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);
5432 #include <isl/map.h>
5433 __isl_give isl_basic_map *isl_basic_map_reverse(
5434 __isl_take isl_basic_map *bmap);
5435 __isl_give isl_map *isl_map_reverse(
5436 __isl_take isl_map *map);
5437 __isl_give isl_map *isl_map_range_reverse(
5438 __isl_take isl_map *map);
5440 #include <isl/union_map.h>
5441 __isl_give isl_union_map *isl_union_map_reverse(
5442 __isl_take isl_union_map *umap);
5443 __isl_give isl_union_map *isl_union_map_range_reverse(
5444 __isl_take isl_union_map *umap);
5446 The function C<isl_space_range_reverse> reverses the relation
5447 that is embedded in the range of the input map space.
5448 The identifier of the range, if any, is only preserved
5449 if this embedded relation has identical input and output tuples.
5450 Similarly for C<isl_space_domain_reverse>.
5451 Along the same lines, C<isl_space_wrapped_reverse> reverses
5452 the relation that is embedded in a set space.
5454 =item * Tuple binding
5456 The following function binds
5457 a tuple to a sequence of parameter identifiers, equating
5458 the tuple dimensions to the parameters with those identifiers and
5459 subsequently projecting out the tuple.
5460 If the original object did not reference any such parameters,
5461 then this means that the tuple dimensions are reinterpreted
5463 The space of C<tuple> needs to match that of the bound tuple.
5465 #include <isl/set.h>
5466 __isl_give isl_set *isl_set_bind(
5467 __isl_take isl_set *set,
5468 __isl_take isl_multi_id *tuple);
5470 #include <isl/map.h>
5471 __isl_give isl_set *isl_map_bind_domain(
5472 __isl_take isl_map *map,
5473 __isl_take isl_multi_id *tuple);
5474 __isl_give isl_set *isl_map_bind_range(
5475 __isl_take isl_map *map,
5476 __isl_take isl_multi_id *tuple);
5478 #include <isl/union_map.h>
5479 __isl_give isl_union_set *isl_union_map_bind_range(
5480 __isl_take isl_union_map *umap,
5481 __isl_take isl_multi_id *tuple);
5483 #include <isl/aff.h>
5484 __isl_give isl_pw_aff *isl_pw_aff_bind_domain(
5485 __isl_take isl_pw_aff *pa,
5486 __isl_take isl_multi_id *tuple);
5487 __isl_give isl_multi_aff *isl_multi_aff_bind_domain(
5488 __isl_take isl_multi_aff *ma,
5489 __isl_take isl_multi_id *tuple);
5490 __isl_give isl_pw_multi_aff *
5491 isl_pw_multi_aff_bind_domain(
5492 __isl_take isl_pw_multi_aff *pma,
5493 __isl_take isl_multi_id *tuple);
5494 __isl_give isl_multi_pw_aff *
5495 isl_multi_pw_aff_bind_domain(
5496 __isl_take isl_multi_pw_aff *mpa,
5497 __isl_take isl_multi_id *tuple);
5498 __isl_give isl_pw_aff *
5499 isl_pw_aff_bind_domain_wrapped_domain(
5500 __isl_take isl_pw_aff *pa,
5501 __isl_take isl_multi_id *tuple);
5502 __isl_give isl_multi_aff *
5503 isl_multi_aff_bind_domain_wrapped_domain(
5504 __isl_take isl_multi_aff *ma,
5505 __isl_take isl_multi_id *tuple);
5506 __isl_give isl_pw_multi_aff *
5507 isl_pw_multi_aff_bind_domain_wrapped_domain(
5508 __isl_take isl_pw_multi_aff *pma,
5509 __isl_take isl_multi_id *tuple);
5510 __isl_give isl_multi_pw_aff *
5511 isl_multi_pw_aff_bind_domain_wrapped_domain(
5512 __isl_take isl_multi_pw_aff *mpa,
5513 __isl_take isl_multi_id *tuple);
5514 __isl_give isl_basic_set *isl_aff_bind_id(
5515 __isl_take isl_aff *aff,
5516 __isl_take isl_id *id);
5517 __isl_give isl_set *isl_pw_aff_bind_id(
5518 __isl_take isl_pw_aff *pa,
5519 __isl_take isl_id *id);
5520 __isl_give isl_basic_set *isl_multi_aff_bind(
5521 __isl_take isl_multi_aff *ma,
5522 __isl_take isl_multi_id *tuple);
5523 __isl_give isl_set *isl_multi_pw_aff_bind(
5524 __isl_take isl_multi_pw_aff *mpa,
5525 __isl_take isl_multi_id *tuple);
5526 __isl_give isl_union_set *isl_union_pw_aff_bind_id(
5527 __isl_take isl_union_pw_aff *upa,
5528 __isl_take isl_id *id);
5529 __isl_give isl_union_set *
5530 isl_multi_union_pw_aff_bind(
5531 __isl_take isl_multi_union_pw_aff *mupa,
5532 __isl_take isl_multi_id *tuple);
5534 Projecting out the domain of the wrapped relation in the domain
5535 of a function leaves the range of that wrapped relation
5536 in the domain of the resulting function.
5537 In the case of C<isl_aff_bind_id>, C<isl_pw_aff_bind_id>,
5538 C<isl_multi_aff_bind>, C<isl_multi_pw_aff_bind>,
5539 C<isl_union_pw_aff_bind_id> and
5540 C<isl_multi_union_pw_aff_bind>, the parameters
5541 are bound to the function values and the result lives
5542 in the domain of the input function.
5546 #include <isl/space.h>
5547 __isl_give isl_space *isl_space_domain(
5548 __isl_take isl_space *space);
5549 __isl_give isl_space *isl_space_range(
5550 __isl_take isl_space *space);
5551 __isl_give isl_space *isl_space_params(
5552 __isl_take isl_space *space);
5553 __isl_give isl_space *
5554 isl_space_domain_wrapped_domain(
5555 __isl_take isl_space *space);
5556 __isl_give isl_space *
5557 isl_space_domain_wrapped_range(
5558 __isl_take isl_space *space);
5559 __isl_give isl_space *
5560 isl_space_range_wrapped_domain(
5561 __isl_take isl_space *space);
5562 __isl_give isl_space *
5563 isl_space_range_wrapped_range(
5564 __isl_take isl_space *space);
5566 #include <isl/local_space.h>
5567 __isl_give isl_local_space *isl_local_space_domain(
5568 __isl_take isl_local_space *ls);
5569 __isl_give isl_local_space *isl_local_space_range(
5570 __isl_take isl_local_space *ls);
5572 #include <isl/set.h>
5573 __isl_give isl_basic_set *isl_basic_set_project_out(
5574 __isl_take isl_basic_set *bset,
5575 enum isl_dim_type type, unsigned first, unsigned n);
5576 __isl_give isl_set *isl_set_project_out_param_id(
5577 __isl_take isl_set *set,
5578 __isl_take isl_id *id);
5579 __isl_give isl_set *
5580 isl_set_project_out_param_id_list(
5581 __isl_take isl_set *set,
5582 __isl_take isl_id_list *list);
5583 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
5584 enum isl_dim_type type, unsigned first, unsigned n);
5585 __isl_give isl_set *isl_set_project_out_all_params(
5586 __isl_take isl_set *set);
5587 __isl_give isl_map *isl_set_project_onto_map(
5588 __isl_take isl_set *set,
5589 enum isl_dim_type type, unsigned first,
5591 __isl_give isl_basic_set *isl_basic_set_params(
5592 __isl_take isl_basic_set *bset);
5593 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
5595 The function C<isl_space_domain_wrapped_domain> returns the domain
5596 of the binary relation wrapped inside the domain of the input.
5597 The function C<isl_set_project_onto_map> returns a relation
5598 that projects the input set onto the given set dimensions.
5600 #include <isl/map.h>
5601 __isl_give isl_basic_map *isl_basic_map_project_out(
5602 __isl_take isl_basic_map *bmap,
5603 enum isl_dim_type type, unsigned first, unsigned n);
5604 __isl_give isl_map *isl_map_project_out_param_id(
5605 __isl_take isl_map *map,
5606 __isl_take isl_id *id);
5607 __isl_give isl_map *isl_map_project_out_param_id_list(
5608 __isl_take isl_map *map,
5609 __isl_take isl_id_list *list);
5610 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
5611 enum isl_dim_type type, unsigned first, unsigned n);
5612 __isl_give isl_map *isl_map_project_out_all_params(
5613 __isl_take isl_map *map);
5614 __isl_give isl_basic_set *isl_basic_map_domain(
5615 __isl_take isl_basic_map *bmap);
5616 __isl_give isl_basic_set *isl_basic_map_range(
5617 __isl_take isl_basic_map *bmap);
5618 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
5619 __isl_give isl_set *isl_map_domain(
5620 __isl_take isl_map *bmap);
5621 __isl_give isl_set *isl_map_range(
5622 __isl_take isl_map *map);
5624 #include <isl/union_set.h>
5625 __isl_give isl_union_set *isl_union_set_project_out(
5626 __isl_take isl_union_set *uset,
5627 enum isl_dim_type type,
5628 unsigned first, unsigned n);
5629 __isl_give isl_union_set *
5630 isl_union_set_project_out_all_params(
5631 __isl_take isl_union_set *uset);
5632 __isl_give isl_set *isl_union_set_params(
5633 __isl_take isl_union_set *uset);
5635 The function C<isl_union_set_project_out> can only project out
5638 #include <isl/union_map.h>
5639 __isl_give isl_union_map *
5640 isl_union_map_project_out_param_id(
5641 __isl_take isl_union_map *umap,
5642 __isl_take isl_id *id);
5643 __isl_give isl_union_map *
5644 isl_union_map_project_out_param_id_list(
5645 __isl_take isl_union_map *umap,
5646 __isl_take isl_id_list *list);
5647 __isl_give isl_union_map *isl_union_map_project_out(
5648 __isl_take isl_union_map *umap,
5649 enum isl_dim_type type, unsigned first, unsigned n);
5650 __isl_give isl_union_map *
5651 isl_union_map_project_out_all_params(
5652 __isl_take isl_union_map *umap);
5653 __isl_give isl_set *isl_union_map_params(
5654 __isl_take isl_union_map *umap);
5655 __isl_give isl_union_set *isl_union_map_domain(
5656 __isl_take isl_union_map *umap);
5657 __isl_give isl_union_set *isl_union_map_range(
5658 __isl_take isl_union_map *umap);
5660 The function C<isl_union_map_project_out> can only project out
5663 #include <isl/aff.h>
5664 __isl_give isl_aff *isl_aff_project_domain_on_params(
5665 __isl_take isl_aff *aff);
5666 __isl_give isl_multi_aff *
5667 isl_multi_aff_project_domain_on_params(
5668 __isl_take isl_multi_aff *ma);
5669 __isl_give isl_pw_aff *
5670 isl_pw_aff_project_domain_on_params(
5671 __isl_take isl_pw_aff *pa);
5672 __isl_give isl_multi_pw_aff *
5673 isl_multi_pw_aff_project_domain_on_params(
5674 __isl_take isl_multi_pw_aff *mpa);
5675 __isl_give isl_pw_multi_aff *
5676 isl_pw_multi_aff_project_domain_on_params(
5677 __isl_take isl_pw_multi_aff *pma);
5678 __isl_give isl_set *isl_pw_aff_domain(
5679 __isl_take isl_pw_aff *pwaff);
5680 __isl_give isl_set *isl_pw_multi_aff_domain(
5681 __isl_take isl_pw_multi_aff *pma);
5682 __isl_give isl_set *isl_multi_pw_aff_domain(
5683 __isl_take isl_multi_pw_aff *mpa);
5684 __isl_give isl_union_set *isl_union_pw_aff_domain(
5685 __isl_take isl_union_pw_aff *upa);
5686 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
5687 __isl_take isl_union_pw_multi_aff *upma);
5688 __isl_give isl_union_set *
5689 isl_multi_union_pw_aff_domain(
5690 __isl_take isl_multi_union_pw_aff *mupa);
5691 __isl_give isl_set *isl_pw_aff_params(
5692 __isl_take isl_pw_aff *pwa);
5694 If no explicit domain was set on a zero-dimensional input to
5695 C<isl_multi_union_pw_aff_domain>, then this function will
5696 return a parameter set.
5698 #include <isl/polynomial.h>
5699 __isl_give isl_qpolynomial *
5700 isl_qpolynomial_project_domain_on_params(
5701 __isl_take isl_qpolynomial *qp);
5702 __isl_give isl_pw_qpolynomial *
5703 isl_pw_qpolynomial_project_domain_on_params(
5704 __isl_take isl_pw_qpolynomial *pwqp);
5705 __isl_give isl_pw_qpolynomial_fold *
5706 isl_pw_qpolynomial_fold_project_domain_on_params(
5707 __isl_take isl_pw_qpolynomial_fold *pwf);
5708 __isl_give isl_set *isl_pw_qpolynomial_domain(
5709 __isl_take isl_pw_qpolynomial *pwqp);
5710 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5711 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5712 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5713 __isl_take isl_union_pw_qpolynomial *upwqp);
5715 #include <isl/space.h>
5716 __isl_give isl_space *isl_space_domain_map(
5717 __isl_take isl_space *space);
5718 __isl_give isl_space *isl_space_range_map(
5719 __isl_take isl_space *space);
5721 #include <isl/map.h>
5722 __isl_give isl_map *isl_set_wrapped_domain_map(
5723 __isl_take isl_set *set);
5724 __isl_give isl_basic_map *isl_basic_map_domain_map(
5725 __isl_take isl_basic_map *bmap);
5726 __isl_give isl_basic_map *isl_basic_map_range_map(
5727 __isl_take isl_basic_map *bmap);
5728 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
5729 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
5731 #include <isl/union_map.h>
5732 __isl_give isl_union_map *isl_union_map_domain_map(
5733 __isl_take isl_union_map *umap);
5734 __isl_give isl_union_pw_multi_aff *
5735 isl_union_map_domain_map_union_pw_multi_aff(
5736 __isl_take isl_union_map *umap);
5737 __isl_give isl_union_map *isl_union_map_range_map(
5738 __isl_take isl_union_map *umap);
5739 __isl_give isl_union_map *
5740 isl_union_set_wrapped_domain_map(
5741 __isl_take isl_union_set *uset);
5743 The functions above construct a (basic, regular or union) relation
5744 that maps (a wrapped version of) the input relation to its domain or range.
5745 C<isl_set_wrapped_domain_map> maps the input set to the domain
5746 of its wrapped relation.
5750 __isl_give isl_basic_set *isl_basic_set_eliminate(
5751 __isl_take isl_basic_set *bset,
5752 enum isl_dim_type type,
5753 unsigned first, unsigned n);
5754 __isl_give isl_set *isl_set_eliminate(
5755 __isl_take isl_set *set, enum isl_dim_type type,
5756 unsigned first, unsigned n);
5757 __isl_give isl_basic_map *isl_basic_map_eliminate(
5758 __isl_take isl_basic_map *bmap,
5759 enum isl_dim_type type,
5760 unsigned first, unsigned n);
5761 __isl_give isl_map *isl_map_eliminate(
5762 __isl_take isl_map *map, enum isl_dim_type type,
5763 unsigned first, unsigned n);
5765 Eliminate the coefficients for the given dimensions from the constraints,
5766 without removing the dimensions.
5768 =item * Constructing a set from a parameter domain
5770 A set space of a given dimension and with an optional name
5771 can be created from a parameter space using the following functions.
5773 #include <isl/space.h>
5774 __isl_give isl_space *isl_space_add_unnamed_tuple_ui(
5775 __isl_take isl_space *space, unsigned dim);
5776 __isl_give isl_space *
5777 isl_space_add_named_tuple_id_ui(
5778 __isl_take isl_space *space,
5779 __isl_take isl_id *tuple_id, unsigned dim);
5781 A set with a given tuple can be created from a parameter domain
5782 using the following function.
5784 #include <isl/set.h>
5785 __isl_give isl_set *isl_set_unbind_params(
5786 __isl_take isl_set *set,
5787 __isl_take isl_multi_id *tuple);
5789 Any parameters with identifiers in C<tuple> are reinterpreted
5790 as the corresponding set dimensions.
5792 A zero-dimensional (local) space or (basic) set can be constructed
5793 on a given parameter domain using the following functions.
5795 #include <isl/space.h>
5796 __isl_give isl_space *isl_space_set_from_params(
5797 __isl_take isl_space *space);
5799 #include <isl/local_space.h>
5800 __isl_give isl_local_space *
5801 isl_local_space_set_from_params(
5802 __isl_take isl_local_space *ls);
5804 #include <isl/set.h>
5805 __isl_give isl_basic_set *isl_basic_set_from_params(
5806 __isl_take isl_basic_set *bset);
5807 __isl_give isl_set *isl_set_from_params(
5808 __isl_take isl_set *set);
5810 =item * Constructing a relation from one or two sets
5812 A map space with a range of a given dimension and with an optional name
5813 can be created from a domain space using the functions
5814 C<isl_space_add_unnamed_tuple_ui> and C<isl_space_add_named_tuple_id_ui>
5817 A relation with a given domain tuple can be created from a set
5818 that will become the range of the relation
5819 using the following function.
5821 #include <isl/set.h>
5822 __isl_give isl_map *
5823 isl_set_unbind_params_insert_domain(
5824 __isl_take isl_set *set,
5825 __isl_take isl_multi_id *domain);
5827 Any parameters with identifiers in C<domain> are reinterpreted
5828 as the corresponding input dimensions.
5830 Similarly, a function defined over a parameter domain can
5831 be converted into one defined over a set domain
5832 using the following functions.
5834 #include <isl/aff.h>
5835 __isl_give isl_aff *
5836 isl_aff_unbind_params_insert_domain(
5837 __isl_take isl_aff *aff,
5838 __isl_take isl_multi_id *domain);
5839 __isl_give isl_multi_aff *
5840 isl_multi_aff_unbind_params_insert_domain(
5841 __isl_take isl_multi_aff *ma,
5842 __isl_take isl_multi_id *domain);
5843 __isl_give isl_multi_pw_aff *
5844 isl_multi_pw_aff_unbind_params_insert_domain(
5845 __isl_take isl_multi_pw_aff *mpa,
5846 __isl_take isl_multi_id *domain);
5849 any parameters with identifiers in C<domain> are reinterpreted
5850 as the corresponding input dimensions.
5852 Create a relation with the given set(s) as domain and/or range.
5853 If only the domain or the range is specified, then
5854 the range or domain of the created relation is a zero-dimensional
5855 flat anonymous space.
5856 If the case of C<isl_space_map_from_set>, the input space
5857 specifies both the domain and the range of the result.
5859 #include <isl/space.h>
5860 __isl_give isl_space *isl_space_from_domain(
5861 __isl_take isl_space *space);
5862 __isl_give isl_space *isl_space_from_range(
5863 __isl_take isl_space *space);
5864 __isl_give isl_space *isl_space_map_from_set(
5865 __isl_take isl_space *space);
5866 __isl_give isl_space *isl_space_map_from_domain_and_range(
5867 __isl_take isl_space *domain,
5868 __isl_take isl_space *range);
5870 #include <isl/local_space.h>
5871 __isl_give isl_local_space *isl_local_space_from_domain(
5872 __isl_take isl_local_space *ls);
5874 #include <isl/map.h>
5875 __isl_give isl_map *isl_set_insert_domain(
5876 __isl_take isl_set *set,
5877 __isl_take isl_space *domain);
5878 __isl_give isl_map *isl_map_from_domain(
5879 __isl_take isl_set *set);
5880 __isl_give isl_map *isl_map_from_range(
5881 __isl_take isl_set *set);
5883 #include <isl/union_map.h>
5884 __isl_give isl_union_map *isl_union_map_from_domain(
5885 __isl_take isl_union_set *uset);
5886 __isl_give isl_union_map *isl_union_map_from_range(
5887 __isl_take isl_union_set *uset);
5888 __isl_give isl_union_map *
5889 isl_union_map_from_domain_and_range(
5890 __isl_take isl_union_set *domain,
5891 __isl_take isl_union_set *range);
5894 __isl_give isl_multi_id *isl_multi_id_from_range(
5895 __isl_take isl_multi_id *mi);
5897 #include <isl/val.h>
5898 __isl_give isl_multi_val *isl_multi_val_from_range(
5899 __isl_take isl_multi_val *mv);
5901 #include <isl/aff.h>
5902 __isl_give isl_multi_aff *
5903 isl_multi_aff_insert_domain(
5904 __isl_take isl_multi_aff *ma,
5905 __isl_take isl_space *domain);
5906 __isl_give isl_pw_aff *isl_pw_aff_insert_domain(
5907 __isl_take isl_pw_aff *pa,
5908 __isl_take isl_space *domain);
5909 __isl_give isl_pw_multi_aff *
5910 isl_pw_multi_aff_insert_domain(
5911 __isl_take isl_pw_multi_aff *pma,
5912 __isl_take isl_space *domain);
5913 __isl_give isl_multi_pw_aff *
5914 isl_multi_pw_aff_insert_domain(
5915 __isl_take isl_multi_pw_aff *mpa,
5916 __isl_take isl_space *domain);
5917 __isl_give isl_aff *isl_aff_from_range(
5918 __isl_take isl_aff *aff);
5919 __isl_give isl_multi_aff *isl_multi_aff_from_range(
5920 __isl_take isl_multi_aff *ma);
5921 __isl_give isl_pw_aff *isl_pw_aff_from_range(
5922 __isl_take isl_pw_aff *pwa);
5923 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
5924 __isl_take isl_multi_pw_aff *mpa);
5925 __isl_give isl_multi_union_pw_aff *
5926 isl_multi_union_pw_aff_from_range(
5927 __isl_take isl_multi_union_pw_aff *mupa);
5928 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
5929 __isl_take isl_set *set);
5930 __isl_give isl_union_pw_multi_aff *
5931 isl_union_pw_multi_aff_from_domain(
5932 __isl_take isl_union_set *uset);
5934 #include <isl/polynomial.h>
5935 __isl_give isl_pw_qpolynomial *
5936 isl_pw_qpolynomial_from_range(
5937 __isl_take isl_pw_qpolynomial *pwqp);
5938 __isl_give isl_pw_qpolynomial_fold *
5939 isl_pw_qpolynomial_fold_from_range(
5940 __isl_take isl_pw_qpolynomial_fold *pwf);
5944 #include <isl/set.h>
5945 __isl_give isl_basic_set *isl_basic_set_fix_si(
5946 __isl_take isl_basic_set *bset,
5947 enum isl_dim_type type, unsigned pos, int value);
5948 __isl_give isl_basic_set *isl_basic_set_fix_val(
5949 __isl_take isl_basic_set *bset,
5950 enum isl_dim_type type, unsigned pos,
5951 __isl_take isl_val *v);
5952 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
5953 enum isl_dim_type type, unsigned pos, int value);
5954 __isl_give isl_set *isl_set_fix_val(
5955 __isl_take isl_set *set,
5956 enum isl_dim_type type, unsigned pos,
5957 __isl_take isl_val *v);
5959 #include <isl/map.h>
5960 __isl_give isl_basic_map *isl_basic_map_fix_si(
5961 __isl_take isl_basic_map *bmap,
5962 enum isl_dim_type type, unsigned pos, int value);
5963 __isl_give isl_basic_map *isl_basic_map_fix_val(
5964 __isl_take isl_basic_map *bmap,
5965 enum isl_dim_type type, unsigned pos,
5966 __isl_take isl_val *v);
5967 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
5968 enum isl_dim_type type, unsigned pos, int value);
5969 __isl_give isl_map *isl_map_fix_val(
5970 __isl_take isl_map *map,
5971 enum isl_dim_type type, unsigned pos,
5972 __isl_take isl_val *v);
5974 #include <isl/aff.h>
5975 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
5976 __isl_take isl_pw_multi_aff *pma,
5977 enum isl_dim_type type, unsigned pos, int value);
5979 #include <isl/polynomial.h>
5980 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
5981 __isl_take isl_pw_qpolynomial *pwqp,
5982 enum isl_dim_type type, unsigned n,
5983 __isl_take isl_val *v);
5984 __isl_give isl_pw_qpolynomial_fold *
5985 isl_pw_qpolynomial_fold_fix_val(
5986 __isl_take isl_pw_qpolynomial_fold *pwf,
5987 enum isl_dim_type type, unsigned n,
5988 __isl_take isl_val *v);
5990 Intersect the set, relation or function domain
5991 with the hyperplane where the given
5992 dimension has the fixed given value.
5994 #include <isl/set.h>
5995 __isl_give isl_basic_set *
5996 isl_basic_set_lower_bound_val(
5997 __isl_take isl_basic_set *bset,
5998 enum isl_dim_type type, unsigned pos,
5999 __isl_take isl_val *value);
6000 __isl_give isl_basic_set *
6001 isl_basic_set_upper_bound_val(
6002 __isl_take isl_basic_set *bset,
6003 enum isl_dim_type type, unsigned pos,
6004 __isl_take isl_val *value);
6005 __isl_give isl_set *isl_set_lower_bound_si(
6006 __isl_take isl_set *set,
6007 enum isl_dim_type type, unsigned pos, int value);
6008 __isl_give isl_set *isl_set_lower_bound_val(
6009 __isl_take isl_set *set,
6010 enum isl_dim_type type, unsigned pos,
6011 __isl_take isl_val *value);
6012 __isl_give isl_set *isl_set_upper_bound_si(
6013 __isl_take isl_set *set,
6014 enum isl_dim_type type, unsigned pos, int value);
6015 __isl_give isl_set *isl_set_upper_bound_val(
6016 __isl_take isl_set *set,
6017 enum isl_dim_type type, unsigned pos,
6018 __isl_take isl_val *value);
6019 __isl_give isl_set *isl_set_lower_bound_multi_val(
6020 __isl_take isl_set *set,
6021 __isl_take isl_multi_val *lower);
6022 __isl_give isl_set *isl_set_upper_bound_multi_val(
6023 __isl_take isl_set *set,
6024 __isl_take isl_multi_val *upper);
6025 __isl_give isl_set *isl_set_lower_bound_multi_pw_aff(
6026 __isl_take isl_set *set,
6027 __isl_take isl_multi_pw_aff *lower);
6028 __isl_give isl_set *isl_set_upper_bound_multi_pw_aff(
6029 __isl_take isl_set *set,
6030 __isl_take isl_multi_pw_aff *upper);
6032 #include <isl/map.h>
6033 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
6034 __isl_take isl_basic_map *bmap,
6035 enum isl_dim_type type, unsigned pos, int value);
6036 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
6037 __isl_take isl_basic_map *bmap,
6038 enum isl_dim_type type, unsigned pos, int value);
6039 __isl_give isl_map *isl_map_lower_bound_si(
6040 __isl_take isl_map *map,
6041 enum isl_dim_type type, unsigned pos, int value);
6042 __isl_give isl_map *isl_map_upper_bound_si(
6043 __isl_take isl_map *map,
6044 enum isl_dim_type type, unsigned pos, int value);
6045 __isl_give isl_map *isl_map_lower_bound_val(
6046 __isl_take isl_map *map,
6047 enum isl_dim_type type, unsigned pos,
6048 __isl_take isl_val *value);
6049 __isl_give isl_map *isl_map_upper_bound_val(
6050 __isl_take isl_map *map,
6051 enum isl_dim_type type, unsigned pos,
6052 __isl_take isl_val *value);
6053 __isl_give isl_map *isl_map_lower_bound_multi_pw_aff(
6054 __isl_take isl_map *map,
6055 __isl_take isl_multi_pw_aff *lower);
6056 __isl_give isl_map *isl_map_upper_bound_multi_pw_aff(
6057 __isl_take isl_map *map,
6058 __isl_take isl_multi_pw_aff *upper);
6060 Intersect the set or relation with the half-space where the given
6061 dimension has a value bounded by the given fixed integer value or
6062 symbolic constant expression.
6063 For functions taking a multi expression,
6064 this applies to all set dimensions.
6065 Those that bound a map, bound the range of that map.
6066 If the multi expression is zero-dimensional but has an explicit domain,
6067 then the (parameter) domain of the set or map is intersected
6068 with this explicit domain.
6070 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
6071 enum isl_dim_type type1, int pos1,
6072 enum isl_dim_type type2, int pos2);
6073 __isl_give isl_basic_map *isl_basic_map_equate(
6074 __isl_take isl_basic_map *bmap,
6075 enum isl_dim_type type1, int pos1,
6076 enum isl_dim_type type2, int pos2);
6077 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
6078 enum isl_dim_type type1, int pos1,
6079 enum isl_dim_type type2, int pos2);
6081 Intersect the set or relation with the hyperplane where the given
6082 dimensions are equal to each other.
6084 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
6085 enum isl_dim_type type1, int pos1,
6086 enum isl_dim_type type2, int pos2);
6088 Intersect the relation with the hyperplane where the given
6089 dimensions have opposite values.
6091 __isl_give isl_map *isl_map_order_le(
6092 __isl_take isl_map *map,
6093 enum isl_dim_type type1, int pos1,
6094 enum isl_dim_type type2, int pos2);
6095 __isl_give isl_basic_map *isl_basic_map_order_ge(
6096 __isl_take isl_basic_map *bmap,
6097 enum isl_dim_type type1, int pos1,
6098 enum isl_dim_type type2, int pos2);
6099 __isl_give isl_map *isl_map_order_ge(
6100 __isl_take isl_map *map,
6101 enum isl_dim_type type1, int pos1,
6102 enum isl_dim_type type2, int pos2);
6103 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
6104 enum isl_dim_type type1, int pos1,
6105 enum isl_dim_type type2, int pos2);
6106 __isl_give isl_basic_map *isl_basic_map_order_gt(
6107 __isl_take isl_basic_map *bmap,
6108 enum isl_dim_type type1, int pos1,
6109 enum isl_dim_type type2, int pos2);
6110 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
6111 enum isl_dim_type type1, int pos1,
6112 enum isl_dim_type type2, int pos2);
6114 Intersect the relation with the half-space where the given
6115 dimensions satisfy the given ordering.
6117 #include <isl/union_set.h>
6118 __isl_give isl_union_map *isl_union_map_remove_map_if(
6119 __isl_take isl_union_map *umap,
6120 isl_bool (*fn)(__isl_keep isl_map *map,
6121 void *user), void *user);
6123 This function calls the callback function once for each
6124 pair of spaces for which there are elements in the input.
6125 If the callback returns C<isl_bool_true>, then all those elements
6126 are removed from the result. The only remaining elements in the output
6127 are then those for which the callback returns C<isl_bool_false>.
6131 #include <isl/aff.h>
6132 __isl_give isl_basic_set *isl_aff_zero_basic_set(
6133 __isl_take isl_aff *aff);
6134 __isl_give isl_basic_set *isl_aff_neg_basic_set(
6135 __isl_take isl_aff *aff);
6136 __isl_give isl_set *isl_pw_aff_pos_set(
6137 __isl_take isl_pw_aff *pa);
6138 __isl_give isl_set *isl_pw_aff_nonneg_set(
6139 __isl_take isl_pw_aff *pwaff);
6140 __isl_give isl_set *isl_pw_aff_zero_set(
6141 __isl_take isl_pw_aff *pwaff);
6142 __isl_give isl_set *isl_pw_aff_non_zero_set(
6143 __isl_take isl_pw_aff *pwaff);
6144 __isl_give isl_union_set *
6145 isl_union_pw_aff_zero_union_set(
6146 __isl_take isl_union_pw_aff *upa);
6147 __isl_give isl_union_set *
6148 isl_multi_union_pw_aff_zero_union_set(
6149 __isl_take isl_multi_union_pw_aff *mupa);
6151 The function C<isl_aff_neg_basic_set> returns a basic set
6152 containing those elements in the domain space
6153 of C<aff> where C<aff> is negative.
6154 The function C<isl_pw_aff_nonneg_set> returns a set
6155 containing those elements in the domain
6156 of C<pwaff> where C<pwaff> is non-negative.
6157 The function C<isl_multi_union_pw_aff_zero_union_set>
6158 returns a union set containing those elements
6159 in the domains of its elements where they are all zero.
6163 __isl_give isl_map *isl_set_identity(
6164 __isl_take isl_set *set);
6165 __isl_give isl_union_map *isl_union_set_identity(
6166 __isl_take isl_union_set *uset);
6167 __isl_give isl_union_pw_multi_aff *
6168 isl_union_set_identity_union_pw_multi_aff(
6169 __isl_take isl_union_set *uset);
6171 Construct an identity relation on the given (union) set.
6173 =item * Function Extraction
6175 A piecewise quasi affine expression that is equal to 1 on a set
6176 and 0 outside the set can be created using the following function.
6178 #include <isl/aff.h>
6179 __isl_give isl_pw_aff *isl_set_indicator_function(
6180 __isl_take isl_set *set);
6182 A piecewise multiple quasi affine expression can be extracted
6183 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
6184 and the C<isl_map> is single-valued.
6185 In case of a conversion from an C<isl_union_map>
6186 to an C<isl_union_pw_multi_aff>, these properties need to hold
6187 in each domain space.
6188 A conversion to a C<isl_multi_union_pw_aff> additionally
6189 requires that the input is non-empty and involves only a single
6192 #include <isl/aff.h>
6193 __isl_give isl_pw_multi_aff *isl_set_as_pw_multi_aff(
6194 __isl_take isl_set *set);
6195 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
6196 __isl_take isl_set *set);
6197 __isl_give isl_pw_multi_aff *isl_map_as_pw_multi_aff(
6198 __isl_take isl_map *map);
6199 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
6200 __isl_take isl_map *map);
6202 __isl_give isl_union_pw_multi_aff *
6203 isl_union_pw_multi_aff_from_union_set(
6204 __isl_take isl_union_set *uset);
6205 __isl_give isl_union_pw_multi_aff *
6206 isl_union_map_as_union_pw_multi_aff(
6207 __isl_take isl_union_map *umap);
6208 __isl_give isl_union_pw_multi_aff *
6209 isl_union_pw_multi_aff_from_union_map(
6210 __isl_take isl_union_map *umap);
6212 __isl_give isl_multi_union_pw_aff *
6213 isl_union_map_as_multi_union_pw_aff(
6214 __isl_take isl_union_map *umap);
6215 __isl_give isl_multi_union_pw_aff *
6216 isl_multi_union_pw_aff_from_union_map(
6217 __isl_take isl_union_map *umap);
6219 C<isl_map_as_pw_multi_aff> and C<isl_pw_multi_aff_from_map> perform
6221 Similarly for C<isl_set_as_pw_multi_aff> and
6222 C<isl_pw_multi_aff_from_set>,
6223 for C<isl_union_map_as_union_pw_multi_aff> and
6224 C<isl_union_pw_multi_aff_from_union_map> and
6225 for C<isl_union_map_as_multi_union_pw_aff> and
6226 C<isl_multi_union_pw_aff_from_union_map>.
6230 __isl_give isl_basic_set *isl_basic_map_deltas(
6231 __isl_take isl_basic_map *bmap);
6232 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
6233 __isl_give isl_union_set *isl_union_map_deltas(
6234 __isl_take isl_union_map *umap);
6236 These functions return a (basic) set containing the differences
6237 between image elements and corresponding domain elements in the input.
6239 __isl_give isl_basic_map *isl_basic_map_deltas_map(
6240 __isl_take isl_basic_map *bmap);
6241 __isl_give isl_map *isl_map_deltas_map(
6242 __isl_take isl_map *map);
6243 __isl_give isl_union_map *isl_union_map_deltas_map(
6244 __isl_take isl_union_map *umap);
6246 The functions above construct a (basic, regular or union) relation
6247 that maps (a wrapped version of) the input relation to its delta set.
6251 #include <isl/map.h>
6252 __isl_give isl_map *isl_set_translation(
6253 __isl_take isl_set *deltas);
6255 This function performs essentially the opposite operation
6256 of C<isl_map_deltas>. In particular, it returns pairs
6257 of elements in the same space that have a difference in C<deltas>.
6261 Simplify the representation of a set, relation or functions by trying
6262 to combine pairs of basic sets or relations into a single
6263 basic set or relation.
6265 #include <isl/set.h>
6266 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
6268 #include <isl/map.h>
6269 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
6271 #include <isl/union_set.h>
6272 __isl_give isl_union_set *isl_union_set_coalesce(
6273 __isl_take isl_union_set *uset);
6275 #include <isl/union_map.h>
6276 __isl_give isl_union_map *isl_union_map_coalesce(
6277 __isl_take isl_union_map *umap);
6279 #include <isl/aff.h>
6280 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
6281 __isl_take isl_pw_aff *pa);
6282 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
6283 __isl_take isl_pw_multi_aff *pma);
6284 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
6285 __isl_take isl_multi_pw_aff *mpa);
6286 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
6287 __isl_take isl_union_pw_aff *upa);
6288 __isl_give isl_union_pw_multi_aff *
6289 isl_union_pw_multi_aff_coalesce(
6290 __isl_take isl_union_pw_multi_aff *upma);
6291 __isl_give isl_multi_union_pw_aff *
6292 isl_multi_union_pw_aff_coalesce(
6293 __isl_take isl_multi_union_pw_aff *mupa);
6295 #include <isl/polynomial.h>
6296 __isl_give isl_pw_qpolynomial_fold *
6297 isl_pw_qpolynomial_fold_coalesce(
6298 __isl_take isl_pw_qpolynomial_fold *pwf);
6299 __isl_give isl_union_pw_qpolynomial *
6300 isl_union_pw_qpolynomial_coalesce(
6301 __isl_take isl_union_pw_qpolynomial *upwqp);
6302 __isl_give isl_union_pw_qpolynomial_fold *
6303 isl_union_pw_qpolynomial_fold_coalesce(
6304 __isl_take isl_union_pw_qpolynomial_fold *upwf);
6306 One of the methods for combining pairs of basic sets or relations
6307 can result in coefficients that are much larger than those that appear
6308 in the constraints of the input. By default, the coefficients are
6309 not allowed to grow larger, but this can be changed by unsetting
6310 the following option.
6312 isl_stat isl_options_set_coalesce_bounded_wrapping(
6313 isl_ctx *ctx, int val);
6314 int isl_options_get_coalesce_bounded_wrapping(
6317 One of the other methods tries to combine pairs of basic sets
6318 with different local variables, treating them as existentially
6319 quantified variables even if they have known (but different)
6320 integer division expressions. The result may then also have
6321 existentially quantified variables. Turning on the following
6322 option prevents this from happening.
6324 isl_stat isl_options_set_coalesce_preserve_locals(
6325 isl_ctx *ctx, int val);
6326 int isl_options_get_coalesce_preserve_locals(isl_ctx *ctx);
6328 =item * Detecting equalities
6330 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
6331 __isl_take isl_basic_set *bset);
6332 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
6333 __isl_take isl_basic_map *bmap);
6334 __isl_give isl_set *isl_set_detect_equalities(
6335 __isl_take isl_set *set);
6336 __isl_give isl_map *isl_map_detect_equalities(
6337 __isl_take isl_map *map);
6338 __isl_give isl_union_set *isl_union_set_detect_equalities(
6339 __isl_take isl_union_set *uset);
6340 __isl_give isl_union_map *isl_union_map_detect_equalities(
6341 __isl_take isl_union_map *umap);
6343 Simplify the representation of a set or relation by detecting implicit
6346 =item * Removing redundant constraints
6348 #include <isl/set.h>
6349 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
6350 __isl_take isl_basic_set *bset);
6351 __isl_give isl_set *isl_set_remove_redundancies(
6352 __isl_take isl_set *set);
6354 #include <isl/union_set.h>
6355 __isl_give isl_union_set *
6356 isl_union_set_remove_redundancies(
6357 __isl_take isl_union_set *uset);
6359 #include <isl/map.h>
6360 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
6361 __isl_take isl_basic_map *bmap);
6362 __isl_give isl_map *isl_map_remove_redundancies(
6363 __isl_take isl_map *map);
6365 #include <isl/union_map.h>
6366 __isl_give isl_union_map *
6367 isl_union_map_remove_redundancies(
6368 __isl_take isl_union_map *umap);
6372 __isl_give isl_basic_set *isl_set_convex_hull(
6373 __isl_take isl_set *set);
6374 __isl_give isl_basic_map *isl_map_convex_hull(
6375 __isl_take isl_map *map);
6377 If the input set or relation has any existentially quantified
6378 variables, then the result of these operations is currently undefined.
6382 #include <isl/set.h>
6383 __isl_give isl_basic_set *
6384 isl_set_unshifted_simple_hull(
6385 __isl_take isl_set *set);
6386 __isl_give isl_basic_set *isl_set_simple_hull(
6387 __isl_take isl_set *set);
6388 __isl_give isl_basic_set *
6389 isl_set_plain_unshifted_simple_hull(
6390 __isl_take isl_set *set);
6391 __isl_give isl_basic_set *
6392 isl_set_unshifted_simple_hull_from_set_list(
6393 __isl_take isl_set *set,
6394 __isl_take isl_set_list *list);
6396 #include <isl/map.h>
6397 __isl_give isl_basic_map *
6398 isl_map_unshifted_simple_hull(
6399 __isl_take isl_map *map);
6400 __isl_give isl_basic_map *isl_map_simple_hull(
6401 __isl_take isl_map *map);
6402 __isl_give isl_basic_map *
6403 isl_map_plain_unshifted_simple_hull(
6404 __isl_take isl_map *map);
6405 __isl_give isl_basic_map *
6406 isl_map_unshifted_simple_hull_from_map_list(
6407 __isl_take isl_map *map,
6408 __isl_take isl_map_list *list);
6410 #include <isl/union_map.h>
6411 __isl_give isl_union_map *isl_union_map_simple_hull(
6412 __isl_take isl_union_map *umap);
6414 These functions compute a single basic set or relation
6415 that contains the whole input set or relation.
6416 In particular, the output is described by translates
6417 of the constraints describing the basic sets or relations in the input.
6418 In case of C<isl_set_unshifted_simple_hull>, only the original
6419 constraints are used, without any translation.
6420 In case of C<isl_set_plain_unshifted_simple_hull> and
6421 C<isl_map_plain_unshifted_simple_hull>, the result is described
6422 by original constraints that are obviously satisfied
6423 by the entire input set or relation.
6424 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
6425 C<isl_map_unshifted_simple_hull_from_map_list>, the
6426 constraints are taken from the elements of the second argument.
6430 (See \autoref{s:simple hull}.)
6436 __isl_give isl_basic_set *isl_basic_set_affine_hull(
6437 __isl_take isl_basic_set *bset);
6438 __isl_give isl_basic_set *isl_set_affine_hull(
6439 __isl_take isl_set *set);
6440 __isl_give isl_union_set *isl_union_set_affine_hull(
6441 __isl_take isl_union_set *uset);
6442 __isl_give isl_basic_map *isl_basic_map_affine_hull(
6443 __isl_take isl_basic_map *bmap);
6444 __isl_give isl_basic_map *isl_map_affine_hull(
6445 __isl_take isl_map *map);
6446 __isl_give isl_union_map *isl_union_map_affine_hull(
6447 __isl_take isl_union_map *umap);
6449 In case of union sets and relations, the affine hull is computed
6452 =item * Polyhedral hull
6454 __isl_give isl_basic_set *isl_set_polyhedral_hull(
6455 __isl_take isl_set *set);
6456 __isl_give isl_basic_map *isl_map_polyhedral_hull(
6457 __isl_take isl_map *map);
6458 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
6459 __isl_take isl_union_set *uset);
6460 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
6461 __isl_take isl_union_map *umap);
6463 These functions compute a single basic set or relation
6464 not involving any existentially quantified variables
6465 that contains the whole input set or relation.
6466 In case of union sets and relations, the polyhedral hull is computed
6471 #include <isl/set.h>
6472 __isl_give isl_fixed_box *
6473 isl_set_get_simple_fixed_box_hull(
6474 __isl_keep isl_set *set)
6476 #include <isl/map.h>
6477 __isl_give isl_fixed_box *
6478 isl_map_get_range_simple_fixed_box_hull(
6479 __isl_keep isl_map *map);
6481 These functions try to approximate the set or
6482 the range of the map by a box of fixed size.
6483 The box is described in terms of an offset living in the same space as
6484 the input and a size living in the set or range space. For any element
6485 in the input map, the range value is greater than or equal to
6486 the offset applied to the domain value and the difference with
6487 this offset is strictly smaller than the size.
6488 The same holds for the elements of the input set, where
6489 the offset is a parametric constant value.
6490 If no fixed-size approximation can be found,
6491 an I<invalid> box is returned, i.e., one for which
6492 C<isl_fixed_box_is_valid> below returns false.
6494 The validity, the offset and the size of the box can be obtained using
6495 the following functions.
6497 #include <isl/fixed_box.h>
6498 isl_bool isl_fixed_box_is_valid(
6499 __isl_keep isl_fixed_box *box);
6500 __isl_give isl_multi_aff *isl_fixed_box_get_offset(
6501 __isl_keep isl_fixed_box *box);
6502 __isl_give isl_multi_val *isl_fixed_box_get_size(
6503 __isl_keep isl_fixed_box *box);
6505 The box can be copied and freed using the following functions.
6507 #include <isl/fixed_box.h>
6508 __isl_give isl_fixed_box *isl_fixed_box_copy(
6509 __isl_keep isl_fixed_box *box);
6510 __isl_null isl_fixed_box *isl_fixed_box_free(
6511 __isl_take isl_fixed_box *box);
6513 An object of type C<isl_fixed_box> can be read from input
6514 using the following function.
6516 #include <isl/fixed_box.h>
6517 __isl_give isl_fixed_box *
6518 isl_fixed_box_read_from_str(isl_ctx *ctx,
6521 A representation of the information contained in an object
6522 of type C<isl_fixed_box> can be obtained using
6524 #include <isl/fixed_box.h>
6525 __isl_give isl_printer *isl_printer_print_fixed_box(
6526 __isl_take isl_printer *p,
6527 __isl_keep isl_fixed_box *box);
6528 __isl_give char *isl_fixed_box_to_str(
6529 __isl_keep isl_fixed_box *box);
6531 C<isl_fixed_box_to_str> prints the information in flow format.
6533 =item * Other approximations
6535 #include <isl/set.h>
6536 __isl_give isl_basic_set *
6537 isl_basic_set_drop_constraints_involving_dims(
6538 __isl_take isl_basic_set *bset,
6539 enum isl_dim_type type,
6540 unsigned first, unsigned n);
6541 __isl_give isl_basic_set *
6542 isl_basic_set_drop_constraints_not_involving_dims(
6543 __isl_take isl_basic_set *bset,
6544 enum isl_dim_type type,
6545 unsigned first, unsigned n);
6546 __isl_give isl_set *
6547 isl_set_drop_constraints_involving_dims(
6548 __isl_take isl_set *set,
6549 enum isl_dim_type type,
6550 unsigned first, unsigned n);
6551 __isl_give isl_set *
6552 isl_set_drop_constraints_not_involving_dims(
6553 __isl_take isl_set *set,
6554 enum isl_dim_type type,
6555 unsigned first, unsigned n);
6557 #include <isl/map.h>
6558 __isl_give isl_basic_map *
6559 isl_basic_map_drop_constraints_involving_dims(
6560 __isl_take isl_basic_map *bmap,
6561 enum isl_dim_type type,
6562 unsigned first, unsigned n);
6563 __isl_give isl_basic_map *
6564 isl_basic_map_drop_constraints_not_involving_dims(
6565 __isl_take isl_basic_map *bmap,
6566 enum isl_dim_type type,
6567 unsigned first, unsigned n);
6568 __isl_give isl_map *
6569 isl_map_drop_constraints_involving_dims(
6570 __isl_take isl_map *map,
6571 enum isl_dim_type type,
6572 unsigned first, unsigned n);
6573 __isl_give isl_map *
6574 isl_map_drop_constraints_not_involving_dims(
6575 __isl_take isl_map *map,
6576 enum isl_dim_type type,
6577 unsigned first, unsigned n);
6579 These functions drop any constraints (not) involving the specified dimensions.
6580 Note that the result depends on the representation of the input.
6582 #include <isl/polynomial.h>
6583 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
6584 __isl_take isl_pw_qpolynomial *pwqp, int sign);
6585 __isl_give isl_union_pw_qpolynomial *
6586 isl_union_pw_qpolynomial_to_polynomial(
6587 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
6589 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
6590 the polynomial will be an overapproximation. If C<sign> is negative,
6591 it will be an underapproximation. If C<sign> is zero, the approximation
6592 will lie somewhere in between.
6596 __isl_give isl_basic_set *isl_basic_set_sample(
6597 __isl_take isl_basic_set *bset);
6598 __isl_give isl_basic_set *isl_set_sample(
6599 __isl_take isl_set *set);
6600 __isl_give isl_basic_map *isl_basic_map_sample(
6601 __isl_take isl_basic_map *bmap);
6602 __isl_give isl_basic_map *isl_map_sample(
6603 __isl_take isl_map *map);
6605 If the input (basic) set or relation is non-empty, then return
6606 a singleton subset of the input. Otherwise, return an empty set.
6608 =item * Optimization
6610 #include <isl/ilp.h>
6611 __isl_give isl_val *isl_basic_set_max_val(
6612 __isl_keep isl_basic_set *bset,
6613 __isl_keep isl_aff *obj);
6614 __isl_give isl_val *isl_set_min_val(
6615 __isl_keep isl_set *set,
6616 __isl_keep isl_aff *obj);
6617 __isl_give isl_val *isl_set_max_val(
6618 __isl_keep isl_set *set,
6619 __isl_keep isl_aff *obj);
6620 __isl_give isl_multi_val *
6621 isl_union_set_min_multi_union_pw_aff(
6622 __isl_keep isl_union_set *uset,
6623 __isl_keep isl_multi_union_pw_aff *obj);
6625 Compute the minimum or maximum of the integer affine expression C<obj>
6626 over the points in C<set>.
6627 The result is C<NULL> in case of an error, the optimal value in case
6628 there is one, negative infinity or infinity if the problem is unbounded and
6629 NaN if the problem is empty.
6631 #include <isl/ilp.h>
6632 __isl_give isl_val *isl_pw_aff_min_val(
6633 __isl_take isl_pw_aff *pa);
6634 __isl_give isl_val *isl_pw_aff_max_val(
6635 __isl_take isl_pw_aff *pa);
6636 __isl_give isl_multi_val *
6637 isl_pw_multi_aff_min_multi_val(
6638 __isl_take isl_pw_multi_aff *pma);
6639 __isl_give isl_multi_val *
6640 isl_pw_multi_aff_max_multi_val(
6641 __isl_take isl_pw_multi_aff *pma);
6642 __isl_give isl_multi_val *
6643 isl_multi_pw_aff_min_multi_val(
6644 __isl_take isl_multi_pw_aff *mpa);
6645 __isl_give isl_multi_val *
6646 isl_multi_pw_aff_max_multi_val(
6647 __isl_take isl_multi_pw_aff *mpa);
6648 __isl_give isl_val *isl_union_pw_aff_min_val(
6649 __isl_take isl_union_pw_aff *upa);
6650 __isl_give isl_val *isl_union_pw_aff_max_val(
6651 __isl_take isl_union_pw_aff *upa);
6652 __isl_give isl_multi_val *
6653 isl_multi_union_pw_aff_min_multi_val(
6654 __isl_take isl_multi_union_pw_aff *mupa);
6655 __isl_give isl_multi_val *
6656 isl_multi_union_pw_aff_max_multi_val(
6657 __isl_take isl_multi_union_pw_aff *mupa);
6659 Compute the minimum or maximum of the integer affine expression
6660 over its definition domain.
6661 The result is C<NULL> in case of an error, the optimal value in case
6662 there is one, negative infinity or infinity if the problem is unbounded and
6663 NaN if the problem is empty.
6665 #include <isl/ilp.h>
6666 __isl_give isl_val *isl_basic_set_dim_max_val(
6667 __isl_take isl_basic_set *bset, int pos);
6668 __isl_give isl_val *isl_set_dim_min_val(
6669 __isl_take isl_set *set, int pos);
6670 __isl_give isl_val *isl_set_dim_max_val(
6671 __isl_take isl_set *set, int pos);
6673 Return the minimal or maximal value attained by the given set dimension,
6674 independently of the parameter values and of any other dimensions.
6675 The result is C<NULL> in case of an error, the optimal value in case
6676 there is one, (negative) infinity if the problem is unbounded and
6677 NaN if the input is empty.
6679 =item * Parametric optimization
6681 __isl_give isl_pw_aff *isl_set_dim_min(
6682 __isl_take isl_set *set, int pos);
6683 __isl_give isl_pw_aff *isl_set_dim_max(
6684 __isl_take isl_set *set, int pos);
6685 __isl_give isl_pw_aff *isl_map_dim_min(
6686 __isl_take isl_map *map, int pos);
6687 __isl_give isl_pw_aff *isl_map_dim_max(
6688 __isl_take isl_map *map, int pos);
6689 __isl_give isl_multi_pw_aff *
6690 isl_set_min_multi_pw_aff(
6691 __isl_take isl_set *set);
6692 __isl_give isl_multi_pw_aff *
6693 isl_set_max_multi_pw_aff(
6694 __isl_take isl_set *set);
6695 __isl_give isl_multi_pw_aff *
6696 isl_map_min_multi_pw_aff(
6697 __isl_take isl_map *map);
6698 __isl_give isl_multi_pw_aff *
6699 isl_map_max_multi_pw_aff(
6700 __isl_take isl_map *map);
6702 Compute the minimum or maximum of the (given) set or output dimension(s)
6703 as a function of the parameters (and input dimensions), but independently
6704 of the other set or output dimensions.
6705 For lexicographic optimization, see L<"Lexicographic Optimization">.
6709 The following functions compute either the set of (rational) coefficient
6710 values of valid constraints for the given set or the set of (rational)
6711 values satisfying the constraints with coefficients from the given set.
6712 Internally, these two sets of functions perform essentially the
6713 same operations, except that the set of coefficients is assumed to
6714 be a cone, while the set of values may be any polyhedron.
6715 The current implementation is based on the Farkas lemma and
6716 Fourier-Motzkin elimination, but this may change or be made optional
6717 in future. In particular, future implementations may use different
6718 dualization algorithms or skip the elimination step.
6720 #include <isl/set.h>
6721 __isl_give isl_basic_set *isl_basic_set_coefficients(
6722 __isl_take isl_basic_set *bset);
6723 __isl_give isl_basic_set_list *
6724 isl_basic_set_list_coefficients(
6725 __isl_take isl_basic_set_list *list);
6726 __isl_give isl_basic_set *isl_set_coefficients(
6727 __isl_take isl_set *set);
6728 __isl_give isl_union_set *isl_union_set_coefficients(
6729 __isl_take isl_union_set *bset);
6730 __isl_give isl_basic_set *isl_basic_set_solutions(
6731 __isl_take isl_basic_set *bset);
6732 __isl_give isl_basic_set *isl_set_solutions(
6733 __isl_take isl_set *set);
6734 __isl_give isl_union_set *isl_union_set_solutions(
6735 __isl_take isl_union_set *bset);
6739 __isl_give isl_map *isl_map_fixed_power_val(
6740 __isl_take isl_map *map,
6741 __isl_take isl_val *exp);
6742 __isl_give isl_union_map *
6743 isl_union_map_fixed_power_val(
6744 __isl_take isl_union_map *umap,
6745 __isl_take isl_val *exp);
6747 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
6748 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
6749 of C<map> is computed.
6751 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
6753 __isl_give isl_union_map *isl_union_map_power(
6754 __isl_take isl_union_map *umap, isl_bool *exact);
6756 Compute a parametric representation for all positive powers I<k> of C<map>.
6757 The result maps I<k> to a nested relation corresponding to the
6758 I<k>th power of C<map>.
6759 The result may be an overapproximation. If the result is known to be exact,
6760 then C<*exact> is set to C<1>.
6762 =item * Transitive closure
6764 __isl_give isl_map *isl_map_transitive_closure(
6765 __isl_take isl_map *map, isl_bool *exact);
6766 __isl_give isl_union_map *isl_union_map_transitive_closure(
6767 __isl_take isl_union_map *umap, isl_bool *exact);
6769 Compute the transitive closure of C<map>.
6770 The result may be an overapproximation. If the result is known to be exact,
6771 then C<*exact> is set to C<1>.
6773 =item * Reaching path lengths
6775 __isl_give isl_map *isl_map_reaching_path_lengths(
6776 __isl_take isl_map *map, isl_bool *exact);
6778 Compute a relation that maps each element in the range of C<map>
6779 to the lengths of all paths composed of edges in C<map> that
6780 end up in the given element.
6781 The result may be an overapproximation. If the result is known to be exact,
6782 then C<*exact> is set to C<1>.
6783 To compute the I<maximal> path length, the resulting relation
6784 should be postprocessed by C<isl_map_lexmax>.
6785 In particular, if the input relation is a dependence relation
6786 (mapping sources to sinks), then the maximal path length corresponds
6787 to the free schedule.
6788 Note, however, that C<isl_map_lexmax> expects the maximum to be
6789 finite, so if the path lengths are unbounded (possibly due to
6790 the overapproximation), then you will get an error message.
6794 #include <isl/space.h>
6795 __isl_give isl_space *isl_space_wrap(
6796 __isl_take isl_space *space);
6797 __isl_give isl_space *isl_space_unwrap(
6798 __isl_take isl_space *space);
6800 #include <isl/local_space.h>
6801 __isl_give isl_local_space *isl_local_space_wrap(
6802 __isl_take isl_local_space *ls);
6804 #include <isl/set.h>
6805 __isl_give isl_basic_map *isl_basic_set_unwrap(
6806 __isl_take isl_basic_set *bset);
6807 __isl_give isl_map *isl_set_unwrap(
6808 __isl_take isl_set *set);
6810 #include <isl/map.h>
6811 __isl_give isl_basic_set *isl_basic_map_wrap(
6812 __isl_take isl_basic_map *bmap);
6813 __isl_give isl_set *isl_map_wrap(
6814 __isl_take isl_map *map);
6816 #include <isl/union_set.h>
6817 __isl_give isl_union_map *isl_union_set_unwrap(
6818 __isl_take isl_union_set *uset);
6820 #include <isl/union_map.h>
6821 __isl_give isl_union_set *isl_union_map_wrap(
6822 __isl_take isl_union_map *umap);
6824 The input to C<isl_space_unwrap> should
6825 be the space of a set, while that of
6826 C<isl_space_wrap> should be the space of a relation.
6827 Conversely, the output of C<isl_space_unwrap> is the space
6828 of a relation, while that of C<isl_space_wrap> is the space of a set.
6832 Remove any internal structure of domain (and range) of the given
6833 set or relation. If there is any such internal structure in the input,
6834 then the name of the space is also removed.
6836 #include <isl/space.h>
6837 __isl_give isl_space *isl_space_flatten_domain(
6838 __isl_take isl_space *space);
6839 __isl_give isl_space *isl_space_flatten_range(
6840 __isl_take isl_space *space);
6842 #include <isl/local_space.h>
6843 __isl_give isl_local_space *
6844 isl_local_space_flatten_domain(
6845 __isl_take isl_local_space *ls);
6846 __isl_give isl_local_space *
6847 isl_local_space_flatten_range(
6848 __isl_take isl_local_space *ls);
6850 #include <isl/set.h>
6851 __isl_give isl_basic_set *isl_basic_set_flatten(
6852 __isl_take isl_basic_set *bset);
6853 __isl_give isl_set *isl_set_flatten(
6854 __isl_take isl_set *set);
6856 #include <isl/map.h>
6857 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
6858 __isl_take isl_basic_map *bmap);
6859 __isl_give isl_basic_map *isl_basic_map_flatten_range(
6860 __isl_take isl_basic_map *bmap);
6861 __isl_give isl_map *isl_map_flatten_range(
6862 __isl_take isl_map *map);
6863 __isl_give isl_map *isl_map_flatten_domain(
6864 __isl_take isl_map *map);
6865 __isl_give isl_basic_map *isl_basic_map_flatten(
6866 __isl_take isl_basic_map *bmap);
6867 __isl_give isl_map *isl_map_flatten(
6868 __isl_take isl_map *map);
6871 __isl_give isl_multi_id *isl_multi_id_flatten_range(
6872 __isl_take isl_multi_id *mi);
6874 #include <isl/val.h>
6875 __isl_give isl_multi_val *isl_multi_val_flatten_range(
6876 __isl_take isl_multi_val *mv);
6878 #include <isl/aff.h>
6879 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
6880 __isl_take isl_multi_aff *ma);
6881 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
6882 __isl_take isl_multi_aff *ma);
6883 __isl_give isl_multi_pw_aff *
6884 isl_multi_pw_aff_flatten_range(
6885 __isl_take isl_multi_pw_aff *mpa);
6886 __isl_give isl_multi_union_pw_aff *
6887 isl_multi_union_pw_aff_flatten_range(
6888 __isl_take isl_multi_union_pw_aff *mupa);
6890 #include <isl/map.h>
6891 __isl_give isl_map *isl_set_flatten_map(
6892 __isl_take isl_set *set);
6894 The function above constructs a relation
6895 that maps the input set to a flattened version of the set.
6899 Lift the input set to a space with extra dimensions corresponding
6900 to the existentially quantified variables in the input.
6901 In particular, the result lives in a wrapped map where the domain
6902 is the original space and the range corresponds to the original
6903 existentially quantified variables.
6905 #include <isl/set.h>
6906 __isl_give isl_basic_set *isl_basic_set_lift(
6907 __isl_take isl_basic_set *bset);
6908 __isl_give isl_set *isl_set_lift(
6909 __isl_take isl_set *set);
6910 __isl_give isl_union_set *isl_union_set_lift(
6911 __isl_take isl_union_set *uset);
6913 Given a local space that contains the existentially quantified
6914 variables of a set, a basic relation that, when applied to
6915 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
6916 can be constructed using the following function.
6918 #include <isl/local_space.h>
6919 __isl_give isl_basic_map *isl_local_space_lifting(
6920 __isl_take isl_local_space *ls);
6922 #include <isl/aff.h>
6923 __isl_give isl_multi_aff *isl_multi_aff_lift(
6924 __isl_take isl_multi_aff *maff,
6925 __isl_give isl_local_space **ls);
6927 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
6928 then it is assigned the local space that lies at the basis of
6929 the lifting applied.
6931 =item * Internal Product
6933 #include <isl/space.h>
6934 __isl_give isl_space *isl_space_zip(
6935 __isl_take isl_space *space);
6937 #include <isl/map.h>
6938 __isl_give isl_basic_map *isl_basic_map_zip(
6939 __isl_take isl_basic_map *bmap);
6940 __isl_give isl_map *isl_map_zip(
6941 __isl_take isl_map *map);
6943 #include <isl/union_map.h>
6944 __isl_give isl_union_map *isl_union_map_zip(
6945 __isl_take isl_union_map *umap);
6947 Given a relation with nested relations for domain and range,
6948 interchange the range of the domain with the domain of the range.
6952 #include <isl/space.h>
6953 __isl_give isl_space *isl_space_curry(
6954 __isl_take isl_space *space);
6955 __isl_give isl_space *isl_space_uncurry(
6956 __isl_take isl_space *space);
6958 #include <isl/map.h>
6959 __isl_give isl_basic_map *isl_basic_map_curry(
6960 __isl_take isl_basic_map *bmap);
6961 __isl_give isl_basic_map *isl_basic_map_uncurry(
6962 __isl_take isl_basic_map *bmap);
6963 __isl_give isl_map *isl_map_curry(
6964 __isl_take isl_map *map);
6965 __isl_give isl_map *isl_map_uncurry(
6966 __isl_take isl_map *map);
6968 #include <isl/union_map.h>
6969 __isl_give isl_union_map *isl_union_map_curry(
6970 __isl_take isl_union_map *umap);
6971 __isl_give isl_union_map *isl_union_map_uncurry(
6972 __isl_take isl_union_map *umap);
6974 Given a relation with a nested relation for domain,
6975 the C<curry> functions
6976 move the range of the nested relation out of the domain
6977 and use it as the domain of a nested relation in the range,
6978 with the original range as range of this nested relation.
6979 The C<uncurry> functions perform the inverse operation.
6981 #include <isl/space.h>
6982 __isl_give isl_space *isl_space_range_curry(
6983 __isl_take isl_space *space);
6985 #include <isl/map.h>
6986 __isl_give isl_map *isl_map_range_curry(
6987 __isl_take isl_map *map);
6989 #include <isl/union_map.h>
6990 __isl_give isl_union_map *isl_union_map_range_curry(
6991 __isl_take isl_union_map *umap);
6993 These functions apply the currying to the relation that
6994 is nested inside the range of the input.
6996 =item * Aligning parameters
6998 Change the order of the parameters of the given set, relation
7000 such that the first parameters match those of C<model>.
7001 This may involve the introduction of extra parameters.
7002 All parameters need to be named.
7004 #include <isl/space.h>
7005 __isl_give isl_space *isl_space_align_params(
7006 __isl_take isl_space *space1,
7007 __isl_take isl_space *space2)
7009 #include <isl/set.h>
7010 __isl_give isl_basic_set *isl_basic_set_align_params(
7011 __isl_take isl_basic_set *bset,
7012 __isl_take isl_space *model);
7013 __isl_give isl_set *isl_set_align_params(
7014 __isl_take isl_set *set,
7015 __isl_take isl_space *model);
7017 #include <isl/map.h>
7018 __isl_give isl_basic_map *isl_basic_map_align_params(
7019 __isl_take isl_basic_map *bmap,
7020 __isl_take isl_space *model);
7021 __isl_give isl_map *isl_map_align_params(
7022 __isl_take isl_map *map,
7023 __isl_take isl_space *model);
7026 __isl_give isl_multi_id *isl_multi_id_align_params(
7027 __isl_take isl_multi_id *mi,
7028 __isl_take isl_space *model);
7030 #include <isl/val.h>
7031 __isl_give isl_multi_val *isl_multi_val_align_params(
7032 __isl_take isl_multi_val *mv,
7033 __isl_take isl_space *model);
7035 #include <isl/aff.h>
7036 __isl_give isl_aff *isl_aff_align_params(
7037 __isl_take isl_aff *aff,
7038 __isl_take isl_space *model);
7039 __isl_give isl_multi_aff *isl_multi_aff_align_params(
7040 __isl_take isl_multi_aff *multi,
7041 __isl_take isl_space *model);
7042 __isl_give isl_pw_aff *isl_pw_aff_align_params(
7043 __isl_take isl_pw_aff *pwaff,
7044 __isl_take isl_space *model);
7045 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
7046 __isl_take isl_pw_multi_aff *pma,
7047 __isl_take isl_space *model);
7048 __isl_give isl_union_pw_aff *
7049 isl_union_pw_aff_align_params(
7050 __isl_take isl_union_pw_aff *upa,
7051 __isl_take isl_space *model);
7052 __isl_give isl_union_pw_multi_aff *
7053 isl_union_pw_multi_aff_align_params(
7054 __isl_take isl_union_pw_multi_aff *upma,
7055 __isl_take isl_space *model);
7056 __isl_give isl_multi_union_pw_aff *
7057 isl_multi_union_pw_aff_align_params(
7058 __isl_take isl_multi_union_pw_aff *mupa,
7059 __isl_take isl_space *model);
7061 #include <isl/polynomial.h>
7062 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
7063 __isl_take isl_qpolynomial *qp,
7064 __isl_take isl_space *model);
7066 =item * Drop unused parameters
7068 Drop parameters that are not referenced by the isl object.
7069 All parameters need to be named.
7071 #include <isl/set.h>
7072 __isl_give isl_basic_set *
7073 isl_basic_set_drop_unused_params(
7074 __isl_take isl_basic_set *bset);
7075 __isl_give isl_set *isl_set_drop_unused_params(
7076 __isl_take isl_set *set);
7078 #include <isl/map.h>
7079 __isl_give isl_basic_map *
7080 isl_basic_map_drop_unused_params(
7081 __isl_take isl_basic_map *bmap);
7082 __isl_give isl_map *isl_map_drop_unused_params(
7083 __isl_take isl_map *map);
7085 #include <isl/union_set.h>
7086 __isl_give isl_union_set *
7087 isl_union_set_drop_unused_params(
7088 __isl_take isl_union_set *uset);
7090 #include <isl/union_map.h>
7091 __isl_give isl_union_map *
7092 isl_union_map_drop_unused_params(
7093 __isl_take isl_union_map *umap);
7095 #include <isl/aff.h>
7096 __isl_give isl_pw_aff *isl_pw_aff_drop_unused_params(
7097 __isl_take isl_pw_aff *pa);
7098 __isl_give isl_pw_multi_aff *
7099 isl_pw_multi_aff_drop_unused_params(
7100 __isl_take isl_pw_multi_aff *pma);
7101 __isl_give isl_union_pw_aff *
7102 isl_union_pw_aff_drop_unused_params(
7103 __isl_take isl_union_pw_aff *upa);
7104 __isl_give isl_union_pw_multi_aff *
7105 isl_union_pw_multi_aff_drop_unused_params(
7106 __isl_take isl_union_pw_multi_aff *upma);
7108 #include <isl/polynomial.h>
7109 __isl_give isl_pw_qpolynomial *
7110 isl_pw_qpolynomial_drop_unused_params(
7111 __isl_take isl_pw_qpolynomial *pwqp);
7112 __isl_give isl_pw_qpolynomial_fold *
7113 isl_pw_qpolynomial_fold_drop_unused_params(
7114 __isl_take isl_pw_qpolynomial_fold *pwf);
7115 __isl_give isl_union_pw_qpolynomial *
7116 isl_union_pw_qpolynomial_drop_unused_params(
7117 __isl_take isl_union_pw_qpolynomial *upwqp);
7118 __isl_give isl_union_pw_qpolynomial_fold *
7119 isl_union_pw_qpolynomial_fold_drop_unused_params(
7120 __isl_take isl_union_pw_qpolynomial_fold *upwf);
7122 =item * Unary Arithmetic Operations
7124 #include <isl/set.h>
7125 __isl_give isl_set *isl_set_neg(
7126 __isl_take isl_set *set);
7127 #include <isl/map.h>
7128 __isl_give isl_map *isl_map_neg(
7129 __isl_take isl_map *map);
7131 C<isl_set_neg> constructs a set containing the opposites of
7132 the elements in its argument.
7133 The domain of the result of C<isl_map_neg> is the same
7134 as the domain of its argument. The corresponding range
7135 elements are the opposites of the corresponding range
7136 elements in the argument.
7138 #include <isl/val.h>
7139 __isl_give isl_multi_val *isl_multi_val_neg(
7140 __isl_take isl_multi_val *mv);
7142 #include <isl/aff.h>
7143 __isl_give isl_aff *isl_aff_neg(
7144 __isl_take isl_aff *aff);
7145 __isl_give isl_multi_aff *isl_multi_aff_neg(
7146 __isl_take isl_multi_aff *ma);
7147 __isl_give isl_pw_aff *isl_pw_aff_neg(
7148 __isl_take isl_pw_aff *pwaff);
7149 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
7150 __isl_take isl_pw_multi_aff *pma);
7151 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
7152 __isl_take isl_multi_pw_aff *mpa);
7153 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
7154 __isl_take isl_union_pw_aff *upa);
7155 __isl_give isl_union_pw_multi_aff *
7156 isl_union_pw_multi_aff_neg(
7157 __isl_take isl_union_pw_multi_aff *upma);
7158 __isl_give isl_multi_union_pw_aff *
7159 isl_multi_union_pw_aff_neg(
7160 __isl_take isl_multi_union_pw_aff *mupa);
7161 __isl_give isl_aff *isl_aff_ceil(
7162 __isl_take isl_aff *aff);
7163 __isl_give isl_pw_aff *isl_pw_aff_ceil(
7164 __isl_take isl_pw_aff *pwaff);
7165 __isl_give isl_aff *isl_aff_floor(
7166 __isl_take isl_aff *aff);
7167 __isl_give isl_multi_aff *isl_multi_aff_floor(
7168 __isl_take isl_multi_aff *ma);
7169 __isl_give isl_pw_aff *isl_pw_aff_floor(
7170 __isl_take isl_pw_aff *pwaff);
7171 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
7172 __isl_take isl_union_pw_aff *upa);
7173 __isl_give isl_multi_union_pw_aff *
7174 isl_multi_union_pw_aff_floor(
7175 __isl_take isl_multi_union_pw_aff *mupa);
7177 #include <isl/aff.h>
7178 __isl_give isl_pw_aff *isl_pw_aff_list_min(
7179 __isl_take isl_pw_aff_list *list);
7180 __isl_give isl_pw_aff *isl_pw_aff_list_max(
7181 __isl_take isl_pw_aff_list *list);
7183 #include <isl/polynomial.h>
7184 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
7185 __isl_take isl_qpolynomial *qp);
7186 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
7187 __isl_take isl_pw_qpolynomial *pwqp);
7188 __isl_give isl_union_pw_qpolynomial *
7189 isl_union_pw_qpolynomial_neg(
7190 __isl_take isl_union_pw_qpolynomial *upwqp);
7191 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
7192 __isl_take isl_qpolynomial *qp,
7194 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
7195 __isl_take isl_pw_qpolynomial *pwqp,
7200 The following functions evaluate a function in a point.
7202 #include <isl/aff.h>
7203 __isl_give isl_val *isl_aff_eval(
7204 __isl_take isl_aff *aff,
7205 __isl_take isl_point *pnt);
7206 __isl_give isl_val *isl_pw_aff_eval(
7207 __isl_take isl_pw_aff *pa,
7208 __isl_take isl_point *pnt);
7210 #include <isl/polynomial.h>
7211 __isl_give isl_val *isl_pw_qpolynomial_eval(
7212 __isl_take isl_pw_qpolynomial *pwqp,
7213 __isl_take isl_point *pnt);
7214 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
7215 __isl_take isl_pw_qpolynomial_fold *pwf,
7216 __isl_take isl_point *pnt);
7217 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
7218 __isl_take isl_union_pw_qpolynomial *upwqp,
7219 __isl_take isl_point *pnt);
7220 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
7221 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7222 __isl_take isl_point *pnt);
7224 These functions return NaN when evaluated at a void point.
7225 Note that C<isl_pw_aff_eval> returns NaN when the function is evaluated outside
7226 its definition domain, while C<isl_pw_qpolynomial_eval> returns zero
7227 when the function is evaluated outside its explicit domain.
7229 =item * Dimension manipulation
7231 It is usually not advisable to directly change the (input or output)
7232 space of a set or a relation as this removes the name and the internal
7233 structure of the space. However, the functions below can be useful
7234 to add new parameters, assuming
7235 C<isl_set_align_params> and C<isl_map_align_params>
7238 #include <isl/space.h>
7239 __isl_give isl_space *isl_space_add_dims(
7240 __isl_take isl_space *space,
7241 enum isl_dim_type type, unsigned n);
7242 __isl_give isl_space *isl_space_insert_dims(
7243 __isl_take isl_space *space,
7244 enum isl_dim_type type, unsigned pos, unsigned n);
7245 __isl_give isl_space *isl_space_drop_dims(
7246 __isl_take isl_space *space,
7247 enum isl_dim_type type, unsigned first, unsigned n);
7248 __isl_give isl_space *isl_space_move_dims(
7249 __isl_take isl_space *space,
7250 enum isl_dim_type dst_type, unsigned dst_pos,
7251 enum isl_dim_type src_type, unsigned src_pos,
7254 #include <isl/local_space.h>
7255 __isl_give isl_local_space *isl_local_space_add_dims(
7256 __isl_take isl_local_space *ls,
7257 enum isl_dim_type type, unsigned n);
7258 __isl_give isl_local_space *isl_local_space_insert_dims(
7259 __isl_take isl_local_space *ls,
7260 enum isl_dim_type type, unsigned first, unsigned n);
7261 __isl_give isl_local_space *isl_local_space_drop_dims(
7262 __isl_take isl_local_space *ls,
7263 enum isl_dim_type type, unsigned first, unsigned n);
7265 #include <isl/set.h>
7266 __isl_give isl_basic_set *isl_basic_set_add_dims(
7267 __isl_take isl_basic_set *bset,
7268 enum isl_dim_type type, unsigned n);
7269 __isl_give isl_set *isl_set_add_dims(
7270 __isl_take isl_set *set,
7271 enum isl_dim_type type, unsigned n);
7272 __isl_give isl_basic_set *isl_basic_set_insert_dims(
7273 __isl_take isl_basic_set *bset,
7274 enum isl_dim_type type, unsigned pos,
7276 __isl_give isl_set *isl_set_insert_dims(
7277 __isl_take isl_set *set,
7278 enum isl_dim_type type, unsigned pos, unsigned n);
7279 __isl_give isl_basic_set *isl_basic_set_move_dims(
7280 __isl_take isl_basic_set *bset,
7281 enum isl_dim_type dst_type, unsigned dst_pos,
7282 enum isl_dim_type src_type, unsigned src_pos,
7284 __isl_give isl_set *isl_set_move_dims(
7285 __isl_take isl_set *set,
7286 enum isl_dim_type dst_type, unsigned dst_pos,
7287 enum isl_dim_type src_type, unsigned src_pos,
7290 #include <isl/map.h>
7291 __isl_give isl_basic_map *isl_basic_map_add_dims(
7292 __isl_take isl_basic_map *bmap,
7293 enum isl_dim_type type, unsigned n);
7294 __isl_give isl_map *isl_map_add_dims(
7295 __isl_take isl_map *map,
7296 enum isl_dim_type type, unsigned n);
7297 __isl_give isl_basic_map *isl_basic_map_insert_dims(
7298 __isl_take isl_basic_map *bmap,
7299 enum isl_dim_type type, unsigned pos,
7301 __isl_give isl_map *isl_map_insert_dims(
7302 __isl_take isl_map *map,
7303 enum isl_dim_type type, unsigned pos, unsigned n);
7304 __isl_give isl_basic_map *isl_basic_map_move_dims(
7305 __isl_take isl_basic_map *bmap,
7306 enum isl_dim_type dst_type, unsigned dst_pos,
7307 enum isl_dim_type src_type, unsigned src_pos,
7309 __isl_give isl_map *isl_map_move_dims(
7310 __isl_take isl_map *map,
7311 enum isl_dim_type dst_type, unsigned dst_pos,
7312 enum isl_dim_type src_type, unsigned src_pos,
7315 #include <isl/val.h>
7316 __isl_give isl_multi_val *isl_multi_val_insert_dims(
7317 __isl_take isl_multi_val *mv,
7318 enum isl_dim_type type, unsigned first, unsigned n);
7319 __isl_give isl_multi_val *isl_multi_val_add_dims(
7320 __isl_take isl_multi_val *mv,
7321 enum isl_dim_type type, unsigned n);
7322 __isl_give isl_multi_val *isl_multi_val_drop_dims(
7323 __isl_take isl_multi_val *mv,
7324 enum isl_dim_type type, unsigned first, unsigned n);
7326 #include <isl/aff.h>
7327 __isl_give isl_aff *isl_aff_insert_dims(
7328 __isl_take isl_aff *aff,
7329 enum isl_dim_type type, unsigned first, unsigned n);
7330 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
7331 __isl_take isl_multi_aff *ma,
7332 enum isl_dim_type type, unsigned first, unsigned n);
7333 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
7334 __isl_take isl_pw_aff *pwaff,
7335 enum isl_dim_type type, unsigned first, unsigned n);
7336 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
7337 __isl_take isl_multi_pw_aff *mpa,
7338 enum isl_dim_type type, unsigned first, unsigned n);
7339 __isl_give isl_aff *isl_aff_add_dims(
7340 __isl_take isl_aff *aff,
7341 enum isl_dim_type type, unsigned n);
7342 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
7343 __isl_take isl_multi_aff *ma,
7344 enum isl_dim_type type, unsigned n);
7345 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
7346 __isl_take isl_pw_aff *pwaff,
7347 enum isl_dim_type type, unsigned n);
7348 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
7349 __isl_take isl_multi_pw_aff *mpa,
7350 enum isl_dim_type type, unsigned n);
7351 __isl_give isl_aff *isl_aff_drop_dims(
7352 __isl_take isl_aff *aff,
7353 enum isl_dim_type type, unsigned first, unsigned n);
7354 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
7355 __isl_take isl_multi_aff *maff,
7356 enum isl_dim_type type, unsigned first, unsigned n);
7357 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
7358 __isl_take isl_pw_aff *pwaff,
7359 enum isl_dim_type type, unsigned first, unsigned n);
7360 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
7361 __isl_take isl_pw_multi_aff *pma,
7362 enum isl_dim_type type, unsigned first, unsigned n);
7363 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
7364 __isl_take isl_union_pw_aff *upa,
7365 enum isl_dim_type type, unsigned first, unsigned n);
7366 __isl_give isl_union_pw_multi_aff *
7367 isl_union_pw_multi_aff_drop_dims(
7368 __isl_take isl_union_pw_multi_aff *upma,
7369 enum isl_dim_type type,
7370 unsigned first, unsigned n);
7371 __isl_give isl_multi_union_pw_aff *
7372 isl_multi_union_pw_aff_drop_dims(
7373 __isl_take isl_multi_union_pw_aff *mupa,
7374 enum isl_dim_type type, unsigned first,
7376 __isl_give isl_aff *isl_aff_move_dims(
7377 __isl_take isl_aff *aff,
7378 enum isl_dim_type dst_type, unsigned dst_pos,
7379 enum isl_dim_type src_type, unsigned src_pos,
7381 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
7382 __isl_take isl_multi_aff *ma,
7383 enum isl_dim_type dst_type, unsigned dst_pos,
7384 enum isl_dim_type src_type, unsigned src_pos,
7386 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
7387 __isl_take isl_pw_aff *pa,
7388 enum isl_dim_type dst_type, unsigned dst_pos,
7389 enum isl_dim_type src_type, unsigned src_pos,
7391 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
7392 __isl_take isl_multi_pw_aff *pma,
7393 enum isl_dim_type dst_type, unsigned dst_pos,
7394 enum isl_dim_type src_type, unsigned src_pos,
7397 #include <isl/polynomial.h>
7398 __isl_give isl_union_pw_qpolynomial *
7399 isl_union_pw_qpolynomial_drop_dims(
7400 __isl_take isl_union_pw_qpolynomial *upwqp,
7401 enum isl_dim_type type,
7402 unsigned first, unsigned n);
7403 __isl_give isl_union_pw_qpolynomial_fold *
7404 isl_union_pw_qpolynomial_fold_drop_dims(
7405 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7406 enum isl_dim_type type,
7407 unsigned first, unsigned n);
7409 The operations on union expressions can only manipulate parameters.
7413 =head2 Binary Operations
7415 The two arguments of a binary operation not only need to live
7416 in the same C<isl_ctx>, they currently also need to have
7417 the same (number of) parameters.
7419 =head3 Basic Operations
7423 =item * Intersection
7425 #include <isl/local_space.h>
7426 __isl_give isl_local_space *isl_local_space_intersect(
7427 __isl_take isl_local_space *ls1,
7428 __isl_take isl_local_space *ls2);
7430 #include <isl/set.h>
7431 __isl_give isl_basic_set *isl_basic_set_intersect_params(
7432 __isl_take isl_basic_set *bset1,
7433 __isl_take isl_basic_set *bset2);
7434 __isl_give isl_basic_set *isl_basic_set_intersect(
7435 __isl_take isl_basic_set *bset1,
7436 __isl_take isl_basic_set *bset2);
7437 __isl_give isl_basic_set *isl_basic_set_list_intersect(
7438 __isl_take struct isl_basic_set_list *list);
7439 __isl_give isl_set *isl_set_intersect_params(
7440 __isl_take isl_set *set,
7441 __isl_take isl_set *params);
7442 __isl_give isl_set *isl_set_intersect(
7443 __isl_take isl_set *set1,
7444 __isl_take isl_set *set2);
7445 __isl_give isl_set *isl_set_intersect_factor_domain(
7446 __isl_take isl_set *set,
7447 __isl_take isl_set *domain);
7448 __isl_give isl_set *isl_set_intersect_factor_range(
7449 __isl_take isl_set *set,
7450 __isl_take isl_set *range);
7452 #include <isl/map.h>
7453 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
7454 __isl_take isl_basic_map *bmap,
7455 __isl_take isl_basic_set *bset);
7456 __isl_give isl_basic_map *isl_basic_map_intersect_range(
7457 __isl_take isl_basic_map *bmap,
7458 __isl_take isl_basic_set *bset);
7459 __isl_give isl_basic_map *isl_basic_map_intersect(
7460 __isl_take isl_basic_map *bmap1,
7461 __isl_take isl_basic_map *bmap2);
7462 __isl_give isl_basic_map *isl_basic_map_list_intersect(
7463 __isl_take isl_basic_map_list *list);
7464 __isl_give isl_map *isl_map_intersect_params(
7465 __isl_take isl_map *map,
7466 __isl_take isl_set *params);
7467 __isl_give isl_map *isl_map_intersect_domain(
7468 __isl_take isl_map *map,
7469 __isl_take isl_set *set);
7470 __isl_give isl_map *isl_map_intersect_range(
7471 __isl_take isl_map *map,
7472 __isl_take isl_set *set);
7473 __isl_give isl_map *isl_map_intersect(
7474 __isl_take isl_map *map1,
7475 __isl_take isl_map *map2);
7476 __isl_give isl_map *
7477 isl_map_intersect_domain_factor_domain(
7478 __isl_take isl_map *map,
7479 __isl_take isl_map *factor);
7480 __isl_give isl_map *
7481 isl_map_intersect_domain_factor_range(
7482 __isl_take isl_map *map,
7483 __isl_take isl_map *factor);
7484 __isl_give isl_map *
7485 isl_map_intersect_range_factor_domain(
7486 __isl_take isl_map *map,
7487 __isl_take isl_map *factor);
7488 __isl_give isl_map *
7489 isl_map_intersect_range_factor_range(
7490 __isl_take isl_map *map,
7491 __isl_take isl_map *factor);
7492 __isl_give isl_map *
7493 isl_map_intersect_domain_wrapped_domain(
7494 __isl_take isl_map *map,
7495 __isl_take isl_set *domain);
7496 __isl_give isl_map *
7497 isl_map_intersect_range_wrapped_domain(
7498 __isl_take isl_map *map,
7499 __isl_take isl_set *domain);
7501 #include <isl/union_set.h>
7502 __isl_give isl_union_set *isl_union_set_intersect_params(
7503 __isl_take isl_union_set *uset,
7504 __isl_take isl_set *set);
7505 __isl_give isl_union_set *isl_union_set_intersect(
7506 __isl_take isl_union_set *uset1,
7507 __isl_take isl_union_set *uset2);
7509 #include <isl/union_map.h>
7510 __isl_give isl_union_map *isl_union_map_intersect_params(
7511 __isl_take isl_union_map *umap,
7512 __isl_take isl_set *set);
7513 __isl_give isl_union_map *
7514 isl_union_map_intersect_domain_union_set(
7515 __isl_take isl_union_map *umap,
7516 __isl_take isl_union_set *uset);
7517 __isl_give isl_union_map *
7518 isl_union_map_intersect_domain_space(
7519 __isl_take isl_union_map *umap,
7520 __isl_take isl_space *space);
7521 __isl_give isl_union_map *isl_union_map_intersect_domain(
7522 __isl_take isl_union_map *umap,
7523 __isl_take isl_union_set *uset);
7524 __isl_give isl_union_map *
7525 isl_union_map_intersect_range_union_set(
7526 __isl_take isl_union_map *umap,
7527 __isl_take isl_union_set *uset);
7528 __isl_give isl_union_map *
7529 isl_union_map_intersect_range_space(
7530 __isl_take isl_union_map *umap,
7531 __isl_take isl_space *space);
7532 __isl_give isl_union_map *isl_union_map_intersect_range(
7533 __isl_take isl_union_map *umap,
7534 __isl_take isl_union_set *uset);
7535 __isl_give isl_union_map *isl_union_map_intersect(
7536 __isl_take isl_union_map *umap1,
7537 __isl_take isl_union_map *umap2);
7538 __isl_give isl_union_map *
7539 isl_union_map_intersect_domain_factor_domain(
7540 __isl_take isl_union_map *umap,
7541 __isl_take isl_union_map *factor);
7542 __isl_give isl_union_map *
7543 isl_union_map_intersect_domain_factor_range(
7544 __isl_take isl_union_map *umap,
7545 __isl_take isl_union_map *factor);
7546 __isl_give isl_union_map *
7547 isl_union_map_intersect_range_factor_domain(
7548 __isl_take isl_union_map *umap,
7549 __isl_take isl_union_map *factor);
7550 __isl_give isl_union_map *
7551 isl_union_map_intersect_range_factor_range(
7552 __isl_take isl_union_map *umap,
7553 __isl_take isl_union_map *factor);
7554 __isl_give isl_union_map *
7555 isl_union_map_intersect_domain_wrapped_domain_union_set(
7556 __isl_take isl_union_map *umap,
7557 __isl_take isl_union_set *domain);
7558 __isl_give isl_union_map *
7559 isl_union_map_intersect_range_wrapped_domain_union_set(
7560 __isl_take isl_union_map *umap,
7561 __isl_take isl_union_set *domain);
7563 #include <isl/aff.h>
7564 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
7565 __isl_take isl_pw_aff *pa,
7566 __isl_take isl_set *set);
7567 __isl_give isl_multi_pw_aff *
7568 isl_multi_pw_aff_intersect_domain(
7569 __isl_take isl_multi_pw_aff *mpa,
7570 __isl_take isl_set *domain);
7571 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
7572 __isl_take isl_pw_multi_aff *pma,
7573 __isl_take isl_set *set);
7574 __isl_give isl_union_pw_aff *
7575 isl_union_pw_aff_intersect_domain_space(
7576 __isl_take isl_union_pw_aff *upa,
7577 __isl_take isl_space *space);
7578 __isl_give isl_union_pw_aff *
7579 isl_union_pw_aff_intersect_domain_union_set(
7580 __isl_take isl_union_pw_aff *upa,
7581 __isl_take isl_union_set *uset);
7582 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
7583 __isl_take isl_union_pw_aff *upa,
7584 __isl_take isl_union_set *uset);
7585 __isl_give isl_union_pw_multi_aff *
7586 isl_union_pw_multi_aff_intersect_domain_space(
7587 __isl_take isl_union_pw_multi_aff *upma,
7588 __isl_take isl_space *space);
7589 __isl_give isl_union_pw_multi_aff *
7590 isl_union_pw_multi_aff_intersect_domain_union_set(
7591 __isl_take isl_union_pw_multi_aff *upma,
7592 __isl_take isl_union_set *uset);
7593 __isl_give isl_union_pw_multi_aff *
7594 isl_union_pw_multi_aff_intersect_domain(
7595 __isl_take isl_union_pw_multi_aff *upma,
7596 __isl_take isl_union_set *uset);
7597 __isl_give isl_multi_union_pw_aff *
7598 isl_multi_union_pw_aff_intersect_domain(
7599 __isl_take isl_multi_union_pw_aff *mupa,
7600 __isl_take isl_union_set *uset);
7601 __isl_give isl_pw_aff *
7602 isl_pw_aff_intersect_domain_wrapped_domain(
7603 __isl_take isl_pw_aff *pa,
7604 __isl_take isl_set *set);
7605 __isl_give isl_pw_multi_aff *
7606 isl_pw_multi_aff_intersect_domain_wrapped_domain(
7607 __isl_take isl_pw_multi_aff *pma,
7608 __isl_take isl_set *set);
7609 __isl_give isl_union_pw_aff *
7610 isl_union_pw_aff_intersect_domain_wrapped_domain(
7611 __isl_take isl_union_pw_aff *upa,
7612 __isl_take isl_union_set *uset);
7613 __isl_give isl_union_pw_multi_aff *
7614 isl_union_pw_multi_aff_intersect_domain_wrapped_domain(
7615 __isl_take isl_union_pw_multi_aff *upma,
7616 __isl_take isl_union_set *uset);
7617 __isl_give isl_pw_aff *
7618 isl_pw_aff_intersect_domain_wrapped_range(
7619 __isl_take isl_pw_aff *pa,
7620 __isl_take isl_set *set);
7621 __isl_give isl_pw_multi_aff *
7622 isl_pw_multi_aff_intersect_domain_wrapped_range(
7623 __isl_take isl_pw_multi_aff *pma,
7624 __isl_take isl_set *set);
7625 __isl_give isl_union_pw_multi_aff *
7626 isl_union_pw_multi_aff_intersect_domain_wrapped_range(
7627 __isl_take isl_union_pw_multi_aff *upma,
7628 __isl_take isl_union_set *uset);
7629 __isl_give isl_union_pw_aff *
7630 isl_union_pw_aff_intersect_domain_wrapped_range(
7631 __isl_take isl_union_pw_aff *upa,
7632 __isl_take isl_union_set *uset);
7633 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
7634 __isl_take isl_pw_aff *pa,
7635 __isl_take isl_set *set);
7636 __isl_give isl_multi_pw_aff *
7637 isl_multi_pw_aff_intersect_params(
7638 __isl_take isl_multi_pw_aff *mpa,
7639 __isl_take isl_set *set);
7640 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
7641 __isl_take isl_pw_multi_aff *pma,
7642 __isl_take isl_set *set);
7643 __isl_give isl_union_pw_aff *
7644 isl_union_pw_aff_intersect_params(
7645 __isl_take isl_union_pw_aff *upa,
7646 __isl_take isl_set *set);
7647 __isl_give isl_union_pw_multi_aff *
7648 isl_union_pw_multi_aff_intersect_params(
7649 __isl_take isl_union_pw_multi_aff *upma,
7650 __isl_take isl_set *set);
7651 __isl_give isl_multi_union_pw_aff *
7652 isl_multi_union_pw_aff_intersect_params(
7653 __isl_take isl_multi_union_pw_aff *mupa,
7654 __isl_take isl_set *params);
7655 __isl_give isl_multi_union_pw_aff *
7656 isl_multi_union_pw_aff_intersect_range(
7657 __isl_take isl_multi_union_pw_aff *mupa,
7658 __isl_take isl_set *set);
7660 #include <isl/polynomial.h>
7661 __isl_give isl_pw_qpolynomial *
7662 isl_pw_qpolynomial_intersect_domain(
7663 __isl_take isl_pw_qpolynomial *pwpq,
7664 __isl_take isl_set *set);
7665 __isl_give isl_union_pw_qpolynomial *
7666 isl_union_pw_qpolynomial_intersect_domain_space(
7667 __isl_take isl_union_pw_qpolynomial *upwpq,
7668 __isl_take isl_space *space);
7669 __isl_give isl_union_pw_qpolynomial *
7670 isl_union_pw_qpolynomial_intersect_domain_union_set(
7671 __isl_take isl_union_pw_qpolynomial *upwpq,
7672 __isl_take isl_union_set *uset);
7673 __isl_give isl_union_pw_qpolynomial *
7674 isl_union_pw_qpolynomial_intersect_domain(
7675 __isl_take isl_union_pw_qpolynomial *upwpq,
7676 __isl_take isl_union_set *uset);
7677 __isl_give isl_union_pw_qpolynomial_fold *
7678 isl_union_pw_qpolynomial_fold_intersect_domain_space(
7679 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7680 __isl_take isl_space *space);
7681 __isl_give isl_union_pw_qpolynomial_fold *
7682 isl_union_pw_qpolynomial_fold_intersect_domain_union_set(
7683 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7684 __isl_take isl_union_set *uset);
7685 __isl_give isl_union_pw_qpolynomial_fold *
7686 isl_union_pw_qpolynomial_fold_intersect_domain(
7687 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7688 __isl_take isl_union_set *uset);
7689 __isl_give isl_pw_qpolynomial *
7690 isl_pw_qpolynomial_intersect_domain_wrapped_domain(
7691 __isl_take isl_pw_qpolynomial *pwpq,
7692 __isl_take isl_set *set);
7693 __isl_give isl_pw_qpolynomial_fold *
7694 isl_pw_qpolynomial_fold_intersect_domain_wrapped_domain(
7695 __isl_take isl_pw_qpolynomial_fold *pwf,
7696 __isl_take isl_set *set);
7697 __isl_give isl_union_pw_qpolynomial *
7698 isl_union_pw_qpolynomial_intersect_domain_wrapped_domain(
7699 __isl_take isl_union_pw_qpolynomial *upwpq,
7700 __isl_take isl_union_set *uset);
7701 __isl_give isl_union_pw_qpolynomial_fold *
7702 isl_union_pw_qpolynomial_fold_intersect_domain_wrapped_domain(
7703 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7704 __isl_take isl_union_set *uset);
7705 __isl_give isl_pw_qpolynomial *
7706 isl_pw_qpolynomial_intersect_domain_wrapped_range(
7707 __isl_take isl_pw_qpolynomial *pwpq,
7708 __isl_take isl_set *set);
7709 __isl_give isl_pw_qpolynomial_fold *
7710 isl_pw_qpolynomial_fold_intersect_domain_wrapped_range(
7711 __isl_take isl_pw_qpolynomial_fold *pwf,
7712 __isl_take isl_set *set);
7713 __isl_give isl_union_pw_qpolynomial *
7714 isl_union_pw_qpolynomial_intersect_domain_wrapped_range(
7715 __isl_take isl_union_pw_qpolynomial *upwpq,
7716 __isl_take isl_union_set *uset);
7717 __isl_give isl_union_pw_qpolynomial_fold *
7718 isl_union_pw_qpolynomial_fold_intersect_domain_wrapped_range(
7719 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7720 __isl_take isl_union_set *uset);
7721 __isl_give isl_pw_qpolynomial *
7722 isl_pw_qpolynomial_intersect_params(
7723 __isl_take isl_pw_qpolynomial *pwpq,
7724 __isl_take isl_set *set);
7725 __isl_give isl_pw_qpolynomial_fold *
7726 isl_pw_qpolynomial_fold_intersect_params(
7727 __isl_take isl_pw_qpolynomial_fold *pwf,
7728 __isl_take isl_set *set);
7729 __isl_give isl_union_pw_qpolynomial *
7730 isl_union_pw_qpolynomial_intersect_params(
7731 __isl_take isl_union_pw_qpolynomial *upwpq,
7732 __isl_take isl_set *set);
7733 __isl_give isl_union_pw_qpolynomial_fold *
7734 isl_union_pw_qpolynomial_fold_intersect_params(
7735 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7736 __isl_take isl_set *set);
7738 The second argument to the C<_params> functions needs to be
7739 a parametric (basic) set. For the other functions, a parametric set
7740 for either argument is only allowed if the other argument is
7741 a parametric set as well.
7742 The list passed to C<isl_basic_set_list_intersect> needs to have
7743 at least one element and all elements need to live in the same space.
7744 The function C<isl_multi_union_pw_aff_intersect_range>
7745 restricts the input function to those shared domain elements
7746 that map to the specified range.
7747 C<isl_union_map_intersect_domain> is an alternative name for
7748 C<isl_union_map_intersect_domain_union_set>.
7749 Similarly for the other pairs of functions.
7753 #include <isl/set.h>
7754 __isl_give isl_set *isl_basic_set_union(
7755 __isl_take isl_basic_set *bset1,
7756 __isl_take isl_basic_set *bset2);
7757 __isl_give isl_set *isl_set_union(
7758 __isl_take isl_set *set1,
7759 __isl_take isl_set *set2);
7760 __isl_give isl_set *isl_set_list_union(
7761 __isl_take isl_set_list *list);
7763 #include <isl/map.h>
7764 __isl_give isl_map *isl_basic_map_union(
7765 __isl_take isl_basic_map *bmap1,
7766 __isl_take isl_basic_map *bmap2);
7767 __isl_give isl_map *isl_map_union(
7768 __isl_take isl_map *map1,
7769 __isl_take isl_map *map2);
7771 #include <isl/union_set.h>
7772 __isl_give isl_union_set *isl_union_set_union(
7773 __isl_take isl_union_set *uset1,
7774 __isl_take isl_union_set *uset2);
7775 __isl_give isl_union_set *isl_union_set_list_union(
7776 __isl_take isl_union_set_list *list);
7778 #include <isl/union_map.h>
7779 __isl_give isl_union_map *isl_union_map_union(
7780 __isl_take isl_union_map *umap1,
7781 __isl_take isl_union_map *umap2);
7783 The list passed to C<isl_set_list_union> needs to have
7784 at least one element and all elements need to live in the same space.
7786 =item * Set difference
7788 #include <isl/set.h>
7789 __isl_give isl_set *isl_set_subtract(
7790 __isl_take isl_set *set1,
7791 __isl_take isl_set *set2);
7793 #include <isl/map.h>
7794 __isl_give isl_map *isl_map_subtract(
7795 __isl_take isl_map *map1,
7796 __isl_take isl_map *map2);
7797 __isl_give isl_map *isl_map_subtract_domain(
7798 __isl_take isl_map *map,
7799 __isl_take isl_set *dom);
7800 __isl_give isl_map *isl_map_subtract_range(
7801 __isl_take isl_map *map,
7802 __isl_take isl_set *dom);
7804 #include <isl/union_set.h>
7805 __isl_give isl_union_set *isl_union_set_subtract(
7806 __isl_take isl_union_set *uset1,
7807 __isl_take isl_union_set *uset2);
7809 #include <isl/union_map.h>
7810 __isl_give isl_union_map *isl_union_map_subtract(
7811 __isl_take isl_union_map *umap1,
7812 __isl_take isl_union_map *umap2);
7813 __isl_give isl_union_map *isl_union_map_subtract_domain(
7814 __isl_take isl_union_map *umap,
7815 __isl_take isl_union_set *dom);
7816 __isl_give isl_union_map *isl_union_map_subtract_range(
7817 __isl_take isl_union_map *umap,
7818 __isl_take isl_union_set *dom);
7820 #include <isl/aff.h>
7821 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
7822 __isl_take isl_pw_aff *pa,
7823 __isl_take isl_set *set);
7824 __isl_give isl_pw_multi_aff *
7825 isl_pw_multi_aff_subtract_domain(
7826 __isl_take isl_pw_multi_aff *pma,
7827 __isl_take isl_set *set);
7828 __isl_give isl_union_pw_aff *
7829 isl_union_pw_aff_subtract_domain_union_set(
7830 __isl_take isl_union_pw_aff *upa,
7831 __isl_take isl_union_set *uset);
7832 __isl_give isl_union_pw_aff *
7833 isl_union_pw_aff_subtract_domain_space(
7834 __isl_take isl_union_pw_aff *upa,
7835 __isl_take isl_space *space);
7836 __isl_give isl_union_pw_aff *
7837 isl_union_pw_aff_subtract_domain(
7838 __isl_take isl_union_pw_aff *upa,
7839 __isl_take isl_union_set *uset);
7840 __isl_give isl_union_pw_multi_aff *
7841 isl_union_pw_multi_aff_subtract_domain_union_set(
7842 __isl_take isl_union_pw_multi_aff *upma,
7843 __isl_take isl_set *set);
7844 __isl_give isl_union_pw_multi_aff *
7845 isl_union_pw_multi_aff_subtract_domain_space(
7846 __isl_take isl_union_pw_multi_aff *upma,
7847 __isl_take isl_space *space);
7848 __isl_give isl_union_pw_multi_aff *
7849 isl_union_pw_multi_aff_subtract_domain(
7850 __isl_take isl_union_pw_multi_aff *upma,
7851 __isl_take isl_union_set *uset);
7853 #include <isl/polynomial.h>
7854 __isl_give isl_pw_qpolynomial *
7855 isl_pw_qpolynomial_subtract_domain(
7856 __isl_take isl_pw_qpolynomial *pwpq,
7857 __isl_take isl_set *set);
7858 __isl_give isl_pw_qpolynomial_fold *
7859 isl_pw_qpolynomial_fold_subtract_domain(
7860 __isl_take isl_pw_qpolynomial_fold *pwf,
7861 __isl_take isl_set *set);
7862 __isl_give isl_union_pw_qpolynomial *
7863 isl_union_pw_qpolynomial_subtract_domain_union_set(
7864 __isl_take isl_union_pw_qpolynomial *upwpq,
7865 __isl_take isl_union_set *uset);
7866 __isl_give isl_union_pw_qpolynomial *
7867 isl_union_pw_qpolynomial_subtract_domain_space(
7868 __isl_take isl_union_pw_qpolynomial *upwpq,
7869 __isl_take isl_space *space);
7870 __isl_give isl_union_pw_qpolynomial *
7871 isl_union_pw_qpolynomial_subtract_domain(
7872 __isl_take isl_union_pw_qpolynomial *upwpq,
7873 __isl_take isl_union_set *uset);
7874 __isl_give isl_union_pw_qpolynomial_fold *
7875 isl_union_pw_qpolynomial_fold_subtract_domain_union_set(
7876 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7877 __isl_take isl_union_set *uset);
7878 __isl_give isl_union_pw_qpolynomial_fold *
7879 isl_union_pw_qpolynomial_fold_subtract_domain_space(
7880 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7881 __isl_take isl_space *space);
7882 __isl_give isl_union_pw_qpolynomial_fold *
7883 isl_union_pw_qpolynomial_fold_subtract_domain(
7884 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7885 __isl_take isl_union_set *uset);
7887 C<isl_union_pw_aff_subtract_domain> is an alternative name for
7888 C<isl_union_pw_aff_subtract_domain_union_set>.
7889 Similarly for the other pairs of functions.
7893 #include <isl/space.h>
7894 __isl_give isl_space *isl_space_join(
7895 __isl_take isl_space *left,
7896 __isl_take isl_space *right);
7898 #include <isl/set.h>
7899 __isl_give isl_basic_set *isl_basic_set_apply(
7900 __isl_take isl_basic_set *bset,
7901 __isl_take isl_basic_map *bmap);
7902 __isl_give isl_set *isl_set_apply(
7903 __isl_take isl_set *set,
7904 __isl_take isl_map *map);
7906 #include <isl/union_set.h>
7907 __isl_give isl_union_set *isl_union_set_apply(
7908 __isl_take isl_union_set *uset,
7909 __isl_take isl_union_map *umap);
7911 #include <isl/map.h>
7912 __isl_give isl_basic_map *isl_basic_map_apply_domain(
7913 __isl_take isl_basic_map *bmap1,
7914 __isl_take isl_basic_map *bmap2);
7915 __isl_give isl_basic_map *isl_basic_map_apply_range(
7916 __isl_take isl_basic_map *bmap1,
7917 __isl_take isl_basic_map *bmap2);
7918 __isl_give isl_map *isl_map_apply_domain(
7919 __isl_take isl_map *map1,
7920 __isl_take isl_map *map2);
7921 __isl_give isl_map *isl_map_apply_range(
7922 __isl_take isl_map *map1,
7923 __isl_take isl_map *map2);
7925 #include <isl/union_map.h>
7926 __isl_give isl_union_map *isl_union_map_apply_domain(
7927 __isl_take isl_union_map *umap1,
7928 __isl_take isl_union_map *umap2);
7929 __isl_give isl_union_map *isl_union_map_apply_range(
7930 __isl_take isl_union_map *umap1,
7931 __isl_take isl_union_map *umap2);
7933 #include <isl/aff.h>
7934 __isl_give isl_union_pw_multi_aff *
7935 isl_union_pw_multi_aff_apply_union_pw_multi_aff(
7936 __isl_take isl_union_pw_multi_aff *upma1,
7937 __isl_take isl_union_pw_multi_aff *upma2);
7938 __isl_give isl_union_pw_aff *
7939 isl_multi_union_pw_aff_apply_aff(
7940 __isl_take isl_multi_union_pw_aff *mupa,
7941 __isl_take isl_aff *aff);
7942 __isl_give isl_union_pw_aff *
7943 isl_multi_union_pw_aff_apply_pw_aff(
7944 __isl_take isl_multi_union_pw_aff *mupa,
7945 __isl_take isl_pw_aff *pa);
7946 __isl_give isl_multi_union_pw_aff *
7947 isl_multi_union_pw_aff_apply_multi_aff(
7948 __isl_take isl_multi_union_pw_aff *mupa,
7949 __isl_take isl_multi_aff *ma);
7950 __isl_give isl_multi_union_pw_aff *
7951 isl_multi_union_pw_aff_apply_pw_multi_aff(
7952 __isl_take isl_multi_union_pw_aff *mupa,
7953 __isl_take isl_pw_multi_aff *pma);
7955 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
7956 over the shared domain of the elements of the input. The dimension is
7957 required to be greater than zero.
7958 The C<isl_multi_union_pw_aff> argument of
7959 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
7960 but only if the range of the C<isl_multi_aff> argument
7961 is also zero-dimensional.
7962 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
7964 #include <isl/polynomial.h>
7965 __isl_give isl_pw_qpolynomial_fold *
7966 isl_set_apply_pw_qpolynomial_fold(
7967 __isl_take isl_set *set,
7968 __isl_take isl_pw_qpolynomial_fold *pwf,
7970 __isl_give isl_pw_qpolynomial_fold *
7971 isl_map_apply_pw_qpolynomial_fold(
7972 __isl_take isl_map *map,
7973 __isl_take isl_pw_qpolynomial_fold *pwf,
7975 __isl_give isl_union_pw_qpolynomial_fold *
7976 isl_union_set_apply_union_pw_qpolynomial_fold(
7977 __isl_take isl_union_set *uset,
7978 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7980 __isl_give isl_union_pw_qpolynomial_fold *
7981 isl_union_map_apply_union_pw_qpolynomial_fold(
7982 __isl_take isl_union_map *umap,
7983 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7986 The functions taking a map
7987 compose the given map with the given piecewise quasipolynomial reduction.
7988 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
7989 over all elements in the intersection of the range of the map
7990 and the domain of the piecewise quasipolynomial reduction
7991 as a function of an element in the domain of the map.
7992 The functions taking a set compute a bound over all elements in the
7993 intersection of the set and the domain of the
7994 piecewise quasipolynomial reduction.
7998 #include <isl/set.h>
7999 __isl_give isl_basic_set *
8000 isl_basic_set_preimage_multi_aff(
8001 __isl_take isl_basic_set *bset,
8002 __isl_take isl_multi_aff *ma);
8003 __isl_give isl_set *isl_set_preimage_multi_aff(
8004 __isl_take isl_set *set,
8005 __isl_take isl_multi_aff *ma);
8006 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
8007 __isl_take isl_set *set,
8008 __isl_take isl_pw_multi_aff *pma);
8009 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
8010 __isl_take isl_set *set,
8011 __isl_take isl_multi_pw_aff *mpa);
8013 #include <isl/union_set.h>
8014 __isl_give isl_union_set *
8015 isl_union_set_preimage_multi_aff(
8016 __isl_take isl_union_set *uset,
8017 __isl_take isl_multi_aff *ma);
8018 __isl_give isl_union_set *
8019 isl_union_set_preimage_pw_multi_aff(
8020 __isl_take isl_union_set *uset,
8021 __isl_take isl_pw_multi_aff *pma);
8022 __isl_give isl_union_set *
8023 isl_union_set_preimage_union_pw_multi_aff(
8024 __isl_take isl_union_set *uset,
8025 __isl_take isl_union_pw_multi_aff *upma);
8027 #include <isl/map.h>
8028 __isl_give isl_basic_map *
8029 isl_basic_map_preimage_domain_multi_aff(
8030 __isl_take isl_basic_map *bmap,
8031 __isl_take isl_multi_aff *ma);
8032 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
8033 __isl_take isl_map *map,
8034 __isl_take isl_multi_aff *ma);
8035 __isl_give isl_map *isl_map_preimage_range_multi_aff(
8036 __isl_take isl_map *map,
8037 __isl_take isl_multi_aff *ma);
8038 __isl_give isl_map *
8039 isl_map_preimage_domain_pw_multi_aff(
8040 __isl_take isl_map *map,
8041 __isl_take isl_pw_multi_aff *pma);
8042 __isl_give isl_map *
8043 isl_map_preimage_range_pw_multi_aff(
8044 __isl_take isl_map *map,
8045 __isl_take isl_pw_multi_aff *pma);
8046 __isl_give isl_map *
8047 isl_map_preimage_domain_multi_pw_aff(
8048 __isl_take isl_map *map,
8049 __isl_take isl_multi_pw_aff *mpa);
8050 __isl_give isl_basic_map *
8051 isl_basic_map_preimage_range_multi_aff(
8052 __isl_take isl_basic_map *bmap,
8053 __isl_take isl_multi_aff *ma);
8055 #include <isl/union_map.h>
8056 __isl_give isl_union_map *
8057 isl_union_map_preimage_domain_multi_aff(
8058 __isl_take isl_union_map *umap,
8059 __isl_take isl_multi_aff *ma);
8060 __isl_give isl_union_map *
8061 isl_union_map_preimage_range_multi_aff(
8062 __isl_take isl_union_map *umap,
8063 __isl_take isl_multi_aff *ma);
8064 __isl_give isl_union_map *
8065 isl_union_map_preimage_domain_pw_multi_aff(
8066 __isl_take isl_union_map *umap,
8067 __isl_take isl_pw_multi_aff *pma);
8068 __isl_give isl_union_map *
8069 isl_union_map_preimage_range_pw_multi_aff(
8070 __isl_take isl_union_map *umap,
8071 __isl_take isl_pw_multi_aff *pma);
8072 __isl_give isl_union_map *
8073 isl_union_map_preimage_domain_union_pw_multi_aff(
8074 __isl_take isl_union_map *umap,
8075 __isl_take isl_union_pw_multi_aff *upma);
8076 __isl_give isl_union_map *
8077 isl_union_map_preimage_range_union_pw_multi_aff(
8078 __isl_take isl_union_map *umap,
8079 __isl_take isl_union_pw_multi_aff *upma);
8081 #include <isl/aff.h>
8082 __isl_give isl_pw_multi_aff *
8083 isl_pw_multi_aff_preimage_domain_wrapped_domain_pw_multi_aff(
8084 __isl_take isl_pw_multi_aff *pma1,
8085 __isl_take isl_pw_multi_aff *pma2);
8086 __isl_give isl_union_pw_multi_aff *
8087 isl_union_pw_multi_aff_preimage_domain_wrapped_domain_union_pw_multi_aff(
8088 __isl_take isl_union_pw_multi_aff *upma1,
8089 __isl_take isl_union_pw_multi_aff *upma2);
8091 These functions compute the preimage of the given set or map domain/range under
8092 the given function. In other words, the expression is plugged
8093 into the set description or into the domain/range of the map or function.
8097 #include <isl/aff.h>
8098 __isl_give isl_aff *isl_aff_pullback_aff(
8099 __isl_take isl_aff *aff1,
8100 __isl_take isl_aff *aff2);
8101 __isl_give isl_aff *isl_aff_pullback_multi_aff(
8102 __isl_take isl_aff *aff,
8103 __isl_take isl_multi_aff *ma);
8104 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
8105 __isl_take isl_pw_aff *pa,
8106 __isl_take isl_multi_aff *ma);
8107 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
8108 __isl_take isl_pw_aff *pa,
8109 __isl_take isl_pw_multi_aff *pma);
8110 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
8111 __isl_take isl_pw_aff *pa,
8112 __isl_take isl_multi_pw_aff *mpa);
8113 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
8114 __isl_take isl_multi_aff *ma1,
8115 __isl_take isl_multi_aff *ma2);
8116 __isl_give isl_pw_multi_aff *
8117 isl_pw_multi_aff_pullback_multi_aff(
8118 __isl_take isl_pw_multi_aff *pma,
8119 __isl_take isl_multi_aff *ma);
8120 __isl_give isl_multi_pw_aff *
8121 isl_multi_pw_aff_pullback_multi_aff(
8122 __isl_take isl_multi_pw_aff *mpa,
8123 __isl_take isl_multi_aff *ma);
8124 __isl_give isl_pw_multi_aff *
8125 isl_pw_multi_aff_pullback_pw_multi_aff(
8126 __isl_take isl_pw_multi_aff *pma1,
8127 __isl_take isl_pw_multi_aff *pma2);
8128 __isl_give isl_multi_pw_aff *
8129 isl_multi_pw_aff_pullback_pw_multi_aff(
8130 __isl_take isl_multi_pw_aff *mpa,
8131 __isl_take isl_pw_multi_aff *pma);
8132 __isl_give isl_multi_pw_aff *
8133 isl_multi_pw_aff_pullback_multi_pw_aff(
8134 __isl_take isl_multi_pw_aff *mpa1,
8135 __isl_take isl_multi_pw_aff *mpa2);
8136 __isl_give isl_union_pw_aff *
8137 isl_union_pw_aff_pullback_union_pw_multi_aff(
8138 __isl_take isl_union_pw_aff *upa,
8139 __isl_take isl_union_pw_multi_aff *upma);
8140 __isl_give isl_union_pw_multi_aff *
8141 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
8142 __isl_take isl_union_pw_multi_aff *upma1,
8143 __isl_take isl_union_pw_multi_aff *upma2);
8144 __isl_give isl_multi_union_pw_aff *
8145 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
8146 __isl_take isl_multi_union_pw_aff *mupa,
8147 __isl_take isl_union_pw_multi_aff *upma);
8149 These functions precompose the first expression by the second function.
8150 In other words, the second function is plugged
8151 into the first expression.
8155 #include <isl/aff.h>
8156 __isl_give isl_basic_set *isl_aff_eq_basic_set(
8157 __isl_take isl_aff *aff1,
8158 __isl_take isl_aff *aff2);
8159 __isl_give isl_set *isl_aff_eq_set(
8160 __isl_take isl_aff *aff1,
8161 __isl_take isl_aff *aff2);
8162 __isl_give isl_set *isl_aff_ne_set(
8163 __isl_take isl_aff *aff1,
8164 __isl_take isl_aff *aff2);
8165 __isl_give isl_basic_set *isl_aff_le_basic_set(
8166 __isl_take isl_aff *aff1,
8167 __isl_take isl_aff *aff2);
8168 __isl_give isl_set *isl_aff_le_set(
8169 __isl_take isl_aff *aff1,
8170 __isl_take isl_aff *aff2);
8171 __isl_give isl_basic_set *isl_aff_lt_basic_set(
8172 __isl_take isl_aff *aff1,
8173 __isl_take isl_aff *aff2);
8174 __isl_give isl_set *isl_aff_lt_set(
8175 __isl_take isl_aff *aff1,
8176 __isl_take isl_aff *aff2);
8177 __isl_give isl_basic_set *isl_aff_ge_basic_set(
8178 __isl_take isl_aff *aff1,
8179 __isl_take isl_aff *aff2);
8180 __isl_give isl_set *isl_aff_ge_set(
8181 __isl_take isl_aff *aff1,
8182 __isl_take isl_aff *aff2);
8183 __isl_give isl_basic_set *isl_aff_gt_basic_set(
8184 __isl_take isl_aff *aff1,
8185 __isl_take isl_aff *aff2);
8186 __isl_give isl_set *isl_aff_gt_set(
8187 __isl_take isl_aff *aff1,
8188 __isl_take isl_aff *aff2);
8189 __isl_give isl_set *isl_pw_aff_eq_set(
8190 __isl_take isl_pw_aff *pwaff1,
8191 __isl_take isl_pw_aff *pwaff2);
8192 __isl_give isl_set *isl_pw_aff_ne_set(
8193 __isl_take isl_pw_aff *pwaff1,
8194 __isl_take isl_pw_aff *pwaff2);
8195 __isl_give isl_set *isl_pw_aff_le_set(
8196 __isl_take isl_pw_aff *pwaff1,
8197 __isl_take isl_pw_aff *pwaff2);
8198 __isl_give isl_set *isl_pw_aff_lt_set(
8199 __isl_take isl_pw_aff *pwaff1,
8200 __isl_take isl_pw_aff *pwaff2);
8201 __isl_give isl_set *isl_pw_aff_ge_set(
8202 __isl_take isl_pw_aff *pwaff1,
8203 __isl_take isl_pw_aff *pwaff2);
8204 __isl_give isl_set *isl_pw_aff_gt_set(
8205 __isl_take isl_pw_aff *pwaff1,
8206 __isl_take isl_pw_aff *pwaff2);
8208 __isl_give isl_set *isl_multi_aff_lex_le_set(
8209 __isl_take isl_multi_aff *ma1,
8210 __isl_take isl_multi_aff *ma2);
8211 __isl_give isl_set *isl_multi_aff_lex_lt_set(
8212 __isl_take isl_multi_aff *ma1,
8213 __isl_take isl_multi_aff *ma2);
8214 __isl_give isl_set *isl_multi_aff_lex_ge_set(
8215 __isl_take isl_multi_aff *ma1,
8216 __isl_take isl_multi_aff *ma2);
8217 __isl_give isl_set *isl_multi_aff_lex_gt_set(
8218 __isl_take isl_multi_aff *ma1,
8219 __isl_take isl_multi_aff *ma2);
8221 __isl_give isl_set *isl_pw_aff_list_eq_set(
8222 __isl_take isl_pw_aff_list *list1,
8223 __isl_take isl_pw_aff_list *list2);
8224 __isl_give isl_set *isl_pw_aff_list_ne_set(
8225 __isl_take isl_pw_aff_list *list1,
8226 __isl_take isl_pw_aff_list *list2);
8227 __isl_give isl_set *isl_pw_aff_list_le_set(
8228 __isl_take isl_pw_aff_list *list1,
8229 __isl_take isl_pw_aff_list *list2);
8230 __isl_give isl_set *isl_pw_aff_list_lt_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_ge_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_gt_set(
8237 __isl_take isl_pw_aff_list *list1,
8238 __isl_take isl_pw_aff_list *list2);
8240 The function C<isl_aff_ge_basic_set> returns a basic set
8241 containing those elements in the shared space
8242 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
8243 The function C<isl_pw_aff_ge_set> returns a set
8244 containing those elements in the shared domain
8245 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
8246 greater than or equal to C<pwaff2>.
8247 The function C<isl_multi_aff_lex_le_set> returns a set
8248 containing those elements in the shared domain space
8249 where C<ma1> is lexicographically smaller than or
8251 The functions operating on C<isl_pw_aff_list> apply the corresponding
8252 C<isl_pw_aff> function to each pair of elements in the two lists.
8254 #include <isl/aff.h>
8255 __isl_give isl_map *isl_pw_aff_eq_map(
8256 __isl_take isl_pw_aff *pa1,
8257 __isl_take isl_pw_aff *pa2);
8258 __isl_give isl_map *isl_pw_aff_le_map(
8259 __isl_take isl_pw_aff *pa1,
8260 __isl_take isl_pw_aff *pa2);
8261 __isl_give isl_map *isl_pw_aff_lt_map(
8262 __isl_take isl_pw_aff *pa1,
8263 __isl_take isl_pw_aff *pa2);
8264 __isl_give isl_map *isl_pw_aff_ge_map(
8265 __isl_take isl_pw_aff *pa1,
8266 __isl_take isl_pw_aff *pa2);
8267 __isl_give isl_map *isl_pw_aff_gt_map(
8268 __isl_take isl_pw_aff *pa1,
8269 __isl_take isl_pw_aff *pa2);
8271 __isl_give isl_map *isl_multi_pw_aff_eq_map(
8272 __isl_take isl_multi_pw_aff *mpa1,
8273 __isl_take isl_multi_pw_aff *mpa2);
8274 __isl_give isl_map *isl_multi_pw_aff_lex_le_map(
8275 __isl_take isl_multi_pw_aff *mpa1,
8276 __isl_take isl_multi_pw_aff *mpa2);
8277 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
8278 __isl_take isl_multi_pw_aff *mpa1,
8279 __isl_take isl_multi_pw_aff *mpa2);
8280 __isl_give isl_map *isl_multi_pw_aff_lex_ge_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_gt_map(
8284 __isl_take isl_multi_pw_aff *mpa1,
8285 __isl_take isl_multi_pw_aff *mpa2);
8287 These functions return a map between domain elements of the arguments
8288 where the function values satisfy the given relation.
8290 #include <isl/map.h>
8291 __isl_give isl_map *isl_map_eq_at_multi_pw_aff(
8292 __isl_take isl_map *map,
8293 __isl_take isl_multi_pw_aff *mpa);
8294 __isl_give isl_map *isl_map_lex_lt_at_multi_pw_aff(
8295 __isl_take isl_map *map,
8296 __isl_take isl_multi_pw_aff *mpa);
8297 __isl_give isl_map *isl_map_lex_le_at_multi_pw_aff(
8298 __isl_take isl_map *map,
8299 __isl_take isl_multi_pw_aff *mpa);
8300 __isl_give isl_map *isl_map_lex_gt_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_ge_at_multi_pw_aff(
8304 __isl_take isl_map *map,
8305 __isl_take isl_multi_pw_aff *mpa);
8307 #include <isl/union_map.h>
8308 __isl_give isl_union_map *
8309 isl_union_map_eq_at_multi_union_pw_aff(
8310 __isl_take isl_union_map *umap,
8311 __isl_take isl_multi_union_pw_aff *mupa);
8312 __isl_give isl_union_map *
8313 isl_union_map_lex_lt_at_multi_union_pw_aff(
8314 __isl_take isl_union_map *umap,
8315 __isl_take isl_multi_union_pw_aff *mupa);
8316 __isl_give isl_union_map *
8317 isl_union_map_lex_le_at_multi_union_pw_aff(
8318 __isl_take isl_union_map *umap,
8319 __isl_take isl_multi_union_pw_aff *mupa);
8320 __isl_give isl_union_map *
8321 isl_union_map_lex_gt_at_multi_union_pw_aff(
8322 __isl_take isl_union_map *umap,
8323 __isl_take isl_multi_union_pw_aff *mupa);
8324 __isl_give isl_union_map *
8325 isl_union_map_lex_ge_at_multi_union_pw_aff(
8326 __isl_take isl_union_map *umap,
8327 __isl_take isl_multi_union_pw_aff *mupa);
8329 These functions select the subset of elements in the union map
8330 that have an equal or lexicographically smaller or greater function value.
8332 =item * Cartesian Product
8334 #include <isl/space.h>
8335 __isl_give isl_space *isl_space_product(
8336 __isl_take isl_space *space1,
8337 __isl_take isl_space *space2);
8338 __isl_give isl_space *isl_space_domain_product(
8339 __isl_take isl_space *space1,
8340 __isl_take isl_space *space2);
8341 __isl_give isl_space *isl_space_range_product(
8342 __isl_take isl_space *space1,
8343 __isl_take isl_space *space2);
8346 C<isl_space_product>, C<isl_space_domain_product>
8347 and C<isl_space_range_product> take pairs or relation spaces and
8348 produce a single relations space, where either the domain, the range
8349 or both domain and range are wrapped spaces of relations between
8350 the domains and/or ranges of the input spaces.
8351 If the product is only constructed over the domain or the range
8352 then the ranges or the domains of the inputs should be the same.
8353 The function C<isl_space_product> also accepts a pair of set spaces,
8354 in which case it returns a wrapped space of a relation between the
8357 #include <isl/set.h>
8358 __isl_give isl_set *isl_set_product(
8359 __isl_take isl_set *set1,
8360 __isl_take isl_set *set2);
8362 #include <isl/map.h>
8363 __isl_give isl_basic_map *isl_basic_map_domain_product(
8364 __isl_take isl_basic_map *bmap1,
8365 __isl_take isl_basic_map *bmap2);
8366 __isl_give isl_basic_map *isl_basic_map_range_product(
8367 __isl_take isl_basic_map *bmap1,
8368 __isl_take isl_basic_map *bmap2);
8369 __isl_give isl_basic_map *isl_basic_map_product(
8370 __isl_take isl_basic_map *bmap1,
8371 __isl_take isl_basic_map *bmap2);
8372 __isl_give isl_map *isl_map_domain_product(
8373 __isl_take isl_map *map1,
8374 __isl_take isl_map *map2);
8375 __isl_give isl_map *isl_map_range_product(
8376 __isl_take isl_map *map1,
8377 __isl_take isl_map *map2);
8378 __isl_give isl_map *isl_map_product(
8379 __isl_take isl_map *map1,
8380 __isl_take isl_map *map2);
8382 #include <isl/union_set.h>
8383 __isl_give isl_union_set *isl_union_set_product(
8384 __isl_take isl_union_set *uset1,
8385 __isl_take isl_union_set *uset2);
8387 #include <isl/union_map.h>
8388 __isl_give isl_union_map *isl_union_map_domain_product(
8389 __isl_take isl_union_map *umap1,
8390 __isl_take isl_union_map *umap2);
8391 __isl_give isl_union_map *isl_union_map_range_product(
8392 __isl_take isl_union_map *umap1,
8393 __isl_take isl_union_map *umap2);
8394 __isl_give isl_union_map *isl_union_map_product(
8395 __isl_take isl_union_map *umap1,
8396 __isl_take isl_union_map *umap2);
8399 __isl_give isl_multi_id *isl_multi_id_range_product(
8400 __isl_take isl_multi_id *mi1,
8401 __isl_take isl_multi_id *mi2);
8403 #include <isl/val.h>
8404 __isl_give isl_multi_val *isl_multi_val_range_product(
8405 __isl_take isl_multi_val *mv1,
8406 __isl_take isl_multi_val *mv2);
8407 __isl_give isl_multi_val *isl_multi_val_product(
8408 __isl_take isl_multi_val *mv1,
8409 __isl_take isl_multi_val *mv2);
8411 #include <isl/aff.h>
8412 __isl_give isl_multi_aff *isl_multi_aff_range_product(
8413 __isl_take isl_multi_aff *ma1,
8414 __isl_take isl_multi_aff *ma2);
8415 __isl_give isl_multi_aff *isl_multi_aff_product(
8416 __isl_take isl_multi_aff *ma1,
8417 __isl_take isl_multi_aff *ma2);
8418 __isl_give isl_multi_pw_aff *
8419 isl_multi_pw_aff_range_product(
8420 __isl_take isl_multi_pw_aff *mpa1,
8421 __isl_take isl_multi_pw_aff *mpa2);
8422 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
8423 __isl_take isl_multi_pw_aff *mpa1,
8424 __isl_take isl_multi_pw_aff *mpa2);
8425 __isl_give isl_pw_multi_aff *
8426 isl_pw_multi_aff_range_product(
8427 __isl_take isl_pw_multi_aff *pma1,
8428 __isl_take isl_pw_multi_aff *pma2);
8429 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
8430 __isl_take isl_pw_multi_aff *pma1,
8431 __isl_take isl_pw_multi_aff *pma2);
8432 __isl_give isl_union_pw_multi_aff *
8433 isl_union_pw_multi_aff_range_product(
8434 __isl_take isl_union_pw_multi_aff *upma1,
8435 __isl_take isl_union_pw_multi_aff *upma2);
8436 __isl_give isl_multi_union_pw_aff *
8437 isl_multi_union_pw_aff_range_product(
8438 __isl_take isl_multi_union_pw_aff *mupa1,
8439 __isl_take isl_multi_union_pw_aff *mupa2);
8441 The above functions compute the cross product of the given
8442 sets, relations or functions. The domains and ranges of the results
8443 are wrapped maps between domains and ranges of the inputs.
8444 To obtain a ``flat'' product, use the following functions
8447 #include <isl/set.h>
8448 __isl_give isl_basic_set *isl_basic_set_flat_product(
8449 __isl_take isl_basic_set *bset1,
8450 __isl_take isl_basic_set *bset2);
8451 __isl_give isl_set *isl_set_flat_product(
8452 __isl_take isl_set *set1,
8453 __isl_take isl_set *set2);
8455 #include <isl/map.h>
8456 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
8457 __isl_take isl_basic_map *bmap1,
8458 __isl_take isl_basic_map *bmap2);
8459 __isl_give isl_map *isl_map_flat_domain_product(
8460 __isl_take isl_map *map1,
8461 __isl_take isl_map *map2);
8462 __isl_give isl_map *isl_map_flat_range_product(
8463 __isl_take isl_map *map1,
8464 __isl_take isl_map *map2);
8465 __isl_give isl_basic_map *isl_basic_map_flat_product(
8466 __isl_take isl_basic_map *bmap1,
8467 __isl_take isl_basic_map *bmap2);
8468 __isl_give isl_map *isl_map_flat_product(
8469 __isl_take isl_map *map1,
8470 __isl_take isl_map *map2);
8472 #include <isl/union_map.h>
8473 __isl_give isl_union_map *
8474 isl_union_map_flat_domain_product(
8475 __isl_take isl_union_map *umap1,
8476 __isl_take isl_union_map *umap2);
8477 __isl_give isl_union_map *
8478 isl_union_map_flat_range_product(
8479 __isl_take isl_union_map *umap1,
8480 __isl_take isl_union_map *umap2);
8483 __isl_give isl_multi_id *
8484 isl_multi_id_flat_range_product(
8485 __isl_take isl_multi_id *mi1,
8486 __isl_take isl_multi_id *mi2);
8488 #include <isl/val.h>
8489 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
8490 __isl_take isl_multi_val *mv1,
8491 __isl_take isl_multi_val *mv2);
8493 #include <isl/aff.h>
8494 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
8495 __isl_take isl_multi_aff *ma1,
8496 __isl_take isl_multi_aff *ma2);
8497 __isl_give isl_pw_multi_aff *
8498 isl_pw_multi_aff_flat_range_product(
8499 __isl_take isl_pw_multi_aff *pma1,
8500 __isl_take isl_pw_multi_aff *pma2);
8501 __isl_give isl_multi_pw_aff *
8502 isl_multi_pw_aff_flat_range_product(
8503 __isl_take isl_multi_pw_aff *mpa1,
8504 __isl_take isl_multi_pw_aff *mpa2);
8505 __isl_give isl_union_pw_multi_aff *
8506 isl_union_pw_multi_aff_flat_range_product(
8507 __isl_take isl_union_pw_multi_aff *upma1,
8508 __isl_take isl_union_pw_multi_aff *upma2);
8509 __isl_give isl_multi_union_pw_aff *
8510 isl_multi_union_pw_aff_flat_range_product(
8511 __isl_take isl_multi_union_pw_aff *mupa1,
8512 __isl_take isl_multi_union_pw_aff *mupa2);
8514 #include <isl/space.h>
8515 __isl_give isl_space *isl_space_factor_domain(
8516 __isl_take isl_space *space);
8517 __isl_give isl_space *isl_space_factor_range(
8518 __isl_take isl_space *space);
8519 __isl_give isl_space *isl_space_domain_factor_domain(
8520 __isl_take isl_space *space);
8521 __isl_give isl_space *isl_space_domain_factor_range(
8522 __isl_take isl_space *space);
8523 __isl_give isl_space *isl_space_range_factor_domain(
8524 __isl_take isl_space *space);
8525 __isl_give isl_space *isl_space_range_factor_range(
8526 __isl_take isl_space *space);
8528 The functions C<isl_space_range_factor_domain> and
8529 C<isl_space_range_factor_range> extract the two arguments from
8530 the result of a call to C<isl_space_range_product>.
8532 The arguments of a call to a product can be extracted
8533 from the result using the following functions.
8535 #include <isl/map.h>
8536 __isl_give isl_map *isl_map_factor_domain(
8537 __isl_take isl_map *map);
8538 __isl_give isl_map *isl_map_factor_range(
8539 __isl_take isl_map *map);
8540 __isl_give isl_map *isl_map_domain_factor_domain(
8541 __isl_take isl_map *map);
8542 __isl_give isl_map *isl_map_domain_factor_range(
8543 __isl_take isl_map *map);
8544 __isl_give isl_map *isl_map_range_factor_domain(
8545 __isl_take isl_map *map);
8546 __isl_give isl_map *isl_map_range_factor_range(
8547 __isl_take isl_map *map);
8549 #include <isl/union_map.h>
8550 __isl_give isl_union_map *isl_union_map_factor_domain(
8551 __isl_take isl_union_map *umap);
8552 __isl_give isl_union_map *isl_union_map_factor_range(
8553 __isl_take isl_union_map *umap);
8554 __isl_give isl_union_map *
8555 isl_union_map_domain_factor_domain(
8556 __isl_take isl_union_map *umap);
8557 __isl_give isl_union_map *
8558 isl_union_map_domain_factor_range(
8559 __isl_take isl_union_map *umap);
8560 __isl_give isl_union_map *
8561 isl_union_map_range_factor_domain(
8562 __isl_take isl_union_map *umap);
8563 __isl_give isl_union_map *
8564 isl_union_map_range_factor_range(
8565 __isl_take isl_union_map *umap);
8568 __isl_give isl_multi_id *isl_multi_id_factor_range(
8569 __isl_take isl_multi_id *mi);
8570 __isl_give isl_multi_id *
8571 isl_multi_id_range_factor_domain(
8572 __isl_take isl_multi_id *mi);
8573 __isl_give isl_multi_id *
8574 isl_multi_id_range_factor_range(
8575 __isl_take isl_multi_id *mi);
8577 #include <isl/val.h>
8578 __isl_give isl_multi_val *isl_multi_val_factor_range(
8579 __isl_take isl_multi_val *mv);
8580 __isl_give isl_multi_val *
8581 isl_multi_val_range_factor_domain(
8582 __isl_take isl_multi_val *mv);
8583 __isl_give isl_multi_val *
8584 isl_multi_val_range_factor_range(
8585 __isl_take isl_multi_val *mv);
8587 #include <isl/aff.h>
8588 __isl_give isl_multi_aff *isl_multi_aff_factor_range(
8589 __isl_take isl_multi_aff *ma);
8590 __isl_give isl_multi_aff *
8591 isl_multi_aff_range_factor_domain(
8592 __isl_take isl_multi_aff *ma);
8593 __isl_give isl_multi_aff *
8594 isl_multi_aff_range_factor_range(
8595 __isl_take isl_multi_aff *ma);
8596 __isl_give isl_multi_pw_aff *
8597 isl_multi_pw_aff_factor_range(
8598 __isl_take isl_multi_pw_aff *mpa);
8599 __isl_give isl_multi_pw_aff *
8600 isl_multi_pw_aff_range_factor_domain(
8601 __isl_take isl_multi_pw_aff *mpa);
8602 __isl_give isl_multi_pw_aff *
8603 isl_multi_pw_aff_range_factor_range(
8604 __isl_take isl_multi_pw_aff *mpa);
8605 __isl_give isl_pw_multi_aff *
8606 isl_pw_multi_aff_range_factor_domain(
8607 __isl_take isl_pw_multi_aff *pma);
8608 __isl_give isl_pw_multi_aff *
8609 isl_pw_multi_aff_range_factor_range(
8610 __isl_take isl_pw_multi_aff *pma);
8611 __isl_give isl_union_pw_multi_aff *
8612 isl_union_pw_multi_aff_range_factor_domain(
8613 __isl_take isl_union_pw_multi_aff *upma);
8614 __isl_give isl_union_pw_multi_aff *
8615 isl_union_pw_multi_aff_range_factor_range(
8616 __isl_take isl_union_pw_multi_aff *upma);
8617 __isl_give isl_multi_union_pw_aff *
8618 isl_multi_union_pw_aff_factor_range(
8619 __isl_take isl_multi_union_pw_aff *mupa);
8620 __isl_give isl_multi_union_pw_aff *
8621 isl_multi_union_pw_aff_range_factor_domain(
8622 __isl_take isl_multi_union_pw_aff *mupa);
8623 __isl_give isl_multi_union_pw_aff *
8624 isl_multi_union_pw_aff_range_factor_range(
8625 __isl_take isl_multi_union_pw_aff *mupa);
8627 The splice functions are a generalization of the flat product functions,
8628 where the second argument may be inserted at any position inside
8629 the first argument rather than being placed at the end.
8630 The functions C<isl_multi_val_factor_range>,
8631 C<isl_multi_aff_factor_range>,
8632 C<isl_multi_pw_aff_factor_range> and
8633 C<isl_multi_union_pw_aff_factor_range>
8634 take functions that live in a set space.
8637 __isl_give isl_multi_id *isl_multi_id_range_splice(
8638 __isl_take isl_multi_id *mi1, unsigned pos,
8639 __isl_take isl_multi_id *mi2);
8641 #include <isl/val.h>
8642 __isl_give isl_multi_val *isl_multi_val_range_splice(
8643 __isl_take isl_multi_val *mv1, unsigned pos,
8644 __isl_take isl_multi_val *mv2);
8646 #include <isl/aff.h>
8647 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
8648 __isl_take isl_multi_aff *ma1, unsigned pos,
8649 __isl_take isl_multi_aff *ma2);
8650 __isl_give isl_multi_aff *isl_multi_aff_splice(
8651 __isl_take isl_multi_aff *ma1,
8652 unsigned in_pos, unsigned out_pos,
8653 __isl_take isl_multi_aff *ma2);
8654 __isl_give isl_multi_pw_aff *
8655 isl_multi_pw_aff_range_splice(
8656 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
8657 __isl_take isl_multi_pw_aff *mpa2);
8658 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
8659 __isl_take isl_multi_pw_aff *mpa1,
8660 unsigned in_pos, unsigned out_pos,
8661 __isl_take isl_multi_pw_aff *mpa2);
8662 __isl_give isl_multi_union_pw_aff *
8663 isl_multi_union_pw_aff_range_splice(
8664 __isl_take isl_multi_union_pw_aff *mupa1,
8666 __isl_take isl_multi_union_pw_aff *mupa2);
8668 =item * Simplification
8670 When applied to a set or relation,
8671 the gist operation returns a set or relation that has the
8672 same intersection with the context as the input set or relation.
8673 Any implicit equality in the intersection is made explicit in the result,
8674 while all inequalities that are redundant with respect to the intersection
8676 In case of union sets and relations, the gist operation is performed
8679 When applied to a function,
8680 the gist operation applies the set gist operation to each of
8681 the cells in the domain of the input piecewise expression.
8682 The context is also exploited
8683 to simplify the expression associated to each cell.
8685 #include <isl/set.h>
8686 __isl_give isl_basic_set *isl_basic_set_gist(
8687 __isl_take isl_basic_set *bset,
8688 __isl_take isl_basic_set *context);
8689 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
8690 __isl_take isl_set *context);
8691 __isl_give isl_set *isl_set_gist_params(
8692 __isl_take isl_set *set,
8693 __isl_take isl_set *context);
8695 #include <isl/map.h>
8696 __isl_give isl_basic_map *isl_basic_map_gist(
8697 __isl_take isl_basic_map *bmap,
8698 __isl_take isl_basic_map *context);
8699 __isl_give isl_basic_map *isl_basic_map_gist_domain(
8700 __isl_take isl_basic_map *bmap,
8701 __isl_take isl_basic_set *context);
8702 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
8703 __isl_take isl_map *context);
8704 __isl_give isl_map *isl_map_gist_params(
8705 __isl_take isl_map *map,
8706 __isl_take isl_set *context);
8707 __isl_give isl_map *isl_map_gist_domain(
8708 __isl_take isl_map *map,
8709 __isl_take isl_set *context);
8710 __isl_give isl_map *isl_map_gist_range(
8711 __isl_take isl_map *map,
8712 __isl_take isl_set *context);
8714 #include <isl/union_set.h>
8715 __isl_give isl_union_set *isl_union_set_gist(
8716 __isl_take isl_union_set *uset,
8717 __isl_take isl_union_set *context);
8718 __isl_give isl_union_set *isl_union_set_gist_params(
8719 __isl_take isl_union_set *uset,
8720 __isl_take isl_set *set);
8722 #include <isl/union_map.h>
8723 __isl_give isl_union_map *isl_union_map_gist(
8724 __isl_take isl_union_map *umap,
8725 __isl_take isl_union_map *context);
8726 __isl_give isl_union_map *isl_union_map_gist_params(
8727 __isl_take isl_union_map *umap,
8728 __isl_take isl_set *set);
8729 __isl_give isl_union_map *isl_union_map_gist_domain(
8730 __isl_take isl_union_map *umap,
8731 __isl_take isl_union_set *uset);
8732 __isl_give isl_union_map *isl_union_map_gist_range(
8733 __isl_take isl_union_map *umap,
8734 __isl_take isl_union_set *uset);
8736 #include <isl/aff.h>
8737 __isl_give isl_aff *isl_aff_gist_params(
8738 __isl_take isl_aff *aff,
8739 __isl_take isl_set *context);
8740 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
8741 __isl_take isl_set *context);
8742 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
8743 __isl_take isl_multi_aff *maff,
8744 __isl_take isl_set *context);
8745 __isl_give isl_multi_aff *isl_multi_aff_gist(
8746 __isl_take isl_multi_aff *maff,
8747 __isl_take isl_set *context);
8748 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
8749 __isl_take isl_pw_aff *pwaff,
8750 __isl_take isl_set *context);
8751 __isl_give isl_pw_aff *isl_pw_aff_gist(
8752 __isl_take isl_pw_aff *pwaff,
8753 __isl_take isl_set *context);
8754 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
8755 __isl_take isl_pw_multi_aff *pma,
8756 __isl_take isl_set *set);
8757 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
8758 __isl_take isl_pw_multi_aff *pma,
8759 __isl_take isl_set *set);
8760 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
8761 __isl_take isl_multi_pw_aff *mpa,
8762 __isl_take isl_set *set);
8763 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
8764 __isl_take isl_multi_pw_aff *mpa,
8765 __isl_take isl_set *set);
8766 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
8767 __isl_take isl_union_pw_aff *upa,
8768 __isl_take isl_union_set *context);
8769 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
8770 __isl_take isl_union_pw_aff *upa,
8771 __isl_take isl_set *context);
8772 __isl_give isl_union_pw_multi_aff *
8773 isl_union_pw_multi_aff_gist_params(
8774 __isl_take isl_union_pw_multi_aff *upma,
8775 __isl_take isl_set *context);
8776 __isl_give isl_union_pw_multi_aff *
8777 isl_union_pw_multi_aff_gist(
8778 __isl_take isl_union_pw_multi_aff *upma,
8779 __isl_take isl_union_set *context);
8780 __isl_give isl_multi_union_pw_aff *
8781 isl_multi_union_pw_aff_gist_params(
8782 __isl_take isl_multi_union_pw_aff *mupa,
8783 __isl_take isl_set *context);
8784 __isl_give isl_multi_union_pw_aff *
8785 isl_multi_union_pw_aff_gist(
8786 __isl_take isl_multi_union_pw_aff *mupa,
8787 __isl_take isl_union_set *context);
8789 #include <isl/polynomial.h>
8790 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
8791 __isl_take isl_qpolynomial *qp,
8792 __isl_take isl_set *context);
8793 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
8794 __isl_take isl_qpolynomial *qp,
8795 __isl_take isl_set *context);
8796 __isl_give isl_qpolynomial_fold *
8797 isl_qpolynomial_fold_gist_params(
8798 __isl_take isl_qpolynomial_fold *fold,
8799 __isl_take isl_set *context);
8800 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
8801 __isl_take isl_qpolynomial_fold *fold,
8802 __isl_take isl_set *context);
8803 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
8804 __isl_take isl_pw_qpolynomial *pwqp,
8805 __isl_take isl_set *context);
8806 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
8807 __isl_take isl_pw_qpolynomial *pwqp,
8808 __isl_take isl_set *context);
8809 __isl_give isl_pw_qpolynomial_fold *
8810 isl_pw_qpolynomial_fold_gist(
8811 __isl_take isl_pw_qpolynomial_fold *pwf,
8812 __isl_take isl_set *context);
8813 __isl_give isl_pw_qpolynomial_fold *
8814 isl_pw_qpolynomial_fold_gist_params(
8815 __isl_take isl_pw_qpolynomial_fold *pwf,
8816 __isl_take isl_set *context);
8817 __isl_give isl_union_pw_qpolynomial *
8818 isl_union_pw_qpolynomial_gist_params(
8819 __isl_take isl_union_pw_qpolynomial *upwqp,
8820 __isl_take isl_set *context);
8821 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
8822 __isl_take isl_union_pw_qpolynomial *upwqp,
8823 __isl_take isl_union_set *context);
8824 __isl_give isl_union_pw_qpolynomial_fold *
8825 isl_union_pw_qpolynomial_fold_gist(
8826 __isl_take isl_union_pw_qpolynomial_fold *upwf,
8827 __isl_take isl_union_set *context);
8828 __isl_give isl_union_pw_qpolynomial_fold *
8829 isl_union_pw_qpolynomial_fold_gist_params(
8830 __isl_take isl_union_pw_qpolynomial_fold *upwf,
8831 __isl_take isl_set *context);
8833 =item * Binary Arithmetic Operations
8835 #include <isl/set.h>
8836 __isl_give isl_set *isl_set_sum(
8837 __isl_take isl_set *set1,
8838 __isl_take isl_set *set2);
8839 #include <isl/map.h>
8840 __isl_give isl_map *isl_map_sum(
8841 __isl_take isl_map *map1,
8842 __isl_take isl_map *map2);
8844 C<isl_set_sum> computes the Minkowski sum of its two arguments,
8845 i.e., the set containing the sums of pairs of elements from
8846 C<set1> and C<set2>.
8847 The domain of the result of C<isl_map_sum> is the intersection
8848 of the domains of its two arguments. The corresponding range
8849 elements are the sums of the corresponding range elements
8850 in the two arguments.
8852 #include <isl/val.h>
8853 __isl_give isl_multi_val *isl_multi_val_add(
8854 __isl_take isl_multi_val *mv1,
8855 __isl_take isl_multi_val *mv2);
8856 __isl_give isl_multi_val *isl_multi_val_sub(
8857 __isl_take isl_multi_val *mv1,
8858 __isl_take isl_multi_val *mv2);
8859 __isl_give isl_multi_val *isl_multi_val_min(
8860 __isl_take isl_multi_val *mv1,
8861 __isl_take isl_multi_val *mv2);
8862 __isl_give isl_multi_val *isl_multi_val_max(
8863 __isl_take isl_multi_val *mv1,
8864 __isl_take isl_multi_val *mv2);
8866 #include <isl/aff.h>
8867 __isl_give isl_aff *isl_aff_add(
8868 __isl_take isl_aff *aff1,
8869 __isl_take isl_aff *aff2);
8870 __isl_give isl_multi_aff *isl_multi_aff_add(
8871 __isl_take isl_multi_aff *maff1,
8872 __isl_take isl_multi_aff *maff2);
8873 __isl_give isl_pw_aff *isl_pw_aff_add(
8874 __isl_take isl_pw_aff *pwaff1,
8875 __isl_take isl_pw_aff *pwaff2);
8876 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add(
8877 __isl_take isl_multi_pw_aff *mpa1,
8878 __isl_take isl_multi_pw_aff *mpa2);
8879 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
8880 __isl_take isl_pw_multi_aff *pma1,
8881 __isl_take isl_pw_multi_aff *pma2);
8882 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
8883 __isl_take isl_union_pw_aff *upa1,
8884 __isl_take isl_union_pw_aff *upa2);
8885 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
8886 __isl_take isl_union_pw_multi_aff *upma1,
8887 __isl_take isl_union_pw_multi_aff *upma2);
8888 __isl_give isl_multi_union_pw_aff *
8889 isl_multi_union_pw_aff_add(
8890 __isl_take isl_multi_union_pw_aff *mupa1,
8891 __isl_take isl_multi_union_pw_aff *mupa2);
8892 __isl_give isl_pw_aff *isl_pw_aff_add_constant_val(
8893 __isl_take isl_pw_aff *pa,
8894 __isl_take isl_val *v);
8895 __isl_give isl_multi_aff *
8896 isl_multi_aff_add_constant_val(
8897 __isl_take isl_multi_aff *pa,
8898 __isl_take isl_val *v);
8899 __isl_give isl_pw_multi_aff *
8900 isl_pw_multi_aff_add_constant_val(
8901 __isl_take isl_pw_multi_aff *pma,
8902 __isl_take isl_val *v);
8903 __isl_give isl_pw_multi_aff *
8904 isl_pw_multi_aff_add_constant_multi_val(
8905 __isl_take isl_pw_multi_aff *pma,
8906 __isl_take isl_multi_val *mv);
8907 __isl_give isl_multi_pw_aff *
8908 isl_multi_pw_aff_add_constant_val(
8909 __isl_take isl_multi_pw_aff *mpa,
8910 __isl_take isl_val *v);
8911 __isl_give isl_multi_aff *
8912 isl_multi_aff_add_constant_multi_val(
8913 __isl_take isl_multi_aff *pa,
8914 __isl_take isl_multi_val *mv);
8915 __isl_give isl_multi_pw_aff *
8916 isl_multi_pw_aff_add_constant_multi_val(
8917 __isl_take isl_multi_pw_aff *mpa,
8918 __isl_take isl_multi_val *mv);
8919 __isl_give isl_pw_aff *isl_pw_aff_min(
8920 __isl_take isl_pw_aff *pwaff1,
8921 __isl_take isl_pw_aff *pwaff2);
8922 __isl_give isl_pw_aff *isl_pw_aff_max(
8923 __isl_take isl_pw_aff *pwaff1,
8924 __isl_take isl_pw_aff *pwaff2);
8925 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_min(
8926 __isl_take isl_multi_pw_aff *mpa1,
8927 __isl_take isl_multi_pw_aff *mpa2);
8928 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_max(
8929 __isl_take isl_multi_pw_aff *mpa1,
8930 __isl_take isl_multi_pw_aff *mpa2);
8931 __isl_give isl_aff *isl_aff_sub(
8932 __isl_take isl_aff *aff1,
8933 __isl_take isl_aff *aff2);
8934 __isl_give isl_multi_aff *isl_multi_aff_sub(
8935 __isl_take isl_multi_aff *ma1,
8936 __isl_take isl_multi_aff *ma2);
8937 __isl_give isl_pw_aff *isl_pw_aff_sub(
8938 __isl_take isl_pw_aff *pwaff1,
8939 __isl_take isl_pw_aff *pwaff2);
8940 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
8941 __isl_take isl_multi_pw_aff *mpa1,
8942 __isl_take isl_multi_pw_aff *mpa2);
8943 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
8944 __isl_take isl_pw_multi_aff *pma1,
8945 __isl_take isl_pw_multi_aff *pma2);
8946 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
8947 __isl_take isl_union_pw_aff *upa1,
8948 __isl_take isl_union_pw_aff *upa2);
8949 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
8950 __isl_take isl_union_pw_multi_aff *upma1,
8951 __isl_take isl_union_pw_multi_aff *upma2);
8952 __isl_give isl_multi_union_pw_aff *
8953 isl_multi_union_pw_aff_sub(
8954 __isl_take isl_multi_union_pw_aff *mupa1,
8955 __isl_take isl_multi_union_pw_aff *mupa2);
8957 C<isl_aff_sub> subtracts the second argument from the first.
8959 #include <isl/polynomial.h>
8960 __isl_give isl_qpolynomial *isl_qpolynomial_add(
8961 __isl_take isl_qpolynomial *qp1,
8962 __isl_take isl_qpolynomial *qp2);
8963 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
8964 __isl_take isl_pw_qpolynomial *pwqp1,
8965 __isl_take isl_pw_qpolynomial *pwqp2);
8966 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
8967 __isl_take isl_pw_qpolynomial *pwqp1,
8968 __isl_take isl_pw_qpolynomial *pwqp2);
8969 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
8970 __isl_take isl_pw_qpolynomial_fold *pwf1,
8971 __isl_take isl_pw_qpolynomial_fold *pwf2);
8972 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
8973 __isl_take isl_union_pw_qpolynomial *upwqp1,
8974 __isl_take isl_union_pw_qpolynomial *upwqp2);
8975 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
8976 __isl_take isl_qpolynomial *qp1,
8977 __isl_take isl_qpolynomial *qp2);
8978 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
8979 __isl_take isl_pw_qpolynomial *pwqp1,
8980 __isl_take isl_pw_qpolynomial *pwqp2);
8981 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
8982 __isl_take isl_union_pw_qpolynomial *upwqp1,
8983 __isl_take isl_union_pw_qpolynomial *upwqp2);
8984 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
8985 __isl_take isl_pw_qpolynomial_fold *pwf1,
8986 __isl_take isl_pw_qpolynomial_fold *pwf2);
8987 __isl_give isl_union_pw_qpolynomial_fold *
8988 isl_union_pw_qpolynomial_fold_fold(
8989 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
8990 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
8992 #include <isl/aff.h>
8993 __isl_give isl_pw_aff *isl_pw_aff_union_add(
8994 __isl_take isl_pw_aff *pwaff1,
8995 __isl_take isl_pw_aff *pwaff2);
8996 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_union_add(
8997 __isl_take isl_multi_pw_aff *mpa1,
8998 __isl_take isl_multi_pw_aff *mpa2);
8999 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
9000 __isl_take isl_pw_multi_aff *pma1,
9001 __isl_take isl_pw_multi_aff *pma2);
9002 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
9003 __isl_take isl_union_pw_aff *upa1,
9004 __isl_take isl_union_pw_aff *upa2);
9005 __isl_give isl_union_pw_multi_aff *
9006 isl_union_pw_multi_aff_union_add(
9007 __isl_take isl_union_pw_multi_aff *upma1,
9008 __isl_take isl_union_pw_multi_aff *upma2);
9009 __isl_give isl_multi_union_pw_aff *
9010 isl_multi_union_pw_aff_union_add(
9011 __isl_take isl_multi_union_pw_aff *mupa1,
9012 __isl_take isl_multi_union_pw_aff *mupa2);
9013 __isl_give isl_pw_aff *isl_pw_aff_union_min(
9014 __isl_take isl_pw_aff *pwaff1,
9015 __isl_take isl_pw_aff *pwaff2);
9016 __isl_give isl_pw_aff *isl_pw_aff_union_max(
9017 __isl_take isl_pw_aff *pwaff1,
9018 __isl_take isl_pw_aff *pwaff2);
9020 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
9021 expression with a domain that is the union of those of C<pwaff1> and
9022 C<pwaff2> and such that on each cell, the quasi-affine expression is
9023 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
9024 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
9025 associated expression is the defined one.
9026 This in contrast to the C<isl_pw_aff_max> function, which is
9027 only defined on the shared definition domain of the arguments.
9029 #include <isl/val.h>
9030 __isl_give isl_multi_val *isl_multi_val_add_val(
9031 __isl_take isl_multi_val *mv,
9032 __isl_take isl_val *v);
9033 __isl_give isl_multi_val *isl_multi_val_mod_val(
9034 __isl_take isl_multi_val *mv,
9035 __isl_take isl_val *v);
9036 __isl_give isl_multi_val *isl_multi_val_scale_val(
9037 __isl_take isl_multi_val *mv,
9038 __isl_take isl_val *v);
9039 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
9040 __isl_take isl_multi_val *mv,
9041 __isl_take isl_val *v);
9043 #include <isl/aff.h>
9044 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
9045 __isl_take isl_val *mod);
9046 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
9047 __isl_take isl_pw_aff *pa,
9048 __isl_take isl_val *mod);
9049 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
9050 __isl_take isl_union_pw_aff *upa,
9051 __isl_take isl_val *f);
9052 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
9053 __isl_take isl_val *v);
9054 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
9055 __isl_take isl_multi_aff *ma,
9056 __isl_take isl_val *v);
9057 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
9058 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
9059 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
9060 __isl_take isl_multi_pw_aff *mpa,
9061 __isl_take isl_val *v);
9062 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
9063 __isl_take isl_pw_multi_aff *pma,
9064 __isl_take isl_val *v);
9065 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
9066 __isl_take isl_union_pw_aff *upa,
9067 __isl_take isl_val *f);
9068 __isl_give isl_union_pw_multi_aff *
9069 isl_union_pw_multi_aff_scale_val(
9070 __isl_take isl_union_pw_multi_aff *upma,
9071 __isl_take isl_val *val);
9072 __isl_give isl_multi_union_pw_aff *
9073 isl_multi_union_pw_aff_scale_val(
9074 __isl_take isl_multi_union_pw_aff *mupa,
9075 __isl_take isl_val *v);
9076 __isl_give isl_aff *isl_aff_scale_down_ui(
9077 __isl_take isl_aff *aff, unsigned f);
9078 __isl_give isl_aff *isl_aff_scale_down_val(
9079 __isl_take isl_aff *aff, __isl_take isl_val *v);
9080 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
9081 __isl_take isl_multi_aff *ma,
9082 __isl_take isl_val *v);
9083 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
9084 __isl_take isl_pw_aff *pa,
9085 __isl_take isl_val *f);
9086 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
9087 __isl_take isl_multi_pw_aff *mpa,
9088 __isl_take isl_val *v);
9089 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
9090 __isl_take isl_pw_multi_aff *pma,
9091 __isl_take isl_val *v);
9092 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
9093 __isl_take isl_union_pw_aff *upa,
9094 __isl_take isl_val *v);
9095 __isl_give isl_union_pw_multi_aff *
9096 isl_union_pw_multi_aff_scale_down_val(
9097 __isl_take isl_union_pw_multi_aff *upma,
9098 __isl_take isl_val *val);
9099 __isl_give isl_multi_union_pw_aff *
9100 isl_multi_union_pw_aff_scale_down_val(
9101 __isl_take isl_multi_union_pw_aff *mupa,
9102 __isl_take isl_val *v);
9104 #include <isl/polynomial.h>
9105 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
9106 __isl_take isl_qpolynomial *qp,
9107 __isl_take isl_val *v);
9108 __isl_give isl_qpolynomial_fold *
9109 isl_qpolynomial_fold_scale_val(
9110 __isl_take isl_qpolynomial_fold *fold,
9111 __isl_take isl_val *v);
9112 __isl_give isl_pw_qpolynomial *
9113 isl_pw_qpolynomial_scale_val(
9114 __isl_take isl_pw_qpolynomial *pwqp,
9115 __isl_take isl_val *v);
9116 __isl_give isl_pw_qpolynomial_fold *
9117 isl_pw_qpolynomial_fold_scale_val(
9118 __isl_take isl_pw_qpolynomial_fold *pwf,
9119 __isl_take isl_val *v);
9120 __isl_give isl_union_pw_qpolynomial *
9121 isl_union_pw_qpolynomial_scale_val(
9122 __isl_take isl_union_pw_qpolynomial *upwqp,
9123 __isl_take isl_val *v);
9124 __isl_give isl_union_pw_qpolynomial_fold *
9125 isl_union_pw_qpolynomial_fold_scale_val(
9126 __isl_take isl_union_pw_qpolynomial_fold *upwf,
9127 __isl_take isl_val *v);
9128 __isl_give isl_qpolynomial *
9129 isl_qpolynomial_scale_down_val(
9130 __isl_take isl_qpolynomial *qp,
9131 __isl_take isl_val *v);
9132 __isl_give isl_qpolynomial_fold *
9133 isl_qpolynomial_fold_scale_down_val(
9134 __isl_take isl_qpolynomial_fold *fold,
9135 __isl_take isl_val *v);
9136 __isl_give isl_pw_qpolynomial *
9137 isl_pw_qpolynomial_scale_down_val(
9138 __isl_take isl_pw_qpolynomial *pwqp,
9139 __isl_take isl_val *v);
9140 __isl_give isl_pw_qpolynomial_fold *
9141 isl_pw_qpolynomial_fold_scale_down_val(
9142 __isl_take isl_pw_qpolynomial_fold *pwf,
9143 __isl_take isl_val *v);
9144 __isl_give isl_union_pw_qpolynomial *
9145 isl_union_pw_qpolynomial_scale_down_val(
9146 __isl_take isl_union_pw_qpolynomial *upwqp,
9147 __isl_take isl_val *v);
9148 __isl_give isl_union_pw_qpolynomial_fold *
9149 isl_union_pw_qpolynomial_fold_scale_down_val(
9150 __isl_take isl_union_pw_qpolynomial_fold *upwf,
9151 __isl_take isl_val *v);
9153 #include <isl/val.h>
9154 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
9155 __isl_take isl_multi_val *mv1,
9156 __isl_take isl_multi_val *mv2);
9157 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
9158 __isl_take isl_multi_val *mv1,
9159 __isl_take isl_multi_val *mv2);
9160 __isl_give isl_multi_val *
9161 isl_multi_val_scale_down_multi_val(
9162 __isl_take isl_multi_val *mv1,
9163 __isl_take isl_multi_val *mv2);
9165 #include <isl/aff.h>
9166 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
9167 __isl_take isl_multi_aff *ma,
9168 __isl_take isl_multi_val *mv);
9169 __isl_give isl_multi_union_pw_aff *
9170 isl_multi_union_pw_aff_mod_multi_val(
9171 __isl_take isl_multi_union_pw_aff *upma,
9172 __isl_take isl_multi_val *mv);
9173 __isl_give isl_multi_pw_aff *
9174 isl_multi_pw_aff_mod_multi_val(
9175 __isl_take isl_multi_pw_aff *mpa,
9176 __isl_take isl_multi_val *mv);
9177 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
9178 __isl_take isl_multi_aff *ma,
9179 __isl_take isl_multi_val *mv);
9180 __isl_give isl_pw_multi_aff *
9181 isl_pw_multi_aff_scale_multi_val(
9182 __isl_take isl_pw_multi_aff *pma,
9183 __isl_take isl_multi_val *mv);
9184 __isl_give isl_multi_pw_aff *
9185 isl_multi_pw_aff_scale_multi_val(
9186 __isl_take isl_multi_pw_aff *mpa,
9187 __isl_take isl_multi_val *mv);
9188 __isl_give isl_multi_union_pw_aff *
9189 isl_multi_union_pw_aff_scale_multi_val(
9190 __isl_take isl_multi_union_pw_aff *mupa,
9191 __isl_take isl_multi_val *mv);
9192 __isl_give isl_union_pw_multi_aff *
9193 isl_union_pw_multi_aff_scale_multi_val(
9194 __isl_take isl_union_pw_multi_aff *upma,
9195 __isl_take isl_multi_val *mv);
9196 __isl_give isl_multi_aff *
9197 isl_multi_aff_scale_down_multi_val(
9198 __isl_take isl_multi_aff *ma,
9199 __isl_take isl_multi_val *mv);
9200 __isl_give isl_pw_multi_aff *
9201 isl_pw_multi_aff_scale_down_multi_val(
9202 __isl_take isl_pw_multi_aff *pma,
9203 __isl_take isl_multi_val *mv);
9204 __isl_give isl_multi_pw_aff *
9205 isl_multi_pw_aff_scale_down_multi_val(
9206 __isl_take isl_multi_pw_aff *mpa,
9207 __isl_take isl_multi_val *mv);
9208 __isl_give isl_multi_union_pw_aff *
9209 isl_multi_union_pw_aff_scale_down_multi_val(
9210 __isl_take isl_multi_union_pw_aff *mupa,
9211 __isl_take isl_multi_val *mv);
9213 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
9214 by the corresponding elements of C<mv>.
9216 #include <isl/aff.h>
9217 __isl_give isl_aff *isl_aff_mul(
9218 __isl_take isl_aff *aff1,
9219 __isl_take isl_aff *aff2);
9220 __isl_give isl_aff *isl_aff_div(
9221 __isl_take isl_aff *aff1,
9222 __isl_take isl_aff *aff2);
9223 __isl_give isl_pw_aff *isl_pw_aff_mul(
9224 __isl_take isl_pw_aff *pwaff1,
9225 __isl_take isl_pw_aff *pwaff2);
9226 __isl_give isl_pw_aff *isl_pw_aff_div(
9227 __isl_take isl_pw_aff *pa1,
9228 __isl_take isl_pw_aff *pa2);
9229 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
9230 __isl_take isl_pw_aff *pa1,
9231 __isl_take isl_pw_aff *pa2);
9232 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
9233 __isl_take isl_pw_aff *pa1,
9234 __isl_take isl_pw_aff *pa2);
9236 When multiplying two affine expressions, at least one of the two needs
9237 to be a constant. Similarly, when dividing an affine expression by another,
9238 the second expression needs to be a constant.
9239 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
9240 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
9243 #include <isl/polynomial.h>
9244 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
9245 __isl_take isl_qpolynomial *qp1,
9246 __isl_take isl_qpolynomial *qp2);
9247 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
9248 __isl_take isl_pw_qpolynomial *pwqp1,
9249 __isl_take isl_pw_qpolynomial *pwqp2);
9250 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
9251 __isl_take isl_union_pw_qpolynomial *upwqp1,
9252 __isl_take isl_union_pw_qpolynomial *upwqp2);
9256 =head3 Lexicographic Optimization
9258 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
9259 the following functions
9260 compute a set that contains the lexicographic minimum or maximum
9261 of the elements in C<set> (or C<bset>) for those values of the parameters
9262 that satisfy C<dom>.
9263 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
9264 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
9266 In other words, the union of the parameter values
9267 for which the result is non-empty and of C<*empty>
9270 #include <isl/set.h>
9271 __isl_give isl_set *isl_basic_set_partial_lexmin(
9272 __isl_take isl_basic_set *bset,
9273 __isl_take isl_basic_set *dom,
9274 __isl_give isl_set **empty);
9275 __isl_give isl_set *isl_basic_set_partial_lexmax(
9276 __isl_take isl_basic_set *bset,
9277 __isl_take isl_basic_set *dom,
9278 __isl_give isl_set **empty);
9279 __isl_give isl_set *isl_set_partial_lexmin(
9280 __isl_take isl_set *set, __isl_take isl_set *dom,
9281 __isl_give isl_set **empty);
9282 __isl_give isl_set *isl_set_partial_lexmax(
9283 __isl_take isl_set *set, __isl_take isl_set *dom,
9284 __isl_give isl_set **empty);
9286 Given a (basic) set C<set> (or C<bset>), the following functions simply
9287 return a set containing the lexicographic minimum or maximum
9288 of the elements in C<set> (or C<bset>).
9289 In case of union sets, the optimum is computed per space.
9291 #include <isl/set.h>
9292 __isl_give isl_set *isl_basic_set_lexmin(
9293 __isl_take isl_basic_set *bset);
9294 __isl_give isl_set *isl_basic_set_lexmax(
9295 __isl_take isl_basic_set *bset);
9296 __isl_give isl_set *isl_set_lexmin(
9297 __isl_take isl_set *set);
9298 __isl_give isl_set *isl_set_lexmax(
9299 __isl_take isl_set *set);
9300 __isl_give isl_union_set *isl_union_set_lexmin(
9301 __isl_take isl_union_set *uset);
9302 __isl_give isl_union_set *isl_union_set_lexmax(
9303 __isl_take isl_union_set *uset);
9305 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
9306 the following functions
9307 compute a relation that maps each element of C<dom>
9308 to the single lexicographic minimum or maximum
9309 of the elements that are associated to that same
9310 element in C<map> (or C<bmap>).
9311 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
9312 that contains the elements in C<dom> that do not map
9313 to any elements in C<map> (or C<bmap>).
9314 In other words, the union of the domain of the result and of C<*empty>
9317 #include <isl/map.h>
9318 __isl_give isl_map *isl_basic_map_partial_lexmax(
9319 __isl_take isl_basic_map *bmap,
9320 __isl_take isl_basic_set *dom,
9321 __isl_give isl_set **empty);
9322 __isl_give isl_map *isl_basic_map_partial_lexmin(
9323 __isl_take isl_basic_map *bmap,
9324 __isl_take isl_basic_set *dom,
9325 __isl_give isl_set **empty);
9326 __isl_give isl_map *isl_map_partial_lexmax(
9327 __isl_take isl_map *map, __isl_take isl_set *dom,
9328 __isl_give isl_set **empty);
9329 __isl_give isl_map *isl_map_partial_lexmin(
9330 __isl_take isl_map *map, __isl_take isl_set *dom,
9331 __isl_give isl_set **empty);
9333 Given a (basic) map C<map> (or C<bmap>), the following functions simply
9334 return a map mapping each element in the domain of
9335 C<map> (or C<bmap>) to the lexicographic minimum or maximum
9336 of all elements associated to that element.
9337 In case of union relations, the optimum is computed per space.
9339 #include <isl/map.h>
9340 __isl_give isl_map *isl_basic_map_lexmin(
9341 __isl_take isl_basic_map *bmap);
9342 __isl_give isl_map *isl_basic_map_lexmax(
9343 __isl_take isl_basic_map *bmap);
9344 __isl_give isl_map *isl_map_lexmin(
9345 __isl_take isl_map *map);
9346 __isl_give isl_map *isl_map_lexmax(
9347 __isl_take isl_map *map);
9348 __isl_give isl_union_map *isl_union_map_lexmin(
9349 __isl_take isl_union_map *umap);
9350 __isl_give isl_union_map *isl_union_map_lexmax(
9351 __isl_take isl_union_map *umap);
9353 The following functions return their result in the form of
9354 a piecewise multi-affine expression,
9355 but are otherwise equivalent to the corresponding functions
9356 returning a basic set or relation.
9358 #include <isl/set.h>
9359 __isl_give isl_pw_multi_aff *
9360 isl_basic_set_partial_lexmin_pw_multi_aff(
9361 __isl_take isl_basic_set *bset,
9362 __isl_take isl_basic_set *dom,
9363 __isl_give isl_set **empty);
9364 __isl_give isl_pw_multi_aff *
9365 isl_basic_set_partial_lexmax_pw_multi_aff(
9366 __isl_take isl_basic_set *bset,
9367 __isl_take isl_basic_set *dom,
9368 __isl_give isl_set **empty);
9369 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
9370 __isl_take isl_set *set);
9371 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
9372 __isl_take isl_set *set);
9374 #include <isl/map.h>
9375 __isl_give isl_pw_multi_aff *
9376 isl_basic_map_lexmin_pw_multi_aff(
9377 __isl_take isl_basic_map *bmap);
9378 __isl_give isl_pw_multi_aff *
9379 isl_basic_map_partial_lexmin_pw_multi_aff(
9380 __isl_take isl_basic_map *bmap,
9381 __isl_take isl_basic_set *dom,
9382 __isl_give isl_set **empty);
9383 __isl_give isl_pw_multi_aff *
9384 isl_basic_map_partial_lexmax_pw_multi_aff(
9385 __isl_take isl_basic_map *bmap,
9386 __isl_take isl_basic_set *dom,
9387 __isl_give isl_set **empty);
9388 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
9389 __isl_take isl_map *map);
9390 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
9391 __isl_take isl_map *map);
9393 The following functions return the lexicographic minimum or maximum
9394 on the shared domain of the inputs and the single defined function
9395 on those parts of the domain where only a single function is defined.
9397 #include <isl/aff.h>
9398 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
9399 __isl_take isl_pw_multi_aff *pma1,
9400 __isl_take isl_pw_multi_aff *pma2);
9401 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
9402 __isl_take isl_pw_multi_aff *pma1,
9403 __isl_take isl_pw_multi_aff *pma2);
9405 If the input to a lexicographic optimization problem has
9406 multiple constraints with the same coefficients for the optimized
9407 variables, then, by default, this symmetry is exploited by
9408 replacing those constraints by a single constraint with
9409 an abstract bound, which is in turn bounded by the corresponding terms
9410 in the original constraints.
9411 Without this optimization, the solver would typically consider
9412 all possible orderings of those original bounds, resulting in a needless
9413 decomposition of the domain.
9414 However, the optimization can also result in slowdowns since
9415 an extra parameter is introduced that may get used in additional
9417 The following option determines whether symmetry detection is applied
9418 during lexicographic optimization.
9420 #include <isl/options.h>
9421 isl_stat isl_options_set_pip_symmetry(isl_ctx *ctx,
9423 int isl_options_get_pip_symmetry(isl_ctx *ctx);
9427 See also \autoref{s:offline}.
9431 =head2 Ternary Operations
9433 #include <isl/aff.h>
9434 __isl_give isl_pw_aff *isl_pw_aff_cond(
9435 __isl_take isl_pw_aff *cond,
9436 __isl_take isl_pw_aff *pwaff_true,
9437 __isl_take isl_pw_aff *pwaff_false);
9439 The function C<isl_pw_aff_cond> performs a conditional operator
9440 and returns an expression that is equal to C<pwaff_true>
9441 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
9442 where C<cond> is zero.
9446 Lists are defined over several element types, including
9447 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_pw_multi_aff>,
9448 C<isl_union_pw_aff>,
9449 C<isl_union_pw_multi_aff>,
9450 C<isl_qpolynomial>, C<isl_pw_qpolynomial>, C<isl_pw_qpolynomial_fold>,
9452 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
9453 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
9454 Here we take lists of C<isl_set>s as an example.
9455 Lists can be created, copied, modified and freed using the following functions.
9457 #include <isl/set.h>
9458 __isl_give isl_set_list *isl_set_to_list(
9459 __isl_take isl_set *el);
9460 __isl_give isl_set_list *isl_set_list_from_set(
9461 __isl_take isl_set *el);
9462 __isl_give isl_set_list *isl_set_list_alloc(
9463 isl_ctx *ctx, int n);
9464 __isl_give isl_set_list *isl_set_list_copy(
9465 __isl_keep isl_set_list *list);
9466 __isl_give isl_set_list *isl_set_list_insert(
9467 __isl_take isl_set_list *list, unsigned pos,
9468 __isl_take isl_set *el);
9469 __isl_give isl_set_list *isl_set_list_add(
9470 __isl_take isl_set_list *list,
9471 __isl_take isl_set *el);
9472 __isl_give isl_set_list *isl_set_list_drop(
9473 __isl_take isl_set_list *list,
9474 unsigned first, unsigned n);
9475 __isl_give isl_set_list *isl_set_list_clear(
9476 __isl_take isl_set_list *list);
9477 __isl_give isl_set_list *isl_set_list_swap(
9478 __isl_take isl_set_list *list,
9479 unsigned pos1, unsigned pos2);
9480 __isl_give isl_set_list *isl_set_list_reverse(
9481 __isl_take isl_set_list *list);
9482 __isl_give isl_set_list *isl_set_list_set_at(
9483 __isl_take isl_set_list *list, int index,
9484 __isl_take isl_set *set);
9485 __isl_give isl_set_list *isl_set_list_set_set(
9486 __isl_take isl_set_list *list, int index,
9487 __isl_take isl_set *set);
9488 __isl_give isl_set_list *isl_set_list_concat(
9489 __isl_take isl_set_list *list1,
9490 __isl_take isl_set_list *list2);
9491 __isl_give isl_set_list *isl_set_list_map(
9492 __isl_take isl_set_list *list,
9493 __isl_give isl_set *(*fn)(__isl_take isl_set *el,
9496 __isl_give isl_set_list *isl_set_list_sort(
9497 __isl_take isl_set_list *list,
9498 int (*cmp)(__isl_keep isl_set *a,
9499 __isl_keep isl_set *b, void *user),
9501 __isl_null isl_set_list *isl_set_list_free(
9502 __isl_take isl_set_list *list);
9504 C<isl_set_list_alloc> creates an empty list with an initial capacity
9505 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
9506 add elements to a list, increasing its capacity as needed.
9507 C<isl_set_to_list> creates a list with a single element.
9508 C<isl_set_list_from_set> performs the same operation.
9509 C<isl_set_list_clear> removes all elements from a list.
9510 C<isl_set_list_swap> swaps the elements at the specified locations.
9511 C<isl_set_list_reverse> reverses the elements in the list.
9512 C<isl_set_list_set_set> is an alternative name for C<isl_set_list_set_at>.
9514 Lists can be inspected using the following functions.
9516 #include <isl/set.h>
9517 isl_size isl_set_list_size(__isl_keep isl_set_list *list);
9518 isl_size isl_set_list_n_set(__isl_keep isl_set_list *list);
9519 __isl_give isl_set *isl_set_list_get_at(
9520 __isl_keep isl_set_list *list, int index);
9521 __isl_give isl_set *isl_set_list_get_set(
9522 __isl_keep isl_set_list *list, int index);
9523 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list,
9524 isl_stat (*fn)(__isl_take isl_set *el, void *user),
9526 isl_bool isl_set_list_every(__isl_keep isl_set_list *list,
9527 isl_bool (*test)(__isl_take isl_set *el,
9530 isl_stat isl_set_list_foreach_scc(
9531 __isl_keep isl_set_list *list,
9532 isl_bool (*follows)(__isl_keep isl_set *a,
9533 __isl_keep isl_set *b, void *user),
9535 isl_stat (*fn)(__isl_take isl_set_list *scc,
9539 C<isl_set_list_n_set> is an alternative name for C<isl_set_list_size>.
9541 C<isl_set_list_get_set> is an alternative name for C<isl_set_list_get_at>.
9542 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
9543 strongly connected components of the graph with as vertices the elements
9544 of C<list> and a directed edge from vertex C<b> to vertex C<a>
9545 iff C<follows(a, b)> returns C<isl_bool_true>. The callbacks C<follows> and
9546 C<fn> should return C<isl_bool_error> or C<isl_stat_error> on error.
9548 Lists can be printed using
9550 #include <isl/set.h>
9551 __isl_give isl_printer *isl_printer_print_set_list(
9552 __isl_take isl_printer *p,
9553 __isl_keep isl_set_list *list);
9555 Alternatively, a string representation can be obtained
9556 directly using the following function, which always prints
9559 #include <isl/set.h>
9560 __isl_give char *isl_set_list_to_str(
9561 __isl_keep isl_set_list *list);
9563 An C<isl_val_list>, C<isl_id_list>,
9564 C<isl_aff_list>, C<isl_pw_aff_list>, C<isl_pw_multi_aff_list>,
9565 C<isl_union_pw_aff_list>,
9566 C<isl_set_list>, C<isl_map_list> or C<isl_union_set_list> object
9567 can also be read from input using the following functions.
9569 #include <isl/val.h>
9570 __isl_give isl_val_list *isl_val_list_read_from_str(
9571 isl_ctx *ctx, const char *str);
9574 __isl_give isl_id_list *isl_id_list_read_from_str(
9575 isl_ctx *ctx, const char *str);
9577 #include <isl/aff.h>
9578 __isl_give isl_aff_list *
9579 isl_aff_list_read_from_str(isl_ctx *ctx,
9581 __isl_give isl_pw_aff_list *
9582 isl_pw_aff_list_read_from_str(isl_ctx *ctx,
9584 __isl_give isl_pw_multi_aff_list *
9585 isl_pw_multi_aff_list_read_from_str(isl_ctx *ctx,
9587 __isl_give isl_union_pw_aff_list *
9588 isl_union_pw_aff_list_read_from_str(isl_ctx *ctx,
9591 #include <isl/set.h>
9592 __isl_give isl_set_list *isl_set_list_read_from_str(
9593 isl_ctx *ctx, const char *str);
9595 #include <isl/map.h>
9596 __isl_give isl_map_list *isl_map_list_read_from_str(
9597 isl_ctx *ctx, const char *str);
9599 #include <isl/union_set.h>
9600 __isl_give isl_union_set_list *
9601 isl_union_set_list_read_from_str(isl_ctx *ctx,
9604 =head2 Associative arrays
9606 Associative arrays map isl objects of a specific type to isl objects
9607 of some (other) specific type. They are defined for several pairs
9608 of types, including (C<isl_map>, C<isl_basic_set>),
9609 (C<isl_id>, C<isl_ast_expr>),
9610 (C<isl_id>, C<isl_id>) and
9611 (C<isl_id>, C<isl_pw_aff>).
9612 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
9615 Associative arrays can be created, copied and freed using
9616 the following functions.
9618 #include <isl/id_to_ast_expr.h>
9619 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
9620 isl_ctx *ctx, int min_size);
9621 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
9622 __isl_keep isl_id_to_ast_expr *id2expr);
9623 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
9624 __isl_take isl_id_to_ast_expr *id2expr);
9626 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
9627 to specify the expected size of the associative array.
9628 The associative array will be grown automatically as needed.
9630 Associative arrays can be inspected using the following functions.
9632 #include <isl/id_to_ast_expr.h>
9633 __isl_give isl_maybe_isl_ast_expr
9634 isl_id_to_ast_expr_try_get(
9635 __isl_keep isl_id_to_ast_expr *id2expr,
9636 __isl_keep isl_id *key);
9637 isl_bool isl_id_to_ast_expr_has(
9638 __isl_keep isl_id_to_ast_expr *id2expr,
9639 __isl_keep isl_id *key);
9640 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
9641 __isl_keep isl_id_to_ast_expr *id2expr,
9642 __isl_take isl_id *key);
9643 isl_stat isl_id_to_ast_expr_foreach(
9644 __isl_keep isl_id_to_ast_expr *id2expr,
9645 isl_stat (*fn)(__isl_take isl_id *key,
9646 __isl_take isl_ast_expr *val, void *user),
9648 isl_bool isl_id_to_ast_expr_every(
9649 __isl_keep isl_id_to_ast_expr *id2expr,
9650 isl_bool (*test)(__isl_keep isl_id *key,
9651 __isl_keep isl_ast_expr *val, void *user),
9654 The function C<isl_id_to_ast_expr_try_get> returns a structure
9655 containing two elements, C<valid> and C<value>.
9656 If there is a value associated to the key, then C<valid>
9657 is set to C<isl_bool_true> and C<value> contains a copy of
9658 the associated value. Otherwise C<value> is C<NULL> and
9659 C<valid> may be C<isl_bool_error> or C<isl_bool_false> depending
9660 on whether some error has occurred or there simply is no associated value.
9661 The function C<isl_id_to_ast_expr_has> returns the C<valid> field
9662 in the structure and
9663 the function C<isl_id_to_ast_expr_get> returns the C<value> field.
9665 Associative arrays can be modified using the following functions.
9667 #include <isl/id_to_ast_expr.h>
9668 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
9669 __isl_take isl_id_to_ast_expr *id2expr,
9670 __isl_take isl_id *key,
9671 __isl_take isl_ast_expr *val);
9672 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
9673 __isl_take isl_id_to_ast_expr *id2expr,
9674 __isl_take isl_id *key);
9676 Associative arrays can be checked for (obvious) equality
9677 using the following function.
9679 #include <isl/id_to_ast_expr.h>
9680 isl_bool isl_id_to_ast_expr_is_equal(
9681 __isl_take isl_id_to_ast_expr *id2expr1,
9682 __isl_take isl_id_to_ast_expr *id2expr2);
9684 Note that depending on how the keys and values are being compared,
9685 for other types of keys and/or values, this function may be called
9686 C<plain_is_equal> rather than C<is_equal>.
9688 Associative arrays can be printed using the following functions.
9690 #include <isl/id_to_ast_expr.h>
9691 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
9692 __isl_take isl_printer *p,
9693 __isl_keep isl_id_to_ast_expr *id2expr);
9694 __isl_give char *isl_id_to_ast_expr_to_str(
9695 __isl_keep isl_id_to_ast_expr *id2expr);
9697 They can be read from input using the following function.
9699 #include <isl/id_to_ast_expr.h>
9700 __isl_give isl_id_to_ast_expr *
9701 isl_id_to_ast_expr_read_from_str(isl_ctx *ctx,
9706 Vectors can be created, copied and freed using the following functions.
9708 #include <isl/vec.h>
9709 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
9711 __isl_give isl_vec *isl_vec_zero(isl_ctx *ctx,
9713 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
9714 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
9716 Note that the elements of a vector created by C<isl_vec_alloc>
9717 may have arbitrary values.
9718 A vector created by C<isl_vec_zero> has elements with value zero.
9719 The elements can be changed and inspected using the following functions.
9721 isl_size isl_vec_size(__isl_keep isl_vec *vec);
9722 __isl_give isl_val *isl_vec_get_element_val(
9723 __isl_keep isl_vec *vec, int pos);
9724 __isl_give isl_vec *isl_vec_set_element_si(
9725 __isl_take isl_vec *vec, int pos, int v);
9726 __isl_give isl_vec *isl_vec_set_element_val(
9727 __isl_take isl_vec *vec, int pos,
9728 __isl_take isl_val *v);
9729 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
9731 __isl_give isl_vec *isl_vec_set_val(
9732 __isl_take isl_vec *vec, __isl_take isl_val *v);
9733 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
9734 __isl_keep isl_vec *vec2, int pos);
9736 C<isl_vec_get_element> will return a negative value if anything went wrong.
9737 In that case, the value of C<*v> is undefined.
9739 The following function can be used to concatenate two vectors.
9741 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
9742 __isl_take isl_vec *vec2);
9746 Matrices can be created, copied and freed using the following functions.
9748 #include <isl/mat.h>
9749 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
9750 unsigned n_row, unsigned n_col);
9751 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
9752 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
9754 Note that the elements of a newly created matrix may have arbitrary values.
9755 The elements can be changed and inspected using the following functions.
9757 isl_size isl_mat_rows(__isl_keep isl_mat *mat);
9758 isl_size isl_mat_cols(__isl_keep isl_mat *mat);
9759 __isl_give isl_val *isl_mat_get_element_val(
9760 __isl_keep isl_mat *mat, int row, int col);
9761 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
9762 int row, int col, int v);
9763 __isl_give isl_mat *isl_mat_set_element_val(
9764 __isl_take isl_mat *mat, int row, int col,
9765 __isl_take isl_val *v);
9767 The following function computes the rank of a matrix.
9768 The return value may be -1 if some error occurred.
9770 #include <isl/mat.h>
9771 isl_size isl_mat_rank(__isl_keep isl_mat *mat);
9773 The following function can be used to compute the (right) inverse
9774 of a matrix, i.e., a matrix such that the product of the original
9775 and the inverse (in that order) is a multiple of the identity matrix.
9776 The input matrix is assumed to be of full row-rank.
9778 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
9780 The following function can be used to compute the (right) kernel
9781 (or null space) of a matrix, i.e., a matrix such that the product of
9782 the original and the kernel (in that order) is the zero matrix.
9784 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
9786 The following function computes a basis for the space spanned
9787 by the rows of a matrix.
9789 __isl_give isl_mat *isl_mat_row_basis(
9790 __isl_take isl_mat *mat);
9792 The following function computes rows that extend a basis of C<mat1>
9793 to a basis that also covers C<mat2>.
9795 __isl_give isl_mat *isl_mat_row_basis_extension(
9796 __isl_take isl_mat *mat1,
9797 __isl_take isl_mat *mat2);
9799 The following function checks whether there is no linear dependence
9800 among the combined rows of "mat1" and "mat2" that is not already present
9801 in "mat1" or "mat2" individually.
9802 If "mat1" and "mat2" have linearly independent rows by themselves,
9803 then this means that there is no linear dependence among all rows together.
9805 isl_bool isl_mat_has_linearly_independent_rows(
9806 __isl_keep isl_mat *mat1,
9807 __isl_keep isl_mat *mat2);
9809 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
9811 The following functions determine
9812 an upper or lower bound on a quasipolynomial over its domain.
9814 __isl_give isl_pw_qpolynomial_fold *
9815 isl_pw_qpolynomial_bound(
9816 __isl_take isl_pw_qpolynomial *pwqp,
9817 enum isl_fold type, isl_bool *tight);
9819 __isl_give isl_union_pw_qpolynomial_fold *
9820 isl_union_pw_qpolynomial_bound(
9821 __isl_take isl_union_pw_qpolynomial *upwqp,
9822 enum isl_fold type, isl_bool *tight);
9824 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
9825 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
9826 is the returned bound is known be tight, i.e., for each value
9827 of the parameters there is at least
9828 one element in the domain that reaches the bound.
9829 If the domain of C<pwqp> is not wrapping, then the bound is computed
9830 over all elements in that domain and the result has a purely parametric
9831 domain. If the domain of C<pwqp> is wrapping, then the bound is
9832 computed over the range of the wrapped relation. The domain of the
9833 wrapped relation becomes the domain of the result.
9835 =head2 Parametric Vertex Enumeration
9837 The parametric vertex enumeration described in this section
9838 is mainly intended to be used internally and by the C<barvinok>
9841 #include <isl/vertices.h>
9842 __isl_give isl_vertices *isl_basic_set_compute_vertices(
9843 __isl_keep isl_basic_set *bset);
9845 The function C<isl_basic_set_compute_vertices> performs the
9846 actual computation of the parametric vertices and the chamber
9847 decomposition and stores the result in an C<isl_vertices> object.
9848 This information can be queried by either iterating over all
9849 the vertices or iterating over all the chambers or cells
9850 and then iterating over all vertices that are active on the chamber.
9852 isl_stat isl_vertices_foreach_vertex(
9853 __isl_keep isl_vertices *vertices,
9854 isl_stat (*fn)(__isl_take isl_vertex *vertex,
9855 void *user), void *user);
9857 isl_stat isl_vertices_foreach_cell(
9858 __isl_keep isl_vertices *vertices,
9859 isl_stat (*fn)(__isl_take isl_cell *cell,
9860 void *user), void *user);
9861 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
9862 isl_stat (*fn)(__isl_take isl_vertex *vertex,
9863 void *user), void *user);
9865 Other operations that can be performed on an C<isl_vertices> object are
9868 isl_size isl_vertices_get_n_vertices(
9869 __isl_keep isl_vertices *vertices);
9870 __isl_null isl_vertices *isl_vertices_free(
9871 __isl_take isl_vertices *vertices);
9873 Vertices can be inspected and destroyed using the following functions.
9875 isl_size isl_vertex_get_id(__isl_keep isl_vertex *vertex);
9876 __isl_give isl_basic_set *isl_vertex_get_domain(
9877 __isl_keep isl_vertex *vertex);
9878 __isl_give isl_multi_aff *isl_vertex_get_expr(
9879 __isl_keep isl_vertex *vertex);
9880 __isl_null isl_vertex *isl_vertex_free(
9881 __isl_take isl_vertex *vertex);
9883 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
9884 describing the vertex in terms of the parameters,
9885 while C<isl_vertex_get_domain> returns the activity domain
9888 Chambers can be inspected and destroyed using the following functions.
9890 __isl_give isl_basic_set *isl_cell_get_domain(
9891 __isl_keep isl_cell *cell);
9892 __isl_null isl_cell *isl_cell_free(
9893 __isl_take isl_cell *cell);
9895 =head1 Polyhedral Compilation Library
9897 This section collects functionality in C<isl> that has been specifically
9898 designed for use during polyhedral compilation.
9900 =head2 Schedule Trees
9902 A schedule tree is a structured representation of a schedule,
9903 assigning a relative order to a set of domain elements.
9904 The relative order expressed by the schedule tree is
9905 defined recursively. In particular, the order between
9906 two domain elements is determined by the node that is closest
9907 to the root that refers to both elements and that orders them apart.
9908 Each node in the tree is of one of several types.
9909 The root node is always of type C<isl_schedule_node_domain>
9910 (or C<isl_schedule_node_extension>)
9911 and it describes the (extra) domain elements to which the schedule applies.
9912 The other types of nodes are as follows.
9916 =item C<isl_schedule_node_band>
9918 A band of schedule dimensions. Each schedule dimension is represented
9919 by a union piecewise quasi-affine expression. If this expression
9920 assigns a different value to two domain elements, while all previous
9921 schedule dimensions in the same band assign them the same value,
9922 then the two domain elements are ordered according to these two
9924 Each expression is required to be total in the domain elements
9925 that reach the band node.
9927 =item C<isl_schedule_node_expansion>
9929 An expansion node maps each of the domain elements that reach the node
9930 to one or more domain elements. The image of this mapping forms
9931 the set of domain elements that reach the child of the expansion node.
9932 The function that maps each of the expanded domain elements
9933 to the original domain element from which it was expanded
9934 is called the contraction.
9936 =item C<isl_schedule_node_filter>
9938 A filter node does not impose any ordering, but rather intersects
9939 the set of domain elements that the current subtree refers to
9940 with a given union set. The subtree of the filter node only
9941 refers to domain elements in the intersection.
9942 A filter node is typically only used as a child of a sequence or
9945 =item C<isl_schedule_node_leaf>
9947 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
9949 =item C<isl_schedule_node_mark>
9951 A mark node can be used to attach any kind of information to a subtree
9952 of the schedule tree.
9954 =item C<isl_schedule_node_sequence>
9956 A sequence node has one or more children, each of which is a filter node.
9957 The filters on these filter nodes form a partition of
9958 the domain elements that the current subtree refers to.
9959 If two domain elements appear in distinct filters then the sequence
9960 node orders them according to the child positions of the corresponding
9963 =item C<isl_schedule_node_set>
9965 A set node is similar to a sequence node, except that
9966 it expresses that domain elements appearing in distinct filters
9967 may have any order. The order of the children of a set node
9968 is therefore also immaterial.
9972 The following node types are only supported by the AST generator.
9976 =item C<isl_schedule_node_context>
9978 The context describes constraints on the parameters and
9979 the schedule dimensions of outer
9980 bands that the AST generator may assume to hold. It is also the only
9981 kind of node that may introduce additional parameters.
9982 The space of the context is that of the flat product of the outer
9983 band nodes. In particular, if there are no outer band nodes, then
9984 this space is the unnamed zero-dimensional space.
9985 Since a context node references the outer band nodes, any tree
9986 containing a context node is considered to be anchored.
9988 =item C<isl_schedule_node_extension>
9990 An extension node instructs the AST generator to add additional
9991 domain elements that need to be scheduled.
9992 The additional domain elements are described by the range of
9993 the extension map in terms of the outer schedule dimensions,
9994 i.e., the flat product of the outer band nodes.
9995 Note that domain elements are added whenever the AST generator
9996 reaches the extension node, meaning that there are still some
9997 active domain elements for which an AST needs to be generated.
9998 The conditions under which some domain elements are still active
9999 may however not be completely described by the outer AST nodes
10000 generated at that point.
10001 Since an extension node references the outer band nodes, any tree
10002 containing an extension node is considered to be anchored.
10004 An extension node may also appear as the root of a schedule tree,
10005 when it is intended to be inserted into another tree
10006 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
10007 In this case, the domain of the extension node should
10008 correspond to the flat product of the outer band nodes
10009 in this other schedule tree at the point where the extension tree
10012 =item C<isl_schedule_node_guard>
10014 The guard describes constraints on the parameters and
10015 the schedule dimensions of outer
10016 bands that need to be enforced by the outer nodes
10017 in the generated AST.
10018 That is, the part of the AST that is generated from descendants
10019 of the guard node can assume that these constraints are satisfied.
10020 The space of the guard is that of the flat product of the outer
10021 band nodes. In particular, if there are no outer band nodes, then
10022 this space is the unnamed zero-dimensional space.
10023 Since a guard node references the outer band nodes, any tree
10024 containing a guard node is considered to be anchored.
10028 Except for the C<isl_schedule_node_context> nodes,
10029 none of the nodes may introduce any parameters that were not
10030 already present in the root domain node.
10032 A schedule tree is encapsulated in an C<isl_schedule> object.
10033 The simplest such objects, those with a tree consisting of single domain node,
10034 can be created using the following functions with either an empty
10035 domain or a given domain.
10037 #include <isl/schedule.h>
10038 __isl_give isl_schedule *isl_schedule_empty(
10039 __isl_take isl_space *space);
10040 __isl_give isl_schedule *isl_schedule_from_domain(
10041 __isl_take isl_union_set *domain);
10043 The function C<isl_schedule_constraints_compute_schedule> described
10044 in L</"Scheduling"> can also be used to construct schedules.
10046 C<isl_schedule> objects may be copied and freed using the following functions.
10048 #include <isl/schedule.h>
10049 __isl_give isl_schedule *isl_schedule_copy(
10050 __isl_keep isl_schedule *sched);
10051 __isl_null isl_schedule *isl_schedule_free(
10052 __isl_take isl_schedule *sched);
10054 The following functions checks whether two C<isl_schedule> objects
10055 are obviously the same.
10057 #include <isl/schedule.h>
10058 isl_bool isl_schedule_plain_is_equal(
10059 __isl_keep isl_schedule *schedule1,
10060 __isl_keep isl_schedule *schedule2);
10062 The domain of the schedule, i.e., the domain described by the root node,
10063 can be obtained using the following function.
10065 #include <isl/schedule.h>
10066 __isl_give isl_union_set *isl_schedule_get_domain(
10067 __isl_keep isl_schedule *schedule);
10069 An extra top-level band node (right underneath the domain node) can
10070 be introduced into the schedule using the following function.
10071 The schedule tree is assumed not to have any anchored nodes.
10073 #include <isl/schedule.h>
10074 __isl_give isl_schedule *
10075 isl_schedule_insert_partial_schedule(
10076 __isl_take isl_schedule *schedule,
10077 __isl_take isl_multi_union_pw_aff *partial);
10079 A top-level context node (right underneath the domain node) can
10080 be introduced into the schedule using the following function.
10082 #include <isl/schedule.h>
10083 __isl_give isl_schedule *isl_schedule_insert_context(
10084 __isl_take isl_schedule *schedule,
10085 __isl_take isl_set *context)
10087 A top-level guard node (right underneath the domain node) can
10088 be introduced into the schedule using the following function.
10090 #include <isl/schedule.h>
10091 __isl_give isl_schedule *isl_schedule_insert_guard(
10092 __isl_take isl_schedule *schedule,
10093 __isl_take isl_set *guard)
10095 A schedule that combines two schedules either in the given
10096 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
10097 or an C<isl_schedule_node_set> node,
10098 can be created using the following functions.
10100 #include <isl/schedule.h>
10101 __isl_give isl_schedule *isl_schedule_sequence(
10102 __isl_take isl_schedule *schedule1,
10103 __isl_take isl_schedule *schedule2);
10104 __isl_give isl_schedule *isl_schedule_set(
10105 __isl_take isl_schedule *schedule1,
10106 __isl_take isl_schedule *schedule2);
10108 The domains of the two input schedules need to be disjoint.
10110 The following function can be used to restrict the domain
10111 of a schedule with a domain node as root to be a subset of the given union set.
10112 This operation may remove nodes in the tree that have become
10115 #include <isl/schedule.h>
10116 __isl_give isl_schedule *isl_schedule_intersect_domain(
10117 __isl_take isl_schedule *schedule,
10118 __isl_take isl_union_set *domain);
10120 The following function can be used to simplify the domain
10121 of a schedule with a domain node as root with respect to the given
10124 #include <isl/schedule.h>
10125 __isl_give isl_schedule *isl_schedule_gist_domain_params(
10126 __isl_take isl_schedule *schedule,
10127 __isl_take isl_set *context);
10129 The following function resets the user pointers on all parameter
10130 and tuple identifiers referenced by the nodes of the given schedule.
10132 #include <isl/schedule.h>
10133 __isl_give isl_schedule *isl_schedule_reset_user(
10134 __isl_take isl_schedule *schedule);
10136 The following function aligns the parameters of all nodes
10137 in the given schedule to the given space.
10139 #include <isl/schedule.h>
10140 __isl_give isl_schedule *isl_schedule_align_params(
10141 __isl_take isl_schedule *schedule,
10142 __isl_take isl_space *space);
10144 The following function allows the user to plug in a given function
10145 in the iteration domains. The input schedule is not allowed to contain
10146 any expansion nodes.
10148 #include <isl/schedule.h>
10149 __isl_give isl_schedule *
10150 isl_schedule_pullback_union_pw_multi_aff(
10151 __isl_take isl_schedule *schedule,
10152 __isl_take isl_union_pw_multi_aff *upma);
10154 The following function can be used to plug in the schedule C<expansion>
10155 in the leaves of C<schedule>, where C<contraction> describes how
10156 the domain elements of C<expansion> map to the domain elements
10157 at the original leaves of C<schedule>.
10158 The resulting schedule will contain expansion nodes, unless
10159 C<contraction> is an identity function.
10161 #include <isl/schedule.h>
10162 __isl_give isl_schedule *isl_schedule_expand(
10163 __isl_take isl_schedule *schedule,
10164 __isl_take isl_union_pw_multi_aff *contraction,
10165 __isl_take isl_schedule *expansion);
10167 An C<isl_union_map> representation of the schedule can be obtained
10168 from an C<isl_schedule> using the following function.
10170 #include <isl/schedule.h>
10171 __isl_give isl_union_map *isl_schedule_get_map(
10172 __isl_keep isl_schedule *sched);
10174 The resulting relation encodes the same relative ordering as
10175 the schedule by mapping the domain elements to a common schedule space.
10176 If the schedule_separate_components option is set, then the order
10177 of the children of a set node is explicitly encoded in the result.
10178 If the tree contains any expansion nodes, then the relation
10179 is formulated in terms of the expanded domain elements.
10181 Schedules can be read from input using the following functions.
10183 #include <isl/schedule.h>
10184 __isl_give isl_schedule *isl_schedule_read_from_file(
10185 isl_ctx *ctx, FILE *input);
10186 __isl_give isl_schedule *isl_schedule_read_from_str(
10187 isl_ctx *ctx, const char *str);
10189 A representation of the schedule can be printed using
10191 #include <isl/schedule.h>
10192 __isl_give isl_printer *isl_printer_print_schedule(
10193 __isl_take isl_printer *p,
10194 __isl_keep isl_schedule *schedule);
10195 __isl_give char *isl_schedule_to_str(
10196 __isl_keep isl_schedule *schedule);
10198 C<isl_schedule_to_str> prints the schedule in flow format.
10200 The schedule tree can be traversed through the use of
10201 C<isl_schedule_node> objects that point to a particular
10202 position in the schedule tree. Whenever a C<isl_schedule_node>
10203 is used to modify a node in the schedule tree, the original schedule
10204 tree is left untouched and the modifications are performed to a copy
10205 of the tree. The returned C<isl_schedule_node> then points to
10206 this modified copy of the tree.
10208 The root of the schedule tree can be obtained using the following function.
10210 #include <isl/schedule.h>
10211 __isl_give isl_schedule_node *isl_schedule_get_root(
10212 __isl_keep isl_schedule *schedule);
10214 A pointer to a newly created schedule tree with a single domain
10215 node can be created using the following functions.
10217 #include <isl/schedule_node.h>
10218 __isl_give isl_schedule_node *
10219 isl_schedule_node_from_domain(
10220 __isl_take isl_union_set *domain);
10221 __isl_give isl_schedule_node *
10222 isl_schedule_node_from_extension(
10223 __isl_take isl_union_map *extension);
10225 C<isl_schedule_node_from_extension> creates a tree with an extension
10228 Schedule nodes can be copied and freed using the following functions.
10230 #include <isl/schedule_node.h>
10231 __isl_give isl_schedule_node *isl_schedule_node_copy(
10232 __isl_keep isl_schedule_node *node);
10233 __isl_null isl_schedule_node *isl_schedule_node_free(
10234 __isl_take isl_schedule_node *node);
10236 The following functions can be used to check if two schedule
10237 nodes point to the same position in the same schedule.
10239 #include <isl/schedule_node.h>
10240 isl_bool isl_schedule_node_is_equal(
10241 __isl_keep isl_schedule_node *node1,
10242 __isl_keep isl_schedule_node *node2);
10244 The following properties can be obtained from a schedule node.
10246 #include <isl/schedule_node.h>
10247 enum isl_schedule_node_type isl_schedule_node_get_type(
10248 __isl_keep isl_schedule_node *node);
10249 enum isl_schedule_node_type
10250 isl_schedule_node_get_parent_type(
10251 __isl_keep isl_schedule_node *node);
10252 __isl_give isl_schedule *isl_schedule_node_get_schedule(
10253 __isl_keep isl_schedule_node *node);
10255 The function C<isl_schedule_node_get_type> returns the type of
10256 the node, while C<isl_schedule_node_get_parent_type> returns
10257 type of the parent of the node, which is required to exist.
10258 The function C<isl_schedule_node_get_schedule> returns a copy
10259 to the schedule to which the node belongs.
10261 The following functions can be used to move the schedule node
10262 to a different position in the tree or to check if such a position
10265 #include <isl/schedule_node.h>
10266 isl_bool isl_schedule_node_has_parent(
10267 __isl_keep isl_schedule_node *node);
10268 __isl_give isl_schedule_node *isl_schedule_node_parent(
10269 __isl_take isl_schedule_node *node);
10270 __isl_give isl_schedule_node *
10271 isl_schedule_node_grandparent(
10272 __isl_take isl_schedule_node *node);
10273 __isl_give isl_schedule_node *isl_schedule_node_root(
10274 __isl_take isl_schedule_node *node);
10275 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
10276 __isl_take isl_schedule_node *node,
10278 isl_size isl_schedule_node_n_children(
10279 __isl_keep isl_schedule_node *node);
10280 __isl_give isl_schedule_node *isl_schedule_node_child(
10281 __isl_take isl_schedule_node *node, int pos);
10282 isl_bool isl_schedule_node_has_children(
10283 __isl_keep isl_schedule_node *node);
10284 __isl_give isl_schedule_node *
10285 isl_schedule_node_grandchild(
10286 __isl_take isl_schedule_node *node,
10287 int pos1, int pos2);
10288 __isl_give isl_schedule_node *isl_schedule_node_first_child(
10289 __isl_take isl_schedule_node *node);
10290 isl_bool isl_schedule_node_has_previous_sibling(
10291 __isl_keep isl_schedule_node *node);
10292 __isl_give isl_schedule_node *
10293 isl_schedule_node_previous_sibling(
10294 __isl_take isl_schedule_node *node);
10295 isl_bool isl_schedule_node_has_next_sibling(
10296 __isl_keep isl_schedule_node *node);
10297 __isl_give isl_schedule_node *
10298 isl_schedule_node_next_sibling(
10299 __isl_take isl_schedule_node *node);
10301 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
10302 is the node itself, the ancestor of generation 1 is its parent and so on.
10304 It is also possible to query the number of ancestors of a node,
10305 the position of the current node
10306 within the children of its parent, the position of the subtree
10307 containing a node within the children of an ancestor
10308 or to obtain a copy of a given
10309 child without destroying the current node.
10310 Given two nodes that point to the same schedule, their closest
10311 shared ancestor can be obtained using
10312 C<isl_schedule_node_get_shared_ancestor>.
10314 #include <isl/schedule_node.h>
10315 isl_size isl_schedule_node_get_tree_depth(
10316 __isl_keep isl_schedule_node *node);
10317 isl_size isl_schedule_node_get_child_position(
10318 __isl_keep isl_schedule_node *node);
10319 isl_size isl_schedule_node_get_ancestor_child_position(
10320 __isl_keep isl_schedule_node *node,
10321 __isl_keep isl_schedule_node *ancestor);
10322 __isl_give isl_schedule_node *isl_schedule_node_get_child(
10323 __isl_keep isl_schedule_node *node, int pos);
10324 __isl_give isl_schedule_node *
10325 isl_schedule_node_get_shared_ancestor(
10326 __isl_keep isl_schedule_node *node1,
10327 __isl_keep isl_schedule_node *node2);
10329 All nodes in a schedule tree or
10330 all descendants of a specific node (including the node) can be visited
10331 in depth-first pre-order using the following functions.
10333 #include <isl/schedule.h>
10334 isl_stat isl_schedule_foreach_schedule_node_top_down(
10335 __isl_keep isl_schedule *sched,
10336 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
10337 void *user), void *user);
10339 #include <isl/schedule_node.h>
10340 isl_stat isl_schedule_node_foreach_descendant_top_down(
10341 __isl_keep isl_schedule_node *node,
10342 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
10343 void *user), void *user);
10345 The callback function is slightly different from the usual
10346 callbacks in that it not only indicates success (non-negative result)
10347 or failure (negative result), but also indicates whether the children
10348 of the given node should be visited. In particular, if the callback
10349 returns a positive value, then the children are visited, but if
10350 the callback returns zero, then the children are not visited.
10352 The following functions checks whether
10353 all descendants of a specific node (including the node itself)
10354 satisfy a user-specified test.
10356 #include <isl/schedule_node.h>
10357 isl_bool isl_schedule_node_every_descendant(
10358 __isl_keep isl_schedule_node *node,
10359 isl_bool (*test)(__isl_keep isl_schedule_node *node,
10360 void *user), void *user)
10362 The ancestors of a node in a schedule tree can be visited from
10363 the root down to and including the parent of the node using
10364 the following function.
10366 #include <isl/schedule_node.h>
10367 isl_stat isl_schedule_node_foreach_ancestor_top_down(
10368 __isl_keep isl_schedule_node *node,
10369 isl_stat (*fn)(__isl_keep isl_schedule_node *node,
10370 void *user), void *user);
10372 The following functions allows for a depth-first post-order
10373 traversal of the nodes in a schedule tree or
10374 of the descendants of a specific node (including the node
10375 itself), where the user callback is allowed to modify the
10378 #include <isl/schedule.h>
10379 __isl_give isl_schedule *
10380 isl_schedule_map_schedule_node_bottom_up(
10381 __isl_take isl_schedule *schedule,
10382 __isl_give isl_schedule_node *(*fn)(
10383 __isl_take isl_schedule_node *node,
10384 void *user), void *user);
10386 #include <isl/schedule_node.h>
10387 __isl_give isl_schedule_node *
10388 isl_schedule_node_map_descendant_bottom_up(
10389 __isl_take isl_schedule_node *node,
10390 __isl_give isl_schedule_node *(*fn)(
10391 __isl_take isl_schedule_node *node,
10392 void *user), void *user);
10394 The traversal continues from the node returned by the callback function.
10395 It is the responsibility of the user to ensure that this does not
10396 lead to an infinite loop. It is safest to always return a pointer
10397 to the same position (same ancestors and child positions) as the input node.
10399 The following function removes a node (along with its descendants)
10400 from a schedule tree and returns a pointer to the leaf at the
10401 same position in the updated tree.
10402 It is not allowed to remove the root of a schedule tree or
10403 a child of a set or sequence node.
10405 #include <isl/schedule_node.h>
10406 __isl_give isl_schedule_node *isl_schedule_node_cut(
10407 __isl_take isl_schedule_node *node);
10409 The following function removes a single node
10410 from a schedule tree and returns a pointer to the child
10411 of the node, now located at the position of the original node
10412 or to a leaf node at that position if there was no child.
10413 It is not allowed to remove the root of a schedule tree,
10414 a set or sequence node, a child of a set or sequence node or
10415 a band node with an anchored subtree.
10417 #include <isl/schedule_node.h>
10418 __isl_give isl_schedule_node *isl_schedule_node_delete(
10419 __isl_take isl_schedule_node *node);
10421 Most nodes in a schedule tree only contain local information.
10422 In some cases, however, a node may also refer to the schedule dimensions
10423 of its outer band nodes.
10424 This means that the position of the node within the tree should
10425 not be changed, or at least that no changes are performed to the
10426 outer band nodes. The following function can be used to test
10427 whether the subtree rooted at a given node contains any such nodes.
10429 #include <isl/schedule_node.h>
10430 isl_bool isl_schedule_node_is_subtree_anchored(
10431 __isl_keep isl_schedule_node *node);
10433 The following function resets the user pointers on all parameter
10434 and tuple identifiers referenced by the given schedule node.
10436 #include <isl/schedule_node.h>
10437 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
10438 __isl_take isl_schedule_node *node);
10440 The following function aligns the parameters of the given schedule
10441 node to the given space.
10443 #include <isl/schedule_node.h>
10444 __isl_give isl_schedule_node *
10445 isl_schedule_node_align_params(
10446 __isl_take isl_schedule_node *node,
10447 __isl_take isl_space *space);
10449 Several node types have their own functions for querying
10450 (and in some cases setting) some node type specific properties.
10452 #include <isl/schedule_node.h>
10453 __isl_give isl_space *isl_schedule_node_band_get_space(
10454 __isl_keep isl_schedule_node *node);
10455 __isl_give isl_multi_union_pw_aff *
10456 isl_schedule_node_band_get_partial_schedule(
10457 __isl_keep isl_schedule_node *node);
10458 __isl_give isl_union_map *
10459 isl_schedule_node_band_get_partial_schedule_union_map(
10460 __isl_keep isl_schedule_node *node);
10461 isl_size isl_schedule_node_band_n_member(
10462 __isl_keep isl_schedule_node *node);
10463 isl_bool isl_schedule_node_band_member_get_coincident(
10464 __isl_keep isl_schedule_node *node, int pos);
10465 __isl_give isl_schedule_node *
10466 isl_schedule_node_band_member_set_coincident(
10467 __isl_take isl_schedule_node *node, int pos,
10469 isl_bool isl_schedule_node_band_get_permutable(
10470 __isl_keep isl_schedule_node *node);
10471 __isl_give isl_schedule_node *
10472 isl_schedule_node_band_set_permutable(
10473 __isl_take isl_schedule_node *node, int permutable);
10474 enum isl_ast_loop_type
10475 isl_schedule_node_band_member_get_ast_loop_type(
10476 __isl_keep isl_schedule_node *node, int pos);
10477 __isl_give isl_schedule_node *
10478 isl_schedule_node_band_member_set_ast_loop_type(
10479 __isl_take isl_schedule_node *node, int pos,
10480 enum isl_ast_loop_type type);
10481 enum isl_ast_loop_type
10482 isl_schedule_node_band_member_get_isolate_ast_loop_type(
10483 __isl_keep isl_schedule_node *node, int pos);
10484 __isl_give isl_schedule_node *
10485 isl_schedule_node_band_member_set_isolate_ast_loop_type(
10486 __isl_take isl_schedule_node *node, int pos,
10487 enum isl_ast_loop_type type);
10488 __isl_give isl_union_set *
10489 isl_schedule_node_band_get_ast_build_options(
10490 __isl_keep isl_schedule_node *node);
10491 __isl_give isl_schedule_node *
10492 isl_schedule_node_band_set_ast_build_options(
10493 __isl_take isl_schedule_node *node,
10494 __isl_take isl_union_set *options);
10495 __isl_give isl_set *
10496 isl_schedule_node_band_get_ast_isolate_option(
10497 __isl_keep isl_schedule_node *node);
10499 The function C<isl_schedule_node_band_get_space> returns the space
10500 of the partial schedule of the band.
10501 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
10502 returns a representation of the partial schedule of the band node
10503 in the form of an C<isl_union_map>.
10504 The coincident and permutable properties are set by
10505 C<isl_schedule_constraints_compute_schedule> on the schedule tree
10507 A scheduling dimension is considered to be ``coincident''
10508 if it satisfies the coincidence constraints within its band.
10509 That is, if the dependence distances of the coincidence
10510 constraints are all zero in that direction (for fixed
10511 iterations of outer bands).
10512 A band is marked permutable if it was produced using the Pluto-like scheduler.
10513 Note that the scheduler may have to resort to a Feautrier style scheduling
10514 step even if the default scheduler is used.
10515 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
10516 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
10517 For the meaning of these loop AST generation types and the difference
10518 between the regular loop AST generation type and the isolate
10519 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
10520 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
10521 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
10522 may return C<isl_ast_loop_error> if an error occurs.
10523 The AST build options govern how an AST is generated for
10524 the individual schedule dimensions during AST generation.
10525 See L</"AST Generation Options (Schedule Tree)">.
10526 The isolate option for the given node can be extracted from these
10527 AST build options using the function
10528 C<isl_schedule_node_band_get_ast_isolate_option>.
10530 #include <isl/schedule_node.h>
10531 __isl_give isl_set *
10532 isl_schedule_node_context_get_context(
10533 __isl_keep isl_schedule_node *node);
10535 #include <isl/schedule_node.h>
10536 __isl_give isl_union_set *
10537 isl_schedule_node_domain_get_domain(
10538 __isl_keep isl_schedule_node *node);
10540 #include <isl/schedule_node.h>
10541 __isl_give isl_union_map *
10542 isl_schedule_node_expansion_get_expansion(
10543 __isl_keep isl_schedule_node *node);
10544 __isl_give isl_union_pw_multi_aff *
10545 isl_schedule_node_expansion_get_contraction(
10546 __isl_keep isl_schedule_node *node);
10548 #include <isl/schedule_node.h>
10549 __isl_give isl_union_map *
10550 isl_schedule_node_extension_get_extension(
10551 __isl_keep isl_schedule_node *node);
10553 #include <isl/schedule_node.h>
10554 __isl_give isl_union_set *
10555 isl_schedule_node_filter_get_filter(
10556 __isl_keep isl_schedule_node *node);
10558 #include <isl/schedule_node.h>
10559 __isl_give isl_set *isl_schedule_node_guard_get_guard(
10560 __isl_keep isl_schedule_node *node);
10562 #include <isl/schedule_node.h>
10563 __isl_give isl_id *isl_schedule_node_mark_get_id(
10564 __isl_keep isl_schedule_node *node);
10566 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
10567 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
10568 partial schedules related to the node.
10570 #include <isl/schedule_node.h>
10571 __isl_give isl_multi_union_pw_aff *
10572 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
10573 __isl_keep isl_schedule_node *node);
10574 __isl_give isl_union_pw_multi_aff *
10575 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
10576 __isl_keep isl_schedule_node *node);
10577 __isl_give isl_union_map *
10578 isl_schedule_node_get_prefix_schedule_union_map(
10579 __isl_keep isl_schedule_node *node);
10580 __isl_give isl_union_map *
10581 isl_schedule_node_get_prefix_schedule_relation(
10582 __isl_keep isl_schedule_node *node);
10583 __isl_give isl_union_map *
10584 isl_schedule_node_get_subtree_schedule_union_map(
10585 __isl_keep isl_schedule_node *node);
10587 In particular, the functions
10588 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
10589 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
10590 and C<isl_schedule_node_get_prefix_schedule_union_map>
10591 return a relative ordering on the domain elements that reach the given
10592 node determined by its ancestors.
10593 The function C<isl_schedule_node_get_prefix_schedule_relation>
10594 additionally includes the domain constraints in the result.
10595 The function C<isl_schedule_node_get_subtree_schedule_union_map>
10596 returns a representation of the partial schedule defined by the
10597 subtree rooted at the given node.
10598 If the tree contains any expansion nodes, then the subtree schedule
10599 is formulated in terms of the expanded domain elements.
10600 The tree passed to functions returning a prefix schedule
10601 may only contain extension nodes if these would not affect
10602 the result of these functions. That is, if one of the ancestors
10603 is an extension node, then all of the domain elements that were
10604 added by the extension node need to have been filtered out
10605 by filter nodes between the extension node and the input node.
10606 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
10607 may not contain in extension nodes in the selected subtree.
10609 The expansion/contraction defined by an entire subtree, combining
10610 the expansions/contractions
10611 on the expansion nodes in the subtree, can be obtained using
10612 the following functions.
10614 #include <isl/schedule_node.h>
10615 __isl_give isl_union_map *
10616 isl_schedule_node_get_subtree_expansion(
10617 __isl_keep isl_schedule_node *node);
10618 __isl_give isl_union_pw_multi_aff *
10619 isl_schedule_node_get_subtree_contraction(
10620 __isl_keep isl_schedule_node *node);
10622 The total number of outer band members of given node, i.e.,
10623 the shared output dimension of the maps in the result
10624 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
10625 using the following function.
10627 #include <isl/schedule_node.h>
10628 isl_size isl_schedule_node_get_schedule_depth(
10629 __isl_keep isl_schedule_node *node);
10631 The following functions return the elements that reach the given node
10632 or the union of universes in the spaces that contain these elements.
10634 #include <isl/schedule_node.h>
10635 __isl_give isl_union_set *
10636 isl_schedule_node_get_domain(
10637 __isl_keep isl_schedule_node *node);
10638 __isl_give isl_union_set *
10639 isl_schedule_node_get_universe_domain(
10640 __isl_keep isl_schedule_node *node);
10642 The input tree of C<isl_schedule_node_get_domain>
10643 may only contain extension nodes if these would not affect
10644 the result of this function. That is, if one of the ancestors
10645 is an extension node, then all of the domain elements that were
10646 added by the extension node need to have been filtered out
10647 by filter nodes between the extension node and the input node.
10649 The following functions can be used to introduce additional nodes
10650 in the schedule tree. The new node is introduced at the point
10651 in the tree where the C<isl_schedule_node> points to and
10652 the results points to the new node.
10654 #include <isl/schedule_node.h>
10655 __isl_give isl_schedule_node *
10656 isl_schedule_node_insert_partial_schedule(
10657 __isl_take isl_schedule_node *node,
10658 __isl_take isl_multi_union_pw_aff *schedule);
10660 This function inserts a new band node with (the greatest integer
10661 part of) the given partial schedule.
10662 The subtree rooted at the given node is assumed not to have
10663 any anchored nodes.
10665 #include <isl/schedule_node.h>
10666 __isl_give isl_schedule_node *
10667 isl_schedule_node_insert_context(
10668 __isl_take isl_schedule_node *node,
10669 __isl_take isl_set *context);
10671 This function inserts a new context node with the given context constraints.
10673 #include <isl/schedule_node.h>
10674 __isl_give isl_schedule_node *
10675 isl_schedule_node_insert_filter(
10676 __isl_take isl_schedule_node *node,
10677 __isl_take isl_union_set *filter);
10679 This function inserts a new filter node with the given filter.
10680 If the original node already pointed to a filter node, then the
10681 two filter nodes are merged into one.
10683 #include <isl/schedule_node.h>
10684 __isl_give isl_schedule_node *
10685 isl_schedule_node_insert_guard(
10686 __isl_take isl_schedule_node *node,
10687 __isl_take isl_set *guard);
10689 This function inserts a new guard node with the given guard constraints.
10691 #include <isl/schedule_node.h>
10692 __isl_give isl_schedule_node *
10693 isl_schedule_node_insert_mark(
10694 __isl_take isl_schedule_node *node,
10695 __isl_take isl_id *mark);
10697 This function inserts a new mark node with the give mark identifier.
10699 #include <isl/schedule_node.h>
10700 __isl_give isl_schedule_node *
10701 isl_schedule_node_insert_sequence(
10702 __isl_take isl_schedule_node *node,
10703 __isl_take isl_union_set_list *filters);
10704 __isl_give isl_schedule_node *
10705 isl_schedule_node_insert_set(
10706 __isl_take isl_schedule_node *node,
10707 __isl_take isl_union_set_list *filters);
10709 These functions insert a new sequence or set node with the given
10710 filters as children.
10712 #include <isl/schedule_node.h>
10713 __isl_give isl_schedule_node *isl_schedule_node_group(
10714 __isl_take isl_schedule_node *node,
10715 __isl_take isl_id *group_id);
10717 This function introduces an expansion node in between the current
10718 node and its parent that expands instances of a space with tuple
10719 identifier C<group_id> to the original domain elements that reach
10720 the node. The group instances are identified by the prefix schedule
10721 of those domain elements. The ancestors of the node are adjusted
10722 to refer to the group instances instead of the original domain
10723 elements. The return value points to the same node in the updated
10724 schedule tree as the input node, i.e., to the child of the newly
10725 introduced expansion node. Grouping instances of different statements
10726 ensures that they will be treated as a single statement by the
10727 AST generator up to the point of the expansion node.
10729 The following functions can be used to flatten a nested
10732 #include <isl/schedule_node.h>
10733 __isl_give isl_schedule_node *
10734 isl_schedule_node_sequence_splice_child(
10735 __isl_take isl_schedule_node *node, int pos);
10736 __isl_give isl_schedule_node *
10737 isl_schedule_node_sequence_splice_children(
10738 __isl_take isl_schedule_node *node);
10740 That is, given a sequence node C<node> that has another sequence node
10741 in its child at position C<pos> (in particular, the child of that filter
10742 node is a sequence node), the function
10743 C<isl_schedule_node_sequence_splice_child>
10744 attaches the children of that other sequence
10745 node as children of C<node>, replacing the original child at position
10747 C<isl_schedule_node_sequence_splice_children> does this for all
10750 The partial schedule of a band node can be scaled (down) or reduced using
10751 the following functions.
10753 #include <isl/schedule_node.h>
10754 __isl_give isl_schedule_node *
10755 isl_schedule_node_band_scale(
10756 __isl_take isl_schedule_node *node,
10757 __isl_take isl_multi_val *mv);
10758 __isl_give isl_schedule_node *
10759 isl_schedule_node_band_scale_down(
10760 __isl_take isl_schedule_node *node,
10761 __isl_take isl_multi_val *mv);
10762 __isl_give isl_schedule_node *
10763 isl_schedule_node_band_mod(
10764 __isl_take isl_schedule_node *node,
10765 __isl_take isl_multi_val *mv);
10767 The spaces of the two arguments need to match.
10768 After scaling, the partial schedule is replaced by its greatest
10769 integer part to ensure that the schedule remains integral.
10771 The partial schedule of a band node can be shifted by an
10772 C<isl_multi_union_pw_aff> with a domain that is a superset
10773 of the domain of the partial schedule using
10774 the following function.
10776 #include <isl/schedule_node.h>
10777 __isl_give isl_schedule_node *
10778 isl_schedule_node_band_shift(
10779 __isl_take isl_schedule_node *node,
10780 __isl_take isl_multi_union_pw_aff *shift);
10782 A band node can be tiled using the following function.
10784 #include <isl/schedule_node.h>
10785 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
10786 __isl_take isl_schedule_node *node,
10787 __isl_take isl_multi_val *sizes);
10789 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
10791 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
10792 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
10794 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
10796 The C<isl_schedule_node_band_tile> function tiles
10797 the band using the given tile sizes inside its schedule.
10798 A new child band node is created to represent the point loops and it is
10799 inserted between the modified band and its children.
10800 The subtree rooted at the given node is assumed not to have
10801 any anchored nodes.
10802 The C<tile_scale_tile_loops> option specifies whether the tile
10803 loops iterators should be scaled by the tile sizes.
10804 If the C<tile_shift_point_loops> option is set, then the point loops
10805 are shifted to start at zero.
10807 A band node can be split into two nested band nodes
10808 using the following function.
10810 #include <isl/schedule_node.h>
10811 __isl_give isl_schedule_node *isl_schedule_node_band_split(
10812 __isl_take isl_schedule_node *node, int pos);
10814 The resulting outer band node contains the first C<pos> dimensions of
10815 the schedule of C<node> while the inner band contains the remaining dimensions.
10816 The schedules of the two band nodes live in anonymous spaces.
10817 The loop AST generation type options and the isolate option
10818 are split over the two band nodes.
10820 A band node can be moved down to the leaves of the subtree rooted
10821 at the band node using the following function.
10823 #include <isl/schedule_node.h>
10824 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
10825 __isl_take isl_schedule_node *node);
10827 The subtree rooted at the given node is assumed not to have
10828 any anchored nodes.
10829 The result points to the node in the resulting tree that is in the same
10830 position as the node pointed to by C<node> in the original tree.
10832 #include <isl/schedule_node.h>
10833 __isl_give isl_schedule_node *
10834 isl_schedule_node_order_before(
10835 __isl_take isl_schedule_node *node,
10836 __isl_take isl_union_set *filter);
10837 __isl_give isl_schedule_node *
10838 isl_schedule_node_order_after(
10839 __isl_take isl_schedule_node *node,
10840 __isl_take isl_union_set *filter);
10842 These functions split the domain elements that reach C<node>
10843 into those that satisfy C<filter> and those that do not and
10844 arranges for the elements that do satisfy the filter to be
10845 executed before (in case of C<isl_schedule_node_order_before>)
10846 or after (in case of C<isl_schedule_node_order_after>)
10847 those that do not. The order is imposed by
10848 a sequence node, possibly reusing the grandparent of C<node>
10849 on two copies of the subtree attached to the original C<node>.
10850 Both copies are simplified with respect to their filter.
10852 Return a pointer to the copy of the subtree that does not
10853 satisfy C<filter>. If there is no such copy (because all
10854 reaching domain elements satisfy the filter), then return
10855 the original pointer.
10857 #include <isl/schedule_node.h>
10858 __isl_give isl_schedule_node *
10859 isl_schedule_node_graft_before(
10860 __isl_take isl_schedule_node *node,
10861 __isl_take isl_schedule_node *graft);
10862 __isl_give isl_schedule_node *
10863 isl_schedule_node_graft_after(
10864 __isl_take isl_schedule_node *node,
10865 __isl_take isl_schedule_node *graft);
10867 This function inserts the C<graft> tree into the tree containing C<node>
10868 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
10869 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
10870 The root node of C<graft>
10871 should be an extension node where the domain of the extension
10872 is the flat product of all outer band nodes of C<node>.
10873 The root node may also be a domain node.
10874 The elements of the domain or the range of the extension may not
10875 intersect with the domain elements that reach "node".
10876 The schedule tree of C<graft> may not be anchored.
10878 The schedule tree of C<node> is modified to include an extension node
10879 corresponding to the root node of C<graft> as a child of the original
10880 parent of C<node>. The original node that C<node> points to and the
10881 child of the root node of C<graft> are attached to this extension node
10882 through a sequence, with appropriate filters and with the child
10883 of C<graft> appearing before or after the original C<node>.
10885 If C<node> already appears inside a sequence that is the child of
10886 an extension node and if the spaces of the new domain elements
10887 do not overlap with those of the original domain elements,
10888 then that extension node is extended with the new extension
10889 rather than introducing a new segment of extension and sequence nodes.
10891 Return a pointer to the same node in the modified tree that
10892 C<node> pointed to in the original tree.
10894 A representation of the schedule node can be printed using
10896 #include <isl/schedule_node.h>
10897 __isl_give isl_printer *isl_printer_print_schedule_node(
10898 __isl_take isl_printer *p,
10899 __isl_keep isl_schedule_node *node);
10900 __isl_give char *isl_schedule_node_to_str(
10901 __isl_keep isl_schedule_node *node);
10903 C<isl_schedule_node_to_str> prints the schedule node in block format.
10905 =head2 Dependence Analysis
10907 C<isl> contains specialized functionality for performing
10908 array dataflow analysis. That is, given a I<sink> access relation,
10909 a collection of possible I<source> accesses and
10910 a collection of I<kill> accesses,
10911 C<isl> can compute relations that describe
10912 for each iteration of the sink access, which iterations
10913 of which of the source access relations may have
10914 accessed the same data element before the given iteration
10915 of the sink access without any intermediate kill of that data element.
10916 The resulting dependence relations map source iterations
10917 to either the corresponding sink iterations or
10918 pairs of corresponding sink iterations and accessed data elements.
10919 To compute standard flow dependences, the sink should be
10920 a read, while the sources should be writes.
10921 If no kills are specified,
10922 then memory based dependence analysis is performed.
10923 If, on the other hand, all sources are also kills,
10924 then value based dependence analysis is performed.
10925 If any of the source accesses are marked as being I<must>
10926 accesses, then they are also treated as kills.
10927 Furthermore, the specification of must-sources results
10928 in the computation of must-dependences.
10929 Only dependences originating in a must access not coscheduled
10930 with any other access to the same element and without
10931 any may accesses between the must access and the sink access
10932 are considered to be must dependences.
10934 =head3 High-level Interface
10936 A high-level interface to dependence analysis is provided
10937 by the following function.
10939 #include <isl/flow.h>
10940 __isl_give isl_union_flow *
10941 isl_union_access_info_compute_flow(
10942 __isl_take isl_union_access_info *access);
10944 The input C<isl_union_access_info> object describes the sink
10945 access relations, the source access relations and a schedule,
10946 while the output C<isl_union_flow> object describes
10947 the resulting dependence relations and the subsets of the
10948 sink relations for which no source was found.
10950 An C<isl_union_access_info> is created, modified, copied and freed using
10951 the following functions.
10953 #include <isl/flow.h>
10954 __isl_give isl_union_access_info *
10955 isl_union_access_info_from_sink(
10956 __isl_take isl_union_map *sink);
10957 __isl_give isl_union_access_info *
10958 isl_union_access_info_set_kill(
10959 __isl_take isl_union_access_info *access,
10960 __isl_take isl_union_map *kill);
10961 __isl_give isl_union_access_info *
10962 isl_union_access_info_set_may_source(
10963 __isl_take isl_union_access_info *access,
10964 __isl_take isl_union_map *may_source);
10965 __isl_give isl_union_access_info *
10966 isl_union_access_info_set_must_source(
10967 __isl_take isl_union_access_info *access,
10968 __isl_take isl_union_map *must_source);
10969 __isl_give isl_union_access_info *
10970 isl_union_access_info_set_schedule(
10971 __isl_take isl_union_access_info *access,
10972 __isl_take isl_schedule *schedule);
10973 __isl_give isl_union_access_info *
10974 isl_union_access_info_set_schedule_map(
10975 __isl_take isl_union_access_info *access,
10976 __isl_take isl_union_map *schedule_map);
10977 __isl_give isl_union_access_info *
10978 isl_union_access_info_copy(
10979 __isl_keep isl_union_access_info *access);
10980 __isl_null isl_union_access_info *
10981 isl_union_access_info_free(
10982 __isl_take isl_union_access_info *access);
10984 The may sources set by C<isl_union_access_info_set_may_source>
10985 do not need to include the must sources set by
10986 C<isl_union_access_info_set_must_source> as a subset.
10987 The kills set by C<isl_union_access_info_set_kill> may overlap
10988 with the may-sources and/or must-sources.
10989 The user is free not to call one (or more) of these functions,
10990 in which case the corresponding set is kept to its empty default.
10991 Similarly, the default schedule initialized by
10992 C<isl_union_access_info_from_sink> is empty.
10993 The current schedule is determined by the last call to either
10994 C<isl_union_access_info_set_schedule> or
10995 C<isl_union_access_info_set_schedule_map>.
10996 The domain of the schedule corresponds to the domains of
10997 the access relations. In particular, the domains of the access
10998 relations are effectively intersected with the domain of the schedule
10999 and only the resulting accesses are considered by the dependence analysis.
11001 An C<isl_union_access_info> object can be read from input
11002 using the following function.
11004 #include <isl/flow.h>
11005 __isl_give isl_union_access_info *
11006 isl_union_access_info_read_from_file(isl_ctx *ctx,
11009 A representation of the information contained in an object
11010 of type C<isl_union_access_info> can be obtained using
11012 #include <isl/flow.h>
11013 __isl_give isl_printer *
11014 isl_printer_print_union_access_info(
11015 __isl_take isl_printer *p,
11016 __isl_keep isl_union_access_info *access);
11017 __isl_give char *isl_union_access_info_to_str(
11018 __isl_keep isl_union_access_info *access);
11020 C<isl_union_access_info_to_str> prints the information in flow format.
11022 The output of C<isl_union_access_info_compute_flow> can be examined,
11023 copied, and freed using the following functions.
11025 #include <isl/flow.h>
11026 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
11027 __isl_keep isl_union_flow *flow);
11028 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
11029 __isl_keep isl_union_flow *flow);
11030 __isl_give isl_union_map *
11031 isl_union_flow_get_full_must_dependence(
11032 __isl_keep isl_union_flow *flow);
11033 __isl_give isl_union_map *
11034 isl_union_flow_get_full_may_dependence(
11035 __isl_keep isl_union_flow *flow);
11036 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
11037 __isl_keep isl_union_flow *flow);
11038 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
11039 __isl_keep isl_union_flow *flow);
11040 __isl_give isl_union_flow *isl_union_flow_copy(
11041 __isl_keep isl_union_flow *flow);
11042 __isl_null isl_union_flow *isl_union_flow_free(
11043 __isl_take isl_union_flow *flow);
11045 The relation returned by C<isl_union_flow_get_must_dependence>
11046 relates domain elements of must sources to domain elements of the sink.
11047 The relation returned by C<isl_union_flow_get_may_dependence>
11048 relates domain elements of must or may sources to domain elements of the sink
11049 and includes the previous relation as a subset.
11050 The relation returned by C<isl_union_flow_get_full_must_dependence>
11051 relates domain elements of must sources to pairs of domain elements of the sink
11052 and accessed data elements.
11053 The relation returned by C<isl_union_flow_get_full_may_dependence>
11054 relates domain elements of must or may sources to pairs of
11055 domain elements of the sink and accessed data elements.
11056 This relation includes the previous relation as a subset.
11057 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
11058 of the sink relation for which no dependences have been found.
11059 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
11060 of the sink relation for which no definite dependences have been found.
11061 That is, it contains those sink access that do not contribute to any
11062 of the elements in the relation returned
11063 by C<isl_union_flow_get_must_dependence>.
11065 A representation of the information contained in an object
11066 of type C<isl_union_flow> can be obtained using
11068 #include <isl/flow.h>
11069 __isl_give isl_printer *isl_printer_print_union_flow(
11070 __isl_take isl_printer *p,
11071 __isl_keep isl_union_flow *flow);
11072 __isl_give char *isl_union_flow_to_str(
11073 __isl_keep isl_union_flow *flow);
11075 C<isl_union_flow_to_str> prints the information in flow format.
11077 =head3 Low-level Interface
11079 A lower-level interface is provided by the following functions.
11081 #include <isl/flow.h>
11083 typedef int (*isl_access_level_before)(void *first, void *second);
11085 __isl_give isl_access_info *isl_access_info_alloc(
11086 __isl_take isl_map *sink,
11087 void *sink_user, isl_access_level_before fn,
11089 __isl_give isl_access_info *isl_access_info_add_source(
11090 __isl_take isl_access_info *acc,
11091 __isl_take isl_map *source, int must,
11092 void *source_user);
11093 __isl_null isl_access_info *isl_access_info_free(
11094 __isl_take isl_access_info *acc);
11096 __isl_give isl_flow *isl_access_info_compute_flow(
11097 __isl_take isl_access_info *acc);
11099 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,
11100 isl_stat (*fn)(__isl_take isl_map *dep, int must,
11101 void *dep_user, void *user),
11103 __isl_give isl_map *isl_flow_get_no_source(
11104 __isl_keep isl_flow *deps, int must);
11105 __isl_null isl_flow *isl_flow_free(
11106 __isl_take isl_flow *deps);
11108 The function C<isl_access_info_compute_flow> performs the actual
11109 dependence analysis. The other functions are used to construct
11110 the input for this function or to read off the output.
11112 The input is collected in an C<isl_access_info>, which can
11113 be created through a call to C<isl_access_info_alloc>.
11114 The arguments to this functions are the sink access relation
11115 C<sink>, a token C<sink_user> used to identify the sink
11116 access to the user, a callback function for specifying the
11117 relative order of source and sink accesses, and the number
11118 of source access relations that will be added.
11120 The callback function has type C<int (*)(void *first, void *second)>.
11121 The function is called with two user supplied tokens identifying
11122 either a source or the sink and it should return the shared nesting
11123 level and the relative order of the two accesses.
11124 In particular, let I<n> be the number of loops shared by
11125 the two accesses. If C<first> precedes C<second> textually,
11126 then the function should return I<2 * n + 1>; otherwise,
11127 it should return I<2 * n>.
11128 The low-level interface assumes that no sources are coscheduled.
11129 If the information returned by the callback does not allow
11130 the relative order to be determined, then one of the sources
11131 is arbitrarily taken to be executed after the other(s).
11133 The sources can be added to the C<isl_access_info> object by performing
11134 (at most) C<max_source> calls to C<isl_access_info_add_source>.
11135 C<must> indicates whether the source is a I<must> access
11136 or a I<may> access. Note that a multi-valued access relation
11137 should only be marked I<must> if every iteration in the domain
11138 of the relation accesses I<all> elements in its image.
11139 The C<source_user> token is again used to identify
11140 the source access. The range of the source access relation
11141 C<source> should have the same dimension as the range
11142 of the sink access relation.
11143 The C<isl_access_info_free> function should usually not be
11144 called explicitly, because it is already called implicitly by
11145 C<isl_access_info_compute_flow>.
11147 The result of the dependence analysis is collected in an
11148 C<isl_flow>. There may be elements of
11149 the sink access for which no preceding source access could be
11150 found or for which all preceding sources are I<may> accesses.
11151 The relations containing these elements can be obtained through
11152 calls to C<isl_flow_get_no_source>, the first with C<must> set
11153 and the second with C<must> unset.
11154 In the case of standard flow dependence analysis,
11155 with the sink a read and the sources I<must> writes,
11156 the first relation corresponds to the reads from uninitialized
11157 array elements and the second relation is empty.
11158 The actual flow dependences can be extracted using
11159 C<isl_flow_foreach>. This function will call the user-specified
11160 callback function C<fn> for each B<non-empty> dependence between
11161 a source and the sink. The callback function is called
11162 with four arguments, the actual flow dependence relation
11163 mapping source iterations to sink iterations, a boolean that
11164 indicates whether it is a I<must> or I<may> dependence, a token
11165 identifying the source and an additional C<void *> with value
11166 equal to the third argument of the C<isl_flow_foreach> call.
11167 A dependence is marked I<must> if it originates from a I<must>
11168 source and if it is not followed by any I<may> sources.
11170 After finishing with an C<isl_flow>, the user should call
11171 C<isl_flow_free> to free all associated memory.
11173 =head3 Interaction with the Low-level Interface
11175 During the dependence analysis, we frequently need to perform
11176 the following operation. Given a relation between sink iterations
11177 and potential source iterations from a particular source domain,
11178 what is the last potential source iteration corresponding to each
11179 sink iteration. It can sometimes be convenient to adjust
11180 the set of potential source iterations before or after each such operation.
11181 The prototypical example is fuzzy array dataflow analysis,
11182 where we need to analyze if, based on data-dependent constraints,
11183 the sink iteration can ever be executed without one or more of
11184 the corresponding potential source iterations being executed.
11185 If so, we can introduce extra parameters and select an unknown
11186 but fixed source iteration from the potential source iterations.
11187 To be able to perform such manipulations, C<isl> provides the following
11190 #include <isl/flow.h>
11192 typedef __isl_give isl_restriction *(*isl_access_restrict)(
11193 __isl_keep isl_map *source_map,
11194 __isl_keep isl_set *sink, void *source_user,
11196 __isl_give isl_access_info *isl_access_info_set_restrict(
11197 __isl_take isl_access_info *acc,
11198 isl_access_restrict fn, void *user);
11200 The function C<isl_access_info_set_restrict> should be called
11201 before calling C<isl_access_info_compute_flow> and registers a callback function
11202 that will be called any time C<isl> is about to compute the last
11203 potential source. The first argument is the (reverse) proto-dependence,
11204 mapping sink iterations to potential source iterations.
11205 The second argument represents the sink iterations for which
11206 we want to compute the last source iteration.
11207 The third argument is the token corresponding to the source
11208 and the final argument is the token passed to C<isl_access_info_set_restrict>.
11209 The callback is expected to return a restriction on either the input or
11210 the output of the operation computing the last potential source.
11211 If the input needs to be restricted then restrictions are needed
11212 for both the source and the sink iterations. The sink iterations
11213 and the potential source iterations will be intersected with these sets.
11214 If the output needs to be restricted then only a restriction on the source
11215 iterations is required.
11216 If any error occurs, the callback should return C<NULL>.
11217 An C<isl_restriction> object can be created, freed and inspected
11218 using the following functions.
11220 #include <isl/flow.h>
11222 __isl_give isl_restriction *isl_restriction_input(
11223 __isl_take isl_set *source_restr,
11224 __isl_take isl_set *sink_restr);
11225 __isl_give isl_restriction *isl_restriction_output(
11226 __isl_take isl_set *source_restr);
11227 __isl_give isl_restriction *isl_restriction_none(
11228 __isl_take isl_map *source_map);
11229 __isl_give isl_restriction *isl_restriction_empty(
11230 __isl_take isl_map *source_map);
11231 __isl_null isl_restriction *isl_restriction_free(
11232 __isl_take isl_restriction *restr);
11234 C<isl_restriction_none> and C<isl_restriction_empty> are special
11235 cases of C<isl_restriction_input>. C<isl_restriction_none>
11236 is essentially equivalent to
11238 isl_restriction_input(isl_set_universe(
11239 isl_space_range(isl_map_get_space(source_map))),
11241 isl_space_domain(isl_map_get_space(source_map))));
11243 whereas C<isl_restriction_empty> is essentially equivalent to
11245 isl_restriction_input(isl_set_empty(
11246 isl_space_range(isl_map_get_space(source_map))),
11248 isl_space_domain(isl_map_get_space(source_map))));
11252 #include <isl/schedule.h>
11253 __isl_give isl_schedule *
11254 isl_schedule_constraints_compute_schedule(
11255 __isl_take isl_schedule_constraints *sc);
11257 The function C<isl_schedule_constraints_compute_schedule> can be
11258 used to compute a schedule that satisfies the given schedule constraints.
11259 These schedule constraints include the iteration domain for which
11260 a schedule should be computed and dependences between pairs of
11261 iterations. In particular, these dependences include
11262 I<validity> dependences and I<proximity> dependences.
11263 By default, the algorithm used to construct the schedule is similar
11264 to that of C<Pluto>.
11265 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
11267 The generated schedule respects all validity dependences.
11268 That is, all dependence distances over these dependences in the
11269 scheduled space are lexicographically positive.
11271 The default algorithm tries to ensure that the dependence distances
11272 over coincidence constraints are zero and to minimize the
11273 dependence distances over proximity dependences.
11274 Moreover, it tries to obtain sequences (bands) of schedule dimensions
11275 for groups of domains where the dependence distances over validity
11276 dependences have only non-negative values.
11277 Note that when minimizing the maximal dependence distance
11278 over proximity dependences, a single affine expression in the parameters
11279 is constructed that bounds all dependence distances. If no such expression
11280 exists, then the algorithm will fail and resort to an alternative
11281 scheduling algorithm. In particular, this means that adding proximity
11282 dependences may eliminate valid solutions. A typical example where this
11283 phenomenon may occur is when some subset of the proximity dependences
11284 has no restriction on some parameter, forcing the coefficient of that
11285 parameter to be zero, while some other subset forces the dependence
11286 distance to depend on that parameter, requiring the same coefficient
11288 When using Feautrier's algorithm, the coincidence and proximity constraints
11289 are only taken into account during the extension to a
11290 full-dimensional schedule.
11292 An C<isl_schedule_constraints> object can be constructed
11293 and manipulated using the following functions.
11295 #include <isl/schedule.h>
11296 __isl_give isl_schedule_constraints *
11297 isl_schedule_constraints_copy(
11298 __isl_keep isl_schedule_constraints *sc);
11299 __isl_give isl_schedule_constraints *
11300 isl_schedule_constraints_on_domain(
11301 __isl_take isl_union_set *domain);
11302 __isl_give isl_schedule_constraints *
11303 isl_schedule_constraints_set_context(
11304 __isl_take isl_schedule_constraints *sc,
11305 __isl_take isl_set *context);
11306 __isl_give isl_schedule_constraints *
11307 isl_schedule_constraints_set_validity(
11308 __isl_take isl_schedule_constraints *sc,
11309 __isl_take isl_union_map *validity);
11310 __isl_give isl_schedule_constraints *
11311 isl_schedule_constraints_set_coincidence(
11312 __isl_take isl_schedule_constraints *sc,
11313 __isl_take isl_union_map *coincidence);
11314 __isl_give isl_schedule_constraints *
11315 isl_schedule_constraints_set_proximity(
11316 __isl_take isl_schedule_constraints *sc,
11317 __isl_take isl_union_map *proximity);
11318 __isl_give isl_schedule_constraints *
11319 isl_schedule_constraints_set_conditional_validity(
11320 __isl_take isl_schedule_constraints *sc,
11321 __isl_take isl_union_map *condition,
11322 __isl_take isl_union_map *validity);
11323 __isl_give isl_schedule_constraints *
11324 isl_schedule_constraints_apply(
11325 __isl_take isl_schedule_constraints *sc,
11326 __isl_take isl_union_map *umap);
11327 __isl_null isl_schedule_constraints *
11328 isl_schedule_constraints_free(
11329 __isl_take isl_schedule_constraints *sc);
11331 The initial C<isl_schedule_constraints> object created by
11332 C<isl_schedule_constraints_on_domain> does not impose any constraints.
11333 That is, it has an empty set of dependences.
11334 The function C<isl_schedule_constraints_set_context> allows the user
11335 to specify additional constraints on the parameters that may
11336 be assumed to hold during the construction of the schedule.
11337 The function C<isl_schedule_constraints_set_validity> replaces the
11338 validity dependences, mapping domain elements I<i> to domain
11339 elements that should be scheduled after I<i>.
11340 The function C<isl_schedule_constraints_set_coincidence> replaces the
11341 coincidence dependences, mapping domain elements I<i> to domain
11342 elements that should be scheduled together with I<I>, if possible.
11343 The function C<isl_schedule_constraints_set_proximity> replaces the
11344 proximity dependences, mapping domain elements I<i> to domain
11345 elements that should be scheduled either before I<I>
11346 or as early as possible after I<i>.
11348 The function C<isl_schedule_constraints_set_conditional_validity>
11349 replaces the conditional validity constraints.
11350 A conditional validity constraint is only imposed when any of the corresponding
11351 conditions is satisfied, i.e., when any of them is non-zero.
11352 That is, the scheduler ensures that within each band if the dependence
11353 distances over the condition constraints are not all zero
11354 then all corresponding conditional validity constraints are respected.
11355 A conditional validity constraint corresponds to a condition
11356 if the two are adjacent, i.e., if the domain of one relation intersect
11357 the range of the other relation.
11358 The typical use case of conditional validity constraints is
11359 to allow order constraints between live ranges to be violated
11360 as long as the live ranges themselves are local to the band.
11361 To allow more fine-grained control over which conditions correspond
11362 to which conditional validity constraints, the domains and ranges
11363 of these relations may include I<tags>. That is, the domains and
11364 ranges of those relation may themselves be wrapped relations
11365 where the iteration domain appears in the domain of those wrapped relations
11366 and the range of the wrapped relations can be arbitrarily chosen
11367 by the user. Conditions and conditional validity constraints are only
11368 considered adjacent to each other if the entire wrapped relation matches.
11369 In particular, a relation with a tag will never be considered adjacent
11370 to a relation without a tag.
11372 The function C<isl_schedule_constraints_apply> takes
11373 schedule constraints that are defined on some set of domain elements
11374 and transforms them to schedule constraints on the elements
11375 to which these domain elements are mapped by the given transformation.
11377 An C<isl_schedule_constraints> object can be inspected
11378 using the following functions.
11380 #include <isl/schedule.h>
11381 __isl_give isl_union_set *
11382 isl_schedule_constraints_get_domain(
11383 __isl_keep isl_schedule_constraints *sc);
11384 __isl_give isl_set *isl_schedule_constraints_get_context(
11385 __isl_keep isl_schedule_constraints *sc);
11386 __isl_give isl_union_map *
11387 isl_schedule_constraints_get_validity(
11388 __isl_keep isl_schedule_constraints *sc);
11389 __isl_give isl_union_map *
11390 isl_schedule_constraints_get_coincidence(
11391 __isl_keep isl_schedule_constraints *sc);
11392 __isl_give isl_union_map *
11393 isl_schedule_constraints_get_proximity(
11394 __isl_keep isl_schedule_constraints *sc);
11395 __isl_give isl_union_map *
11396 isl_schedule_constraints_get_conditional_validity(
11397 __isl_keep isl_schedule_constraints *sc);
11398 __isl_give isl_union_map *
11399 isl_schedule_constraints_get_conditional_validity_condition(
11400 __isl_keep isl_schedule_constraints *sc);
11402 An C<isl_schedule_constraints> object can be read from input
11403 using the following functions.
11405 #include <isl/schedule.h>
11406 __isl_give isl_schedule_constraints *
11407 isl_schedule_constraints_read_from_str(isl_ctx *ctx,
11409 __isl_give isl_schedule_constraints *
11410 isl_schedule_constraints_read_from_file(isl_ctx *ctx,
11413 The contents of an C<isl_schedule_constraints> object can be printed
11414 using the following functions.
11416 #include <isl/schedule.h>
11417 __isl_give isl_printer *
11418 isl_printer_print_schedule_constraints(
11419 __isl_take isl_printer *p,
11420 __isl_keep isl_schedule_constraints *sc);
11421 __isl_give char *isl_schedule_constraints_to_str(
11422 __isl_keep isl_schedule_constraints *sc);
11424 The following function computes a schedule directly from
11425 an iteration domain and validity and proximity dependences
11426 and is implemented in terms of the functions described above.
11427 The use of C<isl_union_set_compute_schedule> is discouraged.
11429 #include <isl/schedule.h>
11430 __isl_give isl_schedule *isl_union_set_compute_schedule(
11431 __isl_take isl_union_set *domain,
11432 __isl_take isl_union_map *validity,
11433 __isl_take isl_union_map *proximity);
11435 The generated schedule represents a schedule tree.
11436 For more information on schedule trees, see
11437 L</"Schedule Trees">.
11441 #include <isl/schedule.h>
11442 isl_stat isl_options_set_schedule_max_coefficient(
11443 isl_ctx *ctx, int val);
11444 int isl_options_get_schedule_max_coefficient(
11446 isl_stat isl_options_set_schedule_max_constant_term(
11447 isl_ctx *ctx, int val);
11448 int isl_options_get_schedule_max_constant_term(
11450 isl_stat isl_options_set_schedule_serialize_sccs(
11451 isl_ctx *ctx, int val);
11452 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx);
11453 isl_stat isl_options_set_schedule_whole_component(
11454 isl_ctx *ctx, int val);
11455 int isl_options_get_schedule_whole_component(
11457 isl_stat isl_options_set_schedule_maximize_band_depth(
11458 isl_ctx *ctx, int val);
11459 int isl_options_get_schedule_maximize_band_depth(
11461 isl_stat isl_options_set_schedule_maximize_coincidence(
11462 isl_ctx *ctx, int val);
11463 int isl_options_get_schedule_maximize_coincidence(
11465 isl_stat isl_options_set_schedule_outer_coincidence(
11466 isl_ctx *ctx, int val);
11467 int isl_options_get_schedule_outer_coincidence(
11469 isl_stat isl_options_set_schedule_split_scaled(
11470 isl_ctx *ctx, int val);
11471 int isl_options_get_schedule_split_scaled(
11473 isl_stat isl_options_set_schedule_treat_coalescing(
11474 isl_ctx *ctx, int val);
11475 int isl_options_get_schedule_treat_coalescing(
11477 isl_stat isl_options_set_schedule_algorithm(
11478 isl_ctx *ctx, int val);
11479 int isl_options_get_schedule_algorithm(
11481 isl_stat isl_options_set_schedule_carry_self_first(
11482 isl_ctx *ctx, int val);
11483 int isl_options_get_schedule_carry_self_first(
11485 isl_stat isl_options_set_schedule_separate_components(
11486 isl_ctx *ctx, int val);
11487 int isl_options_get_schedule_separate_components(
11492 =item * schedule_max_coefficient
11494 This option enforces that the coefficients for variable and parameter
11495 dimensions in the calculated schedule are not larger than the specified value.
11496 This option can significantly increase the speed of the scheduling calculation
11497 and may also prevent fusing of unrelated dimensions. A value of -1 means that
11498 this option does not introduce bounds on the variable or parameter
11500 This option has no effect on the Feautrier style scheduler.
11502 =item * schedule_max_constant_term
11504 This option enforces that the constant coefficients in the calculated schedule
11505 are not larger than the maximal constant term. This option can significantly
11506 increase the speed of the scheduling calculation and may also prevent fusing of
11507 unrelated dimensions. A value of -1 means that this option does not introduce
11508 bounds on the constant coefficients.
11510 =item * schedule_serialize_sccs
11512 If this option is set, then all strongly connected components
11513 in the dependence graph are serialized as soon as they are detected.
11514 This means in particular that instances of statements will only
11515 appear in the same band node if these statements belong
11516 to the same strongly connected component at the point where
11517 the band node is constructed.
11519 =item * schedule_whole_component
11521 If this option is set, then entire (weakly) connected
11522 components in the dependence graph are scheduled together
11524 Otherwise, each strongly connected component within
11525 such a weakly connected component is first scheduled separately
11526 and then combined with other strongly connected components.
11527 This option has no effect if C<schedule_serialize_sccs> is set.
11529 =item * schedule_maximize_band_depth
11531 If this option is set, then the scheduler tries to maximize
11532 the width of the bands. Wider bands give more possibilities for tiling.
11533 In particular, if the C<schedule_whole_component> option is set,
11534 then bands are split if this might result in wider bands.
11535 Otherwise, the effect of this option is to only allow
11536 strongly connected components to be combined if this does
11537 not reduce the width of the bands.
11538 Note that if the C<schedule_serialize_sccs> options is set, then
11539 the C<schedule_maximize_band_depth> option therefore has no effect.
11541 =item * schedule_maximize_coincidence
11543 This option is only effective if the C<schedule_whole_component>
11544 option is turned off.
11545 If the C<schedule_maximize_coincidence> option is set, then (clusters of)
11546 strongly connected components are only combined with each other
11547 if this does not reduce the number of coincident band members.
11549 =item * schedule_outer_coincidence
11551 If this option is set, then we try to construct schedules
11552 where the outermost scheduling dimension in each band
11553 satisfies the coincidence constraints.
11555 =item * schedule_algorithm
11557 Selects the scheduling algorithm to be used.
11558 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
11559 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
11561 =item * schedule_split_scaled
11563 If this option is set, then we try to construct schedules in which the
11564 constant term is split off from the linear part if the linear parts of
11565 the scheduling rows for all nodes in the graph have a common non-trivial
11567 The constant term is then dropped and the linear
11569 This option is only effective when the Feautrier style scheduler is
11570 being used, either as the main scheduler or as a fallback for the
11571 Pluto-like scheduler.
11573 =item * schedule_treat_coalescing
11575 If this option is set, then the scheduler will try and avoid
11576 producing schedules that perform loop coalescing.
11577 In particular, for the Pluto-like scheduler, this option places
11578 bounds on the schedule coefficients based on the sizes of the instance sets.
11579 For the Feautrier style scheduler, this option detects potentially
11580 coalescing schedules and then tries to adjust the schedule to avoid
11583 =item * schedule_carry_self_first
11585 If this option is set, then the Feautrier style scheduler
11586 (when used as a fallback for the Pluto-like scheduler) will
11587 first try to only carry self-dependences.
11589 =item * schedule_separate_components
11591 If this option is set then the function C<isl_schedule_get_map>
11592 will treat set nodes in the same way as sequence nodes.
11596 =head2 AST Generation
11598 This section describes the C<isl> functionality for generating
11599 ASTs that visit all the elements
11600 in a domain in an order specified by a schedule tree or
11602 In case the schedule given as a C<isl_union_map>, an AST is generated
11603 that visits all the elements in the domain of the C<isl_union_map>
11604 according to the lexicographic order of the corresponding image
11605 element(s). If the range of the C<isl_union_map> consists of
11606 elements in more than one space, then each of these spaces is handled
11607 separately in an arbitrary order.
11608 It should be noted that the schedule tree or the image elements
11609 in a schedule map only specify the I<order>
11610 in which the corresponding domain elements should be visited.
11611 No direct relation between the partial schedule values
11612 or the image elements on the one hand and the loop iterators
11613 in the generated AST on the other hand should be assumed.
11615 Each AST is generated within a build. The initial build
11616 simply specifies the constraints on the parameters (if any)
11617 and can be created, inspected, copied and freed using the following functions.
11619 #include <isl/ast_build.h>
11620 __isl_give isl_ast_build *isl_ast_build_alloc(
11622 __isl_give isl_ast_build *isl_ast_build_from_context(
11623 __isl_take isl_set *set);
11624 __isl_give isl_ast_build *isl_ast_build_copy(
11625 __isl_keep isl_ast_build *build);
11626 __isl_null isl_ast_build *isl_ast_build_free(
11627 __isl_take isl_ast_build *build);
11629 The C<set> argument is usually a parameter set with zero or more parameters.
11630 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
11631 this set is required to be a parameter set.
11632 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
11633 specify any parameter constraints.
11634 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
11635 and L</"Fine-grained Control over AST Generation">.
11636 Finally, the AST itself can be constructed using one of the following
11639 #include <isl/ast_build.h>
11640 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
11641 __isl_keep isl_ast_build *build,
11642 __isl_take isl_schedule *schedule);
11643 __isl_give isl_ast_node *
11644 isl_ast_build_node_from_schedule_map(
11645 __isl_keep isl_ast_build *build,
11646 __isl_take isl_union_map *schedule);
11648 =head3 Inspecting the AST
11650 The basic properties of an AST node can be obtained as follows.
11652 #include <isl/ast.h>
11653 enum isl_ast_node_type isl_ast_node_get_type(
11654 __isl_keep isl_ast_node *node);
11656 The type of an AST node is one of
11657 C<isl_ast_node_for>,
11658 C<isl_ast_node_if>,
11659 C<isl_ast_node_block>,
11660 C<isl_ast_node_mark> or
11661 C<isl_ast_node_user>.
11662 An C<isl_ast_node_for> represents a for node.
11663 An C<isl_ast_node_if> represents an if node.
11664 An C<isl_ast_node_block> represents a compound node.
11665 An C<isl_ast_node_mark> introduces a mark in the AST.
11666 An C<isl_ast_node_user> represents an expression statement.
11667 An expression statement typically corresponds to a domain element, i.e.,
11668 one of the elements that is visited by the AST.
11670 Each type of node has its own additional properties.
11672 #include <isl/ast.h>
11673 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
11674 __isl_keep isl_ast_node *node);
11675 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
11676 __isl_keep isl_ast_node *node);
11677 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
11678 __isl_keep isl_ast_node *node);
11679 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
11680 __isl_keep isl_ast_node *node);
11681 __isl_give isl_ast_node *isl_ast_node_for_get_body(
11682 __isl_keep isl_ast_node *node);
11683 isl_bool isl_ast_node_for_is_degenerate(
11684 __isl_keep isl_ast_node *node);
11686 An C<isl_ast_for> is considered degenerate if it is known to execute
11689 #include <isl/ast.h>
11690 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
11691 __isl_keep isl_ast_node *node);
11692 __isl_give isl_ast_node *isl_ast_node_if_get_then_node(
11693 __isl_keep isl_ast_node *node);
11694 __isl_give isl_ast_node *isl_ast_node_if_get_then(
11695 __isl_keep isl_ast_node *node);
11696 isl_bool isl_ast_node_if_has_else_node(
11697 __isl_keep isl_ast_node *node);
11698 isl_bool isl_ast_node_if_has_else(
11699 __isl_keep isl_ast_node *node);
11700 __isl_give isl_ast_node *isl_ast_node_if_get_else_node(
11701 __isl_keep isl_ast_node *node);
11702 __isl_give isl_ast_node *isl_ast_node_if_get_else(
11703 __isl_keep isl_ast_node *node);
11705 C<isl_ast_node_if_get_then>,
11706 C<isl_ast_node_if_has_else> and
11707 C<isl_ast_node_if_get_else>
11708 are alternative names for
11709 C<isl_ast_node_if_get_then_node>,
11710 C<isl_ast_node_if_has_else_node> and
11711 C<isl_ast_node_if_get_else_node>, respectively.
11713 __isl_give isl_ast_node_list *
11714 isl_ast_node_block_get_children(
11715 __isl_keep isl_ast_node *node);
11717 __isl_give isl_id *isl_ast_node_mark_get_id(
11718 __isl_keep isl_ast_node *node);
11719 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
11720 __isl_keep isl_ast_node *node);
11722 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
11723 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
11725 #include <isl/ast.h>
11726 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
11727 __isl_keep isl_ast_node *node);
11729 All descendants of a specific node in the AST (including the node itself)
11731 in depth-first pre-order using the following function.
11733 #include <isl/ast.h>
11734 isl_stat isl_ast_node_foreach_descendant_top_down(
11735 __isl_keep isl_ast_node *node,
11736 isl_bool (*fn)(__isl_keep isl_ast_node *node,
11737 void *user), void *user);
11739 The callback function should return C<isl_bool_true> if the children
11740 of the given node should be visited and C<isl_bool_false> if they should not.
11741 It should return C<isl_bool_error> in case of failure, in which case
11742 the entire traversal is aborted.
11744 Each of the returned C<isl_ast_expr>s can in turn be inspected using
11745 the following functions.
11747 #include <isl/ast.h>
11748 enum isl_ast_expr_type isl_ast_expr_get_type(
11749 __isl_keep isl_ast_expr *expr);
11751 The type of an AST expression is one of
11752 C<isl_ast_expr_op>,
11753 C<isl_ast_expr_id> or
11754 C<isl_ast_expr_int>.
11755 An C<isl_ast_expr_op> represents the result of an operation.
11756 An C<isl_ast_expr_id> represents an identifier.
11757 An C<isl_ast_expr_int> represents an integer value.
11759 Each type of expression has its own additional properties.
11761 #include <isl/ast.h>
11762 enum isl_ast_expr_op_type isl_ast_expr_op_get_type(
11763 __isl_keep isl_ast_expr *expr);
11764 enum isl_ast_expr_op_type isl_ast_expr_get_op_type(
11765 __isl_keep isl_ast_expr *expr);
11766 isl_size isl_ast_expr_op_get_n_arg(__isl_keep isl_ast_expr *expr);
11767 isl_size isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
11768 __isl_give isl_ast_expr *isl_ast_expr_op_get_arg(
11769 __isl_keep isl_ast_expr *expr, int pos);
11770 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
11771 __isl_keep isl_ast_expr *expr, int pos);
11772 isl_stat isl_ast_expr_foreach_ast_expr_op_type(
11773 __isl_keep isl_ast_expr *expr,
11774 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11775 void *user), void *user);
11776 isl_stat isl_ast_expr_foreach_ast_op_type(
11777 __isl_keep isl_ast_expr *expr,
11778 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11779 void *user), void *user);
11780 isl_stat isl_ast_node_foreach_ast_expr_op_type(
11781 __isl_keep isl_ast_node *node,
11782 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11783 void *user), void *user);
11784 isl_stat isl_ast_node_foreach_ast_op_type(
11785 __isl_keep isl_ast_node *node,
11786 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11787 void *user), void *user);
11789 C<isl_ast_expr_op_get_type> returns the type of the operation
11790 performed. C<isl_ast_expr_op_get_n_arg> returns the number of
11791 arguments. C<isl_ast_expr_get_op_arg> returns the specified
11793 C<isl_ast_expr_get_op_type> is an alternative name for
11794 C<isl_ast_expr_op_get_type>.
11796 C<isl_ast_expr_get_op_n_arg> is an alternative name for
11797 C<isl_ast_expr_op_get_n_arg> and
11798 C<isl_ast_expr_get_op_arg> is an alternative name for
11799 C<isl_ast_expr_op_get_arg>.
11801 C<isl_ast_expr_foreach_ast_expr_op_type> calls C<fn> for each distinct
11802 C<isl_ast_expr_op_type> that appears in C<expr>.
11803 C<isl_ast_expr_foreach_ast_op_type> is an alternative name for
11804 C<isl_ast_expr_foreach_ast_expr_op_type>.
11805 C<isl_ast_node_foreach_ast_expr_op_type> does the same for each distinct
11806 C<isl_ast_expr_op_type> that appears in C<node>.
11807 C<isl_ast_node_foreach_ast_op_type> is an alternative name for
11808 C<isl_ast_node_foreach_ast_expr_op_type>.
11809 The operation type is one of the following.
11813 =item C<isl_ast_expr_op_and>
11815 Logical I<and> of two arguments.
11816 Both arguments can be evaluated.
11818 =item C<isl_ast_expr_op_and_then>
11820 Logical I<and> of two arguments.
11821 The second argument can only be evaluated if the first evaluates to true.
11823 =item C<isl_ast_expr_op_or>
11825 Logical I<or> of two arguments.
11826 Both arguments can be evaluated.
11828 =item C<isl_ast_expr_op_or_else>
11830 Logical I<or> of two arguments.
11831 The second argument can only be evaluated if the first evaluates to false.
11833 =item C<isl_ast_expr_op_max>
11835 Maximum of two or more arguments.
11837 =item C<isl_ast_expr_op_min>
11839 Minimum of two or more arguments.
11841 =item C<isl_ast_expr_op_minus>
11845 =item C<isl_ast_expr_op_add>
11847 Sum of two arguments.
11849 =item C<isl_ast_expr_op_sub>
11851 Difference of two arguments.
11853 =item C<isl_ast_expr_op_mul>
11855 Product of two arguments.
11857 =item C<isl_ast_expr_op_div>
11859 Exact division. That is, the result is known to be an integer.
11861 =item C<isl_ast_expr_op_fdiv_q>
11863 Result of integer division, rounded towards negative
11865 The divisor is known to be positive.
11867 =item C<isl_ast_expr_op_pdiv_q>
11869 Result of integer division, where dividend is known to be non-negative.
11870 The divisor is known to be positive.
11872 =item C<isl_ast_expr_op_pdiv_r>
11874 Remainder of integer division, where dividend is known to be non-negative.
11875 The divisor is known to be positive.
11877 =item C<isl_ast_expr_op_zdiv_r>
11879 Equal to zero iff the remainder on integer division is zero.
11880 The divisor is known to be positive.
11882 =item C<isl_ast_expr_op_cond>
11884 Conditional operator defined on three arguments.
11885 If the first argument evaluates to true, then the result
11886 is equal to the second argument. Otherwise, the result
11887 is equal to the third argument.
11888 The second and third argument may only be evaluated if
11889 the first argument evaluates to true and false, respectively.
11890 Corresponds to C<a ? b : c> in C.
11892 =item C<isl_ast_expr_op_select>
11894 Conditional operator defined on three arguments.
11895 If the first argument evaluates to true, then the result
11896 is equal to the second argument. Otherwise, the result
11897 is equal to the third argument.
11898 The second and third argument may be evaluated independently
11899 of the value of the first argument.
11900 Corresponds to C<a * b + (1 - a) * c> in C.
11902 =item C<isl_ast_expr_op_eq>
11906 =item C<isl_ast_expr_op_le>
11908 Less than or equal relation.
11910 =item C<isl_ast_expr_op_lt>
11912 Less than relation.
11914 =item C<isl_ast_expr_op_ge>
11916 Greater than or equal relation.
11918 =item C<isl_ast_expr_op_gt>
11920 Greater than relation.
11922 =item C<isl_ast_expr_op_call>
11925 The number of arguments of the C<isl_ast_expr> is one more than
11926 the number of arguments in the function call, the first argument
11927 representing the function being called.
11929 =item C<isl_ast_expr_op_access>
11932 The number of arguments of the C<isl_ast_expr> is one more than
11933 the number of index expressions in the array access, the first argument
11934 representing the array being accessed.
11936 =item C<isl_ast_expr_op_member>
11939 This operation has two arguments, a structure and the name of
11940 the member of the structure being accessed.
11942 =item C<isl_ast_expr_op_address_of>
11944 The address of its single argument, which is always an array access.
11948 #include <isl/ast.h>
11949 __isl_give isl_id *isl_ast_expr_id_get_id(
11950 __isl_keep isl_ast_expr *expr);
11951 __isl_give isl_id *isl_ast_expr_get_id(
11952 __isl_keep isl_ast_expr *expr);
11954 Return the identifier represented by the AST expression.
11955 C<isl_ast_expr_get_id> is an alternative name for
11956 C<isl_ast_expr_id_get_id>.
11958 #include <isl/ast.h>
11959 __isl_give isl_val *isl_ast_expr_int_get_val(
11960 __isl_keep isl_ast_expr *expr);
11961 __isl_give isl_val *isl_ast_expr_get_val(
11962 __isl_keep isl_ast_expr *expr);
11964 Return the integer represented by the AST expression.
11965 C<isl_ast_expr_get_val> is an alternative name for
11966 C<isl_ast_expr_int_get_val>.
11968 =head3 Properties of ASTs
11970 #include <isl/ast.h>
11971 isl_bool isl_ast_expr_is_equal(
11972 __isl_keep isl_ast_expr *expr1,
11973 __isl_keep isl_ast_expr *expr2);
11975 Check if two C<isl_ast_expr>s are equal to each other.
11977 =head3 Manipulating and printing the AST
11979 AST nodes can be copied and freed using the following functions.
11981 #include <isl/ast.h>
11982 __isl_give isl_ast_node *isl_ast_node_copy(
11983 __isl_keep isl_ast_node *node);
11984 __isl_null isl_ast_node *isl_ast_node_free(
11985 __isl_take isl_ast_node *node);
11987 AST expressions can be copied and freed using the following functions.
11989 #include <isl/ast.h>
11990 __isl_give isl_ast_expr *isl_ast_expr_copy(
11991 __isl_keep isl_ast_expr *expr);
11992 __isl_null isl_ast_expr *isl_ast_expr_free(
11993 __isl_take isl_ast_expr *expr);
11995 New AST expressions can be created either directly or within
11996 the context of an C<isl_ast_build>.
11998 #include <isl/ast.h>
11999 __isl_give isl_ast_expr *isl_ast_expr_from_val(
12000 __isl_take isl_val *v);
12001 __isl_give isl_ast_expr *isl_ast_expr_from_id(
12002 __isl_take isl_id *id);
12003 __isl_give isl_ast_expr *isl_ast_expr_neg(
12004 __isl_take isl_ast_expr *expr);
12005 __isl_give isl_ast_expr *isl_ast_expr_address_of(
12006 __isl_take isl_ast_expr *expr);
12007 __isl_give isl_ast_expr *isl_ast_expr_add(
12008 __isl_take isl_ast_expr *expr1,
12009 __isl_take isl_ast_expr *expr2);
12010 __isl_give isl_ast_expr *isl_ast_expr_sub(
12011 __isl_take isl_ast_expr *expr1,
12012 __isl_take isl_ast_expr *expr2);
12013 __isl_give isl_ast_expr *isl_ast_expr_mul(
12014 __isl_take isl_ast_expr *expr1,
12015 __isl_take isl_ast_expr *expr2);
12016 __isl_give isl_ast_expr *isl_ast_expr_div(
12017 __isl_take isl_ast_expr *expr1,
12018 __isl_take isl_ast_expr *expr2);
12019 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
12020 __isl_take isl_ast_expr *expr1,
12021 __isl_take isl_ast_expr *expr2);
12022 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
12023 __isl_take isl_ast_expr *expr1,
12024 __isl_take isl_ast_expr *expr2);
12025 __isl_give isl_ast_expr *isl_ast_expr_and(
12026 __isl_take isl_ast_expr *expr1,
12027 __isl_take isl_ast_expr *expr2)
12028 __isl_give isl_ast_expr *isl_ast_expr_and_then(
12029 __isl_take isl_ast_expr *expr1,
12030 __isl_take isl_ast_expr *expr2)
12031 __isl_give isl_ast_expr *isl_ast_expr_or(
12032 __isl_take isl_ast_expr *expr1,
12033 __isl_take isl_ast_expr *expr2)
12034 __isl_give isl_ast_expr *isl_ast_expr_or_else(
12035 __isl_take isl_ast_expr *expr1,
12036 __isl_take isl_ast_expr *expr2)
12037 __isl_give isl_ast_expr *isl_ast_expr_eq(
12038 __isl_take isl_ast_expr *expr1,
12039 __isl_take isl_ast_expr *expr2);
12040 __isl_give isl_ast_expr *isl_ast_expr_le(
12041 __isl_take isl_ast_expr *expr1,
12042 __isl_take isl_ast_expr *expr2);
12043 __isl_give isl_ast_expr *isl_ast_expr_lt(
12044 __isl_take isl_ast_expr *expr1,
12045 __isl_take isl_ast_expr *expr2);
12046 __isl_give isl_ast_expr *isl_ast_expr_ge(
12047 __isl_take isl_ast_expr *expr1,
12048 __isl_take isl_ast_expr *expr2);
12049 __isl_give isl_ast_expr *isl_ast_expr_gt(
12050 __isl_take isl_ast_expr *expr1,
12051 __isl_take isl_ast_expr *expr2);
12052 __isl_give isl_ast_expr *isl_ast_expr_access(
12053 __isl_take isl_ast_expr *array,
12054 __isl_take isl_ast_expr_list *indices);
12055 __isl_give isl_ast_expr *isl_ast_expr_call(
12056 __isl_take isl_ast_expr *function,
12057 __isl_take isl_ast_expr_list *arguments);
12059 The function C<isl_ast_expr_address_of> can be applied to an
12060 C<isl_ast_expr> of type C<isl_ast_expr_op_access> only. It is meant
12061 to represent the address of the C<isl_ast_expr_access>.
12062 The second argument of the functions C<isl_ast_expr_pdiv_q> and
12063 C<isl_ast_expr_pdiv_r> should always evaluate to a positive number.
12065 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
12066 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
12068 #include <isl/ast_build.h>
12069 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
12070 __isl_keep isl_ast_build *build,
12071 __isl_take isl_set *set);
12072 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
12073 __isl_keep isl_ast_build *build,
12074 __isl_take isl_pw_aff *pa);
12075 __isl_give isl_ast_expr *
12076 isl_ast_build_access_from_pw_multi_aff(
12077 __isl_keep isl_ast_build *build,
12078 __isl_take isl_pw_multi_aff *pma);
12079 __isl_give isl_ast_expr *
12080 isl_ast_build_access_from_multi_pw_aff(
12081 __isl_keep isl_ast_build *build,
12082 __isl_take isl_multi_pw_aff *mpa);
12083 __isl_give isl_ast_expr *
12084 isl_ast_build_call_from_pw_multi_aff(
12085 __isl_keep isl_ast_build *build,
12086 __isl_take isl_pw_multi_aff *pma);
12087 __isl_give isl_ast_expr *
12088 isl_ast_build_call_from_multi_pw_aff(
12089 __isl_keep isl_ast_build *build,
12090 __isl_take isl_multi_pw_aff *mpa);
12093 the domains of C<pa>, C<mpa> and C<pma> should correspond
12094 to the schedule space of C<build>.
12095 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
12096 the function being called.
12097 If the accessed space is a nested relation, then it is taken
12098 to represent an access of the member specified by the range
12099 of this nested relation of the structure specified by the domain
12100 of the nested relation.
12102 The following functions can be used to modify an C<isl_ast_expr>.
12104 #include <isl/ast.h>
12105 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
12106 __isl_take isl_ast_expr *expr, int pos,
12107 __isl_take isl_ast_expr *arg);
12109 Replace the argument of C<expr> at position C<pos> by C<arg>.
12111 #include <isl/ast.h>
12112 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
12113 __isl_take isl_ast_expr *expr,
12114 __isl_take isl_id_to_ast_expr *id2expr);
12116 The function C<isl_ast_expr_substitute_ids> replaces the
12117 subexpressions of C<expr> of type C<isl_ast_expr_id>
12118 by the corresponding expression in C<id2expr>, if there is any.
12121 The following function can be used to modify the descendants
12122 of a specific node in an AST using a depth-first post-order
12123 traversal of those descendants (including the node itself).
12125 #include <isl/ast.h>
12126 __isl_give isl_ast_node *
12127 isl_ast_node_map_descendant_bottom_up(
12128 __isl_take isl_ast_node *node,
12129 __isl_give isl_ast_node *(*fn)(
12130 __isl_take isl_ast_node *node,
12131 void *user), void *user);
12133 User specified data can be attached to an C<isl_ast_node> and obtained
12134 from the same C<isl_ast_node> using the following functions.
12136 #include <isl/ast.h>
12137 __isl_give isl_ast_node *isl_ast_node_set_annotation(
12138 __isl_take isl_ast_node *node,
12139 __isl_take isl_id *annotation);
12140 __isl_give isl_id *isl_ast_node_get_annotation(
12141 __isl_keep isl_ast_node *node);
12143 Basic printing can be performed using the following functions.
12145 #include <isl/ast.h>
12146 __isl_give isl_printer *isl_printer_print_ast_expr(
12147 __isl_take isl_printer *p,
12148 __isl_keep isl_ast_expr *expr);
12149 __isl_give isl_printer *isl_printer_print_ast_node(
12150 __isl_take isl_printer *p,
12151 __isl_keep isl_ast_node *node);
12152 __isl_give char *isl_ast_expr_to_str(
12153 __isl_keep isl_ast_expr *expr);
12154 __isl_give char *isl_ast_node_to_str(
12155 __isl_keep isl_ast_node *node);
12156 __isl_give char *isl_ast_expr_to_C_str(
12157 __isl_keep isl_ast_expr *expr);
12158 __isl_give char *isl_ast_node_to_C_str(
12159 __isl_keep isl_ast_node *node);
12161 The functions C<isl_ast_expr_to_C_str> and
12162 C<isl_ast_node_to_C_str> are convenience functions
12163 that return a string representation of the input in C format.
12165 More advanced printing can be performed using the following functions.
12167 #include <isl/ast.h>
12168 __isl_give isl_printer *
12169 isl_ast_expr_op_type_set_print_name(
12170 __isl_take isl_printer *p,
12171 enum isl_ast_expr_op_type type,
12172 __isl_keep const char *name);
12173 __isl_give isl_printer *isl_ast_op_type_set_print_name(
12174 __isl_take isl_printer *p,
12175 enum isl_ast_expr_op_type type,
12176 __isl_keep const char *name);
12177 isl_stat isl_options_set_ast_print_macro_once(
12178 isl_ctx *ctx, int val);
12179 int isl_options_get_ast_print_macro_once(isl_ctx *ctx);
12180 __isl_give isl_printer *isl_ast_expr_op_type_print_macro(
12181 enum isl_ast_expr_op_type type,
12182 __isl_take isl_printer *p);
12183 __isl_give isl_printer *isl_ast_op_type_print_macro(
12184 enum isl_ast_expr_op_type type,
12185 __isl_take isl_printer *p);
12186 __isl_give isl_printer *isl_ast_expr_print_macros(
12187 __isl_keep isl_ast_expr *expr,
12188 __isl_take isl_printer *p);
12189 __isl_give isl_printer *isl_ast_node_print_macros(
12190 __isl_keep isl_ast_node *node,
12191 __isl_take isl_printer *p);
12192 __isl_give isl_printer *isl_ast_node_print(
12193 __isl_keep isl_ast_node *node,
12194 __isl_take isl_printer *p,
12195 __isl_take isl_ast_print_options *options);
12196 __isl_give isl_printer *isl_ast_node_for_print(
12197 __isl_keep isl_ast_node *node,
12198 __isl_take isl_printer *p,
12199 __isl_take isl_ast_print_options *options);
12200 __isl_give isl_printer *isl_ast_node_if_print(
12201 __isl_keep isl_ast_node *node,
12202 __isl_take isl_printer *p,
12203 __isl_take isl_ast_print_options *options);
12205 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
12206 C<isl> may print out an AST that makes use of macros such
12207 as C<floord>, C<min> and C<max>.
12208 The names of these macros may be modified by a call
12209 to C<isl_ast_expr_op_type_set_print_name>. The user-specified
12210 names are associated to the printer object.
12211 C<isl_ast_op_type_set_print_name> is an alternative name for
12212 C<isl_ast_expr_op_type_set_print_name>.
12213 C<isl_ast_expr_op_type_print_macro> prints out the macro
12214 corresponding to a specific C<isl_ast_expr_op_type>.
12215 If the print-macro-once option is set, then a given macro definition
12216 is only printed once to any given printer object.
12217 C<isl_ast_op_type_print_macro> is an alternative name for
12218 C<isl_ast_expr_op_type_print_macro>.
12219 C<isl_ast_expr_print_macros> scans the C<isl_ast_expr>
12220 for subexpressions where these macros would be used and prints
12221 out the required macro definitions.
12222 Essentially, C<isl_ast_expr_print_macros> calls
12223 C<isl_ast_expr_foreach_ast_expr_op_type> with
12224 C<isl_ast_expr_op_type_print_macro>
12225 as function argument.
12226 C<isl_ast_node_print_macros> does the same
12227 for expressions in its C<isl_ast_node> argument.
12228 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
12229 C<isl_ast_node_if_print> print an C<isl_ast_node>
12230 in C<ISL_FORMAT_C>, but allow for some extra control
12231 through an C<isl_ast_print_options> object.
12232 This object can be created using the following functions.
12234 #include <isl/ast.h>
12235 __isl_give isl_ast_print_options *
12236 isl_ast_print_options_alloc(isl_ctx *ctx);
12237 __isl_give isl_ast_print_options *
12238 isl_ast_print_options_copy(
12239 __isl_keep isl_ast_print_options *options);
12240 __isl_null isl_ast_print_options *
12241 isl_ast_print_options_free(
12242 __isl_take isl_ast_print_options *options);
12244 __isl_give isl_ast_print_options *
12245 isl_ast_print_options_set_print_user(
12246 __isl_take isl_ast_print_options *options,
12247 __isl_give isl_printer *(*print_user)(
12248 __isl_take isl_printer *p,
12249 __isl_take isl_ast_print_options *options,
12250 __isl_keep isl_ast_node *node, void *user),
12252 __isl_give isl_ast_print_options *
12253 isl_ast_print_options_set_print_for(
12254 __isl_take isl_ast_print_options *options,
12255 __isl_give isl_printer *(*print_for)(
12256 __isl_take isl_printer *p,
12257 __isl_take isl_ast_print_options *options,
12258 __isl_keep isl_ast_node *node, void *user),
12261 The callback set by C<isl_ast_print_options_set_print_user>
12262 is called whenever a node of type C<isl_ast_node_user> needs to
12264 The callback set by C<isl_ast_print_options_set_print_for>
12265 is called whenever a node of type C<isl_ast_node_for> needs to
12267 Note that C<isl_ast_node_for_print> will I<not> call the
12268 callback set by C<isl_ast_print_options_set_print_for> on the node
12269 on which C<isl_ast_node_for_print> is called, but only on nested
12270 nodes of type C<isl_ast_node_for>. It is therefore safe to
12271 call C<isl_ast_node_for_print> from within the callback set by
12272 C<isl_ast_print_options_set_print_for>.
12274 The following option determines the type to be used for iterators
12275 while printing the AST.
12277 isl_stat isl_options_set_ast_iterator_type(
12278 isl_ctx *ctx, const char *val);
12279 const char *isl_options_get_ast_iterator_type(
12282 The AST printer only prints body nodes of C<if> and C<for> nodes
12284 blocks cannot be safely omitted.
12285 For example, a C<for> node with one body node will not be
12286 surrounded with braces in C<ISL_FORMAT_C>.
12287 A block will always be printed by setting the following option.
12289 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx,
12291 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
12293 Explicit block nodes that appear inside the AST are always printed as blocks.
12294 If the block node appears as the outermost node,
12295 then it is only printed if the following option is set.
12297 isl_stat isl_options_set_ast_print_outermost_block(
12298 isl_ctx *ctx, int val);
12299 int isl_options_get_ast_print_outermost_block(
12304 #include <isl/ast_build.h>
12305 isl_stat isl_options_set_ast_build_atomic_upper_bound(
12306 isl_ctx *ctx, int val);
12307 int isl_options_get_ast_build_atomic_upper_bound(
12309 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
12311 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
12312 isl_stat isl_options_set_ast_build_detect_min_max(
12313 isl_ctx *ctx, int val);
12314 int isl_options_get_ast_build_detect_min_max(
12316 isl_stat isl_options_set_ast_build_exploit_nested_bounds(
12317 isl_ctx *ctx, int val);
12318 int isl_options_get_ast_build_exploit_nested_bounds(
12320 isl_stat isl_options_set_ast_build_group_coscheduled(
12321 isl_ctx *ctx, int val);
12322 int isl_options_get_ast_build_group_coscheduled(
12324 isl_stat isl_options_set_ast_build_separation_bounds(
12325 isl_ctx *ctx, int val);
12326 int isl_options_get_ast_build_separation_bounds(
12328 isl_stat isl_options_set_ast_build_scale_strides(
12329 isl_ctx *ctx, int val);
12330 int isl_options_get_ast_build_scale_strides(
12332 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx,
12334 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
12335 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx,
12337 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
12341 =item * ast_build_atomic_upper_bound
12343 Generate loop upper bounds that consist of the current loop iterator,
12344 an operator and an expression not involving the iterator.
12345 If this option is not set, then the current loop iterator may appear
12346 several times in the upper bound.
12347 For example, when this option is turned off, AST generation
12350 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
12354 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
12357 When the option is turned on, the following AST is generated
12359 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
12362 =item * ast_build_prefer_pdiv
12364 If this option is turned off, then the AST generation will
12365 produce ASTs that may only contain C<isl_ast_expr_op_fdiv_q>
12366 operators, but no C<isl_ast_expr_op_pdiv_q> or
12367 C<isl_ast_expr_op_pdiv_r> operators.
12368 If this option is turned on, then C<isl> will try to convert
12369 some of the C<isl_ast_expr_op_fdiv_q> operators to (expressions containing)
12370 C<isl_ast_expr_op_pdiv_q> or C<isl_ast_expr_op_pdiv_r> operators.
12372 =item * ast_build_detect_min_max
12374 If this option is turned on, then C<isl> will try and detect
12375 min or max-expressions when building AST expressions from
12376 piecewise affine expressions.
12378 =item * ast_build_exploit_nested_bounds
12380 Simplify conditions based on bounds of nested for loops.
12381 In particular, remove conditions that are implied by the fact
12382 that one or more nested loops have at least one iteration,
12383 meaning that the upper bound is at least as large as the lower bound.
12384 For example, when this option is turned off, AST generation
12387 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
12393 for (int c0 = 0; c0 <= N; c0 += 1)
12394 for (int c1 = 0; c1 <= M; c1 += 1)
12397 When the option is turned on, the following AST is generated
12399 for (int c0 = 0; c0 <= N; c0 += 1)
12400 for (int c1 = 0; c1 <= M; c1 += 1)
12403 =item * ast_build_group_coscheduled
12405 If two domain elements are assigned the same schedule point, then
12406 they may be executed in any order and they may even appear in different
12407 loops. If this options is set, then the AST generator will make
12408 sure that coscheduled domain elements do not appear in separate parts
12409 of the AST. This is useful in case of nested AST generation
12410 if the outer AST generation is given only part of a schedule
12411 and the inner AST generation should handle the domains that are
12412 coscheduled by this initial part of the schedule together.
12413 For example if an AST is generated for a schedule
12415 { A[i] -> [0]; B[i] -> [0] }
12417 then the C<isl_ast_build_set_create_leaf> callback described
12418 below may get called twice, once for each domain.
12419 Setting this option ensures that the callback is only called once
12420 on both domains together.
12422 =item * ast_build_separation_bounds
12424 This option specifies which bounds to use during separation.
12425 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
12426 then all (possibly implicit) bounds on the current dimension will
12427 be used during separation.
12428 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
12429 then only those bounds that are explicitly available will
12430 be used during separation.
12432 =item * ast_build_scale_strides
12434 This option specifies whether the AST generator is allowed
12435 to scale down iterators of strided loops.
12437 =item * ast_build_allow_else
12439 This option specifies whether the AST generator is allowed
12440 to construct if statements with else branches.
12442 =item * ast_build_allow_or
12444 This option specifies whether the AST generator is allowed
12445 to construct if conditions with disjunctions.
12449 =head3 AST Generation Options (Schedule Tree)
12451 In case of AST construction from a schedule tree, the options
12452 that control how an AST is created from the individual schedule
12453 dimensions are stored in the band nodes of the tree
12454 (see L</"Schedule Trees">).
12456 In particular, a schedule dimension can be handled in four
12457 different ways, atomic, separate, unroll or the default.
12458 This loop AST generation type can be set using
12459 C<isl_schedule_node_band_member_set_ast_loop_type>.
12461 the first three can be selected by including a one-dimensional
12462 element with as value the position of the schedule dimension
12463 within the band and as name one of C<atomic>, C<separate>
12464 or C<unroll> in the options
12465 set by C<isl_schedule_node_band_set_ast_build_options>.
12466 Only one of these three may be specified for
12467 any given schedule dimension within a band node.
12468 If none of these is specified, then the default
12469 is used. The meaning of the options is as follows.
12475 When this option is specified, the AST generator will make
12476 sure that a given domain space only appears in a single
12477 loop at the specified level.
12479 For example, for the schedule tree
12481 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
12483 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
12484 options: "{ atomic[x] }"
12486 the following AST will be generated
12488 for (int c0 = 0; c0 <= 10; c0 += 1) {
12495 On the other hand, for the schedule tree
12497 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
12499 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
12500 options: "{ separate[x] }"
12502 the following AST will be generated
12506 for (int c0 = 1; c0 <= 9; c0 += 1) {
12513 If neither C<atomic> nor C<separate> is specified, then the AST generator
12514 may produce either of these two results or some intermediate form.
12518 When this option is specified, the AST generator will
12519 split the domain of the specified schedule dimension
12520 into pieces with a fixed set of statements for which
12521 instances need to be executed by the iterations in
12522 the schedule domain part. This option tends to avoid
12523 the generation of guards inside the corresponding loops.
12524 See also the C<atomic> option.
12528 When this option is specified, the AST generator will
12529 I<completely> unroll the corresponding schedule dimension.
12530 It is the responsibility of the user to ensure that such
12531 unrolling is possible.
12532 To obtain a partial unrolling, the user should apply an additional
12533 strip-mining to the schedule and fully unroll the inner schedule
12538 The C<isolate> option is a bit more involved. It allows the user
12539 to isolate a range of schedule dimension values from smaller and
12540 greater values. Additionally, the user may specify a different
12541 atomic/separate/unroll choice for the isolated part and the remaining
12542 parts. The typical use case of the C<isolate> option is to isolate
12543 full tiles from partial tiles.
12544 The part that needs to be isolated may depend on outer schedule dimensions.
12545 The option therefore needs to be able to reference those outer schedule
12546 dimensions. In particular, the space of the C<isolate> option is that
12547 of a wrapped map with as domain the flat product of all outer band nodes
12548 and as range the space of the current band node.
12549 The atomic/separate/unroll choice for the isolated part is determined
12550 by an option that lives in an unnamed wrapped space with as domain
12551 a zero-dimensional C<isolate> space and as range the regular
12552 C<atomic>, C<separate> or C<unroll> space.
12553 This option may also be set directly using
12554 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
12555 The atomic/separate/unroll choice for the remaining part is determined
12556 by the regular C<atomic>, C<separate> or C<unroll> option.
12557 Since the C<isolate> option references outer schedule dimensions,
12558 its use in a band node causes any tree containing the node
12559 to be considered anchored.
12561 As an example, consider the isolation of full tiles from partial tiles
12562 in a tiling of a triangular domain. The original schedule is as follows.
12564 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
12566 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
12567 { A[i,j] -> [floor(j/10)] }, \
12568 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
12572 for (int c0 = 0; c0 <= 10; c0 += 1)
12573 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12574 for (int c2 = 10 * c0;
12575 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12576 for (int c3 = 10 * c1;
12577 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12580 Isolating the full tiles, we have the following input
12582 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
12584 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
12585 { A[i,j] -> [floor(j/10)] }, \
12586 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
12587 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
12588 10a+9+10b+9 <= 100 }"
12593 for (int c0 = 0; c0 <= 8; c0 += 1) {
12594 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
12595 for (int c2 = 10 * c0;
12596 c2 <= 10 * c0 + 9; c2 += 1)
12597 for (int c3 = 10 * c1;
12598 c3 <= 10 * c1 + 9; c3 += 1)
12600 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
12601 for (int c2 = 10 * c0;
12602 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12603 for (int c3 = 10 * c1;
12604 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12607 for (int c0 = 9; c0 <= 10; c0 += 1)
12608 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12609 for (int c2 = 10 * c0;
12610 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12611 for (int c3 = 10 * c1;
12612 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12616 We may then additionally unroll the innermost loop of the isolated part
12618 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
12620 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
12621 { A[i,j] -> [floor(j/10)] }, \
12622 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
12623 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
12624 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
12629 for (int c0 = 0; c0 <= 8; c0 += 1) {
12630 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
12631 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
12633 A(c2, 10 * c1 + 1);
12634 A(c2, 10 * c1 + 2);
12635 A(c2, 10 * c1 + 3);
12636 A(c2, 10 * c1 + 4);
12637 A(c2, 10 * c1 + 5);
12638 A(c2, 10 * c1 + 6);
12639 A(c2, 10 * c1 + 7);
12640 A(c2, 10 * c1 + 8);
12641 A(c2, 10 * c1 + 9);
12643 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
12644 for (int c2 = 10 * c0;
12645 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12646 for (int c3 = 10 * c1;
12647 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12650 for (int c0 = 9; c0 <= 10; c0 += 1)
12651 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12652 for (int c2 = 10 * c0;
12653 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12654 for (int c3 = 10 * c1;
12655 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12660 =head3 AST Generation Options (Schedule Map)
12662 In case of AST construction using
12663 C<isl_ast_build_node_from_schedule_map>, the options
12664 that control how an AST is created from the individual schedule
12665 dimensions are stored in the C<isl_ast_build>.
12666 They can be set using the following function.
12668 #include <isl/ast_build.h>
12669 __isl_give isl_ast_build *
12670 isl_ast_build_set_options(
12671 __isl_take isl_ast_build *build,
12672 __isl_take isl_union_map *options);
12674 The options are encoded in an C<isl_union_map>.
12675 The domain of this union relation refers to the schedule domain,
12676 i.e., the range of the schedule passed
12677 to C<isl_ast_build_node_from_schedule_map>.
12678 In the case of nested AST generation (see L</"Nested AST Generation">),
12679 the domain of C<options> should refer to the extra piece of the schedule.
12680 That is, it should be equal to the range of the wrapped relation in the
12681 range of the schedule.
12682 The range of the options can consist of elements in one or more spaces,
12683 the names of which determine the effect of the option.
12684 The values of the range typically also refer to the schedule dimension
12685 to which the option applies, with value C<0> representing
12686 the outermost schedule dimension. In case of nested AST generation
12687 (see L</"Nested AST Generation">), these values refer to the position
12688 of the schedule dimension within the innermost AST generation.
12689 The constraints on the domain elements of
12690 the option should only refer to this dimension and earlier dimensions.
12691 We consider the following spaces.
12695 =item C<separation_class>
12697 B<This option has been deprecated. Use the isolate option on
12698 schedule trees instead.>
12700 This space is a wrapped relation between two one dimensional spaces.
12701 The input space represents the schedule dimension to which the option
12702 applies and the output space represents the separation class.
12703 While constructing a loop corresponding to the specified schedule
12704 dimension(s), the AST generator will try to generate separate loops
12705 for domain elements that are assigned different classes.
12706 If only some of the elements are assigned a class, then those elements
12707 that are not assigned any class will be treated as belonging to a class
12708 that is separate from the explicitly assigned classes.
12709 The typical use case for this option is to separate full tiles from
12711 The other options, described below, are applied after the separation
12714 As an example, consider the separation into full and partial tiles
12715 of a tiling of a triangular domain.
12716 Take, for example, the domain
12718 { A[i,j] : 0 <= i,j and i + j <= 100 }
12720 and a tiling into tiles of 10 by 10. The input to the AST generator
12721 is then the schedule
12723 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
12726 Without any options, the following AST is generated
12728 for (int c0 = 0; c0 <= 10; c0 += 1)
12729 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12730 for (int c2 = 10 * c0;
12731 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
12733 for (int c3 = 10 * c1;
12734 c3 <= min(10 * c1 + 9, -c2 + 100);
12738 Separation into full and partial tiles can be obtained by assigning
12739 a class, say C<0>, to the full tiles. The full tiles are represented by those
12740 values of the first and second schedule dimensions for which there are
12741 values of the third and fourth dimensions to cover an entire tile.
12742 That is, we need to specify the following option
12744 { [a,b,c,d] -> separation_class[[0]->[0]] :
12745 exists b': 0 <= 10a,10b' and
12746 10a+9+10b'+9 <= 100;
12747 [a,b,c,d] -> separation_class[[1]->[0]] :
12748 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
12750 which simplifies to
12752 { [a, b, c, d] -> separation_class[[1] -> [0]] :
12753 a >= 0 and b >= 0 and b <= 8 - a;
12754 [a, b, c, d] -> separation_class[[0] -> [0]] :
12755 a >= 0 and a <= 8 }
12757 With this option, the generated AST is as follows
12760 for (int c0 = 0; c0 <= 8; c0 += 1) {
12761 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
12762 for (int c2 = 10 * c0;
12763 c2 <= 10 * c0 + 9; c2 += 1)
12764 for (int c3 = 10 * c1;
12765 c3 <= 10 * c1 + 9; c3 += 1)
12767 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
12768 for (int c2 = 10 * c0;
12769 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
12771 for (int c3 = 10 * c1;
12772 c3 <= min(-c2 + 100, 10 * c1 + 9);
12776 for (int c0 = 9; c0 <= 10; c0 += 1)
12777 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12778 for (int c2 = 10 * c0;
12779 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
12781 for (int c3 = 10 * c1;
12782 c3 <= min(10 * c1 + 9, -c2 + 100);
12789 This is a single-dimensional space representing the schedule dimension(s)
12790 to which ``separation'' should be applied. Separation tries to split
12791 a loop into several pieces if this can avoid the generation of guards
12793 See also the C<atomic> option.
12797 This is a single-dimensional space representing the schedule dimension(s)
12798 for which the domains should be considered ``atomic''. That is, the
12799 AST generator will make sure that any given domain space will only appear
12800 in a single loop at the specified level.
12802 Consider the following schedule
12804 { a[i] -> [i] : 0 <= i < 10;
12805 b[i] -> [i+1] : 0 <= i < 10 }
12807 If the following option is specified
12809 { [i] -> separate[x] }
12811 then the following AST will be generated
12815 for (int c0 = 1; c0 <= 9; c0 += 1) {
12822 If, on the other hand, the following option is specified
12824 { [i] -> atomic[x] }
12826 then the following AST will be generated
12828 for (int c0 = 0; c0 <= 10; c0 += 1) {
12835 If neither C<atomic> nor C<separate> is specified, then the AST generator
12836 may produce either of these two results or some intermediate form.
12840 This is a single-dimensional space representing the schedule dimension(s)
12841 that should be I<completely> unrolled.
12842 To obtain a partial unrolling, the user should apply an additional
12843 strip-mining to the schedule and fully unroll the inner loop.
12847 =head3 Fine-grained Control over AST Generation
12849 Besides specifying the constraints on the parameters,
12850 an C<isl_ast_build> object can be used to control
12851 various aspects of the AST generation process.
12852 In case of AST construction using
12853 C<isl_ast_build_node_from_schedule_map>,
12854 the most prominent way of control is through ``options'',
12855 as explained above.
12857 Additional control is available through the following functions.
12859 #include <isl/ast_build.h>
12860 __isl_give isl_ast_build *
12861 isl_ast_build_set_iterators(
12862 __isl_take isl_ast_build *build,
12863 __isl_take isl_id_list *iterators);
12865 The function C<isl_ast_build_set_iterators> allows the user to
12866 specify a list of iterator C<isl_id>s to be used as iterators.
12867 If the input schedule is injective, then
12868 the number of elements in this list should be as large as the dimension
12869 of the schedule space, but no direct correspondence should be assumed
12870 between dimensions and elements.
12871 If the input schedule is not injective, then an additional number
12872 of C<isl_id>s equal to the largest dimension of the input domains
12874 If the number of provided C<isl_id>s is insufficient, then additional
12875 names are automatically generated.
12877 #include <isl/ast_build.h>
12878 __isl_give isl_ast_build *
12879 isl_ast_build_set_create_leaf(
12880 __isl_take isl_ast_build *build,
12881 __isl_give isl_ast_node *(*fn)(
12882 __isl_take isl_ast_build *build,
12883 void *user), void *user);
12886 C<isl_ast_build_set_create_leaf> function allows for the
12887 specification of a callback that should be called whenever the AST
12888 generator arrives at an element of the schedule domain.
12889 The callback should return an AST node that should be inserted
12890 at the corresponding position of the AST. The default action (when
12891 the callback is not set) is to continue generating parts of the AST to scan
12892 all the domain elements associated to the schedule domain element
12893 and to insert user nodes, ``calling'' the domain element, for each of them.
12894 The C<build> argument contains the current state of the C<isl_ast_build>.
12895 To ease nested AST generation (see L</"Nested AST Generation">),
12896 all control information that is
12897 specific to the current AST generation such as the options and
12898 the callbacks has been removed from this C<isl_ast_build>.
12899 The callback would typically return the result of a nested
12900 AST generation or a
12901 user defined node created using the following function.
12903 #include <isl/ast.h>
12904 __isl_give isl_ast_node *isl_ast_node_user_from_expr(
12905 __isl_take isl_ast_expr *expr);
12906 __isl_give isl_ast_node *isl_ast_node_alloc_user(
12907 __isl_take isl_ast_expr *expr);
12909 C<isl_ast_node_alloc_user> is an alternative name for
12910 C<isl_ast_node_user_from_expr>.
12912 In some cases, a single user defined node is not enough,
12913 in which case the following function can be used
12914 to create a block node from multiple AST nodes.
12916 #include <isl/ast.h>
12917 __isl_give isl_ast_node *isl_ast_node_block_from_children(
12918 __isl_take isl_ast_node_list *list);
12920 #include <isl/ast_build.h>
12921 __isl_give isl_ast_build *
12922 isl_ast_build_set_at_each_domain(
12923 __isl_take isl_ast_build *build,
12924 __isl_give isl_ast_node *(*fn)(
12925 __isl_take isl_ast_node *node,
12926 __isl_keep isl_ast_build *build,
12927 void *user), void *user);
12928 __isl_give isl_ast_build *
12929 isl_ast_build_set_before_each_for(
12930 __isl_take isl_ast_build *build,
12931 __isl_give isl_id *(*fn)(
12932 __isl_keep isl_ast_build *build,
12933 void *user), void *user);
12934 __isl_give isl_ast_build *
12935 isl_ast_build_set_after_each_for(
12936 __isl_take isl_ast_build *build,
12937 __isl_give isl_ast_node *(*fn)(
12938 __isl_take isl_ast_node *node,
12939 __isl_keep isl_ast_build *build,
12940 void *user), void *user);
12941 __isl_give isl_ast_build *
12942 isl_ast_build_set_before_each_mark(
12943 __isl_take isl_ast_build *build,
12944 isl_stat (*fn)(__isl_keep isl_id *mark,
12945 __isl_keep isl_ast_build *build,
12946 void *user), void *user);
12947 __isl_give isl_ast_build *
12948 isl_ast_build_set_after_each_mark(
12949 __isl_take isl_ast_build *build,
12950 __isl_give isl_ast_node *(*fn)(
12951 __isl_take isl_ast_node *node,
12952 __isl_keep isl_ast_build *build,
12953 void *user), void *user);
12955 The callback set by C<isl_ast_build_set_at_each_domain> will
12956 be called for each domain AST node.
12957 The callbacks set by C<isl_ast_build_set_before_each_for>
12958 and C<isl_ast_build_set_after_each_for> will be called
12959 for each for AST node. The first will be called in depth-first
12960 pre-order, while the second will be called in depth-first post-order.
12961 Since C<isl_ast_build_set_before_each_for> is called before the for
12962 node is actually constructed, it is only passed an C<isl_ast_build>.
12963 The returned C<isl_id> will be added as an annotation (using
12964 C<isl_ast_node_set_annotation>) to the constructed for node.
12965 In particular, if the user has also specified an C<after_each_for>
12966 callback, then the annotation can be retrieved from the node passed to
12967 that callback using C<isl_ast_node_get_annotation>.
12968 The callbacks set by C<isl_ast_build_set_before_each_mark>
12969 and C<isl_ast_build_set_after_each_mark> will be called for each
12970 mark AST node that is created, i.e., for each mark schedule node
12971 in the input schedule tree. The first will be called in depth-first
12972 pre-order, while the second will be called in depth-first post-order.
12973 Since the callback set by C<isl_ast_build_set_before_each_mark>
12974 is called before the mark AST node is actually constructed, it is passed
12975 the identifier of the mark node.
12976 All callbacks should C<NULL> (or C<isl_stat_error>) on failure.
12977 The given C<isl_ast_build> can be used to create new
12978 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
12979 or C<isl_ast_build_call_from_pw_multi_aff>.
12981 =head3 Nested AST Generation
12983 C<isl> allows the user to create an AST within the context
12984 of another AST. These nested ASTs are created using the
12985 same C<isl_ast_build_node_from_schedule_map> function that is used to create
12986 the outer AST. The C<build> argument should be an C<isl_ast_build>
12987 passed to a callback set by
12988 C<isl_ast_build_set_create_leaf>.
12989 The space of the range of the C<schedule> argument should refer
12990 to this build. In particular, the space should be a wrapped
12991 relation and the domain of this wrapped relation should be the
12992 same as that of the range of the schedule returned by
12993 C<isl_ast_build_get_schedule> below.
12994 In practice, the new schedule is typically
12995 created by calling C<isl_union_map_range_product> on the old schedule
12996 and some extra piece of the schedule.
12997 The space of the schedule domain is also available from
12998 the C<isl_ast_build>.
13000 #include <isl/ast_build.h>
13001 __isl_give isl_union_map *isl_ast_build_get_schedule(
13002 __isl_keep isl_ast_build *build);
13003 __isl_give isl_space *isl_ast_build_get_schedule_space(
13004 __isl_keep isl_ast_build *build);
13005 __isl_give isl_ast_build *isl_ast_build_restrict(
13006 __isl_take isl_ast_build *build,
13007 __isl_take isl_set *set);
13009 The C<isl_ast_build_get_schedule> function returns a (partial)
13010 schedule for the domains elements for which part of the AST still needs to
13011 be generated in the current build.
13012 In particular, the domain elements are mapped to those iterations of the loops
13013 enclosing the current point of the AST generation inside which
13014 the domain elements are executed.
13015 No direct correspondence between
13016 the input schedule and this schedule should be assumed.
13017 The space obtained from C<isl_ast_build_get_schedule_space> can be used
13018 to create a set for C<isl_ast_build_restrict> to intersect
13019 with the current build. In particular, the set passed to
13020 C<isl_ast_build_restrict> can have additional parameters.
13021 The ids of the set dimensions in the space returned by
13022 C<isl_ast_build_get_schedule_space> correspond to the
13023 iterators of the already generated loops.
13024 The user should not rely on the ids of the output dimensions
13025 of the relations in the union relation returned by
13026 C<isl_ast_build_get_schedule> having any particular value.
13028 =head1 Applications
13030 Although C<isl> is mainly meant to be used as a library,
13031 it also contains some basic applications that use some
13032 of the functionality of C<isl>.
13033 For applications that take one or more polytopes or polyhedra
13034 as input, this input may be specified in either the L<isl format>
13035 or the L<PolyLib format>.
13037 =head2 C<isl_polyhedron_sample>
13039 C<isl_polyhedron_sample> takes a polyhedron as input and prints
13040 an integer element of the polyhedron, if there is any.
13041 The first column in the output is the denominator and is always
13042 equal to 1. If the polyhedron contains no integer points,
13043 then a vector of length zero is printed.
13047 C<isl_pip> takes the same input as the C<example> program
13048 from the C<piplib> distribution, i.e., a set of constraints
13049 on the parameters, a line containing only -1 and finally a set
13050 of constraints on a parametric polyhedron.
13051 The coefficients of the parameters appear in the last columns
13052 (but before the final constant column).
13053 The output is the lexicographic minimum of the parametric polyhedron.
13054 As C<isl> currently does not have its own output format, the output
13055 is just a dump of the internal state.
13057 =head2 C<isl_polyhedron_minimize>
13059 C<isl_polyhedron_minimize> computes the minimum of some linear
13060 or affine objective function over the integer points in a polyhedron.
13061 If an affine objective function
13062 is given, then the constant should appear in the last column.
13064 =head2 C<isl_polytope_scan>
13066 Given a polytope, C<isl_polytope_scan> prints
13067 all integer points in the polytope.
13071 Given an C<isl_union_access_info> object as input,
13072 C<isl_flow> prints out the corresponding dependences,
13073 as computed by C<isl_union_access_info_compute_flow>.
13075 =head2 C<isl_codegen>
13077 Given either a schedule tree or a sequence consisting of
13078 a schedule map, a context set and an options relation,
13079 C<isl_codegen> prints out an AST that scans the domain elements
13080 of the schedule in the order of their image(s) taking into account
13081 the constraints in the context set.
13083 =head2 C<isl_schedule>
13085 Given an C<isl_schedule_constraints> object as input,
13086 C<isl_schedule> prints out a schedule that satisfies the given