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);
5437 #include <isl/set.h>
5438 __isl_give isl_set *isl_set_wrapped_reverse(
5439 __isl_take isl_set *set);
5441 #include <isl/map.h>
5442 __isl_give isl_basic_map *isl_basic_map_reverse(
5443 __isl_take isl_basic_map *bmap);
5444 __isl_give isl_map *isl_map_reverse(
5445 __isl_take isl_map *map);
5446 __isl_give isl_map *isl_map_range_reverse(
5447 __isl_take isl_map *map);
5449 #include <isl/union_map.h>
5450 __isl_give isl_union_map *isl_union_map_reverse(
5451 __isl_take isl_union_map *umap);
5452 __isl_give isl_union_map *isl_union_map_range_reverse(
5453 __isl_take isl_union_map *umap);
5455 The function C<isl_space_range_reverse> reverses the relation
5456 that is embedded in the range of the input map space.
5457 The identifier of the range, if any, is only preserved
5458 if this embedded relation has identical input and output tuples.
5459 Similarly for C<isl_space_domain_reverse>.
5460 Along the same lines, C<isl_space_wrapped_reverse> reverses
5461 the relation that is embedded in a set space.
5463 =item * Tuple binding
5465 The following function binds
5466 a tuple to a sequence of parameter identifiers, equating
5467 the tuple dimensions to the parameters with those identifiers and
5468 subsequently projecting out the tuple.
5469 If the original object did not reference any such parameters,
5470 then this means that the tuple dimensions are reinterpreted
5472 The space of C<tuple> needs to match that of the bound tuple.
5474 #include <isl/set.h>
5475 __isl_give isl_set *isl_set_bind(
5476 __isl_take isl_set *set,
5477 __isl_take isl_multi_id *tuple);
5479 #include <isl/map.h>
5480 __isl_give isl_set *isl_map_bind_domain(
5481 __isl_take isl_map *map,
5482 __isl_take isl_multi_id *tuple);
5483 __isl_give isl_set *isl_map_bind_range(
5484 __isl_take isl_map *map,
5485 __isl_take isl_multi_id *tuple);
5487 #include <isl/union_map.h>
5488 __isl_give isl_union_set *isl_union_map_bind_range(
5489 __isl_take isl_union_map *umap,
5490 __isl_take isl_multi_id *tuple);
5492 #include <isl/aff.h>
5493 __isl_give isl_pw_aff *isl_pw_aff_bind_domain(
5494 __isl_take isl_pw_aff *pa,
5495 __isl_take isl_multi_id *tuple);
5496 __isl_give isl_multi_aff *isl_multi_aff_bind_domain(
5497 __isl_take isl_multi_aff *ma,
5498 __isl_take isl_multi_id *tuple);
5499 __isl_give isl_pw_multi_aff *
5500 isl_pw_multi_aff_bind_domain(
5501 __isl_take isl_pw_multi_aff *pma,
5502 __isl_take isl_multi_id *tuple);
5503 __isl_give isl_multi_pw_aff *
5504 isl_multi_pw_aff_bind_domain(
5505 __isl_take isl_multi_pw_aff *mpa,
5506 __isl_take isl_multi_id *tuple);
5507 __isl_give isl_pw_aff *
5508 isl_pw_aff_bind_domain_wrapped_domain(
5509 __isl_take isl_pw_aff *pa,
5510 __isl_take isl_multi_id *tuple);
5511 __isl_give isl_multi_aff *
5512 isl_multi_aff_bind_domain_wrapped_domain(
5513 __isl_take isl_multi_aff *ma,
5514 __isl_take isl_multi_id *tuple);
5515 __isl_give isl_pw_multi_aff *
5516 isl_pw_multi_aff_bind_domain_wrapped_domain(
5517 __isl_take isl_pw_multi_aff *pma,
5518 __isl_take isl_multi_id *tuple);
5519 __isl_give isl_multi_pw_aff *
5520 isl_multi_pw_aff_bind_domain_wrapped_domain(
5521 __isl_take isl_multi_pw_aff *mpa,
5522 __isl_take isl_multi_id *tuple);
5523 __isl_give isl_basic_set *isl_aff_bind_id(
5524 __isl_take isl_aff *aff,
5525 __isl_take isl_id *id);
5526 __isl_give isl_set *isl_pw_aff_bind_id(
5527 __isl_take isl_pw_aff *pa,
5528 __isl_take isl_id *id);
5529 __isl_give isl_basic_set *isl_multi_aff_bind(
5530 __isl_take isl_multi_aff *ma,
5531 __isl_take isl_multi_id *tuple);
5532 __isl_give isl_set *isl_multi_pw_aff_bind(
5533 __isl_take isl_multi_pw_aff *mpa,
5534 __isl_take isl_multi_id *tuple);
5535 __isl_give isl_union_set *isl_union_pw_aff_bind_id(
5536 __isl_take isl_union_pw_aff *upa,
5537 __isl_take isl_id *id);
5538 __isl_give isl_union_set *
5539 isl_multi_union_pw_aff_bind(
5540 __isl_take isl_multi_union_pw_aff *mupa,
5541 __isl_take isl_multi_id *tuple);
5543 Projecting out the domain of the wrapped relation in the domain
5544 of a function leaves the range of that wrapped relation
5545 in the domain of the resulting function.
5546 In the case of C<isl_aff_bind_id>, C<isl_pw_aff_bind_id>,
5547 C<isl_multi_aff_bind>, C<isl_multi_pw_aff_bind>,
5548 C<isl_union_pw_aff_bind_id> and
5549 C<isl_multi_union_pw_aff_bind>, the parameters
5550 are bound to the function values and the result lives
5551 in the domain of the input function.
5555 #include <isl/space.h>
5556 __isl_give isl_space *isl_space_domain(
5557 __isl_take isl_space *space);
5558 __isl_give isl_space *isl_space_range(
5559 __isl_take isl_space *space);
5560 __isl_give isl_space *isl_space_params(
5561 __isl_take isl_space *space);
5562 __isl_give isl_space *
5563 isl_space_domain_wrapped_domain(
5564 __isl_take isl_space *space);
5565 __isl_give isl_space *
5566 isl_space_domain_wrapped_range(
5567 __isl_take isl_space *space);
5568 __isl_give isl_space *
5569 isl_space_range_wrapped_domain(
5570 __isl_take isl_space *space);
5571 __isl_give isl_space *
5572 isl_space_range_wrapped_range(
5573 __isl_take isl_space *space);
5575 #include <isl/local_space.h>
5576 __isl_give isl_local_space *isl_local_space_domain(
5577 __isl_take isl_local_space *ls);
5578 __isl_give isl_local_space *isl_local_space_range(
5579 __isl_take isl_local_space *ls);
5581 #include <isl/set.h>
5582 __isl_give isl_basic_set *isl_basic_set_project_out(
5583 __isl_take isl_basic_set *bset,
5584 enum isl_dim_type type, unsigned first, unsigned n);
5585 __isl_give isl_set *isl_set_project_out_param_id(
5586 __isl_take isl_set *set,
5587 __isl_take isl_id *id);
5588 __isl_give isl_set *
5589 isl_set_project_out_param_id_list(
5590 __isl_take isl_set *set,
5591 __isl_take isl_id_list *list);
5592 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
5593 enum isl_dim_type type, unsigned first, unsigned n);
5594 __isl_give isl_set *isl_set_project_out_all_params(
5595 __isl_take isl_set *set);
5596 __isl_give isl_map *isl_set_project_onto_map(
5597 __isl_take isl_set *set,
5598 enum isl_dim_type type, unsigned first,
5600 __isl_give isl_basic_set *isl_basic_set_params(
5601 __isl_take isl_basic_set *bset);
5602 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
5604 The function C<isl_space_domain_wrapped_domain> returns the domain
5605 of the binary relation wrapped inside the domain of the input.
5606 The function C<isl_set_project_onto_map> returns a relation
5607 that projects the input set onto the given set dimensions.
5609 #include <isl/map.h>
5610 __isl_give isl_basic_map *isl_basic_map_project_out(
5611 __isl_take isl_basic_map *bmap,
5612 enum isl_dim_type type, unsigned first, unsigned n);
5613 __isl_give isl_map *isl_map_project_out_param_id(
5614 __isl_take isl_map *map,
5615 __isl_take isl_id *id);
5616 __isl_give isl_map *isl_map_project_out_param_id_list(
5617 __isl_take isl_map *map,
5618 __isl_take isl_id_list *list);
5619 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
5620 enum isl_dim_type type, unsigned first, unsigned n);
5621 __isl_give isl_map *isl_map_project_out_all_params(
5622 __isl_take isl_map *map);
5623 __isl_give isl_basic_set *isl_basic_map_domain(
5624 __isl_take isl_basic_map *bmap);
5625 __isl_give isl_basic_set *isl_basic_map_range(
5626 __isl_take isl_basic_map *bmap);
5627 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
5628 __isl_give isl_set *isl_map_domain(
5629 __isl_take isl_map *bmap);
5630 __isl_give isl_set *isl_map_range(
5631 __isl_take isl_map *map);
5633 #include <isl/union_set.h>
5634 __isl_give isl_union_set *isl_union_set_project_out(
5635 __isl_take isl_union_set *uset,
5636 enum isl_dim_type type,
5637 unsigned first, unsigned n);
5638 __isl_give isl_union_set *
5639 isl_union_set_project_out_all_params(
5640 __isl_take isl_union_set *uset);
5641 __isl_give isl_set *isl_union_set_params(
5642 __isl_take isl_union_set *uset);
5644 The function C<isl_union_set_project_out> can only project out
5647 #include <isl/union_map.h>
5648 __isl_give isl_union_map *
5649 isl_union_map_project_out_param_id(
5650 __isl_take isl_union_map *umap,
5651 __isl_take isl_id *id);
5652 __isl_give isl_union_map *
5653 isl_union_map_project_out_param_id_list(
5654 __isl_take isl_union_map *umap,
5655 __isl_take isl_id_list *list);
5656 __isl_give isl_union_map *isl_union_map_project_out(
5657 __isl_take isl_union_map *umap,
5658 enum isl_dim_type type, unsigned first, unsigned n);
5659 __isl_give isl_union_map *
5660 isl_union_map_project_out_all_params(
5661 __isl_take isl_union_map *umap);
5662 __isl_give isl_set *isl_union_map_params(
5663 __isl_take isl_union_map *umap);
5664 __isl_give isl_union_set *isl_union_map_domain(
5665 __isl_take isl_union_map *umap);
5666 __isl_give isl_union_set *isl_union_map_range(
5667 __isl_take isl_union_map *umap);
5669 The function C<isl_union_map_project_out> can only project out
5672 #include <isl/aff.h>
5673 __isl_give isl_aff *isl_aff_project_domain_on_params(
5674 __isl_take isl_aff *aff);
5675 __isl_give isl_multi_aff *
5676 isl_multi_aff_project_domain_on_params(
5677 __isl_take isl_multi_aff *ma);
5678 __isl_give isl_pw_aff *
5679 isl_pw_aff_project_domain_on_params(
5680 __isl_take isl_pw_aff *pa);
5681 __isl_give isl_multi_pw_aff *
5682 isl_multi_pw_aff_project_domain_on_params(
5683 __isl_take isl_multi_pw_aff *mpa);
5684 __isl_give isl_pw_multi_aff *
5685 isl_pw_multi_aff_project_domain_on_params(
5686 __isl_take isl_pw_multi_aff *pma);
5687 __isl_give isl_set *isl_pw_aff_domain(
5688 __isl_take isl_pw_aff *pwaff);
5689 __isl_give isl_set *isl_pw_multi_aff_domain(
5690 __isl_take isl_pw_multi_aff *pma);
5691 __isl_give isl_set *isl_multi_pw_aff_domain(
5692 __isl_take isl_multi_pw_aff *mpa);
5693 __isl_give isl_union_set *isl_union_pw_aff_domain(
5694 __isl_take isl_union_pw_aff *upa);
5695 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
5696 __isl_take isl_union_pw_multi_aff *upma);
5697 __isl_give isl_union_set *
5698 isl_multi_union_pw_aff_domain(
5699 __isl_take isl_multi_union_pw_aff *mupa);
5700 __isl_give isl_set *isl_pw_aff_params(
5701 __isl_take isl_pw_aff *pwa);
5703 If no explicit domain was set on a zero-dimensional input to
5704 C<isl_multi_union_pw_aff_domain>, then this function will
5705 return a parameter set.
5707 #include <isl/polynomial.h>
5708 __isl_give isl_qpolynomial *
5709 isl_qpolynomial_project_domain_on_params(
5710 __isl_take isl_qpolynomial *qp);
5711 __isl_give isl_pw_qpolynomial *
5712 isl_pw_qpolynomial_project_domain_on_params(
5713 __isl_take isl_pw_qpolynomial *pwqp);
5714 __isl_give isl_pw_qpolynomial_fold *
5715 isl_pw_qpolynomial_fold_project_domain_on_params(
5716 __isl_take isl_pw_qpolynomial_fold *pwf);
5717 __isl_give isl_set *isl_pw_qpolynomial_domain(
5718 __isl_take isl_pw_qpolynomial *pwqp);
5719 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5720 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5721 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5722 __isl_take isl_union_pw_qpolynomial *upwqp);
5724 #include <isl/space.h>
5725 __isl_give isl_space *isl_space_domain_map(
5726 __isl_take isl_space *space);
5727 __isl_give isl_space *isl_space_range_map(
5728 __isl_take isl_space *space);
5730 #include <isl/map.h>
5731 __isl_give isl_map *isl_set_wrapped_domain_map(
5732 __isl_take isl_set *set);
5733 __isl_give isl_basic_map *isl_basic_map_domain_map(
5734 __isl_take isl_basic_map *bmap);
5735 __isl_give isl_basic_map *isl_basic_map_range_map(
5736 __isl_take isl_basic_map *bmap);
5737 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
5738 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
5740 #include <isl/union_map.h>
5741 __isl_give isl_union_map *isl_union_map_domain_map(
5742 __isl_take isl_union_map *umap);
5743 __isl_give isl_union_pw_multi_aff *
5744 isl_union_map_domain_map_union_pw_multi_aff(
5745 __isl_take isl_union_map *umap);
5746 __isl_give isl_union_map *isl_union_map_range_map(
5747 __isl_take isl_union_map *umap);
5748 __isl_give isl_union_map *
5749 isl_union_set_wrapped_domain_map(
5750 __isl_take isl_union_set *uset);
5752 The functions above construct a (basic, regular or union) relation
5753 that maps (a wrapped version of) the input relation to its domain or range.
5754 C<isl_set_wrapped_domain_map> maps the input set to the domain
5755 of its wrapped relation.
5759 __isl_give isl_basic_set *isl_basic_set_eliminate(
5760 __isl_take isl_basic_set *bset,
5761 enum isl_dim_type type,
5762 unsigned first, unsigned n);
5763 __isl_give isl_set *isl_set_eliminate(
5764 __isl_take isl_set *set, enum isl_dim_type type,
5765 unsigned first, unsigned n);
5766 __isl_give isl_basic_map *isl_basic_map_eliminate(
5767 __isl_take isl_basic_map *bmap,
5768 enum isl_dim_type type,
5769 unsigned first, unsigned n);
5770 __isl_give isl_map *isl_map_eliminate(
5771 __isl_take isl_map *map, enum isl_dim_type type,
5772 unsigned first, unsigned n);
5774 Eliminate the coefficients for the given dimensions from the constraints,
5775 without removing the dimensions.
5777 =item * Constructing a set from a parameter domain
5779 A set space of a given dimension and with an optional name
5780 can be created from a parameter space using the following functions.
5782 #include <isl/space.h>
5783 __isl_give isl_space *isl_space_add_unnamed_tuple_ui(
5784 __isl_take isl_space *space, unsigned dim);
5785 __isl_give isl_space *
5786 isl_space_add_named_tuple_id_ui(
5787 __isl_take isl_space *space,
5788 __isl_take isl_id *tuple_id, unsigned dim);
5790 A set with a given tuple can be created from a parameter domain
5791 using the following function.
5793 #include <isl/set.h>
5794 __isl_give isl_set *isl_set_unbind_params(
5795 __isl_take isl_set *set,
5796 __isl_take isl_multi_id *tuple);
5798 Any parameters with identifiers in C<tuple> are reinterpreted
5799 as the corresponding set dimensions.
5801 A zero-dimensional (local) space or (basic) set can be constructed
5802 on a given parameter domain using the following functions.
5804 #include <isl/space.h>
5805 __isl_give isl_space *isl_space_set_from_params(
5806 __isl_take isl_space *space);
5808 #include <isl/local_space.h>
5809 __isl_give isl_local_space *
5810 isl_local_space_set_from_params(
5811 __isl_take isl_local_space *ls);
5813 #include <isl/set.h>
5814 __isl_give isl_basic_set *isl_basic_set_from_params(
5815 __isl_take isl_basic_set *bset);
5816 __isl_give isl_set *isl_set_from_params(
5817 __isl_take isl_set *set);
5819 =item * Constructing a relation from one or two sets
5821 A map space with a range of a given dimension and with an optional name
5822 can be created from a domain space using the functions
5823 C<isl_space_add_unnamed_tuple_ui> and C<isl_space_add_named_tuple_id_ui>
5826 A relation with a given domain tuple can be created from a set
5827 that will become the range of the relation
5828 using the following function.
5830 #include <isl/set.h>
5831 __isl_give isl_map *
5832 isl_set_unbind_params_insert_domain(
5833 __isl_take isl_set *set,
5834 __isl_take isl_multi_id *domain);
5836 Any parameters with identifiers in C<domain> are reinterpreted
5837 as the corresponding input dimensions.
5839 Similarly, a function defined over a parameter domain can
5840 be converted into one defined over a set domain
5841 using the following functions.
5843 #include <isl/aff.h>
5844 __isl_give isl_aff *
5845 isl_aff_unbind_params_insert_domain(
5846 __isl_take isl_aff *aff,
5847 __isl_take isl_multi_id *domain);
5848 __isl_give isl_multi_aff *
5849 isl_multi_aff_unbind_params_insert_domain(
5850 __isl_take isl_multi_aff *ma,
5851 __isl_take isl_multi_id *domain);
5852 __isl_give isl_multi_pw_aff *
5853 isl_multi_pw_aff_unbind_params_insert_domain(
5854 __isl_take isl_multi_pw_aff *mpa,
5855 __isl_take isl_multi_id *domain);
5858 any parameters with identifiers in C<domain> are reinterpreted
5859 as the corresponding input dimensions.
5861 Create a relation with the given set(s) as domain and/or range.
5862 If only the domain or the range is specified, then
5863 the range or domain of the created relation is a zero-dimensional
5864 flat anonymous space.
5865 If the case of C<isl_space_map_from_set>, the input space
5866 specifies both the domain and the range of the result.
5868 #include <isl/space.h>
5869 __isl_give isl_space *isl_space_from_domain(
5870 __isl_take isl_space *space);
5871 __isl_give isl_space *isl_space_from_range(
5872 __isl_take isl_space *space);
5873 __isl_give isl_space *isl_space_map_from_set(
5874 __isl_take isl_space *space);
5875 __isl_give isl_space *isl_space_map_from_domain_and_range(
5876 __isl_take isl_space *domain,
5877 __isl_take isl_space *range);
5879 #include <isl/local_space.h>
5880 __isl_give isl_local_space *isl_local_space_from_domain(
5881 __isl_take isl_local_space *ls);
5883 #include <isl/map.h>
5884 __isl_give isl_map *isl_set_insert_domain(
5885 __isl_take isl_set *set,
5886 __isl_take isl_space *domain);
5887 __isl_give isl_map *isl_map_from_domain(
5888 __isl_take isl_set *set);
5889 __isl_give isl_map *isl_map_from_range(
5890 __isl_take isl_set *set);
5892 #include <isl/union_map.h>
5893 __isl_give isl_union_map *isl_union_map_from_domain(
5894 __isl_take isl_union_set *uset);
5895 __isl_give isl_union_map *isl_union_map_from_range(
5896 __isl_take isl_union_set *uset);
5897 __isl_give isl_union_map *
5898 isl_union_map_from_domain_and_range(
5899 __isl_take isl_union_set *domain,
5900 __isl_take isl_union_set *range);
5903 __isl_give isl_multi_id *isl_multi_id_from_range(
5904 __isl_take isl_multi_id *mi);
5906 #include <isl/val.h>
5907 __isl_give isl_multi_val *isl_multi_val_from_range(
5908 __isl_take isl_multi_val *mv);
5910 #include <isl/aff.h>
5911 __isl_give isl_multi_aff *
5912 isl_multi_aff_insert_domain(
5913 __isl_take isl_multi_aff *ma,
5914 __isl_take isl_space *domain);
5915 __isl_give isl_pw_aff *isl_pw_aff_insert_domain(
5916 __isl_take isl_pw_aff *pa,
5917 __isl_take isl_space *domain);
5918 __isl_give isl_pw_multi_aff *
5919 isl_pw_multi_aff_insert_domain(
5920 __isl_take isl_pw_multi_aff *pma,
5921 __isl_take isl_space *domain);
5922 __isl_give isl_multi_pw_aff *
5923 isl_multi_pw_aff_insert_domain(
5924 __isl_take isl_multi_pw_aff *mpa,
5925 __isl_take isl_space *domain);
5926 __isl_give isl_aff *isl_aff_from_range(
5927 __isl_take isl_aff *aff);
5928 __isl_give isl_multi_aff *isl_multi_aff_from_range(
5929 __isl_take isl_multi_aff *ma);
5930 __isl_give isl_pw_aff *isl_pw_aff_from_range(
5931 __isl_take isl_pw_aff *pwa);
5932 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
5933 __isl_take isl_multi_pw_aff *mpa);
5934 __isl_give isl_multi_union_pw_aff *
5935 isl_multi_union_pw_aff_from_range(
5936 __isl_take isl_multi_union_pw_aff *mupa);
5937 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
5938 __isl_take isl_set *set);
5939 __isl_give isl_union_pw_multi_aff *
5940 isl_union_pw_multi_aff_from_domain(
5941 __isl_take isl_union_set *uset);
5943 #include <isl/polynomial.h>
5944 __isl_give isl_pw_qpolynomial *
5945 isl_pw_qpolynomial_from_range(
5946 __isl_take isl_pw_qpolynomial *pwqp);
5947 __isl_give isl_pw_qpolynomial_fold *
5948 isl_pw_qpolynomial_fold_from_range(
5949 __isl_take isl_pw_qpolynomial_fold *pwf);
5953 #include <isl/set.h>
5954 __isl_give isl_basic_set *isl_basic_set_fix_si(
5955 __isl_take isl_basic_set *bset,
5956 enum isl_dim_type type, unsigned pos, int value);
5957 __isl_give isl_basic_set *isl_basic_set_fix_val(
5958 __isl_take isl_basic_set *bset,
5959 enum isl_dim_type type, unsigned pos,
5960 __isl_take isl_val *v);
5961 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
5962 enum isl_dim_type type, unsigned pos, int value);
5963 __isl_give isl_set *isl_set_fix_val(
5964 __isl_take isl_set *set,
5965 enum isl_dim_type type, unsigned pos,
5966 __isl_take isl_val *v);
5968 #include <isl/map.h>
5969 __isl_give isl_basic_map *isl_basic_map_fix_si(
5970 __isl_take isl_basic_map *bmap,
5971 enum isl_dim_type type, unsigned pos, int value);
5972 __isl_give isl_basic_map *isl_basic_map_fix_val(
5973 __isl_take isl_basic_map *bmap,
5974 enum isl_dim_type type, unsigned pos,
5975 __isl_take isl_val *v);
5976 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
5977 enum isl_dim_type type, unsigned pos, int value);
5978 __isl_give isl_map *isl_map_fix_val(
5979 __isl_take isl_map *map,
5980 enum isl_dim_type type, unsigned pos,
5981 __isl_take isl_val *v);
5983 #include <isl/aff.h>
5984 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
5985 __isl_take isl_pw_multi_aff *pma,
5986 enum isl_dim_type type, unsigned pos, int value);
5988 #include <isl/polynomial.h>
5989 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
5990 __isl_take isl_pw_qpolynomial *pwqp,
5991 enum isl_dim_type type, unsigned n,
5992 __isl_take isl_val *v);
5993 __isl_give isl_pw_qpolynomial_fold *
5994 isl_pw_qpolynomial_fold_fix_val(
5995 __isl_take isl_pw_qpolynomial_fold *pwf,
5996 enum isl_dim_type type, unsigned n,
5997 __isl_take isl_val *v);
5999 Intersect the set, relation or function domain
6000 with the hyperplane where the given
6001 dimension has the fixed given value.
6003 #include <isl/set.h>
6004 __isl_give isl_basic_set *
6005 isl_basic_set_lower_bound_val(
6006 __isl_take isl_basic_set *bset,
6007 enum isl_dim_type type, unsigned pos,
6008 __isl_take isl_val *value);
6009 __isl_give isl_basic_set *
6010 isl_basic_set_upper_bound_val(
6011 __isl_take isl_basic_set *bset,
6012 enum isl_dim_type type, unsigned pos,
6013 __isl_take isl_val *value);
6014 __isl_give isl_set *isl_set_lower_bound_si(
6015 __isl_take isl_set *set,
6016 enum isl_dim_type type, unsigned pos, int value);
6017 __isl_give isl_set *isl_set_lower_bound_val(
6018 __isl_take isl_set *set,
6019 enum isl_dim_type type, unsigned pos,
6020 __isl_take isl_val *value);
6021 __isl_give isl_set *isl_set_upper_bound_si(
6022 __isl_take isl_set *set,
6023 enum isl_dim_type type, unsigned pos, int value);
6024 __isl_give isl_set *isl_set_upper_bound_val(
6025 __isl_take isl_set *set,
6026 enum isl_dim_type type, unsigned pos,
6027 __isl_take isl_val *value);
6028 __isl_give isl_set *isl_set_lower_bound_multi_val(
6029 __isl_take isl_set *set,
6030 __isl_take isl_multi_val *lower);
6031 __isl_give isl_set *isl_set_upper_bound_multi_val(
6032 __isl_take isl_set *set,
6033 __isl_take isl_multi_val *upper);
6034 __isl_give isl_set *isl_set_lower_bound_multi_pw_aff(
6035 __isl_take isl_set *set,
6036 __isl_take isl_multi_pw_aff *lower);
6037 __isl_give isl_set *isl_set_upper_bound_multi_pw_aff(
6038 __isl_take isl_set *set,
6039 __isl_take isl_multi_pw_aff *upper);
6041 #include <isl/map.h>
6042 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
6043 __isl_take isl_basic_map *bmap,
6044 enum isl_dim_type type, unsigned pos, int value);
6045 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
6046 __isl_take isl_basic_map *bmap,
6047 enum isl_dim_type type, unsigned pos, int value);
6048 __isl_give isl_map *isl_map_lower_bound_si(
6049 __isl_take isl_map *map,
6050 enum isl_dim_type type, unsigned pos, int value);
6051 __isl_give isl_map *isl_map_upper_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_lower_bound_val(
6055 __isl_take isl_map *map,
6056 enum isl_dim_type type, unsigned pos,
6057 __isl_take isl_val *value);
6058 __isl_give isl_map *isl_map_upper_bound_val(
6059 __isl_take isl_map *map,
6060 enum isl_dim_type type, unsigned pos,
6061 __isl_take isl_val *value);
6062 __isl_give isl_map *isl_map_lower_bound_multi_pw_aff(
6063 __isl_take isl_map *map,
6064 __isl_take isl_multi_pw_aff *lower);
6065 __isl_give isl_map *isl_map_upper_bound_multi_pw_aff(
6066 __isl_take isl_map *map,
6067 __isl_take isl_multi_pw_aff *upper);
6069 Intersect the set or relation with the half-space where the given
6070 dimension has a value bounded by the given fixed integer value or
6071 symbolic constant expression.
6072 For functions taking a multi expression,
6073 this applies to all set dimensions.
6074 Those that bound a map, bound the range of that map.
6075 If the multi expression is zero-dimensional but has an explicit domain,
6076 then the (parameter) domain of the set or map is intersected
6077 with this explicit domain.
6079 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
6080 enum isl_dim_type type1, int pos1,
6081 enum isl_dim_type type2, int pos2);
6082 __isl_give isl_basic_map *isl_basic_map_equate(
6083 __isl_take isl_basic_map *bmap,
6084 enum isl_dim_type type1, int pos1,
6085 enum isl_dim_type type2, int pos2);
6086 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
6087 enum isl_dim_type type1, int pos1,
6088 enum isl_dim_type type2, int pos2);
6090 Intersect the set or relation with the hyperplane where the given
6091 dimensions are equal to each other.
6093 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
6094 enum isl_dim_type type1, int pos1,
6095 enum isl_dim_type type2, int pos2);
6097 Intersect the relation with the hyperplane where the given
6098 dimensions have opposite values.
6100 __isl_give isl_map *isl_map_order_le(
6101 __isl_take isl_map *map,
6102 enum isl_dim_type type1, int pos1,
6103 enum isl_dim_type type2, int pos2);
6104 __isl_give isl_basic_map *isl_basic_map_order_ge(
6105 __isl_take isl_basic_map *bmap,
6106 enum isl_dim_type type1, int pos1,
6107 enum isl_dim_type type2, int pos2);
6108 __isl_give isl_map *isl_map_order_ge(
6109 __isl_take isl_map *map,
6110 enum isl_dim_type type1, int pos1,
6111 enum isl_dim_type type2, int pos2);
6112 __isl_give isl_map *isl_map_order_lt(__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_basic_map *isl_basic_map_order_gt(
6116 __isl_take isl_basic_map *bmap,
6117 enum isl_dim_type type1, int pos1,
6118 enum isl_dim_type type2, int pos2);
6119 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
6120 enum isl_dim_type type1, int pos1,
6121 enum isl_dim_type type2, int pos2);
6123 Intersect the relation with the half-space where the given
6124 dimensions satisfy the given ordering.
6126 #include <isl/union_set.h>
6127 __isl_give isl_union_map *isl_union_map_remove_map_if(
6128 __isl_take isl_union_map *umap,
6129 isl_bool (*fn)(__isl_keep isl_map *map,
6130 void *user), void *user);
6132 This function calls the callback function once for each
6133 pair of spaces for which there are elements in the input.
6134 If the callback returns C<isl_bool_true>, then all those elements
6135 are removed from the result. The only remaining elements in the output
6136 are then those for which the callback returns C<isl_bool_false>.
6140 #include <isl/aff.h>
6141 __isl_give isl_basic_set *isl_aff_zero_basic_set(
6142 __isl_take isl_aff *aff);
6143 __isl_give isl_basic_set *isl_aff_neg_basic_set(
6144 __isl_take isl_aff *aff);
6145 __isl_give isl_set *isl_pw_aff_pos_set(
6146 __isl_take isl_pw_aff *pa);
6147 __isl_give isl_set *isl_pw_aff_nonneg_set(
6148 __isl_take isl_pw_aff *pwaff);
6149 __isl_give isl_set *isl_pw_aff_zero_set(
6150 __isl_take isl_pw_aff *pwaff);
6151 __isl_give isl_set *isl_pw_aff_non_zero_set(
6152 __isl_take isl_pw_aff *pwaff);
6153 __isl_give isl_union_set *
6154 isl_union_pw_aff_zero_union_set(
6155 __isl_take isl_union_pw_aff *upa);
6156 __isl_give isl_union_set *
6157 isl_multi_union_pw_aff_zero_union_set(
6158 __isl_take isl_multi_union_pw_aff *mupa);
6160 The function C<isl_aff_neg_basic_set> returns a basic set
6161 containing those elements in the domain space
6162 of C<aff> where C<aff> is negative.
6163 The function C<isl_pw_aff_nonneg_set> returns a set
6164 containing those elements in the domain
6165 of C<pwaff> where C<pwaff> is non-negative.
6166 The function C<isl_multi_union_pw_aff_zero_union_set>
6167 returns a union set containing those elements
6168 in the domains of its elements where they are all zero.
6172 __isl_give isl_map *isl_set_identity(
6173 __isl_take isl_set *set);
6174 __isl_give isl_union_map *isl_union_set_identity(
6175 __isl_take isl_union_set *uset);
6176 __isl_give isl_union_pw_multi_aff *
6177 isl_union_set_identity_union_pw_multi_aff(
6178 __isl_take isl_union_set *uset);
6180 Construct an identity relation on the given (union) set.
6182 =item * Function Extraction
6184 A piecewise quasi affine expression that is equal to 1 on a set
6185 and 0 outside the set can be created using the following function.
6187 #include <isl/aff.h>
6188 __isl_give isl_pw_aff *isl_set_indicator_function(
6189 __isl_take isl_set *set);
6191 A piecewise multiple quasi affine expression can be extracted
6192 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
6193 and the C<isl_map> is single-valued.
6194 In case of a conversion from an C<isl_union_map>
6195 to an C<isl_union_pw_multi_aff>, these properties need to hold
6196 in each domain space.
6197 A conversion to a C<isl_multi_union_pw_aff> additionally
6198 requires that the input is non-empty and involves only a single
6201 #include <isl/aff.h>
6202 __isl_give isl_pw_multi_aff *isl_set_as_pw_multi_aff(
6203 __isl_take isl_set *set);
6204 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
6205 __isl_take isl_set *set);
6206 __isl_give isl_pw_multi_aff *isl_map_as_pw_multi_aff(
6207 __isl_take isl_map *map);
6208 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
6209 __isl_take isl_map *map);
6211 __isl_give isl_union_pw_multi_aff *
6212 isl_union_pw_multi_aff_from_union_set(
6213 __isl_take isl_union_set *uset);
6214 __isl_give isl_union_pw_multi_aff *
6215 isl_union_map_as_union_pw_multi_aff(
6216 __isl_take isl_union_map *umap);
6217 __isl_give isl_union_pw_multi_aff *
6218 isl_union_pw_multi_aff_from_union_map(
6219 __isl_take isl_union_map *umap);
6221 __isl_give isl_multi_union_pw_aff *
6222 isl_union_map_as_multi_union_pw_aff(
6223 __isl_take isl_union_map *umap);
6224 __isl_give isl_multi_union_pw_aff *
6225 isl_multi_union_pw_aff_from_union_map(
6226 __isl_take isl_union_map *umap);
6228 C<isl_map_as_pw_multi_aff> and C<isl_pw_multi_aff_from_map> perform
6230 Similarly for C<isl_set_as_pw_multi_aff> and
6231 C<isl_pw_multi_aff_from_set>,
6232 for C<isl_union_map_as_union_pw_multi_aff> and
6233 C<isl_union_pw_multi_aff_from_union_map> and
6234 for C<isl_union_map_as_multi_union_pw_aff> and
6235 C<isl_multi_union_pw_aff_from_union_map>.
6239 __isl_give isl_basic_set *isl_basic_map_deltas(
6240 __isl_take isl_basic_map *bmap);
6241 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
6242 __isl_give isl_union_set *isl_union_map_deltas(
6243 __isl_take isl_union_map *umap);
6245 These functions return a (basic) set containing the differences
6246 between image elements and corresponding domain elements in the input.
6248 __isl_give isl_basic_map *isl_basic_map_deltas_map(
6249 __isl_take isl_basic_map *bmap);
6250 __isl_give isl_map *isl_map_deltas_map(
6251 __isl_take isl_map *map);
6252 __isl_give isl_union_map *isl_union_map_deltas_map(
6253 __isl_take isl_union_map *umap);
6255 The functions above construct a (basic, regular or union) relation
6256 that maps (a wrapped version of) the input relation to its delta set.
6260 #include <isl/map.h>
6261 __isl_give isl_map *isl_set_translation(
6262 __isl_take isl_set *deltas);
6264 This function performs essentially the opposite operation
6265 of C<isl_map_deltas>. In particular, it returns pairs
6266 of elements in the same space that have a difference in C<deltas>.
6270 Simplify the representation of a set, relation or functions by trying
6271 to combine pairs of basic sets or relations into a single
6272 basic set or relation.
6274 #include <isl/set.h>
6275 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
6277 #include <isl/map.h>
6278 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
6280 #include <isl/union_set.h>
6281 __isl_give isl_union_set *isl_union_set_coalesce(
6282 __isl_take isl_union_set *uset);
6284 #include <isl/union_map.h>
6285 __isl_give isl_union_map *isl_union_map_coalesce(
6286 __isl_take isl_union_map *umap);
6288 #include <isl/aff.h>
6289 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
6290 __isl_take isl_pw_aff *pa);
6291 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
6292 __isl_take isl_pw_multi_aff *pma);
6293 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
6294 __isl_take isl_multi_pw_aff *mpa);
6295 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
6296 __isl_take isl_union_pw_aff *upa);
6297 __isl_give isl_union_pw_multi_aff *
6298 isl_union_pw_multi_aff_coalesce(
6299 __isl_take isl_union_pw_multi_aff *upma);
6300 __isl_give isl_multi_union_pw_aff *
6301 isl_multi_union_pw_aff_coalesce(
6302 __isl_take isl_multi_union_pw_aff *mupa);
6304 #include <isl/polynomial.h>
6305 __isl_give isl_pw_qpolynomial_fold *
6306 isl_pw_qpolynomial_fold_coalesce(
6307 __isl_take isl_pw_qpolynomial_fold *pwf);
6308 __isl_give isl_union_pw_qpolynomial *
6309 isl_union_pw_qpolynomial_coalesce(
6310 __isl_take isl_union_pw_qpolynomial *upwqp);
6311 __isl_give isl_union_pw_qpolynomial_fold *
6312 isl_union_pw_qpolynomial_fold_coalesce(
6313 __isl_take isl_union_pw_qpolynomial_fold *upwf);
6315 One of the methods for combining pairs of basic sets or relations
6316 can result in coefficients that are much larger than those that appear
6317 in the constraints of the input. By default, the coefficients are
6318 not allowed to grow larger, but this can be changed by unsetting
6319 the following option.
6321 isl_stat isl_options_set_coalesce_bounded_wrapping(
6322 isl_ctx *ctx, int val);
6323 int isl_options_get_coalesce_bounded_wrapping(
6326 One of the other methods tries to combine pairs of basic sets
6327 with different local variables, treating them as existentially
6328 quantified variables even if they have known (but different)
6329 integer division expressions. The result may then also have
6330 existentially quantified variables. Turning on the following
6331 option prevents this from happening.
6333 isl_stat isl_options_set_coalesce_preserve_locals(
6334 isl_ctx *ctx, int val);
6335 int isl_options_get_coalesce_preserve_locals(isl_ctx *ctx);
6337 =item * Detecting equalities
6339 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
6340 __isl_take isl_basic_set *bset);
6341 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
6342 __isl_take isl_basic_map *bmap);
6343 __isl_give isl_set *isl_set_detect_equalities(
6344 __isl_take isl_set *set);
6345 __isl_give isl_map *isl_map_detect_equalities(
6346 __isl_take isl_map *map);
6347 __isl_give isl_union_set *isl_union_set_detect_equalities(
6348 __isl_take isl_union_set *uset);
6349 __isl_give isl_union_map *isl_union_map_detect_equalities(
6350 __isl_take isl_union_map *umap);
6352 Simplify the representation of a set or relation by detecting implicit
6355 =item * Removing redundant constraints
6357 #include <isl/set.h>
6358 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
6359 __isl_take isl_basic_set *bset);
6360 __isl_give isl_set *isl_set_remove_redundancies(
6361 __isl_take isl_set *set);
6363 #include <isl/union_set.h>
6364 __isl_give isl_union_set *
6365 isl_union_set_remove_redundancies(
6366 __isl_take isl_union_set *uset);
6368 #include <isl/map.h>
6369 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
6370 __isl_take isl_basic_map *bmap);
6371 __isl_give isl_map *isl_map_remove_redundancies(
6372 __isl_take isl_map *map);
6374 #include <isl/union_map.h>
6375 __isl_give isl_union_map *
6376 isl_union_map_remove_redundancies(
6377 __isl_take isl_union_map *umap);
6381 __isl_give isl_basic_set *isl_set_convex_hull(
6382 __isl_take isl_set *set);
6383 __isl_give isl_basic_map *isl_map_convex_hull(
6384 __isl_take isl_map *map);
6386 If the input set or relation has any existentially quantified
6387 variables, then the result of these operations is currently undefined.
6391 #include <isl/set.h>
6392 __isl_give isl_basic_set *
6393 isl_set_unshifted_simple_hull(
6394 __isl_take isl_set *set);
6395 __isl_give isl_basic_set *isl_set_simple_hull(
6396 __isl_take isl_set *set);
6397 __isl_give isl_basic_set *
6398 isl_set_plain_unshifted_simple_hull(
6399 __isl_take isl_set *set);
6400 __isl_give isl_basic_set *
6401 isl_set_unshifted_simple_hull_from_set_list(
6402 __isl_take isl_set *set,
6403 __isl_take isl_set_list *list);
6405 #include <isl/map.h>
6406 __isl_give isl_basic_map *
6407 isl_map_unshifted_simple_hull(
6408 __isl_take isl_map *map);
6409 __isl_give isl_basic_map *isl_map_simple_hull(
6410 __isl_take isl_map *map);
6411 __isl_give isl_basic_map *
6412 isl_map_plain_unshifted_simple_hull(
6413 __isl_take isl_map *map);
6414 __isl_give isl_basic_map *
6415 isl_map_unshifted_simple_hull_from_map_list(
6416 __isl_take isl_map *map,
6417 __isl_take isl_map_list *list);
6419 #include <isl/union_map.h>
6420 __isl_give isl_union_map *isl_union_map_simple_hull(
6421 __isl_take isl_union_map *umap);
6423 These functions compute a single basic set or relation
6424 that contains the whole input set or relation.
6425 In particular, the output is described by translates
6426 of the constraints describing the basic sets or relations in the input.
6427 In case of C<isl_set_unshifted_simple_hull>, only the original
6428 constraints are used, without any translation.
6429 In case of C<isl_set_plain_unshifted_simple_hull> and
6430 C<isl_map_plain_unshifted_simple_hull>, the result is described
6431 by original constraints that are obviously satisfied
6432 by the entire input set or relation.
6433 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
6434 C<isl_map_unshifted_simple_hull_from_map_list>, the
6435 constraints are taken from the elements of the second argument.
6439 (See \autoref{s:simple hull}.)
6445 __isl_give isl_basic_set *isl_basic_set_affine_hull(
6446 __isl_take isl_basic_set *bset);
6447 __isl_give isl_basic_set *isl_set_affine_hull(
6448 __isl_take isl_set *set);
6449 __isl_give isl_union_set *isl_union_set_affine_hull(
6450 __isl_take isl_union_set *uset);
6451 __isl_give isl_basic_map *isl_basic_map_affine_hull(
6452 __isl_take isl_basic_map *bmap);
6453 __isl_give isl_basic_map *isl_map_affine_hull(
6454 __isl_take isl_map *map);
6455 __isl_give isl_union_map *isl_union_map_affine_hull(
6456 __isl_take isl_union_map *umap);
6458 In case of union sets and relations, the affine hull is computed
6461 =item * Polyhedral hull
6463 __isl_give isl_basic_set *isl_set_polyhedral_hull(
6464 __isl_take isl_set *set);
6465 __isl_give isl_basic_map *isl_map_polyhedral_hull(
6466 __isl_take isl_map *map);
6467 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
6468 __isl_take isl_union_set *uset);
6469 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
6470 __isl_take isl_union_map *umap);
6472 These functions compute a single basic set or relation
6473 not involving any existentially quantified variables
6474 that contains the whole input set or relation.
6475 In case of union sets and relations, the polyhedral hull is computed
6480 #include <isl/set.h>
6481 __isl_give isl_fixed_box *
6482 isl_set_get_simple_fixed_box_hull(
6483 __isl_keep isl_set *set)
6485 #include <isl/map.h>
6486 __isl_give isl_fixed_box *
6487 isl_map_get_range_simple_fixed_box_hull(
6488 __isl_keep isl_map *map);
6490 These functions try to approximate the set or
6491 the range of the map by a box of fixed size.
6492 The box is described in terms of an offset living in the same space as
6493 the input and a size living in the set or range space. For any element
6494 in the input map, the range value is greater than or equal to
6495 the offset applied to the domain value and the difference with
6496 this offset is strictly smaller than the size.
6497 The same holds for the elements of the input set, where
6498 the offset is a parametric constant value.
6499 If no fixed-size approximation can be found,
6500 an I<invalid> box is returned, i.e., one for which
6501 C<isl_fixed_box_is_valid> below returns false.
6503 The validity, the offset and the size of the box can be obtained using
6504 the following functions.
6506 #include <isl/fixed_box.h>
6507 isl_bool isl_fixed_box_is_valid(
6508 __isl_keep isl_fixed_box *box);
6509 __isl_give isl_multi_aff *isl_fixed_box_get_offset(
6510 __isl_keep isl_fixed_box *box);
6511 __isl_give isl_multi_val *isl_fixed_box_get_size(
6512 __isl_keep isl_fixed_box *box);
6514 The box can be copied and freed using the following functions.
6516 #include <isl/fixed_box.h>
6517 __isl_give isl_fixed_box *isl_fixed_box_copy(
6518 __isl_keep isl_fixed_box *box);
6519 __isl_null isl_fixed_box *isl_fixed_box_free(
6520 __isl_take isl_fixed_box *box);
6522 An object of type C<isl_fixed_box> can be read from input
6523 using the following function.
6525 #include <isl/fixed_box.h>
6526 __isl_give isl_fixed_box *
6527 isl_fixed_box_read_from_str(isl_ctx *ctx,
6530 A representation of the information contained in an object
6531 of type C<isl_fixed_box> can be obtained using
6533 #include <isl/fixed_box.h>
6534 __isl_give isl_printer *isl_printer_print_fixed_box(
6535 __isl_take isl_printer *p,
6536 __isl_keep isl_fixed_box *box);
6537 __isl_give char *isl_fixed_box_to_str(
6538 __isl_keep isl_fixed_box *box);
6540 C<isl_fixed_box_to_str> prints the information in flow format.
6542 =item * Other approximations
6544 #include <isl/set.h>
6545 __isl_give isl_basic_set *
6546 isl_basic_set_drop_constraints_involving_dims(
6547 __isl_take isl_basic_set *bset,
6548 enum isl_dim_type type,
6549 unsigned first, unsigned n);
6550 __isl_give isl_basic_set *
6551 isl_basic_set_drop_constraints_not_involving_dims(
6552 __isl_take isl_basic_set *bset,
6553 enum isl_dim_type type,
6554 unsigned first, unsigned n);
6555 __isl_give isl_set *
6556 isl_set_drop_constraints_involving_dims(
6557 __isl_take isl_set *set,
6558 enum isl_dim_type type,
6559 unsigned first, unsigned n);
6560 __isl_give isl_set *
6561 isl_set_drop_constraints_not_involving_dims(
6562 __isl_take isl_set *set,
6563 enum isl_dim_type type,
6564 unsigned first, unsigned n);
6566 #include <isl/map.h>
6567 __isl_give isl_basic_map *
6568 isl_basic_map_drop_constraints_involving_dims(
6569 __isl_take isl_basic_map *bmap,
6570 enum isl_dim_type type,
6571 unsigned first, unsigned n);
6572 __isl_give isl_basic_map *
6573 isl_basic_map_drop_constraints_not_involving_dims(
6574 __isl_take isl_basic_map *bmap,
6575 enum isl_dim_type type,
6576 unsigned first, unsigned n);
6577 __isl_give isl_map *
6578 isl_map_drop_constraints_involving_dims(
6579 __isl_take isl_map *map,
6580 enum isl_dim_type type,
6581 unsigned first, unsigned n);
6582 __isl_give isl_map *
6583 isl_map_drop_constraints_not_involving_dims(
6584 __isl_take isl_map *map,
6585 enum isl_dim_type type,
6586 unsigned first, unsigned n);
6588 These functions drop any constraints (not) involving the specified dimensions.
6589 Note that the result depends on the representation of the input.
6591 #include <isl/polynomial.h>
6592 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
6593 __isl_take isl_pw_qpolynomial *pwqp, int sign);
6594 __isl_give isl_union_pw_qpolynomial *
6595 isl_union_pw_qpolynomial_to_polynomial(
6596 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
6598 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
6599 the polynomial will be an overapproximation. If C<sign> is negative,
6600 it will be an underapproximation. If C<sign> is zero, the approximation
6601 will lie somewhere in between.
6605 __isl_give isl_basic_set *isl_basic_set_sample(
6606 __isl_take isl_basic_set *bset);
6607 __isl_give isl_basic_set *isl_set_sample(
6608 __isl_take isl_set *set);
6609 __isl_give isl_basic_map *isl_basic_map_sample(
6610 __isl_take isl_basic_map *bmap);
6611 __isl_give isl_basic_map *isl_map_sample(
6612 __isl_take isl_map *map);
6614 If the input (basic) set or relation is non-empty, then return
6615 a singleton subset of the input. Otherwise, return an empty set.
6617 =item * Optimization
6619 #include <isl/ilp.h>
6620 __isl_give isl_val *isl_basic_set_max_val(
6621 __isl_keep isl_basic_set *bset,
6622 __isl_keep isl_aff *obj);
6623 __isl_give isl_val *isl_set_min_val(
6624 __isl_keep isl_set *set,
6625 __isl_keep isl_aff *obj);
6626 __isl_give isl_val *isl_set_max_val(
6627 __isl_keep isl_set *set,
6628 __isl_keep isl_aff *obj);
6629 __isl_give isl_multi_val *
6630 isl_union_set_min_multi_union_pw_aff(
6631 __isl_keep isl_union_set *uset,
6632 __isl_keep isl_multi_union_pw_aff *obj);
6634 Compute the minimum or maximum of the integer affine expression C<obj>
6635 over the points in C<set>.
6636 The result is C<NULL> in case of an error, the optimal value in case
6637 there is one, negative infinity or infinity if the problem is unbounded and
6638 NaN if the problem is empty.
6640 #include <isl/ilp.h>
6641 __isl_give isl_val *isl_pw_aff_min_val(
6642 __isl_take isl_pw_aff *pa);
6643 __isl_give isl_val *isl_pw_aff_max_val(
6644 __isl_take isl_pw_aff *pa);
6645 __isl_give isl_multi_val *
6646 isl_pw_multi_aff_min_multi_val(
6647 __isl_take isl_pw_multi_aff *pma);
6648 __isl_give isl_multi_val *
6649 isl_pw_multi_aff_max_multi_val(
6650 __isl_take isl_pw_multi_aff *pma);
6651 __isl_give isl_multi_val *
6652 isl_multi_pw_aff_min_multi_val(
6653 __isl_take isl_multi_pw_aff *mpa);
6654 __isl_give isl_multi_val *
6655 isl_multi_pw_aff_max_multi_val(
6656 __isl_take isl_multi_pw_aff *mpa);
6657 __isl_give isl_val *isl_union_pw_aff_min_val(
6658 __isl_take isl_union_pw_aff *upa);
6659 __isl_give isl_val *isl_union_pw_aff_max_val(
6660 __isl_take isl_union_pw_aff *upa);
6661 __isl_give isl_multi_val *
6662 isl_multi_union_pw_aff_min_multi_val(
6663 __isl_take isl_multi_union_pw_aff *mupa);
6664 __isl_give isl_multi_val *
6665 isl_multi_union_pw_aff_max_multi_val(
6666 __isl_take isl_multi_union_pw_aff *mupa);
6668 Compute the minimum or maximum of the integer affine expression
6669 over its definition domain.
6670 The result is C<NULL> in case of an error, the optimal value in case
6671 there is one, negative infinity or infinity if the problem is unbounded and
6672 NaN if the problem is empty.
6674 #include <isl/ilp.h>
6675 __isl_give isl_val *isl_basic_set_dim_max_val(
6676 __isl_take isl_basic_set *bset, int pos);
6677 __isl_give isl_val *isl_set_dim_min_val(
6678 __isl_take isl_set *set, int pos);
6679 __isl_give isl_val *isl_set_dim_max_val(
6680 __isl_take isl_set *set, int pos);
6682 Return the minimal or maximal value attained by the given set dimension,
6683 independently of the parameter values and of any other dimensions.
6684 The result is C<NULL> in case of an error, the optimal value in case
6685 there is one, (negative) infinity if the problem is unbounded and
6686 NaN if the input is empty.
6688 =item * Parametric optimization
6690 __isl_give isl_pw_aff *isl_set_dim_min(
6691 __isl_take isl_set *set, int pos);
6692 __isl_give isl_pw_aff *isl_set_dim_max(
6693 __isl_take isl_set *set, int pos);
6694 __isl_give isl_pw_aff *isl_map_dim_min(
6695 __isl_take isl_map *map, int pos);
6696 __isl_give isl_pw_aff *isl_map_dim_max(
6697 __isl_take isl_map *map, int pos);
6698 __isl_give isl_multi_pw_aff *
6699 isl_set_min_multi_pw_aff(
6700 __isl_take isl_set *set);
6701 __isl_give isl_multi_pw_aff *
6702 isl_set_max_multi_pw_aff(
6703 __isl_take isl_set *set);
6704 __isl_give isl_multi_pw_aff *
6705 isl_map_min_multi_pw_aff(
6706 __isl_take isl_map *map);
6707 __isl_give isl_multi_pw_aff *
6708 isl_map_max_multi_pw_aff(
6709 __isl_take isl_map *map);
6711 Compute the minimum or maximum of the (given) set or output dimension(s)
6712 as a function of the parameters (and input dimensions), but independently
6713 of the other set or output dimensions.
6714 For lexicographic optimization, see L<"Lexicographic Optimization">.
6718 The following functions compute either the set of (rational) coefficient
6719 values of valid constraints for the given set or the set of (rational)
6720 values satisfying the constraints with coefficients from the given set.
6721 Internally, these two sets of functions perform essentially the
6722 same operations, except that the set of coefficients is assumed to
6723 be a cone, while the set of values may be any polyhedron.
6724 The current implementation is based on the Farkas lemma and
6725 Fourier-Motzkin elimination, but this may change or be made optional
6726 in future. In particular, future implementations may use different
6727 dualization algorithms or skip the elimination step.
6729 #include <isl/set.h>
6730 __isl_give isl_basic_set *isl_basic_set_coefficients(
6731 __isl_take isl_basic_set *bset);
6732 __isl_give isl_basic_set_list *
6733 isl_basic_set_list_coefficients(
6734 __isl_take isl_basic_set_list *list);
6735 __isl_give isl_basic_set *isl_set_coefficients(
6736 __isl_take isl_set *set);
6737 __isl_give isl_union_set *isl_union_set_coefficients(
6738 __isl_take isl_union_set *bset);
6739 __isl_give isl_basic_set *isl_basic_set_solutions(
6740 __isl_take isl_basic_set *bset);
6741 __isl_give isl_basic_set *isl_set_solutions(
6742 __isl_take isl_set *set);
6743 __isl_give isl_union_set *isl_union_set_solutions(
6744 __isl_take isl_union_set *bset);
6748 __isl_give isl_map *isl_map_fixed_power_val(
6749 __isl_take isl_map *map,
6750 __isl_take isl_val *exp);
6751 __isl_give isl_union_map *
6752 isl_union_map_fixed_power_val(
6753 __isl_take isl_union_map *umap,
6754 __isl_take isl_val *exp);
6756 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
6757 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
6758 of C<map> is computed.
6760 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
6762 __isl_give isl_union_map *isl_union_map_power(
6763 __isl_take isl_union_map *umap, isl_bool *exact);
6765 Compute a parametric representation for all positive powers I<k> of C<map>.
6766 The result maps I<k> to a nested relation corresponding to the
6767 I<k>th power of C<map>.
6768 The result may be an overapproximation. If the result is known to be exact,
6769 then C<*exact> is set to C<1>.
6771 =item * Transitive closure
6773 __isl_give isl_map *isl_map_transitive_closure(
6774 __isl_take isl_map *map, isl_bool *exact);
6775 __isl_give isl_union_map *isl_union_map_transitive_closure(
6776 __isl_take isl_union_map *umap, isl_bool *exact);
6778 Compute the transitive closure of C<map>.
6779 The result may be an overapproximation. If the result is known to be exact,
6780 then C<*exact> is set to C<1>.
6782 =item * Reaching path lengths
6784 __isl_give isl_map *isl_map_reaching_path_lengths(
6785 __isl_take isl_map *map, isl_bool *exact);
6787 Compute a relation that maps each element in the range of C<map>
6788 to the lengths of all paths composed of edges in C<map> that
6789 end up in the given element.
6790 The result may be an overapproximation. If the result is known to be exact,
6791 then C<*exact> is set to C<1>.
6792 To compute the I<maximal> path length, the resulting relation
6793 should be postprocessed by C<isl_map_lexmax>.
6794 In particular, if the input relation is a dependence relation
6795 (mapping sources to sinks), then the maximal path length corresponds
6796 to the free schedule.
6797 Note, however, that C<isl_map_lexmax> expects the maximum to be
6798 finite, so if the path lengths are unbounded (possibly due to
6799 the overapproximation), then you will get an error message.
6803 #include <isl/space.h>
6804 __isl_give isl_space *isl_space_wrap(
6805 __isl_take isl_space *space);
6806 __isl_give isl_space *isl_space_unwrap(
6807 __isl_take isl_space *space);
6809 #include <isl/local_space.h>
6810 __isl_give isl_local_space *isl_local_space_wrap(
6811 __isl_take isl_local_space *ls);
6813 #include <isl/set.h>
6814 __isl_give isl_basic_map *isl_basic_set_unwrap(
6815 __isl_take isl_basic_set *bset);
6816 __isl_give isl_map *isl_set_unwrap(
6817 __isl_take isl_set *set);
6819 #include <isl/map.h>
6820 __isl_give isl_basic_set *isl_basic_map_wrap(
6821 __isl_take isl_basic_map *bmap);
6822 __isl_give isl_set *isl_map_wrap(
6823 __isl_take isl_map *map);
6825 #include <isl/union_set.h>
6826 __isl_give isl_union_map *isl_union_set_unwrap(
6827 __isl_take isl_union_set *uset);
6829 #include <isl/union_map.h>
6830 __isl_give isl_union_set *isl_union_map_wrap(
6831 __isl_take isl_union_map *umap);
6833 The input to C<isl_space_unwrap> should
6834 be the space of a set, while that of
6835 C<isl_space_wrap> should be the space of a relation.
6836 Conversely, the output of C<isl_space_unwrap> is the space
6837 of a relation, while that of C<isl_space_wrap> is the space of a set.
6841 Remove any internal structure of domain (and range) of the given
6842 set or relation. If there is any such internal structure in the input,
6843 then the name of the space is also removed.
6845 #include <isl/space.h>
6846 __isl_give isl_space *isl_space_flatten_domain(
6847 __isl_take isl_space *space);
6848 __isl_give isl_space *isl_space_flatten_range(
6849 __isl_take isl_space *space);
6851 #include <isl/local_space.h>
6852 __isl_give isl_local_space *
6853 isl_local_space_flatten_domain(
6854 __isl_take isl_local_space *ls);
6855 __isl_give isl_local_space *
6856 isl_local_space_flatten_range(
6857 __isl_take isl_local_space *ls);
6859 #include <isl/set.h>
6860 __isl_give isl_basic_set *isl_basic_set_flatten(
6861 __isl_take isl_basic_set *bset);
6862 __isl_give isl_set *isl_set_flatten(
6863 __isl_take isl_set *set);
6865 #include <isl/map.h>
6866 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
6867 __isl_take isl_basic_map *bmap);
6868 __isl_give isl_basic_map *isl_basic_map_flatten_range(
6869 __isl_take isl_basic_map *bmap);
6870 __isl_give isl_map *isl_map_flatten_range(
6871 __isl_take isl_map *map);
6872 __isl_give isl_map *isl_map_flatten_domain(
6873 __isl_take isl_map *map);
6874 __isl_give isl_basic_map *isl_basic_map_flatten(
6875 __isl_take isl_basic_map *bmap);
6876 __isl_give isl_map *isl_map_flatten(
6877 __isl_take isl_map *map);
6880 __isl_give isl_multi_id *isl_multi_id_flatten_range(
6881 __isl_take isl_multi_id *mi);
6883 #include <isl/val.h>
6884 __isl_give isl_multi_val *isl_multi_val_flatten_range(
6885 __isl_take isl_multi_val *mv);
6887 #include <isl/aff.h>
6888 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
6889 __isl_take isl_multi_aff *ma);
6890 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
6891 __isl_take isl_multi_aff *ma);
6892 __isl_give isl_multi_pw_aff *
6893 isl_multi_pw_aff_flatten_range(
6894 __isl_take isl_multi_pw_aff *mpa);
6895 __isl_give isl_multi_union_pw_aff *
6896 isl_multi_union_pw_aff_flatten_range(
6897 __isl_take isl_multi_union_pw_aff *mupa);
6899 #include <isl/map.h>
6900 __isl_give isl_map *isl_set_flatten_map(
6901 __isl_take isl_set *set);
6903 The function above constructs a relation
6904 that maps the input set to a flattened version of the set.
6908 Lift the input set to a space with extra dimensions corresponding
6909 to the existentially quantified variables in the input.
6910 In particular, the result lives in a wrapped map where the domain
6911 is the original space and the range corresponds to the original
6912 existentially quantified variables.
6914 #include <isl/set.h>
6915 __isl_give isl_basic_set *isl_basic_set_lift(
6916 __isl_take isl_basic_set *bset);
6917 __isl_give isl_set *isl_set_lift(
6918 __isl_take isl_set *set);
6919 __isl_give isl_union_set *isl_union_set_lift(
6920 __isl_take isl_union_set *uset);
6922 Given a local space that contains the existentially quantified
6923 variables of a set, a basic relation that, when applied to
6924 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
6925 can be constructed using the following function.
6927 #include <isl/local_space.h>
6928 __isl_give isl_basic_map *isl_local_space_lifting(
6929 __isl_take isl_local_space *ls);
6931 #include <isl/aff.h>
6932 __isl_give isl_multi_aff *isl_multi_aff_lift(
6933 __isl_take isl_multi_aff *maff,
6934 __isl_give isl_local_space **ls);
6936 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
6937 then it is assigned the local space that lies at the basis of
6938 the lifting applied.
6940 =item * Internal Product
6942 #include <isl/space.h>
6943 __isl_give isl_space *isl_space_zip(
6944 __isl_take isl_space *space);
6946 #include <isl/map.h>
6947 __isl_give isl_basic_map *isl_basic_map_zip(
6948 __isl_take isl_basic_map *bmap);
6949 __isl_give isl_map *isl_map_zip(
6950 __isl_take isl_map *map);
6952 #include <isl/union_map.h>
6953 __isl_give isl_union_map *isl_union_map_zip(
6954 __isl_take isl_union_map *umap);
6956 Given a relation with nested relations for domain and range,
6957 interchange the range of the domain with the domain of the range.
6961 #include <isl/space.h>
6962 __isl_give isl_space *isl_space_curry(
6963 __isl_take isl_space *space);
6964 __isl_give isl_space *isl_space_uncurry(
6965 __isl_take isl_space *space);
6967 #include <isl/map.h>
6968 __isl_give isl_basic_map *isl_basic_map_curry(
6969 __isl_take isl_basic_map *bmap);
6970 __isl_give isl_basic_map *isl_basic_map_uncurry(
6971 __isl_take isl_basic_map *bmap);
6972 __isl_give isl_map *isl_map_curry(
6973 __isl_take isl_map *map);
6974 __isl_give isl_map *isl_map_uncurry(
6975 __isl_take isl_map *map);
6977 #include <isl/union_map.h>
6978 __isl_give isl_union_map *isl_union_map_curry(
6979 __isl_take isl_union_map *umap);
6980 __isl_give isl_union_map *isl_union_map_uncurry(
6981 __isl_take isl_union_map *umap);
6983 Given a relation with a nested relation for domain,
6984 the C<curry> functions
6985 move the range of the nested relation out of the domain
6986 and use it as the domain of a nested relation in the range,
6987 with the original range as range of this nested relation.
6988 The C<uncurry> functions perform the inverse operation.
6990 #include <isl/space.h>
6991 __isl_give isl_space *isl_space_range_curry(
6992 __isl_take isl_space *space);
6994 #include <isl/map.h>
6995 __isl_give isl_map *isl_map_range_curry(
6996 __isl_take isl_map *map);
6998 #include <isl/union_map.h>
6999 __isl_give isl_union_map *isl_union_map_range_curry(
7000 __isl_take isl_union_map *umap);
7002 These functions apply the currying to the relation that
7003 is nested inside the range of the input.
7005 =item * Aligning parameters
7007 Change the order of the parameters of the given set, relation
7009 such that the first parameters match those of C<model>.
7010 This may involve the introduction of extra parameters.
7011 All parameters need to be named.
7013 #include <isl/space.h>
7014 __isl_give isl_space *isl_space_align_params(
7015 __isl_take isl_space *space1,
7016 __isl_take isl_space *space2)
7018 #include <isl/set.h>
7019 __isl_give isl_basic_set *isl_basic_set_align_params(
7020 __isl_take isl_basic_set *bset,
7021 __isl_take isl_space *model);
7022 __isl_give isl_set *isl_set_align_params(
7023 __isl_take isl_set *set,
7024 __isl_take isl_space *model);
7026 #include <isl/map.h>
7027 __isl_give isl_basic_map *isl_basic_map_align_params(
7028 __isl_take isl_basic_map *bmap,
7029 __isl_take isl_space *model);
7030 __isl_give isl_map *isl_map_align_params(
7031 __isl_take isl_map *map,
7032 __isl_take isl_space *model);
7035 __isl_give isl_multi_id *isl_multi_id_align_params(
7036 __isl_take isl_multi_id *mi,
7037 __isl_take isl_space *model);
7039 #include <isl/val.h>
7040 __isl_give isl_multi_val *isl_multi_val_align_params(
7041 __isl_take isl_multi_val *mv,
7042 __isl_take isl_space *model);
7044 #include <isl/aff.h>
7045 __isl_give isl_aff *isl_aff_align_params(
7046 __isl_take isl_aff *aff,
7047 __isl_take isl_space *model);
7048 __isl_give isl_multi_aff *isl_multi_aff_align_params(
7049 __isl_take isl_multi_aff *multi,
7050 __isl_take isl_space *model);
7051 __isl_give isl_pw_aff *isl_pw_aff_align_params(
7052 __isl_take isl_pw_aff *pwaff,
7053 __isl_take isl_space *model);
7054 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
7055 __isl_take isl_pw_multi_aff *pma,
7056 __isl_take isl_space *model);
7057 __isl_give isl_union_pw_aff *
7058 isl_union_pw_aff_align_params(
7059 __isl_take isl_union_pw_aff *upa,
7060 __isl_take isl_space *model);
7061 __isl_give isl_union_pw_multi_aff *
7062 isl_union_pw_multi_aff_align_params(
7063 __isl_take isl_union_pw_multi_aff *upma,
7064 __isl_take isl_space *model);
7065 __isl_give isl_multi_union_pw_aff *
7066 isl_multi_union_pw_aff_align_params(
7067 __isl_take isl_multi_union_pw_aff *mupa,
7068 __isl_take isl_space *model);
7070 #include <isl/polynomial.h>
7071 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
7072 __isl_take isl_qpolynomial *qp,
7073 __isl_take isl_space *model);
7075 =item * Drop unused parameters
7077 Drop parameters that are not referenced by the isl object.
7078 All parameters need to be named.
7080 #include <isl/set.h>
7081 __isl_give isl_basic_set *
7082 isl_basic_set_drop_unused_params(
7083 __isl_take isl_basic_set *bset);
7084 __isl_give isl_set *isl_set_drop_unused_params(
7085 __isl_take isl_set *set);
7087 #include <isl/map.h>
7088 __isl_give isl_basic_map *
7089 isl_basic_map_drop_unused_params(
7090 __isl_take isl_basic_map *bmap);
7091 __isl_give isl_map *isl_map_drop_unused_params(
7092 __isl_take isl_map *map);
7094 #include <isl/union_set.h>
7095 __isl_give isl_union_set *
7096 isl_union_set_drop_unused_params(
7097 __isl_take isl_union_set *uset);
7099 #include <isl/union_map.h>
7100 __isl_give isl_union_map *
7101 isl_union_map_drop_unused_params(
7102 __isl_take isl_union_map *umap);
7104 #include <isl/aff.h>
7105 __isl_give isl_pw_aff *isl_pw_aff_drop_unused_params(
7106 __isl_take isl_pw_aff *pa);
7107 __isl_give isl_pw_multi_aff *
7108 isl_pw_multi_aff_drop_unused_params(
7109 __isl_take isl_pw_multi_aff *pma);
7110 __isl_give isl_union_pw_aff *
7111 isl_union_pw_aff_drop_unused_params(
7112 __isl_take isl_union_pw_aff *upa);
7113 __isl_give isl_union_pw_multi_aff *
7114 isl_union_pw_multi_aff_drop_unused_params(
7115 __isl_take isl_union_pw_multi_aff *upma);
7117 #include <isl/polynomial.h>
7118 __isl_give isl_pw_qpolynomial *
7119 isl_pw_qpolynomial_drop_unused_params(
7120 __isl_take isl_pw_qpolynomial *pwqp);
7121 __isl_give isl_pw_qpolynomial_fold *
7122 isl_pw_qpolynomial_fold_drop_unused_params(
7123 __isl_take isl_pw_qpolynomial_fold *pwf);
7124 __isl_give isl_union_pw_qpolynomial *
7125 isl_union_pw_qpolynomial_drop_unused_params(
7126 __isl_take isl_union_pw_qpolynomial *upwqp);
7127 __isl_give isl_union_pw_qpolynomial_fold *
7128 isl_union_pw_qpolynomial_fold_drop_unused_params(
7129 __isl_take isl_union_pw_qpolynomial_fold *upwf);
7131 =item * Unary Arithmetic Operations
7133 #include <isl/set.h>
7134 __isl_give isl_set *isl_set_neg(
7135 __isl_take isl_set *set);
7136 #include <isl/map.h>
7137 __isl_give isl_map *isl_map_neg(
7138 __isl_take isl_map *map);
7140 C<isl_set_neg> constructs a set containing the opposites of
7141 the elements in its argument.
7142 The domain of the result of C<isl_map_neg> is the same
7143 as the domain of its argument. The corresponding range
7144 elements are the opposites of the corresponding range
7145 elements in the argument.
7147 #include <isl/val.h>
7148 __isl_give isl_multi_val *isl_multi_val_neg(
7149 __isl_take isl_multi_val *mv);
7151 #include <isl/aff.h>
7152 __isl_give isl_aff *isl_aff_neg(
7153 __isl_take isl_aff *aff);
7154 __isl_give isl_multi_aff *isl_multi_aff_neg(
7155 __isl_take isl_multi_aff *ma);
7156 __isl_give isl_pw_aff *isl_pw_aff_neg(
7157 __isl_take isl_pw_aff *pwaff);
7158 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
7159 __isl_take isl_pw_multi_aff *pma);
7160 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
7161 __isl_take isl_multi_pw_aff *mpa);
7162 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
7163 __isl_take isl_union_pw_aff *upa);
7164 __isl_give isl_union_pw_multi_aff *
7165 isl_union_pw_multi_aff_neg(
7166 __isl_take isl_union_pw_multi_aff *upma);
7167 __isl_give isl_multi_union_pw_aff *
7168 isl_multi_union_pw_aff_neg(
7169 __isl_take isl_multi_union_pw_aff *mupa);
7170 __isl_give isl_aff *isl_aff_ceil(
7171 __isl_take isl_aff *aff);
7172 __isl_give isl_pw_aff *isl_pw_aff_ceil(
7173 __isl_take isl_pw_aff *pwaff);
7174 __isl_give isl_aff *isl_aff_floor(
7175 __isl_take isl_aff *aff);
7176 __isl_give isl_multi_aff *isl_multi_aff_floor(
7177 __isl_take isl_multi_aff *ma);
7178 __isl_give isl_pw_aff *isl_pw_aff_floor(
7179 __isl_take isl_pw_aff *pwaff);
7180 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
7181 __isl_take isl_union_pw_aff *upa);
7182 __isl_give isl_multi_union_pw_aff *
7183 isl_multi_union_pw_aff_floor(
7184 __isl_take isl_multi_union_pw_aff *mupa);
7186 #include <isl/aff.h>
7187 __isl_give isl_pw_aff *isl_pw_aff_list_min(
7188 __isl_take isl_pw_aff_list *list);
7189 __isl_give isl_pw_aff *isl_pw_aff_list_max(
7190 __isl_take isl_pw_aff_list *list);
7192 #include <isl/polynomial.h>
7193 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
7194 __isl_take isl_qpolynomial *qp);
7195 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
7196 __isl_take isl_pw_qpolynomial *pwqp);
7197 __isl_give isl_union_pw_qpolynomial *
7198 isl_union_pw_qpolynomial_neg(
7199 __isl_take isl_union_pw_qpolynomial *upwqp);
7200 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
7201 __isl_take isl_qpolynomial *qp,
7203 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
7204 __isl_take isl_pw_qpolynomial *pwqp,
7209 The following functions evaluate a function in a point.
7211 #include <isl/aff.h>
7212 __isl_give isl_val *isl_aff_eval(
7213 __isl_take isl_aff *aff,
7214 __isl_take isl_point *pnt);
7215 __isl_give isl_val *isl_pw_aff_eval(
7216 __isl_take isl_pw_aff *pa,
7217 __isl_take isl_point *pnt);
7219 #include <isl/polynomial.h>
7220 __isl_give isl_val *isl_pw_qpolynomial_eval(
7221 __isl_take isl_pw_qpolynomial *pwqp,
7222 __isl_take isl_point *pnt);
7223 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
7224 __isl_take isl_pw_qpolynomial_fold *pwf,
7225 __isl_take isl_point *pnt);
7226 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
7227 __isl_take isl_union_pw_qpolynomial *upwqp,
7228 __isl_take isl_point *pnt);
7229 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
7230 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7231 __isl_take isl_point *pnt);
7233 These functions return NaN when evaluated at a void point.
7234 Note that C<isl_pw_aff_eval> returns NaN when the function is evaluated outside
7235 its definition domain, while C<isl_pw_qpolynomial_eval> returns zero
7236 when the function is evaluated outside its explicit domain.
7238 =item * Dimension manipulation
7240 It is usually not advisable to directly change the (input or output)
7241 space of a set or a relation as this removes the name and the internal
7242 structure of the space. However, the functions below can be useful
7243 to add new parameters, assuming
7244 C<isl_set_align_params> and C<isl_map_align_params>
7247 #include <isl/space.h>
7248 __isl_give isl_space *isl_space_add_dims(
7249 __isl_take isl_space *space,
7250 enum isl_dim_type type, unsigned n);
7251 __isl_give isl_space *isl_space_insert_dims(
7252 __isl_take isl_space *space,
7253 enum isl_dim_type type, unsigned pos, unsigned n);
7254 __isl_give isl_space *isl_space_drop_dims(
7255 __isl_take isl_space *space,
7256 enum isl_dim_type type, unsigned first, unsigned n);
7257 __isl_give isl_space *isl_space_move_dims(
7258 __isl_take isl_space *space,
7259 enum isl_dim_type dst_type, unsigned dst_pos,
7260 enum isl_dim_type src_type, unsigned src_pos,
7263 #include <isl/local_space.h>
7264 __isl_give isl_local_space *isl_local_space_add_dims(
7265 __isl_take isl_local_space *ls,
7266 enum isl_dim_type type, unsigned n);
7267 __isl_give isl_local_space *isl_local_space_insert_dims(
7268 __isl_take isl_local_space *ls,
7269 enum isl_dim_type type, unsigned first, unsigned n);
7270 __isl_give isl_local_space *isl_local_space_drop_dims(
7271 __isl_take isl_local_space *ls,
7272 enum isl_dim_type type, unsigned first, unsigned n);
7274 #include <isl/set.h>
7275 __isl_give isl_basic_set *isl_basic_set_add_dims(
7276 __isl_take isl_basic_set *bset,
7277 enum isl_dim_type type, unsigned n);
7278 __isl_give isl_set *isl_set_add_dims(
7279 __isl_take isl_set *set,
7280 enum isl_dim_type type, unsigned n);
7281 __isl_give isl_basic_set *isl_basic_set_insert_dims(
7282 __isl_take isl_basic_set *bset,
7283 enum isl_dim_type type, unsigned pos,
7285 __isl_give isl_set *isl_set_insert_dims(
7286 __isl_take isl_set *set,
7287 enum isl_dim_type type, unsigned pos, unsigned n);
7288 __isl_give isl_basic_set *isl_basic_set_move_dims(
7289 __isl_take isl_basic_set *bset,
7290 enum isl_dim_type dst_type, unsigned dst_pos,
7291 enum isl_dim_type src_type, unsigned src_pos,
7293 __isl_give isl_set *isl_set_move_dims(
7294 __isl_take isl_set *set,
7295 enum isl_dim_type dst_type, unsigned dst_pos,
7296 enum isl_dim_type src_type, unsigned src_pos,
7299 #include <isl/map.h>
7300 __isl_give isl_basic_map *isl_basic_map_add_dims(
7301 __isl_take isl_basic_map *bmap,
7302 enum isl_dim_type type, unsigned n);
7303 __isl_give isl_map *isl_map_add_dims(
7304 __isl_take isl_map *map,
7305 enum isl_dim_type type, unsigned n);
7306 __isl_give isl_basic_map *isl_basic_map_insert_dims(
7307 __isl_take isl_basic_map *bmap,
7308 enum isl_dim_type type, unsigned pos,
7310 __isl_give isl_map *isl_map_insert_dims(
7311 __isl_take isl_map *map,
7312 enum isl_dim_type type, unsigned pos, unsigned n);
7313 __isl_give isl_basic_map *isl_basic_map_move_dims(
7314 __isl_take isl_basic_map *bmap,
7315 enum isl_dim_type dst_type, unsigned dst_pos,
7316 enum isl_dim_type src_type, unsigned src_pos,
7318 __isl_give isl_map *isl_map_move_dims(
7319 __isl_take isl_map *map,
7320 enum isl_dim_type dst_type, unsigned dst_pos,
7321 enum isl_dim_type src_type, unsigned src_pos,
7324 #include <isl/val.h>
7325 __isl_give isl_multi_val *isl_multi_val_insert_dims(
7326 __isl_take isl_multi_val *mv,
7327 enum isl_dim_type type, unsigned first, unsigned n);
7328 __isl_give isl_multi_val *isl_multi_val_add_dims(
7329 __isl_take isl_multi_val *mv,
7330 enum isl_dim_type type, unsigned n);
7331 __isl_give isl_multi_val *isl_multi_val_drop_dims(
7332 __isl_take isl_multi_val *mv,
7333 enum isl_dim_type type, unsigned first, unsigned n);
7335 #include <isl/aff.h>
7336 __isl_give isl_aff *isl_aff_insert_dims(
7337 __isl_take isl_aff *aff,
7338 enum isl_dim_type type, unsigned first, unsigned n);
7339 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
7340 __isl_take isl_multi_aff *ma,
7341 enum isl_dim_type type, unsigned first, unsigned n);
7342 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
7343 __isl_take isl_pw_aff *pwaff,
7344 enum isl_dim_type type, unsigned first, unsigned n);
7345 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
7346 __isl_take isl_multi_pw_aff *mpa,
7347 enum isl_dim_type type, unsigned first, unsigned n);
7348 __isl_give isl_aff *isl_aff_add_dims(
7349 __isl_take isl_aff *aff,
7350 enum isl_dim_type type, unsigned n);
7351 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
7352 __isl_take isl_multi_aff *ma,
7353 enum isl_dim_type type, unsigned n);
7354 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
7355 __isl_take isl_pw_aff *pwaff,
7356 enum isl_dim_type type, unsigned n);
7357 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
7358 __isl_take isl_multi_pw_aff *mpa,
7359 enum isl_dim_type type, unsigned n);
7360 __isl_give isl_aff *isl_aff_drop_dims(
7361 __isl_take isl_aff *aff,
7362 enum isl_dim_type type, unsigned first, unsigned n);
7363 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
7364 __isl_take isl_multi_aff *maff,
7365 enum isl_dim_type type, unsigned first, unsigned n);
7366 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
7367 __isl_take isl_pw_aff *pwaff,
7368 enum isl_dim_type type, unsigned first, unsigned n);
7369 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
7370 __isl_take isl_pw_multi_aff *pma,
7371 enum isl_dim_type type, unsigned first, unsigned n);
7372 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
7373 __isl_take isl_union_pw_aff *upa,
7374 enum isl_dim_type type, unsigned first, unsigned n);
7375 __isl_give isl_union_pw_multi_aff *
7376 isl_union_pw_multi_aff_drop_dims(
7377 __isl_take isl_union_pw_multi_aff *upma,
7378 enum isl_dim_type type,
7379 unsigned first, unsigned n);
7380 __isl_give isl_multi_union_pw_aff *
7381 isl_multi_union_pw_aff_drop_dims(
7382 __isl_take isl_multi_union_pw_aff *mupa,
7383 enum isl_dim_type type, unsigned first,
7385 __isl_give isl_aff *isl_aff_move_dims(
7386 __isl_take isl_aff *aff,
7387 enum isl_dim_type dst_type, unsigned dst_pos,
7388 enum isl_dim_type src_type, unsigned src_pos,
7390 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
7391 __isl_take isl_multi_aff *ma,
7392 enum isl_dim_type dst_type, unsigned dst_pos,
7393 enum isl_dim_type src_type, unsigned src_pos,
7395 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
7396 __isl_take isl_pw_aff *pa,
7397 enum isl_dim_type dst_type, unsigned dst_pos,
7398 enum isl_dim_type src_type, unsigned src_pos,
7400 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
7401 __isl_take isl_multi_pw_aff *pma,
7402 enum isl_dim_type dst_type, unsigned dst_pos,
7403 enum isl_dim_type src_type, unsigned src_pos,
7406 #include <isl/polynomial.h>
7407 __isl_give isl_union_pw_qpolynomial *
7408 isl_union_pw_qpolynomial_drop_dims(
7409 __isl_take isl_union_pw_qpolynomial *upwqp,
7410 enum isl_dim_type type,
7411 unsigned first, unsigned n);
7412 __isl_give isl_union_pw_qpolynomial_fold *
7413 isl_union_pw_qpolynomial_fold_drop_dims(
7414 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7415 enum isl_dim_type type,
7416 unsigned first, unsigned n);
7418 The operations on union expressions can only manipulate parameters.
7422 =head2 Binary Operations
7424 The two arguments of a binary operation not only need to live
7425 in the same C<isl_ctx>, they currently also need to have
7426 the same (number of) parameters.
7428 =head3 Basic Operations
7432 =item * Intersection
7434 #include <isl/local_space.h>
7435 __isl_give isl_local_space *isl_local_space_intersect(
7436 __isl_take isl_local_space *ls1,
7437 __isl_take isl_local_space *ls2);
7439 #include <isl/set.h>
7440 __isl_give isl_basic_set *isl_basic_set_intersect_params(
7441 __isl_take isl_basic_set *bset1,
7442 __isl_take isl_basic_set *bset2);
7443 __isl_give isl_basic_set *isl_basic_set_intersect(
7444 __isl_take isl_basic_set *bset1,
7445 __isl_take isl_basic_set *bset2);
7446 __isl_give isl_basic_set *isl_basic_set_list_intersect(
7447 __isl_take struct isl_basic_set_list *list);
7448 __isl_give isl_set *isl_set_intersect_params(
7449 __isl_take isl_set *set,
7450 __isl_take isl_set *params);
7451 __isl_give isl_set *isl_set_intersect(
7452 __isl_take isl_set *set1,
7453 __isl_take isl_set *set2);
7454 __isl_give isl_set *isl_set_intersect_factor_domain(
7455 __isl_take isl_set *set,
7456 __isl_take isl_set *domain);
7457 __isl_give isl_set *isl_set_intersect_factor_range(
7458 __isl_take isl_set *set,
7459 __isl_take isl_set *range);
7461 #include <isl/map.h>
7462 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
7463 __isl_take isl_basic_map *bmap,
7464 __isl_take isl_basic_set *bset);
7465 __isl_give isl_basic_map *isl_basic_map_intersect_range(
7466 __isl_take isl_basic_map *bmap,
7467 __isl_take isl_basic_set *bset);
7468 __isl_give isl_basic_map *isl_basic_map_intersect(
7469 __isl_take isl_basic_map *bmap1,
7470 __isl_take isl_basic_map *bmap2);
7471 __isl_give isl_basic_map *isl_basic_map_list_intersect(
7472 __isl_take isl_basic_map_list *list);
7473 __isl_give isl_map *isl_map_intersect_params(
7474 __isl_take isl_map *map,
7475 __isl_take isl_set *params);
7476 __isl_give isl_map *isl_map_intersect_domain(
7477 __isl_take isl_map *map,
7478 __isl_take isl_set *set);
7479 __isl_give isl_map *isl_map_intersect_range(
7480 __isl_take isl_map *map,
7481 __isl_take isl_set *set);
7482 __isl_give isl_map *isl_map_intersect(
7483 __isl_take isl_map *map1,
7484 __isl_take isl_map *map2);
7485 __isl_give isl_map *
7486 isl_map_intersect_domain_factor_domain(
7487 __isl_take isl_map *map,
7488 __isl_take isl_map *factor);
7489 __isl_give isl_map *
7490 isl_map_intersect_domain_factor_range(
7491 __isl_take isl_map *map,
7492 __isl_take isl_map *factor);
7493 __isl_give isl_map *
7494 isl_map_intersect_range_factor_domain(
7495 __isl_take isl_map *map,
7496 __isl_take isl_map *factor);
7497 __isl_give isl_map *
7498 isl_map_intersect_range_factor_range(
7499 __isl_take isl_map *map,
7500 __isl_take isl_map *factor);
7501 __isl_give isl_map *
7502 isl_map_intersect_domain_wrapped_domain(
7503 __isl_take isl_map *map,
7504 __isl_take isl_set *domain);
7505 __isl_give isl_map *
7506 isl_map_intersect_range_wrapped_domain(
7507 __isl_take isl_map *map,
7508 __isl_take isl_set *domain);
7510 #include <isl/union_set.h>
7511 __isl_give isl_union_set *isl_union_set_intersect_params(
7512 __isl_take isl_union_set *uset,
7513 __isl_take isl_set *set);
7514 __isl_give isl_union_set *isl_union_set_intersect(
7515 __isl_take isl_union_set *uset1,
7516 __isl_take isl_union_set *uset2);
7518 #include <isl/union_map.h>
7519 __isl_give isl_union_map *isl_union_map_intersect_params(
7520 __isl_take isl_union_map *umap,
7521 __isl_take isl_set *set);
7522 __isl_give isl_union_map *
7523 isl_union_map_intersect_domain_union_set(
7524 __isl_take isl_union_map *umap,
7525 __isl_take isl_union_set *uset);
7526 __isl_give isl_union_map *
7527 isl_union_map_intersect_domain_space(
7528 __isl_take isl_union_map *umap,
7529 __isl_take isl_space *space);
7530 __isl_give isl_union_map *isl_union_map_intersect_domain(
7531 __isl_take isl_union_map *umap,
7532 __isl_take isl_union_set *uset);
7533 __isl_give isl_union_map *
7534 isl_union_map_intersect_range_union_set(
7535 __isl_take isl_union_map *umap,
7536 __isl_take isl_union_set *uset);
7537 __isl_give isl_union_map *
7538 isl_union_map_intersect_range_space(
7539 __isl_take isl_union_map *umap,
7540 __isl_take isl_space *space);
7541 __isl_give isl_union_map *isl_union_map_intersect_range(
7542 __isl_take isl_union_map *umap,
7543 __isl_take isl_union_set *uset);
7544 __isl_give isl_union_map *isl_union_map_intersect(
7545 __isl_take isl_union_map *umap1,
7546 __isl_take isl_union_map *umap2);
7547 __isl_give isl_union_map *
7548 isl_union_map_intersect_domain_factor_domain(
7549 __isl_take isl_union_map *umap,
7550 __isl_take isl_union_map *factor);
7551 __isl_give isl_union_map *
7552 isl_union_map_intersect_domain_factor_range(
7553 __isl_take isl_union_map *umap,
7554 __isl_take isl_union_map *factor);
7555 __isl_give isl_union_map *
7556 isl_union_map_intersect_range_factor_domain(
7557 __isl_take isl_union_map *umap,
7558 __isl_take isl_union_map *factor);
7559 __isl_give isl_union_map *
7560 isl_union_map_intersect_range_factor_range(
7561 __isl_take isl_union_map *umap,
7562 __isl_take isl_union_map *factor);
7563 __isl_give isl_union_map *
7564 isl_union_map_intersect_domain_wrapped_domain_union_set(
7565 __isl_take isl_union_map *umap,
7566 __isl_take isl_union_set *domain);
7567 __isl_give isl_union_map *
7568 isl_union_map_intersect_range_wrapped_domain_union_set(
7569 __isl_take isl_union_map *umap,
7570 __isl_take isl_union_set *domain);
7572 #include <isl/aff.h>
7573 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
7574 __isl_take isl_pw_aff *pa,
7575 __isl_take isl_set *set);
7576 __isl_give isl_multi_pw_aff *
7577 isl_multi_pw_aff_intersect_domain(
7578 __isl_take isl_multi_pw_aff *mpa,
7579 __isl_take isl_set *domain);
7580 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
7581 __isl_take isl_pw_multi_aff *pma,
7582 __isl_take isl_set *set);
7583 __isl_give isl_union_pw_aff *
7584 isl_union_pw_aff_intersect_domain_space(
7585 __isl_take isl_union_pw_aff *upa,
7586 __isl_take isl_space *space);
7587 __isl_give isl_union_pw_aff *
7588 isl_union_pw_aff_intersect_domain_union_set(
7589 __isl_take isl_union_pw_aff *upa,
7590 __isl_take isl_union_set *uset);
7591 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
7592 __isl_take isl_union_pw_aff *upa,
7593 __isl_take isl_union_set *uset);
7594 __isl_give isl_union_pw_multi_aff *
7595 isl_union_pw_multi_aff_intersect_domain_space(
7596 __isl_take isl_union_pw_multi_aff *upma,
7597 __isl_take isl_space *space);
7598 __isl_give isl_union_pw_multi_aff *
7599 isl_union_pw_multi_aff_intersect_domain_union_set(
7600 __isl_take isl_union_pw_multi_aff *upma,
7601 __isl_take isl_union_set *uset);
7602 __isl_give isl_union_pw_multi_aff *
7603 isl_union_pw_multi_aff_intersect_domain(
7604 __isl_take isl_union_pw_multi_aff *upma,
7605 __isl_take isl_union_set *uset);
7606 __isl_give isl_multi_union_pw_aff *
7607 isl_multi_union_pw_aff_intersect_domain(
7608 __isl_take isl_multi_union_pw_aff *mupa,
7609 __isl_take isl_union_set *uset);
7610 __isl_give isl_pw_aff *
7611 isl_pw_aff_intersect_domain_wrapped_domain(
7612 __isl_take isl_pw_aff *pa,
7613 __isl_take isl_set *set);
7614 __isl_give isl_pw_multi_aff *
7615 isl_pw_multi_aff_intersect_domain_wrapped_domain(
7616 __isl_take isl_pw_multi_aff *pma,
7617 __isl_take isl_set *set);
7618 __isl_give isl_union_pw_aff *
7619 isl_union_pw_aff_intersect_domain_wrapped_domain(
7620 __isl_take isl_union_pw_aff *upa,
7621 __isl_take isl_union_set *uset);
7622 __isl_give isl_union_pw_multi_aff *
7623 isl_union_pw_multi_aff_intersect_domain_wrapped_domain(
7624 __isl_take isl_union_pw_multi_aff *upma,
7625 __isl_take isl_union_set *uset);
7626 __isl_give isl_pw_aff *
7627 isl_pw_aff_intersect_domain_wrapped_range(
7628 __isl_take isl_pw_aff *pa,
7629 __isl_take isl_set *set);
7630 __isl_give isl_pw_multi_aff *
7631 isl_pw_multi_aff_intersect_domain_wrapped_range(
7632 __isl_take isl_pw_multi_aff *pma,
7633 __isl_take isl_set *set);
7634 __isl_give isl_union_pw_multi_aff *
7635 isl_union_pw_multi_aff_intersect_domain_wrapped_range(
7636 __isl_take isl_union_pw_multi_aff *upma,
7637 __isl_take isl_union_set *uset);
7638 __isl_give isl_union_pw_aff *
7639 isl_union_pw_aff_intersect_domain_wrapped_range(
7640 __isl_take isl_union_pw_aff *upa,
7641 __isl_take isl_union_set *uset);
7642 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
7643 __isl_take isl_pw_aff *pa,
7644 __isl_take isl_set *set);
7645 __isl_give isl_multi_pw_aff *
7646 isl_multi_pw_aff_intersect_params(
7647 __isl_take isl_multi_pw_aff *mpa,
7648 __isl_take isl_set *set);
7649 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
7650 __isl_take isl_pw_multi_aff *pma,
7651 __isl_take isl_set *set);
7652 __isl_give isl_union_pw_aff *
7653 isl_union_pw_aff_intersect_params(
7654 __isl_take isl_union_pw_aff *upa,
7655 __isl_take isl_set *set);
7656 __isl_give isl_union_pw_multi_aff *
7657 isl_union_pw_multi_aff_intersect_params(
7658 __isl_take isl_union_pw_multi_aff *upma,
7659 __isl_take isl_set *set);
7660 __isl_give isl_multi_union_pw_aff *
7661 isl_multi_union_pw_aff_intersect_params(
7662 __isl_take isl_multi_union_pw_aff *mupa,
7663 __isl_take isl_set *params);
7664 __isl_give isl_multi_union_pw_aff *
7665 isl_multi_union_pw_aff_intersect_range(
7666 __isl_take isl_multi_union_pw_aff *mupa,
7667 __isl_take isl_set *set);
7669 #include <isl/polynomial.h>
7670 __isl_give isl_pw_qpolynomial *
7671 isl_pw_qpolynomial_intersect_domain(
7672 __isl_take isl_pw_qpolynomial *pwpq,
7673 __isl_take isl_set *set);
7674 __isl_give isl_union_pw_qpolynomial *
7675 isl_union_pw_qpolynomial_intersect_domain_space(
7676 __isl_take isl_union_pw_qpolynomial *upwpq,
7677 __isl_take isl_space *space);
7678 __isl_give isl_union_pw_qpolynomial *
7679 isl_union_pw_qpolynomial_intersect_domain_union_set(
7680 __isl_take isl_union_pw_qpolynomial *upwpq,
7681 __isl_take isl_union_set *uset);
7682 __isl_give isl_union_pw_qpolynomial *
7683 isl_union_pw_qpolynomial_intersect_domain(
7684 __isl_take isl_union_pw_qpolynomial *upwpq,
7685 __isl_take isl_union_set *uset);
7686 __isl_give isl_union_pw_qpolynomial_fold *
7687 isl_union_pw_qpolynomial_fold_intersect_domain_space(
7688 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7689 __isl_take isl_space *space);
7690 __isl_give isl_union_pw_qpolynomial_fold *
7691 isl_union_pw_qpolynomial_fold_intersect_domain_union_set(
7692 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7693 __isl_take isl_union_set *uset);
7694 __isl_give isl_union_pw_qpolynomial_fold *
7695 isl_union_pw_qpolynomial_fold_intersect_domain(
7696 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7697 __isl_take isl_union_set *uset);
7698 __isl_give isl_pw_qpolynomial *
7699 isl_pw_qpolynomial_intersect_domain_wrapped_domain(
7700 __isl_take isl_pw_qpolynomial *pwpq,
7701 __isl_take isl_set *set);
7702 __isl_give isl_pw_qpolynomial_fold *
7703 isl_pw_qpolynomial_fold_intersect_domain_wrapped_domain(
7704 __isl_take isl_pw_qpolynomial_fold *pwf,
7705 __isl_take isl_set *set);
7706 __isl_give isl_union_pw_qpolynomial *
7707 isl_union_pw_qpolynomial_intersect_domain_wrapped_domain(
7708 __isl_take isl_union_pw_qpolynomial *upwpq,
7709 __isl_take isl_union_set *uset);
7710 __isl_give isl_union_pw_qpolynomial_fold *
7711 isl_union_pw_qpolynomial_fold_intersect_domain_wrapped_domain(
7712 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7713 __isl_take isl_union_set *uset);
7714 __isl_give isl_pw_qpolynomial *
7715 isl_pw_qpolynomial_intersect_domain_wrapped_range(
7716 __isl_take isl_pw_qpolynomial *pwpq,
7717 __isl_take isl_set *set);
7718 __isl_give isl_pw_qpolynomial_fold *
7719 isl_pw_qpolynomial_fold_intersect_domain_wrapped_range(
7720 __isl_take isl_pw_qpolynomial_fold *pwf,
7721 __isl_take isl_set *set);
7722 __isl_give isl_union_pw_qpolynomial *
7723 isl_union_pw_qpolynomial_intersect_domain_wrapped_range(
7724 __isl_take isl_union_pw_qpolynomial *upwpq,
7725 __isl_take isl_union_set *uset);
7726 __isl_give isl_union_pw_qpolynomial_fold *
7727 isl_union_pw_qpolynomial_fold_intersect_domain_wrapped_range(
7728 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7729 __isl_take isl_union_set *uset);
7730 __isl_give isl_pw_qpolynomial *
7731 isl_pw_qpolynomial_intersect_params(
7732 __isl_take isl_pw_qpolynomial *pwpq,
7733 __isl_take isl_set *set);
7734 __isl_give isl_pw_qpolynomial_fold *
7735 isl_pw_qpolynomial_fold_intersect_params(
7736 __isl_take isl_pw_qpolynomial_fold *pwf,
7737 __isl_take isl_set *set);
7738 __isl_give isl_union_pw_qpolynomial *
7739 isl_union_pw_qpolynomial_intersect_params(
7740 __isl_take isl_union_pw_qpolynomial *upwpq,
7741 __isl_take isl_set *set);
7742 __isl_give isl_union_pw_qpolynomial_fold *
7743 isl_union_pw_qpolynomial_fold_intersect_params(
7744 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7745 __isl_take isl_set *set);
7747 The second argument to the C<_params> functions needs to be
7748 a parametric (basic) set. For the other functions, a parametric set
7749 for either argument is only allowed if the other argument is
7750 a parametric set as well.
7751 The list passed to C<isl_basic_set_list_intersect> needs to have
7752 at least one element and all elements need to live in the same space.
7753 The function C<isl_multi_union_pw_aff_intersect_range>
7754 restricts the input function to those shared domain elements
7755 that map to the specified range.
7756 C<isl_union_map_intersect_domain> is an alternative name for
7757 C<isl_union_map_intersect_domain_union_set>.
7758 Similarly for the other pairs of functions.
7762 #include <isl/set.h>
7763 __isl_give isl_set *isl_basic_set_union(
7764 __isl_take isl_basic_set *bset1,
7765 __isl_take isl_basic_set *bset2);
7766 __isl_give isl_set *isl_set_union(
7767 __isl_take isl_set *set1,
7768 __isl_take isl_set *set2);
7769 __isl_give isl_set *isl_set_list_union(
7770 __isl_take isl_set_list *list);
7772 #include <isl/map.h>
7773 __isl_give isl_map *isl_basic_map_union(
7774 __isl_take isl_basic_map *bmap1,
7775 __isl_take isl_basic_map *bmap2);
7776 __isl_give isl_map *isl_map_union(
7777 __isl_take isl_map *map1,
7778 __isl_take isl_map *map2);
7780 #include <isl/union_set.h>
7781 __isl_give isl_union_set *isl_union_set_union(
7782 __isl_take isl_union_set *uset1,
7783 __isl_take isl_union_set *uset2);
7784 __isl_give isl_union_set *isl_union_set_list_union(
7785 __isl_take isl_union_set_list *list);
7787 #include <isl/union_map.h>
7788 __isl_give isl_union_map *isl_union_map_union(
7789 __isl_take isl_union_map *umap1,
7790 __isl_take isl_union_map *umap2);
7792 The list passed to C<isl_set_list_union> needs to have
7793 at least one element and all elements need to live in the same space.
7795 =item * Set difference
7797 #include <isl/set.h>
7798 __isl_give isl_set *isl_set_subtract(
7799 __isl_take isl_set *set1,
7800 __isl_take isl_set *set2);
7802 #include <isl/map.h>
7803 __isl_give isl_map *isl_map_subtract(
7804 __isl_take isl_map *map1,
7805 __isl_take isl_map *map2);
7806 __isl_give isl_map *isl_map_subtract_domain(
7807 __isl_take isl_map *map,
7808 __isl_take isl_set *dom);
7809 __isl_give isl_map *isl_map_subtract_range(
7810 __isl_take isl_map *map,
7811 __isl_take isl_set *dom);
7813 #include <isl/union_set.h>
7814 __isl_give isl_union_set *isl_union_set_subtract(
7815 __isl_take isl_union_set *uset1,
7816 __isl_take isl_union_set *uset2);
7818 #include <isl/union_map.h>
7819 __isl_give isl_union_map *isl_union_map_subtract(
7820 __isl_take isl_union_map *umap1,
7821 __isl_take isl_union_map *umap2);
7822 __isl_give isl_union_map *isl_union_map_subtract_domain(
7823 __isl_take isl_union_map *umap,
7824 __isl_take isl_union_set *dom);
7825 __isl_give isl_union_map *isl_union_map_subtract_range(
7826 __isl_take isl_union_map *umap,
7827 __isl_take isl_union_set *dom);
7829 #include <isl/aff.h>
7830 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
7831 __isl_take isl_pw_aff *pa,
7832 __isl_take isl_set *set);
7833 __isl_give isl_pw_multi_aff *
7834 isl_pw_multi_aff_subtract_domain(
7835 __isl_take isl_pw_multi_aff *pma,
7836 __isl_take isl_set *set);
7837 __isl_give isl_union_pw_aff *
7838 isl_union_pw_aff_subtract_domain_union_set(
7839 __isl_take isl_union_pw_aff *upa,
7840 __isl_take isl_union_set *uset);
7841 __isl_give isl_union_pw_aff *
7842 isl_union_pw_aff_subtract_domain_space(
7843 __isl_take isl_union_pw_aff *upa,
7844 __isl_take isl_space *space);
7845 __isl_give isl_union_pw_aff *
7846 isl_union_pw_aff_subtract_domain(
7847 __isl_take isl_union_pw_aff *upa,
7848 __isl_take isl_union_set *uset);
7849 __isl_give isl_union_pw_multi_aff *
7850 isl_union_pw_multi_aff_subtract_domain_union_set(
7851 __isl_take isl_union_pw_multi_aff *upma,
7852 __isl_take isl_set *set);
7853 __isl_give isl_union_pw_multi_aff *
7854 isl_union_pw_multi_aff_subtract_domain_space(
7855 __isl_take isl_union_pw_multi_aff *upma,
7856 __isl_take isl_space *space);
7857 __isl_give isl_union_pw_multi_aff *
7858 isl_union_pw_multi_aff_subtract_domain(
7859 __isl_take isl_union_pw_multi_aff *upma,
7860 __isl_take isl_union_set *uset);
7862 #include <isl/polynomial.h>
7863 __isl_give isl_pw_qpolynomial *
7864 isl_pw_qpolynomial_subtract_domain(
7865 __isl_take isl_pw_qpolynomial *pwpq,
7866 __isl_take isl_set *set);
7867 __isl_give isl_pw_qpolynomial_fold *
7868 isl_pw_qpolynomial_fold_subtract_domain(
7869 __isl_take isl_pw_qpolynomial_fold *pwf,
7870 __isl_take isl_set *set);
7871 __isl_give isl_union_pw_qpolynomial *
7872 isl_union_pw_qpolynomial_subtract_domain_union_set(
7873 __isl_take isl_union_pw_qpolynomial *upwpq,
7874 __isl_take isl_union_set *uset);
7875 __isl_give isl_union_pw_qpolynomial *
7876 isl_union_pw_qpolynomial_subtract_domain_space(
7877 __isl_take isl_union_pw_qpolynomial *upwpq,
7878 __isl_take isl_space *space);
7879 __isl_give isl_union_pw_qpolynomial *
7880 isl_union_pw_qpolynomial_subtract_domain(
7881 __isl_take isl_union_pw_qpolynomial *upwpq,
7882 __isl_take isl_union_set *uset);
7883 __isl_give isl_union_pw_qpolynomial_fold *
7884 isl_union_pw_qpolynomial_fold_subtract_domain_union_set(
7885 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7886 __isl_take isl_union_set *uset);
7887 __isl_give isl_union_pw_qpolynomial_fold *
7888 isl_union_pw_qpolynomial_fold_subtract_domain_space(
7889 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7890 __isl_take isl_space *space);
7891 __isl_give isl_union_pw_qpolynomial_fold *
7892 isl_union_pw_qpolynomial_fold_subtract_domain(
7893 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7894 __isl_take isl_union_set *uset);
7896 C<isl_union_pw_aff_subtract_domain> is an alternative name for
7897 C<isl_union_pw_aff_subtract_domain_union_set>.
7898 Similarly for the other pairs of functions.
7902 #include <isl/space.h>
7903 __isl_give isl_space *isl_space_join(
7904 __isl_take isl_space *left,
7905 __isl_take isl_space *right);
7907 #include <isl/set.h>
7908 __isl_give isl_basic_set *isl_basic_set_apply(
7909 __isl_take isl_basic_set *bset,
7910 __isl_take isl_basic_map *bmap);
7911 __isl_give isl_set *isl_set_apply(
7912 __isl_take isl_set *set,
7913 __isl_take isl_map *map);
7915 #include <isl/union_set.h>
7916 __isl_give isl_union_set *isl_union_set_apply(
7917 __isl_take isl_union_set *uset,
7918 __isl_take isl_union_map *umap);
7920 #include <isl/map.h>
7921 __isl_give isl_basic_map *isl_basic_map_apply_domain(
7922 __isl_take isl_basic_map *bmap1,
7923 __isl_take isl_basic_map *bmap2);
7924 __isl_give isl_basic_map *isl_basic_map_apply_range(
7925 __isl_take isl_basic_map *bmap1,
7926 __isl_take isl_basic_map *bmap2);
7927 __isl_give isl_map *isl_map_apply_domain(
7928 __isl_take isl_map *map1,
7929 __isl_take isl_map *map2);
7930 __isl_give isl_map *isl_map_apply_range(
7931 __isl_take isl_map *map1,
7932 __isl_take isl_map *map2);
7934 #include <isl/union_map.h>
7935 __isl_give isl_union_map *isl_union_map_apply_domain(
7936 __isl_take isl_union_map *umap1,
7937 __isl_take isl_union_map *umap2);
7938 __isl_give isl_union_map *isl_union_map_apply_range(
7939 __isl_take isl_union_map *umap1,
7940 __isl_take isl_union_map *umap2);
7942 #include <isl/aff.h>
7943 __isl_give isl_union_pw_multi_aff *
7944 isl_union_pw_multi_aff_apply_union_pw_multi_aff(
7945 __isl_take isl_union_pw_multi_aff *upma1,
7946 __isl_take isl_union_pw_multi_aff *upma2);
7947 __isl_give isl_union_pw_aff *
7948 isl_multi_union_pw_aff_apply_aff(
7949 __isl_take isl_multi_union_pw_aff *mupa,
7950 __isl_take isl_aff *aff);
7951 __isl_give isl_union_pw_aff *
7952 isl_multi_union_pw_aff_apply_pw_aff(
7953 __isl_take isl_multi_union_pw_aff *mupa,
7954 __isl_take isl_pw_aff *pa);
7955 __isl_give isl_multi_union_pw_aff *
7956 isl_multi_union_pw_aff_apply_multi_aff(
7957 __isl_take isl_multi_union_pw_aff *mupa,
7958 __isl_take isl_multi_aff *ma);
7959 __isl_give isl_multi_union_pw_aff *
7960 isl_multi_union_pw_aff_apply_pw_multi_aff(
7961 __isl_take isl_multi_union_pw_aff *mupa,
7962 __isl_take isl_pw_multi_aff *pma);
7964 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
7965 over the shared domain of the elements of the input. The dimension is
7966 required to be greater than zero.
7967 The C<isl_multi_union_pw_aff> argument of
7968 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
7969 but only if the range of the C<isl_multi_aff> argument
7970 is also zero-dimensional.
7971 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
7973 #include <isl/polynomial.h>
7974 __isl_give isl_pw_qpolynomial_fold *
7975 isl_set_apply_pw_qpolynomial_fold(
7976 __isl_take isl_set *set,
7977 __isl_take isl_pw_qpolynomial_fold *pwf,
7979 __isl_give isl_pw_qpolynomial_fold *
7980 isl_map_apply_pw_qpolynomial_fold(
7981 __isl_take isl_map *map,
7982 __isl_take isl_pw_qpolynomial_fold *pwf,
7984 __isl_give isl_union_pw_qpolynomial_fold *
7985 isl_union_set_apply_union_pw_qpolynomial_fold(
7986 __isl_take isl_union_set *uset,
7987 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7989 __isl_give isl_union_pw_qpolynomial_fold *
7990 isl_union_map_apply_union_pw_qpolynomial_fold(
7991 __isl_take isl_union_map *umap,
7992 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7995 The functions taking a map
7996 compose the given map with the given piecewise quasipolynomial reduction.
7997 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
7998 over all elements in the intersection of the range of the map
7999 and the domain of the piecewise quasipolynomial reduction
8000 as a function of an element in the domain of the map.
8001 The functions taking a set compute a bound over all elements in the
8002 intersection of the set and the domain of the
8003 piecewise quasipolynomial reduction.
8007 #include <isl/set.h>
8008 __isl_give isl_basic_set *
8009 isl_basic_set_preimage_multi_aff(
8010 __isl_take isl_basic_set *bset,
8011 __isl_take isl_multi_aff *ma);
8012 __isl_give isl_set *isl_set_preimage_multi_aff(
8013 __isl_take isl_set *set,
8014 __isl_take isl_multi_aff *ma);
8015 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
8016 __isl_take isl_set *set,
8017 __isl_take isl_pw_multi_aff *pma);
8018 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
8019 __isl_take isl_set *set,
8020 __isl_take isl_multi_pw_aff *mpa);
8022 #include <isl/union_set.h>
8023 __isl_give isl_union_set *
8024 isl_union_set_preimage_multi_aff(
8025 __isl_take isl_union_set *uset,
8026 __isl_take isl_multi_aff *ma);
8027 __isl_give isl_union_set *
8028 isl_union_set_preimage_pw_multi_aff(
8029 __isl_take isl_union_set *uset,
8030 __isl_take isl_pw_multi_aff *pma);
8031 __isl_give isl_union_set *
8032 isl_union_set_preimage_union_pw_multi_aff(
8033 __isl_take isl_union_set *uset,
8034 __isl_take isl_union_pw_multi_aff *upma);
8036 #include <isl/map.h>
8037 __isl_give isl_basic_map *
8038 isl_basic_map_preimage_domain_multi_aff(
8039 __isl_take isl_basic_map *bmap,
8040 __isl_take isl_multi_aff *ma);
8041 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
8042 __isl_take isl_map *map,
8043 __isl_take isl_multi_aff *ma);
8044 __isl_give isl_map *isl_map_preimage_range_multi_aff(
8045 __isl_take isl_map *map,
8046 __isl_take isl_multi_aff *ma);
8047 __isl_give isl_map *
8048 isl_map_preimage_domain_pw_multi_aff(
8049 __isl_take isl_map *map,
8050 __isl_take isl_pw_multi_aff *pma);
8051 __isl_give isl_map *
8052 isl_map_preimage_range_pw_multi_aff(
8053 __isl_take isl_map *map,
8054 __isl_take isl_pw_multi_aff *pma);
8055 __isl_give isl_map *
8056 isl_map_preimage_domain_multi_pw_aff(
8057 __isl_take isl_map *map,
8058 __isl_take isl_multi_pw_aff *mpa);
8059 __isl_give isl_basic_map *
8060 isl_basic_map_preimage_range_multi_aff(
8061 __isl_take isl_basic_map *bmap,
8062 __isl_take isl_multi_aff *ma);
8064 #include <isl/union_map.h>
8065 __isl_give isl_union_map *
8066 isl_union_map_preimage_domain_multi_aff(
8067 __isl_take isl_union_map *umap,
8068 __isl_take isl_multi_aff *ma);
8069 __isl_give isl_union_map *
8070 isl_union_map_preimage_range_multi_aff(
8071 __isl_take isl_union_map *umap,
8072 __isl_take isl_multi_aff *ma);
8073 __isl_give isl_union_map *
8074 isl_union_map_preimage_domain_pw_multi_aff(
8075 __isl_take isl_union_map *umap,
8076 __isl_take isl_pw_multi_aff *pma);
8077 __isl_give isl_union_map *
8078 isl_union_map_preimage_range_pw_multi_aff(
8079 __isl_take isl_union_map *umap,
8080 __isl_take isl_pw_multi_aff *pma);
8081 __isl_give isl_union_map *
8082 isl_union_map_preimage_domain_union_pw_multi_aff(
8083 __isl_take isl_union_map *umap,
8084 __isl_take isl_union_pw_multi_aff *upma);
8085 __isl_give isl_union_map *
8086 isl_union_map_preimage_range_union_pw_multi_aff(
8087 __isl_take isl_union_map *umap,
8088 __isl_take isl_union_pw_multi_aff *upma);
8090 #include <isl/aff.h>
8091 __isl_give isl_pw_multi_aff *
8092 isl_pw_multi_aff_preimage_domain_wrapped_domain_pw_multi_aff(
8093 __isl_take isl_pw_multi_aff *pma1,
8094 __isl_take isl_pw_multi_aff *pma2);
8095 __isl_give isl_union_pw_multi_aff *
8096 isl_union_pw_multi_aff_preimage_domain_wrapped_domain_union_pw_multi_aff(
8097 __isl_take isl_union_pw_multi_aff *upma1,
8098 __isl_take isl_union_pw_multi_aff *upma2);
8100 These functions compute the preimage of the given set or map domain/range under
8101 the given function. In other words, the expression is plugged
8102 into the set description or into the domain/range of the map or function.
8106 #include <isl/aff.h>
8107 __isl_give isl_aff *isl_aff_pullback_aff(
8108 __isl_take isl_aff *aff1,
8109 __isl_take isl_aff *aff2);
8110 __isl_give isl_aff *isl_aff_pullback_multi_aff(
8111 __isl_take isl_aff *aff,
8112 __isl_take isl_multi_aff *ma);
8113 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
8114 __isl_take isl_pw_aff *pa,
8115 __isl_take isl_multi_aff *ma);
8116 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
8117 __isl_take isl_pw_aff *pa,
8118 __isl_take isl_pw_multi_aff *pma);
8119 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
8120 __isl_take isl_pw_aff *pa,
8121 __isl_take isl_multi_pw_aff *mpa);
8122 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
8123 __isl_take isl_multi_aff *ma1,
8124 __isl_take isl_multi_aff *ma2);
8125 __isl_give isl_pw_multi_aff *
8126 isl_pw_multi_aff_pullback_multi_aff(
8127 __isl_take isl_pw_multi_aff *pma,
8128 __isl_take isl_multi_aff *ma);
8129 __isl_give isl_multi_pw_aff *
8130 isl_multi_pw_aff_pullback_multi_aff(
8131 __isl_take isl_multi_pw_aff *mpa,
8132 __isl_take isl_multi_aff *ma);
8133 __isl_give isl_pw_multi_aff *
8134 isl_pw_multi_aff_pullback_pw_multi_aff(
8135 __isl_take isl_pw_multi_aff *pma1,
8136 __isl_take isl_pw_multi_aff *pma2);
8137 __isl_give isl_multi_pw_aff *
8138 isl_multi_pw_aff_pullback_pw_multi_aff(
8139 __isl_take isl_multi_pw_aff *mpa,
8140 __isl_take isl_pw_multi_aff *pma);
8141 __isl_give isl_multi_pw_aff *
8142 isl_multi_pw_aff_pullback_multi_pw_aff(
8143 __isl_take isl_multi_pw_aff *mpa1,
8144 __isl_take isl_multi_pw_aff *mpa2);
8145 __isl_give isl_union_pw_aff *
8146 isl_union_pw_aff_pullback_union_pw_multi_aff(
8147 __isl_take isl_union_pw_aff *upa,
8148 __isl_take isl_union_pw_multi_aff *upma);
8149 __isl_give isl_union_pw_multi_aff *
8150 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
8151 __isl_take isl_union_pw_multi_aff *upma1,
8152 __isl_take isl_union_pw_multi_aff *upma2);
8153 __isl_give isl_multi_union_pw_aff *
8154 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
8155 __isl_take isl_multi_union_pw_aff *mupa,
8156 __isl_take isl_union_pw_multi_aff *upma);
8158 These functions precompose the first expression by the second function.
8159 In other words, the second function is plugged
8160 into the first expression.
8164 #include <isl/aff.h>
8165 __isl_give isl_basic_set *isl_aff_eq_basic_set(
8166 __isl_take isl_aff *aff1,
8167 __isl_take isl_aff *aff2);
8168 __isl_give isl_set *isl_aff_eq_set(
8169 __isl_take isl_aff *aff1,
8170 __isl_take isl_aff *aff2);
8171 __isl_give isl_set *isl_aff_ne_set(
8172 __isl_take isl_aff *aff1,
8173 __isl_take isl_aff *aff2);
8174 __isl_give isl_basic_set *isl_aff_le_basic_set(
8175 __isl_take isl_aff *aff1,
8176 __isl_take isl_aff *aff2);
8177 __isl_give isl_set *isl_aff_le_set(
8178 __isl_take isl_aff *aff1,
8179 __isl_take isl_aff *aff2);
8180 __isl_give isl_basic_set *isl_aff_lt_basic_set(
8181 __isl_take isl_aff *aff1,
8182 __isl_take isl_aff *aff2);
8183 __isl_give isl_set *isl_aff_lt_set(
8184 __isl_take isl_aff *aff1,
8185 __isl_take isl_aff *aff2);
8186 __isl_give isl_basic_set *isl_aff_ge_basic_set(
8187 __isl_take isl_aff *aff1,
8188 __isl_take isl_aff *aff2);
8189 __isl_give isl_set *isl_aff_ge_set(
8190 __isl_take isl_aff *aff1,
8191 __isl_take isl_aff *aff2);
8192 __isl_give isl_basic_set *isl_aff_gt_basic_set(
8193 __isl_take isl_aff *aff1,
8194 __isl_take isl_aff *aff2);
8195 __isl_give isl_set *isl_aff_gt_set(
8196 __isl_take isl_aff *aff1,
8197 __isl_take isl_aff *aff2);
8198 __isl_give isl_set *isl_pw_aff_eq_set(
8199 __isl_take isl_pw_aff *pwaff1,
8200 __isl_take isl_pw_aff *pwaff2);
8201 __isl_give isl_set *isl_pw_aff_ne_set(
8202 __isl_take isl_pw_aff *pwaff1,
8203 __isl_take isl_pw_aff *pwaff2);
8204 __isl_give isl_set *isl_pw_aff_le_set(
8205 __isl_take isl_pw_aff *pwaff1,
8206 __isl_take isl_pw_aff *pwaff2);
8207 __isl_give isl_set *isl_pw_aff_lt_set(
8208 __isl_take isl_pw_aff *pwaff1,
8209 __isl_take isl_pw_aff *pwaff2);
8210 __isl_give isl_set *isl_pw_aff_ge_set(
8211 __isl_take isl_pw_aff *pwaff1,
8212 __isl_take isl_pw_aff *pwaff2);
8213 __isl_give isl_set *isl_pw_aff_gt_set(
8214 __isl_take isl_pw_aff *pwaff1,
8215 __isl_take isl_pw_aff *pwaff2);
8217 __isl_give isl_set *isl_multi_aff_lex_le_set(
8218 __isl_take isl_multi_aff *ma1,
8219 __isl_take isl_multi_aff *ma2);
8220 __isl_give isl_set *isl_multi_aff_lex_lt_set(
8221 __isl_take isl_multi_aff *ma1,
8222 __isl_take isl_multi_aff *ma2);
8223 __isl_give isl_set *isl_multi_aff_lex_ge_set(
8224 __isl_take isl_multi_aff *ma1,
8225 __isl_take isl_multi_aff *ma2);
8226 __isl_give isl_set *isl_multi_aff_lex_gt_set(
8227 __isl_take isl_multi_aff *ma1,
8228 __isl_take isl_multi_aff *ma2);
8230 __isl_give isl_set *isl_pw_aff_list_eq_set(
8231 __isl_take isl_pw_aff_list *list1,
8232 __isl_take isl_pw_aff_list *list2);
8233 __isl_give isl_set *isl_pw_aff_list_ne_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_le_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_lt_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_ge_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_gt_set(
8246 __isl_take isl_pw_aff_list *list1,
8247 __isl_take isl_pw_aff_list *list2);
8249 The function C<isl_aff_ge_basic_set> returns a basic set
8250 containing those elements in the shared space
8251 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
8252 The function C<isl_pw_aff_ge_set> returns a set
8253 containing those elements in the shared domain
8254 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
8255 greater than or equal to C<pwaff2>.
8256 The function C<isl_multi_aff_lex_le_set> returns a set
8257 containing those elements in the shared domain space
8258 where C<ma1> is lexicographically smaller than or
8260 The functions operating on C<isl_pw_aff_list> apply the corresponding
8261 C<isl_pw_aff> function to each pair of elements in the two lists.
8263 #include <isl/aff.h>
8264 __isl_give isl_map *isl_pw_aff_eq_map(
8265 __isl_take isl_pw_aff *pa1,
8266 __isl_take isl_pw_aff *pa2);
8267 __isl_give isl_map *isl_pw_aff_le_map(
8268 __isl_take isl_pw_aff *pa1,
8269 __isl_take isl_pw_aff *pa2);
8270 __isl_give isl_map *isl_pw_aff_lt_map(
8271 __isl_take isl_pw_aff *pa1,
8272 __isl_take isl_pw_aff *pa2);
8273 __isl_give isl_map *isl_pw_aff_ge_map(
8274 __isl_take isl_pw_aff *pa1,
8275 __isl_take isl_pw_aff *pa2);
8276 __isl_give isl_map *isl_pw_aff_gt_map(
8277 __isl_take isl_pw_aff *pa1,
8278 __isl_take isl_pw_aff *pa2);
8280 __isl_give isl_map *isl_multi_pw_aff_eq_map(
8281 __isl_take isl_multi_pw_aff *mpa1,
8282 __isl_take isl_multi_pw_aff *mpa2);
8283 __isl_give isl_map *isl_multi_pw_aff_lex_le_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_lt_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_ge_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_gt_map(
8293 __isl_take isl_multi_pw_aff *mpa1,
8294 __isl_take isl_multi_pw_aff *mpa2);
8296 These functions return a map between domain elements of the arguments
8297 where the function values satisfy the given relation.
8299 #include <isl/map.h>
8300 __isl_give isl_map *isl_map_eq_at_multi_pw_aff(
8301 __isl_take isl_map *map,
8302 __isl_take isl_multi_pw_aff *mpa);
8303 __isl_give isl_map *isl_map_lex_lt_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_le_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_gt_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_ge_at_multi_pw_aff(
8313 __isl_take isl_map *map,
8314 __isl_take isl_multi_pw_aff *mpa);
8316 #include <isl/union_map.h>
8317 __isl_give isl_union_map *
8318 isl_union_map_eq_at_multi_union_pw_aff(
8319 __isl_take isl_union_map *umap,
8320 __isl_take isl_multi_union_pw_aff *mupa);
8321 __isl_give isl_union_map *
8322 isl_union_map_lex_lt_at_multi_union_pw_aff(
8323 __isl_take isl_union_map *umap,
8324 __isl_take isl_multi_union_pw_aff *mupa);
8325 __isl_give isl_union_map *
8326 isl_union_map_lex_le_at_multi_union_pw_aff(
8327 __isl_take isl_union_map *umap,
8328 __isl_take isl_multi_union_pw_aff *mupa);
8329 __isl_give isl_union_map *
8330 isl_union_map_lex_gt_at_multi_union_pw_aff(
8331 __isl_take isl_union_map *umap,
8332 __isl_take isl_multi_union_pw_aff *mupa);
8333 __isl_give isl_union_map *
8334 isl_union_map_lex_ge_at_multi_union_pw_aff(
8335 __isl_take isl_union_map *umap,
8336 __isl_take isl_multi_union_pw_aff *mupa);
8338 These functions select the subset of elements in the union map
8339 that have an equal or lexicographically smaller or greater function value.
8341 =item * Cartesian Product
8343 #include <isl/space.h>
8344 __isl_give isl_space *isl_space_product(
8345 __isl_take isl_space *space1,
8346 __isl_take isl_space *space2);
8347 __isl_give isl_space *isl_space_domain_product(
8348 __isl_take isl_space *space1,
8349 __isl_take isl_space *space2);
8350 __isl_give isl_space *isl_space_range_product(
8351 __isl_take isl_space *space1,
8352 __isl_take isl_space *space2);
8355 C<isl_space_product>, C<isl_space_domain_product>
8356 and C<isl_space_range_product> take pairs or relation spaces and
8357 produce a single relations space, where either the domain, the range
8358 or both domain and range are wrapped spaces of relations between
8359 the domains and/or ranges of the input spaces.
8360 If the product is only constructed over the domain or the range
8361 then the ranges or the domains of the inputs should be the same.
8362 The function C<isl_space_product> also accepts a pair of set spaces,
8363 in which case it returns a wrapped space of a relation between the
8366 #include <isl/set.h>
8367 __isl_give isl_set *isl_set_product(
8368 __isl_take isl_set *set1,
8369 __isl_take isl_set *set2);
8371 #include <isl/map.h>
8372 __isl_give isl_basic_map *isl_basic_map_domain_product(
8373 __isl_take isl_basic_map *bmap1,
8374 __isl_take isl_basic_map *bmap2);
8375 __isl_give isl_basic_map *isl_basic_map_range_product(
8376 __isl_take isl_basic_map *bmap1,
8377 __isl_take isl_basic_map *bmap2);
8378 __isl_give isl_basic_map *isl_basic_map_product(
8379 __isl_take isl_basic_map *bmap1,
8380 __isl_take isl_basic_map *bmap2);
8381 __isl_give isl_map *isl_map_domain_product(
8382 __isl_take isl_map *map1,
8383 __isl_take isl_map *map2);
8384 __isl_give isl_map *isl_map_range_product(
8385 __isl_take isl_map *map1,
8386 __isl_take isl_map *map2);
8387 __isl_give isl_map *isl_map_product(
8388 __isl_take isl_map *map1,
8389 __isl_take isl_map *map2);
8391 #include <isl/union_set.h>
8392 __isl_give isl_union_set *isl_union_set_product(
8393 __isl_take isl_union_set *uset1,
8394 __isl_take isl_union_set *uset2);
8396 #include <isl/union_map.h>
8397 __isl_give isl_union_map *isl_union_map_domain_product(
8398 __isl_take isl_union_map *umap1,
8399 __isl_take isl_union_map *umap2);
8400 __isl_give isl_union_map *isl_union_map_range_product(
8401 __isl_take isl_union_map *umap1,
8402 __isl_take isl_union_map *umap2);
8403 __isl_give isl_union_map *isl_union_map_product(
8404 __isl_take isl_union_map *umap1,
8405 __isl_take isl_union_map *umap2);
8408 __isl_give isl_multi_id *isl_multi_id_range_product(
8409 __isl_take isl_multi_id *mi1,
8410 __isl_take isl_multi_id *mi2);
8412 #include <isl/val.h>
8413 __isl_give isl_multi_val *isl_multi_val_range_product(
8414 __isl_take isl_multi_val *mv1,
8415 __isl_take isl_multi_val *mv2);
8416 __isl_give isl_multi_val *isl_multi_val_product(
8417 __isl_take isl_multi_val *mv1,
8418 __isl_take isl_multi_val *mv2);
8420 #include <isl/aff.h>
8421 __isl_give isl_multi_aff *isl_multi_aff_range_product(
8422 __isl_take isl_multi_aff *ma1,
8423 __isl_take isl_multi_aff *ma2);
8424 __isl_give isl_multi_aff *isl_multi_aff_product(
8425 __isl_take isl_multi_aff *ma1,
8426 __isl_take isl_multi_aff *ma2);
8427 __isl_give isl_multi_pw_aff *
8428 isl_multi_pw_aff_range_product(
8429 __isl_take isl_multi_pw_aff *mpa1,
8430 __isl_take isl_multi_pw_aff *mpa2);
8431 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
8432 __isl_take isl_multi_pw_aff *mpa1,
8433 __isl_take isl_multi_pw_aff *mpa2);
8434 __isl_give isl_pw_multi_aff *
8435 isl_pw_multi_aff_range_product(
8436 __isl_take isl_pw_multi_aff *pma1,
8437 __isl_take isl_pw_multi_aff *pma2);
8438 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
8439 __isl_take isl_pw_multi_aff *pma1,
8440 __isl_take isl_pw_multi_aff *pma2);
8441 __isl_give isl_union_pw_multi_aff *
8442 isl_union_pw_multi_aff_range_product(
8443 __isl_take isl_union_pw_multi_aff *upma1,
8444 __isl_take isl_union_pw_multi_aff *upma2);
8445 __isl_give isl_multi_union_pw_aff *
8446 isl_multi_union_pw_aff_range_product(
8447 __isl_take isl_multi_union_pw_aff *mupa1,
8448 __isl_take isl_multi_union_pw_aff *mupa2);
8450 The above functions compute the cross product of the given
8451 sets, relations or functions. The domains and ranges of the results
8452 are wrapped maps between domains and ranges of the inputs.
8453 To obtain a ``flat'' product, use the following functions
8456 #include <isl/set.h>
8457 __isl_give isl_basic_set *isl_basic_set_flat_product(
8458 __isl_take isl_basic_set *bset1,
8459 __isl_take isl_basic_set *bset2);
8460 __isl_give isl_set *isl_set_flat_product(
8461 __isl_take isl_set *set1,
8462 __isl_take isl_set *set2);
8464 #include <isl/map.h>
8465 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
8466 __isl_take isl_basic_map *bmap1,
8467 __isl_take isl_basic_map *bmap2);
8468 __isl_give isl_map *isl_map_flat_domain_product(
8469 __isl_take isl_map *map1,
8470 __isl_take isl_map *map2);
8471 __isl_give isl_map *isl_map_flat_range_product(
8472 __isl_take isl_map *map1,
8473 __isl_take isl_map *map2);
8474 __isl_give isl_basic_map *isl_basic_map_flat_product(
8475 __isl_take isl_basic_map *bmap1,
8476 __isl_take isl_basic_map *bmap2);
8477 __isl_give isl_map *isl_map_flat_product(
8478 __isl_take isl_map *map1,
8479 __isl_take isl_map *map2);
8481 #include <isl/union_map.h>
8482 __isl_give isl_union_map *
8483 isl_union_map_flat_domain_product(
8484 __isl_take isl_union_map *umap1,
8485 __isl_take isl_union_map *umap2);
8486 __isl_give isl_union_map *
8487 isl_union_map_flat_range_product(
8488 __isl_take isl_union_map *umap1,
8489 __isl_take isl_union_map *umap2);
8492 __isl_give isl_multi_id *
8493 isl_multi_id_flat_range_product(
8494 __isl_take isl_multi_id *mi1,
8495 __isl_take isl_multi_id *mi2);
8497 #include <isl/val.h>
8498 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
8499 __isl_take isl_multi_val *mv1,
8500 __isl_take isl_multi_val *mv2);
8502 #include <isl/aff.h>
8503 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
8504 __isl_take isl_multi_aff *ma1,
8505 __isl_take isl_multi_aff *ma2);
8506 __isl_give isl_pw_multi_aff *
8507 isl_pw_multi_aff_flat_range_product(
8508 __isl_take isl_pw_multi_aff *pma1,
8509 __isl_take isl_pw_multi_aff *pma2);
8510 __isl_give isl_multi_pw_aff *
8511 isl_multi_pw_aff_flat_range_product(
8512 __isl_take isl_multi_pw_aff *mpa1,
8513 __isl_take isl_multi_pw_aff *mpa2);
8514 __isl_give isl_union_pw_multi_aff *
8515 isl_union_pw_multi_aff_flat_range_product(
8516 __isl_take isl_union_pw_multi_aff *upma1,
8517 __isl_take isl_union_pw_multi_aff *upma2);
8518 __isl_give isl_multi_union_pw_aff *
8519 isl_multi_union_pw_aff_flat_range_product(
8520 __isl_take isl_multi_union_pw_aff *mupa1,
8521 __isl_take isl_multi_union_pw_aff *mupa2);
8523 #include <isl/space.h>
8524 __isl_give isl_space *isl_space_factor_domain(
8525 __isl_take isl_space *space);
8526 __isl_give isl_space *isl_space_factor_range(
8527 __isl_take isl_space *space);
8528 __isl_give isl_space *isl_space_domain_factor_domain(
8529 __isl_take isl_space *space);
8530 __isl_give isl_space *isl_space_domain_factor_range(
8531 __isl_take isl_space *space);
8532 __isl_give isl_space *isl_space_range_factor_domain(
8533 __isl_take isl_space *space);
8534 __isl_give isl_space *isl_space_range_factor_range(
8535 __isl_take isl_space *space);
8537 The functions C<isl_space_range_factor_domain> and
8538 C<isl_space_range_factor_range> extract the two arguments from
8539 the result of a call to C<isl_space_range_product>.
8541 The arguments of a call to a product can be extracted
8542 from the result using the following functions.
8544 #include <isl/map.h>
8545 __isl_give isl_map *isl_map_factor_domain(
8546 __isl_take isl_map *map);
8547 __isl_give isl_map *isl_map_factor_range(
8548 __isl_take isl_map *map);
8549 __isl_give isl_map *isl_map_domain_factor_domain(
8550 __isl_take isl_map *map);
8551 __isl_give isl_map *isl_map_domain_factor_range(
8552 __isl_take isl_map *map);
8553 __isl_give isl_map *isl_map_range_factor_domain(
8554 __isl_take isl_map *map);
8555 __isl_give isl_map *isl_map_range_factor_range(
8556 __isl_take isl_map *map);
8558 #include <isl/union_map.h>
8559 __isl_give isl_union_map *isl_union_map_factor_domain(
8560 __isl_take isl_union_map *umap);
8561 __isl_give isl_union_map *isl_union_map_factor_range(
8562 __isl_take isl_union_map *umap);
8563 __isl_give isl_union_map *
8564 isl_union_map_domain_factor_domain(
8565 __isl_take isl_union_map *umap);
8566 __isl_give isl_union_map *
8567 isl_union_map_domain_factor_range(
8568 __isl_take isl_union_map *umap);
8569 __isl_give isl_union_map *
8570 isl_union_map_range_factor_domain(
8571 __isl_take isl_union_map *umap);
8572 __isl_give isl_union_map *
8573 isl_union_map_range_factor_range(
8574 __isl_take isl_union_map *umap);
8577 __isl_give isl_multi_id *isl_multi_id_factor_range(
8578 __isl_take isl_multi_id *mi);
8579 __isl_give isl_multi_id *
8580 isl_multi_id_range_factor_domain(
8581 __isl_take isl_multi_id *mi);
8582 __isl_give isl_multi_id *
8583 isl_multi_id_range_factor_range(
8584 __isl_take isl_multi_id *mi);
8586 #include <isl/val.h>
8587 __isl_give isl_multi_val *isl_multi_val_factor_range(
8588 __isl_take isl_multi_val *mv);
8589 __isl_give isl_multi_val *
8590 isl_multi_val_range_factor_domain(
8591 __isl_take isl_multi_val *mv);
8592 __isl_give isl_multi_val *
8593 isl_multi_val_range_factor_range(
8594 __isl_take isl_multi_val *mv);
8596 #include <isl/aff.h>
8597 __isl_give isl_multi_aff *isl_multi_aff_factor_range(
8598 __isl_take isl_multi_aff *ma);
8599 __isl_give isl_multi_aff *
8600 isl_multi_aff_range_factor_domain(
8601 __isl_take isl_multi_aff *ma);
8602 __isl_give isl_multi_aff *
8603 isl_multi_aff_range_factor_range(
8604 __isl_take isl_multi_aff *ma);
8605 __isl_give isl_multi_pw_aff *
8606 isl_multi_pw_aff_factor_range(
8607 __isl_take isl_multi_pw_aff *mpa);
8608 __isl_give isl_multi_pw_aff *
8609 isl_multi_pw_aff_range_factor_domain(
8610 __isl_take isl_multi_pw_aff *mpa);
8611 __isl_give isl_multi_pw_aff *
8612 isl_multi_pw_aff_range_factor_range(
8613 __isl_take isl_multi_pw_aff *mpa);
8614 __isl_give isl_pw_multi_aff *
8615 isl_pw_multi_aff_range_factor_domain(
8616 __isl_take isl_pw_multi_aff *pma);
8617 __isl_give isl_pw_multi_aff *
8618 isl_pw_multi_aff_range_factor_range(
8619 __isl_take isl_pw_multi_aff *pma);
8620 __isl_give isl_union_pw_multi_aff *
8621 isl_union_pw_multi_aff_range_factor_domain(
8622 __isl_take isl_union_pw_multi_aff *upma);
8623 __isl_give isl_union_pw_multi_aff *
8624 isl_union_pw_multi_aff_range_factor_range(
8625 __isl_take isl_union_pw_multi_aff *upma);
8626 __isl_give isl_multi_union_pw_aff *
8627 isl_multi_union_pw_aff_factor_range(
8628 __isl_take isl_multi_union_pw_aff *mupa);
8629 __isl_give isl_multi_union_pw_aff *
8630 isl_multi_union_pw_aff_range_factor_domain(
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_range(
8634 __isl_take isl_multi_union_pw_aff *mupa);
8636 The splice functions are a generalization of the flat product functions,
8637 where the second argument may be inserted at any position inside
8638 the first argument rather than being placed at the end.
8639 The functions C<isl_multi_val_factor_range>,
8640 C<isl_multi_aff_factor_range>,
8641 C<isl_multi_pw_aff_factor_range> and
8642 C<isl_multi_union_pw_aff_factor_range>
8643 take functions that live in a set space.
8646 __isl_give isl_multi_id *isl_multi_id_range_splice(
8647 __isl_take isl_multi_id *mi1, unsigned pos,
8648 __isl_take isl_multi_id *mi2);
8650 #include <isl/val.h>
8651 __isl_give isl_multi_val *isl_multi_val_range_splice(
8652 __isl_take isl_multi_val *mv1, unsigned pos,
8653 __isl_take isl_multi_val *mv2);
8655 #include <isl/aff.h>
8656 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
8657 __isl_take isl_multi_aff *ma1, unsigned pos,
8658 __isl_take isl_multi_aff *ma2);
8659 __isl_give isl_multi_aff *isl_multi_aff_splice(
8660 __isl_take isl_multi_aff *ma1,
8661 unsigned in_pos, unsigned out_pos,
8662 __isl_take isl_multi_aff *ma2);
8663 __isl_give isl_multi_pw_aff *
8664 isl_multi_pw_aff_range_splice(
8665 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
8666 __isl_take isl_multi_pw_aff *mpa2);
8667 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
8668 __isl_take isl_multi_pw_aff *mpa1,
8669 unsigned in_pos, unsigned out_pos,
8670 __isl_take isl_multi_pw_aff *mpa2);
8671 __isl_give isl_multi_union_pw_aff *
8672 isl_multi_union_pw_aff_range_splice(
8673 __isl_take isl_multi_union_pw_aff *mupa1,
8675 __isl_take isl_multi_union_pw_aff *mupa2);
8677 =item * Simplification
8679 When applied to a set or relation,
8680 the gist operation returns a set or relation that has the
8681 same intersection with the context as the input set or relation.
8682 Any implicit equality in the intersection is made explicit in the result,
8683 while all inequalities that are redundant with respect to the intersection
8685 In case of union sets and relations, the gist operation is performed
8688 When applied to a function,
8689 the gist operation applies the set gist operation to each of
8690 the cells in the domain of the input piecewise expression.
8691 The context is also exploited
8692 to simplify the expression associated to each cell.
8694 #include <isl/set.h>
8695 __isl_give isl_basic_set *isl_basic_set_gist(
8696 __isl_take isl_basic_set *bset,
8697 __isl_take isl_basic_set *context);
8698 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
8699 __isl_take isl_set *context);
8700 __isl_give isl_set *isl_set_gist_params(
8701 __isl_take isl_set *set,
8702 __isl_take isl_set *context);
8704 #include <isl/map.h>
8705 __isl_give isl_basic_map *isl_basic_map_gist(
8706 __isl_take isl_basic_map *bmap,
8707 __isl_take isl_basic_map *context);
8708 __isl_give isl_basic_map *isl_basic_map_gist_domain(
8709 __isl_take isl_basic_map *bmap,
8710 __isl_take isl_basic_set *context);
8711 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
8712 __isl_take isl_map *context);
8713 __isl_give isl_map *isl_map_gist_params(
8714 __isl_take isl_map *map,
8715 __isl_take isl_set *context);
8716 __isl_give isl_map *isl_map_gist_domain(
8717 __isl_take isl_map *map,
8718 __isl_take isl_set *context);
8719 __isl_give isl_map *isl_map_gist_range(
8720 __isl_take isl_map *map,
8721 __isl_take isl_set *context);
8723 #include <isl/union_set.h>
8724 __isl_give isl_union_set *isl_union_set_gist(
8725 __isl_take isl_union_set *uset,
8726 __isl_take isl_union_set *context);
8727 __isl_give isl_union_set *isl_union_set_gist_params(
8728 __isl_take isl_union_set *uset,
8729 __isl_take isl_set *set);
8731 #include <isl/union_map.h>
8732 __isl_give isl_union_map *isl_union_map_gist(
8733 __isl_take isl_union_map *umap,
8734 __isl_take isl_union_map *context);
8735 __isl_give isl_union_map *isl_union_map_gist_params(
8736 __isl_take isl_union_map *umap,
8737 __isl_take isl_set *set);
8738 __isl_give isl_union_map *isl_union_map_gist_domain(
8739 __isl_take isl_union_map *umap,
8740 __isl_take isl_union_set *uset);
8741 __isl_give isl_union_map *isl_union_map_gist_range(
8742 __isl_take isl_union_map *umap,
8743 __isl_take isl_union_set *uset);
8745 #include <isl/aff.h>
8746 __isl_give isl_aff *isl_aff_gist_params(
8747 __isl_take isl_aff *aff,
8748 __isl_take isl_set *context);
8749 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
8750 __isl_take isl_set *context);
8751 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
8752 __isl_take isl_multi_aff *maff,
8753 __isl_take isl_set *context);
8754 __isl_give isl_multi_aff *isl_multi_aff_gist(
8755 __isl_take isl_multi_aff *maff,
8756 __isl_take isl_set *context);
8757 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
8758 __isl_take isl_pw_aff *pwaff,
8759 __isl_take isl_set *context);
8760 __isl_give isl_pw_aff *isl_pw_aff_gist(
8761 __isl_take isl_pw_aff *pwaff,
8762 __isl_take isl_set *context);
8763 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
8764 __isl_take isl_pw_multi_aff *pma,
8765 __isl_take isl_set *set);
8766 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
8767 __isl_take isl_pw_multi_aff *pma,
8768 __isl_take isl_set *set);
8769 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
8770 __isl_take isl_multi_pw_aff *mpa,
8771 __isl_take isl_set *set);
8772 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
8773 __isl_take isl_multi_pw_aff *mpa,
8774 __isl_take isl_set *set);
8775 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
8776 __isl_take isl_union_pw_aff *upa,
8777 __isl_take isl_union_set *context);
8778 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
8779 __isl_take isl_union_pw_aff *upa,
8780 __isl_take isl_set *context);
8781 __isl_give isl_union_pw_multi_aff *
8782 isl_union_pw_multi_aff_gist_params(
8783 __isl_take isl_union_pw_multi_aff *upma,
8784 __isl_take isl_set *context);
8785 __isl_give isl_union_pw_multi_aff *
8786 isl_union_pw_multi_aff_gist(
8787 __isl_take isl_union_pw_multi_aff *upma,
8788 __isl_take isl_union_set *context);
8789 __isl_give isl_multi_union_pw_aff *
8790 isl_multi_union_pw_aff_gist_params(
8791 __isl_take isl_multi_union_pw_aff *mupa,
8792 __isl_take isl_set *context);
8793 __isl_give isl_multi_union_pw_aff *
8794 isl_multi_union_pw_aff_gist(
8795 __isl_take isl_multi_union_pw_aff *mupa,
8796 __isl_take isl_union_set *context);
8798 #include <isl/polynomial.h>
8799 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
8800 __isl_take isl_qpolynomial *qp,
8801 __isl_take isl_set *context);
8802 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
8803 __isl_take isl_qpolynomial *qp,
8804 __isl_take isl_set *context);
8805 __isl_give isl_qpolynomial_fold *
8806 isl_qpolynomial_fold_gist_params(
8807 __isl_take isl_qpolynomial_fold *fold,
8808 __isl_take isl_set *context);
8809 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
8810 __isl_take isl_qpolynomial_fold *fold,
8811 __isl_take isl_set *context);
8812 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
8813 __isl_take isl_pw_qpolynomial *pwqp,
8814 __isl_take isl_set *context);
8815 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
8816 __isl_take isl_pw_qpolynomial *pwqp,
8817 __isl_take isl_set *context);
8818 __isl_give isl_pw_qpolynomial_fold *
8819 isl_pw_qpolynomial_fold_gist(
8820 __isl_take isl_pw_qpolynomial_fold *pwf,
8821 __isl_take isl_set *context);
8822 __isl_give isl_pw_qpolynomial_fold *
8823 isl_pw_qpolynomial_fold_gist_params(
8824 __isl_take isl_pw_qpolynomial_fold *pwf,
8825 __isl_take isl_set *context);
8826 __isl_give isl_union_pw_qpolynomial *
8827 isl_union_pw_qpolynomial_gist_params(
8828 __isl_take isl_union_pw_qpolynomial *upwqp,
8829 __isl_take isl_set *context);
8830 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
8831 __isl_take isl_union_pw_qpolynomial *upwqp,
8832 __isl_take isl_union_set *context);
8833 __isl_give isl_union_pw_qpolynomial_fold *
8834 isl_union_pw_qpolynomial_fold_gist(
8835 __isl_take isl_union_pw_qpolynomial_fold *upwf,
8836 __isl_take isl_union_set *context);
8837 __isl_give isl_union_pw_qpolynomial_fold *
8838 isl_union_pw_qpolynomial_fold_gist_params(
8839 __isl_take isl_union_pw_qpolynomial_fold *upwf,
8840 __isl_take isl_set *context);
8842 =item * Binary Arithmetic Operations
8844 #include <isl/set.h>
8845 __isl_give isl_set *isl_set_sum(
8846 __isl_take isl_set *set1,
8847 __isl_take isl_set *set2);
8848 #include <isl/map.h>
8849 __isl_give isl_map *isl_map_sum(
8850 __isl_take isl_map *map1,
8851 __isl_take isl_map *map2);
8853 C<isl_set_sum> computes the Minkowski sum of its two arguments,
8854 i.e., the set containing the sums of pairs of elements from
8855 C<set1> and C<set2>.
8856 The domain of the result of C<isl_map_sum> is the intersection
8857 of the domains of its two arguments. The corresponding range
8858 elements are the sums of the corresponding range elements
8859 in the two arguments.
8861 #include <isl/val.h>
8862 __isl_give isl_multi_val *isl_multi_val_add(
8863 __isl_take isl_multi_val *mv1,
8864 __isl_take isl_multi_val *mv2);
8865 __isl_give isl_multi_val *isl_multi_val_sub(
8866 __isl_take isl_multi_val *mv1,
8867 __isl_take isl_multi_val *mv2);
8868 __isl_give isl_multi_val *isl_multi_val_min(
8869 __isl_take isl_multi_val *mv1,
8870 __isl_take isl_multi_val *mv2);
8871 __isl_give isl_multi_val *isl_multi_val_max(
8872 __isl_take isl_multi_val *mv1,
8873 __isl_take isl_multi_val *mv2);
8875 #include <isl/aff.h>
8876 __isl_give isl_aff *isl_aff_add(
8877 __isl_take isl_aff *aff1,
8878 __isl_take isl_aff *aff2);
8879 __isl_give isl_multi_aff *isl_multi_aff_add(
8880 __isl_take isl_multi_aff *maff1,
8881 __isl_take isl_multi_aff *maff2);
8882 __isl_give isl_pw_aff *isl_pw_aff_add(
8883 __isl_take isl_pw_aff *pwaff1,
8884 __isl_take isl_pw_aff *pwaff2);
8885 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add(
8886 __isl_take isl_multi_pw_aff *mpa1,
8887 __isl_take isl_multi_pw_aff *mpa2);
8888 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
8889 __isl_take isl_pw_multi_aff *pma1,
8890 __isl_take isl_pw_multi_aff *pma2);
8891 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
8892 __isl_take isl_union_pw_aff *upa1,
8893 __isl_take isl_union_pw_aff *upa2);
8894 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
8895 __isl_take isl_union_pw_multi_aff *upma1,
8896 __isl_take isl_union_pw_multi_aff *upma2);
8897 __isl_give isl_multi_union_pw_aff *
8898 isl_multi_union_pw_aff_add(
8899 __isl_take isl_multi_union_pw_aff *mupa1,
8900 __isl_take isl_multi_union_pw_aff *mupa2);
8901 __isl_give isl_pw_aff *isl_pw_aff_add_constant_val(
8902 __isl_take isl_pw_aff *pa,
8903 __isl_take isl_val *v);
8904 __isl_give isl_multi_aff *
8905 isl_multi_aff_add_constant_val(
8906 __isl_take isl_multi_aff *pa,
8907 __isl_take isl_val *v);
8908 __isl_give isl_pw_multi_aff *
8909 isl_pw_multi_aff_add_constant_val(
8910 __isl_take isl_pw_multi_aff *pma,
8911 __isl_take isl_val *v);
8912 __isl_give isl_pw_multi_aff *
8913 isl_pw_multi_aff_add_constant_multi_val(
8914 __isl_take isl_pw_multi_aff *pma,
8915 __isl_take isl_multi_val *mv);
8916 __isl_give isl_multi_pw_aff *
8917 isl_multi_pw_aff_add_constant_val(
8918 __isl_take isl_multi_pw_aff *mpa,
8919 __isl_take isl_val *v);
8920 __isl_give isl_multi_aff *
8921 isl_multi_aff_add_constant_multi_val(
8922 __isl_take isl_multi_aff *pa,
8923 __isl_take isl_multi_val *mv);
8924 __isl_give isl_multi_pw_aff *
8925 isl_multi_pw_aff_add_constant_multi_val(
8926 __isl_take isl_multi_pw_aff *mpa,
8927 __isl_take isl_multi_val *mv);
8928 __isl_give isl_pw_aff *isl_pw_aff_min(
8929 __isl_take isl_pw_aff *pwaff1,
8930 __isl_take isl_pw_aff *pwaff2);
8931 __isl_give isl_pw_aff *isl_pw_aff_max(
8932 __isl_take isl_pw_aff *pwaff1,
8933 __isl_take isl_pw_aff *pwaff2);
8934 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_min(
8935 __isl_take isl_multi_pw_aff *mpa1,
8936 __isl_take isl_multi_pw_aff *mpa2);
8937 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_max(
8938 __isl_take isl_multi_pw_aff *mpa1,
8939 __isl_take isl_multi_pw_aff *mpa2);
8940 __isl_give isl_aff *isl_aff_sub(
8941 __isl_take isl_aff *aff1,
8942 __isl_take isl_aff *aff2);
8943 __isl_give isl_multi_aff *isl_multi_aff_sub(
8944 __isl_take isl_multi_aff *ma1,
8945 __isl_take isl_multi_aff *ma2);
8946 __isl_give isl_pw_aff *isl_pw_aff_sub(
8947 __isl_take isl_pw_aff *pwaff1,
8948 __isl_take isl_pw_aff *pwaff2);
8949 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
8950 __isl_take isl_multi_pw_aff *mpa1,
8951 __isl_take isl_multi_pw_aff *mpa2);
8952 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
8953 __isl_take isl_pw_multi_aff *pma1,
8954 __isl_take isl_pw_multi_aff *pma2);
8955 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
8956 __isl_take isl_union_pw_aff *upa1,
8957 __isl_take isl_union_pw_aff *upa2);
8958 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
8959 __isl_take isl_union_pw_multi_aff *upma1,
8960 __isl_take isl_union_pw_multi_aff *upma2);
8961 __isl_give isl_multi_union_pw_aff *
8962 isl_multi_union_pw_aff_sub(
8963 __isl_take isl_multi_union_pw_aff *mupa1,
8964 __isl_take isl_multi_union_pw_aff *mupa2);
8966 C<isl_aff_sub> subtracts the second argument from the first.
8968 #include <isl/polynomial.h>
8969 __isl_give isl_qpolynomial *isl_qpolynomial_add(
8970 __isl_take isl_qpolynomial *qp1,
8971 __isl_take isl_qpolynomial *qp2);
8972 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
8973 __isl_take isl_pw_qpolynomial *pwqp1,
8974 __isl_take isl_pw_qpolynomial *pwqp2);
8975 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
8976 __isl_take isl_pw_qpolynomial *pwqp1,
8977 __isl_take isl_pw_qpolynomial *pwqp2);
8978 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
8979 __isl_take isl_pw_qpolynomial_fold *pwf1,
8980 __isl_take isl_pw_qpolynomial_fold *pwf2);
8981 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
8982 __isl_take isl_union_pw_qpolynomial *upwqp1,
8983 __isl_take isl_union_pw_qpolynomial *upwqp2);
8984 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
8985 __isl_take isl_qpolynomial *qp1,
8986 __isl_take isl_qpolynomial *qp2);
8987 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
8988 __isl_take isl_pw_qpolynomial *pwqp1,
8989 __isl_take isl_pw_qpolynomial *pwqp2);
8990 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
8991 __isl_take isl_union_pw_qpolynomial *upwqp1,
8992 __isl_take isl_union_pw_qpolynomial *upwqp2);
8993 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
8994 __isl_take isl_pw_qpolynomial_fold *pwf1,
8995 __isl_take isl_pw_qpolynomial_fold *pwf2);
8996 __isl_give isl_union_pw_qpolynomial_fold *
8997 isl_union_pw_qpolynomial_fold_fold(
8998 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
8999 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
9001 #include <isl/aff.h>
9002 __isl_give isl_pw_aff *isl_pw_aff_union_add(
9003 __isl_take isl_pw_aff *pwaff1,
9004 __isl_take isl_pw_aff *pwaff2);
9005 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_union_add(
9006 __isl_take isl_multi_pw_aff *mpa1,
9007 __isl_take isl_multi_pw_aff *mpa2);
9008 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
9009 __isl_take isl_pw_multi_aff *pma1,
9010 __isl_take isl_pw_multi_aff *pma2);
9011 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
9012 __isl_take isl_union_pw_aff *upa1,
9013 __isl_take isl_union_pw_aff *upa2);
9014 __isl_give isl_union_pw_multi_aff *
9015 isl_union_pw_multi_aff_union_add(
9016 __isl_take isl_union_pw_multi_aff *upma1,
9017 __isl_take isl_union_pw_multi_aff *upma2);
9018 __isl_give isl_multi_union_pw_aff *
9019 isl_multi_union_pw_aff_union_add(
9020 __isl_take isl_multi_union_pw_aff *mupa1,
9021 __isl_take isl_multi_union_pw_aff *mupa2);
9022 __isl_give isl_pw_aff *isl_pw_aff_union_min(
9023 __isl_take isl_pw_aff *pwaff1,
9024 __isl_take isl_pw_aff *pwaff2);
9025 __isl_give isl_pw_aff *isl_pw_aff_union_max(
9026 __isl_take isl_pw_aff *pwaff1,
9027 __isl_take isl_pw_aff *pwaff2);
9029 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
9030 expression with a domain that is the union of those of C<pwaff1> and
9031 C<pwaff2> and such that on each cell, the quasi-affine expression is
9032 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
9033 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
9034 associated expression is the defined one.
9035 This in contrast to the C<isl_pw_aff_max> function, which is
9036 only defined on the shared definition domain of the arguments.
9038 #include <isl/val.h>
9039 __isl_give isl_multi_val *isl_multi_val_add_val(
9040 __isl_take isl_multi_val *mv,
9041 __isl_take isl_val *v);
9042 __isl_give isl_multi_val *isl_multi_val_mod_val(
9043 __isl_take isl_multi_val *mv,
9044 __isl_take isl_val *v);
9045 __isl_give isl_multi_val *isl_multi_val_scale_val(
9046 __isl_take isl_multi_val *mv,
9047 __isl_take isl_val *v);
9048 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
9049 __isl_take isl_multi_val *mv,
9050 __isl_take isl_val *v);
9052 #include <isl/aff.h>
9053 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
9054 __isl_take isl_val *mod);
9055 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
9056 __isl_take isl_pw_aff *pa,
9057 __isl_take isl_val *mod);
9058 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
9059 __isl_take isl_union_pw_aff *upa,
9060 __isl_take isl_val *f);
9061 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
9062 __isl_take isl_val *v);
9063 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
9064 __isl_take isl_multi_aff *ma,
9065 __isl_take isl_val *v);
9066 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
9067 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
9068 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
9069 __isl_take isl_multi_pw_aff *mpa,
9070 __isl_take isl_val *v);
9071 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
9072 __isl_take isl_pw_multi_aff *pma,
9073 __isl_take isl_val *v);
9074 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
9075 __isl_take isl_union_pw_aff *upa,
9076 __isl_take isl_val *f);
9077 __isl_give isl_union_pw_multi_aff *
9078 isl_union_pw_multi_aff_scale_val(
9079 __isl_take isl_union_pw_multi_aff *upma,
9080 __isl_take isl_val *val);
9081 __isl_give isl_multi_union_pw_aff *
9082 isl_multi_union_pw_aff_scale_val(
9083 __isl_take isl_multi_union_pw_aff *mupa,
9084 __isl_take isl_val *v);
9085 __isl_give isl_aff *isl_aff_scale_down_ui(
9086 __isl_take isl_aff *aff, unsigned f);
9087 __isl_give isl_aff *isl_aff_scale_down_val(
9088 __isl_take isl_aff *aff, __isl_take isl_val *v);
9089 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
9090 __isl_take isl_multi_aff *ma,
9091 __isl_take isl_val *v);
9092 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
9093 __isl_take isl_pw_aff *pa,
9094 __isl_take isl_val *f);
9095 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
9096 __isl_take isl_multi_pw_aff *mpa,
9097 __isl_take isl_val *v);
9098 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
9099 __isl_take isl_pw_multi_aff *pma,
9100 __isl_take isl_val *v);
9101 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
9102 __isl_take isl_union_pw_aff *upa,
9103 __isl_take isl_val *v);
9104 __isl_give isl_union_pw_multi_aff *
9105 isl_union_pw_multi_aff_scale_down_val(
9106 __isl_take isl_union_pw_multi_aff *upma,
9107 __isl_take isl_val *val);
9108 __isl_give isl_multi_union_pw_aff *
9109 isl_multi_union_pw_aff_scale_down_val(
9110 __isl_take isl_multi_union_pw_aff *mupa,
9111 __isl_take isl_val *v);
9113 #include <isl/polynomial.h>
9114 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
9115 __isl_take isl_qpolynomial *qp,
9116 __isl_take isl_val *v);
9117 __isl_give isl_qpolynomial_fold *
9118 isl_qpolynomial_fold_scale_val(
9119 __isl_take isl_qpolynomial_fold *fold,
9120 __isl_take isl_val *v);
9121 __isl_give isl_pw_qpolynomial *
9122 isl_pw_qpolynomial_scale_val(
9123 __isl_take isl_pw_qpolynomial *pwqp,
9124 __isl_take isl_val *v);
9125 __isl_give isl_pw_qpolynomial_fold *
9126 isl_pw_qpolynomial_fold_scale_val(
9127 __isl_take isl_pw_qpolynomial_fold *pwf,
9128 __isl_take isl_val *v);
9129 __isl_give isl_union_pw_qpolynomial *
9130 isl_union_pw_qpolynomial_scale_val(
9131 __isl_take isl_union_pw_qpolynomial *upwqp,
9132 __isl_take isl_val *v);
9133 __isl_give isl_union_pw_qpolynomial_fold *
9134 isl_union_pw_qpolynomial_fold_scale_val(
9135 __isl_take isl_union_pw_qpolynomial_fold *upwf,
9136 __isl_take isl_val *v);
9137 __isl_give isl_qpolynomial *
9138 isl_qpolynomial_scale_down_val(
9139 __isl_take isl_qpolynomial *qp,
9140 __isl_take isl_val *v);
9141 __isl_give isl_qpolynomial_fold *
9142 isl_qpolynomial_fold_scale_down_val(
9143 __isl_take isl_qpolynomial_fold *fold,
9144 __isl_take isl_val *v);
9145 __isl_give isl_pw_qpolynomial *
9146 isl_pw_qpolynomial_scale_down_val(
9147 __isl_take isl_pw_qpolynomial *pwqp,
9148 __isl_take isl_val *v);
9149 __isl_give isl_pw_qpolynomial_fold *
9150 isl_pw_qpolynomial_fold_scale_down_val(
9151 __isl_take isl_pw_qpolynomial_fold *pwf,
9152 __isl_take isl_val *v);
9153 __isl_give isl_union_pw_qpolynomial *
9154 isl_union_pw_qpolynomial_scale_down_val(
9155 __isl_take isl_union_pw_qpolynomial *upwqp,
9156 __isl_take isl_val *v);
9157 __isl_give isl_union_pw_qpolynomial_fold *
9158 isl_union_pw_qpolynomial_fold_scale_down_val(
9159 __isl_take isl_union_pw_qpolynomial_fold *upwf,
9160 __isl_take isl_val *v);
9162 #include <isl/val.h>
9163 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
9164 __isl_take isl_multi_val *mv1,
9165 __isl_take isl_multi_val *mv2);
9166 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
9167 __isl_take isl_multi_val *mv1,
9168 __isl_take isl_multi_val *mv2);
9169 __isl_give isl_multi_val *
9170 isl_multi_val_scale_down_multi_val(
9171 __isl_take isl_multi_val *mv1,
9172 __isl_take isl_multi_val *mv2);
9174 #include <isl/aff.h>
9175 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
9176 __isl_take isl_multi_aff *ma,
9177 __isl_take isl_multi_val *mv);
9178 __isl_give isl_multi_union_pw_aff *
9179 isl_multi_union_pw_aff_mod_multi_val(
9180 __isl_take isl_multi_union_pw_aff *upma,
9181 __isl_take isl_multi_val *mv);
9182 __isl_give isl_multi_pw_aff *
9183 isl_multi_pw_aff_mod_multi_val(
9184 __isl_take isl_multi_pw_aff *mpa,
9185 __isl_take isl_multi_val *mv);
9186 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
9187 __isl_take isl_multi_aff *ma,
9188 __isl_take isl_multi_val *mv);
9189 __isl_give isl_pw_multi_aff *
9190 isl_pw_multi_aff_scale_multi_val(
9191 __isl_take isl_pw_multi_aff *pma,
9192 __isl_take isl_multi_val *mv);
9193 __isl_give isl_multi_pw_aff *
9194 isl_multi_pw_aff_scale_multi_val(
9195 __isl_take isl_multi_pw_aff *mpa,
9196 __isl_take isl_multi_val *mv);
9197 __isl_give isl_multi_union_pw_aff *
9198 isl_multi_union_pw_aff_scale_multi_val(
9199 __isl_take isl_multi_union_pw_aff *mupa,
9200 __isl_take isl_multi_val *mv);
9201 __isl_give isl_union_pw_multi_aff *
9202 isl_union_pw_multi_aff_scale_multi_val(
9203 __isl_take isl_union_pw_multi_aff *upma,
9204 __isl_take isl_multi_val *mv);
9205 __isl_give isl_multi_aff *
9206 isl_multi_aff_scale_down_multi_val(
9207 __isl_take isl_multi_aff *ma,
9208 __isl_take isl_multi_val *mv);
9209 __isl_give isl_pw_multi_aff *
9210 isl_pw_multi_aff_scale_down_multi_val(
9211 __isl_take isl_pw_multi_aff *pma,
9212 __isl_take isl_multi_val *mv);
9213 __isl_give isl_multi_pw_aff *
9214 isl_multi_pw_aff_scale_down_multi_val(
9215 __isl_take isl_multi_pw_aff *mpa,
9216 __isl_take isl_multi_val *mv);
9217 __isl_give isl_multi_union_pw_aff *
9218 isl_multi_union_pw_aff_scale_down_multi_val(
9219 __isl_take isl_multi_union_pw_aff *mupa,
9220 __isl_take isl_multi_val *mv);
9222 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
9223 by the corresponding elements of C<mv>.
9225 #include <isl/aff.h>
9226 __isl_give isl_aff *isl_aff_mul(
9227 __isl_take isl_aff *aff1,
9228 __isl_take isl_aff *aff2);
9229 __isl_give isl_aff *isl_aff_div(
9230 __isl_take isl_aff *aff1,
9231 __isl_take isl_aff *aff2);
9232 __isl_give isl_pw_aff *isl_pw_aff_mul(
9233 __isl_take isl_pw_aff *pwaff1,
9234 __isl_take isl_pw_aff *pwaff2);
9235 __isl_give isl_pw_aff *isl_pw_aff_div(
9236 __isl_take isl_pw_aff *pa1,
9237 __isl_take isl_pw_aff *pa2);
9238 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
9239 __isl_take isl_pw_aff *pa1,
9240 __isl_take isl_pw_aff *pa2);
9241 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
9242 __isl_take isl_pw_aff *pa1,
9243 __isl_take isl_pw_aff *pa2);
9245 When multiplying two affine expressions, at least one of the two needs
9246 to be a constant. Similarly, when dividing an affine expression by another,
9247 the second expression needs to be a constant.
9248 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
9249 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
9252 #include <isl/polynomial.h>
9253 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
9254 __isl_take isl_qpolynomial *qp1,
9255 __isl_take isl_qpolynomial *qp2);
9256 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
9257 __isl_take isl_pw_qpolynomial *pwqp1,
9258 __isl_take isl_pw_qpolynomial *pwqp2);
9259 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
9260 __isl_take isl_union_pw_qpolynomial *upwqp1,
9261 __isl_take isl_union_pw_qpolynomial *upwqp2);
9265 =head3 Lexicographic Optimization
9267 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
9268 the following functions
9269 compute a set that contains the lexicographic minimum or maximum
9270 of the elements in C<set> (or C<bset>) for those values of the parameters
9271 that satisfy C<dom>.
9272 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
9273 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
9275 In other words, the union of the parameter values
9276 for which the result is non-empty and of C<*empty>
9279 #include <isl/set.h>
9280 __isl_give isl_set *isl_basic_set_partial_lexmin(
9281 __isl_take isl_basic_set *bset,
9282 __isl_take isl_basic_set *dom,
9283 __isl_give isl_set **empty);
9284 __isl_give isl_set *isl_basic_set_partial_lexmax(
9285 __isl_take isl_basic_set *bset,
9286 __isl_take isl_basic_set *dom,
9287 __isl_give isl_set **empty);
9288 __isl_give isl_set *isl_set_partial_lexmin(
9289 __isl_take isl_set *set, __isl_take isl_set *dom,
9290 __isl_give isl_set **empty);
9291 __isl_give isl_set *isl_set_partial_lexmax(
9292 __isl_take isl_set *set, __isl_take isl_set *dom,
9293 __isl_give isl_set **empty);
9295 Given a (basic) set C<set> (or C<bset>), the following functions simply
9296 return a set containing the lexicographic minimum or maximum
9297 of the elements in C<set> (or C<bset>).
9298 In case of union sets, the optimum is computed per space.
9300 #include <isl/set.h>
9301 __isl_give isl_set *isl_basic_set_lexmin(
9302 __isl_take isl_basic_set *bset);
9303 __isl_give isl_set *isl_basic_set_lexmax(
9304 __isl_take isl_basic_set *bset);
9305 __isl_give isl_set *isl_set_lexmin(
9306 __isl_take isl_set *set);
9307 __isl_give isl_set *isl_set_lexmax(
9308 __isl_take isl_set *set);
9309 __isl_give isl_union_set *isl_union_set_lexmin(
9310 __isl_take isl_union_set *uset);
9311 __isl_give isl_union_set *isl_union_set_lexmax(
9312 __isl_take isl_union_set *uset);
9314 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
9315 the following functions
9316 compute a relation that maps each element of C<dom>
9317 to the single lexicographic minimum or maximum
9318 of the elements that are associated to that same
9319 element in C<map> (or C<bmap>).
9320 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
9321 that contains the elements in C<dom> that do not map
9322 to any elements in C<map> (or C<bmap>).
9323 In other words, the union of the domain of the result and of C<*empty>
9326 #include <isl/map.h>
9327 __isl_give isl_map *isl_basic_map_partial_lexmax(
9328 __isl_take isl_basic_map *bmap,
9329 __isl_take isl_basic_set *dom,
9330 __isl_give isl_set **empty);
9331 __isl_give isl_map *isl_basic_map_partial_lexmin(
9332 __isl_take isl_basic_map *bmap,
9333 __isl_take isl_basic_set *dom,
9334 __isl_give isl_set **empty);
9335 __isl_give isl_map *isl_map_partial_lexmax(
9336 __isl_take isl_map *map, __isl_take isl_set *dom,
9337 __isl_give isl_set **empty);
9338 __isl_give isl_map *isl_map_partial_lexmin(
9339 __isl_take isl_map *map, __isl_take isl_set *dom,
9340 __isl_give isl_set **empty);
9342 Given a (basic) map C<map> (or C<bmap>), the following functions simply
9343 return a map mapping each element in the domain of
9344 C<map> (or C<bmap>) to the lexicographic minimum or maximum
9345 of all elements associated to that element.
9346 In case of union relations, the optimum is computed per space.
9348 #include <isl/map.h>
9349 __isl_give isl_map *isl_basic_map_lexmin(
9350 __isl_take isl_basic_map *bmap);
9351 __isl_give isl_map *isl_basic_map_lexmax(
9352 __isl_take isl_basic_map *bmap);
9353 __isl_give isl_map *isl_map_lexmin(
9354 __isl_take isl_map *map);
9355 __isl_give isl_map *isl_map_lexmax(
9356 __isl_take isl_map *map);
9357 __isl_give isl_union_map *isl_union_map_lexmin(
9358 __isl_take isl_union_map *umap);
9359 __isl_give isl_union_map *isl_union_map_lexmax(
9360 __isl_take isl_union_map *umap);
9362 The following functions return their result in the form of
9363 a piecewise multi-affine expression,
9364 but are otherwise equivalent to the corresponding functions
9365 returning a basic set or relation.
9367 #include <isl/set.h>
9368 __isl_give isl_pw_multi_aff *
9369 isl_basic_set_partial_lexmin_pw_multi_aff(
9370 __isl_take isl_basic_set *bset,
9371 __isl_take isl_basic_set *dom,
9372 __isl_give isl_set **empty);
9373 __isl_give isl_pw_multi_aff *
9374 isl_basic_set_partial_lexmax_pw_multi_aff(
9375 __isl_take isl_basic_set *bset,
9376 __isl_take isl_basic_set *dom,
9377 __isl_give isl_set **empty);
9378 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
9379 __isl_take isl_set *set);
9380 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
9381 __isl_take isl_set *set);
9383 #include <isl/map.h>
9384 __isl_give isl_pw_multi_aff *
9385 isl_basic_map_lexmin_pw_multi_aff(
9386 __isl_take isl_basic_map *bmap);
9387 __isl_give isl_pw_multi_aff *
9388 isl_basic_map_partial_lexmin_pw_multi_aff(
9389 __isl_take isl_basic_map *bmap,
9390 __isl_take isl_basic_set *dom,
9391 __isl_give isl_set **empty);
9392 __isl_give isl_pw_multi_aff *
9393 isl_basic_map_partial_lexmax_pw_multi_aff(
9394 __isl_take isl_basic_map *bmap,
9395 __isl_take isl_basic_set *dom,
9396 __isl_give isl_set **empty);
9397 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
9398 __isl_take isl_map *map);
9399 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
9400 __isl_take isl_map *map);
9402 The following functions return the lexicographic minimum or maximum
9403 on the shared domain of the inputs and the single defined function
9404 on those parts of the domain where only a single function is defined.
9406 #include <isl/aff.h>
9407 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
9408 __isl_take isl_pw_multi_aff *pma1,
9409 __isl_take isl_pw_multi_aff *pma2);
9410 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
9411 __isl_take isl_pw_multi_aff *pma1,
9412 __isl_take isl_pw_multi_aff *pma2);
9414 If the input to a lexicographic optimization problem has
9415 multiple constraints with the same coefficients for the optimized
9416 variables, then, by default, this symmetry is exploited by
9417 replacing those constraints by a single constraint with
9418 an abstract bound, which is in turn bounded by the corresponding terms
9419 in the original constraints.
9420 Without this optimization, the solver would typically consider
9421 all possible orderings of those original bounds, resulting in a needless
9422 decomposition of the domain.
9423 However, the optimization can also result in slowdowns since
9424 an extra parameter is introduced that may get used in additional
9426 The following option determines whether symmetry detection is applied
9427 during lexicographic optimization.
9429 #include <isl/options.h>
9430 isl_stat isl_options_set_pip_symmetry(isl_ctx *ctx,
9432 int isl_options_get_pip_symmetry(isl_ctx *ctx);
9436 See also \autoref{s:offline}.
9440 =head2 Ternary Operations
9442 #include <isl/aff.h>
9443 __isl_give isl_pw_aff *isl_pw_aff_cond(
9444 __isl_take isl_pw_aff *cond,
9445 __isl_take isl_pw_aff *pwaff_true,
9446 __isl_take isl_pw_aff *pwaff_false);
9448 The function C<isl_pw_aff_cond> performs a conditional operator
9449 and returns an expression that is equal to C<pwaff_true>
9450 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
9451 where C<cond> is zero.
9455 Lists are defined over several element types, including
9456 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_pw_multi_aff>,
9457 C<isl_union_pw_aff>,
9458 C<isl_union_pw_multi_aff>,
9459 C<isl_qpolynomial>, C<isl_pw_qpolynomial>, C<isl_pw_qpolynomial_fold>,
9461 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
9462 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
9463 Here we take lists of C<isl_set>s as an example.
9464 Lists can be created, copied, modified and freed using the following functions.
9466 #include <isl/set.h>
9467 __isl_give isl_set_list *isl_set_to_list(
9468 __isl_take isl_set *el);
9469 __isl_give isl_set_list *isl_set_list_from_set(
9470 __isl_take isl_set *el);
9471 __isl_give isl_set_list *isl_set_list_alloc(
9472 isl_ctx *ctx, int n);
9473 __isl_give isl_set_list *isl_set_list_copy(
9474 __isl_keep isl_set_list *list);
9475 __isl_give isl_set_list *isl_set_list_insert(
9476 __isl_take isl_set_list *list, unsigned pos,
9477 __isl_take isl_set *el);
9478 __isl_give isl_set_list *isl_set_list_add(
9479 __isl_take isl_set_list *list,
9480 __isl_take isl_set *el);
9481 __isl_give isl_set_list *isl_set_list_drop(
9482 __isl_take isl_set_list *list,
9483 unsigned first, unsigned n);
9484 __isl_give isl_set_list *isl_set_list_clear(
9485 __isl_take isl_set_list *list);
9486 __isl_give isl_set_list *isl_set_list_swap(
9487 __isl_take isl_set_list *list,
9488 unsigned pos1, unsigned pos2);
9489 __isl_give isl_set_list *isl_set_list_reverse(
9490 __isl_take isl_set_list *list);
9491 __isl_give isl_set_list *isl_set_list_set_at(
9492 __isl_take isl_set_list *list, int index,
9493 __isl_take isl_set *set);
9494 __isl_give isl_set_list *isl_set_list_set_set(
9495 __isl_take isl_set_list *list, int index,
9496 __isl_take isl_set *set);
9497 __isl_give isl_set_list *isl_set_list_concat(
9498 __isl_take isl_set_list *list1,
9499 __isl_take isl_set_list *list2);
9500 __isl_give isl_set_list *isl_set_list_map(
9501 __isl_take isl_set_list *list,
9502 __isl_give isl_set *(*fn)(__isl_take isl_set *el,
9505 __isl_give isl_set_list *isl_set_list_sort(
9506 __isl_take isl_set_list *list,
9507 int (*cmp)(__isl_keep isl_set *a,
9508 __isl_keep isl_set *b, void *user),
9510 __isl_null isl_set_list *isl_set_list_free(
9511 __isl_take isl_set_list *list);
9513 C<isl_set_list_alloc> creates an empty list with an initial capacity
9514 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
9515 add elements to a list, increasing its capacity as needed.
9516 C<isl_set_to_list> creates a list with a single element.
9517 C<isl_set_list_from_set> performs the same operation.
9518 C<isl_set_list_clear> removes all elements from a list.
9519 C<isl_set_list_swap> swaps the elements at the specified locations.
9520 C<isl_set_list_reverse> reverses the elements in the list.
9521 C<isl_set_list_set_set> is an alternative name for C<isl_set_list_set_at>.
9523 Lists can be inspected using the following functions.
9525 #include <isl/set.h>
9526 isl_size isl_set_list_size(__isl_keep isl_set_list *list);
9527 isl_size isl_set_list_n_set(__isl_keep isl_set_list *list);
9528 __isl_give isl_set *isl_set_list_get_at(
9529 __isl_keep isl_set_list *list, int index);
9530 __isl_give isl_set *isl_set_list_get_set(
9531 __isl_keep isl_set_list *list, int index);
9532 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list,
9533 isl_stat (*fn)(__isl_take isl_set *el, void *user),
9535 isl_bool isl_set_list_every(__isl_keep isl_set_list *list,
9536 isl_bool (*test)(__isl_take isl_set *el,
9539 isl_stat isl_set_list_foreach_scc(
9540 __isl_keep isl_set_list *list,
9541 isl_bool (*follows)(__isl_keep isl_set *a,
9542 __isl_keep isl_set *b, void *user),
9544 isl_stat (*fn)(__isl_take isl_set_list *scc,
9548 C<isl_set_list_n_set> is an alternative name for C<isl_set_list_size>.
9550 C<isl_set_list_get_set> is an alternative name for C<isl_set_list_get_at>.
9551 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
9552 strongly connected components of the graph with as vertices the elements
9553 of C<list> and a directed edge from vertex C<b> to vertex C<a>
9554 iff C<follows(a, b)> returns C<isl_bool_true>. The callbacks C<follows> and
9555 C<fn> should return C<isl_bool_error> or C<isl_stat_error> on error.
9557 Lists can be printed using
9559 #include <isl/set.h>
9560 __isl_give isl_printer *isl_printer_print_set_list(
9561 __isl_take isl_printer *p,
9562 __isl_keep isl_set_list *list);
9564 Alternatively, a string representation can be obtained
9565 directly using the following function, which always prints
9568 #include <isl/set.h>
9569 __isl_give char *isl_set_list_to_str(
9570 __isl_keep isl_set_list *list);
9572 An C<isl_val_list>, C<isl_id_list>,
9573 C<isl_aff_list>, C<isl_pw_aff_list>, C<isl_pw_multi_aff_list>,
9574 C<isl_union_pw_aff_list>,
9575 C<isl_set_list>, C<isl_map_list> or C<isl_union_set_list> object
9576 can also be read from input using the following functions.
9578 #include <isl/val.h>
9579 __isl_give isl_val_list *isl_val_list_read_from_str(
9580 isl_ctx *ctx, const char *str);
9583 __isl_give isl_id_list *isl_id_list_read_from_str(
9584 isl_ctx *ctx, const char *str);
9586 #include <isl/aff.h>
9587 __isl_give isl_aff_list *
9588 isl_aff_list_read_from_str(isl_ctx *ctx,
9590 __isl_give isl_pw_aff_list *
9591 isl_pw_aff_list_read_from_str(isl_ctx *ctx,
9593 __isl_give isl_pw_multi_aff_list *
9594 isl_pw_multi_aff_list_read_from_str(isl_ctx *ctx,
9596 __isl_give isl_union_pw_aff_list *
9597 isl_union_pw_aff_list_read_from_str(isl_ctx *ctx,
9600 #include <isl/set.h>
9601 __isl_give isl_set_list *isl_set_list_read_from_str(
9602 isl_ctx *ctx, const char *str);
9604 #include <isl/map.h>
9605 __isl_give isl_map_list *isl_map_list_read_from_str(
9606 isl_ctx *ctx, const char *str);
9608 #include <isl/union_set.h>
9609 __isl_give isl_union_set_list *
9610 isl_union_set_list_read_from_str(isl_ctx *ctx,
9613 =head2 Associative arrays
9615 Associative arrays map isl objects of a specific type to isl objects
9616 of some (other) specific type. They are defined for several pairs
9617 of types, including (C<isl_map>, C<isl_basic_set>),
9618 (C<isl_id>, C<isl_ast_expr>),
9619 (C<isl_id>, C<isl_id>) and
9620 (C<isl_id>, C<isl_pw_aff>).
9621 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
9624 Associative arrays can be created, copied and freed using
9625 the following functions.
9627 #include <isl/id_to_ast_expr.h>
9628 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
9629 isl_ctx *ctx, int min_size);
9630 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
9631 __isl_keep isl_id_to_ast_expr *id2expr);
9632 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
9633 __isl_take isl_id_to_ast_expr *id2expr);
9635 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
9636 to specify the expected size of the associative array.
9637 The associative array will be grown automatically as needed.
9639 Associative arrays can be inspected using the following functions.
9641 #include <isl/id_to_ast_expr.h>
9642 __isl_give isl_maybe_isl_ast_expr
9643 isl_id_to_ast_expr_try_get(
9644 __isl_keep isl_id_to_ast_expr *id2expr,
9645 __isl_keep isl_id *key);
9646 isl_bool isl_id_to_ast_expr_has(
9647 __isl_keep isl_id_to_ast_expr *id2expr,
9648 __isl_keep isl_id *key);
9649 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
9650 __isl_keep isl_id_to_ast_expr *id2expr,
9651 __isl_take isl_id *key);
9652 isl_stat isl_id_to_ast_expr_foreach(
9653 __isl_keep isl_id_to_ast_expr *id2expr,
9654 isl_stat (*fn)(__isl_take isl_id *key,
9655 __isl_take isl_ast_expr *val, void *user),
9657 isl_bool isl_id_to_ast_expr_every(
9658 __isl_keep isl_id_to_ast_expr *id2expr,
9659 isl_bool (*test)(__isl_keep isl_id *key,
9660 __isl_keep isl_ast_expr *val, void *user),
9663 The function C<isl_id_to_ast_expr_try_get> returns a structure
9664 containing two elements, C<valid> and C<value>.
9665 If there is a value associated to the key, then C<valid>
9666 is set to C<isl_bool_true> and C<value> contains a copy of
9667 the associated value. Otherwise C<value> is C<NULL> and
9668 C<valid> may be C<isl_bool_error> or C<isl_bool_false> depending
9669 on whether some error has occurred or there simply is no associated value.
9670 The function C<isl_id_to_ast_expr_has> returns the C<valid> field
9671 in the structure and
9672 the function C<isl_id_to_ast_expr_get> returns the C<value> field.
9674 Associative arrays can be modified using the following functions.
9676 #include <isl/id_to_ast_expr.h>
9677 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
9678 __isl_take isl_id_to_ast_expr *id2expr,
9679 __isl_take isl_id *key,
9680 __isl_take isl_ast_expr *val);
9681 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
9682 __isl_take isl_id_to_ast_expr *id2expr,
9683 __isl_take isl_id *key);
9685 Associative arrays can be checked for (obvious) equality
9686 using the following function.
9688 #include <isl/id_to_ast_expr.h>
9689 isl_bool isl_id_to_ast_expr_is_equal(
9690 __isl_take isl_id_to_ast_expr *id2expr1,
9691 __isl_take isl_id_to_ast_expr *id2expr2);
9693 Note that depending on how the keys and values are being compared,
9694 for other types of keys and/or values, this function may be called
9695 C<plain_is_equal> rather than C<is_equal>.
9697 Associative arrays can be printed using the following functions.
9699 #include <isl/id_to_ast_expr.h>
9700 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
9701 __isl_take isl_printer *p,
9702 __isl_keep isl_id_to_ast_expr *id2expr);
9703 __isl_give char *isl_id_to_ast_expr_to_str(
9704 __isl_keep isl_id_to_ast_expr *id2expr);
9706 They can be read from input using the following function.
9708 #include <isl/id_to_ast_expr.h>
9709 __isl_give isl_id_to_ast_expr *
9710 isl_id_to_ast_expr_read_from_str(isl_ctx *ctx,
9715 Vectors can be created, copied and freed using the following functions.
9717 #include <isl/vec.h>
9718 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
9720 __isl_give isl_vec *isl_vec_zero(isl_ctx *ctx,
9722 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
9723 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
9725 Note that the elements of a vector created by C<isl_vec_alloc>
9726 may have arbitrary values.
9727 A vector created by C<isl_vec_zero> has elements with value zero.
9728 The elements can be changed and inspected using the following functions.
9730 isl_size isl_vec_size(__isl_keep isl_vec *vec);
9731 __isl_give isl_val *isl_vec_get_element_val(
9732 __isl_keep isl_vec *vec, int pos);
9733 __isl_give isl_vec *isl_vec_set_element_si(
9734 __isl_take isl_vec *vec, int pos, int v);
9735 __isl_give isl_vec *isl_vec_set_element_val(
9736 __isl_take isl_vec *vec, int pos,
9737 __isl_take isl_val *v);
9738 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
9740 __isl_give isl_vec *isl_vec_set_val(
9741 __isl_take isl_vec *vec, __isl_take isl_val *v);
9742 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
9743 __isl_keep isl_vec *vec2, int pos);
9745 C<isl_vec_get_element> will return a negative value if anything went wrong.
9746 In that case, the value of C<*v> is undefined.
9748 The following function can be used to concatenate two vectors.
9750 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
9751 __isl_take isl_vec *vec2);
9755 Matrices can be created, copied and freed using the following functions.
9757 #include <isl/mat.h>
9758 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
9759 unsigned n_row, unsigned n_col);
9760 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
9761 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
9763 Note that the elements of a newly created matrix may have arbitrary values.
9764 The elements can be changed and inspected using the following functions.
9766 isl_size isl_mat_rows(__isl_keep isl_mat *mat);
9767 isl_size isl_mat_cols(__isl_keep isl_mat *mat);
9768 __isl_give isl_val *isl_mat_get_element_val(
9769 __isl_keep isl_mat *mat, int row, int col);
9770 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
9771 int row, int col, int v);
9772 __isl_give isl_mat *isl_mat_set_element_val(
9773 __isl_take isl_mat *mat, int row, int col,
9774 __isl_take isl_val *v);
9776 The following function computes the rank of a matrix.
9777 The return value may be -1 if some error occurred.
9779 #include <isl/mat.h>
9780 isl_size isl_mat_rank(__isl_keep isl_mat *mat);
9782 The following function can be used to compute the (right) inverse
9783 of a matrix, i.e., a matrix such that the product of the original
9784 and the inverse (in that order) is a multiple of the identity matrix.
9785 The input matrix is assumed to be of full row-rank.
9787 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
9789 The following function can be used to compute the (right) kernel
9790 (or null space) of a matrix, i.e., a matrix such that the product of
9791 the original and the kernel (in that order) is the zero matrix.
9793 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
9795 The following function computes a basis for the space spanned
9796 by the rows of a matrix.
9798 __isl_give isl_mat *isl_mat_row_basis(
9799 __isl_take isl_mat *mat);
9801 The following function computes rows that extend a basis of C<mat1>
9802 to a basis that also covers C<mat2>.
9804 __isl_give isl_mat *isl_mat_row_basis_extension(
9805 __isl_take isl_mat *mat1,
9806 __isl_take isl_mat *mat2);
9808 The following function checks whether there is no linear dependence
9809 among the combined rows of "mat1" and "mat2" that is not already present
9810 in "mat1" or "mat2" individually.
9811 If "mat1" and "mat2" have linearly independent rows by themselves,
9812 then this means that there is no linear dependence among all rows together.
9814 isl_bool isl_mat_has_linearly_independent_rows(
9815 __isl_keep isl_mat *mat1,
9816 __isl_keep isl_mat *mat2);
9818 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
9820 The following functions determine
9821 an upper or lower bound on a quasipolynomial over its domain.
9823 __isl_give isl_pw_qpolynomial_fold *
9824 isl_pw_qpolynomial_bound(
9825 __isl_take isl_pw_qpolynomial *pwqp,
9826 enum isl_fold type, isl_bool *tight);
9828 __isl_give isl_union_pw_qpolynomial_fold *
9829 isl_union_pw_qpolynomial_bound(
9830 __isl_take isl_union_pw_qpolynomial *upwqp,
9831 enum isl_fold type, isl_bool *tight);
9833 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
9834 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
9835 is the returned bound is known be tight, i.e., for each value
9836 of the parameters there is at least
9837 one element in the domain that reaches the bound.
9838 If the domain of C<pwqp> is not wrapping, then the bound is computed
9839 over all elements in that domain and the result has a purely parametric
9840 domain. If the domain of C<pwqp> is wrapping, then the bound is
9841 computed over the range of the wrapped relation. The domain of the
9842 wrapped relation becomes the domain of the result.
9844 =head2 Parametric Vertex Enumeration
9846 The parametric vertex enumeration described in this section
9847 is mainly intended to be used internally and by the C<barvinok>
9850 #include <isl/vertices.h>
9851 __isl_give isl_vertices *isl_basic_set_compute_vertices(
9852 __isl_keep isl_basic_set *bset);
9854 The function C<isl_basic_set_compute_vertices> performs the
9855 actual computation of the parametric vertices and the chamber
9856 decomposition and stores the result in an C<isl_vertices> object.
9857 This information can be queried by either iterating over all
9858 the vertices or iterating over all the chambers or cells
9859 and then iterating over all vertices that are active on the chamber.
9861 isl_stat isl_vertices_foreach_vertex(
9862 __isl_keep isl_vertices *vertices,
9863 isl_stat (*fn)(__isl_take isl_vertex *vertex,
9864 void *user), void *user);
9866 isl_stat isl_vertices_foreach_cell(
9867 __isl_keep isl_vertices *vertices,
9868 isl_stat (*fn)(__isl_take isl_cell *cell,
9869 void *user), void *user);
9870 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
9871 isl_stat (*fn)(__isl_take isl_vertex *vertex,
9872 void *user), void *user);
9874 Other operations that can be performed on an C<isl_vertices> object are
9877 isl_size isl_vertices_get_n_vertices(
9878 __isl_keep isl_vertices *vertices);
9879 __isl_null isl_vertices *isl_vertices_free(
9880 __isl_take isl_vertices *vertices);
9882 Vertices can be inspected and destroyed using the following functions.
9884 isl_size isl_vertex_get_id(__isl_keep isl_vertex *vertex);
9885 __isl_give isl_basic_set *isl_vertex_get_domain(
9886 __isl_keep isl_vertex *vertex);
9887 __isl_give isl_multi_aff *isl_vertex_get_expr(
9888 __isl_keep isl_vertex *vertex);
9889 __isl_null isl_vertex *isl_vertex_free(
9890 __isl_take isl_vertex *vertex);
9892 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
9893 describing the vertex in terms of the parameters,
9894 while C<isl_vertex_get_domain> returns the activity domain
9897 Chambers can be inspected and destroyed using the following functions.
9899 __isl_give isl_basic_set *isl_cell_get_domain(
9900 __isl_keep isl_cell *cell);
9901 __isl_null isl_cell *isl_cell_free(
9902 __isl_take isl_cell *cell);
9904 =head1 Polyhedral Compilation Library
9906 This section collects functionality in C<isl> that has been specifically
9907 designed for use during polyhedral compilation.
9909 =head2 Schedule Trees
9911 A schedule tree is a structured representation of a schedule,
9912 assigning a relative order to a set of domain elements.
9913 The relative order expressed by the schedule tree is
9914 defined recursively. In particular, the order between
9915 two domain elements is determined by the node that is closest
9916 to the root that refers to both elements and that orders them apart.
9917 Each node in the tree is of one of several types.
9918 The root node is always of type C<isl_schedule_node_domain>
9919 (or C<isl_schedule_node_extension>)
9920 and it describes the (extra) domain elements to which the schedule applies.
9921 The other types of nodes are as follows.
9925 =item C<isl_schedule_node_band>
9927 A band of schedule dimensions. Each schedule dimension is represented
9928 by a union piecewise quasi-affine expression. If this expression
9929 assigns a different value to two domain elements, while all previous
9930 schedule dimensions in the same band assign them the same value,
9931 then the two domain elements are ordered according to these two
9933 Each expression is required to be total in the domain elements
9934 that reach the band node.
9936 =item C<isl_schedule_node_expansion>
9938 An expansion node maps each of the domain elements that reach the node
9939 to one or more domain elements. The image of this mapping forms
9940 the set of domain elements that reach the child of the expansion node.
9941 The function that maps each of the expanded domain elements
9942 to the original domain element from which it was expanded
9943 is called the contraction.
9945 =item C<isl_schedule_node_filter>
9947 A filter node does not impose any ordering, but rather intersects
9948 the set of domain elements that the current subtree refers to
9949 with a given union set. The subtree of the filter node only
9950 refers to domain elements in the intersection.
9951 A filter node is typically only used as a child of a sequence or
9954 =item C<isl_schedule_node_leaf>
9956 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
9958 =item C<isl_schedule_node_mark>
9960 A mark node can be used to attach any kind of information to a subtree
9961 of the schedule tree.
9963 =item C<isl_schedule_node_sequence>
9965 A sequence node has one or more children, each of which is a filter node.
9966 The filters on these filter nodes form a partition of
9967 the domain elements that the current subtree refers to.
9968 If two domain elements appear in distinct filters then the sequence
9969 node orders them according to the child positions of the corresponding
9972 =item C<isl_schedule_node_set>
9974 A set node is similar to a sequence node, except that
9975 it expresses that domain elements appearing in distinct filters
9976 may have any order. The order of the children of a set node
9977 is therefore also immaterial.
9981 The following node types are only supported by the AST generator.
9985 =item C<isl_schedule_node_context>
9987 The context describes constraints on the parameters and
9988 the schedule dimensions of outer
9989 bands that the AST generator may assume to hold. It is also the only
9990 kind of node that may introduce additional parameters.
9991 The space of the context is that of the flat product of the outer
9992 band nodes. In particular, if there are no outer band nodes, then
9993 this space is the unnamed zero-dimensional space.
9994 Since a context node references the outer band nodes, any tree
9995 containing a context node is considered to be anchored.
9997 =item C<isl_schedule_node_extension>
9999 An extension node instructs the AST generator to add additional
10000 domain elements that need to be scheduled.
10001 The additional domain elements are described by the range of
10002 the extension map in terms of the outer schedule dimensions,
10003 i.e., the flat product of the outer band nodes.
10004 Note that domain elements are added whenever the AST generator
10005 reaches the extension node, meaning that there are still some
10006 active domain elements for which an AST needs to be generated.
10007 The conditions under which some domain elements are still active
10008 may however not be completely described by the outer AST nodes
10009 generated at that point.
10010 Since an extension node references the outer band nodes, any tree
10011 containing an extension node is considered to be anchored.
10013 An extension node may also appear as the root of a schedule tree,
10014 when it is intended to be inserted into another tree
10015 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
10016 In this case, the domain of the extension node should
10017 correspond to the flat product of the outer band nodes
10018 in this other schedule tree at the point where the extension tree
10021 =item C<isl_schedule_node_guard>
10023 The guard describes constraints on the parameters and
10024 the schedule dimensions of outer
10025 bands that need to be enforced by the outer nodes
10026 in the generated AST.
10027 That is, the part of the AST that is generated from descendants
10028 of the guard node can assume that these constraints are satisfied.
10029 The space of the guard is that of the flat product of the outer
10030 band nodes. In particular, if there are no outer band nodes, then
10031 this space is the unnamed zero-dimensional space.
10032 Since a guard node references the outer band nodes, any tree
10033 containing a guard node is considered to be anchored.
10037 Except for the C<isl_schedule_node_context> nodes,
10038 none of the nodes may introduce any parameters that were not
10039 already present in the root domain node.
10041 A schedule tree is encapsulated in an C<isl_schedule> object.
10042 The simplest such objects, those with a tree consisting of single domain node,
10043 can be created using the following functions with either an empty
10044 domain or a given domain.
10046 #include <isl/schedule.h>
10047 __isl_give isl_schedule *isl_schedule_empty(
10048 __isl_take isl_space *space);
10049 __isl_give isl_schedule *isl_schedule_from_domain(
10050 __isl_take isl_union_set *domain);
10052 The function C<isl_schedule_constraints_compute_schedule> described
10053 in L</"Scheduling"> can also be used to construct schedules.
10055 C<isl_schedule> objects may be copied and freed using the following functions.
10057 #include <isl/schedule.h>
10058 __isl_give isl_schedule *isl_schedule_copy(
10059 __isl_keep isl_schedule *sched);
10060 __isl_null isl_schedule *isl_schedule_free(
10061 __isl_take isl_schedule *sched);
10063 The following functions checks whether two C<isl_schedule> objects
10064 are obviously the same.
10066 #include <isl/schedule.h>
10067 isl_bool isl_schedule_plain_is_equal(
10068 __isl_keep isl_schedule *schedule1,
10069 __isl_keep isl_schedule *schedule2);
10071 The domain of the schedule, i.e., the domain described by the root node,
10072 can be obtained using the following function.
10074 #include <isl/schedule.h>
10075 __isl_give isl_union_set *isl_schedule_get_domain(
10076 __isl_keep isl_schedule *schedule);
10078 An extra top-level band node (right underneath the domain node) can
10079 be introduced into the schedule using the following function.
10080 The schedule tree is assumed not to have any anchored nodes.
10082 #include <isl/schedule.h>
10083 __isl_give isl_schedule *
10084 isl_schedule_insert_partial_schedule(
10085 __isl_take isl_schedule *schedule,
10086 __isl_take isl_multi_union_pw_aff *partial);
10088 A top-level context node (right underneath the domain node) can
10089 be introduced into the schedule using the following function.
10091 #include <isl/schedule.h>
10092 __isl_give isl_schedule *isl_schedule_insert_context(
10093 __isl_take isl_schedule *schedule,
10094 __isl_take isl_set *context)
10096 A top-level guard node (right underneath the domain node) can
10097 be introduced into the schedule using the following function.
10099 #include <isl/schedule.h>
10100 __isl_give isl_schedule *isl_schedule_insert_guard(
10101 __isl_take isl_schedule *schedule,
10102 __isl_take isl_set *guard)
10104 A schedule that combines two schedules either in the given
10105 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
10106 or an C<isl_schedule_node_set> node,
10107 can be created using the following functions.
10109 #include <isl/schedule.h>
10110 __isl_give isl_schedule *isl_schedule_sequence(
10111 __isl_take isl_schedule *schedule1,
10112 __isl_take isl_schedule *schedule2);
10113 __isl_give isl_schedule *isl_schedule_set(
10114 __isl_take isl_schedule *schedule1,
10115 __isl_take isl_schedule *schedule2);
10117 The domains of the two input schedules need to be disjoint.
10119 The following function can be used to restrict the domain
10120 of a schedule with a domain node as root to be a subset of the given union set.
10121 This operation may remove nodes in the tree that have become
10124 #include <isl/schedule.h>
10125 __isl_give isl_schedule *isl_schedule_intersect_domain(
10126 __isl_take isl_schedule *schedule,
10127 __isl_take isl_union_set *domain);
10129 The following function can be used to simplify the domain
10130 of a schedule with a domain node as root with respect to the given
10133 #include <isl/schedule.h>
10134 __isl_give isl_schedule *isl_schedule_gist_domain_params(
10135 __isl_take isl_schedule *schedule,
10136 __isl_take isl_set *context);
10138 The following function resets the user pointers on all parameter
10139 and tuple identifiers referenced by the nodes of the given schedule.
10141 #include <isl/schedule.h>
10142 __isl_give isl_schedule *isl_schedule_reset_user(
10143 __isl_take isl_schedule *schedule);
10145 The following function aligns the parameters of all nodes
10146 in the given schedule to the given space.
10148 #include <isl/schedule.h>
10149 __isl_give isl_schedule *isl_schedule_align_params(
10150 __isl_take isl_schedule *schedule,
10151 __isl_take isl_space *space);
10153 The following function allows the user to plug in a given function
10154 in the iteration domains. The input schedule is not allowed to contain
10155 any expansion nodes.
10157 #include <isl/schedule.h>
10158 __isl_give isl_schedule *
10159 isl_schedule_pullback_union_pw_multi_aff(
10160 __isl_take isl_schedule *schedule,
10161 __isl_take isl_union_pw_multi_aff *upma);
10163 The following function can be used to plug in the schedule C<expansion>
10164 in the leaves of C<schedule>, where C<contraction> describes how
10165 the domain elements of C<expansion> map to the domain elements
10166 at the original leaves of C<schedule>.
10167 The resulting schedule will contain expansion nodes, unless
10168 C<contraction> is an identity function.
10170 #include <isl/schedule.h>
10171 __isl_give isl_schedule *isl_schedule_expand(
10172 __isl_take isl_schedule *schedule,
10173 __isl_take isl_union_pw_multi_aff *contraction,
10174 __isl_take isl_schedule *expansion);
10176 An C<isl_union_map> representation of the schedule can be obtained
10177 from an C<isl_schedule> using the following function.
10179 #include <isl/schedule.h>
10180 __isl_give isl_union_map *isl_schedule_get_map(
10181 __isl_keep isl_schedule *sched);
10183 The resulting relation encodes the same relative ordering as
10184 the schedule by mapping the domain elements to a common schedule space.
10185 If the schedule_separate_components option is set, then the order
10186 of the children of a set node is explicitly encoded in the result.
10187 If the tree contains any expansion nodes, then the relation
10188 is formulated in terms of the expanded domain elements.
10190 Schedules can be read from input using the following functions.
10192 #include <isl/schedule.h>
10193 __isl_give isl_schedule *isl_schedule_read_from_file(
10194 isl_ctx *ctx, FILE *input);
10195 __isl_give isl_schedule *isl_schedule_read_from_str(
10196 isl_ctx *ctx, const char *str);
10198 A representation of the schedule can be printed using
10200 #include <isl/schedule.h>
10201 __isl_give isl_printer *isl_printer_print_schedule(
10202 __isl_take isl_printer *p,
10203 __isl_keep isl_schedule *schedule);
10204 __isl_give char *isl_schedule_to_str(
10205 __isl_keep isl_schedule *schedule);
10207 C<isl_schedule_to_str> prints the schedule in flow format.
10209 The schedule tree can be traversed through the use of
10210 C<isl_schedule_node> objects that point to a particular
10211 position in the schedule tree. Whenever a C<isl_schedule_node>
10212 is used to modify a node in the schedule tree, the original schedule
10213 tree is left untouched and the modifications are performed to a copy
10214 of the tree. The returned C<isl_schedule_node> then points to
10215 this modified copy of the tree.
10217 The root of the schedule tree can be obtained using the following function.
10219 #include <isl/schedule.h>
10220 __isl_give isl_schedule_node *isl_schedule_get_root(
10221 __isl_keep isl_schedule *schedule);
10223 A pointer to a newly created schedule tree with a single domain
10224 node can be created using the following functions.
10226 #include <isl/schedule_node.h>
10227 __isl_give isl_schedule_node *
10228 isl_schedule_node_from_domain(
10229 __isl_take isl_union_set *domain);
10230 __isl_give isl_schedule_node *
10231 isl_schedule_node_from_extension(
10232 __isl_take isl_union_map *extension);
10234 C<isl_schedule_node_from_extension> creates a tree with an extension
10237 Schedule nodes can be copied and freed using the following functions.
10239 #include <isl/schedule_node.h>
10240 __isl_give isl_schedule_node *isl_schedule_node_copy(
10241 __isl_keep isl_schedule_node *node);
10242 __isl_null isl_schedule_node *isl_schedule_node_free(
10243 __isl_take isl_schedule_node *node);
10245 The following functions can be used to check if two schedule
10246 nodes point to the same position in the same schedule.
10248 #include <isl/schedule_node.h>
10249 isl_bool isl_schedule_node_is_equal(
10250 __isl_keep isl_schedule_node *node1,
10251 __isl_keep isl_schedule_node *node2);
10253 The following properties can be obtained from a schedule node.
10255 #include <isl/schedule_node.h>
10256 enum isl_schedule_node_type isl_schedule_node_get_type(
10257 __isl_keep isl_schedule_node *node);
10258 enum isl_schedule_node_type
10259 isl_schedule_node_get_parent_type(
10260 __isl_keep isl_schedule_node *node);
10261 __isl_give isl_schedule *isl_schedule_node_get_schedule(
10262 __isl_keep isl_schedule_node *node);
10264 The function C<isl_schedule_node_get_type> returns the type of
10265 the node, while C<isl_schedule_node_get_parent_type> returns
10266 type of the parent of the node, which is required to exist.
10267 The function C<isl_schedule_node_get_schedule> returns a copy
10268 to the schedule to which the node belongs.
10270 The following functions can be used to move the schedule node
10271 to a different position in the tree or to check if such a position
10274 #include <isl/schedule_node.h>
10275 isl_bool isl_schedule_node_has_parent(
10276 __isl_keep isl_schedule_node *node);
10277 __isl_give isl_schedule_node *isl_schedule_node_parent(
10278 __isl_take isl_schedule_node *node);
10279 __isl_give isl_schedule_node *
10280 isl_schedule_node_grandparent(
10281 __isl_take isl_schedule_node *node);
10282 __isl_give isl_schedule_node *isl_schedule_node_root(
10283 __isl_take isl_schedule_node *node);
10284 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
10285 __isl_take isl_schedule_node *node,
10287 isl_size isl_schedule_node_n_children(
10288 __isl_keep isl_schedule_node *node);
10289 __isl_give isl_schedule_node *isl_schedule_node_child(
10290 __isl_take isl_schedule_node *node, int pos);
10291 isl_bool isl_schedule_node_has_children(
10292 __isl_keep isl_schedule_node *node);
10293 __isl_give isl_schedule_node *
10294 isl_schedule_node_grandchild(
10295 __isl_take isl_schedule_node *node,
10296 int pos1, int pos2);
10297 __isl_give isl_schedule_node *isl_schedule_node_first_child(
10298 __isl_take isl_schedule_node *node);
10299 isl_bool isl_schedule_node_has_previous_sibling(
10300 __isl_keep isl_schedule_node *node);
10301 __isl_give isl_schedule_node *
10302 isl_schedule_node_previous_sibling(
10303 __isl_take isl_schedule_node *node);
10304 isl_bool isl_schedule_node_has_next_sibling(
10305 __isl_keep isl_schedule_node *node);
10306 __isl_give isl_schedule_node *
10307 isl_schedule_node_next_sibling(
10308 __isl_take isl_schedule_node *node);
10310 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
10311 is the node itself, the ancestor of generation 1 is its parent and so on.
10313 It is also possible to query the number of ancestors of a node,
10314 the position of the current node
10315 within the children of its parent, the position of the subtree
10316 containing a node within the children of an ancestor
10317 or to obtain a copy of a given
10318 child without destroying the current node.
10319 Given two nodes that point to the same schedule, their closest
10320 shared ancestor can be obtained using
10321 C<isl_schedule_node_get_shared_ancestor>.
10323 #include <isl/schedule_node.h>
10324 isl_size isl_schedule_node_get_tree_depth(
10325 __isl_keep isl_schedule_node *node);
10326 isl_size isl_schedule_node_get_child_position(
10327 __isl_keep isl_schedule_node *node);
10328 isl_size isl_schedule_node_get_ancestor_child_position(
10329 __isl_keep isl_schedule_node *node,
10330 __isl_keep isl_schedule_node *ancestor);
10331 __isl_give isl_schedule_node *isl_schedule_node_get_child(
10332 __isl_keep isl_schedule_node *node, int pos);
10333 __isl_give isl_schedule_node *
10334 isl_schedule_node_get_shared_ancestor(
10335 __isl_keep isl_schedule_node *node1,
10336 __isl_keep isl_schedule_node *node2);
10338 All nodes in a schedule tree or
10339 all descendants of a specific node (including the node) can be visited
10340 in depth-first pre-order using the following functions.
10342 #include <isl/schedule.h>
10343 isl_stat isl_schedule_foreach_schedule_node_top_down(
10344 __isl_keep isl_schedule *sched,
10345 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
10346 void *user), void *user);
10348 #include <isl/schedule_node.h>
10349 isl_stat isl_schedule_node_foreach_descendant_top_down(
10350 __isl_keep isl_schedule_node *node,
10351 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
10352 void *user), void *user);
10354 The callback function is slightly different from the usual
10355 callbacks in that it not only indicates success (non-negative result)
10356 or failure (negative result), but also indicates whether the children
10357 of the given node should be visited. In particular, if the callback
10358 returns a positive value, then the children are visited, but if
10359 the callback returns zero, then the children are not visited.
10361 The following functions checks whether
10362 all descendants of a specific node (including the node itself)
10363 satisfy a user-specified test.
10365 #include <isl/schedule_node.h>
10366 isl_bool isl_schedule_node_every_descendant(
10367 __isl_keep isl_schedule_node *node,
10368 isl_bool (*test)(__isl_keep isl_schedule_node *node,
10369 void *user), void *user)
10371 The ancestors of a node in a schedule tree can be visited from
10372 the root down to and including the parent of the node using
10373 the following function.
10375 #include <isl/schedule_node.h>
10376 isl_stat isl_schedule_node_foreach_ancestor_top_down(
10377 __isl_keep isl_schedule_node *node,
10378 isl_stat (*fn)(__isl_keep isl_schedule_node *node,
10379 void *user), void *user);
10381 The following functions allows for a depth-first post-order
10382 traversal of the nodes in a schedule tree or
10383 of the descendants of a specific node (including the node
10384 itself), where the user callback is allowed to modify the
10387 #include <isl/schedule.h>
10388 __isl_give isl_schedule *
10389 isl_schedule_map_schedule_node_bottom_up(
10390 __isl_take isl_schedule *schedule,
10391 __isl_give isl_schedule_node *(*fn)(
10392 __isl_take isl_schedule_node *node,
10393 void *user), void *user);
10395 #include <isl/schedule_node.h>
10396 __isl_give isl_schedule_node *
10397 isl_schedule_node_map_descendant_bottom_up(
10398 __isl_take isl_schedule_node *node,
10399 __isl_give isl_schedule_node *(*fn)(
10400 __isl_take isl_schedule_node *node,
10401 void *user), void *user);
10403 The traversal continues from the node returned by the callback function.
10404 It is the responsibility of the user to ensure that this does not
10405 lead to an infinite loop. It is safest to always return a pointer
10406 to the same position (same ancestors and child positions) as the input node.
10408 The following function removes a node (along with its descendants)
10409 from a schedule tree and returns a pointer to the leaf at the
10410 same position in the updated tree.
10411 It is not allowed to remove the root of a schedule tree or
10412 a child of a set or sequence node.
10414 #include <isl/schedule_node.h>
10415 __isl_give isl_schedule_node *isl_schedule_node_cut(
10416 __isl_take isl_schedule_node *node);
10418 The following function removes a single node
10419 from a schedule tree and returns a pointer to the child
10420 of the node, now located at the position of the original node
10421 or to a leaf node at that position if there was no child.
10422 It is not allowed to remove the root of a schedule tree,
10423 a set or sequence node, a child of a set or sequence node or
10424 a band node with an anchored subtree.
10426 #include <isl/schedule_node.h>
10427 __isl_give isl_schedule_node *isl_schedule_node_delete(
10428 __isl_take isl_schedule_node *node);
10430 Most nodes in a schedule tree only contain local information.
10431 In some cases, however, a node may also refer to the schedule dimensions
10432 of its outer band nodes.
10433 This means that the position of the node within the tree should
10434 not be changed, or at least that no changes are performed to the
10435 outer band nodes. The following function can be used to test
10436 whether the subtree rooted at a given node contains any such nodes.
10438 #include <isl/schedule_node.h>
10439 isl_bool isl_schedule_node_is_subtree_anchored(
10440 __isl_keep isl_schedule_node *node);
10442 The following function resets the user pointers on all parameter
10443 and tuple identifiers referenced by the given schedule node.
10445 #include <isl/schedule_node.h>
10446 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
10447 __isl_take isl_schedule_node *node);
10449 The following function aligns the parameters of the given schedule
10450 node to the given space.
10452 #include <isl/schedule_node.h>
10453 __isl_give isl_schedule_node *
10454 isl_schedule_node_align_params(
10455 __isl_take isl_schedule_node *node,
10456 __isl_take isl_space *space);
10458 Several node types have their own functions for querying
10459 (and in some cases setting) some node type specific properties.
10461 #include <isl/schedule_node.h>
10462 __isl_give isl_space *isl_schedule_node_band_get_space(
10463 __isl_keep isl_schedule_node *node);
10464 __isl_give isl_multi_union_pw_aff *
10465 isl_schedule_node_band_get_partial_schedule(
10466 __isl_keep isl_schedule_node *node);
10467 __isl_give isl_union_map *
10468 isl_schedule_node_band_get_partial_schedule_union_map(
10469 __isl_keep isl_schedule_node *node);
10470 isl_size isl_schedule_node_band_n_member(
10471 __isl_keep isl_schedule_node *node);
10472 isl_bool isl_schedule_node_band_member_get_coincident(
10473 __isl_keep isl_schedule_node *node, int pos);
10474 __isl_give isl_schedule_node *
10475 isl_schedule_node_band_member_set_coincident(
10476 __isl_take isl_schedule_node *node, int pos,
10478 isl_bool isl_schedule_node_band_get_permutable(
10479 __isl_keep isl_schedule_node *node);
10480 __isl_give isl_schedule_node *
10481 isl_schedule_node_band_set_permutable(
10482 __isl_take isl_schedule_node *node, int permutable);
10483 enum isl_ast_loop_type
10484 isl_schedule_node_band_member_get_ast_loop_type(
10485 __isl_keep isl_schedule_node *node, int pos);
10486 __isl_give isl_schedule_node *
10487 isl_schedule_node_band_member_set_ast_loop_type(
10488 __isl_take isl_schedule_node *node, int pos,
10489 enum isl_ast_loop_type type);
10490 enum isl_ast_loop_type
10491 isl_schedule_node_band_member_get_isolate_ast_loop_type(
10492 __isl_keep isl_schedule_node *node, int pos);
10493 __isl_give isl_schedule_node *
10494 isl_schedule_node_band_member_set_isolate_ast_loop_type(
10495 __isl_take isl_schedule_node *node, int pos,
10496 enum isl_ast_loop_type type);
10497 __isl_give isl_union_set *
10498 isl_schedule_node_band_get_ast_build_options(
10499 __isl_keep isl_schedule_node *node);
10500 __isl_give isl_schedule_node *
10501 isl_schedule_node_band_set_ast_build_options(
10502 __isl_take isl_schedule_node *node,
10503 __isl_take isl_union_set *options);
10504 __isl_give isl_set *
10505 isl_schedule_node_band_get_ast_isolate_option(
10506 __isl_keep isl_schedule_node *node);
10508 The function C<isl_schedule_node_band_get_space> returns the space
10509 of the partial schedule of the band.
10510 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
10511 returns a representation of the partial schedule of the band node
10512 in the form of an C<isl_union_map>.
10513 The coincident and permutable properties are set by
10514 C<isl_schedule_constraints_compute_schedule> on the schedule tree
10516 A scheduling dimension is considered to be ``coincident''
10517 if it satisfies the coincidence constraints within its band.
10518 That is, if the dependence distances of the coincidence
10519 constraints are all zero in that direction (for fixed
10520 iterations of outer bands).
10521 A band is marked permutable if it was produced using the Pluto-like scheduler.
10522 Note that the scheduler may have to resort to a Feautrier style scheduling
10523 step even if the default scheduler is used.
10524 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
10525 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
10526 For the meaning of these loop AST generation types and the difference
10527 between the regular loop AST generation type and the isolate
10528 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
10529 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
10530 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
10531 may return C<isl_ast_loop_error> if an error occurs.
10532 The AST build options govern how an AST is generated for
10533 the individual schedule dimensions during AST generation.
10534 See L</"AST Generation Options (Schedule Tree)">.
10535 The isolate option for the given node can be extracted from these
10536 AST build options using the function
10537 C<isl_schedule_node_band_get_ast_isolate_option>.
10539 #include <isl/schedule_node.h>
10540 __isl_give isl_set *
10541 isl_schedule_node_context_get_context(
10542 __isl_keep isl_schedule_node *node);
10544 #include <isl/schedule_node.h>
10545 __isl_give isl_union_set *
10546 isl_schedule_node_domain_get_domain(
10547 __isl_keep isl_schedule_node *node);
10549 #include <isl/schedule_node.h>
10550 __isl_give isl_union_map *
10551 isl_schedule_node_expansion_get_expansion(
10552 __isl_keep isl_schedule_node *node);
10553 __isl_give isl_union_pw_multi_aff *
10554 isl_schedule_node_expansion_get_contraction(
10555 __isl_keep isl_schedule_node *node);
10557 #include <isl/schedule_node.h>
10558 __isl_give isl_union_map *
10559 isl_schedule_node_extension_get_extension(
10560 __isl_keep isl_schedule_node *node);
10562 #include <isl/schedule_node.h>
10563 __isl_give isl_union_set *
10564 isl_schedule_node_filter_get_filter(
10565 __isl_keep isl_schedule_node *node);
10567 #include <isl/schedule_node.h>
10568 __isl_give isl_set *isl_schedule_node_guard_get_guard(
10569 __isl_keep isl_schedule_node *node);
10571 #include <isl/schedule_node.h>
10572 __isl_give isl_id *isl_schedule_node_mark_get_id(
10573 __isl_keep isl_schedule_node *node);
10575 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
10576 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
10577 partial schedules related to the node.
10579 #include <isl/schedule_node.h>
10580 __isl_give isl_multi_union_pw_aff *
10581 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
10582 __isl_keep isl_schedule_node *node);
10583 __isl_give isl_union_pw_multi_aff *
10584 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
10585 __isl_keep isl_schedule_node *node);
10586 __isl_give isl_union_map *
10587 isl_schedule_node_get_prefix_schedule_union_map(
10588 __isl_keep isl_schedule_node *node);
10589 __isl_give isl_union_map *
10590 isl_schedule_node_get_prefix_schedule_relation(
10591 __isl_keep isl_schedule_node *node);
10592 __isl_give isl_union_map *
10593 isl_schedule_node_get_subtree_schedule_union_map(
10594 __isl_keep isl_schedule_node *node);
10596 In particular, the functions
10597 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
10598 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
10599 and C<isl_schedule_node_get_prefix_schedule_union_map>
10600 return a relative ordering on the domain elements that reach the given
10601 node determined by its ancestors.
10602 The function C<isl_schedule_node_get_prefix_schedule_relation>
10603 additionally includes the domain constraints in the result.
10604 The function C<isl_schedule_node_get_subtree_schedule_union_map>
10605 returns a representation of the partial schedule defined by the
10606 subtree rooted at the given node.
10607 If the tree contains any expansion nodes, then the subtree schedule
10608 is formulated in terms of the expanded domain elements.
10609 The tree passed to functions returning a prefix schedule
10610 may only contain extension nodes if these would not affect
10611 the result of these functions. That is, if one of the ancestors
10612 is an extension node, then all of the domain elements that were
10613 added by the extension node need to have been filtered out
10614 by filter nodes between the extension node and the input node.
10615 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
10616 may not contain in extension nodes in the selected subtree.
10618 The expansion/contraction defined by an entire subtree, combining
10619 the expansions/contractions
10620 on the expansion nodes in the subtree, can be obtained using
10621 the following functions.
10623 #include <isl/schedule_node.h>
10624 __isl_give isl_union_map *
10625 isl_schedule_node_get_subtree_expansion(
10626 __isl_keep isl_schedule_node *node);
10627 __isl_give isl_union_pw_multi_aff *
10628 isl_schedule_node_get_subtree_contraction(
10629 __isl_keep isl_schedule_node *node);
10631 The total number of outer band members of given node, i.e.,
10632 the shared output dimension of the maps in the result
10633 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
10634 using the following function.
10636 #include <isl/schedule_node.h>
10637 isl_size isl_schedule_node_get_schedule_depth(
10638 __isl_keep isl_schedule_node *node);
10640 The following functions return the elements that reach the given node
10641 or the union of universes in the spaces that contain these elements.
10643 #include <isl/schedule_node.h>
10644 __isl_give isl_union_set *
10645 isl_schedule_node_get_domain(
10646 __isl_keep isl_schedule_node *node);
10647 __isl_give isl_union_set *
10648 isl_schedule_node_get_universe_domain(
10649 __isl_keep isl_schedule_node *node);
10651 The input tree of C<isl_schedule_node_get_domain>
10652 may only contain extension nodes if these would not affect
10653 the result of this function. That is, if one of the ancestors
10654 is an extension node, then all of the domain elements that were
10655 added by the extension node need to have been filtered out
10656 by filter nodes between the extension node and the input node.
10658 The following functions can be used to introduce additional nodes
10659 in the schedule tree. The new node is introduced at the point
10660 in the tree where the C<isl_schedule_node> points to and
10661 the results points to the new node.
10663 #include <isl/schedule_node.h>
10664 __isl_give isl_schedule_node *
10665 isl_schedule_node_insert_partial_schedule(
10666 __isl_take isl_schedule_node *node,
10667 __isl_take isl_multi_union_pw_aff *schedule);
10669 This function inserts a new band node with (the greatest integer
10670 part of) the given partial schedule.
10671 The subtree rooted at the given node is assumed not to have
10672 any anchored nodes.
10674 #include <isl/schedule_node.h>
10675 __isl_give isl_schedule_node *
10676 isl_schedule_node_insert_context(
10677 __isl_take isl_schedule_node *node,
10678 __isl_take isl_set *context);
10680 This function inserts a new context node with the given context constraints.
10682 #include <isl/schedule_node.h>
10683 __isl_give isl_schedule_node *
10684 isl_schedule_node_insert_filter(
10685 __isl_take isl_schedule_node *node,
10686 __isl_take isl_union_set *filter);
10688 This function inserts a new filter node with the given filter.
10689 If the original node already pointed to a filter node, then the
10690 two filter nodes are merged into one.
10692 #include <isl/schedule_node.h>
10693 __isl_give isl_schedule_node *
10694 isl_schedule_node_insert_guard(
10695 __isl_take isl_schedule_node *node,
10696 __isl_take isl_set *guard);
10698 This function inserts a new guard node with the given guard constraints.
10700 #include <isl/schedule_node.h>
10701 __isl_give isl_schedule_node *
10702 isl_schedule_node_insert_mark(
10703 __isl_take isl_schedule_node *node,
10704 __isl_take isl_id *mark);
10706 This function inserts a new mark node with the give mark identifier.
10708 #include <isl/schedule_node.h>
10709 __isl_give isl_schedule_node *
10710 isl_schedule_node_insert_sequence(
10711 __isl_take isl_schedule_node *node,
10712 __isl_take isl_union_set_list *filters);
10713 __isl_give isl_schedule_node *
10714 isl_schedule_node_insert_set(
10715 __isl_take isl_schedule_node *node,
10716 __isl_take isl_union_set_list *filters);
10718 These functions insert a new sequence or set node with the given
10719 filters as children.
10721 #include <isl/schedule_node.h>
10722 __isl_give isl_schedule_node *isl_schedule_node_group(
10723 __isl_take isl_schedule_node *node,
10724 __isl_take isl_id *group_id);
10726 This function introduces an expansion node in between the current
10727 node and its parent that expands instances of a space with tuple
10728 identifier C<group_id> to the original domain elements that reach
10729 the node. The group instances are identified by the prefix schedule
10730 of those domain elements. The ancestors of the node are adjusted
10731 to refer to the group instances instead of the original domain
10732 elements. The return value points to the same node in the updated
10733 schedule tree as the input node, i.e., to the child of the newly
10734 introduced expansion node. Grouping instances of different statements
10735 ensures that they will be treated as a single statement by the
10736 AST generator up to the point of the expansion node.
10738 The following functions can be used to flatten a nested
10741 #include <isl/schedule_node.h>
10742 __isl_give isl_schedule_node *
10743 isl_schedule_node_sequence_splice_child(
10744 __isl_take isl_schedule_node *node, int pos);
10745 __isl_give isl_schedule_node *
10746 isl_schedule_node_sequence_splice_children(
10747 __isl_take isl_schedule_node *node);
10749 That is, given a sequence node C<node> that has another sequence node
10750 in its child at position C<pos> (in particular, the child of that filter
10751 node is a sequence node), the function
10752 C<isl_schedule_node_sequence_splice_child>
10753 attaches the children of that other sequence
10754 node as children of C<node>, replacing the original child at position
10756 C<isl_schedule_node_sequence_splice_children> does this for all
10759 The partial schedule of a band node can be scaled (down) or reduced using
10760 the following functions.
10762 #include <isl/schedule_node.h>
10763 __isl_give isl_schedule_node *
10764 isl_schedule_node_band_scale(
10765 __isl_take isl_schedule_node *node,
10766 __isl_take isl_multi_val *mv);
10767 __isl_give isl_schedule_node *
10768 isl_schedule_node_band_scale_down(
10769 __isl_take isl_schedule_node *node,
10770 __isl_take isl_multi_val *mv);
10771 __isl_give isl_schedule_node *
10772 isl_schedule_node_band_mod(
10773 __isl_take isl_schedule_node *node,
10774 __isl_take isl_multi_val *mv);
10776 The spaces of the two arguments need to match.
10777 After scaling, the partial schedule is replaced by its greatest
10778 integer part to ensure that the schedule remains integral.
10780 The partial schedule of a band node can be shifted by an
10781 C<isl_multi_union_pw_aff> with a domain that is a superset
10782 of the domain of the partial schedule using
10783 the following function.
10785 #include <isl/schedule_node.h>
10786 __isl_give isl_schedule_node *
10787 isl_schedule_node_band_shift(
10788 __isl_take isl_schedule_node *node,
10789 __isl_take isl_multi_union_pw_aff *shift);
10791 A band node can be tiled using the following function.
10793 #include <isl/schedule_node.h>
10794 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
10795 __isl_take isl_schedule_node *node,
10796 __isl_take isl_multi_val *sizes);
10798 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
10800 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
10801 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
10803 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
10805 The C<isl_schedule_node_band_tile> function tiles
10806 the band using the given tile sizes inside its schedule.
10807 A new child band node is created to represent the point loops and it is
10808 inserted between the modified band and its children.
10809 The subtree rooted at the given node is assumed not to have
10810 any anchored nodes.
10811 The C<tile_scale_tile_loops> option specifies whether the tile
10812 loops iterators should be scaled by the tile sizes.
10813 If the C<tile_shift_point_loops> option is set, then the point loops
10814 are shifted to start at zero.
10816 A band node can be split into two nested band nodes
10817 using the following function.
10819 #include <isl/schedule_node.h>
10820 __isl_give isl_schedule_node *isl_schedule_node_band_split(
10821 __isl_take isl_schedule_node *node, int pos);
10823 The resulting outer band node contains the first C<pos> dimensions of
10824 the schedule of C<node> while the inner band contains the remaining dimensions.
10825 The schedules of the two band nodes live in anonymous spaces.
10826 The loop AST generation type options and the isolate option
10827 are split over the two band nodes.
10829 A band node can be moved down to the leaves of the subtree rooted
10830 at the band node using the following function.
10832 #include <isl/schedule_node.h>
10833 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
10834 __isl_take isl_schedule_node *node);
10836 The subtree rooted at the given node is assumed not to have
10837 any anchored nodes.
10838 The result points to the node in the resulting tree that is in the same
10839 position as the node pointed to by C<node> in the original tree.
10841 #include <isl/schedule_node.h>
10842 __isl_give isl_schedule_node *
10843 isl_schedule_node_order_before(
10844 __isl_take isl_schedule_node *node,
10845 __isl_take isl_union_set *filter);
10846 __isl_give isl_schedule_node *
10847 isl_schedule_node_order_after(
10848 __isl_take isl_schedule_node *node,
10849 __isl_take isl_union_set *filter);
10851 These functions split the domain elements that reach C<node>
10852 into those that satisfy C<filter> and those that do not and
10853 arranges for the elements that do satisfy the filter to be
10854 executed before (in case of C<isl_schedule_node_order_before>)
10855 or after (in case of C<isl_schedule_node_order_after>)
10856 those that do not. The order is imposed by
10857 a sequence node, possibly reusing the grandparent of C<node>
10858 on two copies of the subtree attached to the original C<node>.
10859 Both copies are simplified with respect to their filter.
10861 Return a pointer to the copy of the subtree that does not
10862 satisfy C<filter>. If there is no such copy (because all
10863 reaching domain elements satisfy the filter), then return
10864 the original pointer.
10866 #include <isl/schedule_node.h>
10867 __isl_give isl_schedule_node *
10868 isl_schedule_node_graft_before(
10869 __isl_take isl_schedule_node *node,
10870 __isl_take isl_schedule_node *graft);
10871 __isl_give isl_schedule_node *
10872 isl_schedule_node_graft_after(
10873 __isl_take isl_schedule_node *node,
10874 __isl_take isl_schedule_node *graft);
10876 This function inserts the C<graft> tree into the tree containing C<node>
10877 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
10878 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
10879 The root node of C<graft>
10880 should be an extension node where the domain of the extension
10881 is the flat product of all outer band nodes of C<node>.
10882 The root node may also be a domain node.
10883 The elements of the domain or the range of the extension may not
10884 intersect with the domain elements that reach "node".
10885 The schedule tree of C<graft> may not be anchored.
10887 The schedule tree of C<node> is modified to include an extension node
10888 corresponding to the root node of C<graft> as a child of the original
10889 parent of C<node>. The original node that C<node> points to and the
10890 child of the root node of C<graft> are attached to this extension node
10891 through a sequence, with appropriate filters and with the child
10892 of C<graft> appearing before or after the original C<node>.
10894 If C<node> already appears inside a sequence that is the child of
10895 an extension node and if the spaces of the new domain elements
10896 do not overlap with those of the original domain elements,
10897 then that extension node is extended with the new extension
10898 rather than introducing a new segment of extension and sequence nodes.
10900 Return a pointer to the same node in the modified tree that
10901 C<node> pointed to in the original tree.
10903 A representation of the schedule node can be printed using
10905 #include <isl/schedule_node.h>
10906 __isl_give isl_printer *isl_printer_print_schedule_node(
10907 __isl_take isl_printer *p,
10908 __isl_keep isl_schedule_node *node);
10909 __isl_give char *isl_schedule_node_to_str(
10910 __isl_keep isl_schedule_node *node);
10912 C<isl_schedule_node_to_str> prints the schedule node in block format.
10914 =head2 Dependence Analysis
10916 C<isl> contains specialized functionality for performing
10917 array dataflow analysis. That is, given a I<sink> access relation,
10918 a collection of possible I<source> accesses and
10919 a collection of I<kill> accesses,
10920 C<isl> can compute relations that describe
10921 for each iteration of the sink access, which iterations
10922 of which of the source access relations may have
10923 accessed the same data element before the given iteration
10924 of the sink access without any intermediate kill of that data element.
10925 The resulting dependence relations map source iterations
10926 to either the corresponding sink iterations or
10927 pairs of corresponding sink iterations and accessed data elements.
10928 To compute standard flow dependences, the sink should be
10929 a read, while the sources should be writes.
10930 If no kills are specified,
10931 then memory based dependence analysis is performed.
10932 If, on the other hand, all sources are also kills,
10933 then value based dependence analysis is performed.
10934 If any of the source accesses are marked as being I<must>
10935 accesses, then they are also treated as kills.
10936 Furthermore, the specification of must-sources results
10937 in the computation of must-dependences.
10938 Only dependences originating in a must access not coscheduled
10939 with any other access to the same element and without
10940 any may accesses between the must access and the sink access
10941 are considered to be must dependences.
10943 =head3 High-level Interface
10945 A high-level interface to dependence analysis is provided
10946 by the following function.
10948 #include <isl/flow.h>
10949 __isl_give isl_union_flow *
10950 isl_union_access_info_compute_flow(
10951 __isl_take isl_union_access_info *access);
10953 The input C<isl_union_access_info> object describes the sink
10954 access relations, the source access relations and a schedule,
10955 while the output C<isl_union_flow> object describes
10956 the resulting dependence relations and the subsets of the
10957 sink relations for which no source was found.
10959 An C<isl_union_access_info> is created, modified, copied and freed using
10960 the following functions.
10962 #include <isl/flow.h>
10963 __isl_give isl_union_access_info *
10964 isl_union_access_info_from_sink(
10965 __isl_take isl_union_map *sink);
10966 __isl_give isl_union_access_info *
10967 isl_union_access_info_set_kill(
10968 __isl_take isl_union_access_info *access,
10969 __isl_take isl_union_map *kill);
10970 __isl_give isl_union_access_info *
10971 isl_union_access_info_set_may_source(
10972 __isl_take isl_union_access_info *access,
10973 __isl_take isl_union_map *may_source);
10974 __isl_give isl_union_access_info *
10975 isl_union_access_info_set_must_source(
10976 __isl_take isl_union_access_info *access,
10977 __isl_take isl_union_map *must_source);
10978 __isl_give isl_union_access_info *
10979 isl_union_access_info_set_schedule(
10980 __isl_take isl_union_access_info *access,
10981 __isl_take isl_schedule *schedule);
10982 __isl_give isl_union_access_info *
10983 isl_union_access_info_set_schedule_map(
10984 __isl_take isl_union_access_info *access,
10985 __isl_take isl_union_map *schedule_map);
10986 __isl_give isl_union_access_info *
10987 isl_union_access_info_copy(
10988 __isl_keep isl_union_access_info *access);
10989 __isl_null isl_union_access_info *
10990 isl_union_access_info_free(
10991 __isl_take isl_union_access_info *access);
10993 The may sources set by C<isl_union_access_info_set_may_source>
10994 do not need to include the must sources set by
10995 C<isl_union_access_info_set_must_source> as a subset.
10996 The kills set by C<isl_union_access_info_set_kill> may overlap
10997 with the may-sources and/or must-sources.
10998 The user is free not to call one (or more) of these functions,
10999 in which case the corresponding set is kept to its empty default.
11000 Similarly, the default schedule initialized by
11001 C<isl_union_access_info_from_sink> is empty.
11002 The current schedule is determined by the last call to either
11003 C<isl_union_access_info_set_schedule> or
11004 C<isl_union_access_info_set_schedule_map>.
11005 The domain of the schedule corresponds to the domains of
11006 the access relations. In particular, the domains of the access
11007 relations are effectively intersected with the domain of the schedule
11008 and only the resulting accesses are considered by the dependence analysis.
11010 An C<isl_union_access_info> object can be read from input
11011 using the following function.
11013 #include <isl/flow.h>
11014 __isl_give isl_union_access_info *
11015 isl_union_access_info_read_from_file(isl_ctx *ctx,
11018 A representation of the information contained in an object
11019 of type C<isl_union_access_info> can be obtained using
11021 #include <isl/flow.h>
11022 __isl_give isl_printer *
11023 isl_printer_print_union_access_info(
11024 __isl_take isl_printer *p,
11025 __isl_keep isl_union_access_info *access);
11026 __isl_give char *isl_union_access_info_to_str(
11027 __isl_keep isl_union_access_info *access);
11029 C<isl_union_access_info_to_str> prints the information in flow format.
11031 The output of C<isl_union_access_info_compute_flow> can be examined,
11032 copied, and freed using the following functions.
11034 #include <isl/flow.h>
11035 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
11036 __isl_keep isl_union_flow *flow);
11037 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
11038 __isl_keep isl_union_flow *flow);
11039 __isl_give isl_union_map *
11040 isl_union_flow_get_full_must_dependence(
11041 __isl_keep isl_union_flow *flow);
11042 __isl_give isl_union_map *
11043 isl_union_flow_get_full_may_dependence(
11044 __isl_keep isl_union_flow *flow);
11045 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
11046 __isl_keep isl_union_flow *flow);
11047 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
11048 __isl_keep isl_union_flow *flow);
11049 __isl_give isl_union_flow *isl_union_flow_copy(
11050 __isl_keep isl_union_flow *flow);
11051 __isl_null isl_union_flow *isl_union_flow_free(
11052 __isl_take isl_union_flow *flow);
11054 The relation returned by C<isl_union_flow_get_must_dependence>
11055 relates domain elements of must sources to domain elements of the sink.
11056 The relation returned by C<isl_union_flow_get_may_dependence>
11057 relates domain elements of must or may sources to domain elements of the sink
11058 and includes the previous relation as a subset.
11059 The relation returned by C<isl_union_flow_get_full_must_dependence>
11060 relates domain elements of must sources to pairs of domain elements of the sink
11061 and accessed data elements.
11062 The relation returned by C<isl_union_flow_get_full_may_dependence>
11063 relates domain elements of must or may sources to pairs of
11064 domain elements of the sink and accessed data elements.
11065 This relation includes the previous relation as a subset.
11066 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
11067 of the sink relation for which no dependences have been found.
11068 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
11069 of the sink relation for which no definite dependences have been found.
11070 That is, it contains those sink access that do not contribute to any
11071 of the elements in the relation returned
11072 by C<isl_union_flow_get_must_dependence>.
11074 A representation of the information contained in an object
11075 of type C<isl_union_flow> can be obtained using
11077 #include <isl/flow.h>
11078 __isl_give isl_printer *isl_printer_print_union_flow(
11079 __isl_take isl_printer *p,
11080 __isl_keep isl_union_flow *flow);
11081 __isl_give char *isl_union_flow_to_str(
11082 __isl_keep isl_union_flow *flow);
11084 C<isl_union_flow_to_str> prints the information in flow format.
11086 =head3 Low-level Interface
11088 A lower-level interface is provided by the following functions.
11090 #include <isl/flow.h>
11092 typedef int (*isl_access_level_before)(void *first, void *second);
11094 __isl_give isl_access_info *isl_access_info_alloc(
11095 __isl_take isl_map *sink,
11096 void *sink_user, isl_access_level_before fn,
11098 __isl_give isl_access_info *isl_access_info_add_source(
11099 __isl_take isl_access_info *acc,
11100 __isl_take isl_map *source, int must,
11101 void *source_user);
11102 __isl_null isl_access_info *isl_access_info_free(
11103 __isl_take isl_access_info *acc);
11105 __isl_give isl_flow *isl_access_info_compute_flow(
11106 __isl_take isl_access_info *acc);
11108 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,
11109 isl_stat (*fn)(__isl_take isl_map *dep, int must,
11110 void *dep_user, void *user),
11112 __isl_give isl_map *isl_flow_get_no_source(
11113 __isl_keep isl_flow *deps, int must);
11114 __isl_null isl_flow *isl_flow_free(
11115 __isl_take isl_flow *deps);
11117 The function C<isl_access_info_compute_flow> performs the actual
11118 dependence analysis. The other functions are used to construct
11119 the input for this function or to read off the output.
11121 The input is collected in an C<isl_access_info>, which can
11122 be created through a call to C<isl_access_info_alloc>.
11123 The arguments to this functions are the sink access relation
11124 C<sink>, a token C<sink_user> used to identify the sink
11125 access to the user, a callback function for specifying the
11126 relative order of source and sink accesses, and the number
11127 of source access relations that will be added.
11129 The callback function has type C<int (*)(void *first, void *second)>.
11130 The function is called with two user supplied tokens identifying
11131 either a source or the sink and it should return the shared nesting
11132 level and the relative order of the two accesses.
11133 In particular, let I<n> be the number of loops shared by
11134 the two accesses. If C<first> precedes C<second> textually,
11135 then the function should return I<2 * n + 1>; otherwise,
11136 it should return I<2 * n>.
11137 The low-level interface assumes that no sources are coscheduled.
11138 If the information returned by the callback does not allow
11139 the relative order to be determined, then one of the sources
11140 is arbitrarily taken to be executed after the other(s).
11142 The sources can be added to the C<isl_access_info> object by performing
11143 (at most) C<max_source> calls to C<isl_access_info_add_source>.
11144 C<must> indicates whether the source is a I<must> access
11145 or a I<may> access. Note that a multi-valued access relation
11146 should only be marked I<must> if every iteration in the domain
11147 of the relation accesses I<all> elements in its image.
11148 The C<source_user> token is again used to identify
11149 the source access. The range of the source access relation
11150 C<source> should have the same dimension as the range
11151 of the sink access relation.
11152 The C<isl_access_info_free> function should usually not be
11153 called explicitly, because it is already called implicitly by
11154 C<isl_access_info_compute_flow>.
11156 The result of the dependence analysis is collected in an
11157 C<isl_flow>. There may be elements of
11158 the sink access for which no preceding source access could be
11159 found or for which all preceding sources are I<may> accesses.
11160 The relations containing these elements can be obtained through
11161 calls to C<isl_flow_get_no_source>, the first with C<must> set
11162 and the second with C<must> unset.
11163 In the case of standard flow dependence analysis,
11164 with the sink a read and the sources I<must> writes,
11165 the first relation corresponds to the reads from uninitialized
11166 array elements and the second relation is empty.
11167 The actual flow dependences can be extracted using
11168 C<isl_flow_foreach>. This function will call the user-specified
11169 callback function C<fn> for each B<non-empty> dependence between
11170 a source and the sink. The callback function is called
11171 with four arguments, the actual flow dependence relation
11172 mapping source iterations to sink iterations, a boolean that
11173 indicates whether it is a I<must> or I<may> dependence, a token
11174 identifying the source and an additional C<void *> with value
11175 equal to the third argument of the C<isl_flow_foreach> call.
11176 A dependence is marked I<must> if it originates from a I<must>
11177 source and if it is not followed by any I<may> sources.
11179 After finishing with an C<isl_flow>, the user should call
11180 C<isl_flow_free> to free all associated memory.
11182 =head3 Interaction with the Low-level Interface
11184 During the dependence analysis, we frequently need to perform
11185 the following operation. Given a relation between sink iterations
11186 and potential source iterations from a particular source domain,
11187 what is the last potential source iteration corresponding to each
11188 sink iteration. It can sometimes be convenient to adjust
11189 the set of potential source iterations before or after each such operation.
11190 The prototypical example is fuzzy array dataflow analysis,
11191 where we need to analyze if, based on data-dependent constraints,
11192 the sink iteration can ever be executed without one or more of
11193 the corresponding potential source iterations being executed.
11194 If so, we can introduce extra parameters and select an unknown
11195 but fixed source iteration from the potential source iterations.
11196 To be able to perform such manipulations, C<isl> provides the following
11199 #include <isl/flow.h>
11201 typedef __isl_give isl_restriction *(*isl_access_restrict)(
11202 __isl_keep isl_map *source_map,
11203 __isl_keep isl_set *sink, void *source_user,
11205 __isl_give isl_access_info *isl_access_info_set_restrict(
11206 __isl_take isl_access_info *acc,
11207 isl_access_restrict fn, void *user);
11209 The function C<isl_access_info_set_restrict> should be called
11210 before calling C<isl_access_info_compute_flow> and registers a callback function
11211 that will be called any time C<isl> is about to compute the last
11212 potential source. The first argument is the (reverse) proto-dependence,
11213 mapping sink iterations to potential source iterations.
11214 The second argument represents the sink iterations for which
11215 we want to compute the last source iteration.
11216 The third argument is the token corresponding to the source
11217 and the final argument is the token passed to C<isl_access_info_set_restrict>.
11218 The callback is expected to return a restriction on either the input or
11219 the output of the operation computing the last potential source.
11220 If the input needs to be restricted then restrictions are needed
11221 for both the source and the sink iterations. The sink iterations
11222 and the potential source iterations will be intersected with these sets.
11223 If the output needs to be restricted then only a restriction on the source
11224 iterations is required.
11225 If any error occurs, the callback should return C<NULL>.
11226 An C<isl_restriction> object can be created, freed and inspected
11227 using the following functions.
11229 #include <isl/flow.h>
11231 __isl_give isl_restriction *isl_restriction_input(
11232 __isl_take isl_set *source_restr,
11233 __isl_take isl_set *sink_restr);
11234 __isl_give isl_restriction *isl_restriction_output(
11235 __isl_take isl_set *source_restr);
11236 __isl_give isl_restriction *isl_restriction_none(
11237 __isl_take isl_map *source_map);
11238 __isl_give isl_restriction *isl_restriction_empty(
11239 __isl_take isl_map *source_map);
11240 __isl_null isl_restriction *isl_restriction_free(
11241 __isl_take isl_restriction *restr);
11243 C<isl_restriction_none> and C<isl_restriction_empty> are special
11244 cases of C<isl_restriction_input>. C<isl_restriction_none>
11245 is essentially equivalent to
11247 isl_restriction_input(isl_set_universe(
11248 isl_space_range(isl_map_get_space(source_map))),
11250 isl_space_domain(isl_map_get_space(source_map))));
11252 whereas C<isl_restriction_empty> is essentially equivalent to
11254 isl_restriction_input(isl_set_empty(
11255 isl_space_range(isl_map_get_space(source_map))),
11257 isl_space_domain(isl_map_get_space(source_map))));
11261 #include <isl/schedule.h>
11262 __isl_give isl_schedule *
11263 isl_schedule_constraints_compute_schedule(
11264 __isl_take isl_schedule_constraints *sc);
11266 The function C<isl_schedule_constraints_compute_schedule> can be
11267 used to compute a schedule that satisfies the given schedule constraints.
11268 These schedule constraints include the iteration domain for which
11269 a schedule should be computed and dependences between pairs of
11270 iterations. In particular, these dependences include
11271 I<validity> dependences and I<proximity> dependences.
11272 By default, the algorithm used to construct the schedule is similar
11273 to that of C<Pluto>.
11274 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
11276 The generated schedule respects all validity dependences.
11277 That is, all dependence distances over these dependences in the
11278 scheduled space are lexicographically positive.
11280 The default algorithm tries to ensure that the dependence distances
11281 over coincidence constraints are zero and to minimize the
11282 dependence distances over proximity dependences.
11283 Moreover, it tries to obtain sequences (bands) of schedule dimensions
11284 for groups of domains where the dependence distances over validity
11285 dependences have only non-negative values.
11286 Note that when minimizing the maximal dependence distance
11287 over proximity dependences, a single affine expression in the parameters
11288 is constructed that bounds all dependence distances. If no such expression
11289 exists, then the algorithm will fail and resort to an alternative
11290 scheduling algorithm. In particular, this means that adding proximity
11291 dependences may eliminate valid solutions. A typical example where this
11292 phenomenon may occur is when some subset of the proximity dependences
11293 has no restriction on some parameter, forcing the coefficient of that
11294 parameter to be zero, while some other subset forces the dependence
11295 distance to depend on that parameter, requiring the same coefficient
11297 When using Feautrier's algorithm, the coincidence and proximity constraints
11298 are only taken into account during the extension to a
11299 full-dimensional schedule.
11301 An C<isl_schedule_constraints> object can be constructed
11302 and manipulated using the following functions.
11304 #include <isl/schedule.h>
11305 __isl_give isl_schedule_constraints *
11306 isl_schedule_constraints_copy(
11307 __isl_keep isl_schedule_constraints *sc);
11308 __isl_give isl_schedule_constraints *
11309 isl_schedule_constraints_on_domain(
11310 __isl_take isl_union_set *domain);
11311 __isl_give isl_schedule_constraints *
11312 isl_schedule_constraints_set_context(
11313 __isl_take isl_schedule_constraints *sc,
11314 __isl_take isl_set *context);
11315 __isl_give isl_schedule_constraints *
11316 isl_schedule_constraints_set_validity(
11317 __isl_take isl_schedule_constraints *sc,
11318 __isl_take isl_union_map *validity);
11319 __isl_give isl_schedule_constraints *
11320 isl_schedule_constraints_set_coincidence(
11321 __isl_take isl_schedule_constraints *sc,
11322 __isl_take isl_union_map *coincidence);
11323 __isl_give isl_schedule_constraints *
11324 isl_schedule_constraints_set_proximity(
11325 __isl_take isl_schedule_constraints *sc,
11326 __isl_take isl_union_map *proximity);
11327 __isl_give isl_schedule_constraints *
11328 isl_schedule_constraints_set_conditional_validity(
11329 __isl_take isl_schedule_constraints *sc,
11330 __isl_take isl_union_map *condition,
11331 __isl_take isl_union_map *validity);
11332 __isl_give isl_schedule_constraints *
11333 isl_schedule_constraints_apply(
11334 __isl_take isl_schedule_constraints *sc,
11335 __isl_take isl_union_map *umap);
11336 __isl_null isl_schedule_constraints *
11337 isl_schedule_constraints_free(
11338 __isl_take isl_schedule_constraints *sc);
11340 The initial C<isl_schedule_constraints> object created by
11341 C<isl_schedule_constraints_on_domain> does not impose any constraints.
11342 That is, it has an empty set of dependences.
11343 The function C<isl_schedule_constraints_set_context> allows the user
11344 to specify additional constraints on the parameters that may
11345 be assumed to hold during the construction of the schedule.
11346 The function C<isl_schedule_constraints_set_validity> replaces the
11347 validity dependences, mapping domain elements I<i> to domain
11348 elements that should be scheduled after I<i>.
11349 The function C<isl_schedule_constraints_set_coincidence> replaces the
11350 coincidence dependences, mapping domain elements I<i> to domain
11351 elements that should be scheduled together with I<I>, if possible.
11352 The function C<isl_schedule_constraints_set_proximity> replaces the
11353 proximity dependences, mapping domain elements I<i> to domain
11354 elements that should be scheduled either before I<I>
11355 or as early as possible after I<i>.
11357 The function C<isl_schedule_constraints_set_conditional_validity>
11358 replaces the conditional validity constraints.
11359 A conditional validity constraint is only imposed when any of the corresponding
11360 conditions is satisfied, i.e., when any of them is non-zero.
11361 That is, the scheduler ensures that within each band if the dependence
11362 distances over the condition constraints are not all zero
11363 then all corresponding conditional validity constraints are respected.
11364 A conditional validity constraint corresponds to a condition
11365 if the two are adjacent, i.e., if the domain of one relation intersect
11366 the range of the other relation.
11367 The typical use case of conditional validity constraints is
11368 to allow order constraints between live ranges to be violated
11369 as long as the live ranges themselves are local to the band.
11370 To allow more fine-grained control over which conditions correspond
11371 to which conditional validity constraints, the domains and ranges
11372 of these relations may include I<tags>. That is, the domains and
11373 ranges of those relation may themselves be wrapped relations
11374 where the iteration domain appears in the domain of those wrapped relations
11375 and the range of the wrapped relations can be arbitrarily chosen
11376 by the user. Conditions and conditional validity constraints are only
11377 considered adjacent to each other if the entire wrapped relation matches.
11378 In particular, a relation with a tag will never be considered adjacent
11379 to a relation without a tag.
11381 The function C<isl_schedule_constraints_apply> takes
11382 schedule constraints that are defined on some set of domain elements
11383 and transforms them to schedule constraints on the elements
11384 to which these domain elements are mapped by the given transformation.
11386 An C<isl_schedule_constraints> object can be inspected
11387 using the following functions.
11389 #include <isl/schedule.h>
11390 __isl_give isl_union_set *
11391 isl_schedule_constraints_get_domain(
11392 __isl_keep isl_schedule_constraints *sc);
11393 __isl_give isl_set *isl_schedule_constraints_get_context(
11394 __isl_keep isl_schedule_constraints *sc);
11395 __isl_give isl_union_map *
11396 isl_schedule_constraints_get_validity(
11397 __isl_keep isl_schedule_constraints *sc);
11398 __isl_give isl_union_map *
11399 isl_schedule_constraints_get_coincidence(
11400 __isl_keep isl_schedule_constraints *sc);
11401 __isl_give isl_union_map *
11402 isl_schedule_constraints_get_proximity(
11403 __isl_keep isl_schedule_constraints *sc);
11404 __isl_give isl_union_map *
11405 isl_schedule_constraints_get_conditional_validity(
11406 __isl_keep isl_schedule_constraints *sc);
11407 __isl_give isl_union_map *
11408 isl_schedule_constraints_get_conditional_validity_condition(
11409 __isl_keep isl_schedule_constraints *sc);
11411 An C<isl_schedule_constraints> object can be read from input
11412 using the following functions.
11414 #include <isl/schedule.h>
11415 __isl_give isl_schedule_constraints *
11416 isl_schedule_constraints_read_from_str(isl_ctx *ctx,
11418 __isl_give isl_schedule_constraints *
11419 isl_schedule_constraints_read_from_file(isl_ctx *ctx,
11422 The contents of an C<isl_schedule_constraints> object can be printed
11423 using the following functions.
11425 #include <isl/schedule.h>
11426 __isl_give isl_printer *
11427 isl_printer_print_schedule_constraints(
11428 __isl_take isl_printer *p,
11429 __isl_keep isl_schedule_constraints *sc);
11430 __isl_give char *isl_schedule_constraints_to_str(
11431 __isl_keep isl_schedule_constraints *sc);
11433 The following function computes a schedule directly from
11434 an iteration domain and validity and proximity dependences
11435 and is implemented in terms of the functions described above.
11436 The use of C<isl_union_set_compute_schedule> is discouraged.
11438 #include <isl/schedule.h>
11439 __isl_give isl_schedule *isl_union_set_compute_schedule(
11440 __isl_take isl_union_set *domain,
11441 __isl_take isl_union_map *validity,
11442 __isl_take isl_union_map *proximity);
11444 The generated schedule represents a schedule tree.
11445 For more information on schedule trees, see
11446 L</"Schedule Trees">.
11450 #include <isl/schedule.h>
11451 isl_stat isl_options_set_schedule_max_coefficient(
11452 isl_ctx *ctx, int val);
11453 int isl_options_get_schedule_max_coefficient(
11455 isl_stat isl_options_set_schedule_max_constant_term(
11456 isl_ctx *ctx, int val);
11457 int isl_options_get_schedule_max_constant_term(
11459 isl_stat isl_options_set_schedule_serialize_sccs(
11460 isl_ctx *ctx, int val);
11461 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx);
11462 isl_stat isl_options_set_schedule_whole_component(
11463 isl_ctx *ctx, int val);
11464 int isl_options_get_schedule_whole_component(
11466 isl_stat isl_options_set_schedule_maximize_band_depth(
11467 isl_ctx *ctx, int val);
11468 int isl_options_get_schedule_maximize_band_depth(
11470 isl_stat isl_options_set_schedule_maximize_coincidence(
11471 isl_ctx *ctx, int val);
11472 int isl_options_get_schedule_maximize_coincidence(
11474 isl_stat isl_options_set_schedule_outer_coincidence(
11475 isl_ctx *ctx, int val);
11476 int isl_options_get_schedule_outer_coincidence(
11478 isl_stat isl_options_set_schedule_split_scaled(
11479 isl_ctx *ctx, int val);
11480 int isl_options_get_schedule_split_scaled(
11482 isl_stat isl_options_set_schedule_treat_coalescing(
11483 isl_ctx *ctx, int val);
11484 int isl_options_get_schedule_treat_coalescing(
11486 isl_stat isl_options_set_schedule_algorithm(
11487 isl_ctx *ctx, int val);
11488 int isl_options_get_schedule_algorithm(
11490 isl_stat isl_options_set_schedule_carry_self_first(
11491 isl_ctx *ctx, int val);
11492 int isl_options_get_schedule_carry_self_first(
11494 isl_stat isl_options_set_schedule_separate_components(
11495 isl_ctx *ctx, int val);
11496 int isl_options_get_schedule_separate_components(
11501 =item * schedule_max_coefficient
11503 This option enforces that the coefficients for variable and parameter
11504 dimensions in the calculated schedule are not larger than the specified value.
11505 This option can significantly increase the speed of the scheduling calculation
11506 and may also prevent fusing of unrelated dimensions. A value of -1 means that
11507 this option does not introduce bounds on the variable or parameter
11509 This option has no effect on the Feautrier style scheduler.
11511 =item * schedule_max_constant_term
11513 This option enforces that the constant coefficients in the calculated schedule
11514 are not larger than the maximal constant term. This option can significantly
11515 increase the speed of the scheduling calculation and may also prevent fusing of
11516 unrelated dimensions. A value of -1 means that this option does not introduce
11517 bounds on the constant coefficients.
11519 =item * schedule_serialize_sccs
11521 If this option is set, then all strongly connected components
11522 in the dependence graph are serialized as soon as they are detected.
11523 This means in particular that instances of statements will only
11524 appear in the same band node if these statements belong
11525 to the same strongly connected component at the point where
11526 the band node is constructed.
11528 =item * schedule_whole_component
11530 If this option is set, then entire (weakly) connected
11531 components in the dependence graph are scheduled together
11533 Otherwise, each strongly connected component within
11534 such a weakly connected component is first scheduled separately
11535 and then combined with other strongly connected components.
11536 This option has no effect if C<schedule_serialize_sccs> is set.
11538 =item * schedule_maximize_band_depth
11540 If this option is set, then the scheduler tries to maximize
11541 the width of the bands. Wider bands give more possibilities for tiling.
11542 In particular, if the C<schedule_whole_component> option is set,
11543 then bands are split if this might result in wider bands.
11544 Otherwise, the effect of this option is to only allow
11545 strongly connected components to be combined if this does
11546 not reduce the width of the bands.
11547 Note that if the C<schedule_serialize_sccs> options is set, then
11548 the C<schedule_maximize_band_depth> option therefore has no effect.
11550 =item * schedule_maximize_coincidence
11552 This option is only effective if the C<schedule_whole_component>
11553 option is turned off.
11554 If the C<schedule_maximize_coincidence> option is set, then (clusters of)
11555 strongly connected components are only combined with each other
11556 if this does not reduce the number of coincident band members.
11558 =item * schedule_outer_coincidence
11560 If this option is set, then we try to construct schedules
11561 where the outermost scheduling dimension in each band
11562 satisfies the coincidence constraints.
11564 =item * schedule_algorithm
11566 Selects the scheduling algorithm to be used.
11567 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
11568 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
11570 =item * schedule_split_scaled
11572 If this option is set, then we try to construct schedules in which the
11573 constant term is split off from the linear part if the linear parts of
11574 the scheduling rows for all nodes in the graph have a common non-trivial
11576 The constant term is then dropped and the linear
11578 This option is only effective when the Feautrier style scheduler is
11579 being used, either as the main scheduler or as a fallback for the
11580 Pluto-like scheduler.
11582 =item * schedule_treat_coalescing
11584 If this option is set, then the scheduler will try and avoid
11585 producing schedules that perform loop coalescing.
11586 In particular, for the Pluto-like scheduler, this option places
11587 bounds on the schedule coefficients based on the sizes of the instance sets.
11588 For the Feautrier style scheduler, this option detects potentially
11589 coalescing schedules and then tries to adjust the schedule to avoid
11592 =item * schedule_carry_self_first
11594 If this option is set, then the Feautrier style scheduler
11595 (when used as a fallback for the Pluto-like scheduler) will
11596 first try to only carry self-dependences.
11598 =item * schedule_separate_components
11600 If this option is set then the function C<isl_schedule_get_map>
11601 will treat set nodes in the same way as sequence nodes.
11605 =head2 AST Generation
11607 This section describes the C<isl> functionality for generating
11608 ASTs that visit all the elements
11609 in a domain in an order specified by a schedule tree or
11611 In case the schedule given as a C<isl_union_map>, an AST is generated
11612 that visits all the elements in the domain of the C<isl_union_map>
11613 according to the lexicographic order of the corresponding image
11614 element(s). If the range of the C<isl_union_map> consists of
11615 elements in more than one space, then each of these spaces is handled
11616 separately in an arbitrary order.
11617 It should be noted that the schedule tree or the image elements
11618 in a schedule map only specify the I<order>
11619 in which the corresponding domain elements should be visited.
11620 No direct relation between the partial schedule values
11621 or the image elements on the one hand and the loop iterators
11622 in the generated AST on the other hand should be assumed.
11624 Each AST is generated within a build. The initial build
11625 simply specifies the constraints on the parameters (if any)
11626 and can be created, inspected, copied and freed using the following functions.
11628 #include <isl/ast_build.h>
11629 __isl_give isl_ast_build *isl_ast_build_alloc(
11631 __isl_give isl_ast_build *isl_ast_build_from_context(
11632 __isl_take isl_set *set);
11633 __isl_give isl_ast_build *isl_ast_build_copy(
11634 __isl_keep isl_ast_build *build);
11635 __isl_null isl_ast_build *isl_ast_build_free(
11636 __isl_take isl_ast_build *build);
11638 The C<set> argument is usually a parameter set with zero or more parameters.
11639 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
11640 this set is required to be a parameter set.
11641 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
11642 specify any parameter constraints.
11643 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
11644 and L</"Fine-grained Control over AST Generation">.
11645 Finally, the AST itself can be constructed using one of the following
11648 #include <isl/ast_build.h>
11649 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
11650 __isl_keep isl_ast_build *build,
11651 __isl_take isl_schedule *schedule);
11652 __isl_give isl_ast_node *
11653 isl_ast_build_node_from_schedule_map(
11654 __isl_keep isl_ast_build *build,
11655 __isl_take isl_union_map *schedule);
11657 =head3 Inspecting the AST
11659 The basic properties of an AST node can be obtained as follows.
11661 #include <isl/ast.h>
11662 enum isl_ast_node_type isl_ast_node_get_type(
11663 __isl_keep isl_ast_node *node);
11665 The type of an AST node is one of
11666 C<isl_ast_node_for>,
11667 C<isl_ast_node_if>,
11668 C<isl_ast_node_block>,
11669 C<isl_ast_node_mark> or
11670 C<isl_ast_node_user>.
11671 An C<isl_ast_node_for> represents a for node.
11672 An C<isl_ast_node_if> represents an if node.
11673 An C<isl_ast_node_block> represents a compound node.
11674 An C<isl_ast_node_mark> introduces a mark in the AST.
11675 An C<isl_ast_node_user> represents an expression statement.
11676 An expression statement typically corresponds to a domain element, i.e.,
11677 one of the elements that is visited by the AST.
11679 Each type of node has its own additional properties.
11681 #include <isl/ast.h>
11682 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
11683 __isl_keep isl_ast_node *node);
11684 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
11685 __isl_keep isl_ast_node *node);
11686 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
11687 __isl_keep isl_ast_node *node);
11688 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
11689 __isl_keep isl_ast_node *node);
11690 __isl_give isl_ast_node *isl_ast_node_for_get_body(
11691 __isl_keep isl_ast_node *node);
11692 isl_bool isl_ast_node_for_is_degenerate(
11693 __isl_keep isl_ast_node *node);
11695 An C<isl_ast_for> is considered degenerate if it is known to execute
11698 #include <isl/ast.h>
11699 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
11700 __isl_keep isl_ast_node *node);
11701 __isl_give isl_ast_node *isl_ast_node_if_get_then_node(
11702 __isl_keep isl_ast_node *node);
11703 __isl_give isl_ast_node *isl_ast_node_if_get_then(
11704 __isl_keep isl_ast_node *node);
11705 isl_bool isl_ast_node_if_has_else_node(
11706 __isl_keep isl_ast_node *node);
11707 isl_bool isl_ast_node_if_has_else(
11708 __isl_keep isl_ast_node *node);
11709 __isl_give isl_ast_node *isl_ast_node_if_get_else_node(
11710 __isl_keep isl_ast_node *node);
11711 __isl_give isl_ast_node *isl_ast_node_if_get_else(
11712 __isl_keep isl_ast_node *node);
11714 C<isl_ast_node_if_get_then>,
11715 C<isl_ast_node_if_has_else> and
11716 C<isl_ast_node_if_get_else>
11717 are alternative names for
11718 C<isl_ast_node_if_get_then_node>,
11719 C<isl_ast_node_if_has_else_node> and
11720 C<isl_ast_node_if_get_else_node>, respectively.
11722 __isl_give isl_ast_node_list *
11723 isl_ast_node_block_get_children(
11724 __isl_keep isl_ast_node *node);
11726 __isl_give isl_id *isl_ast_node_mark_get_id(
11727 __isl_keep isl_ast_node *node);
11728 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
11729 __isl_keep isl_ast_node *node);
11731 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
11732 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
11734 #include <isl/ast.h>
11735 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
11736 __isl_keep isl_ast_node *node);
11738 All descendants of a specific node in the AST (including the node itself)
11740 in depth-first pre-order using the following function.
11742 #include <isl/ast.h>
11743 isl_stat isl_ast_node_foreach_descendant_top_down(
11744 __isl_keep isl_ast_node *node,
11745 isl_bool (*fn)(__isl_keep isl_ast_node *node,
11746 void *user), void *user);
11748 The callback function should return C<isl_bool_true> if the children
11749 of the given node should be visited and C<isl_bool_false> if they should not.
11750 It should return C<isl_bool_error> in case of failure, in which case
11751 the entire traversal is aborted.
11753 Each of the returned C<isl_ast_expr>s can in turn be inspected using
11754 the following functions.
11756 #include <isl/ast.h>
11757 enum isl_ast_expr_type isl_ast_expr_get_type(
11758 __isl_keep isl_ast_expr *expr);
11760 The type of an AST expression is one of
11761 C<isl_ast_expr_op>,
11762 C<isl_ast_expr_id> or
11763 C<isl_ast_expr_int>.
11764 An C<isl_ast_expr_op> represents the result of an operation.
11765 An C<isl_ast_expr_id> represents an identifier.
11766 An C<isl_ast_expr_int> represents an integer value.
11768 Each type of expression has its own additional properties.
11770 #include <isl/ast.h>
11771 enum isl_ast_expr_op_type isl_ast_expr_op_get_type(
11772 __isl_keep isl_ast_expr *expr);
11773 enum isl_ast_expr_op_type isl_ast_expr_get_op_type(
11774 __isl_keep isl_ast_expr *expr);
11775 isl_size isl_ast_expr_op_get_n_arg(__isl_keep isl_ast_expr *expr);
11776 isl_size isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
11777 __isl_give isl_ast_expr *isl_ast_expr_op_get_arg(
11778 __isl_keep isl_ast_expr *expr, int pos);
11779 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
11780 __isl_keep isl_ast_expr *expr, int pos);
11781 isl_stat isl_ast_expr_foreach_ast_expr_op_type(
11782 __isl_keep isl_ast_expr *expr,
11783 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11784 void *user), void *user);
11785 isl_stat isl_ast_expr_foreach_ast_op_type(
11786 __isl_keep isl_ast_expr *expr,
11787 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11788 void *user), void *user);
11789 isl_stat isl_ast_node_foreach_ast_expr_op_type(
11790 __isl_keep isl_ast_node *node,
11791 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11792 void *user), void *user);
11793 isl_stat isl_ast_node_foreach_ast_op_type(
11794 __isl_keep isl_ast_node *node,
11795 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11796 void *user), void *user);
11798 C<isl_ast_expr_op_get_type> returns the type of the operation
11799 performed. C<isl_ast_expr_op_get_n_arg> returns the number of
11800 arguments. C<isl_ast_expr_get_op_arg> returns the specified
11802 C<isl_ast_expr_get_op_type> is an alternative name for
11803 C<isl_ast_expr_op_get_type>.
11805 C<isl_ast_expr_get_op_n_arg> is an alternative name for
11806 C<isl_ast_expr_op_get_n_arg> and
11807 C<isl_ast_expr_get_op_arg> is an alternative name for
11808 C<isl_ast_expr_op_get_arg>.
11810 C<isl_ast_expr_foreach_ast_expr_op_type> calls C<fn> for each distinct
11811 C<isl_ast_expr_op_type> that appears in C<expr>.
11812 C<isl_ast_expr_foreach_ast_op_type> is an alternative name for
11813 C<isl_ast_expr_foreach_ast_expr_op_type>.
11814 C<isl_ast_node_foreach_ast_expr_op_type> does the same for each distinct
11815 C<isl_ast_expr_op_type> that appears in C<node>.
11816 C<isl_ast_node_foreach_ast_op_type> is an alternative name for
11817 C<isl_ast_node_foreach_ast_expr_op_type>.
11818 The operation type is one of the following.
11822 =item C<isl_ast_expr_op_and>
11824 Logical I<and> of two arguments.
11825 Both arguments can be evaluated.
11827 =item C<isl_ast_expr_op_and_then>
11829 Logical I<and> of two arguments.
11830 The second argument can only be evaluated if the first evaluates to true.
11832 =item C<isl_ast_expr_op_or>
11834 Logical I<or> of two arguments.
11835 Both arguments can be evaluated.
11837 =item C<isl_ast_expr_op_or_else>
11839 Logical I<or> of two arguments.
11840 The second argument can only be evaluated if the first evaluates to false.
11842 =item C<isl_ast_expr_op_max>
11844 Maximum of two or more arguments.
11846 =item C<isl_ast_expr_op_min>
11848 Minimum of two or more arguments.
11850 =item C<isl_ast_expr_op_minus>
11854 =item C<isl_ast_expr_op_add>
11856 Sum of two arguments.
11858 =item C<isl_ast_expr_op_sub>
11860 Difference of two arguments.
11862 =item C<isl_ast_expr_op_mul>
11864 Product of two arguments.
11866 =item C<isl_ast_expr_op_div>
11868 Exact division. That is, the result is known to be an integer.
11870 =item C<isl_ast_expr_op_fdiv_q>
11872 Result of integer division, rounded towards negative
11874 The divisor is known to be positive.
11876 =item C<isl_ast_expr_op_pdiv_q>
11878 Result of integer division, where dividend is known to be non-negative.
11879 The divisor is known to be positive.
11881 =item C<isl_ast_expr_op_pdiv_r>
11883 Remainder of integer division, where dividend is known to be non-negative.
11884 The divisor is known to be positive.
11886 =item C<isl_ast_expr_op_zdiv_r>
11888 Equal to zero iff the remainder on integer division is zero.
11889 The divisor is known to be positive.
11891 =item C<isl_ast_expr_op_cond>
11893 Conditional operator defined on three arguments.
11894 If the first argument evaluates to true, then the result
11895 is equal to the second argument. Otherwise, the result
11896 is equal to the third argument.
11897 The second and third argument may only be evaluated if
11898 the first argument evaluates to true and false, respectively.
11899 Corresponds to C<a ? b : c> in C.
11901 =item C<isl_ast_expr_op_select>
11903 Conditional operator defined on three arguments.
11904 If the first argument evaluates to true, then the result
11905 is equal to the second argument. Otherwise, the result
11906 is equal to the third argument.
11907 The second and third argument may be evaluated independently
11908 of the value of the first argument.
11909 Corresponds to C<a * b + (1 - a) * c> in C.
11911 =item C<isl_ast_expr_op_eq>
11915 =item C<isl_ast_expr_op_le>
11917 Less than or equal relation.
11919 =item C<isl_ast_expr_op_lt>
11921 Less than relation.
11923 =item C<isl_ast_expr_op_ge>
11925 Greater than or equal relation.
11927 =item C<isl_ast_expr_op_gt>
11929 Greater than relation.
11931 =item C<isl_ast_expr_op_call>
11934 The number of arguments of the C<isl_ast_expr> is one more than
11935 the number of arguments in the function call, the first argument
11936 representing the function being called.
11938 =item C<isl_ast_expr_op_access>
11941 The number of arguments of the C<isl_ast_expr> is one more than
11942 the number of index expressions in the array access, the first argument
11943 representing the array being accessed.
11945 =item C<isl_ast_expr_op_member>
11948 This operation has two arguments, a structure and the name of
11949 the member of the structure being accessed.
11951 =item C<isl_ast_expr_op_address_of>
11953 The address of its single argument, which is always an array access.
11957 #include <isl/ast.h>
11958 __isl_give isl_id *isl_ast_expr_id_get_id(
11959 __isl_keep isl_ast_expr *expr);
11960 __isl_give isl_id *isl_ast_expr_get_id(
11961 __isl_keep isl_ast_expr *expr);
11963 Return the identifier represented by the AST expression.
11964 C<isl_ast_expr_get_id> is an alternative name for
11965 C<isl_ast_expr_id_get_id>.
11967 #include <isl/ast.h>
11968 __isl_give isl_val *isl_ast_expr_int_get_val(
11969 __isl_keep isl_ast_expr *expr);
11970 __isl_give isl_val *isl_ast_expr_get_val(
11971 __isl_keep isl_ast_expr *expr);
11973 Return the integer represented by the AST expression.
11974 C<isl_ast_expr_get_val> is an alternative name for
11975 C<isl_ast_expr_int_get_val>.
11977 =head3 Properties of ASTs
11979 #include <isl/ast.h>
11980 isl_bool isl_ast_expr_is_equal(
11981 __isl_keep isl_ast_expr *expr1,
11982 __isl_keep isl_ast_expr *expr2);
11984 Check if two C<isl_ast_expr>s are equal to each other.
11986 =head3 Manipulating and printing the AST
11988 AST nodes can be copied and freed using the following functions.
11990 #include <isl/ast.h>
11991 __isl_give isl_ast_node *isl_ast_node_copy(
11992 __isl_keep isl_ast_node *node);
11993 __isl_null isl_ast_node *isl_ast_node_free(
11994 __isl_take isl_ast_node *node);
11996 AST expressions can be copied and freed using the following functions.
11998 #include <isl/ast.h>
11999 __isl_give isl_ast_expr *isl_ast_expr_copy(
12000 __isl_keep isl_ast_expr *expr);
12001 __isl_null isl_ast_expr *isl_ast_expr_free(
12002 __isl_take isl_ast_expr *expr);
12004 New AST expressions can be created either directly or within
12005 the context of an C<isl_ast_build>.
12007 #include <isl/ast.h>
12008 __isl_give isl_ast_expr *isl_ast_expr_from_val(
12009 __isl_take isl_val *v);
12010 __isl_give isl_ast_expr *isl_ast_expr_from_id(
12011 __isl_take isl_id *id);
12012 __isl_give isl_ast_expr *isl_ast_expr_neg(
12013 __isl_take isl_ast_expr *expr);
12014 __isl_give isl_ast_expr *isl_ast_expr_address_of(
12015 __isl_take isl_ast_expr *expr);
12016 __isl_give isl_ast_expr *isl_ast_expr_add(
12017 __isl_take isl_ast_expr *expr1,
12018 __isl_take isl_ast_expr *expr2);
12019 __isl_give isl_ast_expr *isl_ast_expr_sub(
12020 __isl_take isl_ast_expr *expr1,
12021 __isl_take isl_ast_expr *expr2);
12022 __isl_give isl_ast_expr *isl_ast_expr_mul(
12023 __isl_take isl_ast_expr *expr1,
12024 __isl_take isl_ast_expr *expr2);
12025 __isl_give isl_ast_expr *isl_ast_expr_div(
12026 __isl_take isl_ast_expr *expr1,
12027 __isl_take isl_ast_expr *expr2);
12028 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
12029 __isl_take isl_ast_expr *expr1,
12030 __isl_take isl_ast_expr *expr2);
12031 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
12032 __isl_take isl_ast_expr *expr1,
12033 __isl_take isl_ast_expr *expr2);
12034 __isl_give isl_ast_expr *isl_ast_expr_and(
12035 __isl_take isl_ast_expr *expr1,
12036 __isl_take isl_ast_expr *expr2)
12037 __isl_give isl_ast_expr *isl_ast_expr_and_then(
12038 __isl_take isl_ast_expr *expr1,
12039 __isl_take isl_ast_expr *expr2)
12040 __isl_give isl_ast_expr *isl_ast_expr_or(
12041 __isl_take isl_ast_expr *expr1,
12042 __isl_take isl_ast_expr *expr2)
12043 __isl_give isl_ast_expr *isl_ast_expr_or_else(
12044 __isl_take isl_ast_expr *expr1,
12045 __isl_take isl_ast_expr *expr2)
12046 __isl_give isl_ast_expr *isl_ast_expr_eq(
12047 __isl_take isl_ast_expr *expr1,
12048 __isl_take isl_ast_expr *expr2);
12049 __isl_give isl_ast_expr *isl_ast_expr_le(
12050 __isl_take isl_ast_expr *expr1,
12051 __isl_take isl_ast_expr *expr2);
12052 __isl_give isl_ast_expr *isl_ast_expr_lt(
12053 __isl_take isl_ast_expr *expr1,
12054 __isl_take isl_ast_expr *expr2);
12055 __isl_give isl_ast_expr *isl_ast_expr_ge(
12056 __isl_take isl_ast_expr *expr1,
12057 __isl_take isl_ast_expr *expr2);
12058 __isl_give isl_ast_expr *isl_ast_expr_gt(
12059 __isl_take isl_ast_expr *expr1,
12060 __isl_take isl_ast_expr *expr2);
12061 __isl_give isl_ast_expr *isl_ast_expr_access(
12062 __isl_take isl_ast_expr *array,
12063 __isl_take isl_ast_expr_list *indices);
12064 __isl_give isl_ast_expr *isl_ast_expr_call(
12065 __isl_take isl_ast_expr *function,
12066 __isl_take isl_ast_expr_list *arguments);
12068 The function C<isl_ast_expr_address_of> can be applied to an
12069 C<isl_ast_expr> of type C<isl_ast_expr_op_access> only. It is meant
12070 to represent the address of the C<isl_ast_expr_access>.
12071 The second argument of the functions C<isl_ast_expr_pdiv_q> and
12072 C<isl_ast_expr_pdiv_r> should always evaluate to a positive number.
12074 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
12075 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
12077 #include <isl/ast_build.h>
12078 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
12079 __isl_keep isl_ast_build *build,
12080 __isl_take isl_set *set);
12081 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
12082 __isl_keep isl_ast_build *build,
12083 __isl_take isl_pw_aff *pa);
12084 __isl_give isl_ast_expr *
12085 isl_ast_build_access_from_pw_multi_aff(
12086 __isl_keep isl_ast_build *build,
12087 __isl_take isl_pw_multi_aff *pma);
12088 __isl_give isl_ast_expr *
12089 isl_ast_build_access_from_multi_pw_aff(
12090 __isl_keep isl_ast_build *build,
12091 __isl_take isl_multi_pw_aff *mpa);
12092 __isl_give isl_ast_expr *
12093 isl_ast_build_call_from_pw_multi_aff(
12094 __isl_keep isl_ast_build *build,
12095 __isl_take isl_pw_multi_aff *pma);
12096 __isl_give isl_ast_expr *
12097 isl_ast_build_call_from_multi_pw_aff(
12098 __isl_keep isl_ast_build *build,
12099 __isl_take isl_multi_pw_aff *mpa);
12102 the domains of C<pa>, C<mpa> and C<pma> should correspond
12103 to the schedule space of C<build>.
12104 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
12105 the function being called.
12106 If the accessed space is a nested relation, then it is taken
12107 to represent an access of the member specified by the range
12108 of this nested relation of the structure specified by the domain
12109 of the nested relation.
12111 The following functions can be used to modify an C<isl_ast_expr>.
12113 #include <isl/ast.h>
12114 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
12115 __isl_take isl_ast_expr *expr, int pos,
12116 __isl_take isl_ast_expr *arg);
12118 Replace the argument of C<expr> at position C<pos> by C<arg>.
12120 #include <isl/ast.h>
12121 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
12122 __isl_take isl_ast_expr *expr,
12123 __isl_take isl_id_to_ast_expr *id2expr);
12125 The function C<isl_ast_expr_substitute_ids> replaces the
12126 subexpressions of C<expr> of type C<isl_ast_expr_id>
12127 by the corresponding expression in C<id2expr>, if there is any.
12130 The following function can be used to modify the descendants
12131 of a specific node in an AST using a depth-first post-order
12132 traversal of those descendants (including the node itself).
12134 #include <isl/ast.h>
12135 __isl_give isl_ast_node *
12136 isl_ast_node_map_descendant_bottom_up(
12137 __isl_take isl_ast_node *node,
12138 __isl_give isl_ast_node *(*fn)(
12139 __isl_take isl_ast_node *node,
12140 void *user), void *user);
12142 User specified data can be attached to an C<isl_ast_node> and obtained
12143 from the same C<isl_ast_node> using the following functions.
12145 #include <isl/ast.h>
12146 __isl_give isl_ast_node *isl_ast_node_set_annotation(
12147 __isl_take isl_ast_node *node,
12148 __isl_take isl_id *annotation);
12149 __isl_give isl_id *isl_ast_node_get_annotation(
12150 __isl_keep isl_ast_node *node);
12152 Basic printing can be performed using the following functions.
12154 #include <isl/ast.h>
12155 __isl_give isl_printer *isl_printer_print_ast_expr(
12156 __isl_take isl_printer *p,
12157 __isl_keep isl_ast_expr *expr);
12158 __isl_give isl_printer *isl_printer_print_ast_node(
12159 __isl_take isl_printer *p,
12160 __isl_keep isl_ast_node *node);
12161 __isl_give char *isl_ast_expr_to_str(
12162 __isl_keep isl_ast_expr *expr);
12163 __isl_give char *isl_ast_node_to_str(
12164 __isl_keep isl_ast_node *node);
12165 __isl_give char *isl_ast_expr_to_C_str(
12166 __isl_keep isl_ast_expr *expr);
12167 __isl_give char *isl_ast_node_to_C_str(
12168 __isl_keep isl_ast_node *node);
12170 The functions C<isl_ast_expr_to_C_str> and
12171 C<isl_ast_node_to_C_str> are convenience functions
12172 that return a string representation of the input in C format.
12174 More advanced printing can be performed using the following functions.
12176 #include <isl/ast.h>
12177 __isl_give isl_printer *
12178 isl_ast_expr_op_type_set_print_name(
12179 __isl_take isl_printer *p,
12180 enum isl_ast_expr_op_type type,
12181 __isl_keep const char *name);
12182 __isl_give isl_printer *isl_ast_op_type_set_print_name(
12183 __isl_take isl_printer *p,
12184 enum isl_ast_expr_op_type type,
12185 __isl_keep const char *name);
12186 isl_stat isl_options_set_ast_print_macro_once(
12187 isl_ctx *ctx, int val);
12188 int isl_options_get_ast_print_macro_once(isl_ctx *ctx);
12189 __isl_give isl_printer *isl_ast_expr_op_type_print_macro(
12190 enum isl_ast_expr_op_type type,
12191 __isl_take isl_printer *p);
12192 __isl_give isl_printer *isl_ast_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_expr_print_macros(
12196 __isl_keep isl_ast_expr *expr,
12197 __isl_take isl_printer *p);
12198 __isl_give isl_printer *isl_ast_node_print_macros(
12199 __isl_keep isl_ast_node *node,
12200 __isl_take isl_printer *p);
12201 __isl_give isl_printer *isl_ast_node_print(
12202 __isl_keep isl_ast_node *node,
12203 __isl_take isl_printer *p,
12204 __isl_take isl_ast_print_options *options);
12205 __isl_give isl_printer *isl_ast_node_for_print(
12206 __isl_keep isl_ast_node *node,
12207 __isl_take isl_printer *p,
12208 __isl_take isl_ast_print_options *options);
12209 __isl_give isl_printer *isl_ast_node_if_print(
12210 __isl_keep isl_ast_node *node,
12211 __isl_take isl_printer *p,
12212 __isl_take isl_ast_print_options *options);
12214 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
12215 C<isl> may print out an AST that makes use of macros such
12216 as C<floord>, C<min> and C<max>.
12217 The names of these macros may be modified by a call
12218 to C<isl_ast_expr_op_type_set_print_name>. The user-specified
12219 names are associated to the printer object.
12220 C<isl_ast_op_type_set_print_name> is an alternative name for
12221 C<isl_ast_expr_op_type_set_print_name>.
12222 C<isl_ast_expr_op_type_print_macro> prints out the macro
12223 corresponding to a specific C<isl_ast_expr_op_type>.
12224 If the print-macro-once option is set, then a given macro definition
12225 is only printed once to any given printer object.
12226 C<isl_ast_op_type_print_macro> is an alternative name for
12227 C<isl_ast_expr_op_type_print_macro>.
12228 C<isl_ast_expr_print_macros> scans the C<isl_ast_expr>
12229 for subexpressions where these macros would be used and prints
12230 out the required macro definitions.
12231 Essentially, C<isl_ast_expr_print_macros> calls
12232 C<isl_ast_expr_foreach_ast_expr_op_type> with
12233 C<isl_ast_expr_op_type_print_macro>
12234 as function argument.
12235 C<isl_ast_node_print_macros> does the same
12236 for expressions in its C<isl_ast_node> argument.
12237 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
12238 C<isl_ast_node_if_print> print an C<isl_ast_node>
12239 in C<ISL_FORMAT_C>, but allow for some extra control
12240 through an C<isl_ast_print_options> object.
12241 This object can be created using the following functions.
12243 #include <isl/ast.h>
12244 __isl_give isl_ast_print_options *
12245 isl_ast_print_options_alloc(isl_ctx *ctx);
12246 __isl_give isl_ast_print_options *
12247 isl_ast_print_options_copy(
12248 __isl_keep isl_ast_print_options *options);
12249 __isl_null isl_ast_print_options *
12250 isl_ast_print_options_free(
12251 __isl_take isl_ast_print_options *options);
12253 __isl_give isl_ast_print_options *
12254 isl_ast_print_options_set_print_user(
12255 __isl_take isl_ast_print_options *options,
12256 __isl_give isl_printer *(*print_user)(
12257 __isl_take isl_printer *p,
12258 __isl_take isl_ast_print_options *options,
12259 __isl_keep isl_ast_node *node, void *user),
12261 __isl_give isl_ast_print_options *
12262 isl_ast_print_options_set_print_for(
12263 __isl_take isl_ast_print_options *options,
12264 __isl_give isl_printer *(*print_for)(
12265 __isl_take isl_printer *p,
12266 __isl_take isl_ast_print_options *options,
12267 __isl_keep isl_ast_node *node, void *user),
12270 The callback set by C<isl_ast_print_options_set_print_user>
12271 is called whenever a node of type C<isl_ast_node_user> needs to
12273 The callback set by C<isl_ast_print_options_set_print_for>
12274 is called whenever a node of type C<isl_ast_node_for> needs to
12276 Note that C<isl_ast_node_for_print> will I<not> call the
12277 callback set by C<isl_ast_print_options_set_print_for> on the node
12278 on which C<isl_ast_node_for_print> is called, but only on nested
12279 nodes of type C<isl_ast_node_for>. It is therefore safe to
12280 call C<isl_ast_node_for_print> from within the callback set by
12281 C<isl_ast_print_options_set_print_for>.
12283 The following option determines the type to be used for iterators
12284 while printing the AST.
12286 isl_stat isl_options_set_ast_iterator_type(
12287 isl_ctx *ctx, const char *val);
12288 const char *isl_options_get_ast_iterator_type(
12291 The AST printer only prints body nodes of C<if> and C<for> nodes
12293 blocks cannot be safely omitted.
12294 For example, a C<for> node with one body node will not be
12295 surrounded with braces in C<ISL_FORMAT_C>.
12296 A block will always be printed by setting the following option.
12298 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx,
12300 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
12302 Explicit block nodes that appear inside the AST are always printed as blocks.
12303 If the block node appears as the outermost node,
12304 then it is only printed if the following option is set.
12306 isl_stat isl_options_set_ast_print_outermost_block(
12307 isl_ctx *ctx, int val);
12308 int isl_options_get_ast_print_outermost_block(
12313 #include <isl/ast_build.h>
12314 isl_stat isl_options_set_ast_build_atomic_upper_bound(
12315 isl_ctx *ctx, int val);
12316 int isl_options_get_ast_build_atomic_upper_bound(
12318 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
12320 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
12321 isl_stat isl_options_set_ast_build_detect_min_max(
12322 isl_ctx *ctx, int val);
12323 int isl_options_get_ast_build_detect_min_max(
12325 isl_stat isl_options_set_ast_build_exploit_nested_bounds(
12326 isl_ctx *ctx, int val);
12327 int isl_options_get_ast_build_exploit_nested_bounds(
12329 isl_stat isl_options_set_ast_build_group_coscheduled(
12330 isl_ctx *ctx, int val);
12331 int isl_options_get_ast_build_group_coscheduled(
12333 isl_stat isl_options_set_ast_build_separation_bounds(
12334 isl_ctx *ctx, int val);
12335 int isl_options_get_ast_build_separation_bounds(
12337 isl_stat isl_options_set_ast_build_scale_strides(
12338 isl_ctx *ctx, int val);
12339 int isl_options_get_ast_build_scale_strides(
12341 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx,
12343 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
12344 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx,
12346 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
12350 =item * ast_build_atomic_upper_bound
12352 Generate loop upper bounds that consist of the current loop iterator,
12353 an operator and an expression not involving the iterator.
12354 If this option is not set, then the current loop iterator may appear
12355 several times in the upper bound.
12356 For example, when this option is turned off, AST generation
12359 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
12363 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
12366 When the option is turned on, the following AST is generated
12368 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
12371 =item * ast_build_prefer_pdiv
12373 If this option is turned off, then the AST generation will
12374 produce ASTs that may only contain C<isl_ast_expr_op_fdiv_q>
12375 operators, but no C<isl_ast_expr_op_pdiv_q> or
12376 C<isl_ast_expr_op_pdiv_r> operators.
12377 If this option is turned on, then C<isl> will try to convert
12378 some of the C<isl_ast_expr_op_fdiv_q> operators to (expressions containing)
12379 C<isl_ast_expr_op_pdiv_q> or C<isl_ast_expr_op_pdiv_r> operators.
12381 =item * ast_build_detect_min_max
12383 If this option is turned on, then C<isl> will try and detect
12384 min or max-expressions when building AST expressions from
12385 piecewise affine expressions.
12387 =item * ast_build_exploit_nested_bounds
12389 Simplify conditions based on bounds of nested for loops.
12390 In particular, remove conditions that are implied by the fact
12391 that one or more nested loops have at least one iteration,
12392 meaning that the upper bound is at least as large as the lower bound.
12393 For example, when this option is turned off, AST generation
12396 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
12402 for (int c0 = 0; c0 <= N; c0 += 1)
12403 for (int c1 = 0; c1 <= M; c1 += 1)
12406 When the option is turned on, the following AST is generated
12408 for (int c0 = 0; c0 <= N; c0 += 1)
12409 for (int c1 = 0; c1 <= M; c1 += 1)
12412 =item * ast_build_group_coscheduled
12414 If two domain elements are assigned the same schedule point, then
12415 they may be executed in any order and they may even appear in different
12416 loops. If this options is set, then the AST generator will make
12417 sure that coscheduled domain elements do not appear in separate parts
12418 of the AST. This is useful in case of nested AST generation
12419 if the outer AST generation is given only part of a schedule
12420 and the inner AST generation should handle the domains that are
12421 coscheduled by this initial part of the schedule together.
12422 For example if an AST is generated for a schedule
12424 { A[i] -> [0]; B[i] -> [0] }
12426 then the C<isl_ast_build_set_create_leaf> callback described
12427 below may get called twice, once for each domain.
12428 Setting this option ensures that the callback is only called once
12429 on both domains together.
12431 =item * ast_build_separation_bounds
12433 This option specifies which bounds to use during separation.
12434 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
12435 then all (possibly implicit) bounds on the current dimension will
12436 be used during separation.
12437 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
12438 then only those bounds that are explicitly available will
12439 be used during separation.
12441 =item * ast_build_scale_strides
12443 This option specifies whether the AST generator is allowed
12444 to scale down iterators of strided loops.
12446 =item * ast_build_allow_else
12448 This option specifies whether the AST generator is allowed
12449 to construct if statements with else branches.
12451 =item * ast_build_allow_or
12453 This option specifies whether the AST generator is allowed
12454 to construct if conditions with disjunctions.
12458 =head3 AST Generation Options (Schedule Tree)
12460 In case of AST construction from a schedule tree, the options
12461 that control how an AST is created from the individual schedule
12462 dimensions are stored in the band nodes of the tree
12463 (see L</"Schedule Trees">).
12465 In particular, a schedule dimension can be handled in four
12466 different ways, atomic, separate, unroll or the default.
12467 This loop AST generation type can be set using
12468 C<isl_schedule_node_band_member_set_ast_loop_type>.
12470 the first three can be selected by including a one-dimensional
12471 element with as value the position of the schedule dimension
12472 within the band and as name one of C<atomic>, C<separate>
12473 or C<unroll> in the options
12474 set by C<isl_schedule_node_band_set_ast_build_options>.
12475 Only one of these three may be specified for
12476 any given schedule dimension within a band node.
12477 If none of these is specified, then the default
12478 is used. The meaning of the options is as follows.
12484 When this option is specified, the AST generator will make
12485 sure that a given domain space only appears in a single
12486 loop at the specified level.
12488 For example, for the schedule tree
12490 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
12492 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
12493 options: "{ atomic[x] }"
12495 the following AST will be generated
12497 for (int c0 = 0; c0 <= 10; c0 += 1) {
12504 On the other hand, for the schedule tree
12506 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
12508 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
12509 options: "{ separate[x] }"
12511 the following AST will be generated
12515 for (int c0 = 1; c0 <= 9; c0 += 1) {
12522 If neither C<atomic> nor C<separate> is specified, then the AST generator
12523 may produce either of these two results or some intermediate form.
12527 When this option is specified, the AST generator will
12528 split the domain of the specified schedule dimension
12529 into pieces with a fixed set of statements for which
12530 instances need to be executed by the iterations in
12531 the schedule domain part. This option tends to avoid
12532 the generation of guards inside the corresponding loops.
12533 See also the C<atomic> option.
12537 When this option is specified, the AST generator will
12538 I<completely> unroll the corresponding schedule dimension.
12539 It is the responsibility of the user to ensure that such
12540 unrolling is possible.
12541 To obtain a partial unrolling, the user should apply an additional
12542 strip-mining to the schedule and fully unroll the inner schedule
12547 The C<isolate> option is a bit more involved. It allows the user
12548 to isolate a range of schedule dimension values from smaller and
12549 greater values. Additionally, the user may specify a different
12550 atomic/separate/unroll choice for the isolated part and the remaining
12551 parts. The typical use case of the C<isolate> option is to isolate
12552 full tiles from partial tiles.
12553 The part that needs to be isolated may depend on outer schedule dimensions.
12554 The option therefore needs to be able to reference those outer schedule
12555 dimensions. In particular, the space of the C<isolate> option is that
12556 of a wrapped map with as domain the flat product of all outer band nodes
12557 and as range the space of the current band node.
12558 The atomic/separate/unroll choice for the isolated part is determined
12559 by an option that lives in an unnamed wrapped space with as domain
12560 a zero-dimensional C<isolate> space and as range the regular
12561 C<atomic>, C<separate> or C<unroll> space.
12562 This option may also be set directly using
12563 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
12564 The atomic/separate/unroll choice for the remaining part is determined
12565 by the regular C<atomic>, C<separate> or C<unroll> option.
12566 Since the C<isolate> option references outer schedule dimensions,
12567 its use in a band node causes any tree containing the node
12568 to be considered anchored.
12570 As an example, consider the isolation of full tiles from partial tiles
12571 in a tiling of a triangular domain. The original schedule is as follows.
12573 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
12575 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
12576 { A[i,j] -> [floor(j/10)] }, \
12577 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
12581 for (int c0 = 0; c0 <= 10; c0 += 1)
12582 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12583 for (int c2 = 10 * c0;
12584 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12585 for (int c3 = 10 * c1;
12586 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12589 Isolating the full tiles, we have the following input
12591 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
12593 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
12594 { A[i,j] -> [floor(j/10)] }, \
12595 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
12596 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
12597 10a+9+10b+9 <= 100 }"
12602 for (int c0 = 0; c0 <= 8; c0 += 1) {
12603 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
12604 for (int c2 = 10 * c0;
12605 c2 <= 10 * c0 + 9; c2 += 1)
12606 for (int c3 = 10 * c1;
12607 c3 <= 10 * c1 + 9; c3 += 1)
12609 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
12610 for (int c2 = 10 * c0;
12611 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12612 for (int c3 = 10 * c1;
12613 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12616 for (int c0 = 9; c0 <= 10; c0 += 1)
12617 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12618 for (int c2 = 10 * c0;
12619 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12620 for (int c3 = 10 * c1;
12621 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12625 We may then additionally unroll the innermost loop of the isolated part
12627 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
12629 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
12630 { A[i,j] -> [floor(j/10)] }, \
12631 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
12632 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
12633 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
12638 for (int c0 = 0; c0 <= 8; c0 += 1) {
12639 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
12640 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
12642 A(c2, 10 * c1 + 1);
12643 A(c2, 10 * c1 + 2);
12644 A(c2, 10 * c1 + 3);
12645 A(c2, 10 * c1 + 4);
12646 A(c2, 10 * c1 + 5);
12647 A(c2, 10 * c1 + 6);
12648 A(c2, 10 * c1 + 7);
12649 A(c2, 10 * c1 + 8);
12650 A(c2, 10 * c1 + 9);
12652 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
12653 for (int c2 = 10 * c0;
12654 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12655 for (int c3 = 10 * c1;
12656 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12659 for (int c0 = 9; c0 <= 10; c0 += 1)
12660 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12661 for (int c2 = 10 * c0;
12662 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12663 for (int c3 = 10 * c1;
12664 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12669 =head3 AST Generation Options (Schedule Map)
12671 In case of AST construction using
12672 C<isl_ast_build_node_from_schedule_map>, the options
12673 that control how an AST is created from the individual schedule
12674 dimensions are stored in the C<isl_ast_build>.
12675 They can be set using the following function.
12677 #include <isl/ast_build.h>
12678 __isl_give isl_ast_build *
12679 isl_ast_build_set_options(
12680 __isl_take isl_ast_build *build,
12681 __isl_take isl_union_map *options);
12683 The options are encoded in an C<isl_union_map>.
12684 The domain of this union relation refers to the schedule domain,
12685 i.e., the range of the schedule passed
12686 to C<isl_ast_build_node_from_schedule_map>.
12687 In the case of nested AST generation (see L</"Nested AST Generation">),
12688 the domain of C<options> should refer to the extra piece of the schedule.
12689 That is, it should be equal to the range of the wrapped relation in the
12690 range of the schedule.
12691 The range of the options can consist of elements in one or more spaces,
12692 the names of which determine the effect of the option.
12693 The values of the range typically also refer to the schedule dimension
12694 to which the option applies, with value C<0> representing
12695 the outermost schedule dimension. In case of nested AST generation
12696 (see L</"Nested AST Generation">), these values refer to the position
12697 of the schedule dimension within the innermost AST generation.
12698 The constraints on the domain elements of
12699 the option should only refer to this dimension and earlier dimensions.
12700 We consider the following spaces.
12704 =item C<separation_class>
12706 B<This option has been deprecated. Use the isolate option on
12707 schedule trees instead.>
12709 This space is a wrapped relation between two one dimensional spaces.
12710 The input space represents the schedule dimension to which the option
12711 applies and the output space represents the separation class.
12712 While constructing a loop corresponding to the specified schedule
12713 dimension(s), the AST generator will try to generate separate loops
12714 for domain elements that are assigned different classes.
12715 If only some of the elements are assigned a class, then those elements
12716 that are not assigned any class will be treated as belonging to a class
12717 that is separate from the explicitly assigned classes.
12718 The typical use case for this option is to separate full tiles from
12720 The other options, described below, are applied after the separation
12723 As an example, consider the separation into full and partial tiles
12724 of a tiling of a triangular domain.
12725 Take, for example, the domain
12727 { A[i,j] : 0 <= i,j and i + j <= 100 }
12729 and a tiling into tiles of 10 by 10. The input to the AST generator
12730 is then the schedule
12732 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
12735 Without any options, the following AST is generated
12737 for (int c0 = 0; c0 <= 10; c0 += 1)
12738 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12739 for (int c2 = 10 * c0;
12740 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
12742 for (int c3 = 10 * c1;
12743 c3 <= min(10 * c1 + 9, -c2 + 100);
12747 Separation into full and partial tiles can be obtained by assigning
12748 a class, say C<0>, to the full tiles. The full tiles are represented by those
12749 values of the first and second schedule dimensions for which there are
12750 values of the third and fourth dimensions to cover an entire tile.
12751 That is, we need to specify the following option
12753 { [a,b,c,d] -> separation_class[[0]->[0]] :
12754 exists b': 0 <= 10a,10b' and
12755 10a+9+10b'+9 <= 100;
12756 [a,b,c,d] -> separation_class[[1]->[0]] :
12757 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
12759 which simplifies to
12761 { [a, b, c, d] -> separation_class[[1] -> [0]] :
12762 a >= 0 and b >= 0 and b <= 8 - a;
12763 [a, b, c, d] -> separation_class[[0] -> [0]] :
12764 a >= 0 and a <= 8 }
12766 With this option, the generated AST is as follows
12769 for (int c0 = 0; c0 <= 8; c0 += 1) {
12770 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
12771 for (int c2 = 10 * c0;
12772 c2 <= 10 * c0 + 9; c2 += 1)
12773 for (int c3 = 10 * c1;
12774 c3 <= 10 * c1 + 9; c3 += 1)
12776 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
12777 for (int c2 = 10 * c0;
12778 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
12780 for (int c3 = 10 * c1;
12781 c3 <= min(-c2 + 100, 10 * c1 + 9);
12785 for (int c0 = 9; c0 <= 10; c0 += 1)
12786 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12787 for (int c2 = 10 * c0;
12788 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
12790 for (int c3 = 10 * c1;
12791 c3 <= min(10 * c1 + 9, -c2 + 100);
12798 This is a single-dimensional space representing the schedule dimension(s)
12799 to which ``separation'' should be applied. Separation tries to split
12800 a loop into several pieces if this can avoid the generation of guards
12802 See also the C<atomic> option.
12806 This is a single-dimensional space representing the schedule dimension(s)
12807 for which the domains should be considered ``atomic''. That is, the
12808 AST generator will make sure that any given domain space will only appear
12809 in a single loop at the specified level.
12811 Consider the following schedule
12813 { a[i] -> [i] : 0 <= i < 10;
12814 b[i] -> [i+1] : 0 <= i < 10 }
12816 If the following option is specified
12818 { [i] -> separate[x] }
12820 then the following AST will be generated
12824 for (int c0 = 1; c0 <= 9; c0 += 1) {
12831 If, on the other hand, the following option is specified
12833 { [i] -> atomic[x] }
12835 then the following AST will be generated
12837 for (int c0 = 0; c0 <= 10; c0 += 1) {
12844 If neither C<atomic> nor C<separate> is specified, then the AST generator
12845 may produce either of these two results or some intermediate form.
12849 This is a single-dimensional space representing the schedule dimension(s)
12850 that should be I<completely> unrolled.
12851 To obtain a partial unrolling, the user should apply an additional
12852 strip-mining to the schedule and fully unroll the inner loop.
12856 =head3 Fine-grained Control over AST Generation
12858 Besides specifying the constraints on the parameters,
12859 an C<isl_ast_build> object can be used to control
12860 various aspects of the AST generation process.
12861 In case of AST construction using
12862 C<isl_ast_build_node_from_schedule_map>,
12863 the most prominent way of control is through ``options'',
12864 as explained above.
12866 Additional control is available through the following functions.
12868 #include <isl/ast_build.h>
12869 __isl_give isl_ast_build *
12870 isl_ast_build_set_iterators(
12871 __isl_take isl_ast_build *build,
12872 __isl_take isl_id_list *iterators);
12874 The function C<isl_ast_build_set_iterators> allows the user to
12875 specify a list of iterator C<isl_id>s to be used as iterators.
12876 If the input schedule is injective, then
12877 the number of elements in this list should be as large as the dimension
12878 of the schedule space, but no direct correspondence should be assumed
12879 between dimensions and elements.
12880 If the input schedule is not injective, then an additional number
12881 of C<isl_id>s equal to the largest dimension of the input domains
12883 If the number of provided C<isl_id>s is insufficient, then additional
12884 names are automatically generated.
12886 #include <isl/ast_build.h>
12887 __isl_give isl_ast_build *
12888 isl_ast_build_set_create_leaf(
12889 __isl_take isl_ast_build *build,
12890 __isl_give isl_ast_node *(*fn)(
12891 __isl_take isl_ast_build *build,
12892 void *user), void *user);
12895 C<isl_ast_build_set_create_leaf> function allows for the
12896 specification of a callback that should be called whenever the AST
12897 generator arrives at an element of the schedule domain.
12898 The callback should return an AST node that should be inserted
12899 at the corresponding position of the AST. The default action (when
12900 the callback is not set) is to continue generating parts of the AST to scan
12901 all the domain elements associated to the schedule domain element
12902 and to insert user nodes, ``calling'' the domain element, for each of them.
12903 The C<build> argument contains the current state of the C<isl_ast_build>.
12904 To ease nested AST generation (see L</"Nested AST Generation">),
12905 all control information that is
12906 specific to the current AST generation such as the options and
12907 the callbacks has been removed from this C<isl_ast_build>.
12908 The callback would typically return the result of a nested
12909 AST generation or a
12910 user defined node created using the following function.
12912 #include <isl/ast.h>
12913 __isl_give isl_ast_node *isl_ast_node_user_from_expr(
12914 __isl_take isl_ast_expr *expr);
12915 __isl_give isl_ast_node *isl_ast_node_alloc_user(
12916 __isl_take isl_ast_expr *expr);
12918 C<isl_ast_node_alloc_user> is an alternative name for
12919 C<isl_ast_node_user_from_expr>.
12921 In some cases, a single user defined node is not enough,
12922 in which case the following function can be used
12923 to create a block node from multiple AST nodes.
12925 #include <isl/ast.h>
12926 __isl_give isl_ast_node *isl_ast_node_block_from_children(
12927 __isl_take isl_ast_node_list *list);
12929 #include <isl/ast_build.h>
12930 __isl_give isl_ast_build *
12931 isl_ast_build_set_at_each_domain(
12932 __isl_take isl_ast_build *build,
12933 __isl_give isl_ast_node *(*fn)(
12934 __isl_take isl_ast_node *node,
12935 __isl_keep isl_ast_build *build,
12936 void *user), void *user);
12937 __isl_give isl_ast_build *
12938 isl_ast_build_set_before_each_for(
12939 __isl_take isl_ast_build *build,
12940 __isl_give isl_id *(*fn)(
12941 __isl_keep isl_ast_build *build,
12942 void *user), void *user);
12943 __isl_give isl_ast_build *
12944 isl_ast_build_set_after_each_for(
12945 __isl_take isl_ast_build *build,
12946 __isl_give isl_ast_node *(*fn)(
12947 __isl_take isl_ast_node *node,
12948 __isl_keep isl_ast_build *build,
12949 void *user), void *user);
12950 __isl_give isl_ast_build *
12951 isl_ast_build_set_before_each_mark(
12952 __isl_take isl_ast_build *build,
12953 isl_stat (*fn)(__isl_keep isl_id *mark,
12954 __isl_keep isl_ast_build *build,
12955 void *user), void *user);
12956 __isl_give isl_ast_build *
12957 isl_ast_build_set_after_each_mark(
12958 __isl_take isl_ast_build *build,
12959 __isl_give isl_ast_node *(*fn)(
12960 __isl_take isl_ast_node *node,
12961 __isl_keep isl_ast_build *build,
12962 void *user), void *user);
12964 The callback set by C<isl_ast_build_set_at_each_domain> will
12965 be called for each domain AST node.
12966 The callbacks set by C<isl_ast_build_set_before_each_for>
12967 and C<isl_ast_build_set_after_each_for> will be called
12968 for each for AST node. The first will be called in depth-first
12969 pre-order, while the second will be called in depth-first post-order.
12970 Since C<isl_ast_build_set_before_each_for> is called before the for
12971 node is actually constructed, it is only passed an C<isl_ast_build>.
12972 The returned C<isl_id> will be added as an annotation (using
12973 C<isl_ast_node_set_annotation>) to the constructed for node.
12974 In particular, if the user has also specified an C<after_each_for>
12975 callback, then the annotation can be retrieved from the node passed to
12976 that callback using C<isl_ast_node_get_annotation>.
12977 The callbacks set by C<isl_ast_build_set_before_each_mark>
12978 and C<isl_ast_build_set_after_each_mark> will be called for each
12979 mark AST node that is created, i.e., for each mark schedule node
12980 in the input schedule tree. The first will be called in depth-first
12981 pre-order, while the second will be called in depth-first post-order.
12982 Since the callback set by C<isl_ast_build_set_before_each_mark>
12983 is called before the mark AST node is actually constructed, it is passed
12984 the identifier of the mark node.
12985 All callbacks should C<NULL> (or C<isl_stat_error>) on failure.
12986 The given C<isl_ast_build> can be used to create new
12987 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
12988 or C<isl_ast_build_call_from_pw_multi_aff>.
12990 =head3 Nested AST Generation
12992 C<isl> allows the user to create an AST within the context
12993 of another AST. These nested ASTs are created using the
12994 same C<isl_ast_build_node_from_schedule_map> function that is used to create
12995 the outer AST. The C<build> argument should be an C<isl_ast_build>
12996 passed to a callback set by
12997 C<isl_ast_build_set_create_leaf>.
12998 The space of the range of the C<schedule> argument should refer
12999 to this build. In particular, the space should be a wrapped
13000 relation and the domain of this wrapped relation should be the
13001 same as that of the range of the schedule returned by
13002 C<isl_ast_build_get_schedule> below.
13003 In practice, the new schedule is typically
13004 created by calling C<isl_union_map_range_product> on the old schedule
13005 and some extra piece of the schedule.
13006 The space of the schedule domain is also available from
13007 the C<isl_ast_build>.
13009 #include <isl/ast_build.h>
13010 __isl_give isl_union_map *isl_ast_build_get_schedule(
13011 __isl_keep isl_ast_build *build);
13012 __isl_give isl_space *isl_ast_build_get_schedule_space(
13013 __isl_keep isl_ast_build *build);
13014 __isl_give isl_ast_build *isl_ast_build_restrict(
13015 __isl_take isl_ast_build *build,
13016 __isl_take isl_set *set);
13018 The C<isl_ast_build_get_schedule> function returns a (partial)
13019 schedule for the domains elements for which part of the AST still needs to
13020 be generated in the current build.
13021 In particular, the domain elements are mapped to those iterations of the loops
13022 enclosing the current point of the AST generation inside which
13023 the domain elements are executed.
13024 No direct correspondence between
13025 the input schedule and this schedule should be assumed.
13026 The space obtained from C<isl_ast_build_get_schedule_space> can be used
13027 to create a set for C<isl_ast_build_restrict> to intersect
13028 with the current build. In particular, the set passed to
13029 C<isl_ast_build_restrict> can have additional parameters.
13030 The ids of the set dimensions in the space returned by
13031 C<isl_ast_build_get_schedule_space> correspond to the
13032 iterators of the already generated loops.
13033 The user should not rely on the ids of the output dimensions
13034 of the relations in the union relation returned by
13035 C<isl_ast_build_get_schedule> having any particular value.
13037 =head1 Applications
13039 Although C<isl> is mainly meant to be used as a library,
13040 it also contains some basic applications that use some
13041 of the functionality of C<isl>.
13042 For applications that take one or more polytopes or polyhedra
13043 as input, this input may be specified in either the L<isl format>
13044 or the L<PolyLib format>.
13046 =head2 C<isl_polyhedron_sample>
13048 C<isl_polyhedron_sample> takes a polyhedron as input and prints
13049 an integer element of the polyhedron, if there is any.
13050 The first column in the output is the denominator and is always
13051 equal to 1. If the polyhedron contains no integer points,
13052 then a vector of length zero is printed.
13056 C<isl_pip> takes the same input as the C<example> program
13057 from the C<piplib> distribution, i.e., a set of constraints
13058 on the parameters, a line containing only -1 and finally a set
13059 of constraints on a parametric polyhedron.
13060 The coefficients of the parameters appear in the last columns
13061 (but before the final constant column).
13062 The output is the lexicographic minimum of the parametric polyhedron.
13063 As C<isl> currently does not have its own output format, the output
13064 is just a dump of the internal state.
13066 =head2 C<isl_polyhedron_minimize>
13068 C<isl_polyhedron_minimize> computes the minimum of some linear
13069 or affine objective function over the integer points in a polyhedron.
13070 If an affine objective function
13071 is given, then the constant should appear in the last column.
13073 =head2 C<isl_polytope_scan>
13075 Given a polytope, C<isl_polytope_scan> prints
13076 all integer points in the polytope.
13080 Given an C<isl_union_access_info> object as input,
13081 C<isl_flow> prints out the corresponding dependences,
13082 as computed by C<isl_union_access_info_compute_flow>.
13084 =head2 C<isl_codegen>
13086 Given either a schedule tree or a sequence consisting of
13087 a schedule map, a context set and an options relation,
13088 C<isl_codegen> prints out an AST that scans the domain elements
13089 of the schedule in the order of their image(s) taking into account
13090 the constraints in the context set.
13092 =head2 C<isl_schedule>
13094 Given an C<isl_schedule_constraints> object as input,
13095 C<isl_schedule> prints out a schedule that satisfies the given