3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
8 using C<GMP> or C<imath>.
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
171 =head3 Changes since isl-0.10
175 =item * The functions C<isl_set_dim_has_lower_bound> and
176 C<isl_set_dim_has_upper_bound> have been renamed to
177 C<isl_set_dim_has_any_lower_bound> and
178 C<isl_set_dim_has_any_upper_bound>.
179 The new C<isl_set_dim_has_lower_bound> and
180 C<isl_set_dim_has_upper_bound> have slightly different meanings.
184 =head3 Changes since isl-0.12
188 =item * C<isl_int> has been replaced by C<isl_val>.
189 Some of the old functions are still available in C<isl/deprecated/*.h>
190 but they will be removed in the future.
192 =item * The functions C<isl_pw_qpolynomial_eval>,
193 C<isl_union_pw_qpolynomial_eval>, C<isl_pw_qpolynomial_fold_eval>
194 and C<isl_union_pw_qpolynomial_fold_eval> have been changed to return
195 an C<isl_val> instead of an C<isl_qpolynomial>.
197 =item * The function C<isl_band_member_is_zero_distance>
198 has been removed. Essentially the same functionality is available
199 through C<isl_band_member_is_coincident>, except that it requires
200 setting up coincidence constraints.
201 The option C<schedule_outer_zero_distance> has accordingly been
202 replaced by the option C<schedule_outer_coincidence>.
204 =item * The function C<isl_vertex_get_expr> has been changed
205 to return an C<isl_multi_aff> instead of a rational C<isl_basic_set>.
206 The function C<isl_vertex_get_domain> has been changed to return
207 a regular basic set, rather than a rational basic set.
211 =head3 Changes since isl-0.14
215 =item * The function C<isl_union_pw_multi_aff_add> now consistently
216 computes the sum on the shared definition domain.
217 The function C<isl_union_pw_multi_aff_union_add> has been added
218 to compute the sum on the union of definition domains.
219 The original behavior of C<isl_union_pw_multi_aff_add> was
220 confused and is no longer available.
222 =item * Band forests have been replaced by schedule trees.
224 =item * The function C<isl_union_map_compute_flow> has been
225 replaced by the function C<isl_union_access_info_compute_flow>.
226 Note that the may dependence relation returned by
227 C<isl_union_flow_get_may_dependence> is the union of
228 the two dependence relations returned by
229 C<isl_union_map_compute_flow>. Similarly for the no source relations.
230 The function C<isl_union_map_compute_flow> is still available
231 for backward compatibility, but it will be removed in the future.
233 =item * The function C<isl_basic_set_drop_constraint> has been
236 =item * The function C<isl_ast_build_ast_from_schedule> has been
237 renamed to C<isl_ast_build_node_from_schedule_map>.
238 The original name is still available
239 for backward compatibility, but it will be removed in the future.
241 =item * The C<separation_class> AST generation option has been
244 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
245 have been renamed to C<isl_constraint_alloc_equality> and
246 C<isl_constraint_alloc_inequality>. The original names have been
247 kept for backward compatibility, but they will be removed in the future.
249 =item * The C<schedule_fuse> option has been replaced
250 by the C<schedule_serialize_sccs> option. The effect
251 of setting the C<schedule_fuse> option to C<ISL_SCHEDULE_FUSE_MIN>
252 is now obtained by turning on the C<schedule_serialize_sccs> option.
256 =head3 Changes since isl-0.17
260 =item * The function C<isl_printer_print_ast_expr> no longer prints
261 in C format by default. To print in C format, the output format
262 of the printer needs to have been explicitly set to C<ISL_FORMAT_C>.
263 As a result, the function C<isl_ast_expr_to_str> no longer prints
264 the expression in C format. Use C<isl_ast_expr_to_C_str> instead.
266 =item * The functions C<isl_set_align_divs> and C<isl_map_align_divs>
267 have been deprecated. The function C<isl_set_lift> has an effect
268 that is similar to C<isl_set_align_divs> and could in some cases
269 be used as an alternative.
273 =head3 Changes since isl-0.19
277 =item * Zero-dimensional objects of type C<isl_multi_pw_aff> or
278 C<isl_multi_union_pw_aff> can now keep track of an explicit domain.
279 This explicit domain, if present, is taken into account
280 by various operations that take such objects as input.
284 =head3 Changes since isl-0.20
288 =item * Several functions that used to return C<unsigned>
289 now return C<isl_size>. This means that these functions may
290 now return a negative value in case an error occurred.
291 The same holds for functions that used to return C<int>,
292 although some of those were already returning
293 a negative value in case of error.
295 =item * The C<isl_ast_op_type> enumeration type has been
296 renamed to C<isl_ast_expr_op_type>. The corresponding
297 enumeration constants have been similarly renamed.
298 The old names are defined to the new names for backward
301 =item * Several functions returning an extra boolean value
302 through an C<int *> argument now do so through an C<isl_bool *>
303 argument. The returned values are the same, only the type
304 of the pointer has been changed.
310 C<isl> is released under the MIT license.
314 Permission is hereby granted, free of charge, to any person obtaining a copy of
315 this software and associated documentation files (the "Software"), to deal in
316 the Software without restriction, including without limitation the rights to
317 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
318 of the Software, and to permit persons to whom the Software is furnished to do
319 so, subject to the following conditions:
321 The above copyright notice and this permission notice shall be included in all
322 copies or substantial portions of the Software.
324 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
325 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
326 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
327 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
328 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
329 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
334 Note that by default C<isl> requires C<GMP>, which is released
335 under the GNU Lesser General Public License (LGPL). This means
336 that code linked against C<isl> is also linked against LGPL code.
338 When configuring with C<--with-int=imath> or C<--with-int=imath-32>, C<isl>
339 will link against C<imath>, a library for exact integer arithmetic released
340 under the MIT license.
344 The source of C<isl> can be obtained either as a tarball
345 or from the git repository. Both are available from
346 L<https://libisl.sourceforge.io/>.
347 The installation process depends on how you obtained
350 =head2 Installation from the git repository
354 =item 1 Clone or update the repository
356 The first time the source is obtained, you need to clone
359 git clone git://repo.or.cz/isl.git
361 To obtain updates, you need to pull in the latest changes
365 =item 2 Optionally get C<imath> submodule
367 To build C<isl> with C<imath>, you need to obtain the C<imath>
368 submodule by running in the git source tree of C<isl>
373 This will fetch the required version of C<imath> in a subdirectory of C<isl>.
375 =item 2 Generate C<configure>
381 After performing the above steps, continue
382 with the L<Common installation instructions>.
384 =head2 Common installation instructions
388 =item 1 Obtain C<GMP>
390 By default, building C<isl> requires C<GMP>, including its headers files.
391 Your distribution may not provide these header files by default
392 and you may need to install a package called C<gmp-devel> or something
393 similar. Alternatively, C<GMP> can be built from
394 source, available from L<http://gmplib.org/>.
395 C<GMP> is not needed if you build C<isl> with C<imath>.
399 C<isl> uses the standard C<autoconf> C<configure> script.
404 optionally followed by some configure options.
405 A complete list of options can be obtained by running
409 Below we discuss some of the more common options.
415 Installation prefix for C<isl>
417 =item C<--with-int=[gmp|imath|imath-32]>
419 Select the integer library to be used by C<isl>, the default is C<gmp>.
420 With C<imath-32>, C<isl> will use 32 bit integers, but fall back to C<imath>
421 for values out of the 32 bit range. In most applications, C<isl> will run
422 fastest with the C<imath-32> option, followed by C<gmp> and C<imath>, the
425 =item C<--with-gmp-prefix=>I<path>
427 Installation prefix for C<GMP> (architecture-independent files).
429 =item C<--with-gmp-exec-prefix=>I<path>
431 Installation prefix for C<GMP> (architecture-dependent files).
439 =item 4 Test (optional)
443 =item 5 Install (optional)
449 =head2 Building the foreign language bindings
451 The tarball already contains the generated foreign language bindings,
452 but they are not included in the git repository.
453 Building the C++ and Python bindings relies on the LLVM/clang libraries,
454 see C<http://clang.llvm.org/get_started.html>.
455 The C<configure> script will not assume that these are available
457 To enable building the foreign language bindings,
458 one of the following options needs to be specified.
462 =item C<--with-clang=system>
464 Use the system clang libraries (installed in a default location).
466 =item C<--with-clang-prefix=>I<path>
468 Use the system clang libraries installed in I<path>.
472 It is best to use the latest release of the clang libraries (14.0),
473 although any release since 2.9 should work as well.
474 Note that if you build the clang libraries from source,
475 then you need to make sure they are also installed (using C<make install>).
476 If the compiler that was used to compile the clang libraries
477 is different from the default C++ compiler, then use C<CXX_FOR_BUILD>
478 to specify this non-default C++ compiler when running C<isl>'s C<./configure>.
480 =head1 Integer Set Library
482 =head2 Memory Management
484 Since a high-level operation on isl objects usually involves
485 several substeps and since the user is usually not interested in
486 the intermediate results, most functions that return a new object
487 will also release all the objects passed as arguments.
488 If the user still wants to use one or more of these arguments
489 after the function call, she should pass along a copy of the
490 object rather than the object itself.
491 The user is then responsible for making sure that the original
492 object gets used somewhere else or is explicitly freed.
494 The arguments and return values of all documented functions are
495 annotated to make clear which arguments are released and which
496 arguments are preserved. In particular, the following annotations
503 C<__isl_give> means that a new object is returned.
504 The user should make sure that the returned pointer is
505 used exactly once as a value for an C<__isl_take> argument.
506 In between, it can be used as a value for as many
507 C<__isl_keep> arguments as the user likes.
508 There is one exception, and that is the case where the
509 pointer returned is C<NULL>. In this case, the user
510 is free to use it as an C<__isl_take> argument or not.
511 When applied to a C<char *>, the returned pointer needs to be
516 C<__isl_null> means that a C<NULL> value is returned.
520 C<__isl_take> means that the object the argument points to
521 is taken over by the function and may no longer be used
522 by the user as an argument to any other function.
523 The pointer value must be one returned by a function
524 returning an C<__isl_give> pointer.
525 If the user passes in a C<NULL> value, then this will
526 be treated as an error in the sense that the function will
527 not perform its usual operation. However, it will still
528 make sure that all the other C<__isl_take> arguments
533 C<__isl_keep> means that the function will only use the object
534 temporarily. After the function has finished, the user
535 can still use it as an argument to other functions.
536 A C<NULL> value will be treated in the same way as
537 a C<NULL> value for an C<__isl_take> argument.
538 This annotation may also be used on return values of
539 type C<const char *>, in which case the returned pointer should
540 not be freed by the user and is only valid until the object
541 from which it was derived is updated or freed.
545 =head2 Initialization
547 All manipulations of integer sets and relations occur within
548 the context of an C<isl_ctx>.
549 A given C<isl_ctx> can only be used within a single thread.
550 All arguments of a function are required to have been allocated
551 within the same context.
552 There are currently no functions available for moving an object
553 from one C<isl_ctx> to another C<isl_ctx>. This means that
554 there is currently no way of safely moving an object from one
555 thread to another, unless the whole C<isl_ctx> is moved.
557 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
558 freed using C<isl_ctx_free>.
559 All objects allocated within an C<isl_ctx> should be freed
560 before the C<isl_ctx> itself is freed.
562 isl_ctx *isl_ctx_alloc();
563 void isl_ctx_free(isl_ctx *ctx);
565 The user can impose a bound on the number of low-level I<operations>
566 that can be performed by an C<isl_ctx>. This bound can be set and
567 retrieved using the following functions. A bound of zero means that
568 no bound is imposed. The number of operations performed can be
569 reset using C<isl_ctx_reset_operations>. Note that the number
570 of low-level operations needed to perform a high-level computation
571 may differ significantly across different versions
572 of C<isl>, but it should be the same across different platforms
573 for the same version of C<isl>.
575 Warning: This feature is experimental. C<isl> has good support to abort and
576 bail out during the computation, but this feature may exercise error code paths
577 that are normally not used that much. Consequently, it is not unlikely that
578 hidden bugs will be exposed.
580 void isl_ctx_set_max_operations(isl_ctx *ctx,
581 unsigned long max_operations);
582 unsigned long isl_ctx_get_max_operations(isl_ctx *ctx);
583 void isl_ctx_reset_operations(isl_ctx *ctx);
585 In order to be able to create an object in the same context
586 as another object, most object types (described later in
587 this document) provide a function to obtain the context
588 in which the object was created.
591 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
592 isl_ctx *isl_multi_val_get_ctx(
593 __isl_keep isl_multi_val *mv);
596 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
597 isl_ctx *isl_multi_id_get_ctx(
598 __isl_keep isl_multi_id *mi);
600 #include <isl/local_space.h>
601 isl_ctx *isl_local_space_get_ctx(
602 __isl_keep isl_local_space *ls);
605 isl_ctx *isl_set_list_get_ctx(
606 __isl_keep isl_set_list *list);
609 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
610 isl_ctx *isl_multi_aff_get_ctx(
611 __isl_keep isl_multi_aff *maff);
612 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pa);
613 isl_ctx *isl_pw_multi_aff_get_ctx(
614 __isl_keep isl_pw_multi_aff *pma);
615 isl_ctx *isl_multi_pw_aff_get_ctx(
616 __isl_keep isl_multi_pw_aff *mpa);
617 isl_ctx *isl_union_pw_aff_get_ctx(
618 __isl_keep isl_union_pw_aff *upa);
619 isl_ctx *isl_union_pw_multi_aff_get_ctx(
620 __isl_keep isl_union_pw_multi_aff *upma);
621 isl_ctx *isl_multi_union_pw_aff_get_ctx(
622 __isl_keep isl_multi_union_pw_aff *mupa);
624 #include <isl/id_to_ast_expr.h>
625 isl_ctx *isl_id_to_ast_expr_get_ctx(
626 __isl_keep isl_id_to_ast_expr *id2expr);
628 #include <isl/point.h>
629 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
632 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
635 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
637 #include <isl/vertices.h>
638 isl_ctx *isl_vertices_get_ctx(
639 __isl_keep isl_vertices *vertices);
640 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
641 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
643 #include <isl/flow.h>
644 isl_ctx *isl_restriction_get_ctx(
645 __isl_keep isl_restriction *restr);
646 isl_ctx *isl_union_access_info_get_ctx(
647 __isl_keep isl_union_access_info *access);
648 isl_ctx *isl_union_flow_get_ctx(
649 __isl_keep isl_union_flow *flow);
651 #include <isl/schedule.h>
652 isl_ctx *isl_schedule_get_ctx(
653 __isl_keep isl_schedule *sched);
654 isl_ctx *isl_schedule_constraints_get_ctx(
655 __isl_keep isl_schedule_constraints *sc);
657 #include <isl/schedule_node.h>
658 isl_ctx *isl_schedule_node_get_ctx(
659 __isl_keep isl_schedule_node *node);
661 #include <isl/ast_build.h>
662 isl_ctx *isl_ast_build_get_ctx(
663 __isl_keep isl_ast_build *build);
666 isl_ctx *isl_ast_expr_get_ctx(
667 __isl_keep isl_ast_expr *expr);
668 isl_ctx *isl_ast_node_get_ctx(
669 __isl_keep isl_ast_node *node);
671 #include <isl/stride_info.h>
672 isl_ctx *isl_stride_info_get_ctx(
673 __isl_keep isl_stride_info *si);
675 #include <isl/fixed_box.h>
676 isl_ctx *isl_fixed_box_get_ctx(
677 __isl_keep isl_fixed_box *box);
681 C<isl> uses the special return type C<isl_size> for functions
682 that return a non-negative value, typically a number or a position.
683 Besides the regular non-negative return values, a special (negative)
684 value C<isl_size_error> may be returned, indicating that something
687 C<isl> also uses two special return types for functions that either return
688 a boolean or that in principle do not return anything.
689 In particular, the C<isl_bool> type has three possible values:
690 C<isl_bool_true> (a positive integer value), indicating I<true> or I<yes>;
691 C<isl_bool_false> (the integer value zero), indicating I<false> or I<no>; and
692 C<isl_bool_error> (a negative integer value), indicating that something
693 went wrong. The following operations are defined on C<isl_bool>. The function
694 C<isl_bool_not> can be used to negate an C<isl_bool>, where the negation of
695 C<isl_bool_error> is C<isl_bool_error> again. The function C<isl_bool_ok>
696 converts an integer to an C<isl_bool>. Any non-zero values yields
697 C<isl_bool_true> and zero yields C<isl_bool_false>.
700 isl_bool isl_bool_not(isl_bool b);
701 isl_bool isl_bool_ok(int b);
703 The C<isl_stat> type has two possible values:
704 C<isl_stat_ok> (the integer value zero), indicating a successful
706 C<isl_stat_error> (a negative integer value), indicating that something
708 The function C<isl_stat_non_null> converts an isl object pointer
709 to an C<isl_stat>, returning C<isl_stat_ok> if the object pointer is valid and
710 C<isl_stat_error> if it is C<NULL>.
713 isl_stat isl_stat_non_null(void *obj);
715 See L</"Error Handling"> for more information on
716 C<isl_size_error>, C<isl_bool_error> and C<isl_stat_error>.
720 An C<isl_val> represents an integer value, a rational value
721 or one of three special values, infinity, negative infinity and NaN.
722 Some predefined values can be created using the following functions.
725 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
726 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
727 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
728 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
729 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
730 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
732 Specific integer values can be created using the following functions.
735 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
737 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
739 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
740 size_t n, size_t size, const void *chunks);
742 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
743 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
744 The least significant digit is assumed to be stored first.
746 Value objects can be copied and freed using the following functions.
749 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
750 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
752 They can be inspected using the following functions.
755 long isl_val_get_num_si(__isl_keep isl_val *v);
756 long isl_val_get_den_si(__isl_keep isl_val *v);
757 __isl_give isl_val *isl_val_get_den_val(
758 __isl_keep isl_val *v);
759 double isl_val_get_d(__isl_keep isl_val *v);
760 isl_size isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
762 isl_stat isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
763 size_t size, void *chunks);
765 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
766 of C<size> bytes needed to store the absolute value of the
768 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
769 which is assumed to have been preallocated by the caller.
770 The least significant digit is stored first.
771 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
772 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
773 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
775 An C<isl_val> can be modified using the following function.
778 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
781 The following unary properties are defined on C<isl_val>s.
784 int isl_val_sgn(__isl_keep isl_val *v);
785 isl_bool isl_val_is_zero(__isl_keep isl_val *v);
786 isl_bool isl_val_is_one(__isl_keep isl_val *v);
787 isl_bool isl_val_is_negone(__isl_keep isl_val *v);
788 isl_bool isl_val_is_nonneg(__isl_keep isl_val *v);
789 isl_bool isl_val_is_nonpos(__isl_keep isl_val *v);
790 isl_bool isl_val_is_pos(__isl_keep isl_val *v);
791 isl_bool isl_val_is_neg(__isl_keep isl_val *v);
792 isl_bool isl_val_is_int(__isl_keep isl_val *v);
793 isl_bool isl_val_is_rat(__isl_keep isl_val *v);
794 isl_bool isl_val_is_nan(__isl_keep isl_val *v);
795 isl_bool isl_val_is_infty(__isl_keep isl_val *v);
796 isl_bool isl_val_is_neginfty(__isl_keep isl_val *v);
798 Note that the sign of NaN is undefined.
800 The following binary properties are defined on pairs of C<isl_val>s.
803 isl_bool isl_val_lt(__isl_keep isl_val *v1,
804 __isl_keep isl_val *v2);
805 isl_bool isl_val_le(__isl_keep isl_val *v1,
806 __isl_keep isl_val *v2);
807 isl_bool isl_val_gt(__isl_keep isl_val *v1,
808 __isl_keep isl_val *v2);
809 isl_bool isl_val_ge(__isl_keep isl_val *v1,
810 __isl_keep isl_val *v2);
811 isl_bool isl_val_eq(__isl_keep isl_val *v1,
812 __isl_keep isl_val *v2);
813 isl_bool isl_val_ne(__isl_keep isl_val *v1,
814 __isl_keep isl_val *v2);
815 isl_bool isl_val_abs_eq(__isl_keep isl_val *v1,
816 __isl_keep isl_val *v2);
818 Comparisons to NaN always return false.
819 That is, a NaN is not considered to hold any relative position
820 with respect to any value. In particular, a NaN
821 is neither considered to be equal to nor to be different from
822 any value (including another NaN).
823 The function C<isl_val_abs_eq> checks whether its two arguments
824 are equal in absolute value.
826 For integer C<isl_val>s we additionally have the following binary property.
829 isl_bool isl_val_is_divisible_by(__isl_keep isl_val *v1,
830 __isl_keep isl_val *v2);
832 An C<isl_val> can also be compared to an integer using the following
833 functions. The result of C<isl_val_cmp_si> is undefined for NaN.
836 isl_bool isl_val_gt_si(__isl_keep isl_val *v, long i);
837 isl_bool isl_val_eq_si(__isl_keep isl_val *v, long i);
838 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
840 The following unary operations are available on C<isl_val>s.
843 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
844 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
845 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
846 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
847 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
848 __isl_give isl_val *isl_val_inv(__isl_take isl_val *v);
850 The following binary operations are available on C<isl_val>s.
853 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
854 __isl_take isl_val *v2);
855 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
856 __isl_take isl_val *v2);
857 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
858 __isl_take isl_val *v2);
859 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
861 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
862 __isl_take isl_val *v2);
863 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
865 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
866 __isl_take isl_val *v2);
867 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
869 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
870 __isl_take isl_val *v2);
871 __isl_give isl_val *isl_val_div_ui(__isl_take isl_val *v1,
874 On integer values, we additionally have the following operations.
877 __isl_give isl_val *isl_val_pow2(__isl_take isl_val *v);
878 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
879 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
880 __isl_take isl_val *v2);
881 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
882 __isl_take isl_val *v2);
883 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
884 __isl_take isl_val *v2, __isl_give isl_val **x,
885 __isl_give isl_val **y);
887 C<isl_val_2exp> is an alternative name for C<isl_val_pow2>.
888 The function C<isl_val_gcdext> returns the greatest common divisor g
889 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
890 that C<*x> * C<v1> + C<*y> * C<v2> = g.
892 =head3 GMP specific functions
894 These functions are only available if C<isl> has been compiled with C<GMP>
897 Specific integer and rational values can be created from C<GMP> values using
898 the following functions.
900 #include <isl/val_gmp.h>
901 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
903 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
904 const mpz_t n, const mpz_t d);
906 The numerator and denominator of a rational value can be extracted as
907 C<GMP> values using the following functions.
909 #include <isl/val_gmp.h>
910 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
911 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
913 =head2 Sets and Relations
915 C<isl> uses six types of objects for representing sets and relations,
916 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
917 C<isl_union_set> and C<isl_union_map>.
918 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
919 can be described as a conjunction of affine constraints, while
920 C<isl_set> and C<isl_map> represent unions of
921 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
922 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
923 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
924 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
925 where spaces are considered different if they have a different number
926 of dimensions and/or different names (see L<"Spaces">).
927 The difference between sets and relations (maps) is that sets have
928 one set of variables, while relations have two sets of variables,
929 input variables and output variables.
931 =head2 Error Handling
933 C<isl> supports different ways to react in case a runtime error is triggered.
934 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
935 with two maps that have incompatible spaces. There are three possible ways
936 to react on error: to warn, to continue or to abort.
938 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
939 the last error in the corresponding C<isl_ctx> and the function in which the
940 error was triggered returns a value indicating that some error has
941 occurred. In case of functions returning a pointer, this value is
942 C<NULL>. In case of functions returning an C<isl_size>, C<isl_bool> or an
943 C<isl_stat>, this value is C<isl_size_error>,
944 C<isl_bool_error> or C<isl_stat_error>.
945 An error does not corrupt internal state,
946 such that isl can continue to be used. C<isl> also provides functions to
947 read the last error, including the specific error message,
948 the isl source file where the error occurred and the line number,
949 and to reset all information about the last error. The
950 last error is only stored for information purposes. Its presence does not
951 change the behavior of C<isl>. Hence, resetting an error is not required to
952 continue to use isl, but only to observe new errors.
955 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
956 const char *isl_ctx_last_error_msg(isl_ctx *ctx);
957 const char *isl_ctx_last_error_file(isl_ctx *ctx);
958 int isl_ctx_last_error_line(isl_ctx *ctx);
959 void isl_ctx_reset_error(isl_ctx *ctx);
961 If no error has occurred since the last call to C<isl_ctx_reset_error>,
962 then the functions C<isl_ctx_last_error_msg> and
963 C<isl_ctx_last_error_file> return C<NULL>.
965 Another option is to continue on error. This is similar to warn on error mode,
966 except that C<isl> does not print any warning. This allows a program to
967 implement its own error reporting.
969 The last option is to directly abort the execution of the program from within
970 the isl library. This makes it obviously impossible to recover from an error,
971 but it allows to directly spot the error location. By aborting on error,
972 debuggers break at the location the error occurred and can provide a stack
973 trace. Other tools that automatically provide stack traces on abort or that do
974 not want to continue execution after an error was triggered may also prefer to
977 The on error behavior of isl can be specified by calling
978 C<isl_options_set_on_error> or by setting the command line option
979 C<--isl-on-error>. Valid arguments for the function call are
980 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
981 choices for the command line option are C<warn>, C<continue> and C<abort>.
982 It is also possible to query the current error mode.
984 #include <isl/options.h>
985 isl_stat isl_options_set_on_error(isl_ctx *ctx, int val);
986 int isl_options_get_on_error(isl_ctx *ctx);
990 Identifiers are used to identify both individual dimensions
991 and tuples of dimensions. They consist of an optional name and an optional
992 user pointer. The name and the user pointer cannot both be C<NULL>, however.
993 Identifiers with the same name but different pointer values
994 are considered to be distinct.
995 Similarly, identifiers with different names but the same pointer value
996 are also considered to be distinct.
997 Equal identifiers are represented using the same object.
998 Pairs of identifiers can therefore be tested for equality using the
1000 Identifiers can be constructed, copied, freed, inspected and printed
1001 using the following functions.
1004 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
1005 __isl_keep const char *name, void *user);
1006 __isl_give isl_id *isl_id_set_free_user(
1007 __isl_take isl_id *id,
1008 void (*free_user)(void *user));
1009 void (*isl_id_get_free_user(__isl_keep isl_id *id))
1011 __isl_give isl_id *isl_id_copy(isl_id *id);
1012 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
1014 void *isl_id_get_user(__isl_keep isl_id *id);
1015 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
1017 __isl_give isl_printer *isl_printer_print_id(
1018 __isl_take isl_printer *p, __isl_keep isl_id *id);
1020 The callback set by C<isl_id_set_free_user> is called on the user
1021 pointer when the last reference to the C<isl_id> is freed.
1022 This callback can be retrieved using C<isl_id_get_free_user>.
1023 Note that C<isl_id_get_name> returns a pointer to some internal
1024 data structure, so the result can only be used while the
1025 corresponding C<isl_id> is alive.
1029 Whenever a new set, relation or similar object is created from scratch,
1030 the space in which it lives needs to be specified using an C<isl_space>.
1031 Each space involves zero or more parameters and zero, one or two
1032 tuples of set or input/output dimensions. The parameters and dimensions
1033 are identified by an C<isl_dim_type> and a position.
1034 The type C<isl_dim_param> refers to parameters,
1035 the type C<isl_dim_set> refers to set dimensions (for spaces
1036 with a single tuple of dimensions) and the types C<isl_dim_in>
1037 and C<isl_dim_out> refer to input and output dimensions
1038 (for spaces with two tuples of dimensions).
1039 Local spaces (see L</"Local Spaces">) also contain dimensions
1040 of type C<isl_dim_div>.
1041 Note that parameters are only identified by their position within
1042 a given object. Across different objects, parameters are (usually)
1043 identified by their names or identifiers. Only unnamed parameters
1044 are identified by their positions across objects. The use of unnamed
1045 parameters is discouraged.
1047 #include <isl/space.h>
1048 __isl_give isl_space *isl_space_unit(isl_ctx *ctx);
1049 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
1050 unsigned nparam, unsigned n_in, unsigned n_out);
1051 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
1053 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
1054 unsigned nparam, unsigned dim);
1055 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
1056 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
1058 The space used for creating a parameter domain
1059 needs to be created using C<isl_space_unit> or C<isl_space_params_alloc>.
1060 For other sets, the space
1061 needs to be created using C<isl_space_set_alloc>, while
1062 for a relation, the space
1063 needs to be created using C<isl_space_alloc>.
1064 The use of C<isl_space_params_alloc>,
1065 C<isl_space_set_alloc> and C<isl_space_alloc> is discouraged as they allow
1066 for the introduction of unnamed parameters.
1068 To check whether a given space is that of a set or a map
1069 or whether it is a parameter space, use these functions:
1071 #include <isl/space.h>
1072 isl_bool isl_space_is_params(__isl_keep isl_space *space);
1073 isl_bool isl_space_is_set(__isl_keep isl_space *space);
1074 isl_bool isl_space_is_map(__isl_keep isl_space *space);
1076 Spaces can be compared using the following functions:
1078 #include <isl/space.h>
1079 isl_bool isl_space_is_equal(__isl_keep isl_space *space1,
1080 __isl_keep isl_space *space2);
1081 isl_bool isl_space_has_equal_params(
1082 __isl_keep isl_space *space1,
1083 __isl_keep isl_space *space2);
1084 isl_bool isl_space_has_equal_tuples(
1085 __isl_keep isl_space *space1,
1086 __isl_keep isl_space *space2);
1087 isl_bool isl_space_is_domain(__isl_keep isl_space *space1,
1088 __isl_keep isl_space *space2);
1089 isl_bool isl_space_is_range(__isl_keep isl_space *space1,
1090 __isl_keep isl_space *space2);
1091 isl_bool isl_space_tuple_is_equal(
1092 __isl_keep isl_space *space1,
1093 enum isl_dim_type type1,
1094 __isl_keep isl_space *space2,
1095 enum isl_dim_type type2);
1097 C<isl_space_is_domain> checks whether the first argument is equal
1098 to the domain of the second argument. This requires in particular that
1099 the first argument is a set space and that the second argument
1100 is a map space. C<isl_space_tuple_is_equal> checks whether the given
1101 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
1102 spaces are the same. That is, it checks if they have the same
1103 identifier (if any), the same dimension and the same internal structure
1106 C<isl_space_has_equal_params> checks whether two spaces
1107 have the same parameters in the same order.
1108 C<isl_space_has_equal_tuples> check whether two spaces have
1109 the same tuples. In contrast to C<isl_space_is_equal> below,
1110 it does not check the
1111 parameters. This is useful because many C<isl> functions align the
1112 parameters before they perform their operations, such that equivalence
1114 C<isl_space_is_equal> checks whether two spaces are identical,
1115 meaning that they have the same parameters and the same tuples.
1116 That is, it checks whether both C<isl_space_has_equal_params> and
1117 C<isl_space_has_equal_tuples> hold.
1119 It is often useful to create objects that live in the
1120 same space as some other object. This can be accomplished
1121 by creating the new objects
1122 (see L</"Creating New Sets and Relations"> or
1123 L</"Functions">) based on the space
1124 of the original object.
1126 #include <isl/set.h>
1127 __isl_give isl_space *isl_basic_set_get_space(
1128 __isl_keep isl_basic_set *bset);
1129 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
1131 #include <isl/union_set.h>
1132 __isl_give isl_space *isl_union_set_get_space(
1133 __isl_keep isl_union_set *uset);
1135 #include <isl/map.h>
1136 __isl_give isl_space *isl_basic_map_get_space(
1137 __isl_keep isl_basic_map *bmap);
1138 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
1140 #include <isl/union_map.h>
1141 __isl_give isl_space *isl_union_map_get_space(
1142 __isl_keep isl_union_map *umap);
1144 #include <isl/constraint.h>
1145 __isl_give isl_space *isl_constraint_get_space(
1146 __isl_keep isl_constraint *constraint);
1148 #include <isl/polynomial.h>
1149 __isl_give isl_space *isl_qpolynomial_get_domain_space(
1150 __isl_keep isl_qpolynomial *qp);
1151 __isl_give isl_space *isl_qpolynomial_get_space(
1152 __isl_keep isl_qpolynomial *qp);
1153 __isl_give isl_space *
1154 isl_qpolynomial_fold_get_domain_space(
1155 __isl_keep isl_qpolynomial_fold *fold);
1156 __isl_give isl_space *isl_qpolynomial_fold_get_space(
1157 __isl_keep isl_qpolynomial_fold *fold);
1158 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
1159 __isl_keep isl_pw_qpolynomial *pwqp);
1160 __isl_give isl_space *isl_pw_qpolynomial_get_space(
1161 __isl_keep isl_pw_qpolynomial *pwqp);
1162 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
1163 __isl_keep isl_pw_qpolynomial_fold *pwf);
1164 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
1165 __isl_keep isl_pw_qpolynomial_fold *pwf);
1166 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
1167 __isl_keep isl_union_pw_qpolynomial *upwqp);
1168 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
1169 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1172 __isl_give isl_space *isl_multi_id_get_space(
1173 __isl_keep isl_multi_id *mi);
1175 #include <isl/val.h>
1176 __isl_give isl_space *isl_multi_val_get_space(
1177 __isl_keep isl_multi_val *mv);
1179 #include <isl/aff.h>
1180 __isl_give isl_space *isl_aff_get_domain_space(
1181 __isl_keep isl_aff *aff);
1182 __isl_give isl_space *isl_aff_get_space(
1183 __isl_keep isl_aff *aff);
1184 __isl_give isl_space *isl_pw_aff_get_domain_space(
1185 __isl_keep isl_pw_aff *pwaff);
1186 __isl_give isl_space *isl_pw_aff_get_space(
1187 __isl_keep isl_pw_aff *pwaff);
1188 __isl_give isl_space *isl_multi_aff_get_domain_space(
1189 __isl_keep isl_multi_aff *maff);
1190 __isl_give isl_space *isl_multi_aff_get_space(
1191 __isl_keep isl_multi_aff *maff);
1192 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
1193 __isl_keep isl_pw_multi_aff *pma);
1194 __isl_give isl_space *isl_pw_multi_aff_get_space(
1195 __isl_keep isl_pw_multi_aff *pma);
1196 __isl_give isl_space *isl_union_pw_aff_get_space(
1197 __isl_keep isl_union_pw_aff *upa);
1198 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
1199 __isl_keep isl_union_pw_multi_aff *upma);
1200 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
1201 __isl_keep isl_multi_pw_aff *mpa);
1202 __isl_give isl_space *isl_multi_pw_aff_get_space(
1203 __isl_keep isl_multi_pw_aff *mpa);
1204 __isl_give isl_space *
1205 isl_multi_union_pw_aff_get_domain_space(
1206 __isl_keep isl_multi_union_pw_aff *mupa);
1207 __isl_give isl_space *
1208 isl_multi_union_pw_aff_get_space(
1209 __isl_keep isl_multi_union_pw_aff *mupa);
1211 #include <isl/point.h>
1212 __isl_give isl_space *isl_point_get_space(
1213 __isl_keep isl_point *pnt);
1215 #include <isl/fixed_box.h>
1216 __isl_give isl_space *isl_fixed_box_get_space(
1217 __isl_keep isl_fixed_box *box);
1219 The number of dimensions of a given type of space
1220 may be read off from a space or an object that lives
1221 in a space using the following functions.
1222 In case of C<isl_space_dim>, type may be
1223 C<isl_dim_param>, C<isl_dim_in> (only for relations),
1224 C<isl_dim_out> (only for relations), C<isl_dim_set>
1225 (only for sets) or C<isl_dim_all>.
1227 #include <isl/space.h>
1228 isl_size isl_space_dim(__isl_keep isl_space *space,
1229 enum isl_dim_type type);
1231 #include <isl/local_space.h>
1232 isl_size isl_local_space_dim(__isl_keep isl_local_space *ls,
1233 enum isl_dim_type type);
1235 #include <isl/set.h>
1236 isl_size isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1237 enum isl_dim_type type);
1238 isl_size isl_set_tuple_dim(__isl_keep isl_set *set);
1239 isl_size isl_set_dim(__isl_keep isl_set *set,
1240 enum isl_dim_type type);
1242 #include <isl/union_set.h>
1243 isl_size isl_union_set_dim(__isl_keep isl_union_set *uset,
1244 enum isl_dim_type type);
1246 #include <isl/map.h>
1247 isl_size isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1248 enum isl_dim_type type);
1249 isl_size isl_map_domain_tuple_dim(
1250 __isl_keep isl_map *map);
1251 isl_size isl_map_range_tuple_dim(
1252 __isl_keep isl_map *map);
1253 isl_size isl_map_dim(__isl_keep isl_map *map,
1254 enum isl_dim_type type);
1256 #include <isl/union_map.h>
1257 isl_size isl_union_map_dim(__isl_keep isl_union_map *umap,
1258 enum isl_dim_type type);
1260 #include <isl/val.h>
1261 isl_size isl_multi_val_dim(__isl_keep isl_multi_val *mv,
1262 enum isl_dim_type type);
1264 #include <isl/aff.h>
1265 isl_size isl_aff_dim(__isl_keep isl_aff *aff,
1266 enum isl_dim_type type);
1267 isl_size isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1268 enum isl_dim_type type);
1269 isl_size isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1270 enum isl_dim_type type);
1271 isl_size isl_pw_multi_aff_dim(
1272 __isl_keep isl_pw_multi_aff *pma,
1273 enum isl_dim_type type);
1274 isl_size isl_multi_pw_aff_dim(
1275 __isl_keep isl_multi_pw_aff *mpa,
1276 enum isl_dim_type type);
1277 isl_size isl_union_pw_aff_dim(
1278 __isl_keep isl_union_pw_aff *upa,
1279 enum isl_dim_type type);
1280 isl_size isl_union_pw_multi_aff_dim(
1281 __isl_keep isl_union_pw_multi_aff *upma,
1282 enum isl_dim_type type);
1283 isl_size isl_multi_union_pw_aff_dim(
1284 __isl_keep isl_multi_union_pw_aff *mupa,
1285 enum isl_dim_type type);
1287 #include <isl/polynomial.h>
1288 isl_size isl_union_pw_qpolynomial_dim(
1289 __isl_keep isl_union_pw_qpolynomial *upwqp,
1290 enum isl_dim_type type);
1291 isl_size isl_union_pw_qpolynomial_fold_dim(
1292 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1293 enum isl_dim_type type);
1295 Note that an C<isl_union_set>, an C<isl_union_map>,
1296 an C<isl_union_pw_multi_aff>,
1297 an C<isl_union_pw_qpolynomial> and
1298 an C<isl_union_pw_qpolynomial_fold>
1299 only have parameters.
1301 Additional parameters can be added to a space using the following function.
1303 #include <isl/space.h>
1304 __isl_give isl_space *isl_space_add_param_id(
1305 __isl_take isl_space *space,
1306 __isl_take isl_id *id);
1308 If a parameter with the given identifier already appears in the space,
1309 then it is not added again.
1311 Conversely, all parameters can be removed from a space
1312 using the following function.
1314 #include <isl/space.h>
1315 __isl_give isl_space *isl_space_drop_all_params(
1316 __isl_take isl_space *space);
1318 The identifiers or names of the individual dimensions of spaces
1319 may be set or read off using the following functions on spaces
1320 or objects that live in spaces.
1321 These functions are mostly useful to obtain the identifiers, positions
1322 or names of the parameters. Identifiers of individual dimensions are
1323 essentially only useful for printing. They are ignored by all other
1324 operations and may not be preserved across those operations.
1325 To keep track of a space along with names/identifiers of
1326 the set dimensions, use an C<isl_multi_id> as described in
1329 #include <isl/space.h>
1330 __isl_give isl_space *isl_space_set_dim_id(
1331 __isl_take isl_space *space,
1332 enum isl_dim_type type, unsigned pos,
1333 __isl_take isl_id *id);
1334 isl_bool isl_space_has_dim_id(__isl_keep isl_space *space,
1335 enum isl_dim_type type, unsigned pos);
1336 __isl_give isl_id *isl_space_get_dim_id(
1337 __isl_keep isl_space *space,
1338 enum isl_dim_type type, unsigned pos);
1339 __isl_give isl_space *isl_space_set_dim_name(
1340 __isl_take isl_space *space,
1341 enum isl_dim_type type, unsigned pos,
1342 __isl_keep const char *name);
1343 isl_bool isl_space_has_dim_name(__isl_keep isl_space *space,
1344 enum isl_dim_type type, unsigned pos);
1345 __isl_keep const char *isl_space_get_dim_name(
1346 __isl_keep isl_space *space,
1347 enum isl_dim_type type, unsigned pos);
1349 #include <isl/local_space.h>
1350 __isl_give isl_local_space *isl_local_space_set_dim_id(
1351 __isl_take isl_local_space *ls,
1352 enum isl_dim_type type, unsigned pos,
1353 __isl_take isl_id *id);
1354 isl_bool isl_local_space_has_dim_id(
1355 __isl_keep isl_local_space *ls,
1356 enum isl_dim_type type, unsigned pos);
1357 __isl_give isl_id *isl_local_space_get_dim_id(
1358 __isl_keep isl_local_space *ls,
1359 enum isl_dim_type type, unsigned pos);
1360 __isl_give isl_local_space *isl_local_space_set_dim_name(
1361 __isl_take isl_local_space *ls,
1362 enum isl_dim_type type, unsigned pos, const char *s);
1363 isl_bool isl_local_space_has_dim_name(
1364 __isl_keep isl_local_space *ls,
1365 enum isl_dim_type type, unsigned pos)
1366 const char *isl_local_space_get_dim_name(
1367 __isl_keep isl_local_space *ls,
1368 enum isl_dim_type type, unsigned pos);
1370 #include <isl/constraint.h>
1371 const char *isl_constraint_get_dim_name(
1372 __isl_keep isl_constraint *constraint,
1373 enum isl_dim_type type, unsigned pos);
1375 #include <isl/set.h>
1376 __isl_give isl_id *isl_basic_set_get_dim_id(
1377 __isl_keep isl_basic_set *bset,
1378 enum isl_dim_type type, unsigned pos);
1379 __isl_give isl_set *isl_set_set_dim_id(
1380 __isl_take isl_set *set, enum isl_dim_type type,
1381 unsigned pos, __isl_take isl_id *id);
1382 isl_bool isl_set_has_dim_id(__isl_keep isl_set *set,
1383 enum isl_dim_type type, unsigned pos);
1384 __isl_give isl_id *isl_set_get_dim_id(
1385 __isl_keep isl_set *set, enum isl_dim_type type,
1387 const char *isl_basic_set_get_dim_name(
1388 __isl_keep isl_basic_set *bset,
1389 enum isl_dim_type type, unsigned pos);
1390 isl_bool isl_set_has_dim_name(__isl_keep isl_set *set,
1391 enum isl_dim_type type, unsigned pos);
1392 const char *isl_set_get_dim_name(
1393 __isl_keep isl_set *set,
1394 enum isl_dim_type type, unsigned pos);
1396 #include <isl/map.h>
1397 __isl_give isl_map *isl_map_set_dim_id(
1398 __isl_take isl_map *map, enum isl_dim_type type,
1399 unsigned pos, __isl_take isl_id *id);
1400 isl_bool isl_basic_map_has_dim_id(
1401 __isl_keep isl_basic_map *bmap,
1402 enum isl_dim_type type, unsigned pos);
1403 isl_bool isl_map_has_dim_id(__isl_keep isl_map *map,
1404 enum isl_dim_type type, unsigned pos);
1405 __isl_give isl_id *isl_map_get_dim_id(
1406 __isl_keep isl_map *map, enum isl_dim_type type,
1408 __isl_give isl_id *isl_union_map_get_dim_id(
1409 __isl_keep isl_union_map *umap,
1410 enum isl_dim_type type, unsigned pos);
1411 const char *isl_basic_map_get_dim_name(
1412 __isl_keep isl_basic_map *bmap,
1413 enum isl_dim_type type, unsigned pos);
1414 isl_bool isl_map_has_dim_name(__isl_keep isl_map *map,
1415 enum isl_dim_type type, unsigned pos);
1416 const char *isl_map_get_dim_name(
1417 __isl_keep isl_map *map,
1418 enum isl_dim_type type, unsigned pos);
1420 #include <isl/val.h>
1421 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1422 __isl_take isl_multi_val *mv,
1423 enum isl_dim_type type, unsigned pos,
1424 __isl_take isl_id *id);
1425 __isl_give isl_id *isl_multi_val_get_dim_id(
1426 __isl_keep isl_multi_val *mv,
1427 enum isl_dim_type type, unsigned pos);
1428 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1429 __isl_take isl_multi_val *mv,
1430 enum isl_dim_type type, unsigned pos, const char *s);
1432 #include <isl/aff.h>
1433 __isl_give isl_aff *isl_aff_set_dim_id(
1434 __isl_take isl_aff *aff, enum isl_dim_type type,
1435 unsigned pos, __isl_take isl_id *id);
1436 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1437 __isl_take isl_multi_aff *maff,
1438 enum isl_dim_type type, unsigned pos,
1439 __isl_take isl_id *id);
1440 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1441 __isl_take isl_pw_aff *pma,
1442 enum isl_dim_type type, unsigned pos,
1443 __isl_take isl_id *id);
1444 __isl_give isl_multi_pw_aff *
1445 isl_multi_pw_aff_set_dim_id(
1446 __isl_take isl_multi_pw_aff *mpa,
1447 enum isl_dim_type type, unsigned pos,
1448 __isl_take isl_id *id);
1449 __isl_give isl_multi_union_pw_aff *
1450 isl_multi_union_pw_aff_set_dim_id(
1451 __isl_take isl_multi_union_pw_aff *mupa,
1452 enum isl_dim_type type, unsigned pos,
1453 __isl_take isl_id *id);
1454 __isl_give isl_id *isl_multi_aff_get_dim_id(
1455 __isl_keep isl_multi_aff *ma,
1456 enum isl_dim_type type, unsigned pos);
1457 isl_bool isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1458 enum isl_dim_type type, unsigned pos);
1459 __isl_give isl_id *isl_pw_aff_get_dim_id(
1460 __isl_keep isl_pw_aff *pa,
1461 enum isl_dim_type type, unsigned pos);
1462 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1463 __isl_keep isl_pw_multi_aff *pma,
1464 enum isl_dim_type type, unsigned pos);
1465 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1466 __isl_keep isl_multi_pw_aff *mpa,
1467 enum isl_dim_type type, unsigned pos);
1468 __isl_give isl_id *isl_multi_union_pw_aff_get_dim_id(
1469 __isl_keep isl_multi_union_pw_aff *mupa,
1470 enum isl_dim_type type, unsigned pos);
1471 __isl_give isl_aff *isl_aff_set_dim_name(
1472 __isl_take isl_aff *aff, enum isl_dim_type type,
1473 unsigned pos, const char *s);
1474 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1475 __isl_take isl_multi_aff *maff,
1476 enum isl_dim_type type, unsigned pos, const char *s);
1477 __isl_give isl_multi_pw_aff *
1478 isl_multi_pw_aff_set_dim_name(
1479 __isl_take isl_multi_pw_aff *mpa,
1480 enum isl_dim_type type, unsigned pos, const char *s);
1481 __isl_give isl_union_pw_aff *
1482 isl_union_pw_aff_set_dim_name(
1483 __isl_take isl_union_pw_aff *upa,
1484 enum isl_dim_type type, unsigned pos,
1486 __isl_give isl_union_pw_multi_aff *
1487 isl_union_pw_multi_aff_set_dim_name(
1488 __isl_take isl_union_pw_multi_aff *upma,
1489 enum isl_dim_type type, unsigned pos,
1491 __isl_give isl_multi_union_pw_aff *
1492 isl_multi_union_pw_aff_set_dim_name(
1493 __isl_take isl_multi_union_pw_aff *mupa,
1494 enum isl_dim_type type, unsigned pos,
1496 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1497 enum isl_dim_type type, unsigned pos);
1498 const char *isl_pw_aff_get_dim_name(
1499 __isl_keep isl_pw_aff *pa,
1500 enum isl_dim_type type, unsigned pos);
1501 const char *isl_pw_multi_aff_get_dim_name(
1502 __isl_keep isl_pw_multi_aff *pma,
1503 enum isl_dim_type type, unsigned pos);
1505 #include <isl/polynomial.h>
1506 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1507 __isl_take isl_qpolynomial *qp,
1508 enum isl_dim_type type, unsigned pos,
1510 __isl_give isl_pw_qpolynomial *
1511 isl_pw_qpolynomial_set_dim_name(
1512 __isl_take isl_pw_qpolynomial *pwqp,
1513 enum isl_dim_type type, unsigned pos,
1515 __isl_give isl_pw_qpolynomial_fold *
1516 isl_pw_qpolynomial_fold_set_dim_name(
1517 __isl_take isl_pw_qpolynomial_fold *pwf,
1518 enum isl_dim_type type, unsigned pos,
1520 __isl_give isl_union_pw_qpolynomial *
1521 isl_union_pw_qpolynomial_set_dim_name(
1522 __isl_take isl_union_pw_qpolynomial *upwqp,
1523 enum isl_dim_type type, unsigned pos,
1525 __isl_give isl_union_pw_qpolynomial_fold *
1526 isl_union_pw_qpolynomial_fold_set_dim_name(
1527 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1528 enum isl_dim_type type, unsigned pos,
1531 Note that C<isl_space_get_name> returns a pointer to some internal
1532 data structure, so the result can only be used while the
1533 corresponding C<isl_space> is alive.
1534 Also note that every function that operates on two sets or relations
1535 requires that both arguments have the same parameters. This also
1536 means that if one of the arguments has named parameters, then the
1537 other needs to have named parameters too and the names need to match.
1538 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1539 arguments may have different parameters (as long as they are named),
1540 in which case the result will have as parameters the union of the parameters of
1543 Given the identifier or name of a dimension (typically a parameter),
1544 its position can be obtained from the following functions.
1546 #include <isl/space.h>
1547 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1548 enum isl_dim_type type, __isl_keep isl_id *id);
1549 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1550 enum isl_dim_type type, const char *name);
1552 #include <isl/local_space.h>
1553 int isl_local_space_find_dim_by_name(
1554 __isl_keep isl_local_space *ls,
1555 enum isl_dim_type type, const char *name);
1557 #include <isl/val.h>
1558 int isl_multi_val_find_dim_by_id(
1559 __isl_keep isl_multi_val *mv,
1560 enum isl_dim_type type, __isl_keep isl_id *id);
1561 int isl_multi_val_find_dim_by_name(
1562 __isl_keep isl_multi_val *mv,
1563 enum isl_dim_type type, const char *name);
1565 #include <isl/set.h>
1566 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1567 enum isl_dim_type type, __isl_keep isl_id *id);
1568 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1569 enum isl_dim_type type, const char *name);
1571 #include <isl/map.h>
1572 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1573 enum isl_dim_type type, __isl_keep isl_id *id);
1574 int isl_basic_map_find_dim_by_name(
1575 __isl_keep isl_basic_map *bmap,
1576 enum isl_dim_type type, const char *name);
1577 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1578 enum isl_dim_type type, const char *name);
1579 int isl_union_map_find_dim_by_name(
1580 __isl_keep isl_union_map *umap,
1581 enum isl_dim_type type, const char *name);
1583 #include <isl/aff.h>
1584 int isl_multi_aff_find_dim_by_id(
1585 __isl_keep isl_multi_aff *ma,
1586 enum isl_dim_type type, __isl_keep isl_id *id);
1587 int isl_multi_pw_aff_find_dim_by_id(
1588 __isl_keep isl_multi_pw_aff *mpa,
1589 enum isl_dim_type type, __isl_keep isl_id *id);
1590 int isl_multi_union_pw_aff_find_dim_by_id(
1591 __isl_keep isl_multi_union_pw_aff *mupa,
1592 enum isl_dim_type type, __isl_keep isl_id *id);
1593 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff,
1594 enum isl_dim_type type, const char *name);
1595 int isl_multi_aff_find_dim_by_name(
1596 __isl_keep isl_multi_aff *ma,
1597 enum isl_dim_type type, const char *name);
1598 int isl_pw_aff_find_dim_by_name(__isl_keep isl_pw_aff *pa,
1599 enum isl_dim_type type, const char *name);
1600 int isl_multi_pw_aff_find_dim_by_name(
1601 __isl_keep isl_multi_pw_aff *mpa,
1602 enum isl_dim_type type, const char *name);
1603 int isl_pw_multi_aff_find_dim_by_name(
1604 __isl_keep isl_pw_multi_aff *pma,
1605 enum isl_dim_type type, const char *name);
1606 int isl_union_pw_aff_find_dim_by_name(
1607 __isl_keep isl_union_pw_aff *upa,
1608 enum isl_dim_type type, const char *name);
1609 int isl_union_pw_multi_aff_find_dim_by_name(
1610 __isl_keep isl_union_pw_multi_aff *upma,
1611 enum isl_dim_type type, const char *name);
1612 int isl_multi_union_pw_aff_find_dim_by_name(
1613 __isl_keep isl_multi_union_pw_aff *mupa,
1614 enum isl_dim_type type, const char *name);
1616 #include <isl/polynomial.h>
1617 int isl_pw_qpolynomial_find_dim_by_name(
1618 __isl_keep isl_pw_qpolynomial *pwqp,
1619 enum isl_dim_type type, const char *name);
1620 int isl_pw_qpolynomial_fold_find_dim_by_name(
1621 __isl_keep isl_pw_qpolynomial_fold *pwf,
1622 enum isl_dim_type type, const char *name);
1623 int isl_union_pw_qpolynomial_find_dim_by_name(
1624 __isl_keep isl_union_pw_qpolynomial *upwqp,
1625 enum isl_dim_type type, const char *name);
1626 int isl_union_pw_qpolynomial_fold_find_dim_by_name(
1627 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1628 enum isl_dim_type type, const char *name);
1630 The identifiers or names of entire spaces may be set or read off
1631 using the following functions.
1633 #include <isl/space.h>
1634 __isl_give isl_space *isl_space_set_domain_tuple_id(
1635 __isl_take isl_space *space,
1636 __isl_take isl_id *id);
1637 __isl_give isl_space *isl_space_set_range_tuple_id(
1638 __isl_take isl_space *space,
1639 __isl_take isl_id *id);
1640 __isl_give isl_space *isl_space_set_tuple_id(
1641 __isl_take isl_space *space,
1642 enum isl_dim_type type, __isl_take isl_id *id);
1643 __isl_give isl_space *isl_space_reset_tuple_id(
1644 __isl_take isl_space *space, enum isl_dim_type type);
1645 isl_bool isl_space_has_domain_tuple_id(
1646 __isl_keep isl_space *space);
1647 isl_bool isl_space_has_range_tuple_id(
1648 __isl_keep isl_space *space);
1649 isl_bool isl_space_has_tuple_id(
1650 __isl_keep isl_space *space,
1651 enum isl_dim_type type);
1652 __isl_give isl_id *isl_space_get_domain_tuple_id(
1653 __isl_keep isl_space *space);
1654 __isl_give isl_id *isl_space_get_range_tuple_id(
1655 __isl_keep isl_space *space);
1656 __isl_give isl_id *isl_space_get_tuple_id(
1657 __isl_keep isl_space *space, enum isl_dim_type type);
1658 __isl_give isl_space *isl_space_set_tuple_name(
1659 __isl_take isl_space *space,
1660 enum isl_dim_type type, const char *s);
1661 isl_bool isl_space_has_tuple_name(
1662 __isl_keep isl_space *space,
1663 enum isl_dim_type type);
1664 __isl_keep const char *isl_space_get_tuple_name(
1665 __isl_keep isl_space *space,
1666 enum isl_dim_type type);
1668 #include <isl/local_space.h>
1669 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1670 __isl_take isl_local_space *ls,
1671 enum isl_dim_type type, __isl_take isl_id *id);
1673 #include <isl/set.h>
1674 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1675 __isl_take isl_basic_set *bset,
1676 __isl_take isl_id *id);
1677 __isl_give isl_set *isl_set_set_tuple_id(
1678 __isl_take isl_set *set, __isl_take isl_id *id);
1679 __isl_give isl_set *isl_set_reset_tuple_id(
1680 __isl_take isl_set *set);
1681 isl_bool isl_set_has_tuple_id(__isl_keep isl_set *set);
1682 __isl_give isl_id *isl_set_get_tuple_id(
1683 __isl_keep isl_set *set);
1684 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1685 __isl_take isl_basic_set *set, const char *s);
1686 __isl_give isl_set *isl_set_set_tuple_name(
1687 __isl_take isl_set *set, const char *s);
1688 const char *isl_basic_set_get_tuple_name(
1689 __isl_keep isl_basic_set *bset);
1690 isl_bool isl_set_has_tuple_name(__isl_keep isl_set *set);
1691 const char *isl_set_get_tuple_name(
1692 __isl_keep isl_set *set);
1694 #include <isl/map.h>
1695 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1696 __isl_take isl_basic_map *bmap,
1697 enum isl_dim_type type, __isl_take isl_id *id);
1698 __isl_give isl_map *isl_map_set_domain_tuple_id(
1699 __isl_take isl_map *map, __isl_take isl_id *id);
1700 __isl_give isl_map *isl_map_set_range_tuple_id(
1701 __isl_take isl_map *map, __isl_take isl_id *id);
1702 __isl_give isl_map *isl_map_set_tuple_id(
1703 __isl_take isl_map *map, enum isl_dim_type type,
1704 __isl_take isl_id *id);
1705 __isl_give isl_map *isl_map_reset_tuple_id(
1706 __isl_take isl_map *map, enum isl_dim_type type);
1707 isl_bool isl_map_has_domain_tuple_id(
1708 __isl_keep isl_map *map);
1709 isl_bool isl_map_has_range_tuple_id(
1710 __isl_keep isl_map *map);
1711 isl_bool isl_map_has_tuple_id(__isl_keep isl_map *map,
1712 enum isl_dim_type type);
1713 __isl_give isl_id *isl_map_get_domain_tuple_id(
1714 __isl_keep isl_map *map);
1715 __isl_give isl_id *isl_map_get_range_tuple_id(
1716 __isl_keep isl_map *map);
1717 __isl_give isl_id *isl_map_get_tuple_id(
1718 __isl_keep isl_map *map, enum isl_dim_type type);
1719 __isl_give isl_map *isl_map_set_tuple_name(
1720 __isl_take isl_map *map,
1721 enum isl_dim_type type, const char *s);
1722 const char *isl_basic_map_get_tuple_name(
1723 __isl_keep isl_basic_map *bmap,
1724 enum isl_dim_type type);
1725 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1726 __isl_take isl_basic_map *bmap,
1727 enum isl_dim_type type, const char *s);
1728 isl_bool isl_map_has_tuple_name(__isl_keep isl_map *map,
1729 enum isl_dim_type type);
1730 const char *isl_map_get_tuple_name(
1731 __isl_keep isl_map *map,
1732 enum isl_dim_type type);
1734 #include <isl/val.h>
1735 __isl_give isl_multi_val *isl_multi_val_set_range_tuple_id(
1736 __isl_take isl_multi_val *mv,
1737 __isl_take isl_id *id);
1738 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1739 __isl_take isl_multi_val *mv,
1740 enum isl_dim_type type, __isl_take isl_id *id);
1741 __isl_give isl_multi_val *
1742 isl_multi_val_reset_range_tuple_id(
1743 __isl_take isl_multi_val *mv);
1744 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1745 __isl_take isl_multi_val *mv,
1746 enum isl_dim_type type);
1747 isl_bool isl_multi_val_has_range_tuple_id(
1748 __isl_keep isl_multi_val *mv);
1749 __isl_give isl_id *isl_multi_val_get_range_tuple_id(
1750 __isl_keep isl_multi_val *mv);
1751 isl_bool isl_multi_val_has_tuple_id(
1752 __isl_keep isl_multi_val *mv,
1753 enum isl_dim_type type);
1754 __isl_give isl_id *isl_multi_val_get_tuple_id(
1755 __isl_keep isl_multi_val *mv,
1756 enum isl_dim_type type);
1757 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1758 __isl_take isl_multi_val *mv,
1759 enum isl_dim_type type, const char *s);
1760 const char *isl_multi_val_get_tuple_name(
1761 __isl_keep isl_multi_val *mv,
1762 enum isl_dim_type type);
1764 #include <isl/aff.h>
1765 __isl_give isl_aff *isl_aff_set_tuple_id(
1766 __isl_take isl_aff *aff,
1767 enum isl_dim_type type, __isl_take isl_id *id);
1768 __isl_give isl_multi_aff *isl_multi_aff_set_range_tuple_id(
1769 __isl_take isl_multi_aff *ma,
1770 __isl_take isl_id *id);
1771 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1772 __isl_take isl_multi_aff *maff,
1773 enum isl_dim_type type, __isl_take isl_id *id);
1774 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1775 __isl_take isl_pw_aff *pwaff,
1776 enum isl_dim_type type, __isl_take isl_id *id);
1777 __isl_give isl_pw_multi_aff *
1778 isl_pw_multi_aff_set_range_tuple_id(
1779 __isl_take isl_pw_multi_aff *pma,
1780 __isl_take isl_id *id);
1781 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1782 __isl_take isl_pw_multi_aff *pma,
1783 enum isl_dim_type type, __isl_take isl_id *id);
1784 __isl_give isl_multi_pw_aff *
1785 isl_multi_pw_aff_set_range_tuple_id(
1786 __isl_take isl_multi_pw_aff *mpa,
1787 __isl_take isl_id *id);
1788 __isl_give isl_multi_union_pw_aff *
1789 isl_multi_union_pw_aff_set_range_tuple_id(
1790 __isl_take isl_multi_union_pw_aff *mupa,
1791 __isl_take isl_id *id);
1792 __isl_give isl_multi_union_pw_aff *
1793 isl_multi_union_pw_aff_set_tuple_id(
1794 __isl_take isl_multi_union_pw_aff *mupa,
1795 enum isl_dim_type type, __isl_take isl_id *id);
1796 __isl_give isl_multi_aff *
1797 isl_multi_aff_reset_range_tuple_id(
1798 __isl_take isl_multi_aff *ma);
1799 __isl_give isl_multi_pw_aff *
1800 isl_multi_pw_aff_reset_range_tuple_id(
1801 __isl_take isl_multi_pw_aff *mpa);
1802 __isl_give isl_multi_union_pw_aff *
1803 isl_multi_union_pw_aff_reset_range_tuple_id(
1804 __isl_take isl_multi_union_pw_aff *mupa);
1805 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1806 __isl_take isl_multi_aff *ma,
1807 enum isl_dim_type type);
1808 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1809 __isl_take isl_pw_aff *pa,
1810 enum isl_dim_type type);
1811 __isl_give isl_multi_pw_aff *
1812 isl_multi_pw_aff_reset_tuple_id(
1813 __isl_take isl_multi_pw_aff *mpa,
1814 enum isl_dim_type type);
1815 __isl_give isl_pw_multi_aff *
1816 isl_pw_multi_aff_reset_tuple_id(
1817 __isl_take isl_pw_multi_aff *pma,
1818 enum isl_dim_type type);
1819 __isl_give isl_multi_union_pw_aff *
1820 isl_multi_union_pw_aff_reset_tuple_id(
1821 __isl_take isl_multi_union_pw_aff *mupa,
1822 enum isl_dim_type type);
1823 isl_bool isl_multi_aff_has_range_tuple_id(
1824 __isl_keep isl_multi_aff *ma);
1825 __isl_give isl_id *isl_multi_aff_get_range_tuple_id(
1826 __isl_keep isl_multi_aff *ma);
1827 isl_bool isl_multi_aff_has_tuple_id(
1828 __isl_keep isl_multi_aff *ma,
1829 enum isl_dim_type type);
1830 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1831 __isl_keep isl_multi_aff *ma,
1832 enum isl_dim_type type);
1833 isl_bool isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1834 enum isl_dim_type type);
1835 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1836 __isl_keep isl_pw_aff *pa,
1837 enum isl_dim_type type);
1838 isl_bool isl_pw_multi_aff_has_range_tuple_id(
1839 __isl_keep isl_pw_multi_aff *pma);
1840 isl_bool isl_pw_multi_aff_has_tuple_id(
1841 __isl_keep isl_pw_multi_aff *pma,
1842 enum isl_dim_type type);
1843 __isl_give isl_id *isl_pw_multi_aff_get_range_tuple_id(
1844 __isl_keep isl_pw_multi_aff *pma);
1845 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1846 __isl_keep isl_pw_multi_aff *pma,
1847 enum isl_dim_type type);
1848 isl_bool isl_multi_pw_aff_has_range_tuple_id(
1849 __isl_keep isl_multi_pw_aff *mpa);
1850 __isl_give isl_id *isl_multi_pw_aff_get_range_tuple_id(
1851 __isl_keep isl_multi_pw_aff *mpa);
1852 isl_bool isl_multi_pw_aff_has_tuple_id(
1853 __isl_keep isl_multi_pw_aff *mpa,
1854 enum isl_dim_type type);
1855 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1856 __isl_keep isl_multi_pw_aff *mpa,
1857 enum isl_dim_type type);
1858 isl_bool isl_multi_union_pw_aff_has_range_tuple_id(
1859 __isl_keep isl_multi_union_pw_aff *mupa);
1861 isl_multi_union_pw_aff_get_range_tuple_id(
1862 __isl_keep isl_multi_union_pw_aff *mupa);
1863 isl_bool isl_multi_union_pw_aff_has_tuple_id(
1864 __isl_keep isl_multi_union_pw_aff *mupa,
1865 enum isl_dim_type type);
1866 __isl_give isl_id *isl_multi_union_pw_aff_get_tuple_id(
1867 __isl_keep isl_multi_union_pw_aff *mupa,
1868 enum isl_dim_type type);
1869 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1870 __isl_take isl_multi_aff *maff,
1871 enum isl_dim_type type, const char *s);
1872 __isl_give isl_multi_pw_aff *
1873 isl_multi_pw_aff_set_tuple_name(
1874 __isl_take isl_multi_pw_aff *mpa,
1875 enum isl_dim_type type, const char *s);
1876 __isl_give isl_multi_union_pw_aff *
1877 isl_multi_union_pw_aff_set_tuple_name(
1878 __isl_take isl_multi_union_pw_aff *mupa,
1879 enum isl_dim_type type, const char *s);
1880 const char *isl_multi_aff_get_tuple_name(
1881 __isl_keep isl_multi_aff *multi,
1882 enum isl_dim_type type);
1883 isl_bool isl_pw_multi_aff_has_tuple_name(
1884 __isl_keep isl_pw_multi_aff *pma,
1885 enum isl_dim_type type);
1886 const char *isl_pw_multi_aff_get_tuple_name(
1887 __isl_keep isl_pw_multi_aff *pma,
1888 enum isl_dim_type type);
1889 const char *isl_multi_union_pw_aff_get_tuple_name(
1890 __isl_keep isl_multi_union_pw_aff *mupa,
1891 enum isl_dim_type type);
1893 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1894 or C<isl_dim_set>. As with C<isl_space_get_name>,
1895 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1897 Binary operations require the corresponding spaces of their arguments
1898 to have the same name.
1900 To keep the names of all parameters and tuples, but reset the user pointers
1901 of all the corresponding identifiers, use the following function.
1903 #include <isl/space.h>
1904 __isl_give isl_space *isl_space_reset_user(
1905 __isl_take isl_space *space);
1907 #include <isl/set.h>
1908 __isl_give isl_set *isl_set_reset_user(
1909 __isl_take isl_set *set);
1911 #include <isl/map.h>
1912 __isl_give isl_map *isl_map_reset_user(
1913 __isl_take isl_map *map);
1915 #include <isl/union_set.h>
1916 __isl_give isl_union_set *isl_union_set_reset_user(
1917 __isl_take isl_union_set *uset);
1919 #include <isl/union_map.h>
1920 __isl_give isl_union_map *isl_union_map_reset_user(
1921 __isl_take isl_union_map *umap);
1924 __isl_give isl_multi_id *isl_multi_id_reset_user(
1925 __isl_take isl_multi_id *mi);
1927 #include <isl/val.h>
1928 __isl_give isl_multi_val *isl_multi_val_reset_user(
1929 __isl_take isl_multi_val *mv);
1931 #include <isl/aff.h>
1932 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1933 __isl_take isl_multi_aff *ma);
1934 __isl_give isl_pw_aff *isl_pw_aff_reset_user(
1935 __isl_take isl_pw_aff *pa);
1936 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1937 __isl_take isl_multi_pw_aff *mpa);
1938 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_reset_user(
1939 __isl_take isl_pw_multi_aff *pma);
1940 __isl_give isl_union_pw_aff *isl_union_pw_aff_reset_user(
1941 __isl_take isl_union_pw_aff *upa);
1942 __isl_give isl_multi_union_pw_aff *
1943 isl_multi_union_pw_aff_reset_user(
1944 __isl_take isl_multi_union_pw_aff *mupa);
1945 __isl_give isl_union_pw_multi_aff *
1946 isl_union_pw_multi_aff_reset_user(
1947 __isl_take isl_union_pw_multi_aff *upma);
1949 #include <isl/polynomial.h>
1950 __isl_give isl_pw_qpolynomial *
1951 isl_pw_qpolynomial_reset_user(
1952 __isl_take isl_pw_qpolynomial *pwqp);
1953 __isl_give isl_union_pw_qpolynomial *
1954 isl_union_pw_qpolynomial_reset_user(
1955 __isl_take isl_union_pw_qpolynomial *upwqp);
1956 __isl_give isl_pw_qpolynomial_fold *
1957 isl_pw_qpolynomial_fold_reset_user(
1958 __isl_take isl_pw_qpolynomial_fold *pwf);
1959 __isl_give isl_union_pw_qpolynomial_fold *
1960 isl_union_pw_qpolynomial_fold_reset_user(
1961 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1963 Spaces can be nested. In particular, the domain of a set or
1964 the domain or range of a relation can be a nested relation.
1965 This process is also called I<wrapping>.
1966 The functions for detecting, constructing and deconstructing
1967 such nested spaces can be found in the wrapping properties
1968 of L</"Unary Properties">, the wrapping operations
1969 of L</"Unary Operations"> and the Cartesian product operations
1970 of L</"Basic Operations">.
1972 Spaces can be created from other spaces
1973 using the functions described in L</"Unary Operations">
1974 and L</"Binary Operations">.
1978 A local space is essentially a space with
1979 zero or more existentially quantified variables.
1980 The local space of various objects can be obtained
1981 using the following functions.
1983 #include <isl/constraint.h>
1984 __isl_give isl_local_space *isl_constraint_get_local_space(
1985 __isl_keep isl_constraint *constraint);
1987 #include <isl/set.h>
1988 __isl_give isl_local_space *isl_basic_set_get_local_space(
1989 __isl_keep isl_basic_set *bset);
1991 #include <isl/map.h>
1992 __isl_give isl_local_space *isl_basic_map_get_local_space(
1993 __isl_keep isl_basic_map *bmap);
1995 #include <isl/aff.h>
1996 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1997 __isl_keep isl_aff *aff);
1998 __isl_give isl_local_space *isl_aff_get_local_space(
1999 __isl_keep isl_aff *aff);
2001 A new local space can be created from a space using
2003 #include <isl/local_space.h>
2004 __isl_give isl_local_space *isl_local_space_from_space(
2005 __isl_take isl_space *space);
2007 They can be inspected, modified, copied and freed using the following functions.
2009 #include <isl/local_space.h>
2010 isl_bool isl_local_space_is_params(
2011 __isl_keep isl_local_space *ls);
2012 isl_bool isl_local_space_is_set(
2013 __isl_keep isl_local_space *ls);
2014 __isl_give isl_space *isl_local_space_get_space(
2015 __isl_keep isl_local_space *ls);
2016 __isl_give isl_aff *isl_local_space_get_div(
2017 __isl_keep isl_local_space *ls, int pos);
2018 __isl_give isl_local_space *isl_local_space_copy(
2019 __isl_keep isl_local_space *ls);
2020 __isl_null isl_local_space *isl_local_space_free(
2021 __isl_take isl_local_space *ls);
2023 Note that C<isl_local_space_get_div> can only be used on local spaces
2026 Two local spaces can be compared using
2028 isl_bool isl_local_space_is_equal(
2029 __isl_keep isl_local_space *ls1,
2030 __isl_keep isl_local_space *ls2);
2032 Local spaces can be created from other local spaces
2033 using the functions described in L</"Unary Operations">
2034 and L</"Binary Operations">.
2036 =head2 Creating New Sets and Relations
2038 C<isl> has functions for creating some standard sets and relations.
2042 =item * Empty sets and relations
2044 __isl_give isl_basic_set *isl_basic_set_empty(
2045 __isl_take isl_space *space);
2046 __isl_give isl_basic_map *isl_basic_map_empty(
2047 __isl_take isl_space *space);
2048 __isl_give isl_set *isl_set_empty(
2049 __isl_take isl_space *space);
2050 __isl_give isl_map *isl_map_empty(
2051 __isl_take isl_space *space);
2052 __isl_give isl_union_set *isl_union_set_empty_ctx(
2054 __isl_give isl_union_set *isl_union_set_empty_space(
2055 __isl_take isl_space *space);
2056 __isl_give isl_union_set *isl_union_set_empty(
2057 __isl_take isl_space *space);
2058 __isl_give isl_union_map *isl_union_map_empty_ctx(
2060 __isl_give isl_union_map *isl_union_map_empty_space(
2061 __isl_take isl_space *space);
2062 __isl_give isl_union_map *isl_union_map_empty(
2063 __isl_take isl_space *space);
2065 For C<isl_union_set>s and C<isl_union_map>s, the space
2066 is only used to specify the parameters.
2067 C<isl_union_set_empty> is an alternative name for
2068 C<isl_union_set_empty_space>.
2069 Similarly for the other pair of functions.
2071 =item * Universe sets and relations
2073 #include <isl/set.h>
2074 __isl_give isl_basic_set *isl_basic_set_universe(
2075 __isl_take isl_space *space);
2076 __isl_give isl_set *isl_set_universe(
2077 __isl_take isl_space *space);
2078 __isl_give isl_set *isl_space_universe_set(
2079 __isl_take isl_space *space);
2081 #include <isl/map.h>
2082 __isl_give isl_basic_map *isl_basic_map_universe(
2083 __isl_take isl_space *space);
2084 __isl_give isl_map *isl_map_universe(
2085 __isl_take isl_space *space);
2086 __isl_give isl_map *isl_space_universe_map(
2087 __isl_take isl_space *space);
2089 #include <isl/union_set.h>
2090 __isl_give isl_union_set *isl_union_set_universe(
2091 __isl_take isl_union_set *uset);
2093 #include <isl/union_map.h>
2094 __isl_give isl_union_map *isl_union_map_universe(
2095 __isl_take isl_union_map *umap);
2097 C<isl_set_universe> and C<isl_space_universe_set>
2098 perform the same operation.
2100 for the pair C<isl_map_universe> and C<isl_space_universe_map>.
2102 The sets and relations constructed by the functions above
2103 contain all integer values, while those constructed by the
2104 functions below only contain non-negative values.
2106 __isl_give isl_basic_set *isl_basic_set_nat_universe(
2107 __isl_take isl_space *space);
2108 __isl_give isl_basic_map *isl_basic_map_nat_universe(
2109 __isl_take isl_space *space);
2110 __isl_give isl_set *isl_set_nat_universe(
2111 __isl_take isl_space *space);
2112 __isl_give isl_map *isl_map_nat_universe(
2113 __isl_take isl_space *space);
2115 =item * Identity relations
2117 __isl_give isl_basic_map *isl_basic_map_identity(
2118 __isl_take isl_space *space);
2119 __isl_give isl_map *isl_map_identity(
2120 __isl_take isl_space *space);
2122 The number of input and output dimensions in C<space> needs
2125 =item * Lexicographic order
2127 __isl_give isl_map *isl_map_lex_lt(
2128 __isl_take isl_space *set_space);
2129 __isl_give isl_map *isl_map_lex_le(
2130 __isl_take isl_space *set_space);
2131 __isl_give isl_map *isl_map_lex_gt(
2132 __isl_take isl_space *set_space);
2133 __isl_give isl_map *isl_map_lex_ge(
2134 __isl_take isl_space *set_space);
2135 __isl_give isl_map *isl_map_lex_lt_first(
2136 __isl_take isl_space *space, unsigned n);
2137 __isl_give isl_map *isl_map_lex_le_first(
2138 __isl_take isl_space *space, unsigned n);
2139 __isl_give isl_map *isl_map_lex_gt_first(
2140 __isl_take isl_space *space, unsigned n);
2141 __isl_give isl_map *isl_map_lex_ge_first(
2142 __isl_take isl_space *space, unsigned n);
2144 The first four functions take a space for a B<set>
2145 and return relations that express that the elements in the domain
2146 are lexicographically less
2147 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
2148 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
2149 than the elements in the range.
2150 The last four functions take a space for a map
2151 and return relations that express that the first C<n> dimensions
2152 in the domain are lexicographically less
2153 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
2154 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
2155 than the first C<n> dimensions in the range.
2159 A basic set or relation can be converted to a set or relation
2160 using the following functions.
2162 __isl_give isl_set *isl_basic_set_to_set(
2163 __isl_take isl_basic_set *bset);
2164 __isl_give isl_set *isl_set_from_basic_set(
2165 __isl_take isl_basic_set *bset);
2166 __isl_give isl_map *isl_map_from_basic_map(
2167 __isl_take isl_basic_map *bmap);
2169 C<isl_basic_set_to_set> and C<isl_set_from_basic_set> perform
2172 Sets and relations can be converted to union sets and relations
2173 using the following functions.
2175 __isl_give isl_union_set *isl_union_set_from_basic_set(
2176 __isl_take isl_basic_set *bset);
2177 __isl_give isl_union_map *isl_union_map_from_basic_map(
2178 __isl_take isl_basic_map *bmap);
2179 __isl_give isl_union_set *isl_set_to_union_set(
2180 __isl_take isl_set *set);
2181 __isl_give isl_union_set *isl_union_set_from_set(
2182 __isl_take isl_set *set);
2183 __isl_give isl_union_map *isl_map_to_union_map(
2184 __isl_take isl_map *map);
2185 __isl_give isl_union_map *isl_union_map_from_map(
2186 __isl_take isl_map *map);
2188 C<isl_map_to_union_map> and C<isl_union_map_from_map> perform
2190 Similarly for C<isl_set_to_union_set> and C<isl_union_set_from_set>.
2192 The inverse conversions below can only be used if the input
2193 union set or relation is known to contain elements in exactly one
2196 #include <isl/union_set.h>
2197 isl_bool isl_union_set_isa_set(
2198 __isl_keep isl_union_set *uset);
2199 __isl_give isl_set *isl_union_set_as_set(
2200 __isl_take isl_union_set *uset);
2201 __isl_give isl_set *isl_set_from_union_set(
2202 __isl_take isl_union_set *uset);
2204 #include <isl/union_map.h>
2205 isl_bool isl_union_map_isa_map(
2206 __isl_keep isl_union_map *umap);
2207 __isl_give isl_map *isl_union_map_as_map(
2208 __isl_take isl_union_map *umap);
2209 __isl_give isl_map *isl_map_from_union_map(
2210 __isl_take isl_union_map *umap);
2212 C<isl_union_map_as_map> and C<isl_map_from_union_map> perform
2214 Similarly for C<isl_union_set_as_set> and C<isl_set_from_union_set>.
2216 Sets and relations can be copied and freed again using the following
2219 __isl_give isl_basic_set *isl_basic_set_copy(
2220 __isl_keep isl_basic_set *bset);
2221 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
2222 __isl_give isl_union_set *isl_union_set_copy(
2223 __isl_keep isl_union_set *uset);
2224 __isl_give isl_basic_map *isl_basic_map_copy(
2225 __isl_keep isl_basic_map *bmap);
2226 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
2227 __isl_give isl_union_map *isl_union_map_copy(
2228 __isl_keep isl_union_map *umap);
2229 __isl_null isl_basic_set *isl_basic_set_free(
2230 __isl_take isl_basic_set *bset);
2231 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
2232 __isl_null isl_union_set *isl_union_set_free(
2233 __isl_take isl_union_set *uset);
2234 __isl_null isl_basic_map *isl_basic_map_free(
2235 __isl_take isl_basic_map *bmap);
2236 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
2237 __isl_null isl_union_map *isl_union_map_free(
2238 __isl_take isl_union_map *umap);
2240 Other sets and relations can be constructed by starting
2241 from a universe set or relation, adding equality and/or
2242 inequality constraints and then projecting out the
2243 existentially quantified variables, if any.
2244 Constraints can be constructed, manipulated and
2245 added to (or removed from) (basic) sets and relations
2246 using the following functions.
2248 #include <isl/constraint.h>
2249 __isl_give isl_constraint *isl_constraint_alloc_equality(
2250 __isl_take isl_local_space *ls);
2251 __isl_give isl_constraint *isl_constraint_alloc_inequality(
2252 __isl_take isl_local_space *ls);
2253 __isl_give isl_constraint *isl_constraint_set_constant_si(
2254 __isl_take isl_constraint *constraint, int v);
2255 __isl_give isl_constraint *isl_constraint_set_constant_val(
2256 __isl_take isl_constraint *constraint,
2257 __isl_take isl_val *v);
2258 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
2259 __isl_take isl_constraint *constraint,
2260 enum isl_dim_type type, int pos, int v);
2261 __isl_give isl_constraint *
2262 isl_constraint_set_coefficient_val(
2263 __isl_take isl_constraint *constraint,
2264 enum isl_dim_type type, int pos,
2265 __isl_take isl_val *v);
2266 __isl_give isl_basic_map *isl_basic_map_add_constraint(
2267 __isl_take isl_basic_map *bmap,
2268 __isl_take isl_constraint *constraint);
2269 __isl_give isl_basic_set *isl_basic_set_add_constraint(
2270 __isl_take isl_basic_set *bset,
2271 __isl_take isl_constraint *constraint);
2272 __isl_give isl_map *isl_map_add_constraint(
2273 __isl_take isl_map *map,
2274 __isl_take isl_constraint *constraint);
2275 __isl_give isl_set *isl_set_add_constraint(
2276 __isl_take isl_set *set,
2277 __isl_take isl_constraint *constraint);
2279 For example, to create a set containing the even integers
2280 between 10 and 42, you could use the following code.
2283 isl_local_space *ls;
2285 isl_basic_set *bset;
2287 space = isl_space_set_alloc(ctx, 0, 2);
2288 bset = isl_basic_set_universe(isl_space_copy(space));
2289 ls = isl_local_space_from_space(space);
2291 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
2292 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2293 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
2294 bset = isl_basic_set_add_constraint(bset, c);
2296 c = isl_constraint_alloc_inequality(isl_local_space_copy(ls));
2297 c = isl_constraint_set_constant_si(c, -10);
2298 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
2299 bset = isl_basic_set_add_constraint(bset, c);
2301 c = isl_constraint_alloc_inequality(ls);
2302 c = isl_constraint_set_constant_si(c, 42);
2303 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2304 bset = isl_basic_set_add_constraint(bset, c);
2306 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
2308 However, this is considered to be a fairly low-level approach.
2309 It is more appropriate to construct a (basic) set by means
2310 of affine expressions (defined below in L</"Functions">).
2311 For example, the same set could be constructed as follows.
2317 isl_basic_set *bset;
2319 space = isl_space_unit(ctx);
2320 space = isl_space_add_unnamed_tuple_ui(space, 1);
2321 ma = isl_multi_aff_identity_on_domain_space(
2322 isl_space_copy(space));
2323 var = isl_multi_aff_get_at(ma, 0);
2324 v = isl_val_int_from_si(ctx, 10);
2325 cst = isl_aff_val_on_domain_space(isl_space_copy(space), v);
2326 bset = isl_aff_ge_basic_set(isl_aff_copy(var), cst);
2328 v = isl_val_int_from_si(ctx, 42);
2329 cst = isl_aff_val_on_domain_space(space, v);
2330 bset = isl_basic_set_intersect(bset,
2331 isl_aff_le_basic_set(var, cst));
2333 two = isl_val_int_from_si(ctx, 2);
2334 ma = isl_multi_aff_scale_val(ma, isl_val_copy(two));
2335 bset = isl_basic_set_preimage_multi_aff(bset,
2336 isl_multi_aff_copy(ma));
2337 ma = isl_multi_aff_scale_down_val(ma, isl_val_copy(two));
2338 ma = isl_multi_aff_scale_down_val(ma, two);
2339 bset = isl_basic_set_preimage_multi_aff(bset, ma);
2341 Alternatively, the set can be parsed from a string representation.
2343 isl_basic_set *bset;
2344 bset = isl_basic_set_read_from_str(ctx,
2345 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
2347 A basic set or relation can also be constructed from two matrices
2348 describing the equalities and the inequalities.
2350 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
2351 __isl_take isl_space *space,
2352 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2353 enum isl_dim_type c1,
2354 enum isl_dim_type c2, enum isl_dim_type c3,
2355 enum isl_dim_type c4);
2356 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
2357 __isl_take isl_space *space,
2358 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2359 enum isl_dim_type c1,
2360 enum isl_dim_type c2, enum isl_dim_type c3,
2361 enum isl_dim_type c4, enum isl_dim_type c5);
2363 The C<isl_dim_type> arguments indicate the order in which
2364 different kinds of variables appear in the input matrices
2365 and should be a permutation of C<isl_dim_cst> (the constant term),
2366 C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div> for sets and
2367 of C<isl_dim_cst>, C<isl_dim_param>,
2368 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
2370 A (basic or union) set or relation can also be constructed from a
2371 (union) (piecewise) (multiple) affine expression
2372 or a list of affine expressions
2373 (See L</"Functions">), provided these affine expressions do not
2376 #include <isl/set.h>
2377 __isl_give isl_basic_set *isl_basic_set_from_multi_aff(
2378 __isl_take isl_multi_aff *ma);
2379 __isl_give isl_set *isl_multi_aff_as_set(
2380 __isl_take isl_multi_aff *ma);
2381 __isl_give isl_set *isl_set_from_multi_aff(
2382 __isl_take isl_multi_aff *ma);
2384 #include <isl/map.h>
2385 __isl_give isl_basic_map *isl_basic_map_from_aff(
2386 __isl_take isl_aff *aff);
2387 __isl_give isl_map *isl_map_from_aff(
2388 __isl_take isl_aff *aff);
2389 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
2390 __isl_take isl_space *domain_space,
2391 __isl_take isl_aff_list *list);
2392 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
2393 __isl_take isl_multi_aff *maff)
2394 __isl_give isl_map *isl_multi_aff_as_map(
2395 __isl_take isl_multi_aff *ma);
2396 __isl_give isl_map *isl_map_from_multi_aff(
2397 __isl_take isl_multi_aff *maff)
2399 #include <isl/aff.h>
2400 __isl_give isl_set *isl_set_from_pw_aff(
2401 __isl_take isl_pw_aff *pwaff);
2402 __isl_give isl_map *isl_pw_aff_as_map(
2403 __isl_take isl_pw_aff *pa);
2404 __isl_give isl_map *isl_map_from_pw_aff(
2405 __isl_take isl_pw_aff *pwaff);
2406 __isl_give isl_set *isl_pw_multi_aff_as_set(
2407 __isl_take isl_pw_multi_aff *pma);
2408 __isl_give isl_set *isl_set_from_pw_multi_aff(
2409 __isl_take isl_pw_multi_aff *pma);
2410 __isl_give isl_map *isl_pw_multi_aff_as_map(
2411 __isl_take isl_pw_multi_aff *pma);
2412 __isl_give isl_map *isl_map_from_pw_multi_aff(
2413 __isl_take isl_pw_multi_aff *pma);
2414 __isl_give isl_set *isl_multi_pw_aff_as_set(
2415 __isl_take isl_multi_pw_aff *mpa);
2416 __isl_give isl_set *isl_set_from_multi_pw_aff(
2417 __isl_take isl_multi_pw_aff *mpa);
2418 __isl_give isl_map *isl_multi_pw_aff_as_map(
2419 __isl_take isl_multi_pw_aff *mpa);
2420 __isl_give isl_map *isl_map_from_multi_pw_aff(
2421 __isl_take isl_multi_pw_aff *mpa);
2422 __isl_give isl_union_map *isl_union_map_from_union_pw_aff(
2423 __isl_take isl_union_pw_aff *upa);
2424 __isl_give isl_union_map *
2425 isl_union_pw_multi_aff_as_union_map(
2426 __isl_take isl_union_pw_multi_aff *upma);
2427 __isl_give isl_union_map *
2428 isl_union_map_from_union_pw_multi_aff(
2429 __isl_take isl_union_pw_multi_aff *upma);
2430 __isl_give isl_union_map *
2431 isl_union_map_from_multi_union_pw_aff(
2432 __isl_take isl_multi_union_pw_aff *mupa);
2434 The C<domain_space> argument describes the domain of the resulting
2435 basic relation. It is required because the C<list> may consist
2436 of zero affine expressions.
2437 The C<mupa> passed to C<isl_union_map_from_multi_union_pw_aff>
2438 is not allowed to be zero-dimensional. The domain of the result
2439 is the shared domain of the union piecewise affine elements.
2440 C<isl_multi_aff_as_set> and C<isl_set_from_multi_aff> perform
2442 Similarly for the pair C<isl_multi_aff_as_map> and C<isl_map_from_multi_aff>,
2443 for the pair C<isl_pw_aff_as_map> and C<isl_map_from_pw_aff>,
2444 for the pair C<isl_pw_multi_aff_as_set> and C<isl_set_from_pw_multi_aff>,
2445 for the pair C<isl_pw_multi_aff_as_map> and C<isl_map_from_pw_multi_aff>,
2446 the pair C<isl_multi_pw_aff_as_set> and C<isl_set_from_multi_pw_aff>,
2447 the pair C<isl_multi_pw_aff_as_map> and C<isl_map_from_multi_pw_aff>,
2449 C<isl_union_pw_multi_aff_as_union_map> and
2450 C<isl_union_map_from_union_pw_multi_aff>.
2452 =head2 Inspecting Sets and Relations
2454 Usually, the user should not have to care about the actual constraints
2455 of the sets and maps, but should instead apply the abstract operations
2456 explained in the following sections.
2457 Occasionally, however, it may be required to inspect the individual
2458 coefficients of the constraints. This section explains how to do so.
2459 In these cases, it may also be useful to have C<isl> compute
2460 an explicit representation of the existentially quantified variables.
2462 __isl_give isl_set *isl_set_compute_divs(
2463 __isl_take isl_set *set);
2464 __isl_give isl_map *isl_map_compute_divs(
2465 __isl_take isl_map *map);
2466 __isl_give isl_union_set *isl_union_set_compute_divs(
2467 __isl_take isl_union_set *uset);
2468 __isl_give isl_union_map *isl_union_map_compute_divs(
2469 __isl_take isl_union_map *umap);
2471 This explicit representation defines the existentially quantified
2472 variables as integer divisions of the other variables, possibly
2473 including earlier existentially quantified variables.
2474 An explicitly represented existentially quantified variable therefore
2475 has a unique value when the values of the other variables are known.
2477 Alternatively, the existentially quantified variables can be removed
2478 using the following functions, which compute an overapproximation.
2480 #include <isl/set.h>
2481 __isl_give isl_basic_set *isl_basic_set_remove_divs(
2482 __isl_take isl_basic_set *bset);
2483 __isl_give isl_set *isl_set_remove_divs(
2484 __isl_take isl_set *set);
2486 #include <isl/map.h>
2487 __isl_give isl_basic_map *isl_basic_map_remove_divs(
2488 __isl_take isl_basic_map *bmap);
2489 __isl_give isl_map *isl_map_remove_divs(
2490 __isl_take isl_map *map);
2492 #include <isl/union_set.h>
2493 __isl_give isl_union_set *isl_union_set_remove_divs(
2494 __isl_take isl_union_set *bset);
2496 #include <isl/union_map.h>
2497 __isl_give isl_union_map *isl_union_map_remove_divs(
2498 __isl_take isl_union_map *bmap);
2500 It is also possible to only remove those divs that are defined
2501 in terms of a given range of dimensions or only those for which
2502 no explicit representation is known.
2504 __isl_give isl_basic_set *
2505 isl_basic_set_remove_divs_involving_dims(
2506 __isl_take isl_basic_set *bset,
2507 enum isl_dim_type type,
2508 unsigned first, unsigned n);
2509 __isl_give isl_basic_map *
2510 isl_basic_map_remove_divs_involving_dims(
2511 __isl_take isl_basic_map *bmap,
2512 enum isl_dim_type type,
2513 unsigned first, unsigned n);
2514 __isl_give isl_set *isl_set_remove_divs_involving_dims(
2515 __isl_take isl_set *set, enum isl_dim_type type,
2516 unsigned first, unsigned n);
2517 __isl_give isl_map *isl_map_remove_divs_involving_dims(
2518 __isl_take isl_map *map, enum isl_dim_type type,
2519 unsigned first, unsigned n);
2521 __isl_give isl_basic_set *
2522 isl_basic_set_remove_unknown_divs(
2523 __isl_take isl_basic_set *bset);
2524 __isl_give isl_set *isl_set_remove_unknown_divs(
2525 __isl_take isl_set *set);
2526 __isl_give isl_map *isl_map_remove_unknown_divs(
2527 __isl_take isl_map *map);
2529 To iterate over all the sets or maps in a union set or map, use
2531 #include <isl/union_set.h>
2532 isl_stat isl_union_set_foreach_set(
2533 __isl_keep isl_union_set *uset,
2534 isl_stat (*fn)(__isl_take isl_set *set, void *user),
2536 isl_bool isl_union_set_every_set(
2537 __isl_keep isl_union_set *uset,
2538 isl_bool (*test)(__isl_keep isl_set *set,
2542 #include <isl/union_map.h>
2543 isl_stat isl_union_map_foreach_map(
2544 __isl_keep isl_union_map *umap,
2545 isl_stat (*fn)(__isl_take isl_map *map, void *user),
2547 isl_bool isl_union_map_every_map(
2548 __isl_keep isl_union_map *umap,
2549 isl_bool (*test)(__isl_keep isl_map *map,
2553 These functions call the callback function once for each
2554 (pair of) space(s) for which there are elements in the input.
2555 The argument to the callback contains all elements in the input
2556 with that (pair of) space(s).
2557 The C<isl_union_set_every_set> and
2558 C<isl_union_map_every_map> variants check whether each
2559 call to the callback returns true and stops checking as soon as one
2560 of these calls returns false.
2562 The number of sets or maps in a union set or map can be obtained
2565 isl_size isl_union_set_n_set(__isl_keep isl_union_set *uset);
2566 isl_size isl_union_map_n_map(__isl_keep isl_union_map *umap);
2568 To extract the set or map in a given space from a union, use
2570 __isl_give isl_set *isl_union_set_extract_set(
2571 __isl_keep isl_union_set *uset,
2572 __isl_take isl_space *space);
2573 __isl_give isl_map *isl_union_map_extract_map(
2574 __isl_keep isl_union_map *umap,
2575 __isl_take isl_space *space);
2577 To iterate over all the basic sets or maps in a set or map, use
2579 isl_stat isl_set_foreach_basic_set(__isl_keep isl_set *set,
2580 isl_stat (*fn)(__isl_take isl_basic_set *bset,
2583 isl_stat isl_map_foreach_basic_map(__isl_keep isl_map *map,
2584 isl_stat (*fn)(__isl_take isl_basic_map *bmap,
2588 The callback function C<fn> should return C<isl_stat_ok> if successful and
2589 C<isl_stat_error> if an error occurs. In the latter case, or if any other error
2590 occurs, the above functions will return C<isl_stat_error>.
2592 It should be noted that C<isl> does not guarantee that
2593 the basic sets or maps passed to C<fn> are disjoint.
2594 If this is required, then the user should call one of
2595 the following functions first.
2597 __isl_give isl_set *isl_set_make_disjoint(
2598 __isl_take isl_set *set);
2599 __isl_give isl_map *isl_map_make_disjoint(
2600 __isl_take isl_map *map);
2602 The number of basic sets in a set can be obtained
2603 or the number of basic maps in a map can be obtained
2606 #include <isl/set.h>
2607 isl_size isl_set_n_basic_set(__isl_keep isl_set *set);
2609 #include <isl/map.h>
2610 isl_size isl_map_n_basic_map(__isl_keep isl_map *map);
2612 It is also possible to obtain a list of (basic) sets from a set
2613 or union set, a list of basic maps from a map and a list of maps from a union
2616 #include <isl/set.h>
2617 __isl_give isl_basic_set_list *isl_set_get_basic_set_list(
2618 __isl_keep isl_set *set);
2620 #include <isl/union_set.h>
2621 __isl_give isl_basic_set_list *
2622 isl_union_set_get_basic_set_list(
2623 __isl_keep isl_union_set *uset);
2624 __isl_give isl_set_list *isl_union_set_get_set_list(
2625 __isl_keep isl_union_set *uset);
2627 #include <isl/map.h>
2628 __isl_give isl_basic_map_list *isl_map_get_basic_map_list(
2629 __isl_keep isl_map *map);
2631 #include <isl/union_map.h>
2632 __isl_give isl_map_list *isl_union_map_get_map_list(
2633 __isl_keep isl_union_map *umap);
2635 The returned list can be manipulated using the functions in L<"Lists">.
2637 To iterate over the constraints of a basic set or map, use
2639 #include <isl/constraint.h>
2641 isl_size isl_basic_set_n_constraint(
2642 __isl_keep isl_basic_set *bset);
2643 isl_stat isl_basic_set_foreach_constraint(
2644 __isl_keep isl_basic_set *bset,
2645 isl_stat (*fn)(__isl_take isl_constraint *c,
2648 isl_size isl_basic_map_n_constraint(
2649 __isl_keep isl_basic_map *bmap);
2650 isl_stat isl_basic_map_foreach_constraint(
2651 __isl_keep isl_basic_map *bmap,
2652 isl_stat (*fn)(__isl_take isl_constraint *c,
2655 __isl_null isl_constraint *isl_constraint_free(
2656 __isl_take isl_constraint *c);
2658 Again, the callback function C<fn> should return C<isl_stat_ok>
2660 C<isl_stat_error> if an error occurs. In the latter case, or if any other error
2661 occurs, the above functions will return C<isl_stat_error>.
2662 The constraint C<c> represents either an equality or an inequality.
2663 Use the following function to find out whether a constraint
2664 represents an equality. If not, it represents an inequality.
2666 isl_bool isl_constraint_is_equality(
2667 __isl_keep isl_constraint *constraint);
2669 It is also possible to obtain a list of constraints from a basic
2672 #include <isl/constraint.h>
2673 __isl_give isl_constraint_list *
2674 isl_basic_map_get_constraint_list(
2675 __isl_keep isl_basic_map *bmap);
2676 __isl_give isl_constraint_list *
2677 isl_basic_set_get_constraint_list(
2678 __isl_keep isl_basic_set *bset);
2680 These functions require that all existentially quantified variables
2681 have an explicit representation.
2682 The returned list can be manipulated using the functions in L<"Lists">.
2684 The coefficients of the constraints can be inspected using
2685 the following functions.
2687 isl_bool isl_constraint_is_lower_bound(
2688 __isl_keep isl_constraint *constraint,
2689 enum isl_dim_type type, unsigned pos);
2690 isl_bool isl_constraint_is_upper_bound(
2691 __isl_keep isl_constraint *constraint,
2692 enum isl_dim_type type, unsigned pos);
2693 __isl_give isl_val *isl_constraint_get_constant_val(
2694 __isl_keep isl_constraint *constraint);
2695 __isl_give isl_val *isl_constraint_get_coefficient_val(
2696 __isl_keep isl_constraint *constraint,
2697 enum isl_dim_type type, int pos);
2699 The explicit representations of the existentially quantified
2700 variables can be inspected using the following function.
2701 Note that the user is only allowed to use this function
2702 if the inspected set or map is the result of a call
2703 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2704 The existentially quantified variable is equal to the floor
2705 of the returned affine expression. The affine expression
2706 itself can be inspected using the functions in
2709 __isl_give isl_aff *isl_constraint_get_div(
2710 __isl_keep isl_constraint *constraint, int pos);
2712 To obtain the constraints of a basic set or map in matrix
2713 form, use the following functions.
2715 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2716 __isl_keep isl_basic_set *bset,
2717 enum isl_dim_type c1, enum isl_dim_type c2,
2718 enum isl_dim_type c3, enum isl_dim_type c4);
2719 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2720 __isl_keep isl_basic_set *bset,
2721 enum isl_dim_type c1, enum isl_dim_type c2,
2722 enum isl_dim_type c3, enum isl_dim_type c4);
2723 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2724 __isl_keep isl_basic_map *bmap,
2725 enum isl_dim_type c1,
2726 enum isl_dim_type c2, enum isl_dim_type c3,
2727 enum isl_dim_type c4, enum isl_dim_type c5);
2728 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2729 __isl_keep isl_basic_map *bmap,
2730 enum isl_dim_type c1,
2731 enum isl_dim_type c2, enum isl_dim_type c3,
2732 enum isl_dim_type c4, enum isl_dim_type c5);
2734 The C<isl_dim_type> arguments dictate the order in which
2735 different kinds of variables appear in the resulting matrix.
2736 For set inputs, they should be a permutation of
2737 C<isl_dim_cst> (the constant term), C<isl_dim_param>, C<isl_dim_set> and
2739 For map inputs, they should be a permutation of
2740 C<isl_dim_cst>, C<isl_dim_param>,
2741 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2745 Points are elements of a set. They can be used to construct
2746 simple sets (boxes) or they can be used to represent the
2747 individual elements of a set.
2748 The zero point (the origin) can be created using
2750 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2752 The coordinates of a point can be inspected, set and changed
2755 #include <isl/point.h>
2756 __isl_give isl_multi_val *isl_point_get_multi_val(
2757 __isl_keep isl_point *pnt);
2758 __isl_give isl_val *isl_point_get_coordinate_val(
2759 __isl_keep isl_point *pnt,
2760 enum isl_dim_type type, int pos);
2761 __isl_give isl_point *isl_point_set_coordinate_val(
2762 __isl_take isl_point *pnt,
2763 enum isl_dim_type type, int pos,
2764 __isl_take isl_val *v);
2766 __isl_give isl_point *isl_point_add_ui(
2767 __isl_take isl_point *pnt,
2768 enum isl_dim_type type, int pos, unsigned val);
2769 __isl_give isl_point *isl_point_sub_ui(
2770 __isl_take isl_point *pnt,
2771 enum isl_dim_type type, int pos, unsigned val);
2773 Points can be copied or freed using
2775 __isl_give isl_point *isl_point_copy(
2776 __isl_keep isl_point *pnt);
2777 __isl_null isl_point *isl_point_free(
2778 __isl_take isl_point *pnt);
2780 A singleton set can be created from a point using the following functions.
2782 __isl_give isl_basic_set *isl_basic_set_from_point(
2783 __isl_take isl_point *pnt);
2784 __isl_give isl_set *isl_point_to_set(
2785 __isl_take isl_point *pnt);
2786 __isl_give isl_set *isl_set_from_point(
2787 __isl_take isl_point *pnt);
2788 __isl_give isl_union_set *isl_union_set_from_point(
2789 __isl_take isl_point *pnt);
2791 C<isl_point_to_set> and C<isl_set_from_point> perform
2794 A box can be created from two opposite extremal points using
2796 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2797 __isl_take isl_point *pnt1,
2798 __isl_take isl_point *pnt2);
2799 __isl_give isl_set *isl_set_box_from_points(
2800 __isl_take isl_point *pnt1,
2801 __isl_take isl_point *pnt2);
2803 All elements of a B<bounded> (union) set can be enumerated using
2804 the following functions.
2806 isl_stat isl_set_foreach_point(__isl_keep isl_set *set,
2807 isl_stat (*fn)(__isl_take isl_point *pnt,
2810 isl_stat isl_union_set_foreach_point(
2811 __isl_keep isl_union_set *uset,
2812 isl_stat (*fn)(__isl_take isl_point *pnt,
2816 The function C<fn> is called for each integer point in
2817 C<set> with as second argument the last argument of
2818 the C<isl_set_foreach_point> call. The function C<fn>
2819 should return C<isl_stat_ok> on success and C<isl_stat_error> on failure.
2820 In the latter case, C<isl_set_foreach_point> will stop
2821 enumerating and return C<isl_stat_error> as well.
2822 If the enumeration is performed successfully and to completion,
2823 then C<isl_set_foreach_point> returns C<isl_stat_ok>.
2825 To obtain a single point of a (basic or union) set, use
2827 __isl_give isl_point *isl_basic_set_sample_point(
2828 __isl_take isl_basic_set *bset);
2829 __isl_give isl_point *isl_set_sample_point(
2830 __isl_take isl_set *set);
2831 __isl_give isl_point *isl_union_set_sample_point(
2832 __isl_take isl_union_set *uset);
2834 If C<set> does not contain any (integer) points, then the
2835 resulting point will be ``void'', a property that can be
2838 isl_bool isl_point_is_void(__isl_keep isl_point *pnt);
2842 Besides sets and relation, C<isl> also supports various types of functions.
2843 Each of these types is derived from the value type (see L</"Values">)
2844 or from one of two primitive function types
2845 through the application of zero or more type constructors.
2846 As a special case, a multiple expression can also be derived
2847 from an identifier (see L</"Identifiers">) although the result
2848 is not really a function.
2849 We first describe the primitive type and then we describe
2850 the types derived from these primitive types.
2852 =head3 Primitive Functions
2854 C<isl> support two primitive function types, quasi-affine
2855 expressions and quasipolynomials.
2856 A quasi-affine expression is defined either over a parameter
2857 space or over a set and is composed of integer constants,
2858 parameters and set variables, addition, subtraction and
2859 integer division by an integer constant.
2860 For example, the quasi-affine expression
2862 [n] -> { [x] -> [2*floor((4 n + x)/9)] }
2864 maps C<x> to C<2*floor((4 n + x)/9>.
2865 A quasipolynomial is a polynomial expression in quasi-affine
2866 expression. That is, it additionally allows for multiplication.
2867 Note, though, that it is not allowed to construct an integer
2868 division of an expression involving multiplications.
2869 Here is an example of a quasipolynomial that is not
2870 quasi-affine expression
2872 [n] -> { [x] -> (n*floor((4 n + x)/9)) }
2874 Note that the external representations of quasi-affine expressions
2875 and quasipolynomials are different. Quasi-affine expressions
2876 use a notation with square brackets just like binary relations,
2877 while quasipolynomials do not. This might change at some point.
2879 If a primitive function is defined over a parameter space,
2880 then the space of the function itself is that of a set.
2881 If it is defined over a set, then the space of the function
2882 is that of a relation. In both cases, the set space (or
2883 the output space) is single-dimensional, anonymous and unstructured.
2884 To create functions with multiple dimensions or with other kinds
2885 of set or output spaces, use multiple expressions
2886 (see L</"Multiple Expressions">).
2890 =item * Quasi-affine Expressions
2892 Besides the expressions described above, a quasi-affine
2893 expression can also be set to NaN. Such expressions
2894 typically represent a failure to represent a result
2895 as a quasi-affine expression.
2897 The zero quasi affine expression or the quasi affine expression
2898 that is equal to a given value, parameter or
2899 a specified dimension on a given domain can be created using
2901 #include <isl/aff.h>
2902 __isl_give isl_aff *isl_aff_zero_on_domain_space(
2903 __isl_take isl_space *space);
2904 __isl_give isl_aff *isl_space_zero_aff_on_domain(
2905 __isl_take isl_space *space);
2906 __isl_give isl_aff *isl_aff_zero_on_domain(
2907 __isl_take isl_local_space *ls);
2908 __isl_give isl_aff *isl_aff_val_on_domain_space(
2909 __isl_take isl_space *space,
2910 __isl_take isl_val *val);
2911 __isl_give isl_aff *isl_aff_val_on_domain(
2912 __isl_take isl_local_space *ls,
2913 __isl_take isl_val *val);
2914 __isl_give isl_aff *isl_aff_param_on_domain_space_id(
2915 __isl_take isl_space *space,
2916 __isl_take isl_id *id);
2917 __isl_give isl_aff *isl_space_param_aff_on_domain_id(
2918 __isl_take isl_space *space,
2919 __isl_take isl_id *id);
2920 __isl_give isl_aff *isl_aff_var_on_domain(
2921 __isl_take isl_local_space *ls,
2922 enum isl_dim_type type, unsigned pos);
2923 __isl_give isl_aff *isl_aff_nan_on_domain_space(
2924 __isl_take isl_space *space);
2925 __isl_give isl_aff *isl_aff_nan_on_domain(
2926 __isl_take isl_local_space *ls);
2928 The space passed to C<isl_aff_param_on_domain_space_id>
2929 is required to have a parameter with the given identifier.
2930 C<isl_aff_param_on_domain_space_id> and
2931 C<isl_space_param_aff_on_domain_id> perform the same operation.
2933 C<isl_aff_zero_on_domain_space> and C<isl_space_zero_aff_on_domain>
2934 perform the same operation.
2936 Quasi affine expressions can be copied and freed using
2938 #include <isl/aff.h>
2939 __isl_give isl_aff *isl_aff_copy(
2940 __isl_keep isl_aff *aff);
2941 __isl_null isl_aff *isl_aff_free(
2942 __isl_take isl_aff *aff);
2944 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2945 using the following function. The constraint is required to have
2946 a non-zero coefficient for the specified dimension.
2948 #include <isl/constraint.h>
2949 __isl_give isl_aff *isl_constraint_get_bound(
2950 __isl_keep isl_constraint *constraint,
2951 enum isl_dim_type type, int pos);
2953 The entire affine expression of the constraint can also be extracted
2954 using the following function.
2956 #include <isl/constraint.h>
2957 __isl_give isl_aff *isl_constraint_get_aff(
2958 __isl_keep isl_constraint *constraint);
2960 Conversely, an equality constraint equating
2961 the affine expression to zero or an inequality constraint enforcing
2962 the affine expression to be non-negative, can be constructed using
2964 __isl_give isl_constraint *isl_equality_from_aff(
2965 __isl_take isl_aff *aff);
2966 __isl_give isl_constraint *isl_inequality_from_aff(
2967 __isl_take isl_aff *aff);
2969 The coefficients and the integer divisions of an affine expression
2970 can be inspected using the following functions.
2972 #include <isl/aff.h>
2973 __isl_give isl_val *isl_aff_get_constant_val(
2974 __isl_keep isl_aff *aff);
2975 __isl_give isl_val *isl_aff_get_coefficient_val(
2976 __isl_keep isl_aff *aff,
2977 enum isl_dim_type type, int pos);
2978 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2979 enum isl_dim_type type, int pos);
2980 __isl_give isl_val *isl_aff_get_denominator_val(
2981 __isl_keep isl_aff *aff);
2982 __isl_give isl_aff *isl_aff_get_div(
2983 __isl_keep isl_aff *aff, int pos);
2985 They can be modified using the following functions.
2987 #include <isl/aff.h>
2988 __isl_give isl_aff *isl_aff_set_constant_si(
2989 __isl_take isl_aff *aff, int v);
2990 __isl_give isl_aff *isl_aff_set_constant_val(
2991 __isl_take isl_aff *aff, __isl_take isl_val *v);
2992 __isl_give isl_aff *isl_aff_set_coefficient_si(
2993 __isl_take isl_aff *aff,
2994 enum isl_dim_type type, int pos, int v);
2995 __isl_give isl_aff *isl_aff_set_coefficient_val(
2996 __isl_take isl_aff *aff,
2997 enum isl_dim_type type, int pos,
2998 __isl_take isl_val *v);
3000 __isl_give isl_aff *isl_aff_add_constant_si(
3001 __isl_take isl_aff *aff, int v);
3002 __isl_give isl_aff *isl_aff_add_constant_val(
3003 __isl_take isl_aff *aff, __isl_take isl_val *v);
3004 __isl_give isl_aff *isl_aff_add_constant_num_si(
3005 __isl_take isl_aff *aff, int v);
3006 __isl_give isl_aff *isl_aff_add_coefficient_si(
3007 __isl_take isl_aff *aff,
3008 enum isl_dim_type type, int pos, int v);
3009 __isl_give isl_aff *isl_aff_add_coefficient_val(
3010 __isl_take isl_aff *aff,
3011 enum isl_dim_type type, int pos,
3012 __isl_take isl_val *v);
3014 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
3015 set the I<numerator> of the constant or coefficient, while
3016 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
3017 the constant or coefficient as a whole.
3018 The C<add_constant> and C<add_coefficient> functions add an integer
3019 or rational value to
3020 the possibly rational constant or coefficient.
3021 The C<add_constant_num> functions add an integer value to
3024 =item * Quasipolynomials
3026 Some simple quasipolynomials can be created using the following functions.
3028 #include <isl/polynomial.h>
3029 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3030 __isl_take isl_space *domain);
3031 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3032 __isl_take isl_space *domain);
3033 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3034 __isl_take isl_space *domain);
3035 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3036 __isl_take isl_space *domain);
3037 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3038 __isl_take isl_space *domain);
3039 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
3040 __isl_take isl_space *domain,
3041 __isl_take isl_val *val);
3042 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3043 __isl_take isl_space *domain,
3044 enum isl_dim_type type, unsigned pos);
3045 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3046 __isl_take isl_aff *aff);
3048 Recall that the space in which a quasipolynomial lives is a map space
3049 with a one-dimensional range. The C<domain> argument in some of
3050 the functions above corresponds to the domain of this map space.
3052 Quasipolynomials can be copied and freed again using the following
3055 #include <isl/polynomial.h>
3056 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3057 __isl_keep isl_qpolynomial *qp);
3058 __isl_null isl_qpolynomial *isl_qpolynomial_free(
3059 __isl_take isl_qpolynomial *qp);
3061 The constant term of a quasipolynomial can be extracted using
3063 __isl_give isl_val *isl_qpolynomial_get_constant_val(
3064 __isl_keep isl_qpolynomial *qp);
3066 To iterate over all terms in a quasipolynomial,
3069 isl_stat isl_qpolynomial_foreach_term(
3070 __isl_keep isl_qpolynomial *qp,
3071 isl_stat (*fn)(__isl_take isl_term *term,
3072 void *user), void *user);
3074 The terms themselves can be inspected and freed using
3077 isl_size isl_term_dim(__isl_keep isl_term *term,
3078 enum isl_dim_type type);
3079 __isl_give isl_val *isl_term_get_coefficient_val(
3080 __isl_keep isl_term *term);
3081 isl_size isl_term_get_exp(__isl_keep isl_term *term,
3082 enum isl_dim_type type, unsigned pos);
3083 __isl_give isl_aff *isl_term_get_div(
3084 __isl_keep isl_term *term, unsigned pos);
3085 __isl_null isl_term *isl_term_free(
3086 __isl_take isl_term *term);
3088 Each term is a product of parameters, set variables and
3089 integer divisions. The function C<isl_term_get_exp>
3090 returns the exponent of a given dimensions in the given term.
3096 A reduction represents a maximum or a minimum of its
3098 The only reduction type defined by C<isl> is
3099 C<isl_qpolynomial_fold>.
3101 There are currently no functions to directly create such
3102 objects, but they do appear in the piecewise quasipolynomial
3103 reductions returned by the C<isl_pw_qpolynomial_bound> function.
3105 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
3107 Reductions can be copied and freed using
3108 the following functions.
3110 #include <isl/polynomial.h>
3111 __isl_give isl_qpolynomial_fold *
3112 isl_qpolynomial_fold_copy(
3113 __isl_keep isl_qpolynomial_fold *fold);
3114 __isl_null isl_qpolynomial_fold *
3115 isl_qpolynomial_fold_free(
3116 __isl_take isl_qpolynomial_fold *fold);
3118 The type of a (union piecewise) reduction
3119 can be obtained using the following functions.
3121 #include <isl/polynomial.h>
3122 enum isl_fold isl_qpolynomial_fold_get_type(
3123 __isl_keep isl_qpolynomial_fold *fold);
3124 enum isl_fold isl_pw_qpolynomial_fold_get_type(
3125 __isl_keep isl_pw_qpolynomial_fold *pwf);
3126 enum isl_fold isl_union_pw_qpolynomial_fold_get_type(
3127 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3129 The type may be either C<isl_fold_min> or C<isl_fold_max>
3130 (or C<isl_fold_error> in case of error).
3132 To iterate over all quasipolynomials in a reduction, use
3134 isl_stat isl_qpolynomial_fold_foreach_qpolynomial(
3135 __isl_keep isl_qpolynomial_fold *fold,
3136 isl_stat (*fn)(__isl_take isl_qpolynomial *qp,
3137 void *user), void *user);
3139 =head3 Multiple Expressions
3141 A multiple expression represents a sequence of zero or
3142 more base expressions, all defined on the same domain space.
3143 The domain space of the multiple expression is the same
3144 as that of the base expressions, but the range space
3145 can be any space. In case the base expressions have
3146 a set space, the corresponding multiple expression
3147 also has a set space.
3148 Objects of the value or identifier type do not have an associated space.
3149 The space of a multiple value or
3150 multiple identifier is therefore always a set space.
3151 Similarly, the space of a multiple union piecewise
3152 affine expression is always a set space.
3153 If the base expressions are not total, then
3154 a corresponding zero-dimensional multiple expression may
3155 have an explicit domain that keeps track of the domain
3156 outside of any base expressions.
3158 The multiple expression types defined by C<isl>
3159 are C<isl_multi_val>, C<isl_multi_id>, C<isl_multi_aff>, C<isl_multi_pw_aff>,
3160 C<isl_multi_union_pw_aff>.
3162 A multiple expression with the value zero for
3163 each output (or set) dimension can be created
3164 using the following functions.
3166 #include <isl/val.h>
3167 __isl_give isl_multi_val *isl_multi_val_zero(
3168 __isl_take isl_space *space);
3169 __isl_give isl_multi_val *isl_space_zero_multi_val(
3170 __isl_take isl_space *space);
3172 #include <isl/aff.h>
3173 __isl_give isl_multi_aff *isl_multi_aff_zero(
3174 __isl_take isl_space *space);
3175 __isl_give isl_multi_aff *isl_space_zero_multi_aff(
3176 __isl_take isl_space *space);
3177 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
3178 __isl_take isl_space *space);
3179 __isl_give isl_multi_pw_aff *isl_space_zero_multi_pw_aff(
3180 __isl_take isl_space *space);
3181 __isl_give isl_multi_union_pw_aff *
3182 isl_multi_union_pw_aff_zero(
3183 __isl_take isl_space *space);
3184 __isl_give isl_multi_union_pw_aff *
3185 isl_space_zero_multi_union_pw_aff(
3186 __isl_take isl_space *space);
3188 Since there is no canonical way of representing a zero
3189 value of type C<isl_union_pw_aff>, the space passed
3190 to C<isl_multi_union_pw_aff_zero> needs to be zero-dimensional.
3191 C<isl_multi_val_zero> and C<isl_space_zero_multi_val>
3192 perform the same operation.
3194 for the pair C<isl_multi_aff_zero> and C<isl_space_zero_multi_aff>,
3195 for the pair C<isl_multi_pw_aff_zero> and C<isl_space_zero_multi_pw_aff> and
3196 for the pair C<isl_multi_union_pw_aff_zero> and
3197 C<isl_space_zero_multi_union_pw_aff>.
3200 An identity function can be created using the following
3202 For the first group of functions, the space needs to be that of a set.
3203 For the second group,
3204 the space needs to be that of a relation
3205 with the same number of input and output dimensions.
3206 For the third group, the input function needs to live in a space
3207 with the same number of input and output dimensions and
3208 the identity function is created in that space.
3210 #include <isl/aff.h>
3211 __isl_give isl_multi_aff *
3212 isl_multi_aff_identity_on_domain_space(
3213 __isl_take isl_space *space);
3214 __isl_give isl_multi_aff *
3215 isl_space_identity_multi_aff_on_domain(
3216 __isl_take isl_space *space);
3217 __isl_give isl_multi_pw_aff *
3218 isl_multi_pw_aff_identity_on_domain_space(
3219 __isl_take isl_space *space);
3220 __isl_give isl_multi_pw_aff *
3221 isl_space_identity_multi_pw_aff_on_domain(
3222 __isl_take isl_space *space);
3223 __isl_give isl_multi_aff *isl_multi_aff_identity(
3224 __isl_take isl_space *space);
3225 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
3226 __isl_take isl_space *space);
3227 __isl_give isl_multi_aff *
3228 isl_multi_aff_identity_multi_aff(
3229 __isl_take isl_multi_aff *ma);
3230 __isl_give isl_multi_pw_aff *
3231 isl_multi_pw_aff_identity_multi_pw_aff(
3232 __isl_take isl_multi_pw_aff *mpa);
3234 C<isl_multi_aff_identity_on_domain_space> and
3235 C<isl_space_identity_multi_aff_on_domain>
3236 perform the same operation.
3238 for the pair C<isl_multi_pw_aff_identity_on_domain_space> and
3239 C<isl_space_identity_multi_pw_aff_on_domain>.
3241 A function that performs a projection on a universe
3242 relation or set can be created using the following functions.
3243 See also the corresponding
3244 projection operations in L</"Unary Operations">.
3246 #include <isl/aff.h>
3247 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
3248 __isl_take isl_space *space);
3249 __isl_give isl_multi_aff *isl_space_domain_map_multi_aff(
3250 __isl_take isl_space *space);
3251 __isl_give isl_multi_aff *isl_multi_aff_range_map(
3252 __isl_take isl_space *space);
3253 __isl_give isl_multi_aff *isl_space_range_map_multi_aff(
3254 __isl_take isl_space *space);
3255 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
3256 __isl_take isl_space *space,
3257 enum isl_dim_type type,
3258 unsigned first, unsigned n);
3260 C<isl_multi_aff_domain_map> and C<isl_space_domain_map_multi_aff> perform
3263 for the pair C<isl_multi_aff_range_map> and C<isl_space_range_map_multi_aff>.
3265 A multiple expression can be created from a single
3266 base expression using the following functions.
3267 The space of the created multiple expression is the same
3268 as that of the base expression, except for
3269 C<isl_multi_union_pw_aff_from_union_pw_aff> where the input
3270 lives in a parameter space and the output lives
3271 in a single-dimensional set space.
3273 #include <isl/aff.h>
3274 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
3275 __isl_take isl_aff *aff);
3276 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
3277 __isl_take isl_pw_aff *pa);
3278 __isl_give isl_multi_union_pw_aff *
3279 isl_multi_union_pw_aff_from_union_pw_aff(
3280 __isl_take isl_union_pw_aff *upa);
3282 A multiple expression can be created from a list
3283 of base expression in a specified space.
3284 The domain of this space needs to be the same
3285 as the domains of the base expressions in the list.
3286 If the base expressions have a set space (or no associated space),
3287 then this space also needs to be a set space.
3290 __isl_give isl_multi_id *isl_multi_id_from_id_list(
3291 __isl_take isl_space *space,
3292 __isl_take isl_id_list *list);
3293 __isl_give isl_multi_id *isl_space_multi_id(
3294 __isl_take isl_space *space,
3295 __isl_take isl_id_list *list);
3297 #include <isl/val.h>
3298 __isl_give isl_multi_val *isl_multi_val_from_val_list(
3299 __isl_take isl_space *space,
3300 __isl_take isl_val_list *list);
3301 __isl_give isl_multi_val *isl_space_multi_val(
3302 __isl_take isl_space *space,
3303 __isl_take isl_val_list *list);
3305 #include <isl/aff.h>
3306 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3307 __isl_take isl_space *space,
3308 __isl_take isl_aff_list *list);
3309 __isl_give isl_multi_aff *isl_space_multi_aff(
3310 __isl_take isl_space *space,
3311 __isl_take isl_aff_list *list);
3312 __isl_give isl_multi_pw_aff *
3313 isl_multi_pw_aff_from_pw_aff_list(
3314 __isl_take isl_space *space,
3315 __isl_take isl_pw_aff_list *list);
3316 __isl_give isl_multi_pw_aff *
3317 isl_space_multi_pw_aff(
3318 __isl_take isl_space *space,
3319 __isl_take isl_pw_aff_list *list);
3320 __isl_give isl_multi_union_pw_aff *
3321 isl_multi_union_pw_aff_from_union_pw_aff_list(
3322 __isl_take isl_space *space,
3323 __isl_take isl_union_pw_aff_list *list);
3324 __isl_give isl_multi_union_pw_aff *
3325 isl_space_multi_union_pw_aff(
3326 __isl_take isl_space *space,
3327 __isl_take isl_union_pw_aff_list *list);
3329 C<isl_multi_id_from_id_list> and C<isl_space_multi_id> perform
3331 Similarly for the pair C<isl_multi_val_from_val_list> and
3332 C<isl_space_multi_val>,
3333 for the pair C<isl_multi_aff_from_aff_list> and
3334 C<isl_space_multi_aff>,
3335 for the pair C<isl_multi_pw_aff_from_pw_aff_list> and
3336 C<isl_space_multi_pw_aff> and
3337 for the pair C<isl_multi_union_pw_aff_from_union_pw_aff_list> and
3338 C<isl_space_multi_union_pw_aff>.
3340 As a convenience, a multiple piecewise expression can
3341 also be created from a multiple expression,
3342 or even directly from a single base expression.
3343 Each piecewise expression in the result has a single
3346 #include <isl/aff.h>
3347 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_aff(
3348 __isl_take isl_aff *aff);
3349 __isl_give isl_multi_pw_aff *
3350 isl_multi_aff_to_multi_pw_aff(
3351 __isl_take isl_multi_aff *ma);
3352 __isl_give isl_multi_pw_aff *
3353 isl_multi_pw_aff_from_multi_aff(
3354 __isl_take isl_multi_aff *ma);
3356 C<isl_multi_aff_to_multi_pw_aff> and
3357 C<isl_multi_pw_aff_from_multi_aff> perform the same operation.
3359 Similarly, a multiple union expression can be
3360 created from a multiple expression.
3362 #include <isl/aff.h>
3363 __isl_give isl_multi_union_pw_aff *
3364 isl_multi_union_pw_aff_from_multi_aff(
3365 __isl_take isl_multi_aff *ma);
3366 __isl_give isl_multi_union_pw_aff *
3367 isl_multi_aff_to_multi_union_pw_aff(
3368 __isl_take isl_multi_aff *ma);
3369 __isl_give isl_multi_union_pw_aff *
3370 isl_multi_union_pw_aff_from_multi_pw_aff(
3371 __isl_take isl_multi_pw_aff *mpa);
3373 C<isl_multi_aff_to_multi_union_pw_aff> and
3374 C<isl_multi_union_pw_aff_from_multi_aff> perform the same operation.
3376 A multiple quasi-affine expression can be created from
3377 a multiple value with a given domain space using the following
3380 #include <isl/aff.h>
3381 __isl_give isl_multi_aff *
3382 isl_multi_aff_multi_val_on_domain_space(
3383 __isl_take isl_space *space,
3384 __isl_take isl_multi_val *mv);
3385 __isl_give isl_multi_aff *
3386 isl_space_multi_aff_on_domain_multi_val(
3387 __isl_take isl_space *space,
3388 __isl_take isl_multi_val *mv);
3389 __isl_give isl_multi_aff *
3390 isl_multi_aff_multi_val_on_space(
3391 __isl_take isl_space *space,
3392 __isl_take isl_multi_val *mv);
3394 C<isl_space_multi_aff_on_domain_multi_val> and
3395 C<isl_multi_aff_multi_val_on_space> are alternative names
3396 for C<isl_multi_aff_multi_val_on_domain_space>.
3399 a multiple union piecewise affine expression can be created from
3400 a multiple value with a given domain or
3401 a (piecewise) multiple affine expression with a given domain
3402 using the following functions.
3404 #include <isl/aff.h>
3405 __isl_give isl_multi_union_pw_aff *
3406 isl_multi_union_pw_aff_multi_val_on_domain(
3407 __isl_take isl_union_set *domain,
3408 __isl_take isl_multi_val *mv);
3409 __isl_give isl_multi_union_pw_aff *
3410 isl_multi_union_pw_aff_multi_aff_on_domain(
3411 __isl_take isl_union_set *domain,
3412 __isl_take isl_multi_aff *ma);
3413 __isl_give isl_multi_union_pw_aff *
3414 isl_multi_union_pw_aff_pw_multi_aff_on_domain(
3415 __isl_take isl_union_set *domain,
3416 __isl_take isl_pw_multi_aff *pma);
3418 Multiple expressions can be copied and freed using
3419 the following functions.
3422 __isl_give isl_multi_id *isl_multi_id_copy(
3423 __isl_keep isl_multi_id *mi);
3424 __isl_null isl_multi_id *isl_multi_id_free(
3425 __isl_take isl_multi_id *mi);
3427 #include <isl/val.h>
3428 __isl_give isl_multi_val *isl_multi_val_copy(
3429 __isl_keep isl_multi_val *mv);
3430 __isl_null isl_multi_val *isl_multi_val_free(
3431 __isl_take isl_multi_val *mv);
3433 #include <isl/aff.h>
3434 __isl_give isl_multi_aff *isl_multi_aff_copy(
3435 __isl_keep isl_multi_aff *maff);
3436 __isl_null isl_multi_aff *isl_multi_aff_free(
3437 __isl_take isl_multi_aff *maff);
3438 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
3439 __isl_keep isl_multi_pw_aff *mpa);
3440 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
3441 __isl_take isl_multi_pw_aff *mpa);
3442 __isl_give isl_multi_union_pw_aff *
3443 isl_multi_union_pw_aff_copy(
3444 __isl_keep isl_multi_union_pw_aff *mupa);
3445 __isl_null isl_multi_union_pw_aff *
3446 isl_multi_union_pw_aff_free(
3447 __isl_take isl_multi_union_pw_aff *mupa);
3449 The number of base expressions in a multiple
3450 expression can be obtained using the following functions.
3453 int isl_multi_id_size(__isl_keep isl_multi_id *mi);
3455 #include <isl/val.h>
3456 isl_size isl_multi_val_size(__isl_keep isl_multi_val *mv);
3458 #include <isl/aff.h>
3459 isl_size isl_multi_aff_size(
3460 __isl_keep isl_multi_aff *multi);
3461 isl_size isl_multi_pw_aff_size(
3462 __isl_keep isl_multi_pw_aff *mpa);
3463 isl_size isl_multi_union_pw_aff_size(
3464 __isl_keep isl_multi_union_pw_aff *mupa);
3466 The base expression at a given position of a multiple
3467 expression can be extracted using the following functions.
3470 __isl_give isl_id *isl_multi_id_get_at(
3471 __isl_keep isl_multi_id *mi, int pos);
3472 __isl_give isl_id *isl_multi_id_get_id(
3473 __isl_keep isl_multi_id *mi, int pos);
3475 #include <isl/val.h>
3476 __isl_give isl_val *isl_multi_val_get_at(
3477 __isl_keep isl_multi_val *mv, int pos);
3478 __isl_give isl_val *isl_multi_val_get_val(
3479 __isl_keep isl_multi_val *mv, int pos);
3481 #include <isl/aff.h>
3482 __isl_give isl_aff *isl_multi_aff_get_at(
3483 __isl_keep isl_multi_aff *ma, int pos);
3484 __isl_give isl_aff *isl_multi_aff_get_aff(
3485 __isl_keep isl_multi_aff *multi, int pos);
3486 __isl_give isl_pw_aff *isl_multi_pw_aff_get_at(
3487 __isl_keep isl_multi_pw_aff *mpa, int pos);
3488 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
3489 __isl_keep isl_multi_pw_aff *mpa, int pos);
3490 __isl_give isl_union_pw_aff *
3491 isl_multi_union_pw_aff_get_at(
3492 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
3493 __isl_give isl_union_pw_aff *
3494 isl_multi_union_pw_aff_get_union_pw_aff(
3495 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
3497 C<isl_multi_id_get_id> is an alternative name for C<isl_multi_id_get_at>.
3498 Similarly for the other pairs of functions.
3500 The base expression can be replaced using the following functions.
3503 __isl_give isl_multi_id *isl_multi_id_set_at(
3504 __isl_take isl_multi_id *mi, int pos,
3505 __isl_take isl_id *id);
3506 __isl_give isl_multi_id *isl_multi_id_set_id(
3507 __isl_take isl_multi_id *mi, int pos,
3508 __isl_take isl_id *id);
3510 #include <isl/val.h>
3511 __isl_give isl_multi_val *isl_multi_val_set_at(
3512 __isl_take isl_multi_val *mv, int pos,
3513 __isl_take isl_val *val);
3514 __isl_give isl_multi_val *isl_multi_val_set_val(
3515 __isl_take isl_multi_val *mv, int pos,
3516 __isl_take isl_val *val);
3518 #include <isl/aff.h>
3519 __isl_give isl_multi_aff *isl_multi_aff_set_at(
3520 __isl_take isl_multi_aff *ma, int pos,
3521 __isl_take isl_aff *aff);
3522 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3523 __isl_take isl_multi_aff *multi, int pos,
3524 __isl_take isl_aff *aff);
3525 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_set_at(
3526 __isl_take isl_multi_pw_aff *mpa, int pos,
3527 __isl_take isl_pw_aff *pa);
3528 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_set_pw_aff(
3529 __isl_take isl_multi_pw_aff *mpa, int pos,
3530 __isl_take isl_pw_aff *pa);
3531 __isl_give isl_multi_union_pw_aff *
3532 isl_multi_union_pw_aff_set_at(
3533 __isl_take isl_multi_union_pw_aff *mupa, int pos,
3534 __isl_take isl_union_pw_aff *upa);
3535 __isl_give isl_multi_union_pw_aff *
3536 isl_multi_union_pw_aff_set_union_pw_aff(
3537 __isl_take isl_multi_union_pw_aff *mupa, int pos,
3538 __isl_take isl_union_pw_aff *upa);
3540 C<isl_multi_id_set_id> is an alternative name for C<isl_multi_id_set_at>.
3541 Similarly for the other pairs of functions.
3543 A list of all base expressions of a multiple
3544 expression can be extracted using the following functions.
3547 __isl_give isl_id_list *isl_multi_id_get_list(
3548 __isl_keep isl_multi_id *mi);
3550 #include <isl/val.h>
3551 __isl_give isl_val_list *isl_multi_val_get_list(
3552 __isl_keep isl_multi_val *mv);
3554 #include <isl/aff.h>
3555 __isl_give isl_aff_list *isl_multi_aff_get_list(
3556 __isl_keep isl_multi_aff *multi);
3557 __isl_give isl_pw_aff_list *isl_multi_pw_aff_get_list(
3558 __isl_keep isl_multi_pw_aff *mpa);
3559 __isl_give isl_union_pw_aff_list *
3560 isl_multi_union_pw_aff_list(
3561 __isl_keep isl_multi_union_pw_aff *mupa);
3563 The constant terms of the base expressions can be obtained using
3564 the following function.
3566 #include <isl/aff.h>
3567 __isl_give isl_multi_val *
3568 isl_multi_aff_get_constant_multi_val(
3569 __isl_keep isl_multi_aff *ma);
3571 As a convenience, a sequence of base expressions that have
3572 their domains in a given space can be extracted from a sequence
3573 of union expressions using the following function.
3575 #include <isl/aff.h>
3576 __isl_give isl_multi_pw_aff *
3577 isl_multi_union_pw_aff_extract_multi_pw_aff(
3578 __isl_keep isl_multi_union_pw_aff *mupa,
3579 __isl_take isl_space *space);
3581 Note that there is a difference between C<isl_multi_union_pw_aff>
3582 and C<isl_union_pw_multi_aff> objects. The first is a sequence
3583 of unions of piecewise expressions, while the second is a union
3584 of piecewise sequences. In particular, multiple affine expressions
3585 in an C<isl_union_pw_multi_aff> may live in different spaces,
3586 while there is only a single multiple expression in
3587 an C<isl_multi_union_pw_aff>, which can therefore only live
3588 in a single space. This means that not every
3589 C<isl_union_pw_multi_aff> can be converted to
3590 an C<isl_multi_union_pw_aff>. Conversely, the elements
3591 of an C<isl_multi_union_pw_aff> may be defined over different domains,
3592 while each multiple expression inside an C<isl_union_pw_multi_aff>
3593 has a single domain. The conversion of an C<isl_union_pw_multi_aff>
3594 of dimension greater than one may therefore not be exact.
3595 The following functions can
3596 be used to perform these conversions when they are possible.
3598 #include <isl/aff.h>
3599 __isl_give isl_multi_union_pw_aff *
3600 isl_union_pw_multi_aff_as_multi_union_pw_aff(
3601 __isl_take isl_union_pw_multi_aff *upma);
3602 __isl_give isl_multi_union_pw_aff *
3603 isl_multi_union_pw_aff_from_union_pw_multi_aff(
3604 __isl_take isl_union_pw_multi_aff *upma);
3605 __isl_give isl_union_pw_multi_aff *
3606 isl_union_pw_multi_aff_from_multi_union_pw_aff(
3607 __isl_take isl_multi_union_pw_aff *mupa);
3609 C<isl_union_pw_multi_aff_as_multi_union_pw_aff> and
3610 C<isl_multi_union_pw_aff_from_union_pw_multi_aff>
3611 perform the same operation.
3613 =head3 Piecewise Expressions
3615 A piecewise expression is an expression that is described
3616 using zero or more base expression defined over the same
3617 number of cells in the domain space of the base expressions.
3618 All base expressions are defined over the same
3619 domain space and the cells are disjoint.
3620 The space of a piecewise expression is the same as
3621 that of the base expressions.
3622 If the union of the cells is a strict subset of the domain
3623 space, then the value of the piecewise expression outside
3624 this union is different for types derived from quasi-affine
3625 expressions and those derived from quasipolynomials.
3626 Piecewise expressions derived from quasi-affine expressions
3627 are considered to be undefined outside the union of their cells.
3628 Piecewise expressions derived from quasipolynomials
3629 are considered to be zero outside the union of their cells.
3631 Piecewise quasipolynomials are mainly used by the C<barvinok>
3632 library for representing the number of elements in a parametric set or map.
3633 For example, the piecewise quasipolynomial
3635 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3637 represents the number of points in the map
3639 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3641 The piecewise expression types defined by C<isl>
3642 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
3643 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
3645 A piecewise expression with no cells can be created using
3646 the following functions.
3648 #include <isl/aff.h>
3649 __isl_give isl_pw_aff *isl_pw_aff_empty(
3650 __isl_take isl_space *space);
3651 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3652 __isl_take isl_space *space);
3654 A piecewise expression with a single universe cell can be
3655 created using the following functions.
3657 #include <isl/aff.h>
3658 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3659 __isl_take isl_aff *aff);
3660 __isl_give isl_pw_multi_aff *
3661 isl_multi_aff_to_pw_multi_aff(
3662 __isl_take isl_multi_aff *ma);
3663 __isl_give isl_pw_multi_aff *
3664 isl_pw_multi_aff_from_multi_aff(
3665 __isl_take isl_multi_aff *ma);
3667 #include <isl/polynomial.h>
3668 __isl_give isl_pw_qpolynomial *
3669 isl_pw_qpolynomial_from_qpolynomial(
3670 __isl_take isl_qpolynomial *qp);
3671 __isl_give isl_pw_qpolynomial_fold *
3672 isl_pw_qpolynomial_fold_from_qpolynomial_fold(
3673 __isl_take isl_qpolynomial_fold *fold);
3675 C<isl_multi_aff_to_pw_multi_aff> and C<isl_pw_multi_aff_from_multi_aff> perform
3678 The inverse conversions below can only be used if the input
3679 expression is known to be defined over a single universe domain.
3681 #include <isl/aff.h>
3682 isl_bool isl_pw_aff_isa_aff(__isl_keep isl_pw_aff *pa);
3683 __isl_give isl_aff *isl_pw_aff_as_aff(
3684 __isl_take isl_pw_aff *pa);
3685 isl_bool isl_multi_pw_aff_isa_multi_aff(
3686 __isl_keep isl_multi_pw_aff *mpa);
3687 __isl_give isl_multi_aff *isl_multi_pw_aff_as_multi_aff(
3688 __isl_take isl_multi_pw_aff *mpa);
3689 isl_bool isl_pw_multi_aff_isa_multi_aff(
3690 __isl_keep isl_pw_multi_aff *pma);
3691 __isl_give isl_multi_aff *isl_pw_multi_aff_as_multi_aff(
3692 __isl_take isl_pw_multi_aff *pma);
3694 #include <isl/polynomial.h>
3695 isl_bool isl_pw_qpolynomial_isa_qpolynomial(
3696 __isl_keep isl_pw_qpolynomial *pwqp);
3697 __isl_give isl_qpolynomial *
3698 isl_pw_qpolynomial_as_qpolynomial(
3699 __isl_take isl_pw_qpolynomial *pwqp);
3700 isl_bool isl_pw_qpolynomial_fold_isa_qpolynomial_fold(
3701 __isl_keep isl_pw_qpolynomial_fold *pwf);
3702 __isl_give isl_qpolynomial_fold *
3703 isl_pw_qpolynomial_fold_as_qpolynomial_fold(
3704 __isl_take isl_pw_qpolynomial_fold *pwf);
3706 A piecewise expression with a single specified cell can be
3707 created using the following functions.
3709 #include <isl/aff.h>
3710 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3711 __isl_take isl_set *set, __isl_take isl_aff *aff);
3712 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3713 __isl_take isl_set *set,
3714 __isl_take isl_multi_aff *maff);
3716 #include <isl/polynomial.h>
3717 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3718 __isl_take isl_set *set,
3719 __isl_take isl_qpolynomial *qp);
3721 The following convenience functions first create a base expression and
3722 then create a piecewise expression over a universe domain.
3724 #include <isl/aff.h>
3725 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3726 __isl_take isl_local_space *ls);
3727 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3728 __isl_take isl_local_space *ls,
3729 enum isl_dim_type type, unsigned pos);
3730 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain_space(
3731 __isl_take isl_space *space);
3732 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3733 __isl_take isl_local_space *ls);
3734 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
3735 __isl_take isl_space *space);
3736 __isl_give isl_pw_multi_aff *
3737 isl_pw_multi_aff_identity_on_domain_space(
3738 __isl_take isl_space *space)
3739 __isl_give isl_pw_multi_aff *
3740 isl_space_identity_pw_multi_aff_on_domain(
3741 __isl_take isl_space *space)
3742 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3743 __isl_take isl_space *space);
3744 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_domain_map(
3745 __isl_take isl_space *space);
3746 __isl_give isl_pw_multi_aff *
3747 isl_space_domain_map_pw_multi_aff(
3748 __isl_take isl_space *space);
3749 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
3750 __isl_take isl_space *space);
3751 __isl_give isl_pw_multi_aff *
3752 isl_space_range_map_pw_multi_aff(
3753 __isl_take isl_space *space);
3754 __isl_give isl_pw_multi_aff *
3755 isl_pw_multi_aff_project_out_map(
3756 __isl_take isl_space *space,
3757 enum isl_dim_type type,
3758 unsigned first, unsigned n);
3760 #include <isl/polynomial.h>
3761 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3762 __isl_take isl_space *space);
3764 C<isl_pw_multi_aff_identity_on_domain_space> and
3765 C<isl_space_identity_pw_multi_aff_on_domain>
3766 perform the same operation.
3768 for the pair C<isl_pw_multi_aff_domain_map> and
3769 C<isl_space_domain_map_pw_multi_aff> and
3770 for the pair C<isl_pw_multi_aff_range_map> and
3771 C<isl_space_range_map_pw_multi_aff>.
3773 The following convenience functions first create a base expression and
3774 then create a piecewise expression over a given domain.
3776 #include <isl/aff.h>
3777 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
3778 __isl_take isl_set *domain,
3779 __isl_take isl_val *v);
3780 __isl_give isl_pw_aff *isl_set_pw_aff_on_domain_val(
3781 __isl_take isl_set *domain,
3782 __isl_take isl_val *v);
3783 __isl_give isl_pw_multi_aff *
3784 isl_pw_multi_aff_multi_val_on_domain(
3785 __isl_take isl_set *domain,
3786 __isl_take isl_multi_val *mv);
3787 __isl_give isl_pw_multi_aff *
3788 isl_set_pw_multi_aff_on_domain_multi_val(
3789 __isl_take isl_set *domain,
3790 __isl_take isl_multi_val *mv);
3791 __isl_give isl_pw_aff *isl_pw_aff_param_on_domain_id(
3792 __isl_take isl_set *domain,
3793 __isl_take isl_id *id);
3794 __isl_give isl_pw_aff *isl_set_param_pw_aff_on_domain_id(
3795 __isl_take isl_set *domain,
3796 __isl_take isl_id *id);
3798 C<isl_set_pw_aff_on_domain_val> is an alternative name
3799 for C<isl_pw_aff_val_on_domain>.
3800 Similarly for the pair
3801 C<isl_set_pw_multi_aff_on_domain_multi_val> and
3802 C<isl_pw_multi_aff_multi_val_on_domain> and
3803 for the pair C<isl_set_param_pw_aff_on_domain_id> and
3804 C<isl_pw_aff_param_on_domain_id>.
3806 As a convenience, a piecewise multiple expression can
3807 also be created from a piecewise expression.
3808 Each multiple expression in the result is derived
3809 from the corresponding base expression.
3811 #include <isl/aff.h>
3812 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
3813 __isl_take isl_pw_aff *pa);
3815 Similarly, a piecewise quasipolynomial can be
3816 created from a piecewise quasi-affine expression using
3817 the following function.
3819 #include <isl/polynomial.h>
3820 __isl_give isl_pw_qpolynomial *
3821 isl_pw_qpolynomial_from_pw_aff(
3822 __isl_take isl_pw_aff *pwaff);
3824 Piecewise expressions can be copied and freed using the following functions.
3826 #include <isl/aff.h>
3827 __isl_give isl_pw_aff *isl_pw_aff_copy(
3828 __isl_keep isl_pw_aff *pwaff);
3829 __isl_null isl_pw_aff *isl_pw_aff_free(
3830 __isl_take isl_pw_aff *pwaff);
3831 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3832 __isl_keep isl_pw_multi_aff *pma);
3833 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
3834 __isl_take isl_pw_multi_aff *pma);
3836 #include <isl/polynomial.h>
3837 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3838 __isl_keep isl_pw_qpolynomial *pwqp);
3839 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
3840 __isl_take isl_pw_qpolynomial *pwqp);
3841 __isl_give isl_pw_qpolynomial_fold *
3842 isl_pw_qpolynomial_fold_copy(
3843 __isl_keep isl_pw_qpolynomial_fold *pwf);
3844 __isl_null isl_pw_qpolynomial_fold *
3845 isl_pw_qpolynomial_fold_free(
3846 __isl_take isl_pw_qpolynomial_fold *pwf);
3848 To iterate over the different cells of a piecewise expression,
3849 use the following functions.
3851 #include <isl/aff.h>
3852 isl_bool isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3853 isl_size isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3854 isl_stat isl_pw_aff_foreach_piece(
3855 __isl_keep isl_pw_aff *pwaff,
3856 isl_stat (*fn)(__isl_take isl_set *set,
3857 __isl_take isl_aff *aff,
3858 void *user), void *user);
3859 isl_bool isl_pw_aff_every_piece(__isl_keep isl_pw_aff *pa,
3860 isl_bool (*test)(__isl_keep isl_set *set,
3861 __isl_keep isl_aff *aff, void *user),
3863 isl_size isl_pw_multi_aff_n_piece(
3864 __isl_keep isl_pw_multi_aff *pma);
3865 isl_stat isl_pw_multi_aff_foreach_piece(
3866 __isl_keep isl_pw_multi_aff *pma,
3867 isl_stat (*fn)(__isl_take isl_set *set,
3868 __isl_take isl_multi_aff *maff,
3869 void *user), void *user);
3870 isl_bool isl_pw_multi_aff_every_piece(
3871 __isl_keep isl_pw_multi_aff *pma,
3872 isl_bool (*test)(__isl_keep isl_set *set,
3873 __isl_keep isl_multi_aff *ma, void *user),
3876 #include <isl/polynomial.h>
3877 isl_size isl_pw_qpolynomial_n_piece(
3878 __isl_keep isl_pw_qpolynomial *pwqp);
3879 isl_stat isl_pw_qpolynomial_foreach_piece(
3880 __isl_keep isl_pw_qpolynomial *pwqp,
3881 isl_stat (*fn)(__isl_take isl_set *set,
3882 __isl_take isl_qpolynomial *qp,
3883 void *user), void *user);
3884 isl_bool isl_pw_qpolynomial_every_piece(
3885 __isl_keep isl_pw_qpolynomial *pwqp,
3886 isl_bool (*test)(__isl_keep isl_set *set,
3887 __isl_keep isl_qpolynomial *qp,
3888 void *user), void *user);
3889 isl_stat isl_pw_qpolynomial_foreach_lifted_piece(
3890 __isl_keep isl_pw_qpolynomial *pwqp,
3891 isl_stat (*fn)(__isl_take isl_set *set,
3892 __isl_take isl_qpolynomial *qp,
3893 void *user), void *user);
3894 isl_size isl_pw_qpolynomial_fold_n_piece(
3895 __isl_keep isl_pw_qpolynomial_fold *pwf);
3896 isl_stat isl_pw_qpolynomial_fold_foreach_piece(
3897 __isl_keep isl_pw_qpolynomial_fold *pwf,
3898 isl_stat (*fn)(__isl_take isl_set *set,
3899 __isl_take isl_qpolynomial_fold *fold,
3900 void *user), void *user);
3901 isl_bool isl_pw_qpolynomial_fold_every_piece(
3902 __isl_keep isl_pw_qpolynomial_fold *pwf,
3903 isl_bool (*test)(__isl_keep isl_set *set,
3904 __isl_keep isl_qpolynomial_fold *fold,
3905 void *user), void *user);
3906 isl_stat isl_pw_qpolynomial_fold_foreach_lifted_piece(
3907 __isl_keep isl_pw_qpolynomial_fold *pwf,
3908 isl_stat (*fn)(__isl_take isl_set *set,
3909 __isl_take isl_qpolynomial_fold *fold,
3910 void *user), void *user);
3912 As usual, the function C<fn> should return C<isl_stat_ok> on success
3913 and C<isl_stat_error> on failure. The difference between
3914 C<isl_pw_qpolynomial_foreach_piece> and
3915 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3916 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3917 compute unique representations for all existentially quantified
3918 variables and then turn these existentially quantified variables
3919 into extra set variables, adapting the associated quasipolynomial
3920 accordingly. This means that the C<set> passed to C<fn>
3921 will not have any existentially quantified variables, but that
3922 the dimensions of the sets may be different for different
3923 invocations of C<fn>.
3924 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
3925 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
3926 The function C<isl_pw_aff_every_piece> and its variants
3927 check whether each call to the callback returns true and
3928 stop checking as soon as one of these calls returns false (or error).
3930 A piecewise expression consisting of the expressions at a given
3931 position of a piecewise multiple expression can be extracted
3932 using the following function.
3934 #include <isl/aff.h>
3935 __isl_give isl_pw_aff *isl_pw_multi_aff_get_at(
3936 __isl_keep isl_pw_multi_aff *pma, int pos);
3937 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3938 __isl_keep isl_pw_multi_aff *pma, int pos);
3940 C<isl_pw_multi_aff_get_pw_aff> is an alternative name for
3941 C<isl_pw_multi_aff_get_at>.
3943 These expressions can be replaced using the following function.
3945 #include <isl/aff.h>
3946 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3947 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3948 __isl_take isl_pw_aff *pa);
3950 Note that there is a difference between C<isl_multi_pw_aff> and
3951 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
3952 affine expressions, while the second is a piecewise sequence
3953 of affine expressions. In particular, each of the piecewise
3954 affine expressions in an C<isl_multi_pw_aff> may have a different
3955 domain, while all multiple expressions associated to a cell
3956 in an C<isl_pw_multi_aff> have the same domain.
3957 It is possible to convert between the two, but when converting
3958 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
3959 of the result is the intersection of the domains of the input.
3960 The reverse conversion is exact.
3962 #include <isl/aff.h>
3963 __isl_give isl_pw_multi_aff *
3964 isl_pw_multi_aff_from_multi_pw_aff(
3965 __isl_take isl_multi_pw_aff *mpa);
3966 __isl_give isl_multi_pw_aff *
3967 isl_pw_multi_aff_to_multi_pw_aff(
3968 __isl_take isl_pw_multi_aff *pma);
3969 __isl_give isl_multi_pw_aff *
3970 isl_multi_pw_aff_from_pw_multi_aff(
3971 __isl_take isl_pw_multi_aff *pma);
3973 C<isl_pw_multi_aff_to_multi_pw_aff> and
3974 C<isl_multi_pw_aff_from_pw_multi_aff> perform the same operation.
3976 =head3 Union Expressions
3978 A union expression collects base expressions defined
3979 over different domains. The space of a union expression
3980 is that of the shared parameter space.
3982 The union expression types defined by C<isl>
3983 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
3984 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
3986 C<isl_union_pw_aff>,
3987 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>,
3988 there can be at most one base expression for a given domain space.
3990 C<isl_union_pw_multi_aff>,
3991 there can be multiple such expressions for a given domain space,
3992 but the domains of these expressions need to be disjoint.
3994 An empty union expression can be created using the following functions.
3996 #include <isl/aff.h>
3997 __isl_give isl_union_pw_aff *
3998 isl_union_pw_aff_empty_ctx(
4000 __isl_give isl_union_pw_aff *
4001 isl_union_pw_aff_empty_space(
4002 __isl_take isl_space *space);
4003 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
4004 __isl_take isl_space *space);
4005 __isl_give isl_union_pw_multi_aff *
4006 isl_union_pw_multi_aff_empty_ctx(
4008 __isl_give isl_union_pw_multi_aff *
4009 isl_union_pw_multi_aff_empty_space(
4010 __isl_take isl_space *space);
4011 __isl_give isl_union_pw_multi_aff *
4012 isl_union_pw_multi_aff_empty(
4013 __isl_take isl_space *space);
4015 #include <isl/polynomial.h>
4016 __isl_give isl_union_pw_qpolynomial *
4017 isl_union_pw_qpolynomial_zero_ctx(
4019 __isl_give isl_union_pw_qpolynomial *
4020 isl_union_pw_qpolynomial_zero_space(
4021 __isl_take isl_space *space);
4022 __isl_give isl_union_pw_qpolynomial *
4023 isl_union_pw_qpolynomial_zero(
4024 __isl_take isl_space *space);
4026 C<isl_union_pw_aff_empty> is an alternative name for
4027 C<isl_union_pw_aff_empty_space>.
4028 Similarly for the other pairs of functions.
4030 A union expression containing a single base expression
4031 can be created using the following functions.
4033 #include <isl/aff.h>
4034 __isl_give isl_union_pw_aff *
4035 isl_pw_aff_to_union_pw_aff(
4036 __isl_take isl_pw_aff *pa);
4037 __isl_give isl_union_pw_aff *
4038 isl_union_pw_aff_from_pw_aff(
4039 __isl_take isl_pw_aff *pa);
4040 __isl_give isl_union_pw_multi_aff *
4041 isl_union_pw_multi_aff_from_aff(
4042 __isl_take isl_aff *aff);
4043 __isl_give isl_union_pw_multi_aff *
4044 isl_pw_multi_aff_to_union_pw_multi_aff(
4045 __isl_take isl_pw_multi_aff *pma);
4046 __isl_give isl_union_pw_multi_aff *
4047 isl_union_pw_multi_aff_from_pw_multi_aff(
4048 __isl_take isl_pw_multi_aff *pma);
4050 #include <isl/polynomial.h>
4051 __isl_give isl_union_pw_qpolynomial *
4052 isl_pw_qpolynomial_to_union_pw_qpolynomial(
4053 __isl_take isl_pw_qpolynomial *pwqp);
4054 __isl_give isl_union_pw_qpolynomial *
4055 isl_union_pw_qpolynomial_from_pw_qpolynomial(
4056 __isl_take isl_pw_qpolynomial *pwqp);
4057 __isl_give isl_union_pw_qpolynomial_fold *
4058 isl_pw_qpolynomial_fold_to_union_pw_qpolynomial_fold(
4059 __isl_take isl_pw_qpolynomial_fold *pwf);
4060 __isl_give isl_union_pw_qpolynomial_fold *
4061 isl_union_pw_qpolynomial_fold_from_pw_qpolynomial_fold(
4062 __isl_take isl_pw_qpolynomial_fold *pwf);
4064 C<isl_pw_aff_to_union_pw_aff> and C<isl_union_pw_aff_from_pw_aff> perform
4066 Similarly for C<isl_pw_multi_aff_to_union_pw_multi_aff> and
4067 C<isl_union_pw_multi_aff_from_pw_multi_aff>,
4069 C<isl_pw_qpolynomial_to_union_pw_qpolynomial> and
4070 C<isl_union_pw_qpolynomial_from_pw_qpolynomial>, and
4072 C<isl_pw_qpolynomial_fold_to_union_pw_qpolynomial_fold> and
4073 C<isl_union_pw_qpolynomial_fold_from_pw_qpolynomial_fold>.
4075 The inverse conversions below can only be used if the input
4076 expression is known to live in exactly one space.
4078 #include <isl/aff.h>
4079 isl_bool isl_union_pw_multi_aff_isa_pw_multi_aff(
4080 __isl_keep isl_union_pw_multi_aff *upma);
4081 __isl_give isl_pw_multi_aff *
4082 isl_union_pw_multi_aff_as_pw_multi_aff(
4083 __isl_take isl_union_pw_multi_aff *upma);
4085 A union piecewise expression containing a single base expression
4086 on a universe domain can also be created directly from
4087 a base expression using the following functions.
4089 #include <isl/aff.h>
4090 __isl_give isl_union_pw_aff *isl_union_pw_aff_from_aff(
4091 __isl_take isl_aff *aff);
4092 __isl_give isl_union_pw_multi_aff *
4093 isl_union_pw_multi_aff_from_multi_aff(
4094 __isl_take isl_multi_aff *ma);
4096 The following functions create a base expression on each
4097 of the sets in the union set and collect the results.
4099 #include <isl/aff.h>
4100 __isl_give isl_union_pw_multi_aff *
4101 isl_union_pw_multi_aff_from_union_pw_aff(
4102 __isl_take isl_union_pw_aff *upa);
4103 __isl_give isl_union_pw_aff *
4104 isl_union_pw_multi_aff_get_union_pw_aff(
4105 __isl_keep isl_union_pw_multi_aff *upma, int pos);
4106 __isl_give isl_union_pw_aff *
4107 isl_union_pw_aff_val_on_domain(
4108 __isl_take isl_union_set *domain,
4109 __isl_take isl_val *v);
4110 __isl_give isl_union_pw_multi_aff *
4111 isl_union_pw_multi_aff_multi_val_on_domain(
4112 __isl_take isl_union_set *domain,
4113 __isl_take isl_multi_val *mv);
4114 __isl_give isl_union_pw_aff *
4115 isl_union_pw_aff_param_on_domain_id(
4116 __isl_take isl_union_set *domain,
4117 __isl_take isl_id *id);
4119 The C<id> argument of C<isl_union_pw_aff_param_on_domain_id>
4120 is the identifier of a parameter that may or may not already
4121 be present in C<domain>.
4123 An C<isl_union_pw_aff> that is equal to a (parametric) affine
4125 expression on a given domain can be created using the following
4128 #include <isl/aff.h>
4129 __isl_give isl_union_pw_aff *
4130 isl_union_pw_aff_aff_on_domain(
4131 __isl_take isl_union_set *domain,
4132 __isl_take isl_aff *aff);
4133 __isl_give isl_union_pw_aff *
4134 isl_union_pw_aff_pw_aff_on_domain(
4135 __isl_take isl_union_set *domain,
4136 __isl_take isl_pw_aff *pa);
4138 A base expression can be added to a union expression using
4139 the following functions.
4141 #include <isl/aff.h>
4142 __isl_give isl_union_pw_aff *
4143 isl_union_pw_aff_add_pw_aff(
4144 __isl_take isl_union_pw_aff *upa,
4145 __isl_take isl_pw_aff *pa);
4146 __isl_give isl_union_pw_multi_aff *
4147 isl_union_pw_multi_aff_add_pw_multi_aff(
4148 __isl_take isl_union_pw_multi_aff *upma,
4149 __isl_take isl_pw_multi_aff *pma);
4151 #include <isl/polynomial.h>
4152 __isl_give isl_union_pw_qpolynomial *
4153 isl_union_pw_qpolynomial_add_pw_qpolynomial(
4154 __isl_take isl_union_pw_qpolynomial *upwqp,
4155 __isl_take isl_pw_qpolynomial *pwqp);
4157 Union expressions can be copied and freed using
4158 the following functions.
4160 #include <isl/aff.h>
4161 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
4162 __isl_keep isl_union_pw_aff *upa);
4163 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
4164 __isl_take isl_union_pw_aff *upa);
4165 __isl_give isl_union_pw_multi_aff *
4166 isl_union_pw_multi_aff_copy(
4167 __isl_keep isl_union_pw_multi_aff *upma);
4168 __isl_null isl_union_pw_multi_aff *
4169 isl_union_pw_multi_aff_free(
4170 __isl_take isl_union_pw_multi_aff *upma);
4172 #include <isl/polynomial.h>
4173 __isl_give isl_union_pw_qpolynomial *
4174 isl_union_pw_qpolynomial_copy(
4175 __isl_keep isl_union_pw_qpolynomial *upwqp);
4176 __isl_null isl_union_pw_qpolynomial *
4177 isl_union_pw_qpolynomial_free(
4178 __isl_take isl_union_pw_qpolynomial *upwqp);
4179 __isl_give isl_union_pw_qpolynomial_fold *
4180 isl_union_pw_qpolynomial_fold_copy(
4181 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4182 __isl_null isl_union_pw_qpolynomial_fold *
4183 isl_union_pw_qpolynomial_fold_free(
4184 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4186 To iterate over the base expressions in a union expression,
4187 use the following functions.
4189 #include <isl/aff.h>
4190 isl_size isl_union_pw_aff_n_pw_aff(
4191 __isl_keep isl_union_pw_aff *upa);
4192 isl_stat isl_union_pw_aff_foreach_pw_aff(
4193 __isl_keep isl_union_pw_aff *upa,
4194 isl_stat (*fn)(__isl_take isl_pw_aff *pa,
4195 void *user), void *user);
4196 isl_bool isl_union_pw_aff_every_pw_aff(
4197 __isl_keep isl_union_pw_aff *upa,
4198 isl_bool (*test)(__isl_keep isl_pw_aff *pa,
4199 void *user), void *user);
4200 isl_size isl_union_pw_multi_aff_n_pw_multi_aff(
4201 __isl_keep isl_union_pw_multi_aff *upma);
4202 isl_stat isl_union_pw_multi_aff_foreach_pw_multi_aff(
4203 __isl_keep isl_union_pw_multi_aff *upma,
4204 isl_stat (*fn)(__isl_take isl_pw_multi_aff *pma,
4205 void *user), void *user);
4206 isl_bool isl_union_pw_multi_aff_every_pw_multi_aff(
4207 __isl_keep isl_union_pw_multi_aff *upma,
4209 __isl_keep isl_pw_multi_aff *pma,
4210 void *user), void *user);
4212 #include <isl/polynomial.h>
4213 isl_size isl_union_pw_qpolynomial_n_pw_qpolynomial(
4214 __isl_keep isl_union_pw_qpolynomial *upwqp);
4215 isl_stat isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4216 __isl_keep isl_union_pw_qpolynomial *upwqp,
4217 isl_stat (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
4218 void *user), void *user);
4219 isl_bool isl_union_pw_qpolynomial_every_pw_qpolynomial(
4220 __isl_keep isl_union_pw_qpolynomial *upwqp,
4222 __isl_keep isl_pw_qpolynomial *pwqp,
4223 void *user), void *user);
4224 isl_size isl_union_pw_qpolynomial_fold_n_pw_qpolynomial_fold(
4225 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4226 isl_stat isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4227 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4228 isl_stat (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4229 void *user), void *user);
4231 isl_union_pw_qpolynomial_fold_every_pw_qpolynomial_fold(
4232 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4234 __isl_keep isl_pw_qpolynomial_fold *pwf,
4235 void *user), void *user);
4237 To extract the base expression in a given space from a union, use
4238 the following functions.
4240 #include <isl/aff.h>
4241 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
4242 __isl_keep isl_union_pw_aff *upa,
4243 __isl_take isl_space *space);
4244 __isl_give isl_pw_multi_aff *
4245 isl_union_pw_multi_aff_extract_pw_multi_aff(
4246 __isl_keep isl_union_pw_multi_aff *upma,
4247 __isl_take isl_space *space);
4249 #include <isl/polynomial.h>
4250 __isl_give isl_pw_qpolynomial *
4251 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4252 __isl_keep isl_union_pw_qpolynomial *upwqp,
4253 __isl_take isl_space *space);
4255 It is also possible to obtain a list of the base expressions using
4256 the following functions.
4258 #include <isl/aff.h>
4259 __isl_give isl_pw_aff_list *
4260 isl_union_pw_aff_get_pw_aff_list(
4261 __isl_keep isl_union_pw_aff *upa);
4262 __isl_give isl_pw_multi_aff_list *
4263 isl_union_pw_multi_aff_get_pw_multi_aff_list(
4264 __isl_keep isl_union_pw_multi_aff *upma);
4266 #include <isl/polynomial.h>
4267 __isl_give isl_pw_qpolynomial_list *
4268 isl_union_pw_qpolynomial_get_pw_qpolynomial_list(
4269 __isl_keep isl_union_pw_qpolynomial *upwqp);
4270 __isl_give isl_pw_qpolynomial_fold_list *
4271 isl_union_pw_qpolynomial_fold_get_pw_qpolynomial_fold_list(
4272 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4274 The returned list can be manipulated using the functions in L<"Lists">.
4276 =head2 Input and Output
4278 For set and relation,
4279 C<isl> supports its own input/output format, which is similar
4280 to the C<Omega> format, but also supports the C<PolyLib> format
4282 For other object types, typically only an C<isl> format is supported.
4284 =head3 C<isl> format
4286 The C<isl> format is similar to that of C<Omega>, but has a different
4287 syntax for describing the parameters and allows for the definition
4288 of an existentially quantified variable as the integer division
4289 of an affine expression.
4290 For example, the set of integers C<i> between C<0> and C<n>
4291 such that C<i % 10 <= 6> can be described as
4293 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
4296 A set or relation can have several disjuncts, separated
4297 by the keyword C<or>. Each disjunct is either a conjunction
4298 of constraints or a projection (C<exists>) of a conjunction
4299 of constraints. The constraints are separated by the keyword
4302 =head3 C<PolyLib> format
4304 If the represented set is a union, then the first line
4305 contains a single number representing the number of disjuncts.
4306 Otherwise, a line containing the number C<1> is optional.
4308 Each disjunct is represented by a matrix of constraints.
4309 The first line contains two numbers representing
4310 the number of rows and columns,
4311 where the number of rows is equal to the number of constraints
4312 and the number of columns is equal to two plus the number of variables.
4313 The following lines contain the actual rows of the constraint matrix.
4314 In each row, the first column indicates whether the constraint
4315 is an equality (C<0>) or inequality (C<1>). The final column
4316 corresponds to the constant term.
4318 If the set is parametric, then the coefficients of the parameters
4319 appear in the last columns before the constant column.
4320 The coefficients of any existentially quantified variables appear
4321 between those of the set variables and those of the parameters.
4323 =head3 Extended C<PolyLib> format
4325 The extended C<PolyLib> format is nearly identical to the
4326 C<PolyLib> format. The only difference is that the line
4327 containing the number of rows and columns of a constraint matrix
4328 also contains four additional numbers:
4329 the number of output dimensions, the number of input dimensions,
4330 the number of local dimensions (i.e., the number of existentially
4331 quantified variables) and the number of parameters.
4332 For sets, the number of ``output'' dimensions is equal
4333 to the number of set dimensions, while the number of ``input''
4338 Objects can be read from input using the following functions.
4341 __isl_give isl_id *isl_id_read_from_str(isl_ctx *ctx,
4343 __isl_give isl_multi_id *isl_multi_id_read_from_str(
4344 isl_ctx *ctx, const char *str);
4346 #include <isl/val.h>
4347 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
4349 __isl_give isl_multi_val *isl_multi_val_read_from_str(
4350 isl_ctx *ctx, const char *str);
4352 #include <isl/space.h>
4353 __isl_give isl_space *isl_space_read_from_str(
4354 isl_ctx *ctx, const char *str);
4356 #include <isl/set.h>
4357 __isl_give isl_basic_set *isl_basic_set_read_from_file(
4358 isl_ctx *ctx, FILE *input);
4359 __isl_give isl_basic_set *isl_basic_set_read_from_str(
4360 isl_ctx *ctx, const char *str);
4361 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
4363 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
4366 #include <isl/map.h>
4367 __isl_give isl_basic_map *isl_basic_map_read_from_file(
4368 isl_ctx *ctx, FILE *input);
4369 __isl_give isl_basic_map *isl_basic_map_read_from_str(
4370 isl_ctx *ctx, const char *str);
4371 __isl_give isl_map *isl_map_read_from_file(
4372 isl_ctx *ctx, FILE *input);
4373 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
4376 #include <isl/union_set.h>
4377 __isl_give isl_union_set *isl_union_set_read_from_file(
4378 isl_ctx *ctx, FILE *input);
4379 __isl_give isl_union_set *isl_union_set_read_from_str(
4380 isl_ctx *ctx, const char *str);
4382 #include <isl/union_map.h>
4383 __isl_give isl_union_map *isl_union_map_read_from_file(
4384 isl_ctx *ctx, FILE *input);
4385 __isl_give isl_union_map *isl_union_map_read_from_str(
4386 isl_ctx *ctx, const char *str);
4388 #include <isl/aff.h>
4389 __isl_give isl_aff *isl_aff_read_from_str(
4390 isl_ctx *ctx, const char *str);
4391 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4392 isl_ctx *ctx, const char *str);
4393 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
4394 isl_ctx *ctx, const char *str);
4395 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4396 isl_ctx *ctx, const char *str);
4397 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
4398 isl_ctx *ctx, const char *str);
4399 __isl_give isl_union_pw_aff *
4400 isl_union_pw_aff_read_from_str(
4401 isl_ctx *ctx, const char *str);
4402 __isl_give isl_union_pw_multi_aff *
4403 isl_union_pw_multi_aff_read_from_str(
4404 isl_ctx *ctx, const char *str);
4405 __isl_give isl_multi_union_pw_aff *
4406 isl_multi_union_pw_aff_read_from_str(
4407 isl_ctx *ctx, const char *str);
4409 #include <isl/polynomial.h>
4410 __isl_give isl_union_pw_qpolynomial *
4411 isl_union_pw_qpolynomial_read_from_str(
4412 isl_ctx *ctx, const char *str);
4414 __isl_give isl_pw_qpolynomial_fold *
4415 isl_pw_qpolynomial_fold_read_from_str(
4416 isl_ctx *ctx, const char *str);
4418 For sets and relations,
4419 the input format is autodetected and may be either the C<PolyLib> format
4420 or the C<isl> format.
4424 Before anything can be printed, an C<isl_printer> needs to
4427 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
4429 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
4430 __isl_null isl_printer *isl_printer_free(
4431 __isl_take isl_printer *printer);
4433 C<isl_printer_to_file> prints to the given file, while
4434 C<isl_printer_to_str> prints to a string that can be extracted
4435 using the following function.
4437 #include <isl/printer.h>
4438 __isl_give char *isl_printer_get_str(
4439 __isl_keep isl_printer *printer);
4441 The printer can be inspected using the following functions.
4443 FILE *isl_printer_get_file(
4444 __isl_keep isl_printer *printer);
4445 int isl_printer_get_output_format(
4446 __isl_keep isl_printer *p);
4447 int isl_printer_get_yaml_style(__isl_keep isl_printer *p);
4449 The behavior of the printer can be modified in various ways
4451 __isl_give isl_printer *isl_printer_set_output_format(
4452 __isl_take isl_printer *p, int output_format);
4453 __isl_give isl_printer *isl_printer_set_indent(
4454 __isl_take isl_printer *p, int indent);
4455 __isl_give isl_printer *isl_printer_set_indent_prefix(
4456 __isl_take isl_printer *p, const char *prefix);
4457 __isl_give isl_printer *isl_printer_indent(
4458 __isl_take isl_printer *p, int indent);
4459 __isl_give isl_printer *isl_printer_set_prefix(
4460 __isl_take isl_printer *p, const char *prefix);
4461 __isl_give isl_printer *isl_printer_set_suffix(
4462 __isl_take isl_printer *p, const char *suffix);
4463 __isl_give isl_printer *isl_printer_set_yaml_style(
4464 __isl_take isl_printer *p, int yaml_style);
4466 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
4467 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
4468 and defaults to C<ISL_FORMAT_ISL>.
4469 Each line in the output is prefixed by C<indent_prefix>,
4470 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
4471 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
4472 In the C<PolyLib> format output,
4473 the coefficients of the existentially quantified variables
4474 appear between those of the set variables and those
4476 The function C<isl_printer_indent> increases the indentation
4477 by the specified amount (which may be negative).
4478 The YAML style may be either C<ISL_YAML_STYLE_BLOCK> or
4479 C<ISL_YAML_STYLE_FLOW> and when we are printing something
4482 To actually print something, use
4484 #include <isl/printer.h>
4485 __isl_give isl_printer *isl_printer_print_double(
4486 __isl_take isl_printer *p, double d);
4488 #include <isl/val.h>
4489 __isl_give isl_printer *isl_printer_print_val(
4490 __isl_take isl_printer *p, __isl_keep isl_val *v);
4491 __isl_give isl_printer *isl_printer_print_multi_val(
4492 __isl_take isl_printer *p,
4493 __isl_keep isl_multi_val *mv);
4495 #include <isl/set.h>
4496 __isl_give isl_printer *isl_printer_print_basic_set(
4497 __isl_take isl_printer *printer,
4498 __isl_keep isl_basic_set *bset);
4499 __isl_give isl_printer *isl_printer_print_set(
4500 __isl_take isl_printer *printer,
4501 __isl_keep isl_set *set);
4503 #include <isl/map.h>
4504 __isl_give isl_printer *isl_printer_print_basic_map(
4505 __isl_take isl_printer *printer,
4506 __isl_keep isl_basic_map *bmap);
4507 __isl_give isl_printer *isl_printer_print_map(
4508 __isl_take isl_printer *printer,
4509 __isl_keep isl_map *map);
4511 #include <isl/union_set.h>
4512 __isl_give isl_printer *isl_printer_print_union_set(
4513 __isl_take isl_printer *p,
4514 __isl_keep isl_union_set *uset);
4516 #include <isl/union_map.h>
4517 __isl_give isl_printer *isl_printer_print_union_map(
4518 __isl_take isl_printer *p,
4519 __isl_keep isl_union_map *umap);
4522 __isl_give isl_printer *isl_printer_print_multi_id(
4523 __isl_take isl_printer *p,
4524 __isl_keep isl_multi_id *mi);
4526 #include <isl/aff.h>
4527 __isl_give isl_printer *isl_printer_print_aff(
4528 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
4529 __isl_give isl_printer *isl_printer_print_multi_aff(
4530 __isl_take isl_printer *p,
4531 __isl_keep isl_multi_aff *maff);
4532 __isl_give isl_printer *isl_printer_print_pw_aff(
4533 __isl_take isl_printer *p,
4534 __isl_keep isl_pw_aff *pwaff);
4535 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4536 __isl_take isl_printer *p,
4537 __isl_keep isl_pw_multi_aff *pma);
4538 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4539 __isl_take isl_printer *p,
4540 __isl_keep isl_multi_pw_aff *mpa);
4541 __isl_give isl_printer *isl_printer_print_union_pw_aff(
4542 __isl_take isl_printer *p,
4543 __isl_keep isl_union_pw_aff *upa);
4544 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4545 __isl_take isl_printer *p,
4546 __isl_keep isl_union_pw_multi_aff *upma);
4547 __isl_give isl_printer *
4548 isl_printer_print_multi_union_pw_aff(
4549 __isl_take isl_printer *p,
4550 __isl_keep isl_multi_union_pw_aff *mupa);
4552 #include <isl/polynomial.h>
4553 __isl_give isl_printer *isl_printer_print_qpolynomial(
4554 __isl_take isl_printer *p,
4555 __isl_keep isl_qpolynomial *qp);
4556 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4557 __isl_take isl_printer *p,
4558 __isl_keep isl_pw_qpolynomial *pwqp);
4559 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4560 __isl_take isl_printer *p,
4561 __isl_keep isl_union_pw_qpolynomial *upwqp);
4563 __isl_give isl_printer *
4564 isl_printer_print_pw_qpolynomial_fold(
4565 __isl_take isl_printer *p,
4566 __isl_keep isl_pw_qpolynomial_fold *pwf);
4567 __isl_give isl_printer *
4568 isl_printer_print_union_pw_qpolynomial_fold(
4569 __isl_take isl_printer *p,
4570 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4572 For C<isl_printer_print_qpolynomial>,
4573 C<isl_printer_print_pw_qpolynomial> and
4574 C<isl_printer_print_pw_qpolynomial_fold>,
4575 the output format of the printer
4576 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4577 For C<isl_printer_print_union_pw_qpolynomial> and
4578 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
4580 In case of printing in C<ISL_FORMAT_C>, the user may want
4581 to set the names of all dimensions first.
4583 C<isl> also provides limited support for printing YAML documents,
4584 just enough for the internal use for printing such documents.
4586 #include <isl/printer.h>
4587 __isl_give isl_printer *isl_printer_yaml_start_mapping(
4588 __isl_take isl_printer *p);
4589 __isl_give isl_printer *isl_printer_yaml_end_mapping(
4590 __isl_take isl_printer *p);
4591 __isl_give isl_printer *isl_printer_yaml_start_sequence(
4592 __isl_take isl_printer *p);
4593 __isl_give isl_printer *isl_printer_yaml_end_sequence(
4594 __isl_take isl_printer *p);
4595 __isl_give isl_printer *isl_printer_yaml_next(
4596 __isl_take isl_printer *p);
4598 A document is started by a call to either
4599 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
4600 Anything printed to the printer after such a call belong to the
4601 first key of the mapping or the first element in the sequence.
4602 The function C<isl_printer_yaml_next> moves to the value if
4603 we are currently printing a mapping key, the next key if we
4604 are printing a value or the next element if we are printing
4605 an element in a sequence.
4606 Nested mappings and sequences are initiated by the same
4607 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
4608 Each call to these functions needs to have a corresponding call to
4609 C<isl_printer_yaml_end_mapping> or C<isl_printer_yaml_end_sequence>.
4611 When called on a file printer, the following function flushes
4612 the file. When called on a string printer, the buffer is cleared.
4614 __isl_give isl_printer *isl_printer_flush(
4615 __isl_take isl_printer *p);
4617 The following functions allow the user to attach
4618 notes to a printer in order to keep track of additional state.
4620 #include <isl/printer.h>
4621 isl_bool isl_printer_has_note(__isl_keep isl_printer *p,
4622 __isl_keep isl_id *id);
4623 __isl_give isl_id *isl_printer_get_note(
4624 __isl_keep isl_printer *p, __isl_take isl_id *id);
4625 __isl_give isl_printer *isl_printer_set_note(
4626 __isl_take isl_printer *p,
4627 __isl_take isl_id *id, __isl_take isl_id *note);
4629 C<isl_printer_set_note> associates the given note to the given
4630 identifier in the printer.
4631 C<isl_printer_get_note> retrieves a note associated to an
4633 C<isl_printer_has_note> checks if there is such a note.
4634 C<isl_printer_get_note> fails if the requested note does not exist.
4636 Alternatively, a string representation can be obtained
4637 directly using the following functions, which always print
4641 __isl_give char *isl_id_to_str(
4642 __isl_keep isl_id *id);
4643 __isl_give char *isl_multi_id_to_str(
4644 __isl_keep isl_multi_id *mi);
4646 #include <isl/space.h>
4647 __isl_give char *isl_space_to_str(
4648 __isl_keep isl_space *space);
4650 #include <isl/val.h>
4651 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
4652 __isl_give char *isl_multi_val_to_str(
4653 __isl_keep isl_multi_val *mv);
4655 #include <isl/set.h>
4656 __isl_give char *isl_basic_set_to_str(
4657 __isl_keep isl_basic_set *bset);
4658 __isl_give char *isl_set_to_str(
4659 __isl_keep isl_set *set);
4661 #include <isl/union_set.h>
4662 __isl_give char *isl_union_set_to_str(
4663 __isl_keep isl_union_set *uset);
4665 #include <isl/map.h>
4666 __isl_give char *isl_basic_map_to_str(
4667 __isl_keep isl_basic_map *bmap);
4668 __isl_give char *isl_map_to_str(
4669 __isl_keep isl_map *map);
4671 #include <isl/union_map.h>
4672 __isl_give char *isl_union_map_to_str(
4673 __isl_keep isl_union_map *umap);
4675 #include <isl/aff.h>
4676 __isl_give char *isl_aff_to_str(__isl_keep isl_aff *aff);
4677 __isl_give char *isl_pw_aff_to_str(
4678 __isl_keep isl_pw_aff *pa);
4679 __isl_give char *isl_multi_aff_to_str(
4680 __isl_keep isl_multi_aff *ma);
4681 __isl_give char *isl_pw_multi_aff_to_str(
4682 __isl_keep isl_pw_multi_aff *pma);
4683 __isl_give char *isl_multi_pw_aff_to_str(
4684 __isl_keep isl_multi_pw_aff *mpa);
4685 __isl_give char *isl_union_pw_aff_to_str(
4686 __isl_keep isl_union_pw_aff *upa);
4687 __isl_give char *isl_union_pw_multi_aff_to_str(
4688 __isl_keep isl_union_pw_multi_aff *upma);
4689 __isl_give char *isl_multi_union_pw_aff_to_str(
4690 __isl_keep isl_multi_union_pw_aff *mupa);
4692 #include <isl/point.h>
4693 __isl_give char *isl_point_to_str(
4694 __isl_keep isl_point *pnt);
4696 #include <isl/polynomial.h>
4697 __isl_give char *isl_pw_qpolynomial_to_str(
4698 __isl_keep isl_pw_qpolynomial *pwqp);
4699 __isl_give char *isl_union_pw_qpolynomial_to_str(
4700 __isl_keep isl_union_pw_qpolynomial *upwqp);
4704 =head3 Unary Properties
4710 The following functions test whether the given set or relation
4711 contains any integer points. The ``plain'' variants do not perform
4712 any computations, but simply check if the given set or relation
4713 is already known to be empty.
4715 #include <isl/set.h>
4716 isl_bool isl_basic_set_plain_is_empty(
4717 __isl_keep isl_basic_set *bset);
4718 isl_bool isl_basic_set_is_empty(
4719 __isl_keep isl_basic_set *bset);
4720 isl_bool isl_set_plain_is_empty(
4721 __isl_keep isl_set *set);
4722 isl_bool isl_set_is_empty(__isl_keep isl_set *set);
4724 #include <isl/union_set.h>
4725 isl_bool isl_union_set_is_empty(
4726 __isl_keep isl_union_set *uset);
4728 #include <isl/map.h>
4729 isl_bool isl_basic_map_plain_is_empty(
4730 __isl_keep isl_basic_map *bmap);
4731 isl_bool isl_basic_map_is_empty(
4732 __isl_keep isl_basic_map *bmap);
4733 isl_bool isl_map_plain_is_empty(
4734 __isl_keep isl_map *map);
4735 isl_bool isl_map_is_empty(__isl_keep isl_map *map);
4737 #include <isl/union_map.h>
4738 isl_bool isl_union_map_plain_is_empty(
4739 __isl_keep isl_union_map *umap);
4740 isl_bool isl_union_map_is_empty(
4741 __isl_keep isl_union_map *umap);
4743 #include <isl/aff.h>
4744 isl_bool isl_union_pw_multi_aff_plain_is_empty(
4745 __isl_keep isl_union_pw_multi_aff *upma);
4747 =item * Universality
4749 isl_bool isl_basic_set_plain_is_universe(
4750 __isl_keep isl_basic_set *bset);
4751 isl_bool isl_basic_set_is_universe(
4752 __isl_keep isl_basic_set *bset);
4753 isl_bool isl_basic_map_plain_is_universe(
4754 __isl_keep isl_basic_map *bmap);
4755 isl_bool isl_basic_map_is_universe(
4756 __isl_keep isl_basic_map *bmap);
4757 isl_bool isl_set_plain_is_universe(
4758 __isl_keep isl_set *set);
4759 isl_bool isl_map_plain_is_universe(
4760 __isl_keep isl_map *map);
4762 =item * Single-valuedness
4764 #include <isl/set.h>
4765 isl_bool isl_set_is_singleton(__isl_keep isl_set *set);
4767 #include <isl/map.h>
4768 isl_bool isl_basic_map_is_single_valued(
4769 __isl_keep isl_basic_map *bmap);
4770 isl_bool isl_map_plain_is_single_valued(
4771 __isl_keep isl_map *map);
4772 isl_bool isl_map_is_single_valued(__isl_keep isl_map *map);
4774 #include <isl/union_map.h>
4775 isl_bool isl_union_map_is_single_valued(
4776 __isl_keep isl_union_map *umap);
4780 isl_bool isl_map_plain_is_injective(
4781 __isl_keep isl_map *map);
4782 isl_bool isl_map_is_injective(
4783 __isl_keep isl_map *map);
4784 isl_bool isl_union_map_plain_is_injective(
4785 __isl_keep isl_union_map *umap);
4786 isl_bool isl_union_map_is_injective(
4787 __isl_keep isl_union_map *umap);
4791 isl_bool isl_map_is_bijective(
4792 __isl_keep isl_map *map);
4793 isl_bool isl_union_map_is_bijective(
4794 __isl_keep isl_union_map *umap);
4798 The following functions test whether the given relation
4799 only maps elements to themselves.
4801 #include <isl/map.h>
4802 isl_bool isl_map_is_identity(
4803 __isl_keep isl_map *map);
4805 #include <isl/union_map.h>
4806 isl_bool isl_union_map_is_identity(
4807 __isl_keep isl_union_map *umap);
4811 __isl_give isl_val *
4812 isl_basic_map_plain_get_val_if_fixed(
4813 __isl_keep isl_basic_map *bmap,
4814 enum isl_dim_type type, unsigned pos);
4815 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
4816 __isl_keep isl_set *set,
4817 enum isl_dim_type type, unsigned pos);
4818 __isl_give isl_multi_val *
4819 isl_set_get_plain_multi_val_if_fixed(
4820 __isl_keep isl_set *set);
4821 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
4822 __isl_keep isl_map *map,
4823 enum isl_dim_type type, unsigned pos);
4825 If the set or relation obviously lies on a hyperplane where the given dimension
4826 has a fixed value, then return that value.
4827 Otherwise return NaN.
4828 C<isl_set_get_plain_multi_val_if_fixed> collects the results over
4833 Stride detection is based on heuristics.
4834 The strides returned by the functions below are always valid,
4835 but there may be larger valid strides that are not detected.
4837 isl_stat isl_set_dim_residue_class_val(
4838 __isl_keep isl_set *set,
4839 int pos, __isl_give isl_val **modulo,
4840 __isl_give isl_val **residue);
4842 Check if the values of the given set dimension are equal to a fixed
4843 value modulo some integer value. If so, assign the modulo to C<*modulo>
4844 and the fixed value to C<*residue>. If the given dimension attains only
4845 a single value, then assign C<0> to C<*modulo> and the fixed value to
4847 If the dimension does not attain only a single value and if no modulo
4848 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
4850 #include <isl/set.h>
4851 __isl_give isl_stride_info *isl_set_get_stride_info(
4852 __isl_keep isl_set *set, int pos);
4853 __isl_give isl_val *isl_set_get_stride(
4854 __isl_keep isl_set *set, int pos);
4855 __isl_give isl_fixed_box *isl_set_get_lattice_tile(
4856 __isl_keep isl_set *set);
4858 #include <isl/map.h>
4859 __isl_give isl_stride_info *
4860 isl_map_get_range_stride_info(
4861 __isl_keep isl_map *map, int pos);
4862 __isl_give isl_fixed_box *
4863 isl_map_get_range_lattice_tile(
4864 __isl_keep isl_map *map);
4866 Check if the values of the given set dimension are equal to
4867 some affine expression of the other dimensions (the offset)
4868 modulo some integer stride or
4869 check if the values of the given output dimensions are equal to
4870 some affine expression of the input dimensions (the offset)
4871 modulo some integer stride.
4872 If no more specific information can be found, then the stride
4873 is taken to be one and the offset is taken to be the zero expression.
4874 The function C<isl_set_get_stride> performs the same
4875 computation as C<isl_set_get_stride_info> but only returns the stride.
4876 The function C<isl_map_get_range_lattice_tile> collects the stride
4877 information over all output dimensions.
4878 In particular, it returns a tile of a rectangular lattice
4879 (possibly of size 1 in all directions)
4880 containing the output in terms of the parameters and the input dimensions.
4881 The size and the offset of this tile correspond to
4882 the strides and the offsets of the stride information and
4883 can be extracted from the returned
4884 C<isl_fixed_box> using the functions described under "Box hull" in
4885 L</"Unary Operations">. Note that the C<isl_fixed_box> object returned by
4886 C<isl_map_get_range_lattice_tile> is always valid.
4887 The function C<isl_set_get_lattice_tile> collects the same stride
4888 information over all set dimensions.
4889 For the other functions,
4890 the stride and offset can be extracted from the returned object
4891 using the following functions.
4893 #include <isl/stride_info.h>
4894 __isl_give isl_val *isl_stride_info_get_stride(
4895 __isl_keep isl_stride_info *si);
4896 __isl_give isl_aff *isl_stride_info_get_offset(
4897 __isl_keep isl_stride_info *si);
4899 The stride info object can be copied and released using the following
4902 #include <isl/stride_info.h>
4903 __isl_give isl_stride_info *isl_stride_info_copy(
4904 __isl_keep isl_stride_info *si);
4905 __isl_null isl_stride_info *isl_stride_info_free(
4906 __isl_take isl_stride_info *si);
4910 To check whether a function involves any local variables,
4911 i.e., integer divisions,
4912 the following functions can be used.
4914 #include <isl/set.h>
4915 isl_bool isl_set_involves_locals(
4916 __isl_keep isl_set *set);
4918 #include <isl/aff.h>
4919 isl_bool isl_aff_involves_locals(
4920 __isl_keep isl_aff *aff);
4921 isl_bool isl_multi_aff_involves_locals(
4922 __isl_keep isl_multi_aff *ma);
4923 isl_bool isl_pw_multi_aff_involves_locals(
4924 __isl_keep isl_pw_multi_aff *pma);
4925 isl_bool isl_union_pw_multi_aff_involves_locals(
4926 __isl_keep isl_union_pw_multi_aff *upma);
4928 To check whether the description of a set, relation or function depends
4929 on a parameter or one or more given dimensions,
4930 the following functions can be used.
4932 #include <isl/constraint.h>
4933 isl_bool isl_constraint_involves_dims(
4934 __isl_keep isl_constraint *constraint,
4935 enum isl_dim_type type, unsigned first, unsigned n);
4937 #include <isl/set.h>
4938 isl_bool isl_basic_set_involves_dims(
4939 __isl_keep isl_basic_set *bset,
4940 enum isl_dim_type type, unsigned first, unsigned n);
4941 isl_bool isl_set_involves_dims(__isl_keep isl_set *set,
4942 enum isl_dim_type type, unsigned first, unsigned n);
4944 #include <isl/map.h>
4945 isl_bool isl_basic_map_involves_dims(
4946 __isl_keep isl_basic_map *bmap,
4947 enum isl_dim_type type, unsigned first, unsigned n);
4948 isl_bool isl_map_involves_dims(__isl_keep isl_map *map,
4949 enum isl_dim_type type, unsigned first, unsigned n);
4951 #include <isl/union_map.h>
4952 isl_bool isl_union_map_involves_dims(
4953 __isl_keep isl_union_map *umap,
4954 enum isl_dim_type type, unsigned first, unsigned n);
4956 #include <isl/aff.h>
4957 isl_bool isl_aff_involves_dims(__isl_keep isl_aff *aff,
4958 enum isl_dim_type type, unsigned first, unsigned n);
4959 isl_bool isl_pw_aff_involves_param_id(
4960 __isl_keep isl_pw_aff *pa,
4961 __isl_keep isl_id *id);
4962 isl_bool isl_pw_aff_involves_dims(
4963 __isl_keep isl_pw_aff *pwaff,
4964 enum isl_dim_type type, unsigned first, unsigned n);
4965 isl_bool isl_multi_aff_involves_dims(
4966 __isl_keep isl_multi_aff *ma,
4967 enum isl_dim_type type, unsigned first, unsigned n);
4968 isl_bool isl_pw_multi_aff_involves_param_id(
4969 __isl_keep isl_pw_multi_aff *pma,
4970 __isl_keep isl_id *id);
4971 isl_bool isl_pw_multi_aff_involves_dims(
4972 __isl_keep isl_pw_multi_aff *pma,
4973 enum isl_dim_type type, unsigned first, unsigned n);
4974 isl_bool isl_multi_pw_aff_involves_dims(
4975 __isl_keep isl_multi_pw_aff *mpa,
4976 enum isl_dim_type type, unsigned first, unsigned n);
4977 isl_bool isl_multi_pw_aff_involves_param_id(
4978 __isl_keep isl_multi_pw_aff *mpa,
4979 __isl_keep isl_id *id);
4980 isl_bool isl_multi_pw_aff_involves_param_id_list(
4981 __isl_keep isl_multi_pw_aff *mpa,
4982 __isl_keep isl_id_list *list);
4984 #include <isl/polynomial.h>
4985 isl_bool isl_qpolynomial_involves_dims(
4986 __isl_keep isl_qpolynomial *qp,
4987 enum isl_dim_type type, unsigned first, unsigned n);
4988 isl_bool isl_pw_qpolynomial_involves_param_id(
4989 __isl_keep isl_pw_qpolynomial *pwqp,
4990 __isl_keep isl_id *id);
4991 isl_bool isl_pw_qpolynomial_fold_involves_param_id(
4992 __isl_keep isl_pw_qpolynomial_fold *pwf,
4993 __isl_keep isl_id *id);
4995 Similarly, the following functions can be used to check whether
4996 a given dimension is involved in any lower or upper bound.
4998 #include <isl/set.h>
4999 isl_bool isl_set_dim_has_any_lower_bound(
5000 __isl_keep isl_set *set,
5001 enum isl_dim_type type, unsigned pos);
5002 isl_bool isl_set_dim_has_any_upper_bound(
5003 __isl_keep isl_set *set,
5004 enum isl_dim_type type, unsigned pos);
5006 Note that these functions return true even if there is a bound on
5007 the dimension on only some of the basic sets of C<set>.
5008 To check if they have a bound for all of the basic sets in C<set>,
5009 use the following functions instead.
5011 #include <isl/set.h>
5012 isl_bool isl_set_dim_has_lower_bound(
5013 __isl_keep isl_set *set,
5014 enum isl_dim_type type, unsigned pos);
5015 isl_bool isl_set_dim_has_upper_bound(
5016 __isl_keep isl_set *set,
5017 enum isl_dim_type type, unsigned pos);
5021 To check whether a set is a parameter domain, use this function:
5023 isl_bool isl_set_is_params(__isl_keep isl_set *set);
5024 isl_bool isl_union_set_is_params(
5025 __isl_keep isl_union_set *uset);
5029 The following functions check whether the space of the given
5030 (basic) set or relation domain and/or range is a wrapped relation.
5032 #include <isl/space.h>
5033 isl_bool isl_space_is_wrapping(
5034 __isl_keep isl_space *space);
5035 isl_bool isl_space_domain_is_wrapping(
5036 __isl_keep isl_space *space);
5037 isl_bool isl_space_range_is_wrapping(
5038 __isl_keep isl_space *space);
5039 isl_bool isl_space_is_product(
5040 __isl_keep isl_space *space);
5042 #include <isl/set.h>
5043 isl_bool isl_basic_set_is_wrapping(
5044 __isl_keep isl_basic_set *bset);
5045 isl_bool isl_set_is_wrapping(__isl_keep isl_set *set);
5047 #include <isl/map.h>
5048 isl_bool isl_map_domain_is_wrapping(
5049 __isl_keep isl_map *map);
5050 isl_bool isl_map_range_is_wrapping(
5051 __isl_keep isl_map *map);
5052 isl_bool isl_map_is_product(__isl_keep isl_map *map);
5055 isl_bool isl_multi_id_range_is_wrapping(
5056 __isl_keep isl_multi_id *mi);
5058 #include <isl/val.h>
5059 isl_bool isl_multi_val_range_is_wrapping(
5060 __isl_keep isl_multi_val *mv);
5062 #include <isl/aff.h>
5063 isl_bool isl_multi_aff_range_is_wrapping(
5064 __isl_keep isl_multi_aff *ma);
5065 isl_bool isl_multi_pw_aff_range_is_wrapping(
5066 __isl_keep isl_multi_pw_aff *mpa);
5067 isl_bool isl_multi_union_pw_aff_range_is_wrapping(
5068 __isl_keep isl_multi_union_pw_aff *mupa);
5070 The input to C<isl_space_is_wrapping> should
5071 be the space of a set, while that of
5072 C<isl_space_domain_is_wrapping> and
5073 C<isl_space_range_is_wrapping> should be the space of a relation.
5074 The input to C<isl_space_is_product> can be either the space
5075 of a set or that of a binary relation.
5076 In case the input is the space of a binary relation, it checks
5077 whether both domain and range are wrapping.
5079 =item * Internal Product
5081 isl_bool isl_basic_map_can_zip(
5082 __isl_keep isl_basic_map *bmap);
5083 isl_bool isl_map_can_zip(__isl_keep isl_map *map);
5085 Check whether the product of domain and range of the given relation
5087 i.e., whether both domain and range are nested relations.
5091 #include <isl/space.h>
5092 isl_bool isl_space_can_curry(
5093 __isl_keep isl_space *space);
5095 #include <isl/map.h>
5096 isl_bool isl_basic_map_can_curry(
5097 __isl_keep isl_basic_map *bmap);
5098 isl_bool isl_map_can_curry(__isl_keep isl_map *map);
5100 Check whether the domain of the (basic) relation is a wrapped relation.
5102 #include <isl/space.h>
5103 isl_bool isl_space_can_uncurry(
5104 __isl_keep isl_space *space);
5106 #include <isl/map.h>
5107 isl_bool isl_basic_map_can_uncurry(
5108 __isl_keep isl_basic_map *bmap);
5109 isl_bool isl_map_can_uncurry(__isl_keep isl_map *map);
5111 Check whether the range of the (basic) relation is a wrapped relation.
5113 #include <isl/space.h>
5114 isl_bool isl_space_can_range_curry(
5115 __isl_keep isl_space *space);
5117 #include <isl/map.h>
5118 isl_bool isl_map_can_range_curry(
5119 __isl_keep isl_map *map);
5121 Check whether the domain of the relation wrapped in the range of
5122 the input is itself a wrapped relation.
5124 =item * Special Values
5126 #include <isl/aff.h>
5127 isl_bool isl_aff_is_cst(__isl_keep isl_aff *aff);
5128 isl_bool isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
5129 isl_bool isl_multi_pw_aff_is_cst(
5130 __isl_keep isl_multi_pw_aff *mpa);
5132 Check whether the given expression is a constant.
5134 #include <isl/val.h>
5135 isl_bool isl_multi_val_involves_nan(
5136 __isl_keep isl_multi_val *mv);
5138 #include <isl/aff.h>
5139 isl_bool isl_aff_is_nan(__isl_keep isl_aff *aff);
5140 isl_bool isl_multi_aff_involves_nan(
5141 __isl_keep isl_multi_aff *ma);
5142 isl_bool isl_pw_aff_involves_nan(
5143 __isl_keep isl_pw_aff *pa);
5144 isl_bool isl_pw_multi_aff_involves_nan(
5145 __isl_keep isl_pw_multi_aff *pma);
5146 isl_bool isl_multi_pw_aff_involves_nan(
5147 __isl_keep isl_multi_pw_aff *mpa);
5148 isl_bool isl_union_pw_aff_involves_nan(
5149 __isl_keep isl_union_pw_aff *upa);
5150 isl_bool isl_union_pw_multi_aff_involves_nan(
5151 __isl_keep isl_union_pw_multi_aff *upma);
5152 isl_bool isl_multi_union_pw_aff_involves_nan(
5153 __isl_keep isl_multi_union_pw_aff *mupa);
5155 #include <isl/polynomial.h>
5156 isl_bool isl_qpolynomial_is_nan(
5157 __isl_keep isl_qpolynomial *qp);
5158 isl_bool isl_qpolynomial_fold_is_nan(
5159 __isl_keep isl_qpolynomial_fold *fold);
5160 isl_bool isl_pw_qpolynomial_involves_nan(
5161 __isl_keep isl_pw_qpolynomial *pwqp);
5162 isl_bool isl_pw_qpolynomial_fold_involves_nan(
5163 __isl_keep isl_pw_qpolynomial_fold *pwf);
5164 isl_bool isl_union_pw_qpolynomial_involves_nan(
5165 __isl_keep isl_union_pw_qpolynomial *upwqp);
5166 isl_bool isl_union_pw_qpolynomial_fold_involves_nan(
5167 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
5169 Check whether the given expression is equal to or involves NaN.
5171 #include <isl/val.h>
5172 isl_bool isl_multi_val_is_zero(
5173 __isl_keep isl_multi_val *mv);
5175 Check whether the multiple value is zero.
5177 #include <isl/aff.h>
5178 isl_bool isl_aff_plain_is_zero(
5179 __isl_keep isl_aff *aff);
5181 Check whether the affine expression is obviously zero.
5185 =head3 Binary Properties
5191 The following functions check whether two objects
5192 represent the same set, relation or function.
5193 The C<plain> variants only return true if the objects
5194 are obviously the same. That is, they may return false
5195 even if the objects are the same, but they will never
5196 return true if the objects are not the same.
5198 #include <isl/set.h>
5199 isl_bool isl_basic_set_plain_is_equal(
5200 __isl_keep isl_basic_set *bset1,
5201 __isl_keep isl_basic_set *bset2);
5202 isl_bool isl_basic_set_is_equal(
5203 __isl_keep isl_basic_set *bset1,
5204 __isl_keep isl_basic_set *bset2);
5205 isl_bool isl_set_plain_is_equal(
5206 __isl_keep isl_set *set1,
5207 __isl_keep isl_set *set2);
5208 isl_bool isl_set_is_equal(__isl_keep isl_set *set1,
5209 __isl_keep isl_set *set2);
5211 #include <isl/map.h>
5212 isl_bool isl_basic_map_is_equal(
5213 __isl_keep isl_basic_map *bmap1,
5214 __isl_keep isl_basic_map *bmap2);
5215 isl_bool isl_map_is_equal(__isl_keep isl_map *map1,
5216 __isl_keep isl_map *map2);
5217 isl_bool isl_map_plain_is_equal(
5218 __isl_keep isl_map *map1,
5219 __isl_keep isl_map *map2);
5221 #include <isl/union_set.h>
5222 isl_bool isl_union_set_is_equal(
5223 __isl_keep isl_union_set *uset1,
5224 __isl_keep isl_union_set *uset2);
5226 #include <isl/union_map.h>
5227 isl_bool isl_union_map_is_equal(
5228 __isl_keep isl_union_map *umap1,
5229 __isl_keep isl_union_map *umap2);
5232 isl_bool isl_multi_id_plain_is_equal(
5233 __isl_keep isl_multi_id *mi1,
5234 __isl_keep isl_multi_id *mi2);
5236 #include <isl/val.h>
5237 isl_bool isl_multi_val_plain_is_equal(
5238 __isl_keep isl_multi_val *mv1,
5239 __isl_keep isl_multi_val *mv2);
5241 #include <isl/aff.h>
5242 isl_bool isl_aff_plain_is_equal(
5243 __isl_keep isl_aff *aff1,
5244 __isl_keep isl_aff *aff2);
5245 isl_bool isl_multi_aff_plain_is_equal(
5246 __isl_keep isl_multi_aff *maff1,
5247 __isl_keep isl_multi_aff *maff2);
5248 isl_bool isl_pw_aff_plain_is_equal(
5249 __isl_keep isl_pw_aff *pwaff1,
5250 __isl_keep isl_pw_aff *pwaff2);
5251 isl_bool isl_pw_aff_is_equal(
5252 __isl_keep isl_pw_aff *pa1,
5253 __isl_keep isl_pw_aff *pa2);
5254 isl_bool isl_pw_multi_aff_plain_is_equal(
5255 __isl_keep isl_pw_multi_aff *pma1,
5256 __isl_keep isl_pw_multi_aff *pma2);
5257 isl_bool isl_pw_multi_aff_is_equal(
5258 __isl_keep isl_pw_multi_aff *pma1,
5259 __isl_keep isl_pw_multi_aff *pma2);
5260 isl_bool isl_multi_pw_aff_plain_is_equal(
5261 __isl_keep isl_multi_pw_aff *mpa1,
5262 __isl_keep isl_multi_pw_aff *mpa2);
5263 isl_bool isl_multi_pw_aff_is_equal(
5264 __isl_keep isl_multi_pw_aff *mpa1,
5265 __isl_keep isl_multi_pw_aff *mpa2);
5266 isl_bool isl_union_pw_aff_plain_is_equal(
5267 __isl_keep isl_union_pw_aff *upa1,
5268 __isl_keep isl_union_pw_aff *upa2);
5269 isl_bool isl_union_pw_multi_aff_plain_is_equal(
5270 __isl_keep isl_union_pw_multi_aff *upma1,
5271 __isl_keep isl_union_pw_multi_aff *upma2);
5272 isl_bool isl_multi_union_pw_aff_plain_is_equal(
5273 __isl_keep isl_multi_union_pw_aff *mupa1,
5274 __isl_keep isl_multi_union_pw_aff *mupa2);
5276 #include <isl/polynomial.h>
5277 isl_bool isl_union_pw_qpolynomial_plain_is_equal(
5278 __isl_keep isl_union_pw_qpolynomial *upwqp1,
5279 __isl_keep isl_union_pw_qpolynomial *upwqp2);
5280 isl_bool isl_union_pw_qpolynomial_fold_plain_is_equal(
5281 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
5282 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
5284 =item * Disjointness
5286 #include <isl/set.h>
5287 isl_bool isl_basic_set_is_disjoint(
5288 __isl_keep isl_basic_set *bset1,
5289 __isl_keep isl_basic_set *bset2);
5290 isl_bool isl_set_plain_is_disjoint(
5291 __isl_keep isl_set *set1,
5292 __isl_keep isl_set *set2);
5293 isl_bool isl_set_is_disjoint(__isl_keep isl_set *set1,
5294 __isl_keep isl_set *set2);
5296 #include <isl/map.h>
5297 isl_bool isl_basic_map_is_disjoint(
5298 __isl_keep isl_basic_map *bmap1,
5299 __isl_keep isl_basic_map *bmap2);
5300 isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1,
5301 __isl_keep isl_map *map2);
5303 #include <isl/union_set.h>
5304 isl_bool isl_union_set_is_disjoint(
5305 __isl_keep isl_union_set *uset1,
5306 __isl_keep isl_union_set *uset2);
5308 #include <isl/union_map.h>
5309 isl_bool isl_union_map_is_disjoint(
5310 __isl_keep isl_union_map *umap1,
5311 __isl_keep isl_union_map *umap2);
5315 isl_bool isl_basic_set_is_subset(
5316 __isl_keep isl_basic_set *bset1,
5317 __isl_keep isl_basic_set *bset2);
5318 isl_bool isl_set_is_subset(__isl_keep isl_set *set1,
5319 __isl_keep isl_set *set2);
5320 isl_bool isl_set_is_strict_subset(
5321 __isl_keep isl_set *set1,
5322 __isl_keep isl_set *set2);
5323 isl_bool isl_union_set_is_subset(
5324 __isl_keep isl_union_set *uset1,
5325 __isl_keep isl_union_set *uset2);
5326 isl_bool isl_union_set_is_strict_subset(
5327 __isl_keep isl_union_set *uset1,
5328 __isl_keep isl_union_set *uset2);
5329 isl_bool isl_basic_map_is_subset(
5330 __isl_keep isl_basic_map *bmap1,
5331 __isl_keep isl_basic_map *bmap2);
5332 isl_bool isl_basic_map_is_strict_subset(
5333 __isl_keep isl_basic_map *bmap1,
5334 __isl_keep isl_basic_map *bmap2);
5335 isl_bool isl_map_is_subset(
5336 __isl_keep isl_map *map1,
5337 __isl_keep isl_map *map2);
5338 isl_bool isl_map_is_strict_subset(
5339 __isl_keep isl_map *map1,
5340 __isl_keep isl_map *map2);
5341 isl_bool isl_union_map_is_subset(
5342 __isl_keep isl_union_map *umap1,
5343 __isl_keep isl_union_map *umap2);
5344 isl_bool isl_union_map_is_strict_subset(
5345 __isl_keep isl_union_map *umap1,
5346 __isl_keep isl_union_map *umap2);
5348 Check whether the first argument is a (strict) subset of the
5353 Every comparison function returns a negative value if the first
5354 argument is considered smaller than the second, a positive value
5355 if the first argument is considered greater and zero if the two
5356 constraints are considered the same by the comparison criterion.
5358 #include <isl/constraint.h>
5359 int isl_constraint_plain_cmp(
5360 __isl_keep isl_constraint *c1,
5361 __isl_keep isl_constraint *c2);
5363 This function is useful for sorting C<isl_constraint>s.
5364 The order depends on the internal representation of the inputs.
5365 The order is fixed over different calls to the function (assuming
5366 the internal representation of the inputs has not changed), but may
5367 change over different versions of C<isl>.
5369 #include <isl/constraint.h>
5370 int isl_constraint_cmp_last_non_zero(
5371 __isl_keep isl_constraint *c1,
5372 __isl_keep isl_constraint *c2);
5374 This function can be used to sort constraints that live in the same
5375 local space. Constraints that involve ``earlier'' dimensions or
5376 that have a smaller coefficient for the shared latest dimension
5377 are considered smaller than other constraints.
5378 This function only defines a B<partial> order.
5380 #include <isl/set.h>
5381 int isl_set_plain_cmp(__isl_keep isl_set *set1,
5382 __isl_keep isl_set *set2);
5384 This function is useful for sorting C<isl_set>s.
5385 The order depends on the internal representation of the inputs.
5386 The order is fixed over different calls to the function (assuming
5387 the internal representation of the inputs has not changed), but may
5388 change over different versions of C<isl>.
5390 #include <isl/aff.h>
5391 int isl_multi_aff_plain_cmp(
5392 __isl_keep isl_multi_aff *ma1,
5393 __isl_keep isl_multi_aff *ma2);
5394 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
5395 __isl_keep isl_pw_aff *pa2);
5397 The functions C<isl_multi_aff_plain_cmp> and
5398 C<isl_pw_aff_plain_cmp> can be used to sort C<isl_multi_aff>s and
5399 C<isl_pw_aff>s. The order is not strictly defined.
5400 The current order sorts expressions that only involve
5401 earlier dimensions before those that involve later dimensions.
5405 =head2 Unary Operations
5411 __isl_give isl_set *isl_set_complement(
5412 __isl_take isl_set *set);
5413 __isl_give isl_map *isl_map_complement(
5414 __isl_take isl_map *map);
5418 #include <isl/space.h>
5419 __isl_give isl_space *isl_space_reverse(
5420 __isl_take isl_space *space);
5421 __isl_give isl_space *isl_space_wrapped_reverse(
5422 __isl_take isl_space *space);
5423 __isl_give isl_space *isl_space_domain_reverse(
5424 __isl_take isl_space *space);
5425 __isl_give isl_space *isl_space_range_reverse(
5426 __isl_take isl_space *space);
5428 #include <isl/aff.h>
5429 __isl_give isl_aff *isl_aff_domain_reverse(
5430 __isl_take isl_aff *aff);
5431 __isl_give isl_multi_aff *
5432 isl_multi_aff_domain_reverse(
5433 __isl_take isl_multi_aff *ma);
5434 __isl_give isl_pw_aff *isl_pw_aff_domain_reverse(
5435 __isl_take isl_pw_aff *pa);
5436 __isl_give isl_pw_multi_aff *
5437 isl_pw_multi_aff_domain_reverse(
5438 __isl_take isl_pw_multi_aff *pma);
5439 __isl_give isl_multi_pw_aff *
5440 isl_multi_pw_aff_domain_reverse(
5441 __isl_take isl_multi_pw_aff *mpa);
5443 #include <isl/set.h>
5444 __isl_give isl_set *isl_set_wrapped_reverse(
5445 __isl_take isl_set *set);
5447 #include <isl/map.h>
5448 __isl_give isl_basic_map *isl_basic_map_reverse(
5449 __isl_take isl_basic_map *bmap);
5450 __isl_give isl_map *isl_map_reverse(
5451 __isl_take isl_map *map);
5452 __isl_give isl_map *isl_map_domain_reverse(
5453 __isl_take isl_map *map);
5454 __isl_give isl_map *isl_map_range_reverse(
5455 __isl_take isl_map *map);
5457 #include <isl/union_map.h>
5458 __isl_give isl_union_map *isl_union_map_reverse(
5459 __isl_take isl_union_map *umap);
5460 __isl_give isl_union_map *isl_union_map_range_reverse(
5461 __isl_take isl_union_map *umap);
5463 The function C<isl_space_range_reverse> reverses the relation
5464 that is embedded in the range of the input map space.
5465 The identifier of the range, if any, is only preserved
5466 if this embedded relation has identical input and output tuples.
5467 Similarly for C<isl_space_domain_reverse>.
5468 Along the same lines, C<isl_space_wrapped_reverse> reverses
5469 the relation that is embedded in a set space.
5471 =item * Tuple binding
5473 The following function binds
5474 a tuple to a sequence of parameter identifiers, equating
5475 the tuple dimensions to the parameters with those identifiers and
5476 subsequently projecting out the tuple.
5477 If the original object did not reference any such parameters,
5478 then this means that the tuple dimensions are reinterpreted
5480 The space of C<tuple> needs to match that of the bound tuple.
5482 #include <isl/set.h>
5483 __isl_give isl_set *isl_set_bind(
5484 __isl_take isl_set *set,
5485 __isl_take isl_multi_id *tuple);
5487 #include <isl/map.h>
5488 __isl_give isl_set *isl_map_bind_domain(
5489 __isl_take isl_map *map,
5490 __isl_take isl_multi_id *tuple);
5491 __isl_give isl_set *isl_map_bind_range(
5492 __isl_take isl_map *map,
5493 __isl_take isl_multi_id *tuple);
5495 #include <isl/union_map.h>
5496 __isl_give isl_union_set *isl_union_map_bind_range(
5497 __isl_take isl_union_map *umap,
5498 __isl_take isl_multi_id *tuple);
5500 #include <isl/aff.h>
5501 __isl_give isl_pw_aff *isl_pw_aff_bind_domain(
5502 __isl_take isl_pw_aff *pa,
5503 __isl_take isl_multi_id *tuple);
5504 __isl_give isl_multi_aff *isl_multi_aff_bind_domain(
5505 __isl_take isl_multi_aff *ma,
5506 __isl_take isl_multi_id *tuple);
5507 __isl_give isl_pw_multi_aff *
5508 isl_pw_multi_aff_bind_domain(
5509 __isl_take isl_pw_multi_aff *pma,
5510 __isl_take isl_multi_id *tuple);
5511 __isl_give isl_multi_pw_aff *
5512 isl_multi_pw_aff_bind_domain(
5513 __isl_take isl_multi_pw_aff *mpa,
5514 __isl_take isl_multi_id *tuple);
5515 __isl_give isl_pw_aff *
5516 isl_pw_aff_bind_domain_wrapped_domain(
5517 __isl_take isl_pw_aff *pa,
5518 __isl_take isl_multi_id *tuple);
5519 __isl_give isl_multi_aff *
5520 isl_multi_aff_bind_domain_wrapped_domain(
5521 __isl_take isl_multi_aff *ma,
5522 __isl_take isl_multi_id *tuple);
5523 __isl_give isl_pw_multi_aff *
5524 isl_pw_multi_aff_bind_domain_wrapped_domain(
5525 __isl_take isl_pw_multi_aff *pma,
5526 __isl_take isl_multi_id *tuple);
5527 __isl_give isl_multi_pw_aff *
5528 isl_multi_pw_aff_bind_domain_wrapped_domain(
5529 __isl_take isl_multi_pw_aff *mpa,
5530 __isl_take isl_multi_id *tuple);
5531 __isl_give isl_basic_set *isl_aff_bind_id(
5532 __isl_take isl_aff *aff,
5533 __isl_take isl_id *id);
5534 __isl_give isl_set *isl_pw_aff_bind_id(
5535 __isl_take isl_pw_aff *pa,
5536 __isl_take isl_id *id);
5537 __isl_give isl_basic_set *isl_multi_aff_bind(
5538 __isl_take isl_multi_aff *ma,
5539 __isl_take isl_multi_id *tuple);
5540 __isl_give isl_set *isl_multi_pw_aff_bind(
5541 __isl_take isl_multi_pw_aff *mpa,
5542 __isl_take isl_multi_id *tuple);
5543 __isl_give isl_union_set *isl_union_pw_aff_bind_id(
5544 __isl_take isl_union_pw_aff *upa,
5545 __isl_take isl_id *id);
5546 __isl_give isl_union_set *
5547 isl_multi_union_pw_aff_bind(
5548 __isl_take isl_multi_union_pw_aff *mupa,
5549 __isl_take isl_multi_id *tuple);
5551 Projecting out the domain of the wrapped relation in the domain
5552 of a function leaves the range of that wrapped relation
5553 in the domain of the resulting function.
5554 In the case of C<isl_aff_bind_id>, C<isl_pw_aff_bind_id>,
5555 C<isl_multi_aff_bind>, C<isl_multi_pw_aff_bind>,
5556 C<isl_union_pw_aff_bind_id> and
5557 C<isl_multi_union_pw_aff_bind>, the parameters
5558 are bound to the function values and the result lives
5559 in the domain of the input function.
5563 #include <isl/space.h>
5564 __isl_give isl_space *isl_space_domain(
5565 __isl_take isl_space *space);
5566 __isl_give isl_space *isl_space_range(
5567 __isl_take isl_space *space);
5568 __isl_give isl_space *isl_space_params(
5569 __isl_take isl_space *space);
5570 __isl_give isl_space *
5571 isl_space_domain_wrapped_domain(
5572 __isl_take isl_space *space);
5573 __isl_give isl_space *
5574 isl_space_domain_wrapped_range(
5575 __isl_take isl_space *space);
5576 __isl_give isl_space *
5577 isl_space_range_wrapped_domain(
5578 __isl_take isl_space *space);
5579 __isl_give isl_space *
5580 isl_space_range_wrapped_range(
5581 __isl_take isl_space *space);
5583 #include <isl/local_space.h>
5584 __isl_give isl_local_space *isl_local_space_domain(
5585 __isl_take isl_local_space *ls);
5586 __isl_give isl_local_space *isl_local_space_range(
5587 __isl_take isl_local_space *ls);
5589 #include <isl/set.h>
5590 __isl_give isl_basic_set *isl_basic_set_project_out(
5591 __isl_take isl_basic_set *bset,
5592 enum isl_dim_type type, unsigned first, unsigned n);
5593 __isl_give isl_set *isl_set_project_out_param_id(
5594 __isl_take isl_set *set,
5595 __isl_take isl_id *id);
5596 __isl_give isl_set *
5597 isl_set_project_out_param_id_list(
5598 __isl_take isl_set *set,
5599 __isl_take isl_id_list *list);
5600 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
5601 enum isl_dim_type type, unsigned first, unsigned n);
5602 __isl_give isl_set *isl_set_project_out_all_params(
5603 __isl_take isl_set *set);
5604 __isl_give isl_map *isl_set_project_onto_map(
5605 __isl_take isl_set *set,
5606 enum isl_dim_type type, unsigned first,
5608 __isl_give isl_basic_set *isl_basic_set_params(
5609 __isl_take isl_basic_set *bset);
5610 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
5612 The function C<isl_space_domain_wrapped_domain> returns the domain
5613 of the binary relation wrapped inside the domain of the input.
5614 The function C<isl_set_project_onto_map> returns a relation
5615 that projects the input set onto the given set dimensions.
5617 #include <isl/map.h>
5618 __isl_give isl_basic_map *isl_basic_map_project_out(
5619 __isl_take isl_basic_map *bmap,
5620 enum isl_dim_type type, unsigned first, unsigned n);
5621 __isl_give isl_map *isl_map_project_out_param_id(
5622 __isl_take isl_map *map,
5623 __isl_take isl_id *id);
5624 __isl_give isl_map *isl_map_project_out_param_id_list(
5625 __isl_take isl_map *map,
5626 __isl_take isl_id_list *list);
5627 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
5628 enum isl_dim_type type, unsigned first, unsigned n);
5629 __isl_give isl_map *isl_map_project_out_all_params(
5630 __isl_take isl_map *map);
5631 __isl_give isl_basic_set *isl_basic_map_domain(
5632 __isl_take isl_basic_map *bmap);
5633 __isl_give isl_basic_set *isl_basic_map_range(
5634 __isl_take isl_basic_map *bmap);
5635 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
5636 __isl_give isl_set *isl_map_domain(
5637 __isl_take isl_map *bmap);
5638 __isl_give isl_set *isl_map_range(
5639 __isl_take isl_map *map);
5641 #include <isl/union_set.h>
5642 __isl_give isl_union_set *isl_union_set_project_out(
5643 __isl_take isl_union_set *uset,
5644 enum isl_dim_type type,
5645 unsigned first, unsigned n);
5646 __isl_give isl_union_set *
5647 isl_union_set_project_out_all_params(
5648 __isl_take isl_union_set *uset);
5649 __isl_give isl_set *isl_union_set_params(
5650 __isl_take isl_union_set *uset);
5652 The function C<isl_union_set_project_out> can only project out
5655 #include <isl/union_map.h>
5656 __isl_give isl_union_map *
5657 isl_union_map_project_out_param_id(
5658 __isl_take isl_union_map *umap,
5659 __isl_take isl_id *id);
5660 __isl_give isl_union_map *
5661 isl_union_map_project_out_param_id_list(
5662 __isl_take isl_union_map *umap,
5663 __isl_take isl_id_list *list);
5664 __isl_give isl_union_map *isl_union_map_project_out(
5665 __isl_take isl_union_map *umap,
5666 enum isl_dim_type type, unsigned first, unsigned n);
5667 __isl_give isl_union_map *
5668 isl_union_map_project_out_all_params(
5669 __isl_take isl_union_map *umap);
5670 __isl_give isl_set *isl_union_map_params(
5671 __isl_take isl_union_map *umap);
5672 __isl_give isl_union_set *isl_union_map_domain(
5673 __isl_take isl_union_map *umap);
5674 __isl_give isl_union_set *isl_union_map_range(
5675 __isl_take isl_union_map *umap);
5677 The function C<isl_union_map_project_out> can only project out
5680 #include <isl/aff.h>
5681 __isl_give isl_aff *isl_aff_project_domain_on_params(
5682 __isl_take isl_aff *aff);
5683 __isl_give isl_multi_aff *
5684 isl_multi_aff_project_domain_on_params(
5685 __isl_take isl_multi_aff *ma);
5686 __isl_give isl_pw_aff *
5687 isl_pw_aff_project_domain_on_params(
5688 __isl_take isl_pw_aff *pa);
5689 __isl_give isl_multi_pw_aff *
5690 isl_multi_pw_aff_project_domain_on_params(
5691 __isl_take isl_multi_pw_aff *mpa);
5692 __isl_give isl_pw_multi_aff *
5693 isl_pw_multi_aff_project_domain_on_params(
5694 __isl_take isl_pw_multi_aff *pma);
5695 __isl_give isl_set *isl_pw_aff_domain(
5696 __isl_take isl_pw_aff *pwaff);
5697 __isl_give isl_set *isl_pw_multi_aff_domain(
5698 __isl_take isl_pw_multi_aff *pma);
5699 __isl_give isl_set *isl_multi_pw_aff_domain(
5700 __isl_take isl_multi_pw_aff *mpa);
5701 __isl_give isl_union_set *isl_union_pw_aff_domain(
5702 __isl_take isl_union_pw_aff *upa);
5703 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
5704 __isl_take isl_union_pw_multi_aff *upma);
5705 __isl_give isl_union_set *
5706 isl_multi_union_pw_aff_domain(
5707 __isl_take isl_multi_union_pw_aff *mupa);
5708 __isl_give isl_set *isl_pw_aff_params(
5709 __isl_take isl_pw_aff *pwa);
5711 If no explicit domain was set on a zero-dimensional input to
5712 C<isl_multi_union_pw_aff_domain>, then this function will
5713 return a parameter set.
5715 #include <isl/polynomial.h>
5716 __isl_give isl_qpolynomial *
5717 isl_qpolynomial_project_domain_on_params(
5718 __isl_take isl_qpolynomial *qp);
5719 __isl_give isl_pw_qpolynomial *
5720 isl_pw_qpolynomial_project_domain_on_params(
5721 __isl_take isl_pw_qpolynomial *pwqp);
5722 __isl_give isl_pw_qpolynomial_fold *
5723 isl_pw_qpolynomial_fold_project_domain_on_params(
5724 __isl_take isl_pw_qpolynomial_fold *pwf);
5725 __isl_give isl_set *isl_pw_qpolynomial_domain(
5726 __isl_take isl_pw_qpolynomial *pwqp);
5727 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5728 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5729 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5730 __isl_take isl_union_pw_qpolynomial *upwqp);
5732 #include <isl/space.h>
5733 __isl_give isl_space *isl_space_domain_map(
5734 __isl_take isl_space *space);
5735 __isl_give isl_space *isl_space_range_map(
5736 __isl_take isl_space *space);
5738 #include <isl/map.h>
5739 __isl_give isl_map *isl_set_wrapped_domain_map(
5740 __isl_take isl_set *set);
5741 __isl_give isl_basic_map *isl_basic_map_domain_map(
5742 __isl_take isl_basic_map *bmap);
5743 __isl_give isl_basic_map *isl_basic_map_range_map(
5744 __isl_take isl_basic_map *bmap);
5745 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
5746 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
5748 #include <isl/union_map.h>
5749 __isl_give isl_union_map *isl_union_map_domain_map(
5750 __isl_take isl_union_map *umap);
5751 __isl_give isl_union_pw_multi_aff *
5752 isl_union_map_domain_map_union_pw_multi_aff(
5753 __isl_take isl_union_map *umap);
5754 __isl_give isl_union_map *isl_union_map_range_map(
5755 __isl_take isl_union_map *umap);
5756 __isl_give isl_union_map *
5757 isl_union_set_wrapped_domain_map(
5758 __isl_take isl_union_set *uset);
5760 The functions above construct a (basic, regular or union) relation
5761 that maps (a wrapped version of) the input relation to its domain or range.
5762 C<isl_set_wrapped_domain_map> maps the input set to the domain
5763 of its wrapped relation.
5767 __isl_give isl_basic_set *isl_basic_set_eliminate(
5768 __isl_take isl_basic_set *bset,
5769 enum isl_dim_type type,
5770 unsigned first, unsigned n);
5771 __isl_give isl_set *isl_set_eliminate(
5772 __isl_take isl_set *set, enum isl_dim_type type,
5773 unsigned first, unsigned n);
5774 __isl_give isl_basic_map *isl_basic_map_eliminate(
5775 __isl_take isl_basic_map *bmap,
5776 enum isl_dim_type type,
5777 unsigned first, unsigned n);
5778 __isl_give isl_map *isl_map_eliminate(
5779 __isl_take isl_map *map, enum isl_dim_type type,
5780 unsigned first, unsigned n);
5782 Eliminate the coefficients for the given dimensions from the constraints,
5783 without removing the dimensions.
5785 =item * Constructing a set from a parameter domain
5787 A set space of a given dimension and with an optional name
5788 can be created from a parameter space using the following functions.
5790 #include <isl/space.h>
5791 __isl_give isl_space *isl_space_add_unnamed_tuple_ui(
5792 __isl_take isl_space *space, unsigned dim);
5793 __isl_give isl_space *
5794 isl_space_add_named_tuple_id_ui(
5795 __isl_take isl_space *space,
5796 __isl_take isl_id *tuple_id, unsigned dim);
5798 A set with a given tuple can be created from a parameter domain
5799 using the following function.
5801 #include <isl/set.h>
5802 __isl_give isl_set *isl_set_unbind_params(
5803 __isl_take isl_set *set,
5804 __isl_take isl_multi_id *tuple);
5806 Any parameters with identifiers in C<tuple> are reinterpreted
5807 as the corresponding set dimensions.
5809 A zero-dimensional (local) space or (basic) set can be constructed
5810 on a given parameter domain using the following functions.
5812 #include <isl/space.h>
5813 __isl_give isl_space *isl_space_set_from_params(
5814 __isl_take isl_space *space);
5816 #include <isl/local_space.h>
5817 __isl_give isl_local_space *
5818 isl_local_space_set_from_params(
5819 __isl_take isl_local_space *ls);
5821 #include <isl/set.h>
5822 __isl_give isl_basic_set *isl_basic_set_from_params(
5823 __isl_take isl_basic_set *bset);
5824 __isl_give isl_set *isl_set_from_params(
5825 __isl_take isl_set *set);
5827 =item * Constructing a relation from one or two sets
5829 A map space with a range of a given dimension and with an optional name
5830 can be created from a domain space using the functions
5831 C<isl_space_add_unnamed_tuple_ui> and C<isl_space_add_named_tuple_id_ui>
5834 A relation with a given domain tuple can be created from a set
5835 that will become the range of the relation
5836 using the following function.
5838 #include <isl/set.h>
5839 __isl_give isl_map *
5840 isl_set_unbind_params_insert_domain(
5841 __isl_take isl_set *set,
5842 __isl_take isl_multi_id *domain);
5844 Any parameters with identifiers in C<domain> are reinterpreted
5845 as the corresponding input dimensions.
5847 Similarly, a function defined over a parameter domain can
5848 be converted into one defined over a set domain
5849 using the following functions.
5851 #include <isl/aff.h>
5852 __isl_give isl_aff *
5853 isl_aff_unbind_params_insert_domain(
5854 __isl_take isl_aff *aff,
5855 __isl_take isl_multi_id *domain);
5856 __isl_give isl_multi_aff *
5857 isl_multi_aff_unbind_params_insert_domain(
5858 __isl_take isl_multi_aff *ma,
5859 __isl_take isl_multi_id *domain);
5860 __isl_give isl_multi_pw_aff *
5861 isl_multi_pw_aff_unbind_params_insert_domain(
5862 __isl_take isl_multi_pw_aff *mpa,
5863 __isl_take isl_multi_id *domain);
5866 any parameters with identifiers in C<domain> are reinterpreted
5867 as the corresponding input dimensions.
5869 Create a relation with the given set(s) as domain and/or range.
5870 If only the domain or the range is specified, then
5871 the range or domain of the created relation is a zero-dimensional
5872 flat anonymous space.
5873 If the case of C<isl_space_map_from_set>, the input space
5874 specifies both the domain and the range of the result.
5876 #include <isl/space.h>
5877 __isl_give isl_space *isl_space_from_domain(
5878 __isl_take isl_space *space);
5879 __isl_give isl_space *isl_space_from_range(
5880 __isl_take isl_space *space);
5881 __isl_give isl_space *isl_space_map_from_set(
5882 __isl_take isl_space *space);
5883 __isl_give isl_space *isl_space_map_from_domain_and_range(
5884 __isl_take isl_space *domain,
5885 __isl_take isl_space *range);
5887 #include <isl/local_space.h>
5888 __isl_give isl_local_space *isl_local_space_from_domain(
5889 __isl_take isl_local_space *ls);
5891 #include <isl/map.h>
5892 __isl_give isl_map *isl_set_insert_domain(
5893 __isl_take isl_set *set,
5894 __isl_take isl_space *domain);
5895 __isl_give isl_map *isl_map_from_domain(
5896 __isl_take isl_set *set);
5897 __isl_give isl_map *isl_map_from_range(
5898 __isl_take isl_set *set);
5900 #include <isl/union_map.h>
5901 __isl_give isl_union_map *isl_union_map_from_domain(
5902 __isl_take isl_union_set *uset);
5903 __isl_give isl_union_map *isl_union_map_from_range(
5904 __isl_take isl_union_set *uset);
5905 __isl_give isl_union_map *
5906 isl_union_map_from_domain_and_range(
5907 __isl_take isl_union_set *domain,
5908 __isl_take isl_union_set *range);
5911 __isl_give isl_multi_id *isl_multi_id_from_range(
5912 __isl_take isl_multi_id *mi);
5914 #include <isl/val.h>
5915 __isl_give isl_multi_val *isl_multi_val_from_range(
5916 __isl_take isl_multi_val *mv);
5918 #include <isl/aff.h>
5919 __isl_give isl_multi_aff *
5920 isl_multi_aff_insert_domain(
5921 __isl_take isl_multi_aff *ma,
5922 __isl_take isl_space *domain);
5923 __isl_give isl_pw_aff *isl_pw_aff_insert_domain(
5924 __isl_take isl_pw_aff *pa,
5925 __isl_take isl_space *domain);
5926 __isl_give isl_pw_multi_aff *
5927 isl_pw_multi_aff_insert_domain(
5928 __isl_take isl_pw_multi_aff *pma,
5929 __isl_take isl_space *domain);
5930 __isl_give isl_multi_pw_aff *
5931 isl_multi_pw_aff_insert_domain(
5932 __isl_take isl_multi_pw_aff *mpa,
5933 __isl_take isl_space *domain);
5934 __isl_give isl_aff *isl_aff_from_range(
5935 __isl_take isl_aff *aff);
5936 __isl_give isl_multi_aff *isl_multi_aff_from_range(
5937 __isl_take isl_multi_aff *ma);
5938 __isl_give isl_pw_aff *isl_pw_aff_from_range(
5939 __isl_take isl_pw_aff *pwa);
5940 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
5941 __isl_take isl_multi_pw_aff *mpa);
5942 __isl_give isl_multi_union_pw_aff *
5943 isl_multi_union_pw_aff_from_range(
5944 __isl_take isl_multi_union_pw_aff *mupa);
5945 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
5946 __isl_take isl_set *set);
5947 __isl_give isl_union_pw_multi_aff *
5948 isl_union_pw_multi_aff_from_domain(
5949 __isl_take isl_union_set *uset);
5951 #include <isl/polynomial.h>
5952 __isl_give isl_pw_qpolynomial *
5953 isl_pw_qpolynomial_from_range(
5954 __isl_take isl_pw_qpolynomial *pwqp);
5955 __isl_give isl_pw_qpolynomial_fold *
5956 isl_pw_qpolynomial_fold_from_range(
5957 __isl_take isl_pw_qpolynomial_fold *pwf);
5961 #include <isl/set.h>
5962 __isl_give isl_basic_set *isl_basic_set_fix_si(
5963 __isl_take isl_basic_set *bset,
5964 enum isl_dim_type type, unsigned pos, int value);
5965 __isl_give isl_basic_set *isl_basic_set_fix_val(
5966 __isl_take isl_basic_set *bset,
5967 enum isl_dim_type type, unsigned pos,
5968 __isl_take isl_val *v);
5969 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
5970 enum isl_dim_type type, unsigned pos, int value);
5971 __isl_give isl_set *isl_set_fix_val(
5972 __isl_take isl_set *set,
5973 enum isl_dim_type type, unsigned pos,
5974 __isl_take isl_val *v);
5976 #include <isl/map.h>
5977 __isl_give isl_basic_map *isl_basic_map_fix_si(
5978 __isl_take isl_basic_map *bmap,
5979 enum isl_dim_type type, unsigned pos, int value);
5980 __isl_give isl_basic_map *isl_basic_map_fix_val(
5981 __isl_take isl_basic_map *bmap,
5982 enum isl_dim_type type, unsigned pos,
5983 __isl_take isl_val *v);
5984 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
5985 enum isl_dim_type type, unsigned pos, int value);
5986 __isl_give isl_map *isl_map_fix_val(
5987 __isl_take isl_map *map,
5988 enum isl_dim_type type, unsigned pos,
5989 __isl_take isl_val *v);
5991 #include <isl/aff.h>
5992 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
5993 __isl_take isl_pw_multi_aff *pma,
5994 enum isl_dim_type type, unsigned pos, int value);
5996 #include <isl/polynomial.h>
5997 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
5998 __isl_take isl_pw_qpolynomial *pwqp,
5999 enum isl_dim_type type, unsigned n,
6000 __isl_take isl_val *v);
6001 __isl_give isl_pw_qpolynomial_fold *
6002 isl_pw_qpolynomial_fold_fix_val(
6003 __isl_take isl_pw_qpolynomial_fold *pwf,
6004 enum isl_dim_type type, unsigned n,
6005 __isl_take isl_val *v);
6007 Intersect the set, relation or function domain
6008 with the hyperplane where the given
6009 dimension has the fixed given value.
6011 #include <isl/set.h>
6012 __isl_give isl_basic_set *
6013 isl_basic_set_lower_bound_val(
6014 __isl_take isl_basic_set *bset,
6015 enum isl_dim_type type, unsigned pos,
6016 __isl_take isl_val *value);
6017 __isl_give isl_basic_set *
6018 isl_basic_set_upper_bound_val(
6019 __isl_take isl_basic_set *bset,
6020 enum isl_dim_type type, unsigned pos,
6021 __isl_take isl_val *value);
6022 __isl_give isl_set *isl_set_lower_bound_si(
6023 __isl_take isl_set *set,
6024 enum isl_dim_type type, unsigned pos, int value);
6025 __isl_give isl_set *isl_set_lower_bound_val(
6026 __isl_take isl_set *set,
6027 enum isl_dim_type type, unsigned pos,
6028 __isl_take isl_val *value);
6029 __isl_give isl_set *isl_set_upper_bound_si(
6030 __isl_take isl_set *set,
6031 enum isl_dim_type type, unsigned pos, int value);
6032 __isl_give isl_set *isl_set_upper_bound_val(
6033 __isl_take isl_set *set,
6034 enum isl_dim_type type, unsigned pos,
6035 __isl_take isl_val *value);
6036 __isl_give isl_set *isl_set_lower_bound_multi_val(
6037 __isl_take isl_set *set,
6038 __isl_take isl_multi_val *lower);
6039 __isl_give isl_set *isl_set_upper_bound_multi_val(
6040 __isl_take isl_set *set,
6041 __isl_take isl_multi_val *upper);
6042 __isl_give isl_set *isl_set_lower_bound_multi_pw_aff(
6043 __isl_take isl_set *set,
6044 __isl_take isl_multi_pw_aff *lower);
6045 __isl_give isl_set *isl_set_upper_bound_multi_pw_aff(
6046 __isl_take isl_set *set,
6047 __isl_take isl_multi_pw_aff *upper);
6049 #include <isl/map.h>
6050 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
6051 __isl_take isl_basic_map *bmap,
6052 enum isl_dim_type type, unsigned pos, int value);
6053 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
6054 __isl_take isl_basic_map *bmap,
6055 enum isl_dim_type type, unsigned pos, int value);
6056 __isl_give isl_map *isl_map_lower_bound_si(
6057 __isl_take isl_map *map,
6058 enum isl_dim_type type, unsigned pos, int value);
6059 __isl_give isl_map *isl_map_upper_bound_si(
6060 __isl_take isl_map *map,
6061 enum isl_dim_type type, unsigned pos, int value);
6062 __isl_give isl_map *isl_map_lower_bound_val(
6063 __isl_take isl_map *map,
6064 enum isl_dim_type type, unsigned pos,
6065 __isl_take isl_val *value);
6066 __isl_give isl_map *isl_map_upper_bound_val(
6067 __isl_take isl_map *map,
6068 enum isl_dim_type type, unsigned pos,
6069 __isl_take isl_val *value);
6070 __isl_give isl_map *isl_map_lower_bound_multi_pw_aff(
6071 __isl_take isl_map *map,
6072 __isl_take isl_multi_pw_aff *lower);
6073 __isl_give isl_map *isl_map_upper_bound_multi_pw_aff(
6074 __isl_take isl_map *map,
6075 __isl_take isl_multi_pw_aff *upper);
6077 Intersect the set or relation with the half-space where the given
6078 dimension has a value bounded by the given fixed integer value or
6079 symbolic constant expression.
6080 For functions taking a multi expression,
6081 this applies to all set dimensions.
6082 Those that bound a map, bound the range of that map.
6083 If the multi expression is zero-dimensional but has an explicit domain,
6084 then the (parameter) domain of the set or map is intersected
6085 with this explicit domain.
6087 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
6088 enum isl_dim_type type1, int pos1,
6089 enum isl_dim_type type2, int pos2);
6090 __isl_give isl_basic_map *isl_basic_map_equate(
6091 __isl_take isl_basic_map *bmap,
6092 enum isl_dim_type type1, int pos1,
6093 enum isl_dim_type type2, int pos2);
6094 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
6095 enum isl_dim_type type1, int pos1,
6096 enum isl_dim_type type2, int pos2);
6098 Intersect the set or relation with the hyperplane where the given
6099 dimensions are equal to each other.
6101 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
6102 enum isl_dim_type type1, int pos1,
6103 enum isl_dim_type type2, int pos2);
6105 Intersect the relation with the hyperplane where the given
6106 dimensions have opposite values.
6108 __isl_give isl_map *isl_map_order_le(
6109 __isl_take isl_map *map,
6110 enum isl_dim_type type1, int pos1,
6111 enum isl_dim_type type2, int pos2);
6112 __isl_give isl_basic_map *isl_basic_map_order_ge(
6113 __isl_take isl_basic_map *bmap,
6114 enum isl_dim_type type1, int pos1,
6115 enum isl_dim_type type2, int pos2);
6116 __isl_give isl_map *isl_map_order_ge(
6117 __isl_take isl_map *map,
6118 enum isl_dim_type type1, int pos1,
6119 enum isl_dim_type type2, int pos2);
6120 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
6121 enum isl_dim_type type1, int pos1,
6122 enum isl_dim_type type2, int pos2);
6123 __isl_give isl_basic_map *isl_basic_map_order_gt(
6124 __isl_take isl_basic_map *bmap,
6125 enum isl_dim_type type1, int pos1,
6126 enum isl_dim_type type2, int pos2);
6127 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
6128 enum isl_dim_type type1, int pos1,
6129 enum isl_dim_type type2, int pos2);
6131 Intersect the relation with the half-space where the given
6132 dimensions satisfy the given ordering.
6134 #include <isl/union_set.h>
6135 __isl_give isl_union_map *isl_union_map_remove_map_if(
6136 __isl_take isl_union_map *umap,
6137 isl_bool (*fn)(__isl_keep isl_map *map,
6138 void *user), void *user);
6140 This function calls the callback function once for each
6141 pair of spaces for which there are elements in the input.
6142 If the callback returns C<isl_bool_true>, then all those elements
6143 are removed from the result. The only remaining elements in the output
6144 are then those for which the callback returns C<isl_bool_false>.
6148 #include <isl/aff.h>
6149 __isl_give isl_basic_set *isl_aff_zero_basic_set(
6150 __isl_take isl_aff *aff);
6151 __isl_give isl_basic_set *isl_aff_neg_basic_set(
6152 __isl_take isl_aff *aff);
6153 __isl_give isl_set *isl_pw_aff_pos_set(
6154 __isl_take isl_pw_aff *pa);
6155 __isl_give isl_set *isl_pw_aff_nonneg_set(
6156 __isl_take isl_pw_aff *pwaff);
6157 __isl_give isl_set *isl_pw_aff_zero_set(
6158 __isl_take isl_pw_aff *pwaff);
6159 __isl_give isl_set *isl_pw_aff_non_zero_set(
6160 __isl_take isl_pw_aff *pwaff);
6161 __isl_give isl_union_set *
6162 isl_union_pw_aff_zero_union_set(
6163 __isl_take isl_union_pw_aff *upa);
6164 __isl_give isl_union_set *
6165 isl_multi_union_pw_aff_zero_union_set(
6166 __isl_take isl_multi_union_pw_aff *mupa);
6168 The function C<isl_aff_neg_basic_set> returns a basic set
6169 containing those elements in the domain space
6170 of C<aff> where C<aff> is negative.
6171 The function C<isl_pw_aff_nonneg_set> returns a set
6172 containing those elements in the domain
6173 of C<pwaff> where C<pwaff> is non-negative.
6174 The function C<isl_multi_union_pw_aff_zero_union_set>
6175 returns a union set containing those elements
6176 in the domains of its elements where they are all zero.
6180 __isl_give isl_map *isl_set_identity(
6181 __isl_take isl_set *set);
6182 __isl_give isl_union_map *isl_union_set_identity(
6183 __isl_take isl_union_set *uset);
6184 __isl_give isl_union_pw_multi_aff *
6185 isl_union_set_identity_union_pw_multi_aff(
6186 __isl_take isl_union_set *uset);
6188 Construct an identity relation on the given (union) set.
6190 =item * Function Extraction
6192 A piecewise quasi affine expression that is equal to 1 on a set
6193 and 0 outside the set can be created using the following function.
6195 #include <isl/aff.h>
6196 __isl_give isl_pw_aff *isl_set_indicator_function(
6197 __isl_take isl_set *set);
6199 A piecewise multiple quasi affine expression can be extracted
6200 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
6201 and the C<isl_map> is single-valued.
6202 In case of a conversion from an C<isl_union_map>
6203 to an C<isl_union_pw_multi_aff>, these properties need to hold
6204 in each domain space.
6205 A conversion to a C<isl_multi_union_pw_aff> additionally
6206 requires that the input is non-empty and involves only a single
6209 #include <isl/aff.h>
6210 __isl_give isl_pw_multi_aff *isl_set_as_pw_multi_aff(
6211 __isl_take isl_set *set);
6212 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
6213 __isl_take isl_set *set);
6214 __isl_give isl_pw_multi_aff *isl_map_as_pw_multi_aff(
6215 __isl_take isl_map *map);
6216 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
6217 __isl_take isl_map *map);
6219 __isl_give isl_union_pw_multi_aff *
6220 isl_union_pw_multi_aff_from_union_set(
6221 __isl_take isl_union_set *uset);
6222 __isl_give isl_union_pw_multi_aff *
6223 isl_union_map_as_union_pw_multi_aff(
6224 __isl_take isl_union_map *umap);
6225 __isl_give isl_union_pw_multi_aff *
6226 isl_union_pw_multi_aff_from_union_map(
6227 __isl_take isl_union_map *umap);
6229 __isl_give isl_multi_union_pw_aff *
6230 isl_union_map_as_multi_union_pw_aff(
6231 __isl_take isl_union_map *umap);
6232 __isl_give isl_multi_union_pw_aff *
6233 isl_multi_union_pw_aff_from_union_map(
6234 __isl_take isl_union_map *umap);
6236 C<isl_map_as_pw_multi_aff> and C<isl_pw_multi_aff_from_map> perform
6238 Similarly for C<isl_set_as_pw_multi_aff> and
6239 C<isl_pw_multi_aff_from_set>,
6240 for C<isl_union_map_as_union_pw_multi_aff> and
6241 C<isl_union_pw_multi_aff_from_union_map> and
6242 for C<isl_union_map_as_multi_union_pw_aff> and
6243 C<isl_multi_union_pw_aff_from_union_map>.
6247 __isl_give isl_basic_set *isl_basic_map_deltas(
6248 __isl_take isl_basic_map *bmap);
6249 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
6250 __isl_give isl_union_set *isl_union_map_deltas(
6251 __isl_take isl_union_map *umap);
6253 These functions return a (basic) set containing the differences
6254 between image elements and corresponding domain elements in the input.
6256 __isl_give isl_basic_map *isl_basic_map_deltas_map(
6257 __isl_take isl_basic_map *bmap);
6258 __isl_give isl_map *isl_map_deltas_map(
6259 __isl_take isl_map *map);
6260 __isl_give isl_union_map *isl_union_map_deltas_map(
6261 __isl_take isl_union_map *umap);
6263 The functions above construct a (basic, regular or union) relation
6264 that maps (a wrapped version of) the input relation to its delta set.
6268 #include <isl/map.h>
6269 __isl_give isl_map *isl_set_translation(
6270 __isl_take isl_set *deltas);
6272 This function performs essentially the opposite operation
6273 of C<isl_map_deltas>. In particular, it returns pairs
6274 of elements in the same space that have a difference in C<deltas>.
6278 Simplify the representation of a set, relation or functions by trying
6279 to combine pairs of basic sets or relations into a single
6280 basic set or relation.
6282 #include <isl/set.h>
6283 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
6285 #include <isl/map.h>
6286 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
6288 #include <isl/union_set.h>
6289 __isl_give isl_union_set *isl_union_set_coalesce(
6290 __isl_take isl_union_set *uset);
6292 #include <isl/union_map.h>
6293 __isl_give isl_union_map *isl_union_map_coalesce(
6294 __isl_take isl_union_map *umap);
6296 #include <isl/aff.h>
6297 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
6298 __isl_take isl_pw_aff *pa);
6299 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
6300 __isl_take isl_pw_multi_aff *pma);
6301 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
6302 __isl_take isl_multi_pw_aff *mpa);
6303 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
6304 __isl_take isl_union_pw_aff *upa);
6305 __isl_give isl_union_pw_multi_aff *
6306 isl_union_pw_multi_aff_coalesce(
6307 __isl_take isl_union_pw_multi_aff *upma);
6308 __isl_give isl_multi_union_pw_aff *
6309 isl_multi_union_pw_aff_coalesce(
6310 __isl_take isl_multi_union_pw_aff *mupa);
6312 #include <isl/polynomial.h>
6313 __isl_give isl_pw_qpolynomial_fold *
6314 isl_pw_qpolynomial_fold_coalesce(
6315 __isl_take isl_pw_qpolynomial_fold *pwf);
6316 __isl_give isl_union_pw_qpolynomial *
6317 isl_union_pw_qpolynomial_coalesce(
6318 __isl_take isl_union_pw_qpolynomial *upwqp);
6319 __isl_give isl_union_pw_qpolynomial_fold *
6320 isl_union_pw_qpolynomial_fold_coalesce(
6321 __isl_take isl_union_pw_qpolynomial_fold *upwf);
6323 One of the methods for combining pairs of basic sets or relations
6324 can result in coefficients that are much larger than those that appear
6325 in the constraints of the input. By default, the coefficients are
6326 not allowed to grow larger, but this can be changed by unsetting
6327 the following option.
6329 isl_stat isl_options_set_coalesce_bounded_wrapping(
6330 isl_ctx *ctx, int val);
6331 int isl_options_get_coalesce_bounded_wrapping(
6334 One of the other methods tries to combine pairs of basic sets
6335 with different local variables, treating them as existentially
6336 quantified variables even if they have known (but different)
6337 integer division expressions. The result may then also have
6338 existentially quantified variables. Turning on the following
6339 option prevents this from happening.
6341 isl_stat isl_options_set_coalesce_preserve_locals(
6342 isl_ctx *ctx, int val);
6343 int isl_options_get_coalesce_preserve_locals(isl_ctx *ctx);
6345 =item * Detecting equalities
6347 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
6348 __isl_take isl_basic_set *bset);
6349 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
6350 __isl_take isl_basic_map *bmap);
6351 __isl_give isl_set *isl_set_detect_equalities(
6352 __isl_take isl_set *set);
6353 __isl_give isl_map *isl_map_detect_equalities(
6354 __isl_take isl_map *map);
6355 __isl_give isl_union_set *isl_union_set_detect_equalities(
6356 __isl_take isl_union_set *uset);
6357 __isl_give isl_union_map *isl_union_map_detect_equalities(
6358 __isl_take isl_union_map *umap);
6360 Simplify the representation of a set or relation by detecting implicit
6363 =item * Removing redundant constraints
6365 #include <isl/set.h>
6366 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
6367 __isl_take isl_basic_set *bset);
6368 __isl_give isl_set *isl_set_remove_redundancies(
6369 __isl_take isl_set *set);
6371 #include <isl/union_set.h>
6372 __isl_give isl_union_set *
6373 isl_union_set_remove_redundancies(
6374 __isl_take isl_union_set *uset);
6376 #include <isl/map.h>
6377 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
6378 __isl_take isl_basic_map *bmap);
6379 __isl_give isl_map *isl_map_remove_redundancies(
6380 __isl_take isl_map *map);
6382 #include <isl/union_map.h>
6383 __isl_give isl_union_map *
6384 isl_union_map_remove_redundancies(
6385 __isl_take isl_union_map *umap);
6389 __isl_give isl_basic_set *isl_set_convex_hull(
6390 __isl_take isl_set *set);
6391 __isl_give isl_basic_map *isl_map_convex_hull(
6392 __isl_take isl_map *map);
6394 If the input set or relation has any existentially quantified
6395 variables, then the result of these operations is currently undefined.
6399 #include <isl/set.h>
6400 __isl_give isl_basic_set *
6401 isl_set_unshifted_simple_hull(
6402 __isl_take isl_set *set);
6403 __isl_give isl_basic_set *isl_set_simple_hull(
6404 __isl_take isl_set *set);
6405 __isl_give isl_basic_set *
6406 isl_set_plain_unshifted_simple_hull(
6407 __isl_take isl_set *set);
6408 __isl_give isl_basic_set *
6409 isl_set_unshifted_simple_hull_from_set_list(
6410 __isl_take isl_set *set,
6411 __isl_take isl_set_list *list);
6413 #include <isl/map.h>
6414 __isl_give isl_basic_map *
6415 isl_map_unshifted_simple_hull(
6416 __isl_take isl_map *map);
6417 __isl_give isl_basic_map *isl_map_simple_hull(
6418 __isl_take isl_map *map);
6419 __isl_give isl_basic_map *
6420 isl_map_plain_unshifted_simple_hull(
6421 __isl_take isl_map *map);
6422 __isl_give isl_basic_map *
6423 isl_map_unshifted_simple_hull_from_map_list(
6424 __isl_take isl_map *map,
6425 __isl_take isl_map_list *list);
6427 #include <isl/union_map.h>
6428 __isl_give isl_union_map *isl_union_map_simple_hull(
6429 __isl_take isl_union_map *umap);
6431 These functions compute a single basic set or relation
6432 that contains the whole input set or relation.
6433 In particular, the output is described by translates
6434 of the constraints describing the basic sets or relations in the input.
6435 In case of C<isl_set_unshifted_simple_hull>, only the original
6436 constraints are used, without any translation.
6437 In case of C<isl_set_plain_unshifted_simple_hull> and
6438 C<isl_map_plain_unshifted_simple_hull>, the result is described
6439 by original constraints that are obviously satisfied
6440 by the entire input set or relation.
6441 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
6442 C<isl_map_unshifted_simple_hull_from_map_list>, the
6443 constraints are taken from the elements of the second argument.
6447 (See \autoref{s:simple hull}.)
6453 __isl_give isl_basic_set *isl_basic_set_affine_hull(
6454 __isl_take isl_basic_set *bset);
6455 __isl_give isl_basic_set *isl_set_affine_hull(
6456 __isl_take isl_set *set);
6457 __isl_give isl_union_set *isl_union_set_affine_hull(
6458 __isl_take isl_union_set *uset);
6459 __isl_give isl_basic_map *isl_basic_map_affine_hull(
6460 __isl_take isl_basic_map *bmap);
6461 __isl_give isl_basic_map *isl_map_affine_hull(
6462 __isl_take isl_map *map);
6463 __isl_give isl_union_map *isl_union_map_affine_hull(
6464 __isl_take isl_union_map *umap);
6466 In case of union sets and relations, the affine hull is computed
6469 =item * Polyhedral hull
6471 __isl_give isl_basic_set *isl_set_polyhedral_hull(
6472 __isl_take isl_set *set);
6473 __isl_give isl_basic_map *isl_map_polyhedral_hull(
6474 __isl_take isl_map *map);
6475 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
6476 __isl_take isl_union_set *uset);
6477 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
6478 __isl_take isl_union_map *umap);
6480 These functions compute a single basic set or relation
6481 not involving any existentially quantified variables
6482 that contains the whole input set or relation.
6483 In case of union sets and relations, the polyhedral hull is computed
6488 #include <isl/set.h>
6489 __isl_give isl_fixed_box *
6490 isl_set_get_simple_fixed_box_hull(
6491 __isl_keep isl_set *set)
6493 #include <isl/map.h>
6494 __isl_give isl_fixed_box *
6495 isl_map_get_range_simple_fixed_box_hull(
6496 __isl_keep isl_map *map);
6498 These functions try to approximate the set or
6499 the range of the map by a box of fixed size.
6500 The box is described in terms of an offset living in the same space as
6501 the input and a size living in the set or range space. For any element
6502 in the input map, the range value is greater than or equal to
6503 the offset applied to the domain value and the difference with
6504 this offset is strictly smaller than the size.
6505 The same holds for the elements of the input set, where
6506 the offset is a parametric constant value.
6507 If no fixed-size approximation can be found,
6508 an I<invalid> box is returned, i.e., one for which
6509 C<isl_fixed_box_is_valid> below returns false.
6511 The validity, the offset and the size of the box can be obtained using
6512 the following functions.
6514 #include <isl/fixed_box.h>
6515 isl_bool isl_fixed_box_is_valid(
6516 __isl_keep isl_fixed_box *box);
6517 __isl_give isl_multi_aff *isl_fixed_box_get_offset(
6518 __isl_keep isl_fixed_box *box);
6519 __isl_give isl_multi_val *isl_fixed_box_get_size(
6520 __isl_keep isl_fixed_box *box);
6522 The box can be copied and freed using the following functions.
6524 #include <isl/fixed_box.h>
6525 __isl_give isl_fixed_box *isl_fixed_box_copy(
6526 __isl_keep isl_fixed_box *box);
6527 __isl_null isl_fixed_box *isl_fixed_box_free(
6528 __isl_take isl_fixed_box *box);
6530 An object of type C<isl_fixed_box> can be read from input
6531 using the following function.
6533 #include <isl/fixed_box.h>
6534 __isl_give isl_fixed_box *
6535 isl_fixed_box_read_from_str(isl_ctx *ctx,
6538 A representation of the information contained in an object
6539 of type C<isl_fixed_box> can be obtained using
6541 #include <isl/fixed_box.h>
6542 __isl_give isl_printer *isl_printer_print_fixed_box(
6543 __isl_take isl_printer *p,
6544 __isl_keep isl_fixed_box *box);
6545 __isl_give char *isl_fixed_box_to_str(
6546 __isl_keep isl_fixed_box *box);
6548 C<isl_fixed_box_to_str> prints the information in flow format.
6550 =item * Other approximations
6552 #include <isl/set.h>
6553 __isl_give isl_basic_set *
6554 isl_basic_set_drop_constraints_involving_dims(
6555 __isl_take isl_basic_set *bset,
6556 enum isl_dim_type type,
6557 unsigned first, unsigned n);
6558 __isl_give isl_basic_set *
6559 isl_basic_set_drop_constraints_not_involving_dims(
6560 __isl_take isl_basic_set *bset,
6561 enum isl_dim_type type,
6562 unsigned first, unsigned n);
6563 __isl_give isl_set *
6564 isl_set_drop_constraints_involving_dims(
6565 __isl_take isl_set *set,
6566 enum isl_dim_type type,
6567 unsigned first, unsigned n);
6568 __isl_give isl_set *
6569 isl_set_drop_constraints_not_involving_dims(
6570 __isl_take isl_set *set,
6571 enum isl_dim_type type,
6572 unsigned first, unsigned n);
6574 #include <isl/map.h>
6575 __isl_give isl_basic_map *
6576 isl_basic_map_drop_constraints_involving_dims(
6577 __isl_take isl_basic_map *bmap,
6578 enum isl_dim_type type,
6579 unsigned first, unsigned n);
6580 __isl_give isl_basic_map *
6581 isl_basic_map_drop_constraints_not_involving_dims(
6582 __isl_take isl_basic_map *bmap,
6583 enum isl_dim_type type,
6584 unsigned first, unsigned n);
6585 __isl_give isl_map *
6586 isl_map_drop_constraints_involving_dims(
6587 __isl_take isl_map *map,
6588 enum isl_dim_type type,
6589 unsigned first, unsigned n);
6590 __isl_give isl_map *
6591 isl_map_drop_constraints_not_involving_dims(
6592 __isl_take isl_map *map,
6593 enum isl_dim_type type,
6594 unsigned first, unsigned n);
6596 These functions drop any constraints (not) involving the specified dimensions.
6597 Note that the result depends on the representation of the input.
6599 #include <isl/polynomial.h>
6600 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
6601 __isl_take isl_pw_qpolynomial *pwqp, int sign);
6602 __isl_give isl_union_pw_qpolynomial *
6603 isl_union_pw_qpolynomial_to_polynomial(
6604 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
6606 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
6607 the polynomial will be an overapproximation. If C<sign> is negative,
6608 it will be an underapproximation. If C<sign> is zero, the approximation
6609 will lie somewhere in between.
6613 __isl_give isl_basic_set *isl_basic_set_sample(
6614 __isl_take isl_basic_set *bset);
6615 __isl_give isl_basic_set *isl_set_sample(
6616 __isl_take isl_set *set);
6617 __isl_give isl_basic_map *isl_basic_map_sample(
6618 __isl_take isl_basic_map *bmap);
6619 __isl_give isl_basic_map *isl_map_sample(
6620 __isl_take isl_map *map);
6622 If the input (basic) set or relation is non-empty, then return
6623 a singleton subset of the input. Otherwise, return an empty set.
6625 =item * Optimization
6627 #include <isl/ilp.h>
6628 __isl_give isl_val *isl_basic_set_max_val(
6629 __isl_keep isl_basic_set *bset,
6630 __isl_keep isl_aff *obj);
6631 __isl_give isl_val *isl_set_min_val(
6632 __isl_keep isl_set *set,
6633 __isl_keep isl_aff *obj);
6634 __isl_give isl_val *isl_set_max_val(
6635 __isl_keep isl_set *set,
6636 __isl_keep isl_aff *obj);
6637 __isl_give isl_multi_val *
6638 isl_union_set_min_multi_union_pw_aff(
6639 __isl_keep isl_union_set *uset,
6640 __isl_keep isl_multi_union_pw_aff *obj);
6642 Compute the minimum or maximum of the integer affine expression C<obj>
6643 over the points in C<set>.
6644 The result is C<NULL> in case of an error, the optimal value in case
6645 there is one, negative infinity or infinity if the problem is unbounded and
6646 NaN if the problem is empty.
6648 #include <isl/ilp.h>
6649 __isl_give isl_val *isl_pw_aff_min_val(
6650 __isl_take isl_pw_aff *pa);
6651 __isl_give isl_val *isl_pw_aff_max_val(
6652 __isl_take isl_pw_aff *pa);
6653 __isl_give isl_multi_val *
6654 isl_pw_multi_aff_min_multi_val(
6655 __isl_take isl_pw_multi_aff *pma);
6656 __isl_give isl_multi_val *
6657 isl_pw_multi_aff_max_multi_val(
6658 __isl_take isl_pw_multi_aff *pma);
6659 __isl_give isl_multi_val *
6660 isl_multi_pw_aff_min_multi_val(
6661 __isl_take isl_multi_pw_aff *mpa);
6662 __isl_give isl_multi_val *
6663 isl_multi_pw_aff_max_multi_val(
6664 __isl_take isl_multi_pw_aff *mpa);
6665 __isl_give isl_val *isl_union_pw_aff_min_val(
6666 __isl_take isl_union_pw_aff *upa);
6667 __isl_give isl_val *isl_union_pw_aff_max_val(
6668 __isl_take isl_union_pw_aff *upa);
6669 __isl_give isl_multi_val *
6670 isl_multi_union_pw_aff_min_multi_val(
6671 __isl_take isl_multi_union_pw_aff *mupa);
6672 __isl_give isl_multi_val *
6673 isl_multi_union_pw_aff_max_multi_val(
6674 __isl_take isl_multi_union_pw_aff *mupa);
6676 Compute the minimum or maximum of the integer affine expression
6677 over its definition domain.
6678 The result is C<NULL> in case of an error, the optimal value in case
6679 there is one, negative infinity or infinity if the problem is unbounded and
6680 NaN if the problem is empty.
6682 #include <isl/ilp.h>
6683 __isl_give isl_val *isl_basic_set_dim_max_val(
6684 __isl_take isl_basic_set *bset, int pos);
6685 __isl_give isl_val *isl_set_dim_min_val(
6686 __isl_take isl_set *set, int pos);
6687 __isl_give isl_val *isl_set_dim_max_val(
6688 __isl_take isl_set *set, int pos);
6690 Return the minimal or maximal value attained by the given set dimension,
6691 independently of the parameter values and of any other dimensions.
6692 The result is C<NULL> in case of an error, the optimal value in case
6693 there is one, (negative) infinity if the problem is unbounded and
6694 NaN if the input is empty.
6696 =item * Parametric optimization
6698 __isl_give isl_pw_aff *isl_set_dim_min(
6699 __isl_take isl_set *set, int pos);
6700 __isl_give isl_pw_aff *isl_set_dim_max(
6701 __isl_take isl_set *set, int pos);
6702 __isl_give isl_pw_aff *isl_map_dim_min(
6703 __isl_take isl_map *map, int pos);
6704 __isl_give isl_pw_aff *isl_map_dim_max(
6705 __isl_take isl_map *map, int pos);
6706 __isl_give isl_multi_pw_aff *
6707 isl_set_min_multi_pw_aff(
6708 __isl_take isl_set *set);
6709 __isl_give isl_multi_pw_aff *
6710 isl_set_max_multi_pw_aff(
6711 __isl_take isl_set *set);
6712 __isl_give isl_multi_pw_aff *
6713 isl_map_min_multi_pw_aff(
6714 __isl_take isl_map *map);
6715 __isl_give isl_multi_pw_aff *
6716 isl_map_max_multi_pw_aff(
6717 __isl_take isl_map *map);
6719 Compute the minimum or maximum of the (given) set or output dimension(s)
6720 as a function of the parameters (and input dimensions), but independently
6721 of the other set or output dimensions.
6722 For lexicographic optimization, see L<"Lexicographic Optimization">.
6726 The following functions compute either the set of (rational) coefficient
6727 values of valid constraints for the given set or the set of (rational)
6728 values satisfying the constraints with coefficients from the given set.
6729 Internally, these two sets of functions perform essentially the
6730 same operations, except that the set of coefficients is assumed to
6731 be a cone, while the set of values may be any polyhedron.
6732 The current implementation is based on the Farkas lemma and
6733 Fourier-Motzkin elimination, but this may change or be made optional
6734 in future. In particular, future implementations may use different
6735 dualization algorithms or skip the elimination step.
6737 #include <isl/set.h>
6738 __isl_give isl_basic_set *isl_basic_set_coefficients(
6739 __isl_take isl_basic_set *bset);
6740 __isl_give isl_basic_set_list *
6741 isl_basic_set_list_coefficients(
6742 __isl_take isl_basic_set_list *list);
6743 __isl_give isl_basic_set *isl_set_coefficients(
6744 __isl_take isl_set *set);
6745 __isl_give isl_union_set *isl_union_set_coefficients(
6746 __isl_take isl_union_set *bset);
6747 __isl_give isl_basic_set *isl_basic_set_solutions(
6748 __isl_take isl_basic_set *bset);
6749 __isl_give isl_basic_set *isl_set_solutions(
6750 __isl_take isl_set *set);
6751 __isl_give isl_union_set *isl_union_set_solutions(
6752 __isl_take isl_union_set *bset);
6756 __isl_give isl_map *isl_map_fixed_power_val(
6757 __isl_take isl_map *map,
6758 __isl_take isl_val *exp);
6759 __isl_give isl_union_map *
6760 isl_union_map_fixed_power_val(
6761 __isl_take isl_union_map *umap,
6762 __isl_take isl_val *exp);
6764 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
6765 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
6766 of C<map> is computed.
6768 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
6770 __isl_give isl_union_map *isl_union_map_power(
6771 __isl_take isl_union_map *umap, isl_bool *exact);
6773 Compute a parametric representation for all positive powers I<k> of C<map>.
6774 The result maps I<k> to a nested relation corresponding to the
6775 I<k>th power of C<map>.
6776 The result may be an overapproximation. If the result is known to be exact,
6777 then C<*exact> is set to C<1>.
6779 =item * Transitive closure
6781 __isl_give isl_map *isl_map_transitive_closure(
6782 __isl_take isl_map *map, isl_bool *exact);
6783 __isl_give isl_union_map *isl_union_map_transitive_closure(
6784 __isl_take isl_union_map *umap, isl_bool *exact);
6786 Compute the transitive closure of C<map>.
6787 The result may be an overapproximation. If the result is known to be exact,
6788 then C<*exact> is set to C<1>.
6790 =item * Reaching path lengths
6792 __isl_give isl_map *isl_map_reaching_path_lengths(
6793 __isl_take isl_map *map, isl_bool *exact);
6795 Compute a relation that maps each element in the range of C<map>
6796 to the lengths of all paths composed of edges in C<map> that
6797 end up in the given element.
6798 The result may be an overapproximation. If the result is known to be exact,
6799 then C<*exact> is set to C<1>.
6800 To compute the I<maximal> path length, the resulting relation
6801 should be postprocessed by C<isl_map_lexmax>.
6802 In particular, if the input relation is a dependence relation
6803 (mapping sources to sinks), then the maximal path length corresponds
6804 to the free schedule.
6805 Note, however, that C<isl_map_lexmax> expects the maximum to be
6806 finite, so if the path lengths are unbounded (possibly due to
6807 the overapproximation), then you will get an error message.
6811 #include <isl/space.h>
6812 __isl_give isl_space *isl_space_wrap(
6813 __isl_take isl_space *space);
6814 __isl_give isl_space *isl_space_unwrap(
6815 __isl_take isl_space *space);
6817 #include <isl/local_space.h>
6818 __isl_give isl_local_space *isl_local_space_wrap(
6819 __isl_take isl_local_space *ls);
6821 #include <isl/set.h>
6822 __isl_give isl_basic_map *isl_basic_set_unwrap(
6823 __isl_take isl_basic_set *bset);
6824 __isl_give isl_map *isl_set_unwrap(
6825 __isl_take isl_set *set);
6827 #include <isl/map.h>
6828 __isl_give isl_basic_set *isl_basic_map_wrap(
6829 __isl_take isl_basic_map *bmap);
6830 __isl_give isl_set *isl_map_wrap(
6831 __isl_take isl_map *map);
6833 #include <isl/union_set.h>
6834 __isl_give isl_union_map *isl_union_set_unwrap(
6835 __isl_take isl_union_set *uset);
6837 #include <isl/union_map.h>
6838 __isl_give isl_union_set *isl_union_map_wrap(
6839 __isl_take isl_union_map *umap);
6841 The input to C<isl_space_unwrap> should
6842 be the space of a set, while that of
6843 C<isl_space_wrap> should be the space of a relation.
6844 Conversely, the output of C<isl_space_unwrap> is the space
6845 of a relation, while that of C<isl_space_wrap> is the space of a set.
6849 Remove any internal structure of domain (and range) of the given
6850 set or relation. If there is any such internal structure in the input,
6851 then the name of the space is also removed.
6853 #include <isl/space.h>
6854 __isl_give isl_space *isl_space_flatten_domain(
6855 __isl_take isl_space *space);
6856 __isl_give isl_space *isl_space_flatten_range(
6857 __isl_take isl_space *space);
6859 #include <isl/local_space.h>
6860 __isl_give isl_local_space *
6861 isl_local_space_flatten_domain(
6862 __isl_take isl_local_space *ls);
6863 __isl_give isl_local_space *
6864 isl_local_space_flatten_range(
6865 __isl_take isl_local_space *ls);
6867 #include <isl/set.h>
6868 __isl_give isl_basic_set *isl_basic_set_flatten(
6869 __isl_take isl_basic_set *bset);
6870 __isl_give isl_set *isl_set_flatten(
6871 __isl_take isl_set *set);
6873 #include <isl/map.h>
6874 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
6875 __isl_take isl_basic_map *bmap);
6876 __isl_give isl_basic_map *isl_basic_map_flatten_range(
6877 __isl_take isl_basic_map *bmap);
6878 __isl_give isl_map *isl_map_flatten_range(
6879 __isl_take isl_map *map);
6880 __isl_give isl_map *isl_map_flatten_domain(
6881 __isl_take isl_map *map);
6882 __isl_give isl_basic_map *isl_basic_map_flatten(
6883 __isl_take isl_basic_map *bmap);
6884 __isl_give isl_map *isl_map_flatten(
6885 __isl_take isl_map *map);
6888 __isl_give isl_multi_id *isl_multi_id_flatten_range(
6889 __isl_take isl_multi_id *mi);
6891 #include <isl/val.h>
6892 __isl_give isl_multi_val *isl_multi_val_flatten_range(
6893 __isl_take isl_multi_val *mv);
6895 #include <isl/aff.h>
6896 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
6897 __isl_take isl_multi_aff *ma);
6898 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
6899 __isl_take isl_multi_aff *ma);
6900 __isl_give isl_multi_pw_aff *
6901 isl_multi_pw_aff_flatten_range(
6902 __isl_take isl_multi_pw_aff *mpa);
6903 __isl_give isl_multi_union_pw_aff *
6904 isl_multi_union_pw_aff_flatten_range(
6905 __isl_take isl_multi_union_pw_aff *mupa);
6907 #include <isl/map.h>
6908 __isl_give isl_map *isl_set_flatten_map(
6909 __isl_take isl_set *set);
6911 The function above constructs a relation
6912 that maps the input set to a flattened version of the set.
6916 Lift the input set to a space with extra dimensions corresponding
6917 to the existentially quantified variables in the input.
6918 In particular, the result lives in a wrapped map where the domain
6919 is the original space and the range corresponds to the original
6920 existentially quantified variables.
6922 #include <isl/set.h>
6923 __isl_give isl_basic_set *isl_basic_set_lift(
6924 __isl_take isl_basic_set *bset);
6925 __isl_give isl_set *isl_set_lift(
6926 __isl_take isl_set *set);
6927 __isl_give isl_union_set *isl_union_set_lift(
6928 __isl_take isl_union_set *uset);
6930 Given a local space that contains the existentially quantified
6931 variables of a set, a basic relation that, when applied to
6932 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
6933 can be constructed using the following function.
6935 #include <isl/local_space.h>
6936 __isl_give isl_basic_map *isl_local_space_lifting(
6937 __isl_take isl_local_space *ls);
6939 #include <isl/aff.h>
6940 __isl_give isl_multi_aff *isl_multi_aff_lift(
6941 __isl_take isl_multi_aff *maff,
6942 __isl_give isl_local_space **ls);
6944 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
6945 then it is assigned the local space that lies at the basis of
6946 the lifting applied.
6948 =item * Internal Product
6950 #include <isl/space.h>
6951 __isl_give isl_space *isl_space_zip(
6952 __isl_take isl_space *space);
6954 #include <isl/map.h>
6955 __isl_give isl_basic_map *isl_basic_map_zip(
6956 __isl_take isl_basic_map *bmap);
6957 __isl_give isl_map *isl_map_zip(
6958 __isl_take isl_map *map);
6960 #include <isl/union_map.h>
6961 __isl_give isl_union_map *isl_union_map_zip(
6962 __isl_take isl_union_map *umap);
6964 Given a relation with nested relations for domain and range,
6965 interchange the range of the domain with the domain of the range.
6969 #include <isl/space.h>
6970 __isl_give isl_space *isl_space_curry(
6971 __isl_take isl_space *space);
6972 __isl_give isl_space *isl_space_uncurry(
6973 __isl_take isl_space *space);
6975 #include <isl/map.h>
6976 __isl_give isl_basic_map *isl_basic_map_curry(
6977 __isl_take isl_basic_map *bmap);
6978 __isl_give isl_basic_map *isl_basic_map_uncurry(
6979 __isl_take isl_basic_map *bmap);
6980 __isl_give isl_map *isl_map_curry(
6981 __isl_take isl_map *map);
6982 __isl_give isl_map *isl_map_uncurry(
6983 __isl_take isl_map *map);
6985 #include <isl/union_map.h>
6986 __isl_give isl_union_map *isl_union_map_curry(
6987 __isl_take isl_union_map *umap);
6988 __isl_give isl_union_map *isl_union_map_uncurry(
6989 __isl_take isl_union_map *umap);
6991 Given a relation with a nested relation for domain,
6992 the C<curry> functions
6993 move the range of the nested relation out of the domain
6994 and use it as the domain of a nested relation in the range,
6995 with the original range as range of this nested relation.
6996 The C<uncurry> functions perform the inverse operation.
6998 #include <isl/space.h>
6999 __isl_give isl_space *isl_space_range_curry(
7000 __isl_take isl_space *space);
7002 #include <isl/map.h>
7003 __isl_give isl_map *isl_map_range_curry(
7004 __isl_take isl_map *map);
7006 #include <isl/union_map.h>
7007 __isl_give isl_union_map *isl_union_map_range_curry(
7008 __isl_take isl_union_map *umap);
7010 These functions apply the currying to the relation that
7011 is nested inside the range of the input.
7013 =item * Aligning parameters
7015 Change the order of the parameters of the given set, relation
7017 such that the first parameters match those of C<model>.
7018 This may involve the introduction of extra parameters.
7019 All parameters need to be named.
7021 #include <isl/space.h>
7022 __isl_give isl_space *isl_space_align_params(
7023 __isl_take isl_space *space1,
7024 __isl_take isl_space *space2)
7026 #include <isl/set.h>
7027 __isl_give isl_basic_set *isl_basic_set_align_params(
7028 __isl_take isl_basic_set *bset,
7029 __isl_take isl_space *model);
7030 __isl_give isl_set *isl_set_align_params(
7031 __isl_take isl_set *set,
7032 __isl_take isl_space *model);
7034 #include <isl/map.h>
7035 __isl_give isl_basic_map *isl_basic_map_align_params(
7036 __isl_take isl_basic_map *bmap,
7037 __isl_take isl_space *model);
7038 __isl_give isl_map *isl_map_align_params(
7039 __isl_take isl_map *map,
7040 __isl_take isl_space *model);
7043 __isl_give isl_multi_id *isl_multi_id_align_params(
7044 __isl_take isl_multi_id *mi,
7045 __isl_take isl_space *model);
7047 #include <isl/val.h>
7048 __isl_give isl_multi_val *isl_multi_val_align_params(
7049 __isl_take isl_multi_val *mv,
7050 __isl_take isl_space *model);
7052 #include <isl/aff.h>
7053 __isl_give isl_aff *isl_aff_align_params(
7054 __isl_take isl_aff *aff,
7055 __isl_take isl_space *model);
7056 __isl_give isl_multi_aff *isl_multi_aff_align_params(
7057 __isl_take isl_multi_aff *multi,
7058 __isl_take isl_space *model);
7059 __isl_give isl_pw_aff *isl_pw_aff_align_params(
7060 __isl_take isl_pw_aff *pwaff,
7061 __isl_take isl_space *model);
7062 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
7063 __isl_take isl_pw_multi_aff *pma,
7064 __isl_take isl_space *model);
7065 __isl_give isl_union_pw_aff *
7066 isl_union_pw_aff_align_params(
7067 __isl_take isl_union_pw_aff *upa,
7068 __isl_take isl_space *model);
7069 __isl_give isl_union_pw_multi_aff *
7070 isl_union_pw_multi_aff_align_params(
7071 __isl_take isl_union_pw_multi_aff *upma,
7072 __isl_take isl_space *model);
7073 __isl_give isl_multi_union_pw_aff *
7074 isl_multi_union_pw_aff_align_params(
7075 __isl_take isl_multi_union_pw_aff *mupa,
7076 __isl_take isl_space *model);
7078 #include <isl/polynomial.h>
7079 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
7080 __isl_take isl_qpolynomial *qp,
7081 __isl_take isl_space *model);
7083 =item * Drop unused parameters
7085 Drop parameters that are not referenced by the isl object.
7086 All parameters need to be named.
7088 #include <isl/set.h>
7089 __isl_give isl_basic_set *
7090 isl_basic_set_drop_unused_params(
7091 __isl_take isl_basic_set *bset);
7092 __isl_give isl_set *isl_set_drop_unused_params(
7093 __isl_take isl_set *set);
7095 #include <isl/map.h>
7096 __isl_give isl_basic_map *
7097 isl_basic_map_drop_unused_params(
7098 __isl_take isl_basic_map *bmap);
7099 __isl_give isl_map *isl_map_drop_unused_params(
7100 __isl_take isl_map *map);
7102 #include <isl/union_set.h>
7103 __isl_give isl_union_set *
7104 isl_union_set_drop_unused_params(
7105 __isl_take isl_union_set *uset);
7107 #include <isl/union_map.h>
7108 __isl_give isl_union_map *
7109 isl_union_map_drop_unused_params(
7110 __isl_take isl_union_map *umap);
7112 #include <isl/aff.h>
7113 __isl_give isl_pw_aff *isl_pw_aff_drop_unused_params(
7114 __isl_take isl_pw_aff *pa);
7115 __isl_give isl_pw_multi_aff *
7116 isl_pw_multi_aff_drop_unused_params(
7117 __isl_take isl_pw_multi_aff *pma);
7118 __isl_give isl_union_pw_aff *
7119 isl_union_pw_aff_drop_unused_params(
7120 __isl_take isl_union_pw_aff *upa);
7121 __isl_give isl_union_pw_multi_aff *
7122 isl_union_pw_multi_aff_drop_unused_params(
7123 __isl_take isl_union_pw_multi_aff *upma);
7125 #include <isl/polynomial.h>
7126 __isl_give isl_pw_qpolynomial *
7127 isl_pw_qpolynomial_drop_unused_params(
7128 __isl_take isl_pw_qpolynomial *pwqp);
7129 __isl_give isl_pw_qpolynomial_fold *
7130 isl_pw_qpolynomial_fold_drop_unused_params(
7131 __isl_take isl_pw_qpolynomial_fold *pwf);
7132 __isl_give isl_union_pw_qpolynomial *
7133 isl_union_pw_qpolynomial_drop_unused_params(
7134 __isl_take isl_union_pw_qpolynomial *upwqp);
7135 __isl_give isl_union_pw_qpolynomial_fold *
7136 isl_union_pw_qpolynomial_fold_drop_unused_params(
7137 __isl_take isl_union_pw_qpolynomial_fold *upwf);
7139 =item * Unary Arithmetic Operations
7141 #include <isl/set.h>
7142 __isl_give isl_set *isl_set_neg(
7143 __isl_take isl_set *set);
7144 #include <isl/map.h>
7145 __isl_give isl_map *isl_map_neg(
7146 __isl_take isl_map *map);
7148 C<isl_set_neg> constructs a set containing the opposites of
7149 the elements in its argument.
7150 The domain of the result of C<isl_map_neg> is the same
7151 as the domain of its argument. The corresponding range
7152 elements are the opposites of the corresponding range
7153 elements in the argument.
7155 #include <isl/val.h>
7156 __isl_give isl_multi_val *isl_multi_val_neg(
7157 __isl_take isl_multi_val *mv);
7159 #include <isl/aff.h>
7160 __isl_give isl_aff *isl_aff_neg(
7161 __isl_take isl_aff *aff);
7162 __isl_give isl_multi_aff *isl_multi_aff_neg(
7163 __isl_take isl_multi_aff *ma);
7164 __isl_give isl_pw_aff *isl_pw_aff_neg(
7165 __isl_take isl_pw_aff *pwaff);
7166 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
7167 __isl_take isl_pw_multi_aff *pma);
7168 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
7169 __isl_take isl_multi_pw_aff *mpa);
7170 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
7171 __isl_take isl_union_pw_aff *upa);
7172 __isl_give isl_union_pw_multi_aff *
7173 isl_union_pw_multi_aff_neg(
7174 __isl_take isl_union_pw_multi_aff *upma);
7175 __isl_give isl_multi_union_pw_aff *
7176 isl_multi_union_pw_aff_neg(
7177 __isl_take isl_multi_union_pw_aff *mupa);
7178 __isl_give isl_aff *isl_aff_ceil(
7179 __isl_take isl_aff *aff);
7180 __isl_give isl_pw_aff *isl_pw_aff_ceil(
7181 __isl_take isl_pw_aff *pwaff);
7182 __isl_give isl_aff *isl_aff_floor(
7183 __isl_take isl_aff *aff);
7184 __isl_give isl_multi_aff *isl_multi_aff_floor(
7185 __isl_take isl_multi_aff *ma);
7186 __isl_give isl_pw_aff *isl_pw_aff_floor(
7187 __isl_take isl_pw_aff *pwaff);
7188 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
7189 __isl_take isl_union_pw_aff *upa);
7190 __isl_give isl_multi_union_pw_aff *
7191 isl_multi_union_pw_aff_floor(
7192 __isl_take isl_multi_union_pw_aff *mupa);
7194 #include <isl/aff.h>
7195 __isl_give isl_pw_aff *isl_pw_aff_list_min(
7196 __isl_take isl_pw_aff_list *list);
7197 __isl_give isl_pw_aff *isl_pw_aff_list_max(
7198 __isl_take isl_pw_aff_list *list);
7200 #include <isl/polynomial.h>
7201 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
7202 __isl_take isl_qpolynomial *qp);
7203 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
7204 __isl_take isl_pw_qpolynomial *pwqp);
7205 __isl_give isl_union_pw_qpolynomial *
7206 isl_union_pw_qpolynomial_neg(
7207 __isl_take isl_union_pw_qpolynomial *upwqp);
7208 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
7209 __isl_take isl_qpolynomial *qp,
7211 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
7212 __isl_take isl_pw_qpolynomial *pwqp,
7217 The following functions evaluate a function in a point.
7219 #include <isl/aff.h>
7220 __isl_give isl_val *isl_aff_eval(
7221 __isl_take isl_aff *aff,
7222 __isl_take isl_point *pnt);
7223 __isl_give isl_val *isl_pw_aff_eval(
7224 __isl_take isl_pw_aff *pa,
7225 __isl_take isl_point *pnt);
7227 #include <isl/polynomial.h>
7228 __isl_give isl_val *isl_pw_qpolynomial_eval(
7229 __isl_take isl_pw_qpolynomial *pwqp,
7230 __isl_take isl_point *pnt);
7231 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
7232 __isl_take isl_pw_qpolynomial_fold *pwf,
7233 __isl_take isl_point *pnt);
7234 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
7235 __isl_take isl_union_pw_qpolynomial *upwqp,
7236 __isl_take isl_point *pnt);
7237 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
7238 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7239 __isl_take isl_point *pnt);
7241 These functions return NaN when evaluated at a void point.
7242 Note that C<isl_pw_aff_eval> returns NaN when the function is evaluated outside
7243 its definition domain, while C<isl_pw_qpolynomial_eval> returns zero
7244 when the function is evaluated outside its explicit domain.
7246 =item * Dimension manipulation
7248 It is usually not advisable to directly change the (input or output)
7249 space of a set or a relation as this removes the name and the internal
7250 structure of the space. However, the functions below can be useful
7251 to add new parameters, assuming
7252 C<isl_set_align_params> and C<isl_map_align_params>
7255 #include <isl/space.h>
7256 __isl_give isl_space *isl_space_add_dims(
7257 __isl_take isl_space *space,
7258 enum isl_dim_type type, unsigned n);
7259 __isl_give isl_space *isl_space_insert_dims(
7260 __isl_take isl_space *space,
7261 enum isl_dim_type type, unsigned pos, unsigned n);
7262 __isl_give isl_space *isl_space_drop_dims(
7263 __isl_take isl_space *space,
7264 enum isl_dim_type type, unsigned first, unsigned n);
7265 __isl_give isl_space *isl_space_move_dims(
7266 __isl_take isl_space *space,
7267 enum isl_dim_type dst_type, unsigned dst_pos,
7268 enum isl_dim_type src_type, unsigned src_pos,
7271 #include <isl/local_space.h>
7272 __isl_give isl_local_space *isl_local_space_add_dims(
7273 __isl_take isl_local_space *ls,
7274 enum isl_dim_type type, unsigned n);
7275 __isl_give isl_local_space *isl_local_space_insert_dims(
7276 __isl_take isl_local_space *ls,
7277 enum isl_dim_type type, unsigned first, unsigned n);
7278 __isl_give isl_local_space *isl_local_space_drop_dims(
7279 __isl_take isl_local_space *ls,
7280 enum isl_dim_type type, unsigned first, unsigned n);
7282 #include <isl/set.h>
7283 __isl_give isl_basic_set *isl_basic_set_add_dims(
7284 __isl_take isl_basic_set *bset,
7285 enum isl_dim_type type, unsigned n);
7286 __isl_give isl_set *isl_set_add_dims(
7287 __isl_take isl_set *set,
7288 enum isl_dim_type type, unsigned n);
7289 __isl_give isl_basic_set *isl_basic_set_insert_dims(
7290 __isl_take isl_basic_set *bset,
7291 enum isl_dim_type type, unsigned pos,
7293 __isl_give isl_set *isl_set_insert_dims(
7294 __isl_take isl_set *set,
7295 enum isl_dim_type type, unsigned pos, unsigned n);
7296 __isl_give isl_basic_set *isl_basic_set_move_dims(
7297 __isl_take isl_basic_set *bset,
7298 enum isl_dim_type dst_type, unsigned dst_pos,
7299 enum isl_dim_type src_type, unsigned src_pos,
7301 __isl_give isl_set *isl_set_move_dims(
7302 __isl_take isl_set *set,
7303 enum isl_dim_type dst_type, unsigned dst_pos,
7304 enum isl_dim_type src_type, unsigned src_pos,
7307 #include <isl/map.h>
7308 __isl_give isl_basic_map *isl_basic_map_add_dims(
7309 __isl_take isl_basic_map *bmap,
7310 enum isl_dim_type type, unsigned n);
7311 __isl_give isl_map *isl_map_add_dims(
7312 __isl_take isl_map *map,
7313 enum isl_dim_type type, unsigned n);
7314 __isl_give isl_basic_map *isl_basic_map_insert_dims(
7315 __isl_take isl_basic_map *bmap,
7316 enum isl_dim_type type, unsigned pos,
7318 __isl_give isl_map *isl_map_insert_dims(
7319 __isl_take isl_map *map,
7320 enum isl_dim_type type, unsigned pos, unsigned n);
7321 __isl_give isl_basic_map *isl_basic_map_move_dims(
7322 __isl_take isl_basic_map *bmap,
7323 enum isl_dim_type dst_type, unsigned dst_pos,
7324 enum isl_dim_type src_type, unsigned src_pos,
7326 __isl_give isl_map *isl_map_move_dims(
7327 __isl_take isl_map *map,
7328 enum isl_dim_type dst_type, unsigned dst_pos,
7329 enum isl_dim_type src_type, unsigned src_pos,
7332 #include <isl/val.h>
7333 __isl_give isl_multi_val *isl_multi_val_insert_dims(
7334 __isl_take isl_multi_val *mv,
7335 enum isl_dim_type type, unsigned first, unsigned n);
7336 __isl_give isl_multi_val *isl_multi_val_add_dims(
7337 __isl_take isl_multi_val *mv,
7338 enum isl_dim_type type, unsigned n);
7339 __isl_give isl_multi_val *isl_multi_val_drop_dims(
7340 __isl_take isl_multi_val *mv,
7341 enum isl_dim_type type, unsigned first, unsigned n);
7343 #include <isl/aff.h>
7344 __isl_give isl_aff *isl_aff_insert_dims(
7345 __isl_take isl_aff *aff,
7346 enum isl_dim_type type, unsigned first, unsigned n);
7347 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
7348 __isl_take isl_multi_aff *ma,
7349 enum isl_dim_type type, unsigned first, unsigned n);
7350 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
7351 __isl_take isl_pw_aff *pwaff,
7352 enum isl_dim_type type, unsigned first, unsigned n);
7353 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
7354 __isl_take isl_multi_pw_aff *mpa,
7355 enum isl_dim_type type, unsigned first, unsigned n);
7356 __isl_give isl_aff *isl_aff_add_dims(
7357 __isl_take isl_aff *aff,
7358 enum isl_dim_type type, unsigned n);
7359 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
7360 __isl_take isl_multi_aff *ma,
7361 enum isl_dim_type type, unsigned n);
7362 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
7363 __isl_take isl_pw_aff *pwaff,
7364 enum isl_dim_type type, unsigned n);
7365 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
7366 __isl_take isl_multi_pw_aff *mpa,
7367 enum isl_dim_type type, unsigned n);
7368 __isl_give isl_aff *isl_aff_drop_dims(
7369 __isl_take isl_aff *aff,
7370 enum isl_dim_type type, unsigned first, unsigned n);
7371 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
7372 __isl_take isl_multi_aff *maff,
7373 enum isl_dim_type type, unsigned first, unsigned n);
7374 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
7375 __isl_take isl_pw_aff *pwaff,
7376 enum isl_dim_type type, unsigned first, unsigned n);
7377 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
7378 __isl_take isl_pw_multi_aff *pma,
7379 enum isl_dim_type type, unsigned first, unsigned n);
7380 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
7381 __isl_take isl_union_pw_aff *upa,
7382 enum isl_dim_type type, unsigned first, unsigned n);
7383 __isl_give isl_union_pw_multi_aff *
7384 isl_union_pw_multi_aff_drop_dims(
7385 __isl_take isl_union_pw_multi_aff *upma,
7386 enum isl_dim_type type,
7387 unsigned first, unsigned n);
7388 __isl_give isl_multi_union_pw_aff *
7389 isl_multi_union_pw_aff_drop_dims(
7390 __isl_take isl_multi_union_pw_aff *mupa,
7391 enum isl_dim_type type, unsigned first,
7393 __isl_give isl_aff *isl_aff_move_dims(
7394 __isl_take isl_aff *aff,
7395 enum isl_dim_type dst_type, unsigned dst_pos,
7396 enum isl_dim_type src_type, unsigned src_pos,
7398 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
7399 __isl_take isl_multi_aff *ma,
7400 enum isl_dim_type dst_type, unsigned dst_pos,
7401 enum isl_dim_type src_type, unsigned src_pos,
7403 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
7404 __isl_take isl_pw_aff *pa,
7405 enum isl_dim_type dst_type, unsigned dst_pos,
7406 enum isl_dim_type src_type, unsigned src_pos,
7408 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
7409 __isl_take isl_multi_pw_aff *pma,
7410 enum isl_dim_type dst_type, unsigned dst_pos,
7411 enum isl_dim_type src_type, unsigned src_pos,
7414 #include <isl/polynomial.h>
7415 __isl_give isl_union_pw_qpolynomial *
7416 isl_union_pw_qpolynomial_drop_dims(
7417 __isl_take isl_union_pw_qpolynomial *upwqp,
7418 enum isl_dim_type type,
7419 unsigned first, unsigned n);
7420 __isl_give isl_union_pw_qpolynomial_fold *
7421 isl_union_pw_qpolynomial_fold_drop_dims(
7422 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7423 enum isl_dim_type type,
7424 unsigned first, unsigned n);
7426 The operations on union expressions can only manipulate parameters.
7430 =head2 Binary Operations
7432 The two arguments of a binary operation not only need to live
7433 in the same C<isl_ctx>, they currently also need to have
7434 the same (number of) parameters.
7436 =head3 Basic Operations
7440 =item * Intersection
7442 #include <isl/local_space.h>
7443 __isl_give isl_local_space *isl_local_space_intersect(
7444 __isl_take isl_local_space *ls1,
7445 __isl_take isl_local_space *ls2);
7447 #include <isl/set.h>
7448 __isl_give isl_basic_set *isl_basic_set_intersect_params(
7449 __isl_take isl_basic_set *bset1,
7450 __isl_take isl_basic_set *bset2);
7451 __isl_give isl_basic_set *isl_basic_set_intersect(
7452 __isl_take isl_basic_set *bset1,
7453 __isl_take isl_basic_set *bset2);
7454 __isl_give isl_basic_set *isl_basic_set_list_intersect(
7455 __isl_take struct isl_basic_set_list *list);
7456 __isl_give isl_set *isl_set_intersect_params(
7457 __isl_take isl_set *set,
7458 __isl_take isl_set *params);
7459 __isl_give isl_set *isl_set_intersect(
7460 __isl_take isl_set *set1,
7461 __isl_take isl_set *set2);
7462 __isl_give isl_set *isl_set_intersect_factor_domain(
7463 __isl_take isl_set *set,
7464 __isl_take isl_set *domain);
7465 __isl_give isl_set *isl_set_intersect_factor_range(
7466 __isl_take isl_set *set,
7467 __isl_take isl_set *range);
7469 #include <isl/map.h>
7470 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
7471 __isl_take isl_basic_map *bmap,
7472 __isl_take isl_basic_set *bset);
7473 __isl_give isl_basic_map *isl_basic_map_intersect_range(
7474 __isl_take isl_basic_map *bmap,
7475 __isl_take isl_basic_set *bset);
7476 __isl_give isl_basic_map *isl_basic_map_intersect(
7477 __isl_take isl_basic_map *bmap1,
7478 __isl_take isl_basic_map *bmap2);
7479 __isl_give isl_basic_map *isl_basic_map_list_intersect(
7480 __isl_take isl_basic_map_list *list);
7481 __isl_give isl_map *isl_map_intersect_params(
7482 __isl_take isl_map *map,
7483 __isl_take isl_set *params);
7484 __isl_give isl_map *isl_map_intersect_domain(
7485 __isl_take isl_map *map,
7486 __isl_take isl_set *set);
7487 __isl_give isl_map *isl_map_intersect_range(
7488 __isl_take isl_map *map,
7489 __isl_take isl_set *set);
7490 __isl_give isl_map *isl_map_intersect(
7491 __isl_take isl_map *map1,
7492 __isl_take isl_map *map2);
7493 __isl_give isl_map *
7494 isl_map_intersect_domain_factor_domain(
7495 __isl_take isl_map *map,
7496 __isl_take isl_map *factor);
7497 __isl_give isl_map *
7498 isl_map_intersect_domain_factor_range(
7499 __isl_take isl_map *map,
7500 __isl_take isl_map *factor);
7501 __isl_give isl_map *
7502 isl_map_intersect_range_factor_domain(
7503 __isl_take isl_map *map,
7504 __isl_take isl_map *factor);
7505 __isl_give isl_map *
7506 isl_map_intersect_range_factor_range(
7507 __isl_take isl_map *map,
7508 __isl_take isl_map *factor);
7509 __isl_give isl_map *
7510 isl_map_intersect_domain_wrapped_domain(
7511 __isl_take isl_map *map,
7512 __isl_take isl_set *domain);
7513 __isl_give isl_map *
7514 isl_map_intersect_range_wrapped_domain(
7515 __isl_take isl_map *map,
7516 __isl_take isl_set *domain);
7518 #include <isl/union_set.h>
7519 __isl_give isl_union_set *isl_union_set_intersect_params(
7520 __isl_take isl_union_set *uset,
7521 __isl_take isl_set *set);
7522 __isl_give isl_union_set *isl_union_set_intersect(
7523 __isl_take isl_union_set *uset1,
7524 __isl_take isl_union_set *uset2);
7526 #include <isl/union_map.h>
7527 __isl_give isl_union_map *isl_union_map_intersect_params(
7528 __isl_take isl_union_map *umap,
7529 __isl_take isl_set *set);
7530 __isl_give isl_union_map *
7531 isl_union_map_intersect_domain_union_set(
7532 __isl_take isl_union_map *umap,
7533 __isl_take isl_union_set *uset);
7534 __isl_give isl_union_map *
7535 isl_union_map_intersect_domain_space(
7536 __isl_take isl_union_map *umap,
7537 __isl_take isl_space *space);
7538 __isl_give isl_union_map *isl_union_map_intersect_domain(
7539 __isl_take isl_union_map *umap,
7540 __isl_take isl_union_set *uset);
7541 __isl_give isl_union_map *
7542 isl_union_map_intersect_range_union_set(
7543 __isl_take isl_union_map *umap,
7544 __isl_take isl_union_set *uset);
7545 __isl_give isl_union_map *
7546 isl_union_map_intersect_range_space(
7547 __isl_take isl_union_map *umap,
7548 __isl_take isl_space *space);
7549 __isl_give isl_union_map *isl_union_map_intersect_range(
7550 __isl_take isl_union_map *umap,
7551 __isl_take isl_union_set *uset);
7552 __isl_give isl_union_map *isl_union_map_intersect(
7553 __isl_take isl_union_map *umap1,
7554 __isl_take isl_union_map *umap2);
7555 __isl_give isl_union_map *
7556 isl_union_map_intersect_domain_factor_domain(
7557 __isl_take isl_union_map *umap,
7558 __isl_take isl_union_map *factor);
7559 __isl_give isl_union_map *
7560 isl_union_map_intersect_domain_factor_range(
7561 __isl_take isl_union_map *umap,
7562 __isl_take isl_union_map *factor);
7563 __isl_give isl_union_map *
7564 isl_union_map_intersect_range_factor_domain(
7565 __isl_take isl_union_map *umap,
7566 __isl_take isl_union_map *factor);
7567 __isl_give isl_union_map *
7568 isl_union_map_intersect_range_factor_range(
7569 __isl_take isl_union_map *umap,
7570 __isl_take isl_union_map *factor);
7571 __isl_give isl_union_map *
7572 isl_union_map_intersect_domain_wrapped_domain_union_set(
7573 __isl_take isl_union_map *umap,
7574 __isl_take isl_union_set *domain);
7575 __isl_give isl_union_map *
7576 isl_union_map_intersect_range_wrapped_domain_union_set(
7577 __isl_take isl_union_map *umap,
7578 __isl_take isl_union_set *domain);
7580 #include <isl/aff.h>
7581 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
7582 __isl_take isl_pw_aff *pa,
7583 __isl_take isl_set *set);
7584 __isl_give isl_multi_pw_aff *
7585 isl_multi_pw_aff_intersect_domain(
7586 __isl_take isl_multi_pw_aff *mpa,
7587 __isl_take isl_set *domain);
7588 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
7589 __isl_take isl_pw_multi_aff *pma,
7590 __isl_take isl_set *set);
7591 __isl_give isl_union_pw_aff *
7592 isl_union_pw_aff_intersect_domain_space(
7593 __isl_take isl_union_pw_aff *upa,
7594 __isl_take isl_space *space);
7595 __isl_give isl_union_pw_aff *
7596 isl_union_pw_aff_intersect_domain_union_set(
7597 __isl_take isl_union_pw_aff *upa,
7598 __isl_take isl_union_set *uset);
7599 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
7600 __isl_take isl_union_pw_aff *upa,
7601 __isl_take isl_union_set *uset);
7602 __isl_give isl_union_pw_multi_aff *
7603 isl_union_pw_multi_aff_intersect_domain_space(
7604 __isl_take isl_union_pw_multi_aff *upma,
7605 __isl_take isl_space *space);
7606 __isl_give isl_union_pw_multi_aff *
7607 isl_union_pw_multi_aff_intersect_domain_union_set(
7608 __isl_take isl_union_pw_multi_aff *upma,
7609 __isl_take isl_union_set *uset);
7610 __isl_give isl_union_pw_multi_aff *
7611 isl_union_pw_multi_aff_intersect_domain(
7612 __isl_take isl_union_pw_multi_aff *upma,
7613 __isl_take isl_union_set *uset);
7614 __isl_give isl_multi_union_pw_aff *
7615 isl_multi_union_pw_aff_intersect_domain(
7616 __isl_take isl_multi_union_pw_aff *mupa,
7617 __isl_take isl_union_set *uset);
7618 __isl_give isl_pw_aff *
7619 isl_pw_aff_intersect_domain_wrapped_domain(
7620 __isl_take isl_pw_aff *pa,
7621 __isl_take isl_set *set);
7622 __isl_give isl_pw_multi_aff *
7623 isl_pw_multi_aff_intersect_domain_wrapped_domain(
7624 __isl_take isl_pw_multi_aff *pma,
7625 __isl_take isl_set *set);
7626 __isl_give isl_union_pw_aff *
7627 isl_union_pw_aff_intersect_domain_wrapped_domain(
7628 __isl_take isl_union_pw_aff *upa,
7629 __isl_take isl_union_set *uset);
7630 __isl_give isl_union_pw_multi_aff *
7631 isl_union_pw_multi_aff_intersect_domain_wrapped_domain(
7632 __isl_take isl_union_pw_multi_aff *upma,
7633 __isl_take isl_union_set *uset);
7634 __isl_give isl_pw_aff *
7635 isl_pw_aff_intersect_domain_wrapped_range(
7636 __isl_take isl_pw_aff *pa,
7637 __isl_take isl_set *set);
7638 __isl_give isl_pw_multi_aff *
7639 isl_pw_multi_aff_intersect_domain_wrapped_range(
7640 __isl_take isl_pw_multi_aff *pma,
7641 __isl_take isl_set *set);
7642 __isl_give isl_union_pw_multi_aff *
7643 isl_union_pw_multi_aff_intersect_domain_wrapped_range(
7644 __isl_take isl_union_pw_multi_aff *upma,
7645 __isl_take isl_union_set *uset);
7646 __isl_give isl_union_pw_aff *
7647 isl_union_pw_aff_intersect_domain_wrapped_range(
7648 __isl_take isl_union_pw_aff *upa,
7649 __isl_take isl_union_set *uset);
7650 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
7651 __isl_take isl_pw_aff *pa,
7652 __isl_take isl_set *set);
7653 __isl_give isl_multi_pw_aff *
7654 isl_multi_pw_aff_intersect_params(
7655 __isl_take isl_multi_pw_aff *mpa,
7656 __isl_take isl_set *set);
7657 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
7658 __isl_take isl_pw_multi_aff *pma,
7659 __isl_take isl_set *set);
7660 __isl_give isl_union_pw_aff *
7661 isl_union_pw_aff_intersect_params(
7662 __isl_take isl_union_pw_aff *upa,
7663 __isl_take isl_set *set);
7664 __isl_give isl_union_pw_multi_aff *
7665 isl_union_pw_multi_aff_intersect_params(
7666 __isl_take isl_union_pw_multi_aff *upma,
7667 __isl_take isl_set *set);
7668 __isl_give isl_multi_union_pw_aff *
7669 isl_multi_union_pw_aff_intersect_params(
7670 __isl_take isl_multi_union_pw_aff *mupa,
7671 __isl_take isl_set *params);
7672 __isl_give isl_multi_union_pw_aff *
7673 isl_multi_union_pw_aff_intersect_range(
7674 __isl_take isl_multi_union_pw_aff *mupa,
7675 __isl_take isl_set *set);
7677 #include <isl/polynomial.h>
7678 __isl_give isl_pw_qpolynomial *
7679 isl_pw_qpolynomial_intersect_domain(
7680 __isl_take isl_pw_qpolynomial *pwpq,
7681 __isl_take isl_set *set);
7682 __isl_give isl_union_pw_qpolynomial *
7683 isl_union_pw_qpolynomial_intersect_domain_space(
7684 __isl_take isl_union_pw_qpolynomial *upwpq,
7685 __isl_take isl_space *space);
7686 __isl_give isl_union_pw_qpolynomial *
7687 isl_union_pw_qpolynomial_intersect_domain_union_set(
7688 __isl_take isl_union_pw_qpolynomial *upwpq,
7689 __isl_take isl_union_set *uset);
7690 __isl_give isl_union_pw_qpolynomial *
7691 isl_union_pw_qpolynomial_intersect_domain(
7692 __isl_take isl_union_pw_qpolynomial *upwpq,
7693 __isl_take isl_union_set *uset);
7694 __isl_give isl_union_pw_qpolynomial_fold *
7695 isl_union_pw_qpolynomial_fold_intersect_domain_space(
7696 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7697 __isl_take isl_space *space);
7698 __isl_give isl_union_pw_qpolynomial_fold *
7699 isl_union_pw_qpolynomial_fold_intersect_domain_union_set(
7700 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7701 __isl_take isl_union_set *uset);
7702 __isl_give isl_union_pw_qpolynomial_fold *
7703 isl_union_pw_qpolynomial_fold_intersect_domain(
7704 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7705 __isl_take isl_union_set *uset);
7706 __isl_give isl_pw_qpolynomial *
7707 isl_pw_qpolynomial_intersect_domain_wrapped_domain(
7708 __isl_take isl_pw_qpolynomial *pwpq,
7709 __isl_take isl_set *set);
7710 __isl_give isl_pw_qpolynomial_fold *
7711 isl_pw_qpolynomial_fold_intersect_domain_wrapped_domain(
7712 __isl_take isl_pw_qpolynomial_fold *pwf,
7713 __isl_take isl_set *set);
7714 __isl_give isl_union_pw_qpolynomial *
7715 isl_union_pw_qpolynomial_intersect_domain_wrapped_domain(
7716 __isl_take isl_union_pw_qpolynomial *upwpq,
7717 __isl_take isl_union_set *uset);
7718 __isl_give isl_union_pw_qpolynomial_fold *
7719 isl_union_pw_qpolynomial_fold_intersect_domain_wrapped_domain(
7720 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7721 __isl_take isl_union_set *uset);
7722 __isl_give isl_pw_qpolynomial *
7723 isl_pw_qpolynomial_intersect_domain_wrapped_range(
7724 __isl_take isl_pw_qpolynomial *pwpq,
7725 __isl_take isl_set *set);
7726 __isl_give isl_pw_qpolynomial_fold *
7727 isl_pw_qpolynomial_fold_intersect_domain_wrapped_range(
7728 __isl_take isl_pw_qpolynomial_fold *pwf,
7729 __isl_take isl_set *set);
7730 __isl_give isl_union_pw_qpolynomial *
7731 isl_union_pw_qpolynomial_intersect_domain_wrapped_range(
7732 __isl_take isl_union_pw_qpolynomial *upwpq,
7733 __isl_take isl_union_set *uset);
7734 __isl_give isl_union_pw_qpolynomial_fold *
7735 isl_union_pw_qpolynomial_fold_intersect_domain_wrapped_range(
7736 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7737 __isl_take isl_union_set *uset);
7738 __isl_give isl_pw_qpolynomial *
7739 isl_pw_qpolynomial_intersect_params(
7740 __isl_take isl_pw_qpolynomial *pwpq,
7741 __isl_take isl_set *set);
7742 __isl_give isl_pw_qpolynomial_fold *
7743 isl_pw_qpolynomial_fold_intersect_params(
7744 __isl_take isl_pw_qpolynomial_fold *pwf,
7745 __isl_take isl_set *set);
7746 __isl_give isl_union_pw_qpolynomial *
7747 isl_union_pw_qpolynomial_intersect_params(
7748 __isl_take isl_union_pw_qpolynomial *upwpq,
7749 __isl_take isl_set *set);
7750 __isl_give isl_union_pw_qpolynomial_fold *
7751 isl_union_pw_qpolynomial_fold_intersect_params(
7752 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7753 __isl_take isl_set *set);
7755 The second argument to the C<_params> functions needs to be
7756 a parametric (basic) set. For the other functions, a parametric set
7757 for either argument is only allowed if the other argument is
7758 a parametric set as well.
7759 The list passed to C<isl_basic_set_list_intersect> needs to have
7760 at least one element and all elements need to live in the same space.
7761 The function C<isl_multi_union_pw_aff_intersect_range>
7762 restricts the input function to those shared domain elements
7763 that map to the specified range.
7764 C<isl_union_map_intersect_domain> is an alternative name for
7765 C<isl_union_map_intersect_domain_union_set>.
7766 Similarly for the other pairs of functions.
7770 #include <isl/set.h>
7771 __isl_give isl_set *isl_basic_set_union(
7772 __isl_take isl_basic_set *bset1,
7773 __isl_take isl_basic_set *bset2);
7774 __isl_give isl_set *isl_set_union(
7775 __isl_take isl_set *set1,
7776 __isl_take isl_set *set2);
7777 __isl_give isl_set *isl_set_list_union(
7778 __isl_take isl_set_list *list);
7780 #include <isl/map.h>
7781 __isl_give isl_map *isl_basic_map_union(
7782 __isl_take isl_basic_map *bmap1,
7783 __isl_take isl_basic_map *bmap2);
7784 __isl_give isl_map *isl_map_union(
7785 __isl_take isl_map *map1,
7786 __isl_take isl_map *map2);
7788 #include <isl/union_set.h>
7789 __isl_give isl_union_set *isl_union_set_union(
7790 __isl_take isl_union_set *uset1,
7791 __isl_take isl_union_set *uset2);
7792 __isl_give isl_union_set *isl_union_set_list_union(
7793 __isl_take isl_union_set_list *list);
7795 #include <isl/union_map.h>
7796 __isl_give isl_union_map *isl_union_map_union(
7797 __isl_take isl_union_map *umap1,
7798 __isl_take isl_union_map *umap2);
7800 The list passed to C<isl_set_list_union> needs to have
7801 at least one element and all elements need to live in the same space.
7803 =item * Set difference
7805 #include <isl/set.h>
7806 __isl_give isl_set *isl_set_subtract(
7807 __isl_take isl_set *set1,
7808 __isl_take isl_set *set2);
7810 #include <isl/map.h>
7811 __isl_give isl_map *isl_map_subtract(
7812 __isl_take isl_map *map1,
7813 __isl_take isl_map *map2);
7814 __isl_give isl_map *isl_map_subtract_domain(
7815 __isl_take isl_map *map,
7816 __isl_take isl_set *dom);
7817 __isl_give isl_map *isl_map_subtract_range(
7818 __isl_take isl_map *map,
7819 __isl_take isl_set *dom);
7821 #include <isl/union_set.h>
7822 __isl_give isl_union_set *isl_union_set_subtract(
7823 __isl_take isl_union_set *uset1,
7824 __isl_take isl_union_set *uset2);
7826 #include <isl/union_map.h>
7827 __isl_give isl_union_map *isl_union_map_subtract(
7828 __isl_take isl_union_map *umap1,
7829 __isl_take isl_union_map *umap2);
7830 __isl_give isl_union_map *isl_union_map_subtract_domain(
7831 __isl_take isl_union_map *umap,
7832 __isl_take isl_union_set *dom);
7833 __isl_give isl_union_map *isl_union_map_subtract_range(
7834 __isl_take isl_union_map *umap,
7835 __isl_take isl_union_set *dom);
7837 #include <isl/aff.h>
7838 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
7839 __isl_take isl_pw_aff *pa,
7840 __isl_take isl_set *set);
7841 __isl_give isl_pw_multi_aff *
7842 isl_pw_multi_aff_subtract_domain(
7843 __isl_take isl_pw_multi_aff *pma,
7844 __isl_take isl_set *set);
7845 __isl_give isl_union_pw_aff *
7846 isl_union_pw_aff_subtract_domain_union_set(
7847 __isl_take isl_union_pw_aff *upa,
7848 __isl_take isl_union_set *uset);
7849 __isl_give isl_union_pw_aff *
7850 isl_union_pw_aff_subtract_domain_space(
7851 __isl_take isl_union_pw_aff *upa,
7852 __isl_take isl_space *space);
7853 __isl_give isl_union_pw_aff *
7854 isl_union_pw_aff_subtract_domain(
7855 __isl_take isl_union_pw_aff *upa,
7856 __isl_take isl_union_set *uset);
7857 __isl_give isl_union_pw_multi_aff *
7858 isl_union_pw_multi_aff_subtract_domain_union_set(
7859 __isl_take isl_union_pw_multi_aff *upma,
7860 __isl_take isl_set *set);
7861 __isl_give isl_union_pw_multi_aff *
7862 isl_union_pw_multi_aff_subtract_domain_space(
7863 __isl_take isl_union_pw_multi_aff *upma,
7864 __isl_take isl_space *space);
7865 __isl_give isl_union_pw_multi_aff *
7866 isl_union_pw_multi_aff_subtract_domain(
7867 __isl_take isl_union_pw_multi_aff *upma,
7868 __isl_take isl_union_set *uset);
7870 #include <isl/polynomial.h>
7871 __isl_give isl_pw_qpolynomial *
7872 isl_pw_qpolynomial_subtract_domain(
7873 __isl_take isl_pw_qpolynomial *pwpq,
7874 __isl_take isl_set *set);
7875 __isl_give isl_pw_qpolynomial_fold *
7876 isl_pw_qpolynomial_fold_subtract_domain(
7877 __isl_take isl_pw_qpolynomial_fold *pwf,
7878 __isl_take isl_set *set);
7879 __isl_give isl_union_pw_qpolynomial *
7880 isl_union_pw_qpolynomial_subtract_domain_union_set(
7881 __isl_take isl_union_pw_qpolynomial *upwpq,
7882 __isl_take isl_union_set *uset);
7883 __isl_give isl_union_pw_qpolynomial *
7884 isl_union_pw_qpolynomial_subtract_domain_space(
7885 __isl_take isl_union_pw_qpolynomial *upwpq,
7886 __isl_take isl_space *space);
7887 __isl_give isl_union_pw_qpolynomial *
7888 isl_union_pw_qpolynomial_subtract_domain(
7889 __isl_take isl_union_pw_qpolynomial *upwpq,
7890 __isl_take isl_union_set *uset);
7891 __isl_give isl_union_pw_qpolynomial_fold *
7892 isl_union_pw_qpolynomial_fold_subtract_domain_union_set(
7893 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7894 __isl_take isl_union_set *uset);
7895 __isl_give isl_union_pw_qpolynomial_fold *
7896 isl_union_pw_qpolynomial_fold_subtract_domain_space(
7897 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7898 __isl_take isl_space *space);
7899 __isl_give isl_union_pw_qpolynomial_fold *
7900 isl_union_pw_qpolynomial_fold_subtract_domain(
7901 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7902 __isl_take isl_union_set *uset);
7904 C<isl_union_pw_aff_subtract_domain> is an alternative name for
7905 C<isl_union_pw_aff_subtract_domain_union_set>.
7906 Similarly for the other pairs of functions.
7910 #include <isl/space.h>
7911 __isl_give isl_space *isl_space_join(
7912 __isl_take isl_space *left,
7913 __isl_take isl_space *right);
7915 #include <isl/set.h>
7916 __isl_give isl_basic_set *isl_basic_set_apply(
7917 __isl_take isl_basic_set *bset,
7918 __isl_take isl_basic_map *bmap);
7919 __isl_give isl_set *isl_set_apply(
7920 __isl_take isl_set *set,
7921 __isl_take isl_map *map);
7923 #include <isl/union_set.h>
7924 __isl_give isl_union_set *isl_union_set_apply(
7925 __isl_take isl_union_set *uset,
7926 __isl_take isl_union_map *umap);
7928 #include <isl/map.h>
7929 __isl_give isl_basic_map *isl_basic_map_apply_domain(
7930 __isl_take isl_basic_map *bmap1,
7931 __isl_take isl_basic_map *bmap2);
7932 __isl_give isl_basic_map *isl_basic_map_apply_range(
7933 __isl_take isl_basic_map *bmap1,
7934 __isl_take isl_basic_map *bmap2);
7935 __isl_give isl_map *isl_map_apply_domain(
7936 __isl_take isl_map *map1,
7937 __isl_take isl_map *map2);
7938 __isl_give isl_map *isl_map_apply_range(
7939 __isl_take isl_map *map1,
7940 __isl_take isl_map *map2);
7942 #include <isl/union_map.h>
7943 __isl_give isl_union_map *isl_union_map_apply_domain(
7944 __isl_take isl_union_map *umap1,
7945 __isl_take isl_union_map *umap2);
7946 __isl_give isl_union_map *isl_union_map_apply_range(
7947 __isl_take isl_union_map *umap1,
7948 __isl_take isl_union_map *umap2);
7950 #include <isl/aff.h>
7951 __isl_give isl_union_pw_multi_aff *
7952 isl_union_pw_multi_aff_apply_union_pw_multi_aff(
7953 __isl_take isl_union_pw_multi_aff *upma1,
7954 __isl_take isl_union_pw_multi_aff *upma2);
7955 __isl_give isl_union_pw_aff *
7956 isl_multi_union_pw_aff_apply_aff(
7957 __isl_take isl_multi_union_pw_aff *mupa,
7958 __isl_take isl_aff *aff);
7959 __isl_give isl_union_pw_aff *
7960 isl_multi_union_pw_aff_apply_pw_aff(
7961 __isl_take isl_multi_union_pw_aff *mupa,
7962 __isl_take isl_pw_aff *pa);
7963 __isl_give isl_multi_union_pw_aff *
7964 isl_multi_union_pw_aff_apply_multi_aff(
7965 __isl_take isl_multi_union_pw_aff *mupa,
7966 __isl_take isl_multi_aff *ma);
7967 __isl_give isl_multi_union_pw_aff *
7968 isl_multi_union_pw_aff_apply_pw_multi_aff(
7969 __isl_take isl_multi_union_pw_aff *mupa,
7970 __isl_take isl_pw_multi_aff *pma);
7972 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
7973 over the shared domain of the elements of the input. The dimension is
7974 required to be greater than zero.
7975 The C<isl_multi_union_pw_aff> argument of
7976 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
7977 but only if the range of the C<isl_multi_aff> argument
7978 is also zero-dimensional.
7979 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
7981 #include <isl/polynomial.h>
7982 __isl_give isl_pw_qpolynomial_fold *
7983 isl_set_apply_pw_qpolynomial_fold(
7984 __isl_take isl_set *set,
7985 __isl_take isl_pw_qpolynomial_fold *pwf,
7987 __isl_give isl_pw_qpolynomial_fold *
7988 isl_map_apply_pw_qpolynomial_fold(
7989 __isl_take isl_map *map,
7990 __isl_take isl_pw_qpolynomial_fold *pwf,
7992 __isl_give isl_union_pw_qpolynomial_fold *
7993 isl_union_set_apply_union_pw_qpolynomial_fold(
7994 __isl_take isl_union_set *uset,
7995 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7997 __isl_give isl_union_pw_qpolynomial_fold *
7998 isl_union_map_apply_union_pw_qpolynomial_fold(
7999 __isl_take isl_union_map *umap,
8000 __isl_take isl_union_pw_qpolynomial_fold *upwf,
8003 The functions taking a map
8004 compose the given map with the given piecewise quasipolynomial reduction.
8005 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
8006 over all elements in the intersection of the range of the map
8007 and the domain of the piecewise quasipolynomial reduction
8008 as a function of an element in the domain of the map.
8009 The functions taking a set compute a bound over all elements in the
8010 intersection of the set and the domain of the
8011 piecewise quasipolynomial reduction.
8015 #include <isl/set.h>
8016 __isl_give isl_basic_set *
8017 isl_basic_set_preimage_multi_aff(
8018 __isl_take isl_basic_set *bset,
8019 __isl_take isl_multi_aff *ma);
8020 __isl_give isl_set *isl_set_preimage_multi_aff(
8021 __isl_take isl_set *set,
8022 __isl_take isl_multi_aff *ma);
8023 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
8024 __isl_take isl_set *set,
8025 __isl_take isl_pw_multi_aff *pma);
8026 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
8027 __isl_take isl_set *set,
8028 __isl_take isl_multi_pw_aff *mpa);
8030 #include <isl/union_set.h>
8031 __isl_give isl_union_set *
8032 isl_union_set_preimage_multi_aff(
8033 __isl_take isl_union_set *uset,
8034 __isl_take isl_multi_aff *ma);
8035 __isl_give isl_union_set *
8036 isl_union_set_preimage_pw_multi_aff(
8037 __isl_take isl_union_set *uset,
8038 __isl_take isl_pw_multi_aff *pma);
8039 __isl_give isl_union_set *
8040 isl_union_set_preimage_union_pw_multi_aff(
8041 __isl_take isl_union_set *uset,
8042 __isl_take isl_union_pw_multi_aff *upma);
8044 #include <isl/map.h>
8045 __isl_give isl_basic_map *
8046 isl_basic_map_preimage_domain_multi_aff(
8047 __isl_take isl_basic_map *bmap,
8048 __isl_take isl_multi_aff *ma);
8049 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
8050 __isl_take isl_map *map,
8051 __isl_take isl_multi_aff *ma);
8052 __isl_give isl_map *isl_map_preimage_range_multi_aff(
8053 __isl_take isl_map *map,
8054 __isl_take isl_multi_aff *ma);
8055 __isl_give isl_map *
8056 isl_map_preimage_domain_pw_multi_aff(
8057 __isl_take isl_map *map,
8058 __isl_take isl_pw_multi_aff *pma);
8059 __isl_give isl_map *
8060 isl_map_preimage_range_pw_multi_aff(
8061 __isl_take isl_map *map,
8062 __isl_take isl_pw_multi_aff *pma);
8063 __isl_give isl_map *
8064 isl_map_preimage_domain_multi_pw_aff(
8065 __isl_take isl_map *map,
8066 __isl_take isl_multi_pw_aff *mpa);
8067 __isl_give isl_basic_map *
8068 isl_basic_map_preimage_range_multi_aff(
8069 __isl_take isl_basic_map *bmap,
8070 __isl_take isl_multi_aff *ma);
8072 #include <isl/union_map.h>
8073 __isl_give isl_union_map *
8074 isl_union_map_preimage_domain_multi_aff(
8075 __isl_take isl_union_map *umap,
8076 __isl_take isl_multi_aff *ma);
8077 __isl_give isl_union_map *
8078 isl_union_map_preimage_range_multi_aff(
8079 __isl_take isl_union_map *umap,
8080 __isl_take isl_multi_aff *ma);
8081 __isl_give isl_union_map *
8082 isl_union_map_preimage_domain_pw_multi_aff(
8083 __isl_take isl_union_map *umap,
8084 __isl_take isl_pw_multi_aff *pma);
8085 __isl_give isl_union_map *
8086 isl_union_map_preimage_range_pw_multi_aff(
8087 __isl_take isl_union_map *umap,
8088 __isl_take isl_pw_multi_aff *pma);
8089 __isl_give isl_union_map *
8090 isl_union_map_preimage_domain_union_pw_multi_aff(
8091 __isl_take isl_union_map *umap,
8092 __isl_take isl_union_pw_multi_aff *upma);
8093 __isl_give isl_union_map *
8094 isl_union_map_preimage_range_union_pw_multi_aff(
8095 __isl_take isl_union_map *umap,
8096 __isl_take isl_union_pw_multi_aff *upma);
8098 #include <isl/aff.h>
8099 __isl_give isl_pw_multi_aff *
8100 isl_pw_multi_aff_preimage_domain_wrapped_domain_pw_multi_aff(
8101 __isl_take isl_pw_multi_aff *pma1,
8102 __isl_take isl_pw_multi_aff *pma2);
8103 __isl_give isl_union_pw_multi_aff *
8104 isl_union_pw_multi_aff_preimage_domain_wrapped_domain_union_pw_multi_aff(
8105 __isl_take isl_union_pw_multi_aff *upma1,
8106 __isl_take isl_union_pw_multi_aff *upma2);
8108 These functions compute the preimage of the given set or map domain/range under
8109 the given function. In other words, the expression is plugged
8110 into the set description or into the domain/range of the map or function.
8114 #include <isl/aff.h>
8115 __isl_give isl_aff *isl_aff_pullback_aff(
8116 __isl_take isl_aff *aff1,
8117 __isl_take isl_aff *aff2);
8118 __isl_give isl_aff *isl_aff_pullback_multi_aff(
8119 __isl_take isl_aff *aff,
8120 __isl_take isl_multi_aff *ma);
8121 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
8122 __isl_take isl_pw_aff *pa,
8123 __isl_take isl_multi_aff *ma);
8124 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
8125 __isl_take isl_pw_aff *pa,
8126 __isl_take isl_pw_multi_aff *pma);
8127 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
8128 __isl_take isl_pw_aff *pa,
8129 __isl_take isl_multi_pw_aff *mpa);
8130 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
8131 __isl_take isl_multi_aff *ma1,
8132 __isl_take isl_multi_aff *ma2);
8133 __isl_give isl_pw_multi_aff *
8134 isl_pw_multi_aff_pullback_multi_aff(
8135 __isl_take isl_pw_multi_aff *pma,
8136 __isl_take isl_multi_aff *ma);
8137 __isl_give isl_multi_pw_aff *
8138 isl_multi_pw_aff_pullback_multi_aff(
8139 __isl_take isl_multi_pw_aff *mpa,
8140 __isl_take isl_multi_aff *ma);
8141 __isl_give isl_pw_multi_aff *
8142 isl_pw_multi_aff_pullback_pw_multi_aff(
8143 __isl_take isl_pw_multi_aff *pma1,
8144 __isl_take isl_pw_multi_aff *pma2);
8145 __isl_give isl_multi_pw_aff *
8146 isl_multi_pw_aff_pullback_pw_multi_aff(
8147 __isl_take isl_multi_pw_aff *mpa,
8148 __isl_take isl_pw_multi_aff *pma);
8149 __isl_give isl_multi_pw_aff *
8150 isl_multi_pw_aff_pullback_multi_pw_aff(
8151 __isl_take isl_multi_pw_aff *mpa1,
8152 __isl_take isl_multi_pw_aff *mpa2);
8153 __isl_give isl_union_pw_aff *
8154 isl_union_pw_aff_pullback_union_pw_multi_aff(
8155 __isl_take isl_union_pw_aff *upa,
8156 __isl_take isl_union_pw_multi_aff *upma);
8157 __isl_give isl_union_pw_multi_aff *
8158 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
8159 __isl_take isl_union_pw_multi_aff *upma1,
8160 __isl_take isl_union_pw_multi_aff *upma2);
8161 __isl_give isl_multi_union_pw_aff *
8162 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
8163 __isl_take isl_multi_union_pw_aff *mupa,
8164 __isl_take isl_union_pw_multi_aff *upma);
8166 These functions precompose the first expression by the second function.
8167 In other words, the second function is plugged
8168 into the first expression.
8172 #include <isl/aff.h>
8173 __isl_give isl_basic_set *isl_aff_eq_basic_set(
8174 __isl_take isl_aff *aff1,
8175 __isl_take isl_aff *aff2);
8176 __isl_give isl_set *isl_aff_eq_set(
8177 __isl_take isl_aff *aff1,
8178 __isl_take isl_aff *aff2);
8179 __isl_give isl_set *isl_aff_ne_set(
8180 __isl_take isl_aff *aff1,
8181 __isl_take isl_aff *aff2);
8182 __isl_give isl_basic_set *isl_aff_le_basic_set(
8183 __isl_take isl_aff *aff1,
8184 __isl_take isl_aff *aff2);
8185 __isl_give isl_set *isl_aff_le_set(
8186 __isl_take isl_aff *aff1,
8187 __isl_take isl_aff *aff2);
8188 __isl_give isl_basic_set *isl_aff_lt_basic_set(
8189 __isl_take isl_aff *aff1,
8190 __isl_take isl_aff *aff2);
8191 __isl_give isl_set *isl_aff_lt_set(
8192 __isl_take isl_aff *aff1,
8193 __isl_take isl_aff *aff2);
8194 __isl_give isl_basic_set *isl_aff_ge_basic_set(
8195 __isl_take isl_aff *aff1,
8196 __isl_take isl_aff *aff2);
8197 __isl_give isl_set *isl_aff_ge_set(
8198 __isl_take isl_aff *aff1,
8199 __isl_take isl_aff *aff2);
8200 __isl_give isl_basic_set *isl_aff_gt_basic_set(
8201 __isl_take isl_aff *aff1,
8202 __isl_take isl_aff *aff2);
8203 __isl_give isl_set *isl_aff_gt_set(
8204 __isl_take isl_aff *aff1,
8205 __isl_take isl_aff *aff2);
8206 __isl_give isl_set *isl_pw_aff_eq_set(
8207 __isl_take isl_pw_aff *pwaff1,
8208 __isl_take isl_pw_aff *pwaff2);
8209 __isl_give isl_set *isl_pw_aff_ne_set(
8210 __isl_take isl_pw_aff *pwaff1,
8211 __isl_take isl_pw_aff *pwaff2);
8212 __isl_give isl_set *isl_pw_aff_le_set(
8213 __isl_take isl_pw_aff *pwaff1,
8214 __isl_take isl_pw_aff *pwaff2);
8215 __isl_give isl_set *isl_pw_aff_lt_set(
8216 __isl_take isl_pw_aff *pwaff1,
8217 __isl_take isl_pw_aff *pwaff2);
8218 __isl_give isl_set *isl_pw_aff_ge_set(
8219 __isl_take isl_pw_aff *pwaff1,
8220 __isl_take isl_pw_aff *pwaff2);
8221 __isl_give isl_set *isl_pw_aff_gt_set(
8222 __isl_take isl_pw_aff *pwaff1,
8223 __isl_take isl_pw_aff *pwaff2);
8225 __isl_give isl_set *isl_multi_aff_lex_le_set(
8226 __isl_take isl_multi_aff *ma1,
8227 __isl_take isl_multi_aff *ma2);
8228 __isl_give isl_set *isl_multi_aff_lex_lt_set(
8229 __isl_take isl_multi_aff *ma1,
8230 __isl_take isl_multi_aff *ma2);
8231 __isl_give isl_set *isl_multi_aff_lex_ge_set(
8232 __isl_take isl_multi_aff *ma1,
8233 __isl_take isl_multi_aff *ma2);
8234 __isl_give isl_set *isl_multi_aff_lex_gt_set(
8235 __isl_take isl_multi_aff *ma1,
8236 __isl_take isl_multi_aff *ma2);
8238 __isl_give isl_set *isl_pw_aff_list_eq_set(
8239 __isl_take isl_pw_aff_list *list1,
8240 __isl_take isl_pw_aff_list *list2);
8241 __isl_give isl_set *isl_pw_aff_list_ne_set(
8242 __isl_take isl_pw_aff_list *list1,
8243 __isl_take isl_pw_aff_list *list2);
8244 __isl_give isl_set *isl_pw_aff_list_le_set(
8245 __isl_take isl_pw_aff_list *list1,
8246 __isl_take isl_pw_aff_list *list2);
8247 __isl_give isl_set *isl_pw_aff_list_lt_set(
8248 __isl_take isl_pw_aff_list *list1,
8249 __isl_take isl_pw_aff_list *list2);
8250 __isl_give isl_set *isl_pw_aff_list_ge_set(
8251 __isl_take isl_pw_aff_list *list1,
8252 __isl_take isl_pw_aff_list *list2);
8253 __isl_give isl_set *isl_pw_aff_list_gt_set(
8254 __isl_take isl_pw_aff_list *list1,
8255 __isl_take isl_pw_aff_list *list2);
8257 The function C<isl_aff_ge_basic_set> returns a basic set
8258 containing those elements in the shared space
8259 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
8260 The function C<isl_pw_aff_ge_set> returns a set
8261 containing those elements in the shared domain
8262 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
8263 greater than or equal to C<pwaff2>.
8264 The function C<isl_multi_aff_lex_le_set> returns a set
8265 containing those elements in the shared domain space
8266 where C<ma1> is lexicographically smaller than or
8268 The functions operating on C<isl_pw_aff_list> apply the corresponding
8269 C<isl_pw_aff> function to each pair of elements in the two lists.
8271 #include <isl/aff.h>
8272 __isl_give isl_map *isl_pw_aff_eq_map(
8273 __isl_take isl_pw_aff *pa1,
8274 __isl_take isl_pw_aff *pa2);
8275 __isl_give isl_map *isl_pw_aff_le_map(
8276 __isl_take isl_pw_aff *pa1,
8277 __isl_take isl_pw_aff *pa2);
8278 __isl_give isl_map *isl_pw_aff_lt_map(
8279 __isl_take isl_pw_aff *pa1,
8280 __isl_take isl_pw_aff *pa2);
8281 __isl_give isl_map *isl_pw_aff_ge_map(
8282 __isl_take isl_pw_aff *pa1,
8283 __isl_take isl_pw_aff *pa2);
8284 __isl_give isl_map *isl_pw_aff_gt_map(
8285 __isl_take isl_pw_aff *pa1,
8286 __isl_take isl_pw_aff *pa2);
8288 __isl_give isl_map *isl_multi_pw_aff_eq_map(
8289 __isl_take isl_multi_pw_aff *mpa1,
8290 __isl_take isl_multi_pw_aff *mpa2);
8291 __isl_give isl_map *isl_multi_pw_aff_lex_le_map(
8292 __isl_take isl_multi_pw_aff *mpa1,
8293 __isl_take isl_multi_pw_aff *mpa2);
8294 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
8295 __isl_take isl_multi_pw_aff *mpa1,
8296 __isl_take isl_multi_pw_aff *mpa2);
8297 __isl_give isl_map *isl_multi_pw_aff_lex_ge_map(
8298 __isl_take isl_multi_pw_aff *mpa1,
8299 __isl_take isl_multi_pw_aff *mpa2);
8300 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
8301 __isl_take isl_multi_pw_aff *mpa1,
8302 __isl_take isl_multi_pw_aff *mpa2);
8304 These functions return a map between domain elements of the arguments
8305 where the function values satisfy the given relation.
8307 #include <isl/map.h>
8308 __isl_give isl_map *isl_map_eq_at_multi_pw_aff(
8309 __isl_take isl_map *map,
8310 __isl_take isl_multi_pw_aff *mpa);
8311 __isl_give isl_map *isl_map_lex_lt_at_multi_pw_aff(
8312 __isl_take isl_map *map,
8313 __isl_take isl_multi_pw_aff *mpa);
8314 __isl_give isl_map *isl_map_lex_le_at_multi_pw_aff(
8315 __isl_take isl_map *map,
8316 __isl_take isl_multi_pw_aff *mpa);
8317 __isl_give isl_map *isl_map_lex_gt_at_multi_pw_aff(
8318 __isl_take isl_map *map,
8319 __isl_take isl_multi_pw_aff *mpa);
8320 __isl_give isl_map *isl_map_lex_ge_at_multi_pw_aff(
8321 __isl_take isl_map *map,
8322 __isl_take isl_multi_pw_aff *mpa);
8324 #include <isl/union_map.h>
8325 __isl_give isl_union_map *
8326 isl_union_map_eq_at_multi_union_pw_aff(
8327 __isl_take isl_union_map *umap,
8328 __isl_take isl_multi_union_pw_aff *mupa);
8329 __isl_give isl_union_map *
8330 isl_union_map_lex_lt_at_multi_union_pw_aff(
8331 __isl_take isl_union_map *umap,
8332 __isl_take isl_multi_union_pw_aff *mupa);
8333 __isl_give isl_union_map *
8334 isl_union_map_lex_le_at_multi_union_pw_aff(
8335 __isl_take isl_union_map *umap,
8336 __isl_take isl_multi_union_pw_aff *mupa);
8337 __isl_give isl_union_map *
8338 isl_union_map_lex_gt_at_multi_union_pw_aff(
8339 __isl_take isl_union_map *umap,
8340 __isl_take isl_multi_union_pw_aff *mupa);
8341 __isl_give isl_union_map *
8342 isl_union_map_lex_ge_at_multi_union_pw_aff(
8343 __isl_take isl_union_map *umap,
8344 __isl_take isl_multi_union_pw_aff *mupa);
8346 These functions select the subset of elements in the union map
8347 that have an equal or lexicographically smaller or greater function value.
8349 =item * Cartesian Product
8351 #include <isl/space.h>
8352 __isl_give isl_space *isl_space_product(
8353 __isl_take isl_space *space1,
8354 __isl_take isl_space *space2);
8355 __isl_give isl_space *isl_space_domain_product(
8356 __isl_take isl_space *space1,
8357 __isl_take isl_space *space2);
8358 __isl_give isl_space *isl_space_range_product(
8359 __isl_take isl_space *space1,
8360 __isl_take isl_space *space2);
8363 C<isl_space_product>, C<isl_space_domain_product>
8364 and C<isl_space_range_product> take pairs or relation spaces and
8365 produce a single relations space, where either the domain, the range
8366 or both domain and range are wrapped spaces of relations between
8367 the domains and/or ranges of the input spaces.
8368 If the product is only constructed over the domain or the range
8369 then the ranges or the domains of the inputs should be the same.
8370 The function C<isl_space_product> also accepts a pair of set spaces,
8371 in which case it returns a wrapped space of a relation between the
8374 #include <isl/set.h>
8375 __isl_give isl_set *isl_set_product(
8376 __isl_take isl_set *set1,
8377 __isl_take isl_set *set2);
8379 #include <isl/map.h>
8380 __isl_give isl_basic_map *isl_basic_map_domain_product(
8381 __isl_take isl_basic_map *bmap1,
8382 __isl_take isl_basic_map *bmap2);
8383 __isl_give isl_basic_map *isl_basic_map_range_product(
8384 __isl_take isl_basic_map *bmap1,
8385 __isl_take isl_basic_map *bmap2);
8386 __isl_give isl_basic_map *isl_basic_map_product(
8387 __isl_take isl_basic_map *bmap1,
8388 __isl_take isl_basic_map *bmap2);
8389 __isl_give isl_map *isl_map_domain_product(
8390 __isl_take isl_map *map1,
8391 __isl_take isl_map *map2);
8392 __isl_give isl_map *isl_map_range_product(
8393 __isl_take isl_map *map1,
8394 __isl_take isl_map *map2);
8395 __isl_give isl_map *isl_map_product(
8396 __isl_take isl_map *map1,
8397 __isl_take isl_map *map2);
8399 #include <isl/union_set.h>
8400 __isl_give isl_union_set *isl_union_set_product(
8401 __isl_take isl_union_set *uset1,
8402 __isl_take isl_union_set *uset2);
8404 #include <isl/union_map.h>
8405 __isl_give isl_union_map *isl_union_map_domain_product(
8406 __isl_take isl_union_map *umap1,
8407 __isl_take isl_union_map *umap2);
8408 __isl_give isl_union_map *isl_union_map_range_product(
8409 __isl_take isl_union_map *umap1,
8410 __isl_take isl_union_map *umap2);
8411 __isl_give isl_union_map *isl_union_map_product(
8412 __isl_take isl_union_map *umap1,
8413 __isl_take isl_union_map *umap2);
8416 __isl_give isl_multi_id *isl_multi_id_range_product(
8417 __isl_take isl_multi_id *mi1,
8418 __isl_take isl_multi_id *mi2);
8420 #include <isl/val.h>
8421 __isl_give isl_multi_val *isl_multi_val_range_product(
8422 __isl_take isl_multi_val *mv1,
8423 __isl_take isl_multi_val *mv2);
8424 __isl_give isl_multi_val *isl_multi_val_product(
8425 __isl_take isl_multi_val *mv1,
8426 __isl_take isl_multi_val *mv2);
8428 #include <isl/aff.h>
8429 __isl_give isl_multi_aff *isl_multi_aff_range_product(
8430 __isl_take isl_multi_aff *ma1,
8431 __isl_take isl_multi_aff *ma2);
8432 __isl_give isl_multi_aff *isl_multi_aff_product(
8433 __isl_take isl_multi_aff *ma1,
8434 __isl_take isl_multi_aff *ma2);
8435 __isl_give isl_multi_pw_aff *
8436 isl_multi_pw_aff_range_product(
8437 __isl_take isl_multi_pw_aff *mpa1,
8438 __isl_take isl_multi_pw_aff *mpa2);
8439 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
8440 __isl_take isl_multi_pw_aff *mpa1,
8441 __isl_take isl_multi_pw_aff *mpa2);
8442 __isl_give isl_pw_multi_aff *
8443 isl_pw_multi_aff_range_product(
8444 __isl_take isl_pw_multi_aff *pma1,
8445 __isl_take isl_pw_multi_aff *pma2);
8446 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
8447 __isl_take isl_pw_multi_aff *pma1,
8448 __isl_take isl_pw_multi_aff *pma2);
8449 __isl_give isl_union_pw_multi_aff *
8450 isl_union_pw_multi_aff_range_product(
8451 __isl_take isl_union_pw_multi_aff *upma1,
8452 __isl_take isl_union_pw_multi_aff *upma2);
8453 __isl_give isl_multi_union_pw_aff *
8454 isl_multi_union_pw_aff_range_product(
8455 __isl_take isl_multi_union_pw_aff *mupa1,
8456 __isl_take isl_multi_union_pw_aff *mupa2);
8458 The above functions compute the cross product of the given
8459 sets, relations or functions. The domains and ranges of the results
8460 are wrapped maps between domains and ranges of the inputs.
8461 To obtain a ``flat'' product, use the following functions
8464 #include <isl/set.h>
8465 __isl_give isl_basic_set *isl_basic_set_flat_product(
8466 __isl_take isl_basic_set *bset1,
8467 __isl_take isl_basic_set *bset2);
8468 __isl_give isl_set *isl_set_flat_product(
8469 __isl_take isl_set *set1,
8470 __isl_take isl_set *set2);
8472 #include <isl/map.h>
8473 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
8474 __isl_take isl_basic_map *bmap1,
8475 __isl_take isl_basic_map *bmap2);
8476 __isl_give isl_map *isl_map_flat_domain_product(
8477 __isl_take isl_map *map1,
8478 __isl_take isl_map *map2);
8479 __isl_give isl_map *isl_map_flat_range_product(
8480 __isl_take isl_map *map1,
8481 __isl_take isl_map *map2);
8482 __isl_give isl_basic_map *isl_basic_map_flat_product(
8483 __isl_take isl_basic_map *bmap1,
8484 __isl_take isl_basic_map *bmap2);
8485 __isl_give isl_map *isl_map_flat_product(
8486 __isl_take isl_map *map1,
8487 __isl_take isl_map *map2);
8489 #include <isl/union_map.h>
8490 __isl_give isl_union_map *
8491 isl_union_map_flat_domain_product(
8492 __isl_take isl_union_map *umap1,
8493 __isl_take isl_union_map *umap2);
8494 __isl_give isl_union_map *
8495 isl_union_map_flat_range_product(
8496 __isl_take isl_union_map *umap1,
8497 __isl_take isl_union_map *umap2);
8500 __isl_give isl_multi_id *
8501 isl_multi_id_flat_range_product(
8502 __isl_take isl_multi_id *mi1,
8503 __isl_take isl_multi_id *mi2);
8505 #include <isl/val.h>
8506 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
8507 __isl_take isl_multi_val *mv1,
8508 __isl_take isl_multi_val *mv2);
8510 #include <isl/aff.h>
8511 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
8512 __isl_take isl_multi_aff *ma1,
8513 __isl_take isl_multi_aff *ma2);
8514 __isl_give isl_pw_multi_aff *
8515 isl_pw_multi_aff_flat_range_product(
8516 __isl_take isl_pw_multi_aff *pma1,
8517 __isl_take isl_pw_multi_aff *pma2);
8518 __isl_give isl_multi_pw_aff *
8519 isl_multi_pw_aff_flat_range_product(
8520 __isl_take isl_multi_pw_aff *mpa1,
8521 __isl_take isl_multi_pw_aff *mpa2);
8522 __isl_give isl_union_pw_multi_aff *
8523 isl_union_pw_multi_aff_flat_range_product(
8524 __isl_take isl_union_pw_multi_aff *upma1,
8525 __isl_take isl_union_pw_multi_aff *upma2);
8526 __isl_give isl_multi_union_pw_aff *
8527 isl_multi_union_pw_aff_flat_range_product(
8528 __isl_take isl_multi_union_pw_aff *mupa1,
8529 __isl_take isl_multi_union_pw_aff *mupa2);
8531 #include <isl/space.h>
8532 __isl_give isl_space *isl_space_factor_domain(
8533 __isl_take isl_space *space);
8534 __isl_give isl_space *isl_space_factor_range(
8535 __isl_take isl_space *space);
8536 __isl_give isl_space *isl_space_domain_factor_domain(
8537 __isl_take isl_space *space);
8538 __isl_give isl_space *isl_space_domain_factor_range(
8539 __isl_take isl_space *space);
8540 __isl_give isl_space *isl_space_range_factor_domain(
8541 __isl_take isl_space *space);
8542 __isl_give isl_space *isl_space_range_factor_range(
8543 __isl_take isl_space *space);
8545 The functions C<isl_space_range_factor_domain> and
8546 C<isl_space_range_factor_range> extract the two arguments from
8547 the result of a call to C<isl_space_range_product>.
8549 The arguments of a call to a product can be extracted
8550 from the result using the following functions.
8552 #include <isl/map.h>
8553 __isl_give isl_map *isl_map_factor_domain(
8554 __isl_take isl_map *map);
8555 __isl_give isl_map *isl_map_factor_range(
8556 __isl_take isl_map *map);
8557 __isl_give isl_map *isl_map_domain_factor_domain(
8558 __isl_take isl_map *map);
8559 __isl_give isl_map *isl_map_domain_factor_range(
8560 __isl_take isl_map *map);
8561 __isl_give isl_map *isl_map_range_factor_domain(
8562 __isl_take isl_map *map);
8563 __isl_give isl_map *isl_map_range_factor_range(
8564 __isl_take isl_map *map);
8566 #include <isl/union_map.h>
8567 __isl_give isl_union_map *isl_union_map_factor_domain(
8568 __isl_take isl_union_map *umap);
8569 __isl_give isl_union_map *isl_union_map_factor_range(
8570 __isl_take isl_union_map *umap);
8571 __isl_give isl_union_map *
8572 isl_union_map_domain_factor_domain(
8573 __isl_take isl_union_map *umap);
8574 __isl_give isl_union_map *
8575 isl_union_map_domain_factor_range(
8576 __isl_take isl_union_map *umap);
8577 __isl_give isl_union_map *
8578 isl_union_map_range_factor_domain(
8579 __isl_take isl_union_map *umap);
8580 __isl_give isl_union_map *
8581 isl_union_map_range_factor_range(
8582 __isl_take isl_union_map *umap);
8585 __isl_give isl_multi_id *isl_multi_id_factor_range(
8586 __isl_take isl_multi_id *mi);
8587 __isl_give isl_multi_id *
8588 isl_multi_id_range_factor_domain(
8589 __isl_take isl_multi_id *mi);
8590 __isl_give isl_multi_id *
8591 isl_multi_id_range_factor_range(
8592 __isl_take isl_multi_id *mi);
8594 #include <isl/val.h>
8595 __isl_give isl_multi_val *isl_multi_val_factor_range(
8596 __isl_take isl_multi_val *mv);
8597 __isl_give isl_multi_val *
8598 isl_multi_val_range_factor_domain(
8599 __isl_take isl_multi_val *mv);
8600 __isl_give isl_multi_val *
8601 isl_multi_val_range_factor_range(
8602 __isl_take isl_multi_val *mv);
8604 #include <isl/aff.h>
8605 __isl_give isl_multi_aff *isl_multi_aff_factor_range(
8606 __isl_take isl_multi_aff *ma);
8607 __isl_give isl_multi_aff *
8608 isl_multi_aff_range_factor_domain(
8609 __isl_take isl_multi_aff *ma);
8610 __isl_give isl_multi_aff *
8611 isl_multi_aff_range_factor_range(
8612 __isl_take isl_multi_aff *ma);
8613 __isl_give isl_multi_pw_aff *
8614 isl_multi_pw_aff_factor_range(
8615 __isl_take isl_multi_pw_aff *mpa);
8616 __isl_give isl_multi_pw_aff *
8617 isl_multi_pw_aff_range_factor_domain(
8618 __isl_take isl_multi_pw_aff *mpa);
8619 __isl_give isl_multi_pw_aff *
8620 isl_multi_pw_aff_range_factor_range(
8621 __isl_take isl_multi_pw_aff *mpa);
8622 __isl_give isl_pw_multi_aff *
8623 isl_pw_multi_aff_range_factor_domain(
8624 __isl_take isl_pw_multi_aff *pma);
8625 __isl_give isl_pw_multi_aff *
8626 isl_pw_multi_aff_range_factor_range(
8627 __isl_take isl_pw_multi_aff *pma);
8628 __isl_give isl_union_pw_multi_aff *
8629 isl_union_pw_multi_aff_range_factor_domain(
8630 __isl_take isl_union_pw_multi_aff *upma);
8631 __isl_give isl_union_pw_multi_aff *
8632 isl_union_pw_multi_aff_range_factor_range(
8633 __isl_take isl_union_pw_multi_aff *upma);
8634 __isl_give isl_multi_union_pw_aff *
8635 isl_multi_union_pw_aff_factor_range(
8636 __isl_take isl_multi_union_pw_aff *mupa);
8637 __isl_give isl_multi_union_pw_aff *
8638 isl_multi_union_pw_aff_range_factor_domain(
8639 __isl_take isl_multi_union_pw_aff *mupa);
8640 __isl_give isl_multi_union_pw_aff *
8641 isl_multi_union_pw_aff_range_factor_range(
8642 __isl_take isl_multi_union_pw_aff *mupa);
8644 The splice functions are a generalization of the flat product functions,
8645 where the second argument may be inserted at any position inside
8646 the first argument rather than being placed at the end.
8647 The functions C<isl_multi_val_factor_range>,
8648 C<isl_multi_aff_factor_range>,
8649 C<isl_multi_pw_aff_factor_range> and
8650 C<isl_multi_union_pw_aff_factor_range>
8651 take functions that live in a set space.
8654 __isl_give isl_multi_id *isl_multi_id_range_splice(
8655 __isl_take isl_multi_id *mi1, unsigned pos,
8656 __isl_take isl_multi_id *mi2);
8658 #include <isl/val.h>
8659 __isl_give isl_multi_val *isl_multi_val_range_splice(
8660 __isl_take isl_multi_val *mv1, unsigned pos,
8661 __isl_take isl_multi_val *mv2);
8663 #include <isl/aff.h>
8664 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
8665 __isl_take isl_multi_aff *ma1, unsigned pos,
8666 __isl_take isl_multi_aff *ma2);
8667 __isl_give isl_multi_aff *isl_multi_aff_splice(
8668 __isl_take isl_multi_aff *ma1,
8669 unsigned in_pos, unsigned out_pos,
8670 __isl_take isl_multi_aff *ma2);
8671 __isl_give isl_multi_pw_aff *
8672 isl_multi_pw_aff_range_splice(
8673 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
8674 __isl_take isl_multi_pw_aff *mpa2);
8675 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
8676 __isl_take isl_multi_pw_aff *mpa1,
8677 unsigned in_pos, unsigned out_pos,
8678 __isl_take isl_multi_pw_aff *mpa2);
8679 __isl_give isl_multi_union_pw_aff *
8680 isl_multi_union_pw_aff_range_splice(
8681 __isl_take isl_multi_union_pw_aff *mupa1,
8683 __isl_take isl_multi_union_pw_aff *mupa2);
8685 =item * Simplification
8687 When applied to a set or relation,
8688 the gist operation returns a set or relation that has the
8689 same intersection with the context as the input set or relation.
8690 Any implicit equality in the intersection is made explicit in the result,
8691 while all inequalities that are redundant with respect to the intersection
8693 In case of union sets and relations, the gist operation is performed
8696 When applied to a function,
8697 the gist operation applies the set gist operation to each of
8698 the cells in the domain of the input piecewise expression.
8699 The context is also exploited
8700 to simplify the expression associated to each cell.
8702 #include <isl/set.h>
8703 __isl_give isl_basic_set *isl_basic_set_gist(
8704 __isl_take isl_basic_set *bset,
8705 __isl_take isl_basic_set *context);
8706 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
8707 __isl_take isl_set *context);
8708 __isl_give isl_set *isl_set_gist_params(
8709 __isl_take isl_set *set,
8710 __isl_take isl_set *context);
8712 #include <isl/map.h>
8713 __isl_give isl_basic_map *isl_basic_map_gist(
8714 __isl_take isl_basic_map *bmap,
8715 __isl_take isl_basic_map *context);
8716 __isl_give isl_basic_map *isl_basic_map_gist_domain(
8717 __isl_take isl_basic_map *bmap,
8718 __isl_take isl_basic_set *context);
8719 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
8720 __isl_take isl_map *context);
8721 __isl_give isl_map *isl_map_gist_params(
8722 __isl_take isl_map *map,
8723 __isl_take isl_set *context);
8724 __isl_give isl_map *isl_map_gist_domain(
8725 __isl_take isl_map *map,
8726 __isl_take isl_set *context);
8727 __isl_give isl_map *isl_map_gist_range(
8728 __isl_take isl_map *map,
8729 __isl_take isl_set *context);
8731 #include <isl/union_set.h>
8732 __isl_give isl_union_set *isl_union_set_gist(
8733 __isl_take isl_union_set *uset,
8734 __isl_take isl_union_set *context);
8735 __isl_give isl_union_set *isl_union_set_gist_params(
8736 __isl_take isl_union_set *uset,
8737 __isl_take isl_set *set);
8739 #include <isl/union_map.h>
8740 __isl_give isl_union_map *isl_union_map_gist(
8741 __isl_take isl_union_map *umap,
8742 __isl_take isl_union_map *context);
8743 __isl_give isl_union_map *isl_union_map_gist_params(
8744 __isl_take isl_union_map *umap,
8745 __isl_take isl_set *set);
8746 __isl_give isl_union_map *isl_union_map_gist_domain(
8747 __isl_take isl_union_map *umap,
8748 __isl_take isl_union_set *uset);
8749 __isl_give isl_union_map *isl_union_map_gist_range(
8750 __isl_take isl_union_map *umap,
8751 __isl_take isl_union_set *uset);
8753 #include <isl/aff.h>
8754 __isl_give isl_aff *isl_aff_gist_params(
8755 __isl_take isl_aff *aff,
8756 __isl_take isl_set *context);
8757 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
8758 __isl_take isl_set *context);
8759 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
8760 __isl_take isl_multi_aff *maff,
8761 __isl_take isl_set *context);
8762 __isl_give isl_multi_aff *isl_multi_aff_gist(
8763 __isl_take isl_multi_aff *maff,
8764 __isl_take isl_set *context);
8765 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
8766 __isl_take isl_pw_aff *pwaff,
8767 __isl_take isl_set *context);
8768 __isl_give isl_pw_aff *isl_pw_aff_gist(
8769 __isl_take isl_pw_aff *pwaff,
8770 __isl_take isl_set *context);
8771 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
8772 __isl_take isl_pw_multi_aff *pma,
8773 __isl_take isl_set *set);
8774 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
8775 __isl_take isl_pw_multi_aff *pma,
8776 __isl_take isl_set *set);
8777 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
8778 __isl_take isl_multi_pw_aff *mpa,
8779 __isl_take isl_set *set);
8780 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
8781 __isl_take isl_multi_pw_aff *mpa,
8782 __isl_take isl_set *set);
8783 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
8784 __isl_take isl_union_pw_aff *upa,
8785 __isl_take isl_union_set *context);
8786 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
8787 __isl_take isl_union_pw_aff *upa,
8788 __isl_take isl_set *context);
8789 __isl_give isl_union_pw_multi_aff *
8790 isl_union_pw_multi_aff_gist_params(
8791 __isl_take isl_union_pw_multi_aff *upma,
8792 __isl_take isl_set *context);
8793 __isl_give isl_union_pw_multi_aff *
8794 isl_union_pw_multi_aff_gist(
8795 __isl_take isl_union_pw_multi_aff *upma,
8796 __isl_take isl_union_set *context);
8797 __isl_give isl_multi_union_pw_aff *
8798 isl_multi_union_pw_aff_gist_params(
8799 __isl_take isl_multi_union_pw_aff *mupa,
8800 __isl_take isl_set *context);
8801 __isl_give isl_multi_union_pw_aff *
8802 isl_multi_union_pw_aff_gist(
8803 __isl_take isl_multi_union_pw_aff *mupa,
8804 __isl_take isl_union_set *context);
8806 #include <isl/polynomial.h>
8807 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
8808 __isl_take isl_qpolynomial *qp,
8809 __isl_take isl_set *context);
8810 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
8811 __isl_take isl_qpolynomial *qp,
8812 __isl_take isl_set *context);
8813 __isl_give isl_qpolynomial_fold *
8814 isl_qpolynomial_fold_gist_params(
8815 __isl_take isl_qpolynomial_fold *fold,
8816 __isl_take isl_set *context);
8817 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
8818 __isl_take isl_qpolynomial_fold *fold,
8819 __isl_take isl_set *context);
8820 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
8821 __isl_take isl_pw_qpolynomial *pwqp,
8822 __isl_take isl_set *context);
8823 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
8824 __isl_take isl_pw_qpolynomial *pwqp,
8825 __isl_take isl_set *context);
8826 __isl_give isl_pw_qpolynomial_fold *
8827 isl_pw_qpolynomial_fold_gist(
8828 __isl_take isl_pw_qpolynomial_fold *pwf,
8829 __isl_take isl_set *context);
8830 __isl_give isl_pw_qpolynomial_fold *
8831 isl_pw_qpolynomial_fold_gist_params(
8832 __isl_take isl_pw_qpolynomial_fold *pwf,
8833 __isl_take isl_set *context);
8834 __isl_give isl_union_pw_qpolynomial *
8835 isl_union_pw_qpolynomial_gist_params(
8836 __isl_take isl_union_pw_qpolynomial *upwqp,
8837 __isl_take isl_set *context);
8838 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
8839 __isl_take isl_union_pw_qpolynomial *upwqp,
8840 __isl_take isl_union_set *context);
8841 __isl_give isl_union_pw_qpolynomial_fold *
8842 isl_union_pw_qpolynomial_fold_gist(
8843 __isl_take isl_union_pw_qpolynomial_fold *upwf,
8844 __isl_take isl_union_set *context);
8845 __isl_give isl_union_pw_qpolynomial_fold *
8846 isl_union_pw_qpolynomial_fold_gist_params(
8847 __isl_take isl_union_pw_qpolynomial_fold *upwf,
8848 __isl_take isl_set *context);
8850 =item * Binary Arithmetic Operations
8852 #include <isl/set.h>
8853 __isl_give isl_set *isl_set_sum(
8854 __isl_take isl_set *set1,
8855 __isl_take isl_set *set2);
8856 #include <isl/map.h>
8857 __isl_give isl_map *isl_map_sum(
8858 __isl_take isl_map *map1,
8859 __isl_take isl_map *map2);
8861 C<isl_set_sum> computes the Minkowski sum of its two arguments,
8862 i.e., the set containing the sums of pairs of elements from
8863 C<set1> and C<set2>.
8864 The domain of the result of C<isl_map_sum> is the intersection
8865 of the domains of its two arguments. The corresponding range
8866 elements are the sums of the corresponding range elements
8867 in the two arguments.
8869 #include <isl/val.h>
8870 __isl_give isl_multi_val *isl_multi_val_add(
8871 __isl_take isl_multi_val *mv1,
8872 __isl_take isl_multi_val *mv2);
8873 __isl_give isl_multi_val *isl_multi_val_sub(
8874 __isl_take isl_multi_val *mv1,
8875 __isl_take isl_multi_val *mv2);
8876 __isl_give isl_multi_val *isl_multi_val_min(
8877 __isl_take isl_multi_val *mv1,
8878 __isl_take isl_multi_val *mv2);
8879 __isl_give isl_multi_val *isl_multi_val_max(
8880 __isl_take isl_multi_val *mv1,
8881 __isl_take isl_multi_val *mv2);
8883 #include <isl/aff.h>
8884 __isl_give isl_aff *isl_aff_add(
8885 __isl_take isl_aff *aff1,
8886 __isl_take isl_aff *aff2);
8887 __isl_give isl_multi_aff *isl_multi_aff_add(
8888 __isl_take isl_multi_aff *maff1,
8889 __isl_take isl_multi_aff *maff2);
8890 __isl_give isl_pw_aff *isl_pw_aff_add(
8891 __isl_take isl_pw_aff *pwaff1,
8892 __isl_take isl_pw_aff *pwaff2);
8893 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add(
8894 __isl_take isl_multi_pw_aff *mpa1,
8895 __isl_take isl_multi_pw_aff *mpa2);
8896 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
8897 __isl_take isl_pw_multi_aff *pma1,
8898 __isl_take isl_pw_multi_aff *pma2);
8899 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
8900 __isl_take isl_union_pw_aff *upa1,
8901 __isl_take isl_union_pw_aff *upa2);
8902 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
8903 __isl_take isl_union_pw_multi_aff *upma1,
8904 __isl_take isl_union_pw_multi_aff *upma2);
8905 __isl_give isl_multi_union_pw_aff *
8906 isl_multi_union_pw_aff_add(
8907 __isl_take isl_multi_union_pw_aff *mupa1,
8908 __isl_take isl_multi_union_pw_aff *mupa2);
8909 __isl_give isl_pw_aff *isl_pw_aff_add_constant_val(
8910 __isl_take isl_pw_aff *pa,
8911 __isl_take isl_val *v);
8912 __isl_give isl_multi_aff *
8913 isl_multi_aff_add_constant_val(
8914 __isl_take isl_multi_aff *pa,
8915 __isl_take isl_val *v);
8916 __isl_give isl_pw_multi_aff *
8917 isl_pw_multi_aff_add_constant_val(
8918 __isl_take isl_pw_multi_aff *pma,
8919 __isl_take isl_val *v);
8920 __isl_give isl_pw_multi_aff *
8921 isl_pw_multi_aff_add_constant_multi_val(
8922 __isl_take isl_pw_multi_aff *pma,
8923 __isl_take isl_multi_val *mv);
8924 __isl_give isl_multi_pw_aff *
8925 isl_multi_pw_aff_add_constant_val(
8926 __isl_take isl_multi_pw_aff *mpa,
8927 __isl_take isl_val *v);
8928 __isl_give isl_multi_aff *
8929 isl_multi_aff_add_constant_multi_val(
8930 __isl_take isl_multi_aff *pa,
8931 __isl_take isl_multi_val *mv);
8932 __isl_give isl_multi_pw_aff *
8933 isl_multi_pw_aff_add_constant_multi_val(
8934 __isl_take isl_multi_pw_aff *mpa,
8935 __isl_take isl_multi_val *mv);
8936 __isl_give isl_pw_aff *isl_pw_aff_min(
8937 __isl_take isl_pw_aff *pwaff1,
8938 __isl_take isl_pw_aff *pwaff2);
8939 __isl_give isl_pw_aff *isl_pw_aff_max(
8940 __isl_take isl_pw_aff *pwaff1,
8941 __isl_take isl_pw_aff *pwaff2);
8942 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_min(
8943 __isl_take isl_multi_pw_aff *mpa1,
8944 __isl_take isl_multi_pw_aff *mpa2);
8945 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_max(
8946 __isl_take isl_multi_pw_aff *mpa1,
8947 __isl_take isl_multi_pw_aff *mpa2);
8948 __isl_give isl_aff *isl_aff_sub(
8949 __isl_take isl_aff *aff1,
8950 __isl_take isl_aff *aff2);
8951 __isl_give isl_multi_aff *isl_multi_aff_sub(
8952 __isl_take isl_multi_aff *ma1,
8953 __isl_take isl_multi_aff *ma2);
8954 __isl_give isl_pw_aff *isl_pw_aff_sub(
8955 __isl_take isl_pw_aff *pwaff1,
8956 __isl_take isl_pw_aff *pwaff2);
8957 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
8958 __isl_take isl_multi_pw_aff *mpa1,
8959 __isl_take isl_multi_pw_aff *mpa2);
8960 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
8961 __isl_take isl_pw_multi_aff *pma1,
8962 __isl_take isl_pw_multi_aff *pma2);
8963 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
8964 __isl_take isl_union_pw_aff *upa1,
8965 __isl_take isl_union_pw_aff *upa2);
8966 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
8967 __isl_take isl_union_pw_multi_aff *upma1,
8968 __isl_take isl_union_pw_multi_aff *upma2);
8969 __isl_give isl_multi_union_pw_aff *
8970 isl_multi_union_pw_aff_sub(
8971 __isl_take isl_multi_union_pw_aff *mupa1,
8972 __isl_take isl_multi_union_pw_aff *mupa2);
8974 C<isl_aff_sub> subtracts the second argument from the first.
8976 #include <isl/polynomial.h>
8977 __isl_give isl_qpolynomial *isl_qpolynomial_add(
8978 __isl_take isl_qpolynomial *qp1,
8979 __isl_take isl_qpolynomial *qp2);
8980 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
8981 __isl_take isl_pw_qpolynomial *pwqp1,
8982 __isl_take isl_pw_qpolynomial *pwqp2);
8983 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
8984 __isl_take isl_pw_qpolynomial *pwqp1,
8985 __isl_take isl_pw_qpolynomial *pwqp2);
8986 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
8987 __isl_take isl_pw_qpolynomial_fold *pwf1,
8988 __isl_take isl_pw_qpolynomial_fold *pwf2);
8989 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
8990 __isl_take isl_union_pw_qpolynomial *upwqp1,
8991 __isl_take isl_union_pw_qpolynomial *upwqp2);
8992 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
8993 __isl_take isl_qpolynomial *qp1,
8994 __isl_take isl_qpolynomial *qp2);
8995 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
8996 __isl_take isl_pw_qpolynomial *pwqp1,
8997 __isl_take isl_pw_qpolynomial *pwqp2);
8998 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
8999 __isl_take isl_union_pw_qpolynomial *upwqp1,
9000 __isl_take isl_union_pw_qpolynomial *upwqp2);
9001 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
9002 __isl_take isl_pw_qpolynomial_fold *pwf1,
9003 __isl_take isl_pw_qpolynomial_fold *pwf2);
9004 __isl_give isl_union_pw_qpolynomial_fold *
9005 isl_union_pw_qpolynomial_fold_fold(
9006 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
9007 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
9009 #include <isl/aff.h>
9010 __isl_give isl_pw_aff *isl_pw_aff_union_add(
9011 __isl_take isl_pw_aff *pwaff1,
9012 __isl_take isl_pw_aff *pwaff2);
9013 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_union_add(
9014 __isl_take isl_multi_pw_aff *mpa1,
9015 __isl_take isl_multi_pw_aff *mpa2);
9016 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
9017 __isl_take isl_pw_multi_aff *pma1,
9018 __isl_take isl_pw_multi_aff *pma2);
9019 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
9020 __isl_take isl_union_pw_aff *upa1,
9021 __isl_take isl_union_pw_aff *upa2);
9022 __isl_give isl_union_pw_multi_aff *
9023 isl_union_pw_multi_aff_union_add(
9024 __isl_take isl_union_pw_multi_aff *upma1,
9025 __isl_take isl_union_pw_multi_aff *upma2);
9026 __isl_give isl_multi_union_pw_aff *
9027 isl_multi_union_pw_aff_union_add(
9028 __isl_take isl_multi_union_pw_aff *mupa1,
9029 __isl_take isl_multi_union_pw_aff *mupa2);
9030 __isl_give isl_pw_aff *isl_pw_aff_union_min(
9031 __isl_take isl_pw_aff *pwaff1,
9032 __isl_take isl_pw_aff *pwaff2);
9033 __isl_give isl_pw_aff *isl_pw_aff_union_max(
9034 __isl_take isl_pw_aff *pwaff1,
9035 __isl_take isl_pw_aff *pwaff2);
9037 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
9038 expression with a domain that is the union of those of C<pwaff1> and
9039 C<pwaff2> and such that on each cell, the quasi-affine expression is
9040 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
9041 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
9042 associated expression is the defined one.
9043 This in contrast to the C<isl_pw_aff_max> function, which is
9044 only defined on the shared definition domain of the arguments.
9046 #include <isl/val.h>
9047 __isl_give isl_multi_val *isl_multi_val_add_val(
9048 __isl_take isl_multi_val *mv,
9049 __isl_take isl_val *v);
9050 __isl_give isl_multi_val *isl_multi_val_mod_val(
9051 __isl_take isl_multi_val *mv,
9052 __isl_take isl_val *v);
9053 __isl_give isl_multi_val *isl_multi_val_scale_val(
9054 __isl_take isl_multi_val *mv,
9055 __isl_take isl_val *v);
9056 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
9057 __isl_take isl_multi_val *mv,
9058 __isl_take isl_val *v);
9060 #include <isl/aff.h>
9061 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
9062 __isl_take isl_val *mod);
9063 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
9064 __isl_take isl_pw_aff *pa,
9065 __isl_take isl_val *mod);
9066 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
9067 __isl_take isl_union_pw_aff *upa,
9068 __isl_take isl_val *f);
9069 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
9070 __isl_take isl_val *v);
9071 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
9072 __isl_take isl_multi_aff *ma,
9073 __isl_take isl_val *v);
9074 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
9075 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
9076 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
9077 __isl_take isl_multi_pw_aff *mpa,
9078 __isl_take isl_val *v);
9079 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
9080 __isl_take isl_pw_multi_aff *pma,
9081 __isl_take isl_val *v);
9082 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
9083 __isl_take isl_union_pw_aff *upa,
9084 __isl_take isl_val *f);
9085 __isl_give isl_union_pw_multi_aff *
9086 isl_union_pw_multi_aff_scale_val(
9087 __isl_take isl_union_pw_multi_aff *upma,
9088 __isl_take isl_val *val);
9089 __isl_give isl_multi_union_pw_aff *
9090 isl_multi_union_pw_aff_scale_val(
9091 __isl_take isl_multi_union_pw_aff *mupa,
9092 __isl_take isl_val *v);
9093 __isl_give isl_aff *isl_aff_scale_down_ui(
9094 __isl_take isl_aff *aff, unsigned f);
9095 __isl_give isl_aff *isl_aff_scale_down_val(
9096 __isl_take isl_aff *aff, __isl_take isl_val *v);
9097 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
9098 __isl_take isl_multi_aff *ma,
9099 __isl_take isl_val *v);
9100 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
9101 __isl_take isl_pw_aff *pa,
9102 __isl_take isl_val *f);
9103 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
9104 __isl_take isl_multi_pw_aff *mpa,
9105 __isl_take isl_val *v);
9106 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
9107 __isl_take isl_pw_multi_aff *pma,
9108 __isl_take isl_val *v);
9109 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
9110 __isl_take isl_union_pw_aff *upa,
9111 __isl_take isl_val *v);
9112 __isl_give isl_union_pw_multi_aff *
9113 isl_union_pw_multi_aff_scale_down_val(
9114 __isl_take isl_union_pw_multi_aff *upma,
9115 __isl_take isl_val *val);
9116 __isl_give isl_multi_union_pw_aff *
9117 isl_multi_union_pw_aff_scale_down_val(
9118 __isl_take isl_multi_union_pw_aff *mupa,
9119 __isl_take isl_val *v);
9121 #include <isl/polynomial.h>
9122 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
9123 __isl_take isl_qpolynomial *qp,
9124 __isl_take isl_val *v);
9125 __isl_give isl_qpolynomial_fold *
9126 isl_qpolynomial_fold_scale_val(
9127 __isl_take isl_qpolynomial_fold *fold,
9128 __isl_take isl_val *v);
9129 __isl_give isl_pw_qpolynomial *
9130 isl_pw_qpolynomial_scale_val(
9131 __isl_take isl_pw_qpolynomial *pwqp,
9132 __isl_take isl_val *v);
9133 __isl_give isl_pw_qpolynomial_fold *
9134 isl_pw_qpolynomial_fold_scale_val(
9135 __isl_take isl_pw_qpolynomial_fold *pwf,
9136 __isl_take isl_val *v);
9137 __isl_give isl_union_pw_qpolynomial *
9138 isl_union_pw_qpolynomial_scale_val(
9139 __isl_take isl_union_pw_qpolynomial *upwqp,
9140 __isl_take isl_val *v);
9141 __isl_give isl_union_pw_qpolynomial_fold *
9142 isl_union_pw_qpolynomial_fold_scale_val(
9143 __isl_take isl_union_pw_qpolynomial_fold *upwf,
9144 __isl_take isl_val *v);
9145 __isl_give isl_qpolynomial *
9146 isl_qpolynomial_scale_down_val(
9147 __isl_take isl_qpolynomial *qp,
9148 __isl_take isl_val *v);
9149 __isl_give isl_qpolynomial_fold *
9150 isl_qpolynomial_fold_scale_down_val(
9151 __isl_take isl_qpolynomial_fold *fold,
9152 __isl_take isl_val *v);
9153 __isl_give isl_pw_qpolynomial *
9154 isl_pw_qpolynomial_scale_down_val(
9155 __isl_take isl_pw_qpolynomial *pwqp,
9156 __isl_take isl_val *v);
9157 __isl_give isl_pw_qpolynomial_fold *
9158 isl_pw_qpolynomial_fold_scale_down_val(
9159 __isl_take isl_pw_qpolynomial_fold *pwf,
9160 __isl_take isl_val *v);
9161 __isl_give isl_union_pw_qpolynomial *
9162 isl_union_pw_qpolynomial_scale_down_val(
9163 __isl_take isl_union_pw_qpolynomial *upwqp,
9164 __isl_take isl_val *v);
9165 __isl_give isl_union_pw_qpolynomial_fold *
9166 isl_union_pw_qpolynomial_fold_scale_down_val(
9167 __isl_take isl_union_pw_qpolynomial_fold *upwf,
9168 __isl_take isl_val *v);
9170 #include <isl/val.h>
9171 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
9172 __isl_take isl_multi_val *mv1,
9173 __isl_take isl_multi_val *mv2);
9174 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
9175 __isl_take isl_multi_val *mv1,
9176 __isl_take isl_multi_val *mv2);
9177 __isl_give isl_multi_val *
9178 isl_multi_val_scale_down_multi_val(
9179 __isl_take isl_multi_val *mv1,
9180 __isl_take isl_multi_val *mv2);
9182 #include <isl/aff.h>
9183 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
9184 __isl_take isl_multi_aff *ma,
9185 __isl_take isl_multi_val *mv);
9186 __isl_give isl_multi_union_pw_aff *
9187 isl_multi_union_pw_aff_mod_multi_val(
9188 __isl_take isl_multi_union_pw_aff *upma,
9189 __isl_take isl_multi_val *mv);
9190 __isl_give isl_multi_pw_aff *
9191 isl_multi_pw_aff_mod_multi_val(
9192 __isl_take isl_multi_pw_aff *mpa,
9193 __isl_take isl_multi_val *mv);
9194 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
9195 __isl_take isl_multi_aff *ma,
9196 __isl_take isl_multi_val *mv);
9197 __isl_give isl_pw_multi_aff *
9198 isl_pw_multi_aff_scale_multi_val(
9199 __isl_take isl_pw_multi_aff *pma,
9200 __isl_take isl_multi_val *mv);
9201 __isl_give isl_multi_pw_aff *
9202 isl_multi_pw_aff_scale_multi_val(
9203 __isl_take isl_multi_pw_aff *mpa,
9204 __isl_take isl_multi_val *mv);
9205 __isl_give isl_multi_union_pw_aff *
9206 isl_multi_union_pw_aff_scale_multi_val(
9207 __isl_take isl_multi_union_pw_aff *mupa,
9208 __isl_take isl_multi_val *mv);
9209 __isl_give isl_union_pw_multi_aff *
9210 isl_union_pw_multi_aff_scale_multi_val(
9211 __isl_take isl_union_pw_multi_aff *upma,
9212 __isl_take isl_multi_val *mv);
9213 __isl_give isl_multi_aff *
9214 isl_multi_aff_scale_down_multi_val(
9215 __isl_take isl_multi_aff *ma,
9216 __isl_take isl_multi_val *mv);
9217 __isl_give isl_pw_multi_aff *
9218 isl_pw_multi_aff_scale_down_multi_val(
9219 __isl_take isl_pw_multi_aff *pma,
9220 __isl_take isl_multi_val *mv);
9221 __isl_give isl_multi_pw_aff *
9222 isl_multi_pw_aff_scale_down_multi_val(
9223 __isl_take isl_multi_pw_aff *mpa,
9224 __isl_take isl_multi_val *mv);
9225 __isl_give isl_multi_union_pw_aff *
9226 isl_multi_union_pw_aff_scale_down_multi_val(
9227 __isl_take isl_multi_union_pw_aff *mupa,
9228 __isl_take isl_multi_val *mv);
9230 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
9231 by the corresponding elements of C<mv>.
9233 #include <isl/aff.h>
9234 __isl_give isl_aff *isl_aff_mul(
9235 __isl_take isl_aff *aff1,
9236 __isl_take isl_aff *aff2);
9237 __isl_give isl_aff *isl_aff_div(
9238 __isl_take isl_aff *aff1,
9239 __isl_take isl_aff *aff2);
9240 __isl_give isl_pw_aff *isl_pw_aff_mul(
9241 __isl_take isl_pw_aff *pwaff1,
9242 __isl_take isl_pw_aff *pwaff2);
9243 __isl_give isl_pw_aff *isl_pw_aff_div(
9244 __isl_take isl_pw_aff *pa1,
9245 __isl_take isl_pw_aff *pa2);
9246 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
9247 __isl_take isl_pw_aff *pa1,
9248 __isl_take isl_pw_aff *pa2);
9249 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
9250 __isl_take isl_pw_aff *pa1,
9251 __isl_take isl_pw_aff *pa2);
9253 When multiplying two affine expressions, at least one of the two needs
9254 to be a constant. Similarly, when dividing an affine expression by another,
9255 the second expression needs to be a constant.
9256 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
9257 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
9260 #include <isl/polynomial.h>
9261 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
9262 __isl_take isl_qpolynomial *qp1,
9263 __isl_take isl_qpolynomial *qp2);
9264 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
9265 __isl_take isl_pw_qpolynomial *pwqp1,
9266 __isl_take isl_pw_qpolynomial *pwqp2);
9267 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
9268 __isl_take isl_union_pw_qpolynomial *upwqp1,
9269 __isl_take isl_union_pw_qpolynomial *upwqp2);
9273 =head3 Lexicographic Optimization
9275 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
9276 the following functions
9277 compute a set that contains the lexicographic minimum or maximum
9278 of the elements in C<set> (or C<bset>) for those values of the parameters
9279 that satisfy C<dom>.
9280 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
9281 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
9283 In other words, the union of the parameter values
9284 for which the result is non-empty and of C<*empty>
9287 #include <isl/set.h>
9288 __isl_give isl_set *isl_basic_set_partial_lexmin(
9289 __isl_take isl_basic_set *bset,
9290 __isl_take isl_basic_set *dom,
9291 __isl_give isl_set **empty);
9292 __isl_give isl_set *isl_basic_set_partial_lexmax(
9293 __isl_take isl_basic_set *bset,
9294 __isl_take isl_basic_set *dom,
9295 __isl_give isl_set **empty);
9296 __isl_give isl_set *isl_set_partial_lexmin(
9297 __isl_take isl_set *set, __isl_take isl_set *dom,
9298 __isl_give isl_set **empty);
9299 __isl_give isl_set *isl_set_partial_lexmax(
9300 __isl_take isl_set *set, __isl_take isl_set *dom,
9301 __isl_give isl_set **empty);
9303 Given a (basic) set C<set> (or C<bset>), the following functions simply
9304 return a set containing the lexicographic minimum or maximum
9305 of the elements in C<set> (or C<bset>).
9306 In case of union sets, the optimum is computed per space.
9308 #include <isl/set.h>
9309 __isl_give isl_set *isl_basic_set_lexmin(
9310 __isl_take isl_basic_set *bset);
9311 __isl_give isl_set *isl_basic_set_lexmax(
9312 __isl_take isl_basic_set *bset);
9313 __isl_give isl_set *isl_set_lexmin(
9314 __isl_take isl_set *set);
9315 __isl_give isl_set *isl_set_lexmax(
9316 __isl_take isl_set *set);
9317 __isl_give isl_union_set *isl_union_set_lexmin(
9318 __isl_take isl_union_set *uset);
9319 __isl_give isl_union_set *isl_union_set_lexmax(
9320 __isl_take isl_union_set *uset);
9322 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
9323 the following functions
9324 compute a relation that maps each element of C<dom>
9325 to the single lexicographic minimum or maximum
9326 of the elements that are associated to that same
9327 element in C<map> (or C<bmap>).
9328 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
9329 that contains the elements in C<dom> that do not map
9330 to any elements in C<map> (or C<bmap>).
9331 In other words, the union of the domain of the result and of C<*empty>
9334 #include <isl/map.h>
9335 __isl_give isl_map *isl_basic_map_partial_lexmax(
9336 __isl_take isl_basic_map *bmap,
9337 __isl_take isl_basic_set *dom,
9338 __isl_give isl_set **empty);
9339 __isl_give isl_map *isl_basic_map_partial_lexmin(
9340 __isl_take isl_basic_map *bmap,
9341 __isl_take isl_basic_set *dom,
9342 __isl_give isl_set **empty);
9343 __isl_give isl_map *isl_map_partial_lexmax(
9344 __isl_take isl_map *map, __isl_take isl_set *dom,
9345 __isl_give isl_set **empty);
9346 __isl_give isl_map *isl_map_partial_lexmin(
9347 __isl_take isl_map *map, __isl_take isl_set *dom,
9348 __isl_give isl_set **empty);
9350 Given a (basic) map C<map> (or C<bmap>), the following functions simply
9351 return a map mapping each element in the domain of
9352 C<map> (or C<bmap>) to the lexicographic minimum or maximum
9353 of all elements associated to that element.
9354 In case of union relations, the optimum is computed per space.
9356 #include <isl/map.h>
9357 __isl_give isl_map *isl_basic_map_lexmin(
9358 __isl_take isl_basic_map *bmap);
9359 __isl_give isl_map *isl_basic_map_lexmax(
9360 __isl_take isl_basic_map *bmap);
9361 __isl_give isl_map *isl_map_lexmin(
9362 __isl_take isl_map *map);
9363 __isl_give isl_map *isl_map_lexmax(
9364 __isl_take isl_map *map);
9365 __isl_give isl_union_map *isl_union_map_lexmin(
9366 __isl_take isl_union_map *umap);
9367 __isl_give isl_union_map *isl_union_map_lexmax(
9368 __isl_take isl_union_map *umap);
9370 The following functions return their result in the form of
9371 a piecewise multi-affine expression,
9372 but are otherwise equivalent to the corresponding functions
9373 returning a basic set or relation.
9375 #include <isl/set.h>
9376 __isl_give isl_pw_multi_aff *
9377 isl_basic_set_partial_lexmin_pw_multi_aff(
9378 __isl_take isl_basic_set *bset,
9379 __isl_take isl_basic_set *dom,
9380 __isl_give isl_set **empty);
9381 __isl_give isl_pw_multi_aff *
9382 isl_basic_set_partial_lexmax_pw_multi_aff(
9383 __isl_take isl_basic_set *bset,
9384 __isl_take isl_basic_set *dom,
9385 __isl_give isl_set **empty);
9386 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
9387 __isl_take isl_set *set);
9388 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
9389 __isl_take isl_set *set);
9391 #include <isl/map.h>
9392 __isl_give isl_pw_multi_aff *
9393 isl_basic_map_lexmin_pw_multi_aff(
9394 __isl_take isl_basic_map *bmap);
9395 __isl_give isl_pw_multi_aff *
9396 isl_basic_map_partial_lexmin_pw_multi_aff(
9397 __isl_take isl_basic_map *bmap,
9398 __isl_take isl_basic_set *dom,
9399 __isl_give isl_set **empty);
9400 __isl_give isl_pw_multi_aff *
9401 isl_basic_map_partial_lexmax_pw_multi_aff(
9402 __isl_take isl_basic_map *bmap,
9403 __isl_take isl_basic_set *dom,
9404 __isl_give isl_set **empty);
9405 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
9406 __isl_take isl_map *map);
9407 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
9408 __isl_take isl_map *map);
9410 The following functions return the lexicographic minimum or maximum
9411 on the shared domain of the inputs and the single defined function
9412 on those parts of the domain where only a single function is defined.
9414 #include <isl/aff.h>
9415 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
9416 __isl_take isl_pw_multi_aff *pma1,
9417 __isl_take isl_pw_multi_aff *pma2);
9418 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
9419 __isl_take isl_pw_multi_aff *pma1,
9420 __isl_take isl_pw_multi_aff *pma2);
9422 If the input to a lexicographic optimization problem has
9423 multiple constraints with the same coefficients for the optimized
9424 variables, then, by default, this symmetry is exploited by
9425 replacing those constraints by a single constraint with
9426 an abstract bound, which is in turn bounded by the corresponding terms
9427 in the original constraints.
9428 Without this optimization, the solver would typically consider
9429 all possible orderings of those original bounds, resulting in a needless
9430 decomposition of the domain.
9431 However, the optimization can also result in slowdowns since
9432 an extra parameter is introduced that may get used in additional
9434 The following option determines whether symmetry detection is applied
9435 during lexicographic optimization.
9437 #include <isl/options.h>
9438 isl_stat isl_options_set_pip_symmetry(isl_ctx *ctx,
9440 int isl_options_get_pip_symmetry(isl_ctx *ctx);
9444 See also \autoref{s:offline}.
9448 =head2 Ternary Operations
9450 #include <isl/aff.h>
9451 __isl_give isl_pw_aff *isl_pw_aff_cond(
9452 __isl_take isl_pw_aff *cond,
9453 __isl_take isl_pw_aff *pwaff_true,
9454 __isl_take isl_pw_aff *pwaff_false);
9456 The function C<isl_pw_aff_cond> performs a conditional operator
9457 and returns an expression that is equal to C<pwaff_true>
9458 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
9459 where C<cond> is zero.
9463 Lists are defined over several element types, including
9464 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_pw_multi_aff>,
9465 C<isl_union_pw_aff>,
9466 C<isl_union_pw_multi_aff>,
9467 C<isl_qpolynomial>, C<isl_pw_qpolynomial>, C<isl_pw_qpolynomial_fold>,
9469 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
9470 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
9471 Here we take lists of C<isl_set>s as an example.
9472 Lists can be created, copied, modified and freed using the following functions.
9474 #include <isl/set.h>
9475 __isl_give isl_set_list *isl_set_to_list(
9476 __isl_take isl_set *el);
9477 __isl_give isl_set_list *isl_set_list_from_set(
9478 __isl_take isl_set *el);
9479 __isl_give isl_set_list *isl_set_list_alloc(
9480 isl_ctx *ctx, int n);
9481 __isl_give isl_set_list *isl_set_list_copy(
9482 __isl_keep isl_set_list *list);
9483 __isl_give isl_set_list *isl_set_list_insert(
9484 __isl_take isl_set_list *list, unsigned pos,
9485 __isl_take isl_set *el);
9486 __isl_give isl_set_list *isl_set_list_add(
9487 __isl_take isl_set_list *list,
9488 __isl_take isl_set *el);
9489 __isl_give isl_set_list *isl_set_list_drop(
9490 __isl_take isl_set_list *list,
9491 unsigned first, unsigned n);
9492 __isl_give isl_set_list *isl_set_list_clear(
9493 __isl_take isl_set_list *list);
9494 __isl_give isl_set_list *isl_set_list_swap(
9495 __isl_take isl_set_list *list,
9496 unsigned pos1, unsigned pos2);
9497 __isl_give isl_set_list *isl_set_list_reverse(
9498 __isl_take isl_set_list *list);
9499 __isl_give isl_set_list *isl_set_list_set_at(
9500 __isl_take isl_set_list *list, int index,
9501 __isl_take isl_set *set);
9502 __isl_give isl_set_list *isl_set_list_set_set(
9503 __isl_take isl_set_list *list, int index,
9504 __isl_take isl_set *set);
9505 __isl_give isl_set_list *isl_set_list_concat(
9506 __isl_take isl_set_list *list1,
9507 __isl_take isl_set_list *list2);
9508 __isl_give isl_set_list *isl_set_list_map(
9509 __isl_take isl_set_list *list,
9510 __isl_give isl_set *(*fn)(__isl_take isl_set *el,
9513 __isl_give isl_set_list *isl_set_list_sort(
9514 __isl_take isl_set_list *list,
9515 int (*cmp)(__isl_keep isl_set *a,
9516 __isl_keep isl_set *b, void *user),
9518 __isl_null isl_set_list *isl_set_list_free(
9519 __isl_take isl_set_list *list);
9521 C<isl_set_list_alloc> creates an empty list with an initial capacity
9522 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
9523 add elements to a list, increasing its capacity as needed.
9524 C<isl_set_to_list> creates a list with a single element.
9525 C<isl_set_list_from_set> performs the same operation.
9526 C<isl_set_list_clear> removes all elements from a list.
9527 C<isl_set_list_swap> swaps the elements at the specified locations.
9528 C<isl_set_list_reverse> reverses the elements in the list.
9529 C<isl_set_list_set_set> is an alternative name for C<isl_set_list_set_at>.
9531 Lists can be inspected using the following functions.
9533 #include <isl/set.h>
9534 isl_size isl_set_list_size(__isl_keep isl_set_list *list);
9535 isl_size isl_set_list_n_set(__isl_keep isl_set_list *list);
9536 __isl_give isl_set *isl_set_list_get_at(
9537 __isl_keep isl_set_list *list, int index);
9538 __isl_give isl_set *isl_set_list_get_set(
9539 __isl_keep isl_set_list *list, int index);
9540 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list,
9541 isl_stat (*fn)(__isl_take isl_set *el, void *user),
9543 isl_bool isl_set_list_every(__isl_keep isl_set_list *list,
9544 isl_bool (*test)(__isl_take isl_set *el,
9547 isl_stat isl_set_list_foreach_scc(
9548 __isl_keep isl_set_list *list,
9549 isl_bool (*follows)(__isl_keep isl_set *a,
9550 __isl_keep isl_set *b, void *user),
9552 isl_stat (*fn)(__isl_take isl_set_list *scc,
9556 C<isl_set_list_n_set> is an alternative name for C<isl_set_list_size>.
9558 C<isl_set_list_get_set> is an alternative name for C<isl_set_list_get_at>.
9559 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
9560 strongly connected components of the graph with as vertices the elements
9561 of C<list> and a directed edge from vertex C<b> to vertex C<a>
9562 iff C<follows(a, b)> returns C<isl_bool_true>. The callbacks C<follows> and
9563 C<fn> should return C<isl_bool_error> or C<isl_stat_error> on error.
9565 Lists can be printed using
9567 #include <isl/set.h>
9568 __isl_give isl_printer *isl_printer_print_set_list(
9569 __isl_take isl_printer *p,
9570 __isl_keep isl_set_list *list);
9572 Alternatively, a string representation can be obtained
9573 directly using the following function, which always prints
9576 #include <isl/set.h>
9577 __isl_give char *isl_set_list_to_str(
9578 __isl_keep isl_set_list *list);
9580 An C<isl_val_list>, C<isl_id_list>,
9581 C<isl_aff_list>, C<isl_pw_aff_list>, C<isl_pw_multi_aff_list>,
9582 C<isl_union_pw_aff_list>,
9583 C<isl_set_list>, C<isl_map_list> or C<isl_union_set_list> object
9584 can also be read from input using the following functions.
9586 #include <isl/val.h>
9587 __isl_give isl_val_list *isl_val_list_read_from_str(
9588 isl_ctx *ctx, const char *str);
9591 __isl_give isl_id_list *isl_id_list_read_from_str(
9592 isl_ctx *ctx, const char *str);
9594 #include <isl/aff.h>
9595 __isl_give isl_aff_list *
9596 isl_aff_list_read_from_str(isl_ctx *ctx,
9598 __isl_give isl_pw_aff_list *
9599 isl_pw_aff_list_read_from_str(isl_ctx *ctx,
9601 __isl_give isl_pw_multi_aff_list *
9602 isl_pw_multi_aff_list_read_from_str(isl_ctx *ctx,
9604 __isl_give isl_union_pw_aff_list *
9605 isl_union_pw_aff_list_read_from_str(isl_ctx *ctx,
9608 #include <isl/set.h>
9609 __isl_give isl_set_list *isl_set_list_read_from_str(
9610 isl_ctx *ctx, const char *str);
9612 #include <isl/map.h>
9613 __isl_give isl_map_list *isl_map_list_read_from_str(
9614 isl_ctx *ctx, const char *str);
9616 #include <isl/union_set.h>
9617 __isl_give isl_union_set_list *
9618 isl_union_set_list_read_from_str(isl_ctx *ctx,
9621 =head2 Associative arrays
9623 Associative arrays map isl objects of a specific type to isl objects
9624 of some (other) specific type. They are defined for several pairs
9625 of types, including (C<isl_map>, C<isl_basic_set>),
9626 (C<isl_id>, C<isl_ast_expr>),
9627 (C<isl_id>, C<isl_id>) and
9628 (C<isl_id>, C<isl_pw_aff>).
9629 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
9632 Associative arrays can be created, copied and freed using
9633 the following functions.
9635 #include <isl/id_to_ast_expr.h>
9636 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
9637 isl_ctx *ctx, int min_size);
9638 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
9639 __isl_keep isl_id_to_ast_expr *id2expr);
9640 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
9641 __isl_take isl_id_to_ast_expr *id2expr);
9643 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
9644 to specify the expected size of the associative array.
9645 The associative array will be grown automatically as needed.
9647 Associative arrays can be inspected using the following functions.
9649 #include <isl/id_to_ast_expr.h>
9650 __isl_give isl_maybe_isl_ast_expr
9651 isl_id_to_ast_expr_try_get(
9652 __isl_keep isl_id_to_ast_expr *id2expr,
9653 __isl_keep isl_id *key);
9654 isl_bool isl_id_to_ast_expr_has(
9655 __isl_keep isl_id_to_ast_expr *id2expr,
9656 __isl_keep isl_id *key);
9657 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
9658 __isl_keep isl_id_to_ast_expr *id2expr,
9659 __isl_take isl_id *key);
9660 isl_stat isl_id_to_ast_expr_foreach(
9661 __isl_keep isl_id_to_ast_expr *id2expr,
9662 isl_stat (*fn)(__isl_take isl_id *key,
9663 __isl_take isl_ast_expr *val, void *user),
9665 isl_bool isl_id_to_ast_expr_every(
9666 __isl_keep isl_id_to_ast_expr *id2expr,
9667 isl_bool (*test)(__isl_keep isl_id *key,
9668 __isl_keep isl_ast_expr *val, void *user),
9671 The function C<isl_id_to_ast_expr_try_get> returns a structure
9672 containing two elements, C<valid> and C<value>.
9673 If there is a value associated to the key, then C<valid>
9674 is set to C<isl_bool_true> and C<value> contains a copy of
9675 the associated value. Otherwise C<value> is C<NULL> and
9676 C<valid> may be C<isl_bool_error> or C<isl_bool_false> depending
9677 on whether some error has occurred or there simply is no associated value.
9678 The function C<isl_id_to_ast_expr_has> returns the C<valid> field
9679 in the structure and
9680 the function C<isl_id_to_ast_expr_get> returns the C<value> field.
9682 Associative arrays can be modified using the following functions.
9684 #include <isl/id_to_ast_expr.h>
9685 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
9686 __isl_take isl_id_to_ast_expr *id2expr,
9687 __isl_take isl_id *key,
9688 __isl_take isl_ast_expr *val);
9689 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
9690 __isl_take isl_id_to_ast_expr *id2expr,
9691 __isl_take isl_id *key);
9693 Associative arrays can be checked for (obvious) equality
9694 using the following function.
9696 #include <isl/id_to_ast_expr.h>
9697 isl_bool isl_id_to_ast_expr_is_equal(
9698 __isl_take isl_id_to_ast_expr *id2expr1,
9699 __isl_take isl_id_to_ast_expr *id2expr2);
9701 Note that depending on how the keys and values are being compared,
9702 for other types of keys and/or values, this function may be called
9703 C<plain_is_equal> rather than C<is_equal>.
9705 Associative arrays can be printed using the following functions.
9707 #include <isl/id_to_ast_expr.h>
9708 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
9709 __isl_take isl_printer *p,
9710 __isl_keep isl_id_to_ast_expr *id2expr);
9711 __isl_give char *isl_id_to_ast_expr_to_str(
9712 __isl_keep isl_id_to_ast_expr *id2expr);
9714 They can be read from input using the following function.
9716 #include <isl/id_to_ast_expr.h>
9717 __isl_give isl_id_to_ast_expr *
9718 isl_id_to_ast_expr_read_from_str(isl_ctx *ctx,
9723 Vectors can be created, copied and freed using the following functions.
9725 #include <isl/vec.h>
9726 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
9728 __isl_give isl_vec *isl_vec_zero(isl_ctx *ctx,
9730 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
9731 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
9733 Note that the elements of a vector created by C<isl_vec_alloc>
9734 may have arbitrary values.
9735 A vector created by C<isl_vec_zero> has elements with value zero.
9736 The elements can be changed and inspected using the following functions.
9738 isl_size isl_vec_size(__isl_keep isl_vec *vec);
9739 __isl_give isl_val *isl_vec_get_element_val(
9740 __isl_keep isl_vec *vec, int pos);
9741 __isl_give isl_vec *isl_vec_set_element_si(
9742 __isl_take isl_vec *vec, int pos, int v);
9743 __isl_give isl_vec *isl_vec_set_element_val(
9744 __isl_take isl_vec *vec, int pos,
9745 __isl_take isl_val *v);
9746 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
9748 __isl_give isl_vec *isl_vec_set_val(
9749 __isl_take isl_vec *vec, __isl_take isl_val *v);
9750 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
9751 __isl_keep isl_vec *vec2, int pos);
9753 C<isl_vec_get_element> will return a negative value if anything went wrong.
9754 In that case, the value of C<*v> is undefined.
9756 The following function can be used to concatenate two vectors.
9758 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
9759 __isl_take isl_vec *vec2);
9763 Matrices can be created, copied and freed using the following functions.
9765 #include <isl/mat.h>
9766 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
9767 unsigned n_row, unsigned n_col);
9768 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
9769 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
9771 Note that the elements of a newly created matrix may have arbitrary values.
9772 The elements can be changed and inspected using the following functions.
9774 isl_size isl_mat_rows(__isl_keep isl_mat *mat);
9775 isl_size isl_mat_cols(__isl_keep isl_mat *mat);
9776 __isl_give isl_val *isl_mat_get_element_val(
9777 __isl_keep isl_mat *mat, int row, int col);
9778 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
9779 int row, int col, int v);
9780 __isl_give isl_mat *isl_mat_set_element_val(
9781 __isl_take isl_mat *mat, int row, int col,
9782 __isl_take isl_val *v);
9784 The following function computes the rank of a matrix.
9785 The return value may be -1 if some error occurred.
9787 #include <isl/mat.h>
9788 isl_size isl_mat_rank(__isl_keep isl_mat *mat);
9790 The following function can be used to compute the (right) inverse
9791 of a matrix, i.e., a matrix such that the product of the original
9792 and the inverse (in that order) is a multiple of the identity matrix.
9793 The input matrix is assumed to be of full row-rank.
9795 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
9797 The following function can be used to compute the (right) kernel
9798 (or null space) of a matrix, i.e., a matrix such that the product of
9799 the original and the kernel (in that order) is the zero matrix.
9801 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
9803 The following function computes a basis for the space spanned
9804 by the rows of a matrix.
9806 __isl_give isl_mat *isl_mat_row_basis(
9807 __isl_take isl_mat *mat);
9809 The following function computes rows that extend a basis of C<mat1>
9810 to a basis that also covers C<mat2>.
9812 __isl_give isl_mat *isl_mat_row_basis_extension(
9813 __isl_take isl_mat *mat1,
9814 __isl_take isl_mat *mat2);
9816 The following function checks whether there is no linear dependence
9817 among the combined rows of "mat1" and "mat2" that is not already present
9818 in "mat1" or "mat2" individually.
9819 If "mat1" and "mat2" have linearly independent rows by themselves,
9820 then this means that there is no linear dependence among all rows together.
9822 isl_bool isl_mat_has_linearly_independent_rows(
9823 __isl_keep isl_mat *mat1,
9824 __isl_keep isl_mat *mat2);
9826 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
9828 The following functions determine
9829 an upper or lower bound on a quasipolynomial over its domain.
9831 __isl_give isl_pw_qpolynomial_fold *
9832 isl_pw_qpolynomial_bound(
9833 __isl_take isl_pw_qpolynomial *pwqp,
9834 enum isl_fold type, isl_bool *tight);
9836 __isl_give isl_union_pw_qpolynomial_fold *
9837 isl_union_pw_qpolynomial_bound(
9838 __isl_take isl_union_pw_qpolynomial *upwqp,
9839 enum isl_fold type, isl_bool *tight);
9841 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
9842 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
9843 is the returned bound is known be tight, i.e., for each value
9844 of the parameters there is at least
9845 one element in the domain that reaches the bound.
9846 If the domain of C<pwqp> is not wrapping, then the bound is computed
9847 over all elements in that domain and the result has a purely parametric
9848 domain. If the domain of C<pwqp> is wrapping, then the bound is
9849 computed over the range of the wrapped relation. The domain of the
9850 wrapped relation becomes the domain of the result.
9852 =head2 Parametric Vertex Enumeration
9854 The parametric vertex enumeration described in this section
9855 is mainly intended to be used internally and by the C<barvinok>
9858 #include <isl/vertices.h>
9859 __isl_give isl_vertices *isl_basic_set_compute_vertices(
9860 __isl_keep isl_basic_set *bset);
9862 The function C<isl_basic_set_compute_vertices> performs the
9863 actual computation of the parametric vertices and the chamber
9864 decomposition and stores the result in an C<isl_vertices> object.
9865 This information can be queried by either iterating over all
9866 the vertices or iterating over all the chambers or cells
9867 and then iterating over all vertices that are active on the chamber.
9869 isl_stat isl_vertices_foreach_vertex(
9870 __isl_keep isl_vertices *vertices,
9871 isl_stat (*fn)(__isl_take isl_vertex *vertex,
9872 void *user), void *user);
9874 isl_stat isl_vertices_foreach_cell(
9875 __isl_keep isl_vertices *vertices,
9876 isl_stat (*fn)(__isl_take isl_cell *cell,
9877 void *user), void *user);
9878 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
9879 isl_stat (*fn)(__isl_take isl_vertex *vertex,
9880 void *user), void *user);
9882 Other operations that can be performed on an C<isl_vertices> object are
9885 isl_size isl_vertices_get_n_vertices(
9886 __isl_keep isl_vertices *vertices);
9887 __isl_null isl_vertices *isl_vertices_free(
9888 __isl_take isl_vertices *vertices);
9890 Vertices can be inspected and destroyed using the following functions.
9892 isl_size isl_vertex_get_id(__isl_keep isl_vertex *vertex);
9893 __isl_give isl_basic_set *isl_vertex_get_domain(
9894 __isl_keep isl_vertex *vertex);
9895 __isl_give isl_multi_aff *isl_vertex_get_expr(
9896 __isl_keep isl_vertex *vertex);
9897 __isl_null isl_vertex *isl_vertex_free(
9898 __isl_take isl_vertex *vertex);
9900 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
9901 describing the vertex in terms of the parameters,
9902 while C<isl_vertex_get_domain> returns the activity domain
9905 Chambers can be inspected and destroyed using the following functions.
9907 __isl_give isl_basic_set *isl_cell_get_domain(
9908 __isl_keep isl_cell *cell);
9909 __isl_null isl_cell *isl_cell_free(
9910 __isl_take isl_cell *cell);
9912 =head1 Polyhedral Compilation Library
9914 This section collects functionality in C<isl> that has been specifically
9915 designed for use during polyhedral compilation.
9917 =head2 Schedule Trees
9919 A schedule tree is a structured representation of a schedule,
9920 assigning a relative order to a set of domain elements.
9921 The relative order expressed by the schedule tree is
9922 defined recursively. In particular, the order between
9923 two domain elements is determined by the node that is closest
9924 to the root that refers to both elements and that orders them apart.
9925 Each node in the tree is of one of several types.
9926 The root node is always of type C<isl_schedule_node_domain>
9927 (or C<isl_schedule_node_extension>)
9928 and it describes the (extra) domain elements to which the schedule applies.
9929 The other types of nodes are as follows.
9933 =item C<isl_schedule_node_band>
9935 A band of schedule dimensions. Each schedule dimension is represented
9936 by a union piecewise quasi-affine expression. If this expression
9937 assigns a different value to two domain elements, while all previous
9938 schedule dimensions in the same band assign them the same value,
9939 then the two domain elements are ordered according to these two
9941 Each expression is required to be total in the domain elements
9942 that reach the band node.
9944 =item C<isl_schedule_node_expansion>
9946 An expansion node maps each of the domain elements that reach the node
9947 to one or more domain elements. The image of this mapping forms
9948 the set of domain elements that reach the child of the expansion node.
9949 The function that maps each of the expanded domain elements
9950 to the original domain element from which it was expanded
9951 is called the contraction.
9953 =item C<isl_schedule_node_filter>
9955 A filter node does not impose any ordering, but rather intersects
9956 the set of domain elements that the current subtree refers to
9957 with a given union set. The subtree of the filter node only
9958 refers to domain elements in the intersection.
9959 A filter node is typically only used as a child of a sequence or
9962 =item C<isl_schedule_node_leaf>
9964 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
9966 =item C<isl_schedule_node_mark>
9968 A mark node can be used to attach any kind of information to a subtree
9969 of the schedule tree.
9971 =item C<isl_schedule_node_sequence>
9973 A sequence node has one or more children, each of which is a filter node.
9974 The filters on these filter nodes form a partition of
9975 the domain elements that the current subtree refers to.
9976 If two domain elements appear in distinct filters then the sequence
9977 node orders them according to the child positions of the corresponding
9980 =item C<isl_schedule_node_set>
9982 A set node is similar to a sequence node, except that
9983 it expresses that domain elements appearing in distinct filters
9984 may have any order. The order of the children of a set node
9985 is therefore also immaterial.
9989 The following node types are only supported by the AST generator.
9993 =item C<isl_schedule_node_context>
9995 The context describes constraints on the parameters and
9996 the schedule dimensions of outer
9997 bands that the AST generator may assume to hold. It is also the only
9998 kind of node that may introduce additional parameters.
9999 The space of the context is that of the flat product of the outer
10000 band nodes. In particular, if there are no outer band nodes, then
10001 this space is the unnamed zero-dimensional space.
10002 Since a context node references the outer band nodes, any tree
10003 containing a context node is considered to be anchored.
10005 =item C<isl_schedule_node_extension>
10007 An extension node instructs the AST generator to add additional
10008 domain elements that need to be scheduled.
10009 The additional domain elements are described by the range of
10010 the extension map in terms of the outer schedule dimensions,
10011 i.e., the flat product of the outer band nodes.
10012 Note that domain elements are added whenever the AST generator
10013 reaches the extension node, meaning that there are still some
10014 active domain elements for which an AST needs to be generated.
10015 The conditions under which some domain elements are still active
10016 may however not be completely described by the outer AST nodes
10017 generated at that point.
10018 Since an extension node references the outer band nodes, any tree
10019 containing an extension node is considered to be anchored.
10021 An extension node may also appear as the root of a schedule tree,
10022 when it is intended to be inserted into another tree
10023 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
10024 In this case, the domain of the extension node should
10025 correspond to the flat product of the outer band nodes
10026 in this other schedule tree at the point where the extension tree
10029 =item C<isl_schedule_node_guard>
10031 The guard describes constraints on the parameters and
10032 the schedule dimensions of outer
10033 bands that need to be enforced by the outer nodes
10034 in the generated AST.
10035 That is, the part of the AST that is generated from descendants
10036 of the guard node can assume that these constraints are satisfied.
10037 The space of the guard is that of the flat product of the outer
10038 band nodes. In particular, if there are no outer band nodes, then
10039 this space is the unnamed zero-dimensional space.
10040 Since a guard node references the outer band nodes, any tree
10041 containing a guard node is considered to be anchored.
10045 Except for the C<isl_schedule_node_context> nodes,
10046 none of the nodes may introduce any parameters that were not
10047 already present in the root domain node.
10049 A schedule tree is encapsulated in an C<isl_schedule> object.
10050 The simplest such objects, those with a tree consisting of single domain node,
10051 can be created using the following functions with either an empty
10052 domain or a given domain.
10054 #include <isl/schedule.h>
10055 __isl_give isl_schedule *isl_schedule_empty(
10056 __isl_take isl_space *space);
10057 __isl_give isl_schedule *isl_schedule_from_domain(
10058 __isl_take isl_union_set *domain);
10060 The function C<isl_schedule_constraints_compute_schedule> described
10061 in L</"Scheduling"> can also be used to construct schedules.
10063 C<isl_schedule> objects may be copied and freed using the following functions.
10065 #include <isl/schedule.h>
10066 __isl_give isl_schedule *isl_schedule_copy(
10067 __isl_keep isl_schedule *sched);
10068 __isl_null isl_schedule *isl_schedule_free(
10069 __isl_take isl_schedule *sched);
10071 The following functions checks whether two C<isl_schedule> objects
10072 are obviously the same.
10074 #include <isl/schedule.h>
10075 isl_bool isl_schedule_plain_is_equal(
10076 __isl_keep isl_schedule *schedule1,
10077 __isl_keep isl_schedule *schedule2);
10079 The domain of the schedule, i.e., the domain described by the root node,
10080 can be obtained using the following function.
10082 #include <isl/schedule.h>
10083 __isl_give isl_union_set *isl_schedule_get_domain(
10084 __isl_keep isl_schedule *schedule);
10086 An extra top-level band node (right underneath the domain node) can
10087 be introduced into the schedule using the following function.
10088 The schedule tree is assumed not to have any anchored nodes.
10090 #include <isl/schedule.h>
10091 __isl_give isl_schedule *
10092 isl_schedule_insert_partial_schedule(
10093 __isl_take isl_schedule *schedule,
10094 __isl_take isl_multi_union_pw_aff *partial);
10096 A top-level context node (right underneath the domain node) can
10097 be introduced into the schedule using the following function.
10099 #include <isl/schedule.h>
10100 __isl_give isl_schedule *isl_schedule_insert_context(
10101 __isl_take isl_schedule *schedule,
10102 __isl_take isl_set *context)
10104 A top-level guard node (right underneath the domain node) can
10105 be introduced into the schedule using the following function.
10107 #include <isl/schedule.h>
10108 __isl_give isl_schedule *isl_schedule_insert_guard(
10109 __isl_take isl_schedule *schedule,
10110 __isl_take isl_set *guard)
10112 A schedule that combines two schedules either in the given
10113 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
10114 or an C<isl_schedule_node_set> node,
10115 can be created using the following functions.
10117 #include <isl/schedule.h>
10118 __isl_give isl_schedule *isl_schedule_sequence(
10119 __isl_take isl_schedule *schedule1,
10120 __isl_take isl_schedule *schedule2);
10121 __isl_give isl_schedule *isl_schedule_set(
10122 __isl_take isl_schedule *schedule1,
10123 __isl_take isl_schedule *schedule2);
10125 The domains of the two input schedules need to be disjoint.
10127 The following function can be used to restrict the domain
10128 of a schedule with a domain node as root to be a subset of the given union set.
10129 This operation may remove nodes in the tree that have become
10132 #include <isl/schedule.h>
10133 __isl_give isl_schedule *isl_schedule_intersect_domain(
10134 __isl_take isl_schedule *schedule,
10135 __isl_take isl_union_set *domain);
10137 The following function can be used to simplify the domain
10138 of a schedule with a domain node as root with respect to the given
10141 #include <isl/schedule.h>
10142 __isl_give isl_schedule *isl_schedule_gist_domain_params(
10143 __isl_take isl_schedule *schedule,
10144 __isl_take isl_set *context);
10146 The following function resets the user pointers on all parameter
10147 and tuple identifiers referenced by the nodes of the given schedule.
10149 #include <isl/schedule.h>
10150 __isl_give isl_schedule *isl_schedule_reset_user(
10151 __isl_take isl_schedule *schedule);
10153 The following function aligns the parameters of all nodes
10154 in the given schedule to the given space.
10156 #include <isl/schedule.h>
10157 __isl_give isl_schedule *isl_schedule_align_params(
10158 __isl_take isl_schedule *schedule,
10159 __isl_take isl_space *space);
10161 The following function allows the user to plug in a given function
10162 in the iteration domains. The input schedule is not allowed to contain
10163 any expansion nodes.
10165 #include <isl/schedule.h>
10166 __isl_give isl_schedule *
10167 isl_schedule_pullback_union_pw_multi_aff(
10168 __isl_take isl_schedule *schedule,
10169 __isl_take isl_union_pw_multi_aff *upma);
10171 The following function can be used to plug in the schedule C<expansion>
10172 in the leaves of C<schedule>, where C<contraction> describes how
10173 the domain elements of C<expansion> map to the domain elements
10174 at the original leaves of C<schedule>.
10175 The resulting schedule will contain expansion nodes, unless
10176 C<contraction> is an identity function.
10178 #include <isl/schedule.h>
10179 __isl_give isl_schedule *isl_schedule_expand(
10180 __isl_take isl_schedule *schedule,
10181 __isl_take isl_union_pw_multi_aff *contraction,
10182 __isl_take isl_schedule *expansion);
10184 An C<isl_union_map> representation of the schedule can be obtained
10185 from an C<isl_schedule> using the following function.
10187 #include <isl/schedule.h>
10188 __isl_give isl_union_map *isl_schedule_get_map(
10189 __isl_keep isl_schedule *sched);
10191 The resulting relation encodes the same relative ordering as
10192 the schedule by mapping the domain elements to a common schedule space.
10193 If the schedule_separate_components option is set, then the order
10194 of the children of a set node is explicitly encoded in the result.
10195 If the tree contains any expansion nodes, then the relation
10196 is formulated in terms of the expanded domain elements.
10198 Schedules can be read from input using the following functions.
10200 #include <isl/schedule.h>
10201 __isl_give isl_schedule *isl_schedule_read_from_file(
10202 isl_ctx *ctx, FILE *input);
10203 __isl_give isl_schedule *isl_schedule_read_from_str(
10204 isl_ctx *ctx, const char *str);
10206 A representation of the schedule can be printed using
10208 #include <isl/schedule.h>
10209 __isl_give isl_printer *isl_printer_print_schedule(
10210 __isl_take isl_printer *p,
10211 __isl_keep isl_schedule *schedule);
10212 __isl_give char *isl_schedule_to_str(
10213 __isl_keep isl_schedule *schedule);
10215 C<isl_schedule_to_str> prints the schedule in flow format.
10217 The schedule tree can be traversed through the use of
10218 C<isl_schedule_node> objects that point to a particular
10219 position in the schedule tree. Whenever a C<isl_schedule_node>
10220 is used to modify a node in the schedule tree, the original schedule
10221 tree is left untouched and the modifications are performed to a copy
10222 of the tree. The returned C<isl_schedule_node> then points to
10223 this modified copy of the tree.
10225 The root of the schedule tree can be obtained using the following function.
10227 #include <isl/schedule.h>
10228 __isl_give isl_schedule_node *isl_schedule_get_root(
10229 __isl_keep isl_schedule *schedule);
10231 A pointer to a newly created schedule tree with a single domain
10232 node can be created using the following functions.
10234 #include <isl/schedule_node.h>
10235 __isl_give isl_schedule_node *
10236 isl_schedule_node_from_domain(
10237 __isl_take isl_union_set *domain);
10238 __isl_give isl_schedule_node *
10239 isl_schedule_node_from_extension(
10240 __isl_take isl_union_map *extension);
10242 C<isl_schedule_node_from_extension> creates a tree with an extension
10245 Schedule nodes can be copied and freed using the following functions.
10247 #include <isl/schedule_node.h>
10248 __isl_give isl_schedule_node *isl_schedule_node_copy(
10249 __isl_keep isl_schedule_node *node);
10250 __isl_null isl_schedule_node *isl_schedule_node_free(
10251 __isl_take isl_schedule_node *node);
10253 The following functions can be used to check if two schedule
10254 nodes point to the same position in the same schedule.
10256 #include <isl/schedule_node.h>
10257 isl_bool isl_schedule_node_is_equal(
10258 __isl_keep isl_schedule_node *node1,
10259 __isl_keep isl_schedule_node *node2);
10261 The following properties can be obtained from a schedule node.
10263 #include <isl/schedule_node.h>
10264 enum isl_schedule_node_type isl_schedule_node_get_type(
10265 __isl_keep isl_schedule_node *node);
10266 enum isl_schedule_node_type
10267 isl_schedule_node_get_parent_type(
10268 __isl_keep isl_schedule_node *node);
10269 __isl_give isl_schedule *isl_schedule_node_get_schedule(
10270 __isl_keep isl_schedule_node *node);
10272 The function C<isl_schedule_node_get_type> returns the type of
10273 the node, while C<isl_schedule_node_get_parent_type> returns
10274 type of the parent of the node, which is required to exist.
10275 The function C<isl_schedule_node_get_schedule> returns a copy
10276 to the schedule to which the node belongs.
10278 The following functions can be used to move the schedule node
10279 to a different position in the tree or to check if such a position
10282 #include <isl/schedule_node.h>
10283 isl_bool isl_schedule_node_has_parent(
10284 __isl_keep isl_schedule_node *node);
10285 __isl_give isl_schedule_node *isl_schedule_node_parent(
10286 __isl_take isl_schedule_node *node);
10287 __isl_give isl_schedule_node *
10288 isl_schedule_node_grandparent(
10289 __isl_take isl_schedule_node *node);
10290 __isl_give isl_schedule_node *isl_schedule_node_root(
10291 __isl_take isl_schedule_node *node);
10292 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
10293 __isl_take isl_schedule_node *node,
10295 isl_size isl_schedule_node_n_children(
10296 __isl_keep isl_schedule_node *node);
10297 __isl_give isl_schedule_node *isl_schedule_node_child(
10298 __isl_take isl_schedule_node *node, int pos);
10299 isl_bool isl_schedule_node_has_children(
10300 __isl_keep isl_schedule_node *node);
10301 __isl_give isl_schedule_node *
10302 isl_schedule_node_grandchild(
10303 __isl_take isl_schedule_node *node,
10304 int pos1, int pos2);
10305 __isl_give isl_schedule_node *isl_schedule_node_first_child(
10306 __isl_take isl_schedule_node *node);
10307 isl_bool isl_schedule_node_has_previous_sibling(
10308 __isl_keep isl_schedule_node *node);
10309 __isl_give isl_schedule_node *
10310 isl_schedule_node_previous_sibling(
10311 __isl_take isl_schedule_node *node);
10312 isl_bool isl_schedule_node_has_next_sibling(
10313 __isl_keep isl_schedule_node *node);
10314 __isl_give isl_schedule_node *
10315 isl_schedule_node_next_sibling(
10316 __isl_take isl_schedule_node *node);
10318 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
10319 is the node itself, the ancestor of generation 1 is its parent and so on.
10321 It is also possible to query the number of ancestors of a node,
10322 the position of the current node
10323 within the children of its parent, the position of the subtree
10324 containing a node within the children of an ancestor
10325 or to obtain a copy of a given
10326 child without destroying the current node.
10327 Given two nodes that point to the same schedule, their closest
10328 shared ancestor can be obtained using
10329 C<isl_schedule_node_get_shared_ancestor>.
10331 #include <isl/schedule_node.h>
10332 isl_size isl_schedule_node_get_tree_depth(
10333 __isl_keep isl_schedule_node *node);
10334 isl_size isl_schedule_node_get_child_position(
10335 __isl_keep isl_schedule_node *node);
10336 isl_size isl_schedule_node_get_ancestor_child_position(
10337 __isl_keep isl_schedule_node *node,
10338 __isl_keep isl_schedule_node *ancestor);
10339 __isl_give isl_schedule_node *isl_schedule_node_get_child(
10340 __isl_keep isl_schedule_node *node, int pos);
10341 __isl_give isl_schedule_node *
10342 isl_schedule_node_get_shared_ancestor(
10343 __isl_keep isl_schedule_node *node1,
10344 __isl_keep isl_schedule_node *node2);
10346 All nodes in a schedule tree or
10347 all descendants of a specific node (including the node) can be visited
10348 in depth-first pre-order using the following functions.
10350 #include <isl/schedule.h>
10351 isl_stat isl_schedule_foreach_schedule_node_top_down(
10352 __isl_keep isl_schedule *sched,
10353 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
10354 void *user), void *user);
10356 #include <isl/schedule_node.h>
10357 isl_stat isl_schedule_node_foreach_descendant_top_down(
10358 __isl_keep isl_schedule_node *node,
10359 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
10360 void *user), void *user);
10362 The callback function is slightly different from the usual
10363 callbacks in that it not only indicates success (non-negative result)
10364 or failure (negative result), but also indicates whether the children
10365 of the given node should be visited. In particular, if the callback
10366 returns a positive value, then the children are visited, but if
10367 the callback returns zero, then the children are not visited.
10369 The following functions checks whether
10370 all descendants of a specific node (including the node itself)
10371 satisfy a user-specified test.
10373 #include <isl/schedule_node.h>
10374 isl_bool isl_schedule_node_every_descendant(
10375 __isl_keep isl_schedule_node *node,
10376 isl_bool (*test)(__isl_keep isl_schedule_node *node,
10377 void *user), void *user)
10379 The ancestors of a node in a schedule tree can be visited from
10380 the root down to and including the parent of the node using
10381 the following function.
10383 #include <isl/schedule_node.h>
10384 isl_stat isl_schedule_node_foreach_ancestor_top_down(
10385 __isl_keep isl_schedule_node *node,
10386 isl_stat (*fn)(__isl_keep isl_schedule_node *node,
10387 void *user), void *user);
10389 The following functions allows for a depth-first post-order
10390 traversal of the nodes in a schedule tree or
10391 of the descendants of a specific node (including the node
10392 itself), where the user callback is allowed to modify the
10395 #include <isl/schedule.h>
10396 __isl_give isl_schedule *
10397 isl_schedule_map_schedule_node_bottom_up(
10398 __isl_take isl_schedule *schedule,
10399 __isl_give isl_schedule_node *(*fn)(
10400 __isl_take isl_schedule_node *node,
10401 void *user), void *user);
10403 #include <isl/schedule_node.h>
10404 __isl_give isl_schedule_node *
10405 isl_schedule_node_map_descendant_bottom_up(
10406 __isl_take isl_schedule_node *node,
10407 __isl_give isl_schedule_node *(*fn)(
10408 __isl_take isl_schedule_node *node,
10409 void *user), void *user);
10411 The traversal continues from the node returned by the callback function.
10412 It is the responsibility of the user to ensure that this does not
10413 lead to an infinite loop. It is safest to always return a pointer
10414 to the same position (same ancestors and child positions) as the input node.
10416 The following function removes a node (along with its descendants)
10417 from a schedule tree and returns a pointer to the leaf at the
10418 same position in the updated tree.
10419 It is not allowed to remove the root of a schedule tree or
10420 a child of a set or sequence node.
10422 #include <isl/schedule_node.h>
10423 __isl_give isl_schedule_node *isl_schedule_node_cut(
10424 __isl_take isl_schedule_node *node);
10426 The following function removes a single node
10427 from a schedule tree and returns a pointer to the child
10428 of the node, now located at the position of the original node
10429 or to a leaf node at that position if there was no child.
10430 It is not allowed to remove the root of a schedule tree,
10431 a set or sequence node, a child of a set or sequence node or
10432 a band node with an anchored subtree.
10434 #include <isl/schedule_node.h>
10435 __isl_give isl_schedule_node *isl_schedule_node_delete(
10436 __isl_take isl_schedule_node *node);
10438 Most nodes in a schedule tree only contain local information.
10439 In some cases, however, a node may also refer to the schedule dimensions
10440 of its outer band nodes.
10441 This means that the position of the node within the tree should
10442 not be changed, or at least that no changes are performed to the
10443 outer band nodes. The following function can be used to test
10444 whether the subtree rooted at a given node contains any such nodes.
10446 #include <isl/schedule_node.h>
10447 isl_bool isl_schedule_node_is_subtree_anchored(
10448 __isl_keep isl_schedule_node *node);
10450 The following function resets the user pointers on all parameter
10451 and tuple identifiers referenced by the given schedule node.
10453 #include <isl/schedule_node.h>
10454 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
10455 __isl_take isl_schedule_node *node);
10457 The following function aligns the parameters of the given schedule
10458 node to the given space.
10460 #include <isl/schedule_node.h>
10461 __isl_give isl_schedule_node *
10462 isl_schedule_node_align_params(
10463 __isl_take isl_schedule_node *node,
10464 __isl_take isl_space *space);
10466 Several node types have their own functions for querying
10467 (and in some cases setting) some node type specific properties.
10469 #include <isl/schedule_node.h>
10470 __isl_give isl_space *isl_schedule_node_band_get_space(
10471 __isl_keep isl_schedule_node *node);
10472 __isl_give isl_multi_union_pw_aff *
10473 isl_schedule_node_band_get_partial_schedule(
10474 __isl_keep isl_schedule_node *node);
10475 __isl_give isl_union_map *
10476 isl_schedule_node_band_get_partial_schedule_union_map(
10477 __isl_keep isl_schedule_node *node);
10478 isl_size isl_schedule_node_band_n_member(
10479 __isl_keep isl_schedule_node *node);
10480 isl_bool isl_schedule_node_band_member_get_coincident(
10481 __isl_keep isl_schedule_node *node, int pos);
10482 __isl_give isl_schedule_node *
10483 isl_schedule_node_band_member_set_coincident(
10484 __isl_take isl_schedule_node *node, int pos,
10486 isl_bool isl_schedule_node_band_get_permutable(
10487 __isl_keep isl_schedule_node *node);
10488 __isl_give isl_schedule_node *
10489 isl_schedule_node_band_set_permutable(
10490 __isl_take isl_schedule_node *node, int permutable);
10491 enum isl_ast_loop_type
10492 isl_schedule_node_band_member_get_ast_loop_type(
10493 __isl_keep isl_schedule_node *node, int pos);
10494 __isl_give isl_schedule_node *
10495 isl_schedule_node_band_member_set_ast_loop_type(
10496 __isl_take isl_schedule_node *node, int pos,
10497 enum isl_ast_loop_type type);
10498 enum isl_ast_loop_type
10499 isl_schedule_node_band_member_get_isolate_ast_loop_type(
10500 __isl_keep isl_schedule_node *node, int pos);
10501 __isl_give isl_schedule_node *
10502 isl_schedule_node_band_member_set_isolate_ast_loop_type(
10503 __isl_take isl_schedule_node *node, int pos,
10504 enum isl_ast_loop_type type);
10505 __isl_give isl_union_set *
10506 isl_schedule_node_band_get_ast_build_options(
10507 __isl_keep isl_schedule_node *node);
10508 __isl_give isl_schedule_node *
10509 isl_schedule_node_band_set_ast_build_options(
10510 __isl_take isl_schedule_node *node,
10511 __isl_take isl_union_set *options);
10512 __isl_give isl_set *
10513 isl_schedule_node_band_get_ast_isolate_option(
10514 __isl_keep isl_schedule_node *node);
10516 The function C<isl_schedule_node_band_get_space> returns the space
10517 of the partial schedule of the band.
10518 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
10519 returns a representation of the partial schedule of the band node
10520 in the form of an C<isl_union_map>.
10521 The coincident and permutable properties are set by
10522 C<isl_schedule_constraints_compute_schedule> on the schedule tree
10524 A scheduling dimension is considered to be ``coincident''
10525 if it satisfies the coincidence constraints within its band.
10526 That is, if the dependence distances of the coincidence
10527 constraints are all zero in that direction (for fixed
10528 iterations of outer bands).
10529 A band is marked permutable if it was produced using the Pluto-like scheduler.
10530 Note that the scheduler may have to resort to a Feautrier style scheduling
10531 step even if the default scheduler is used.
10532 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
10533 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
10534 For the meaning of these loop AST generation types and the difference
10535 between the regular loop AST generation type and the isolate
10536 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
10537 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
10538 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
10539 may return C<isl_ast_loop_error> if an error occurs.
10540 The AST build options govern how an AST is generated for
10541 the individual schedule dimensions during AST generation.
10542 See L</"AST Generation Options (Schedule Tree)">.
10543 The isolate option for the given node can be extracted from these
10544 AST build options using the function
10545 C<isl_schedule_node_band_get_ast_isolate_option>.
10547 #include <isl/schedule_node.h>
10548 __isl_give isl_set *
10549 isl_schedule_node_context_get_context(
10550 __isl_keep isl_schedule_node *node);
10552 #include <isl/schedule_node.h>
10553 __isl_give isl_union_set *
10554 isl_schedule_node_domain_get_domain(
10555 __isl_keep isl_schedule_node *node);
10557 #include <isl/schedule_node.h>
10558 __isl_give isl_union_map *
10559 isl_schedule_node_expansion_get_expansion(
10560 __isl_keep isl_schedule_node *node);
10561 __isl_give isl_union_pw_multi_aff *
10562 isl_schedule_node_expansion_get_contraction(
10563 __isl_keep isl_schedule_node *node);
10565 #include <isl/schedule_node.h>
10566 __isl_give isl_union_map *
10567 isl_schedule_node_extension_get_extension(
10568 __isl_keep isl_schedule_node *node);
10570 #include <isl/schedule_node.h>
10571 __isl_give isl_union_set *
10572 isl_schedule_node_filter_get_filter(
10573 __isl_keep isl_schedule_node *node);
10575 #include <isl/schedule_node.h>
10576 __isl_give isl_set *isl_schedule_node_guard_get_guard(
10577 __isl_keep isl_schedule_node *node);
10579 #include <isl/schedule_node.h>
10580 __isl_give isl_id *isl_schedule_node_mark_get_id(
10581 __isl_keep isl_schedule_node *node);
10583 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
10584 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
10585 partial schedules related to the node.
10587 #include <isl/schedule_node.h>
10588 __isl_give isl_multi_union_pw_aff *
10589 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
10590 __isl_keep isl_schedule_node *node);
10591 __isl_give isl_union_pw_multi_aff *
10592 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
10593 __isl_keep isl_schedule_node *node);
10594 __isl_give isl_union_map *
10595 isl_schedule_node_get_prefix_schedule_union_map(
10596 __isl_keep isl_schedule_node *node);
10597 __isl_give isl_union_map *
10598 isl_schedule_node_get_prefix_schedule_relation(
10599 __isl_keep isl_schedule_node *node);
10600 __isl_give isl_union_map *
10601 isl_schedule_node_get_subtree_schedule_union_map(
10602 __isl_keep isl_schedule_node *node);
10604 In particular, the functions
10605 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
10606 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
10607 and C<isl_schedule_node_get_prefix_schedule_union_map>
10608 return a relative ordering on the domain elements that reach the given
10609 node determined by its ancestors.
10610 The function C<isl_schedule_node_get_prefix_schedule_relation>
10611 additionally includes the domain constraints in the result.
10612 The function C<isl_schedule_node_get_subtree_schedule_union_map>
10613 returns a representation of the partial schedule defined by the
10614 subtree rooted at the given node.
10615 If the tree contains any expansion nodes, then the subtree schedule
10616 is formulated in terms of the expanded domain elements.
10617 The tree passed to functions returning a prefix schedule
10618 may only contain extension nodes if these would not affect
10619 the result of these functions. That is, if one of the ancestors
10620 is an extension node, then all of the domain elements that were
10621 added by the extension node need to have been filtered out
10622 by filter nodes between the extension node and the input node.
10623 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
10624 may not contain in extension nodes in the selected subtree.
10626 The expansion/contraction defined by an entire subtree, combining
10627 the expansions/contractions
10628 on the expansion nodes in the subtree, can be obtained using
10629 the following functions.
10631 #include <isl/schedule_node.h>
10632 __isl_give isl_union_map *
10633 isl_schedule_node_get_subtree_expansion(
10634 __isl_keep isl_schedule_node *node);
10635 __isl_give isl_union_pw_multi_aff *
10636 isl_schedule_node_get_subtree_contraction(
10637 __isl_keep isl_schedule_node *node);
10639 The total number of outer band members of given node, i.e.,
10640 the shared output dimension of the maps in the result
10641 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
10642 using the following function.
10644 #include <isl/schedule_node.h>
10645 isl_size isl_schedule_node_get_schedule_depth(
10646 __isl_keep isl_schedule_node *node);
10648 The following functions return the elements that reach the given node
10649 or the union of universes in the spaces that contain these elements.
10651 #include <isl/schedule_node.h>
10652 __isl_give isl_union_set *
10653 isl_schedule_node_get_domain(
10654 __isl_keep isl_schedule_node *node);
10655 __isl_give isl_union_set *
10656 isl_schedule_node_get_universe_domain(
10657 __isl_keep isl_schedule_node *node);
10659 The input tree of C<isl_schedule_node_get_domain>
10660 may only contain extension nodes if these would not affect
10661 the result of this function. That is, if one of the ancestors
10662 is an extension node, then all of the domain elements that were
10663 added by the extension node need to have been filtered out
10664 by filter nodes between the extension node and the input node.
10666 The following functions can be used to introduce additional nodes
10667 in the schedule tree. The new node is introduced at the point
10668 in the tree where the C<isl_schedule_node> points to and
10669 the results points to the new node.
10671 #include <isl/schedule_node.h>
10672 __isl_give isl_schedule_node *
10673 isl_schedule_node_insert_partial_schedule(
10674 __isl_take isl_schedule_node *node,
10675 __isl_take isl_multi_union_pw_aff *schedule);
10677 This function inserts a new band node with (the greatest integer
10678 part of) the given partial schedule.
10679 The subtree rooted at the given node is assumed not to have
10680 any anchored nodes.
10682 #include <isl/schedule_node.h>
10683 __isl_give isl_schedule_node *
10684 isl_schedule_node_insert_context(
10685 __isl_take isl_schedule_node *node,
10686 __isl_take isl_set *context);
10688 This function inserts a new context node with the given context constraints.
10690 #include <isl/schedule_node.h>
10691 __isl_give isl_schedule_node *
10692 isl_schedule_node_insert_filter(
10693 __isl_take isl_schedule_node *node,
10694 __isl_take isl_union_set *filter);
10696 This function inserts a new filter node with the given filter.
10697 If the original node already pointed to a filter node, then the
10698 two filter nodes are merged into one.
10700 #include <isl/schedule_node.h>
10701 __isl_give isl_schedule_node *
10702 isl_schedule_node_insert_guard(
10703 __isl_take isl_schedule_node *node,
10704 __isl_take isl_set *guard);
10706 This function inserts a new guard node with the given guard constraints.
10708 #include <isl/schedule_node.h>
10709 __isl_give isl_schedule_node *
10710 isl_schedule_node_insert_mark(
10711 __isl_take isl_schedule_node *node,
10712 __isl_take isl_id *mark);
10714 This function inserts a new mark node with the give mark identifier.
10716 #include <isl/schedule_node.h>
10717 __isl_give isl_schedule_node *
10718 isl_schedule_node_insert_sequence(
10719 __isl_take isl_schedule_node *node,
10720 __isl_take isl_union_set_list *filters);
10721 __isl_give isl_schedule_node *
10722 isl_schedule_node_insert_set(
10723 __isl_take isl_schedule_node *node,
10724 __isl_take isl_union_set_list *filters);
10726 These functions insert a new sequence or set node with the given
10727 filters as children.
10729 #include <isl/schedule_node.h>
10730 __isl_give isl_schedule_node *isl_schedule_node_group(
10731 __isl_take isl_schedule_node *node,
10732 __isl_take isl_id *group_id);
10734 This function introduces an expansion node in between the current
10735 node and its parent that expands instances of a space with tuple
10736 identifier C<group_id> to the original domain elements that reach
10737 the node. The group instances are identified by the prefix schedule
10738 of those domain elements. The ancestors of the node are adjusted
10739 to refer to the group instances instead of the original domain
10740 elements. The return value points to the same node in the updated
10741 schedule tree as the input node, i.e., to the child of the newly
10742 introduced expansion node. Grouping instances of different statements
10743 ensures that they will be treated as a single statement by the
10744 AST generator up to the point of the expansion node.
10746 The following functions can be used to flatten a nested
10749 #include <isl/schedule_node.h>
10750 __isl_give isl_schedule_node *
10751 isl_schedule_node_sequence_splice_child(
10752 __isl_take isl_schedule_node *node, int pos);
10753 __isl_give isl_schedule_node *
10754 isl_schedule_node_sequence_splice_children(
10755 __isl_take isl_schedule_node *node);
10757 That is, given a sequence node C<node> that has another sequence node
10758 in its child at position C<pos> (in particular, the child of that filter
10759 node is a sequence node), the function
10760 C<isl_schedule_node_sequence_splice_child>
10761 attaches the children of that other sequence
10762 node as children of C<node>, replacing the original child at position
10764 C<isl_schedule_node_sequence_splice_children> does this for all
10767 The partial schedule of a band node can be scaled (down) or reduced using
10768 the following functions.
10770 #include <isl/schedule_node.h>
10771 __isl_give isl_schedule_node *
10772 isl_schedule_node_band_scale(
10773 __isl_take isl_schedule_node *node,
10774 __isl_take isl_multi_val *mv);
10775 __isl_give isl_schedule_node *
10776 isl_schedule_node_band_scale_down(
10777 __isl_take isl_schedule_node *node,
10778 __isl_take isl_multi_val *mv);
10779 __isl_give isl_schedule_node *
10780 isl_schedule_node_band_mod(
10781 __isl_take isl_schedule_node *node,
10782 __isl_take isl_multi_val *mv);
10784 The spaces of the two arguments need to match.
10785 After scaling, the partial schedule is replaced by its greatest
10786 integer part to ensure that the schedule remains integral.
10788 The partial schedule of a band node can be shifted by an
10789 C<isl_multi_union_pw_aff> with a domain that is a superset
10790 of the domain of the partial schedule using
10791 the following function.
10793 #include <isl/schedule_node.h>
10794 __isl_give isl_schedule_node *
10795 isl_schedule_node_band_shift(
10796 __isl_take isl_schedule_node *node,
10797 __isl_take isl_multi_union_pw_aff *shift);
10799 A band node can be tiled using the following function.
10801 #include <isl/schedule_node.h>
10802 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
10803 __isl_take isl_schedule_node *node,
10804 __isl_take isl_multi_val *sizes);
10806 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
10808 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
10809 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
10811 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
10813 The C<isl_schedule_node_band_tile> function tiles
10814 the band using the given tile sizes inside its schedule.
10815 A new child band node is created to represent the point loops and it is
10816 inserted between the modified band and its children.
10817 The subtree rooted at the given node is assumed not to have
10818 any anchored nodes.
10819 The C<tile_scale_tile_loops> option specifies whether the tile
10820 loops iterators should be scaled by the tile sizes.
10821 If the C<tile_shift_point_loops> option is set, then the point loops
10822 are shifted to start at zero.
10824 A band node can be split into two nested band nodes
10825 using the following function.
10827 #include <isl/schedule_node.h>
10828 __isl_give isl_schedule_node *isl_schedule_node_band_split(
10829 __isl_take isl_schedule_node *node, int pos);
10831 The resulting outer band node contains the first C<pos> dimensions of
10832 the schedule of C<node> while the inner band contains the remaining dimensions.
10833 The schedules of the two band nodes live in anonymous spaces.
10834 The loop AST generation type options and the isolate option
10835 are split over the two band nodes.
10837 A band node can be moved down to the leaves of the subtree rooted
10838 at the band node using the following function.
10840 #include <isl/schedule_node.h>
10841 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
10842 __isl_take isl_schedule_node *node);
10844 The subtree rooted at the given node is assumed not to have
10845 any anchored nodes.
10846 The result points to the node in the resulting tree that is in the same
10847 position as the node pointed to by C<node> in the original tree.
10849 #include <isl/schedule_node.h>
10850 __isl_give isl_schedule_node *
10851 isl_schedule_node_order_before(
10852 __isl_take isl_schedule_node *node,
10853 __isl_take isl_union_set *filter);
10854 __isl_give isl_schedule_node *
10855 isl_schedule_node_order_after(
10856 __isl_take isl_schedule_node *node,
10857 __isl_take isl_union_set *filter);
10859 These functions split the domain elements that reach C<node>
10860 into those that satisfy C<filter> and those that do not and
10861 arranges for the elements that do satisfy the filter to be
10862 executed before (in case of C<isl_schedule_node_order_before>)
10863 or after (in case of C<isl_schedule_node_order_after>)
10864 those that do not. The order is imposed by
10865 a sequence node, possibly reusing the grandparent of C<node>
10866 on two copies of the subtree attached to the original C<node>.
10867 Both copies are simplified with respect to their filter.
10869 Return a pointer to the copy of the subtree that does not
10870 satisfy C<filter>. If there is no such copy (because all
10871 reaching domain elements satisfy the filter), then return
10872 the original pointer.
10874 #include <isl/schedule_node.h>
10875 __isl_give isl_schedule_node *
10876 isl_schedule_node_graft_before(
10877 __isl_take isl_schedule_node *node,
10878 __isl_take isl_schedule_node *graft);
10879 __isl_give isl_schedule_node *
10880 isl_schedule_node_graft_after(
10881 __isl_take isl_schedule_node *node,
10882 __isl_take isl_schedule_node *graft);
10884 This function inserts the C<graft> tree into the tree containing C<node>
10885 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
10886 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
10887 The root node of C<graft>
10888 should be an extension node where the domain of the extension
10889 is the flat product of all outer band nodes of C<node>.
10890 The root node may also be a domain node.
10891 The elements of the domain or the range of the extension may not
10892 intersect with the domain elements that reach "node".
10893 The schedule tree of C<graft> may not be anchored.
10895 The schedule tree of C<node> is modified to include an extension node
10896 corresponding to the root node of C<graft> as a child of the original
10897 parent of C<node>. The original node that C<node> points to and the
10898 child of the root node of C<graft> are attached to this extension node
10899 through a sequence, with appropriate filters and with the child
10900 of C<graft> appearing before or after the original C<node>.
10902 If C<node> already appears inside a sequence that is the child of
10903 an extension node and if the spaces of the new domain elements
10904 do not overlap with those of the original domain elements,
10905 then that extension node is extended with the new extension
10906 rather than introducing a new segment of extension and sequence nodes.
10908 Return a pointer to the same node in the modified tree that
10909 C<node> pointed to in the original tree.
10911 A representation of the schedule node can be printed using
10913 #include <isl/schedule_node.h>
10914 __isl_give isl_printer *isl_printer_print_schedule_node(
10915 __isl_take isl_printer *p,
10916 __isl_keep isl_schedule_node *node);
10917 __isl_give char *isl_schedule_node_to_str(
10918 __isl_keep isl_schedule_node *node);
10920 C<isl_schedule_node_to_str> prints the schedule node in block format.
10922 =head2 Dependence Analysis
10924 C<isl> contains specialized functionality for performing
10925 array dataflow analysis. That is, given a I<sink> access relation,
10926 a collection of possible I<source> accesses and
10927 a collection of I<kill> accesses,
10928 C<isl> can compute relations that describe
10929 for each iteration of the sink access, which iterations
10930 of which of the source access relations may have
10931 accessed the same data element before the given iteration
10932 of the sink access without any intermediate kill of that data element.
10933 The resulting dependence relations map source iterations
10934 to either the corresponding sink iterations or
10935 pairs of corresponding sink iterations and accessed data elements.
10936 To compute standard flow dependences, the sink should be
10937 a read, while the sources should be writes.
10938 If no kills are specified,
10939 then memory based dependence analysis is performed.
10940 If, on the other hand, all sources are also kills,
10941 then value based dependence analysis is performed.
10942 If any of the source accesses are marked as being I<must>
10943 accesses, then they are also treated as kills.
10944 Furthermore, the specification of must-sources results
10945 in the computation of must-dependences.
10946 Only dependences originating in a must access not coscheduled
10947 with any other access to the same element and without
10948 any may accesses between the must access and the sink access
10949 are considered to be must dependences.
10951 =head3 High-level Interface
10953 A high-level interface to dependence analysis is provided
10954 by the following function.
10956 #include <isl/flow.h>
10957 __isl_give isl_union_flow *
10958 isl_union_access_info_compute_flow(
10959 __isl_take isl_union_access_info *access);
10961 The input C<isl_union_access_info> object describes the sink
10962 access relations, the source access relations and a schedule,
10963 while the output C<isl_union_flow> object describes
10964 the resulting dependence relations and the subsets of the
10965 sink relations for which no source was found.
10967 An C<isl_union_access_info> is created, modified, copied and freed using
10968 the following functions.
10970 #include <isl/flow.h>
10971 __isl_give isl_union_access_info *
10972 isl_union_access_info_from_sink(
10973 __isl_take isl_union_map *sink);
10974 __isl_give isl_union_access_info *
10975 isl_union_access_info_set_kill(
10976 __isl_take isl_union_access_info *access,
10977 __isl_take isl_union_map *kill);
10978 __isl_give isl_union_access_info *
10979 isl_union_access_info_set_may_source(
10980 __isl_take isl_union_access_info *access,
10981 __isl_take isl_union_map *may_source);
10982 __isl_give isl_union_access_info *
10983 isl_union_access_info_set_must_source(
10984 __isl_take isl_union_access_info *access,
10985 __isl_take isl_union_map *must_source);
10986 __isl_give isl_union_access_info *
10987 isl_union_access_info_set_schedule(
10988 __isl_take isl_union_access_info *access,
10989 __isl_take isl_schedule *schedule);
10990 __isl_give isl_union_access_info *
10991 isl_union_access_info_set_schedule_map(
10992 __isl_take isl_union_access_info *access,
10993 __isl_take isl_union_map *schedule_map);
10994 __isl_give isl_union_access_info *
10995 isl_union_access_info_copy(
10996 __isl_keep isl_union_access_info *access);
10997 __isl_null isl_union_access_info *
10998 isl_union_access_info_free(
10999 __isl_take isl_union_access_info *access);
11001 The may sources set by C<isl_union_access_info_set_may_source>
11002 do not need to include the must sources set by
11003 C<isl_union_access_info_set_must_source> as a subset.
11004 The kills set by C<isl_union_access_info_set_kill> may overlap
11005 with the may-sources and/or must-sources.
11006 The user is free not to call one (or more) of these functions,
11007 in which case the corresponding set is kept to its empty default.
11008 Similarly, the default schedule initialized by
11009 C<isl_union_access_info_from_sink> is empty.
11010 The current schedule is determined by the last call to either
11011 C<isl_union_access_info_set_schedule> or
11012 C<isl_union_access_info_set_schedule_map>.
11013 The domain of the schedule corresponds to the domains of
11014 the access relations. In particular, the domains of the access
11015 relations are effectively intersected with the domain of the schedule
11016 and only the resulting accesses are considered by the dependence analysis.
11018 An C<isl_union_access_info> object can be read from input
11019 using the following function.
11021 #include <isl/flow.h>
11022 __isl_give isl_union_access_info *
11023 isl_union_access_info_read_from_file(isl_ctx *ctx,
11026 A representation of the information contained in an object
11027 of type C<isl_union_access_info> can be obtained using
11029 #include <isl/flow.h>
11030 __isl_give isl_printer *
11031 isl_printer_print_union_access_info(
11032 __isl_take isl_printer *p,
11033 __isl_keep isl_union_access_info *access);
11034 __isl_give char *isl_union_access_info_to_str(
11035 __isl_keep isl_union_access_info *access);
11037 C<isl_union_access_info_to_str> prints the information in flow format.
11039 The output of C<isl_union_access_info_compute_flow> can be examined,
11040 copied, and freed using the following functions.
11042 #include <isl/flow.h>
11043 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
11044 __isl_keep isl_union_flow *flow);
11045 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
11046 __isl_keep isl_union_flow *flow);
11047 __isl_give isl_union_map *
11048 isl_union_flow_get_full_must_dependence(
11049 __isl_keep isl_union_flow *flow);
11050 __isl_give isl_union_map *
11051 isl_union_flow_get_full_may_dependence(
11052 __isl_keep isl_union_flow *flow);
11053 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
11054 __isl_keep isl_union_flow *flow);
11055 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
11056 __isl_keep isl_union_flow *flow);
11057 __isl_give isl_union_flow *isl_union_flow_copy(
11058 __isl_keep isl_union_flow *flow);
11059 __isl_null isl_union_flow *isl_union_flow_free(
11060 __isl_take isl_union_flow *flow);
11062 The relation returned by C<isl_union_flow_get_must_dependence>
11063 relates domain elements of must sources to domain elements of the sink.
11064 The relation returned by C<isl_union_flow_get_may_dependence>
11065 relates domain elements of must or may sources to domain elements of the sink
11066 and includes the previous relation as a subset.
11067 The relation returned by C<isl_union_flow_get_full_must_dependence>
11068 relates domain elements of must sources to pairs of domain elements of the sink
11069 and accessed data elements.
11070 The relation returned by C<isl_union_flow_get_full_may_dependence>
11071 relates domain elements of must or may sources to pairs of
11072 domain elements of the sink and accessed data elements.
11073 This relation includes the previous relation as a subset.
11074 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
11075 of the sink relation for which no dependences have been found.
11076 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
11077 of the sink relation for which no definite dependences have been found.
11078 That is, it contains those sink access that do not contribute to any
11079 of the elements in the relation returned
11080 by C<isl_union_flow_get_must_dependence>.
11082 A representation of the information contained in an object
11083 of type C<isl_union_flow> can be obtained using
11085 #include <isl/flow.h>
11086 __isl_give isl_printer *isl_printer_print_union_flow(
11087 __isl_take isl_printer *p,
11088 __isl_keep isl_union_flow *flow);
11089 __isl_give char *isl_union_flow_to_str(
11090 __isl_keep isl_union_flow *flow);
11092 C<isl_union_flow_to_str> prints the information in flow format.
11094 =head3 Low-level Interface
11096 A lower-level interface is provided by the following functions.
11098 #include <isl/flow.h>
11100 typedef int (*isl_access_level_before)(void *first, void *second);
11102 __isl_give isl_access_info *isl_access_info_alloc(
11103 __isl_take isl_map *sink,
11104 void *sink_user, isl_access_level_before fn,
11106 __isl_give isl_access_info *isl_access_info_add_source(
11107 __isl_take isl_access_info *acc,
11108 __isl_take isl_map *source, int must,
11109 void *source_user);
11110 __isl_null isl_access_info *isl_access_info_free(
11111 __isl_take isl_access_info *acc);
11113 __isl_give isl_flow *isl_access_info_compute_flow(
11114 __isl_take isl_access_info *acc);
11116 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,
11117 isl_stat (*fn)(__isl_take isl_map *dep, int must,
11118 void *dep_user, void *user),
11120 __isl_give isl_map *isl_flow_get_no_source(
11121 __isl_keep isl_flow *deps, int must);
11122 __isl_null isl_flow *isl_flow_free(
11123 __isl_take isl_flow *deps);
11125 The function C<isl_access_info_compute_flow> performs the actual
11126 dependence analysis. The other functions are used to construct
11127 the input for this function or to read off the output.
11129 The input is collected in an C<isl_access_info>, which can
11130 be created through a call to C<isl_access_info_alloc>.
11131 The arguments to this functions are the sink access relation
11132 C<sink>, a token C<sink_user> used to identify the sink
11133 access to the user, a callback function for specifying the
11134 relative order of source and sink accesses, and the number
11135 of source access relations that will be added.
11137 The callback function has type C<int (*)(void *first, void *second)>.
11138 The function is called with two user supplied tokens identifying
11139 either a source or the sink and it should return the shared nesting
11140 level and the relative order of the two accesses.
11141 In particular, let I<n> be the number of loops shared by
11142 the two accesses. If C<first> precedes C<second> textually,
11143 then the function should return I<2 * n + 1>; otherwise,
11144 it should return I<2 * n>.
11145 The low-level interface assumes that no sources are coscheduled.
11146 If the information returned by the callback does not allow
11147 the relative order to be determined, then one of the sources
11148 is arbitrarily taken to be executed after the other(s).
11150 The sources can be added to the C<isl_access_info> object by performing
11151 (at most) C<max_source> calls to C<isl_access_info_add_source>.
11152 C<must> indicates whether the source is a I<must> access
11153 or a I<may> access. Note that a multi-valued access relation
11154 should only be marked I<must> if every iteration in the domain
11155 of the relation accesses I<all> elements in its image.
11156 The C<source_user> token is again used to identify
11157 the source access. The range of the source access relation
11158 C<source> should have the same dimension as the range
11159 of the sink access relation.
11160 The C<isl_access_info_free> function should usually not be
11161 called explicitly, because it is already called implicitly by
11162 C<isl_access_info_compute_flow>.
11164 The result of the dependence analysis is collected in an
11165 C<isl_flow>. There may be elements of
11166 the sink access for which no preceding source access could be
11167 found or for which all preceding sources are I<may> accesses.
11168 The relations containing these elements can be obtained through
11169 calls to C<isl_flow_get_no_source>, the first with C<must> set
11170 and the second with C<must> unset.
11171 In the case of standard flow dependence analysis,
11172 with the sink a read and the sources I<must> writes,
11173 the first relation corresponds to the reads from uninitialized
11174 array elements and the second relation is empty.
11175 The actual flow dependences can be extracted using
11176 C<isl_flow_foreach>. This function will call the user-specified
11177 callback function C<fn> for each B<non-empty> dependence between
11178 a source and the sink. The callback function is called
11179 with four arguments, the actual flow dependence relation
11180 mapping source iterations to sink iterations, a boolean that
11181 indicates whether it is a I<must> or I<may> dependence, a token
11182 identifying the source and an additional C<void *> with value
11183 equal to the third argument of the C<isl_flow_foreach> call.
11184 A dependence is marked I<must> if it originates from a I<must>
11185 source and if it is not followed by any I<may> sources.
11187 After finishing with an C<isl_flow>, the user should call
11188 C<isl_flow_free> to free all associated memory.
11190 =head3 Interaction with the Low-level Interface
11192 During the dependence analysis, we frequently need to perform
11193 the following operation. Given a relation between sink iterations
11194 and potential source iterations from a particular source domain,
11195 what is the last potential source iteration corresponding to each
11196 sink iteration. It can sometimes be convenient to adjust
11197 the set of potential source iterations before or after each such operation.
11198 The prototypical example is fuzzy array dataflow analysis,
11199 where we need to analyze if, based on data-dependent constraints,
11200 the sink iteration can ever be executed without one or more of
11201 the corresponding potential source iterations being executed.
11202 If so, we can introduce extra parameters and select an unknown
11203 but fixed source iteration from the potential source iterations.
11204 To be able to perform such manipulations, C<isl> provides the following
11207 #include <isl/flow.h>
11209 typedef __isl_give isl_restriction *(*isl_access_restrict)(
11210 __isl_keep isl_map *source_map,
11211 __isl_keep isl_set *sink, void *source_user,
11213 __isl_give isl_access_info *isl_access_info_set_restrict(
11214 __isl_take isl_access_info *acc,
11215 isl_access_restrict fn, void *user);
11217 The function C<isl_access_info_set_restrict> should be called
11218 before calling C<isl_access_info_compute_flow> and registers a callback function
11219 that will be called any time C<isl> is about to compute the last
11220 potential source. The first argument is the (reverse) proto-dependence,
11221 mapping sink iterations to potential source iterations.
11222 The second argument represents the sink iterations for which
11223 we want to compute the last source iteration.
11224 The third argument is the token corresponding to the source
11225 and the final argument is the token passed to C<isl_access_info_set_restrict>.
11226 The callback is expected to return a restriction on either the input or
11227 the output of the operation computing the last potential source.
11228 If the input needs to be restricted then restrictions are needed
11229 for both the source and the sink iterations. The sink iterations
11230 and the potential source iterations will be intersected with these sets.
11231 If the output needs to be restricted then only a restriction on the source
11232 iterations is required.
11233 If any error occurs, the callback should return C<NULL>.
11234 An C<isl_restriction> object can be created, freed and inspected
11235 using the following functions.
11237 #include <isl/flow.h>
11239 __isl_give isl_restriction *isl_restriction_input(
11240 __isl_take isl_set *source_restr,
11241 __isl_take isl_set *sink_restr);
11242 __isl_give isl_restriction *isl_restriction_output(
11243 __isl_take isl_set *source_restr);
11244 __isl_give isl_restriction *isl_restriction_none(
11245 __isl_take isl_map *source_map);
11246 __isl_give isl_restriction *isl_restriction_empty(
11247 __isl_take isl_map *source_map);
11248 __isl_null isl_restriction *isl_restriction_free(
11249 __isl_take isl_restriction *restr);
11251 C<isl_restriction_none> and C<isl_restriction_empty> are special
11252 cases of C<isl_restriction_input>. C<isl_restriction_none>
11253 is essentially equivalent to
11255 isl_restriction_input(isl_set_universe(
11256 isl_space_range(isl_map_get_space(source_map))),
11258 isl_space_domain(isl_map_get_space(source_map))));
11260 whereas C<isl_restriction_empty> is essentially equivalent to
11262 isl_restriction_input(isl_set_empty(
11263 isl_space_range(isl_map_get_space(source_map))),
11265 isl_space_domain(isl_map_get_space(source_map))));
11269 #include <isl/schedule.h>
11270 __isl_give isl_schedule *
11271 isl_schedule_constraints_compute_schedule(
11272 __isl_take isl_schedule_constraints *sc);
11274 The function C<isl_schedule_constraints_compute_schedule> can be
11275 used to compute a schedule that satisfies the given schedule constraints.
11276 These schedule constraints include the iteration domain for which
11277 a schedule should be computed and dependences between pairs of
11278 iterations. In particular, these dependences include
11279 I<validity> dependences and I<proximity> dependences.
11280 By default, the algorithm used to construct the schedule is similar
11281 to that of C<Pluto>.
11282 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
11284 The generated schedule respects all validity dependences.
11285 That is, all dependence distances over these dependences in the
11286 scheduled space are lexicographically positive.
11288 The default algorithm tries to ensure that the dependence distances
11289 over coincidence constraints are zero and to minimize the
11290 dependence distances over proximity dependences.
11291 Moreover, it tries to obtain sequences (bands) of schedule dimensions
11292 for groups of domains where the dependence distances over validity
11293 dependences have only non-negative values.
11294 Note that when minimizing the maximal dependence distance
11295 over proximity dependences, a single affine expression in the parameters
11296 is constructed that bounds all dependence distances. If no such expression
11297 exists, then the algorithm will fail and resort to an alternative
11298 scheduling algorithm. In particular, this means that adding proximity
11299 dependences may eliminate valid solutions. A typical example where this
11300 phenomenon may occur is when some subset of the proximity dependences
11301 has no restriction on some parameter, forcing the coefficient of that
11302 parameter to be zero, while some other subset forces the dependence
11303 distance to depend on that parameter, requiring the same coefficient
11305 When using Feautrier's algorithm, the coincidence and proximity constraints
11306 are only taken into account during the extension to a
11307 full-dimensional schedule.
11309 An C<isl_schedule_constraints> object can be constructed
11310 and manipulated using the following functions.
11312 #include <isl/schedule.h>
11313 __isl_give isl_schedule_constraints *
11314 isl_schedule_constraints_copy(
11315 __isl_keep isl_schedule_constraints *sc);
11316 __isl_give isl_schedule_constraints *
11317 isl_schedule_constraints_on_domain(
11318 __isl_take isl_union_set *domain);
11319 __isl_give isl_schedule_constraints *
11320 isl_schedule_constraints_set_context(
11321 __isl_take isl_schedule_constraints *sc,
11322 __isl_take isl_set *context);
11323 __isl_give isl_schedule_constraints *
11324 isl_schedule_constraints_set_validity(
11325 __isl_take isl_schedule_constraints *sc,
11326 __isl_take isl_union_map *validity);
11327 __isl_give isl_schedule_constraints *
11328 isl_schedule_constraints_set_coincidence(
11329 __isl_take isl_schedule_constraints *sc,
11330 __isl_take isl_union_map *coincidence);
11331 __isl_give isl_schedule_constraints *
11332 isl_schedule_constraints_set_proximity(
11333 __isl_take isl_schedule_constraints *sc,
11334 __isl_take isl_union_map *proximity);
11335 __isl_give isl_schedule_constraints *
11336 isl_schedule_constraints_set_conditional_validity(
11337 __isl_take isl_schedule_constraints *sc,
11338 __isl_take isl_union_map *condition,
11339 __isl_take isl_union_map *validity);
11340 __isl_give isl_schedule_constraints *
11341 isl_schedule_constraints_apply(
11342 __isl_take isl_schedule_constraints *sc,
11343 __isl_take isl_union_map *umap);
11344 __isl_null isl_schedule_constraints *
11345 isl_schedule_constraints_free(
11346 __isl_take isl_schedule_constraints *sc);
11348 The initial C<isl_schedule_constraints> object created by
11349 C<isl_schedule_constraints_on_domain> does not impose any constraints.
11350 That is, it has an empty set of dependences.
11351 The function C<isl_schedule_constraints_set_context> allows the user
11352 to specify additional constraints on the parameters that may
11353 be assumed to hold during the construction of the schedule.
11354 The function C<isl_schedule_constraints_set_validity> replaces the
11355 validity dependences, mapping domain elements I<i> to domain
11356 elements that should be scheduled after I<i>.
11357 The function C<isl_schedule_constraints_set_coincidence> replaces the
11358 coincidence dependences, mapping domain elements I<i> to domain
11359 elements that should be scheduled together with I<I>, if possible.
11360 The function C<isl_schedule_constraints_set_proximity> replaces the
11361 proximity dependences, mapping domain elements I<i> to domain
11362 elements that should be scheduled either before I<I>
11363 or as early as possible after I<i>.
11365 The function C<isl_schedule_constraints_set_conditional_validity>
11366 replaces the conditional validity constraints.
11367 A conditional validity constraint is only imposed when any of the corresponding
11368 conditions is satisfied, i.e., when any of them is non-zero.
11369 That is, the scheduler ensures that within each band if the dependence
11370 distances over the condition constraints are not all zero
11371 then all corresponding conditional validity constraints are respected.
11372 A conditional validity constraint corresponds to a condition
11373 if the two are adjacent, i.e., if the domain of one relation intersect
11374 the range of the other relation.
11375 The typical use case of conditional validity constraints is
11376 to allow order constraints between live ranges to be violated
11377 as long as the live ranges themselves are local to the band.
11378 To allow more fine-grained control over which conditions correspond
11379 to which conditional validity constraints, the domains and ranges
11380 of these relations may include I<tags>. That is, the domains and
11381 ranges of those relation may themselves be wrapped relations
11382 where the iteration domain appears in the domain of those wrapped relations
11383 and the range of the wrapped relations can be arbitrarily chosen
11384 by the user. Conditions and conditional validity constraints are only
11385 considered adjacent to each other if the entire wrapped relation matches.
11386 In particular, a relation with a tag will never be considered adjacent
11387 to a relation without a tag.
11389 The function C<isl_schedule_constraints_apply> takes
11390 schedule constraints that are defined on some set of domain elements
11391 and transforms them to schedule constraints on the elements
11392 to which these domain elements are mapped by the given transformation.
11394 An C<isl_schedule_constraints> object can be inspected
11395 using the following functions.
11397 #include <isl/schedule.h>
11398 __isl_give isl_union_set *
11399 isl_schedule_constraints_get_domain(
11400 __isl_keep isl_schedule_constraints *sc);
11401 __isl_give isl_set *isl_schedule_constraints_get_context(
11402 __isl_keep isl_schedule_constraints *sc);
11403 __isl_give isl_union_map *
11404 isl_schedule_constraints_get_validity(
11405 __isl_keep isl_schedule_constraints *sc);
11406 __isl_give isl_union_map *
11407 isl_schedule_constraints_get_coincidence(
11408 __isl_keep isl_schedule_constraints *sc);
11409 __isl_give isl_union_map *
11410 isl_schedule_constraints_get_proximity(
11411 __isl_keep isl_schedule_constraints *sc);
11412 __isl_give isl_union_map *
11413 isl_schedule_constraints_get_conditional_validity(
11414 __isl_keep isl_schedule_constraints *sc);
11415 __isl_give isl_union_map *
11416 isl_schedule_constraints_get_conditional_validity_condition(
11417 __isl_keep isl_schedule_constraints *sc);
11419 An C<isl_schedule_constraints> object can be read from input
11420 using the following functions.
11422 #include <isl/schedule.h>
11423 __isl_give isl_schedule_constraints *
11424 isl_schedule_constraints_read_from_str(isl_ctx *ctx,
11426 __isl_give isl_schedule_constraints *
11427 isl_schedule_constraints_read_from_file(isl_ctx *ctx,
11430 The contents of an C<isl_schedule_constraints> object can be printed
11431 using the following functions.
11433 #include <isl/schedule.h>
11434 __isl_give isl_printer *
11435 isl_printer_print_schedule_constraints(
11436 __isl_take isl_printer *p,
11437 __isl_keep isl_schedule_constraints *sc);
11438 __isl_give char *isl_schedule_constraints_to_str(
11439 __isl_keep isl_schedule_constraints *sc);
11441 The following function computes a schedule directly from
11442 an iteration domain and validity and proximity dependences
11443 and is implemented in terms of the functions described above.
11444 The use of C<isl_union_set_compute_schedule> is discouraged.
11446 #include <isl/schedule.h>
11447 __isl_give isl_schedule *isl_union_set_compute_schedule(
11448 __isl_take isl_union_set *domain,
11449 __isl_take isl_union_map *validity,
11450 __isl_take isl_union_map *proximity);
11452 The generated schedule represents a schedule tree.
11453 For more information on schedule trees, see
11454 L</"Schedule Trees">.
11458 #include <isl/schedule.h>
11459 isl_stat isl_options_set_schedule_max_coefficient(
11460 isl_ctx *ctx, int val);
11461 int isl_options_get_schedule_max_coefficient(
11463 isl_stat isl_options_set_schedule_max_constant_term(
11464 isl_ctx *ctx, int val);
11465 int isl_options_get_schedule_max_constant_term(
11467 isl_stat isl_options_set_schedule_serialize_sccs(
11468 isl_ctx *ctx, int val);
11469 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx);
11470 isl_stat isl_options_set_schedule_whole_component(
11471 isl_ctx *ctx, int val);
11472 int isl_options_get_schedule_whole_component(
11474 isl_stat isl_options_set_schedule_maximize_band_depth(
11475 isl_ctx *ctx, int val);
11476 int isl_options_get_schedule_maximize_band_depth(
11478 isl_stat isl_options_set_schedule_maximize_coincidence(
11479 isl_ctx *ctx, int val);
11480 int isl_options_get_schedule_maximize_coincidence(
11482 isl_stat isl_options_set_schedule_outer_coincidence(
11483 isl_ctx *ctx, int val);
11484 int isl_options_get_schedule_outer_coincidence(
11486 isl_stat isl_options_set_schedule_split_scaled(
11487 isl_ctx *ctx, int val);
11488 int isl_options_get_schedule_split_scaled(
11490 isl_stat isl_options_set_schedule_treat_coalescing(
11491 isl_ctx *ctx, int val);
11492 int isl_options_get_schedule_treat_coalescing(
11494 isl_stat isl_options_set_schedule_algorithm(
11495 isl_ctx *ctx, int val);
11496 int isl_options_get_schedule_algorithm(
11498 isl_stat isl_options_set_schedule_carry_self_first(
11499 isl_ctx *ctx, int val);
11500 int isl_options_get_schedule_carry_self_first(
11502 isl_stat isl_options_set_schedule_separate_components(
11503 isl_ctx *ctx, int val);
11504 int isl_options_get_schedule_separate_components(
11509 =item * schedule_max_coefficient
11511 This option enforces that the coefficients for variable and parameter
11512 dimensions in the calculated schedule are not larger than the specified value.
11513 This option can significantly increase the speed of the scheduling calculation
11514 and may also prevent fusing of unrelated dimensions. A value of -1 means that
11515 this option does not introduce bounds on the variable or parameter
11517 This option has no effect on the Feautrier style scheduler.
11519 =item * schedule_max_constant_term
11521 This option enforces that the constant coefficients in the calculated schedule
11522 are not larger than the maximal constant term. This option can significantly
11523 increase the speed of the scheduling calculation and may also prevent fusing of
11524 unrelated dimensions. A value of -1 means that this option does not introduce
11525 bounds on the constant coefficients.
11527 =item * schedule_serialize_sccs
11529 If this option is set, then all strongly connected components
11530 in the dependence graph are serialized as soon as they are detected.
11531 This means in particular that instances of statements will only
11532 appear in the same band node if these statements belong
11533 to the same strongly connected component at the point where
11534 the band node is constructed.
11536 =item * schedule_whole_component
11538 If this option is set, then entire (weakly) connected
11539 components in the dependence graph are scheduled together
11541 Otherwise, each strongly connected component within
11542 such a weakly connected component is first scheduled separately
11543 and then combined with other strongly connected components.
11544 This option has no effect if C<schedule_serialize_sccs> is set.
11546 =item * schedule_maximize_band_depth
11548 If this option is set, then the scheduler tries to maximize
11549 the width of the bands. Wider bands give more possibilities for tiling.
11550 In particular, if the C<schedule_whole_component> option is set,
11551 then bands are split if this might result in wider bands.
11552 Otherwise, the effect of this option is to only allow
11553 strongly connected components to be combined if this does
11554 not reduce the width of the bands.
11555 Note that if the C<schedule_serialize_sccs> options is set, then
11556 the C<schedule_maximize_band_depth> option therefore has no effect.
11558 =item * schedule_maximize_coincidence
11560 This option is only effective if the C<schedule_whole_component>
11561 option is turned off.
11562 If the C<schedule_maximize_coincidence> option is set, then (clusters of)
11563 strongly connected components are only combined with each other
11564 if this does not reduce the number of coincident band members.
11566 =item * schedule_outer_coincidence
11568 If this option is set, then we try to construct schedules
11569 where the outermost scheduling dimension in each band
11570 satisfies the coincidence constraints.
11572 =item * schedule_algorithm
11574 Selects the scheduling algorithm to be used.
11575 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
11576 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
11578 =item * schedule_split_scaled
11580 If this option is set, then we try to construct schedules in which the
11581 constant term is split off from the linear part if the linear parts of
11582 the scheduling rows for all nodes in the graph have a common non-trivial
11584 The constant term is then dropped and the linear
11586 This option is only effective when the Feautrier style scheduler is
11587 being used, either as the main scheduler or as a fallback for the
11588 Pluto-like scheduler.
11590 =item * schedule_treat_coalescing
11592 If this option is set, then the scheduler will try and avoid
11593 producing schedules that perform loop coalescing.
11594 In particular, for the Pluto-like scheduler, this option places
11595 bounds on the schedule coefficients based on the sizes of the instance sets.
11596 For the Feautrier style scheduler, this option detects potentially
11597 coalescing schedules and then tries to adjust the schedule to avoid
11600 =item * schedule_carry_self_first
11602 If this option is set, then the Feautrier style scheduler
11603 (when used as a fallback for the Pluto-like scheduler) will
11604 first try to only carry self-dependences.
11606 =item * schedule_separate_components
11608 If this option is set then the function C<isl_schedule_get_map>
11609 will treat set nodes in the same way as sequence nodes.
11613 =head2 AST Generation
11615 This section describes the C<isl> functionality for generating
11616 ASTs that visit all the elements
11617 in a domain in an order specified by a schedule tree or
11619 In case the schedule given as a C<isl_union_map>, an AST is generated
11620 that visits all the elements in the domain of the C<isl_union_map>
11621 according to the lexicographic order of the corresponding image
11622 element(s). If the range of the C<isl_union_map> consists of
11623 elements in more than one space, then each of these spaces is handled
11624 separately in an arbitrary order.
11625 It should be noted that the schedule tree or the image elements
11626 in a schedule map only specify the I<order>
11627 in which the corresponding domain elements should be visited.
11628 No direct relation between the partial schedule values
11629 or the image elements on the one hand and the loop iterators
11630 in the generated AST on the other hand should be assumed.
11632 Each AST is generated within a build. The initial build
11633 simply specifies the constraints on the parameters (if any)
11634 and can be created, inspected, copied and freed using the following functions.
11636 #include <isl/ast_build.h>
11637 __isl_give isl_ast_build *isl_ast_build_alloc(
11639 __isl_give isl_ast_build *isl_ast_build_from_context(
11640 __isl_take isl_set *set);
11641 __isl_give isl_ast_build *isl_ast_build_copy(
11642 __isl_keep isl_ast_build *build);
11643 __isl_null isl_ast_build *isl_ast_build_free(
11644 __isl_take isl_ast_build *build);
11646 The C<set> argument is usually a parameter set with zero or more parameters.
11647 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
11648 this set is required to be a parameter set.
11649 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
11650 specify any parameter constraints.
11651 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
11652 and L</"Fine-grained Control over AST Generation">.
11653 Finally, the AST itself can be constructed using one of the following
11656 #include <isl/ast_build.h>
11657 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
11658 __isl_keep isl_ast_build *build,
11659 __isl_take isl_schedule *schedule);
11660 __isl_give isl_ast_node *
11661 isl_ast_build_node_from_schedule_map(
11662 __isl_keep isl_ast_build *build,
11663 __isl_take isl_union_map *schedule);
11665 =head3 Inspecting the AST
11667 The basic properties of an AST node can be obtained as follows.
11669 #include <isl/ast.h>
11670 enum isl_ast_node_type isl_ast_node_get_type(
11671 __isl_keep isl_ast_node *node);
11673 The type of an AST node is one of
11674 C<isl_ast_node_for>,
11675 C<isl_ast_node_if>,
11676 C<isl_ast_node_block>,
11677 C<isl_ast_node_mark> or
11678 C<isl_ast_node_user>.
11679 An C<isl_ast_node_for> represents a for node.
11680 An C<isl_ast_node_if> represents an if node.
11681 An C<isl_ast_node_block> represents a compound node.
11682 An C<isl_ast_node_mark> introduces a mark in the AST.
11683 An C<isl_ast_node_user> represents an expression statement.
11684 An expression statement typically corresponds to a domain element, i.e.,
11685 one of the elements that is visited by the AST.
11687 Each type of node has its own additional properties.
11689 #include <isl/ast.h>
11690 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
11691 __isl_keep isl_ast_node *node);
11692 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
11693 __isl_keep isl_ast_node *node);
11694 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
11695 __isl_keep isl_ast_node *node);
11696 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
11697 __isl_keep isl_ast_node *node);
11698 __isl_give isl_ast_node *isl_ast_node_for_get_body(
11699 __isl_keep isl_ast_node *node);
11700 isl_bool isl_ast_node_for_is_degenerate(
11701 __isl_keep isl_ast_node *node);
11703 An C<isl_ast_for> is considered degenerate if it is known to execute
11706 #include <isl/ast.h>
11707 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
11708 __isl_keep isl_ast_node *node);
11709 __isl_give isl_ast_node *isl_ast_node_if_get_then_node(
11710 __isl_keep isl_ast_node *node);
11711 __isl_give isl_ast_node *isl_ast_node_if_get_then(
11712 __isl_keep isl_ast_node *node);
11713 isl_bool isl_ast_node_if_has_else_node(
11714 __isl_keep isl_ast_node *node);
11715 isl_bool isl_ast_node_if_has_else(
11716 __isl_keep isl_ast_node *node);
11717 __isl_give isl_ast_node *isl_ast_node_if_get_else_node(
11718 __isl_keep isl_ast_node *node);
11719 __isl_give isl_ast_node *isl_ast_node_if_get_else(
11720 __isl_keep isl_ast_node *node);
11722 C<isl_ast_node_if_get_then>,
11723 C<isl_ast_node_if_has_else> and
11724 C<isl_ast_node_if_get_else>
11725 are alternative names for
11726 C<isl_ast_node_if_get_then_node>,
11727 C<isl_ast_node_if_has_else_node> and
11728 C<isl_ast_node_if_get_else_node>, respectively.
11730 __isl_give isl_ast_node_list *
11731 isl_ast_node_block_get_children(
11732 __isl_keep isl_ast_node *node);
11734 __isl_give isl_id *isl_ast_node_mark_get_id(
11735 __isl_keep isl_ast_node *node);
11736 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
11737 __isl_keep isl_ast_node *node);
11739 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
11740 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
11742 #include <isl/ast.h>
11743 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
11744 __isl_keep isl_ast_node *node);
11746 All descendants of a specific node in the AST (including the node itself)
11748 in depth-first pre-order using the following function.
11750 #include <isl/ast.h>
11751 isl_stat isl_ast_node_foreach_descendant_top_down(
11752 __isl_keep isl_ast_node *node,
11753 isl_bool (*fn)(__isl_keep isl_ast_node *node,
11754 void *user), void *user);
11756 The callback function should return C<isl_bool_true> if the children
11757 of the given node should be visited and C<isl_bool_false> if they should not.
11758 It should return C<isl_bool_error> in case of failure, in which case
11759 the entire traversal is aborted.
11761 Each of the returned C<isl_ast_expr>s can in turn be inspected using
11762 the following functions.
11764 #include <isl/ast.h>
11765 enum isl_ast_expr_type isl_ast_expr_get_type(
11766 __isl_keep isl_ast_expr *expr);
11768 The type of an AST expression is one of
11769 C<isl_ast_expr_op>,
11770 C<isl_ast_expr_id> or
11771 C<isl_ast_expr_int>.
11772 An C<isl_ast_expr_op> represents the result of an operation.
11773 An C<isl_ast_expr_id> represents an identifier.
11774 An C<isl_ast_expr_int> represents an integer value.
11776 Each type of expression has its own additional properties.
11778 #include <isl/ast.h>
11779 enum isl_ast_expr_op_type isl_ast_expr_op_get_type(
11780 __isl_keep isl_ast_expr *expr);
11781 enum isl_ast_expr_op_type isl_ast_expr_get_op_type(
11782 __isl_keep isl_ast_expr *expr);
11783 isl_size isl_ast_expr_op_get_n_arg(__isl_keep isl_ast_expr *expr);
11784 isl_size isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
11785 __isl_give isl_ast_expr *isl_ast_expr_op_get_arg(
11786 __isl_keep isl_ast_expr *expr, int pos);
11787 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
11788 __isl_keep isl_ast_expr *expr, int pos);
11789 isl_stat isl_ast_expr_foreach_ast_expr_op_type(
11790 __isl_keep isl_ast_expr *expr,
11791 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11792 void *user), void *user);
11793 isl_stat isl_ast_expr_foreach_ast_op_type(
11794 __isl_keep isl_ast_expr *expr,
11795 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11796 void *user), void *user);
11797 isl_stat isl_ast_node_foreach_ast_expr_op_type(
11798 __isl_keep isl_ast_node *node,
11799 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11800 void *user), void *user);
11801 isl_stat isl_ast_node_foreach_ast_op_type(
11802 __isl_keep isl_ast_node *node,
11803 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11804 void *user), void *user);
11806 C<isl_ast_expr_op_get_type> returns the type of the operation
11807 performed. C<isl_ast_expr_op_get_n_arg> returns the number of
11808 arguments. C<isl_ast_expr_get_op_arg> returns the specified
11810 C<isl_ast_expr_get_op_type> is an alternative name for
11811 C<isl_ast_expr_op_get_type>.
11813 C<isl_ast_expr_get_op_n_arg> is an alternative name for
11814 C<isl_ast_expr_op_get_n_arg> and
11815 C<isl_ast_expr_get_op_arg> is an alternative name for
11816 C<isl_ast_expr_op_get_arg>.
11818 C<isl_ast_expr_foreach_ast_expr_op_type> calls C<fn> for each distinct
11819 C<isl_ast_expr_op_type> that appears in C<expr>.
11820 C<isl_ast_expr_foreach_ast_op_type> is an alternative name for
11821 C<isl_ast_expr_foreach_ast_expr_op_type>.
11822 C<isl_ast_node_foreach_ast_expr_op_type> does the same for each distinct
11823 C<isl_ast_expr_op_type> that appears in C<node>.
11824 C<isl_ast_node_foreach_ast_op_type> is an alternative name for
11825 C<isl_ast_node_foreach_ast_expr_op_type>.
11826 The operation type is one of the following.
11830 =item C<isl_ast_expr_op_and>
11832 Logical I<and> of two arguments.
11833 Both arguments can be evaluated.
11835 =item C<isl_ast_expr_op_and_then>
11837 Logical I<and> of two arguments.
11838 The second argument can only be evaluated if the first evaluates to true.
11840 =item C<isl_ast_expr_op_or>
11842 Logical I<or> of two arguments.
11843 Both arguments can be evaluated.
11845 =item C<isl_ast_expr_op_or_else>
11847 Logical I<or> of two arguments.
11848 The second argument can only be evaluated if the first evaluates to false.
11850 =item C<isl_ast_expr_op_max>
11852 Maximum of two or more arguments.
11854 =item C<isl_ast_expr_op_min>
11856 Minimum of two or more arguments.
11858 =item C<isl_ast_expr_op_minus>
11862 =item C<isl_ast_expr_op_add>
11864 Sum of two arguments.
11866 =item C<isl_ast_expr_op_sub>
11868 Difference of two arguments.
11870 =item C<isl_ast_expr_op_mul>
11872 Product of two arguments.
11874 =item C<isl_ast_expr_op_div>
11876 Exact division. That is, the result is known to be an integer.
11878 =item C<isl_ast_expr_op_fdiv_q>
11880 Result of integer division, rounded towards negative
11882 The divisor is known to be positive.
11884 =item C<isl_ast_expr_op_pdiv_q>
11886 Result of integer division, where dividend is known to be non-negative.
11887 The divisor is known to be positive.
11889 =item C<isl_ast_expr_op_pdiv_r>
11891 Remainder of integer division, where dividend is known to be non-negative.
11892 The divisor is known to be positive.
11894 =item C<isl_ast_expr_op_zdiv_r>
11896 Equal to zero iff the remainder on integer division is zero.
11897 The divisor is known to be positive.
11899 =item C<isl_ast_expr_op_cond>
11901 Conditional operator defined on three arguments.
11902 If the first argument evaluates to true, then the result
11903 is equal to the second argument. Otherwise, the result
11904 is equal to the third argument.
11905 The second and third argument may only be evaluated if
11906 the first argument evaluates to true and false, respectively.
11907 Corresponds to C<a ? b : c> in C.
11909 =item C<isl_ast_expr_op_select>
11911 Conditional operator defined on three arguments.
11912 If the first argument evaluates to true, then the result
11913 is equal to the second argument. Otherwise, the result
11914 is equal to the third argument.
11915 The second and third argument may be evaluated independently
11916 of the value of the first argument.
11917 Corresponds to C<a * b + (1 - a) * c> in C.
11919 =item C<isl_ast_expr_op_eq>
11923 =item C<isl_ast_expr_op_le>
11925 Less than or equal relation.
11927 =item C<isl_ast_expr_op_lt>
11929 Less than relation.
11931 =item C<isl_ast_expr_op_ge>
11933 Greater than or equal relation.
11935 =item C<isl_ast_expr_op_gt>
11937 Greater than relation.
11939 =item C<isl_ast_expr_op_call>
11942 The number of arguments of the C<isl_ast_expr> is one more than
11943 the number of arguments in the function call, the first argument
11944 representing the function being called.
11946 =item C<isl_ast_expr_op_access>
11949 The number of arguments of the C<isl_ast_expr> is one more than
11950 the number of index expressions in the array access, the first argument
11951 representing the array being accessed.
11953 =item C<isl_ast_expr_op_member>
11956 This operation has two arguments, a structure and the name of
11957 the member of the structure being accessed.
11959 =item C<isl_ast_expr_op_address_of>
11961 The address of its single argument, which is always an array access.
11965 #include <isl/ast.h>
11966 __isl_give isl_id *isl_ast_expr_id_get_id(
11967 __isl_keep isl_ast_expr *expr);
11968 __isl_give isl_id *isl_ast_expr_get_id(
11969 __isl_keep isl_ast_expr *expr);
11971 Return the identifier represented by the AST expression.
11972 C<isl_ast_expr_get_id> is an alternative name for
11973 C<isl_ast_expr_id_get_id>.
11975 #include <isl/ast.h>
11976 __isl_give isl_val *isl_ast_expr_int_get_val(
11977 __isl_keep isl_ast_expr *expr);
11978 __isl_give isl_val *isl_ast_expr_get_val(
11979 __isl_keep isl_ast_expr *expr);
11981 Return the integer represented by the AST expression.
11982 C<isl_ast_expr_get_val> is an alternative name for
11983 C<isl_ast_expr_int_get_val>.
11985 =head3 Properties of ASTs
11987 #include <isl/ast.h>
11988 isl_bool isl_ast_expr_is_equal(
11989 __isl_keep isl_ast_expr *expr1,
11990 __isl_keep isl_ast_expr *expr2);
11992 Check if two C<isl_ast_expr>s are equal to each other.
11994 =head3 Manipulating and printing the AST
11996 AST nodes can be copied and freed using the following functions.
11998 #include <isl/ast.h>
11999 __isl_give isl_ast_node *isl_ast_node_copy(
12000 __isl_keep isl_ast_node *node);
12001 __isl_null isl_ast_node *isl_ast_node_free(
12002 __isl_take isl_ast_node *node);
12004 AST expressions can be copied and freed using the following functions.
12006 #include <isl/ast.h>
12007 __isl_give isl_ast_expr *isl_ast_expr_copy(
12008 __isl_keep isl_ast_expr *expr);
12009 __isl_null isl_ast_expr *isl_ast_expr_free(
12010 __isl_take isl_ast_expr *expr);
12012 New AST expressions can be created either directly or within
12013 the context of an C<isl_ast_build>.
12015 #include <isl/ast.h>
12016 __isl_give isl_ast_expr *isl_ast_expr_from_val(
12017 __isl_take isl_val *v);
12018 __isl_give isl_ast_expr *isl_ast_expr_from_id(
12019 __isl_take isl_id *id);
12020 __isl_give isl_ast_expr *isl_ast_expr_neg(
12021 __isl_take isl_ast_expr *expr);
12022 __isl_give isl_ast_expr *isl_ast_expr_address_of(
12023 __isl_take isl_ast_expr *expr);
12024 __isl_give isl_ast_expr *isl_ast_expr_add(
12025 __isl_take isl_ast_expr *expr1,
12026 __isl_take isl_ast_expr *expr2);
12027 __isl_give isl_ast_expr *isl_ast_expr_sub(
12028 __isl_take isl_ast_expr *expr1,
12029 __isl_take isl_ast_expr *expr2);
12030 __isl_give isl_ast_expr *isl_ast_expr_mul(
12031 __isl_take isl_ast_expr *expr1,
12032 __isl_take isl_ast_expr *expr2);
12033 __isl_give isl_ast_expr *isl_ast_expr_div(
12034 __isl_take isl_ast_expr *expr1,
12035 __isl_take isl_ast_expr *expr2);
12036 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
12037 __isl_take isl_ast_expr *expr1,
12038 __isl_take isl_ast_expr *expr2);
12039 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
12040 __isl_take isl_ast_expr *expr1,
12041 __isl_take isl_ast_expr *expr2);
12042 __isl_give isl_ast_expr *isl_ast_expr_and(
12043 __isl_take isl_ast_expr *expr1,
12044 __isl_take isl_ast_expr *expr2)
12045 __isl_give isl_ast_expr *isl_ast_expr_and_then(
12046 __isl_take isl_ast_expr *expr1,
12047 __isl_take isl_ast_expr *expr2)
12048 __isl_give isl_ast_expr *isl_ast_expr_or(
12049 __isl_take isl_ast_expr *expr1,
12050 __isl_take isl_ast_expr *expr2)
12051 __isl_give isl_ast_expr *isl_ast_expr_or_else(
12052 __isl_take isl_ast_expr *expr1,
12053 __isl_take isl_ast_expr *expr2)
12054 __isl_give isl_ast_expr *isl_ast_expr_eq(
12055 __isl_take isl_ast_expr *expr1,
12056 __isl_take isl_ast_expr *expr2);
12057 __isl_give isl_ast_expr *isl_ast_expr_le(
12058 __isl_take isl_ast_expr *expr1,
12059 __isl_take isl_ast_expr *expr2);
12060 __isl_give isl_ast_expr *isl_ast_expr_lt(
12061 __isl_take isl_ast_expr *expr1,
12062 __isl_take isl_ast_expr *expr2);
12063 __isl_give isl_ast_expr *isl_ast_expr_ge(
12064 __isl_take isl_ast_expr *expr1,
12065 __isl_take isl_ast_expr *expr2);
12066 __isl_give isl_ast_expr *isl_ast_expr_gt(
12067 __isl_take isl_ast_expr *expr1,
12068 __isl_take isl_ast_expr *expr2);
12069 __isl_give isl_ast_expr *isl_ast_expr_access(
12070 __isl_take isl_ast_expr *array,
12071 __isl_take isl_ast_expr_list *indices);
12072 __isl_give isl_ast_expr *isl_ast_expr_call(
12073 __isl_take isl_ast_expr *function,
12074 __isl_take isl_ast_expr_list *arguments);
12076 The function C<isl_ast_expr_address_of> can be applied to an
12077 C<isl_ast_expr> of type C<isl_ast_expr_op_access> only. It is meant
12078 to represent the address of the C<isl_ast_expr_access>.
12079 The second argument of the functions C<isl_ast_expr_pdiv_q> and
12080 C<isl_ast_expr_pdiv_r> should always evaluate to a positive number.
12082 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
12083 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
12085 #include <isl/ast_build.h>
12086 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
12087 __isl_keep isl_ast_build *build,
12088 __isl_take isl_set *set);
12089 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
12090 __isl_keep isl_ast_build *build,
12091 __isl_take isl_pw_aff *pa);
12092 __isl_give isl_ast_expr *
12093 isl_ast_build_access_from_pw_multi_aff(
12094 __isl_keep isl_ast_build *build,
12095 __isl_take isl_pw_multi_aff *pma);
12096 __isl_give isl_ast_expr *
12097 isl_ast_build_access_from_multi_pw_aff(
12098 __isl_keep isl_ast_build *build,
12099 __isl_take isl_multi_pw_aff *mpa);
12100 __isl_give isl_ast_expr *
12101 isl_ast_build_call_from_pw_multi_aff(
12102 __isl_keep isl_ast_build *build,
12103 __isl_take isl_pw_multi_aff *pma);
12104 __isl_give isl_ast_expr *
12105 isl_ast_build_call_from_multi_pw_aff(
12106 __isl_keep isl_ast_build *build,
12107 __isl_take isl_multi_pw_aff *mpa);
12110 the domains of C<pa>, C<mpa> and C<pma> should correspond
12111 to the schedule space of C<build>.
12112 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
12113 the function being called.
12114 If the accessed space is a nested relation, then it is taken
12115 to represent an access of the member specified by the range
12116 of this nested relation of the structure specified by the domain
12117 of the nested relation.
12119 The following functions can be used to modify an C<isl_ast_expr>.
12121 #include <isl/ast.h>
12122 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
12123 __isl_take isl_ast_expr *expr, int pos,
12124 __isl_take isl_ast_expr *arg);
12126 Replace the argument of C<expr> at position C<pos> by C<arg>.
12128 #include <isl/ast.h>
12129 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
12130 __isl_take isl_ast_expr *expr,
12131 __isl_take isl_id_to_ast_expr *id2expr);
12133 The function C<isl_ast_expr_substitute_ids> replaces the
12134 subexpressions of C<expr> of type C<isl_ast_expr_id>
12135 by the corresponding expression in C<id2expr>, if there is any.
12138 The following function can be used to modify the descendants
12139 of a specific node in an AST using a depth-first post-order
12140 traversal of those descendants (including the node itself).
12142 #include <isl/ast.h>
12143 __isl_give isl_ast_node *
12144 isl_ast_node_map_descendant_bottom_up(
12145 __isl_take isl_ast_node *node,
12146 __isl_give isl_ast_node *(*fn)(
12147 __isl_take isl_ast_node *node,
12148 void *user), void *user);
12150 User specified data can be attached to an C<isl_ast_node> and obtained
12151 from the same C<isl_ast_node> using the following functions.
12153 #include <isl/ast.h>
12154 __isl_give isl_ast_node *isl_ast_node_set_annotation(
12155 __isl_take isl_ast_node *node,
12156 __isl_take isl_id *annotation);
12157 __isl_give isl_id *isl_ast_node_get_annotation(
12158 __isl_keep isl_ast_node *node);
12160 Basic printing can be performed using the following functions.
12162 #include <isl/ast.h>
12163 __isl_give isl_printer *isl_printer_print_ast_expr(
12164 __isl_take isl_printer *p,
12165 __isl_keep isl_ast_expr *expr);
12166 __isl_give isl_printer *isl_printer_print_ast_node(
12167 __isl_take isl_printer *p,
12168 __isl_keep isl_ast_node *node);
12169 __isl_give char *isl_ast_expr_to_str(
12170 __isl_keep isl_ast_expr *expr);
12171 __isl_give char *isl_ast_node_to_str(
12172 __isl_keep isl_ast_node *node);
12173 __isl_give char *isl_ast_expr_to_C_str(
12174 __isl_keep isl_ast_expr *expr);
12175 __isl_give char *isl_ast_node_to_C_str(
12176 __isl_keep isl_ast_node *node);
12178 The functions C<isl_ast_expr_to_C_str> and
12179 C<isl_ast_node_to_C_str> are convenience functions
12180 that return a string representation of the input in C format.
12182 More advanced printing can be performed using the following functions.
12184 #include <isl/ast.h>
12185 __isl_give isl_printer *
12186 isl_ast_expr_op_type_set_print_name(
12187 __isl_take isl_printer *p,
12188 enum isl_ast_expr_op_type type,
12189 __isl_keep const char *name);
12190 __isl_give isl_printer *isl_ast_op_type_set_print_name(
12191 __isl_take isl_printer *p,
12192 enum isl_ast_expr_op_type type,
12193 __isl_keep const char *name);
12194 isl_stat isl_options_set_ast_print_macro_once(
12195 isl_ctx *ctx, int val);
12196 int isl_options_get_ast_print_macro_once(isl_ctx *ctx);
12197 __isl_give isl_printer *isl_ast_expr_op_type_print_macro(
12198 enum isl_ast_expr_op_type type,
12199 __isl_take isl_printer *p);
12200 __isl_give isl_printer *isl_ast_op_type_print_macro(
12201 enum isl_ast_expr_op_type type,
12202 __isl_take isl_printer *p);
12203 __isl_give isl_printer *isl_ast_expr_print_macros(
12204 __isl_keep isl_ast_expr *expr,
12205 __isl_take isl_printer *p);
12206 __isl_give isl_printer *isl_ast_node_print_macros(
12207 __isl_keep isl_ast_node *node,
12208 __isl_take isl_printer *p);
12209 __isl_give isl_printer *isl_ast_node_print(
12210 __isl_keep isl_ast_node *node,
12211 __isl_take isl_printer *p,
12212 __isl_take isl_ast_print_options *options);
12213 __isl_give isl_printer *isl_ast_node_for_print(
12214 __isl_keep isl_ast_node *node,
12215 __isl_take isl_printer *p,
12216 __isl_take isl_ast_print_options *options);
12217 __isl_give isl_printer *isl_ast_node_if_print(
12218 __isl_keep isl_ast_node *node,
12219 __isl_take isl_printer *p,
12220 __isl_take isl_ast_print_options *options);
12222 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
12223 C<isl> may print out an AST that makes use of macros such
12224 as C<floord>, C<min> and C<max>.
12225 The names of these macros may be modified by a call
12226 to C<isl_ast_expr_op_type_set_print_name>. The user-specified
12227 names are associated to the printer object.
12228 C<isl_ast_op_type_set_print_name> is an alternative name for
12229 C<isl_ast_expr_op_type_set_print_name>.
12230 C<isl_ast_expr_op_type_print_macro> prints out the macro
12231 corresponding to a specific C<isl_ast_expr_op_type>.
12232 If the print-macro-once option is set, then a given macro definition
12233 is only printed once to any given printer object.
12234 C<isl_ast_op_type_print_macro> is an alternative name for
12235 C<isl_ast_expr_op_type_print_macro>.
12236 C<isl_ast_expr_print_macros> scans the C<isl_ast_expr>
12237 for subexpressions where these macros would be used and prints
12238 out the required macro definitions.
12239 Essentially, C<isl_ast_expr_print_macros> calls
12240 C<isl_ast_expr_foreach_ast_expr_op_type> with
12241 C<isl_ast_expr_op_type_print_macro>
12242 as function argument.
12243 C<isl_ast_node_print_macros> does the same
12244 for expressions in its C<isl_ast_node> argument.
12245 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
12246 C<isl_ast_node_if_print> print an C<isl_ast_node>
12247 in C<ISL_FORMAT_C>, but allow for some extra control
12248 through an C<isl_ast_print_options> object.
12249 This object can be created using the following functions.
12251 #include <isl/ast.h>
12252 __isl_give isl_ast_print_options *
12253 isl_ast_print_options_alloc(isl_ctx *ctx);
12254 __isl_give isl_ast_print_options *
12255 isl_ast_print_options_copy(
12256 __isl_keep isl_ast_print_options *options);
12257 __isl_null isl_ast_print_options *
12258 isl_ast_print_options_free(
12259 __isl_take isl_ast_print_options *options);
12261 __isl_give isl_ast_print_options *
12262 isl_ast_print_options_set_print_user(
12263 __isl_take isl_ast_print_options *options,
12264 __isl_give isl_printer *(*print_user)(
12265 __isl_take isl_printer *p,
12266 __isl_take isl_ast_print_options *options,
12267 __isl_keep isl_ast_node *node, void *user),
12269 __isl_give isl_ast_print_options *
12270 isl_ast_print_options_set_print_for(
12271 __isl_take isl_ast_print_options *options,
12272 __isl_give isl_printer *(*print_for)(
12273 __isl_take isl_printer *p,
12274 __isl_take isl_ast_print_options *options,
12275 __isl_keep isl_ast_node *node, void *user),
12278 The callback set by C<isl_ast_print_options_set_print_user>
12279 is called whenever a node of type C<isl_ast_node_user> needs to
12281 The callback set by C<isl_ast_print_options_set_print_for>
12282 is called whenever a node of type C<isl_ast_node_for> needs to
12284 Note that C<isl_ast_node_for_print> will I<not> call the
12285 callback set by C<isl_ast_print_options_set_print_for> on the node
12286 on which C<isl_ast_node_for_print> is called, but only on nested
12287 nodes of type C<isl_ast_node_for>. It is therefore safe to
12288 call C<isl_ast_node_for_print> from within the callback set by
12289 C<isl_ast_print_options_set_print_for>.
12291 The following option determines the type to be used for iterators
12292 while printing the AST.
12294 isl_stat isl_options_set_ast_iterator_type(
12295 isl_ctx *ctx, const char *val);
12296 const char *isl_options_get_ast_iterator_type(
12299 The AST printer only prints body nodes of C<if> and C<for> nodes
12301 blocks cannot be safely omitted.
12302 For example, a C<for> node with one body node will not be
12303 surrounded with braces in C<ISL_FORMAT_C>.
12304 A block will always be printed by setting the following option.
12306 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx,
12308 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
12310 Explicit block nodes that appear inside the AST are always printed as blocks.
12311 If the block node appears as the outermost node,
12312 then it is only printed if the following option is set.
12314 isl_stat isl_options_set_ast_print_outermost_block(
12315 isl_ctx *ctx, int val);
12316 int isl_options_get_ast_print_outermost_block(
12321 #include <isl/ast_build.h>
12322 isl_stat isl_options_set_ast_build_atomic_upper_bound(
12323 isl_ctx *ctx, int val);
12324 int isl_options_get_ast_build_atomic_upper_bound(
12326 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
12328 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
12329 isl_stat isl_options_set_ast_build_detect_min_max(
12330 isl_ctx *ctx, int val);
12331 int isl_options_get_ast_build_detect_min_max(
12333 isl_stat isl_options_set_ast_build_exploit_nested_bounds(
12334 isl_ctx *ctx, int val);
12335 int isl_options_get_ast_build_exploit_nested_bounds(
12337 isl_stat isl_options_set_ast_build_group_coscheduled(
12338 isl_ctx *ctx, int val);
12339 int isl_options_get_ast_build_group_coscheduled(
12341 isl_stat isl_options_set_ast_build_separation_bounds(
12342 isl_ctx *ctx, int val);
12343 int isl_options_get_ast_build_separation_bounds(
12345 isl_stat isl_options_set_ast_build_scale_strides(
12346 isl_ctx *ctx, int val);
12347 int isl_options_get_ast_build_scale_strides(
12349 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx,
12351 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
12352 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx,
12354 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
12358 =item * ast_build_atomic_upper_bound
12360 Generate loop upper bounds that consist of the current loop iterator,
12361 an operator and an expression not involving the iterator.
12362 If this option is not set, then the current loop iterator may appear
12363 several times in the upper bound.
12364 For example, when this option is turned off, AST generation
12367 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
12371 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
12374 When the option is turned on, the following AST is generated
12376 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
12379 =item * ast_build_prefer_pdiv
12381 If this option is turned off, then the AST generation will
12382 produce ASTs that may only contain C<isl_ast_expr_op_fdiv_q>
12383 operators, but no C<isl_ast_expr_op_pdiv_q> or
12384 C<isl_ast_expr_op_pdiv_r> operators.
12385 If this option is turned on, then C<isl> will try to convert
12386 some of the C<isl_ast_expr_op_fdiv_q> operators to (expressions containing)
12387 C<isl_ast_expr_op_pdiv_q> or C<isl_ast_expr_op_pdiv_r> operators.
12389 =item * ast_build_detect_min_max
12391 If this option is turned on, then C<isl> will try and detect
12392 min or max-expressions when building AST expressions from
12393 piecewise affine expressions.
12395 =item * ast_build_exploit_nested_bounds
12397 Simplify conditions based on bounds of nested for loops.
12398 In particular, remove conditions that are implied by the fact
12399 that one or more nested loops have at least one iteration,
12400 meaning that the upper bound is at least as large as the lower bound.
12401 For example, when this option is turned off, AST generation
12404 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
12410 for (int c0 = 0; c0 <= N; c0 += 1)
12411 for (int c1 = 0; c1 <= M; c1 += 1)
12414 When the option is turned on, the following AST is generated
12416 for (int c0 = 0; c0 <= N; c0 += 1)
12417 for (int c1 = 0; c1 <= M; c1 += 1)
12420 =item * ast_build_group_coscheduled
12422 If two domain elements are assigned the same schedule point, then
12423 they may be executed in any order and they may even appear in different
12424 loops. If this options is set, then the AST generator will make
12425 sure that coscheduled domain elements do not appear in separate parts
12426 of the AST. This is useful in case of nested AST generation
12427 if the outer AST generation is given only part of a schedule
12428 and the inner AST generation should handle the domains that are
12429 coscheduled by this initial part of the schedule together.
12430 For example if an AST is generated for a schedule
12432 { A[i] -> [0]; B[i] -> [0] }
12434 then the C<isl_ast_build_set_create_leaf> callback described
12435 below may get called twice, once for each domain.
12436 Setting this option ensures that the callback is only called once
12437 on both domains together.
12439 =item * ast_build_separation_bounds
12441 This option specifies which bounds to use during separation.
12442 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
12443 then all (possibly implicit) bounds on the current dimension will
12444 be used during separation.
12445 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
12446 then only those bounds that are explicitly available will
12447 be used during separation.
12449 =item * ast_build_scale_strides
12451 This option specifies whether the AST generator is allowed
12452 to scale down iterators of strided loops.
12454 =item * ast_build_allow_else
12456 This option specifies whether the AST generator is allowed
12457 to construct if statements with else branches.
12459 =item * ast_build_allow_or
12461 This option specifies whether the AST generator is allowed
12462 to construct if conditions with disjunctions.
12466 =head3 AST Generation Options (Schedule Tree)
12468 In case of AST construction from a schedule tree, the options
12469 that control how an AST is created from the individual schedule
12470 dimensions are stored in the band nodes of the tree
12471 (see L</"Schedule Trees">).
12473 In particular, a schedule dimension can be handled in four
12474 different ways, atomic, separate, unroll or the default.
12475 This loop AST generation type can be set using
12476 C<isl_schedule_node_band_member_set_ast_loop_type>.
12478 the first three can be selected by including a one-dimensional
12479 element with as value the position of the schedule dimension
12480 within the band and as name one of C<atomic>, C<separate>
12481 or C<unroll> in the options
12482 set by C<isl_schedule_node_band_set_ast_build_options>.
12483 Only one of these three may be specified for
12484 any given schedule dimension within a band node.
12485 If none of these is specified, then the default
12486 is used. The meaning of the options is as follows.
12492 When this option is specified, the AST generator will make
12493 sure that a given domain space only appears in a single
12494 loop at the specified level.
12496 For example, for the schedule tree
12498 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
12500 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
12501 options: "{ atomic[x] }"
12503 the following AST will be generated
12505 for (int c0 = 0; c0 <= 10; c0 += 1) {
12512 On the other hand, for the schedule tree
12514 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
12516 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
12517 options: "{ separate[x] }"
12519 the following AST will be generated
12523 for (int c0 = 1; c0 <= 9; c0 += 1) {
12530 If neither C<atomic> nor C<separate> is specified, then the AST generator
12531 may produce either of these two results or some intermediate form.
12535 When this option is specified, the AST generator will
12536 split the domain of the specified schedule dimension
12537 into pieces with a fixed set of statements for which
12538 instances need to be executed by the iterations in
12539 the schedule domain part. This option tends to avoid
12540 the generation of guards inside the corresponding loops.
12541 See also the C<atomic> option.
12545 When this option is specified, the AST generator will
12546 I<completely> unroll the corresponding schedule dimension.
12547 It is the responsibility of the user to ensure that such
12548 unrolling is possible.
12549 To obtain a partial unrolling, the user should apply an additional
12550 strip-mining to the schedule and fully unroll the inner schedule
12555 The C<isolate> option is a bit more involved. It allows the user
12556 to isolate a range of schedule dimension values from smaller and
12557 greater values. Additionally, the user may specify a different
12558 atomic/separate/unroll choice for the isolated part and the remaining
12559 parts. The typical use case of the C<isolate> option is to isolate
12560 full tiles from partial tiles.
12561 The part that needs to be isolated may depend on outer schedule dimensions.
12562 The option therefore needs to be able to reference those outer schedule
12563 dimensions. In particular, the space of the C<isolate> option is that
12564 of a wrapped map with as domain the flat product of all outer band nodes
12565 and as range the space of the current band node.
12566 The atomic/separate/unroll choice for the isolated part is determined
12567 by an option that lives in an unnamed wrapped space with as domain
12568 a zero-dimensional C<isolate> space and as range the regular
12569 C<atomic>, C<separate> or C<unroll> space.
12570 This option may also be set directly using
12571 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
12572 The atomic/separate/unroll choice for the remaining part is determined
12573 by the regular C<atomic>, C<separate> or C<unroll> option.
12574 Since the C<isolate> option references outer schedule dimensions,
12575 its use in a band node causes any tree containing the node
12576 to be considered anchored.
12578 As an example, consider the isolation of full tiles from partial tiles
12579 in a tiling of a triangular domain. The original schedule is as follows.
12581 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
12583 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
12584 { A[i,j] -> [floor(j/10)] }, \
12585 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
12589 for (int c0 = 0; c0 <= 10; c0 += 1)
12590 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12591 for (int c2 = 10 * c0;
12592 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12593 for (int c3 = 10 * c1;
12594 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12597 Isolating the full tiles, we have the following input
12599 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
12601 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
12602 { A[i,j] -> [floor(j/10)] }, \
12603 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
12604 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
12605 10a+9+10b+9 <= 100 }"
12610 for (int c0 = 0; c0 <= 8; c0 += 1) {
12611 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
12612 for (int c2 = 10 * c0;
12613 c2 <= 10 * c0 + 9; c2 += 1)
12614 for (int c3 = 10 * c1;
12615 c3 <= 10 * c1 + 9; c3 += 1)
12617 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
12618 for (int c2 = 10 * c0;
12619 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12620 for (int c3 = 10 * c1;
12621 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12624 for (int c0 = 9; c0 <= 10; c0 += 1)
12625 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12626 for (int c2 = 10 * c0;
12627 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12628 for (int c3 = 10 * c1;
12629 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12633 We may then additionally unroll the innermost loop of the isolated part
12635 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
12637 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
12638 { A[i,j] -> [floor(j/10)] }, \
12639 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
12640 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
12641 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
12646 for (int c0 = 0; c0 <= 8; c0 += 1) {
12647 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
12648 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
12650 A(c2, 10 * c1 + 1);
12651 A(c2, 10 * c1 + 2);
12652 A(c2, 10 * c1 + 3);
12653 A(c2, 10 * c1 + 4);
12654 A(c2, 10 * c1 + 5);
12655 A(c2, 10 * c1 + 6);
12656 A(c2, 10 * c1 + 7);
12657 A(c2, 10 * c1 + 8);
12658 A(c2, 10 * c1 + 9);
12660 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
12661 for (int c2 = 10 * c0;
12662 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12663 for (int c3 = 10 * c1;
12664 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12667 for (int c0 = 9; c0 <= 10; c0 += 1)
12668 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12669 for (int c2 = 10 * c0;
12670 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12671 for (int c3 = 10 * c1;
12672 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12677 =head3 AST Generation Options (Schedule Map)
12679 In case of AST construction using
12680 C<isl_ast_build_node_from_schedule_map>, the options
12681 that control how an AST is created from the individual schedule
12682 dimensions are stored in the C<isl_ast_build>.
12683 They can be set using the following function.
12685 #include <isl/ast_build.h>
12686 __isl_give isl_ast_build *
12687 isl_ast_build_set_options(
12688 __isl_take isl_ast_build *build,
12689 __isl_take isl_union_map *options);
12691 The options are encoded in an C<isl_union_map>.
12692 The domain of this union relation refers to the schedule domain,
12693 i.e., the range of the schedule passed
12694 to C<isl_ast_build_node_from_schedule_map>.
12695 In the case of nested AST generation (see L</"Nested AST Generation">),
12696 the domain of C<options> should refer to the extra piece of the schedule.
12697 That is, it should be equal to the range of the wrapped relation in the
12698 range of the schedule.
12699 The range of the options can consist of elements in one or more spaces,
12700 the names of which determine the effect of the option.
12701 The values of the range typically also refer to the schedule dimension
12702 to which the option applies, with value C<0> representing
12703 the outermost schedule dimension. In case of nested AST generation
12704 (see L</"Nested AST Generation">), these values refer to the position
12705 of the schedule dimension within the innermost AST generation.
12706 The constraints on the domain elements of
12707 the option should only refer to this dimension and earlier dimensions.
12708 We consider the following spaces.
12712 =item C<separation_class>
12714 B<This option has been deprecated. Use the isolate option on
12715 schedule trees instead.>
12717 This space is a wrapped relation between two one dimensional spaces.
12718 The input space represents the schedule dimension to which the option
12719 applies and the output space represents the separation class.
12720 While constructing a loop corresponding to the specified schedule
12721 dimension(s), the AST generator will try to generate separate loops
12722 for domain elements that are assigned different classes.
12723 If only some of the elements are assigned a class, then those elements
12724 that are not assigned any class will be treated as belonging to a class
12725 that is separate from the explicitly assigned classes.
12726 The typical use case for this option is to separate full tiles from
12728 The other options, described below, are applied after the separation
12731 As an example, consider the separation into full and partial tiles
12732 of a tiling of a triangular domain.
12733 Take, for example, the domain
12735 { A[i,j] : 0 <= i,j and i + j <= 100 }
12737 and a tiling into tiles of 10 by 10. The input to the AST generator
12738 is then the schedule
12740 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
12743 Without any options, the following AST is generated
12745 for (int c0 = 0; c0 <= 10; c0 += 1)
12746 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12747 for (int c2 = 10 * c0;
12748 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
12750 for (int c3 = 10 * c1;
12751 c3 <= min(10 * c1 + 9, -c2 + 100);
12755 Separation into full and partial tiles can be obtained by assigning
12756 a class, say C<0>, to the full tiles. The full tiles are represented by those
12757 values of the first and second schedule dimensions for which there are
12758 values of the third and fourth dimensions to cover an entire tile.
12759 That is, we need to specify the following option
12761 { [a,b,c,d] -> separation_class[[0]->[0]] :
12762 exists b': 0 <= 10a,10b' and
12763 10a+9+10b'+9 <= 100;
12764 [a,b,c,d] -> separation_class[[1]->[0]] :
12765 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
12767 which simplifies to
12769 { [a, b, c, d] -> separation_class[[1] -> [0]] :
12770 a >= 0 and b >= 0 and b <= 8 - a;
12771 [a, b, c, d] -> separation_class[[0] -> [0]] :
12772 a >= 0 and a <= 8 }
12774 With this option, the generated AST is as follows
12777 for (int c0 = 0; c0 <= 8; c0 += 1) {
12778 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
12779 for (int c2 = 10 * c0;
12780 c2 <= 10 * c0 + 9; c2 += 1)
12781 for (int c3 = 10 * c1;
12782 c3 <= 10 * c1 + 9; c3 += 1)
12784 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
12785 for (int c2 = 10 * c0;
12786 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
12788 for (int c3 = 10 * c1;
12789 c3 <= min(-c2 + 100, 10 * c1 + 9);
12793 for (int c0 = 9; c0 <= 10; c0 += 1)
12794 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12795 for (int c2 = 10 * c0;
12796 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
12798 for (int c3 = 10 * c1;
12799 c3 <= min(10 * c1 + 9, -c2 + 100);
12806 This is a single-dimensional space representing the schedule dimension(s)
12807 to which ``separation'' should be applied. Separation tries to split
12808 a loop into several pieces if this can avoid the generation of guards
12810 See also the C<atomic> option.
12814 This is a single-dimensional space representing the schedule dimension(s)
12815 for which the domains should be considered ``atomic''. That is, the
12816 AST generator will make sure that any given domain space will only appear
12817 in a single loop at the specified level.
12819 Consider the following schedule
12821 { a[i] -> [i] : 0 <= i < 10;
12822 b[i] -> [i+1] : 0 <= i < 10 }
12824 If the following option is specified
12826 { [i] -> separate[x] }
12828 then the following AST will be generated
12832 for (int c0 = 1; c0 <= 9; c0 += 1) {
12839 If, on the other hand, the following option is specified
12841 { [i] -> atomic[x] }
12843 then the following AST will be generated
12845 for (int c0 = 0; c0 <= 10; c0 += 1) {
12852 If neither C<atomic> nor C<separate> is specified, then the AST generator
12853 may produce either of these two results or some intermediate form.
12857 This is a single-dimensional space representing the schedule dimension(s)
12858 that should be I<completely> unrolled.
12859 To obtain a partial unrolling, the user should apply an additional
12860 strip-mining to the schedule and fully unroll the inner loop.
12864 =head3 Fine-grained Control over AST Generation
12866 Besides specifying the constraints on the parameters,
12867 an C<isl_ast_build> object can be used to control
12868 various aspects of the AST generation process.
12869 In case of AST construction using
12870 C<isl_ast_build_node_from_schedule_map>,
12871 the most prominent way of control is through ``options'',
12872 as explained above.
12874 Additional control is available through the following functions.
12876 #include <isl/ast_build.h>
12877 __isl_give isl_ast_build *
12878 isl_ast_build_set_iterators(
12879 __isl_take isl_ast_build *build,
12880 __isl_take isl_id_list *iterators);
12882 The function C<isl_ast_build_set_iterators> allows the user to
12883 specify a list of iterator C<isl_id>s to be used as iterators.
12884 If the input schedule is injective, then
12885 the number of elements in this list should be as large as the dimension
12886 of the schedule space, but no direct correspondence should be assumed
12887 between dimensions and elements.
12888 If the input schedule is not injective, then an additional number
12889 of C<isl_id>s equal to the largest dimension of the input domains
12891 If the number of provided C<isl_id>s is insufficient, then additional
12892 names are automatically generated.
12894 #include <isl/ast_build.h>
12895 __isl_give isl_ast_build *
12896 isl_ast_build_set_create_leaf(
12897 __isl_take isl_ast_build *build,
12898 __isl_give isl_ast_node *(*fn)(
12899 __isl_take isl_ast_build *build,
12900 void *user), void *user);
12903 C<isl_ast_build_set_create_leaf> function allows for the
12904 specification of a callback that should be called whenever the AST
12905 generator arrives at an element of the schedule domain.
12906 The callback should return an AST node that should be inserted
12907 at the corresponding position of the AST. The default action (when
12908 the callback is not set) is to continue generating parts of the AST to scan
12909 all the domain elements associated to the schedule domain element
12910 and to insert user nodes, ``calling'' the domain element, for each of them.
12911 The C<build> argument contains the current state of the C<isl_ast_build>.
12912 To ease nested AST generation (see L</"Nested AST Generation">),
12913 all control information that is
12914 specific to the current AST generation such as the options and
12915 the callbacks has been removed from this C<isl_ast_build>.
12916 The callback would typically return the result of a nested
12917 AST generation or a
12918 user defined node created using the following function.
12920 #include <isl/ast.h>
12921 __isl_give isl_ast_node *isl_ast_node_user_from_expr(
12922 __isl_take isl_ast_expr *expr);
12923 __isl_give isl_ast_node *isl_ast_node_alloc_user(
12924 __isl_take isl_ast_expr *expr);
12926 C<isl_ast_node_alloc_user> is an alternative name for
12927 C<isl_ast_node_user_from_expr>.
12929 In some cases, a single user defined node is not enough,
12930 in which case the following function can be used
12931 to create a block node from multiple AST nodes.
12933 #include <isl/ast.h>
12934 __isl_give isl_ast_node *isl_ast_node_block_from_children(
12935 __isl_take isl_ast_node_list *list);
12937 #include <isl/ast_build.h>
12938 __isl_give isl_ast_build *
12939 isl_ast_build_set_at_each_domain(
12940 __isl_take isl_ast_build *build,
12941 __isl_give isl_ast_node *(*fn)(
12942 __isl_take isl_ast_node *node,
12943 __isl_keep isl_ast_build *build,
12944 void *user), void *user);
12945 __isl_give isl_ast_build *
12946 isl_ast_build_set_before_each_for(
12947 __isl_take isl_ast_build *build,
12948 __isl_give isl_id *(*fn)(
12949 __isl_keep isl_ast_build *build,
12950 void *user), void *user);
12951 __isl_give isl_ast_build *
12952 isl_ast_build_set_after_each_for(
12953 __isl_take isl_ast_build *build,
12954 __isl_give isl_ast_node *(*fn)(
12955 __isl_take isl_ast_node *node,
12956 __isl_keep isl_ast_build *build,
12957 void *user), void *user);
12958 __isl_give isl_ast_build *
12959 isl_ast_build_set_before_each_mark(
12960 __isl_take isl_ast_build *build,
12961 isl_stat (*fn)(__isl_keep isl_id *mark,
12962 __isl_keep isl_ast_build *build,
12963 void *user), void *user);
12964 __isl_give isl_ast_build *
12965 isl_ast_build_set_after_each_mark(
12966 __isl_take isl_ast_build *build,
12967 __isl_give isl_ast_node *(*fn)(
12968 __isl_take isl_ast_node *node,
12969 __isl_keep isl_ast_build *build,
12970 void *user), void *user);
12972 The callback set by C<isl_ast_build_set_at_each_domain> will
12973 be called for each domain AST node.
12974 The callbacks set by C<isl_ast_build_set_before_each_for>
12975 and C<isl_ast_build_set_after_each_for> will be called
12976 for each for AST node. The first will be called in depth-first
12977 pre-order, while the second will be called in depth-first post-order.
12978 Since C<isl_ast_build_set_before_each_for> is called before the for
12979 node is actually constructed, it is only passed an C<isl_ast_build>.
12980 The returned C<isl_id> will be added as an annotation (using
12981 C<isl_ast_node_set_annotation>) to the constructed for node.
12982 In particular, if the user has also specified an C<after_each_for>
12983 callback, then the annotation can be retrieved from the node passed to
12984 that callback using C<isl_ast_node_get_annotation>.
12985 The callbacks set by C<isl_ast_build_set_before_each_mark>
12986 and C<isl_ast_build_set_after_each_mark> will be called for each
12987 mark AST node that is created, i.e., for each mark schedule node
12988 in the input schedule tree. The first will be called in depth-first
12989 pre-order, while the second will be called in depth-first post-order.
12990 Since the callback set by C<isl_ast_build_set_before_each_mark>
12991 is called before the mark AST node is actually constructed, it is passed
12992 the identifier of the mark node.
12993 All callbacks should C<NULL> (or C<isl_stat_error>) on failure.
12994 The given C<isl_ast_build> can be used to create new
12995 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
12996 or C<isl_ast_build_call_from_pw_multi_aff>.
12998 =head3 Nested AST Generation
13000 C<isl> allows the user to create an AST within the context
13001 of another AST. These nested ASTs are created using the
13002 same C<isl_ast_build_node_from_schedule_map> function that is used to create
13003 the outer AST. The C<build> argument should be an C<isl_ast_build>
13004 passed to a callback set by
13005 C<isl_ast_build_set_create_leaf>.
13006 The space of the range of the C<schedule> argument should refer
13007 to this build. In particular, the space should be a wrapped
13008 relation and the domain of this wrapped relation should be the
13009 same as that of the range of the schedule returned by
13010 C<isl_ast_build_get_schedule> below.
13011 In practice, the new schedule is typically
13012 created by calling C<isl_union_map_range_product> on the old schedule
13013 and some extra piece of the schedule.
13014 The space of the schedule domain is also available from
13015 the C<isl_ast_build>.
13017 #include <isl/ast_build.h>
13018 __isl_give isl_union_map *isl_ast_build_get_schedule(
13019 __isl_keep isl_ast_build *build);
13020 __isl_give isl_space *isl_ast_build_get_schedule_space(
13021 __isl_keep isl_ast_build *build);
13022 __isl_give isl_ast_build *isl_ast_build_restrict(
13023 __isl_take isl_ast_build *build,
13024 __isl_take isl_set *set);
13026 The C<isl_ast_build_get_schedule> function returns a (partial)
13027 schedule for the domains elements for which part of the AST still needs to
13028 be generated in the current build.
13029 In particular, the domain elements are mapped to those iterations of the loops
13030 enclosing the current point of the AST generation inside which
13031 the domain elements are executed.
13032 No direct correspondence between
13033 the input schedule and this schedule should be assumed.
13034 The space obtained from C<isl_ast_build_get_schedule_space> can be used
13035 to create a set for C<isl_ast_build_restrict> to intersect
13036 with the current build. In particular, the set passed to
13037 C<isl_ast_build_restrict> can have additional parameters.
13038 The ids of the set dimensions in the space returned by
13039 C<isl_ast_build_get_schedule_space> correspond to the
13040 iterators of the already generated loops.
13041 The user should not rely on the ids of the output dimensions
13042 of the relations in the union relation returned by
13043 C<isl_ast_build_get_schedule> having any particular value.
13045 =head1 Applications
13047 Although C<isl> is mainly meant to be used as a library,
13048 it also contains some basic applications that use some
13049 of the functionality of C<isl>.
13050 For applications that take one or more polytopes or polyhedra
13051 as input, this input may be specified in either the L<isl format>
13052 or the L<PolyLib format>.
13054 =head2 C<isl_polyhedron_sample>
13056 C<isl_polyhedron_sample> takes a polyhedron as input and prints
13057 an integer element of the polyhedron, if there is any.
13058 The first column in the output is the denominator and is always
13059 equal to 1. If the polyhedron contains no integer points,
13060 then a vector of length zero is printed.
13064 C<isl_pip> takes the same input as the C<example> program
13065 from the C<piplib> distribution, i.e., a set of constraints
13066 on the parameters, a line containing only -1 and finally a set
13067 of constraints on a parametric polyhedron.
13068 The coefficients of the parameters appear in the last columns
13069 (but before the final constant column).
13070 The output is the lexicographic minimum of the parametric polyhedron.
13071 As C<isl> currently does not have its own output format, the output
13072 is just a dump of the internal state.
13074 =head2 C<isl_polyhedron_minimize>
13076 C<isl_polyhedron_minimize> computes the minimum of some linear
13077 or affine objective function over the integer points in a polyhedron.
13078 If an affine objective function
13079 is given, then the constant should appear in the last column.
13081 =head2 C<isl_polytope_scan>
13083 Given a polytope, C<isl_polytope_scan> prints
13084 all integer points in the polytope.
13088 Given an C<isl_union_access_info> object as input,
13089 C<isl_flow> prints out the corresponding dependences,
13090 as computed by C<isl_union_access_info_compute_flow>.
13092 =head2 C<isl_codegen>
13094 Given either a schedule tree or a sequence consisting of
13095 a schedule map, a context set and an options relation,
13096 C<isl_codegen> prints out an AST that scans the domain elements
13097 of the schedule in the order of their image(s) taking into account
13098 the constraints in the context set.
13100 =head2 C<isl_schedule>
13102 Given an C<isl_schedule_constraints> object as input,
13103 C<isl_schedule> prints out a schedule that satisfies the given