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 (14.0),
473 although any release since 2.9 should work as well.
474 Note that if you build the clang libraries from source,
475 then you need to make sure they are also installed (using C<make install>).
476 If the compiler that was used to compile the clang libraries
477 is different from the default C++ compiler, then use C<CXX_FOR_BUILD>
478 to specify this non-default C++ compiler when running C<isl>'s C<./configure>.
480 =head1 Integer Set Library
482 =head2 Memory Management
484 Since a high-level operation on isl objects usually involves
485 several substeps and since the user is usually not interested in
486 the intermediate results, most functions that return a new object
487 will also release all the objects passed as arguments.
488 If the user still wants to use one or more of these arguments
489 after the function call, she should pass along a copy of the
490 object rather than the object itself.
491 The user is then responsible for making sure that the original
492 object gets used somewhere else or is explicitly freed.
494 The arguments and return values of all documented functions are
495 annotated to make clear which arguments are released and which
496 arguments are preserved. In particular, the following annotations
503 C<__isl_give> means that a new object is returned.
504 The user should make sure that the returned pointer is
505 used exactly once as a value for an C<__isl_take> argument.
506 In between, it can be used as a value for as many
507 C<__isl_keep> arguments as the user likes.
508 There is one exception, and that is the case where the
509 pointer returned is C<NULL>. In this case, the user
510 is free to use it as an C<__isl_take> argument or not.
511 When applied to a C<char *>, the returned pointer needs to be
516 C<__isl_null> means that a C<NULL> value is returned.
520 C<__isl_take> means that the object the argument points to
521 is taken over by the function and may no longer be used
522 by the user as an argument to any other function.
523 The pointer value must be one returned by a function
524 returning an C<__isl_give> pointer.
525 If the user passes in a C<NULL> value, then this will
526 be treated as an error in the sense that the function will
527 not perform its usual operation. However, it will still
528 make sure that all the other C<__isl_take> arguments
533 C<__isl_keep> means that the function will only use the object
534 temporarily. After the function has finished, the user
535 can still use it as an argument to other functions.
536 A C<NULL> value will be treated in the same way as
537 a C<NULL> value for an C<__isl_take> argument.
538 This annotation may also be used on return values of
539 type C<const char *>, in which case the returned pointer should
540 not be freed by the user and is only valid until the object
541 from which it was derived is updated or freed.
545 =head2 Initialization
547 All manipulations of integer sets and relations occur within
548 the context of an C<isl_ctx>.
549 A given C<isl_ctx> can only be used within a single thread.
550 All arguments of a function are required to have been allocated
551 within the same context.
552 There are currently no functions available for moving an object
553 from one C<isl_ctx> to another C<isl_ctx>. This means that
554 there is currently no way of safely moving an object from one
555 thread to another, unless the whole C<isl_ctx> is moved.
557 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
558 freed using C<isl_ctx_free>.
559 All objects allocated within an C<isl_ctx> should be freed
560 before the C<isl_ctx> itself is freed.
562 isl_ctx *isl_ctx_alloc();
563 void isl_ctx_free(isl_ctx *ctx);
565 The user can impose a bound on the number of low-level I<operations>
566 that can be performed by an C<isl_ctx>. This bound can be set and
567 retrieved using the following functions. A bound of zero means that
568 no bound is imposed. The number of operations performed can be
569 reset using C<isl_ctx_reset_operations>. Note that the number
570 of low-level operations needed to perform a high-level computation
571 may differ significantly across different versions
572 of C<isl>, but it should be the same across different platforms
573 for the same version of C<isl>.
575 Warning: This feature is experimental. C<isl> has good support to abort and
576 bail out during the computation, but this feature may exercise error code paths
577 that are normally not used that much. Consequently, it is not unlikely that
578 hidden bugs will be exposed.
580 void isl_ctx_set_max_operations(isl_ctx *ctx,
581 unsigned long max_operations);
582 unsigned long isl_ctx_get_max_operations(isl_ctx *ctx);
583 void isl_ctx_reset_operations(isl_ctx *ctx);
585 In order to be able to create an object in the same context
586 as another object, most object types (described later in
587 this document) provide a function to obtain the context
588 in which the object was created.
591 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
592 isl_ctx *isl_multi_val_get_ctx(
593 __isl_keep isl_multi_val *mv);
596 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
597 isl_ctx *isl_multi_id_get_ctx(
598 __isl_keep isl_multi_id *mi);
600 #include <isl/local_space.h>
601 isl_ctx *isl_local_space_get_ctx(
602 __isl_keep isl_local_space *ls);
605 isl_ctx *isl_set_list_get_ctx(
606 __isl_keep isl_set_list *list);
609 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
610 isl_ctx *isl_multi_aff_get_ctx(
611 __isl_keep isl_multi_aff *maff);
612 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pa);
613 isl_ctx *isl_pw_multi_aff_get_ctx(
614 __isl_keep isl_pw_multi_aff *pma);
615 isl_ctx *isl_multi_pw_aff_get_ctx(
616 __isl_keep isl_multi_pw_aff *mpa);
617 isl_ctx *isl_union_pw_aff_get_ctx(
618 __isl_keep isl_union_pw_aff *upa);
619 isl_ctx *isl_union_pw_multi_aff_get_ctx(
620 __isl_keep isl_union_pw_multi_aff *upma);
621 isl_ctx *isl_multi_union_pw_aff_get_ctx(
622 __isl_keep isl_multi_union_pw_aff *mupa);
624 #include <isl/id_to_ast_expr.h>
625 isl_ctx *isl_id_to_ast_expr_get_ctx(
626 __isl_keep isl_id_to_ast_expr *id2expr);
628 #include <isl/point.h>
629 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
632 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
635 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
637 #include <isl/vertices.h>
638 isl_ctx *isl_vertices_get_ctx(
639 __isl_keep isl_vertices *vertices);
640 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
641 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
643 #include <isl/flow.h>
644 isl_ctx *isl_restriction_get_ctx(
645 __isl_keep isl_restriction *restr);
646 isl_ctx *isl_union_access_info_get_ctx(
647 __isl_keep isl_union_access_info *access);
648 isl_ctx *isl_union_flow_get_ctx(
649 __isl_keep isl_union_flow *flow);
651 #include <isl/schedule.h>
652 isl_ctx *isl_schedule_get_ctx(
653 __isl_keep isl_schedule *sched);
654 isl_ctx *isl_schedule_constraints_get_ctx(
655 __isl_keep isl_schedule_constraints *sc);
657 #include <isl/schedule_node.h>
658 isl_ctx *isl_schedule_node_get_ctx(
659 __isl_keep isl_schedule_node *node);
661 #include <isl/ast_build.h>
662 isl_ctx *isl_ast_build_get_ctx(
663 __isl_keep isl_ast_build *build);
666 isl_ctx *isl_ast_expr_get_ctx(
667 __isl_keep isl_ast_expr *expr);
668 isl_ctx *isl_ast_node_get_ctx(
669 __isl_keep isl_ast_node *node);
671 #include <isl/stride_info.h>
672 isl_ctx *isl_stride_info_get_ctx(
673 __isl_keep isl_stride_info *si);
675 #include <isl/fixed_box.h>
676 isl_ctx *isl_fixed_box_get_ctx(
677 __isl_keep isl_fixed_box *box);
681 C<isl> uses the special return type C<isl_size> for functions
682 that return a non-negative value, typically a number or a position.
683 Besides the regular non-negative return values, a special (negative)
684 value C<isl_size_error> may be returned, indicating that something
687 C<isl> also uses two special return types for functions that either return
688 a boolean or that in principle do not return anything.
689 In particular, the C<isl_bool> type has three possible values:
690 C<isl_bool_true> (a positive integer value), indicating I<true> or I<yes>;
691 C<isl_bool_false> (the integer value zero), indicating I<false> or I<no>; and
692 C<isl_bool_error> (a negative integer value), indicating that something
693 went wrong. The following operations are defined on C<isl_bool>. The function
694 C<isl_bool_not> can be used to negate an C<isl_bool>, where the negation of
695 C<isl_bool_error> is C<isl_bool_error> again. The function C<isl_bool_ok>
696 converts an integer to an C<isl_bool>. Any non-zero values yields
697 C<isl_bool_true> and zero yields C<isl_bool_false>.
700 isl_bool isl_bool_not(isl_bool b);
701 isl_bool isl_bool_ok(int b);
703 The C<isl_stat> type has two possible values:
704 C<isl_stat_ok> (the integer value zero), indicating a successful
706 C<isl_stat_error> (a negative integer value), indicating that something
708 The function C<isl_stat_non_null> converts an isl object pointer
709 to an C<isl_stat>, returning C<isl_stat_ok> if the object pointer is valid and
710 C<isl_stat_error> if it is C<NULL>.
713 isl_stat isl_stat_non_null(void *obj);
715 See L</"Error Handling"> for more information on
716 C<isl_size_error>, C<isl_bool_error> and C<isl_stat_error>.
720 An C<isl_val> represents an integer value, a rational value
721 or one of three special values, infinity, negative infinity and NaN.
722 Some predefined values can be created using the following functions.
725 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
726 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
727 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
728 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
729 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
730 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
732 Specific integer values can be created using the following functions.
735 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
737 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
739 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
740 size_t n, size_t size, const void *chunks);
742 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
743 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
744 The least significant digit is assumed to be stored first.
746 Value objects can be copied and freed using the following functions.
749 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
750 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
752 They can be inspected using the following functions.
755 long isl_val_get_num_si(__isl_keep isl_val *v);
756 long isl_val_get_den_si(__isl_keep isl_val *v);
757 __isl_give isl_val *isl_val_get_den_val(
758 __isl_keep isl_val *v);
759 double isl_val_get_d(__isl_keep isl_val *v);
760 isl_size isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
762 isl_stat isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
763 size_t size, void *chunks);
765 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
766 of C<size> bytes needed to store the absolute value of the
768 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
769 which is assumed to have been preallocated by the caller.
770 The least significant digit is stored first.
771 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
772 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
773 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
775 An C<isl_val> can be modified using the following function.
778 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
781 The following unary properties are defined on C<isl_val>s.
784 int isl_val_sgn(__isl_keep isl_val *v);
785 isl_bool isl_val_is_zero(__isl_keep isl_val *v);
786 isl_bool isl_val_is_one(__isl_keep isl_val *v);
787 isl_bool isl_val_is_negone(__isl_keep isl_val *v);
788 isl_bool isl_val_is_nonneg(__isl_keep isl_val *v);
789 isl_bool isl_val_is_nonpos(__isl_keep isl_val *v);
790 isl_bool isl_val_is_pos(__isl_keep isl_val *v);
791 isl_bool isl_val_is_neg(__isl_keep isl_val *v);
792 isl_bool isl_val_is_int(__isl_keep isl_val *v);
793 isl_bool isl_val_is_rat(__isl_keep isl_val *v);
794 isl_bool isl_val_is_nan(__isl_keep isl_val *v);
795 isl_bool isl_val_is_infty(__isl_keep isl_val *v);
796 isl_bool isl_val_is_neginfty(__isl_keep isl_val *v);
798 Note that the sign of NaN is undefined.
800 The following binary properties are defined on pairs of C<isl_val>s.
803 isl_bool isl_val_lt(__isl_keep isl_val *v1,
804 __isl_keep isl_val *v2);
805 isl_bool isl_val_le(__isl_keep isl_val *v1,
806 __isl_keep isl_val *v2);
807 isl_bool isl_val_gt(__isl_keep isl_val *v1,
808 __isl_keep isl_val *v2);
809 isl_bool isl_val_ge(__isl_keep isl_val *v1,
810 __isl_keep isl_val *v2);
811 isl_bool isl_val_eq(__isl_keep isl_val *v1,
812 __isl_keep isl_val *v2);
813 isl_bool isl_val_ne(__isl_keep isl_val *v1,
814 __isl_keep isl_val *v2);
815 isl_bool isl_val_abs_eq(__isl_keep isl_val *v1,
816 __isl_keep isl_val *v2);
818 Comparisons to NaN always return false.
819 That is, a NaN is not considered to hold any relative position
820 with respect to any value. In particular, a NaN
821 is neither considered to be equal to nor to be different from
822 any value (including another NaN).
823 The function C<isl_val_abs_eq> checks whether its two arguments
824 are equal in absolute value.
826 For integer C<isl_val>s we additionally have the following binary property.
829 isl_bool isl_val_is_divisible_by(__isl_keep isl_val *v1,
830 __isl_keep isl_val *v2);
832 An C<isl_val> can also be compared to an integer using the following
833 functions. The result of C<isl_val_cmp_si> is undefined for NaN.
836 isl_bool isl_val_gt_si(__isl_keep isl_val *v, long i);
837 isl_bool isl_val_eq_si(__isl_keep isl_val *v, long i);
838 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
840 The following unary operations are available on C<isl_val>s.
843 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
844 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
845 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
846 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
847 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
848 __isl_give isl_val *isl_val_inv(__isl_take isl_val *v);
850 The following binary operations are available on C<isl_val>s.
853 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
854 __isl_take isl_val *v2);
855 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
856 __isl_take isl_val *v2);
857 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
858 __isl_take isl_val *v2);
859 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
861 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
862 __isl_take isl_val *v2);
863 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
865 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
866 __isl_take isl_val *v2);
867 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
869 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
870 __isl_take isl_val *v2);
871 __isl_give isl_val *isl_val_div_ui(__isl_take isl_val *v1,
874 On integer values, we additionally have the following operations.
877 __isl_give isl_val *isl_val_pow2(__isl_take isl_val *v);
878 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
879 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
880 __isl_take isl_val *v2);
881 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
882 __isl_take isl_val *v2);
883 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
884 __isl_take isl_val *v2, __isl_give isl_val **x,
885 __isl_give isl_val **y);
887 C<isl_val_2exp> is an alternative name for C<isl_val_pow2>.
888 The function C<isl_val_gcdext> returns the greatest common divisor g
889 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
890 that C<*x> * C<v1> + C<*y> * C<v2> = g.
892 =head3 GMP specific functions
894 These functions are only available if C<isl> has been compiled with C<GMP>
897 Specific integer and rational values can be created from C<GMP> values using
898 the following functions.
900 #include <isl/val_gmp.h>
901 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
903 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
904 const mpz_t n, const mpz_t d);
906 The numerator and denominator of a rational value can be extracted as
907 C<GMP> values using the following functions.
909 #include <isl/val_gmp.h>
910 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
911 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
913 =head2 Sets and Relations
915 C<isl> uses six types of objects for representing sets and relations,
916 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
917 C<isl_union_set> and C<isl_union_map>.
918 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
919 can be described as a conjunction of affine constraints, while
920 C<isl_set> and C<isl_map> represent unions of
921 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
922 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
923 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
924 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
925 where spaces are considered different if they have a different number
926 of dimensions and/or different names (see L<"Spaces">).
927 The difference between sets and relations (maps) is that sets have
928 one set of variables, while relations have two sets of variables,
929 input variables and output variables.
931 =head2 Error Handling
933 C<isl> supports different ways to react in case a runtime error is triggered.
934 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
935 with two maps that have incompatible spaces. There are three possible ways
936 to react on error: to warn, to continue or to abort.
938 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
939 the last error in the corresponding C<isl_ctx> and the function in which the
940 error was triggered returns a value indicating that some error has
941 occurred. In case of functions returning a pointer, this value is
942 C<NULL>. In case of functions returning an C<isl_size>, C<isl_bool> or an
943 C<isl_stat>, this value is C<isl_size_error>,
944 C<isl_bool_error> or C<isl_stat_error>.
945 An error does not corrupt internal state,
946 such that isl can continue to be used. C<isl> also provides functions to
947 read the last error, including the specific error message,
948 the isl source file where the error occurred and the line number,
949 and to reset all information about the last error. The
950 last error is only stored for information purposes. Its presence does not
951 change the behavior of C<isl>. Hence, resetting an error is not required to
952 continue to use isl, but only to observe new errors.
955 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
956 const char *isl_ctx_last_error_msg(isl_ctx *ctx);
957 const char *isl_ctx_last_error_file(isl_ctx *ctx);
958 int isl_ctx_last_error_line(isl_ctx *ctx);
959 void isl_ctx_reset_error(isl_ctx *ctx);
961 If no error has occurred since the last call to C<isl_ctx_reset_error>,
962 then the functions C<isl_ctx_last_error_msg> and
963 C<isl_ctx_last_error_file> return C<NULL>.
965 Another option is to continue on error. This is similar to warn on error mode,
966 except that C<isl> does not print any warning. This allows a program to
967 implement its own error reporting.
969 The last option is to directly abort the execution of the program from within
970 the isl library. This makes it obviously impossible to recover from an error,
971 but it allows to directly spot the error location. By aborting on error,
972 debuggers break at the location the error occurred and can provide a stack
973 trace. Other tools that automatically provide stack traces on abort or that do
974 not want to continue execution after an error was triggered may also prefer to
977 The on error behavior of isl can be specified by calling
978 C<isl_options_set_on_error> or by setting the command line option
979 C<--isl-on-error>. Valid arguments for the function call are
980 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
981 choices for the command line option are C<warn>, C<continue> and C<abort>.
982 It is also possible to query the current error mode.
984 #include <isl/options.h>
985 isl_stat isl_options_set_on_error(isl_ctx *ctx, int val);
986 int isl_options_get_on_error(isl_ctx *ctx);
990 Identifiers are used to identify both individual dimensions
991 and tuples of dimensions. They consist of an optional name and an optional
992 user pointer. The name and the user pointer cannot both be C<NULL>, however.
993 Identifiers with the same name but different pointer values
994 are considered to be distinct.
995 Similarly, identifiers with different names but the same pointer value
996 are also considered to be distinct.
997 Equal identifiers are represented using the same object.
998 Pairs of identifiers can therefore be tested for equality using the
1000 Identifiers can be constructed, copied, freed, inspected and printed
1001 using the following functions.
1004 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
1005 __isl_keep const char *name, void *user);
1006 __isl_give isl_id *isl_id_set_free_user(
1007 __isl_take isl_id *id,
1008 void (*free_user)(void *user));
1009 void (*isl_id_get_free_user(__isl_keep isl_id *id))
1011 __isl_give isl_id *isl_id_copy(isl_id *id);
1012 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
1014 void *isl_id_get_user(__isl_keep isl_id *id);
1015 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
1017 __isl_give isl_printer *isl_printer_print_id(
1018 __isl_take isl_printer *p, __isl_keep isl_id *id);
1020 The callback set by C<isl_id_set_free_user> is called on the user
1021 pointer when the last reference to the C<isl_id> is freed.
1022 This callback can be retrieved using C<isl_id_get_free_user>.
1023 Note that C<isl_id_get_name> returns a pointer to some internal
1024 data structure, so the result can only be used while the
1025 corresponding C<isl_id> is alive.
1029 Whenever a new set, relation or similar object is created from scratch,
1030 the space in which it lives needs to be specified using an C<isl_space>.
1031 Each space involves zero or more parameters and zero, one or two
1032 tuples of set or input/output dimensions. The parameters and dimensions
1033 are identified by an C<isl_dim_type> and a position.
1034 The type C<isl_dim_param> refers to parameters,
1035 the type C<isl_dim_set> refers to set dimensions (for spaces
1036 with a single tuple of dimensions) and the types C<isl_dim_in>
1037 and C<isl_dim_out> refer to input and output dimensions
1038 (for spaces with two tuples of dimensions).
1039 Local spaces (see L</"Local Spaces">) also contain dimensions
1040 of type C<isl_dim_div>.
1041 Note that parameters are only identified by their position within
1042 a given object. Across different objects, parameters are (usually)
1043 identified by their names or identifiers. Only unnamed parameters
1044 are identified by their positions across objects. The use of unnamed
1045 parameters is discouraged.
1047 #include <isl/space.h>
1048 __isl_give isl_space *isl_space_unit(isl_ctx *ctx);
1049 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
1050 unsigned nparam, unsigned n_in, unsigned n_out);
1051 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
1053 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
1054 unsigned nparam, unsigned dim);
1055 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
1056 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
1058 The space used for creating a parameter domain
1059 needs to be created using C<isl_space_unit> or C<isl_space_params_alloc>.
1060 For other sets, the space
1061 needs to be created using C<isl_space_set_alloc>, while
1062 for a relation, the space
1063 needs to be created using C<isl_space_alloc>.
1064 The use of C<isl_space_params_alloc>,
1065 C<isl_space_set_alloc> and C<isl_space_alloc> is discouraged as they allow
1066 for the introduction of unnamed parameters.
1068 To check whether a given space is that of a set or a map
1069 or whether it is a parameter space, use these functions:
1071 #include <isl/space.h>
1072 isl_bool isl_space_is_params(__isl_keep isl_space *space);
1073 isl_bool isl_space_is_set(__isl_keep isl_space *space);
1074 isl_bool isl_space_is_map(__isl_keep isl_space *space);
1076 Spaces can be compared using the following functions:
1078 #include <isl/space.h>
1079 isl_bool isl_space_is_equal(__isl_keep isl_space *space1,
1080 __isl_keep isl_space *space2);
1081 isl_bool isl_space_has_equal_params(
1082 __isl_keep isl_space *space1,
1083 __isl_keep isl_space *space2);
1084 isl_bool isl_space_has_equal_tuples(
1085 __isl_keep isl_space *space1,
1086 __isl_keep isl_space *space2);
1087 isl_bool isl_space_is_domain(__isl_keep isl_space *space1,
1088 __isl_keep isl_space *space2);
1089 isl_bool isl_space_is_range(__isl_keep isl_space *space1,
1090 __isl_keep isl_space *space2);
1091 isl_bool isl_space_tuple_is_equal(
1092 __isl_keep isl_space *space1,
1093 enum isl_dim_type type1,
1094 __isl_keep isl_space *space2,
1095 enum isl_dim_type type2);
1097 C<isl_space_is_domain> checks whether the first argument is equal
1098 to the domain of the second argument. This requires in particular that
1099 the first argument is a set space and that the second argument
1100 is a map space. C<isl_space_tuple_is_equal> checks whether the given
1101 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
1102 spaces are the same. That is, it checks if they have the same
1103 identifier (if any), the same dimension and the same internal structure
1106 C<isl_space_has_equal_params> checks whether two spaces
1107 have the same parameters in the same order.
1108 C<isl_space_has_equal_tuples> check whether two spaces have
1109 the same tuples. In contrast to C<isl_space_is_equal> below,
1110 it does not check the
1111 parameters. This is useful because many C<isl> functions align the
1112 parameters before they perform their operations, such that equivalence
1114 C<isl_space_is_equal> checks whether two spaces are identical,
1115 meaning that they have the same parameters and the same tuples.
1116 That is, it checks whether both C<isl_space_has_equal_params> and
1117 C<isl_space_has_equal_tuples> hold.
1119 It is often useful to create objects that live in the
1120 same space as some other object. This can be accomplished
1121 by creating the new objects
1122 (see L</"Creating New Sets and Relations"> or
1123 L</"Functions">) based on the space
1124 of the original object.
1126 #include <isl/set.h>
1127 __isl_give isl_space *isl_basic_set_get_space(
1128 __isl_keep isl_basic_set *bset);
1129 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
1131 #include <isl/union_set.h>
1132 __isl_give isl_space *isl_union_set_get_space(
1133 __isl_keep isl_union_set *uset);
1135 #include <isl/map.h>
1136 __isl_give isl_space *isl_basic_map_get_space(
1137 __isl_keep isl_basic_map *bmap);
1138 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
1140 #include <isl/union_map.h>
1141 __isl_give isl_space *isl_union_map_get_space(
1142 __isl_keep isl_union_map *umap);
1144 #include <isl/constraint.h>
1145 __isl_give isl_space *isl_constraint_get_space(
1146 __isl_keep isl_constraint *constraint);
1148 #include <isl/polynomial.h>
1149 __isl_give isl_space *isl_qpolynomial_get_domain_space(
1150 __isl_keep isl_qpolynomial *qp);
1151 __isl_give isl_space *isl_qpolynomial_get_space(
1152 __isl_keep isl_qpolynomial *qp);
1153 __isl_give isl_space *
1154 isl_qpolynomial_fold_get_domain_space(
1155 __isl_keep isl_qpolynomial_fold *fold);
1156 __isl_give isl_space *isl_qpolynomial_fold_get_space(
1157 __isl_keep isl_qpolynomial_fold *fold);
1158 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
1159 __isl_keep isl_pw_qpolynomial *pwqp);
1160 __isl_give isl_space *isl_pw_qpolynomial_get_space(
1161 __isl_keep isl_pw_qpolynomial *pwqp);
1162 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
1163 __isl_keep isl_pw_qpolynomial_fold *pwf);
1164 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
1165 __isl_keep isl_pw_qpolynomial_fold *pwf);
1166 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
1167 __isl_keep isl_union_pw_qpolynomial *upwqp);
1168 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
1169 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1172 __isl_give isl_space *isl_multi_id_get_space(
1173 __isl_keep isl_multi_id *mi);
1175 #include <isl/val.h>
1176 __isl_give isl_space *isl_multi_val_get_space(
1177 __isl_keep isl_multi_val *mv);
1179 #include <isl/aff.h>
1180 __isl_give isl_space *isl_aff_get_domain_space(
1181 __isl_keep isl_aff *aff);
1182 __isl_give isl_space *isl_aff_get_space(
1183 __isl_keep isl_aff *aff);
1184 __isl_give isl_space *isl_pw_aff_get_domain_space(
1185 __isl_keep isl_pw_aff *pwaff);
1186 __isl_give isl_space *isl_pw_aff_get_space(
1187 __isl_keep isl_pw_aff *pwaff);
1188 __isl_give isl_space *isl_multi_aff_get_domain_space(
1189 __isl_keep isl_multi_aff *maff);
1190 __isl_give isl_space *isl_multi_aff_get_space(
1191 __isl_keep isl_multi_aff *maff);
1192 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
1193 __isl_keep isl_pw_multi_aff *pma);
1194 __isl_give isl_space *isl_pw_multi_aff_get_space(
1195 __isl_keep isl_pw_multi_aff *pma);
1196 __isl_give isl_space *isl_union_pw_aff_get_space(
1197 __isl_keep isl_union_pw_aff *upa);
1198 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
1199 __isl_keep isl_union_pw_multi_aff *upma);
1200 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
1201 __isl_keep isl_multi_pw_aff *mpa);
1202 __isl_give isl_space *isl_multi_pw_aff_get_space(
1203 __isl_keep isl_multi_pw_aff *mpa);
1204 __isl_give isl_space *
1205 isl_multi_union_pw_aff_get_domain_space(
1206 __isl_keep isl_multi_union_pw_aff *mupa);
1207 __isl_give isl_space *
1208 isl_multi_union_pw_aff_get_space(
1209 __isl_keep isl_multi_union_pw_aff *mupa);
1211 #include <isl/point.h>
1212 __isl_give isl_space *isl_point_get_space(
1213 __isl_keep isl_point *pnt);
1215 #include <isl/fixed_box.h>
1216 __isl_give isl_space *isl_fixed_box_get_space(
1217 __isl_keep isl_fixed_box *box);
1219 The number of dimensions of a given type of space
1220 may be read off from a space or an object that lives
1221 in a space using the following functions.
1222 In case of C<isl_space_dim>, type may be
1223 C<isl_dim_param>, C<isl_dim_in> (only for relations),
1224 C<isl_dim_out> (only for relations), C<isl_dim_set>
1225 (only for sets) or C<isl_dim_all>.
1227 #include <isl/space.h>
1228 isl_size isl_space_dim(__isl_keep isl_space *space,
1229 enum isl_dim_type type);
1231 #include <isl/local_space.h>
1232 isl_size isl_local_space_dim(__isl_keep isl_local_space *ls,
1233 enum isl_dim_type type);
1235 #include <isl/set.h>
1236 isl_size isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1237 enum isl_dim_type type);
1238 isl_size isl_set_tuple_dim(__isl_keep isl_set *set);
1239 isl_size isl_set_dim(__isl_keep isl_set *set,
1240 enum isl_dim_type type);
1242 #include <isl/union_set.h>
1243 isl_size isl_union_set_dim(__isl_keep isl_union_set *uset,
1244 enum isl_dim_type type);
1246 #include <isl/map.h>
1247 isl_size isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1248 enum isl_dim_type type);
1249 isl_size isl_map_domain_tuple_dim(
1250 __isl_keep isl_map *map);
1251 isl_size isl_map_range_tuple_dim(
1252 __isl_keep isl_map *map);
1253 isl_size isl_map_dim(__isl_keep isl_map *map,
1254 enum isl_dim_type type);
1256 #include <isl/union_map.h>
1257 isl_size isl_union_map_dim(__isl_keep isl_union_map *umap,
1258 enum isl_dim_type type);
1260 #include <isl/val.h>
1261 isl_size isl_multi_val_dim(__isl_keep isl_multi_val *mv,
1262 enum isl_dim_type type);
1264 #include <isl/aff.h>
1265 isl_size isl_aff_dim(__isl_keep isl_aff *aff,
1266 enum isl_dim_type type);
1267 isl_size isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1268 enum isl_dim_type type);
1269 isl_size isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1270 enum isl_dim_type type);
1271 isl_size isl_pw_multi_aff_dim(
1272 __isl_keep isl_pw_multi_aff *pma,
1273 enum isl_dim_type type);
1274 isl_size isl_multi_pw_aff_dim(
1275 __isl_keep isl_multi_pw_aff *mpa,
1276 enum isl_dim_type type);
1277 isl_size isl_union_pw_aff_dim(
1278 __isl_keep isl_union_pw_aff *upa,
1279 enum isl_dim_type type);
1280 isl_size isl_union_pw_multi_aff_dim(
1281 __isl_keep isl_union_pw_multi_aff *upma,
1282 enum isl_dim_type type);
1283 isl_size isl_multi_union_pw_aff_dim(
1284 __isl_keep isl_multi_union_pw_aff *mupa,
1285 enum isl_dim_type type);
1287 #include <isl/polynomial.h>
1288 isl_size isl_union_pw_qpolynomial_dim(
1289 __isl_keep isl_union_pw_qpolynomial *upwqp,
1290 enum isl_dim_type type);
1291 isl_size isl_union_pw_qpolynomial_fold_dim(
1292 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1293 enum isl_dim_type type);
1295 Note that an C<isl_union_set>, an C<isl_union_map>,
1296 an C<isl_union_pw_multi_aff>,
1297 an C<isl_union_pw_qpolynomial> and
1298 an C<isl_union_pw_qpolynomial_fold>
1299 only have parameters.
1301 Additional parameters can be added to a space using the following function.
1303 #include <isl/space.h>
1304 __isl_give isl_space *isl_space_add_param_id(
1305 __isl_take isl_space *space,
1306 __isl_take isl_id *id);
1308 If a parameter with the given identifier already appears in the space,
1309 then it is not added again.
1311 Conversely, all parameters can be removed from a space
1312 using the following function.
1314 #include <isl/space.h>
1315 __isl_give isl_space *isl_space_drop_all_params(
1316 __isl_take isl_space *space);
1318 The identifiers or names of the individual dimensions of spaces
1319 may be set or read off using the following functions on spaces
1320 or objects that live in spaces.
1321 These functions are mostly useful to obtain the identifiers, positions
1322 or names of the parameters. Identifiers of individual dimensions are
1323 essentially only useful for printing. They are ignored by all other
1324 operations and may not be preserved across those operations.
1325 To keep track of a space along with names/identifiers of
1326 the set dimensions, use an C<isl_multi_id> as described in
1329 #include <isl/space.h>
1330 __isl_give isl_space *isl_space_set_dim_id(
1331 __isl_take isl_space *space,
1332 enum isl_dim_type type, unsigned pos,
1333 __isl_take isl_id *id);
1334 isl_bool isl_space_has_dim_id(__isl_keep isl_space *space,
1335 enum isl_dim_type type, unsigned pos);
1336 __isl_give isl_id *isl_space_get_dim_id(
1337 __isl_keep isl_space *space,
1338 enum isl_dim_type type, unsigned pos);
1339 __isl_give isl_space *isl_space_set_dim_name(
1340 __isl_take isl_space *space,
1341 enum isl_dim_type type, unsigned pos,
1342 __isl_keep const char *name);
1343 isl_bool isl_space_has_dim_name(__isl_keep isl_space *space,
1344 enum isl_dim_type type, unsigned pos);
1345 __isl_keep const char *isl_space_get_dim_name(
1346 __isl_keep isl_space *space,
1347 enum isl_dim_type type, unsigned pos);
1349 #include <isl/local_space.h>
1350 __isl_give isl_local_space *isl_local_space_set_dim_id(
1351 __isl_take isl_local_space *ls,
1352 enum isl_dim_type type, unsigned pos,
1353 __isl_take isl_id *id);
1354 isl_bool isl_local_space_has_dim_id(
1355 __isl_keep isl_local_space *ls,
1356 enum isl_dim_type type, unsigned pos);
1357 __isl_give isl_id *isl_local_space_get_dim_id(
1358 __isl_keep isl_local_space *ls,
1359 enum isl_dim_type type, unsigned pos);
1360 __isl_give isl_local_space *isl_local_space_set_dim_name(
1361 __isl_take isl_local_space *ls,
1362 enum isl_dim_type type, unsigned pos, const char *s);
1363 isl_bool isl_local_space_has_dim_name(
1364 __isl_keep isl_local_space *ls,
1365 enum isl_dim_type type, unsigned pos)
1366 const char *isl_local_space_get_dim_name(
1367 __isl_keep isl_local_space *ls,
1368 enum isl_dim_type type, unsigned pos);
1370 #include <isl/constraint.h>
1371 const char *isl_constraint_get_dim_name(
1372 __isl_keep isl_constraint *constraint,
1373 enum isl_dim_type type, unsigned pos);
1375 #include <isl/set.h>
1376 __isl_give isl_id *isl_basic_set_get_dim_id(
1377 __isl_keep isl_basic_set *bset,
1378 enum isl_dim_type type, unsigned pos);
1379 __isl_give isl_set *isl_set_set_dim_id(
1380 __isl_take isl_set *set, enum isl_dim_type type,
1381 unsigned pos, __isl_take isl_id *id);
1382 isl_bool isl_set_has_dim_id(__isl_keep isl_set *set,
1383 enum isl_dim_type type, unsigned pos);
1384 __isl_give isl_id *isl_set_get_dim_id(
1385 __isl_keep isl_set *set, enum isl_dim_type type,
1387 const char *isl_basic_set_get_dim_name(
1388 __isl_keep isl_basic_set *bset,
1389 enum isl_dim_type type, unsigned pos);
1390 isl_bool isl_set_has_dim_name(__isl_keep isl_set *set,
1391 enum isl_dim_type type, unsigned pos);
1392 const char *isl_set_get_dim_name(
1393 __isl_keep isl_set *set,
1394 enum isl_dim_type type, unsigned pos);
1396 #include <isl/map.h>
1397 __isl_give isl_map *isl_map_set_dim_id(
1398 __isl_take isl_map *map, enum isl_dim_type type,
1399 unsigned pos, __isl_take isl_id *id);
1400 isl_bool isl_basic_map_has_dim_id(
1401 __isl_keep isl_basic_map *bmap,
1402 enum isl_dim_type type, unsigned pos);
1403 isl_bool isl_map_has_dim_id(__isl_keep isl_map *map,
1404 enum isl_dim_type type, unsigned pos);
1405 __isl_give isl_id *isl_map_get_dim_id(
1406 __isl_keep isl_map *map, enum isl_dim_type type,
1408 __isl_give isl_id *isl_union_map_get_dim_id(
1409 __isl_keep isl_union_map *umap,
1410 enum isl_dim_type type, unsigned pos);
1411 const char *isl_basic_map_get_dim_name(
1412 __isl_keep isl_basic_map *bmap,
1413 enum isl_dim_type type, unsigned pos);
1414 isl_bool isl_map_has_dim_name(__isl_keep isl_map *map,
1415 enum isl_dim_type type, unsigned pos);
1416 const char *isl_map_get_dim_name(
1417 __isl_keep isl_map *map,
1418 enum isl_dim_type type, unsigned pos);
1420 #include <isl/val.h>
1421 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1422 __isl_take isl_multi_val *mv,
1423 enum isl_dim_type type, unsigned pos,
1424 __isl_take isl_id *id);
1425 __isl_give isl_id *isl_multi_val_get_dim_id(
1426 __isl_keep isl_multi_val *mv,
1427 enum isl_dim_type type, unsigned pos);
1428 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1429 __isl_take isl_multi_val *mv,
1430 enum isl_dim_type type, unsigned pos, const char *s);
1432 #include <isl/aff.h>
1433 __isl_give isl_aff *isl_aff_set_dim_id(
1434 __isl_take isl_aff *aff, enum isl_dim_type type,
1435 unsigned pos, __isl_take isl_id *id);
1436 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1437 __isl_take isl_multi_aff *maff,
1438 enum isl_dim_type type, unsigned pos,
1439 __isl_take isl_id *id);
1440 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1441 __isl_take isl_pw_aff *pma,
1442 enum isl_dim_type type, unsigned pos,
1443 __isl_take isl_id *id);
1444 __isl_give isl_multi_pw_aff *
1445 isl_multi_pw_aff_set_dim_id(
1446 __isl_take isl_multi_pw_aff *mpa,
1447 enum isl_dim_type type, unsigned pos,
1448 __isl_take isl_id *id);
1449 __isl_give isl_multi_union_pw_aff *
1450 isl_multi_union_pw_aff_set_dim_id(
1451 __isl_take isl_multi_union_pw_aff *mupa,
1452 enum isl_dim_type type, unsigned pos,
1453 __isl_take isl_id *id);
1454 __isl_give isl_id *isl_multi_aff_get_dim_id(
1455 __isl_keep isl_multi_aff *ma,
1456 enum isl_dim_type type, unsigned pos);
1457 isl_bool isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1458 enum isl_dim_type type, unsigned pos);
1459 __isl_give isl_id *isl_pw_aff_get_dim_id(
1460 __isl_keep isl_pw_aff *pa,
1461 enum isl_dim_type type, unsigned pos);
1462 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1463 __isl_keep isl_pw_multi_aff *pma,
1464 enum isl_dim_type type, unsigned pos);
1465 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1466 __isl_keep isl_multi_pw_aff *mpa,
1467 enum isl_dim_type type, unsigned pos);
1468 __isl_give isl_id *isl_multi_union_pw_aff_get_dim_id(
1469 __isl_keep isl_multi_union_pw_aff *mupa,
1470 enum isl_dim_type type, unsigned pos);
1471 __isl_give isl_aff *isl_aff_set_dim_name(
1472 __isl_take isl_aff *aff, enum isl_dim_type type,
1473 unsigned pos, const char *s);
1474 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1475 __isl_take isl_multi_aff *maff,
1476 enum isl_dim_type type, unsigned pos, const char *s);
1477 __isl_give isl_multi_pw_aff *
1478 isl_multi_pw_aff_set_dim_name(
1479 __isl_take isl_multi_pw_aff *mpa,
1480 enum isl_dim_type type, unsigned pos, const char *s);
1481 __isl_give isl_union_pw_aff *
1482 isl_union_pw_aff_set_dim_name(
1483 __isl_take isl_union_pw_aff *upa,
1484 enum isl_dim_type type, unsigned pos,
1486 __isl_give isl_union_pw_multi_aff *
1487 isl_union_pw_multi_aff_set_dim_name(
1488 __isl_take isl_union_pw_multi_aff *upma,
1489 enum isl_dim_type type, unsigned pos,
1491 __isl_give isl_multi_union_pw_aff *
1492 isl_multi_union_pw_aff_set_dim_name(
1493 __isl_take isl_multi_union_pw_aff *mupa,
1494 enum isl_dim_type type, unsigned pos,
1496 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1497 enum isl_dim_type type, unsigned pos);
1498 const char *isl_pw_aff_get_dim_name(
1499 __isl_keep isl_pw_aff *pa,
1500 enum isl_dim_type type, unsigned pos);
1501 const char *isl_pw_multi_aff_get_dim_name(
1502 __isl_keep isl_pw_multi_aff *pma,
1503 enum isl_dim_type type, unsigned pos);
1505 #include <isl/polynomial.h>
1506 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1507 __isl_take isl_qpolynomial *qp,
1508 enum isl_dim_type type, unsigned pos,
1510 __isl_give isl_pw_qpolynomial *
1511 isl_pw_qpolynomial_set_dim_name(
1512 __isl_take isl_pw_qpolynomial *pwqp,
1513 enum isl_dim_type type, unsigned pos,
1515 __isl_give isl_pw_qpolynomial_fold *
1516 isl_pw_qpolynomial_fold_set_dim_name(
1517 __isl_take isl_pw_qpolynomial_fold *pwf,
1518 enum isl_dim_type type, unsigned pos,
1520 __isl_give isl_union_pw_qpolynomial *
1521 isl_union_pw_qpolynomial_set_dim_name(
1522 __isl_take isl_union_pw_qpolynomial *upwqp,
1523 enum isl_dim_type type, unsigned pos,
1525 __isl_give isl_union_pw_qpolynomial_fold *
1526 isl_union_pw_qpolynomial_fold_set_dim_name(
1527 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1528 enum isl_dim_type type, unsigned pos,
1531 Note that C<isl_space_get_name> returns a pointer to some internal
1532 data structure, so the result can only be used while the
1533 corresponding C<isl_space> is alive.
1534 Also note that every function that operates on two sets or relations
1535 requires that both arguments have the same parameters. This also
1536 means that if one of the arguments has named parameters, then the
1537 other needs to have named parameters too and the names need to match.
1538 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1539 arguments may have different parameters (as long as they are named),
1540 in which case the result will have as parameters the union of the parameters of
1543 Given the identifier or name of a dimension (typically a parameter),
1544 its position can be obtained from the following functions.
1546 #include <isl/space.h>
1547 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1548 enum isl_dim_type type, __isl_keep isl_id *id);
1549 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1550 enum isl_dim_type type, const char *name);
1552 #include <isl/local_space.h>
1553 int isl_local_space_find_dim_by_name(
1554 __isl_keep isl_local_space *ls,
1555 enum isl_dim_type type, const char *name);
1557 #include <isl/val.h>
1558 int isl_multi_val_find_dim_by_id(
1559 __isl_keep isl_multi_val *mv,
1560 enum isl_dim_type type, __isl_keep isl_id *id);
1561 int isl_multi_val_find_dim_by_name(
1562 __isl_keep isl_multi_val *mv,
1563 enum isl_dim_type type, const char *name);
1565 #include <isl/set.h>
1566 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1567 enum isl_dim_type type, __isl_keep isl_id *id);
1568 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1569 enum isl_dim_type type, const char *name);
1571 #include <isl/map.h>
1572 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1573 enum isl_dim_type type, __isl_keep isl_id *id);
1574 int isl_basic_map_find_dim_by_name(
1575 __isl_keep isl_basic_map *bmap,
1576 enum isl_dim_type type, const char *name);
1577 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1578 enum isl_dim_type type, const char *name);
1579 int isl_union_map_find_dim_by_name(
1580 __isl_keep isl_union_map *umap,
1581 enum isl_dim_type type, const char *name);
1583 #include <isl/aff.h>
1584 int isl_multi_aff_find_dim_by_id(
1585 __isl_keep isl_multi_aff *ma,
1586 enum isl_dim_type type, __isl_keep isl_id *id);
1587 int isl_multi_pw_aff_find_dim_by_id(
1588 __isl_keep isl_multi_pw_aff *mpa,
1589 enum isl_dim_type type, __isl_keep isl_id *id);
1590 int isl_multi_union_pw_aff_find_dim_by_id(
1591 __isl_keep isl_multi_union_pw_aff *mupa,
1592 enum isl_dim_type type, __isl_keep isl_id *id);
1593 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff,
1594 enum isl_dim_type type, const char *name);
1595 int isl_multi_aff_find_dim_by_name(
1596 __isl_keep isl_multi_aff *ma,
1597 enum isl_dim_type type, const char *name);
1598 int isl_pw_aff_find_dim_by_name(__isl_keep isl_pw_aff *pa,
1599 enum isl_dim_type type, const char *name);
1600 int isl_multi_pw_aff_find_dim_by_name(
1601 __isl_keep isl_multi_pw_aff *mpa,
1602 enum isl_dim_type type, const char *name);
1603 int isl_pw_multi_aff_find_dim_by_name(
1604 __isl_keep isl_pw_multi_aff *pma,
1605 enum isl_dim_type type, const char *name);
1606 int isl_union_pw_aff_find_dim_by_name(
1607 __isl_keep isl_union_pw_aff *upa,
1608 enum isl_dim_type type, const char *name);
1609 int isl_union_pw_multi_aff_find_dim_by_name(
1610 __isl_keep isl_union_pw_multi_aff *upma,
1611 enum isl_dim_type type, const char *name);
1612 int isl_multi_union_pw_aff_find_dim_by_name(
1613 __isl_keep isl_multi_union_pw_aff *mupa,
1614 enum isl_dim_type type, const char *name);
1616 #include <isl/polynomial.h>
1617 int isl_pw_qpolynomial_find_dim_by_name(
1618 __isl_keep isl_pw_qpolynomial *pwqp,
1619 enum isl_dim_type type, const char *name);
1620 int isl_pw_qpolynomial_fold_find_dim_by_name(
1621 __isl_keep isl_pw_qpolynomial_fold *pwf,
1622 enum isl_dim_type type, const char *name);
1623 int isl_union_pw_qpolynomial_find_dim_by_name(
1624 __isl_keep isl_union_pw_qpolynomial *upwqp,
1625 enum isl_dim_type type, const char *name);
1626 int isl_union_pw_qpolynomial_fold_find_dim_by_name(
1627 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1628 enum isl_dim_type type, const char *name);
1630 The identifiers or names of entire spaces may be set or read off
1631 using the following functions.
1633 #include <isl/space.h>
1634 __isl_give isl_space *isl_space_set_domain_tuple_id(
1635 __isl_take isl_space *space,
1636 __isl_take isl_id *id);
1637 __isl_give isl_space *isl_space_set_range_tuple_id(
1638 __isl_take isl_space *space,
1639 __isl_take isl_id *id);
1640 __isl_give isl_space *isl_space_set_tuple_id(
1641 __isl_take isl_space *space,
1642 enum isl_dim_type type, __isl_take isl_id *id);
1643 __isl_give isl_space *isl_space_reset_tuple_id(
1644 __isl_take isl_space *space, enum isl_dim_type type);
1645 isl_bool isl_space_has_domain_tuple_id(
1646 __isl_keep isl_space *space);
1647 isl_bool isl_space_has_range_tuple_id(
1648 __isl_keep isl_space *space);
1649 isl_bool isl_space_has_tuple_id(
1650 __isl_keep isl_space *space,
1651 enum isl_dim_type type);
1652 __isl_give isl_id *isl_space_get_domain_tuple_id(
1653 __isl_keep isl_space *space);
1654 __isl_give isl_id *isl_space_get_range_tuple_id(
1655 __isl_keep isl_space *space);
1656 __isl_give isl_id *isl_space_get_tuple_id(
1657 __isl_keep isl_space *space, enum isl_dim_type type);
1658 __isl_give isl_space *isl_space_set_tuple_name(
1659 __isl_take isl_space *space,
1660 enum isl_dim_type type, const char *s);
1661 isl_bool isl_space_has_tuple_name(
1662 __isl_keep isl_space *space,
1663 enum isl_dim_type type);
1664 __isl_keep const char *isl_space_get_tuple_name(
1665 __isl_keep isl_space *space,
1666 enum isl_dim_type type);
1668 #include <isl/local_space.h>
1669 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1670 __isl_take isl_local_space *ls,
1671 enum isl_dim_type type, __isl_take isl_id *id);
1673 #include <isl/set.h>
1674 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1675 __isl_take isl_basic_set *bset,
1676 __isl_take isl_id *id);
1677 __isl_give isl_set *isl_set_set_tuple_id(
1678 __isl_take isl_set *set, __isl_take isl_id *id);
1679 __isl_give isl_set *isl_set_reset_tuple_id(
1680 __isl_take isl_set *set);
1681 isl_bool isl_set_has_tuple_id(__isl_keep isl_set *set);
1682 __isl_give isl_id *isl_set_get_tuple_id(
1683 __isl_keep isl_set *set);
1684 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1685 __isl_take isl_basic_set *set, const char *s);
1686 __isl_give isl_set *isl_set_set_tuple_name(
1687 __isl_take isl_set *set, const char *s);
1688 const char *isl_basic_set_get_tuple_name(
1689 __isl_keep isl_basic_set *bset);
1690 isl_bool isl_set_has_tuple_name(__isl_keep isl_set *set);
1691 const char *isl_set_get_tuple_name(
1692 __isl_keep isl_set *set);
1694 #include <isl/map.h>
1695 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1696 __isl_take isl_basic_map *bmap,
1697 enum isl_dim_type type, __isl_take isl_id *id);
1698 __isl_give isl_map *isl_map_set_domain_tuple_id(
1699 __isl_take isl_map *map, __isl_take isl_id *id);
1700 __isl_give isl_map *isl_map_set_range_tuple_id(
1701 __isl_take isl_map *map, __isl_take isl_id *id);
1702 __isl_give isl_map *isl_map_set_tuple_id(
1703 __isl_take isl_map *map, enum isl_dim_type type,
1704 __isl_take isl_id *id);
1705 __isl_give isl_map *isl_map_reset_tuple_id(
1706 __isl_take isl_map *map, enum isl_dim_type type);
1707 isl_bool isl_map_has_domain_tuple_id(
1708 __isl_keep isl_map *map);
1709 isl_bool isl_map_has_range_tuple_id(
1710 __isl_keep isl_map *map);
1711 isl_bool isl_map_has_tuple_id(__isl_keep isl_map *map,
1712 enum isl_dim_type type);
1713 __isl_give isl_id *isl_map_get_domain_tuple_id(
1714 __isl_keep isl_map *map);
1715 __isl_give isl_id *isl_map_get_range_tuple_id(
1716 __isl_keep isl_map *map);
1717 __isl_give isl_id *isl_map_get_tuple_id(
1718 __isl_keep isl_map *map, enum isl_dim_type type);
1719 __isl_give isl_map *isl_map_set_tuple_name(
1720 __isl_take isl_map *map,
1721 enum isl_dim_type type, const char *s);
1722 const char *isl_basic_map_get_tuple_name(
1723 __isl_keep isl_basic_map *bmap,
1724 enum isl_dim_type type);
1725 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1726 __isl_take isl_basic_map *bmap,
1727 enum isl_dim_type type, const char *s);
1728 isl_bool isl_map_has_tuple_name(__isl_keep isl_map *map,
1729 enum isl_dim_type type);
1730 const char *isl_map_get_tuple_name(
1731 __isl_keep isl_map *map,
1732 enum isl_dim_type type);
1734 #include <isl/val.h>
1735 __isl_give isl_multi_val *isl_multi_val_set_range_tuple_id(
1736 __isl_take isl_multi_val *mv,
1737 __isl_take isl_id *id);
1738 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1739 __isl_take isl_multi_val *mv,
1740 enum isl_dim_type type, __isl_take isl_id *id);
1741 __isl_give isl_multi_val *
1742 isl_multi_val_reset_range_tuple_id(
1743 __isl_take isl_multi_val *mv);
1744 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1745 __isl_take isl_multi_val *mv,
1746 enum isl_dim_type type);
1747 isl_bool isl_multi_val_has_range_tuple_id(
1748 __isl_keep isl_multi_val *mv);
1749 __isl_give isl_id *isl_multi_val_get_range_tuple_id(
1750 __isl_keep isl_multi_val *mv);
1751 isl_bool isl_multi_val_has_tuple_id(
1752 __isl_keep isl_multi_val *mv,
1753 enum isl_dim_type type);
1754 __isl_give isl_id *isl_multi_val_get_tuple_id(
1755 __isl_keep isl_multi_val *mv,
1756 enum isl_dim_type type);
1757 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1758 __isl_take isl_multi_val *mv,
1759 enum isl_dim_type type, const char *s);
1760 const char *isl_multi_val_get_tuple_name(
1761 __isl_keep isl_multi_val *mv,
1762 enum isl_dim_type type);
1764 #include <isl/aff.h>
1765 __isl_give isl_aff *isl_aff_set_tuple_id(
1766 __isl_take isl_aff *aff,
1767 enum isl_dim_type type, __isl_take isl_id *id);
1768 __isl_give isl_multi_aff *isl_multi_aff_set_range_tuple_id(
1769 __isl_take isl_multi_aff *ma,
1770 __isl_take isl_id *id);
1771 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1772 __isl_take isl_multi_aff *maff,
1773 enum isl_dim_type type, __isl_take isl_id *id);
1774 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1775 __isl_take isl_pw_aff *pwaff,
1776 enum isl_dim_type type, __isl_take isl_id *id);
1777 __isl_give isl_pw_multi_aff *
1778 isl_pw_multi_aff_set_range_tuple_id(
1779 __isl_take isl_pw_multi_aff *pma,
1780 __isl_take isl_id *id);
1781 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1782 __isl_take isl_pw_multi_aff *pma,
1783 enum isl_dim_type type, __isl_take isl_id *id);
1784 __isl_give isl_multi_pw_aff *
1785 isl_multi_pw_aff_set_range_tuple_id(
1786 __isl_take isl_multi_pw_aff *mpa,
1787 __isl_take isl_id *id);
1788 __isl_give isl_multi_union_pw_aff *
1789 isl_multi_union_pw_aff_set_range_tuple_id(
1790 __isl_take isl_multi_union_pw_aff *mupa,
1791 __isl_take isl_id *id);
1792 __isl_give isl_multi_union_pw_aff *
1793 isl_multi_union_pw_aff_set_tuple_id(
1794 __isl_take isl_multi_union_pw_aff *mupa,
1795 enum isl_dim_type type, __isl_take isl_id *id);
1796 __isl_give isl_multi_aff *
1797 isl_multi_aff_reset_range_tuple_id(
1798 __isl_take isl_multi_aff *ma);
1799 __isl_give isl_multi_pw_aff *
1800 isl_multi_pw_aff_reset_range_tuple_id(
1801 __isl_take isl_multi_pw_aff *mpa);
1802 __isl_give isl_multi_union_pw_aff *
1803 isl_multi_union_pw_aff_reset_range_tuple_id(
1804 __isl_take isl_multi_union_pw_aff *mupa);
1805 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1806 __isl_take isl_multi_aff *ma,
1807 enum isl_dim_type type);
1808 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1809 __isl_take isl_pw_aff *pa,
1810 enum isl_dim_type type);
1811 __isl_give isl_multi_pw_aff *
1812 isl_multi_pw_aff_reset_tuple_id(
1813 __isl_take isl_multi_pw_aff *mpa,
1814 enum isl_dim_type type);
1815 __isl_give isl_pw_multi_aff *
1816 isl_pw_multi_aff_reset_tuple_id(
1817 __isl_take isl_pw_multi_aff *pma,
1818 enum isl_dim_type type);
1819 __isl_give isl_multi_union_pw_aff *
1820 isl_multi_union_pw_aff_reset_tuple_id(
1821 __isl_take isl_multi_union_pw_aff *mupa,
1822 enum isl_dim_type type);
1823 isl_bool isl_multi_aff_has_range_tuple_id(
1824 __isl_keep isl_multi_aff *ma);
1825 __isl_give isl_id *isl_multi_aff_get_range_tuple_id(
1826 __isl_keep isl_multi_aff *ma);
1827 isl_bool isl_multi_aff_has_tuple_id(
1828 __isl_keep isl_multi_aff *ma,
1829 enum isl_dim_type type);
1830 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1831 __isl_keep isl_multi_aff *ma,
1832 enum isl_dim_type type);
1833 isl_bool isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1834 enum isl_dim_type type);
1835 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1836 __isl_keep isl_pw_aff *pa,
1837 enum isl_dim_type type);
1838 isl_bool isl_pw_multi_aff_has_range_tuple_id(
1839 __isl_keep isl_pw_multi_aff *pma);
1840 isl_bool isl_pw_multi_aff_has_tuple_id(
1841 __isl_keep isl_pw_multi_aff *pma,
1842 enum isl_dim_type type);
1843 __isl_give isl_id *isl_pw_multi_aff_get_range_tuple_id(
1844 __isl_keep isl_pw_multi_aff *pma);
1845 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1846 __isl_keep isl_pw_multi_aff *pma,
1847 enum isl_dim_type type);
1848 isl_bool isl_multi_pw_aff_has_range_tuple_id(
1849 __isl_keep isl_multi_pw_aff *mpa);
1850 __isl_give isl_id *isl_multi_pw_aff_get_range_tuple_id(
1851 __isl_keep isl_multi_pw_aff *mpa);
1852 isl_bool isl_multi_pw_aff_has_tuple_id(
1853 __isl_keep isl_multi_pw_aff *mpa,
1854 enum isl_dim_type type);
1855 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1856 __isl_keep isl_multi_pw_aff *mpa,
1857 enum isl_dim_type type);
1858 isl_bool isl_multi_union_pw_aff_has_range_tuple_id(
1859 __isl_keep isl_multi_union_pw_aff *mupa);
1861 isl_multi_union_pw_aff_get_range_tuple_id(
1862 __isl_keep isl_multi_union_pw_aff *mupa);
1863 isl_bool isl_multi_union_pw_aff_has_tuple_id(
1864 __isl_keep isl_multi_union_pw_aff *mupa,
1865 enum isl_dim_type type);
1866 __isl_give isl_id *isl_multi_union_pw_aff_get_tuple_id(
1867 __isl_keep isl_multi_union_pw_aff *mupa,
1868 enum isl_dim_type type);
1869 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1870 __isl_take isl_multi_aff *maff,
1871 enum isl_dim_type type, const char *s);
1872 __isl_give isl_multi_pw_aff *
1873 isl_multi_pw_aff_set_tuple_name(
1874 __isl_take isl_multi_pw_aff *mpa,
1875 enum isl_dim_type type, const char *s);
1876 __isl_give isl_multi_union_pw_aff *
1877 isl_multi_union_pw_aff_set_tuple_name(
1878 __isl_take isl_multi_union_pw_aff *mupa,
1879 enum isl_dim_type type, const char *s);
1880 const char *isl_multi_aff_get_tuple_name(
1881 __isl_keep isl_multi_aff *multi,
1882 enum isl_dim_type type);
1883 isl_bool isl_pw_multi_aff_has_tuple_name(
1884 __isl_keep isl_pw_multi_aff *pma,
1885 enum isl_dim_type type);
1886 const char *isl_pw_multi_aff_get_tuple_name(
1887 __isl_keep isl_pw_multi_aff *pma,
1888 enum isl_dim_type type);
1889 const char *isl_multi_union_pw_aff_get_tuple_name(
1890 __isl_keep isl_multi_union_pw_aff *mupa,
1891 enum isl_dim_type type);
1893 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1894 or C<isl_dim_set>. As with C<isl_space_get_name>,
1895 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1897 Binary operations require the corresponding spaces of their arguments
1898 to have the same name.
1900 To keep the names of all parameters and tuples, but reset the user pointers
1901 of all the corresponding identifiers, use the following function.
1903 #include <isl/space.h>
1904 __isl_give isl_space *isl_space_reset_user(
1905 __isl_take isl_space *space);
1907 #include <isl/set.h>
1908 __isl_give isl_set *isl_set_reset_user(
1909 __isl_take isl_set *set);
1911 #include <isl/map.h>
1912 __isl_give isl_map *isl_map_reset_user(
1913 __isl_take isl_map *map);
1915 #include <isl/union_set.h>
1916 __isl_give isl_union_set *isl_union_set_reset_user(
1917 __isl_take isl_union_set *uset);
1919 #include <isl/union_map.h>
1920 __isl_give isl_union_map *isl_union_map_reset_user(
1921 __isl_take isl_union_map *umap);
1924 __isl_give isl_multi_id *isl_multi_id_reset_user(
1925 __isl_take isl_multi_id *mi);
1927 #include <isl/val.h>
1928 __isl_give isl_multi_val *isl_multi_val_reset_user(
1929 __isl_take isl_multi_val *mv);
1931 #include <isl/aff.h>
1932 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1933 __isl_take isl_multi_aff *ma);
1934 __isl_give isl_pw_aff *isl_pw_aff_reset_user(
1935 __isl_take isl_pw_aff *pa);
1936 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1937 __isl_take isl_multi_pw_aff *mpa);
1938 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_reset_user(
1939 __isl_take isl_pw_multi_aff *pma);
1940 __isl_give isl_union_pw_aff *isl_union_pw_aff_reset_user(
1941 __isl_take isl_union_pw_aff *upa);
1942 __isl_give isl_multi_union_pw_aff *
1943 isl_multi_union_pw_aff_reset_user(
1944 __isl_take isl_multi_union_pw_aff *mupa);
1945 __isl_give isl_union_pw_multi_aff *
1946 isl_union_pw_multi_aff_reset_user(
1947 __isl_take isl_union_pw_multi_aff *upma);
1949 #include <isl/polynomial.h>
1950 __isl_give isl_pw_qpolynomial *
1951 isl_pw_qpolynomial_reset_user(
1952 __isl_take isl_pw_qpolynomial *pwqp);
1953 __isl_give isl_union_pw_qpolynomial *
1954 isl_union_pw_qpolynomial_reset_user(
1955 __isl_take isl_union_pw_qpolynomial *upwqp);
1956 __isl_give isl_pw_qpolynomial_fold *
1957 isl_pw_qpolynomial_fold_reset_user(
1958 __isl_take isl_pw_qpolynomial_fold *pwf);
1959 __isl_give isl_union_pw_qpolynomial_fold *
1960 isl_union_pw_qpolynomial_fold_reset_user(
1961 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1963 Spaces can be nested. In particular, the domain of a set or
1964 the domain or range of a relation can be a nested relation.
1965 This process is also called I<wrapping>.
1966 The functions for detecting, constructing and deconstructing
1967 such nested spaces can be found in the wrapping properties
1968 of L</"Unary Properties">, the wrapping operations
1969 of L</"Unary Operations"> and the Cartesian product operations
1970 of L</"Basic Operations">.
1972 Spaces can be created from other spaces
1973 using the functions described in L</"Unary Operations">
1974 and L</"Binary Operations">.
1978 A local space is essentially a space with
1979 zero or more existentially quantified variables.
1980 The local space of various objects can be obtained
1981 using the following functions.
1983 #include <isl/constraint.h>
1984 __isl_give isl_local_space *isl_constraint_get_local_space(
1985 __isl_keep isl_constraint *constraint);
1987 #include <isl/set.h>
1988 __isl_give isl_local_space *isl_basic_set_get_local_space(
1989 __isl_keep isl_basic_set *bset);
1991 #include <isl/map.h>
1992 __isl_give isl_local_space *isl_basic_map_get_local_space(
1993 __isl_keep isl_basic_map *bmap);
1995 #include <isl/aff.h>
1996 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1997 __isl_keep isl_aff *aff);
1998 __isl_give isl_local_space *isl_aff_get_local_space(
1999 __isl_keep isl_aff *aff);
2001 A new local space can be created from a space using
2003 #include <isl/local_space.h>
2004 __isl_give isl_local_space *isl_local_space_from_space(
2005 __isl_take isl_space *space);
2007 They can be inspected, modified, copied and freed using the following functions.
2009 #include <isl/local_space.h>
2010 isl_bool isl_local_space_is_params(
2011 __isl_keep isl_local_space *ls);
2012 isl_bool isl_local_space_is_set(
2013 __isl_keep isl_local_space *ls);
2014 __isl_give isl_space *isl_local_space_get_space(
2015 __isl_keep isl_local_space *ls);
2016 __isl_give isl_aff *isl_local_space_get_div(
2017 __isl_keep isl_local_space *ls, int pos);
2018 __isl_give isl_local_space *isl_local_space_copy(
2019 __isl_keep isl_local_space *ls);
2020 __isl_null isl_local_space *isl_local_space_free(
2021 __isl_take isl_local_space *ls);
2023 Note that C<isl_local_space_get_div> can only be used on local spaces
2026 Two local spaces can be compared using
2028 isl_bool isl_local_space_is_equal(
2029 __isl_keep isl_local_space *ls1,
2030 __isl_keep isl_local_space *ls2);
2032 Local spaces can be created from other local spaces
2033 using the functions described in L</"Unary Operations">
2034 and L</"Binary Operations">.
2036 =head2 Creating New Sets and Relations
2038 C<isl> has functions for creating some standard sets and relations.
2042 =item * Empty sets and relations
2044 __isl_give isl_basic_set *isl_basic_set_empty(
2045 __isl_take isl_space *space);
2046 __isl_give isl_basic_map *isl_basic_map_empty(
2047 __isl_take isl_space *space);
2048 __isl_give isl_set *isl_set_empty(
2049 __isl_take isl_space *space);
2050 __isl_give isl_map *isl_map_empty(
2051 __isl_take isl_space *space);
2052 __isl_give isl_union_set *isl_union_set_empty_ctx(
2054 __isl_give isl_union_set *isl_union_set_empty_space(
2055 __isl_take isl_space *space);
2056 __isl_give isl_union_set *isl_union_set_empty(
2057 __isl_take isl_space *space);
2058 __isl_give isl_union_map *isl_union_map_empty_ctx(
2060 __isl_give isl_union_map *isl_union_map_empty_space(
2061 __isl_take isl_space *space);
2062 __isl_give isl_union_map *isl_union_map_empty(
2063 __isl_take isl_space *space);
2065 For C<isl_union_set>s and C<isl_union_map>s, the space
2066 is only used to specify the parameters.
2067 C<isl_union_set_empty> is an alternative name for
2068 C<isl_union_set_empty_space>.
2069 Similarly for the other pair of functions.
2071 =item * Universe sets and relations
2073 #include <isl/set.h>
2074 __isl_give isl_basic_set *isl_basic_set_universe(
2075 __isl_take isl_space *space);
2076 __isl_give isl_set *isl_set_universe(
2077 __isl_take isl_space *space);
2078 __isl_give isl_set *isl_space_universe_set(
2079 __isl_take isl_space *space);
2081 #include <isl/map.h>
2082 __isl_give isl_basic_map *isl_basic_map_universe(
2083 __isl_take isl_space *space);
2084 __isl_give isl_map *isl_map_universe(
2085 __isl_take isl_space *space);
2086 __isl_give isl_map *isl_space_universe_map(
2087 __isl_take isl_space *space);
2089 #include <isl/union_set.h>
2090 __isl_give isl_union_set *isl_union_set_universe(
2091 __isl_take isl_union_set *uset);
2093 #include <isl/union_map.h>
2094 __isl_give isl_union_map *isl_union_map_universe(
2095 __isl_take isl_union_map *umap);
2097 C<isl_set_universe> and C<isl_space_universe_set>
2098 perform the same operation.
2100 for the pair C<isl_map_universe> and C<isl_space_universe_map>.
2102 The sets and relations constructed by the functions above
2103 contain all integer values, while those constructed by the
2104 functions below only contain non-negative values.
2106 __isl_give isl_basic_set *isl_basic_set_nat_universe(
2107 __isl_take isl_space *space);
2108 __isl_give isl_basic_map *isl_basic_map_nat_universe(
2109 __isl_take isl_space *space);
2110 __isl_give isl_set *isl_set_nat_universe(
2111 __isl_take isl_space *space);
2112 __isl_give isl_map *isl_map_nat_universe(
2113 __isl_take isl_space *space);
2115 =item * Identity relations
2117 __isl_give isl_basic_map *isl_basic_map_identity(
2118 __isl_take isl_space *space);
2119 __isl_give isl_map *isl_map_identity(
2120 __isl_take isl_space *space);
2122 The number of input and output dimensions in C<space> needs
2125 =item * Lexicographic order
2127 __isl_give isl_map *isl_map_lex_lt(
2128 __isl_take isl_space *set_space);
2129 __isl_give isl_map *isl_map_lex_le(
2130 __isl_take isl_space *set_space);
2131 __isl_give isl_map *isl_map_lex_gt(
2132 __isl_take isl_space *set_space);
2133 __isl_give isl_map *isl_map_lex_ge(
2134 __isl_take isl_space *set_space);
2135 __isl_give isl_map *isl_map_lex_lt_first(
2136 __isl_take isl_space *space, unsigned n);
2137 __isl_give isl_map *isl_map_lex_le_first(
2138 __isl_take isl_space *space, unsigned n);
2139 __isl_give isl_map *isl_map_lex_gt_first(
2140 __isl_take isl_space *space, unsigned n);
2141 __isl_give isl_map *isl_map_lex_ge_first(
2142 __isl_take isl_space *space, unsigned n);
2144 The first four functions take a space for a B<set>
2145 and return relations that express that the elements in the domain
2146 are lexicographically less
2147 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
2148 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
2149 than the elements in the range.
2150 The last four functions take a space for a map
2151 and return relations that express that the first C<n> dimensions
2152 in the domain are lexicographically less
2153 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
2154 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
2155 than the first C<n> dimensions in the range.
2159 A basic set or relation can be converted to a set or relation
2160 using the following functions.
2162 __isl_give isl_set *isl_basic_set_to_set(
2163 __isl_take isl_basic_set *bset);
2164 __isl_give isl_set *isl_set_from_basic_set(
2165 __isl_take isl_basic_set *bset);
2166 __isl_give isl_map *isl_map_from_basic_map(
2167 __isl_take isl_basic_map *bmap);
2169 C<isl_basic_set_to_set> and C<isl_set_from_basic_set> perform
2172 Sets and relations can be converted to union sets and relations
2173 using the following functions.
2175 __isl_give isl_union_set *isl_union_set_from_basic_set(
2176 __isl_take isl_basic_set *bset);
2177 __isl_give isl_union_map *isl_union_map_from_basic_map(
2178 __isl_take isl_basic_map *bmap);
2179 __isl_give isl_union_set *isl_set_to_union_set(
2180 __isl_take isl_set *set);
2181 __isl_give isl_union_set *isl_union_set_from_set(
2182 __isl_take isl_set *set);
2183 __isl_give isl_union_map *isl_map_to_union_map(
2184 __isl_take isl_map *map);
2185 __isl_give isl_union_map *isl_union_map_from_map(
2186 __isl_take isl_map *map);
2188 C<isl_map_to_union_map> and C<isl_union_map_from_map> perform
2190 Similarly for C<isl_set_to_union_set> and C<isl_union_set_from_set>.
2192 The inverse conversions below can only be used if the input
2193 union set or relation is known to contain elements in exactly one
2196 #include <isl/union_set.h>
2197 isl_bool isl_union_set_isa_set(
2198 __isl_keep isl_union_set *uset);
2199 __isl_give isl_set *isl_union_set_as_set(
2200 __isl_take isl_union_set *uset);
2201 __isl_give isl_set *isl_set_from_union_set(
2202 __isl_take isl_union_set *uset);
2204 #include <isl/union_map.h>
2205 isl_bool isl_union_map_isa_map(
2206 __isl_keep isl_union_map *umap);
2207 __isl_give isl_map *isl_union_map_as_map(
2208 __isl_take isl_union_map *umap);
2209 __isl_give isl_map *isl_map_from_union_map(
2210 __isl_take isl_union_map *umap);
2212 C<isl_union_map_as_map> and C<isl_map_from_union_map> perform
2214 Similarly for C<isl_union_set_as_set> and C<isl_set_from_union_set>.
2216 Sets and relations can be copied and freed again using the following
2219 __isl_give isl_basic_set *isl_basic_set_copy(
2220 __isl_keep isl_basic_set *bset);
2221 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
2222 __isl_give isl_union_set *isl_union_set_copy(
2223 __isl_keep isl_union_set *uset);
2224 __isl_give isl_basic_map *isl_basic_map_copy(
2225 __isl_keep isl_basic_map *bmap);
2226 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
2227 __isl_give isl_union_map *isl_union_map_copy(
2228 __isl_keep isl_union_map *umap);
2229 __isl_null isl_basic_set *isl_basic_set_free(
2230 __isl_take isl_basic_set *bset);
2231 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
2232 __isl_null isl_union_set *isl_union_set_free(
2233 __isl_take isl_union_set *uset);
2234 __isl_null isl_basic_map *isl_basic_map_free(
2235 __isl_take isl_basic_map *bmap);
2236 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
2237 __isl_null isl_union_map *isl_union_map_free(
2238 __isl_take isl_union_map *umap);
2240 Other sets and relations can be constructed by starting
2241 from a universe set or relation, adding equality and/or
2242 inequality constraints and then projecting out the
2243 existentially quantified variables, if any.
2244 Constraints can be constructed, manipulated and
2245 added to (or removed from) (basic) sets and relations
2246 using the following functions.
2248 #include <isl/constraint.h>
2249 __isl_give isl_constraint *isl_constraint_alloc_equality(
2250 __isl_take isl_local_space *ls);
2251 __isl_give isl_constraint *isl_constraint_alloc_inequality(
2252 __isl_take isl_local_space *ls);
2253 __isl_give isl_constraint *isl_constraint_set_constant_si(
2254 __isl_take isl_constraint *constraint, int v);
2255 __isl_give isl_constraint *isl_constraint_set_constant_val(
2256 __isl_take isl_constraint *constraint,
2257 __isl_take isl_val *v);
2258 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
2259 __isl_take isl_constraint *constraint,
2260 enum isl_dim_type type, int pos, int v);
2261 __isl_give isl_constraint *
2262 isl_constraint_set_coefficient_val(
2263 __isl_take isl_constraint *constraint,
2264 enum isl_dim_type type, int pos,
2265 __isl_take isl_val *v);
2266 __isl_give isl_basic_map *isl_basic_map_add_constraint(
2267 __isl_take isl_basic_map *bmap,
2268 __isl_take isl_constraint *constraint);
2269 __isl_give isl_basic_set *isl_basic_set_add_constraint(
2270 __isl_take isl_basic_set *bset,
2271 __isl_take isl_constraint *constraint);
2272 __isl_give isl_map *isl_map_add_constraint(
2273 __isl_take isl_map *map,
2274 __isl_take isl_constraint *constraint);
2275 __isl_give isl_set *isl_set_add_constraint(
2276 __isl_take isl_set *set,
2277 __isl_take isl_constraint *constraint);
2279 For example, to create a set containing the even integers
2280 between 10 and 42, you could use the following code.
2283 isl_local_space *ls;
2285 isl_basic_set *bset;
2287 space = isl_space_set_alloc(ctx, 0, 2);
2288 bset = isl_basic_set_universe(isl_space_copy(space));
2289 ls = isl_local_space_from_space(space);
2291 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
2292 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2293 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
2294 bset = isl_basic_set_add_constraint(bset, c);
2296 c = isl_constraint_alloc_inequality(isl_local_space_copy(ls));
2297 c = isl_constraint_set_constant_si(c, -10);
2298 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
2299 bset = isl_basic_set_add_constraint(bset, c);
2301 c = isl_constraint_alloc_inequality(ls);
2302 c = isl_constraint_set_constant_si(c, 42);
2303 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2304 bset = isl_basic_set_add_constraint(bset, c);
2306 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
2308 However, this is considered to be a fairly low-level approach.
2309 It is more appropriate to construct a (basic) set by means
2310 of affine expressions (defined below in L</"Functions">).
2311 For example, the same set could be constructed as follows.
2317 isl_basic_set *bset;
2319 space = isl_space_unit(ctx);
2320 space = isl_space_add_unnamed_tuple_ui(space, 1);
2321 ma = isl_multi_aff_identity_on_domain_space(
2322 isl_space_copy(space));
2323 var = isl_multi_aff_get_at(ma, 0);
2324 v = isl_val_int_from_si(ctx, 10);
2325 cst = isl_aff_val_on_domain_space(isl_space_copy(space), v);
2326 bset = isl_aff_ge_basic_set(isl_aff_copy(var), cst);
2328 v = isl_val_int_from_si(ctx, 42);
2329 cst = isl_aff_val_on_domain_space(space, v);
2330 bset = isl_basic_set_intersect(bset,
2331 isl_aff_le_basic_set(var, cst));
2333 two = isl_val_int_from_si(ctx, 2);
2334 ma = isl_multi_aff_scale_val(ma, isl_val_copy(two));
2335 bset = isl_basic_set_preimage_multi_aff(bset,
2336 isl_multi_aff_copy(ma));
2337 ma = isl_multi_aff_scale_down_val(ma, isl_val_copy(two));
2338 ma = isl_multi_aff_scale_down_val(ma, two);
2339 bset = isl_basic_set_preimage_multi_aff(bset, ma);
2341 Alternatively, the set can be parsed from a string representation.
2343 isl_basic_set *bset;
2344 bset = isl_basic_set_read_from_str(ctx,
2345 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
2347 A basic set or relation can also be constructed from two matrices
2348 describing the equalities and the inequalities.
2350 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
2351 __isl_take isl_space *space,
2352 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2353 enum isl_dim_type c1,
2354 enum isl_dim_type c2, enum isl_dim_type c3,
2355 enum isl_dim_type c4);
2356 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
2357 __isl_take isl_space *space,
2358 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2359 enum isl_dim_type c1,
2360 enum isl_dim_type c2, enum isl_dim_type c3,
2361 enum isl_dim_type c4, enum isl_dim_type c5);
2363 The C<isl_dim_type> arguments indicate the order in which
2364 different kinds of variables appear in the input matrices
2365 and should be a permutation of C<isl_dim_cst> (the constant term),
2366 C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div> for sets and
2367 of C<isl_dim_cst>, C<isl_dim_param>,
2368 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
2370 A (basic or union) set or relation can also be constructed from a
2371 (union) (piecewise) (multiple) affine expression
2372 or a list of affine expressions
2373 (See L</"Functions">), provided these affine expressions do not
2376 #include <isl/set.h>
2377 __isl_give isl_basic_set *isl_basic_set_from_multi_aff(
2378 __isl_take isl_multi_aff *ma);
2379 __isl_give isl_set *isl_multi_aff_as_set(
2380 __isl_take isl_multi_aff *ma);
2381 __isl_give isl_set *isl_set_from_multi_aff(
2382 __isl_take isl_multi_aff *ma);
2384 #include <isl/map.h>
2385 __isl_give isl_basic_map *isl_basic_map_from_aff(
2386 __isl_take isl_aff *aff);
2387 __isl_give isl_map *isl_map_from_aff(
2388 __isl_take isl_aff *aff);
2389 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
2390 __isl_take isl_space *domain_space,
2391 __isl_take isl_aff_list *list);
2392 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
2393 __isl_take isl_multi_aff *maff)
2394 __isl_give isl_map *isl_multi_aff_as_map(
2395 __isl_take isl_multi_aff *ma);
2396 __isl_give isl_map *isl_map_from_multi_aff(
2397 __isl_take isl_multi_aff *maff)
2399 #include <isl/aff.h>
2400 __isl_give isl_set *isl_set_from_pw_aff(
2401 __isl_take isl_pw_aff *pwaff);
2402 __isl_give isl_map *isl_pw_aff_as_map(
2403 __isl_take isl_pw_aff *pa);
2404 __isl_give isl_map *isl_map_from_pw_aff(
2405 __isl_take isl_pw_aff *pwaff);
2406 __isl_give isl_set *isl_pw_multi_aff_as_set(
2407 __isl_take isl_pw_multi_aff *pma);
2408 __isl_give isl_set *isl_set_from_pw_multi_aff(
2409 __isl_take isl_pw_multi_aff *pma);
2410 __isl_give isl_map *isl_pw_multi_aff_as_map(
2411 __isl_take isl_pw_multi_aff *pma);
2412 __isl_give isl_map *isl_map_from_pw_multi_aff(
2413 __isl_take isl_pw_multi_aff *pma);
2414 __isl_give isl_set *isl_multi_pw_aff_as_set(
2415 __isl_take isl_multi_pw_aff *mpa);
2416 __isl_give isl_set *isl_set_from_multi_pw_aff(
2417 __isl_take isl_multi_pw_aff *mpa);
2418 __isl_give isl_map *isl_multi_pw_aff_as_map(
2419 __isl_take isl_multi_pw_aff *mpa);
2420 __isl_give isl_map *isl_map_from_multi_pw_aff(
2421 __isl_take isl_multi_pw_aff *mpa);
2422 __isl_give isl_union_map *isl_union_map_from_union_pw_aff(
2423 __isl_take isl_union_pw_aff *upa);
2424 __isl_give isl_union_map *
2425 isl_union_pw_multi_aff_as_union_map(
2426 __isl_take isl_union_pw_multi_aff *upma);
2427 __isl_give isl_union_map *
2428 isl_union_map_from_union_pw_multi_aff(
2429 __isl_take isl_union_pw_multi_aff *upma);
2430 __isl_give isl_union_map *
2431 isl_union_map_from_multi_union_pw_aff(
2432 __isl_take isl_multi_union_pw_aff *mupa);
2434 The C<domain_space> argument describes the domain of the resulting
2435 basic relation. It is required because the C<list> may consist
2436 of zero affine expressions.
2437 The C<mupa> passed to C<isl_union_map_from_multi_union_pw_aff>
2438 is not allowed to be zero-dimensional. The domain of the result
2439 is the shared domain of the union piecewise affine elements.
2440 C<isl_multi_aff_as_set> and C<isl_set_from_multi_aff> perform
2442 Similarly for the pair C<isl_multi_aff_as_map> and C<isl_map_from_multi_aff>,
2443 for the pair C<isl_pw_aff_as_map> and C<isl_map_from_pw_aff>,
2444 for the pair C<isl_pw_multi_aff_as_set> and C<isl_set_from_pw_multi_aff>,
2445 for the pair C<isl_pw_multi_aff_as_map> and C<isl_map_from_pw_multi_aff>,
2446 the pair C<isl_multi_pw_aff_as_set> and C<isl_set_from_multi_pw_aff>,
2447 the pair C<isl_multi_pw_aff_as_map> and C<isl_map_from_multi_pw_aff>,
2449 C<isl_union_pw_multi_aff_as_union_map> and
2450 C<isl_union_map_from_union_pw_multi_aff>.
2452 =head2 Inspecting Sets and Relations
2454 Usually, the user should not have to care about the actual constraints
2455 of the sets and maps, but should instead apply the abstract operations
2456 explained in the following sections.
2457 Occasionally, however, it may be required to inspect the individual
2458 coefficients of the constraints. This section explains how to do so.
2459 In these cases, it may also be useful to have C<isl> compute
2460 an explicit representation of the existentially quantified variables.
2462 __isl_give isl_set *isl_set_compute_divs(
2463 __isl_take isl_set *set);
2464 __isl_give isl_map *isl_map_compute_divs(
2465 __isl_take isl_map *map);
2466 __isl_give isl_union_set *isl_union_set_compute_divs(
2467 __isl_take isl_union_set *uset);
2468 __isl_give isl_union_map *isl_union_map_compute_divs(
2469 __isl_take isl_union_map *umap);
2471 This explicit representation defines the existentially quantified
2472 variables as integer divisions of the other variables, possibly
2473 including earlier existentially quantified variables.
2474 An explicitly represented existentially quantified variable therefore
2475 has a unique value when the values of the other variables are known.
2477 Alternatively, the existentially quantified variables can be removed
2478 using the following functions, which compute an overapproximation.
2480 #include <isl/set.h>
2481 __isl_give isl_basic_set *isl_basic_set_remove_divs(
2482 __isl_take isl_basic_set *bset);
2483 __isl_give isl_set *isl_set_remove_divs(
2484 __isl_take isl_set *set);
2486 #include <isl/map.h>
2487 __isl_give isl_basic_map *isl_basic_map_remove_divs(
2488 __isl_take isl_basic_map *bmap);
2489 __isl_give isl_map *isl_map_remove_divs(
2490 __isl_take isl_map *map);
2492 #include <isl/union_set.h>
2493 __isl_give isl_union_set *isl_union_set_remove_divs(
2494 __isl_take isl_union_set *bset);
2496 #include <isl/union_map.h>
2497 __isl_give isl_union_map *isl_union_map_remove_divs(
2498 __isl_take isl_union_map *bmap);
2500 It is also possible to only remove those divs that are defined
2501 in terms of a given range of dimensions or only those for which
2502 no explicit representation is known.
2504 __isl_give isl_basic_set *
2505 isl_basic_set_remove_divs_involving_dims(
2506 __isl_take isl_basic_set *bset,
2507 enum isl_dim_type type,
2508 unsigned first, unsigned n);
2509 __isl_give isl_basic_map *
2510 isl_basic_map_remove_divs_involving_dims(
2511 __isl_take isl_basic_map *bmap,
2512 enum isl_dim_type type,
2513 unsigned first, unsigned n);
2514 __isl_give isl_set *isl_set_remove_divs_involving_dims(
2515 __isl_take isl_set *set, enum isl_dim_type type,
2516 unsigned first, unsigned n);
2517 __isl_give isl_map *isl_map_remove_divs_involving_dims(
2518 __isl_take isl_map *map, enum isl_dim_type type,
2519 unsigned first, unsigned n);
2521 __isl_give isl_basic_set *
2522 isl_basic_set_remove_unknown_divs(
2523 __isl_take isl_basic_set *bset);
2524 __isl_give isl_set *isl_set_remove_unknown_divs(
2525 __isl_take isl_set *set);
2526 __isl_give isl_map *isl_map_remove_unknown_divs(
2527 __isl_take isl_map *map);
2529 To iterate over all the sets or maps in a union set or map, use
2531 #include <isl/union_set.h>
2532 isl_stat isl_union_set_foreach_set(
2533 __isl_keep isl_union_set *uset,
2534 isl_stat (*fn)(__isl_take isl_set *set, void *user),
2536 isl_bool isl_union_set_every_set(
2537 __isl_keep isl_union_set *uset,
2538 isl_bool (*test)(__isl_keep isl_set *set,
2542 #include <isl/union_map.h>
2543 isl_stat isl_union_map_foreach_map(
2544 __isl_keep isl_union_map *umap,
2545 isl_stat (*fn)(__isl_take isl_map *map, void *user),
2547 isl_bool isl_union_map_every_map(
2548 __isl_keep isl_union_map *umap,
2549 isl_bool (*test)(__isl_keep isl_map *map,
2553 These functions call the callback function once for each
2554 (pair of) space(s) for which there are elements in the input.
2555 The argument to the callback contains all elements in the input
2556 with that (pair of) space(s).
2557 The C<isl_union_set_every_set> and
2558 C<isl_union_map_every_map> variants check whether each
2559 call to the callback returns true and stops checking as soon as one
2560 of these calls returns false.
2562 The number of sets or maps in a union set or map can be obtained
2565 isl_size isl_union_set_n_set(__isl_keep isl_union_set *uset);
2566 isl_size isl_union_map_n_map(__isl_keep isl_union_map *umap);
2568 To extract the set or map in a given space from a union, use
2570 __isl_give isl_set *isl_union_set_extract_set(
2571 __isl_keep isl_union_set *uset,
2572 __isl_take isl_space *space);
2573 __isl_give isl_map *isl_union_map_extract_map(
2574 __isl_keep isl_union_map *umap,
2575 __isl_take isl_space *space);
2577 To iterate over all the basic sets or maps in a set or map, use
2579 isl_stat isl_set_foreach_basic_set(__isl_keep isl_set *set,
2580 isl_stat (*fn)(__isl_take isl_basic_set *bset,
2583 isl_stat isl_map_foreach_basic_map(__isl_keep isl_map *map,
2584 isl_stat (*fn)(__isl_take isl_basic_map *bmap,
2588 The callback function C<fn> should return C<isl_stat_ok> if successful and
2589 C<isl_stat_error> if an error occurs. In the latter case, or if any other error
2590 occurs, the above functions will return C<isl_stat_error>.
2592 It should be noted that C<isl> does not guarantee that
2593 the basic sets or maps passed to C<fn> are disjoint.
2594 If this is required, then the user should call one of
2595 the following functions first.
2597 __isl_give isl_set *isl_set_make_disjoint(
2598 __isl_take isl_set *set);
2599 __isl_give isl_map *isl_map_make_disjoint(
2600 __isl_take isl_map *map);
2602 The number of basic sets in a set can be obtained
2603 or the number of basic maps in a map can be obtained
2606 #include <isl/set.h>
2607 isl_size isl_set_n_basic_set(__isl_keep isl_set *set);
2609 #include <isl/map.h>
2610 isl_size isl_map_n_basic_map(__isl_keep isl_map *map);
2612 It is also possible to obtain a list of (basic) sets from a set
2613 or union set, a list of basic maps from a map and a list of maps from a union
2616 #include <isl/set.h>
2617 __isl_give isl_basic_set_list *isl_set_get_basic_set_list(
2618 __isl_keep isl_set *set);
2620 #include <isl/union_set.h>
2621 __isl_give isl_basic_set_list *
2622 isl_union_set_get_basic_set_list(
2623 __isl_keep isl_union_set *uset);
2624 __isl_give isl_set_list *isl_union_set_get_set_list(
2625 __isl_keep isl_union_set *uset);
2627 #include <isl/map.h>
2628 __isl_give isl_basic_map_list *isl_map_get_basic_map_list(
2629 __isl_keep isl_map *map);
2631 #include <isl/union_map.h>
2632 __isl_give isl_map_list *isl_union_map_get_map_list(
2633 __isl_keep isl_union_map *umap);
2635 The returned list can be manipulated using the functions in L<"Lists">.
2637 To iterate over the constraints of a basic set or map, use
2639 #include <isl/constraint.h>
2641 isl_size isl_basic_set_n_constraint(
2642 __isl_keep isl_basic_set *bset);
2643 isl_stat isl_basic_set_foreach_constraint(
2644 __isl_keep isl_basic_set *bset,
2645 isl_stat (*fn)(__isl_take isl_constraint *c,
2648 isl_size isl_basic_map_n_constraint(
2649 __isl_keep isl_basic_map *bmap);
2650 isl_stat isl_basic_map_foreach_constraint(
2651 __isl_keep isl_basic_map *bmap,
2652 isl_stat (*fn)(__isl_take isl_constraint *c,
2655 __isl_null isl_constraint *isl_constraint_free(
2656 __isl_take isl_constraint *c);
2658 Again, the callback function C<fn> should return C<isl_stat_ok>
2660 C<isl_stat_error> if an error occurs. In the latter case, or if any other error
2661 occurs, the above functions will return C<isl_stat_error>.
2662 The constraint C<c> represents either an equality or an inequality.
2663 Use the following function to find out whether a constraint
2664 represents an equality. If not, it represents an inequality.
2666 isl_bool isl_constraint_is_equality(
2667 __isl_keep isl_constraint *constraint);
2669 It is also possible to obtain a list of constraints from a basic
2672 #include <isl/constraint.h>
2673 __isl_give isl_constraint_list *
2674 isl_basic_map_get_constraint_list(
2675 __isl_keep isl_basic_map *bmap);
2676 __isl_give isl_constraint_list *
2677 isl_basic_set_get_constraint_list(
2678 __isl_keep isl_basic_set *bset);
2680 These functions require that all existentially quantified variables
2681 have an explicit representation.
2682 The returned list can be manipulated using the functions in L<"Lists">.
2684 The coefficients of the constraints can be inspected using
2685 the following functions.
2687 isl_bool isl_constraint_is_lower_bound(
2688 __isl_keep isl_constraint *constraint,
2689 enum isl_dim_type type, unsigned pos);
2690 isl_bool isl_constraint_is_upper_bound(
2691 __isl_keep isl_constraint *constraint,
2692 enum isl_dim_type type, unsigned pos);
2693 __isl_give isl_val *isl_constraint_get_constant_val(
2694 __isl_keep isl_constraint *constraint);
2695 __isl_give isl_val *isl_constraint_get_coefficient_val(
2696 __isl_keep isl_constraint *constraint,
2697 enum isl_dim_type type, int pos);
2699 The explicit representations of the existentially quantified
2700 variables can be inspected using the following function.
2701 Note that the user is only allowed to use this function
2702 if the inspected set or map is the result of a call
2703 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2704 The existentially quantified variable is equal to the floor
2705 of the returned affine expression. The affine expression
2706 itself can be inspected using the functions in
2709 __isl_give isl_aff *isl_constraint_get_div(
2710 __isl_keep isl_constraint *constraint, int pos);
2712 To obtain the constraints of a basic set or map in matrix
2713 form, use the following functions.
2715 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2716 __isl_keep isl_basic_set *bset,
2717 enum isl_dim_type c1, enum isl_dim_type c2,
2718 enum isl_dim_type c3, enum isl_dim_type c4);
2719 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2720 __isl_keep isl_basic_set *bset,
2721 enum isl_dim_type c1, enum isl_dim_type c2,
2722 enum isl_dim_type c3, enum isl_dim_type c4);
2723 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2724 __isl_keep isl_basic_map *bmap,
2725 enum isl_dim_type c1,
2726 enum isl_dim_type c2, enum isl_dim_type c3,
2727 enum isl_dim_type c4, enum isl_dim_type c5);
2728 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2729 __isl_keep isl_basic_map *bmap,
2730 enum isl_dim_type c1,
2731 enum isl_dim_type c2, enum isl_dim_type c3,
2732 enum isl_dim_type c4, enum isl_dim_type c5);
2734 The C<isl_dim_type> arguments dictate the order in which
2735 different kinds of variables appear in the resulting matrix.
2736 For set inputs, they should be a permutation of
2737 C<isl_dim_cst> (the constant term), C<isl_dim_param>, C<isl_dim_set> and
2739 For map inputs, they should be a permutation of
2740 C<isl_dim_cst>, C<isl_dim_param>,
2741 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2745 Points are elements of a set. They can be used to construct
2746 simple sets (boxes) or they can be used to represent the
2747 individual elements of a set.
2748 The zero point (the origin) can be created using
2750 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2752 The coordinates of a point can be inspected, set and changed
2755 #include <isl/point.h>
2756 __isl_give isl_multi_val *isl_point_get_multi_val(
2757 __isl_keep isl_point *pnt);
2758 __isl_give isl_val *isl_point_get_coordinate_val(
2759 __isl_keep isl_point *pnt,
2760 enum isl_dim_type type, int pos);
2761 __isl_give isl_point *isl_point_set_coordinate_val(
2762 __isl_take isl_point *pnt,
2763 enum isl_dim_type type, int pos,
2764 __isl_take isl_val *v);
2766 __isl_give isl_point *isl_point_add_ui(
2767 __isl_take isl_point *pnt,
2768 enum isl_dim_type type, int pos, unsigned val);
2769 __isl_give isl_point *isl_point_sub_ui(
2770 __isl_take isl_point *pnt,
2771 enum isl_dim_type type, int pos, unsigned val);
2773 Points can be copied or freed using
2775 __isl_give isl_point *isl_point_copy(
2776 __isl_keep isl_point *pnt);
2777 __isl_null isl_point *isl_point_free(
2778 __isl_take isl_point *pnt);
2780 A singleton set can be created from a point using the following functions.
2782 __isl_give isl_basic_set *isl_basic_set_from_point(
2783 __isl_take isl_point *pnt);
2784 __isl_give isl_set *isl_point_to_set(
2785 __isl_take isl_point *pnt);
2786 __isl_give isl_set *isl_set_from_point(
2787 __isl_take isl_point *pnt);
2788 __isl_give isl_union_set *isl_union_set_from_point(
2789 __isl_take isl_point *pnt);
2791 C<isl_point_to_set> and C<isl_set_from_point> perform
2794 A box can be created from two opposite extremal points using
2796 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2797 __isl_take isl_point *pnt1,
2798 __isl_take isl_point *pnt2);
2799 __isl_give isl_set *isl_set_box_from_points(
2800 __isl_take isl_point *pnt1,
2801 __isl_take isl_point *pnt2);
2803 All elements of a B<bounded> (union) set can be enumerated using
2804 the following functions.
2806 isl_stat isl_set_foreach_point(__isl_keep isl_set *set,
2807 isl_stat (*fn)(__isl_take isl_point *pnt,
2810 isl_stat isl_union_set_foreach_point(
2811 __isl_keep isl_union_set *uset,
2812 isl_stat (*fn)(__isl_take isl_point *pnt,
2816 The function C<fn> is called for each integer point in
2817 C<set> with as second argument the last argument of
2818 the C<isl_set_foreach_point> call. The function C<fn>
2819 should return C<isl_stat_ok> on success and C<isl_stat_error> on failure.
2820 In the latter case, C<isl_set_foreach_point> will stop
2821 enumerating and return C<isl_stat_error> as well.
2822 If the enumeration is performed successfully and to completion,
2823 then C<isl_set_foreach_point> returns C<isl_stat_ok>.
2825 To obtain a single point of a (basic or union) set, use
2827 __isl_give isl_point *isl_basic_set_sample_point(
2828 __isl_take isl_basic_set *bset);
2829 __isl_give isl_point *isl_set_sample_point(
2830 __isl_take isl_set *set);
2831 __isl_give isl_point *isl_union_set_sample_point(
2832 __isl_take isl_union_set *uset);
2834 If C<set> does not contain any (integer) points, then the
2835 resulting point will be ``void'', a property that can be
2838 isl_bool isl_point_is_void(__isl_keep isl_point *pnt);
2842 Besides sets and relation, C<isl> also supports various types of functions.
2843 Each of these types is derived from the value type (see L</"Values">)
2844 or from one of two primitive function types
2845 through the application of zero or more type constructors.
2846 As a special case, a multiple expression can also be derived
2847 from an identifier (see L</"Identifiers">) although the result
2848 is not really a function.
2849 We first describe the primitive type and then we describe
2850 the types derived from these primitive types.
2852 =head3 Primitive Functions
2854 C<isl> support two primitive function types, quasi-affine
2855 expressions and quasipolynomials.
2856 A quasi-affine expression is defined either over a parameter
2857 space or over a set and is composed of integer constants,
2858 parameters and set variables, addition, subtraction and
2859 integer division by an integer constant.
2860 For example, the quasi-affine expression
2862 [n] -> { [x] -> [2*floor((4 n + x)/9)] }
2864 maps C<x> to C<2*floor((4 n + x)/9>.
2865 A quasipolynomial is a polynomial expression in quasi-affine
2866 expression. That is, it additionally allows for multiplication.
2867 Note, though, that it is not allowed to construct an integer
2868 division of an expression involving multiplications.
2869 Here is an example of a quasipolynomial that is not
2870 quasi-affine expression
2872 [n] -> { [x] -> (n*floor((4 n + x)/9)) }
2874 Note that the external representations of quasi-affine expressions
2875 and quasipolynomials are different. Quasi-affine expressions
2876 use a notation with square brackets just like binary relations,
2877 while quasipolynomials do not. This might change at some point.
2879 If a primitive function is defined over a parameter space,
2880 then the space of the function itself is that of a set.
2881 If it is defined over a set, then the space of the function
2882 is that of a relation. In both cases, the set space (or
2883 the output space) is single-dimensional, anonymous and unstructured.
2884 To create functions with multiple dimensions or with other kinds
2885 of set or output spaces, use multiple expressions
2886 (see L</"Multiple Expressions">).
2890 =item * Quasi-affine Expressions
2892 Besides the expressions described above, a quasi-affine
2893 expression can also be set to NaN. Such expressions
2894 typically represent a failure to represent a result
2895 as a quasi-affine expression.
2897 The zero quasi affine expression or the quasi affine expression
2898 that is equal to a given value, parameter or
2899 a specified dimension on a given domain can be created using
2901 #include <isl/aff.h>
2902 __isl_give isl_aff *isl_aff_zero_on_domain_space(
2903 __isl_take isl_space *space);
2904 __isl_give isl_aff *isl_space_zero_aff_on_domain(
2905 __isl_take isl_space *space);
2906 __isl_give isl_aff *isl_aff_zero_on_domain(
2907 __isl_take isl_local_space *ls);
2908 __isl_give isl_aff *isl_aff_val_on_domain_space(
2909 __isl_take isl_space *space,
2910 __isl_take isl_val *val);
2911 __isl_give isl_aff *isl_aff_val_on_domain(
2912 __isl_take isl_local_space *ls,
2913 __isl_take isl_val *val);
2914 __isl_give isl_aff *isl_aff_param_on_domain_space_id(
2915 __isl_take isl_space *space,
2916 __isl_take isl_id *id);
2917 __isl_give isl_aff *isl_space_param_aff_on_domain_id(
2918 __isl_take isl_space *space,
2919 __isl_take isl_id *id);
2920 __isl_give isl_aff *isl_aff_var_on_domain(
2921 __isl_take isl_local_space *ls,
2922 enum isl_dim_type type, unsigned pos);
2923 __isl_give isl_aff *isl_aff_nan_on_domain_space(
2924 __isl_take isl_space *space);
2925 __isl_give isl_aff *isl_aff_nan_on_domain(
2926 __isl_take isl_local_space *ls);
2928 The space passed to C<isl_aff_param_on_domain_space_id>
2929 is required to have a parameter with the given identifier.
2930 C<isl_aff_param_on_domain_space_id> and
2931 C<isl_space_param_aff_on_domain_id> perform the same operation.
2933 C<isl_aff_zero_on_domain_space> and C<isl_space_zero_aff_on_domain>
2934 perform the same operation.
2936 Quasi affine expressions can be copied and freed using
2938 #include <isl/aff.h>
2939 __isl_give isl_aff *isl_aff_copy(
2940 __isl_keep isl_aff *aff);
2941 __isl_null isl_aff *isl_aff_free(
2942 __isl_take isl_aff *aff);
2944 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2945 using the following function. The constraint is required to have
2946 a non-zero coefficient for the specified dimension.
2948 #include <isl/constraint.h>
2949 __isl_give isl_aff *isl_constraint_get_bound(
2950 __isl_keep isl_constraint *constraint,
2951 enum isl_dim_type type, int pos);
2953 The entire affine expression of the constraint can also be extracted
2954 using the following function.
2956 #include <isl/constraint.h>
2957 __isl_give isl_aff *isl_constraint_get_aff(
2958 __isl_keep isl_constraint *constraint);
2960 Conversely, an equality constraint equating
2961 the affine expression to zero or an inequality constraint enforcing
2962 the affine expression to be non-negative, can be constructed using
2964 __isl_give isl_constraint *isl_equality_from_aff(
2965 __isl_take isl_aff *aff);
2966 __isl_give isl_constraint *isl_inequality_from_aff(
2967 __isl_take isl_aff *aff);
2969 The coefficients and the integer divisions of an affine expression
2970 can be inspected using the following functions.
2972 #include <isl/aff.h>
2973 __isl_give isl_val *isl_aff_get_constant_val(
2974 __isl_keep isl_aff *aff);
2975 __isl_give isl_val *isl_aff_get_coefficient_val(
2976 __isl_keep isl_aff *aff,
2977 enum isl_dim_type type, int pos);
2978 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2979 enum isl_dim_type type, int pos);
2980 __isl_give isl_val *isl_aff_get_denominator_val(
2981 __isl_keep isl_aff *aff);
2982 __isl_give isl_aff *isl_aff_get_div(
2983 __isl_keep isl_aff *aff, int pos);
2985 They can be modified using the following functions.
2987 #include <isl/aff.h>
2988 __isl_give isl_aff *isl_aff_set_constant_si(
2989 __isl_take isl_aff *aff, int v);
2990 __isl_give isl_aff *isl_aff_set_constant_val(
2991 __isl_take isl_aff *aff, __isl_take isl_val *v);
2992 __isl_give isl_aff *isl_aff_set_coefficient_si(
2993 __isl_take isl_aff *aff,
2994 enum isl_dim_type type, int pos, int v);
2995 __isl_give isl_aff *isl_aff_set_coefficient_val(
2996 __isl_take isl_aff *aff,
2997 enum isl_dim_type type, int pos,
2998 __isl_take isl_val *v);
3000 __isl_give isl_aff *isl_aff_add_constant_si(
3001 __isl_take isl_aff *aff, int v);
3002 __isl_give isl_aff *isl_aff_add_constant_val(
3003 __isl_take isl_aff *aff, __isl_take isl_val *v);
3004 __isl_give isl_aff *isl_aff_add_constant_num_si(
3005 __isl_take isl_aff *aff, int v);
3006 __isl_give isl_aff *isl_aff_add_coefficient_si(
3007 __isl_take isl_aff *aff,
3008 enum isl_dim_type type, int pos, int v);
3009 __isl_give isl_aff *isl_aff_add_coefficient_val(
3010 __isl_take isl_aff *aff,
3011 enum isl_dim_type type, int pos,
3012 __isl_take isl_val *v);
3014 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
3015 set the I<numerator> of the constant or coefficient, while
3016 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
3017 the constant or coefficient as a whole.
3018 The C<add_constant> and C<add_coefficient> functions add an integer
3019 or rational value to
3020 the possibly rational constant or coefficient.
3021 The C<add_constant_num> functions add an integer value to
3024 =item * Quasipolynomials
3026 Some simple quasipolynomials can be created using the following functions.
3028 #include <isl/polynomial.h>
3029 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3030 __isl_take isl_space *domain);
3031 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3032 __isl_take isl_space *domain);
3033 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3034 __isl_take isl_space *domain);
3035 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3036 __isl_take isl_space *domain);
3037 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3038 __isl_take isl_space *domain);
3039 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
3040 __isl_take isl_space *domain,
3041 __isl_take isl_val *val);
3042 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3043 __isl_take isl_space *domain,
3044 enum isl_dim_type type, unsigned pos);
3045 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3046 __isl_take isl_aff *aff);
3048 Recall that the space in which a quasipolynomial lives is a map space
3049 with a one-dimensional range. The C<domain> argument in some of
3050 the functions above corresponds to the domain of this map space.
3052 Quasipolynomials can be copied and freed again using the following
3055 #include <isl/polynomial.h>
3056 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3057 __isl_keep isl_qpolynomial *qp);
3058 __isl_null isl_qpolynomial *isl_qpolynomial_free(
3059 __isl_take isl_qpolynomial *qp);
3061 The constant term of a quasipolynomial can be extracted using
3063 __isl_give isl_val *isl_qpolynomial_get_constant_val(
3064 __isl_keep isl_qpolynomial *qp);
3066 To iterate over all terms in a quasipolynomial,
3069 isl_stat isl_qpolynomial_foreach_term(
3070 __isl_keep isl_qpolynomial *qp,
3071 isl_stat (*fn)(__isl_take isl_term *term,
3072 void *user), void *user);
3074 The terms themselves can be inspected and freed using
3077 isl_size isl_term_dim(__isl_keep isl_term *term,
3078 enum isl_dim_type type);
3079 __isl_give isl_val *isl_term_get_coefficient_val(
3080 __isl_keep isl_term *term);
3081 isl_size isl_term_get_exp(__isl_keep isl_term *term,
3082 enum isl_dim_type type, unsigned pos);
3083 __isl_give isl_aff *isl_term_get_div(
3084 __isl_keep isl_term *term, unsigned pos);
3085 __isl_null isl_term *isl_term_free(
3086 __isl_take isl_term *term);
3088 Each term is a product of parameters, set variables and
3089 integer divisions. The function C<isl_term_get_exp>
3090 returns the exponent of a given dimensions in the given term.
3096 A reduction represents a maximum or a minimum of its
3098 The only reduction type defined by C<isl> is
3099 C<isl_qpolynomial_fold>.
3101 There are currently no functions to directly create such
3102 objects, but they do appear in the piecewise quasipolynomial
3103 reductions returned by the C<isl_pw_qpolynomial_bound> function.
3105 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
3107 Reductions can be copied and freed using
3108 the following functions.
3110 #include <isl/polynomial.h>
3111 __isl_give isl_qpolynomial_fold *
3112 isl_qpolynomial_fold_copy(
3113 __isl_keep isl_qpolynomial_fold *fold);
3114 __isl_null isl_qpolynomial_fold *
3115 isl_qpolynomial_fold_free(
3116 __isl_take isl_qpolynomial_fold *fold);
3118 The type of a (union piecewise) reduction
3119 can be obtained using the following functions.
3121 #include <isl/polynomial.h>
3122 enum isl_fold isl_qpolynomial_fold_get_type(
3123 __isl_keep isl_qpolynomial_fold *fold);
3124 enum isl_fold isl_pw_qpolynomial_fold_get_type(
3125 __isl_keep isl_pw_qpolynomial_fold *pwf);
3126 enum isl_fold isl_union_pw_qpolynomial_fold_get_type(
3127 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3129 The type may be either C<isl_fold_min> or C<isl_fold_max>
3130 (or C<isl_fold_error> in case of error).
3132 To iterate over all quasipolynomials in a reduction, use
3134 isl_stat isl_qpolynomial_fold_foreach_qpolynomial(
3135 __isl_keep isl_qpolynomial_fold *fold,
3136 isl_stat (*fn)(__isl_take isl_qpolynomial *qp,
3137 void *user), void *user);
3139 =head3 Multiple Expressions
3141 A multiple expression represents a sequence of zero or
3142 more base expressions, all defined on the same domain space.
3143 The domain space of the multiple expression is the same
3144 as that of the base expressions, but the range space
3145 can be any space. In case the base expressions have
3146 a set space, the corresponding multiple expression
3147 also has a set space.
3148 Objects of the value or identifier type do not have an associated space.
3149 The space of a multiple value or
3150 multiple identifier is therefore always a set space.
3151 Similarly, the space of a multiple union piecewise
3152 affine expression is always a set space.
3153 If the base expressions are not total, then
3154 a corresponding zero-dimensional multiple expression may
3155 have an explicit domain that keeps track of the domain
3156 outside of any base expressions.
3158 The multiple expression types defined by C<isl>
3159 are C<isl_multi_val>, C<isl_multi_id>, C<isl_multi_aff>, C<isl_multi_pw_aff>,
3160 C<isl_multi_union_pw_aff>.
3162 A multiple expression with the value zero for
3163 each output (or set) dimension can be created
3164 using the following functions.
3166 #include <isl/val.h>
3167 __isl_give isl_multi_val *isl_multi_val_zero(
3168 __isl_take isl_space *space);
3169 __isl_give isl_multi_val *isl_space_zero_multi_val(
3170 __isl_take isl_space *space);
3172 #include <isl/aff.h>
3173 __isl_give isl_multi_aff *isl_multi_aff_zero(
3174 __isl_take isl_space *space);
3175 __isl_give isl_multi_aff *isl_space_zero_multi_aff(
3176 __isl_take isl_space *space);
3177 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
3178 __isl_take isl_space *space);
3179 __isl_give isl_multi_pw_aff *isl_space_zero_multi_pw_aff(
3180 __isl_take isl_space *space);
3181 __isl_give isl_multi_union_pw_aff *
3182 isl_multi_union_pw_aff_zero(
3183 __isl_take isl_space *space);
3184 __isl_give isl_multi_union_pw_aff *
3185 isl_space_zero_multi_union_pw_aff(
3186 __isl_take isl_space *space);
3188 Since there is no canonical way of representing a zero
3189 value of type C<isl_union_pw_aff>, the space passed
3190 to C<isl_multi_union_pw_aff_zero> needs to be zero-dimensional.
3191 C<isl_multi_val_zero> and C<isl_space_zero_multi_val>
3192 perform the same operation.
3194 for the pair C<isl_multi_aff_zero> and C<isl_space_zero_multi_aff>,
3195 for the pair C<isl_multi_pw_aff_zero> and C<isl_space_zero_multi_pw_aff> and
3196 for the pair C<isl_multi_union_pw_aff_zero> and
3197 C<isl_space_zero_multi_union_pw_aff>.
3200 An identity function can be created using the following
3202 For the first group of functions, the space needs to be that of a set.
3203 For the second group,
3204 the space needs to be that of a relation
3205 with the same number of input and output dimensions.
3206 For the third group, the input function needs to live in a space
3207 with the same number of input and output dimensions and
3208 the identity function is created in that space.
3210 #include <isl/aff.h>
3211 __isl_give isl_multi_aff *
3212 isl_multi_aff_identity_on_domain_space(
3213 __isl_take isl_space *space);
3214 __isl_give isl_multi_aff *
3215 isl_space_identity_multi_aff_on_domain(
3216 __isl_take isl_space *space);
3217 __isl_give isl_multi_pw_aff *
3218 isl_multi_pw_aff_identity_on_domain_space(
3219 __isl_take isl_space *space);
3220 __isl_give isl_multi_pw_aff *
3221 isl_space_identity_multi_pw_aff_on_domain(
3222 __isl_take isl_space *space);
3223 __isl_give isl_multi_aff *isl_multi_aff_identity(
3224 __isl_take isl_space *space);
3225 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
3226 __isl_take isl_space *space);
3227 __isl_give isl_multi_aff *
3228 isl_multi_aff_identity_multi_aff(
3229 __isl_take isl_multi_aff *ma);
3230 __isl_give isl_multi_pw_aff *
3231 isl_multi_pw_aff_identity_multi_pw_aff(
3232 __isl_take isl_multi_pw_aff *mpa);
3234 C<isl_multi_aff_identity_on_domain_space> and
3235 C<isl_space_identity_multi_aff_on_domain>
3236 perform the same operation.
3238 for the pair C<isl_multi_pw_aff_identity_on_domain_space> and
3239 C<isl_space_identity_multi_pw_aff_on_domain>.
3241 A function that performs a projection on a universe
3242 relation or set can be created using the following functions.
3243 See also the corresponding
3244 projection operations in L</"Unary Operations">.
3246 #include <isl/aff.h>
3247 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
3248 __isl_take isl_space *space);
3249 __isl_give isl_multi_aff *isl_space_domain_map_multi_aff(
3250 __isl_take isl_space *space);
3251 __isl_give isl_multi_aff *isl_multi_aff_range_map(
3252 __isl_take isl_space *space);
3253 __isl_give isl_multi_aff *isl_space_range_map_multi_aff(
3254 __isl_take isl_space *space);
3255 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
3256 __isl_take isl_space *space,
3257 enum isl_dim_type type,
3258 unsigned first, unsigned n);
3260 C<isl_multi_aff_domain_map> and C<isl_space_domain_map_multi_aff> perform
3263 for the pair C<isl_multi_aff_range_map> and C<isl_space_range_map_multi_aff>.
3265 A multiple expression can be created from a single
3266 base expression using the following functions.
3267 The space of the created multiple expression is the same
3268 as that of the base expression, except for
3269 C<isl_multi_union_pw_aff_from_union_pw_aff> where the input
3270 lives in a parameter space and the output lives
3271 in a single-dimensional set space.
3273 #include <isl/aff.h>
3274 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
3275 __isl_take isl_aff *aff);
3276 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
3277 __isl_take isl_pw_aff *pa);
3278 __isl_give isl_multi_union_pw_aff *
3279 isl_multi_union_pw_aff_from_union_pw_aff(
3280 __isl_take isl_union_pw_aff *upa);
3282 A multiple expression can be created from a list
3283 of base expression in a specified space.
3284 The domain of this space needs to be the same
3285 as the domains of the base expressions in the list.
3286 If the base expressions have a set space (or no associated space),
3287 then this space also needs to be a set space.
3290 __isl_give isl_multi_id *isl_multi_id_from_id_list(
3291 __isl_take isl_space *space,
3292 __isl_take isl_id_list *list);
3293 __isl_give isl_multi_id *isl_space_multi_id(
3294 __isl_take isl_space *space,
3295 __isl_take isl_id_list *list);
3297 #include <isl/val.h>
3298 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3299 __isl_take isl_space *space,
3300 __isl_take isl_val_list *list);
3301 __isl_give isl_multi_val *isl_space_multi_val(
3302 __isl_take isl_space *space,
3303 __isl_take isl_val_list *list);
3305 #include <isl/aff.h>
3306 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3307 __isl_take isl_space *space,
3308 __isl_take isl_aff_list *list);
3309 __isl_give isl_multi_aff *isl_space_multi_aff(
3310 __isl_take isl_space *space,
3311 __isl_take isl_aff_list *list);
3312 __isl_give isl_multi_pw_aff *
3313 isl_multi_pw_aff_from_pw_aff_list(
3314 __isl_take isl_space *space,
3315 __isl_take isl_pw_aff_list *list);
3316 __isl_give isl_multi_pw_aff *
3317 isl_space_multi_pw_aff(
3318 __isl_take isl_space *space,
3319 __isl_take isl_pw_aff_list *list);
3320 __isl_give isl_multi_union_pw_aff *
3321 isl_multi_union_pw_aff_from_union_pw_aff_list(
3322 __isl_take isl_space *space,
3323 __isl_take isl_union_pw_aff_list *list);
3324 __isl_give isl_multi_union_pw_aff *
3325 isl_space_multi_union_pw_aff(
3326 __isl_take isl_space *space,
3327 __isl_take isl_union_pw_aff_list *list);
3329 C<isl_multi_id_from_id_list> and C<isl_space_multi_id> perform
3331 Similarly for the pair C<isl_multi_val_from_val_list> and
3332 C<isl_space_multi_val>,
3333 for the pair C<isl_multi_aff_from_aff_list> and
3334 C<isl_space_multi_aff>,
3335 for the pair C<isl_multi_pw_aff_from_pw_aff_list> and
3336 C<isl_space_multi_pw_aff> and
3337 for the pair C<isl_multi_union_pw_aff_from_union_pw_aff_list> and
3338 C<isl_space_multi_union_pw_aff>.
3340 As a convenience, a multiple piecewise expression can
3341 also be created from a multiple expression,
3342 or even directly from a single base expression.
3343 Each piecewise expression in the result has a single
3346 #include <isl/aff.h>
3347 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_aff(
3348 __isl_take isl_aff *aff);
3349 __isl_give isl_multi_pw_aff *
3350 isl_multi_aff_to_multi_pw_aff(
3351 __isl_take isl_multi_aff *ma);
3352 __isl_give isl_multi_pw_aff *
3353 isl_multi_pw_aff_from_multi_aff(
3354 __isl_take isl_multi_aff *ma);
3356 C<isl_multi_aff_to_multi_pw_aff> and
3357 C<isl_multi_pw_aff_from_multi_aff> perform the same operation.
3359 Similarly, a multiple union expression can be
3360 created from a multiple expression.
3362 #include <isl/aff.h>
3363 __isl_give isl_multi_union_pw_aff *
3364 isl_multi_union_pw_aff_from_multi_aff(
3365 __isl_take isl_multi_aff *ma);
3366 __isl_give isl_multi_union_pw_aff *
3367 isl_multi_aff_to_multi_union_pw_aff(
3368 __isl_take isl_multi_aff *ma);
3369 __isl_give isl_multi_union_pw_aff *
3370 isl_multi_union_pw_aff_from_multi_pw_aff(
3371 __isl_take isl_multi_pw_aff *mpa);
3373 C<isl_multi_aff_to_multi_union_pw_aff> and
3374 C<isl_multi_union_pw_aff_from_multi_aff> perform the same operation.
3376 A multiple quasi-affine expression can be created from
3377 a multiple value with a given domain space using the following
3380 #include <isl/aff.h>
3381 __isl_give isl_multi_aff *
3382 isl_multi_aff_multi_val_on_domain_space(
3383 __isl_take isl_space *space,
3384 __isl_take isl_multi_val *mv);
3385 __isl_give isl_multi_aff *
3386 isl_space_multi_aff_on_domain_multi_val(
3387 __isl_take isl_space *space,
3388 __isl_take isl_multi_val *mv);
3389 __isl_give isl_multi_aff *
3390 isl_multi_aff_multi_val_on_space(
3391 __isl_take isl_space *space,
3392 __isl_take isl_multi_val *mv);
3394 C<isl_space_multi_aff_on_domain_multi_val> and
3395 C<isl_multi_aff_multi_val_on_space> are alternative names
3396 for C<isl_multi_aff_multi_val_on_domain_space>.
3399 a multiple union piecewise affine expression can be created from
3400 a multiple value with a given domain or
3401 a (piecewise) multiple affine expression with a given domain
3402 using the following functions.
3404 #include <isl/aff.h>
3405 __isl_give isl_multi_union_pw_aff *
3406 isl_multi_union_pw_aff_multi_val_on_domain(
3407 __isl_take isl_union_set *domain,
3408 __isl_take isl_multi_val *mv);
3409 __isl_give isl_multi_union_pw_aff *
3410 isl_multi_union_pw_aff_multi_aff_on_domain(
3411 __isl_take isl_union_set *domain,
3412 __isl_take isl_multi_aff *ma);
3413 __isl_give isl_multi_union_pw_aff *
3414 isl_multi_union_pw_aff_pw_multi_aff_on_domain(
3415 __isl_take isl_union_set *domain,
3416 __isl_take isl_pw_multi_aff *pma);
3418 Multiple expressions can be copied and freed using
3419 the following functions.
3422 __isl_give isl_multi_id *isl_multi_id_copy(
3423 __isl_keep isl_multi_id *mi);
3424 __isl_null isl_multi_id *isl_multi_id_free(
3425 __isl_take isl_multi_id *mi);
3427 #include <isl/val.h>
3428 __isl_give isl_multi_val *isl_multi_val_copy(
3429 __isl_keep isl_multi_val *mv);
3430 __isl_null isl_multi_val *isl_multi_val_free(
3431 __isl_take isl_multi_val *mv);
3433 #include <isl/aff.h>
3434 __isl_give isl_multi_aff *isl_multi_aff_copy(
3435 __isl_keep isl_multi_aff *maff);
3436 __isl_null isl_multi_aff *isl_multi_aff_free(
3437 __isl_take isl_multi_aff *maff);
3438 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
3439 __isl_keep isl_multi_pw_aff *mpa);
3440 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
3441 __isl_take isl_multi_pw_aff *mpa);
3442 __isl_give isl_multi_union_pw_aff *
3443 isl_multi_union_pw_aff_copy(
3444 __isl_keep isl_multi_union_pw_aff *mupa);
3445 __isl_null isl_multi_union_pw_aff *
3446 isl_multi_union_pw_aff_free(
3447 __isl_take isl_multi_union_pw_aff *mupa);
3449 The number of base expressions in a multiple
3450 expression can be obtained using the following functions.
3453 int isl_multi_id_size(__isl_keep isl_multi_id *mi);
3455 #include <isl/val.h>
3456 isl_size isl_multi_val_size(__isl_keep isl_multi_val *mv);
3458 #include <isl/aff.h>
3459 isl_size isl_multi_aff_size(
3460 __isl_keep isl_multi_aff *multi);
3461 isl_size isl_multi_pw_aff_size(
3462 __isl_keep isl_multi_pw_aff *mpa);
3463 isl_size isl_multi_union_pw_aff_size(
3464 __isl_keep isl_multi_union_pw_aff *mupa);
3466 The base expression at a given position of a multiple
3467 expression can be extracted using the following functions.
3470 __isl_give isl_id *isl_multi_id_get_at(
3471 __isl_keep isl_multi_id *mi, int pos);
3472 __isl_give isl_id *isl_multi_id_get_id(
3473 __isl_keep isl_multi_id *mi, int pos);
3475 #include <isl/val.h>
3476 __isl_give isl_val *isl_multi_val_get_at(
3477 __isl_keep isl_multi_val *mv, int pos);
3478 __isl_give isl_val *isl_multi_val_get_val(
3479 __isl_keep isl_multi_val *mv, int pos);
3481 #include <isl/aff.h>
3482 __isl_give isl_aff *isl_multi_aff_get_at(
3483 __isl_keep isl_multi_aff *ma, int pos);
3484 __isl_give isl_aff *isl_multi_aff_get_aff(
3485 __isl_keep isl_multi_aff *multi, int pos);
3486 __isl_give isl_pw_aff *isl_multi_pw_aff_get_at(
3487 __isl_keep isl_multi_pw_aff *mpa, int pos);
3488 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
3489 __isl_keep isl_multi_pw_aff *mpa, int pos);
3490 __isl_give isl_union_pw_aff *
3491 isl_multi_union_pw_aff_get_at(
3492 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
3493 __isl_give isl_union_pw_aff *
3494 isl_multi_union_pw_aff_get_union_pw_aff(
3495 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
3497 C<isl_multi_id_get_id> is an alternative name for C<isl_multi_id_get_at>.
3498 Similarly for the other pairs of functions.
3500 The base expression can be replaced using the following functions.
3503 __isl_give isl_multi_id *isl_multi_id_set_at(
3504 __isl_take isl_multi_id *mi, int pos,
3505 __isl_take isl_id *id);
3506 __isl_give isl_multi_id *isl_multi_id_set_id(
3507 __isl_take isl_multi_id *mi, int pos,
3508 __isl_take isl_id *id);
3510 #include <isl/val.h>
3511 __isl_give isl_multi_val *isl_multi_val_set_at(
3512 __isl_take isl_multi_val *mv, int pos,
3513 __isl_take isl_val *val);
3514 __isl_give isl_multi_val *isl_multi_val_set_val(
3515 __isl_take isl_multi_val *mv, int pos,
3516 __isl_take isl_val *val);
3518 #include <isl/aff.h>
3519 __isl_give isl_multi_aff *isl_multi_aff_set_at(
3520 __isl_take isl_multi_aff *ma, int pos,
3521 __isl_take isl_aff *aff);
3522 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3523 __isl_take isl_multi_aff *multi, int pos,
3524 __isl_take isl_aff *aff);
3525 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_set_at(
3526 __isl_take isl_multi_pw_aff *mpa, int pos,
3527 __isl_take isl_pw_aff *pa);
3528 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_set_pw_aff(
3529 __isl_take isl_multi_pw_aff *mpa, int pos,
3530 __isl_take isl_pw_aff *pa);
3531 __isl_give isl_multi_union_pw_aff *
3532 isl_multi_union_pw_aff_set_at(
3533 __isl_take isl_multi_union_pw_aff *mupa, int pos,
3534 __isl_take isl_union_pw_aff *upa);
3535 __isl_give isl_multi_union_pw_aff *
3536 isl_multi_union_pw_aff_set_union_pw_aff(
3537 __isl_take isl_multi_union_pw_aff *mupa, int pos,
3538 __isl_take isl_union_pw_aff *upa);
3540 C<isl_multi_id_set_id> is an alternative name for C<isl_multi_id_set_at>.
3541 Similarly for the other pairs of functions.
3543 A list of all base expressions of a multiple
3544 expression can be extracted using the following functions.
3547 __isl_give isl_id_list *isl_multi_id_get_list(
3548 __isl_keep isl_multi_id *mi);
3550 #include <isl/val.h>
3551 __isl_give isl_val_list *isl_multi_val_get_list(
3552 __isl_keep isl_multi_val *mv);
3554 #include <isl/aff.h>
3555 __isl_give isl_aff_list *isl_multi_aff_get_list(
3556 __isl_keep isl_multi_aff *multi);
3557 __isl_give isl_pw_aff_list *isl_multi_pw_aff_get_list(
3558 __isl_keep isl_multi_pw_aff *mpa);
3559 __isl_give isl_union_pw_aff_list *
3560 isl_multi_union_pw_aff_list(
3561 __isl_keep isl_multi_union_pw_aff *mupa);
3563 The constant terms of the base expressions can be obtained using
3564 the following function.
3566 #include <isl/aff.h>
3567 __isl_give isl_multi_val *
3568 isl_multi_aff_get_constant_multi_val(
3569 __isl_keep isl_multi_aff *ma);
3571 As a convenience, a sequence of base expressions that have
3572 their domains in a given space can be extracted from a sequence
3573 of union expressions using the following function.
3575 #include <isl/aff.h>
3576 __isl_give isl_multi_pw_aff *
3577 isl_multi_union_pw_aff_extract_multi_pw_aff(
3578 __isl_keep isl_multi_union_pw_aff *mupa,
3579 __isl_take isl_space *space);
3581 Note that there is a difference between C<isl_multi_union_pw_aff>
3582 and C<isl_union_pw_multi_aff> objects. The first is a sequence
3583 of unions of piecewise expressions, while the second is a union
3584 of piecewise sequences. In particular, multiple affine expressions
3585 in an C<isl_union_pw_multi_aff> may live in different spaces,
3586 while there is only a single multiple expression in
3587 an C<isl_multi_union_pw_aff>, which can therefore only live
3588 in a single space. This means that not every
3589 C<isl_union_pw_multi_aff> can be converted to
3590 an C<isl_multi_union_pw_aff>. Conversely, the elements
3591 of an C<isl_multi_union_pw_aff> may be defined over different domains,
3592 while each multiple expression inside an C<isl_union_pw_multi_aff>
3593 has a single domain. The conversion of an C<isl_union_pw_multi_aff>
3594 of dimension greater than one may therefore not be exact.
3595 The following functions can
3596 be used to perform these conversions when they are possible.
3598 #include <isl/aff.h>
3599 __isl_give isl_multi_union_pw_aff *
3600 isl_union_pw_multi_aff_as_multi_union_pw_aff(
3601 __isl_take isl_union_pw_multi_aff *upma);
3602 __isl_give isl_multi_union_pw_aff *
3603 isl_multi_union_pw_aff_from_union_pw_multi_aff(
3604 __isl_take isl_union_pw_multi_aff *upma);
3605 __isl_give isl_union_pw_multi_aff *
3606 isl_union_pw_multi_aff_from_multi_union_pw_aff(
3607 __isl_take isl_multi_union_pw_aff *mupa);
3609 C<isl_union_pw_multi_aff_as_multi_union_pw_aff> and
3610 C<isl_multi_union_pw_aff_from_union_pw_multi_aff>
3611 perform the same operation.
3613 =head3 Piecewise Expressions
3615 A piecewise expression is an expression that is described
3616 using zero or more base expression defined over the same
3617 number of cells in the domain space of the base expressions.
3618 All base expressions are defined over the same
3619 domain space and the cells are disjoint.
3620 The space of a piecewise expression is the same as
3621 that of the base expressions.
3622 If the union of the cells is a strict subset of the domain
3623 space, then the value of the piecewise expression outside
3624 this union is different for types derived from quasi-affine
3625 expressions and those derived from quasipolynomials.
3626 Piecewise expressions derived from quasi-affine expressions
3627 are considered to be undefined outside the union of their cells.
3628 Piecewise expressions derived from quasipolynomials
3629 are considered to be zero outside the union of their cells.
3631 Piecewise quasipolynomials are mainly used by the C<barvinok>
3632 library for representing the number of elements in a parametric set or map.
3633 For example, the piecewise quasipolynomial
3635 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3637 represents the number of points in the map
3639 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3641 The piecewise expression types defined by C<isl>
3642 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
3643 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
3645 A piecewise expression with no cells can be created using
3646 the following functions.
3648 #include <isl/aff.h>
3649 __isl_give isl_pw_aff *isl_pw_aff_empty(
3650 __isl_take isl_space *space);
3651 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3652 __isl_take isl_space *space);
3654 A piecewise expression with a single universe cell can be
3655 created using the following functions.
3657 #include <isl/aff.h>
3658 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3659 __isl_take isl_aff *aff);
3660 __isl_give isl_pw_multi_aff *
3661 isl_multi_aff_to_pw_multi_aff(
3662 __isl_take isl_multi_aff *ma);
3663 __isl_give isl_pw_multi_aff *
3664 isl_pw_multi_aff_from_multi_aff(
3665 __isl_take isl_multi_aff *ma);
3667 #include <isl/polynomial.h>
3668 __isl_give isl_pw_qpolynomial *
3669 isl_pw_qpolynomial_from_qpolynomial(
3670 __isl_take isl_qpolynomial *qp);
3671 __isl_give isl_pw_qpolynomial_fold *
3672 isl_pw_qpolynomial_fold_from_qpolynomial_fold(
3673 __isl_take isl_qpolynomial_fold *fold);
3675 C<isl_multi_aff_to_pw_multi_aff> and C<isl_pw_multi_aff_from_multi_aff> perform
3678 The inverse conversions below can only be used if the input
3679 expression is known to be defined over a single universe domain.
3681 #include <isl/aff.h>
3682 isl_bool isl_pw_aff_isa_aff(__isl_keep isl_pw_aff *pa);
3683 __isl_give isl_aff *isl_pw_aff_as_aff(
3684 __isl_take isl_pw_aff *pa);
3685 isl_bool isl_multi_pw_aff_isa_multi_aff(
3686 __isl_keep isl_multi_pw_aff *mpa);
3687 __isl_give isl_multi_aff *isl_multi_pw_aff_as_multi_aff(
3688 __isl_take isl_multi_pw_aff *mpa);
3689 isl_bool isl_pw_multi_aff_isa_multi_aff(
3690 __isl_keep isl_pw_multi_aff *pma);
3691 __isl_give isl_multi_aff *isl_pw_multi_aff_as_multi_aff(
3692 __isl_take isl_pw_multi_aff *pma);
3694 #include <isl/polynomial.h>
3695 isl_bool isl_pw_qpolynomial_isa_qpolynomial(
3696 __isl_keep isl_pw_qpolynomial *pwqp);
3697 __isl_give isl_qpolynomial *
3698 isl_pw_qpolynomial_as_qpolynomial(
3699 __isl_take isl_pw_qpolynomial *pwqp);
3700 isl_bool isl_pw_qpolynomial_fold_isa_qpolynomial_fold(
3701 __isl_keep isl_pw_qpolynomial_fold *pwf);
3702 __isl_give isl_qpolynomial_fold *
3703 isl_pw_qpolynomial_fold_as_qpolynomial_fold(
3704 __isl_take isl_pw_qpolynomial_fold *pwf);
3706 A piecewise expression with a single specified cell can be
3707 created using the following functions.
3709 #include <isl/aff.h>
3710 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3711 __isl_take isl_set *set, __isl_take isl_aff *aff);
3712 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3713 __isl_take isl_set *set,
3714 __isl_take isl_multi_aff *maff);
3716 #include <isl/polynomial.h>
3717 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3718 __isl_take isl_set *set,
3719 __isl_take isl_qpolynomial *qp);
3721 The following convenience functions first create a base expression and
3722 then create a piecewise expression over a universe domain.
3724 #include <isl/aff.h>
3725 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3726 __isl_take isl_local_space *ls);
3727 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3728 __isl_take isl_local_space *ls,
3729 enum isl_dim_type type, unsigned pos);
3730 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain_space(
3731 __isl_take isl_space *space);
3732 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3733 __isl_take isl_local_space *ls);
3734 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
3735 __isl_take isl_space *space);
3736 __isl_give isl_pw_multi_aff *
3737 isl_pw_multi_aff_identity_on_domain_space(
3738 __isl_take isl_space *space)
3739 __isl_give isl_pw_multi_aff *
3740 isl_space_identity_pw_multi_aff_on_domain(
3741 __isl_take isl_space *space)
3742 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3743 __isl_take isl_space *space);
3744 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_domain_map(
3745 __isl_take isl_space *space);
3746 __isl_give isl_pw_multi_aff *
3747 isl_space_domain_map_pw_multi_aff(
3748 __isl_take isl_space *space);
3749 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
3750 __isl_take isl_space *space);
3751 __isl_give isl_pw_multi_aff *
3752 isl_space_range_map_pw_multi_aff(
3753 __isl_take isl_space *space);
3754 __isl_give isl_pw_multi_aff *
3755 isl_pw_multi_aff_project_out_map(
3756 __isl_take isl_space *space,
3757 enum isl_dim_type type,
3758 unsigned first, unsigned n);
3760 #include <isl/polynomial.h>
3761 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3762 __isl_take isl_space *space);
3764 C<isl_pw_multi_aff_identity_on_domain_space> and
3765 C<isl_space_identity_pw_multi_aff_on_domain>
3766 perform the same operation.
3768 for the pair C<isl_pw_multi_aff_domain_map> and
3769 C<isl_space_domain_map_pw_multi_aff> and
3770 for the pair C<isl_pw_multi_aff_range_map> and
3771 C<isl_space_range_map_pw_multi_aff>.
3773 The following convenience functions first create a base expression and
3774 then create a piecewise expression over a given domain.
3776 #include <isl/aff.h>
3777 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
3778 __isl_take isl_set *domain,
3779 __isl_take isl_val *v);
3780 __isl_give isl_pw_aff *isl_set_pw_aff_on_domain_val(
3781 __isl_take isl_set *domain,
3782 __isl_take isl_val *v);
3783 __isl_give isl_pw_multi_aff *
3784 isl_pw_multi_aff_multi_val_on_domain(
3785 __isl_take isl_set *domain,
3786 __isl_take isl_multi_val *mv);
3787 __isl_give isl_pw_multi_aff *
3788 isl_set_pw_multi_aff_on_domain_multi_val(
3789 __isl_take isl_set *domain,
3790 __isl_take isl_multi_val *mv);
3791 __isl_give isl_pw_aff *isl_pw_aff_param_on_domain_id(
3792 __isl_take isl_set *domain,
3793 __isl_take isl_id *id);
3794 __isl_give isl_pw_aff *isl_set_param_pw_aff_on_domain_id(
3795 __isl_take isl_set *domain,
3796 __isl_take isl_id *id);
3798 C<isl_set_pw_aff_on_domain_val> is an alternative name
3799 for C<isl_pw_aff_val_on_domain>.
3800 Similarly for the pair
3801 C<isl_set_pw_multi_aff_on_domain_multi_val> and
3802 C<isl_pw_multi_aff_multi_val_on_domain> and
3803 for the pair C<isl_set_param_pw_aff_on_domain_id> and
3804 C<isl_pw_aff_param_on_domain_id>.
3806 As a convenience, a piecewise multiple expression can
3807 also be created from a piecewise expression.
3808 Each multiple expression in the result is derived
3809 from the corresponding base expression.
3811 #include <isl/aff.h>
3812 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
3813 __isl_take isl_pw_aff *pa);
3815 Similarly, a piecewise quasipolynomial can be
3816 created from a piecewise quasi-affine expression using
3817 the following function.
3819 #include <isl/polynomial.h>
3820 __isl_give isl_pw_qpolynomial *
3821 isl_pw_qpolynomial_from_pw_aff(
3822 __isl_take isl_pw_aff *pwaff);
3824 Piecewise expressions can be copied and freed using the following functions.
3826 #include <isl/aff.h>
3827 __isl_give isl_pw_aff *isl_pw_aff_copy(
3828 __isl_keep isl_pw_aff *pwaff);
3829 __isl_null isl_pw_aff *isl_pw_aff_free(
3830 __isl_take isl_pw_aff *pwaff);
3831 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3832 __isl_keep isl_pw_multi_aff *pma);
3833 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
3834 __isl_take isl_pw_multi_aff *pma);
3836 #include <isl/polynomial.h>
3837 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3838 __isl_keep isl_pw_qpolynomial *pwqp);
3839 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
3840 __isl_take isl_pw_qpolynomial *pwqp);
3841 __isl_give isl_pw_qpolynomial_fold *
3842 isl_pw_qpolynomial_fold_copy(
3843 __isl_keep isl_pw_qpolynomial_fold *pwf);
3844 __isl_null isl_pw_qpolynomial_fold *
3845 isl_pw_qpolynomial_fold_free(
3846 __isl_take isl_pw_qpolynomial_fold *pwf);
3848 To iterate over the different cells of a piecewise expression,
3849 use the following functions.
3851 #include <isl/aff.h>
3852 isl_bool isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3853 isl_size isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3854 isl_stat isl_pw_aff_foreach_piece(
3855 __isl_keep isl_pw_aff *pwaff,
3856 isl_stat (*fn)(__isl_take isl_set *set,
3857 __isl_take isl_aff *aff,
3858 void *user), void *user);
3859 isl_bool isl_pw_aff_every_piece(__isl_keep isl_pw_aff *pa,
3860 isl_bool (*test)(__isl_keep isl_set *set,
3861 __isl_keep isl_aff *aff, void *user),
3863 isl_size isl_pw_multi_aff_n_piece(
3864 __isl_keep isl_pw_multi_aff *pma);
3865 isl_stat isl_pw_multi_aff_foreach_piece(
3866 __isl_keep isl_pw_multi_aff *pma,
3867 isl_stat (*fn)(__isl_take isl_set *set,
3868 __isl_take isl_multi_aff *maff,
3869 void *user), void *user);
3870 isl_bool isl_pw_multi_aff_every_piece(
3871 __isl_keep isl_pw_multi_aff *pma,
3872 isl_bool (*test)(__isl_keep isl_set *set,
3873 __isl_keep isl_multi_aff *ma, void *user),
3876 #include <isl/polynomial.h>
3877 isl_size isl_pw_qpolynomial_n_piece(
3878 __isl_keep isl_pw_qpolynomial *pwqp);
3879 isl_stat isl_pw_qpolynomial_foreach_piece(
3880 __isl_keep isl_pw_qpolynomial *pwqp,
3881 isl_stat (*fn)(__isl_take isl_set *set,
3882 __isl_take isl_qpolynomial *qp,
3883 void *user), void *user);
3884 isl_bool isl_pw_qpolynomial_every_piece(
3885 __isl_keep isl_pw_qpolynomial *pwqp,
3886 isl_bool (*test)(__isl_keep isl_set *set,
3887 __isl_keep isl_qpolynomial *qp,
3888 void *user), void *user);
3889 isl_stat isl_pw_qpolynomial_foreach_lifted_piece(
3890 __isl_keep isl_pw_qpolynomial *pwqp,
3891 isl_stat (*fn)(__isl_take isl_set *set,
3892 __isl_take isl_qpolynomial *qp,
3893 void *user), void *user);
3894 isl_size isl_pw_qpolynomial_fold_n_piece(
3895 __isl_keep isl_pw_qpolynomial_fold *pwf);
3896 isl_stat isl_pw_qpolynomial_fold_foreach_piece(
3897 __isl_keep isl_pw_qpolynomial_fold *pwf,
3898 isl_stat (*fn)(__isl_take isl_set *set,
3899 __isl_take isl_qpolynomial_fold *fold,
3900 void *user), void *user);
3901 isl_bool isl_pw_qpolynomial_fold_every_piece(
3902 __isl_keep isl_pw_qpolynomial_fold *pwf,
3903 isl_bool (*test)(__isl_keep isl_set *set,
3904 __isl_keep isl_qpolynomial_fold *fold,
3905 void *user), void *user);
3906 isl_stat isl_pw_qpolynomial_fold_foreach_lifted_piece(
3907 __isl_keep isl_pw_qpolynomial_fold *pwf,
3908 isl_stat (*fn)(__isl_take isl_set *set,
3909 __isl_take isl_qpolynomial_fold *fold,
3910 void *user), void *user);
3912 As usual, the function C<fn> should return C<isl_stat_ok> on success
3913 and C<isl_stat_error> on failure. The difference between
3914 C<isl_pw_qpolynomial_foreach_piece> and
3915 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3916 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3917 compute unique representations for all existentially quantified
3918 variables and then turn these existentially quantified variables
3919 into extra set variables, adapting the associated quasipolynomial
3920 accordingly. This means that the C<set> passed to C<fn>
3921 will not have any existentially quantified variables, but that
3922 the dimensions of the sets may be different for different
3923 invocations of C<fn>.
3924 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
3925 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
3926 The function C<isl_pw_aff_every_piece> and its variants
3927 check whether each call to the callback returns true and
3928 stop checking as soon as one of these calls returns false (or error).
3930 A piecewise expression consisting of the expressions at a given
3931 position of a piecewise multiple expression can be extracted
3932 using the following function.
3934 #include <isl/aff.h>
3935 __isl_give isl_pw_aff *isl_pw_multi_aff_get_at(
3936 __isl_keep isl_pw_multi_aff *pma, int pos);
3937 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3938 __isl_keep isl_pw_multi_aff *pma, int pos);
3940 C<isl_pw_multi_aff_get_pw_aff> is an alternative name for
3941 C<isl_pw_multi_aff_get_at>.
3943 These expressions can be replaced using the following function.
3945 #include <isl/aff.h>
3946 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3947 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3948 __isl_take isl_pw_aff *pa);
3950 Note that there is a difference between C<isl_multi_pw_aff> and
3951 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
3952 affine expressions, while the second is a piecewise sequence
3953 of affine expressions. In particular, each of the piecewise
3954 affine expressions in an C<isl_multi_pw_aff> may have a different
3955 domain, while all multiple expressions associated to a cell
3956 in an C<isl_pw_multi_aff> have the same domain.
3957 It is possible to convert between the two, but when converting
3958 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
3959 of the result is the intersection of the domains of the input.
3960 The reverse conversion is exact.
3962 #include <isl/aff.h>
3963 __isl_give isl_pw_multi_aff *
3964 isl_pw_multi_aff_from_multi_pw_aff(
3965 __isl_take isl_multi_pw_aff *mpa);
3966 __isl_give isl_multi_pw_aff *
3967 isl_pw_multi_aff_to_multi_pw_aff(
3968 __isl_take isl_pw_multi_aff *pma);
3969 __isl_give isl_multi_pw_aff *
3970 isl_multi_pw_aff_from_pw_multi_aff(
3971 __isl_take isl_pw_multi_aff *pma);
3973 C<isl_pw_multi_aff_to_multi_pw_aff> and
3974 C<isl_multi_pw_aff_from_pw_multi_aff> perform the same operation.
3976 =head3 Union Expressions
3978 A union expression collects base expressions defined
3979 over different domains. The space of a union expression
3980 is that of the shared parameter space.
3982 The union expression types defined by C<isl>
3983 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
3984 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
3986 C<isl_union_pw_aff>,
3987 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>,
3988 there can be at most one base expression for a given domain space.
3990 C<isl_union_pw_multi_aff>,
3991 there can be multiple such expressions for a given domain space,
3992 but the domains of these expressions need to be disjoint.
3994 An empty union expression can be created using the following functions.
3996 #include <isl/aff.h>
3997 __isl_give isl_union_pw_aff *
3998 isl_union_pw_aff_empty_ctx(
4000 __isl_give isl_union_pw_aff *
4001 isl_union_pw_aff_empty_space(
4002 __isl_take isl_space *space);
4003 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
4004 __isl_take isl_space *space);
4005 __isl_give isl_union_pw_multi_aff *
4006 isl_union_pw_multi_aff_empty_ctx(
4008 __isl_give isl_union_pw_multi_aff *
4009 isl_union_pw_multi_aff_empty_space(
4010 __isl_take isl_space *space);
4011 __isl_give isl_union_pw_multi_aff *
4012 isl_union_pw_multi_aff_empty(
4013 __isl_take isl_space *space);
4015 #include <isl/polynomial.h>
4016 __isl_give isl_union_pw_qpolynomial *
4017 isl_union_pw_qpolynomial_zero_ctx(
4019 __isl_give isl_union_pw_qpolynomial *
4020 isl_union_pw_qpolynomial_zero_space(
4021 __isl_take isl_space *space);
4022 __isl_give isl_union_pw_qpolynomial *
4023 isl_union_pw_qpolynomial_zero(
4024 __isl_take isl_space *space);
4026 C<isl_union_pw_aff_empty> is an alternative name for
4027 C<isl_union_pw_aff_empty_space>.
4028 Similarly for the other pairs of functions.
4030 A union expression containing a single base expression
4031 can be created using the following functions.
4033 #include <isl/aff.h>
4034 __isl_give isl_union_pw_aff *
4035 isl_pw_aff_to_union_pw_aff(
4036 __isl_take isl_pw_aff *pa);
4037 __isl_give isl_union_pw_aff *
4038 isl_union_pw_aff_from_pw_aff(
4039 __isl_take isl_pw_aff *pa);
4040 __isl_give isl_union_pw_multi_aff *
4041 isl_union_pw_multi_aff_from_aff(
4042 __isl_take isl_aff *aff);
4043 __isl_give isl_union_pw_multi_aff *
4044 isl_pw_multi_aff_to_union_pw_multi_aff(
4045 __isl_take isl_pw_multi_aff *pma);
4046 __isl_give isl_union_pw_multi_aff *
4047 isl_union_pw_multi_aff_from_pw_multi_aff(
4048 __isl_take isl_pw_multi_aff *pma);
4050 #include <isl/polynomial.h>
4051 __isl_give isl_union_pw_qpolynomial *
4052 isl_pw_qpolynomial_to_union_pw_qpolynomial(
4053 __isl_take isl_pw_qpolynomial *pwqp);
4054 __isl_give isl_union_pw_qpolynomial *
4055 isl_union_pw_qpolynomial_from_pw_qpolynomial(
4056 __isl_take isl_pw_qpolynomial *pwqp);
4057 __isl_give isl_union_pw_qpolynomial_fold *
4058 isl_pw_qpolynomial_fold_to_union_pw_qpolynomial_fold(
4059 __isl_take isl_pw_qpolynomial_fold *pwf);
4060 __isl_give isl_union_pw_qpolynomial_fold *
4061 isl_union_pw_qpolynomial_fold_from_pw_qpolynomial_fold(
4062 __isl_take isl_pw_qpolynomial_fold *pwf);
4064 C<isl_pw_aff_to_union_pw_aff> and C<isl_union_pw_aff_from_pw_aff> perform
4066 Similarly for C<isl_pw_multi_aff_to_union_pw_multi_aff> and
4067 C<isl_union_pw_multi_aff_from_pw_multi_aff>,
4069 C<isl_pw_qpolynomial_to_union_pw_qpolynomial> and
4070 C<isl_union_pw_qpolynomial_from_pw_qpolynomial>, and
4072 C<isl_pw_qpolynomial_fold_to_union_pw_qpolynomial_fold> and
4073 C<isl_union_pw_qpolynomial_fold_from_pw_qpolynomial_fold>.
4075 The inverse conversions below can only be used if the input
4076 expression is known to live in exactly one space.
4078 #include <isl/aff.h>
4079 isl_bool isl_union_pw_multi_aff_isa_pw_multi_aff(
4080 __isl_keep isl_union_pw_multi_aff *upma);
4081 __isl_give isl_pw_multi_aff *
4082 isl_union_pw_multi_aff_as_pw_multi_aff(
4083 __isl_take isl_union_pw_multi_aff *upma);
4085 A union piecewise expression containing a single base expression
4086 on a universe domain can also be created directly from
4087 a base expression using the following functions.
4089 #include <isl/aff.h>
4090 __isl_give isl_union_pw_aff *isl_union_pw_aff_from_aff(
4091 __isl_take isl_aff *aff);
4092 __isl_give isl_union_pw_multi_aff *
4093 isl_union_pw_multi_aff_from_multi_aff(
4094 __isl_take isl_multi_aff *ma);
4096 The following functions create a base expression on each
4097 of the sets in the union set and collect the results.
4099 #include <isl/aff.h>
4100 __isl_give isl_union_pw_multi_aff *
4101 isl_union_pw_multi_aff_from_union_pw_aff(
4102 __isl_take isl_union_pw_aff *upa);
4103 __isl_give isl_union_pw_aff *
4104 isl_union_pw_multi_aff_get_union_pw_aff(
4105 __isl_keep isl_union_pw_multi_aff *upma, int pos);
4106 __isl_give isl_union_pw_aff *
4107 isl_union_pw_aff_val_on_domain(
4108 __isl_take isl_union_set *domain,
4109 __isl_take isl_val *v);
4110 __isl_give isl_union_pw_multi_aff *
4111 isl_union_pw_multi_aff_multi_val_on_domain(
4112 __isl_take isl_union_set *domain,
4113 __isl_take isl_multi_val *mv);
4114 __isl_give isl_union_pw_aff *
4115 isl_union_pw_aff_param_on_domain_id(
4116 __isl_take isl_union_set *domain,
4117 __isl_take isl_id *id);
4119 The C<id> argument of C<isl_union_pw_aff_param_on_domain_id>
4120 is the identifier of a parameter that may or may not already
4121 be present in C<domain>.
4123 An C<isl_union_pw_aff> that is equal to a (parametric) affine
4125 expression on a given domain can be created using the following
4128 #include <isl/aff.h>
4129 __isl_give isl_union_pw_aff *
4130 isl_union_pw_aff_aff_on_domain(
4131 __isl_take isl_union_set *domain,
4132 __isl_take isl_aff *aff);
4133 __isl_give isl_union_pw_aff *
4134 isl_union_pw_aff_pw_aff_on_domain(
4135 __isl_take isl_union_set *domain,
4136 __isl_take isl_pw_aff *pa);
4138 A base expression can be added to a union expression using
4139 the following functions.
4141 #include <isl/aff.h>
4142 __isl_give isl_union_pw_aff *
4143 isl_union_pw_aff_add_pw_aff(
4144 __isl_take isl_union_pw_aff *upa,
4145 __isl_take isl_pw_aff *pa);
4146 __isl_give isl_union_pw_multi_aff *
4147 isl_union_pw_multi_aff_add_pw_multi_aff(
4148 __isl_take isl_union_pw_multi_aff *upma,
4149 __isl_take isl_pw_multi_aff *pma);
4151 #include <isl/polynomial.h>
4152 __isl_give isl_union_pw_qpolynomial *
4153 isl_union_pw_qpolynomial_add_pw_qpolynomial(
4154 __isl_take isl_union_pw_qpolynomial *upwqp,
4155 __isl_take isl_pw_qpolynomial *pwqp);
4157 Union expressions can be copied and freed using
4158 the following functions.
4160 #include <isl/aff.h>
4161 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
4162 __isl_keep isl_union_pw_aff *upa);
4163 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
4164 __isl_take isl_union_pw_aff *upa);
4165 __isl_give isl_union_pw_multi_aff *
4166 isl_union_pw_multi_aff_copy(
4167 __isl_keep isl_union_pw_multi_aff *upma);
4168 __isl_null isl_union_pw_multi_aff *
4169 isl_union_pw_multi_aff_free(
4170 __isl_take isl_union_pw_multi_aff *upma);
4172 #include <isl/polynomial.h>
4173 __isl_give isl_union_pw_qpolynomial *
4174 isl_union_pw_qpolynomial_copy(
4175 __isl_keep isl_union_pw_qpolynomial *upwqp);
4176 __isl_null isl_union_pw_qpolynomial *
4177 isl_union_pw_qpolynomial_free(
4178 __isl_take isl_union_pw_qpolynomial *upwqp);
4179 __isl_give isl_union_pw_qpolynomial_fold *
4180 isl_union_pw_qpolynomial_fold_copy(
4181 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4182 __isl_null isl_union_pw_qpolynomial_fold *
4183 isl_union_pw_qpolynomial_fold_free(
4184 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4186 To iterate over the base expressions in a union expression,
4187 use the following functions.
4189 #include <isl/aff.h>
4190 isl_size isl_union_pw_aff_n_pw_aff(
4191 __isl_keep isl_union_pw_aff *upa);
4192 isl_stat isl_union_pw_aff_foreach_pw_aff(
4193 __isl_keep isl_union_pw_aff *upa,
4194 isl_stat (*fn)(__isl_take isl_pw_aff *pa,
4195 void *user), void *user);
4196 isl_bool isl_union_pw_aff_every_pw_aff(
4197 __isl_keep isl_union_pw_aff *upa,
4198 isl_bool (*test)(__isl_keep isl_pw_aff *pa,
4199 void *user), void *user);
4200 isl_size isl_union_pw_multi_aff_n_pw_multi_aff(
4201 __isl_keep isl_union_pw_multi_aff *upma);
4202 isl_stat isl_union_pw_multi_aff_foreach_pw_multi_aff(
4203 __isl_keep isl_union_pw_multi_aff *upma,
4204 isl_stat (*fn)(__isl_take isl_pw_multi_aff *pma,
4205 void *user), void *user);
4206 isl_bool isl_union_pw_multi_aff_every_pw_multi_aff(
4207 __isl_keep isl_union_pw_multi_aff *upma,
4209 __isl_keep isl_pw_multi_aff *pma,
4210 void *user), void *user);
4212 #include <isl/polynomial.h>
4213 isl_size isl_union_pw_qpolynomial_n_pw_qpolynomial(
4214 __isl_keep isl_union_pw_qpolynomial *upwqp);
4215 isl_stat isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4216 __isl_keep isl_union_pw_qpolynomial *upwqp,
4217 isl_stat (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
4218 void *user), void *user);
4219 isl_bool isl_union_pw_qpolynomial_every_pw_qpolynomial(
4220 __isl_keep isl_union_pw_qpolynomial *upwqp,
4222 __isl_keep isl_pw_qpolynomial *pwqp,
4223 void *user), void *user);
4224 isl_size isl_union_pw_qpolynomial_fold_n_pw_qpolynomial_fold(
4225 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4226 isl_stat isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4227 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4228 isl_stat (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4229 void *user), void *user);
4231 isl_union_pw_qpolynomial_fold_every_pw_qpolynomial_fold(
4232 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4234 __isl_keep isl_pw_qpolynomial_fold *pwf,
4235 void *user), void *user);
4237 To extract the base expression in a given space from a union, use
4238 the following functions.
4240 #include <isl/aff.h>
4241 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
4242 __isl_keep isl_union_pw_aff *upa,
4243 __isl_take isl_space *space);
4244 __isl_give isl_pw_multi_aff *
4245 isl_union_pw_multi_aff_extract_pw_multi_aff(
4246 __isl_keep isl_union_pw_multi_aff *upma,
4247 __isl_take isl_space *space);
4249 #include <isl/polynomial.h>
4250 __isl_give isl_pw_qpolynomial *
4251 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4252 __isl_keep isl_union_pw_qpolynomial *upwqp,
4253 __isl_take isl_space *space);
4255 It is also possible to obtain a list of the base expressions using
4256 the following functions.
4258 #include <isl/aff.h>
4259 __isl_give isl_pw_aff_list *
4260 isl_union_pw_aff_get_pw_aff_list(
4261 __isl_keep isl_union_pw_aff *upa);
4262 __isl_give isl_pw_multi_aff_list *
4263 isl_union_pw_multi_aff_get_pw_multi_aff_list(
4264 __isl_keep isl_union_pw_multi_aff *upma);
4266 #include <isl/polynomial.h>
4267 __isl_give isl_pw_qpolynomial_list *
4268 isl_union_pw_qpolynomial_get_pw_qpolynomial_list(
4269 __isl_keep isl_union_pw_qpolynomial *upwqp);
4270 __isl_give isl_pw_qpolynomial_fold_list *
4271 isl_union_pw_qpolynomial_fold_get_pw_qpolynomial_fold_list(
4272 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4274 The returned list can be manipulated using the functions in L<"Lists">.
4276 =head2 Input and Output
4278 For set and relation,
4279 C<isl> supports its own input/output format, which is similar
4280 to the C<Omega> format, but also supports the C<PolyLib> format
4282 For other object types, typically only an C<isl> format is supported.
4284 =head3 C<isl> format
4286 The C<isl> format is similar to that of C<Omega>, but has a different
4287 syntax for describing the parameters and allows for the definition
4288 of an existentially quantified variable as the integer division
4289 of an affine expression.
4290 For example, the set of integers C<i> between C<0> and C<n>
4291 such that C<i % 10 <= 6> can be described as
4293 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
4296 A set or relation can have several disjuncts, separated
4297 by the keyword C<or>. Each disjunct is either a conjunction
4298 of constraints or a projection (C<exists>) of a conjunction
4299 of constraints. The constraints are separated by the keyword
4302 =head3 C<PolyLib> format
4304 If the represented set is a union, then the first line
4305 contains a single number representing the number of disjuncts.
4306 Otherwise, a line containing the number C<1> is optional.
4308 Each disjunct is represented by a matrix of constraints.
4309 The first line contains two numbers representing
4310 the number of rows and columns,
4311 where the number of rows is equal to the number of constraints
4312 and the number of columns is equal to two plus the number of variables.
4313 The following lines contain the actual rows of the constraint matrix.
4314 In each row, the first column indicates whether the constraint
4315 is an equality (C<0>) or inequality (C<1>). The final column
4316 corresponds to the constant term.
4318 If the set is parametric, then the coefficients of the parameters
4319 appear in the last columns before the constant column.
4320 The coefficients of any existentially quantified variables appear
4321 between those of the set variables and those of the parameters.
4323 =head3 Extended C<PolyLib> format
4325 The extended C<PolyLib> format is nearly identical to the
4326 C<PolyLib> format. The only difference is that the line
4327 containing the number of rows and columns of a constraint matrix
4328 also contains four additional numbers:
4329 the number of output dimensions, the number of input dimensions,
4330 the number of local dimensions (i.e., the number of existentially
4331 quantified variables) and the number of parameters.
4332 For sets, the number of ``output'' dimensions is equal
4333 to the number of set dimensions, while the number of ``input''
4338 Objects can be read from input using the following functions.
4341 __isl_give isl_id *isl_id_read_from_str(isl_ctx *ctx,
4343 __isl_give isl_multi_id *isl_multi_id_read_from_str(
4344 isl_ctx *ctx, const char *str);
4346 #include <isl/val.h>
4347 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
4349 __isl_give isl_multi_val *isl_multi_val_read_from_str(
4350 isl_ctx *ctx, const char *str);
4352 #include <isl/space.h>
4353 __isl_give isl_space *isl_space_read_from_str(
4354 isl_ctx *ctx, const char *str);
4356 #include <isl/set.h>
4357 __isl_give isl_basic_set *isl_basic_set_read_from_file(
4358 isl_ctx *ctx, FILE *input);
4359 __isl_give isl_basic_set *isl_basic_set_read_from_str(
4360 isl_ctx *ctx, const char *str);
4361 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
4363 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
4366 #include <isl/map.h>
4367 __isl_give isl_basic_map *isl_basic_map_read_from_file(
4368 isl_ctx *ctx, FILE *input);
4369 __isl_give isl_basic_map *isl_basic_map_read_from_str(
4370 isl_ctx *ctx, const char *str);
4371 __isl_give isl_map *isl_map_read_from_file(
4372 isl_ctx *ctx, FILE *input);
4373 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
4376 #include <isl/union_set.h>
4377 __isl_give isl_union_set *isl_union_set_read_from_file(
4378 isl_ctx *ctx, FILE *input);
4379 __isl_give isl_union_set *isl_union_set_read_from_str(
4380 isl_ctx *ctx, const char *str);
4382 #include <isl/union_map.h>
4383 __isl_give isl_union_map *isl_union_map_read_from_file(
4384 isl_ctx *ctx, FILE *input);
4385 __isl_give isl_union_map *isl_union_map_read_from_str(
4386 isl_ctx *ctx, const char *str);
4388 #include <isl/aff.h>
4389 __isl_give isl_aff *isl_aff_read_from_str(
4390 isl_ctx *ctx, const char *str);
4391 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4392 isl_ctx *ctx, const char *str);
4393 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4394 isl_ctx *ctx, const char *str);
4395 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4396 isl_ctx *ctx, const char *str);
4397 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
4398 isl_ctx *ctx, const char *str);
4399 __isl_give isl_union_pw_aff *
4400 isl_union_pw_aff_read_from_str(
4401 isl_ctx *ctx, const char *str);
4402 __isl_give isl_union_pw_multi_aff *
4403 isl_union_pw_multi_aff_read_from_str(
4404 isl_ctx *ctx, const char *str);
4405 __isl_give isl_multi_union_pw_aff *
4406 isl_multi_union_pw_aff_read_from_str(
4407 isl_ctx *ctx, const char *str);
4409 #include <isl/polynomial.h>
4410 __isl_give isl_union_pw_qpolynomial *
4411 isl_union_pw_qpolynomial_read_from_str(
4412 isl_ctx *ctx, const char *str);
4414 __isl_give isl_pw_qpolynomial_fold *
4415 isl_pw_qpolynomial_fold_read_from_str(
4416 isl_ctx *ctx, const char *str);
4418 For sets and relations,
4419 the input format is autodetected and may be either the C<PolyLib> format
4420 or the C<isl> format.
4424 Before anything can be printed, an C<isl_printer> needs to
4427 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
4429 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
4430 __isl_null isl_printer *isl_printer_free(
4431 __isl_take isl_printer *printer);
4433 C<isl_printer_to_file> prints to the given file, while
4434 C<isl_printer_to_str> prints to a string that can be extracted
4435 using the following function.
4437 #include <isl/printer.h>
4438 __isl_give char *isl_printer_get_str(
4439 __isl_keep isl_printer *printer);
4441 The printer can be inspected using the following functions.
4443 FILE *isl_printer_get_file(
4444 __isl_keep isl_printer *printer);
4445 int isl_printer_get_output_format(
4446 __isl_keep isl_printer *p);
4447 int isl_printer_get_yaml_style(__isl_keep isl_printer *p);
4449 The behavior of the printer can be modified in various ways
4451 __isl_give isl_printer *isl_printer_set_output_format(
4452 __isl_take isl_printer *p, int output_format);
4453 __isl_give isl_printer *isl_printer_set_indent(
4454 __isl_take isl_printer *p, int indent);
4455 __isl_give isl_printer *isl_printer_set_indent_prefix(
4456 __isl_take isl_printer *p, const char *prefix);
4457 __isl_give isl_printer *isl_printer_indent(
4458 __isl_take isl_printer *p, int indent);
4459 __isl_give isl_printer *isl_printer_set_prefix(
4460 __isl_take isl_printer *p, const char *prefix);
4461 __isl_give isl_printer *isl_printer_set_suffix(
4462 __isl_take isl_printer *p, const char *suffix);
4463 __isl_give isl_printer *isl_printer_set_yaml_style(
4464 __isl_take isl_printer *p, int yaml_style);
4466 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
4467 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
4468 and defaults to C<ISL_FORMAT_ISL>.
4469 Each line in the output is prefixed by C<indent_prefix>,
4470 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
4471 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
4472 In the C<PolyLib> format output,
4473 the coefficients of the existentially quantified variables
4474 appear between those of the set variables and those
4476 The function C<isl_printer_indent> increases the indentation
4477 by the specified amount (which may be negative).
4478 The YAML style may be either C<ISL_YAML_STYLE_BLOCK> or
4479 C<ISL_YAML_STYLE_FLOW> and when we are printing something
4482 To actually print something, use
4484 #include <isl/printer.h>
4485 __isl_give isl_printer *isl_printer_print_double(
4486 __isl_take isl_printer *p, double d);
4488 #include <isl/val.h>
4489 __isl_give isl_printer *isl_printer_print_val(
4490 __isl_take isl_printer *p, __isl_keep isl_val *v);
4491 __isl_give isl_printer *isl_printer_print_multi_val(
4492 __isl_take isl_printer *p,
4493 __isl_keep isl_multi_val *mv);
4495 #include <isl/set.h>
4496 __isl_give isl_printer *isl_printer_print_basic_set(
4497 __isl_take isl_printer *printer,
4498 __isl_keep isl_basic_set *bset);
4499 __isl_give isl_printer *isl_printer_print_set(
4500 __isl_take isl_printer *printer,
4501 __isl_keep isl_set *set);
4503 #include <isl/map.h>
4504 __isl_give isl_printer *isl_printer_print_basic_map(
4505 __isl_take isl_printer *printer,
4506 __isl_keep isl_basic_map *bmap);
4507 __isl_give isl_printer *isl_printer_print_map(
4508 __isl_take isl_printer *printer,
4509 __isl_keep isl_map *map);
4511 #include <isl/union_set.h>
4512 __isl_give isl_printer *isl_printer_print_union_set(
4513 __isl_take isl_printer *p,
4514 __isl_keep isl_union_set *uset);
4516 #include <isl/union_map.h>
4517 __isl_give isl_printer *isl_printer_print_union_map(
4518 __isl_take isl_printer *p,
4519 __isl_keep isl_union_map *umap);
4522 __isl_give isl_printer *isl_printer_print_multi_id(
4523 __isl_take isl_printer *p,
4524 __isl_keep isl_multi_id *mi);
4526 #include <isl/aff.h>
4527 __isl_give isl_printer *isl_printer_print_aff(
4528 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4529 __isl_give isl_printer *isl_printer_print_multi_aff(
4530 __isl_take isl_printer *p,
4531 __isl_keep isl_multi_aff *maff);
4532 __isl_give isl_printer *isl_printer_print_pw_aff(
4533 __isl_take isl_printer *p,
4534 __isl_keep isl_pw_aff *pwaff);
4535 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4536 __isl_take isl_printer *p,
4537 __isl_keep isl_pw_multi_aff *pma);
4538 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4539 __isl_take isl_printer *p,
4540 __isl_keep isl_multi_pw_aff *mpa);
4541 __isl_give isl_printer *isl_printer_print_union_pw_aff(
4542 __isl_take isl_printer *p,
4543 __isl_keep isl_union_pw_aff *upa);
4544 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4545 __isl_take isl_printer *p,
4546 __isl_keep isl_union_pw_multi_aff *upma);
4547 __isl_give isl_printer *
4548 isl_printer_print_multi_union_pw_aff(
4549 __isl_take isl_printer *p,
4550 __isl_keep isl_multi_union_pw_aff *mupa);
4552 #include <isl/polynomial.h>
4553 __isl_give isl_printer *isl_printer_print_qpolynomial(
4554 __isl_take isl_printer *p,
4555 __isl_keep isl_qpolynomial *qp);
4556 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4557 __isl_take isl_printer *p,
4558 __isl_keep isl_pw_qpolynomial *pwqp);
4559 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4560 __isl_take isl_printer *p,
4561 __isl_keep isl_union_pw_qpolynomial *upwqp);
4563 __isl_give isl_printer *
4564 isl_printer_print_pw_qpolynomial_fold(
4565 __isl_take isl_printer *p,
4566 __isl_keep isl_pw_qpolynomial_fold *pwf);
4567 __isl_give isl_printer *
4568 isl_printer_print_union_pw_qpolynomial_fold(
4569 __isl_take isl_printer *p,
4570 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4572 For C<isl_printer_print_qpolynomial>,
4573 C<isl_printer_print_pw_qpolynomial> and
4574 C<isl_printer_print_pw_qpolynomial_fold>,
4575 the output format of the printer
4576 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4577 For C<isl_printer_print_union_pw_qpolynomial> and
4578 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
4580 In case of printing in C<ISL_FORMAT_C>, the user may want
4581 to set the names of all dimensions first.
4583 C<isl> also provides limited support for printing YAML documents,
4584 just enough for the internal use for printing such documents.
4586 #include <isl/printer.h>
4587 __isl_give isl_printer *isl_printer_yaml_start_mapping(
4588 __isl_take isl_printer *p);
4589 __isl_give isl_printer *isl_printer_yaml_end_mapping(
4590 __isl_take isl_printer *p);
4591 __isl_give isl_printer *isl_printer_yaml_start_sequence(
4592 __isl_take isl_printer *p);
4593 __isl_give isl_printer *isl_printer_yaml_end_sequence(
4594 __isl_take isl_printer *p);
4595 __isl_give isl_printer *isl_printer_yaml_next(
4596 __isl_take isl_printer *p);
4598 A document is started by a call to either
4599 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
4600 Anything printed to the printer after such a call belong to the
4601 first key of the mapping or the first element in the sequence.
4602 The function C<isl_printer_yaml_next> moves to the value if
4603 we are currently printing a mapping key, the next key if we
4604 are printing a value or the next element if we are printing
4605 an element in a sequence.
4606 Nested mappings and sequences are initiated by the same
4607 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
4608 Each call to these functions needs to have a corresponding call to
4609 C<isl_printer_yaml_end_mapping> or C<isl_printer_yaml_end_sequence>.
4611 When called on a file printer, the following function flushes
4612 the file. When called on a string printer, the buffer is cleared.
4614 __isl_give isl_printer *isl_printer_flush(
4615 __isl_take isl_printer *p);
4617 The following functions allow the user to attach
4618 notes to a printer in order to keep track of additional state.
4620 #include <isl/printer.h>
4621 isl_bool isl_printer_has_note(__isl_keep isl_printer *p,
4622 __isl_keep isl_id *id);
4623 __isl_give isl_id *isl_printer_get_note(
4624 __isl_keep isl_printer *p, __isl_take isl_id *id);
4625 __isl_give isl_printer *isl_printer_set_note(
4626 __isl_take isl_printer *p,
4627 __isl_take isl_id *id, __isl_take isl_id *note);
4629 C<isl_printer_set_note> associates the given note to the given
4630 identifier in the printer.
4631 C<isl_printer_get_note> retrieves a note associated to an
4633 C<isl_printer_has_note> checks if there is such a note.
4634 C<isl_printer_get_note> fails if the requested note does not exist.
4636 Alternatively, a string representation can be obtained
4637 directly using the following functions, which always print
4641 __isl_give char *isl_id_to_str(
4642 __isl_keep isl_id *id);
4643 __isl_give char *isl_multi_id_to_str(
4644 __isl_keep isl_multi_id *mi);
4646 #include <isl/space.h>
4647 __isl_give char *isl_space_to_str(
4648 __isl_keep isl_space *space);
4650 #include <isl/val.h>
4651 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
4652 __isl_give char *isl_multi_val_to_str(
4653 __isl_keep isl_multi_val *mv);
4655 #include <isl/set.h>
4656 __isl_give char *isl_basic_set_to_str(
4657 __isl_keep isl_basic_set *bset);
4658 __isl_give char *isl_set_to_str(
4659 __isl_keep isl_set *set);
4661 #include <isl/union_set.h>
4662 __isl_give char *isl_union_set_to_str(
4663 __isl_keep isl_union_set *uset);
4665 #include <isl/map.h>
4666 __isl_give char *isl_basic_map_to_str(
4667 __isl_keep isl_basic_map *bmap);
4668 __isl_give char *isl_map_to_str(
4669 __isl_keep isl_map *map);
4671 #include <isl/union_map.h>
4672 __isl_give char *isl_union_map_to_str(
4673 __isl_keep isl_union_map *umap);
4675 #include <isl/aff.h>
4676 __isl_give char *isl_aff_to_str(__isl_keep isl_aff *aff);
4677 __isl_give char *isl_pw_aff_to_str(
4678 __isl_keep isl_pw_aff *pa);
4679 __isl_give char *isl_multi_aff_to_str(
4680 __isl_keep isl_multi_aff *ma);
4681 __isl_give char *isl_pw_multi_aff_to_str(
4682 __isl_keep isl_pw_multi_aff *pma);
4683 __isl_give char *isl_multi_pw_aff_to_str(
4684 __isl_keep isl_multi_pw_aff *mpa);
4685 __isl_give char *isl_union_pw_aff_to_str(
4686 __isl_keep isl_union_pw_aff *upa);
4687 __isl_give char *isl_union_pw_multi_aff_to_str(
4688 __isl_keep isl_union_pw_multi_aff *upma);
4689 __isl_give char *isl_multi_union_pw_aff_to_str(
4690 __isl_keep isl_multi_union_pw_aff *mupa);
4692 #include <isl/point.h>
4693 __isl_give char *isl_point_to_str(
4694 __isl_keep isl_point *pnt);
4696 #include <isl/polynomial.h>
4697 __isl_give char *isl_pw_qpolynomial_to_str(
4698 __isl_keep isl_pw_qpolynomial *pwqp);
4699 __isl_give char *isl_union_pw_qpolynomial_to_str(
4700 __isl_keep isl_union_pw_qpolynomial *upwqp);
4704 =head3 Unary Properties
4710 The following functions test whether the given set or relation
4711 contains any integer points. The ``plain'' variants do not perform
4712 any computations, but simply check if the given set or relation
4713 is already known to be empty.
4715 #include <isl/set.h>
4716 isl_bool isl_basic_set_plain_is_empty(
4717 __isl_keep isl_basic_set *bset);
4718 isl_bool isl_basic_set_is_empty(
4719 __isl_keep isl_basic_set *bset);
4720 isl_bool isl_set_plain_is_empty(
4721 __isl_keep isl_set *set);
4722 isl_bool isl_set_is_empty(__isl_keep isl_set *set);
4724 #include <isl/union_set.h>
4725 isl_bool isl_union_set_is_empty(
4726 __isl_keep isl_union_set *uset);
4728 #include <isl/map.h>
4729 isl_bool isl_basic_map_plain_is_empty(
4730 __isl_keep isl_basic_map *bmap);
4731 isl_bool isl_basic_map_is_empty(
4732 __isl_keep isl_basic_map *bmap);
4733 isl_bool isl_map_plain_is_empty(
4734 __isl_keep isl_map *map);
4735 isl_bool isl_map_is_empty(__isl_keep isl_map *map);
4737 #include <isl/union_map.h>
4738 isl_bool isl_union_map_plain_is_empty(
4739 __isl_keep isl_union_map *umap);
4740 isl_bool isl_union_map_is_empty(
4741 __isl_keep isl_union_map *umap);
4743 #include <isl/aff.h>
4744 isl_bool isl_union_pw_multi_aff_plain_is_empty(
4745 __isl_keep isl_union_pw_multi_aff *upma);
4747 =item * Universality
4749 isl_bool isl_basic_set_plain_is_universe(
4750 __isl_keep isl_basic_set *bset);
4751 isl_bool isl_basic_set_is_universe(
4752 __isl_keep isl_basic_set *bset);
4753 isl_bool isl_basic_map_plain_is_universe(
4754 __isl_keep isl_basic_map *bmap);
4755 isl_bool isl_basic_map_is_universe(
4756 __isl_keep isl_basic_map *bmap);
4757 isl_bool isl_set_plain_is_universe(
4758 __isl_keep isl_set *set);
4759 isl_bool isl_map_plain_is_universe(
4760 __isl_keep isl_map *map);
4762 =item * Single-valuedness
4764 #include <isl/set.h>
4765 isl_bool isl_set_is_singleton(__isl_keep isl_set *set);
4767 #include <isl/map.h>
4768 isl_bool isl_basic_map_is_single_valued(
4769 __isl_keep isl_basic_map *bmap);
4770 isl_bool isl_map_plain_is_single_valued(
4771 __isl_keep isl_map *map);
4772 isl_bool isl_map_is_single_valued(__isl_keep isl_map *map);
4774 #include <isl/union_map.h>
4775 isl_bool isl_union_map_is_single_valued(
4776 __isl_keep isl_union_map *umap);
4780 isl_bool isl_map_plain_is_injective(
4781 __isl_keep isl_map *map);
4782 isl_bool isl_map_is_injective(
4783 __isl_keep isl_map *map);
4784 isl_bool isl_union_map_plain_is_injective(
4785 __isl_keep isl_union_map *umap);
4786 isl_bool isl_union_map_is_injective(
4787 __isl_keep isl_union_map *umap);
4791 isl_bool isl_map_is_bijective(
4792 __isl_keep isl_map *map);
4793 isl_bool isl_union_map_is_bijective(
4794 __isl_keep isl_union_map *umap);
4798 The following functions test whether the given relation
4799 only maps elements to themselves.
4801 #include <isl/map.h>
4802 isl_bool isl_map_is_identity(
4803 __isl_keep isl_map *map);
4805 #include <isl/union_map.h>
4806 isl_bool isl_union_map_is_identity(
4807 __isl_keep isl_union_map *umap);
4811 __isl_give isl_val *
4812 isl_basic_map_plain_get_val_if_fixed(
4813 __isl_keep isl_basic_map *bmap,
4814 enum isl_dim_type type, unsigned pos);
4815 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
4816 __isl_keep isl_set *set,
4817 enum isl_dim_type type, unsigned pos);
4818 __isl_give isl_multi_val *
4819 isl_set_get_plain_multi_val_if_fixed(
4820 __isl_keep isl_set *set);
4821 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
4822 __isl_keep isl_map *map,
4823 enum isl_dim_type type, unsigned pos);
4825 If the set or relation obviously lies on a hyperplane where the given dimension
4826 has a fixed value, then return that value.
4827 Otherwise return NaN.
4828 C<isl_set_get_plain_multi_val_if_fixed> collects the results over
4833 Stride detection is based on heuristics.
4834 The strides returned by the functions below are always valid,
4835 but there may be larger valid strides that are not detected.
4837 isl_stat isl_set_dim_residue_class_val(
4838 __isl_keep isl_set *set,
4839 int pos, __isl_give isl_val **modulo,
4840 __isl_give isl_val **residue);
4842 Check if the values of the given set dimension are equal to a fixed
4843 value modulo some integer value. If so, assign the modulo to C<*modulo>
4844 and the fixed value to C<*residue>. If the given dimension attains only
4845 a single value, then assign C<0> to C<*modulo> and the fixed value to
4847 If the dimension does not attain only a single value and if no modulo
4848 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
4850 #include <isl/set.h>
4851 __isl_give isl_stride_info *isl_set_get_stride_info(
4852 __isl_keep isl_set *set, int pos);
4853 __isl_give isl_val *isl_set_get_stride(
4854 __isl_keep isl_set *set, int pos);
4855 __isl_give isl_fixed_box *isl_set_get_lattice_tile(
4856 __isl_keep isl_set *set);
4858 #include <isl/map.h>
4859 __isl_give isl_stride_info *
4860 isl_map_get_range_stride_info(
4861 __isl_keep isl_map *map, int pos);
4862 __isl_give isl_fixed_box *
4863 isl_map_get_range_lattice_tile(
4864 __isl_keep isl_map *map);
4866 Check if the values of the given set dimension are equal to
4867 some affine expression of the other dimensions (the offset)
4868 modulo some integer stride or
4869 check if the values of the given output dimensions are equal to
4870 some affine expression of the input dimensions (the offset)
4871 modulo some integer stride.
4872 If no more specific information can be found, then the stride
4873 is taken to be one and the offset is taken to be the zero expression.
4874 The function C<isl_set_get_stride> performs the same
4875 computation as C<isl_set_get_stride_info> but only returns the stride.
4876 The function C<isl_map_get_range_lattice_tile> collects the stride
4877 information over all output dimensions.
4878 In particular, it returns a tile of a rectangular lattice
4879 (possibly of size 1 in all directions)
4880 containing the output in terms of the parameters and the input dimensions.
4881 The size and the offset of this tile correspond to
4882 the strides and the offsets of the stride information and
4883 can be extracted from the returned
4884 C<isl_fixed_box> using the functions described under "Box hull" in
4885 L</"Unary Operations">. Note that the C<isl_fixed_box> object returned by
4886 C<isl_map_get_range_lattice_tile> is always valid.
4887 The function C<isl_set_get_lattice_tile> collects the same stride
4888 information over all set dimensions.
4889 For the other functions,
4890 the stride and offset can be extracted from the returned object
4891 using the following functions.
4893 #include <isl/stride_info.h>
4894 __isl_give isl_val *isl_stride_info_get_stride(
4895 __isl_keep isl_stride_info *si);
4896 __isl_give isl_aff *isl_stride_info_get_offset(
4897 __isl_keep isl_stride_info *si);
4899 The stride info object can be copied and released using the following
4902 #include <isl/stride_info.h>
4903 __isl_give isl_stride_info *isl_stride_info_copy(
4904 __isl_keep isl_stride_info *si);
4905 __isl_null isl_stride_info *isl_stride_info_free(
4906 __isl_take isl_stride_info *si);
4910 To check whether a function involves any local variables,
4911 i.e., integer divisions,
4912 the following functions can be used.
4914 #include <isl/set.h>
4915 isl_bool isl_set_involves_locals(
4916 __isl_keep isl_set *set);
4918 #include <isl/aff.h>
4919 isl_bool isl_aff_involves_locals(
4920 __isl_keep isl_aff *aff);
4921 isl_bool isl_multi_aff_involves_locals(
4922 __isl_keep isl_multi_aff *ma);
4923 isl_bool isl_pw_multi_aff_involves_locals(
4924 __isl_keep isl_pw_multi_aff *pma);
4925 isl_bool isl_union_pw_multi_aff_involves_locals(
4926 __isl_keep isl_union_pw_multi_aff *upma);
4928 To check whether the description of a set, relation or function depends
4929 on a parameter or one or more given dimensions,
4930 the following functions can be used.
4932 #include <isl/constraint.h>
4933 isl_bool isl_constraint_involves_dims(
4934 __isl_keep isl_constraint *constraint,
4935 enum isl_dim_type type, unsigned first, unsigned n);
4937 #include <isl/set.h>
4938 isl_bool isl_basic_set_involves_dims(
4939 __isl_keep isl_basic_set *bset,
4940 enum isl_dim_type type, unsigned first, unsigned n);
4941 isl_bool isl_set_involves_dims(__isl_keep isl_set *set,
4942 enum isl_dim_type type, unsigned first, unsigned n);
4944 #include <isl/map.h>
4945 isl_bool isl_basic_map_involves_dims(
4946 __isl_keep isl_basic_map *bmap,
4947 enum isl_dim_type type, unsigned first, unsigned n);
4948 isl_bool isl_map_involves_dims(__isl_keep isl_map *map,
4949 enum isl_dim_type type, unsigned first, unsigned n);
4951 #include <isl/union_map.h>
4952 isl_bool isl_union_map_involves_dims(
4953 __isl_keep isl_union_map *umap,
4954 enum isl_dim_type type, unsigned first, unsigned n);
4956 #include <isl/aff.h>
4957 isl_bool isl_aff_involves_dims(__isl_keep isl_aff *aff,
4958 enum isl_dim_type type, unsigned first, unsigned n);
4959 isl_bool isl_pw_aff_involves_param_id(
4960 __isl_keep isl_pw_aff *pa,
4961 __isl_keep isl_id *id);
4962 isl_bool isl_pw_aff_involves_dims(
4963 __isl_keep isl_pw_aff *pwaff,
4964 enum isl_dim_type type, unsigned first, unsigned n);
4965 isl_bool isl_multi_aff_involves_dims(
4966 __isl_keep isl_multi_aff *ma,
4967 enum isl_dim_type type, unsigned first, unsigned n);
4968 isl_bool isl_pw_multi_aff_involves_param_id(
4969 __isl_keep isl_pw_multi_aff *pma,
4970 __isl_keep isl_id *id);
4971 isl_bool isl_pw_multi_aff_involves_dims(
4972 __isl_keep isl_pw_multi_aff *pma,
4973 enum isl_dim_type type, unsigned first, unsigned n);
4974 isl_bool isl_multi_pw_aff_involves_dims(
4975 __isl_keep isl_multi_pw_aff *mpa,
4976 enum isl_dim_type type, unsigned first, unsigned n);
4977 isl_bool isl_multi_pw_aff_involves_param_id(
4978 __isl_keep isl_multi_pw_aff *mpa,
4979 __isl_keep isl_id *id);
4980 isl_bool isl_multi_pw_aff_involves_param_id_list(
4981 __isl_keep isl_multi_pw_aff *mpa,
4982 __isl_keep isl_id_list *list);
4984 #include <isl/polynomial.h>
4985 isl_bool isl_qpolynomial_involves_dims(
4986 __isl_keep isl_qpolynomial *qp,
4987 enum isl_dim_type type, unsigned first, unsigned n);
4988 isl_bool isl_pw_qpolynomial_involves_param_id(
4989 __isl_keep isl_pw_qpolynomial *pwqp,
4990 __isl_keep isl_id *id);
4991 isl_bool isl_pw_qpolynomial_fold_involves_param_id(
4992 __isl_keep isl_pw_qpolynomial_fold *pwf,
4993 __isl_keep isl_id *id);
4995 Similarly, the following functions can be used to check whether
4996 a given dimension is involved in any lower or upper bound.
4998 #include <isl/set.h>
4999 isl_bool isl_set_dim_has_any_lower_bound(
5000 __isl_keep isl_set *set,
5001 enum isl_dim_type type, unsigned pos);
5002 isl_bool isl_set_dim_has_any_upper_bound(
5003 __isl_keep isl_set *set,
5004 enum isl_dim_type type, unsigned pos);
5006 Note that these functions return true even if there is a bound on
5007 the dimension on only some of the basic sets of C<set>.
5008 To check if they have a bound for all of the basic sets in C<set>,
5009 use the following functions instead.
5011 #include <isl/set.h>
5012 isl_bool isl_set_dim_has_lower_bound(
5013 __isl_keep isl_set *set,
5014 enum isl_dim_type type, unsigned pos);
5015 isl_bool isl_set_dim_has_upper_bound(
5016 __isl_keep isl_set *set,
5017 enum isl_dim_type type, unsigned pos);
5021 To check whether a set is a parameter domain, use this function:
5023 isl_bool isl_set_is_params(__isl_keep isl_set *set);
5024 isl_bool isl_union_set_is_params(
5025 __isl_keep isl_union_set *uset);
5029 The following functions check whether the space of the given
5030 (basic) set or relation domain and/or range is a wrapped relation.
5032 #include <isl/space.h>
5033 isl_bool isl_space_is_wrapping(
5034 __isl_keep isl_space *space);
5035 isl_bool isl_space_domain_is_wrapping(
5036 __isl_keep isl_space *space);
5037 isl_bool isl_space_range_is_wrapping(
5038 __isl_keep isl_space *space);
5039 isl_bool isl_space_is_product(
5040 __isl_keep isl_space *space);
5042 #include <isl/set.h>
5043 isl_bool isl_basic_set_is_wrapping(
5044 __isl_keep isl_basic_set *bset);
5045 isl_bool isl_set_is_wrapping(__isl_keep isl_set *set);
5047 #include <isl/map.h>
5048 isl_bool isl_map_domain_is_wrapping(
5049 __isl_keep isl_map *map);
5050 isl_bool isl_map_range_is_wrapping(
5051 __isl_keep isl_map *map);
5052 isl_bool isl_map_is_product(__isl_keep isl_map *map);
5055 isl_bool isl_multi_id_range_is_wrapping(
5056 __isl_keep isl_multi_id *mi);
5058 #include <isl/val.h>
5059 isl_bool isl_multi_val_range_is_wrapping(
5060 __isl_keep isl_multi_val *mv);
5062 #include <isl/aff.h>
5063 isl_bool isl_multi_aff_range_is_wrapping(
5064 __isl_keep isl_multi_aff *ma);
5065 isl_bool isl_multi_pw_aff_range_is_wrapping(
5066 __isl_keep isl_multi_pw_aff *mpa);
5067 isl_bool isl_multi_union_pw_aff_range_is_wrapping(
5068 __isl_keep isl_multi_union_pw_aff *mupa);
5070 The input to C<isl_space_is_wrapping> should
5071 be the space of a set, while that of
5072 C<isl_space_domain_is_wrapping> and
5073 C<isl_space_range_is_wrapping> should be the space of a relation.
5074 The input to C<isl_space_is_product> can be either the space
5075 of a set or that of a binary relation.
5076 In case the input is the space of a binary relation, it checks
5077 whether both domain and range are wrapping.
5079 =item * Internal Product
5081 isl_bool isl_basic_map_can_zip(
5082 __isl_keep isl_basic_map *bmap);
5083 isl_bool isl_map_can_zip(__isl_keep isl_map *map);
5085 Check whether the product of domain and range of the given relation
5087 i.e., whether both domain and range are nested relations.
5091 #include <isl/space.h>
5092 isl_bool isl_space_can_curry(
5093 __isl_keep isl_space *space);
5095 #include <isl/map.h>
5096 isl_bool isl_basic_map_can_curry(
5097 __isl_keep isl_basic_map *bmap);
5098 isl_bool isl_map_can_curry(__isl_keep isl_map *map);
5100 Check whether the domain of the (basic) relation is a wrapped relation.
5102 #include <isl/space.h>
5103 isl_bool isl_space_can_uncurry(
5104 __isl_keep isl_space *space);
5106 #include <isl/map.h>
5107 isl_bool isl_basic_map_can_uncurry(
5108 __isl_keep isl_basic_map *bmap);
5109 isl_bool isl_map_can_uncurry(__isl_keep isl_map *map);
5111 Check whether the range of the (basic) relation is a wrapped relation.
5113 #include <isl/space.h>
5114 isl_bool isl_space_can_range_curry(
5115 __isl_keep isl_space *space);
5117 #include <isl/map.h>
5118 isl_bool isl_map_can_range_curry(
5119 __isl_keep isl_map *map);
5121 Check whether the domain of the relation wrapped in the range of
5122 the input is itself a wrapped relation.
5124 =item * Special Values
5126 #include <isl/aff.h>
5127 isl_bool isl_aff_is_cst(__isl_keep isl_aff *aff);
5128 isl_bool isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
5129 isl_bool isl_multi_pw_aff_is_cst(
5130 __isl_keep isl_multi_pw_aff *mpa);
5132 Check whether the given expression is a constant.
5134 #include <isl/val.h>
5135 isl_bool isl_multi_val_involves_nan(
5136 __isl_keep isl_multi_val *mv);
5138 #include <isl/aff.h>
5139 isl_bool isl_aff_is_nan(__isl_keep isl_aff *aff);
5140 isl_bool isl_multi_aff_involves_nan(
5141 __isl_keep isl_multi_aff *ma);
5142 isl_bool isl_pw_aff_involves_nan(
5143 __isl_keep isl_pw_aff *pa);
5144 isl_bool isl_pw_multi_aff_involves_nan(
5145 __isl_keep isl_pw_multi_aff *pma);
5146 isl_bool isl_multi_pw_aff_involves_nan(
5147 __isl_keep isl_multi_pw_aff *mpa);
5148 isl_bool isl_union_pw_aff_involves_nan(
5149 __isl_keep isl_union_pw_aff *upa);
5150 isl_bool isl_union_pw_multi_aff_involves_nan(
5151 __isl_keep isl_union_pw_multi_aff *upma);
5152 isl_bool isl_multi_union_pw_aff_involves_nan(
5153 __isl_keep isl_multi_union_pw_aff *mupa);
5155 #include <isl/polynomial.h>
5156 isl_bool isl_qpolynomial_is_nan(
5157 __isl_keep isl_qpolynomial *qp);
5158 isl_bool isl_qpolynomial_fold_is_nan(
5159 __isl_keep isl_qpolynomial_fold *fold);
5160 isl_bool isl_pw_qpolynomial_involves_nan(
5161 __isl_keep isl_pw_qpolynomial *pwqp);
5162 isl_bool isl_pw_qpolynomial_fold_involves_nan(
5163 __isl_keep isl_pw_qpolynomial_fold *pwf);
5164 isl_bool isl_union_pw_qpolynomial_involves_nan(
5165 __isl_keep isl_union_pw_qpolynomial *upwqp);
5166 isl_bool isl_union_pw_qpolynomial_fold_involves_nan(
5167 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5169 Check whether the given expression is equal to or involves NaN.
5171 #include <isl/val.h>
5172 isl_bool isl_multi_val_is_zero(
5173 __isl_keep isl_multi_val *mv);
5175 Check whether the multiple value is zero.
5177 #include <isl/aff.h>
5178 isl_bool isl_aff_plain_is_zero(
5179 __isl_keep isl_aff *aff);
5181 Check whether the affine expression is obviously zero.
5185 =head3 Binary Properties
5191 The following functions check whether two objects
5192 represent the same set, relation or function.
5193 The C<plain> variants only return true if the objects
5194 are obviously the same. That is, they may return false
5195 even if the objects are the same, but they will never
5196 return true if the objects are not the same.
5198 #include <isl/set.h>
5199 isl_bool isl_basic_set_plain_is_equal(
5200 __isl_keep isl_basic_set *bset1,
5201 __isl_keep isl_basic_set *bset2);
5202 isl_bool isl_basic_set_is_equal(
5203 __isl_keep isl_basic_set *bset1,
5204 __isl_keep isl_basic_set *bset2);
5205 isl_bool isl_set_plain_is_equal(
5206 __isl_keep isl_set *set1,
5207 __isl_keep isl_set *set2);
5208 isl_bool isl_set_is_equal(__isl_keep isl_set *set1,
5209 __isl_keep isl_set *set2);
5211 #include <isl/map.h>
5212 isl_bool isl_basic_map_is_equal(
5213 __isl_keep isl_basic_map *bmap1,
5214 __isl_keep isl_basic_map *bmap2);
5215 isl_bool isl_map_is_equal(__isl_keep isl_map *map1,
5216 __isl_keep isl_map *map2);
5217 isl_bool isl_map_plain_is_equal(
5218 __isl_keep isl_map *map1,
5219 __isl_keep isl_map *map2);
5221 #include <isl/union_set.h>
5222 isl_bool isl_union_set_is_equal(
5223 __isl_keep isl_union_set *uset1,
5224 __isl_keep isl_union_set *uset2);
5226 #include <isl/union_map.h>
5227 isl_bool isl_union_map_is_equal(
5228 __isl_keep isl_union_map *umap1,
5229 __isl_keep isl_union_map *umap2);
5232 isl_bool isl_multi_id_plain_is_equal(
5233 __isl_keep isl_multi_id *mi1,
5234 __isl_keep isl_multi_id *mi2);
5236 #include <isl/val.h>
5237 isl_bool isl_multi_val_plain_is_equal(
5238 __isl_keep isl_multi_val *mv1,
5239 __isl_keep isl_multi_val *mv2);
5241 #include <isl/aff.h>
5242 isl_bool isl_aff_plain_is_equal(
5243 __isl_keep isl_aff *aff1,
5244 __isl_keep isl_aff *aff2);
5245 isl_bool isl_multi_aff_plain_is_equal(
5246 __isl_keep isl_multi_aff *maff1,
5247 __isl_keep isl_multi_aff *maff2);
5248 isl_bool isl_pw_aff_plain_is_equal(
5249 __isl_keep isl_pw_aff *pwaff1,
5250 __isl_keep isl_pw_aff *pwaff2);
5251 isl_bool isl_pw_aff_is_equal(
5252 __isl_keep isl_pw_aff *pa1,
5253 __isl_keep isl_pw_aff *pa2);
5254 isl_bool isl_pw_multi_aff_plain_is_equal(
5255 __isl_keep isl_pw_multi_aff *pma1,
5256 __isl_keep isl_pw_multi_aff *pma2);
5257 isl_bool isl_pw_multi_aff_is_equal(
5258 __isl_keep isl_pw_multi_aff *pma1,
5259 __isl_keep isl_pw_multi_aff *pma2);
5260 isl_bool isl_multi_pw_aff_plain_is_equal(
5261 __isl_keep isl_multi_pw_aff *mpa1,
5262 __isl_keep isl_multi_pw_aff *mpa2);
5263 isl_bool isl_multi_pw_aff_is_equal(
5264 __isl_keep isl_multi_pw_aff *mpa1,
5265 __isl_keep isl_multi_pw_aff *mpa2);
5266 isl_bool isl_union_pw_aff_plain_is_equal(
5267 __isl_keep isl_union_pw_aff *upa1,
5268 __isl_keep isl_union_pw_aff *upa2);
5269 isl_bool isl_union_pw_multi_aff_plain_is_equal(
5270 __isl_keep isl_union_pw_multi_aff *upma1,
5271 __isl_keep isl_union_pw_multi_aff *upma2);
5272 isl_bool isl_multi_union_pw_aff_plain_is_equal(
5273 __isl_keep isl_multi_union_pw_aff *mupa1,
5274 __isl_keep isl_multi_union_pw_aff *mupa2);
5276 #include <isl/polynomial.h>
5277 isl_bool isl_union_pw_qpolynomial_plain_is_equal(
5278 __isl_keep isl_union_pw_qpolynomial *upwqp1,
5279 __isl_keep isl_union_pw_qpolynomial *upwqp2);
5280 isl_bool isl_union_pw_qpolynomial_fold_plain_is_equal(
5281 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5282 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5284 =item * Disjointness
5286 #include <isl/set.h>
5287 isl_bool isl_basic_set_is_disjoint(
5288 __isl_keep isl_basic_set *bset1,
5289 __isl_keep isl_basic_set *bset2);
5290 isl_bool isl_set_plain_is_disjoint(
5291 __isl_keep isl_set *set1,
5292 __isl_keep isl_set *set2);
5293 isl_bool isl_set_is_disjoint(__isl_keep isl_set *set1,
5294 __isl_keep isl_set *set2);
5296 #include <isl/map.h>
5297 isl_bool isl_basic_map_is_disjoint(
5298 __isl_keep isl_basic_map *bmap1,
5299 __isl_keep isl_basic_map *bmap2);
5300 isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1,
5301 __isl_keep isl_map *map2);
5303 #include <isl/union_set.h>
5304 isl_bool isl_union_set_is_disjoint(
5305 __isl_keep isl_union_set *uset1,
5306 __isl_keep isl_union_set *uset2);
5308 #include <isl/union_map.h>
5309 isl_bool isl_union_map_is_disjoint(
5310 __isl_keep isl_union_map *umap1,
5311 __isl_keep isl_union_map *umap2);
5315 isl_bool isl_basic_set_is_subset(
5316 __isl_keep isl_basic_set *bset1,
5317 __isl_keep isl_basic_set *bset2);
5318 isl_bool isl_set_is_subset(__isl_keep isl_set *set1,
5319 __isl_keep isl_set *set2);
5320 isl_bool isl_set_is_strict_subset(
5321 __isl_keep isl_set *set1,
5322 __isl_keep isl_set *set2);
5323 isl_bool isl_union_set_is_subset(
5324 __isl_keep isl_union_set *uset1,
5325 __isl_keep isl_union_set *uset2);
5326 isl_bool isl_union_set_is_strict_subset(
5327 __isl_keep isl_union_set *uset1,
5328 __isl_keep isl_union_set *uset2);
5329 isl_bool isl_basic_map_is_subset(
5330 __isl_keep isl_basic_map *bmap1,
5331 __isl_keep isl_basic_map *bmap2);
5332 isl_bool isl_basic_map_is_strict_subset(
5333 __isl_keep isl_basic_map *bmap1,
5334 __isl_keep isl_basic_map *bmap2);
5335 isl_bool isl_map_is_subset(
5336 __isl_keep isl_map *map1,
5337 __isl_keep isl_map *map2);
5338 isl_bool isl_map_is_strict_subset(
5339 __isl_keep isl_map *map1,
5340 __isl_keep isl_map *map2);
5341 isl_bool isl_union_map_is_subset(
5342 __isl_keep isl_union_map *umap1,
5343 __isl_keep isl_union_map *umap2);
5344 isl_bool isl_union_map_is_strict_subset(
5345 __isl_keep isl_union_map *umap1,
5346 __isl_keep isl_union_map *umap2);
5348 Check whether the first argument is a (strict) subset of the
5353 Every comparison function returns a negative value if the first
5354 argument is considered smaller than the second, a positive value
5355 if the first argument is considered greater and zero if the two
5356 constraints are considered the same by the comparison criterion.
5358 #include <isl/constraint.h>
5359 int isl_constraint_plain_cmp(
5360 __isl_keep isl_constraint *c1,
5361 __isl_keep isl_constraint *c2);
5363 This function is useful for sorting C<isl_constraint>s.
5364 The order depends on the internal representation of the inputs.
5365 The order is fixed over different calls to the function (assuming
5366 the internal representation of the inputs has not changed), but may
5367 change over different versions of C<isl>.
5369 #include <isl/constraint.h>
5370 int isl_constraint_cmp_last_non_zero(
5371 __isl_keep isl_constraint *c1,
5372 __isl_keep isl_constraint *c2);
5374 This function can be used to sort constraints that live in the same
5375 local space. Constraints that involve ``earlier'' dimensions or
5376 that have a smaller coefficient for the shared latest dimension
5377 are considered smaller than other constraints.
5378 This function only defines a B<partial> order.
5380 #include <isl/set.h>
5381 int isl_set_plain_cmp(__isl_keep isl_set *set1,
5382 __isl_keep isl_set *set2);
5384 This function is useful for sorting C<isl_set>s.
5385 The order depends on the internal representation of the inputs.
5386 The order is fixed over different calls to the function (assuming
5387 the internal representation of the inputs has not changed), but may
5388 change over different versions of C<isl>.
5390 #include <isl/aff.h>
5391 int isl_multi_aff_plain_cmp(
5392 __isl_keep isl_multi_aff *ma1,
5393 __isl_keep isl_multi_aff *ma2);
5394 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
5395 __isl_keep isl_pw_aff *pa2);
5397 The functions C<isl_multi_aff_plain_cmp> and
5398 C<isl_pw_aff_plain_cmp> can be used to sort C<isl_multi_aff>s and
5399 C<isl_pw_aff>s. The order is not strictly defined.
5400 The current order sorts expressions that only involve
5401 earlier dimensions before those that involve later dimensions.
5405 =head2 Unary Operations
5411 __isl_give isl_set *isl_set_complement(
5412 __isl_take isl_set *set);
5413 __isl_give isl_map *isl_map_complement(
5414 __isl_take isl_map *map);
5418 #include <isl/space.h>
5419 __isl_give isl_space *isl_space_reverse(
5420 __isl_take isl_space *space);
5421 __isl_give isl_space *isl_space_wrapped_reverse(
5422 __isl_take isl_space *space);
5423 __isl_give isl_space *isl_space_domain_reverse(
5424 __isl_take isl_space *space);
5425 __isl_give isl_space *isl_space_range_reverse(
5426 __isl_take isl_space *space);
5428 #include <isl/aff.h>
5429 __isl_give isl_aff *isl_aff_domain_reverse(
5430 __isl_take isl_aff *aff);
5431 __isl_give isl_multi_aff *
5432 isl_multi_aff_domain_reverse(
5433 __isl_take isl_multi_aff *ma);
5434 __isl_give isl_pw_aff *isl_pw_aff_domain_reverse(
5435 __isl_take isl_pw_aff *pa);
5436 __isl_give isl_pw_multi_aff *
5437 isl_pw_multi_aff_domain_reverse(
5438 __isl_take isl_pw_multi_aff *pma);
5440 #include <isl/set.h>
5441 __isl_give isl_set *isl_set_wrapped_reverse(
5442 __isl_take isl_set *set);
5444 #include <isl/map.h>
5445 __isl_give isl_basic_map *isl_basic_map_reverse(
5446 __isl_take isl_basic_map *bmap);
5447 __isl_give isl_map *isl_map_reverse(
5448 __isl_take isl_map *map);
5449 __isl_give isl_map *isl_map_range_reverse(
5450 __isl_take isl_map *map);
5452 #include <isl/union_map.h>
5453 __isl_give isl_union_map *isl_union_map_reverse(
5454 __isl_take isl_union_map *umap);
5455 __isl_give isl_union_map *isl_union_map_range_reverse(
5456 __isl_take isl_union_map *umap);
5458 The function C<isl_space_range_reverse> reverses the relation
5459 that is embedded in the range of the input map space.
5460 The identifier of the range, if any, is only preserved
5461 if this embedded relation has identical input and output tuples.
5462 Similarly for C<isl_space_domain_reverse>.
5463 Along the same lines, C<isl_space_wrapped_reverse> reverses
5464 the relation that is embedded in a set space.
5466 =item * Tuple binding
5468 The following function binds
5469 a tuple to a sequence of parameter identifiers, equating
5470 the tuple dimensions to the parameters with those identifiers and
5471 subsequently projecting out the tuple.
5472 If the original object did not reference any such parameters,
5473 then this means that the tuple dimensions are reinterpreted
5475 The space of C<tuple> needs to match that of the bound tuple.
5477 #include <isl/set.h>
5478 __isl_give isl_set *isl_set_bind(
5479 __isl_take isl_set *set,
5480 __isl_take isl_multi_id *tuple);
5482 #include <isl/map.h>
5483 __isl_give isl_set *isl_map_bind_domain(
5484 __isl_take isl_map *map,
5485 __isl_take isl_multi_id *tuple);
5486 __isl_give isl_set *isl_map_bind_range(
5487 __isl_take isl_map *map,
5488 __isl_take isl_multi_id *tuple);
5490 #include <isl/union_map.h>
5491 __isl_give isl_union_set *isl_union_map_bind_range(
5492 __isl_take isl_union_map *umap,
5493 __isl_take isl_multi_id *tuple);
5495 #include <isl/aff.h>
5496 __isl_give isl_pw_aff *isl_pw_aff_bind_domain(
5497 __isl_take isl_pw_aff *pa,
5498 __isl_take isl_multi_id *tuple);
5499 __isl_give isl_multi_aff *isl_multi_aff_bind_domain(
5500 __isl_take isl_multi_aff *ma,
5501 __isl_take isl_multi_id *tuple);
5502 __isl_give isl_pw_multi_aff *
5503 isl_pw_multi_aff_bind_domain(
5504 __isl_take isl_pw_multi_aff *pma,
5505 __isl_take isl_multi_id *tuple);
5506 __isl_give isl_multi_pw_aff *
5507 isl_multi_pw_aff_bind_domain(
5508 __isl_take isl_multi_pw_aff *mpa,
5509 __isl_take isl_multi_id *tuple);
5510 __isl_give isl_pw_aff *
5511 isl_pw_aff_bind_domain_wrapped_domain(
5512 __isl_take isl_pw_aff *pa,
5513 __isl_take isl_multi_id *tuple);
5514 __isl_give isl_multi_aff *
5515 isl_multi_aff_bind_domain_wrapped_domain(
5516 __isl_take isl_multi_aff *ma,
5517 __isl_take isl_multi_id *tuple);
5518 __isl_give isl_pw_multi_aff *
5519 isl_pw_multi_aff_bind_domain_wrapped_domain(
5520 __isl_take isl_pw_multi_aff *pma,
5521 __isl_take isl_multi_id *tuple);
5522 __isl_give isl_multi_pw_aff *
5523 isl_multi_pw_aff_bind_domain_wrapped_domain(
5524 __isl_take isl_multi_pw_aff *mpa,
5525 __isl_take isl_multi_id *tuple);
5526 __isl_give isl_basic_set *isl_aff_bind_id(
5527 __isl_take isl_aff *aff,
5528 __isl_take isl_id *id);
5529 __isl_give isl_set *isl_pw_aff_bind_id(
5530 __isl_take isl_pw_aff *pa,
5531 __isl_take isl_id *id);
5532 __isl_give isl_basic_set *isl_multi_aff_bind(
5533 __isl_take isl_multi_aff *ma,
5534 __isl_take isl_multi_id *tuple);
5535 __isl_give isl_set *isl_multi_pw_aff_bind(
5536 __isl_take isl_multi_pw_aff *mpa,
5537 __isl_take isl_multi_id *tuple);
5538 __isl_give isl_union_set *isl_union_pw_aff_bind_id(
5539 __isl_take isl_union_pw_aff *upa,
5540 __isl_take isl_id *id);
5541 __isl_give isl_union_set *
5542 isl_multi_union_pw_aff_bind(
5543 __isl_take isl_multi_union_pw_aff *mupa,
5544 __isl_take isl_multi_id *tuple);
5546 Projecting out the domain of the wrapped relation in the domain
5547 of a function leaves the range of that wrapped relation
5548 in the domain of the resulting function.
5549 In the case of C<isl_aff_bind_id>, C<isl_pw_aff_bind_id>,
5550 C<isl_multi_aff_bind>, C<isl_multi_pw_aff_bind>,
5551 C<isl_union_pw_aff_bind_id> and
5552 C<isl_multi_union_pw_aff_bind>, the parameters
5553 are bound to the function values and the result lives
5554 in the domain of the input function.
5558 #include <isl/space.h>
5559 __isl_give isl_space *isl_space_domain(
5560 __isl_take isl_space *space);
5561 __isl_give isl_space *isl_space_range(
5562 __isl_take isl_space *space);
5563 __isl_give isl_space *isl_space_params(
5564 __isl_take isl_space *space);
5565 __isl_give isl_space *
5566 isl_space_domain_wrapped_domain(
5567 __isl_take isl_space *space);
5568 __isl_give isl_space *
5569 isl_space_domain_wrapped_range(
5570 __isl_take isl_space *space);
5571 __isl_give isl_space *
5572 isl_space_range_wrapped_domain(
5573 __isl_take isl_space *space);
5574 __isl_give isl_space *
5575 isl_space_range_wrapped_range(
5576 __isl_take isl_space *space);
5578 #include <isl/local_space.h>
5579 __isl_give isl_local_space *isl_local_space_domain(
5580 __isl_take isl_local_space *ls);
5581 __isl_give isl_local_space *isl_local_space_range(
5582 __isl_take isl_local_space *ls);
5584 #include <isl/set.h>
5585 __isl_give isl_basic_set *isl_basic_set_project_out(
5586 __isl_take isl_basic_set *bset,
5587 enum isl_dim_type type, unsigned first, unsigned n);
5588 __isl_give isl_set *isl_set_project_out_param_id(
5589 __isl_take isl_set *set,
5590 __isl_take isl_id *id);
5591 __isl_give isl_set *
5592 isl_set_project_out_param_id_list(
5593 __isl_take isl_set *set,
5594 __isl_take isl_id_list *list);
5595 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
5596 enum isl_dim_type type, unsigned first, unsigned n);
5597 __isl_give isl_set *isl_set_project_out_all_params(
5598 __isl_take isl_set *set);
5599 __isl_give isl_map *isl_set_project_onto_map(
5600 __isl_take isl_set *set,
5601 enum isl_dim_type type, unsigned first,
5603 __isl_give isl_basic_set *isl_basic_set_params(
5604 __isl_take isl_basic_set *bset);
5605 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
5607 The function C<isl_space_domain_wrapped_domain> returns the domain
5608 of the binary relation wrapped inside the domain of the input.
5609 The function C<isl_set_project_onto_map> returns a relation
5610 that projects the input set onto the given set dimensions.
5612 #include <isl/map.h>
5613 __isl_give isl_basic_map *isl_basic_map_project_out(
5614 __isl_take isl_basic_map *bmap,
5615 enum isl_dim_type type, unsigned first, unsigned n);
5616 __isl_give isl_map *isl_map_project_out_param_id(
5617 __isl_take isl_map *map,
5618 __isl_take isl_id *id);
5619 __isl_give isl_map *isl_map_project_out_param_id_list(
5620 __isl_take isl_map *map,
5621 __isl_take isl_id_list *list);
5622 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
5623 enum isl_dim_type type, unsigned first, unsigned n);
5624 __isl_give isl_map *isl_map_project_out_all_params(
5625 __isl_take isl_map *map);
5626 __isl_give isl_basic_set *isl_basic_map_domain(
5627 __isl_take isl_basic_map *bmap);
5628 __isl_give isl_basic_set *isl_basic_map_range(
5629 __isl_take isl_basic_map *bmap);
5630 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
5631 __isl_give isl_set *isl_map_domain(
5632 __isl_take isl_map *bmap);
5633 __isl_give isl_set *isl_map_range(
5634 __isl_take isl_map *map);
5636 #include <isl/union_set.h>
5637 __isl_give isl_union_set *isl_union_set_project_out(
5638 __isl_take isl_union_set *uset,
5639 enum isl_dim_type type,
5640 unsigned first, unsigned n);
5641 __isl_give isl_union_set *
5642 isl_union_set_project_out_all_params(
5643 __isl_take isl_union_set *uset);
5644 __isl_give isl_set *isl_union_set_params(
5645 __isl_take isl_union_set *uset);
5647 The function C<isl_union_set_project_out> can only project out
5650 #include <isl/union_map.h>
5651 __isl_give isl_union_map *
5652 isl_union_map_project_out_param_id(
5653 __isl_take isl_union_map *umap,
5654 __isl_take isl_id *id);
5655 __isl_give isl_union_map *
5656 isl_union_map_project_out_param_id_list(
5657 __isl_take isl_union_map *umap,
5658 __isl_take isl_id_list *list);
5659 __isl_give isl_union_map *isl_union_map_project_out(
5660 __isl_take isl_union_map *umap,
5661 enum isl_dim_type type, unsigned first, unsigned n);
5662 __isl_give isl_union_map *
5663 isl_union_map_project_out_all_params(
5664 __isl_take isl_union_map *umap);
5665 __isl_give isl_set *isl_union_map_params(
5666 __isl_take isl_union_map *umap);
5667 __isl_give isl_union_set *isl_union_map_domain(
5668 __isl_take isl_union_map *umap);
5669 __isl_give isl_union_set *isl_union_map_range(
5670 __isl_take isl_union_map *umap);
5672 The function C<isl_union_map_project_out> can only project out
5675 #include <isl/aff.h>
5676 __isl_give isl_aff *isl_aff_project_domain_on_params(
5677 __isl_take isl_aff *aff);
5678 __isl_give isl_multi_aff *
5679 isl_multi_aff_project_domain_on_params(
5680 __isl_take isl_multi_aff *ma);
5681 __isl_give isl_pw_aff *
5682 isl_pw_aff_project_domain_on_params(
5683 __isl_take isl_pw_aff *pa);
5684 __isl_give isl_multi_pw_aff *
5685 isl_multi_pw_aff_project_domain_on_params(
5686 __isl_take isl_multi_pw_aff *mpa);
5687 __isl_give isl_pw_multi_aff *
5688 isl_pw_multi_aff_project_domain_on_params(
5689 __isl_take isl_pw_multi_aff *pma);
5690 __isl_give isl_set *isl_pw_aff_domain(
5691 __isl_take isl_pw_aff *pwaff);
5692 __isl_give isl_set *isl_pw_multi_aff_domain(
5693 __isl_take isl_pw_multi_aff *pma);
5694 __isl_give isl_set *isl_multi_pw_aff_domain(
5695 __isl_take isl_multi_pw_aff *mpa);
5696 __isl_give isl_union_set *isl_union_pw_aff_domain(
5697 __isl_take isl_union_pw_aff *upa);
5698 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
5699 __isl_take isl_union_pw_multi_aff *upma);
5700 __isl_give isl_union_set *
5701 isl_multi_union_pw_aff_domain(
5702 __isl_take isl_multi_union_pw_aff *mupa);
5703 __isl_give isl_set *isl_pw_aff_params(
5704 __isl_take isl_pw_aff *pwa);
5706 If no explicit domain was set on a zero-dimensional input to
5707 C<isl_multi_union_pw_aff_domain>, then this function will
5708 return a parameter set.
5710 #include <isl/polynomial.h>
5711 __isl_give isl_qpolynomial *
5712 isl_qpolynomial_project_domain_on_params(
5713 __isl_take isl_qpolynomial *qp);
5714 __isl_give isl_pw_qpolynomial *
5715 isl_pw_qpolynomial_project_domain_on_params(
5716 __isl_take isl_pw_qpolynomial *pwqp);
5717 __isl_give isl_pw_qpolynomial_fold *
5718 isl_pw_qpolynomial_fold_project_domain_on_params(
5719 __isl_take isl_pw_qpolynomial_fold *pwf);
5720 __isl_give isl_set *isl_pw_qpolynomial_domain(
5721 __isl_take isl_pw_qpolynomial *pwqp);
5722 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5723 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5724 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5725 __isl_take isl_union_pw_qpolynomial *upwqp);
5727 #include <isl/space.h>
5728 __isl_give isl_space *isl_space_domain_map(
5729 __isl_take isl_space *space);
5730 __isl_give isl_space *isl_space_range_map(
5731 __isl_take isl_space *space);
5733 #include <isl/map.h>
5734 __isl_give isl_map *isl_set_wrapped_domain_map(
5735 __isl_take isl_set *set);
5736 __isl_give isl_basic_map *isl_basic_map_domain_map(
5737 __isl_take isl_basic_map *bmap);
5738 __isl_give isl_basic_map *isl_basic_map_range_map(
5739 __isl_take isl_basic_map *bmap);
5740 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
5741 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
5743 #include <isl/union_map.h>
5744 __isl_give isl_union_map *isl_union_map_domain_map(
5745 __isl_take isl_union_map *umap);
5746 __isl_give isl_union_pw_multi_aff *
5747 isl_union_map_domain_map_union_pw_multi_aff(
5748 __isl_take isl_union_map *umap);
5749 __isl_give isl_union_map *isl_union_map_range_map(
5750 __isl_take isl_union_map *umap);
5751 __isl_give isl_union_map *
5752 isl_union_set_wrapped_domain_map(
5753 __isl_take isl_union_set *uset);
5755 The functions above construct a (basic, regular or union) relation
5756 that maps (a wrapped version of) the input relation to its domain or range.
5757 C<isl_set_wrapped_domain_map> maps the input set to the domain
5758 of its wrapped relation.
5762 __isl_give isl_basic_set *isl_basic_set_eliminate(
5763 __isl_take isl_basic_set *bset,
5764 enum isl_dim_type type,
5765 unsigned first, unsigned n);
5766 __isl_give isl_set *isl_set_eliminate(
5767 __isl_take isl_set *set, enum isl_dim_type type,
5768 unsigned first, unsigned n);
5769 __isl_give isl_basic_map *isl_basic_map_eliminate(
5770 __isl_take isl_basic_map *bmap,
5771 enum isl_dim_type type,
5772 unsigned first, unsigned n);
5773 __isl_give isl_map *isl_map_eliminate(
5774 __isl_take isl_map *map, enum isl_dim_type type,
5775 unsigned first, unsigned n);
5777 Eliminate the coefficients for the given dimensions from the constraints,
5778 without removing the dimensions.
5780 =item * Constructing a set from a parameter domain
5782 A set space of a given dimension and with an optional name
5783 can be created from a parameter space using the following functions.
5785 #include <isl/space.h>
5786 __isl_give isl_space *isl_space_add_unnamed_tuple_ui(
5787 __isl_take isl_space *space, unsigned dim);
5788 __isl_give isl_space *
5789 isl_space_add_named_tuple_id_ui(
5790 __isl_take isl_space *space,
5791 __isl_take isl_id *tuple_id, unsigned dim);
5793 A set with a given tuple can be created from a parameter domain
5794 using the following function.
5796 #include <isl/set.h>
5797 __isl_give isl_set *isl_set_unbind_params(
5798 __isl_take isl_set *set,
5799 __isl_take isl_multi_id *tuple);
5801 Any parameters with identifiers in C<tuple> are reinterpreted
5802 as the corresponding set dimensions.
5804 A zero-dimensional (local) space or (basic) set can be constructed
5805 on a given parameter domain using the following functions.
5807 #include <isl/space.h>
5808 __isl_give isl_space *isl_space_set_from_params(
5809 __isl_take isl_space *space);
5811 #include <isl/local_space.h>
5812 __isl_give isl_local_space *
5813 isl_local_space_set_from_params(
5814 __isl_take isl_local_space *ls);
5816 #include <isl/set.h>
5817 __isl_give isl_basic_set *isl_basic_set_from_params(
5818 __isl_take isl_basic_set *bset);
5819 __isl_give isl_set *isl_set_from_params(
5820 __isl_take isl_set *set);
5822 =item * Constructing a relation from one or two sets
5824 A map space with a range of a given dimension and with an optional name
5825 can be created from a domain space using the functions
5826 C<isl_space_add_unnamed_tuple_ui> and C<isl_space_add_named_tuple_id_ui>
5829 A relation with a given domain tuple can be created from a set
5830 that will become the range of the relation
5831 using the following function.
5833 #include <isl/set.h>
5834 __isl_give isl_map *
5835 isl_set_unbind_params_insert_domain(
5836 __isl_take isl_set *set,
5837 __isl_take isl_multi_id *domain);
5839 Any parameters with identifiers in C<domain> are reinterpreted
5840 as the corresponding input dimensions.
5842 Similarly, a function defined over a parameter domain can
5843 be converted into one defined over a set domain
5844 using the following functions.
5846 #include <isl/aff.h>
5847 __isl_give isl_aff *
5848 isl_aff_unbind_params_insert_domain(
5849 __isl_take isl_aff *aff,
5850 __isl_take isl_multi_id *domain);
5851 __isl_give isl_multi_aff *
5852 isl_multi_aff_unbind_params_insert_domain(
5853 __isl_take isl_multi_aff *ma,
5854 __isl_take isl_multi_id *domain);
5855 __isl_give isl_multi_pw_aff *
5856 isl_multi_pw_aff_unbind_params_insert_domain(
5857 __isl_take isl_multi_pw_aff *mpa,
5858 __isl_take isl_multi_id *domain);
5861 any parameters with identifiers in C<domain> are reinterpreted
5862 as the corresponding input dimensions.
5864 Create a relation with the given set(s) as domain and/or range.
5865 If only the domain or the range is specified, then
5866 the range or domain of the created relation is a zero-dimensional
5867 flat anonymous space.
5868 If the case of C<isl_space_map_from_set>, the input space
5869 specifies both the domain and the range of the result.
5871 #include <isl/space.h>
5872 __isl_give isl_space *isl_space_from_domain(
5873 __isl_take isl_space *space);
5874 __isl_give isl_space *isl_space_from_range(
5875 __isl_take isl_space *space);
5876 __isl_give isl_space *isl_space_map_from_set(
5877 __isl_take isl_space *space);
5878 __isl_give isl_space *isl_space_map_from_domain_and_range(
5879 __isl_take isl_space *domain,
5880 __isl_take isl_space *range);
5882 #include <isl/local_space.h>
5883 __isl_give isl_local_space *isl_local_space_from_domain(
5884 __isl_take isl_local_space *ls);
5886 #include <isl/map.h>
5887 __isl_give isl_map *isl_set_insert_domain(
5888 __isl_take isl_set *set,
5889 __isl_take isl_space *domain);
5890 __isl_give isl_map *isl_map_from_domain(
5891 __isl_take isl_set *set);
5892 __isl_give isl_map *isl_map_from_range(
5893 __isl_take isl_set *set);
5895 #include <isl/union_map.h>
5896 __isl_give isl_union_map *isl_union_map_from_domain(
5897 __isl_take isl_union_set *uset);
5898 __isl_give isl_union_map *isl_union_map_from_range(
5899 __isl_take isl_union_set *uset);
5900 __isl_give isl_union_map *
5901 isl_union_map_from_domain_and_range(
5902 __isl_take isl_union_set *domain,
5903 __isl_take isl_union_set *range);
5906 __isl_give isl_multi_id *isl_multi_id_from_range(
5907 __isl_take isl_multi_id *mi);
5909 #include <isl/val.h>
5910 __isl_give isl_multi_val *isl_multi_val_from_range(
5911 __isl_take isl_multi_val *mv);
5913 #include <isl/aff.h>
5914 __isl_give isl_multi_aff *
5915 isl_multi_aff_insert_domain(
5916 __isl_take isl_multi_aff *ma,
5917 __isl_take isl_space *domain);
5918 __isl_give isl_pw_aff *isl_pw_aff_insert_domain(
5919 __isl_take isl_pw_aff *pa,
5920 __isl_take isl_space *domain);
5921 __isl_give isl_pw_multi_aff *
5922 isl_pw_multi_aff_insert_domain(
5923 __isl_take isl_pw_multi_aff *pma,
5924 __isl_take isl_space *domain);
5925 __isl_give isl_multi_pw_aff *
5926 isl_multi_pw_aff_insert_domain(
5927 __isl_take isl_multi_pw_aff *mpa,
5928 __isl_take isl_space *domain);
5929 __isl_give isl_aff *isl_aff_from_range(
5930 __isl_take isl_aff *aff);
5931 __isl_give isl_multi_aff *isl_multi_aff_from_range(
5932 __isl_take isl_multi_aff *ma);
5933 __isl_give isl_pw_aff *isl_pw_aff_from_range(
5934 __isl_take isl_pw_aff *pwa);
5935 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
5936 __isl_take isl_multi_pw_aff *mpa);
5937 __isl_give isl_multi_union_pw_aff *
5938 isl_multi_union_pw_aff_from_range(
5939 __isl_take isl_multi_union_pw_aff *mupa);
5940 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
5941 __isl_take isl_set *set);
5942 __isl_give isl_union_pw_multi_aff *
5943 isl_union_pw_multi_aff_from_domain(
5944 __isl_take isl_union_set *uset);
5946 #include <isl/polynomial.h>
5947 __isl_give isl_pw_qpolynomial *
5948 isl_pw_qpolynomial_from_range(
5949 __isl_take isl_pw_qpolynomial *pwqp);
5950 __isl_give isl_pw_qpolynomial_fold *
5951 isl_pw_qpolynomial_fold_from_range(
5952 __isl_take isl_pw_qpolynomial_fold *pwf);
5956 #include <isl/set.h>
5957 __isl_give isl_basic_set *isl_basic_set_fix_si(
5958 __isl_take isl_basic_set *bset,
5959 enum isl_dim_type type, unsigned pos, int value);
5960 __isl_give isl_basic_set *isl_basic_set_fix_val(
5961 __isl_take isl_basic_set *bset,
5962 enum isl_dim_type type, unsigned pos,
5963 __isl_take isl_val *v);
5964 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
5965 enum isl_dim_type type, unsigned pos, int value);
5966 __isl_give isl_set *isl_set_fix_val(
5967 __isl_take isl_set *set,
5968 enum isl_dim_type type, unsigned pos,
5969 __isl_take isl_val *v);
5971 #include <isl/map.h>
5972 __isl_give isl_basic_map *isl_basic_map_fix_si(
5973 __isl_take isl_basic_map *bmap,
5974 enum isl_dim_type type, unsigned pos, int value);
5975 __isl_give isl_basic_map *isl_basic_map_fix_val(
5976 __isl_take isl_basic_map *bmap,
5977 enum isl_dim_type type, unsigned pos,
5978 __isl_take isl_val *v);
5979 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
5980 enum isl_dim_type type, unsigned pos, int value);
5981 __isl_give isl_map *isl_map_fix_val(
5982 __isl_take isl_map *map,
5983 enum isl_dim_type type, unsigned pos,
5984 __isl_take isl_val *v);
5986 #include <isl/aff.h>
5987 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
5988 __isl_take isl_pw_multi_aff *pma,
5989 enum isl_dim_type type, unsigned pos, int value);
5991 #include <isl/polynomial.h>
5992 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
5993 __isl_take isl_pw_qpolynomial *pwqp,
5994 enum isl_dim_type type, unsigned n,
5995 __isl_take isl_val *v);
5996 __isl_give isl_pw_qpolynomial_fold *
5997 isl_pw_qpolynomial_fold_fix_val(
5998 __isl_take isl_pw_qpolynomial_fold *pwf,
5999 enum isl_dim_type type, unsigned n,
6000 __isl_take isl_val *v);
6002 Intersect the set, relation or function domain
6003 with the hyperplane where the given
6004 dimension has the fixed given value.
6006 #include <isl/set.h>
6007 __isl_give isl_basic_set *
6008 isl_basic_set_lower_bound_val(
6009 __isl_take isl_basic_set *bset,
6010 enum isl_dim_type type, unsigned pos,
6011 __isl_take isl_val *value);
6012 __isl_give isl_basic_set *
6013 isl_basic_set_upper_bound_val(
6014 __isl_take isl_basic_set *bset,
6015 enum isl_dim_type type, unsigned pos,
6016 __isl_take isl_val *value);
6017 __isl_give isl_set *isl_set_lower_bound_si(
6018 __isl_take isl_set *set,
6019 enum isl_dim_type type, unsigned pos, int value);
6020 __isl_give isl_set *isl_set_lower_bound_val(
6021 __isl_take isl_set *set,
6022 enum isl_dim_type type, unsigned pos,
6023 __isl_take isl_val *value);
6024 __isl_give isl_set *isl_set_upper_bound_si(
6025 __isl_take isl_set *set,
6026 enum isl_dim_type type, unsigned pos, int value);
6027 __isl_give isl_set *isl_set_upper_bound_val(
6028 __isl_take isl_set *set,
6029 enum isl_dim_type type, unsigned pos,
6030 __isl_take isl_val *value);
6031 __isl_give isl_set *isl_set_lower_bound_multi_val(
6032 __isl_take isl_set *set,
6033 __isl_take isl_multi_val *lower);
6034 __isl_give isl_set *isl_set_upper_bound_multi_val(
6035 __isl_take isl_set *set,
6036 __isl_take isl_multi_val *upper);
6037 __isl_give isl_set *isl_set_lower_bound_multi_pw_aff(
6038 __isl_take isl_set *set,
6039 __isl_take isl_multi_pw_aff *lower);
6040 __isl_give isl_set *isl_set_upper_bound_multi_pw_aff(
6041 __isl_take isl_set *set,
6042 __isl_take isl_multi_pw_aff *upper);
6044 #include <isl/map.h>
6045 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
6046 __isl_take isl_basic_map *bmap,
6047 enum isl_dim_type type, unsigned pos, int value);
6048 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
6049 __isl_take isl_basic_map *bmap,
6050 enum isl_dim_type type, unsigned pos, int value);
6051 __isl_give isl_map *isl_map_lower_bound_si(
6052 __isl_take isl_map *map,
6053 enum isl_dim_type type, unsigned pos, int value);
6054 __isl_give isl_map *isl_map_upper_bound_si(
6055 __isl_take isl_map *map,
6056 enum isl_dim_type type, unsigned pos, int value);
6057 __isl_give isl_map *isl_map_lower_bound_val(
6058 __isl_take isl_map *map,
6059 enum isl_dim_type type, unsigned pos,
6060 __isl_take isl_val *value);
6061 __isl_give isl_map *isl_map_upper_bound_val(
6062 __isl_take isl_map *map,
6063 enum isl_dim_type type, unsigned pos,
6064 __isl_take isl_val *value);
6065 __isl_give isl_map *isl_map_lower_bound_multi_pw_aff(
6066 __isl_take isl_map *map,
6067 __isl_take isl_multi_pw_aff *lower);
6068 __isl_give isl_map *isl_map_upper_bound_multi_pw_aff(
6069 __isl_take isl_map *map,
6070 __isl_take isl_multi_pw_aff *upper);
6072 Intersect the set or relation with the half-space where the given
6073 dimension has a value bounded by the given fixed integer value or
6074 symbolic constant expression.
6075 For functions taking a multi expression,
6076 this applies to all set dimensions.
6077 Those that bound a map, bound the range of that map.
6078 If the multi expression is zero-dimensional but has an explicit domain,
6079 then the (parameter) domain of the set or map is intersected
6080 with this explicit domain.
6082 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
6083 enum isl_dim_type type1, int pos1,
6084 enum isl_dim_type type2, int pos2);
6085 __isl_give isl_basic_map *isl_basic_map_equate(
6086 __isl_take isl_basic_map *bmap,
6087 enum isl_dim_type type1, int pos1,
6088 enum isl_dim_type type2, int pos2);
6089 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
6090 enum isl_dim_type type1, int pos1,
6091 enum isl_dim_type type2, int pos2);
6093 Intersect the set or relation with the hyperplane where the given
6094 dimensions are equal to each other.
6096 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
6097 enum isl_dim_type type1, int pos1,
6098 enum isl_dim_type type2, int pos2);
6100 Intersect the relation with the hyperplane where the given
6101 dimensions have opposite values.
6103 __isl_give isl_map *isl_map_order_le(
6104 __isl_take isl_map *map,
6105 enum isl_dim_type type1, int pos1,
6106 enum isl_dim_type type2, int pos2);
6107 __isl_give isl_basic_map *isl_basic_map_order_ge(
6108 __isl_take isl_basic_map *bmap,
6109 enum isl_dim_type type1, int pos1,
6110 enum isl_dim_type type2, int pos2);
6111 __isl_give isl_map *isl_map_order_ge(
6112 __isl_take isl_map *map,
6113 enum isl_dim_type type1, int pos1,
6114 enum isl_dim_type type2, int pos2);
6115 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
6116 enum isl_dim_type type1, int pos1,
6117 enum isl_dim_type type2, int pos2);
6118 __isl_give isl_basic_map *isl_basic_map_order_gt(
6119 __isl_take isl_basic_map *bmap,
6120 enum isl_dim_type type1, int pos1,
6121 enum isl_dim_type type2, int pos2);
6122 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
6123 enum isl_dim_type type1, int pos1,
6124 enum isl_dim_type type2, int pos2);
6126 Intersect the relation with the half-space where the given
6127 dimensions satisfy the given ordering.
6129 #include <isl/union_set.h>
6130 __isl_give isl_union_map *isl_union_map_remove_map_if(
6131 __isl_take isl_union_map *umap,
6132 isl_bool (*fn)(__isl_keep isl_map *map,
6133 void *user), void *user);
6135 This function calls the callback function once for each
6136 pair of spaces for which there are elements in the input.
6137 If the callback returns C<isl_bool_true>, then all those elements
6138 are removed from the result. The only remaining elements in the output
6139 are then those for which the callback returns C<isl_bool_false>.
6143 #include <isl/aff.h>
6144 __isl_give isl_basic_set *isl_aff_zero_basic_set(
6145 __isl_take isl_aff *aff);
6146 __isl_give isl_basic_set *isl_aff_neg_basic_set(
6147 __isl_take isl_aff *aff);
6148 __isl_give isl_set *isl_pw_aff_pos_set(
6149 __isl_take isl_pw_aff *pa);
6150 __isl_give isl_set *isl_pw_aff_nonneg_set(
6151 __isl_take isl_pw_aff *pwaff);
6152 __isl_give isl_set *isl_pw_aff_zero_set(
6153 __isl_take isl_pw_aff *pwaff);
6154 __isl_give isl_set *isl_pw_aff_non_zero_set(
6155 __isl_take isl_pw_aff *pwaff);
6156 __isl_give isl_union_set *
6157 isl_union_pw_aff_zero_union_set(
6158 __isl_take isl_union_pw_aff *upa);
6159 __isl_give isl_union_set *
6160 isl_multi_union_pw_aff_zero_union_set(
6161 __isl_take isl_multi_union_pw_aff *mupa);
6163 The function C<isl_aff_neg_basic_set> returns a basic set
6164 containing those elements in the domain space
6165 of C<aff> where C<aff> is negative.
6166 The function C<isl_pw_aff_nonneg_set> returns a set
6167 containing those elements in the domain
6168 of C<pwaff> where C<pwaff> is non-negative.
6169 The function C<isl_multi_union_pw_aff_zero_union_set>
6170 returns a union set containing those elements
6171 in the domains of its elements where they are all zero.
6175 __isl_give isl_map *isl_set_identity(
6176 __isl_take isl_set *set);
6177 __isl_give isl_union_map *isl_union_set_identity(
6178 __isl_take isl_union_set *uset);
6179 __isl_give isl_union_pw_multi_aff *
6180 isl_union_set_identity_union_pw_multi_aff(
6181 __isl_take isl_union_set *uset);
6183 Construct an identity relation on the given (union) set.
6185 =item * Function Extraction
6187 A piecewise quasi affine expression that is equal to 1 on a set
6188 and 0 outside the set can be created using the following function.
6190 #include <isl/aff.h>
6191 __isl_give isl_pw_aff *isl_set_indicator_function(
6192 __isl_take isl_set *set);
6194 A piecewise multiple quasi affine expression can be extracted
6195 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
6196 and the C<isl_map> is single-valued.
6197 In case of a conversion from an C<isl_union_map>
6198 to an C<isl_union_pw_multi_aff>, these properties need to hold
6199 in each domain space.
6200 A conversion to a C<isl_multi_union_pw_aff> additionally
6201 requires that the input is non-empty and involves only a single
6204 #include <isl/aff.h>
6205 __isl_give isl_pw_multi_aff *isl_set_as_pw_multi_aff(
6206 __isl_take isl_set *set);
6207 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
6208 __isl_take isl_set *set);
6209 __isl_give isl_pw_multi_aff *isl_map_as_pw_multi_aff(
6210 __isl_take isl_map *map);
6211 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
6212 __isl_take isl_map *map);
6214 __isl_give isl_union_pw_multi_aff *
6215 isl_union_pw_multi_aff_from_union_set(
6216 __isl_take isl_union_set *uset);
6217 __isl_give isl_union_pw_multi_aff *
6218 isl_union_map_as_union_pw_multi_aff(
6219 __isl_take isl_union_map *umap);
6220 __isl_give isl_union_pw_multi_aff *
6221 isl_union_pw_multi_aff_from_union_map(
6222 __isl_take isl_union_map *umap);
6224 __isl_give isl_multi_union_pw_aff *
6225 isl_union_map_as_multi_union_pw_aff(
6226 __isl_take isl_union_map *umap);
6227 __isl_give isl_multi_union_pw_aff *
6228 isl_multi_union_pw_aff_from_union_map(
6229 __isl_take isl_union_map *umap);
6231 C<isl_map_as_pw_multi_aff> and C<isl_pw_multi_aff_from_map> perform
6233 Similarly for C<isl_set_as_pw_multi_aff> and
6234 C<isl_pw_multi_aff_from_set>,
6235 for C<isl_union_map_as_union_pw_multi_aff> and
6236 C<isl_union_pw_multi_aff_from_union_map> and
6237 for C<isl_union_map_as_multi_union_pw_aff> and
6238 C<isl_multi_union_pw_aff_from_union_map>.
6242 __isl_give isl_basic_set *isl_basic_map_deltas(
6243 __isl_take isl_basic_map *bmap);
6244 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
6245 __isl_give isl_union_set *isl_union_map_deltas(
6246 __isl_take isl_union_map *umap);
6248 These functions return a (basic) set containing the differences
6249 between image elements and corresponding domain elements in the input.
6251 __isl_give isl_basic_map *isl_basic_map_deltas_map(
6252 __isl_take isl_basic_map *bmap);
6253 __isl_give isl_map *isl_map_deltas_map(
6254 __isl_take isl_map *map);
6255 __isl_give isl_union_map *isl_union_map_deltas_map(
6256 __isl_take isl_union_map *umap);
6258 The functions above construct a (basic, regular or union) relation
6259 that maps (a wrapped version of) the input relation to its delta set.
6263 #include <isl/map.h>
6264 __isl_give isl_map *isl_set_translation(
6265 __isl_take isl_set *deltas);
6267 This function performs essentially the opposite operation
6268 of C<isl_map_deltas>. In particular, it returns pairs
6269 of elements in the same space that have a difference in C<deltas>.
6273 Simplify the representation of a set, relation or functions by trying
6274 to combine pairs of basic sets or relations into a single
6275 basic set or relation.
6277 #include <isl/set.h>
6278 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
6280 #include <isl/map.h>
6281 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
6283 #include <isl/union_set.h>
6284 __isl_give isl_union_set *isl_union_set_coalesce(
6285 __isl_take isl_union_set *uset);
6287 #include <isl/union_map.h>
6288 __isl_give isl_union_map *isl_union_map_coalesce(
6289 __isl_take isl_union_map *umap);
6291 #include <isl/aff.h>
6292 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
6293 __isl_take isl_pw_aff *pa);
6294 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
6295 __isl_take isl_pw_multi_aff *pma);
6296 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
6297 __isl_take isl_multi_pw_aff *mpa);
6298 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
6299 __isl_take isl_union_pw_aff *upa);
6300 __isl_give isl_union_pw_multi_aff *
6301 isl_union_pw_multi_aff_coalesce(
6302 __isl_take isl_union_pw_multi_aff *upma);
6303 __isl_give isl_multi_union_pw_aff *
6304 isl_multi_union_pw_aff_coalesce(
6305 __isl_take isl_multi_union_pw_aff *mupa);
6307 #include <isl/polynomial.h>
6308 __isl_give isl_pw_qpolynomial_fold *
6309 isl_pw_qpolynomial_fold_coalesce(
6310 __isl_take isl_pw_qpolynomial_fold *pwf);
6311 __isl_give isl_union_pw_qpolynomial *
6312 isl_union_pw_qpolynomial_coalesce(
6313 __isl_take isl_union_pw_qpolynomial *upwqp);
6314 __isl_give isl_union_pw_qpolynomial_fold *
6315 isl_union_pw_qpolynomial_fold_coalesce(
6316 __isl_take isl_union_pw_qpolynomial_fold *upwf);
6318 One of the methods for combining pairs of basic sets or relations
6319 can result in coefficients that are much larger than those that appear
6320 in the constraints of the input. By default, the coefficients are
6321 not allowed to grow larger, but this can be changed by unsetting
6322 the following option.
6324 isl_stat isl_options_set_coalesce_bounded_wrapping(
6325 isl_ctx *ctx, int val);
6326 int isl_options_get_coalesce_bounded_wrapping(
6329 One of the other methods tries to combine pairs of basic sets
6330 with different local variables, treating them as existentially
6331 quantified variables even if they have known (but different)
6332 integer division expressions. The result may then also have
6333 existentially quantified variables. Turning on the following
6334 option prevents this from happening.
6336 isl_stat isl_options_set_coalesce_preserve_locals(
6337 isl_ctx *ctx, int val);
6338 int isl_options_get_coalesce_preserve_locals(isl_ctx *ctx);
6340 =item * Detecting equalities
6342 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
6343 __isl_take isl_basic_set *bset);
6344 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
6345 __isl_take isl_basic_map *bmap);
6346 __isl_give isl_set *isl_set_detect_equalities(
6347 __isl_take isl_set *set);
6348 __isl_give isl_map *isl_map_detect_equalities(
6349 __isl_take isl_map *map);
6350 __isl_give isl_union_set *isl_union_set_detect_equalities(
6351 __isl_take isl_union_set *uset);
6352 __isl_give isl_union_map *isl_union_map_detect_equalities(
6353 __isl_take isl_union_map *umap);
6355 Simplify the representation of a set or relation by detecting implicit
6358 =item * Removing redundant constraints
6360 #include <isl/set.h>
6361 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
6362 __isl_take isl_basic_set *bset);
6363 __isl_give isl_set *isl_set_remove_redundancies(
6364 __isl_take isl_set *set);
6366 #include <isl/union_set.h>
6367 __isl_give isl_union_set *
6368 isl_union_set_remove_redundancies(
6369 __isl_take isl_union_set *uset);
6371 #include <isl/map.h>
6372 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
6373 __isl_take isl_basic_map *bmap);
6374 __isl_give isl_map *isl_map_remove_redundancies(
6375 __isl_take isl_map *map);
6377 #include <isl/union_map.h>
6378 __isl_give isl_union_map *
6379 isl_union_map_remove_redundancies(
6380 __isl_take isl_union_map *umap);
6384 __isl_give isl_basic_set *isl_set_convex_hull(
6385 __isl_take isl_set *set);
6386 __isl_give isl_basic_map *isl_map_convex_hull(
6387 __isl_take isl_map *map);
6389 If the input set or relation has any existentially quantified
6390 variables, then the result of these operations is currently undefined.
6394 #include <isl/set.h>
6395 __isl_give isl_basic_set *
6396 isl_set_unshifted_simple_hull(
6397 __isl_take isl_set *set);
6398 __isl_give isl_basic_set *isl_set_simple_hull(
6399 __isl_take isl_set *set);
6400 __isl_give isl_basic_set *
6401 isl_set_plain_unshifted_simple_hull(
6402 __isl_take isl_set *set);
6403 __isl_give isl_basic_set *
6404 isl_set_unshifted_simple_hull_from_set_list(
6405 __isl_take isl_set *set,
6406 __isl_take isl_set_list *list);
6408 #include <isl/map.h>
6409 __isl_give isl_basic_map *
6410 isl_map_unshifted_simple_hull(
6411 __isl_take isl_map *map);
6412 __isl_give isl_basic_map *isl_map_simple_hull(
6413 __isl_take isl_map *map);
6414 __isl_give isl_basic_map *
6415 isl_map_plain_unshifted_simple_hull(
6416 __isl_take isl_map *map);
6417 __isl_give isl_basic_map *
6418 isl_map_unshifted_simple_hull_from_map_list(
6419 __isl_take isl_map *map,
6420 __isl_take isl_map_list *list);
6422 #include <isl/union_map.h>
6423 __isl_give isl_union_map *isl_union_map_simple_hull(
6424 __isl_take isl_union_map *umap);
6426 These functions compute a single basic set or relation
6427 that contains the whole input set or relation.
6428 In particular, the output is described by translates
6429 of the constraints describing the basic sets or relations in the input.
6430 In case of C<isl_set_unshifted_simple_hull>, only the original
6431 constraints are used, without any translation.
6432 In case of C<isl_set_plain_unshifted_simple_hull> and
6433 C<isl_map_plain_unshifted_simple_hull>, the result is described
6434 by original constraints that are obviously satisfied
6435 by the entire input set or relation.
6436 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
6437 C<isl_map_unshifted_simple_hull_from_map_list>, the
6438 constraints are taken from the elements of the second argument.
6442 (See \autoref{s:simple hull}.)
6448 __isl_give isl_basic_set *isl_basic_set_affine_hull(
6449 __isl_take isl_basic_set *bset);
6450 __isl_give isl_basic_set *isl_set_affine_hull(
6451 __isl_take isl_set *set);
6452 __isl_give isl_union_set *isl_union_set_affine_hull(
6453 __isl_take isl_union_set *uset);
6454 __isl_give isl_basic_map *isl_basic_map_affine_hull(
6455 __isl_take isl_basic_map *bmap);
6456 __isl_give isl_basic_map *isl_map_affine_hull(
6457 __isl_take isl_map *map);
6458 __isl_give isl_union_map *isl_union_map_affine_hull(
6459 __isl_take isl_union_map *umap);
6461 In case of union sets and relations, the affine hull is computed
6464 =item * Polyhedral hull
6466 __isl_give isl_basic_set *isl_set_polyhedral_hull(
6467 __isl_take isl_set *set);
6468 __isl_give isl_basic_map *isl_map_polyhedral_hull(
6469 __isl_take isl_map *map);
6470 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
6471 __isl_take isl_union_set *uset);
6472 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
6473 __isl_take isl_union_map *umap);
6475 These functions compute a single basic set or relation
6476 not involving any existentially quantified variables
6477 that contains the whole input set or relation.
6478 In case of union sets and relations, the polyhedral hull is computed
6483 #include <isl/set.h>
6484 __isl_give isl_fixed_box *
6485 isl_set_get_simple_fixed_box_hull(
6486 __isl_keep isl_set *set)
6488 #include <isl/map.h>
6489 __isl_give isl_fixed_box *
6490 isl_map_get_range_simple_fixed_box_hull(
6491 __isl_keep isl_map *map);
6493 These functions try to approximate the set or
6494 the range of the map by a box of fixed size.
6495 The box is described in terms of an offset living in the same space as
6496 the input and a size living in the set or range space. For any element
6497 in the input map, the range value is greater than or equal to
6498 the offset applied to the domain value and the difference with
6499 this offset is strictly smaller than the size.
6500 The same holds for the elements of the input set, where
6501 the offset is a parametric constant value.
6502 If no fixed-size approximation can be found,
6503 an I<invalid> box is returned, i.e., one for which
6504 C<isl_fixed_box_is_valid> below returns false.
6506 The validity, the offset and the size of the box can be obtained using
6507 the following functions.
6509 #include <isl/fixed_box.h>
6510 isl_bool isl_fixed_box_is_valid(
6511 __isl_keep isl_fixed_box *box);
6512 __isl_give isl_multi_aff *isl_fixed_box_get_offset(
6513 __isl_keep isl_fixed_box *box);
6514 __isl_give isl_multi_val *isl_fixed_box_get_size(
6515 __isl_keep isl_fixed_box *box);
6517 The box can be copied and freed using the following functions.
6519 #include <isl/fixed_box.h>
6520 __isl_give isl_fixed_box *isl_fixed_box_copy(
6521 __isl_keep isl_fixed_box *box);
6522 __isl_null isl_fixed_box *isl_fixed_box_free(
6523 __isl_take isl_fixed_box *box);
6525 An object of type C<isl_fixed_box> can be read from input
6526 using the following function.
6528 #include <isl/fixed_box.h>
6529 __isl_give isl_fixed_box *
6530 isl_fixed_box_read_from_str(isl_ctx *ctx,
6533 A representation of the information contained in an object
6534 of type C<isl_fixed_box> can be obtained using
6536 #include <isl/fixed_box.h>
6537 __isl_give isl_printer *isl_printer_print_fixed_box(
6538 __isl_take isl_printer *p,
6539 __isl_keep isl_fixed_box *box);
6540 __isl_give char *isl_fixed_box_to_str(
6541 __isl_keep isl_fixed_box *box);
6543 C<isl_fixed_box_to_str> prints the information in flow format.
6545 =item * Other approximations
6547 #include <isl/set.h>
6548 __isl_give isl_basic_set *
6549 isl_basic_set_drop_constraints_involving_dims(
6550 __isl_take isl_basic_set *bset,
6551 enum isl_dim_type type,
6552 unsigned first, unsigned n);
6553 __isl_give isl_basic_set *
6554 isl_basic_set_drop_constraints_not_involving_dims(
6555 __isl_take isl_basic_set *bset,
6556 enum isl_dim_type type,
6557 unsigned first, unsigned n);
6558 __isl_give isl_set *
6559 isl_set_drop_constraints_involving_dims(
6560 __isl_take isl_set *set,
6561 enum isl_dim_type type,
6562 unsigned first, unsigned n);
6563 __isl_give isl_set *
6564 isl_set_drop_constraints_not_involving_dims(
6565 __isl_take isl_set *set,
6566 enum isl_dim_type type,
6567 unsigned first, unsigned n);
6569 #include <isl/map.h>
6570 __isl_give isl_basic_map *
6571 isl_basic_map_drop_constraints_involving_dims(
6572 __isl_take isl_basic_map *bmap,
6573 enum isl_dim_type type,
6574 unsigned first, unsigned n);
6575 __isl_give isl_basic_map *
6576 isl_basic_map_drop_constraints_not_involving_dims(
6577 __isl_take isl_basic_map *bmap,
6578 enum isl_dim_type type,
6579 unsigned first, unsigned n);
6580 __isl_give isl_map *
6581 isl_map_drop_constraints_involving_dims(
6582 __isl_take isl_map *map,
6583 enum isl_dim_type type,
6584 unsigned first, unsigned n);
6585 __isl_give isl_map *
6586 isl_map_drop_constraints_not_involving_dims(
6587 __isl_take isl_map *map,
6588 enum isl_dim_type type,
6589 unsigned first, unsigned n);
6591 These functions drop any constraints (not) involving the specified dimensions.
6592 Note that the result depends on the representation of the input.
6594 #include <isl/polynomial.h>
6595 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
6596 __isl_take isl_pw_qpolynomial *pwqp, int sign);
6597 __isl_give isl_union_pw_qpolynomial *
6598 isl_union_pw_qpolynomial_to_polynomial(
6599 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
6601 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
6602 the polynomial will be an overapproximation. If C<sign> is negative,
6603 it will be an underapproximation. If C<sign> is zero, the approximation
6604 will lie somewhere in between.
6608 __isl_give isl_basic_set *isl_basic_set_sample(
6609 __isl_take isl_basic_set *bset);
6610 __isl_give isl_basic_set *isl_set_sample(
6611 __isl_take isl_set *set);
6612 __isl_give isl_basic_map *isl_basic_map_sample(
6613 __isl_take isl_basic_map *bmap);
6614 __isl_give isl_basic_map *isl_map_sample(
6615 __isl_take isl_map *map);
6617 If the input (basic) set or relation is non-empty, then return
6618 a singleton subset of the input. Otherwise, return an empty set.
6620 =item * Optimization
6622 #include <isl/ilp.h>
6623 __isl_give isl_val *isl_basic_set_max_val(
6624 __isl_keep isl_basic_set *bset,
6625 __isl_keep isl_aff *obj);
6626 __isl_give isl_val *isl_set_min_val(
6627 __isl_keep isl_set *set,
6628 __isl_keep isl_aff *obj);
6629 __isl_give isl_val *isl_set_max_val(
6630 __isl_keep isl_set *set,
6631 __isl_keep isl_aff *obj);
6632 __isl_give isl_multi_val *
6633 isl_union_set_min_multi_union_pw_aff(
6634 __isl_keep isl_union_set *uset,
6635 __isl_keep isl_multi_union_pw_aff *obj);
6637 Compute the minimum or maximum of the integer affine expression C<obj>
6638 over the points in C<set>.
6639 The result is C<NULL> in case of an error, the optimal value in case
6640 there is one, negative infinity or infinity if the problem is unbounded and
6641 NaN if the problem is empty.
6643 #include <isl/ilp.h>
6644 __isl_give isl_val *isl_pw_aff_min_val(
6645 __isl_take isl_pw_aff *pa);
6646 __isl_give isl_val *isl_pw_aff_max_val(
6647 __isl_take isl_pw_aff *pa);
6648 __isl_give isl_multi_val *
6649 isl_pw_multi_aff_min_multi_val(
6650 __isl_take isl_pw_multi_aff *pma);
6651 __isl_give isl_multi_val *
6652 isl_pw_multi_aff_max_multi_val(
6653 __isl_take isl_pw_multi_aff *pma);
6654 __isl_give isl_multi_val *
6655 isl_multi_pw_aff_min_multi_val(
6656 __isl_take isl_multi_pw_aff *mpa);
6657 __isl_give isl_multi_val *
6658 isl_multi_pw_aff_max_multi_val(
6659 __isl_take isl_multi_pw_aff *mpa);
6660 __isl_give isl_val *isl_union_pw_aff_min_val(
6661 __isl_take isl_union_pw_aff *upa);
6662 __isl_give isl_val *isl_union_pw_aff_max_val(
6663 __isl_take isl_union_pw_aff *upa);
6664 __isl_give isl_multi_val *
6665 isl_multi_union_pw_aff_min_multi_val(
6666 __isl_take isl_multi_union_pw_aff *mupa);
6667 __isl_give isl_multi_val *
6668 isl_multi_union_pw_aff_max_multi_val(
6669 __isl_take isl_multi_union_pw_aff *mupa);
6671 Compute the minimum or maximum of the integer affine expression
6672 over its definition domain.
6673 The result is C<NULL> in case of an error, the optimal value in case
6674 there is one, negative infinity or infinity if the problem is unbounded and
6675 NaN if the problem is empty.
6677 #include <isl/ilp.h>
6678 __isl_give isl_val *isl_basic_set_dim_max_val(
6679 __isl_take isl_basic_set *bset, int pos);
6680 __isl_give isl_val *isl_set_dim_min_val(
6681 __isl_take isl_set *set, int pos);
6682 __isl_give isl_val *isl_set_dim_max_val(
6683 __isl_take isl_set *set, int pos);
6685 Return the minimal or maximal value attained by the given set dimension,
6686 independently of the parameter values and of any other dimensions.
6687 The result is C<NULL> in case of an error, the optimal value in case
6688 there is one, (negative) infinity if the problem is unbounded and
6689 NaN if the input is empty.
6691 =item * Parametric optimization
6693 __isl_give isl_pw_aff *isl_set_dim_min(
6694 __isl_take isl_set *set, int pos);
6695 __isl_give isl_pw_aff *isl_set_dim_max(
6696 __isl_take isl_set *set, int pos);
6697 __isl_give isl_pw_aff *isl_map_dim_min(
6698 __isl_take isl_map *map, int pos);
6699 __isl_give isl_pw_aff *isl_map_dim_max(
6700 __isl_take isl_map *map, int pos);
6701 __isl_give isl_multi_pw_aff *
6702 isl_set_min_multi_pw_aff(
6703 __isl_take isl_set *set);
6704 __isl_give isl_multi_pw_aff *
6705 isl_set_max_multi_pw_aff(
6706 __isl_take isl_set *set);
6707 __isl_give isl_multi_pw_aff *
6708 isl_map_min_multi_pw_aff(
6709 __isl_take isl_map *map);
6710 __isl_give isl_multi_pw_aff *
6711 isl_map_max_multi_pw_aff(
6712 __isl_take isl_map *map);
6714 Compute the minimum or maximum of the (given) set or output dimension(s)
6715 as a function of the parameters (and input dimensions), but independently
6716 of the other set or output dimensions.
6717 For lexicographic optimization, see L<"Lexicographic Optimization">.
6721 The following functions compute either the set of (rational) coefficient
6722 values of valid constraints for the given set or the set of (rational)
6723 values satisfying the constraints with coefficients from the given set.
6724 Internally, these two sets of functions perform essentially the
6725 same operations, except that the set of coefficients is assumed to
6726 be a cone, while the set of values may be any polyhedron.
6727 The current implementation is based on the Farkas lemma and
6728 Fourier-Motzkin elimination, but this may change or be made optional
6729 in future. In particular, future implementations may use different
6730 dualization algorithms or skip the elimination step.
6732 #include <isl/set.h>
6733 __isl_give isl_basic_set *isl_basic_set_coefficients(
6734 __isl_take isl_basic_set *bset);
6735 __isl_give isl_basic_set_list *
6736 isl_basic_set_list_coefficients(
6737 __isl_take isl_basic_set_list *list);
6738 __isl_give isl_basic_set *isl_set_coefficients(
6739 __isl_take isl_set *set);
6740 __isl_give isl_union_set *isl_union_set_coefficients(
6741 __isl_take isl_union_set *bset);
6742 __isl_give isl_basic_set *isl_basic_set_solutions(
6743 __isl_take isl_basic_set *bset);
6744 __isl_give isl_basic_set *isl_set_solutions(
6745 __isl_take isl_set *set);
6746 __isl_give isl_union_set *isl_union_set_solutions(
6747 __isl_take isl_union_set *bset);
6751 __isl_give isl_map *isl_map_fixed_power_val(
6752 __isl_take isl_map *map,
6753 __isl_take isl_val *exp);
6754 __isl_give isl_union_map *
6755 isl_union_map_fixed_power_val(
6756 __isl_take isl_union_map *umap,
6757 __isl_take isl_val *exp);
6759 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
6760 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
6761 of C<map> is computed.
6763 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
6765 __isl_give isl_union_map *isl_union_map_power(
6766 __isl_take isl_union_map *umap, isl_bool *exact);
6768 Compute a parametric representation for all positive powers I<k> of C<map>.
6769 The result maps I<k> to a nested relation corresponding to the
6770 I<k>th power of C<map>.
6771 The result may be an overapproximation. If the result is known to be exact,
6772 then C<*exact> is set to C<1>.
6774 =item * Transitive closure
6776 __isl_give isl_map *isl_map_transitive_closure(
6777 __isl_take isl_map *map, isl_bool *exact);
6778 __isl_give isl_union_map *isl_union_map_transitive_closure(
6779 __isl_take isl_union_map *umap, isl_bool *exact);
6781 Compute the transitive closure of C<map>.
6782 The result may be an overapproximation. If the result is known to be exact,
6783 then C<*exact> is set to C<1>.
6785 =item * Reaching path lengths
6787 __isl_give isl_map *isl_map_reaching_path_lengths(
6788 __isl_take isl_map *map, isl_bool *exact);
6790 Compute a relation that maps each element in the range of C<map>
6791 to the lengths of all paths composed of edges in C<map> that
6792 end up in the given element.
6793 The result may be an overapproximation. If the result is known to be exact,
6794 then C<*exact> is set to C<1>.
6795 To compute the I<maximal> path length, the resulting relation
6796 should be postprocessed by C<isl_map_lexmax>.
6797 In particular, if the input relation is a dependence relation
6798 (mapping sources to sinks), then the maximal path length corresponds
6799 to the free schedule.
6800 Note, however, that C<isl_map_lexmax> expects the maximum to be
6801 finite, so if the path lengths are unbounded (possibly due to
6802 the overapproximation), then you will get an error message.
6806 #include <isl/space.h>
6807 __isl_give isl_space *isl_space_wrap(
6808 __isl_take isl_space *space);
6809 __isl_give isl_space *isl_space_unwrap(
6810 __isl_take isl_space *space);
6812 #include <isl/local_space.h>
6813 __isl_give isl_local_space *isl_local_space_wrap(
6814 __isl_take isl_local_space *ls);
6816 #include <isl/set.h>
6817 __isl_give isl_basic_map *isl_basic_set_unwrap(
6818 __isl_take isl_basic_set *bset);
6819 __isl_give isl_map *isl_set_unwrap(
6820 __isl_take isl_set *set);
6822 #include <isl/map.h>
6823 __isl_give isl_basic_set *isl_basic_map_wrap(
6824 __isl_take isl_basic_map *bmap);
6825 __isl_give isl_set *isl_map_wrap(
6826 __isl_take isl_map *map);
6828 #include <isl/union_set.h>
6829 __isl_give isl_union_map *isl_union_set_unwrap(
6830 __isl_take isl_union_set *uset);
6832 #include <isl/union_map.h>
6833 __isl_give isl_union_set *isl_union_map_wrap(
6834 __isl_take isl_union_map *umap);
6836 The input to C<isl_space_unwrap> should
6837 be the space of a set, while that of
6838 C<isl_space_wrap> should be the space of a relation.
6839 Conversely, the output of C<isl_space_unwrap> is the space
6840 of a relation, while that of C<isl_space_wrap> is the space of a set.
6844 Remove any internal structure of domain (and range) of the given
6845 set or relation. If there is any such internal structure in the input,
6846 then the name of the space is also removed.
6848 #include <isl/space.h>
6849 __isl_give isl_space *isl_space_flatten_domain(
6850 __isl_take isl_space *space);
6851 __isl_give isl_space *isl_space_flatten_range(
6852 __isl_take isl_space *space);
6854 #include <isl/local_space.h>
6855 __isl_give isl_local_space *
6856 isl_local_space_flatten_domain(
6857 __isl_take isl_local_space *ls);
6858 __isl_give isl_local_space *
6859 isl_local_space_flatten_range(
6860 __isl_take isl_local_space *ls);
6862 #include <isl/set.h>
6863 __isl_give isl_basic_set *isl_basic_set_flatten(
6864 __isl_take isl_basic_set *bset);
6865 __isl_give isl_set *isl_set_flatten(
6866 __isl_take isl_set *set);
6868 #include <isl/map.h>
6869 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
6870 __isl_take isl_basic_map *bmap);
6871 __isl_give isl_basic_map *isl_basic_map_flatten_range(
6872 __isl_take isl_basic_map *bmap);
6873 __isl_give isl_map *isl_map_flatten_range(
6874 __isl_take isl_map *map);
6875 __isl_give isl_map *isl_map_flatten_domain(
6876 __isl_take isl_map *map);
6877 __isl_give isl_basic_map *isl_basic_map_flatten(
6878 __isl_take isl_basic_map *bmap);
6879 __isl_give isl_map *isl_map_flatten(
6880 __isl_take isl_map *map);
6883 __isl_give isl_multi_id *isl_multi_id_flatten_range(
6884 __isl_take isl_multi_id *mi);
6886 #include <isl/val.h>
6887 __isl_give isl_multi_val *isl_multi_val_flatten_range(
6888 __isl_take isl_multi_val *mv);
6890 #include <isl/aff.h>
6891 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
6892 __isl_take isl_multi_aff *ma);
6893 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
6894 __isl_take isl_multi_aff *ma);
6895 __isl_give isl_multi_pw_aff *
6896 isl_multi_pw_aff_flatten_range(
6897 __isl_take isl_multi_pw_aff *mpa);
6898 __isl_give isl_multi_union_pw_aff *
6899 isl_multi_union_pw_aff_flatten_range(
6900 __isl_take isl_multi_union_pw_aff *mupa);
6902 #include <isl/map.h>
6903 __isl_give isl_map *isl_set_flatten_map(
6904 __isl_take isl_set *set);
6906 The function above constructs a relation
6907 that maps the input set to a flattened version of the set.
6911 Lift the input set to a space with extra dimensions corresponding
6912 to the existentially quantified variables in the input.
6913 In particular, the result lives in a wrapped map where the domain
6914 is the original space and the range corresponds to the original
6915 existentially quantified variables.
6917 #include <isl/set.h>
6918 __isl_give isl_basic_set *isl_basic_set_lift(
6919 __isl_take isl_basic_set *bset);
6920 __isl_give isl_set *isl_set_lift(
6921 __isl_take isl_set *set);
6922 __isl_give isl_union_set *isl_union_set_lift(
6923 __isl_take isl_union_set *uset);
6925 Given a local space that contains the existentially quantified
6926 variables of a set, a basic relation that, when applied to
6927 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
6928 can be constructed using the following function.
6930 #include <isl/local_space.h>
6931 __isl_give isl_basic_map *isl_local_space_lifting(
6932 __isl_take isl_local_space *ls);
6934 #include <isl/aff.h>
6935 __isl_give isl_multi_aff *isl_multi_aff_lift(
6936 __isl_take isl_multi_aff *maff,
6937 __isl_give isl_local_space **ls);
6939 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
6940 then it is assigned the local space that lies at the basis of
6941 the lifting applied.
6943 =item * Internal Product
6945 #include <isl/space.h>
6946 __isl_give isl_space *isl_space_zip(
6947 __isl_take isl_space *space);
6949 #include <isl/map.h>
6950 __isl_give isl_basic_map *isl_basic_map_zip(
6951 __isl_take isl_basic_map *bmap);
6952 __isl_give isl_map *isl_map_zip(
6953 __isl_take isl_map *map);
6955 #include <isl/union_map.h>
6956 __isl_give isl_union_map *isl_union_map_zip(
6957 __isl_take isl_union_map *umap);
6959 Given a relation with nested relations for domain and range,
6960 interchange the range of the domain with the domain of the range.
6964 #include <isl/space.h>
6965 __isl_give isl_space *isl_space_curry(
6966 __isl_take isl_space *space);
6967 __isl_give isl_space *isl_space_uncurry(
6968 __isl_take isl_space *space);
6970 #include <isl/map.h>
6971 __isl_give isl_basic_map *isl_basic_map_curry(
6972 __isl_take isl_basic_map *bmap);
6973 __isl_give isl_basic_map *isl_basic_map_uncurry(
6974 __isl_take isl_basic_map *bmap);
6975 __isl_give isl_map *isl_map_curry(
6976 __isl_take isl_map *map);
6977 __isl_give isl_map *isl_map_uncurry(
6978 __isl_take isl_map *map);
6980 #include <isl/union_map.h>
6981 __isl_give isl_union_map *isl_union_map_curry(
6982 __isl_take isl_union_map *umap);
6983 __isl_give isl_union_map *isl_union_map_uncurry(
6984 __isl_take isl_union_map *umap);
6986 Given a relation with a nested relation for domain,
6987 the C<curry> functions
6988 move the range of the nested relation out of the domain
6989 and use it as the domain of a nested relation in the range,
6990 with the original range as range of this nested relation.
6991 The C<uncurry> functions perform the inverse operation.
6993 #include <isl/space.h>
6994 __isl_give isl_space *isl_space_range_curry(
6995 __isl_take isl_space *space);
6997 #include <isl/map.h>
6998 __isl_give isl_map *isl_map_range_curry(
6999 __isl_take isl_map *map);
7001 #include <isl/union_map.h>
7002 __isl_give isl_union_map *isl_union_map_range_curry(
7003 __isl_take isl_union_map *umap);
7005 These functions apply the currying to the relation that
7006 is nested inside the range of the input.
7008 =item * Aligning parameters
7010 Change the order of the parameters of the given set, relation
7012 such that the first parameters match those of C<model>.
7013 This may involve the introduction of extra parameters.
7014 All parameters need to be named.
7016 #include <isl/space.h>
7017 __isl_give isl_space *isl_space_align_params(
7018 __isl_take isl_space *space1,
7019 __isl_take isl_space *space2)
7021 #include <isl/set.h>
7022 __isl_give isl_basic_set *isl_basic_set_align_params(
7023 __isl_take isl_basic_set *bset,
7024 __isl_take isl_space *model);
7025 __isl_give isl_set *isl_set_align_params(
7026 __isl_take isl_set *set,
7027 __isl_take isl_space *model);
7029 #include <isl/map.h>
7030 __isl_give isl_basic_map *isl_basic_map_align_params(
7031 __isl_take isl_basic_map *bmap,
7032 __isl_take isl_space *model);
7033 __isl_give isl_map *isl_map_align_params(
7034 __isl_take isl_map *map,
7035 __isl_take isl_space *model);
7038 __isl_give isl_multi_id *isl_multi_id_align_params(
7039 __isl_take isl_multi_id *mi,
7040 __isl_take isl_space *model);
7042 #include <isl/val.h>
7043 __isl_give isl_multi_val *isl_multi_val_align_params(
7044 __isl_take isl_multi_val *mv,
7045 __isl_take isl_space *model);
7047 #include <isl/aff.h>
7048 __isl_give isl_aff *isl_aff_align_params(
7049 __isl_take isl_aff *aff,
7050 __isl_take isl_space *model);
7051 __isl_give isl_multi_aff *isl_multi_aff_align_params(
7052 __isl_take isl_multi_aff *multi,
7053 __isl_take isl_space *model);
7054 __isl_give isl_pw_aff *isl_pw_aff_align_params(
7055 __isl_take isl_pw_aff *pwaff,
7056 __isl_take isl_space *model);
7057 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
7058 __isl_take isl_pw_multi_aff *pma,
7059 __isl_take isl_space *model);
7060 __isl_give isl_union_pw_aff *
7061 isl_union_pw_aff_align_params(
7062 __isl_take isl_union_pw_aff *upa,
7063 __isl_take isl_space *model);
7064 __isl_give isl_union_pw_multi_aff *
7065 isl_union_pw_multi_aff_align_params(
7066 __isl_take isl_union_pw_multi_aff *upma,
7067 __isl_take isl_space *model);
7068 __isl_give isl_multi_union_pw_aff *
7069 isl_multi_union_pw_aff_align_params(
7070 __isl_take isl_multi_union_pw_aff *mupa,
7071 __isl_take isl_space *model);
7073 #include <isl/polynomial.h>
7074 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
7075 __isl_take isl_qpolynomial *qp,
7076 __isl_take isl_space *model);
7078 =item * Drop unused parameters
7080 Drop parameters that are not referenced by the isl object.
7081 All parameters need to be named.
7083 #include <isl/set.h>
7084 __isl_give isl_basic_set *
7085 isl_basic_set_drop_unused_params(
7086 __isl_take isl_basic_set *bset);
7087 __isl_give isl_set *isl_set_drop_unused_params(
7088 __isl_take isl_set *set);
7090 #include <isl/map.h>
7091 __isl_give isl_basic_map *
7092 isl_basic_map_drop_unused_params(
7093 __isl_take isl_basic_map *bmap);
7094 __isl_give isl_map *isl_map_drop_unused_params(
7095 __isl_take isl_map *map);
7097 #include <isl/union_set.h>
7098 __isl_give isl_union_set *
7099 isl_union_set_drop_unused_params(
7100 __isl_take isl_union_set *uset);
7102 #include <isl/union_map.h>
7103 __isl_give isl_union_map *
7104 isl_union_map_drop_unused_params(
7105 __isl_take isl_union_map *umap);
7107 #include <isl/aff.h>
7108 __isl_give isl_pw_aff *isl_pw_aff_drop_unused_params(
7109 __isl_take isl_pw_aff *pa);
7110 __isl_give isl_pw_multi_aff *
7111 isl_pw_multi_aff_drop_unused_params(
7112 __isl_take isl_pw_multi_aff *pma);
7113 __isl_give isl_union_pw_aff *
7114 isl_union_pw_aff_drop_unused_params(
7115 __isl_take isl_union_pw_aff *upa);
7116 __isl_give isl_union_pw_multi_aff *
7117 isl_union_pw_multi_aff_drop_unused_params(
7118 __isl_take isl_union_pw_multi_aff *upma);
7120 #include <isl/polynomial.h>
7121 __isl_give isl_pw_qpolynomial *
7122 isl_pw_qpolynomial_drop_unused_params(
7123 __isl_take isl_pw_qpolynomial *pwqp);
7124 __isl_give isl_pw_qpolynomial_fold *
7125 isl_pw_qpolynomial_fold_drop_unused_params(
7126 __isl_take isl_pw_qpolynomial_fold *pwf);
7127 __isl_give isl_union_pw_qpolynomial *
7128 isl_union_pw_qpolynomial_drop_unused_params(
7129 __isl_take isl_union_pw_qpolynomial *upwqp);
7130 __isl_give isl_union_pw_qpolynomial_fold *
7131 isl_union_pw_qpolynomial_fold_drop_unused_params(
7132 __isl_take isl_union_pw_qpolynomial_fold *upwf);
7134 =item * Unary Arithmetic Operations
7136 #include <isl/set.h>
7137 __isl_give isl_set *isl_set_neg(
7138 __isl_take isl_set *set);
7139 #include <isl/map.h>
7140 __isl_give isl_map *isl_map_neg(
7141 __isl_take isl_map *map);
7143 C<isl_set_neg> constructs a set containing the opposites of
7144 the elements in its argument.
7145 The domain of the result of C<isl_map_neg> is the same
7146 as the domain of its argument. The corresponding range
7147 elements are the opposites of the corresponding range
7148 elements in the argument.
7150 #include <isl/val.h>
7151 __isl_give isl_multi_val *isl_multi_val_neg(
7152 __isl_take isl_multi_val *mv);
7154 #include <isl/aff.h>
7155 __isl_give isl_aff *isl_aff_neg(
7156 __isl_take isl_aff *aff);
7157 __isl_give isl_multi_aff *isl_multi_aff_neg(
7158 __isl_take isl_multi_aff *ma);
7159 __isl_give isl_pw_aff *isl_pw_aff_neg(
7160 __isl_take isl_pw_aff *pwaff);
7161 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
7162 __isl_take isl_pw_multi_aff *pma);
7163 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
7164 __isl_take isl_multi_pw_aff *mpa);
7165 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
7166 __isl_take isl_union_pw_aff *upa);
7167 __isl_give isl_union_pw_multi_aff *
7168 isl_union_pw_multi_aff_neg(
7169 __isl_take isl_union_pw_multi_aff *upma);
7170 __isl_give isl_multi_union_pw_aff *
7171 isl_multi_union_pw_aff_neg(
7172 __isl_take isl_multi_union_pw_aff *mupa);
7173 __isl_give isl_aff *isl_aff_ceil(
7174 __isl_take isl_aff *aff);
7175 __isl_give isl_pw_aff *isl_pw_aff_ceil(
7176 __isl_take isl_pw_aff *pwaff);
7177 __isl_give isl_aff *isl_aff_floor(
7178 __isl_take isl_aff *aff);
7179 __isl_give isl_multi_aff *isl_multi_aff_floor(
7180 __isl_take isl_multi_aff *ma);
7181 __isl_give isl_pw_aff *isl_pw_aff_floor(
7182 __isl_take isl_pw_aff *pwaff);
7183 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
7184 __isl_take isl_union_pw_aff *upa);
7185 __isl_give isl_multi_union_pw_aff *
7186 isl_multi_union_pw_aff_floor(
7187 __isl_take isl_multi_union_pw_aff *mupa);
7189 #include <isl/aff.h>
7190 __isl_give isl_pw_aff *isl_pw_aff_list_min(
7191 __isl_take isl_pw_aff_list *list);
7192 __isl_give isl_pw_aff *isl_pw_aff_list_max(
7193 __isl_take isl_pw_aff_list *list);
7195 #include <isl/polynomial.h>
7196 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
7197 __isl_take isl_qpolynomial *qp);
7198 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
7199 __isl_take isl_pw_qpolynomial *pwqp);
7200 __isl_give isl_union_pw_qpolynomial *
7201 isl_union_pw_qpolynomial_neg(
7202 __isl_take isl_union_pw_qpolynomial *upwqp);
7203 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
7204 __isl_take isl_qpolynomial *qp,
7206 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
7207 __isl_take isl_pw_qpolynomial *pwqp,
7212 The following functions evaluate a function in a point.
7214 #include <isl/aff.h>
7215 __isl_give isl_val *isl_aff_eval(
7216 __isl_take isl_aff *aff,
7217 __isl_take isl_point *pnt);
7218 __isl_give isl_val *isl_pw_aff_eval(
7219 __isl_take isl_pw_aff *pa,
7220 __isl_take isl_point *pnt);
7222 #include <isl/polynomial.h>
7223 __isl_give isl_val *isl_pw_qpolynomial_eval(
7224 __isl_take isl_pw_qpolynomial *pwqp,
7225 __isl_take isl_point *pnt);
7226 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
7227 __isl_take isl_pw_qpolynomial_fold *pwf,
7228 __isl_take isl_point *pnt);
7229 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
7230 __isl_take isl_union_pw_qpolynomial *upwqp,
7231 __isl_take isl_point *pnt);
7232 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
7233 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7234 __isl_take isl_point *pnt);
7236 These functions return NaN when evaluated at a void point.
7237 Note that C<isl_pw_aff_eval> returns NaN when the function is evaluated outside
7238 its definition domain, while C<isl_pw_qpolynomial_eval> returns zero
7239 when the function is evaluated outside its explicit domain.
7241 =item * Dimension manipulation
7243 It is usually not advisable to directly change the (input or output)
7244 space of a set or a relation as this removes the name and the internal
7245 structure of the space. However, the functions below can be useful
7246 to add new parameters, assuming
7247 C<isl_set_align_params> and C<isl_map_align_params>
7250 #include <isl/space.h>
7251 __isl_give isl_space *isl_space_add_dims(
7252 __isl_take isl_space *space,
7253 enum isl_dim_type type, unsigned n);
7254 __isl_give isl_space *isl_space_insert_dims(
7255 __isl_take isl_space *space,
7256 enum isl_dim_type type, unsigned pos, unsigned n);
7257 __isl_give isl_space *isl_space_drop_dims(
7258 __isl_take isl_space *space,
7259 enum isl_dim_type type, unsigned first, unsigned n);
7260 __isl_give isl_space *isl_space_move_dims(
7261 __isl_take isl_space *space,
7262 enum isl_dim_type dst_type, unsigned dst_pos,
7263 enum isl_dim_type src_type, unsigned src_pos,
7266 #include <isl/local_space.h>
7267 __isl_give isl_local_space *isl_local_space_add_dims(
7268 __isl_take isl_local_space *ls,
7269 enum isl_dim_type type, unsigned n);
7270 __isl_give isl_local_space *isl_local_space_insert_dims(
7271 __isl_take isl_local_space *ls,
7272 enum isl_dim_type type, unsigned first, unsigned n);
7273 __isl_give isl_local_space *isl_local_space_drop_dims(
7274 __isl_take isl_local_space *ls,
7275 enum isl_dim_type type, unsigned first, unsigned n);
7277 #include <isl/set.h>
7278 __isl_give isl_basic_set *isl_basic_set_add_dims(
7279 __isl_take isl_basic_set *bset,
7280 enum isl_dim_type type, unsigned n);
7281 __isl_give isl_set *isl_set_add_dims(
7282 __isl_take isl_set *set,
7283 enum isl_dim_type type, unsigned n);
7284 __isl_give isl_basic_set *isl_basic_set_insert_dims(
7285 __isl_take isl_basic_set *bset,
7286 enum isl_dim_type type, unsigned pos,
7288 __isl_give isl_set *isl_set_insert_dims(
7289 __isl_take isl_set *set,
7290 enum isl_dim_type type, unsigned pos, unsigned n);
7291 __isl_give isl_basic_set *isl_basic_set_move_dims(
7292 __isl_take isl_basic_set *bset,
7293 enum isl_dim_type dst_type, unsigned dst_pos,
7294 enum isl_dim_type src_type, unsigned src_pos,
7296 __isl_give isl_set *isl_set_move_dims(
7297 __isl_take isl_set *set,
7298 enum isl_dim_type dst_type, unsigned dst_pos,
7299 enum isl_dim_type src_type, unsigned src_pos,
7302 #include <isl/map.h>
7303 __isl_give isl_basic_map *isl_basic_map_add_dims(
7304 __isl_take isl_basic_map *bmap,
7305 enum isl_dim_type type, unsigned n);
7306 __isl_give isl_map *isl_map_add_dims(
7307 __isl_take isl_map *map,
7308 enum isl_dim_type type, unsigned n);
7309 __isl_give isl_basic_map *isl_basic_map_insert_dims(
7310 __isl_take isl_basic_map *bmap,
7311 enum isl_dim_type type, unsigned pos,
7313 __isl_give isl_map *isl_map_insert_dims(
7314 __isl_take isl_map *map,
7315 enum isl_dim_type type, unsigned pos, unsigned n);
7316 __isl_give isl_basic_map *isl_basic_map_move_dims(
7317 __isl_take isl_basic_map *bmap,
7318 enum isl_dim_type dst_type, unsigned dst_pos,
7319 enum isl_dim_type src_type, unsigned src_pos,
7321 __isl_give isl_map *isl_map_move_dims(
7322 __isl_take isl_map *map,
7323 enum isl_dim_type dst_type, unsigned dst_pos,
7324 enum isl_dim_type src_type, unsigned src_pos,
7327 #include <isl/val.h>
7328 __isl_give isl_multi_val *isl_multi_val_insert_dims(
7329 __isl_take isl_multi_val *mv,
7330 enum isl_dim_type type, unsigned first, unsigned n);
7331 __isl_give isl_multi_val *isl_multi_val_add_dims(
7332 __isl_take isl_multi_val *mv,
7333 enum isl_dim_type type, unsigned n);
7334 __isl_give isl_multi_val *isl_multi_val_drop_dims(
7335 __isl_take isl_multi_val *mv,
7336 enum isl_dim_type type, unsigned first, unsigned n);
7338 #include <isl/aff.h>
7339 __isl_give isl_aff *isl_aff_insert_dims(
7340 __isl_take isl_aff *aff,
7341 enum isl_dim_type type, unsigned first, unsigned n);
7342 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
7343 __isl_take isl_multi_aff *ma,
7344 enum isl_dim_type type, unsigned first, unsigned n);
7345 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
7346 __isl_take isl_pw_aff *pwaff,
7347 enum isl_dim_type type, unsigned first, unsigned n);
7348 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
7349 __isl_take isl_multi_pw_aff *mpa,
7350 enum isl_dim_type type, unsigned first, unsigned n);
7351 __isl_give isl_aff *isl_aff_add_dims(
7352 __isl_take isl_aff *aff,
7353 enum isl_dim_type type, unsigned n);
7354 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
7355 __isl_take isl_multi_aff *ma,
7356 enum isl_dim_type type, unsigned n);
7357 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
7358 __isl_take isl_pw_aff *pwaff,
7359 enum isl_dim_type type, unsigned n);
7360 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
7361 __isl_take isl_multi_pw_aff *mpa,
7362 enum isl_dim_type type, unsigned n);
7363 __isl_give isl_aff *isl_aff_drop_dims(
7364 __isl_take isl_aff *aff,
7365 enum isl_dim_type type, unsigned first, unsigned n);
7366 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
7367 __isl_take isl_multi_aff *maff,
7368 enum isl_dim_type type, unsigned first, unsigned n);
7369 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
7370 __isl_take isl_pw_aff *pwaff,
7371 enum isl_dim_type type, unsigned first, unsigned n);
7372 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
7373 __isl_take isl_pw_multi_aff *pma,
7374 enum isl_dim_type type, unsigned first, unsigned n);
7375 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
7376 __isl_take isl_union_pw_aff *upa,
7377 enum isl_dim_type type, unsigned first, unsigned n);
7378 __isl_give isl_union_pw_multi_aff *
7379 isl_union_pw_multi_aff_drop_dims(
7380 __isl_take isl_union_pw_multi_aff *upma,
7381 enum isl_dim_type type,
7382 unsigned first, unsigned n);
7383 __isl_give isl_multi_union_pw_aff *
7384 isl_multi_union_pw_aff_drop_dims(
7385 __isl_take isl_multi_union_pw_aff *mupa,
7386 enum isl_dim_type type, unsigned first,
7388 __isl_give isl_aff *isl_aff_move_dims(
7389 __isl_take isl_aff *aff,
7390 enum isl_dim_type dst_type, unsigned dst_pos,
7391 enum isl_dim_type src_type, unsigned src_pos,
7393 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
7394 __isl_take isl_multi_aff *ma,
7395 enum isl_dim_type dst_type, unsigned dst_pos,
7396 enum isl_dim_type src_type, unsigned src_pos,
7398 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
7399 __isl_take isl_pw_aff *pa,
7400 enum isl_dim_type dst_type, unsigned dst_pos,
7401 enum isl_dim_type src_type, unsigned src_pos,
7403 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
7404 __isl_take isl_multi_pw_aff *pma,
7405 enum isl_dim_type dst_type, unsigned dst_pos,
7406 enum isl_dim_type src_type, unsigned src_pos,
7409 #include <isl/polynomial.h>
7410 __isl_give isl_union_pw_qpolynomial *
7411 isl_union_pw_qpolynomial_drop_dims(
7412 __isl_take isl_union_pw_qpolynomial *upwqp,
7413 enum isl_dim_type type,
7414 unsigned first, unsigned n);
7415 __isl_give isl_union_pw_qpolynomial_fold *
7416 isl_union_pw_qpolynomial_fold_drop_dims(
7417 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7418 enum isl_dim_type type,
7419 unsigned first, unsigned n);
7421 The operations on union expressions can only manipulate parameters.
7425 =head2 Binary Operations
7427 The two arguments of a binary operation not only need to live
7428 in the same C<isl_ctx>, they currently also need to have
7429 the same (number of) parameters.
7431 =head3 Basic Operations
7435 =item * Intersection
7437 #include <isl/local_space.h>
7438 __isl_give isl_local_space *isl_local_space_intersect(
7439 __isl_take isl_local_space *ls1,
7440 __isl_take isl_local_space *ls2);
7442 #include <isl/set.h>
7443 __isl_give isl_basic_set *isl_basic_set_intersect_params(
7444 __isl_take isl_basic_set *bset1,
7445 __isl_take isl_basic_set *bset2);
7446 __isl_give isl_basic_set *isl_basic_set_intersect(
7447 __isl_take isl_basic_set *bset1,
7448 __isl_take isl_basic_set *bset2);
7449 __isl_give isl_basic_set *isl_basic_set_list_intersect(
7450 __isl_take struct isl_basic_set_list *list);
7451 __isl_give isl_set *isl_set_intersect_params(
7452 __isl_take isl_set *set,
7453 __isl_take isl_set *params);
7454 __isl_give isl_set *isl_set_intersect(
7455 __isl_take isl_set *set1,
7456 __isl_take isl_set *set2);
7457 __isl_give isl_set *isl_set_intersect_factor_domain(
7458 __isl_take isl_set *set,
7459 __isl_take isl_set *domain);
7460 __isl_give isl_set *isl_set_intersect_factor_range(
7461 __isl_take isl_set *set,
7462 __isl_take isl_set *range);
7464 #include <isl/map.h>
7465 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
7466 __isl_take isl_basic_map *bmap,
7467 __isl_take isl_basic_set *bset);
7468 __isl_give isl_basic_map *isl_basic_map_intersect_range(
7469 __isl_take isl_basic_map *bmap,
7470 __isl_take isl_basic_set *bset);
7471 __isl_give isl_basic_map *isl_basic_map_intersect(
7472 __isl_take isl_basic_map *bmap1,
7473 __isl_take isl_basic_map *bmap2);
7474 __isl_give isl_basic_map *isl_basic_map_list_intersect(
7475 __isl_take isl_basic_map_list *list);
7476 __isl_give isl_map *isl_map_intersect_params(
7477 __isl_take isl_map *map,
7478 __isl_take isl_set *params);
7479 __isl_give isl_map *isl_map_intersect_domain(
7480 __isl_take isl_map *map,
7481 __isl_take isl_set *set);
7482 __isl_give isl_map *isl_map_intersect_range(
7483 __isl_take isl_map *map,
7484 __isl_take isl_set *set);
7485 __isl_give isl_map *isl_map_intersect(
7486 __isl_take isl_map *map1,
7487 __isl_take isl_map *map2);
7488 __isl_give isl_map *
7489 isl_map_intersect_domain_factor_domain(
7490 __isl_take isl_map *map,
7491 __isl_take isl_map *factor);
7492 __isl_give isl_map *
7493 isl_map_intersect_domain_factor_range(
7494 __isl_take isl_map *map,
7495 __isl_take isl_map *factor);
7496 __isl_give isl_map *
7497 isl_map_intersect_range_factor_domain(
7498 __isl_take isl_map *map,
7499 __isl_take isl_map *factor);
7500 __isl_give isl_map *
7501 isl_map_intersect_range_factor_range(
7502 __isl_take isl_map *map,
7503 __isl_take isl_map *factor);
7504 __isl_give isl_map *
7505 isl_map_intersect_domain_wrapped_domain(
7506 __isl_take isl_map *map,
7507 __isl_take isl_set *domain);
7508 __isl_give isl_map *
7509 isl_map_intersect_range_wrapped_domain(
7510 __isl_take isl_map *map,
7511 __isl_take isl_set *domain);
7513 #include <isl/union_set.h>
7514 __isl_give isl_union_set *isl_union_set_intersect_params(
7515 __isl_take isl_union_set *uset,
7516 __isl_take isl_set *set);
7517 __isl_give isl_union_set *isl_union_set_intersect(
7518 __isl_take isl_union_set *uset1,
7519 __isl_take isl_union_set *uset2);
7521 #include <isl/union_map.h>
7522 __isl_give isl_union_map *isl_union_map_intersect_params(
7523 __isl_take isl_union_map *umap,
7524 __isl_take isl_set *set);
7525 __isl_give isl_union_map *
7526 isl_union_map_intersect_domain_union_set(
7527 __isl_take isl_union_map *umap,
7528 __isl_take isl_union_set *uset);
7529 __isl_give isl_union_map *
7530 isl_union_map_intersect_domain_space(
7531 __isl_take isl_union_map *umap,
7532 __isl_take isl_space *space);
7533 __isl_give isl_union_map *isl_union_map_intersect_domain(
7534 __isl_take isl_union_map *umap,
7535 __isl_take isl_union_set *uset);
7536 __isl_give isl_union_map *
7537 isl_union_map_intersect_range_union_set(
7538 __isl_take isl_union_map *umap,
7539 __isl_take isl_union_set *uset);
7540 __isl_give isl_union_map *
7541 isl_union_map_intersect_range_space(
7542 __isl_take isl_union_map *umap,
7543 __isl_take isl_space *space);
7544 __isl_give isl_union_map *isl_union_map_intersect_range(
7545 __isl_take isl_union_map *umap,
7546 __isl_take isl_union_set *uset);
7547 __isl_give isl_union_map *isl_union_map_intersect(
7548 __isl_take isl_union_map *umap1,
7549 __isl_take isl_union_map *umap2);
7550 __isl_give isl_union_map *
7551 isl_union_map_intersect_domain_factor_domain(
7552 __isl_take isl_union_map *umap,
7553 __isl_take isl_union_map *factor);
7554 __isl_give isl_union_map *
7555 isl_union_map_intersect_domain_factor_range(
7556 __isl_take isl_union_map *umap,
7557 __isl_take isl_union_map *factor);
7558 __isl_give isl_union_map *
7559 isl_union_map_intersect_range_factor_domain(
7560 __isl_take isl_union_map *umap,
7561 __isl_take isl_union_map *factor);
7562 __isl_give isl_union_map *
7563 isl_union_map_intersect_range_factor_range(
7564 __isl_take isl_union_map *umap,
7565 __isl_take isl_union_map *factor);
7566 __isl_give isl_union_map *
7567 isl_union_map_intersect_domain_wrapped_domain_union_set(
7568 __isl_take isl_union_map *umap,
7569 __isl_take isl_union_set *domain);
7570 __isl_give isl_union_map *
7571 isl_union_map_intersect_range_wrapped_domain_union_set(
7572 __isl_take isl_union_map *umap,
7573 __isl_take isl_union_set *domain);
7575 #include <isl/aff.h>
7576 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
7577 __isl_take isl_pw_aff *pa,
7578 __isl_take isl_set *set);
7579 __isl_give isl_multi_pw_aff *
7580 isl_multi_pw_aff_intersect_domain(
7581 __isl_take isl_multi_pw_aff *mpa,
7582 __isl_take isl_set *domain);
7583 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
7584 __isl_take isl_pw_multi_aff *pma,
7585 __isl_take isl_set *set);
7586 __isl_give isl_union_pw_aff *
7587 isl_union_pw_aff_intersect_domain_space(
7588 __isl_take isl_union_pw_aff *upa,
7589 __isl_take isl_space *space);
7590 __isl_give isl_union_pw_aff *
7591 isl_union_pw_aff_intersect_domain_union_set(
7592 __isl_take isl_union_pw_aff *upa,
7593 __isl_take isl_union_set *uset);
7594 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
7595 __isl_take isl_union_pw_aff *upa,
7596 __isl_take isl_union_set *uset);
7597 __isl_give isl_union_pw_multi_aff *
7598 isl_union_pw_multi_aff_intersect_domain_space(
7599 __isl_take isl_union_pw_multi_aff *upma,
7600 __isl_take isl_space *space);
7601 __isl_give isl_union_pw_multi_aff *
7602 isl_union_pw_multi_aff_intersect_domain_union_set(
7603 __isl_take isl_union_pw_multi_aff *upma,
7604 __isl_take isl_union_set *uset);
7605 __isl_give isl_union_pw_multi_aff *
7606 isl_union_pw_multi_aff_intersect_domain(
7607 __isl_take isl_union_pw_multi_aff *upma,
7608 __isl_take isl_union_set *uset);
7609 __isl_give isl_multi_union_pw_aff *
7610 isl_multi_union_pw_aff_intersect_domain(
7611 __isl_take isl_multi_union_pw_aff *mupa,
7612 __isl_take isl_union_set *uset);
7613 __isl_give isl_pw_aff *
7614 isl_pw_aff_intersect_domain_wrapped_domain(
7615 __isl_take isl_pw_aff *pa,
7616 __isl_take isl_set *set);
7617 __isl_give isl_pw_multi_aff *
7618 isl_pw_multi_aff_intersect_domain_wrapped_domain(
7619 __isl_take isl_pw_multi_aff *pma,
7620 __isl_take isl_set *set);
7621 __isl_give isl_union_pw_aff *
7622 isl_union_pw_aff_intersect_domain_wrapped_domain(
7623 __isl_take isl_union_pw_aff *upa,
7624 __isl_take isl_union_set *uset);
7625 __isl_give isl_union_pw_multi_aff *
7626 isl_union_pw_multi_aff_intersect_domain_wrapped_domain(
7627 __isl_take isl_union_pw_multi_aff *upma,
7628 __isl_take isl_union_set *uset);
7629 __isl_give isl_pw_aff *
7630 isl_pw_aff_intersect_domain_wrapped_range(
7631 __isl_take isl_pw_aff *pa,
7632 __isl_take isl_set *set);
7633 __isl_give isl_pw_multi_aff *
7634 isl_pw_multi_aff_intersect_domain_wrapped_range(
7635 __isl_take isl_pw_multi_aff *pma,
7636 __isl_take isl_set *set);
7637 __isl_give isl_union_pw_multi_aff *
7638 isl_union_pw_multi_aff_intersect_domain_wrapped_range(
7639 __isl_take isl_union_pw_multi_aff *upma,
7640 __isl_take isl_union_set *uset);
7641 __isl_give isl_union_pw_aff *
7642 isl_union_pw_aff_intersect_domain_wrapped_range(
7643 __isl_take isl_union_pw_aff *upa,
7644 __isl_take isl_union_set *uset);
7645 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
7646 __isl_take isl_pw_aff *pa,
7647 __isl_take isl_set *set);
7648 __isl_give isl_multi_pw_aff *
7649 isl_multi_pw_aff_intersect_params(
7650 __isl_take isl_multi_pw_aff *mpa,
7651 __isl_take isl_set *set);
7652 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
7653 __isl_take isl_pw_multi_aff *pma,
7654 __isl_take isl_set *set);
7655 __isl_give isl_union_pw_aff *
7656 isl_union_pw_aff_intersect_params(
7657 __isl_take isl_union_pw_aff *upa,
7658 __isl_take isl_set *set);
7659 __isl_give isl_union_pw_multi_aff *
7660 isl_union_pw_multi_aff_intersect_params(
7661 __isl_take isl_union_pw_multi_aff *upma,
7662 __isl_take isl_set *set);
7663 __isl_give isl_multi_union_pw_aff *
7664 isl_multi_union_pw_aff_intersect_params(
7665 __isl_take isl_multi_union_pw_aff *mupa,
7666 __isl_take isl_set *params);
7667 __isl_give isl_multi_union_pw_aff *
7668 isl_multi_union_pw_aff_intersect_range(
7669 __isl_take isl_multi_union_pw_aff *mupa,
7670 __isl_take isl_set *set);
7672 #include <isl/polynomial.h>
7673 __isl_give isl_pw_qpolynomial *
7674 isl_pw_qpolynomial_intersect_domain(
7675 __isl_take isl_pw_qpolynomial *pwpq,
7676 __isl_take isl_set *set);
7677 __isl_give isl_union_pw_qpolynomial *
7678 isl_union_pw_qpolynomial_intersect_domain_space(
7679 __isl_take isl_union_pw_qpolynomial *upwpq,
7680 __isl_take isl_space *space);
7681 __isl_give isl_union_pw_qpolynomial *
7682 isl_union_pw_qpolynomial_intersect_domain_union_set(
7683 __isl_take isl_union_pw_qpolynomial *upwpq,
7684 __isl_take isl_union_set *uset);
7685 __isl_give isl_union_pw_qpolynomial *
7686 isl_union_pw_qpolynomial_intersect_domain(
7687 __isl_take isl_union_pw_qpolynomial *upwpq,
7688 __isl_take isl_union_set *uset);
7689 __isl_give isl_union_pw_qpolynomial_fold *
7690 isl_union_pw_qpolynomial_fold_intersect_domain_space(
7691 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7692 __isl_take isl_space *space);
7693 __isl_give isl_union_pw_qpolynomial_fold *
7694 isl_union_pw_qpolynomial_fold_intersect_domain_union_set(
7695 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7696 __isl_take isl_union_set *uset);
7697 __isl_give isl_union_pw_qpolynomial_fold *
7698 isl_union_pw_qpolynomial_fold_intersect_domain(
7699 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7700 __isl_take isl_union_set *uset);
7701 __isl_give isl_pw_qpolynomial *
7702 isl_pw_qpolynomial_intersect_domain_wrapped_domain(
7703 __isl_take isl_pw_qpolynomial *pwpq,
7704 __isl_take isl_set *set);
7705 __isl_give isl_pw_qpolynomial_fold *
7706 isl_pw_qpolynomial_fold_intersect_domain_wrapped_domain(
7707 __isl_take isl_pw_qpolynomial_fold *pwf,
7708 __isl_take isl_set *set);
7709 __isl_give isl_union_pw_qpolynomial *
7710 isl_union_pw_qpolynomial_intersect_domain_wrapped_domain(
7711 __isl_take isl_union_pw_qpolynomial *upwpq,
7712 __isl_take isl_union_set *uset);
7713 __isl_give isl_union_pw_qpolynomial_fold *
7714 isl_union_pw_qpolynomial_fold_intersect_domain_wrapped_domain(
7715 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7716 __isl_take isl_union_set *uset);
7717 __isl_give isl_pw_qpolynomial *
7718 isl_pw_qpolynomial_intersect_domain_wrapped_range(
7719 __isl_take isl_pw_qpolynomial *pwpq,
7720 __isl_take isl_set *set);
7721 __isl_give isl_pw_qpolynomial_fold *
7722 isl_pw_qpolynomial_fold_intersect_domain_wrapped_range(
7723 __isl_take isl_pw_qpolynomial_fold *pwf,
7724 __isl_take isl_set *set);
7725 __isl_give isl_union_pw_qpolynomial *
7726 isl_union_pw_qpolynomial_intersect_domain_wrapped_range(
7727 __isl_take isl_union_pw_qpolynomial *upwpq,
7728 __isl_take isl_union_set *uset);
7729 __isl_give isl_union_pw_qpolynomial_fold *
7730 isl_union_pw_qpolynomial_fold_intersect_domain_wrapped_range(
7731 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7732 __isl_take isl_union_set *uset);
7733 __isl_give isl_pw_qpolynomial *
7734 isl_pw_qpolynomial_intersect_params(
7735 __isl_take isl_pw_qpolynomial *pwpq,
7736 __isl_take isl_set *set);
7737 __isl_give isl_pw_qpolynomial_fold *
7738 isl_pw_qpolynomial_fold_intersect_params(
7739 __isl_take isl_pw_qpolynomial_fold *pwf,
7740 __isl_take isl_set *set);
7741 __isl_give isl_union_pw_qpolynomial *
7742 isl_union_pw_qpolynomial_intersect_params(
7743 __isl_take isl_union_pw_qpolynomial *upwpq,
7744 __isl_take isl_set *set);
7745 __isl_give isl_union_pw_qpolynomial_fold *
7746 isl_union_pw_qpolynomial_fold_intersect_params(
7747 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7748 __isl_take isl_set *set);
7750 The second argument to the C<_params> functions needs to be
7751 a parametric (basic) set. For the other functions, a parametric set
7752 for either argument is only allowed if the other argument is
7753 a parametric set as well.
7754 The list passed to C<isl_basic_set_list_intersect> needs to have
7755 at least one element and all elements need to live in the same space.
7756 The function C<isl_multi_union_pw_aff_intersect_range>
7757 restricts the input function to those shared domain elements
7758 that map to the specified range.
7759 C<isl_union_map_intersect_domain> is an alternative name for
7760 C<isl_union_map_intersect_domain_union_set>.
7761 Similarly for the other pairs of functions.
7765 #include <isl/set.h>
7766 __isl_give isl_set *isl_basic_set_union(
7767 __isl_take isl_basic_set *bset1,
7768 __isl_take isl_basic_set *bset2);
7769 __isl_give isl_set *isl_set_union(
7770 __isl_take isl_set *set1,
7771 __isl_take isl_set *set2);
7772 __isl_give isl_set *isl_set_list_union(
7773 __isl_take isl_set_list *list);
7775 #include <isl/map.h>
7776 __isl_give isl_map *isl_basic_map_union(
7777 __isl_take isl_basic_map *bmap1,
7778 __isl_take isl_basic_map *bmap2);
7779 __isl_give isl_map *isl_map_union(
7780 __isl_take isl_map *map1,
7781 __isl_take isl_map *map2);
7783 #include <isl/union_set.h>
7784 __isl_give isl_union_set *isl_union_set_union(
7785 __isl_take isl_union_set *uset1,
7786 __isl_take isl_union_set *uset2);
7787 __isl_give isl_union_set *isl_union_set_list_union(
7788 __isl_take isl_union_set_list *list);
7790 #include <isl/union_map.h>
7791 __isl_give isl_union_map *isl_union_map_union(
7792 __isl_take isl_union_map *umap1,
7793 __isl_take isl_union_map *umap2);
7795 The list passed to C<isl_set_list_union> needs to have
7796 at least one element and all elements need to live in the same space.
7798 =item * Set difference
7800 #include <isl/set.h>
7801 __isl_give isl_set *isl_set_subtract(
7802 __isl_take isl_set *set1,
7803 __isl_take isl_set *set2);
7805 #include <isl/map.h>
7806 __isl_give isl_map *isl_map_subtract(
7807 __isl_take isl_map *map1,
7808 __isl_take isl_map *map2);
7809 __isl_give isl_map *isl_map_subtract_domain(
7810 __isl_take isl_map *map,
7811 __isl_take isl_set *dom);
7812 __isl_give isl_map *isl_map_subtract_range(
7813 __isl_take isl_map *map,
7814 __isl_take isl_set *dom);
7816 #include <isl/union_set.h>
7817 __isl_give isl_union_set *isl_union_set_subtract(
7818 __isl_take isl_union_set *uset1,
7819 __isl_take isl_union_set *uset2);
7821 #include <isl/union_map.h>
7822 __isl_give isl_union_map *isl_union_map_subtract(
7823 __isl_take isl_union_map *umap1,
7824 __isl_take isl_union_map *umap2);
7825 __isl_give isl_union_map *isl_union_map_subtract_domain(
7826 __isl_take isl_union_map *umap,
7827 __isl_take isl_union_set *dom);
7828 __isl_give isl_union_map *isl_union_map_subtract_range(
7829 __isl_take isl_union_map *umap,
7830 __isl_take isl_union_set *dom);
7832 #include <isl/aff.h>
7833 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
7834 __isl_take isl_pw_aff *pa,
7835 __isl_take isl_set *set);
7836 __isl_give isl_pw_multi_aff *
7837 isl_pw_multi_aff_subtract_domain(
7838 __isl_take isl_pw_multi_aff *pma,
7839 __isl_take isl_set *set);
7840 __isl_give isl_union_pw_aff *
7841 isl_union_pw_aff_subtract_domain_union_set(
7842 __isl_take isl_union_pw_aff *upa,
7843 __isl_take isl_union_set *uset);
7844 __isl_give isl_union_pw_aff *
7845 isl_union_pw_aff_subtract_domain_space(
7846 __isl_take isl_union_pw_aff *upa,
7847 __isl_take isl_space *space);
7848 __isl_give isl_union_pw_aff *
7849 isl_union_pw_aff_subtract_domain(
7850 __isl_take isl_union_pw_aff *upa,
7851 __isl_take isl_union_set *uset);
7852 __isl_give isl_union_pw_multi_aff *
7853 isl_union_pw_multi_aff_subtract_domain_union_set(
7854 __isl_take isl_union_pw_multi_aff *upma,
7855 __isl_take isl_set *set);
7856 __isl_give isl_union_pw_multi_aff *
7857 isl_union_pw_multi_aff_subtract_domain_space(
7858 __isl_take isl_union_pw_multi_aff *upma,
7859 __isl_take isl_space *space);
7860 __isl_give isl_union_pw_multi_aff *
7861 isl_union_pw_multi_aff_subtract_domain(
7862 __isl_take isl_union_pw_multi_aff *upma,
7863 __isl_take isl_union_set *uset);
7865 #include <isl/polynomial.h>
7866 __isl_give isl_pw_qpolynomial *
7867 isl_pw_qpolynomial_subtract_domain(
7868 __isl_take isl_pw_qpolynomial *pwpq,
7869 __isl_take isl_set *set);
7870 __isl_give isl_pw_qpolynomial_fold *
7871 isl_pw_qpolynomial_fold_subtract_domain(
7872 __isl_take isl_pw_qpolynomial_fold *pwf,
7873 __isl_take isl_set *set);
7874 __isl_give isl_union_pw_qpolynomial *
7875 isl_union_pw_qpolynomial_subtract_domain_union_set(
7876 __isl_take isl_union_pw_qpolynomial *upwpq,
7877 __isl_take isl_union_set *uset);
7878 __isl_give isl_union_pw_qpolynomial *
7879 isl_union_pw_qpolynomial_subtract_domain_space(
7880 __isl_take isl_union_pw_qpolynomial *upwpq,
7881 __isl_take isl_space *space);
7882 __isl_give isl_union_pw_qpolynomial *
7883 isl_union_pw_qpolynomial_subtract_domain(
7884 __isl_take isl_union_pw_qpolynomial *upwpq,
7885 __isl_take isl_union_set *uset);
7886 __isl_give isl_union_pw_qpolynomial_fold *
7887 isl_union_pw_qpolynomial_fold_subtract_domain_union_set(
7888 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7889 __isl_take isl_union_set *uset);
7890 __isl_give isl_union_pw_qpolynomial_fold *
7891 isl_union_pw_qpolynomial_fold_subtract_domain_space(
7892 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7893 __isl_take isl_space *space);
7894 __isl_give isl_union_pw_qpolynomial_fold *
7895 isl_union_pw_qpolynomial_fold_subtract_domain(
7896 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7897 __isl_take isl_union_set *uset);
7899 C<isl_union_pw_aff_subtract_domain> is an alternative name for
7900 C<isl_union_pw_aff_subtract_domain_union_set>.
7901 Similarly for the other pairs of functions.
7905 #include <isl/space.h>
7906 __isl_give isl_space *isl_space_join(
7907 __isl_take isl_space *left,
7908 __isl_take isl_space *right);
7910 #include <isl/set.h>
7911 __isl_give isl_basic_set *isl_basic_set_apply(
7912 __isl_take isl_basic_set *bset,
7913 __isl_take isl_basic_map *bmap);
7914 __isl_give isl_set *isl_set_apply(
7915 __isl_take isl_set *set,
7916 __isl_take isl_map *map);
7918 #include <isl/union_set.h>
7919 __isl_give isl_union_set *isl_union_set_apply(
7920 __isl_take isl_union_set *uset,
7921 __isl_take isl_union_map *umap);
7923 #include <isl/map.h>
7924 __isl_give isl_basic_map *isl_basic_map_apply_domain(
7925 __isl_take isl_basic_map *bmap1,
7926 __isl_take isl_basic_map *bmap2);
7927 __isl_give isl_basic_map *isl_basic_map_apply_range(
7928 __isl_take isl_basic_map *bmap1,
7929 __isl_take isl_basic_map *bmap2);
7930 __isl_give isl_map *isl_map_apply_domain(
7931 __isl_take isl_map *map1,
7932 __isl_take isl_map *map2);
7933 __isl_give isl_map *isl_map_apply_range(
7934 __isl_take isl_map *map1,
7935 __isl_take isl_map *map2);
7937 #include <isl/union_map.h>
7938 __isl_give isl_union_map *isl_union_map_apply_domain(
7939 __isl_take isl_union_map *umap1,
7940 __isl_take isl_union_map *umap2);
7941 __isl_give isl_union_map *isl_union_map_apply_range(
7942 __isl_take isl_union_map *umap1,
7943 __isl_take isl_union_map *umap2);
7945 #include <isl/aff.h>
7946 __isl_give isl_union_pw_multi_aff *
7947 isl_union_pw_multi_aff_apply_union_pw_multi_aff(
7948 __isl_take isl_union_pw_multi_aff *upma1,
7949 __isl_take isl_union_pw_multi_aff *upma2);
7950 __isl_give isl_union_pw_aff *
7951 isl_multi_union_pw_aff_apply_aff(
7952 __isl_take isl_multi_union_pw_aff *mupa,
7953 __isl_take isl_aff *aff);
7954 __isl_give isl_union_pw_aff *
7955 isl_multi_union_pw_aff_apply_pw_aff(
7956 __isl_take isl_multi_union_pw_aff *mupa,
7957 __isl_take isl_pw_aff *pa);
7958 __isl_give isl_multi_union_pw_aff *
7959 isl_multi_union_pw_aff_apply_multi_aff(
7960 __isl_take isl_multi_union_pw_aff *mupa,
7961 __isl_take isl_multi_aff *ma);
7962 __isl_give isl_multi_union_pw_aff *
7963 isl_multi_union_pw_aff_apply_pw_multi_aff(
7964 __isl_take isl_multi_union_pw_aff *mupa,
7965 __isl_take isl_pw_multi_aff *pma);
7967 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
7968 over the shared domain of the elements of the input. The dimension is
7969 required to be greater than zero.
7970 The C<isl_multi_union_pw_aff> argument of
7971 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
7972 but only if the range of the C<isl_multi_aff> argument
7973 is also zero-dimensional.
7974 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
7976 #include <isl/polynomial.h>
7977 __isl_give isl_pw_qpolynomial_fold *
7978 isl_set_apply_pw_qpolynomial_fold(
7979 __isl_take isl_set *set,
7980 __isl_take isl_pw_qpolynomial_fold *pwf,
7982 __isl_give isl_pw_qpolynomial_fold *
7983 isl_map_apply_pw_qpolynomial_fold(
7984 __isl_take isl_map *map,
7985 __isl_take isl_pw_qpolynomial_fold *pwf,
7987 __isl_give isl_union_pw_qpolynomial_fold *
7988 isl_union_set_apply_union_pw_qpolynomial_fold(
7989 __isl_take isl_union_set *uset,
7990 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7992 __isl_give isl_union_pw_qpolynomial_fold *
7993 isl_union_map_apply_union_pw_qpolynomial_fold(
7994 __isl_take isl_union_map *umap,
7995 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7998 The functions taking a map
7999 compose the given map with the given piecewise quasipolynomial reduction.
8000 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
8001 over all elements in the intersection of the range of the map
8002 and the domain of the piecewise quasipolynomial reduction
8003 as a function of an element in the domain of the map.
8004 The functions taking a set compute a bound over all elements in the
8005 intersection of the set and the domain of the
8006 piecewise quasipolynomial reduction.
8010 #include <isl/set.h>
8011 __isl_give isl_basic_set *
8012 isl_basic_set_preimage_multi_aff(
8013 __isl_take isl_basic_set *bset,
8014 __isl_take isl_multi_aff *ma);
8015 __isl_give isl_set *isl_set_preimage_multi_aff(
8016 __isl_take isl_set *set,
8017 __isl_take isl_multi_aff *ma);
8018 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
8019 __isl_take isl_set *set,
8020 __isl_take isl_pw_multi_aff *pma);
8021 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
8022 __isl_take isl_set *set,
8023 __isl_take isl_multi_pw_aff *mpa);
8025 #include <isl/union_set.h>
8026 __isl_give isl_union_set *
8027 isl_union_set_preimage_multi_aff(
8028 __isl_take isl_union_set *uset,
8029 __isl_take isl_multi_aff *ma);
8030 __isl_give isl_union_set *
8031 isl_union_set_preimage_pw_multi_aff(
8032 __isl_take isl_union_set *uset,
8033 __isl_take isl_pw_multi_aff *pma);
8034 __isl_give isl_union_set *
8035 isl_union_set_preimage_union_pw_multi_aff(
8036 __isl_take isl_union_set *uset,
8037 __isl_take isl_union_pw_multi_aff *upma);
8039 #include <isl/map.h>
8040 __isl_give isl_basic_map *
8041 isl_basic_map_preimage_domain_multi_aff(
8042 __isl_take isl_basic_map *bmap,
8043 __isl_take isl_multi_aff *ma);
8044 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
8045 __isl_take isl_map *map,
8046 __isl_take isl_multi_aff *ma);
8047 __isl_give isl_map *isl_map_preimage_range_multi_aff(
8048 __isl_take isl_map *map,
8049 __isl_take isl_multi_aff *ma);
8050 __isl_give isl_map *
8051 isl_map_preimage_domain_pw_multi_aff(
8052 __isl_take isl_map *map,
8053 __isl_take isl_pw_multi_aff *pma);
8054 __isl_give isl_map *
8055 isl_map_preimage_range_pw_multi_aff(
8056 __isl_take isl_map *map,
8057 __isl_take isl_pw_multi_aff *pma);
8058 __isl_give isl_map *
8059 isl_map_preimage_domain_multi_pw_aff(
8060 __isl_take isl_map *map,
8061 __isl_take isl_multi_pw_aff *mpa);
8062 __isl_give isl_basic_map *
8063 isl_basic_map_preimage_range_multi_aff(
8064 __isl_take isl_basic_map *bmap,
8065 __isl_take isl_multi_aff *ma);
8067 #include <isl/union_map.h>
8068 __isl_give isl_union_map *
8069 isl_union_map_preimage_domain_multi_aff(
8070 __isl_take isl_union_map *umap,
8071 __isl_take isl_multi_aff *ma);
8072 __isl_give isl_union_map *
8073 isl_union_map_preimage_range_multi_aff(
8074 __isl_take isl_union_map *umap,
8075 __isl_take isl_multi_aff *ma);
8076 __isl_give isl_union_map *
8077 isl_union_map_preimage_domain_pw_multi_aff(
8078 __isl_take isl_union_map *umap,
8079 __isl_take isl_pw_multi_aff *pma);
8080 __isl_give isl_union_map *
8081 isl_union_map_preimage_range_pw_multi_aff(
8082 __isl_take isl_union_map *umap,
8083 __isl_take isl_pw_multi_aff *pma);
8084 __isl_give isl_union_map *
8085 isl_union_map_preimage_domain_union_pw_multi_aff(
8086 __isl_take isl_union_map *umap,
8087 __isl_take isl_union_pw_multi_aff *upma);
8088 __isl_give isl_union_map *
8089 isl_union_map_preimage_range_union_pw_multi_aff(
8090 __isl_take isl_union_map *umap,
8091 __isl_take isl_union_pw_multi_aff *upma);
8093 #include <isl/aff.h>
8094 __isl_give isl_pw_multi_aff *
8095 isl_pw_multi_aff_preimage_domain_wrapped_domain_pw_multi_aff(
8096 __isl_take isl_pw_multi_aff *pma1,
8097 __isl_take isl_pw_multi_aff *pma2);
8098 __isl_give isl_union_pw_multi_aff *
8099 isl_union_pw_multi_aff_preimage_domain_wrapped_domain_union_pw_multi_aff(
8100 __isl_take isl_union_pw_multi_aff *upma1,
8101 __isl_take isl_union_pw_multi_aff *upma2);
8103 These functions compute the preimage of the given set or map domain/range under
8104 the given function. In other words, the expression is plugged
8105 into the set description or into the domain/range of the map or function.
8109 #include <isl/aff.h>
8110 __isl_give isl_aff *isl_aff_pullback_aff(
8111 __isl_take isl_aff *aff1,
8112 __isl_take isl_aff *aff2);
8113 __isl_give isl_aff *isl_aff_pullback_multi_aff(
8114 __isl_take isl_aff *aff,
8115 __isl_take isl_multi_aff *ma);
8116 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
8117 __isl_take isl_pw_aff *pa,
8118 __isl_take isl_multi_aff *ma);
8119 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
8120 __isl_take isl_pw_aff *pa,
8121 __isl_take isl_pw_multi_aff *pma);
8122 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
8123 __isl_take isl_pw_aff *pa,
8124 __isl_take isl_multi_pw_aff *mpa);
8125 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
8126 __isl_take isl_multi_aff *ma1,
8127 __isl_take isl_multi_aff *ma2);
8128 __isl_give isl_pw_multi_aff *
8129 isl_pw_multi_aff_pullback_multi_aff(
8130 __isl_take isl_pw_multi_aff *pma,
8131 __isl_take isl_multi_aff *ma);
8132 __isl_give isl_multi_pw_aff *
8133 isl_multi_pw_aff_pullback_multi_aff(
8134 __isl_take isl_multi_pw_aff *mpa,
8135 __isl_take isl_multi_aff *ma);
8136 __isl_give isl_pw_multi_aff *
8137 isl_pw_multi_aff_pullback_pw_multi_aff(
8138 __isl_take isl_pw_multi_aff *pma1,
8139 __isl_take isl_pw_multi_aff *pma2);
8140 __isl_give isl_multi_pw_aff *
8141 isl_multi_pw_aff_pullback_pw_multi_aff(
8142 __isl_take isl_multi_pw_aff *mpa,
8143 __isl_take isl_pw_multi_aff *pma);
8144 __isl_give isl_multi_pw_aff *
8145 isl_multi_pw_aff_pullback_multi_pw_aff(
8146 __isl_take isl_multi_pw_aff *mpa1,
8147 __isl_take isl_multi_pw_aff *mpa2);
8148 __isl_give isl_union_pw_aff *
8149 isl_union_pw_aff_pullback_union_pw_multi_aff(
8150 __isl_take isl_union_pw_aff *upa,
8151 __isl_take isl_union_pw_multi_aff *upma);
8152 __isl_give isl_union_pw_multi_aff *
8153 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
8154 __isl_take isl_union_pw_multi_aff *upma1,
8155 __isl_take isl_union_pw_multi_aff *upma2);
8156 __isl_give isl_multi_union_pw_aff *
8157 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
8158 __isl_take isl_multi_union_pw_aff *mupa,
8159 __isl_take isl_union_pw_multi_aff *upma);
8161 These functions precompose the first expression by the second function.
8162 In other words, the second function is plugged
8163 into the first expression.
8167 #include <isl/aff.h>
8168 __isl_give isl_basic_set *isl_aff_eq_basic_set(
8169 __isl_take isl_aff *aff1,
8170 __isl_take isl_aff *aff2);
8171 __isl_give isl_set *isl_aff_eq_set(
8172 __isl_take isl_aff *aff1,
8173 __isl_take isl_aff *aff2);
8174 __isl_give isl_set *isl_aff_ne_set(
8175 __isl_take isl_aff *aff1,
8176 __isl_take isl_aff *aff2);
8177 __isl_give isl_basic_set *isl_aff_le_basic_set(
8178 __isl_take isl_aff *aff1,
8179 __isl_take isl_aff *aff2);
8180 __isl_give isl_set *isl_aff_le_set(
8181 __isl_take isl_aff *aff1,
8182 __isl_take isl_aff *aff2);
8183 __isl_give isl_basic_set *isl_aff_lt_basic_set(
8184 __isl_take isl_aff *aff1,
8185 __isl_take isl_aff *aff2);
8186 __isl_give isl_set *isl_aff_lt_set(
8187 __isl_take isl_aff *aff1,
8188 __isl_take isl_aff *aff2);
8189 __isl_give isl_basic_set *isl_aff_ge_basic_set(
8190 __isl_take isl_aff *aff1,
8191 __isl_take isl_aff *aff2);
8192 __isl_give isl_set *isl_aff_ge_set(
8193 __isl_take isl_aff *aff1,
8194 __isl_take isl_aff *aff2);
8195 __isl_give isl_basic_set *isl_aff_gt_basic_set(
8196 __isl_take isl_aff *aff1,
8197 __isl_take isl_aff *aff2);
8198 __isl_give isl_set *isl_aff_gt_set(
8199 __isl_take isl_aff *aff1,
8200 __isl_take isl_aff *aff2);
8201 __isl_give isl_set *isl_pw_aff_eq_set(
8202 __isl_take isl_pw_aff *pwaff1,
8203 __isl_take isl_pw_aff *pwaff2);
8204 __isl_give isl_set *isl_pw_aff_ne_set(
8205 __isl_take isl_pw_aff *pwaff1,
8206 __isl_take isl_pw_aff *pwaff2);
8207 __isl_give isl_set *isl_pw_aff_le_set(
8208 __isl_take isl_pw_aff *pwaff1,
8209 __isl_take isl_pw_aff *pwaff2);
8210 __isl_give isl_set *isl_pw_aff_lt_set(
8211 __isl_take isl_pw_aff *pwaff1,
8212 __isl_take isl_pw_aff *pwaff2);
8213 __isl_give isl_set *isl_pw_aff_ge_set(
8214 __isl_take isl_pw_aff *pwaff1,
8215 __isl_take isl_pw_aff *pwaff2);
8216 __isl_give isl_set *isl_pw_aff_gt_set(
8217 __isl_take isl_pw_aff *pwaff1,
8218 __isl_take isl_pw_aff *pwaff2);
8220 __isl_give isl_set *isl_multi_aff_lex_le_set(
8221 __isl_take isl_multi_aff *ma1,
8222 __isl_take isl_multi_aff *ma2);
8223 __isl_give isl_set *isl_multi_aff_lex_lt_set(
8224 __isl_take isl_multi_aff *ma1,
8225 __isl_take isl_multi_aff *ma2);
8226 __isl_give isl_set *isl_multi_aff_lex_ge_set(
8227 __isl_take isl_multi_aff *ma1,
8228 __isl_take isl_multi_aff *ma2);
8229 __isl_give isl_set *isl_multi_aff_lex_gt_set(
8230 __isl_take isl_multi_aff *ma1,
8231 __isl_take isl_multi_aff *ma2);
8233 __isl_give isl_set *isl_pw_aff_list_eq_set(
8234 __isl_take isl_pw_aff_list *list1,
8235 __isl_take isl_pw_aff_list *list2);
8236 __isl_give isl_set *isl_pw_aff_list_ne_set(
8237 __isl_take isl_pw_aff_list *list1,
8238 __isl_take isl_pw_aff_list *list2);
8239 __isl_give isl_set *isl_pw_aff_list_le_set(
8240 __isl_take isl_pw_aff_list *list1,
8241 __isl_take isl_pw_aff_list *list2);
8242 __isl_give isl_set *isl_pw_aff_list_lt_set(
8243 __isl_take isl_pw_aff_list *list1,
8244 __isl_take isl_pw_aff_list *list2);
8245 __isl_give isl_set *isl_pw_aff_list_ge_set(
8246 __isl_take isl_pw_aff_list *list1,
8247 __isl_take isl_pw_aff_list *list2);
8248 __isl_give isl_set *isl_pw_aff_list_gt_set(
8249 __isl_take isl_pw_aff_list *list1,
8250 __isl_take isl_pw_aff_list *list2);
8252 The function C<isl_aff_ge_basic_set> returns a basic set
8253 containing those elements in the shared space
8254 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
8255 The function C<isl_pw_aff_ge_set> returns a set
8256 containing those elements in the shared domain
8257 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
8258 greater than or equal to C<pwaff2>.
8259 The function C<isl_multi_aff_lex_le_set> returns a set
8260 containing those elements in the shared domain space
8261 where C<ma1> is lexicographically smaller than or
8263 The functions operating on C<isl_pw_aff_list> apply the corresponding
8264 C<isl_pw_aff> function to each pair of elements in the two lists.
8266 #include <isl/aff.h>
8267 __isl_give isl_map *isl_pw_aff_eq_map(
8268 __isl_take isl_pw_aff *pa1,
8269 __isl_take isl_pw_aff *pa2);
8270 __isl_give isl_map *isl_pw_aff_le_map(
8271 __isl_take isl_pw_aff *pa1,
8272 __isl_take isl_pw_aff *pa2);
8273 __isl_give isl_map *isl_pw_aff_lt_map(
8274 __isl_take isl_pw_aff *pa1,
8275 __isl_take isl_pw_aff *pa2);
8276 __isl_give isl_map *isl_pw_aff_ge_map(
8277 __isl_take isl_pw_aff *pa1,
8278 __isl_take isl_pw_aff *pa2);
8279 __isl_give isl_map *isl_pw_aff_gt_map(
8280 __isl_take isl_pw_aff *pa1,
8281 __isl_take isl_pw_aff *pa2);
8283 __isl_give isl_map *isl_multi_pw_aff_eq_map(
8284 __isl_take isl_multi_pw_aff *mpa1,
8285 __isl_take isl_multi_pw_aff *mpa2);
8286 __isl_give isl_map *isl_multi_pw_aff_lex_le_map(
8287 __isl_take isl_multi_pw_aff *mpa1,
8288 __isl_take isl_multi_pw_aff *mpa2);
8289 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
8290 __isl_take isl_multi_pw_aff *mpa1,
8291 __isl_take isl_multi_pw_aff *mpa2);
8292 __isl_give isl_map *isl_multi_pw_aff_lex_ge_map(
8293 __isl_take isl_multi_pw_aff *mpa1,
8294 __isl_take isl_multi_pw_aff *mpa2);
8295 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
8296 __isl_take isl_multi_pw_aff *mpa1,
8297 __isl_take isl_multi_pw_aff *mpa2);
8299 These functions return a map between domain elements of the arguments
8300 where the function values satisfy the given relation.
8302 #include <isl/map.h>
8303 __isl_give isl_map *isl_map_eq_at_multi_pw_aff(
8304 __isl_take isl_map *map,
8305 __isl_take isl_multi_pw_aff *mpa);
8306 __isl_give isl_map *isl_map_lex_lt_at_multi_pw_aff(
8307 __isl_take isl_map *map,
8308 __isl_take isl_multi_pw_aff *mpa);
8309 __isl_give isl_map *isl_map_lex_le_at_multi_pw_aff(
8310 __isl_take isl_map *map,
8311 __isl_take isl_multi_pw_aff *mpa);
8312 __isl_give isl_map *isl_map_lex_gt_at_multi_pw_aff(
8313 __isl_take isl_map *map,
8314 __isl_take isl_multi_pw_aff *mpa);
8315 __isl_give isl_map *isl_map_lex_ge_at_multi_pw_aff(
8316 __isl_take isl_map *map,
8317 __isl_take isl_multi_pw_aff *mpa);
8319 #include <isl/union_map.h>
8320 __isl_give isl_union_map *
8321 isl_union_map_eq_at_multi_union_pw_aff(
8322 __isl_take isl_union_map *umap,
8323 __isl_take isl_multi_union_pw_aff *mupa);
8324 __isl_give isl_union_map *
8325 isl_union_map_lex_lt_at_multi_union_pw_aff(
8326 __isl_take isl_union_map *umap,
8327 __isl_take isl_multi_union_pw_aff *mupa);
8328 __isl_give isl_union_map *
8329 isl_union_map_lex_le_at_multi_union_pw_aff(
8330 __isl_take isl_union_map *umap,
8331 __isl_take isl_multi_union_pw_aff *mupa);
8332 __isl_give isl_union_map *
8333 isl_union_map_lex_gt_at_multi_union_pw_aff(
8334 __isl_take isl_union_map *umap,
8335 __isl_take isl_multi_union_pw_aff *mupa);
8336 __isl_give isl_union_map *
8337 isl_union_map_lex_ge_at_multi_union_pw_aff(
8338 __isl_take isl_union_map *umap,
8339 __isl_take isl_multi_union_pw_aff *mupa);
8341 These functions select the subset of elements in the union map
8342 that have an equal or lexicographically smaller or greater function value.
8344 =item * Cartesian Product
8346 #include <isl/space.h>
8347 __isl_give isl_space *isl_space_product(
8348 __isl_take isl_space *space1,
8349 __isl_take isl_space *space2);
8350 __isl_give isl_space *isl_space_domain_product(
8351 __isl_take isl_space *space1,
8352 __isl_take isl_space *space2);
8353 __isl_give isl_space *isl_space_range_product(
8354 __isl_take isl_space *space1,
8355 __isl_take isl_space *space2);
8358 C<isl_space_product>, C<isl_space_domain_product>
8359 and C<isl_space_range_product> take pairs or relation spaces and
8360 produce a single relations space, where either the domain, the range
8361 or both domain and range are wrapped spaces of relations between
8362 the domains and/or ranges of the input spaces.
8363 If the product is only constructed over the domain or the range
8364 then the ranges or the domains of the inputs should be the same.
8365 The function C<isl_space_product> also accepts a pair of set spaces,
8366 in which case it returns a wrapped space of a relation between the
8369 #include <isl/set.h>
8370 __isl_give isl_set *isl_set_product(
8371 __isl_take isl_set *set1,
8372 __isl_take isl_set *set2);
8374 #include <isl/map.h>
8375 __isl_give isl_basic_map *isl_basic_map_domain_product(
8376 __isl_take isl_basic_map *bmap1,
8377 __isl_take isl_basic_map *bmap2);
8378 __isl_give isl_basic_map *isl_basic_map_range_product(
8379 __isl_take isl_basic_map *bmap1,
8380 __isl_take isl_basic_map *bmap2);
8381 __isl_give isl_basic_map *isl_basic_map_product(
8382 __isl_take isl_basic_map *bmap1,
8383 __isl_take isl_basic_map *bmap2);
8384 __isl_give isl_map *isl_map_domain_product(
8385 __isl_take isl_map *map1,
8386 __isl_take isl_map *map2);
8387 __isl_give isl_map *isl_map_range_product(
8388 __isl_take isl_map *map1,
8389 __isl_take isl_map *map2);
8390 __isl_give isl_map *isl_map_product(
8391 __isl_take isl_map *map1,
8392 __isl_take isl_map *map2);
8394 #include <isl/union_set.h>
8395 __isl_give isl_union_set *isl_union_set_product(
8396 __isl_take isl_union_set *uset1,
8397 __isl_take isl_union_set *uset2);
8399 #include <isl/union_map.h>
8400 __isl_give isl_union_map *isl_union_map_domain_product(
8401 __isl_take isl_union_map *umap1,
8402 __isl_take isl_union_map *umap2);
8403 __isl_give isl_union_map *isl_union_map_range_product(
8404 __isl_take isl_union_map *umap1,
8405 __isl_take isl_union_map *umap2);
8406 __isl_give isl_union_map *isl_union_map_product(
8407 __isl_take isl_union_map *umap1,
8408 __isl_take isl_union_map *umap2);
8411 __isl_give isl_multi_id *isl_multi_id_range_product(
8412 __isl_take isl_multi_id *mi1,
8413 __isl_take isl_multi_id *mi2);
8415 #include <isl/val.h>
8416 __isl_give isl_multi_val *isl_multi_val_range_product(
8417 __isl_take isl_multi_val *mv1,
8418 __isl_take isl_multi_val *mv2);
8419 __isl_give isl_multi_val *isl_multi_val_product(
8420 __isl_take isl_multi_val *mv1,
8421 __isl_take isl_multi_val *mv2);
8423 #include <isl/aff.h>
8424 __isl_give isl_multi_aff *isl_multi_aff_range_product(
8425 __isl_take isl_multi_aff *ma1,
8426 __isl_take isl_multi_aff *ma2);
8427 __isl_give isl_multi_aff *isl_multi_aff_product(
8428 __isl_take isl_multi_aff *ma1,
8429 __isl_take isl_multi_aff *ma2);
8430 __isl_give isl_multi_pw_aff *
8431 isl_multi_pw_aff_range_product(
8432 __isl_take isl_multi_pw_aff *mpa1,
8433 __isl_take isl_multi_pw_aff *mpa2);
8434 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
8435 __isl_take isl_multi_pw_aff *mpa1,
8436 __isl_take isl_multi_pw_aff *mpa2);
8437 __isl_give isl_pw_multi_aff *
8438 isl_pw_multi_aff_range_product(
8439 __isl_take isl_pw_multi_aff *pma1,
8440 __isl_take isl_pw_multi_aff *pma2);
8441 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
8442 __isl_take isl_pw_multi_aff *pma1,
8443 __isl_take isl_pw_multi_aff *pma2);
8444 __isl_give isl_union_pw_multi_aff *
8445 isl_union_pw_multi_aff_range_product(
8446 __isl_take isl_union_pw_multi_aff *upma1,
8447 __isl_take isl_union_pw_multi_aff *upma2);
8448 __isl_give isl_multi_union_pw_aff *
8449 isl_multi_union_pw_aff_range_product(
8450 __isl_take isl_multi_union_pw_aff *mupa1,
8451 __isl_take isl_multi_union_pw_aff *mupa2);
8453 The above functions compute the cross product of the given
8454 sets, relations or functions. The domains and ranges of the results
8455 are wrapped maps between domains and ranges of the inputs.
8456 To obtain a ``flat'' product, use the following functions
8459 #include <isl/set.h>
8460 __isl_give isl_basic_set *isl_basic_set_flat_product(
8461 __isl_take isl_basic_set *bset1,
8462 __isl_take isl_basic_set *bset2);
8463 __isl_give isl_set *isl_set_flat_product(
8464 __isl_take isl_set *set1,
8465 __isl_take isl_set *set2);
8467 #include <isl/map.h>
8468 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
8469 __isl_take isl_basic_map *bmap1,
8470 __isl_take isl_basic_map *bmap2);
8471 __isl_give isl_map *isl_map_flat_domain_product(
8472 __isl_take isl_map *map1,
8473 __isl_take isl_map *map2);
8474 __isl_give isl_map *isl_map_flat_range_product(
8475 __isl_take isl_map *map1,
8476 __isl_take isl_map *map2);
8477 __isl_give isl_basic_map *isl_basic_map_flat_product(
8478 __isl_take isl_basic_map *bmap1,
8479 __isl_take isl_basic_map *bmap2);
8480 __isl_give isl_map *isl_map_flat_product(
8481 __isl_take isl_map *map1,
8482 __isl_take isl_map *map2);
8484 #include <isl/union_map.h>
8485 __isl_give isl_union_map *
8486 isl_union_map_flat_domain_product(
8487 __isl_take isl_union_map *umap1,
8488 __isl_take isl_union_map *umap2);
8489 __isl_give isl_union_map *
8490 isl_union_map_flat_range_product(
8491 __isl_take isl_union_map *umap1,
8492 __isl_take isl_union_map *umap2);
8495 __isl_give isl_multi_id *
8496 isl_multi_id_flat_range_product(
8497 __isl_take isl_multi_id *mi1,
8498 __isl_take isl_multi_id *mi2);
8500 #include <isl/val.h>
8501 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
8502 __isl_take isl_multi_val *mv1,
8503 __isl_take isl_multi_val *mv2);
8505 #include <isl/aff.h>
8506 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
8507 __isl_take isl_multi_aff *ma1,
8508 __isl_take isl_multi_aff *ma2);
8509 __isl_give isl_pw_multi_aff *
8510 isl_pw_multi_aff_flat_range_product(
8511 __isl_take isl_pw_multi_aff *pma1,
8512 __isl_take isl_pw_multi_aff *pma2);
8513 __isl_give isl_multi_pw_aff *
8514 isl_multi_pw_aff_flat_range_product(
8515 __isl_take isl_multi_pw_aff *mpa1,
8516 __isl_take isl_multi_pw_aff *mpa2);
8517 __isl_give isl_union_pw_multi_aff *
8518 isl_union_pw_multi_aff_flat_range_product(
8519 __isl_take isl_union_pw_multi_aff *upma1,
8520 __isl_take isl_union_pw_multi_aff *upma2);
8521 __isl_give isl_multi_union_pw_aff *
8522 isl_multi_union_pw_aff_flat_range_product(
8523 __isl_take isl_multi_union_pw_aff *mupa1,
8524 __isl_take isl_multi_union_pw_aff *mupa2);
8526 #include <isl/space.h>
8527 __isl_give isl_space *isl_space_factor_domain(
8528 __isl_take isl_space *space);
8529 __isl_give isl_space *isl_space_factor_range(
8530 __isl_take isl_space *space);
8531 __isl_give isl_space *isl_space_domain_factor_domain(
8532 __isl_take isl_space *space);
8533 __isl_give isl_space *isl_space_domain_factor_range(
8534 __isl_take isl_space *space);
8535 __isl_give isl_space *isl_space_range_factor_domain(
8536 __isl_take isl_space *space);
8537 __isl_give isl_space *isl_space_range_factor_range(
8538 __isl_take isl_space *space);
8540 The functions C<isl_space_range_factor_domain> and
8541 C<isl_space_range_factor_range> extract the two arguments from
8542 the result of a call to C<isl_space_range_product>.
8544 The arguments of a call to a product can be extracted
8545 from the result using the following functions.
8547 #include <isl/map.h>
8548 __isl_give isl_map *isl_map_factor_domain(
8549 __isl_take isl_map *map);
8550 __isl_give isl_map *isl_map_factor_range(
8551 __isl_take isl_map *map);
8552 __isl_give isl_map *isl_map_domain_factor_domain(
8553 __isl_take isl_map *map);
8554 __isl_give isl_map *isl_map_domain_factor_range(
8555 __isl_take isl_map *map);
8556 __isl_give isl_map *isl_map_range_factor_domain(
8557 __isl_take isl_map *map);
8558 __isl_give isl_map *isl_map_range_factor_range(
8559 __isl_take isl_map *map);
8561 #include <isl/union_map.h>
8562 __isl_give isl_union_map *isl_union_map_factor_domain(
8563 __isl_take isl_union_map *umap);
8564 __isl_give isl_union_map *isl_union_map_factor_range(
8565 __isl_take isl_union_map *umap);
8566 __isl_give isl_union_map *
8567 isl_union_map_domain_factor_domain(
8568 __isl_take isl_union_map *umap);
8569 __isl_give isl_union_map *
8570 isl_union_map_domain_factor_range(
8571 __isl_take isl_union_map *umap);
8572 __isl_give isl_union_map *
8573 isl_union_map_range_factor_domain(
8574 __isl_take isl_union_map *umap);
8575 __isl_give isl_union_map *
8576 isl_union_map_range_factor_range(
8577 __isl_take isl_union_map *umap);
8580 __isl_give isl_multi_id *isl_multi_id_factor_range(
8581 __isl_take isl_multi_id *mi);
8582 __isl_give isl_multi_id *
8583 isl_multi_id_range_factor_domain(
8584 __isl_take isl_multi_id *mi);
8585 __isl_give isl_multi_id *
8586 isl_multi_id_range_factor_range(
8587 __isl_take isl_multi_id *mi);
8589 #include <isl/val.h>
8590 __isl_give isl_multi_val *isl_multi_val_factor_range(
8591 __isl_take isl_multi_val *mv);
8592 __isl_give isl_multi_val *
8593 isl_multi_val_range_factor_domain(
8594 __isl_take isl_multi_val *mv);
8595 __isl_give isl_multi_val *
8596 isl_multi_val_range_factor_range(
8597 __isl_take isl_multi_val *mv);
8599 #include <isl/aff.h>
8600 __isl_give isl_multi_aff *isl_multi_aff_factor_range(
8601 __isl_take isl_multi_aff *ma);
8602 __isl_give isl_multi_aff *
8603 isl_multi_aff_range_factor_domain(
8604 __isl_take isl_multi_aff *ma);
8605 __isl_give isl_multi_aff *
8606 isl_multi_aff_range_factor_range(
8607 __isl_take isl_multi_aff *ma);
8608 __isl_give isl_multi_pw_aff *
8609 isl_multi_pw_aff_factor_range(
8610 __isl_take isl_multi_pw_aff *mpa);
8611 __isl_give isl_multi_pw_aff *
8612 isl_multi_pw_aff_range_factor_domain(
8613 __isl_take isl_multi_pw_aff *mpa);
8614 __isl_give isl_multi_pw_aff *
8615 isl_multi_pw_aff_range_factor_range(
8616 __isl_take isl_multi_pw_aff *mpa);
8617 __isl_give isl_pw_multi_aff *
8618 isl_pw_multi_aff_range_factor_domain(
8619 __isl_take isl_pw_multi_aff *pma);
8620 __isl_give isl_pw_multi_aff *
8621 isl_pw_multi_aff_range_factor_range(
8622 __isl_take isl_pw_multi_aff *pma);
8623 __isl_give isl_union_pw_multi_aff *
8624 isl_union_pw_multi_aff_range_factor_domain(
8625 __isl_take isl_union_pw_multi_aff *upma);
8626 __isl_give isl_union_pw_multi_aff *
8627 isl_union_pw_multi_aff_range_factor_range(
8628 __isl_take isl_union_pw_multi_aff *upma);
8629 __isl_give isl_multi_union_pw_aff *
8630 isl_multi_union_pw_aff_factor_range(
8631 __isl_take isl_multi_union_pw_aff *mupa);
8632 __isl_give isl_multi_union_pw_aff *
8633 isl_multi_union_pw_aff_range_factor_domain(
8634 __isl_take isl_multi_union_pw_aff *mupa);
8635 __isl_give isl_multi_union_pw_aff *
8636 isl_multi_union_pw_aff_range_factor_range(
8637 __isl_take isl_multi_union_pw_aff *mupa);
8639 The splice functions are a generalization of the flat product functions,
8640 where the second argument may be inserted at any position inside
8641 the first argument rather than being placed at the end.
8642 The functions C<isl_multi_val_factor_range>,
8643 C<isl_multi_aff_factor_range>,
8644 C<isl_multi_pw_aff_factor_range> and
8645 C<isl_multi_union_pw_aff_factor_range>
8646 take functions that live in a set space.
8649 __isl_give isl_multi_id *isl_multi_id_range_splice(
8650 __isl_take isl_multi_id *mi1, unsigned pos,
8651 __isl_take isl_multi_id *mi2);
8653 #include <isl/val.h>
8654 __isl_give isl_multi_val *isl_multi_val_range_splice(
8655 __isl_take isl_multi_val *mv1, unsigned pos,
8656 __isl_take isl_multi_val *mv2);
8658 #include <isl/aff.h>
8659 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
8660 __isl_take isl_multi_aff *ma1, unsigned pos,
8661 __isl_take isl_multi_aff *ma2);
8662 __isl_give isl_multi_aff *isl_multi_aff_splice(
8663 __isl_take isl_multi_aff *ma1,
8664 unsigned in_pos, unsigned out_pos,
8665 __isl_take isl_multi_aff *ma2);
8666 __isl_give isl_multi_pw_aff *
8667 isl_multi_pw_aff_range_splice(
8668 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
8669 __isl_take isl_multi_pw_aff *mpa2);
8670 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
8671 __isl_take isl_multi_pw_aff *mpa1,
8672 unsigned in_pos, unsigned out_pos,
8673 __isl_take isl_multi_pw_aff *mpa2);
8674 __isl_give isl_multi_union_pw_aff *
8675 isl_multi_union_pw_aff_range_splice(
8676 __isl_take isl_multi_union_pw_aff *mupa1,
8678 __isl_take isl_multi_union_pw_aff *mupa2);
8680 =item * Simplification
8682 When applied to a set or relation,
8683 the gist operation returns a set or relation that has the
8684 same intersection with the context as the input set or relation.
8685 Any implicit equality in the intersection is made explicit in the result,
8686 while all inequalities that are redundant with respect to the intersection
8688 In case of union sets and relations, the gist operation is performed
8691 When applied to a function,
8692 the gist operation applies the set gist operation to each of
8693 the cells in the domain of the input piecewise expression.
8694 The context is also exploited
8695 to simplify the expression associated to each cell.
8697 #include <isl/set.h>
8698 __isl_give isl_basic_set *isl_basic_set_gist(
8699 __isl_take isl_basic_set *bset,
8700 __isl_take isl_basic_set *context);
8701 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
8702 __isl_take isl_set *context);
8703 __isl_give isl_set *isl_set_gist_params(
8704 __isl_take isl_set *set,
8705 __isl_take isl_set *context);
8707 #include <isl/map.h>
8708 __isl_give isl_basic_map *isl_basic_map_gist(
8709 __isl_take isl_basic_map *bmap,
8710 __isl_take isl_basic_map *context);
8711 __isl_give isl_basic_map *isl_basic_map_gist_domain(
8712 __isl_take isl_basic_map *bmap,
8713 __isl_take isl_basic_set *context);
8714 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
8715 __isl_take isl_map *context);
8716 __isl_give isl_map *isl_map_gist_params(
8717 __isl_take isl_map *map,
8718 __isl_take isl_set *context);
8719 __isl_give isl_map *isl_map_gist_domain(
8720 __isl_take isl_map *map,
8721 __isl_take isl_set *context);
8722 __isl_give isl_map *isl_map_gist_range(
8723 __isl_take isl_map *map,
8724 __isl_take isl_set *context);
8726 #include <isl/union_set.h>
8727 __isl_give isl_union_set *isl_union_set_gist(
8728 __isl_take isl_union_set *uset,
8729 __isl_take isl_union_set *context);
8730 __isl_give isl_union_set *isl_union_set_gist_params(
8731 __isl_take isl_union_set *uset,
8732 __isl_take isl_set *set);
8734 #include <isl/union_map.h>
8735 __isl_give isl_union_map *isl_union_map_gist(
8736 __isl_take isl_union_map *umap,
8737 __isl_take isl_union_map *context);
8738 __isl_give isl_union_map *isl_union_map_gist_params(
8739 __isl_take isl_union_map *umap,
8740 __isl_take isl_set *set);
8741 __isl_give isl_union_map *isl_union_map_gist_domain(
8742 __isl_take isl_union_map *umap,
8743 __isl_take isl_union_set *uset);
8744 __isl_give isl_union_map *isl_union_map_gist_range(
8745 __isl_take isl_union_map *umap,
8746 __isl_take isl_union_set *uset);
8748 #include <isl/aff.h>
8749 __isl_give isl_aff *isl_aff_gist_params(
8750 __isl_take isl_aff *aff,
8751 __isl_take isl_set *context);
8752 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
8753 __isl_take isl_set *context);
8754 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
8755 __isl_take isl_multi_aff *maff,
8756 __isl_take isl_set *context);
8757 __isl_give isl_multi_aff *isl_multi_aff_gist(
8758 __isl_take isl_multi_aff *maff,
8759 __isl_take isl_set *context);
8760 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
8761 __isl_take isl_pw_aff *pwaff,
8762 __isl_take isl_set *context);
8763 __isl_give isl_pw_aff *isl_pw_aff_gist(
8764 __isl_take isl_pw_aff *pwaff,
8765 __isl_take isl_set *context);
8766 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
8767 __isl_take isl_pw_multi_aff *pma,
8768 __isl_take isl_set *set);
8769 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
8770 __isl_take isl_pw_multi_aff *pma,
8771 __isl_take isl_set *set);
8772 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
8773 __isl_take isl_multi_pw_aff *mpa,
8774 __isl_take isl_set *set);
8775 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
8776 __isl_take isl_multi_pw_aff *mpa,
8777 __isl_take isl_set *set);
8778 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
8779 __isl_take isl_union_pw_aff *upa,
8780 __isl_take isl_union_set *context);
8781 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
8782 __isl_take isl_union_pw_aff *upa,
8783 __isl_take isl_set *context);
8784 __isl_give isl_union_pw_multi_aff *
8785 isl_union_pw_multi_aff_gist_params(
8786 __isl_take isl_union_pw_multi_aff *upma,
8787 __isl_take isl_set *context);
8788 __isl_give isl_union_pw_multi_aff *
8789 isl_union_pw_multi_aff_gist(
8790 __isl_take isl_union_pw_multi_aff *upma,
8791 __isl_take isl_union_set *context);
8792 __isl_give isl_multi_union_pw_aff *
8793 isl_multi_union_pw_aff_gist_params(
8794 __isl_take isl_multi_union_pw_aff *mupa,
8795 __isl_take isl_set *context);
8796 __isl_give isl_multi_union_pw_aff *
8797 isl_multi_union_pw_aff_gist(
8798 __isl_take isl_multi_union_pw_aff *mupa,
8799 __isl_take isl_union_set *context);
8801 #include <isl/polynomial.h>
8802 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
8803 __isl_take isl_qpolynomial *qp,
8804 __isl_take isl_set *context);
8805 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
8806 __isl_take isl_qpolynomial *qp,
8807 __isl_take isl_set *context);
8808 __isl_give isl_qpolynomial_fold *
8809 isl_qpolynomial_fold_gist_params(
8810 __isl_take isl_qpolynomial_fold *fold,
8811 __isl_take isl_set *context);
8812 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
8813 __isl_take isl_qpolynomial_fold *fold,
8814 __isl_take isl_set *context);
8815 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
8816 __isl_take isl_pw_qpolynomial *pwqp,
8817 __isl_take isl_set *context);
8818 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
8819 __isl_take isl_pw_qpolynomial *pwqp,
8820 __isl_take isl_set *context);
8821 __isl_give isl_pw_qpolynomial_fold *
8822 isl_pw_qpolynomial_fold_gist(
8823 __isl_take isl_pw_qpolynomial_fold *pwf,
8824 __isl_take isl_set *context);
8825 __isl_give isl_pw_qpolynomial_fold *
8826 isl_pw_qpolynomial_fold_gist_params(
8827 __isl_take isl_pw_qpolynomial_fold *pwf,
8828 __isl_take isl_set *context);
8829 __isl_give isl_union_pw_qpolynomial *
8830 isl_union_pw_qpolynomial_gist_params(
8831 __isl_take isl_union_pw_qpolynomial *upwqp,
8832 __isl_take isl_set *context);
8833 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
8834 __isl_take isl_union_pw_qpolynomial *upwqp,
8835 __isl_take isl_union_set *context);
8836 __isl_give isl_union_pw_qpolynomial_fold *
8837 isl_union_pw_qpolynomial_fold_gist(
8838 __isl_take isl_union_pw_qpolynomial_fold *upwf,
8839 __isl_take isl_union_set *context);
8840 __isl_give isl_union_pw_qpolynomial_fold *
8841 isl_union_pw_qpolynomial_fold_gist_params(
8842 __isl_take isl_union_pw_qpolynomial_fold *upwf,
8843 __isl_take isl_set *context);
8845 =item * Binary Arithmetic Operations
8847 #include <isl/set.h>
8848 __isl_give isl_set *isl_set_sum(
8849 __isl_take isl_set *set1,
8850 __isl_take isl_set *set2);
8851 #include <isl/map.h>
8852 __isl_give isl_map *isl_map_sum(
8853 __isl_take isl_map *map1,
8854 __isl_take isl_map *map2);
8856 C<isl_set_sum> computes the Minkowski sum of its two arguments,
8857 i.e., the set containing the sums of pairs of elements from
8858 C<set1> and C<set2>.
8859 The domain of the result of C<isl_map_sum> is the intersection
8860 of the domains of its two arguments. The corresponding range
8861 elements are the sums of the corresponding range elements
8862 in the two arguments.
8864 #include <isl/val.h>
8865 __isl_give isl_multi_val *isl_multi_val_add(
8866 __isl_take isl_multi_val *mv1,
8867 __isl_take isl_multi_val *mv2);
8868 __isl_give isl_multi_val *isl_multi_val_sub(
8869 __isl_take isl_multi_val *mv1,
8870 __isl_take isl_multi_val *mv2);
8871 __isl_give isl_multi_val *isl_multi_val_min(
8872 __isl_take isl_multi_val *mv1,
8873 __isl_take isl_multi_val *mv2);
8874 __isl_give isl_multi_val *isl_multi_val_max(
8875 __isl_take isl_multi_val *mv1,
8876 __isl_take isl_multi_val *mv2);
8878 #include <isl/aff.h>
8879 __isl_give isl_aff *isl_aff_add(
8880 __isl_take isl_aff *aff1,
8881 __isl_take isl_aff *aff2);
8882 __isl_give isl_multi_aff *isl_multi_aff_add(
8883 __isl_take isl_multi_aff *maff1,
8884 __isl_take isl_multi_aff *maff2);
8885 __isl_give isl_pw_aff *isl_pw_aff_add(
8886 __isl_take isl_pw_aff *pwaff1,
8887 __isl_take isl_pw_aff *pwaff2);
8888 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add(
8889 __isl_take isl_multi_pw_aff *mpa1,
8890 __isl_take isl_multi_pw_aff *mpa2);
8891 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
8892 __isl_take isl_pw_multi_aff *pma1,
8893 __isl_take isl_pw_multi_aff *pma2);
8894 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
8895 __isl_take isl_union_pw_aff *upa1,
8896 __isl_take isl_union_pw_aff *upa2);
8897 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
8898 __isl_take isl_union_pw_multi_aff *upma1,
8899 __isl_take isl_union_pw_multi_aff *upma2);
8900 __isl_give isl_multi_union_pw_aff *
8901 isl_multi_union_pw_aff_add(
8902 __isl_take isl_multi_union_pw_aff *mupa1,
8903 __isl_take isl_multi_union_pw_aff *mupa2);
8904 __isl_give isl_pw_aff *isl_pw_aff_add_constant_val(
8905 __isl_take isl_pw_aff *pa,
8906 __isl_take isl_val *v);
8907 __isl_give isl_multi_aff *
8908 isl_multi_aff_add_constant_val(
8909 __isl_take isl_multi_aff *pa,
8910 __isl_take isl_val *v);
8911 __isl_give isl_pw_multi_aff *
8912 isl_pw_multi_aff_add_constant_val(
8913 __isl_take isl_pw_multi_aff *pma,
8914 __isl_take isl_val *v);
8915 __isl_give isl_pw_multi_aff *
8916 isl_pw_multi_aff_add_constant_multi_val(
8917 __isl_take isl_pw_multi_aff *pma,
8918 __isl_take isl_multi_val *mv);
8919 __isl_give isl_multi_pw_aff *
8920 isl_multi_pw_aff_add_constant_val(
8921 __isl_take isl_multi_pw_aff *mpa,
8922 __isl_take isl_val *v);
8923 __isl_give isl_multi_aff *
8924 isl_multi_aff_add_constant_multi_val(
8925 __isl_take isl_multi_aff *pa,
8926 __isl_take isl_multi_val *mv);
8927 __isl_give isl_multi_pw_aff *
8928 isl_multi_pw_aff_add_constant_multi_val(
8929 __isl_take isl_multi_pw_aff *mpa,
8930 __isl_take isl_multi_val *mv);
8931 __isl_give isl_pw_aff *isl_pw_aff_min(
8932 __isl_take isl_pw_aff *pwaff1,
8933 __isl_take isl_pw_aff *pwaff2);
8934 __isl_give isl_pw_aff *isl_pw_aff_max(
8935 __isl_take isl_pw_aff *pwaff1,
8936 __isl_take isl_pw_aff *pwaff2);
8937 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_min(
8938 __isl_take isl_multi_pw_aff *mpa1,
8939 __isl_take isl_multi_pw_aff *mpa2);
8940 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_max(
8941 __isl_take isl_multi_pw_aff *mpa1,
8942 __isl_take isl_multi_pw_aff *mpa2);
8943 __isl_give isl_aff *isl_aff_sub(
8944 __isl_take isl_aff *aff1,
8945 __isl_take isl_aff *aff2);
8946 __isl_give isl_multi_aff *isl_multi_aff_sub(
8947 __isl_take isl_multi_aff *ma1,
8948 __isl_take isl_multi_aff *ma2);
8949 __isl_give isl_pw_aff *isl_pw_aff_sub(
8950 __isl_take isl_pw_aff *pwaff1,
8951 __isl_take isl_pw_aff *pwaff2);
8952 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
8953 __isl_take isl_multi_pw_aff *mpa1,
8954 __isl_take isl_multi_pw_aff *mpa2);
8955 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
8956 __isl_take isl_pw_multi_aff *pma1,
8957 __isl_take isl_pw_multi_aff *pma2);
8958 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
8959 __isl_take isl_union_pw_aff *upa1,
8960 __isl_take isl_union_pw_aff *upa2);
8961 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
8962 __isl_take isl_union_pw_multi_aff *upma1,
8963 __isl_take isl_union_pw_multi_aff *upma2);
8964 __isl_give isl_multi_union_pw_aff *
8965 isl_multi_union_pw_aff_sub(
8966 __isl_take isl_multi_union_pw_aff *mupa1,
8967 __isl_take isl_multi_union_pw_aff *mupa2);
8969 C<isl_aff_sub> subtracts the second argument from the first.
8971 #include <isl/polynomial.h>
8972 __isl_give isl_qpolynomial *isl_qpolynomial_add(
8973 __isl_take isl_qpolynomial *qp1,
8974 __isl_take isl_qpolynomial *qp2);
8975 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
8976 __isl_take isl_pw_qpolynomial *pwqp1,
8977 __isl_take isl_pw_qpolynomial *pwqp2);
8978 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
8979 __isl_take isl_pw_qpolynomial *pwqp1,
8980 __isl_take isl_pw_qpolynomial *pwqp2);
8981 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
8982 __isl_take isl_pw_qpolynomial_fold *pwf1,
8983 __isl_take isl_pw_qpolynomial_fold *pwf2);
8984 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
8985 __isl_take isl_union_pw_qpolynomial *upwqp1,
8986 __isl_take isl_union_pw_qpolynomial *upwqp2);
8987 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
8988 __isl_take isl_qpolynomial *qp1,
8989 __isl_take isl_qpolynomial *qp2);
8990 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
8991 __isl_take isl_pw_qpolynomial *pwqp1,
8992 __isl_take isl_pw_qpolynomial *pwqp2);
8993 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
8994 __isl_take isl_union_pw_qpolynomial *upwqp1,
8995 __isl_take isl_union_pw_qpolynomial *upwqp2);
8996 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
8997 __isl_take isl_pw_qpolynomial_fold *pwf1,
8998 __isl_take isl_pw_qpolynomial_fold *pwf2);
8999 __isl_give isl_union_pw_qpolynomial_fold *
9000 isl_union_pw_qpolynomial_fold_fold(
9001 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
9002 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
9004 #include <isl/aff.h>
9005 __isl_give isl_pw_aff *isl_pw_aff_union_add(
9006 __isl_take isl_pw_aff *pwaff1,
9007 __isl_take isl_pw_aff *pwaff2);
9008 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_union_add(
9009 __isl_take isl_multi_pw_aff *mpa1,
9010 __isl_take isl_multi_pw_aff *mpa2);
9011 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
9012 __isl_take isl_pw_multi_aff *pma1,
9013 __isl_take isl_pw_multi_aff *pma2);
9014 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
9015 __isl_take isl_union_pw_aff *upa1,
9016 __isl_take isl_union_pw_aff *upa2);
9017 __isl_give isl_union_pw_multi_aff *
9018 isl_union_pw_multi_aff_union_add(
9019 __isl_take isl_union_pw_multi_aff *upma1,
9020 __isl_take isl_union_pw_multi_aff *upma2);
9021 __isl_give isl_multi_union_pw_aff *
9022 isl_multi_union_pw_aff_union_add(
9023 __isl_take isl_multi_union_pw_aff *mupa1,
9024 __isl_take isl_multi_union_pw_aff *mupa2);
9025 __isl_give isl_pw_aff *isl_pw_aff_union_min(
9026 __isl_take isl_pw_aff *pwaff1,
9027 __isl_take isl_pw_aff *pwaff2);
9028 __isl_give isl_pw_aff *isl_pw_aff_union_max(
9029 __isl_take isl_pw_aff *pwaff1,
9030 __isl_take isl_pw_aff *pwaff2);
9032 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
9033 expression with a domain that is the union of those of C<pwaff1> and
9034 C<pwaff2> and such that on each cell, the quasi-affine expression is
9035 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
9036 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
9037 associated expression is the defined one.
9038 This in contrast to the C<isl_pw_aff_max> function, which is
9039 only defined on the shared definition domain of the arguments.
9041 #include <isl/val.h>
9042 __isl_give isl_multi_val *isl_multi_val_add_val(
9043 __isl_take isl_multi_val *mv,
9044 __isl_take isl_val *v);
9045 __isl_give isl_multi_val *isl_multi_val_mod_val(
9046 __isl_take isl_multi_val *mv,
9047 __isl_take isl_val *v);
9048 __isl_give isl_multi_val *isl_multi_val_scale_val(
9049 __isl_take isl_multi_val *mv,
9050 __isl_take isl_val *v);
9051 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
9052 __isl_take isl_multi_val *mv,
9053 __isl_take isl_val *v);
9055 #include <isl/aff.h>
9056 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
9057 __isl_take isl_val *mod);
9058 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
9059 __isl_take isl_pw_aff *pa,
9060 __isl_take isl_val *mod);
9061 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
9062 __isl_take isl_union_pw_aff *upa,
9063 __isl_take isl_val *f);
9064 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
9065 __isl_take isl_val *v);
9066 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
9067 __isl_take isl_multi_aff *ma,
9068 __isl_take isl_val *v);
9069 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
9070 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
9071 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
9072 __isl_take isl_multi_pw_aff *mpa,
9073 __isl_take isl_val *v);
9074 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
9075 __isl_take isl_pw_multi_aff *pma,
9076 __isl_take isl_val *v);
9077 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
9078 __isl_take isl_union_pw_aff *upa,
9079 __isl_take isl_val *f);
9080 __isl_give isl_union_pw_multi_aff *
9081 isl_union_pw_multi_aff_scale_val(
9082 __isl_take isl_union_pw_multi_aff *upma,
9083 __isl_take isl_val *val);
9084 __isl_give isl_multi_union_pw_aff *
9085 isl_multi_union_pw_aff_scale_val(
9086 __isl_take isl_multi_union_pw_aff *mupa,
9087 __isl_take isl_val *v);
9088 __isl_give isl_aff *isl_aff_scale_down_ui(
9089 __isl_take isl_aff *aff, unsigned f);
9090 __isl_give isl_aff *isl_aff_scale_down_val(
9091 __isl_take isl_aff *aff, __isl_take isl_val *v);
9092 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
9093 __isl_take isl_multi_aff *ma,
9094 __isl_take isl_val *v);
9095 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
9096 __isl_take isl_pw_aff *pa,
9097 __isl_take isl_val *f);
9098 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
9099 __isl_take isl_multi_pw_aff *mpa,
9100 __isl_take isl_val *v);
9101 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
9102 __isl_take isl_pw_multi_aff *pma,
9103 __isl_take isl_val *v);
9104 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
9105 __isl_take isl_union_pw_aff *upa,
9106 __isl_take isl_val *v);
9107 __isl_give isl_union_pw_multi_aff *
9108 isl_union_pw_multi_aff_scale_down_val(
9109 __isl_take isl_union_pw_multi_aff *upma,
9110 __isl_take isl_val *val);
9111 __isl_give isl_multi_union_pw_aff *
9112 isl_multi_union_pw_aff_scale_down_val(
9113 __isl_take isl_multi_union_pw_aff *mupa,
9114 __isl_take isl_val *v);
9116 #include <isl/polynomial.h>
9117 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
9118 __isl_take isl_qpolynomial *qp,
9119 __isl_take isl_val *v);
9120 __isl_give isl_qpolynomial_fold *
9121 isl_qpolynomial_fold_scale_val(
9122 __isl_take isl_qpolynomial_fold *fold,
9123 __isl_take isl_val *v);
9124 __isl_give isl_pw_qpolynomial *
9125 isl_pw_qpolynomial_scale_val(
9126 __isl_take isl_pw_qpolynomial *pwqp,
9127 __isl_take isl_val *v);
9128 __isl_give isl_pw_qpolynomial_fold *
9129 isl_pw_qpolynomial_fold_scale_val(
9130 __isl_take isl_pw_qpolynomial_fold *pwf,
9131 __isl_take isl_val *v);
9132 __isl_give isl_union_pw_qpolynomial *
9133 isl_union_pw_qpolynomial_scale_val(
9134 __isl_take isl_union_pw_qpolynomial *upwqp,
9135 __isl_take isl_val *v);
9136 __isl_give isl_union_pw_qpolynomial_fold *
9137 isl_union_pw_qpolynomial_fold_scale_val(
9138 __isl_take isl_union_pw_qpolynomial_fold *upwf,
9139 __isl_take isl_val *v);
9140 __isl_give isl_qpolynomial *
9141 isl_qpolynomial_scale_down_val(
9142 __isl_take isl_qpolynomial *qp,
9143 __isl_take isl_val *v);
9144 __isl_give isl_qpolynomial_fold *
9145 isl_qpolynomial_fold_scale_down_val(
9146 __isl_take isl_qpolynomial_fold *fold,
9147 __isl_take isl_val *v);
9148 __isl_give isl_pw_qpolynomial *
9149 isl_pw_qpolynomial_scale_down_val(
9150 __isl_take isl_pw_qpolynomial *pwqp,
9151 __isl_take isl_val *v);
9152 __isl_give isl_pw_qpolynomial_fold *
9153 isl_pw_qpolynomial_fold_scale_down_val(
9154 __isl_take isl_pw_qpolynomial_fold *pwf,
9155 __isl_take isl_val *v);
9156 __isl_give isl_union_pw_qpolynomial *
9157 isl_union_pw_qpolynomial_scale_down_val(
9158 __isl_take isl_union_pw_qpolynomial *upwqp,
9159 __isl_take isl_val *v);
9160 __isl_give isl_union_pw_qpolynomial_fold *
9161 isl_union_pw_qpolynomial_fold_scale_down_val(
9162 __isl_take isl_union_pw_qpolynomial_fold *upwf,
9163 __isl_take isl_val *v);
9165 #include <isl/val.h>
9166 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
9167 __isl_take isl_multi_val *mv1,
9168 __isl_take isl_multi_val *mv2);
9169 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
9170 __isl_take isl_multi_val *mv1,
9171 __isl_take isl_multi_val *mv2);
9172 __isl_give isl_multi_val *
9173 isl_multi_val_scale_down_multi_val(
9174 __isl_take isl_multi_val *mv1,
9175 __isl_take isl_multi_val *mv2);
9177 #include <isl/aff.h>
9178 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
9179 __isl_take isl_multi_aff *ma,
9180 __isl_take isl_multi_val *mv);
9181 __isl_give isl_multi_union_pw_aff *
9182 isl_multi_union_pw_aff_mod_multi_val(
9183 __isl_take isl_multi_union_pw_aff *upma,
9184 __isl_take isl_multi_val *mv);
9185 __isl_give isl_multi_pw_aff *
9186 isl_multi_pw_aff_mod_multi_val(
9187 __isl_take isl_multi_pw_aff *mpa,
9188 __isl_take isl_multi_val *mv);
9189 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
9190 __isl_take isl_multi_aff *ma,
9191 __isl_take isl_multi_val *mv);
9192 __isl_give isl_pw_multi_aff *
9193 isl_pw_multi_aff_scale_multi_val(
9194 __isl_take isl_pw_multi_aff *pma,
9195 __isl_take isl_multi_val *mv);
9196 __isl_give isl_multi_pw_aff *
9197 isl_multi_pw_aff_scale_multi_val(
9198 __isl_take isl_multi_pw_aff *mpa,
9199 __isl_take isl_multi_val *mv);
9200 __isl_give isl_multi_union_pw_aff *
9201 isl_multi_union_pw_aff_scale_multi_val(
9202 __isl_take isl_multi_union_pw_aff *mupa,
9203 __isl_take isl_multi_val *mv);
9204 __isl_give isl_union_pw_multi_aff *
9205 isl_union_pw_multi_aff_scale_multi_val(
9206 __isl_take isl_union_pw_multi_aff *upma,
9207 __isl_take isl_multi_val *mv);
9208 __isl_give isl_multi_aff *
9209 isl_multi_aff_scale_down_multi_val(
9210 __isl_take isl_multi_aff *ma,
9211 __isl_take isl_multi_val *mv);
9212 __isl_give isl_pw_multi_aff *
9213 isl_pw_multi_aff_scale_down_multi_val(
9214 __isl_take isl_pw_multi_aff *pma,
9215 __isl_take isl_multi_val *mv);
9216 __isl_give isl_multi_pw_aff *
9217 isl_multi_pw_aff_scale_down_multi_val(
9218 __isl_take isl_multi_pw_aff *mpa,
9219 __isl_take isl_multi_val *mv);
9220 __isl_give isl_multi_union_pw_aff *
9221 isl_multi_union_pw_aff_scale_down_multi_val(
9222 __isl_take isl_multi_union_pw_aff *mupa,
9223 __isl_take isl_multi_val *mv);
9225 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
9226 by the corresponding elements of C<mv>.
9228 #include <isl/aff.h>
9229 __isl_give isl_aff *isl_aff_mul(
9230 __isl_take isl_aff *aff1,
9231 __isl_take isl_aff *aff2);
9232 __isl_give isl_aff *isl_aff_div(
9233 __isl_take isl_aff *aff1,
9234 __isl_take isl_aff *aff2);
9235 __isl_give isl_pw_aff *isl_pw_aff_mul(
9236 __isl_take isl_pw_aff *pwaff1,
9237 __isl_take isl_pw_aff *pwaff2);
9238 __isl_give isl_pw_aff *isl_pw_aff_div(
9239 __isl_take isl_pw_aff *pa1,
9240 __isl_take isl_pw_aff *pa2);
9241 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
9242 __isl_take isl_pw_aff *pa1,
9243 __isl_take isl_pw_aff *pa2);
9244 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
9245 __isl_take isl_pw_aff *pa1,
9246 __isl_take isl_pw_aff *pa2);
9248 When multiplying two affine expressions, at least one of the two needs
9249 to be a constant. Similarly, when dividing an affine expression by another,
9250 the second expression needs to be a constant.
9251 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
9252 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
9255 #include <isl/polynomial.h>
9256 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
9257 __isl_take isl_qpolynomial *qp1,
9258 __isl_take isl_qpolynomial *qp2);
9259 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
9260 __isl_take isl_pw_qpolynomial *pwqp1,
9261 __isl_take isl_pw_qpolynomial *pwqp2);
9262 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
9263 __isl_take isl_union_pw_qpolynomial *upwqp1,
9264 __isl_take isl_union_pw_qpolynomial *upwqp2);
9268 =head3 Lexicographic Optimization
9270 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
9271 the following functions
9272 compute a set that contains the lexicographic minimum or maximum
9273 of the elements in C<set> (or C<bset>) for those values of the parameters
9274 that satisfy C<dom>.
9275 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
9276 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
9278 In other words, the union of the parameter values
9279 for which the result is non-empty and of C<*empty>
9282 #include <isl/set.h>
9283 __isl_give isl_set *isl_basic_set_partial_lexmin(
9284 __isl_take isl_basic_set *bset,
9285 __isl_take isl_basic_set *dom,
9286 __isl_give isl_set **empty);
9287 __isl_give isl_set *isl_basic_set_partial_lexmax(
9288 __isl_take isl_basic_set *bset,
9289 __isl_take isl_basic_set *dom,
9290 __isl_give isl_set **empty);
9291 __isl_give isl_set *isl_set_partial_lexmin(
9292 __isl_take isl_set *set, __isl_take isl_set *dom,
9293 __isl_give isl_set **empty);
9294 __isl_give isl_set *isl_set_partial_lexmax(
9295 __isl_take isl_set *set, __isl_take isl_set *dom,
9296 __isl_give isl_set **empty);
9298 Given a (basic) set C<set> (or C<bset>), the following functions simply
9299 return a set containing the lexicographic minimum or maximum
9300 of the elements in C<set> (or C<bset>).
9301 In case of union sets, the optimum is computed per space.
9303 #include <isl/set.h>
9304 __isl_give isl_set *isl_basic_set_lexmin(
9305 __isl_take isl_basic_set *bset);
9306 __isl_give isl_set *isl_basic_set_lexmax(
9307 __isl_take isl_basic_set *bset);
9308 __isl_give isl_set *isl_set_lexmin(
9309 __isl_take isl_set *set);
9310 __isl_give isl_set *isl_set_lexmax(
9311 __isl_take isl_set *set);
9312 __isl_give isl_union_set *isl_union_set_lexmin(
9313 __isl_take isl_union_set *uset);
9314 __isl_give isl_union_set *isl_union_set_lexmax(
9315 __isl_take isl_union_set *uset);
9317 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
9318 the following functions
9319 compute a relation that maps each element of C<dom>
9320 to the single lexicographic minimum or maximum
9321 of the elements that are associated to that same
9322 element in C<map> (or C<bmap>).
9323 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
9324 that contains the elements in C<dom> that do not map
9325 to any elements in C<map> (or C<bmap>).
9326 In other words, the union of the domain of the result and of C<*empty>
9329 #include <isl/map.h>
9330 __isl_give isl_map *isl_basic_map_partial_lexmax(
9331 __isl_take isl_basic_map *bmap,
9332 __isl_take isl_basic_set *dom,
9333 __isl_give isl_set **empty);
9334 __isl_give isl_map *isl_basic_map_partial_lexmin(
9335 __isl_take isl_basic_map *bmap,
9336 __isl_take isl_basic_set *dom,
9337 __isl_give isl_set **empty);
9338 __isl_give isl_map *isl_map_partial_lexmax(
9339 __isl_take isl_map *map, __isl_take isl_set *dom,
9340 __isl_give isl_set **empty);
9341 __isl_give isl_map *isl_map_partial_lexmin(
9342 __isl_take isl_map *map, __isl_take isl_set *dom,
9343 __isl_give isl_set **empty);
9345 Given a (basic) map C<map> (or C<bmap>), the following functions simply
9346 return a map mapping each element in the domain of
9347 C<map> (or C<bmap>) to the lexicographic minimum or maximum
9348 of all elements associated to that element.
9349 In case of union relations, the optimum is computed per space.
9351 #include <isl/map.h>
9352 __isl_give isl_map *isl_basic_map_lexmin(
9353 __isl_take isl_basic_map *bmap);
9354 __isl_give isl_map *isl_basic_map_lexmax(
9355 __isl_take isl_basic_map *bmap);
9356 __isl_give isl_map *isl_map_lexmin(
9357 __isl_take isl_map *map);
9358 __isl_give isl_map *isl_map_lexmax(
9359 __isl_take isl_map *map);
9360 __isl_give isl_union_map *isl_union_map_lexmin(
9361 __isl_take isl_union_map *umap);
9362 __isl_give isl_union_map *isl_union_map_lexmax(
9363 __isl_take isl_union_map *umap);
9365 The following functions return their result in the form of
9366 a piecewise multi-affine expression,
9367 but are otherwise equivalent to the corresponding functions
9368 returning a basic set or relation.
9370 #include <isl/set.h>
9371 __isl_give isl_pw_multi_aff *
9372 isl_basic_set_partial_lexmin_pw_multi_aff(
9373 __isl_take isl_basic_set *bset,
9374 __isl_take isl_basic_set *dom,
9375 __isl_give isl_set **empty);
9376 __isl_give isl_pw_multi_aff *
9377 isl_basic_set_partial_lexmax_pw_multi_aff(
9378 __isl_take isl_basic_set *bset,
9379 __isl_take isl_basic_set *dom,
9380 __isl_give isl_set **empty);
9381 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
9382 __isl_take isl_set *set);
9383 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
9384 __isl_take isl_set *set);
9386 #include <isl/map.h>
9387 __isl_give isl_pw_multi_aff *
9388 isl_basic_map_lexmin_pw_multi_aff(
9389 __isl_take isl_basic_map *bmap);
9390 __isl_give isl_pw_multi_aff *
9391 isl_basic_map_partial_lexmin_pw_multi_aff(
9392 __isl_take isl_basic_map *bmap,
9393 __isl_take isl_basic_set *dom,
9394 __isl_give isl_set **empty);
9395 __isl_give isl_pw_multi_aff *
9396 isl_basic_map_partial_lexmax_pw_multi_aff(
9397 __isl_take isl_basic_map *bmap,
9398 __isl_take isl_basic_set *dom,
9399 __isl_give isl_set **empty);
9400 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
9401 __isl_take isl_map *map);
9402 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
9403 __isl_take isl_map *map);
9405 The following functions return the lexicographic minimum or maximum
9406 on the shared domain of the inputs and the single defined function
9407 on those parts of the domain where only a single function is defined.
9409 #include <isl/aff.h>
9410 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
9411 __isl_take isl_pw_multi_aff *pma1,
9412 __isl_take isl_pw_multi_aff *pma2);
9413 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
9414 __isl_take isl_pw_multi_aff *pma1,
9415 __isl_take isl_pw_multi_aff *pma2);
9417 If the input to a lexicographic optimization problem has
9418 multiple constraints with the same coefficients for the optimized
9419 variables, then, by default, this symmetry is exploited by
9420 replacing those constraints by a single constraint with
9421 an abstract bound, which is in turn bounded by the corresponding terms
9422 in the original constraints.
9423 Without this optimization, the solver would typically consider
9424 all possible orderings of those original bounds, resulting in a needless
9425 decomposition of the domain.
9426 However, the optimization can also result in slowdowns since
9427 an extra parameter is introduced that may get used in additional
9429 The following option determines whether symmetry detection is applied
9430 during lexicographic optimization.
9432 #include <isl/options.h>
9433 isl_stat isl_options_set_pip_symmetry(isl_ctx *ctx,
9435 int isl_options_get_pip_symmetry(isl_ctx *ctx);
9439 See also \autoref{s:offline}.
9443 =head2 Ternary Operations
9445 #include <isl/aff.h>
9446 __isl_give isl_pw_aff *isl_pw_aff_cond(
9447 __isl_take isl_pw_aff *cond,
9448 __isl_take isl_pw_aff *pwaff_true,
9449 __isl_take isl_pw_aff *pwaff_false);
9451 The function C<isl_pw_aff_cond> performs a conditional operator
9452 and returns an expression that is equal to C<pwaff_true>
9453 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
9454 where C<cond> is zero.
9458 Lists are defined over several element types, including
9459 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_pw_multi_aff>,
9460 C<isl_union_pw_aff>,
9461 C<isl_union_pw_multi_aff>,
9462 C<isl_qpolynomial>, C<isl_pw_qpolynomial>, C<isl_pw_qpolynomial_fold>,
9464 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
9465 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
9466 Here we take lists of C<isl_set>s as an example.
9467 Lists can be created, copied, modified and freed using the following functions.
9469 #include <isl/set.h>
9470 __isl_give isl_set_list *isl_set_to_list(
9471 __isl_take isl_set *el);
9472 __isl_give isl_set_list *isl_set_list_from_set(
9473 __isl_take isl_set *el);
9474 __isl_give isl_set_list *isl_set_list_alloc(
9475 isl_ctx *ctx, int n);
9476 __isl_give isl_set_list *isl_set_list_copy(
9477 __isl_keep isl_set_list *list);
9478 __isl_give isl_set_list *isl_set_list_insert(
9479 __isl_take isl_set_list *list, unsigned pos,
9480 __isl_take isl_set *el);
9481 __isl_give isl_set_list *isl_set_list_add(
9482 __isl_take isl_set_list *list,
9483 __isl_take isl_set *el);
9484 __isl_give isl_set_list *isl_set_list_drop(
9485 __isl_take isl_set_list *list,
9486 unsigned first, unsigned n);
9487 __isl_give isl_set_list *isl_set_list_clear(
9488 __isl_take isl_set_list *list);
9489 __isl_give isl_set_list *isl_set_list_swap(
9490 __isl_take isl_set_list *list,
9491 unsigned pos1, unsigned pos2);
9492 __isl_give isl_set_list *isl_set_list_reverse(
9493 __isl_take isl_set_list *list);
9494 __isl_give isl_set_list *isl_set_list_set_at(
9495 __isl_take isl_set_list *list, int index,
9496 __isl_take isl_set *set);
9497 __isl_give isl_set_list *isl_set_list_set_set(
9498 __isl_take isl_set_list *list, int index,
9499 __isl_take isl_set *set);
9500 __isl_give isl_set_list *isl_set_list_concat(
9501 __isl_take isl_set_list *list1,
9502 __isl_take isl_set_list *list2);
9503 __isl_give isl_set_list *isl_set_list_map(
9504 __isl_take isl_set_list *list,
9505 __isl_give isl_set *(*fn)(__isl_take isl_set *el,
9508 __isl_give isl_set_list *isl_set_list_sort(
9509 __isl_take isl_set_list *list,
9510 int (*cmp)(__isl_keep isl_set *a,
9511 __isl_keep isl_set *b, void *user),
9513 __isl_null isl_set_list *isl_set_list_free(
9514 __isl_take isl_set_list *list);
9516 C<isl_set_list_alloc> creates an empty list with an initial capacity
9517 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
9518 add elements to a list, increasing its capacity as needed.
9519 C<isl_set_to_list> creates a list with a single element.
9520 C<isl_set_list_from_set> performs the same operation.
9521 C<isl_set_list_clear> removes all elements from a list.
9522 C<isl_set_list_swap> swaps the elements at the specified locations.
9523 C<isl_set_list_reverse> reverses the elements in the list.
9524 C<isl_set_list_set_set> is an alternative name for C<isl_set_list_set_at>.
9526 Lists can be inspected using the following functions.
9528 #include <isl/set.h>
9529 isl_size isl_set_list_size(__isl_keep isl_set_list *list);
9530 isl_size isl_set_list_n_set(__isl_keep isl_set_list *list);
9531 __isl_give isl_set *isl_set_list_get_at(
9532 __isl_keep isl_set_list *list, int index);
9533 __isl_give isl_set *isl_set_list_get_set(
9534 __isl_keep isl_set_list *list, int index);
9535 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list,
9536 isl_stat (*fn)(__isl_take isl_set *el, void *user),
9538 isl_bool isl_set_list_every(__isl_keep isl_set_list *list,
9539 isl_bool (*test)(__isl_take isl_set *el,
9542 isl_stat isl_set_list_foreach_scc(
9543 __isl_keep isl_set_list *list,
9544 isl_bool (*follows)(__isl_keep isl_set *a,
9545 __isl_keep isl_set *b, void *user),
9547 isl_stat (*fn)(__isl_take isl_set_list *scc,
9551 C<isl_set_list_n_set> is an alternative name for C<isl_set_list_size>.
9553 C<isl_set_list_get_set> is an alternative name for C<isl_set_list_get_at>.
9554 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
9555 strongly connected components of the graph with as vertices the elements
9556 of C<list> and a directed edge from vertex C<b> to vertex C<a>
9557 iff C<follows(a, b)> returns C<isl_bool_true>. The callbacks C<follows> and
9558 C<fn> should return C<isl_bool_error> or C<isl_stat_error> on error.
9560 Lists can be printed using
9562 #include <isl/set.h>
9563 __isl_give isl_printer *isl_printer_print_set_list(
9564 __isl_take isl_printer *p,
9565 __isl_keep isl_set_list *list);
9567 Alternatively, a string representation can be obtained
9568 directly using the following function, which always prints
9571 #include <isl/set.h>
9572 __isl_give char *isl_set_list_to_str(
9573 __isl_keep isl_set_list *list);
9575 An C<isl_val_list>, C<isl_id_list>,
9576 C<isl_aff_list>, C<isl_pw_aff_list>, C<isl_pw_multi_aff_list>,
9577 C<isl_union_pw_aff_list>,
9578 C<isl_set_list>, C<isl_map_list> or C<isl_union_set_list> object
9579 can also be read from input using the following functions.
9581 #include <isl/val.h>
9582 __isl_give isl_val_list *isl_val_list_read_from_str(
9583 isl_ctx *ctx, const char *str);
9586 __isl_give isl_id_list *isl_id_list_read_from_str(
9587 isl_ctx *ctx, const char *str);
9589 #include <isl/aff.h>
9590 __isl_give isl_aff_list *
9591 isl_aff_list_read_from_str(isl_ctx *ctx,
9593 __isl_give isl_pw_aff_list *
9594 isl_pw_aff_list_read_from_str(isl_ctx *ctx,
9596 __isl_give isl_pw_multi_aff_list *
9597 isl_pw_multi_aff_list_read_from_str(isl_ctx *ctx,
9599 __isl_give isl_union_pw_aff_list *
9600 isl_union_pw_aff_list_read_from_str(isl_ctx *ctx,
9603 #include <isl/set.h>
9604 __isl_give isl_set_list *isl_set_list_read_from_str(
9605 isl_ctx *ctx, const char *str);
9607 #include <isl/map.h>
9608 __isl_give isl_map_list *isl_map_list_read_from_str(
9609 isl_ctx *ctx, const char *str);
9611 #include <isl/union_set.h>
9612 __isl_give isl_union_set_list *
9613 isl_union_set_list_read_from_str(isl_ctx *ctx,
9616 =head2 Associative arrays
9618 Associative arrays map isl objects of a specific type to isl objects
9619 of some (other) specific type. They are defined for several pairs
9620 of types, including (C<isl_map>, C<isl_basic_set>),
9621 (C<isl_id>, C<isl_ast_expr>),
9622 (C<isl_id>, C<isl_id>) and
9623 (C<isl_id>, C<isl_pw_aff>).
9624 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
9627 Associative arrays can be created, copied and freed using
9628 the following functions.
9630 #include <isl/id_to_ast_expr.h>
9631 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
9632 isl_ctx *ctx, int min_size);
9633 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
9634 __isl_keep isl_id_to_ast_expr *id2expr);
9635 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
9636 __isl_take isl_id_to_ast_expr *id2expr);
9638 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
9639 to specify the expected size of the associative array.
9640 The associative array will be grown automatically as needed.
9642 Associative arrays can be inspected using the following functions.
9644 #include <isl/id_to_ast_expr.h>
9645 __isl_give isl_maybe_isl_ast_expr
9646 isl_id_to_ast_expr_try_get(
9647 __isl_keep isl_id_to_ast_expr *id2expr,
9648 __isl_keep isl_id *key);
9649 isl_bool isl_id_to_ast_expr_has(
9650 __isl_keep isl_id_to_ast_expr *id2expr,
9651 __isl_keep isl_id *key);
9652 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
9653 __isl_keep isl_id_to_ast_expr *id2expr,
9654 __isl_take isl_id *key);
9655 isl_stat isl_id_to_ast_expr_foreach(
9656 __isl_keep isl_id_to_ast_expr *id2expr,
9657 isl_stat (*fn)(__isl_take isl_id *key,
9658 __isl_take isl_ast_expr *val, void *user),
9660 isl_bool isl_id_to_ast_expr_every(
9661 __isl_keep isl_id_to_ast_expr *id2expr,
9662 isl_bool (*test)(__isl_keep isl_id *key,
9663 __isl_keep isl_ast_expr *val, void *user),
9666 The function C<isl_id_to_ast_expr_try_get> returns a structure
9667 containing two elements, C<valid> and C<value>.
9668 If there is a value associated to the key, then C<valid>
9669 is set to C<isl_bool_true> and C<value> contains a copy of
9670 the associated value. Otherwise C<value> is C<NULL> and
9671 C<valid> may be C<isl_bool_error> or C<isl_bool_false> depending
9672 on whether some error has occurred or there simply is no associated value.
9673 The function C<isl_id_to_ast_expr_has> returns the C<valid> field
9674 in the structure and
9675 the function C<isl_id_to_ast_expr_get> returns the C<value> field.
9677 Associative arrays can be modified using the following functions.
9679 #include <isl/id_to_ast_expr.h>
9680 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
9681 __isl_take isl_id_to_ast_expr *id2expr,
9682 __isl_take isl_id *key,
9683 __isl_take isl_ast_expr *val);
9684 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
9685 __isl_take isl_id_to_ast_expr *id2expr,
9686 __isl_take isl_id *key);
9688 Associative arrays can be checked for (obvious) equality
9689 using the following function.
9691 #include <isl/id_to_ast_expr.h>
9692 isl_bool isl_id_to_ast_expr_is_equal(
9693 __isl_take isl_id_to_ast_expr *id2expr1,
9694 __isl_take isl_id_to_ast_expr *id2expr2);
9696 Note that depending on how the keys and values are being compared,
9697 for other types of keys and/or values, this function may be called
9698 C<plain_is_equal> rather than C<is_equal>.
9700 Associative arrays can be printed using the following functions.
9702 #include <isl/id_to_ast_expr.h>
9703 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
9704 __isl_take isl_printer *p,
9705 __isl_keep isl_id_to_ast_expr *id2expr);
9706 __isl_give char *isl_id_to_ast_expr_to_str(
9707 __isl_keep isl_id_to_ast_expr *id2expr);
9709 They can be read from input using the following function.
9711 #include <isl/id_to_ast_expr.h>
9712 __isl_give isl_id_to_ast_expr *
9713 isl_id_to_ast_expr_read_from_str(isl_ctx *ctx,
9718 Vectors can be created, copied and freed using the following functions.
9720 #include <isl/vec.h>
9721 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
9723 __isl_give isl_vec *isl_vec_zero(isl_ctx *ctx,
9725 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
9726 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
9728 Note that the elements of a vector created by C<isl_vec_alloc>
9729 may have arbitrary values.
9730 A vector created by C<isl_vec_zero> has elements with value zero.
9731 The elements can be changed and inspected using the following functions.
9733 isl_size isl_vec_size(__isl_keep isl_vec *vec);
9734 __isl_give isl_val *isl_vec_get_element_val(
9735 __isl_keep isl_vec *vec, int pos);
9736 __isl_give isl_vec *isl_vec_set_element_si(
9737 __isl_take isl_vec *vec, int pos, int v);
9738 __isl_give isl_vec *isl_vec_set_element_val(
9739 __isl_take isl_vec *vec, int pos,
9740 __isl_take isl_val *v);
9741 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
9743 __isl_give isl_vec *isl_vec_set_val(
9744 __isl_take isl_vec *vec, __isl_take isl_val *v);
9745 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
9746 __isl_keep isl_vec *vec2, int pos);
9748 C<isl_vec_get_element> will return a negative value if anything went wrong.
9749 In that case, the value of C<*v> is undefined.
9751 The following function can be used to concatenate two vectors.
9753 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
9754 __isl_take isl_vec *vec2);
9758 Matrices can be created, copied and freed using the following functions.
9760 #include <isl/mat.h>
9761 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
9762 unsigned n_row, unsigned n_col);
9763 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
9764 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
9766 Note that the elements of a newly created matrix may have arbitrary values.
9767 The elements can be changed and inspected using the following functions.
9769 isl_size isl_mat_rows(__isl_keep isl_mat *mat);
9770 isl_size isl_mat_cols(__isl_keep isl_mat *mat);
9771 __isl_give isl_val *isl_mat_get_element_val(
9772 __isl_keep isl_mat *mat, int row, int col);
9773 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
9774 int row, int col, int v);
9775 __isl_give isl_mat *isl_mat_set_element_val(
9776 __isl_take isl_mat *mat, int row, int col,
9777 __isl_take isl_val *v);
9779 The following function computes the rank of a matrix.
9780 The return value may be -1 if some error occurred.
9782 #include <isl/mat.h>
9783 isl_size isl_mat_rank(__isl_keep isl_mat *mat);
9785 The following function can be used to compute the (right) inverse
9786 of a matrix, i.e., a matrix such that the product of the original
9787 and the inverse (in that order) is a multiple of the identity matrix.
9788 The input matrix is assumed to be of full row-rank.
9790 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
9792 The following function can be used to compute the (right) kernel
9793 (or null space) of a matrix, i.e., a matrix such that the product of
9794 the original and the kernel (in that order) is the zero matrix.
9796 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
9798 The following function computes a basis for the space spanned
9799 by the rows of a matrix.
9801 __isl_give isl_mat *isl_mat_row_basis(
9802 __isl_take isl_mat *mat);
9804 The following function computes rows that extend a basis of C<mat1>
9805 to a basis that also covers C<mat2>.
9807 __isl_give isl_mat *isl_mat_row_basis_extension(
9808 __isl_take isl_mat *mat1,
9809 __isl_take isl_mat *mat2);
9811 The following function checks whether there is no linear dependence
9812 among the combined rows of "mat1" and "mat2" that is not already present
9813 in "mat1" or "mat2" individually.
9814 If "mat1" and "mat2" have linearly independent rows by themselves,
9815 then this means that there is no linear dependence among all rows together.
9817 isl_bool isl_mat_has_linearly_independent_rows(
9818 __isl_keep isl_mat *mat1,
9819 __isl_keep isl_mat *mat2);
9821 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
9823 The following functions determine
9824 an upper or lower bound on a quasipolynomial over its domain.
9826 __isl_give isl_pw_qpolynomial_fold *
9827 isl_pw_qpolynomial_bound(
9828 __isl_take isl_pw_qpolynomial *pwqp,
9829 enum isl_fold type, isl_bool *tight);
9831 __isl_give isl_union_pw_qpolynomial_fold *
9832 isl_union_pw_qpolynomial_bound(
9833 __isl_take isl_union_pw_qpolynomial *upwqp,
9834 enum isl_fold type, isl_bool *tight);
9836 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
9837 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
9838 is the returned bound is known be tight, i.e., for each value
9839 of the parameters there is at least
9840 one element in the domain that reaches the bound.
9841 If the domain of C<pwqp> is not wrapping, then the bound is computed
9842 over all elements in that domain and the result has a purely parametric
9843 domain. If the domain of C<pwqp> is wrapping, then the bound is
9844 computed over the range of the wrapped relation. The domain of the
9845 wrapped relation becomes the domain of the result.
9847 =head2 Parametric Vertex Enumeration
9849 The parametric vertex enumeration described in this section
9850 is mainly intended to be used internally and by the C<barvinok>
9853 #include <isl/vertices.h>
9854 __isl_give isl_vertices *isl_basic_set_compute_vertices(
9855 __isl_keep isl_basic_set *bset);
9857 The function C<isl_basic_set_compute_vertices> performs the
9858 actual computation of the parametric vertices and the chamber
9859 decomposition and stores the result in an C<isl_vertices> object.
9860 This information can be queried by either iterating over all
9861 the vertices or iterating over all the chambers or cells
9862 and then iterating over all vertices that are active on the chamber.
9864 isl_stat isl_vertices_foreach_vertex(
9865 __isl_keep isl_vertices *vertices,
9866 isl_stat (*fn)(__isl_take isl_vertex *vertex,
9867 void *user), void *user);
9869 isl_stat isl_vertices_foreach_cell(
9870 __isl_keep isl_vertices *vertices,
9871 isl_stat (*fn)(__isl_take isl_cell *cell,
9872 void *user), void *user);
9873 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
9874 isl_stat (*fn)(__isl_take isl_vertex *vertex,
9875 void *user), void *user);
9877 Other operations that can be performed on an C<isl_vertices> object are
9880 isl_size isl_vertices_get_n_vertices(
9881 __isl_keep isl_vertices *vertices);
9882 __isl_null isl_vertices *isl_vertices_free(
9883 __isl_take isl_vertices *vertices);
9885 Vertices can be inspected and destroyed using the following functions.
9887 isl_size isl_vertex_get_id(__isl_keep isl_vertex *vertex);
9888 __isl_give isl_basic_set *isl_vertex_get_domain(
9889 __isl_keep isl_vertex *vertex);
9890 __isl_give isl_multi_aff *isl_vertex_get_expr(
9891 __isl_keep isl_vertex *vertex);
9892 __isl_null isl_vertex *isl_vertex_free(
9893 __isl_take isl_vertex *vertex);
9895 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
9896 describing the vertex in terms of the parameters,
9897 while C<isl_vertex_get_domain> returns the activity domain
9900 Chambers can be inspected and destroyed using the following functions.
9902 __isl_give isl_basic_set *isl_cell_get_domain(
9903 __isl_keep isl_cell *cell);
9904 __isl_null isl_cell *isl_cell_free(
9905 __isl_take isl_cell *cell);
9907 =head1 Polyhedral Compilation Library
9909 This section collects functionality in C<isl> that has been specifically
9910 designed for use during polyhedral compilation.
9912 =head2 Schedule Trees
9914 A schedule tree is a structured representation of a schedule,
9915 assigning a relative order to a set of domain elements.
9916 The relative order expressed by the schedule tree is
9917 defined recursively. In particular, the order between
9918 two domain elements is determined by the node that is closest
9919 to the root that refers to both elements and that orders them apart.
9920 Each node in the tree is of one of several types.
9921 The root node is always of type C<isl_schedule_node_domain>
9922 (or C<isl_schedule_node_extension>)
9923 and it describes the (extra) domain elements to which the schedule applies.
9924 The other types of nodes are as follows.
9928 =item C<isl_schedule_node_band>
9930 A band of schedule dimensions. Each schedule dimension is represented
9931 by a union piecewise quasi-affine expression. If this expression
9932 assigns a different value to two domain elements, while all previous
9933 schedule dimensions in the same band assign them the same value,
9934 then the two domain elements are ordered according to these two
9936 Each expression is required to be total in the domain elements
9937 that reach the band node.
9939 =item C<isl_schedule_node_expansion>
9941 An expansion node maps each of the domain elements that reach the node
9942 to one or more domain elements. The image of this mapping forms
9943 the set of domain elements that reach the child of the expansion node.
9944 The function that maps each of the expanded domain elements
9945 to the original domain element from which it was expanded
9946 is called the contraction.
9948 =item C<isl_schedule_node_filter>
9950 A filter node does not impose any ordering, but rather intersects
9951 the set of domain elements that the current subtree refers to
9952 with a given union set. The subtree of the filter node only
9953 refers to domain elements in the intersection.
9954 A filter node is typically only used as a child of a sequence or
9957 =item C<isl_schedule_node_leaf>
9959 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
9961 =item C<isl_schedule_node_mark>
9963 A mark node can be used to attach any kind of information to a subtree
9964 of the schedule tree.
9966 =item C<isl_schedule_node_sequence>
9968 A sequence node has one or more children, each of which is a filter node.
9969 The filters on these filter nodes form a partition of
9970 the domain elements that the current subtree refers to.
9971 If two domain elements appear in distinct filters then the sequence
9972 node orders them according to the child positions of the corresponding
9975 =item C<isl_schedule_node_set>
9977 A set node is similar to a sequence node, except that
9978 it expresses that domain elements appearing in distinct filters
9979 may have any order. The order of the children of a set node
9980 is therefore also immaterial.
9984 The following node types are only supported by the AST generator.
9988 =item C<isl_schedule_node_context>
9990 The context describes constraints on the parameters and
9991 the schedule dimensions of outer
9992 bands that the AST generator may assume to hold. It is also the only
9993 kind of node that may introduce additional parameters.
9994 The space of the context is that of the flat product of the outer
9995 band nodes. In particular, if there are no outer band nodes, then
9996 this space is the unnamed zero-dimensional space.
9997 Since a context node references the outer band nodes, any tree
9998 containing a context node is considered to be anchored.
10000 =item C<isl_schedule_node_extension>
10002 An extension node instructs the AST generator to add additional
10003 domain elements that need to be scheduled.
10004 The additional domain elements are described by the range of
10005 the extension map in terms of the outer schedule dimensions,
10006 i.e., the flat product of the outer band nodes.
10007 Note that domain elements are added whenever the AST generator
10008 reaches the extension node, meaning that there are still some
10009 active domain elements for which an AST needs to be generated.
10010 The conditions under which some domain elements are still active
10011 may however not be completely described by the outer AST nodes
10012 generated at that point.
10013 Since an extension node references the outer band nodes, any tree
10014 containing an extension node is considered to be anchored.
10016 An extension node may also appear as the root of a schedule tree,
10017 when it is intended to be inserted into another tree
10018 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
10019 In this case, the domain of the extension node should
10020 correspond to the flat product of the outer band nodes
10021 in this other schedule tree at the point where the extension tree
10024 =item C<isl_schedule_node_guard>
10026 The guard describes constraints on the parameters and
10027 the schedule dimensions of outer
10028 bands that need to be enforced by the outer nodes
10029 in the generated AST.
10030 That is, the part of the AST that is generated from descendants
10031 of the guard node can assume that these constraints are satisfied.
10032 The space of the guard is that of the flat product of the outer
10033 band nodes. In particular, if there are no outer band nodes, then
10034 this space is the unnamed zero-dimensional space.
10035 Since a guard node references the outer band nodes, any tree
10036 containing a guard node is considered to be anchored.
10040 Except for the C<isl_schedule_node_context> nodes,
10041 none of the nodes may introduce any parameters that were not
10042 already present in the root domain node.
10044 A schedule tree is encapsulated in an C<isl_schedule> object.
10045 The simplest such objects, those with a tree consisting of single domain node,
10046 can be created using the following functions with either an empty
10047 domain or a given domain.
10049 #include <isl/schedule.h>
10050 __isl_give isl_schedule *isl_schedule_empty(
10051 __isl_take isl_space *space);
10052 __isl_give isl_schedule *isl_schedule_from_domain(
10053 __isl_take isl_union_set *domain);
10055 The function C<isl_schedule_constraints_compute_schedule> described
10056 in L</"Scheduling"> can also be used to construct schedules.
10058 C<isl_schedule> objects may be copied and freed using the following functions.
10060 #include <isl/schedule.h>
10061 __isl_give isl_schedule *isl_schedule_copy(
10062 __isl_keep isl_schedule *sched);
10063 __isl_null isl_schedule *isl_schedule_free(
10064 __isl_take isl_schedule *sched);
10066 The following functions checks whether two C<isl_schedule> objects
10067 are obviously the same.
10069 #include <isl/schedule.h>
10070 isl_bool isl_schedule_plain_is_equal(
10071 __isl_keep isl_schedule *schedule1,
10072 __isl_keep isl_schedule *schedule2);
10074 The domain of the schedule, i.e., the domain described by the root node,
10075 can be obtained using the following function.
10077 #include <isl/schedule.h>
10078 __isl_give isl_union_set *isl_schedule_get_domain(
10079 __isl_keep isl_schedule *schedule);
10081 An extra top-level band node (right underneath the domain node) can
10082 be introduced into the schedule using the following function.
10083 The schedule tree is assumed not to have any anchored nodes.
10085 #include <isl/schedule.h>
10086 __isl_give isl_schedule *
10087 isl_schedule_insert_partial_schedule(
10088 __isl_take isl_schedule *schedule,
10089 __isl_take isl_multi_union_pw_aff *partial);
10091 A top-level context node (right underneath the domain node) can
10092 be introduced into the schedule using the following function.
10094 #include <isl/schedule.h>
10095 __isl_give isl_schedule *isl_schedule_insert_context(
10096 __isl_take isl_schedule *schedule,
10097 __isl_take isl_set *context)
10099 A top-level guard node (right underneath the domain node) can
10100 be introduced into the schedule using the following function.
10102 #include <isl/schedule.h>
10103 __isl_give isl_schedule *isl_schedule_insert_guard(
10104 __isl_take isl_schedule *schedule,
10105 __isl_take isl_set *guard)
10107 A schedule that combines two schedules either in the given
10108 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
10109 or an C<isl_schedule_node_set> node,
10110 can be created using the following functions.
10112 #include <isl/schedule.h>
10113 __isl_give isl_schedule *isl_schedule_sequence(
10114 __isl_take isl_schedule *schedule1,
10115 __isl_take isl_schedule *schedule2);
10116 __isl_give isl_schedule *isl_schedule_set(
10117 __isl_take isl_schedule *schedule1,
10118 __isl_take isl_schedule *schedule2);
10120 The domains of the two input schedules need to be disjoint.
10122 The following function can be used to restrict the domain
10123 of a schedule with a domain node as root to be a subset of the given union set.
10124 This operation may remove nodes in the tree that have become
10127 #include <isl/schedule.h>
10128 __isl_give isl_schedule *isl_schedule_intersect_domain(
10129 __isl_take isl_schedule *schedule,
10130 __isl_take isl_union_set *domain);
10132 The following function can be used to simplify the domain
10133 of a schedule with a domain node as root with respect to the given
10136 #include <isl/schedule.h>
10137 __isl_give isl_schedule *isl_schedule_gist_domain_params(
10138 __isl_take isl_schedule *schedule,
10139 __isl_take isl_set *context);
10141 The following function resets the user pointers on all parameter
10142 and tuple identifiers referenced by the nodes of the given schedule.
10144 #include <isl/schedule.h>
10145 __isl_give isl_schedule *isl_schedule_reset_user(
10146 __isl_take isl_schedule *schedule);
10148 The following function aligns the parameters of all nodes
10149 in the given schedule to the given space.
10151 #include <isl/schedule.h>
10152 __isl_give isl_schedule *isl_schedule_align_params(
10153 __isl_take isl_schedule *schedule,
10154 __isl_take isl_space *space);
10156 The following function allows the user to plug in a given function
10157 in the iteration domains. The input schedule is not allowed to contain
10158 any expansion nodes.
10160 #include <isl/schedule.h>
10161 __isl_give isl_schedule *
10162 isl_schedule_pullback_union_pw_multi_aff(
10163 __isl_take isl_schedule *schedule,
10164 __isl_take isl_union_pw_multi_aff *upma);
10166 The following function can be used to plug in the schedule C<expansion>
10167 in the leaves of C<schedule>, where C<contraction> describes how
10168 the domain elements of C<expansion> map to the domain elements
10169 at the original leaves of C<schedule>.
10170 The resulting schedule will contain expansion nodes, unless
10171 C<contraction> is an identity function.
10173 #include <isl/schedule.h>
10174 __isl_give isl_schedule *isl_schedule_expand(
10175 __isl_take isl_schedule *schedule,
10176 __isl_take isl_union_pw_multi_aff *contraction,
10177 __isl_take isl_schedule *expansion);
10179 An C<isl_union_map> representation of the schedule can be obtained
10180 from an C<isl_schedule> using the following function.
10182 #include <isl/schedule.h>
10183 __isl_give isl_union_map *isl_schedule_get_map(
10184 __isl_keep isl_schedule *sched);
10186 The resulting relation encodes the same relative ordering as
10187 the schedule by mapping the domain elements to a common schedule space.
10188 If the schedule_separate_components option is set, then the order
10189 of the children of a set node is explicitly encoded in the result.
10190 If the tree contains any expansion nodes, then the relation
10191 is formulated in terms of the expanded domain elements.
10193 Schedules can be read from input using the following functions.
10195 #include <isl/schedule.h>
10196 __isl_give isl_schedule *isl_schedule_read_from_file(
10197 isl_ctx *ctx, FILE *input);
10198 __isl_give isl_schedule *isl_schedule_read_from_str(
10199 isl_ctx *ctx, const char *str);
10201 A representation of the schedule can be printed using
10203 #include <isl/schedule.h>
10204 __isl_give isl_printer *isl_printer_print_schedule(
10205 __isl_take isl_printer *p,
10206 __isl_keep isl_schedule *schedule);
10207 __isl_give char *isl_schedule_to_str(
10208 __isl_keep isl_schedule *schedule);
10210 C<isl_schedule_to_str> prints the schedule in flow format.
10212 The schedule tree can be traversed through the use of
10213 C<isl_schedule_node> objects that point to a particular
10214 position in the schedule tree. Whenever a C<isl_schedule_node>
10215 is used to modify a node in the schedule tree, the original schedule
10216 tree is left untouched and the modifications are performed to a copy
10217 of the tree. The returned C<isl_schedule_node> then points to
10218 this modified copy of the tree.
10220 The root of the schedule tree can be obtained using the following function.
10222 #include <isl/schedule.h>
10223 __isl_give isl_schedule_node *isl_schedule_get_root(
10224 __isl_keep isl_schedule *schedule);
10226 A pointer to a newly created schedule tree with a single domain
10227 node can be created using the following functions.
10229 #include <isl/schedule_node.h>
10230 __isl_give isl_schedule_node *
10231 isl_schedule_node_from_domain(
10232 __isl_take isl_union_set *domain);
10233 __isl_give isl_schedule_node *
10234 isl_schedule_node_from_extension(
10235 __isl_take isl_union_map *extension);
10237 C<isl_schedule_node_from_extension> creates a tree with an extension
10240 Schedule nodes can be copied and freed using the following functions.
10242 #include <isl/schedule_node.h>
10243 __isl_give isl_schedule_node *isl_schedule_node_copy(
10244 __isl_keep isl_schedule_node *node);
10245 __isl_null isl_schedule_node *isl_schedule_node_free(
10246 __isl_take isl_schedule_node *node);
10248 The following functions can be used to check if two schedule
10249 nodes point to the same position in the same schedule.
10251 #include <isl/schedule_node.h>
10252 isl_bool isl_schedule_node_is_equal(
10253 __isl_keep isl_schedule_node *node1,
10254 __isl_keep isl_schedule_node *node2);
10256 The following properties can be obtained from a schedule node.
10258 #include <isl/schedule_node.h>
10259 enum isl_schedule_node_type isl_schedule_node_get_type(
10260 __isl_keep isl_schedule_node *node);
10261 enum isl_schedule_node_type
10262 isl_schedule_node_get_parent_type(
10263 __isl_keep isl_schedule_node *node);
10264 __isl_give isl_schedule *isl_schedule_node_get_schedule(
10265 __isl_keep isl_schedule_node *node);
10267 The function C<isl_schedule_node_get_type> returns the type of
10268 the node, while C<isl_schedule_node_get_parent_type> returns
10269 type of the parent of the node, which is required to exist.
10270 The function C<isl_schedule_node_get_schedule> returns a copy
10271 to the schedule to which the node belongs.
10273 The following functions can be used to move the schedule node
10274 to a different position in the tree or to check if such a position
10277 #include <isl/schedule_node.h>
10278 isl_bool isl_schedule_node_has_parent(
10279 __isl_keep isl_schedule_node *node);
10280 __isl_give isl_schedule_node *isl_schedule_node_parent(
10281 __isl_take isl_schedule_node *node);
10282 __isl_give isl_schedule_node *
10283 isl_schedule_node_grandparent(
10284 __isl_take isl_schedule_node *node);
10285 __isl_give isl_schedule_node *isl_schedule_node_root(
10286 __isl_take isl_schedule_node *node);
10287 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
10288 __isl_take isl_schedule_node *node,
10290 isl_size isl_schedule_node_n_children(
10291 __isl_keep isl_schedule_node *node);
10292 __isl_give isl_schedule_node *isl_schedule_node_child(
10293 __isl_take isl_schedule_node *node, int pos);
10294 isl_bool isl_schedule_node_has_children(
10295 __isl_keep isl_schedule_node *node);
10296 __isl_give isl_schedule_node *
10297 isl_schedule_node_grandchild(
10298 __isl_take isl_schedule_node *node,
10299 int pos1, int pos2);
10300 __isl_give isl_schedule_node *isl_schedule_node_first_child(
10301 __isl_take isl_schedule_node *node);
10302 isl_bool isl_schedule_node_has_previous_sibling(
10303 __isl_keep isl_schedule_node *node);
10304 __isl_give isl_schedule_node *
10305 isl_schedule_node_previous_sibling(
10306 __isl_take isl_schedule_node *node);
10307 isl_bool isl_schedule_node_has_next_sibling(
10308 __isl_keep isl_schedule_node *node);
10309 __isl_give isl_schedule_node *
10310 isl_schedule_node_next_sibling(
10311 __isl_take isl_schedule_node *node);
10313 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
10314 is the node itself, the ancestor of generation 1 is its parent and so on.
10316 It is also possible to query the number of ancestors of a node,
10317 the position of the current node
10318 within the children of its parent, the position of the subtree
10319 containing a node within the children of an ancestor
10320 or to obtain a copy of a given
10321 child without destroying the current node.
10322 Given two nodes that point to the same schedule, their closest
10323 shared ancestor can be obtained using
10324 C<isl_schedule_node_get_shared_ancestor>.
10326 #include <isl/schedule_node.h>
10327 isl_size isl_schedule_node_get_tree_depth(
10328 __isl_keep isl_schedule_node *node);
10329 isl_size isl_schedule_node_get_child_position(
10330 __isl_keep isl_schedule_node *node);
10331 isl_size isl_schedule_node_get_ancestor_child_position(
10332 __isl_keep isl_schedule_node *node,
10333 __isl_keep isl_schedule_node *ancestor);
10334 __isl_give isl_schedule_node *isl_schedule_node_get_child(
10335 __isl_keep isl_schedule_node *node, int pos);
10336 __isl_give isl_schedule_node *
10337 isl_schedule_node_get_shared_ancestor(
10338 __isl_keep isl_schedule_node *node1,
10339 __isl_keep isl_schedule_node *node2);
10341 All nodes in a schedule tree or
10342 all descendants of a specific node (including the node) can be visited
10343 in depth-first pre-order using the following functions.
10345 #include <isl/schedule.h>
10346 isl_stat isl_schedule_foreach_schedule_node_top_down(
10347 __isl_keep isl_schedule *sched,
10348 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
10349 void *user), void *user);
10351 #include <isl/schedule_node.h>
10352 isl_stat isl_schedule_node_foreach_descendant_top_down(
10353 __isl_keep isl_schedule_node *node,
10354 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
10355 void *user), void *user);
10357 The callback function is slightly different from the usual
10358 callbacks in that it not only indicates success (non-negative result)
10359 or failure (negative result), but also indicates whether the children
10360 of the given node should be visited. In particular, if the callback
10361 returns a positive value, then the children are visited, but if
10362 the callback returns zero, then the children are not visited.
10364 The following functions checks whether
10365 all descendants of a specific node (including the node itself)
10366 satisfy a user-specified test.
10368 #include <isl/schedule_node.h>
10369 isl_bool isl_schedule_node_every_descendant(
10370 __isl_keep isl_schedule_node *node,
10371 isl_bool (*test)(__isl_keep isl_schedule_node *node,
10372 void *user), void *user)
10374 The ancestors of a node in a schedule tree can be visited from
10375 the root down to and including the parent of the node using
10376 the following function.
10378 #include <isl/schedule_node.h>
10379 isl_stat isl_schedule_node_foreach_ancestor_top_down(
10380 __isl_keep isl_schedule_node *node,
10381 isl_stat (*fn)(__isl_keep isl_schedule_node *node,
10382 void *user), void *user);
10384 The following functions allows for a depth-first post-order
10385 traversal of the nodes in a schedule tree or
10386 of the descendants of a specific node (including the node
10387 itself), where the user callback is allowed to modify the
10390 #include <isl/schedule.h>
10391 __isl_give isl_schedule *
10392 isl_schedule_map_schedule_node_bottom_up(
10393 __isl_take isl_schedule *schedule,
10394 __isl_give isl_schedule_node *(*fn)(
10395 __isl_take isl_schedule_node *node,
10396 void *user), void *user);
10398 #include <isl/schedule_node.h>
10399 __isl_give isl_schedule_node *
10400 isl_schedule_node_map_descendant_bottom_up(
10401 __isl_take isl_schedule_node *node,
10402 __isl_give isl_schedule_node *(*fn)(
10403 __isl_take isl_schedule_node *node,
10404 void *user), void *user);
10406 The traversal continues from the node returned by the callback function.
10407 It is the responsibility of the user to ensure that this does not
10408 lead to an infinite loop. It is safest to always return a pointer
10409 to the same position (same ancestors and child positions) as the input node.
10411 The following function removes a node (along with its descendants)
10412 from a schedule tree and returns a pointer to the leaf at the
10413 same position in the updated tree.
10414 It is not allowed to remove the root of a schedule tree or
10415 a child of a set or sequence node.
10417 #include <isl/schedule_node.h>
10418 __isl_give isl_schedule_node *isl_schedule_node_cut(
10419 __isl_take isl_schedule_node *node);
10421 The following function removes a single node
10422 from a schedule tree and returns a pointer to the child
10423 of the node, now located at the position of the original node
10424 or to a leaf node at that position if there was no child.
10425 It is not allowed to remove the root of a schedule tree,
10426 a set or sequence node, a child of a set or sequence node or
10427 a band node with an anchored subtree.
10429 #include <isl/schedule_node.h>
10430 __isl_give isl_schedule_node *isl_schedule_node_delete(
10431 __isl_take isl_schedule_node *node);
10433 Most nodes in a schedule tree only contain local information.
10434 In some cases, however, a node may also refer to the schedule dimensions
10435 of its outer band nodes.
10436 This means that the position of the node within the tree should
10437 not be changed, or at least that no changes are performed to the
10438 outer band nodes. The following function can be used to test
10439 whether the subtree rooted at a given node contains any such nodes.
10441 #include <isl/schedule_node.h>
10442 isl_bool isl_schedule_node_is_subtree_anchored(
10443 __isl_keep isl_schedule_node *node);
10445 The following function resets the user pointers on all parameter
10446 and tuple identifiers referenced by the given schedule node.
10448 #include <isl/schedule_node.h>
10449 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
10450 __isl_take isl_schedule_node *node);
10452 The following function aligns the parameters of the given schedule
10453 node to the given space.
10455 #include <isl/schedule_node.h>
10456 __isl_give isl_schedule_node *
10457 isl_schedule_node_align_params(
10458 __isl_take isl_schedule_node *node,
10459 __isl_take isl_space *space);
10461 Several node types have their own functions for querying
10462 (and in some cases setting) some node type specific properties.
10464 #include <isl/schedule_node.h>
10465 __isl_give isl_space *isl_schedule_node_band_get_space(
10466 __isl_keep isl_schedule_node *node);
10467 __isl_give isl_multi_union_pw_aff *
10468 isl_schedule_node_band_get_partial_schedule(
10469 __isl_keep isl_schedule_node *node);
10470 __isl_give isl_union_map *
10471 isl_schedule_node_band_get_partial_schedule_union_map(
10472 __isl_keep isl_schedule_node *node);
10473 isl_size isl_schedule_node_band_n_member(
10474 __isl_keep isl_schedule_node *node);
10475 isl_bool isl_schedule_node_band_member_get_coincident(
10476 __isl_keep isl_schedule_node *node, int pos);
10477 __isl_give isl_schedule_node *
10478 isl_schedule_node_band_member_set_coincident(
10479 __isl_take isl_schedule_node *node, int pos,
10481 isl_bool isl_schedule_node_band_get_permutable(
10482 __isl_keep isl_schedule_node *node);
10483 __isl_give isl_schedule_node *
10484 isl_schedule_node_band_set_permutable(
10485 __isl_take isl_schedule_node *node, int permutable);
10486 enum isl_ast_loop_type
10487 isl_schedule_node_band_member_get_ast_loop_type(
10488 __isl_keep isl_schedule_node *node, int pos);
10489 __isl_give isl_schedule_node *
10490 isl_schedule_node_band_member_set_ast_loop_type(
10491 __isl_take isl_schedule_node *node, int pos,
10492 enum isl_ast_loop_type type);
10493 enum isl_ast_loop_type
10494 isl_schedule_node_band_member_get_isolate_ast_loop_type(
10495 __isl_keep isl_schedule_node *node, int pos);
10496 __isl_give isl_schedule_node *
10497 isl_schedule_node_band_member_set_isolate_ast_loop_type(
10498 __isl_take isl_schedule_node *node, int pos,
10499 enum isl_ast_loop_type type);
10500 __isl_give isl_union_set *
10501 isl_schedule_node_band_get_ast_build_options(
10502 __isl_keep isl_schedule_node *node);
10503 __isl_give isl_schedule_node *
10504 isl_schedule_node_band_set_ast_build_options(
10505 __isl_take isl_schedule_node *node,
10506 __isl_take isl_union_set *options);
10507 __isl_give isl_set *
10508 isl_schedule_node_band_get_ast_isolate_option(
10509 __isl_keep isl_schedule_node *node);
10511 The function C<isl_schedule_node_band_get_space> returns the space
10512 of the partial schedule of the band.
10513 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
10514 returns a representation of the partial schedule of the band node
10515 in the form of an C<isl_union_map>.
10516 The coincident and permutable properties are set by
10517 C<isl_schedule_constraints_compute_schedule> on the schedule tree
10519 A scheduling dimension is considered to be ``coincident''
10520 if it satisfies the coincidence constraints within its band.
10521 That is, if the dependence distances of the coincidence
10522 constraints are all zero in that direction (for fixed
10523 iterations of outer bands).
10524 A band is marked permutable if it was produced using the Pluto-like scheduler.
10525 Note that the scheduler may have to resort to a Feautrier style scheduling
10526 step even if the default scheduler is used.
10527 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
10528 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
10529 For the meaning of these loop AST generation types and the difference
10530 between the regular loop AST generation type and the isolate
10531 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
10532 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
10533 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
10534 may return C<isl_ast_loop_error> if an error occurs.
10535 The AST build options govern how an AST is generated for
10536 the individual schedule dimensions during AST generation.
10537 See L</"AST Generation Options (Schedule Tree)">.
10538 The isolate option for the given node can be extracted from these
10539 AST build options using the function
10540 C<isl_schedule_node_band_get_ast_isolate_option>.
10542 #include <isl/schedule_node.h>
10543 __isl_give isl_set *
10544 isl_schedule_node_context_get_context(
10545 __isl_keep isl_schedule_node *node);
10547 #include <isl/schedule_node.h>
10548 __isl_give isl_union_set *
10549 isl_schedule_node_domain_get_domain(
10550 __isl_keep isl_schedule_node *node);
10552 #include <isl/schedule_node.h>
10553 __isl_give isl_union_map *
10554 isl_schedule_node_expansion_get_expansion(
10555 __isl_keep isl_schedule_node *node);
10556 __isl_give isl_union_pw_multi_aff *
10557 isl_schedule_node_expansion_get_contraction(
10558 __isl_keep isl_schedule_node *node);
10560 #include <isl/schedule_node.h>
10561 __isl_give isl_union_map *
10562 isl_schedule_node_extension_get_extension(
10563 __isl_keep isl_schedule_node *node);
10565 #include <isl/schedule_node.h>
10566 __isl_give isl_union_set *
10567 isl_schedule_node_filter_get_filter(
10568 __isl_keep isl_schedule_node *node);
10570 #include <isl/schedule_node.h>
10571 __isl_give isl_set *isl_schedule_node_guard_get_guard(
10572 __isl_keep isl_schedule_node *node);
10574 #include <isl/schedule_node.h>
10575 __isl_give isl_id *isl_schedule_node_mark_get_id(
10576 __isl_keep isl_schedule_node *node);
10578 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
10579 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
10580 partial schedules related to the node.
10582 #include <isl/schedule_node.h>
10583 __isl_give isl_multi_union_pw_aff *
10584 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
10585 __isl_keep isl_schedule_node *node);
10586 __isl_give isl_union_pw_multi_aff *
10587 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
10588 __isl_keep isl_schedule_node *node);
10589 __isl_give isl_union_map *
10590 isl_schedule_node_get_prefix_schedule_union_map(
10591 __isl_keep isl_schedule_node *node);
10592 __isl_give isl_union_map *
10593 isl_schedule_node_get_prefix_schedule_relation(
10594 __isl_keep isl_schedule_node *node);
10595 __isl_give isl_union_map *
10596 isl_schedule_node_get_subtree_schedule_union_map(
10597 __isl_keep isl_schedule_node *node);
10599 In particular, the functions
10600 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
10601 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
10602 and C<isl_schedule_node_get_prefix_schedule_union_map>
10603 return a relative ordering on the domain elements that reach the given
10604 node determined by its ancestors.
10605 The function C<isl_schedule_node_get_prefix_schedule_relation>
10606 additionally includes the domain constraints in the result.
10607 The function C<isl_schedule_node_get_subtree_schedule_union_map>
10608 returns a representation of the partial schedule defined by the
10609 subtree rooted at the given node.
10610 If the tree contains any expansion nodes, then the subtree schedule
10611 is formulated in terms of the expanded domain elements.
10612 The tree passed to functions returning a prefix schedule
10613 may only contain extension nodes if these would not affect
10614 the result of these functions. That is, if one of the ancestors
10615 is an extension node, then all of the domain elements that were
10616 added by the extension node need to have been filtered out
10617 by filter nodes between the extension node and the input node.
10618 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
10619 may not contain in extension nodes in the selected subtree.
10621 The expansion/contraction defined by an entire subtree, combining
10622 the expansions/contractions
10623 on the expansion nodes in the subtree, can be obtained using
10624 the following functions.
10626 #include <isl/schedule_node.h>
10627 __isl_give isl_union_map *
10628 isl_schedule_node_get_subtree_expansion(
10629 __isl_keep isl_schedule_node *node);
10630 __isl_give isl_union_pw_multi_aff *
10631 isl_schedule_node_get_subtree_contraction(
10632 __isl_keep isl_schedule_node *node);
10634 The total number of outer band members of given node, i.e.,
10635 the shared output dimension of the maps in the result
10636 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
10637 using the following function.
10639 #include <isl/schedule_node.h>
10640 isl_size isl_schedule_node_get_schedule_depth(
10641 __isl_keep isl_schedule_node *node);
10643 The following functions return the elements that reach the given node
10644 or the union of universes in the spaces that contain these elements.
10646 #include <isl/schedule_node.h>
10647 __isl_give isl_union_set *
10648 isl_schedule_node_get_domain(
10649 __isl_keep isl_schedule_node *node);
10650 __isl_give isl_union_set *
10651 isl_schedule_node_get_universe_domain(
10652 __isl_keep isl_schedule_node *node);
10654 The input tree of C<isl_schedule_node_get_domain>
10655 may only contain extension nodes if these would not affect
10656 the result of this function. That is, if one of the ancestors
10657 is an extension node, then all of the domain elements that were
10658 added by the extension node need to have been filtered out
10659 by filter nodes between the extension node and the input node.
10661 The following functions can be used to introduce additional nodes
10662 in the schedule tree. The new node is introduced at the point
10663 in the tree where the C<isl_schedule_node> points to and
10664 the results points to the new node.
10666 #include <isl/schedule_node.h>
10667 __isl_give isl_schedule_node *
10668 isl_schedule_node_insert_partial_schedule(
10669 __isl_take isl_schedule_node *node,
10670 __isl_take isl_multi_union_pw_aff *schedule);
10672 This function inserts a new band node with (the greatest integer
10673 part of) the given partial schedule.
10674 The subtree rooted at the given node is assumed not to have
10675 any anchored nodes.
10677 #include <isl/schedule_node.h>
10678 __isl_give isl_schedule_node *
10679 isl_schedule_node_insert_context(
10680 __isl_take isl_schedule_node *node,
10681 __isl_take isl_set *context);
10683 This function inserts a new context node with the given context constraints.
10685 #include <isl/schedule_node.h>
10686 __isl_give isl_schedule_node *
10687 isl_schedule_node_insert_filter(
10688 __isl_take isl_schedule_node *node,
10689 __isl_take isl_union_set *filter);
10691 This function inserts a new filter node with the given filter.
10692 If the original node already pointed to a filter node, then the
10693 two filter nodes are merged into one.
10695 #include <isl/schedule_node.h>
10696 __isl_give isl_schedule_node *
10697 isl_schedule_node_insert_guard(
10698 __isl_take isl_schedule_node *node,
10699 __isl_take isl_set *guard);
10701 This function inserts a new guard node with the given guard constraints.
10703 #include <isl/schedule_node.h>
10704 __isl_give isl_schedule_node *
10705 isl_schedule_node_insert_mark(
10706 __isl_take isl_schedule_node *node,
10707 __isl_take isl_id *mark);
10709 This function inserts a new mark node with the give mark identifier.
10711 #include <isl/schedule_node.h>
10712 __isl_give isl_schedule_node *
10713 isl_schedule_node_insert_sequence(
10714 __isl_take isl_schedule_node *node,
10715 __isl_take isl_union_set_list *filters);
10716 __isl_give isl_schedule_node *
10717 isl_schedule_node_insert_set(
10718 __isl_take isl_schedule_node *node,
10719 __isl_take isl_union_set_list *filters);
10721 These functions insert a new sequence or set node with the given
10722 filters as children.
10724 #include <isl/schedule_node.h>
10725 __isl_give isl_schedule_node *isl_schedule_node_group(
10726 __isl_take isl_schedule_node *node,
10727 __isl_take isl_id *group_id);
10729 This function introduces an expansion node in between the current
10730 node and its parent that expands instances of a space with tuple
10731 identifier C<group_id> to the original domain elements that reach
10732 the node. The group instances are identified by the prefix schedule
10733 of those domain elements. The ancestors of the node are adjusted
10734 to refer to the group instances instead of the original domain
10735 elements. The return value points to the same node in the updated
10736 schedule tree as the input node, i.e., to the child of the newly
10737 introduced expansion node. Grouping instances of different statements
10738 ensures that they will be treated as a single statement by the
10739 AST generator up to the point of the expansion node.
10741 The following functions can be used to flatten a nested
10744 #include <isl/schedule_node.h>
10745 __isl_give isl_schedule_node *
10746 isl_schedule_node_sequence_splice_child(
10747 __isl_take isl_schedule_node *node, int pos);
10748 __isl_give isl_schedule_node *
10749 isl_schedule_node_sequence_splice_children(
10750 __isl_take isl_schedule_node *node);
10752 That is, given a sequence node C<node> that has another sequence node
10753 in its child at position C<pos> (in particular, the child of that filter
10754 node is a sequence node), the function
10755 C<isl_schedule_node_sequence_splice_child>
10756 attaches the children of that other sequence
10757 node as children of C<node>, replacing the original child at position
10759 C<isl_schedule_node_sequence_splice_children> does this for all
10762 The partial schedule of a band node can be scaled (down) or reduced using
10763 the following functions.
10765 #include <isl/schedule_node.h>
10766 __isl_give isl_schedule_node *
10767 isl_schedule_node_band_scale(
10768 __isl_take isl_schedule_node *node,
10769 __isl_take isl_multi_val *mv);
10770 __isl_give isl_schedule_node *
10771 isl_schedule_node_band_scale_down(
10772 __isl_take isl_schedule_node *node,
10773 __isl_take isl_multi_val *mv);
10774 __isl_give isl_schedule_node *
10775 isl_schedule_node_band_mod(
10776 __isl_take isl_schedule_node *node,
10777 __isl_take isl_multi_val *mv);
10779 The spaces of the two arguments need to match.
10780 After scaling, the partial schedule is replaced by its greatest
10781 integer part to ensure that the schedule remains integral.
10783 The partial schedule of a band node can be shifted by an
10784 C<isl_multi_union_pw_aff> with a domain that is a superset
10785 of the domain of the partial schedule using
10786 the following function.
10788 #include <isl/schedule_node.h>
10789 __isl_give isl_schedule_node *
10790 isl_schedule_node_band_shift(
10791 __isl_take isl_schedule_node *node,
10792 __isl_take isl_multi_union_pw_aff *shift);
10794 A band node can be tiled using the following function.
10796 #include <isl/schedule_node.h>
10797 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
10798 __isl_take isl_schedule_node *node,
10799 __isl_take isl_multi_val *sizes);
10801 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
10803 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
10804 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
10806 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
10808 The C<isl_schedule_node_band_tile> function tiles
10809 the band using the given tile sizes inside its schedule.
10810 A new child band node is created to represent the point loops and it is
10811 inserted between the modified band and its children.
10812 The subtree rooted at the given node is assumed not to have
10813 any anchored nodes.
10814 The C<tile_scale_tile_loops> option specifies whether the tile
10815 loops iterators should be scaled by the tile sizes.
10816 If the C<tile_shift_point_loops> option is set, then the point loops
10817 are shifted to start at zero.
10819 A band node can be split into two nested band nodes
10820 using the following function.
10822 #include <isl/schedule_node.h>
10823 __isl_give isl_schedule_node *isl_schedule_node_band_split(
10824 __isl_take isl_schedule_node *node, int pos);
10826 The resulting outer band node contains the first C<pos> dimensions of
10827 the schedule of C<node> while the inner band contains the remaining dimensions.
10828 The schedules of the two band nodes live in anonymous spaces.
10829 The loop AST generation type options and the isolate option
10830 are split over the two band nodes.
10832 A band node can be moved down to the leaves of the subtree rooted
10833 at the band node using the following function.
10835 #include <isl/schedule_node.h>
10836 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
10837 __isl_take isl_schedule_node *node);
10839 The subtree rooted at the given node is assumed not to have
10840 any anchored nodes.
10841 The result points to the node in the resulting tree that is in the same
10842 position as the node pointed to by C<node> in the original tree.
10844 #include <isl/schedule_node.h>
10845 __isl_give isl_schedule_node *
10846 isl_schedule_node_order_before(
10847 __isl_take isl_schedule_node *node,
10848 __isl_take isl_union_set *filter);
10849 __isl_give isl_schedule_node *
10850 isl_schedule_node_order_after(
10851 __isl_take isl_schedule_node *node,
10852 __isl_take isl_union_set *filter);
10854 These functions split the domain elements that reach C<node>
10855 into those that satisfy C<filter> and those that do not and
10856 arranges for the elements that do satisfy the filter to be
10857 executed before (in case of C<isl_schedule_node_order_before>)
10858 or after (in case of C<isl_schedule_node_order_after>)
10859 those that do not. The order is imposed by
10860 a sequence node, possibly reusing the grandparent of C<node>
10861 on two copies of the subtree attached to the original C<node>.
10862 Both copies are simplified with respect to their filter.
10864 Return a pointer to the copy of the subtree that does not
10865 satisfy C<filter>. If there is no such copy (because all
10866 reaching domain elements satisfy the filter), then return
10867 the original pointer.
10869 #include <isl/schedule_node.h>
10870 __isl_give isl_schedule_node *
10871 isl_schedule_node_graft_before(
10872 __isl_take isl_schedule_node *node,
10873 __isl_take isl_schedule_node *graft);
10874 __isl_give isl_schedule_node *
10875 isl_schedule_node_graft_after(
10876 __isl_take isl_schedule_node *node,
10877 __isl_take isl_schedule_node *graft);
10879 This function inserts the C<graft> tree into the tree containing C<node>
10880 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
10881 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
10882 The root node of C<graft>
10883 should be an extension node where the domain of the extension
10884 is the flat product of all outer band nodes of C<node>.
10885 The root node may also be a domain node.
10886 The elements of the domain or the range of the extension may not
10887 intersect with the domain elements that reach "node".
10888 The schedule tree of C<graft> may not be anchored.
10890 The schedule tree of C<node> is modified to include an extension node
10891 corresponding to the root node of C<graft> as a child of the original
10892 parent of C<node>. The original node that C<node> points to and the
10893 child of the root node of C<graft> are attached to this extension node
10894 through a sequence, with appropriate filters and with the child
10895 of C<graft> appearing before or after the original C<node>.
10897 If C<node> already appears inside a sequence that is the child of
10898 an extension node and if the spaces of the new domain elements
10899 do not overlap with those of the original domain elements,
10900 then that extension node is extended with the new extension
10901 rather than introducing a new segment of extension and sequence nodes.
10903 Return a pointer to the same node in the modified tree that
10904 C<node> pointed to in the original tree.
10906 A representation of the schedule node can be printed using
10908 #include <isl/schedule_node.h>
10909 __isl_give isl_printer *isl_printer_print_schedule_node(
10910 __isl_take isl_printer *p,
10911 __isl_keep isl_schedule_node *node);
10912 __isl_give char *isl_schedule_node_to_str(
10913 __isl_keep isl_schedule_node *node);
10915 C<isl_schedule_node_to_str> prints the schedule node in block format.
10917 =head2 Dependence Analysis
10919 C<isl> contains specialized functionality for performing
10920 array dataflow analysis. That is, given a I<sink> access relation,
10921 a collection of possible I<source> accesses and
10922 a collection of I<kill> accesses,
10923 C<isl> can compute relations that describe
10924 for each iteration of the sink access, which iterations
10925 of which of the source access relations may have
10926 accessed the same data element before the given iteration
10927 of the sink access without any intermediate kill of that data element.
10928 The resulting dependence relations map source iterations
10929 to either the corresponding sink iterations or
10930 pairs of corresponding sink iterations and accessed data elements.
10931 To compute standard flow dependences, the sink should be
10932 a read, while the sources should be writes.
10933 If no kills are specified,
10934 then memory based dependence analysis is performed.
10935 If, on the other hand, all sources are also kills,
10936 then value based dependence analysis is performed.
10937 If any of the source accesses are marked as being I<must>
10938 accesses, then they are also treated as kills.
10939 Furthermore, the specification of must-sources results
10940 in the computation of must-dependences.
10941 Only dependences originating in a must access not coscheduled
10942 with any other access to the same element and without
10943 any may accesses between the must access and the sink access
10944 are considered to be must dependences.
10946 =head3 High-level Interface
10948 A high-level interface to dependence analysis is provided
10949 by the following function.
10951 #include <isl/flow.h>
10952 __isl_give isl_union_flow *
10953 isl_union_access_info_compute_flow(
10954 __isl_take isl_union_access_info *access);
10956 The input C<isl_union_access_info> object describes the sink
10957 access relations, the source access relations and a schedule,
10958 while the output C<isl_union_flow> object describes
10959 the resulting dependence relations and the subsets of the
10960 sink relations for which no source was found.
10962 An C<isl_union_access_info> is created, modified, copied and freed using
10963 the following functions.
10965 #include <isl/flow.h>
10966 __isl_give isl_union_access_info *
10967 isl_union_access_info_from_sink(
10968 __isl_take isl_union_map *sink);
10969 __isl_give isl_union_access_info *
10970 isl_union_access_info_set_kill(
10971 __isl_take isl_union_access_info *access,
10972 __isl_take isl_union_map *kill);
10973 __isl_give isl_union_access_info *
10974 isl_union_access_info_set_may_source(
10975 __isl_take isl_union_access_info *access,
10976 __isl_take isl_union_map *may_source);
10977 __isl_give isl_union_access_info *
10978 isl_union_access_info_set_must_source(
10979 __isl_take isl_union_access_info *access,
10980 __isl_take isl_union_map *must_source);
10981 __isl_give isl_union_access_info *
10982 isl_union_access_info_set_schedule(
10983 __isl_take isl_union_access_info *access,
10984 __isl_take isl_schedule *schedule);
10985 __isl_give isl_union_access_info *
10986 isl_union_access_info_set_schedule_map(
10987 __isl_take isl_union_access_info *access,
10988 __isl_take isl_union_map *schedule_map);
10989 __isl_give isl_union_access_info *
10990 isl_union_access_info_copy(
10991 __isl_keep isl_union_access_info *access);
10992 __isl_null isl_union_access_info *
10993 isl_union_access_info_free(
10994 __isl_take isl_union_access_info *access);
10996 The may sources set by C<isl_union_access_info_set_may_source>
10997 do not need to include the must sources set by
10998 C<isl_union_access_info_set_must_source> as a subset.
10999 The kills set by C<isl_union_access_info_set_kill> may overlap
11000 with the may-sources and/or must-sources.
11001 The user is free not to call one (or more) of these functions,
11002 in which case the corresponding set is kept to its empty default.
11003 Similarly, the default schedule initialized by
11004 C<isl_union_access_info_from_sink> is empty.
11005 The current schedule is determined by the last call to either
11006 C<isl_union_access_info_set_schedule> or
11007 C<isl_union_access_info_set_schedule_map>.
11008 The domain of the schedule corresponds to the domains of
11009 the access relations. In particular, the domains of the access
11010 relations are effectively intersected with the domain of the schedule
11011 and only the resulting accesses are considered by the dependence analysis.
11013 An C<isl_union_access_info> object can be read from input
11014 using the following function.
11016 #include <isl/flow.h>
11017 __isl_give isl_union_access_info *
11018 isl_union_access_info_read_from_file(isl_ctx *ctx,
11021 A representation of the information contained in an object
11022 of type C<isl_union_access_info> can be obtained using
11024 #include <isl/flow.h>
11025 __isl_give isl_printer *
11026 isl_printer_print_union_access_info(
11027 __isl_take isl_printer *p,
11028 __isl_keep isl_union_access_info *access);
11029 __isl_give char *isl_union_access_info_to_str(
11030 __isl_keep isl_union_access_info *access);
11032 C<isl_union_access_info_to_str> prints the information in flow format.
11034 The output of C<isl_union_access_info_compute_flow> can be examined,
11035 copied, and freed using the following functions.
11037 #include <isl/flow.h>
11038 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
11039 __isl_keep isl_union_flow *flow);
11040 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
11041 __isl_keep isl_union_flow *flow);
11042 __isl_give isl_union_map *
11043 isl_union_flow_get_full_must_dependence(
11044 __isl_keep isl_union_flow *flow);
11045 __isl_give isl_union_map *
11046 isl_union_flow_get_full_may_dependence(
11047 __isl_keep isl_union_flow *flow);
11048 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
11049 __isl_keep isl_union_flow *flow);
11050 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
11051 __isl_keep isl_union_flow *flow);
11052 __isl_give isl_union_flow *isl_union_flow_copy(
11053 __isl_keep isl_union_flow *flow);
11054 __isl_null isl_union_flow *isl_union_flow_free(
11055 __isl_take isl_union_flow *flow);
11057 The relation returned by C<isl_union_flow_get_must_dependence>
11058 relates domain elements of must sources to domain elements of the sink.
11059 The relation returned by C<isl_union_flow_get_may_dependence>
11060 relates domain elements of must or may sources to domain elements of the sink
11061 and includes the previous relation as a subset.
11062 The relation returned by C<isl_union_flow_get_full_must_dependence>
11063 relates domain elements of must sources to pairs of domain elements of the sink
11064 and accessed data elements.
11065 The relation returned by C<isl_union_flow_get_full_may_dependence>
11066 relates domain elements of must or may sources to pairs of
11067 domain elements of the sink and accessed data elements.
11068 This relation includes the previous relation as a subset.
11069 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
11070 of the sink relation for which no dependences have been found.
11071 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
11072 of the sink relation for which no definite dependences have been found.
11073 That is, it contains those sink access that do not contribute to any
11074 of the elements in the relation returned
11075 by C<isl_union_flow_get_must_dependence>.
11077 A representation of the information contained in an object
11078 of type C<isl_union_flow> can be obtained using
11080 #include <isl/flow.h>
11081 __isl_give isl_printer *isl_printer_print_union_flow(
11082 __isl_take isl_printer *p,
11083 __isl_keep isl_union_flow *flow);
11084 __isl_give char *isl_union_flow_to_str(
11085 __isl_keep isl_union_flow *flow);
11087 C<isl_union_flow_to_str> prints the information in flow format.
11089 =head3 Low-level Interface
11091 A lower-level interface is provided by the following functions.
11093 #include <isl/flow.h>
11095 typedef int (*isl_access_level_before)(void *first, void *second);
11097 __isl_give isl_access_info *isl_access_info_alloc(
11098 __isl_take isl_map *sink,
11099 void *sink_user, isl_access_level_before fn,
11101 __isl_give isl_access_info *isl_access_info_add_source(
11102 __isl_take isl_access_info *acc,
11103 __isl_take isl_map *source, int must,
11104 void *source_user);
11105 __isl_null isl_access_info *isl_access_info_free(
11106 __isl_take isl_access_info *acc);
11108 __isl_give isl_flow *isl_access_info_compute_flow(
11109 __isl_take isl_access_info *acc);
11111 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,
11112 isl_stat (*fn)(__isl_take isl_map *dep, int must,
11113 void *dep_user, void *user),
11115 __isl_give isl_map *isl_flow_get_no_source(
11116 __isl_keep isl_flow *deps, int must);
11117 __isl_null isl_flow *isl_flow_free(
11118 __isl_take isl_flow *deps);
11120 The function C<isl_access_info_compute_flow> performs the actual
11121 dependence analysis. The other functions are used to construct
11122 the input for this function or to read off the output.
11124 The input is collected in an C<isl_access_info>, which can
11125 be created through a call to C<isl_access_info_alloc>.
11126 The arguments to this functions are the sink access relation
11127 C<sink>, a token C<sink_user> used to identify the sink
11128 access to the user, a callback function for specifying the
11129 relative order of source and sink accesses, and the number
11130 of source access relations that will be added.
11132 The callback function has type C<int (*)(void *first, void *second)>.
11133 The function is called with two user supplied tokens identifying
11134 either a source or the sink and it should return the shared nesting
11135 level and the relative order of the two accesses.
11136 In particular, let I<n> be the number of loops shared by
11137 the two accesses. If C<first> precedes C<second> textually,
11138 then the function should return I<2 * n + 1>; otherwise,
11139 it should return I<2 * n>.
11140 The low-level interface assumes that no sources are coscheduled.
11141 If the information returned by the callback does not allow
11142 the relative order to be determined, then one of the sources
11143 is arbitrarily taken to be executed after the other(s).
11145 The sources can be added to the C<isl_access_info> object by performing
11146 (at most) C<max_source> calls to C<isl_access_info_add_source>.
11147 C<must> indicates whether the source is a I<must> access
11148 or a I<may> access. Note that a multi-valued access relation
11149 should only be marked I<must> if every iteration in the domain
11150 of the relation accesses I<all> elements in its image.
11151 The C<source_user> token is again used to identify
11152 the source access. The range of the source access relation
11153 C<source> should have the same dimension as the range
11154 of the sink access relation.
11155 The C<isl_access_info_free> function should usually not be
11156 called explicitly, because it is already called implicitly by
11157 C<isl_access_info_compute_flow>.
11159 The result of the dependence analysis is collected in an
11160 C<isl_flow>. There may be elements of
11161 the sink access for which no preceding source access could be
11162 found or for which all preceding sources are I<may> accesses.
11163 The relations containing these elements can be obtained through
11164 calls to C<isl_flow_get_no_source>, the first with C<must> set
11165 and the second with C<must> unset.
11166 In the case of standard flow dependence analysis,
11167 with the sink a read and the sources I<must> writes,
11168 the first relation corresponds to the reads from uninitialized
11169 array elements and the second relation is empty.
11170 The actual flow dependences can be extracted using
11171 C<isl_flow_foreach>. This function will call the user-specified
11172 callback function C<fn> for each B<non-empty> dependence between
11173 a source and the sink. The callback function is called
11174 with four arguments, the actual flow dependence relation
11175 mapping source iterations to sink iterations, a boolean that
11176 indicates whether it is a I<must> or I<may> dependence, a token
11177 identifying the source and an additional C<void *> with value
11178 equal to the third argument of the C<isl_flow_foreach> call.
11179 A dependence is marked I<must> if it originates from a I<must>
11180 source and if it is not followed by any I<may> sources.
11182 After finishing with an C<isl_flow>, the user should call
11183 C<isl_flow_free> to free all associated memory.
11185 =head3 Interaction with the Low-level Interface
11187 During the dependence analysis, we frequently need to perform
11188 the following operation. Given a relation between sink iterations
11189 and potential source iterations from a particular source domain,
11190 what is the last potential source iteration corresponding to each
11191 sink iteration. It can sometimes be convenient to adjust
11192 the set of potential source iterations before or after each such operation.
11193 The prototypical example is fuzzy array dataflow analysis,
11194 where we need to analyze if, based on data-dependent constraints,
11195 the sink iteration can ever be executed without one or more of
11196 the corresponding potential source iterations being executed.
11197 If so, we can introduce extra parameters and select an unknown
11198 but fixed source iteration from the potential source iterations.
11199 To be able to perform such manipulations, C<isl> provides the following
11202 #include <isl/flow.h>
11204 typedef __isl_give isl_restriction *(*isl_access_restrict)(
11205 __isl_keep isl_map *source_map,
11206 __isl_keep isl_set *sink, void *source_user,
11208 __isl_give isl_access_info *isl_access_info_set_restrict(
11209 __isl_take isl_access_info *acc,
11210 isl_access_restrict fn, void *user);
11212 The function C<isl_access_info_set_restrict> should be called
11213 before calling C<isl_access_info_compute_flow> and registers a callback function
11214 that will be called any time C<isl> is about to compute the last
11215 potential source. The first argument is the (reverse) proto-dependence,
11216 mapping sink iterations to potential source iterations.
11217 The second argument represents the sink iterations for which
11218 we want to compute the last source iteration.
11219 The third argument is the token corresponding to the source
11220 and the final argument is the token passed to C<isl_access_info_set_restrict>.
11221 The callback is expected to return a restriction on either the input or
11222 the output of the operation computing the last potential source.
11223 If the input needs to be restricted then restrictions are needed
11224 for both the source and the sink iterations. The sink iterations
11225 and the potential source iterations will be intersected with these sets.
11226 If the output needs to be restricted then only a restriction on the source
11227 iterations is required.
11228 If any error occurs, the callback should return C<NULL>.
11229 An C<isl_restriction> object can be created, freed and inspected
11230 using the following functions.
11232 #include <isl/flow.h>
11234 __isl_give isl_restriction *isl_restriction_input(
11235 __isl_take isl_set *source_restr,
11236 __isl_take isl_set *sink_restr);
11237 __isl_give isl_restriction *isl_restriction_output(
11238 __isl_take isl_set *source_restr);
11239 __isl_give isl_restriction *isl_restriction_none(
11240 __isl_take isl_map *source_map);
11241 __isl_give isl_restriction *isl_restriction_empty(
11242 __isl_take isl_map *source_map);
11243 __isl_null isl_restriction *isl_restriction_free(
11244 __isl_take isl_restriction *restr);
11246 C<isl_restriction_none> and C<isl_restriction_empty> are special
11247 cases of C<isl_restriction_input>. C<isl_restriction_none>
11248 is essentially equivalent to
11250 isl_restriction_input(isl_set_universe(
11251 isl_space_range(isl_map_get_space(source_map))),
11253 isl_space_domain(isl_map_get_space(source_map))));
11255 whereas C<isl_restriction_empty> is essentially equivalent to
11257 isl_restriction_input(isl_set_empty(
11258 isl_space_range(isl_map_get_space(source_map))),
11260 isl_space_domain(isl_map_get_space(source_map))));
11264 #include <isl/schedule.h>
11265 __isl_give isl_schedule *
11266 isl_schedule_constraints_compute_schedule(
11267 __isl_take isl_schedule_constraints *sc);
11269 The function C<isl_schedule_constraints_compute_schedule> can be
11270 used to compute a schedule that satisfies the given schedule constraints.
11271 These schedule constraints include the iteration domain for which
11272 a schedule should be computed and dependences between pairs of
11273 iterations. In particular, these dependences include
11274 I<validity> dependences and I<proximity> dependences.
11275 By default, the algorithm used to construct the schedule is similar
11276 to that of C<Pluto>.
11277 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
11279 The generated schedule respects all validity dependences.
11280 That is, all dependence distances over these dependences in the
11281 scheduled space are lexicographically positive.
11283 The default algorithm tries to ensure that the dependence distances
11284 over coincidence constraints are zero and to minimize the
11285 dependence distances over proximity dependences.
11286 Moreover, it tries to obtain sequences (bands) of schedule dimensions
11287 for groups of domains where the dependence distances over validity
11288 dependences have only non-negative values.
11289 Note that when minimizing the maximal dependence distance
11290 over proximity dependences, a single affine expression in the parameters
11291 is constructed that bounds all dependence distances. If no such expression
11292 exists, then the algorithm will fail and resort to an alternative
11293 scheduling algorithm. In particular, this means that adding proximity
11294 dependences may eliminate valid solutions. A typical example where this
11295 phenomenon may occur is when some subset of the proximity dependences
11296 has no restriction on some parameter, forcing the coefficient of that
11297 parameter to be zero, while some other subset forces the dependence
11298 distance to depend on that parameter, requiring the same coefficient
11300 When using Feautrier's algorithm, the coincidence and proximity constraints
11301 are only taken into account during the extension to a
11302 full-dimensional schedule.
11304 An C<isl_schedule_constraints> object can be constructed
11305 and manipulated using the following functions.
11307 #include <isl/schedule.h>
11308 __isl_give isl_schedule_constraints *
11309 isl_schedule_constraints_copy(
11310 __isl_keep isl_schedule_constraints *sc);
11311 __isl_give isl_schedule_constraints *
11312 isl_schedule_constraints_on_domain(
11313 __isl_take isl_union_set *domain);
11314 __isl_give isl_schedule_constraints *
11315 isl_schedule_constraints_set_context(
11316 __isl_take isl_schedule_constraints *sc,
11317 __isl_take isl_set *context);
11318 __isl_give isl_schedule_constraints *
11319 isl_schedule_constraints_set_validity(
11320 __isl_take isl_schedule_constraints *sc,
11321 __isl_take isl_union_map *validity);
11322 __isl_give isl_schedule_constraints *
11323 isl_schedule_constraints_set_coincidence(
11324 __isl_take isl_schedule_constraints *sc,
11325 __isl_take isl_union_map *coincidence);
11326 __isl_give isl_schedule_constraints *
11327 isl_schedule_constraints_set_proximity(
11328 __isl_take isl_schedule_constraints *sc,
11329 __isl_take isl_union_map *proximity);
11330 __isl_give isl_schedule_constraints *
11331 isl_schedule_constraints_set_conditional_validity(
11332 __isl_take isl_schedule_constraints *sc,
11333 __isl_take isl_union_map *condition,
11334 __isl_take isl_union_map *validity);
11335 __isl_give isl_schedule_constraints *
11336 isl_schedule_constraints_apply(
11337 __isl_take isl_schedule_constraints *sc,
11338 __isl_take isl_union_map *umap);
11339 __isl_null isl_schedule_constraints *
11340 isl_schedule_constraints_free(
11341 __isl_take isl_schedule_constraints *sc);
11343 The initial C<isl_schedule_constraints> object created by
11344 C<isl_schedule_constraints_on_domain> does not impose any constraints.
11345 That is, it has an empty set of dependences.
11346 The function C<isl_schedule_constraints_set_context> allows the user
11347 to specify additional constraints on the parameters that may
11348 be assumed to hold during the construction of the schedule.
11349 The function C<isl_schedule_constraints_set_validity> replaces the
11350 validity dependences, mapping domain elements I<i> to domain
11351 elements that should be scheduled after I<i>.
11352 The function C<isl_schedule_constraints_set_coincidence> replaces the
11353 coincidence dependences, mapping domain elements I<i> to domain
11354 elements that should be scheduled together with I<I>, if possible.
11355 The function C<isl_schedule_constraints_set_proximity> replaces the
11356 proximity dependences, mapping domain elements I<i> to domain
11357 elements that should be scheduled either before I<I>
11358 or as early as possible after I<i>.
11360 The function C<isl_schedule_constraints_set_conditional_validity>
11361 replaces the conditional validity constraints.
11362 A conditional validity constraint is only imposed when any of the corresponding
11363 conditions is satisfied, i.e., when any of them is non-zero.
11364 That is, the scheduler ensures that within each band if the dependence
11365 distances over the condition constraints are not all zero
11366 then all corresponding conditional validity constraints are respected.
11367 A conditional validity constraint corresponds to a condition
11368 if the two are adjacent, i.e., if the domain of one relation intersect
11369 the range of the other relation.
11370 The typical use case of conditional validity constraints is
11371 to allow order constraints between live ranges to be violated
11372 as long as the live ranges themselves are local to the band.
11373 To allow more fine-grained control over which conditions correspond
11374 to which conditional validity constraints, the domains and ranges
11375 of these relations may include I<tags>. That is, the domains and
11376 ranges of those relation may themselves be wrapped relations
11377 where the iteration domain appears in the domain of those wrapped relations
11378 and the range of the wrapped relations can be arbitrarily chosen
11379 by the user. Conditions and conditional validity constraints are only
11380 considered adjacent to each other if the entire wrapped relation matches.
11381 In particular, a relation with a tag will never be considered adjacent
11382 to a relation without a tag.
11384 The function C<isl_schedule_constraints_apply> takes
11385 schedule constraints that are defined on some set of domain elements
11386 and transforms them to schedule constraints on the elements
11387 to which these domain elements are mapped by the given transformation.
11389 An C<isl_schedule_constraints> object can be inspected
11390 using the following functions.
11392 #include <isl/schedule.h>
11393 __isl_give isl_union_set *
11394 isl_schedule_constraints_get_domain(
11395 __isl_keep isl_schedule_constraints *sc);
11396 __isl_give isl_set *isl_schedule_constraints_get_context(
11397 __isl_keep isl_schedule_constraints *sc);
11398 __isl_give isl_union_map *
11399 isl_schedule_constraints_get_validity(
11400 __isl_keep isl_schedule_constraints *sc);
11401 __isl_give isl_union_map *
11402 isl_schedule_constraints_get_coincidence(
11403 __isl_keep isl_schedule_constraints *sc);
11404 __isl_give isl_union_map *
11405 isl_schedule_constraints_get_proximity(
11406 __isl_keep isl_schedule_constraints *sc);
11407 __isl_give isl_union_map *
11408 isl_schedule_constraints_get_conditional_validity(
11409 __isl_keep isl_schedule_constraints *sc);
11410 __isl_give isl_union_map *
11411 isl_schedule_constraints_get_conditional_validity_condition(
11412 __isl_keep isl_schedule_constraints *sc);
11414 An C<isl_schedule_constraints> object can be read from input
11415 using the following functions.
11417 #include <isl/schedule.h>
11418 __isl_give isl_schedule_constraints *
11419 isl_schedule_constraints_read_from_str(isl_ctx *ctx,
11421 __isl_give isl_schedule_constraints *
11422 isl_schedule_constraints_read_from_file(isl_ctx *ctx,
11425 The contents of an C<isl_schedule_constraints> object can be printed
11426 using the following functions.
11428 #include <isl/schedule.h>
11429 __isl_give isl_printer *
11430 isl_printer_print_schedule_constraints(
11431 __isl_take isl_printer *p,
11432 __isl_keep isl_schedule_constraints *sc);
11433 __isl_give char *isl_schedule_constraints_to_str(
11434 __isl_keep isl_schedule_constraints *sc);
11436 The following function computes a schedule directly from
11437 an iteration domain and validity and proximity dependences
11438 and is implemented in terms of the functions described above.
11439 The use of C<isl_union_set_compute_schedule> is discouraged.
11441 #include <isl/schedule.h>
11442 __isl_give isl_schedule *isl_union_set_compute_schedule(
11443 __isl_take isl_union_set *domain,
11444 __isl_take isl_union_map *validity,
11445 __isl_take isl_union_map *proximity);
11447 The generated schedule represents a schedule tree.
11448 For more information on schedule trees, see
11449 L</"Schedule Trees">.
11453 #include <isl/schedule.h>
11454 isl_stat isl_options_set_schedule_max_coefficient(
11455 isl_ctx *ctx, int val);
11456 int isl_options_get_schedule_max_coefficient(
11458 isl_stat isl_options_set_schedule_max_constant_term(
11459 isl_ctx *ctx, int val);
11460 int isl_options_get_schedule_max_constant_term(
11462 isl_stat isl_options_set_schedule_serialize_sccs(
11463 isl_ctx *ctx, int val);
11464 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx);
11465 isl_stat isl_options_set_schedule_whole_component(
11466 isl_ctx *ctx, int val);
11467 int isl_options_get_schedule_whole_component(
11469 isl_stat isl_options_set_schedule_maximize_band_depth(
11470 isl_ctx *ctx, int val);
11471 int isl_options_get_schedule_maximize_band_depth(
11473 isl_stat isl_options_set_schedule_maximize_coincidence(
11474 isl_ctx *ctx, int val);
11475 int isl_options_get_schedule_maximize_coincidence(
11477 isl_stat isl_options_set_schedule_outer_coincidence(
11478 isl_ctx *ctx, int val);
11479 int isl_options_get_schedule_outer_coincidence(
11481 isl_stat isl_options_set_schedule_split_scaled(
11482 isl_ctx *ctx, int val);
11483 int isl_options_get_schedule_split_scaled(
11485 isl_stat isl_options_set_schedule_treat_coalescing(
11486 isl_ctx *ctx, int val);
11487 int isl_options_get_schedule_treat_coalescing(
11489 isl_stat isl_options_set_schedule_algorithm(
11490 isl_ctx *ctx, int val);
11491 int isl_options_get_schedule_algorithm(
11493 isl_stat isl_options_set_schedule_carry_self_first(
11494 isl_ctx *ctx, int val);
11495 int isl_options_get_schedule_carry_self_first(
11497 isl_stat isl_options_set_schedule_separate_components(
11498 isl_ctx *ctx, int val);
11499 int isl_options_get_schedule_separate_components(
11504 =item * schedule_max_coefficient
11506 This option enforces that the coefficients for variable and parameter
11507 dimensions in the calculated schedule are not larger than the specified value.
11508 This option can significantly increase the speed of the scheduling calculation
11509 and may also prevent fusing of unrelated dimensions. A value of -1 means that
11510 this option does not introduce bounds on the variable or parameter
11512 This option has no effect on the Feautrier style scheduler.
11514 =item * schedule_max_constant_term
11516 This option enforces that the constant coefficients in the calculated schedule
11517 are not larger than the maximal constant term. This option can significantly
11518 increase the speed of the scheduling calculation and may also prevent fusing of
11519 unrelated dimensions. A value of -1 means that this option does not introduce
11520 bounds on the constant coefficients.
11522 =item * schedule_serialize_sccs
11524 If this option is set, then all strongly connected components
11525 in the dependence graph are serialized as soon as they are detected.
11526 This means in particular that instances of statements will only
11527 appear in the same band node if these statements belong
11528 to the same strongly connected component at the point where
11529 the band node is constructed.
11531 =item * schedule_whole_component
11533 If this option is set, then entire (weakly) connected
11534 components in the dependence graph are scheduled together
11536 Otherwise, each strongly connected component within
11537 such a weakly connected component is first scheduled separately
11538 and then combined with other strongly connected components.
11539 This option has no effect if C<schedule_serialize_sccs> is set.
11541 =item * schedule_maximize_band_depth
11543 If this option is set, then the scheduler tries to maximize
11544 the width of the bands. Wider bands give more possibilities for tiling.
11545 In particular, if the C<schedule_whole_component> option is set,
11546 then bands are split if this might result in wider bands.
11547 Otherwise, the effect of this option is to only allow
11548 strongly connected components to be combined if this does
11549 not reduce the width of the bands.
11550 Note that if the C<schedule_serialize_sccs> options is set, then
11551 the C<schedule_maximize_band_depth> option therefore has no effect.
11553 =item * schedule_maximize_coincidence
11555 This option is only effective if the C<schedule_whole_component>
11556 option is turned off.
11557 If the C<schedule_maximize_coincidence> option is set, then (clusters of)
11558 strongly connected components are only combined with each other
11559 if this does not reduce the number of coincident band members.
11561 =item * schedule_outer_coincidence
11563 If this option is set, then we try to construct schedules
11564 where the outermost scheduling dimension in each band
11565 satisfies the coincidence constraints.
11567 =item * schedule_algorithm
11569 Selects the scheduling algorithm to be used.
11570 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
11571 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
11573 =item * schedule_split_scaled
11575 If this option is set, then we try to construct schedules in which the
11576 constant term is split off from the linear part if the linear parts of
11577 the scheduling rows for all nodes in the graph have a common non-trivial
11579 The constant term is then dropped and the linear
11581 This option is only effective when the Feautrier style scheduler is
11582 being used, either as the main scheduler or as a fallback for the
11583 Pluto-like scheduler.
11585 =item * schedule_treat_coalescing
11587 If this option is set, then the scheduler will try and avoid
11588 producing schedules that perform loop coalescing.
11589 In particular, for the Pluto-like scheduler, this option places
11590 bounds on the schedule coefficients based on the sizes of the instance sets.
11591 For the Feautrier style scheduler, this option detects potentially
11592 coalescing schedules and then tries to adjust the schedule to avoid
11595 =item * schedule_carry_self_first
11597 If this option is set, then the Feautrier style scheduler
11598 (when used as a fallback for the Pluto-like scheduler) will
11599 first try to only carry self-dependences.
11601 =item * schedule_separate_components
11603 If this option is set then the function C<isl_schedule_get_map>
11604 will treat set nodes in the same way as sequence nodes.
11608 =head2 AST Generation
11610 This section describes the C<isl> functionality for generating
11611 ASTs that visit all the elements
11612 in a domain in an order specified by a schedule tree or
11614 In case the schedule given as a C<isl_union_map>, an AST is generated
11615 that visits all the elements in the domain of the C<isl_union_map>
11616 according to the lexicographic order of the corresponding image
11617 element(s). If the range of the C<isl_union_map> consists of
11618 elements in more than one space, then each of these spaces is handled
11619 separately in an arbitrary order.
11620 It should be noted that the schedule tree or the image elements
11621 in a schedule map only specify the I<order>
11622 in which the corresponding domain elements should be visited.
11623 No direct relation between the partial schedule values
11624 or the image elements on the one hand and the loop iterators
11625 in the generated AST on the other hand should be assumed.
11627 Each AST is generated within a build. The initial build
11628 simply specifies the constraints on the parameters (if any)
11629 and can be created, inspected, copied and freed using the following functions.
11631 #include <isl/ast_build.h>
11632 __isl_give isl_ast_build *isl_ast_build_alloc(
11634 __isl_give isl_ast_build *isl_ast_build_from_context(
11635 __isl_take isl_set *set);
11636 __isl_give isl_ast_build *isl_ast_build_copy(
11637 __isl_keep isl_ast_build *build);
11638 __isl_null isl_ast_build *isl_ast_build_free(
11639 __isl_take isl_ast_build *build);
11641 The C<set> argument is usually a parameter set with zero or more parameters.
11642 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
11643 this set is required to be a parameter set.
11644 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
11645 specify any parameter constraints.
11646 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
11647 and L</"Fine-grained Control over AST Generation">.
11648 Finally, the AST itself can be constructed using one of the following
11651 #include <isl/ast_build.h>
11652 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
11653 __isl_keep isl_ast_build *build,
11654 __isl_take isl_schedule *schedule);
11655 __isl_give isl_ast_node *
11656 isl_ast_build_node_from_schedule_map(
11657 __isl_keep isl_ast_build *build,
11658 __isl_take isl_union_map *schedule);
11660 =head3 Inspecting the AST
11662 The basic properties of an AST node can be obtained as follows.
11664 #include <isl/ast.h>
11665 enum isl_ast_node_type isl_ast_node_get_type(
11666 __isl_keep isl_ast_node *node);
11668 The type of an AST node is one of
11669 C<isl_ast_node_for>,
11670 C<isl_ast_node_if>,
11671 C<isl_ast_node_block>,
11672 C<isl_ast_node_mark> or
11673 C<isl_ast_node_user>.
11674 An C<isl_ast_node_for> represents a for node.
11675 An C<isl_ast_node_if> represents an if node.
11676 An C<isl_ast_node_block> represents a compound node.
11677 An C<isl_ast_node_mark> introduces a mark in the AST.
11678 An C<isl_ast_node_user> represents an expression statement.
11679 An expression statement typically corresponds to a domain element, i.e.,
11680 one of the elements that is visited by the AST.
11682 Each type of node has its own additional properties.
11684 #include <isl/ast.h>
11685 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
11686 __isl_keep isl_ast_node *node);
11687 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
11688 __isl_keep isl_ast_node *node);
11689 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
11690 __isl_keep isl_ast_node *node);
11691 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
11692 __isl_keep isl_ast_node *node);
11693 __isl_give isl_ast_node *isl_ast_node_for_get_body(
11694 __isl_keep isl_ast_node *node);
11695 isl_bool isl_ast_node_for_is_degenerate(
11696 __isl_keep isl_ast_node *node);
11698 An C<isl_ast_for> is considered degenerate if it is known to execute
11701 #include <isl/ast.h>
11702 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
11703 __isl_keep isl_ast_node *node);
11704 __isl_give isl_ast_node *isl_ast_node_if_get_then_node(
11705 __isl_keep isl_ast_node *node);
11706 __isl_give isl_ast_node *isl_ast_node_if_get_then(
11707 __isl_keep isl_ast_node *node);
11708 isl_bool isl_ast_node_if_has_else_node(
11709 __isl_keep isl_ast_node *node);
11710 isl_bool isl_ast_node_if_has_else(
11711 __isl_keep isl_ast_node *node);
11712 __isl_give isl_ast_node *isl_ast_node_if_get_else_node(
11713 __isl_keep isl_ast_node *node);
11714 __isl_give isl_ast_node *isl_ast_node_if_get_else(
11715 __isl_keep isl_ast_node *node);
11717 C<isl_ast_node_if_get_then>,
11718 C<isl_ast_node_if_has_else> and
11719 C<isl_ast_node_if_get_else>
11720 are alternative names for
11721 C<isl_ast_node_if_get_then_node>,
11722 C<isl_ast_node_if_has_else_node> and
11723 C<isl_ast_node_if_get_else_node>, respectively.
11725 __isl_give isl_ast_node_list *
11726 isl_ast_node_block_get_children(
11727 __isl_keep isl_ast_node *node);
11729 __isl_give isl_id *isl_ast_node_mark_get_id(
11730 __isl_keep isl_ast_node *node);
11731 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
11732 __isl_keep isl_ast_node *node);
11734 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
11735 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
11737 #include <isl/ast.h>
11738 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
11739 __isl_keep isl_ast_node *node);
11741 All descendants of a specific node in the AST (including the node itself)
11743 in depth-first pre-order using the following function.
11745 #include <isl/ast.h>
11746 isl_stat isl_ast_node_foreach_descendant_top_down(
11747 __isl_keep isl_ast_node *node,
11748 isl_bool (*fn)(__isl_keep isl_ast_node *node,
11749 void *user), void *user);
11751 The callback function should return C<isl_bool_true> if the children
11752 of the given node should be visited and C<isl_bool_false> if they should not.
11753 It should return C<isl_bool_error> in case of failure, in which case
11754 the entire traversal is aborted.
11756 Each of the returned C<isl_ast_expr>s can in turn be inspected using
11757 the following functions.
11759 #include <isl/ast.h>
11760 enum isl_ast_expr_type isl_ast_expr_get_type(
11761 __isl_keep isl_ast_expr *expr);
11763 The type of an AST expression is one of
11764 C<isl_ast_expr_op>,
11765 C<isl_ast_expr_id> or
11766 C<isl_ast_expr_int>.
11767 An C<isl_ast_expr_op> represents the result of an operation.
11768 An C<isl_ast_expr_id> represents an identifier.
11769 An C<isl_ast_expr_int> represents an integer value.
11771 Each type of expression has its own additional properties.
11773 #include <isl/ast.h>
11774 enum isl_ast_expr_op_type isl_ast_expr_op_get_type(
11775 __isl_keep isl_ast_expr *expr);
11776 enum isl_ast_expr_op_type isl_ast_expr_get_op_type(
11777 __isl_keep isl_ast_expr *expr);
11778 isl_size isl_ast_expr_op_get_n_arg(__isl_keep isl_ast_expr *expr);
11779 isl_size isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
11780 __isl_give isl_ast_expr *isl_ast_expr_op_get_arg(
11781 __isl_keep isl_ast_expr *expr, int pos);
11782 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
11783 __isl_keep isl_ast_expr *expr, int pos);
11784 isl_stat isl_ast_expr_foreach_ast_expr_op_type(
11785 __isl_keep isl_ast_expr *expr,
11786 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11787 void *user), void *user);
11788 isl_stat isl_ast_expr_foreach_ast_op_type(
11789 __isl_keep isl_ast_expr *expr,
11790 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11791 void *user), void *user);
11792 isl_stat isl_ast_node_foreach_ast_expr_op_type(
11793 __isl_keep isl_ast_node *node,
11794 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11795 void *user), void *user);
11796 isl_stat isl_ast_node_foreach_ast_op_type(
11797 __isl_keep isl_ast_node *node,
11798 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11799 void *user), void *user);
11801 C<isl_ast_expr_op_get_type> returns the type of the operation
11802 performed. C<isl_ast_expr_op_get_n_arg> returns the number of
11803 arguments. C<isl_ast_expr_get_op_arg> returns the specified
11805 C<isl_ast_expr_get_op_type> is an alternative name for
11806 C<isl_ast_expr_op_get_type>.
11808 C<isl_ast_expr_get_op_n_arg> is an alternative name for
11809 C<isl_ast_expr_op_get_n_arg> and
11810 C<isl_ast_expr_get_op_arg> is an alternative name for
11811 C<isl_ast_expr_op_get_arg>.
11813 C<isl_ast_expr_foreach_ast_expr_op_type> calls C<fn> for each distinct
11814 C<isl_ast_expr_op_type> that appears in C<expr>.
11815 C<isl_ast_expr_foreach_ast_op_type> is an alternative name for
11816 C<isl_ast_expr_foreach_ast_expr_op_type>.
11817 C<isl_ast_node_foreach_ast_expr_op_type> does the same for each distinct
11818 C<isl_ast_expr_op_type> that appears in C<node>.
11819 C<isl_ast_node_foreach_ast_op_type> is an alternative name for
11820 C<isl_ast_node_foreach_ast_expr_op_type>.
11821 The operation type is one of the following.
11825 =item C<isl_ast_expr_op_and>
11827 Logical I<and> of two arguments.
11828 Both arguments can be evaluated.
11830 =item C<isl_ast_expr_op_and_then>
11832 Logical I<and> of two arguments.
11833 The second argument can only be evaluated if the first evaluates to true.
11835 =item C<isl_ast_expr_op_or>
11837 Logical I<or> of two arguments.
11838 Both arguments can be evaluated.
11840 =item C<isl_ast_expr_op_or_else>
11842 Logical I<or> of two arguments.
11843 The second argument can only be evaluated if the first evaluates to false.
11845 =item C<isl_ast_expr_op_max>
11847 Maximum of two or more arguments.
11849 =item C<isl_ast_expr_op_min>
11851 Minimum of two or more arguments.
11853 =item C<isl_ast_expr_op_minus>
11857 =item C<isl_ast_expr_op_add>
11859 Sum of two arguments.
11861 =item C<isl_ast_expr_op_sub>
11863 Difference of two arguments.
11865 =item C<isl_ast_expr_op_mul>
11867 Product of two arguments.
11869 =item C<isl_ast_expr_op_div>
11871 Exact division. That is, the result is known to be an integer.
11873 =item C<isl_ast_expr_op_fdiv_q>
11875 Result of integer division, rounded towards negative
11877 The divisor is known to be positive.
11879 =item C<isl_ast_expr_op_pdiv_q>
11881 Result of integer division, where dividend is known to be non-negative.
11882 The divisor is known to be positive.
11884 =item C<isl_ast_expr_op_pdiv_r>
11886 Remainder of integer division, where dividend is known to be non-negative.
11887 The divisor is known to be positive.
11889 =item C<isl_ast_expr_op_zdiv_r>
11891 Equal to zero iff the remainder on integer division is zero.
11892 The divisor is known to be positive.
11894 =item C<isl_ast_expr_op_cond>
11896 Conditional operator defined on three arguments.
11897 If the first argument evaluates to true, then the result
11898 is equal to the second argument. Otherwise, the result
11899 is equal to the third argument.
11900 The second and third argument may only be evaluated if
11901 the first argument evaluates to true and false, respectively.
11902 Corresponds to C<a ? b : c> in C.
11904 =item C<isl_ast_expr_op_select>
11906 Conditional operator defined on three arguments.
11907 If the first argument evaluates to true, then the result
11908 is equal to the second argument. Otherwise, the result
11909 is equal to the third argument.
11910 The second and third argument may be evaluated independently
11911 of the value of the first argument.
11912 Corresponds to C<a * b + (1 - a) * c> in C.
11914 =item C<isl_ast_expr_op_eq>
11918 =item C<isl_ast_expr_op_le>
11920 Less than or equal relation.
11922 =item C<isl_ast_expr_op_lt>
11924 Less than relation.
11926 =item C<isl_ast_expr_op_ge>
11928 Greater than or equal relation.
11930 =item C<isl_ast_expr_op_gt>
11932 Greater than relation.
11934 =item C<isl_ast_expr_op_call>
11937 The number of arguments of the C<isl_ast_expr> is one more than
11938 the number of arguments in the function call, the first argument
11939 representing the function being called.
11941 =item C<isl_ast_expr_op_access>
11944 The number of arguments of the C<isl_ast_expr> is one more than
11945 the number of index expressions in the array access, the first argument
11946 representing the array being accessed.
11948 =item C<isl_ast_expr_op_member>
11951 This operation has two arguments, a structure and the name of
11952 the member of the structure being accessed.
11954 =item C<isl_ast_expr_op_address_of>
11956 The address of its single argument, which is always an array access.
11960 #include <isl/ast.h>
11961 __isl_give isl_id *isl_ast_expr_id_get_id(
11962 __isl_keep isl_ast_expr *expr);
11963 __isl_give isl_id *isl_ast_expr_get_id(
11964 __isl_keep isl_ast_expr *expr);
11966 Return the identifier represented by the AST expression.
11967 C<isl_ast_expr_get_id> is an alternative name for
11968 C<isl_ast_expr_id_get_id>.
11970 #include <isl/ast.h>
11971 __isl_give isl_val *isl_ast_expr_int_get_val(
11972 __isl_keep isl_ast_expr *expr);
11973 __isl_give isl_val *isl_ast_expr_get_val(
11974 __isl_keep isl_ast_expr *expr);
11976 Return the integer represented by the AST expression.
11977 C<isl_ast_expr_get_val> is an alternative name for
11978 C<isl_ast_expr_int_get_val>.
11980 =head3 Properties of ASTs
11982 #include <isl/ast.h>
11983 isl_bool isl_ast_expr_is_equal(
11984 __isl_keep isl_ast_expr *expr1,
11985 __isl_keep isl_ast_expr *expr2);
11987 Check if two C<isl_ast_expr>s are equal to each other.
11989 =head3 Manipulating and printing the AST
11991 AST nodes can be copied and freed using the following functions.
11993 #include <isl/ast.h>
11994 __isl_give isl_ast_node *isl_ast_node_copy(
11995 __isl_keep isl_ast_node *node);
11996 __isl_null isl_ast_node *isl_ast_node_free(
11997 __isl_take isl_ast_node *node);
11999 AST expressions can be copied and freed using the following functions.
12001 #include <isl/ast.h>
12002 __isl_give isl_ast_expr *isl_ast_expr_copy(
12003 __isl_keep isl_ast_expr *expr);
12004 __isl_null isl_ast_expr *isl_ast_expr_free(
12005 __isl_take isl_ast_expr *expr);
12007 New AST expressions can be created either directly or within
12008 the context of an C<isl_ast_build>.
12010 #include <isl/ast.h>
12011 __isl_give isl_ast_expr *isl_ast_expr_from_val(
12012 __isl_take isl_val *v);
12013 __isl_give isl_ast_expr *isl_ast_expr_from_id(
12014 __isl_take isl_id *id);
12015 __isl_give isl_ast_expr *isl_ast_expr_neg(
12016 __isl_take isl_ast_expr *expr);
12017 __isl_give isl_ast_expr *isl_ast_expr_address_of(
12018 __isl_take isl_ast_expr *expr);
12019 __isl_give isl_ast_expr *isl_ast_expr_add(
12020 __isl_take isl_ast_expr *expr1,
12021 __isl_take isl_ast_expr *expr2);
12022 __isl_give isl_ast_expr *isl_ast_expr_sub(
12023 __isl_take isl_ast_expr *expr1,
12024 __isl_take isl_ast_expr *expr2);
12025 __isl_give isl_ast_expr *isl_ast_expr_mul(
12026 __isl_take isl_ast_expr *expr1,
12027 __isl_take isl_ast_expr *expr2);
12028 __isl_give isl_ast_expr *isl_ast_expr_div(
12029 __isl_take isl_ast_expr *expr1,
12030 __isl_take isl_ast_expr *expr2);
12031 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
12032 __isl_take isl_ast_expr *expr1,
12033 __isl_take isl_ast_expr *expr2);
12034 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
12035 __isl_take isl_ast_expr *expr1,
12036 __isl_take isl_ast_expr *expr2);
12037 __isl_give isl_ast_expr *isl_ast_expr_and(
12038 __isl_take isl_ast_expr *expr1,
12039 __isl_take isl_ast_expr *expr2)
12040 __isl_give isl_ast_expr *isl_ast_expr_and_then(
12041 __isl_take isl_ast_expr *expr1,
12042 __isl_take isl_ast_expr *expr2)
12043 __isl_give isl_ast_expr *isl_ast_expr_or(
12044 __isl_take isl_ast_expr *expr1,
12045 __isl_take isl_ast_expr *expr2)
12046 __isl_give isl_ast_expr *isl_ast_expr_or_else(
12047 __isl_take isl_ast_expr *expr1,
12048 __isl_take isl_ast_expr *expr2)
12049 __isl_give isl_ast_expr *isl_ast_expr_eq(
12050 __isl_take isl_ast_expr *expr1,
12051 __isl_take isl_ast_expr *expr2);
12052 __isl_give isl_ast_expr *isl_ast_expr_le(
12053 __isl_take isl_ast_expr *expr1,
12054 __isl_take isl_ast_expr *expr2);
12055 __isl_give isl_ast_expr *isl_ast_expr_lt(
12056 __isl_take isl_ast_expr *expr1,
12057 __isl_take isl_ast_expr *expr2);
12058 __isl_give isl_ast_expr *isl_ast_expr_ge(
12059 __isl_take isl_ast_expr *expr1,
12060 __isl_take isl_ast_expr *expr2);
12061 __isl_give isl_ast_expr *isl_ast_expr_gt(
12062 __isl_take isl_ast_expr *expr1,
12063 __isl_take isl_ast_expr *expr2);
12064 __isl_give isl_ast_expr *isl_ast_expr_access(
12065 __isl_take isl_ast_expr *array,
12066 __isl_take isl_ast_expr_list *indices);
12067 __isl_give isl_ast_expr *isl_ast_expr_call(
12068 __isl_take isl_ast_expr *function,
12069 __isl_take isl_ast_expr_list *arguments);
12071 The function C<isl_ast_expr_address_of> can be applied to an
12072 C<isl_ast_expr> of type C<isl_ast_expr_op_access> only. It is meant
12073 to represent the address of the C<isl_ast_expr_access>.
12074 The second argument of the functions C<isl_ast_expr_pdiv_q> and
12075 C<isl_ast_expr_pdiv_r> should always evaluate to a positive number.
12077 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
12078 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
12080 #include <isl/ast_build.h>
12081 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
12082 __isl_keep isl_ast_build *build,
12083 __isl_take isl_set *set);
12084 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
12085 __isl_keep isl_ast_build *build,
12086 __isl_take isl_pw_aff *pa);
12087 __isl_give isl_ast_expr *
12088 isl_ast_build_access_from_pw_multi_aff(
12089 __isl_keep isl_ast_build *build,
12090 __isl_take isl_pw_multi_aff *pma);
12091 __isl_give isl_ast_expr *
12092 isl_ast_build_access_from_multi_pw_aff(
12093 __isl_keep isl_ast_build *build,
12094 __isl_take isl_multi_pw_aff *mpa);
12095 __isl_give isl_ast_expr *
12096 isl_ast_build_call_from_pw_multi_aff(
12097 __isl_keep isl_ast_build *build,
12098 __isl_take isl_pw_multi_aff *pma);
12099 __isl_give isl_ast_expr *
12100 isl_ast_build_call_from_multi_pw_aff(
12101 __isl_keep isl_ast_build *build,
12102 __isl_take isl_multi_pw_aff *mpa);
12105 the domains of C<pa>, C<mpa> and C<pma> should correspond
12106 to the schedule space of C<build>.
12107 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
12108 the function being called.
12109 If the accessed space is a nested relation, then it is taken
12110 to represent an access of the member specified by the range
12111 of this nested relation of the structure specified by the domain
12112 of the nested relation.
12114 The following functions can be used to modify an C<isl_ast_expr>.
12116 #include <isl/ast.h>
12117 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
12118 __isl_take isl_ast_expr *expr, int pos,
12119 __isl_take isl_ast_expr *arg);
12121 Replace the argument of C<expr> at position C<pos> by C<arg>.
12123 #include <isl/ast.h>
12124 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
12125 __isl_take isl_ast_expr *expr,
12126 __isl_take isl_id_to_ast_expr *id2expr);
12128 The function C<isl_ast_expr_substitute_ids> replaces the
12129 subexpressions of C<expr> of type C<isl_ast_expr_id>
12130 by the corresponding expression in C<id2expr>, if there is any.
12133 The following function can be used to modify the descendants
12134 of a specific node in an AST using a depth-first post-order
12135 traversal of those descendants (including the node itself).
12137 #include <isl/ast.h>
12138 __isl_give isl_ast_node *
12139 isl_ast_node_map_descendant_bottom_up(
12140 __isl_take isl_ast_node *node,
12141 __isl_give isl_ast_node *(*fn)(
12142 __isl_take isl_ast_node *node,
12143 void *user), void *user);
12145 User specified data can be attached to an C<isl_ast_node> and obtained
12146 from the same C<isl_ast_node> using the following functions.
12148 #include <isl/ast.h>
12149 __isl_give isl_ast_node *isl_ast_node_set_annotation(
12150 __isl_take isl_ast_node *node,
12151 __isl_take isl_id *annotation);
12152 __isl_give isl_id *isl_ast_node_get_annotation(
12153 __isl_keep isl_ast_node *node);
12155 Basic printing can be performed using the following functions.
12157 #include <isl/ast.h>
12158 __isl_give isl_printer *isl_printer_print_ast_expr(
12159 __isl_take isl_printer *p,
12160 __isl_keep isl_ast_expr *expr);
12161 __isl_give isl_printer *isl_printer_print_ast_node(
12162 __isl_take isl_printer *p,
12163 __isl_keep isl_ast_node *node);
12164 __isl_give char *isl_ast_expr_to_str(
12165 __isl_keep isl_ast_expr *expr);
12166 __isl_give char *isl_ast_node_to_str(
12167 __isl_keep isl_ast_node *node);
12168 __isl_give char *isl_ast_expr_to_C_str(
12169 __isl_keep isl_ast_expr *expr);
12170 __isl_give char *isl_ast_node_to_C_str(
12171 __isl_keep isl_ast_node *node);
12173 The functions C<isl_ast_expr_to_C_str> and
12174 C<isl_ast_node_to_C_str> are convenience functions
12175 that return a string representation of the input in C format.
12177 More advanced printing can be performed using the following functions.
12179 #include <isl/ast.h>
12180 __isl_give isl_printer *
12181 isl_ast_expr_op_type_set_print_name(
12182 __isl_take isl_printer *p,
12183 enum isl_ast_expr_op_type type,
12184 __isl_keep const char *name);
12185 __isl_give isl_printer *isl_ast_op_type_set_print_name(
12186 __isl_take isl_printer *p,
12187 enum isl_ast_expr_op_type type,
12188 __isl_keep const char *name);
12189 isl_stat isl_options_set_ast_print_macro_once(
12190 isl_ctx *ctx, int val);
12191 int isl_options_get_ast_print_macro_once(isl_ctx *ctx);
12192 __isl_give isl_printer *isl_ast_expr_op_type_print_macro(
12193 enum isl_ast_expr_op_type type,
12194 __isl_take isl_printer *p);
12195 __isl_give isl_printer *isl_ast_op_type_print_macro(
12196 enum isl_ast_expr_op_type type,
12197 __isl_take isl_printer *p);
12198 __isl_give isl_printer *isl_ast_expr_print_macros(
12199 __isl_keep isl_ast_expr *expr,
12200 __isl_take isl_printer *p);
12201 __isl_give isl_printer *isl_ast_node_print_macros(
12202 __isl_keep isl_ast_node *node,
12203 __isl_take isl_printer *p);
12204 __isl_give isl_printer *isl_ast_node_print(
12205 __isl_keep isl_ast_node *node,
12206 __isl_take isl_printer *p,
12207 __isl_take isl_ast_print_options *options);
12208 __isl_give isl_printer *isl_ast_node_for_print(
12209 __isl_keep isl_ast_node *node,
12210 __isl_take isl_printer *p,
12211 __isl_take isl_ast_print_options *options);
12212 __isl_give isl_printer *isl_ast_node_if_print(
12213 __isl_keep isl_ast_node *node,
12214 __isl_take isl_printer *p,
12215 __isl_take isl_ast_print_options *options);
12217 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
12218 C<isl> may print out an AST that makes use of macros such
12219 as C<floord>, C<min> and C<max>.
12220 The names of these macros may be modified by a call
12221 to C<isl_ast_expr_op_type_set_print_name>. The user-specified
12222 names are associated to the printer object.
12223 C<isl_ast_op_type_set_print_name> is an alternative name for
12224 C<isl_ast_expr_op_type_set_print_name>.
12225 C<isl_ast_expr_op_type_print_macro> prints out the macro
12226 corresponding to a specific C<isl_ast_expr_op_type>.
12227 If the print-macro-once option is set, then a given macro definition
12228 is only printed once to any given printer object.
12229 C<isl_ast_op_type_print_macro> is an alternative name for
12230 C<isl_ast_expr_op_type_print_macro>.
12231 C<isl_ast_expr_print_macros> scans the C<isl_ast_expr>
12232 for subexpressions where these macros would be used and prints
12233 out the required macro definitions.
12234 Essentially, C<isl_ast_expr_print_macros> calls
12235 C<isl_ast_expr_foreach_ast_expr_op_type> with
12236 C<isl_ast_expr_op_type_print_macro>
12237 as function argument.
12238 C<isl_ast_node_print_macros> does the same
12239 for expressions in its C<isl_ast_node> argument.
12240 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
12241 C<isl_ast_node_if_print> print an C<isl_ast_node>
12242 in C<ISL_FORMAT_C>, but allow for some extra control
12243 through an C<isl_ast_print_options> object.
12244 This object can be created using the following functions.
12246 #include <isl/ast.h>
12247 __isl_give isl_ast_print_options *
12248 isl_ast_print_options_alloc(isl_ctx *ctx);
12249 __isl_give isl_ast_print_options *
12250 isl_ast_print_options_copy(
12251 __isl_keep isl_ast_print_options *options);
12252 __isl_null isl_ast_print_options *
12253 isl_ast_print_options_free(
12254 __isl_take isl_ast_print_options *options);
12256 __isl_give isl_ast_print_options *
12257 isl_ast_print_options_set_print_user(
12258 __isl_take isl_ast_print_options *options,
12259 __isl_give isl_printer *(*print_user)(
12260 __isl_take isl_printer *p,
12261 __isl_take isl_ast_print_options *options,
12262 __isl_keep isl_ast_node *node, void *user),
12264 __isl_give isl_ast_print_options *
12265 isl_ast_print_options_set_print_for(
12266 __isl_take isl_ast_print_options *options,
12267 __isl_give isl_printer *(*print_for)(
12268 __isl_take isl_printer *p,
12269 __isl_take isl_ast_print_options *options,
12270 __isl_keep isl_ast_node *node, void *user),
12273 The callback set by C<isl_ast_print_options_set_print_user>
12274 is called whenever a node of type C<isl_ast_node_user> needs to
12276 The callback set by C<isl_ast_print_options_set_print_for>
12277 is called whenever a node of type C<isl_ast_node_for> needs to
12279 Note that C<isl_ast_node_for_print> will I<not> call the
12280 callback set by C<isl_ast_print_options_set_print_for> on the node
12281 on which C<isl_ast_node_for_print> is called, but only on nested
12282 nodes of type C<isl_ast_node_for>. It is therefore safe to
12283 call C<isl_ast_node_for_print> from within the callback set by
12284 C<isl_ast_print_options_set_print_for>.
12286 The following option determines the type to be used for iterators
12287 while printing the AST.
12289 isl_stat isl_options_set_ast_iterator_type(
12290 isl_ctx *ctx, const char *val);
12291 const char *isl_options_get_ast_iterator_type(
12294 The AST printer only prints body nodes of C<if> and C<for> nodes
12296 blocks cannot be safely omitted.
12297 For example, a C<for> node with one body node will not be
12298 surrounded with braces in C<ISL_FORMAT_C>.
12299 A block will always be printed by setting the following option.
12301 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx,
12303 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
12305 Explicit block nodes that appear inside the AST are always printed as blocks.
12306 If the block node appears as the outermost node,
12307 then it is only printed if the following option is set.
12309 isl_stat isl_options_set_ast_print_outermost_block(
12310 isl_ctx *ctx, int val);
12311 int isl_options_get_ast_print_outermost_block(
12316 #include <isl/ast_build.h>
12317 isl_stat isl_options_set_ast_build_atomic_upper_bound(
12318 isl_ctx *ctx, int val);
12319 int isl_options_get_ast_build_atomic_upper_bound(
12321 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
12323 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
12324 isl_stat isl_options_set_ast_build_detect_min_max(
12325 isl_ctx *ctx, int val);
12326 int isl_options_get_ast_build_detect_min_max(
12328 isl_stat isl_options_set_ast_build_exploit_nested_bounds(
12329 isl_ctx *ctx, int val);
12330 int isl_options_get_ast_build_exploit_nested_bounds(
12332 isl_stat isl_options_set_ast_build_group_coscheduled(
12333 isl_ctx *ctx, int val);
12334 int isl_options_get_ast_build_group_coscheduled(
12336 isl_stat isl_options_set_ast_build_separation_bounds(
12337 isl_ctx *ctx, int val);
12338 int isl_options_get_ast_build_separation_bounds(
12340 isl_stat isl_options_set_ast_build_scale_strides(
12341 isl_ctx *ctx, int val);
12342 int isl_options_get_ast_build_scale_strides(
12344 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx,
12346 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
12347 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx,
12349 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
12353 =item * ast_build_atomic_upper_bound
12355 Generate loop upper bounds that consist of the current loop iterator,
12356 an operator and an expression not involving the iterator.
12357 If this option is not set, then the current loop iterator may appear
12358 several times in the upper bound.
12359 For example, when this option is turned off, AST generation
12362 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
12366 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
12369 When the option is turned on, the following AST is generated
12371 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
12374 =item * ast_build_prefer_pdiv
12376 If this option is turned off, then the AST generation will
12377 produce ASTs that may only contain C<isl_ast_expr_op_fdiv_q>
12378 operators, but no C<isl_ast_expr_op_pdiv_q> or
12379 C<isl_ast_expr_op_pdiv_r> operators.
12380 If this option is turned on, then C<isl> will try to convert
12381 some of the C<isl_ast_expr_op_fdiv_q> operators to (expressions containing)
12382 C<isl_ast_expr_op_pdiv_q> or C<isl_ast_expr_op_pdiv_r> operators.
12384 =item * ast_build_detect_min_max
12386 If this option is turned on, then C<isl> will try and detect
12387 min or max-expressions when building AST expressions from
12388 piecewise affine expressions.
12390 =item * ast_build_exploit_nested_bounds
12392 Simplify conditions based on bounds of nested for loops.
12393 In particular, remove conditions that are implied by the fact
12394 that one or more nested loops have at least one iteration,
12395 meaning that the upper bound is at least as large as the lower bound.
12396 For example, when this option is turned off, AST generation
12399 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
12405 for (int c0 = 0; c0 <= N; c0 += 1)
12406 for (int c1 = 0; c1 <= M; c1 += 1)
12409 When the option is turned on, the following AST is generated
12411 for (int c0 = 0; c0 <= N; c0 += 1)
12412 for (int c1 = 0; c1 <= M; c1 += 1)
12415 =item * ast_build_group_coscheduled
12417 If two domain elements are assigned the same schedule point, then
12418 they may be executed in any order and they may even appear in different
12419 loops. If this options is set, then the AST generator will make
12420 sure that coscheduled domain elements do not appear in separate parts
12421 of the AST. This is useful in case of nested AST generation
12422 if the outer AST generation is given only part of a schedule
12423 and the inner AST generation should handle the domains that are
12424 coscheduled by this initial part of the schedule together.
12425 For example if an AST is generated for a schedule
12427 { A[i] -> [0]; B[i] -> [0] }
12429 then the C<isl_ast_build_set_create_leaf> callback described
12430 below may get called twice, once for each domain.
12431 Setting this option ensures that the callback is only called once
12432 on both domains together.
12434 =item * ast_build_separation_bounds
12436 This option specifies which bounds to use during separation.
12437 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
12438 then all (possibly implicit) bounds on the current dimension will
12439 be used during separation.
12440 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
12441 then only those bounds that are explicitly available will
12442 be used during separation.
12444 =item * ast_build_scale_strides
12446 This option specifies whether the AST generator is allowed
12447 to scale down iterators of strided loops.
12449 =item * ast_build_allow_else
12451 This option specifies whether the AST generator is allowed
12452 to construct if statements with else branches.
12454 =item * ast_build_allow_or
12456 This option specifies whether the AST generator is allowed
12457 to construct if conditions with disjunctions.
12461 =head3 AST Generation Options (Schedule Tree)
12463 In case of AST construction from a schedule tree, the options
12464 that control how an AST is created from the individual schedule
12465 dimensions are stored in the band nodes of the tree
12466 (see L</"Schedule Trees">).
12468 In particular, a schedule dimension can be handled in four
12469 different ways, atomic, separate, unroll or the default.
12470 This loop AST generation type can be set using
12471 C<isl_schedule_node_band_member_set_ast_loop_type>.
12473 the first three can be selected by including a one-dimensional
12474 element with as value the position of the schedule dimension
12475 within the band and as name one of C<atomic>, C<separate>
12476 or C<unroll> in the options
12477 set by C<isl_schedule_node_band_set_ast_build_options>.
12478 Only one of these three may be specified for
12479 any given schedule dimension within a band node.
12480 If none of these is specified, then the default
12481 is used. The meaning of the options is as follows.
12487 When this option is specified, the AST generator will make
12488 sure that a given domain space only appears in a single
12489 loop at the specified level.
12491 For example, for the schedule tree
12493 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
12495 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
12496 options: "{ atomic[x] }"
12498 the following AST will be generated
12500 for (int c0 = 0; c0 <= 10; c0 += 1) {
12507 On the other hand, for the schedule tree
12509 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
12511 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
12512 options: "{ separate[x] }"
12514 the following AST will be generated
12518 for (int c0 = 1; c0 <= 9; c0 += 1) {
12525 If neither C<atomic> nor C<separate> is specified, then the AST generator
12526 may produce either of these two results or some intermediate form.
12530 When this option is specified, the AST generator will
12531 split the domain of the specified schedule dimension
12532 into pieces with a fixed set of statements for which
12533 instances need to be executed by the iterations in
12534 the schedule domain part. This option tends to avoid
12535 the generation of guards inside the corresponding loops.
12536 See also the C<atomic> option.
12540 When this option is specified, the AST generator will
12541 I<completely> unroll the corresponding schedule dimension.
12542 It is the responsibility of the user to ensure that such
12543 unrolling is possible.
12544 To obtain a partial unrolling, the user should apply an additional
12545 strip-mining to the schedule and fully unroll the inner schedule
12550 The C<isolate> option is a bit more involved. It allows the user
12551 to isolate a range of schedule dimension values from smaller and
12552 greater values. Additionally, the user may specify a different
12553 atomic/separate/unroll choice for the isolated part and the remaining
12554 parts. The typical use case of the C<isolate> option is to isolate
12555 full tiles from partial tiles.
12556 The part that needs to be isolated may depend on outer schedule dimensions.
12557 The option therefore needs to be able to reference those outer schedule
12558 dimensions. In particular, the space of the C<isolate> option is that
12559 of a wrapped map with as domain the flat product of all outer band nodes
12560 and as range the space of the current band node.
12561 The atomic/separate/unroll choice for the isolated part is determined
12562 by an option that lives in an unnamed wrapped space with as domain
12563 a zero-dimensional C<isolate> space and as range the regular
12564 C<atomic>, C<separate> or C<unroll> space.
12565 This option may also be set directly using
12566 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
12567 The atomic/separate/unroll choice for the remaining part is determined
12568 by the regular C<atomic>, C<separate> or C<unroll> option.
12569 Since the C<isolate> option references outer schedule dimensions,
12570 its use in a band node causes any tree containing the node
12571 to be considered anchored.
12573 As an example, consider the isolation of full tiles from partial tiles
12574 in a tiling of a triangular domain. The original schedule is as follows.
12576 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
12578 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
12579 { A[i,j] -> [floor(j/10)] }, \
12580 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
12584 for (int c0 = 0; c0 <= 10; c0 += 1)
12585 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12586 for (int c2 = 10 * c0;
12587 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12588 for (int c3 = 10 * c1;
12589 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12592 Isolating the full tiles, we have the following input
12594 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
12596 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
12597 { A[i,j] -> [floor(j/10)] }, \
12598 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
12599 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
12600 10a+9+10b+9 <= 100 }"
12605 for (int c0 = 0; c0 <= 8; c0 += 1) {
12606 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
12607 for (int c2 = 10 * c0;
12608 c2 <= 10 * c0 + 9; c2 += 1)
12609 for (int c3 = 10 * c1;
12610 c3 <= 10 * c1 + 9; c3 += 1)
12612 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
12613 for (int c2 = 10 * c0;
12614 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12615 for (int c3 = 10 * c1;
12616 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12619 for (int c0 = 9; c0 <= 10; c0 += 1)
12620 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12621 for (int c2 = 10 * c0;
12622 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12623 for (int c3 = 10 * c1;
12624 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12628 We may then additionally unroll the innermost loop of the isolated part
12630 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
12632 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
12633 { A[i,j] -> [floor(j/10)] }, \
12634 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
12635 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
12636 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
12641 for (int c0 = 0; c0 <= 8; c0 += 1) {
12642 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
12643 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
12645 A(c2, 10 * c1 + 1);
12646 A(c2, 10 * c1 + 2);
12647 A(c2, 10 * c1 + 3);
12648 A(c2, 10 * c1 + 4);
12649 A(c2, 10 * c1 + 5);
12650 A(c2, 10 * c1 + 6);
12651 A(c2, 10 * c1 + 7);
12652 A(c2, 10 * c1 + 8);
12653 A(c2, 10 * c1 + 9);
12655 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
12656 for (int c2 = 10 * c0;
12657 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12658 for (int c3 = 10 * c1;
12659 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12662 for (int c0 = 9; c0 <= 10; c0 += 1)
12663 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12664 for (int c2 = 10 * c0;
12665 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12666 for (int c3 = 10 * c1;
12667 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12672 =head3 AST Generation Options (Schedule Map)
12674 In case of AST construction using
12675 C<isl_ast_build_node_from_schedule_map>, the options
12676 that control how an AST is created from the individual schedule
12677 dimensions are stored in the C<isl_ast_build>.
12678 They can be set using the following function.
12680 #include <isl/ast_build.h>
12681 __isl_give isl_ast_build *
12682 isl_ast_build_set_options(
12683 __isl_take isl_ast_build *build,
12684 __isl_take isl_union_map *options);
12686 The options are encoded in an C<isl_union_map>.
12687 The domain of this union relation refers to the schedule domain,
12688 i.e., the range of the schedule passed
12689 to C<isl_ast_build_node_from_schedule_map>.
12690 In the case of nested AST generation (see L</"Nested AST Generation">),
12691 the domain of C<options> should refer to the extra piece of the schedule.
12692 That is, it should be equal to the range of the wrapped relation in the
12693 range of the schedule.
12694 The range of the options can consist of elements in one or more spaces,
12695 the names of which determine the effect of the option.
12696 The values of the range typically also refer to the schedule dimension
12697 to which the option applies, with value C<0> representing
12698 the outermost schedule dimension. In case of nested AST generation
12699 (see L</"Nested AST Generation">), these values refer to the position
12700 of the schedule dimension within the innermost AST generation.
12701 The constraints on the domain elements of
12702 the option should only refer to this dimension and earlier dimensions.
12703 We consider the following spaces.
12707 =item C<separation_class>
12709 B<This option has been deprecated. Use the isolate option on
12710 schedule trees instead.>
12712 This space is a wrapped relation between two one dimensional spaces.
12713 The input space represents the schedule dimension to which the option
12714 applies and the output space represents the separation class.
12715 While constructing a loop corresponding to the specified schedule
12716 dimension(s), the AST generator will try to generate separate loops
12717 for domain elements that are assigned different classes.
12718 If only some of the elements are assigned a class, then those elements
12719 that are not assigned any class will be treated as belonging to a class
12720 that is separate from the explicitly assigned classes.
12721 The typical use case for this option is to separate full tiles from
12723 The other options, described below, are applied after the separation
12726 As an example, consider the separation into full and partial tiles
12727 of a tiling of a triangular domain.
12728 Take, for example, the domain
12730 { A[i,j] : 0 <= i,j and i + j <= 100 }
12732 and a tiling into tiles of 10 by 10. The input to the AST generator
12733 is then the schedule
12735 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
12738 Without any options, the following AST is generated
12740 for (int c0 = 0; c0 <= 10; c0 += 1)
12741 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12742 for (int c2 = 10 * c0;
12743 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
12745 for (int c3 = 10 * c1;
12746 c3 <= min(10 * c1 + 9, -c2 + 100);
12750 Separation into full and partial tiles can be obtained by assigning
12751 a class, say C<0>, to the full tiles. The full tiles are represented by those
12752 values of the first and second schedule dimensions for which there are
12753 values of the third and fourth dimensions to cover an entire tile.
12754 That is, we need to specify the following option
12756 { [a,b,c,d] -> separation_class[[0]->[0]] :
12757 exists b': 0 <= 10a,10b' and
12758 10a+9+10b'+9 <= 100;
12759 [a,b,c,d] -> separation_class[[1]->[0]] :
12760 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
12762 which simplifies to
12764 { [a, b, c, d] -> separation_class[[1] -> [0]] :
12765 a >= 0 and b >= 0 and b <= 8 - a;
12766 [a, b, c, d] -> separation_class[[0] -> [0]] :
12767 a >= 0 and a <= 8 }
12769 With this option, the generated AST is as follows
12772 for (int c0 = 0; c0 <= 8; c0 += 1) {
12773 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
12774 for (int c2 = 10 * c0;
12775 c2 <= 10 * c0 + 9; c2 += 1)
12776 for (int c3 = 10 * c1;
12777 c3 <= 10 * c1 + 9; c3 += 1)
12779 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
12780 for (int c2 = 10 * c0;
12781 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
12783 for (int c3 = 10 * c1;
12784 c3 <= min(-c2 + 100, 10 * c1 + 9);
12788 for (int c0 = 9; c0 <= 10; c0 += 1)
12789 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12790 for (int c2 = 10 * c0;
12791 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
12793 for (int c3 = 10 * c1;
12794 c3 <= min(10 * c1 + 9, -c2 + 100);
12801 This is a single-dimensional space representing the schedule dimension(s)
12802 to which ``separation'' should be applied. Separation tries to split
12803 a loop into several pieces if this can avoid the generation of guards
12805 See also the C<atomic> option.
12809 This is a single-dimensional space representing the schedule dimension(s)
12810 for which the domains should be considered ``atomic''. That is, the
12811 AST generator will make sure that any given domain space will only appear
12812 in a single loop at the specified level.
12814 Consider the following schedule
12816 { a[i] -> [i] : 0 <= i < 10;
12817 b[i] -> [i+1] : 0 <= i < 10 }
12819 If the following option is specified
12821 { [i] -> separate[x] }
12823 then the following AST will be generated
12827 for (int c0 = 1; c0 <= 9; c0 += 1) {
12834 If, on the other hand, the following option is specified
12836 { [i] -> atomic[x] }
12838 then the following AST will be generated
12840 for (int c0 = 0; c0 <= 10; c0 += 1) {
12847 If neither C<atomic> nor C<separate> is specified, then the AST generator
12848 may produce either of these two results or some intermediate form.
12852 This is a single-dimensional space representing the schedule dimension(s)
12853 that should be I<completely> unrolled.
12854 To obtain a partial unrolling, the user should apply an additional
12855 strip-mining to the schedule and fully unroll the inner loop.
12859 =head3 Fine-grained Control over AST Generation
12861 Besides specifying the constraints on the parameters,
12862 an C<isl_ast_build> object can be used to control
12863 various aspects of the AST generation process.
12864 In case of AST construction using
12865 C<isl_ast_build_node_from_schedule_map>,
12866 the most prominent way of control is through ``options'',
12867 as explained above.
12869 Additional control is available through the following functions.
12871 #include <isl/ast_build.h>
12872 __isl_give isl_ast_build *
12873 isl_ast_build_set_iterators(
12874 __isl_take isl_ast_build *build,
12875 __isl_take isl_id_list *iterators);
12877 The function C<isl_ast_build_set_iterators> allows the user to
12878 specify a list of iterator C<isl_id>s to be used as iterators.
12879 If the input schedule is injective, then
12880 the number of elements in this list should be as large as the dimension
12881 of the schedule space, but no direct correspondence should be assumed
12882 between dimensions and elements.
12883 If the input schedule is not injective, then an additional number
12884 of C<isl_id>s equal to the largest dimension of the input domains
12886 If the number of provided C<isl_id>s is insufficient, then additional
12887 names are automatically generated.
12889 #include <isl/ast_build.h>
12890 __isl_give isl_ast_build *
12891 isl_ast_build_set_create_leaf(
12892 __isl_take isl_ast_build *build,
12893 __isl_give isl_ast_node *(*fn)(
12894 __isl_take isl_ast_build *build,
12895 void *user), void *user);
12898 C<isl_ast_build_set_create_leaf> function allows for the
12899 specification of a callback that should be called whenever the AST
12900 generator arrives at an element of the schedule domain.
12901 The callback should return an AST node that should be inserted
12902 at the corresponding position of the AST. The default action (when
12903 the callback is not set) is to continue generating parts of the AST to scan
12904 all the domain elements associated to the schedule domain element
12905 and to insert user nodes, ``calling'' the domain element, for each of them.
12906 The C<build> argument contains the current state of the C<isl_ast_build>.
12907 To ease nested AST generation (see L</"Nested AST Generation">),
12908 all control information that is
12909 specific to the current AST generation such as the options and
12910 the callbacks has been removed from this C<isl_ast_build>.
12911 The callback would typically return the result of a nested
12912 AST generation or a
12913 user defined node created using the following function.
12915 #include <isl/ast.h>
12916 __isl_give isl_ast_node *isl_ast_node_user_from_expr(
12917 __isl_take isl_ast_expr *expr);
12918 __isl_give isl_ast_node *isl_ast_node_alloc_user(
12919 __isl_take isl_ast_expr *expr);
12921 C<isl_ast_node_alloc_user> is an alternative name for
12922 C<isl_ast_node_user_from_expr>.
12924 In some cases, a single user defined node is not enough,
12925 in which case the following function can be used
12926 to create a block node from multiple AST nodes.
12928 #include <isl/ast.h>
12929 __isl_give isl_ast_node *isl_ast_node_block_from_children(
12930 __isl_take isl_ast_node_list *list);
12932 #include <isl/ast_build.h>
12933 __isl_give isl_ast_build *
12934 isl_ast_build_set_at_each_domain(
12935 __isl_take isl_ast_build *build,
12936 __isl_give isl_ast_node *(*fn)(
12937 __isl_take isl_ast_node *node,
12938 __isl_keep isl_ast_build *build,
12939 void *user), void *user);
12940 __isl_give isl_ast_build *
12941 isl_ast_build_set_before_each_for(
12942 __isl_take isl_ast_build *build,
12943 __isl_give isl_id *(*fn)(
12944 __isl_keep isl_ast_build *build,
12945 void *user), void *user);
12946 __isl_give isl_ast_build *
12947 isl_ast_build_set_after_each_for(
12948 __isl_take isl_ast_build *build,
12949 __isl_give isl_ast_node *(*fn)(
12950 __isl_take isl_ast_node *node,
12951 __isl_keep isl_ast_build *build,
12952 void *user), void *user);
12953 __isl_give isl_ast_build *
12954 isl_ast_build_set_before_each_mark(
12955 __isl_take isl_ast_build *build,
12956 isl_stat (*fn)(__isl_keep isl_id *mark,
12957 __isl_keep isl_ast_build *build,
12958 void *user), void *user);
12959 __isl_give isl_ast_build *
12960 isl_ast_build_set_after_each_mark(
12961 __isl_take isl_ast_build *build,
12962 __isl_give isl_ast_node *(*fn)(
12963 __isl_take isl_ast_node *node,
12964 __isl_keep isl_ast_build *build,
12965 void *user), void *user);
12967 The callback set by C<isl_ast_build_set_at_each_domain> will
12968 be called for each domain AST node.
12969 The callbacks set by C<isl_ast_build_set_before_each_for>
12970 and C<isl_ast_build_set_after_each_for> will be called
12971 for each for AST node. The first will be called in depth-first
12972 pre-order, while the second will be called in depth-first post-order.
12973 Since C<isl_ast_build_set_before_each_for> is called before the for
12974 node is actually constructed, it is only passed an C<isl_ast_build>.
12975 The returned C<isl_id> will be added as an annotation (using
12976 C<isl_ast_node_set_annotation>) to the constructed for node.
12977 In particular, if the user has also specified an C<after_each_for>
12978 callback, then the annotation can be retrieved from the node passed to
12979 that callback using C<isl_ast_node_get_annotation>.
12980 The callbacks set by C<isl_ast_build_set_before_each_mark>
12981 and C<isl_ast_build_set_after_each_mark> will be called for each
12982 mark AST node that is created, i.e., for each mark schedule node
12983 in the input schedule tree. The first will be called in depth-first
12984 pre-order, while the second will be called in depth-first post-order.
12985 Since the callback set by C<isl_ast_build_set_before_each_mark>
12986 is called before the mark AST node is actually constructed, it is passed
12987 the identifier of the mark node.
12988 All callbacks should C<NULL> (or C<isl_stat_error>) on failure.
12989 The given C<isl_ast_build> can be used to create new
12990 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
12991 or C<isl_ast_build_call_from_pw_multi_aff>.
12993 =head3 Nested AST Generation
12995 C<isl> allows the user to create an AST within the context
12996 of another AST. These nested ASTs are created using the
12997 same C<isl_ast_build_node_from_schedule_map> function that is used to create
12998 the outer AST. The C<build> argument should be an C<isl_ast_build>
12999 passed to a callback set by
13000 C<isl_ast_build_set_create_leaf>.
13001 The space of the range of the C<schedule> argument should refer
13002 to this build. In particular, the space should be a wrapped
13003 relation and the domain of this wrapped relation should be the
13004 same as that of the range of the schedule returned by
13005 C<isl_ast_build_get_schedule> below.
13006 In practice, the new schedule is typically
13007 created by calling C<isl_union_map_range_product> on the old schedule
13008 and some extra piece of the schedule.
13009 The space of the schedule domain is also available from
13010 the C<isl_ast_build>.
13012 #include <isl/ast_build.h>
13013 __isl_give isl_union_map *isl_ast_build_get_schedule(
13014 __isl_keep isl_ast_build *build);
13015 __isl_give isl_space *isl_ast_build_get_schedule_space(
13016 __isl_keep isl_ast_build *build);
13017 __isl_give isl_ast_build *isl_ast_build_restrict(
13018 __isl_take isl_ast_build *build,
13019 __isl_take isl_set *set);
13021 The C<isl_ast_build_get_schedule> function returns a (partial)
13022 schedule for the domains elements for which part of the AST still needs to
13023 be generated in the current build.
13024 In particular, the domain elements are mapped to those iterations of the loops
13025 enclosing the current point of the AST generation inside which
13026 the domain elements are executed.
13027 No direct correspondence between
13028 the input schedule and this schedule should be assumed.
13029 The space obtained from C<isl_ast_build_get_schedule_space> can be used
13030 to create a set for C<isl_ast_build_restrict> to intersect
13031 with the current build. In particular, the set passed to
13032 C<isl_ast_build_restrict> can have additional parameters.
13033 The ids of the set dimensions in the space returned by
13034 C<isl_ast_build_get_schedule_space> correspond to the
13035 iterators of the already generated loops.
13036 The user should not rely on the ids of the output dimensions
13037 of the relations in the union relation returned by
13038 C<isl_ast_build_get_schedule> having any particular value.
13040 =head1 Applications
13042 Although C<isl> is mainly meant to be used as a library,
13043 it also contains some basic applications that use some
13044 of the functionality of C<isl>.
13045 For applications that take one or more polytopes or polyhedra
13046 as input, this input may be specified in either the L<isl format>
13047 or the L<PolyLib format>.
13049 =head2 C<isl_polyhedron_sample>
13051 C<isl_polyhedron_sample> takes a polyhedron as input and prints
13052 an integer element of the polyhedron, if there is any.
13053 The first column in the output is the denominator and is always
13054 equal to 1. If the polyhedron contains no integer points,
13055 then a vector of length zero is printed.
13059 C<isl_pip> takes the same input as the C<example> program
13060 from the C<piplib> distribution, i.e., a set of constraints
13061 on the parameters, a line containing only -1 and finally a set
13062 of constraints on a parametric polyhedron.
13063 The coefficients of the parameters appear in the last columns
13064 (but before the final constant column).
13065 The output is the lexicographic minimum of the parametric polyhedron.
13066 As C<isl> currently does not have its own output format, the output
13067 is just a dump of the internal state.
13069 =head2 C<isl_polyhedron_minimize>
13071 C<isl_polyhedron_minimize> computes the minimum of some linear
13072 or affine objective function over the integer points in a polyhedron.
13073 If an affine objective function
13074 is given, then the constant should appear in the last column.
13076 =head2 C<isl_polytope_scan>
13078 Given a polytope, C<isl_polytope_scan> prints
13079 all integer points in the polytope.
13083 Given an C<isl_union_access_info> object as input,
13084 C<isl_flow> prints out the corresponding dependences,
13085 as computed by C<isl_union_access_info_compute_flow>.
13087 =head2 C<isl_codegen>
13089 Given either a schedule tree or a sequence consisting of
13090 a schedule map, a context set and an options relation,
13091 C<isl_codegen> prints out an AST that scans the domain elements
13092 of the schedule in the order of their image(s) taking into account
13093 the constraints in the context set.
13095 =head2 C<isl_schedule>
13097 Given an C<isl_schedule_constraints> object as input,
13098 C<isl_schedule> prints out a schedule that satisfies the given