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/map.h>
5429 __isl_give isl_basic_map *isl_basic_map_reverse(
5430 __isl_take isl_basic_map *bmap);
5431 __isl_give isl_map *isl_map_reverse(
5432 __isl_take isl_map *map);
5433 __isl_give isl_map *isl_map_range_reverse(
5434 __isl_take isl_map *map);
5436 #include <isl/union_map.h>
5437 __isl_give isl_union_map *isl_union_map_reverse(
5438 __isl_take isl_union_map *umap);
5439 __isl_give isl_union_map *isl_union_map_range_reverse(
5440 __isl_take isl_union_map *umap);
5442 The function C<isl_space_range_reverse> reverses the relation
5443 that is embedded in the range of the input map space.
5444 The identifier of the range, if any, is only preserved
5445 if this embedded relation has identical input and output tuples.
5446 Similarly for C<isl_space_domain_reverse>.
5447 Along the same lines, C<isl_space_wrapped_reverse> reverses
5448 the relation that is embedded in a set space.
5450 =item * Tuple binding
5452 The following function binds
5453 a tuple to a sequence of parameter identifiers, equating
5454 the tuple dimensions to the parameters with those identifiers and
5455 subsequently projecting out the tuple.
5456 If the original object did not reference any such parameters,
5457 then this means that the tuple dimensions are reinterpreted
5459 The space of C<tuple> needs to match that of the bound tuple.
5461 #include <isl/set.h>
5462 __isl_give isl_set *isl_set_bind(
5463 __isl_take isl_set *set,
5464 __isl_take isl_multi_id *tuple);
5466 #include <isl/map.h>
5467 __isl_give isl_set *isl_map_bind_domain(
5468 __isl_take isl_map *map,
5469 __isl_take isl_multi_id *tuple);
5470 __isl_give isl_set *isl_map_bind_range(
5471 __isl_take isl_map *map,
5472 __isl_take isl_multi_id *tuple);
5474 #include <isl/union_map.h>
5475 __isl_give isl_union_set *isl_union_map_bind_range(
5476 __isl_take isl_union_map *umap,
5477 __isl_take isl_multi_id *tuple);
5479 #include <isl/aff.h>
5480 __isl_give isl_pw_aff *isl_pw_aff_bind_domain(
5481 __isl_take isl_pw_aff *pa,
5482 __isl_take isl_multi_id *tuple);
5483 __isl_give isl_multi_aff *isl_multi_aff_bind_domain(
5484 __isl_take isl_multi_aff *ma,
5485 __isl_take isl_multi_id *tuple);
5486 __isl_give isl_pw_multi_aff *
5487 isl_pw_multi_aff_bind_domain(
5488 __isl_take isl_pw_multi_aff *pma,
5489 __isl_take isl_multi_id *tuple);
5490 __isl_give isl_multi_pw_aff *
5491 isl_multi_pw_aff_bind_domain(
5492 __isl_take isl_multi_pw_aff *mpa,
5493 __isl_take isl_multi_id *tuple);
5494 __isl_give isl_pw_aff *
5495 isl_pw_aff_bind_domain_wrapped_domain(
5496 __isl_take isl_pw_aff *pa,
5497 __isl_take isl_multi_id *tuple);
5498 __isl_give isl_multi_aff *
5499 isl_multi_aff_bind_domain_wrapped_domain(
5500 __isl_take isl_multi_aff *ma,
5501 __isl_take isl_multi_id *tuple);
5502 __isl_give isl_pw_multi_aff *
5503 isl_pw_multi_aff_bind_domain_wrapped_domain(
5504 __isl_take isl_pw_multi_aff *pma,
5505 __isl_take isl_multi_id *tuple);
5506 __isl_give isl_multi_pw_aff *
5507 isl_multi_pw_aff_bind_domain_wrapped_domain(
5508 __isl_take isl_multi_pw_aff *mpa,
5509 __isl_take isl_multi_id *tuple);
5510 __isl_give isl_basic_set *isl_aff_bind_id(
5511 __isl_take isl_aff *aff,
5512 __isl_take isl_id *id);
5513 __isl_give isl_set *isl_pw_aff_bind_id(
5514 __isl_take isl_pw_aff *pa,
5515 __isl_take isl_id *id);
5516 __isl_give isl_basic_set *isl_multi_aff_bind(
5517 __isl_take isl_multi_aff *ma,
5518 __isl_take isl_multi_id *tuple);
5519 __isl_give isl_set *isl_multi_pw_aff_bind(
5520 __isl_take isl_multi_pw_aff *mpa,
5521 __isl_take isl_multi_id *tuple);
5522 __isl_give isl_union_set *isl_union_pw_aff_bind_id(
5523 __isl_take isl_union_pw_aff *upa,
5524 __isl_take isl_id *id);
5525 __isl_give isl_union_set *
5526 isl_multi_union_pw_aff_bind(
5527 __isl_take isl_multi_union_pw_aff *mupa,
5528 __isl_take isl_multi_id *tuple);
5530 Projecting out the domain of the wrapped relation in the domain
5531 of a function leaves the range of that wrapped relation
5532 in the domain of the resulting function.
5533 In the case of C<isl_aff_bind_id>, C<isl_pw_aff_bind_id>,
5534 C<isl_multi_aff_bind>, C<isl_multi_pw_aff_bind>,
5535 C<isl_union_pw_aff_bind_id> and
5536 C<isl_multi_union_pw_aff_bind>, the parameters
5537 are bound to the function values and the result lives
5538 in the domain of the input function.
5542 #include <isl/space.h>
5543 __isl_give isl_space *isl_space_domain(
5544 __isl_take isl_space *space);
5545 __isl_give isl_space *isl_space_range(
5546 __isl_take isl_space *space);
5547 __isl_give isl_space *isl_space_params(
5548 __isl_take isl_space *space);
5549 __isl_give isl_space *
5550 isl_space_domain_wrapped_domain(
5551 __isl_take isl_space *space);
5552 __isl_give isl_space *
5553 isl_space_domain_wrapped_range(
5554 __isl_take isl_space *space);
5555 __isl_give isl_space *
5556 isl_space_range_wrapped_domain(
5557 __isl_take isl_space *space);
5558 __isl_give isl_space *
5559 isl_space_range_wrapped_range(
5560 __isl_take isl_space *space);
5562 #include <isl/local_space.h>
5563 __isl_give isl_local_space *isl_local_space_domain(
5564 __isl_take isl_local_space *ls);
5565 __isl_give isl_local_space *isl_local_space_range(
5566 __isl_take isl_local_space *ls);
5568 #include <isl/set.h>
5569 __isl_give isl_basic_set *isl_basic_set_project_out(
5570 __isl_take isl_basic_set *bset,
5571 enum isl_dim_type type, unsigned first, unsigned n);
5572 __isl_give isl_set *isl_set_project_out_param_id(
5573 __isl_take isl_set *set,
5574 __isl_take isl_id *id);
5575 __isl_give isl_set *
5576 isl_set_project_out_param_id_list(
5577 __isl_take isl_set *set,
5578 __isl_take isl_id_list *list);
5579 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
5580 enum isl_dim_type type, unsigned first, unsigned n);
5581 __isl_give isl_set *isl_set_project_out_all_params(
5582 __isl_take isl_set *set);
5583 __isl_give isl_map *isl_set_project_onto_map(
5584 __isl_take isl_set *set,
5585 enum isl_dim_type type, unsigned first,
5587 __isl_give isl_basic_set *isl_basic_set_params(
5588 __isl_take isl_basic_set *bset);
5589 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
5591 The function C<isl_space_domain_wrapped_domain> returns the domain
5592 of the binary relation wrapped inside the domain of the input.
5593 The function C<isl_set_project_onto_map> returns a relation
5594 that projects the input set onto the given set dimensions.
5596 #include <isl/map.h>
5597 __isl_give isl_basic_map *isl_basic_map_project_out(
5598 __isl_take isl_basic_map *bmap,
5599 enum isl_dim_type type, unsigned first, unsigned n);
5600 __isl_give isl_map *isl_map_project_out_param_id(
5601 __isl_take isl_map *map,
5602 __isl_take isl_id *id);
5603 __isl_give isl_map *isl_map_project_out_param_id_list(
5604 __isl_take isl_map *map,
5605 __isl_take isl_id_list *list);
5606 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
5607 enum isl_dim_type type, unsigned first, unsigned n);
5608 __isl_give isl_map *isl_map_project_out_all_params(
5609 __isl_take isl_map *map);
5610 __isl_give isl_basic_set *isl_basic_map_domain(
5611 __isl_take isl_basic_map *bmap);
5612 __isl_give isl_basic_set *isl_basic_map_range(
5613 __isl_take isl_basic_map *bmap);
5614 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
5615 __isl_give isl_set *isl_map_domain(
5616 __isl_take isl_map *bmap);
5617 __isl_give isl_set *isl_map_range(
5618 __isl_take isl_map *map);
5620 #include <isl/union_set.h>
5621 __isl_give isl_union_set *isl_union_set_project_out(
5622 __isl_take isl_union_set *uset,
5623 enum isl_dim_type type,
5624 unsigned first, unsigned n);
5625 __isl_give isl_union_set *
5626 isl_union_set_project_out_all_params(
5627 __isl_take isl_union_set *uset);
5628 __isl_give isl_set *isl_union_set_params(
5629 __isl_take isl_union_set *uset);
5631 The function C<isl_union_set_project_out> can only project out
5634 #include <isl/union_map.h>
5635 __isl_give isl_union_map *
5636 isl_union_map_project_out_param_id(
5637 __isl_take isl_union_map *umap,
5638 __isl_take isl_id *id);
5639 __isl_give isl_union_map *
5640 isl_union_map_project_out_param_id_list(
5641 __isl_take isl_union_map *umap,
5642 __isl_take isl_id_list *list);
5643 __isl_give isl_union_map *isl_union_map_project_out(
5644 __isl_take isl_union_map *umap,
5645 enum isl_dim_type type, unsigned first, unsigned n);
5646 __isl_give isl_union_map *
5647 isl_union_map_project_out_all_params(
5648 __isl_take isl_union_map *umap);
5649 __isl_give isl_set *isl_union_map_params(
5650 __isl_take isl_union_map *umap);
5651 __isl_give isl_union_set *isl_union_map_domain(
5652 __isl_take isl_union_map *umap);
5653 __isl_give isl_union_set *isl_union_map_range(
5654 __isl_take isl_union_map *umap);
5656 The function C<isl_union_map_project_out> can only project out
5659 #include <isl/aff.h>
5660 __isl_give isl_aff *isl_aff_project_domain_on_params(
5661 __isl_take isl_aff *aff);
5662 __isl_give isl_multi_aff *
5663 isl_multi_aff_project_domain_on_params(
5664 __isl_take isl_multi_aff *ma);
5665 __isl_give isl_pw_aff *
5666 isl_pw_aff_project_domain_on_params(
5667 __isl_take isl_pw_aff *pa);
5668 __isl_give isl_multi_pw_aff *
5669 isl_multi_pw_aff_project_domain_on_params(
5670 __isl_take isl_multi_pw_aff *mpa);
5671 __isl_give isl_pw_multi_aff *
5672 isl_pw_multi_aff_project_domain_on_params(
5673 __isl_take isl_pw_multi_aff *pma);
5674 __isl_give isl_set *isl_pw_aff_domain(
5675 __isl_take isl_pw_aff *pwaff);
5676 __isl_give isl_set *isl_pw_multi_aff_domain(
5677 __isl_take isl_pw_multi_aff *pma);
5678 __isl_give isl_set *isl_multi_pw_aff_domain(
5679 __isl_take isl_multi_pw_aff *mpa);
5680 __isl_give isl_union_set *isl_union_pw_aff_domain(
5681 __isl_take isl_union_pw_aff *upa);
5682 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
5683 __isl_take isl_union_pw_multi_aff *upma);
5684 __isl_give isl_union_set *
5685 isl_multi_union_pw_aff_domain(
5686 __isl_take isl_multi_union_pw_aff *mupa);
5687 __isl_give isl_set *isl_pw_aff_params(
5688 __isl_take isl_pw_aff *pwa);
5690 If no explicit domain was set on a zero-dimensional input to
5691 C<isl_multi_union_pw_aff_domain>, then this function will
5692 return a parameter set.
5694 #include <isl/polynomial.h>
5695 __isl_give isl_qpolynomial *
5696 isl_qpolynomial_project_domain_on_params(
5697 __isl_take isl_qpolynomial *qp);
5698 __isl_give isl_pw_qpolynomial *
5699 isl_pw_qpolynomial_project_domain_on_params(
5700 __isl_take isl_pw_qpolynomial *pwqp);
5701 __isl_give isl_pw_qpolynomial_fold *
5702 isl_pw_qpolynomial_fold_project_domain_on_params(
5703 __isl_take isl_pw_qpolynomial_fold *pwf);
5704 __isl_give isl_set *isl_pw_qpolynomial_domain(
5705 __isl_take isl_pw_qpolynomial *pwqp);
5706 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
5707 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5708 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
5709 __isl_take isl_union_pw_qpolynomial *upwqp);
5711 #include <isl/space.h>
5712 __isl_give isl_space *isl_space_domain_map(
5713 __isl_take isl_space *space);
5714 __isl_give isl_space *isl_space_range_map(
5715 __isl_take isl_space *space);
5717 #include <isl/map.h>
5718 __isl_give isl_map *isl_set_wrapped_domain_map(
5719 __isl_take isl_set *set);
5720 __isl_give isl_basic_map *isl_basic_map_domain_map(
5721 __isl_take isl_basic_map *bmap);
5722 __isl_give isl_basic_map *isl_basic_map_range_map(
5723 __isl_take isl_basic_map *bmap);
5724 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
5725 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
5727 #include <isl/union_map.h>
5728 __isl_give isl_union_map *isl_union_map_domain_map(
5729 __isl_take isl_union_map *umap);
5730 __isl_give isl_union_pw_multi_aff *
5731 isl_union_map_domain_map_union_pw_multi_aff(
5732 __isl_take isl_union_map *umap);
5733 __isl_give isl_union_map *isl_union_map_range_map(
5734 __isl_take isl_union_map *umap);
5735 __isl_give isl_union_map *
5736 isl_union_set_wrapped_domain_map(
5737 __isl_take isl_union_set *uset);
5739 The functions above construct a (basic, regular or union) relation
5740 that maps (a wrapped version of) the input relation to its domain or range.
5741 C<isl_set_wrapped_domain_map> maps the input set to the domain
5742 of its wrapped relation.
5746 __isl_give isl_basic_set *isl_basic_set_eliminate(
5747 __isl_take isl_basic_set *bset,
5748 enum isl_dim_type type,
5749 unsigned first, unsigned n);
5750 __isl_give isl_set *isl_set_eliminate(
5751 __isl_take isl_set *set, enum isl_dim_type type,
5752 unsigned first, unsigned n);
5753 __isl_give isl_basic_map *isl_basic_map_eliminate(
5754 __isl_take isl_basic_map *bmap,
5755 enum isl_dim_type type,
5756 unsigned first, unsigned n);
5757 __isl_give isl_map *isl_map_eliminate(
5758 __isl_take isl_map *map, enum isl_dim_type type,
5759 unsigned first, unsigned n);
5761 Eliminate the coefficients for the given dimensions from the constraints,
5762 without removing the dimensions.
5764 =item * Constructing a set from a parameter domain
5766 A set space of a given dimension and with an optional name
5767 can be created from a parameter space using the following functions.
5769 #include <isl/space.h>
5770 __isl_give isl_space *isl_space_add_unnamed_tuple_ui(
5771 __isl_take isl_space *space, unsigned dim);
5772 __isl_give isl_space *
5773 isl_space_add_named_tuple_id_ui(
5774 __isl_take isl_space *space,
5775 __isl_take isl_id *tuple_id, unsigned dim);
5777 A set with a given tuple can be created from a parameter domain
5778 using the following function.
5780 #include <isl/set.h>
5781 __isl_give isl_set *isl_set_unbind_params(
5782 __isl_take isl_set *set,
5783 __isl_take isl_multi_id *tuple);
5785 Any parameters with identifiers in C<tuple> are reinterpreted
5786 as the corresponding set dimensions.
5788 A zero-dimensional (local) space or (basic) set can be constructed
5789 on a given parameter domain using the following functions.
5791 #include <isl/space.h>
5792 __isl_give isl_space *isl_space_set_from_params(
5793 __isl_take isl_space *space);
5795 #include <isl/local_space.h>
5796 __isl_give isl_local_space *
5797 isl_local_space_set_from_params(
5798 __isl_take isl_local_space *ls);
5800 #include <isl/set.h>
5801 __isl_give isl_basic_set *isl_basic_set_from_params(
5802 __isl_take isl_basic_set *bset);
5803 __isl_give isl_set *isl_set_from_params(
5804 __isl_take isl_set *set);
5806 =item * Constructing a relation from one or two sets
5808 A map space with a range of a given dimension and with an optional name
5809 can be created from a domain space using the functions
5810 C<isl_space_add_unnamed_tuple_ui> and C<isl_space_add_named_tuple_id_ui>
5813 A relation with a given domain tuple can be created from a set
5814 that will become the range of the relation
5815 using the following function.
5817 #include <isl/set.h>
5818 __isl_give isl_map *
5819 isl_set_unbind_params_insert_domain(
5820 __isl_take isl_set *set,
5821 __isl_take isl_multi_id *domain);
5823 Any parameters with identifiers in C<domain> are reinterpreted
5824 as the corresponding input dimensions.
5826 Similarly, a function defined over a parameter domain can
5827 be converted into one defined over a set domain
5828 using the following functions.
5830 #include <isl/aff.h>
5831 __isl_give isl_aff *
5832 isl_aff_unbind_params_insert_domain(
5833 __isl_take isl_aff *aff,
5834 __isl_take isl_multi_id *domain);
5835 __isl_give isl_multi_aff *
5836 isl_multi_aff_unbind_params_insert_domain(
5837 __isl_take isl_multi_aff *ma,
5838 __isl_take isl_multi_id *domain);
5839 __isl_give isl_multi_pw_aff *
5840 isl_multi_pw_aff_unbind_params_insert_domain(
5841 __isl_take isl_multi_pw_aff *mpa,
5842 __isl_take isl_multi_id *domain);
5845 any parameters with identifiers in C<domain> are reinterpreted
5846 as the corresponding input dimensions.
5848 Create a relation with the given set(s) as domain and/or range.
5849 If only the domain or the range is specified, then
5850 the range or domain of the created relation is a zero-dimensional
5851 flat anonymous space.
5852 If the case of C<isl_space_map_from_set>, the input space
5853 specifies both the domain and the range of the result.
5855 #include <isl/space.h>
5856 __isl_give isl_space *isl_space_from_domain(
5857 __isl_take isl_space *space);
5858 __isl_give isl_space *isl_space_from_range(
5859 __isl_take isl_space *space);
5860 __isl_give isl_space *isl_space_map_from_set(
5861 __isl_take isl_space *space);
5862 __isl_give isl_space *isl_space_map_from_domain_and_range(
5863 __isl_take isl_space *domain,
5864 __isl_take isl_space *range);
5866 #include <isl/local_space.h>
5867 __isl_give isl_local_space *isl_local_space_from_domain(
5868 __isl_take isl_local_space *ls);
5870 #include <isl/map.h>
5871 __isl_give isl_map *isl_set_insert_domain(
5872 __isl_take isl_set *set,
5873 __isl_take isl_space *domain);
5874 __isl_give isl_map *isl_map_from_domain(
5875 __isl_take isl_set *set);
5876 __isl_give isl_map *isl_map_from_range(
5877 __isl_take isl_set *set);
5879 #include <isl/union_map.h>
5880 __isl_give isl_union_map *isl_union_map_from_domain(
5881 __isl_take isl_union_set *uset);
5882 __isl_give isl_union_map *isl_union_map_from_range(
5883 __isl_take isl_union_set *uset);
5884 __isl_give isl_union_map *
5885 isl_union_map_from_domain_and_range(
5886 __isl_take isl_union_set *domain,
5887 __isl_take isl_union_set *range);
5890 __isl_give isl_multi_id *isl_multi_id_from_range(
5891 __isl_take isl_multi_id *mi);
5893 #include <isl/val.h>
5894 __isl_give isl_multi_val *isl_multi_val_from_range(
5895 __isl_take isl_multi_val *mv);
5897 #include <isl/aff.h>
5898 __isl_give isl_multi_aff *
5899 isl_multi_aff_insert_domain(
5900 __isl_take isl_multi_aff *ma,
5901 __isl_take isl_space *domain);
5902 __isl_give isl_pw_aff *isl_pw_aff_insert_domain(
5903 __isl_take isl_pw_aff *pa,
5904 __isl_take isl_space *domain);
5905 __isl_give isl_pw_multi_aff *
5906 isl_pw_multi_aff_insert_domain(
5907 __isl_take isl_pw_multi_aff *pma,
5908 __isl_take isl_space *domain);
5909 __isl_give isl_multi_pw_aff *
5910 isl_multi_pw_aff_insert_domain(
5911 __isl_take isl_multi_pw_aff *mpa,
5912 __isl_take isl_space *domain);
5913 __isl_give isl_aff *isl_aff_from_range(
5914 __isl_take isl_aff *aff);
5915 __isl_give isl_multi_aff *isl_multi_aff_from_range(
5916 __isl_take isl_multi_aff *ma);
5917 __isl_give isl_pw_aff *isl_pw_aff_from_range(
5918 __isl_take isl_pw_aff *pwa);
5919 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
5920 __isl_take isl_multi_pw_aff *mpa);
5921 __isl_give isl_multi_union_pw_aff *
5922 isl_multi_union_pw_aff_from_range(
5923 __isl_take isl_multi_union_pw_aff *mupa);
5924 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
5925 __isl_take isl_set *set);
5926 __isl_give isl_union_pw_multi_aff *
5927 isl_union_pw_multi_aff_from_domain(
5928 __isl_take isl_union_set *uset);
5930 #include <isl/polynomial.h>
5931 __isl_give isl_pw_qpolynomial *
5932 isl_pw_qpolynomial_from_range(
5933 __isl_take isl_pw_qpolynomial *pwqp);
5934 __isl_give isl_pw_qpolynomial_fold *
5935 isl_pw_qpolynomial_fold_from_range(
5936 __isl_take isl_pw_qpolynomial_fold *pwf);
5940 #include <isl/set.h>
5941 __isl_give isl_basic_set *isl_basic_set_fix_si(
5942 __isl_take isl_basic_set *bset,
5943 enum isl_dim_type type, unsigned pos, int value);
5944 __isl_give isl_basic_set *isl_basic_set_fix_val(
5945 __isl_take isl_basic_set *bset,
5946 enum isl_dim_type type, unsigned pos,
5947 __isl_take isl_val *v);
5948 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
5949 enum isl_dim_type type, unsigned pos, int value);
5950 __isl_give isl_set *isl_set_fix_val(
5951 __isl_take isl_set *set,
5952 enum isl_dim_type type, unsigned pos,
5953 __isl_take isl_val *v);
5955 #include <isl/map.h>
5956 __isl_give isl_basic_map *isl_basic_map_fix_si(
5957 __isl_take isl_basic_map *bmap,
5958 enum isl_dim_type type, unsigned pos, int value);
5959 __isl_give isl_basic_map *isl_basic_map_fix_val(
5960 __isl_take isl_basic_map *bmap,
5961 enum isl_dim_type type, unsigned pos,
5962 __isl_take isl_val *v);
5963 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
5964 enum isl_dim_type type, unsigned pos, int value);
5965 __isl_give isl_map *isl_map_fix_val(
5966 __isl_take isl_map *map,
5967 enum isl_dim_type type, unsigned pos,
5968 __isl_take isl_val *v);
5970 #include <isl/aff.h>
5971 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
5972 __isl_take isl_pw_multi_aff *pma,
5973 enum isl_dim_type type, unsigned pos, int value);
5975 #include <isl/polynomial.h>
5976 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
5977 __isl_take isl_pw_qpolynomial *pwqp,
5978 enum isl_dim_type type, unsigned n,
5979 __isl_take isl_val *v);
5980 __isl_give isl_pw_qpolynomial_fold *
5981 isl_pw_qpolynomial_fold_fix_val(
5982 __isl_take isl_pw_qpolynomial_fold *pwf,
5983 enum isl_dim_type type, unsigned n,
5984 __isl_take isl_val *v);
5986 Intersect the set, relation or function domain
5987 with the hyperplane where the given
5988 dimension has the fixed given value.
5990 #include <isl/set.h>
5991 __isl_give isl_basic_set *
5992 isl_basic_set_lower_bound_val(
5993 __isl_take isl_basic_set *bset,
5994 enum isl_dim_type type, unsigned pos,
5995 __isl_take isl_val *value);
5996 __isl_give isl_basic_set *
5997 isl_basic_set_upper_bound_val(
5998 __isl_take isl_basic_set *bset,
5999 enum isl_dim_type type, unsigned pos,
6000 __isl_take isl_val *value);
6001 __isl_give isl_set *isl_set_lower_bound_si(
6002 __isl_take isl_set *set,
6003 enum isl_dim_type type, unsigned pos, int value);
6004 __isl_give isl_set *isl_set_lower_bound_val(
6005 __isl_take isl_set *set,
6006 enum isl_dim_type type, unsigned pos,
6007 __isl_take isl_val *value);
6008 __isl_give isl_set *isl_set_upper_bound_si(
6009 __isl_take isl_set *set,
6010 enum isl_dim_type type, unsigned pos, int value);
6011 __isl_give isl_set *isl_set_upper_bound_val(
6012 __isl_take isl_set *set,
6013 enum isl_dim_type type, unsigned pos,
6014 __isl_take isl_val *value);
6015 __isl_give isl_set *isl_set_lower_bound_multi_val(
6016 __isl_take isl_set *set,
6017 __isl_take isl_multi_val *lower);
6018 __isl_give isl_set *isl_set_upper_bound_multi_val(
6019 __isl_take isl_set *set,
6020 __isl_take isl_multi_val *upper);
6021 __isl_give isl_set *isl_set_lower_bound_multi_pw_aff(
6022 __isl_take isl_set *set,
6023 __isl_take isl_multi_pw_aff *lower);
6024 __isl_give isl_set *isl_set_upper_bound_multi_pw_aff(
6025 __isl_take isl_set *set,
6026 __isl_take isl_multi_pw_aff *upper);
6028 #include <isl/map.h>
6029 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
6030 __isl_take isl_basic_map *bmap,
6031 enum isl_dim_type type, unsigned pos, int value);
6032 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
6033 __isl_take isl_basic_map *bmap,
6034 enum isl_dim_type type, unsigned pos, int value);
6035 __isl_give isl_map *isl_map_lower_bound_si(
6036 __isl_take isl_map *map,
6037 enum isl_dim_type type, unsigned pos, int value);
6038 __isl_give isl_map *isl_map_upper_bound_si(
6039 __isl_take isl_map *map,
6040 enum isl_dim_type type, unsigned pos, int value);
6041 __isl_give isl_map *isl_map_lower_bound_val(
6042 __isl_take isl_map *map,
6043 enum isl_dim_type type, unsigned pos,
6044 __isl_take isl_val *value);
6045 __isl_give isl_map *isl_map_upper_bound_val(
6046 __isl_take isl_map *map,
6047 enum isl_dim_type type, unsigned pos,
6048 __isl_take isl_val *value);
6049 __isl_give isl_map *isl_map_lower_bound_multi_pw_aff(
6050 __isl_take isl_map *map,
6051 __isl_take isl_multi_pw_aff *lower);
6052 __isl_give isl_map *isl_map_upper_bound_multi_pw_aff(
6053 __isl_take isl_map *map,
6054 __isl_take isl_multi_pw_aff *upper);
6056 Intersect the set or relation with the half-space where the given
6057 dimension has a value bounded by the given fixed integer value or
6058 symbolic constant expression.
6059 For functions taking a multi expression,
6060 this applies to all set dimensions.
6061 Those that bound a map, bound the range of that map.
6062 If the multi expression is zero-dimensional but has an explicit domain,
6063 then the (parameter) domain of the set or map is intersected
6064 with this explicit domain.
6066 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
6067 enum isl_dim_type type1, int pos1,
6068 enum isl_dim_type type2, int pos2);
6069 __isl_give isl_basic_map *isl_basic_map_equate(
6070 __isl_take isl_basic_map *bmap,
6071 enum isl_dim_type type1, int pos1,
6072 enum isl_dim_type type2, int pos2);
6073 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
6074 enum isl_dim_type type1, int pos1,
6075 enum isl_dim_type type2, int pos2);
6077 Intersect the set or relation with the hyperplane where the given
6078 dimensions are equal to each other.
6080 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
6081 enum isl_dim_type type1, int pos1,
6082 enum isl_dim_type type2, int pos2);
6084 Intersect the relation with the hyperplane where the given
6085 dimensions have opposite values.
6087 __isl_give isl_map *isl_map_order_le(
6088 __isl_take isl_map *map,
6089 enum isl_dim_type type1, int pos1,
6090 enum isl_dim_type type2, int pos2);
6091 __isl_give isl_basic_map *isl_basic_map_order_ge(
6092 __isl_take isl_basic_map *bmap,
6093 enum isl_dim_type type1, int pos1,
6094 enum isl_dim_type type2, int pos2);
6095 __isl_give isl_map *isl_map_order_ge(
6096 __isl_take isl_map *map,
6097 enum isl_dim_type type1, int pos1,
6098 enum isl_dim_type type2, int pos2);
6099 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
6100 enum isl_dim_type type1, int pos1,
6101 enum isl_dim_type type2, int pos2);
6102 __isl_give isl_basic_map *isl_basic_map_order_gt(
6103 __isl_take isl_basic_map *bmap,
6104 enum isl_dim_type type1, int pos1,
6105 enum isl_dim_type type2, int pos2);
6106 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
6107 enum isl_dim_type type1, int pos1,
6108 enum isl_dim_type type2, int pos2);
6110 Intersect the relation with the half-space where the given
6111 dimensions satisfy the given ordering.
6113 #include <isl/union_set.h>
6114 __isl_give isl_union_map *isl_union_map_remove_map_if(
6115 __isl_take isl_union_map *umap,
6116 isl_bool (*fn)(__isl_keep isl_map *map,
6117 void *user), void *user);
6119 This function calls the callback function once for each
6120 pair of spaces for which there are elements in the input.
6121 If the callback returns C<isl_bool_true>, then all those elements
6122 are removed from the result. The only remaining elements in the output
6123 are then those for which the callback returns C<isl_bool_false>.
6127 #include <isl/aff.h>
6128 __isl_give isl_basic_set *isl_aff_zero_basic_set(
6129 __isl_take isl_aff *aff);
6130 __isl_give isl_basic_set *isl_aff_neg_basic_set(
6131 __isl_take isl_aff *aff);
6132 __isl_give isl_set *isl_pw_aff_pos_set(
6133 __isl_take isl_pw_aff *pa);
6134 __isl_give isl_set *isl_pw_aff_nonneg_set(
6135 __isl_take isl_pw_aff *pwaff);
6136 __isl_give isl_set *isl_pw_aff_zero_set(
6137 __isl_take isl_pw_aff *pwaff);
6138 __isl_give isl_set *isl_pw_aff_non_zero_set(
6139 __isl_take isl_pw_aff *pwaff);
6140 __isl_give isl_union_set *
6141 isl_union_pw_aff_zero_union_set(
6142 __isl_take isl_union_pw_aff *upa);
6143 __isl_give isl_union_set *
6144 isl_multi_union_pw_aff_zero_union_set(
6145 __isl_take isl_multi_union_pw_aff *mupa);
6147 The function C<isl_aff_neg_basic_set> returns a basic set
6148 containing those elements in the domain space
6149 of C<aff> where C<aff> is negative.
6150 The function C<isl_pw_aff_nonneg_set> returns a set
6151 containing those elements in the domain
6152 of C<pwaff> where C<pwaff> is non-negative.
6153 The function C<isl_multi_union_pw_aff_zero_union_set>
6154 returns a union set containing those elements
6155 in the domains of its elements where they are all zero.
6159 __isl_give isl_map *isl_set_identity(
6160 __isl_take isl_set *set);
6161 __isl_give isl_union_map *isl_union_set_identity(
6162 __isl_take isl_union_set *uset);
6163 __isl_give isl_union_pw_multi_aff *
6164 isl_union_set_identity_union_pw_multi_aff(
6165 __isl_take isl_union_set *uset);
6167 Construct an identity relation on the given (union) set.
6169 =item * Function Extraction
6171 A piecewise quasi affine expression that is equal to 1 on a set
6172 and 0 outside the set can be created using the following function.
6174 #include <isl/aff.h>
6175 __isl_give isl_pw_aff *isl_set_indicator_function(
6176 __isl_take isl_set *set);
6178 A piecewise multiple quasi affine expression can be extracted
6179 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
6180 and the C<isl_map> is single-valued.
6181 In case of a conversion from an C<isl_union_map>
6182 to an C<isl_union_pw_multi_aff>, these properties need to hold
6183 in each domain space.
6184 A conversion to a C<isl_multi_union_pw_aff> additionally
6185 requires that the input is non-empty and involves only a single
6188 #include <isl/aff.h>
6189 __isl_give isl_pw_multi_aff *isl_set_as_pw_multi_aff(
6190 __isl_take isl_set *set);
6191 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
6192 __isl_take isl_set *set);
6193 __isl_give isl_pw_multi_aff *isl_map_as_pw_multi_aff(
6194 __isl_take isl_map *map);
6195 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
6196 __isl_take isl_map *map);
6198 __isl_give isl_union_pw_multi_aff *
6199 isl_union_pw_multi_aff_from_union_set(
6200 __isl_take isl_union_set *uset);
6201 __isl_give isl_union_pw_multi_aff *
6202 isl_union_map_as_union_pw_multi_aff(
6203 __isl_take isl_union_map *umap);
6204 __isl_give isl_union_pw_multi_aff *
6205 isl_union_pw_multi_aff_from_union_map(
6206 __isl_take isl_union_map *umap);
6208 __isl_give isl_multi_union_pw_aff *
6209 isl_union_map_as_multi_union_pw_aff(
6210 __isl_take isl_union_map *umap);
6211 __isl_give isl_multi_union_pw_aff *
6212 isl_multi_union_pw_aff_from_union_map(
6213 __isl_take isl_union_map *umap);
6215 C<isl_map_as_pw_multi_aff> and C<isl_pw_multi_aff_from_map> perform
6217 Similarly for C<isl_set_as_pw_multi_aff> and
6218 C<isl_pw_multi_aff_from_set>,
6219 for C<isl_union_map_as_union_pw_multi_aff> and
6220 C<isl_union_pw_multi_aff_from_union_map> and
6221 for C<isl_union_map_as_multi_union_pw_aff> and
6222 C<isl_multi_union_pw_aff_from_union_map>.
6226 __isl_give isl_basic_set *isl_basic_map_deltas(
6227 __isl_take isl_basic_map *bmap);
6228 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
6229 __isl_give isl_union_set *isl_union_map_deltas(
6230 __isl_take isl_union_map *umap);
6232 These functions return a (basic) set containing the differences
6233 between image elements and corresponding domain elements in the input.
6235 __isl_give isl_basic_map *isl_basic_map_deltas_map(
6236 __isl_take isl_basic_map *bmap);
6237 __isl_give isl_map *isl_map_deltas_map(
6238 __isl_take isl_map *map);
6239 __isl_give isl_union_map *isl_union_map_deltas_map(
6240 __isl_take isl_union_map *umap);
6242 The functions above construct a (basic, regular or union) relation
6243 that maps (a wrapped version of) the input relation to its delta set.
6247 #include <isl/map.h>
6248 __isl_give isl_map *isl_set_translation(
6249 __isl_take isl_set *deltas);
6251 This function performs essentially the opposite operation
6252 of C<isl_map_deltas>. In particular, it returns pairs
6253 of elements in the same space that have a difference in C<deltas>.
6257 Simplify the representation of a set, relation or functions by trying
6258 to combine pairs of basic sets or relations into a single
6259 basic set or relation.
6261 #include <isl/set.h>
6262 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
6264 #include <isl/map.h>
6265 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
6267 #include <isl/union_set.h>
6268 __isl_give isl_union_set *isl_union_set_coalesce(
6269 __isl_take isl_union_set *uset);
6271 #include <isl/union_map.h>
6272 __isl_give isl_union_map *isl_union_map_coalesce(
6273 __isl_take isl_union_map *umap);
6275 #include <isl/aff.h>
6276 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
6277 __isl_take isl_pw_aff *pa);
6278 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
6279 __isl_take isl_pw_multi_aff *pma);
6280 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
6281 __isl_take isl_multi_pw_aff *mpa);
6282 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
6283 __isl_take isl_union_pw_aff *upa);
6284 __isl_give isl_union_pw_multi_aff *
6285 isl_union_pw_multi_aff_coalesce(
6286 __isl_take isl_union_pw_multi_aff *upma);
6287 __isl_give isl_multi_union_pw_aff *
6288 isl_multi_union_pw_aff_coalesce(
6289 __isl_take isl_multi_union_pw_aff *mupa);
6291 #include <isl/polynomial.h>
6292 __isl_give isl_pw_qpolynomial_fold *
6293 isl_pw_qpolynomial_fold_coalesce(
6294 __isl_take isl_pw_qpolynomial_fold *pwf);
6295 __isl_give isl_union_pw_qpolynomial *
6296 isl_union_pw_qpolynomial_coalesce(
6297 __isl_take isl_union_pw_qpolynomial *upwqp);
6298 __isl_give isl_union_pw_qpolynomial_fold *
6299 isl_union_pw_qpolynomial_fold_coalesce(
6300 __isl_take isl_union_pw_qpolynomial_fold *upwf);
6302 One of the methods for combining pairs of basic sets or relations
6303 can result in coefficients that are much larger than those that appear
6304 in the constraints of the input. By default, the coefficients are
6305 not allowed to grow larger, but this can be changed by unsetting
6306 the following option.
6308 isl_stat isl_options_set_coalesce_bounded_wrapping(
6309 isl_ctx *ctx, int val);
6310 int isl_options_get_coalesce_bounded_wrapping(
6313 One of the other methods tries to combine pairs of basic sets
6314 with different local variables, treating them as existentially
6315 quantified variables even if they have known (but different)
6316 integer division expressions. The result may then also have
6317 existentially quantified variables. Turning on the following
6318 option prevents this from happening.
6320 isl_stat isl_options_set_coalesce_preserve_locals(
6321 isl_ctx *ctx, int val);
6322 int isl_options_get_coalesce_preserve_locals(isl_ctx *ctx);
6324 =item * Detecting equalities
6326 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
6327 __isl_take isl_basic_set *bset);
6328 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
6329 __isl_take isl_basic_map *bmap);
6330 __isl_give isl_set *isl_set_detect_equalities(
6331 __isl_take isl_set *set);
6332 __isl_give isl_map *isl_map_detect_equalities(
6333 __isl_take isl_map *map);
6334 __isl_give isl_union_set *isl_union_set_detect_equalities(
6335 __isl_take isl_union_set *uset);
6336 __isl_give isl_union_map *isl_union_map_detect_equalities(
6337 __isl_take isl_union_map *umap);
6339 Simplify the representation of a set or relation by detecting implicit
6342 =item * Removing redundant constraints
6344 #include <isl/set.h>
6345 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
6346 __isl_take isl_basic_set *bset);
6347 __isl_give isl_set *isl_set_remove_redundancies(
6348 __isl_take isl_set *set);
6350 #include <isl/union_set.h>
6351 __isl_give isl_union_set *
6352 isl_union_set_remove_redundancies(
6353 __isl_take isl_union_set *uset);
6355 #include <isl/map.h>
6356 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
6357 __isl_take isl_basic_map *bmap);
6358 __isl_give isl_map *isl_map_remove_redundancies(
6359 __isl_take isl_map *map);
6361 #include <isl/union_map.h>
6362 __isl_give isl_union_map *
6363 isl_union_map_remove_redundancies(
6364 __isl_take isl_union_map *umap);
6368 __isl_give isl_basic_set *isl_set_convex_hull(
6369 __isl_take isl_set *set);
6370 __isl_give isl_basic_map *isl_map_convex_hull(
6371 __isl_take isl_map *map);
6373 If the input set or relation has any existentially quantified
6374 variables, then the result of these operations is currently undefined.
6378 #include <isl/set.h>
6379 __isl_give isl_basic_set *
6380 isl_set_unshifted_simple_hull(
6381 __isl_take isl_set *set);
6382 __isl_give isl_basic_set *isl_set_simple_hull(
6383 __isl_take isl_set *set);
6384 __isl_give isl_basic_set *
6385 isl_set_plain_unshifted_simple_hull(
6386 __isl_take isl_set *set);
6387 __isl_give isl_basic_set *
6388 isl_set_unshifted_simple_hull_from_set_list(
6389 __isl_take isl_set *set,
6390 __isl_take isl_set_list *list);
6392 #include <isl/map.h>
6393 __isl_give isl_basic_map *
6394 isl_map_unshifted_simple_hull(
6395 __isl_take isl_map *map);
6396 __isl_give isl_basic_map *isl_map_simple_hull(
6397 __isl_take isl_map *map);
6398 __isl_give isl_basic_map *
6399 isl_map_plain_unshifted_simple_hull(
6400 __isl_take isl_map *map);
6401 __isl_give isl_basic_map *
6402 isl_map_unshifted_simple_hull_from_map_list(
6403 __isl_take isl_map *map,
6404 __isl_take isl_map_list *list);
6406 #include <isl/union_map.h>
6407 __isl_give isl_union_map *isl_union_map_simple_hull(
6408 __isl_take isl_union_map *umap);
6410 These functions compute a single basic set or relation
6411 that contains the whole input set or relation.
6412 In particular, the output is described by translates
6413 of the constraints describing the basic sets or relations in the input.
6414 In case of C<isl_set_unshifted_simple_hull>, only the original
6415 constraints are used, without any translation.
6416 In case of C<isl_set_plain_unshifted_simple_hull> and
6417 C<isl_map_plain_unshifted_simple_hull>, the result is described
6418 by original constraints that are obviously satisfied
6419 by the entire input set or relation.
6420 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
6421 C<isl_map_unshifted_simple_hull_from_map_list>, the
6422 constraints are taken from the elements of the second argument.
6426 (See \autoref{s:simple hull}.)
6432 __isl_give isl_basic_set *isl_basic_set_affine_hull(
6433 __isl_take isl_basic_set *bset);
6434 __isl_give isl_basic_set *isl_set_affine_hull(
6435 __isl_take isl_set *set);
6436 __isl_give isl_union_set *isl_union_set_affine_hull(
6437 __isl_take isl_union_set *uset);
6438 __isl_give isl_basic_map *isl_basic_map_affine_hull(
6439 __isl_take isl_basic_map *bmap);
6440 __isl_give isl_basic_map *isl_map_affine_hull(
6441 __isl_take isl_map *map);
6442 __isl_give isl_union_map *isl_union_map_affine_hull(
6443 __isl_take isl_union_map *umap);
6445 In case of union sets and relations, the affine hull is computed
6448 =item * Polyhedral hull
6450 __isl_give isl_basic_set *isl_set_polyhedral_hull(
6451 __isl_take isl_set *set);
6452 __isl_give isl_basic_map *isl_map_polyhedral_hull(
6453 __isl_take isl_map *map);
6454 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
6455 __isl_take isl_union_set *uset);
6456 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
6457 __isl_take isl_union_map *umap);
6459 These functions compute a single basic set or relation
6460 not involving any existentially quantified variables
6461 that contains the whole input set or relation.
6462 In case of union sets and relations, the polyhedral hull is computed
6467 #include <isl/set.h>
6468 __isl_give isl_fixed_box *
6469 isl_set_get_simple_fixed_box_hull(
6470 __isl_keep isl_set *set)
6472 #include <isl/map.h>
6473 __isl_give isl_fixed_box *
6474 isl_map_get_range_simple_fixed_box_hull(
6475 __isl_keep isl_map *map);
6477 These functions try to approximate the set or
6478 the range of the map by a box of fixed size.
6479 The box is described in terms of an offset living in the same space as
6480 the input and a size living in the set or range space. For any element
6481 in the input map, the range value is greater than or equal to
6482 the offset applied to the domain value and the difference with
6483 this offset is strictly smaller than the size.
6484 The same holds for the elements of the input set, where
6485 the offset is a parametric constant value.
6486 If no fixed-size approximation can be found,
6487 an I<invalid> box is returned, i.e., one for which
6488 C<isl_fixed_box_is_valid> below returns false.
6490 The validity, the offset and the size of the box can be obtained using
6491 the following functions.
6493 #include <isl/fixed_box.h>
6494 isl_bool isl_fixed_box_is_valid(
6495 __isl_keep isl_fixed_box *box);
6496 __isl_give isl_multi_aff *isl_fixed_box_get_offset(
6497 __isl_keep isl_fixed_box *box);
6498 __isl_give isl_multi_val *isl_fixed_box_get_size(
6499 __isl_keep isl_fixed_box *box);
6501 The box can be copied and freed using the following functions.
6503 #include <isl/fixed_box.h>
6504 __isl_give isl_fixed_box *isl_fixed_box_copy(
6505 __isl_keep isl_fixed_box *box);
6506 __isl_null isl_fixed_box *isl_fixed_box_free(
6507 __isl_take isl_fixed_box *box);
6509 An object of type C<isl_fixed_box> can be read from input
6510 using the following function.
6512 #include <isl/fixed_box.h>
6513 __isl_give isl_fixed_box *
6514 isl_fixed_box_read_from_str(isl_ctx *ctx,
6517 A representation of the information contained in an object
6518 of type C<isl_fixed_box> can be obtained using
6520 #include <isl/fixed_box.h>
6521 __isl_give isl_printer *isl_printer_print_fixed_box(
6522 __isl_take isl_printer *p,
6523 __isl_keep isl_fixed_box *box);
6524 __isl_give char *isl_fixed_box_to_str(
6525 __isl_keep isl_fixed_box *box);
6527 C<isl_fixed_box_to_str> prints the information in flow format.
6529 =item * Other approximations
6531 #include <isl/set.h>
6532 __isl_give isl_basic_set *
6533 isl_basic_set_drop_constraints_involving_dims(
6534 __isl_take isl_basic_set *bset,
6535 enum isl_dim_type type,
6536 unsigned first, unsigned n);
6537 __isl_give isl_basic_set *
6538 isl_basic_set_drop_constraints_not_involving_dims(
6539 __isl_take isl_basic_set *bset,
6540 enum isl_dim_type type,
6541 unsigned first, unsigned n);
6542 __isl_give isl_set *
6543 isl_set_drop_constraints_involving_dims(
6544 __isl_take isl_set *set,
6545 enum isl_dim_type type,
6546 unsigned first, unsigned n);
6547 __isl_give isl_set *
6548 isl_set_drop_constraints_not_involving_dims(
6549 __isl_take isl_set *set,
6550 enum isl_dim_type type,
6551 unsigned first, unsigned n);
6553 #include <isl/map.h>
6554 __isl_give isl_basic_map *
6555 isl_basic_map_drop_constraints_involving_dims(
6556 __isl_take isl_basic_map *bmap,
6557 enum isl_dim_type type,
6558 unsigned first, unsigned n);
6559 __isl_give isl_basic_map *
6560 isl_basic_map_drop_constraints_not_involving_dims(
6561 __isl_take isl_basic_map *bmap,
6562 enum isl_dim_type type,
6563 unsigned first, unsigned n);
6564 __isl_give isl_map *
6565 isl_map_drop_constraints_involving_dims(
6566 __isl_take isl_map *map,
6567 enum isl_dim_type type,
6568 unsigned first, unsigned n);
6569 __isl_give isl_map *
6570 isl_map_drop_constraints_not_involving_dims(
6571 __isl_take isl_map *map,
6572 enum isl_dim_type type,
6573 unsigned first, unsigned n);
6575 These functions drop any constraints (not) involving the specified dimensions.
6576 Note that the result depends on the representation of the input.
6578 #include <isl/polynomial.h>
6579 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
6580 __isl_take isl_pw_qpolynomial *pwqp, int sign);
6581 __isl_give isl_union_pw_qpolynomial *
6582 isl_union_pw_qpolynomial_to_polynomial(
6583 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
6585 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
6586 the polynomial will be an overapproximation. If C<sign> is negative,
6587 it will be an underapproximation. If C<sign> is zero, the approximation
6588 will lie somewhere in between.
6592 __isl_give isl_basic_set *isl_basic_set_sample(
6593 __isl_take isl_basic_set *bset);
6594 __isl_give isl_basic_set *isl_set_sample(
6595 __isl_take isl_set *set);
6596 __isl_give isl_basic_map *isl_basic_map_sample(
6597 __isl_take isl_basic_map *bmap);
6598 __isl_give isl_basic_map *isl_map_sample(
6599 __isl_take isl_map *map);
6601 If the input (basic) set or relation is non-empty, then return
6602 a singleton subset of the input. Otherwise, return an empty set.
6604 =item * Optimization
6606 #include <isl/ilp.h>
6607 __isl_give isl_val *isl_basic_set_max_val(
6608 __isl_keep isl_basic_set *bset,
6609 __isl_keep isl_aff *obj);
6610 __isl_give isl_val *isl_set_min_val(
6611 __isl_keep isl_set *set,
6612 __isl_keep isl_aff *obj);
6613 __isl_give isl_val *isl_set_max_val(
6614 __isl_keep isl_set *set,
6615 __isl_keep isl_aff *obj);
6616 __isl_give isl_multi_val *
6617 isl_union_set_min_multi_union_pw_aff(
6618 __isl_keep isl_union_set *uset,
6619 __isl_keep isl_multi_union_pw_aff *obj);
6621 Compute the minimum or maximum of the integer affine expression C<obj>
6622 over the points in C<set>.
6623 The result is C<NULL> in case of an error, the optimal value in case
6624 there is one, negative infinity or infinity if the problem is unbounded and
6625 NaN if the problem is empty.
6627 #include <isl/ilp.h>
6628 __isl_give isl_val *isl_pw_aff_min_val(
6629 __isl_take isl_pw_aff *pa);
6630 __isl_give isl_val *isl_pw_aff_max_val(
6631 __isl_take isl_pw_aff *pa);
6632 __isl_give isl_multi_val *
6633 isl_pw_multi_aff_min_multi_val(
6634 __isl_take isl_pw_multi_aff *pma);
6635 __isl_give isl_multi_val *
6636 isl_pw_multi_aff_max_multi_val(
6637 __isl_take isl_pw_multi_aff *pma);
6638 __isl_give isl_multi_val *
6639 isl_multi_pw_aff_min_multi_val(
6640 __isl_take isl_multi_pw_aff *mpa);
6641 __isl_give isl_multi_val *
6642 isl_multi_pw_aff_max_multi_val(
6643 __isl_take isl_multi_pw_aff *mpa);
6644 __isl_give isl_val *isl_union_pw_aff_min_val(
6645 __isl_take isl_union_pw_aff *upa);
6646 __isl_give isl_val *isl_union_pw_aff_max_val(
6647 __isl_take isl_union_pw_aff *upa);
6648 __isl_give isl_multi_val *
6649 isl_multi_union_pw_aff_min_multi_val(
6650 __isl_take isl_multi_union_pw_aff *mupa);
6651 __isl_give isl_multi_val *
6652 isl_multi_union_pw_aff_max_multi_val(
6653 __isl_take isl_multi_union_pw_aff *mupa);
6655 Compute the minimum or maximum of the integer affine expression
6656 over its definition domain.
6657 The result is C<NULL> in case of an error, the optimal value in case
6658 there is one, negative infinity or infinity if the problem is unbounded and
6659 NaN if the problem is empty.
6661 #include <isl/ilp.h>
6662 __isl_give isl_val *isl_basic_set_dim_max_val(
6663 __isl_take isl_basic_set *bset, int pos);
6664 __isl_give isl_val *isl_set_dim_min_val(
6665 __isl_take isl_set *set, int pos);
6666 __isl_give isl_val *isl_set_dim_max_val(
6667 __isl_take isl_set *set, int pos);
6669 Return the minimal or maximal value attained by the given set dimension,
6670 independently of the parameter values and of any other dimensions.
6671 The result is C<NULL> in case of an error, the optimal value in case
6672 there is one, (negative) infinity if the problem is unbounded and
6673 NaN if the input is empty.
6675 =item * Parametric optimization
6677 __isl_give isl_pw_aff *isl_set_dim_min(
6678 __isl_take isl_set *set, int pos);
6679 __isl_give isl_pw_aff *isl_set_dim_max(
6680 __isl_take isl_set *set, int pos);
6681 __isl_give isl_pw_aff *isl_map_dim_min(
6682 __isl_take isl_map *map, int pos);
6683 __isl_give isl_pw_aff *isl_map_dim_max(
6684 __isl_take isl_map *map, int pos);
6685 __isl_give isl_multi_pw_aff *
6686 isl_set_min_multi_pw_aff(
6687 __isl_take isl_set *set);
6688 __isl_give isl_multi_pw_aff *
6689 isl_set_max_multi_pw_aff(
6690 __isl_take isl_set *set);
6691 __isl_give isl_multi_pw_aff *
6692 isl_map_min_multi_pw_aff(
6693 __isl_take isl_map *map);
6694 __isl_give isl_multi_pw_aff *
6695 isl_map_max_multi_pw_aff(
6696 __isl_take isl_map *map);
6698 Compute the minimum or maximum of the (given) set or output dimension(s)
6699 as a function of the parameters (and input dimensions), but independently
6700 of the other set or output dimensions.
6701 For lexicographic optimization, see L<"Lexicographic Optimization">.
6705 The following functions compute either the set of (rational) coefficient
6706 values of valid constraints for the given set or the set of (rational)
6707 values satisfying the constraints with coefficients from the given set.
6708 Internally, these two sets of functions perform essentially the
6709 same operations, except that the set of coefficients is assumed to
6710 be a cone, while the set of values may be any polyhedron.
6711 The current implementation is based on the Farkas lemma and
6712 Fourier-Motzkin elimination, but this may change or be made optional
6713 in future. In particular, future implementations may use different
6714 dualization algorithms or skip the elimination step.
6716 #include <isl/set.h>
6717 __isl_give isl_basic_set *isl_basic_set_coefficients(
6718 __isl_take isl_basic_set *bset);
6719 __isl_give isl_basic_set_list *
6720 isl_basic_set_list_coefficients(
6721 __isl_take isl_basic_set_list *list);
6722 __isl_give isl_basic_set *isl_set_coefficients(
6723 __isl_take isl_set *set);
6724 __isl_give isl_union_set *isl_union_set_coefficients(
6725 __isl_take isl_union_set *bset);
6726 __isl_give isl_basic_set *isl_basic_set_solutions(
6727 __isl_take isl_basic_set *bset);
6728 __isl_give isl_basic_set *isl_set_solutions(
6729 __isl_take isl_set *set);
6730 __isl_give isl_union_set *isl_union_set_solutions(
6731 __isl_take isl_union_set *bset);
6735 __isl_give isl_map *isl_map_fixed_power_val(
6736 __isl_take isl_map *map,
6737 __isl_take isl_val *exp);
6738 __isl_give isl_union_map *
6739 isl_union_map_fixed_power_val(
6740 __isl_take isl_union_map *umap,
6741 __isl_take isl_val *exp);
6743 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
6744 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
6745 of C<map> is computed.
6747 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
6749 __isl_give isl_union_map *isl_union_map_power(
6750 __isl_take isl_union_map *umap, isl_bool *exact);
6752 Compute a parametric representation for all positive powers I<k> of C<map>.
6753 The result maps I<k> to a nested relation corresponding to the
6754 I<k>th power of C<map>.
6755 The result may be an overapproximation. If the result is known to be exact,
6756 then C<*exact> is set to C<1>.
6758 =item * Transitive closure
6760 __isl_give isl_map *isl_map_transitive_closure(
6761 __isl_take isl_map *map, isl_bool *exact);
6762 __isl_give isl_union_map *isl_union_map_transitive_closure(
6763 __isl_take isl_union_map *umap, isl_bool *exact);
6765 Compute the transitive closure of C<map>.
6766 The result may be an overapproximation. If the result is known to be exact,
6767 then C<*exact> is set to C<1>.
6769 =item * Reaching path lengths
6771 __isl_give isl_map *isl_map_reaching_path_lengths(
6772 __isl_take isl_map *map, isl_bool *exact);
6774 Compute a relation that maps each element in the range of C<map>
6775 to the lengths of all paths composed of edges in C<map> that
6776 end up in the given element.
6777 The result may be an overapproximation. If the result is known to be exact,
6778 then C<*exact> is set to C<1>.
6779 To compute the I<maximal> path length, the resulting relation
6780 should be postprocessed by C<isl_map_lexmax>.
6781 In particular, if the input relation is a dependence relation
6782 (mapping sources to sinks), then the maximal path length corresponds
6783 to the free schedule.
6784 Note, however, that C<isl_map_lexmax> expects the maximum to be
6785 finite, so if the path lengths are unbounded (possibly due to
6786 the overapproximation), then you will get an error message.
6790 #include <isl/space.h>
6791 __isl_give isl_space *isl_space_wrap(
6792 __isl_take isl_space *space);
6793 __isl_give isl_space *isl_space_unwrap(
6794 __isl_take isl_space *space);
6796 #include <isl/local_space.h>
6797 __isl_give isl_local_space *isl_local_space_wrap(
6798 __isl_take isl_local_space *ls);
6800 #include <isl/set.h>
6801 __isl_give isl_basic_map *isl_basic_set_unwrap(
6802 __isl_take isl_basic_set *bset);
6803 __isl_give isl_map *isl_set_unwrap(
6804 __isl_take isl_set *set);
6806 #include <isl/map.h>
6807 __isl_give isl_basic_set *isl_basic_map_wrap(
6808 __isl_take isl_basic_map *bmap);
6809 __isl_give isl_set *isl_map_wrap(
6810 __isl_take isl_map *map);
6812 #include <isl/union_set.h>
6813 __isl_give isl_union_map *isl_union_set_unwrap(
6814 __isl_take isl_union_set *uset);
6816 #include <isl/union_map.h>
6817 __isl_give isl_union_set *isl_union_map_wrap(
6818 __isl_take isl_union_map *umap);
6820 The input to C<isl_space_unwrap> should
6821 be the space of a set, while that of
6822 C<isl_space_wrap> should be the space of a relation.
6823 Conversely, the output of C<isl_space_unwrap> is the space
6824 of a relation, while that of C<isl_space_wrap> is the space of a set.
6828 Remove any internal structure of domain (and range) of the given
6829 set or relation. If there is any such internal structure in the input,
6830 then the name of the space is also removed.
6832 #include <isl/space.h>
6833 __isl_give isl_space *isl_space_flatten_domain(
6834 __isl_take isl_space *space);
6835 __isl_give isl_space *isl_space_flatten_range(
6836 __isl_take isl_space *space);
6838 #include <isl/local_space.h>
6839 __isl_give isl_local_space *
6840 isl_local_space_flatten_domain(
6841 __isl_take isl_local_space *ls);
6842 __isl_give isl_local_space *
6843 isl_local_space_flatten_range(
6844 __isl_take isl_local_space *ls);
6846 #include <isl/set.h>
6847 __isl_give isl_basic_set *isl_basic_set_flatten(
6848 __isl_take isl_basic_set *bset);
6849 __isl_give isl_set *isl_set_flatten(
6850 __isl_take isl_set *set);
6852 #include <isl/map.h>
6853 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
6854 __isl_take isl_basic_map *bmap);
6855 __isl_give isl_basic_map *isl_basic_map_flatten_range(
6856 __isl_take isl_basic_map *bmap);
6857 __isl_give isl_map *isl_map_flatten_range(
6858 __isl_take isl_map *map);
6859 __isl_give isl_map *isl_map_flatten_domain(
6860 __isl_take isl_map *map);
6861 __isl_give isl_basic_map *isl_basic_map_flatten(
6862 __isl_take isl_basic_map *bmap);
6863 __isl_give isl_map *isl_map_flatten(
6864 __isl_take isl_map *map);
6867 __isl_give isl_multi_id *isl_multi_id_flatten_range(
6868 __isl_take isl_multi_id *mi);
6870 #include <isl/val.h>
6871 __isl_give isl_multi_val *isl_multi_val_flatten_range(
6872 __isl_take isl_multi_val *mv);
6874 #include <isl/aff.h>
6875 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
6876 __isl_take isl_multi_aff *ma);
6877 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
6878 __isl_take isl_multi_aff *ma);
6879 __isl_give isl_multi_pw_aff *
6880 isl_multi_pw_aff_flatten_range(
6881 __isl_take isl_multi_pw_aff *mpa);
6882 __isl_give isl_multi_union_pw_aff *
6883 isl_multi_union_pw_aff_flatten_range(
6884 __isl_take isl_multi_union_pw_aff *mupa);
6886 #include <isl/map.h>
6887 __isl_give isl_map *isl_set_flatten_map(
6888 __isl_take isl_set *set);
6890 The function above constructs a relation
6891 that maps the input set to a flattened version of the set.
6895 Lift the input set to a space with extra dimensions corresponding
6896 to the existentially quantified variables in the input.
6897 In particular, the result lives in a wrapped map where the domain
6898 is the original space and the range corresponds to the original
6899 existentially quantified variables.
6901 #include <isl/set.h>
6902 __isl_give isl_basic_set *isl_basic_set_lift(
6903 __isl_take isl_basic_set *bset);
6904 __isl_give isl_set *isl_set_lift(
6905 __isl_take isl_set *set);
6906 __isl_give isl_union_set *isl_union_set_lift(
6907 __isl_take isl_union_set *uset);
6909 Given a local space that contains the existentially quantified
6910 variables of a set, a basic relation that, when applied to
6911 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
6912 can be constructed using the following function.
6914 #include <isl/local_space.h>
6915 __isl_give isl_basic_map *isl_local_space_lifting(
6916 __isl_take isl_local_space *ls);
6918 #include <isl/aff.h>
6919 __isl_give isl_multi_aff *isl_multi_aff_lift(
6920 __isl_take isl_multi_aff *maff,
6921 __isl_give isl_local_space **ls);
6923 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
6924 then it is assigned the local space that lies at the basis of
6925 the lifting applied.
6927 =item * Internal Product
6929 #include <isl/space.h>
6930 __isl_give isl_space *isl_space_zip(
6931 __isl_take isl_space *space);
6933 #include <isl/map.h>
6934 __isl_give isl_basic_map *isl_basic_map_zip(
6935 __isl_take isl_basic_map *bmap);
6936 __isl_give isl_map *isl_map_zip(
6937 __isl_take isl_map *map);
6939 #include <isl/union_map.h>
6940 __isl_give isl_union_map *isl_union_map_zip(
6941 __isl_take isl_union_map *umap);
6943 Given a relation with nested relations for domain and range,
6944 interchange the range of the domain with the domain of the range.
6948 #include <isl/space.h>
6949 __isl_give isl_space *isl_space_curry(
6950 __isl_take isl_space *space);
6951 __isl_give isl_space *isl_space_uncurry(
6952 __isl_take isl_space *space);
6954 #include <isl/map.h>
6955 __isl_give isl_basic_map *isl_basic_map_curry(
6956 __isl_take isl_basic_map *bmap);
6957 __isl_give isl_basic_map *isl_basic_map_uncurry(
6958 __isl_take isl_basic_map *bmap);
6959 __isl_give isl_map *isl_map_curry(
6960 __isl_take isl_map *map);
6961 __isl_give isl_map *isl_map_uncurry(
6962 __isl_take isl_map *map);
6964 #include <isl/union_map.h>
6965 __isl_give isl_union_map *isl_union_map_curry(
6966 __isl_take isl_union_map *umap);
6967 __isl_give isl_union_map *isl_union_map_uncurry(
6968 __isl_take isl_union_map *umap);
6970 Given a relation with a nested relation for domain,
6971 the C<curry> functions
6972 move the range of the nested relation out of the domain
6973 and use it as the domain of a nested relation in the range,
6974 with the original range as range of this nested relation.
6975 The C<uncurry> functions perform the inverse operation.
6977 #include <isl/space.h>
6978 __isl_give isl_space *isl_space_range_curry(
6979 __isl_take isl_space *space);
6981 #include <isl/map.h>
6982 __isl_give isl_map *isl_map_range_curry(
6983 __isl_take isl_map *map);
6985 #include <isl/union_map.h>
6986 __isl_give isl_union_map *isl_union_map_range_curry(
6987 __isl_take isl_union_map *umap);
6989 These functions apply the currying to the relation that
6990 is nested inside the range of the input.
6992 =item * Aligning parameters
6994 Change the order of the parameters of the given set, relation
6996 such that the first parameters match those of C<model>.
6997 This may involve the introduction of extra parameters.
6998 All parameters need to be named.
7000 #include <isl/space.h>
7001 __isl_give isl_space *isl_space_align_params(
7002 __isl_take isl_space *space1,
7003 __isl_take isl_space *space2)
7005 #include <isl/set.h>
7006 __isl_give isl_basic_set *isl_basic_set_align_params(
7007 __isl_take isl_basic_set *bset,
7008 __isl_take isl_space *model);
7009 __isl_give isl_set *isl_set_align_params(
7010 __isl_take isl_set *set,
7011 __isl_take isl_space *model);
7013 #include <isl/map.h>
7014 __isl_give isl_basic_map *isl_basic_map_align_params(
7015 __isl_take isl_basic_map *bmap,
7016 __isl_take isl_space *model);
7017 __isl_give isl_map *isl_map_align_params(
7018 __isl_take isl_map *map,
7019 __isl_take isl_space *model);
7022 __isl_give isl_multi_id *isl_multi_id_align_params(
7023 __isl_take isl_multi_id *mi,
7024 __isl_take isl_space *model);
7026 #include <isl/val.h>
7027 __isl_give isl_multi_val *isl_multi_val_align_params(
7028 __isl_take isl_multi_val *mv,
7029 __isl_take isl_space *model);
7031 #include <isl/aff.h>
7032 __isl_give isl_aff *isl_aff_align_params(
7033 __isl_take isl_aff *aff,
7034 __isl_take isl_space *model);
7035 __isl_give isl_multi_aff *isl_multi_aff_align_params(
7036 __isl_take isl_multi_aff *multi,
7037 __isl_take isl_space *model);
7038 __isl_give isl_pw_aff *isl_pw_aff_align_params(
7039 __isl_take isl_pw_aff *pwaff,
7040 __isl_take isl_space *model);
7041 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
7042 __isl_take isl_pw_multi_aff *pma,
7043 __isl_take isl_space *model);
7044 __isl_give isl_union_pw_aff *
7045 isl_union_pw_aff_align_params(
7046 __isl_take isl_union_pw_aff *upa,
7047 __isl_take isl_space *model);
7048 __isl_give isl_union_pw_multi_aff *
7049 isl_union_pw_multi_aff_align_params(
7050 __isl_take isl_union_pw_multi_aff *upma,
7051 __isl_take isl_space *model);
7052 __isl_give isl_multi_union_pw_aff *
7053 isl_multi_union_pw_aff_align_params(
7054 __isl_take isl_multi_union_pw_aff *mupa,
7055 __isl_take isl_space *model);
7057 #include <isl/polynomial.h>
7058 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
7059 __isl_take isl_qpolynomial *qp,
7060 __isl_take isl_space *model);
7062 =item * Drop unused parameters
7064 Drop parameters that are not referenced by the isl object.
7065 All parameters need to be named.
7067 #include <isl/set.h>
7068 __isl_give isl_basic_set *
7069 isl_basic_set_drop_unused_params(
7070 __isl_take isl_basic_set *bset);
7071 __isl_give isl_set *isl_set_drop_unused_params(
7072 __isl_take isl_set *set);
7074 #include <isl/map.h>
7075 __isl_give isl_basic_map *
7076 isl_basic_map_drop_unused_params(
7077 __isl_take isl_basic_map *bmap);
7078 __isl_give isl_map *isl_map_drop_unused_params(
7079 __isl_take isl_map *map);
7081 #include <isl/union_set.h>
7082 __isl_give isl_union_set *
7083 isl_union_set_drop_unused_params(
7084 __isl_take isl_union_set *uset);
7086 #include <isl/union_map.h>
7087 __isl_give isl_union_map *
7088 isl_union_map_drop_unused_params(
7089 __isl_take isl_union_map *umap);
7091 #include <isl/aff.h>
7092 __isl_give isl_pw_aff *isl_pw_aff_drop_unused_params(
7093 __isl_take isl_pw_aff *pa);
7094 __isl_give isl_pw_multi_aff *
7095 isl_pw_multi_aff_drop_unused_params(
7096 __isl_take isl_pw_multi_aff *pma);
7097 __isl_give isl_union_pw_aff *
7098 isl_union_pw_aff_drop_unused_params(
7099 __isl_take isl_union_pw_aff *upa);
7100 __isl_give isl_union_pw_multi_aff *
7101 isl_union_pw_multi_aff_drop_unused_params(
7102 __isl_take isl_union_pw_multi_aff *upma);
7104 #include <isl/polynomial.h>
7105 __isl_give isl_pw_qpolynomial *
7106 isl_pw_qpolynomial_drop_unused_params(
7107 __isl_take isl_pw_qpolynomial *pwqp);
7108 __isl_give isl_pw_qpolynomial_fold *
7109 isl_pw_qpolynomial_fold_drop_unused_params(
7110 __isl_take isl_pw_qpolynomial_fold *pwf);
7111 __isl_give isl_union_pw_qpolynomial *
7112 isl_union_pw_qpolynomial_drop_unused_params(
7113 __isl_take isl_union_pw_qpolynomial *upwqp);
7114 __isl_give isl_union_pw_qpolynomial_fold *
7115 isl_union_pw_qpolynomial_fold_drop_unused_params(
7116 __isl_take isl_union_pw_qpolynomial_fold *upwf);
7118 =item * Unary Arithmetic Operations
7120 #include <isl/set.h>
7121 __isl_give isl_set *isl_set_neg(
7122 __isl_take isl_set *set);
7123 #include <isl/map.h>
7124 __isl_give isl_map *isl_map_neg(
7125 __isl_take isl_map *map);
7127 C<isl_set_neg> constructs a set containing the opposites of
7128 the elements in its argument.
7129 The domain of the result of C<isl_map_neg> is the same
7130 as the domain of its argument. The corresponding range
7131 elements are the opposites of the corresponding range
7132 elements in the argument.
7134 #include <isl/val.h>
7135 __isl_give isl_multi_val *isl_multi_val_neg(
7136 __isl_take isl_multi_val *mv);
7138 #include <isl/aff.h>
7139 __isl_give isl_aff *isl_aff_neg(
7140 __isl_take isl_aff *aff);
7141 __isl_give isl_multi_aff *isl_multi_aff_neg(
7142 __isl_take isl_multi_aff *ma);
7143 __isl_give isl_pw_aff *isl_pw_aff_neg(
7144 __isl_take isl_pw_aff *pwaff);
7145 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
7146 __isl_take isl_pw_multi_aff *pma);
7147 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
7148 __isl_take isl_multi_pw_aff *mpa);
7149 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
7150 __isl_take isl_union_pw_aff *upa);
7151 __isl_give isl_union_pw_multi_aff *
7152 isl_union_pw_multi_aff_neg(
7153 __isl_take isl_union_pw_multi_aff *upma);
7154 __isl_give isl_multi_union_pw_aff *
7155 isl_multi_union_pw_aff_neg(
7156 __isl_take isl_multi_union_pw_aff *mupa);
7157 __isl_give isl_aff *isl_aff_ceil(
7158 __isl_take isl_aff *aff);
7159 __isl_give isl_pw_aff *isl_pw_aff_ceil(
7160 __isl_take isl_pw_aff *pwaff);
7161 __isl_give isl_aff *isl_aff_floor(
7162 __isl_take isl_aff *aff);
7163 __isl_give isl_multi_aff *isl_multi_aff_floor(
7164 __isl_take isl_multi_aff *ma);
7165 __isl_give isl_pw_aff *isl_pw_aff_floor(
7166 __isl_take isl_pw_aff *pwaff);
7167 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
7168 __isl_take isl_union_pw_aff *upa);
7169 __isl_give isl_multi_union_pw_aff *
7170 isl_multi_union_pw_aff_floor(
7171 __isl_take isl_multi_union_pw_aff *mupa);
7173 #include <isl/aff.h>
7174 __isl_give isl_pw_aff *isl_pw_aff_list_min(
7175 __isl_take isl_pw_aff_list *list);
7176 __isl_give isl_pw_aff *isl_pw_aff_list_max(
7177 __isl_take isl_pw_aff_list *list);
7179 #include <isl/polynomial.h>
7180 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
7181 __isl_take isl_qpolynomial *qp);
7182 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
7183 __isl_take isl_pw_qpolynomial *pwqp);
7184 __isl_give isl_union_pw_qpolynomial *
7185 isl_union_pw_qpolynomial_neg(
7186 __isl_take isl_union_pw_qpolynomial *upwqp);
7187 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
7188 __isl_take isl_qpolynomial *qp,
7190 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
7191 __isl_take isl_pw_qpolynomial *pwqp,
7196 The following functions evaluate a function in a point.
7198 #include <isl/aff.h>
7199 __isl_give isl_val *isl_aff_eval(
7200 __isl_take isl_aff *aff,
7201 __isl_take isl_point *pnt);
7202 __isl_give isl_val *isl_pw_aff_eval(
7203 __isl_take isl_pw_aff *pa,
7204 __isl_take isl_point *pnt);
7206 #include <isl/polynomial.h>
7207 __isl_give isl_val *isl_pw_qpolynomial_eval(
7208 __isl_take isl_pw_qpolynomial *pwqp,
7209 __isl_take isl_point *pnt);
7210 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
7211 __isl_take isl_pw_qpolynomial_fold *pwf,
7212 __isl_take isl_point *pnt);
7213 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
7214 __isl_take isl_union_pw_qpolynomial *upwqp,
7215 __isl_take isl_point *pnt);
7216 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
7217 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7218 __isl_take isl_point *pnt);
7220 These functions return NaN when evaluated at a void point.
7221 Note that C<isl_pw_aff_eval> returns NaN when the function is evaluated outside
7222 its definition domain, while C<isl_pw_qpolynomial_eval> returns zero
7223 when the function is evaluated outside its explicit domain.
7225 =item * Dimension manipulation
7227 It is usually not advisable to directly change the (input or output)
7228 space of a set or a relation as this removes the name and the internal
7229 structure of the space. However, the functions below can be useful
7230 to add new parameters, assuming
7231 C<isl_set_align_params> and C<isl_map_align_params>
7234 #include <isl/space.h>
7235 __isl_give isl_space *isl_space_add_dims(
7236 __isl_take isl_space *space,
7237 enum isl_dim_type type, unsigned n);
7238 __isl_give isl_space *isl_space_insert_dims(
7239 __isl_take isl_space *space,
7240 enum isl_dim_type type, unsigned pos, unsigned n);
7241 __isl_give isl_space *isl_space_drop_dims(
7242 __isl_take isl_space *space,
7243 enum isl_dim_type type, unsigned first, unsigned n);
7244 __isl_give isl_space *isl_space_move_dims(
7245 __isl_take isl_space *space,
7246 enum isl_dim_type dst_type, unsigned dst_pos,
7247 enum isl_dim_type src_type, unsigned src_pos,
7250 #include <isl/local_space.h>
7251 __isl_give isl_local_space *isl_local_space_add_dims(
7252 __isl_take isl_local_space *ls,
7253 enum isl_dim_type type, unsigned n);
7254 __isl_give isl_local_space *isl_local_space_insert_dims(
7255 __isl_take isl_local_space *ls,
7256 enum isl_dim_type type, unsigned first, unsigned n);
7257 __isl_give isl_local_space *isl_local_space_drop_dims(
7258 __isl_take isl_local_space *ls,
7259 enum isl_dim_type type, unsigned first, unsigned n);
7261 #include <isl/set.h>
7262 __isl_give isl_basic_set *isl_basic_set_add_dims(
7263 __isl_take isl_basic_set *bset,
7264 enum isl_dim_type type, unsigned n);
7265 __isl_give isl_set *isl_set_add_dims(
7266 __isl_take isl_set *set,
7267 enum isl_dim_type type, unsigned n);
7268 __isl_give isl_basic_set *isl_basic_set_insert_dims(
7269 __isl_take isl_basic_set *bset,
7270 enum isl_dim_type type, unsigned pos,
7272 __isl_give isl_set *isl_set_insert_dims(
7273 __isl_take isl_set *set,
7274 enum isl_dim_type type, unsigned pos, unsigned n);
7275 __isl_give isl_basic_set *isl_basic_set_move_dims(
7276 __isl_take isl_basic_set *bset,
7277 enum isl_dim_type dst_type, unsigned dst_pos,
7278 enum isl_dim_type src_type, unsigned src_pos,
7280 __isl_give isl_set *isl_set_move_dims(
7281 __isl_take isl_set *set,
7282 enum isl_dim_type dst_type, unsigned dst_pos,
7283 enum isl_dim_type src_type, unsigned src_pos,
7286 #include <isl/map.h>
7287 __isl_give isl_basic_map *isl_basic_map_add_dims(
7288 __isl_take isl_basic_map *bmap,
7289 enum isl_dim_type type, unsigned n);
7290 __isl_give isl_map *isl_map_add_dims(
7291 __isl_take isl_map *map,
7292 enum isl_dim_type type, unsigned n);
7293 __isl_give isl_basic_map *isl_basic_map_insert_dims(
7294 __isl_take isl_basic_map *bmap,
7295 enum isl_dim_type type, unsigned pos,
7297 __isl_give isl_map *isl_map_insert_dims(
7298 __isl_take isl_map *map,
7299 enum isl_dim_type type, unsigned pos, unsigned n);
7300 __isl_give isl_basic_map *isl_basic_map_move_dims(
7301 __isl_take isl_basic_map *bmap,
7302 enum isl_dim_type dst_type, unsigned dst_pos,
7303 enum isl_dim_type src_type, unsigned src_pos,
7305 __isl_give isl_map *isl_map_move_dims(
7306 __isl_take isl_map *map,
7307 enum isl_dim_type dst_type, unsigned dst_pos,
7308 enum isl_dim_type src_type, unsigned src_pos,
7311 #include <isl/val.h>
7312 __isl_give isl_multi_val *isl_multi_val_insert_dims(
7313 __isl_take isl_multi_val *mv,
7314 enum isl_dim_type type, unsigned first, unsigned n);
7315 __isl_give isl_multi_val *isl_multi_val_add_dims(
7316 __isl_take isl_multi_val *mv,
7317 enum isl_dim_type type, unsigned n);
7318 __isl_give isl_multi_val *isl_multi_val_drop_dims(
7319 __isl_take isl_multi_val *mv,
7320 enum isl_dim_type type, unsigned first, unsigned n);
7322 #include <isl/aff.h>
7323 __isl_give isl_aff *isl_aff_insert_dims(
7324 __isl_take isl_aff *aff,
7325 enum isl_dim_type type, unsigned first, unsigned n);
7326 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
7327 __isl_take isl_multi_aff *ma,
7328 enum isl_dim_type type, unsigned first, unsigned n);
7329 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
7330 __isl_take isl_pw_aff *pwaff,
7331 enum isl_dim_type type, unsigned first, unsigned n);
7332 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
7333 __isl_take isl_multi_pw_aff *mpa,
7334 enum isl_dim_type type, unsigned first, unsigned n);
7335 __isl_give isl_aff *isl_aff_add_dims(
7336 __isl_take isl_aff *aff,
7337 enum isl_dim_type type, unsigned n);
7338 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
7339 __isl_take isl_multi_aff *ma,
7340 enum isl_dim_type type, unsigned n);
7341 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
7342 __isl_take isl_pw_aff *pwaff,
7343 enum isl_dim_type type, unsigned n);
7344 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
7345 __isl_take isl_multi_pw_aff *mpa,
7346 enum isl_dim_type type, unsigned n);
7347 __isl_give isl_aff *isl_aff_drop_dims(
7348 __isl_take isl_aff *aff,
7349 enum isl_dim_type type, unsigned first, unsigned n);
7350 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
7351 __isl_take isl_multi_aff *maff,
7352 enum isl_dim_type type, unsigned first, unsigned n);
7353 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
7354 __isl_take isl_pw_aff *pwaff,
7355 enum isl_dim_type type, unsigned first, unsigned n);
7356 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
7357 __isl_take isl_pw_multi_aff *pma,
7358 enum isl_dim_type type, unsigned first, unsigned n);
7359 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
7360 __isl_take isl_union_pw_aff *upa,
7361 enum isl_dim_type type, unsigned first, unsigned n);
7362 __isl_give isl_union_pw_multi_aff *
7363 isl_union_pw_multi_aff_drop_dims(
7364 __isl_take isl_union_pw_multi_aff *upma,
7365 enum isl_dim_type type,
7366 unsigned first, unsigned n);
7367 __isl_give isl_multi_union_pw_aff *
7368 isl_multi_union_pw_aff_drop_dims(
7369 __isl_take isl_multi_union_pw_aff *mupa,
7370 enum isl_dim_type type, unsigned first,
7372 __isl_give isl_aff *isl_aff_move_dims(
7373 __isl_take isl_aff *aff,
7374 enum isl_dim_type dst_type, unsigned dst_pos,
7375 enum isl_dim_type src_type, unsigned src_pos,
7377 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
7378 __isl_take isl_multi_aff *ma,
7379 enum isl_dim_type dst_type, unsigned dst_pos,
7380 enum isl_dim_type src_type, unsigned src_pos,
7382 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
7383 __isl_take isl_pw_aff *pa,
7384 enum isl_dim_type dst_type, unsigned dst_pos,
7385 enum isl_dim_type src_type, unsigned src_pos,
7387 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
7388 __isl_take isl_multi_pw_aff *pma,
7389 enum isl_dim_type dst_type, unsigned dst_pos,
7390 enum isl_dim_type src_type, unsigned src_pos,
7393 #include <isl/polynomial.h>
7394 __isl_give isl_union_pw_qpolynomial *
7395 isl_union_pw_qpolynomial_drop_dims(
7396 __isl_take isl_union_pw_qpolynomial *upwqp,
7397 enum isl_dim_type type,
7398 unsigned first, unsigned n);
7399 __isl_give isl_union_pw_qpolynomial_fold *
7400 isl_union_pw_qpolynomial_fold_drop_dims(
7401 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7402 enum isl_dim_type type,
7403 unsigned first, unsigned n);
7405 The operations on union expressions can only manipulate parameters.
7409 =head2 Binary Operations
7411 The two arguments of a binary operation not only need to live
7412 in the same C<isl_ctx>, they currently also need to have
7413 the same (number of) parameters.
7415 =head3 Basic Operations
7419 =item * Intersection
7421 #include <isl/local_space.h>
7422 __isl_give isl_local_space *isl_local_space_intersect(
7423 __isl_take isl_local_space *ls1,
7424 __isl_take isl_local_space *ls2);
7426 #include <isl/set.h>
7427 __isl_give isl_basic_set *isl_basic_set_intersect_params(
7428 __isl_take isl_basic_set *bset1,
7429 __isl_take isl_basic_set *bset2);
7430 __isl_give isl_basic_set *isl_basic_set_intersect(
7431 __isl_take isl_basic_set *bset1,
7432 __isl_take isl_basic_set *bset2);
7433 __isl_give isl_basic_set *isl_basic_set_list_intersect(
7434 __isl_take struct isl_basic_set_list *list);
7435 __isl_give isl_set *isl_set_intersect_params(
7436 __isl_take isl_set *set,
7437 __isl_take isl_set *params);
7438 __isl_give isl_set *isl_set_intersect(
7439 __isl_take isl_set *set1,
7440 __isl_take isl_set *set2);
7441 __isl_give isl_set *isl_set_intersect_factor_domain(
7442 __isl_take isl_set *set,
7443 __isl_take isl_set *domain);
7444 __isl_give isl_set *isl_set_intersect_factor_range(
7445 __isl_take isl_set *set,
7446 __isl_take isl_set *range);
7448 #include <isl/map.h>
7449 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
7450 __isl_take isl_basic_map *bmap,
7451 __isl_take isl_basic_set *bset);
7452 __isl_give isl_basic_map *isl_basic_map_intersect_range(
7453 __isl_take isl_basic_map *bmap,
7454 __isl_take isl_basic_set *bset);
7455 __isl_give isl_basic_map *isl_basic_map_intersect(
7456 __isl_take isl_basic_map *bmap1,
7457 __isl_take isl_basic_map *bmap2);
7458 __isl_give isl_basic_map *isl_basic_map_list_intersect(
7459 __isl_take isl_basic_map_list *list);
7460 __isl_give isl_map *isl_map_intersect_params(
7461 __isl_take isl_map *map,
7462 __isl_take isl_set *params);
7463 __isl_give isl_map *isl_map_intersect_domain(
7464 __isl_take isl_map *map,
7465 __isl_take isl_set *set);
7466 __isl_give isl_map *isl_map_intersect_range(
7467 __isl_take isl_map *map,
7468 __isl_take isl_set *set);
7469 __isl_give isl_map *isl_map_intersect(
7470 __isl_take isl_map *map1,
7471 __isl_take isl_map *map2);
7472 __isl_give isl_map *
7473 isl_map_intersect_domain_factor_domain(
7474 __isl_take isl_map *map,
7475 __isl_take isl_map *factor);
7476 __isl_give isl_map *
7477 isl_map_intersect_domain_factor_range(
7478 __isl_take isl_map *map,
7479 __isl_take isl_map *factor);
7480 __isl_give isl_map *
7481 isl_map_intersect_range_factor_domain(
7482 __isl_take isl_map *map,
7483 __isl_take isl_map *factor);
7484 __isl_give isl_map *
7485 isl_map_intersect_range_factor_range(
7486 __isl_take isl_map *map,
7487 __isl_take isl_map *factor);
7488 __isl_give isl_map *
7489 isl_map_intersect_domain_wrapped_domain(
7490 __isl_take isl_map *map,
7491 __isl_take isl_set *domain);
7492 __isl_give isl_map *
7493 isl_map_intersect_range_wrapped_domain(
7494 __isl_take isl_map *map,
7495 __isl_take isl_set *domain);
7497 #include <isl/union_set.h>
7498 __isl_give isl_union_set *isl_union_set_intersect_params(
7499 __isl_take isl_union_set *uset,
7500 __isl_take isl_set *set);
7501 __isl_give isl_union_set *isl_union_set_intersect(
7502 __isl_take isl_union_set *uset1,
7503 __isl_take isl_union_set *uset2);
7505 #include <isl/union_map.h>
7506 __isl_give isl_union_map *isl_union_map_intersect_params(
7507 __isl_take isl_union_map *umap,
7508 __isl_take isl_set *set);
7509 __isl_give isl_union_map *
7510 isl_union_map_intersect_domain_union_set(
7511 __isl_take isl_union_map *umap,
7512 __isl_take isl_union_set *uset);
7513 __isl_give isl_union_map *
7514 isl_union_map_intersect_domain_space(
7515 __isl_take isl_union_map *umap,
7516 __isl_take isl_space *space);
7517 __isl_give isl_union_map *isl_union_map_intersect_domain(
7518 __isl_take isl_union_map *umap,
7519 __isl_take isl_union_set *uset);
7520 __isl_give isl_union_map *
7521 isl_union_map_intersect_range_union_set(
7522 __isl_take isl_union_map *umap,
7523 __isl_take isl_union_set *uset);
7524 __isl_give isl_union_map *
7525 isl_union_map_intersect_range_space(
7526 __isl_take isl_union_map *umap,
7527 __isl_take isl_space *space);
7528 __isl_give isl_union_map *isl_union_map_intersect_range(
7529 __isl_take isl_union_map *umap,
7530 __isl_take isl_union_set *uset);
7531 __isl_give isl_union_map *isl_union_map_intersect(
7532 __isl_take isl_union_map *umap1,
7533 __isl_take isl_union_map *umap2);
7534 __isl_give isl_union_map *
7535 isl_union_map_intersect_domain_factor_domain(
7536 __isl_take isl_union_map *umap,
7537 __isl_take isl_union_map *factor);
7538 __isl_give isl_union_map *
7539 isl_union_map_intersect_domain_factor_range(
7540 __isl_take isl_union_map *umap,
7541 __isl_take isl_union_map *factor);
7542 __isl_give isl_union_map *
7543 isl_union_map_intersect_range_factor_domain(
7544 __isl_take isl_union_map *umap,
7545 __isl_take isl_union_map *factor);
7546 __isl_give isl_union_map *
7547 isl_union_map_intersect_range_factor_range(
7548 __isl_take isl_union_map *umap,
7549 __isl_take isl_union_map *factor);
7550 __isl_give isl_union_map *
7551 isl_union_map_intersect_domain_wrapped_domain_union_set(
7552 __isl_take isl_union_map *umap,
7553 __isl_take isl_union_set *domain);
7554 __isl_give isl_union_map *
7555 isl_union_map_intersect_range_wrapped_domain_union_set(
7556 __isl_take isl_union_map *umap,
7557 __isl_take isl_union_set *domain);
7559 #include <isl/aff.h>
7560 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
7561 __isl_take isl_pw_aff *pa,
7562 __isl_take isl_set *set);
7563 __isl_give isl_multi_pw_aff *
7564 isl_multi_pw_aff_intersect_domain(
7565 __isl_take isl_multi_pw_aff *mpa,
7566 __isl_take isl_set *domain);
7567 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
7568 __isl_take isl_pw_multi_aff *pma,
7569 __isl_take isl_set *set);
7570 __isl_give isl_union_pw_aff *
7571 isl_union_pw_aff_intersect_domain_space(
7572 __isl_take isl_union_pw_aff *upa,
7573 __isl_take isl_space *space);
7574 __isl_give isl_union_pw_aff *
7575 isl_union_pw_aff_intersect_domain_union_set(
7576 __isl_take isl_union_pw_aff *upa,
7577 __isl_take isl_union_set *uset);
7578 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
7579 __isl_take isl_union_pw_aff *upa,
7580 __isl_take isl_union_set *uset);
7581 __isl_give isl_union_pw_multi_aff *
7582 isl_union_pw_multi_aff_intersect_domain_space(
7583 __isl_take isl_union_pw_multi_aff *upma,
7584 __isl_take isl_space *space);
7585 __isl_give isl_union_pw_multi_aff *
7586 isl_union_pw_multi_aff_intersect_domain_union_set(
7587 __isl_take isl_union_pw_multi_aff *upma,
7588 __isl_take isl_union_set *uset);
7589 __isl_give isl_union_pw_multi_aff *
7590 isl_union_pw_multi_aff_intersect_domain(
7591 __isl_take isl_union_pw_multi_aff *upma,
7592 __isl_take isl_union_set *uset);
7593 __isl_give isl_multi_union_pw_aff *
7594 isl_multi_union_pw_aff_intersect_domain(
7595 __isl_take isl_multi_union_pw_aff *mupa,
7596 __isl_take isl_union_set *uset);
7597 __isl_give isl_pw_aff *
7598 isl_pw_aff_intersect_domain_wrapped_domain(
7599 __isl_take isl_pw_aff *pa,
7600 __isl_take isl_set *set);
7601 __isl_give isl_pw_multi_aff *
7602 isl_pw_multi_aff_intersect_domain_wrapped_domain(
7603 __isl_take isl_pw_multi_aff *pma,
7604 __isl_take isl_set *set);
7605 __isl_give isl_union_pw_aff *
7606 isl_union_pw_aff_intersect_domain_wrapped_domain(
7607 __isl_take isl_union_pw_aff *upa,
7608 __isl_take isl_union_set *uset);
7609 __isl_give isl_union_pw_multi_aff *
7610 isl_union_pw_multi_aff_intersect_domain_wrapped_domain(
7611 __isl_take isl_union_pw_multi_aff *upma,
7612 __isl_take isl_union_set *uset);
7613 __isl_give isl_pw_aff *
7614 isl_pw_aff_intersect_domain_wrapped_range(
7615 __isl_take isl_pw_aff *pa,
7616 __isl_take isl_set *set);
7617 __isl_give isl_pw_multi_aff *
7618 isl_pw_multi_aff_intersect_domain_wrapped_range(
7619 __isl_take isl_pw_multi_aff *pma,
7620 __isl_take isl_set *set);
7621 __isl_give isl_union_pw_multi_aff *
7622 isl_union_pw_multi_aff_intersect_domain_wrapped_range(
7623 __isl_take isl_union_pw_multi_aff *upma,
7624 __isl_take isl_union_set *uset);
7625 __isl_give isl_union_pw_aff *
7626 isl_union_pw_aff_intersect_domain_wrapped_range(
7627 __isl_take isl_union_pw_aff *upa,
7628 __isl_take isl_union_set *uset);
7629 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
7630 __isl_take isl_pw_aff *pa,
7631 __isl_take isl_set *set);
7632 __isl_give isl_multi_pw_aff *
7633 isl_multi_pw_aff_intersect_params(
7634 __isl_take isl_multi_pw_aff *mpa,
7635 __isl_take isl_set *set);
7636 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
7637 __isl_take isl_pw_multi_aff *pma,
7638 __isl_take isl_set *set);
7639 __isl_give isl_union_pw_aff *
7640 isl_union_pw_aff_intersect_params(
7641 __isl_take isl_union_pw_aff *upa,
7642 __isl_take isl_set *set);
7643 __isl_give isl_union_pw_multi_aff *
7644 isl_union_pw_multi_aff_intersect_params(
7645 __isl_take isl_union_pw_multi_aff *upma,
7646 __isl_take isl_set *set);
7647 __isl_give isl_multi_union_pw_aff *
7648 isl_multi_union_pw_aff_intersect_params(
7649 __isl_take isl_multi_union_pw_aff *mupa,
7650 __isl_take isl_set *params);
7651 __isl_give isl_multi_union_pw_aff *
7652 isl_multi_union_pw_aff_intersect_range(
7653 __isl_take isl_multi_union_pw_aff *mupa,
7654 __isl_take isl_set *set);
7656 #include <isl/polynomial.h>
7657 __isl_give isl_pw_qpolynomial *
7658 isl_pw_qpolynomial_intersect_domain(
7659 __isl_take isl_pw_qpolynomial *pwpq,
7660 __isl_take isl_set *set);
7661 __isl_give isl_union_pw_qpolynomial *
7662 isl_union_pw_qpolynomial_intersect_domain_space(
7663 __isl_take isl_union_pw_qpolynomial *upwpq,
7664 __isl_take isl_space *space);
7665 __isl_give isl_union_pw_qpolynomial *
7666 isl_union_pw_qpolynomial_intersect_domain_union_set(
7667 __isl_take isl_union_pw_qpolynomial *upwpq,
7668 __isl_take isl_union_set *uset);
7669 __isl_give isl_union_pw_qpolynomial *
7670 isl_union_pw_qpolynomial_intersect_domain(
7671 __isl_take isl_union_pw_qpolynomial *upwpq,
7672 __isl_take isl_union_set *uset);
7673 __isl_give isl_union_pw_qpolynomial_fold *
7674 isl_union_pw_qpolynomial_fold_intersect_domain_space(
7675 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7676 __isl_take isl_space *space);
7677 __isl_give isl_union_pw_qpolynomial_fold *
7678 isl_union_pw_qpolynomial_fold_intersect_domain_union_set(
7679 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7680 __isl_take isl_union_set *uset);
7681 __isl_give isl_union_pw_qpolynomial_fold *
7682 isl_union_pw_qpolynomial_fold_intersect_domain(
7683 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7684 __isl_take isl_union_set *uset);
7685 __isl_give isl_pw_qpolynomial *
7686 isl_pw_qpolynomial_intersect_domain_wrapped_domain(
7687 __isl_take isl_pw_qpolynomial *pwpq,
7688 __isl_take isl_set *set);
7689 __isl_give isl_pw_qpolynomial_fold *
7690 isl_pw_qpolynomial_fold_intersect_domain_wrapped_domain(
7691 __isl_take isl_pw_qpolynomial_fold *pwf,
7692 __isl_take isl_set *set);
7693 __isl_give isl_union_pw_qpolynomial *
7694 isl_union_pw_qpolynomial_intersect_domain_wrapped_domain(
7695 __isl_take isl_union_pw_qpolynomial *upwpq,
7696 __isl_take isl_union_set *uset);
7697 __isl_give isl_union_pw_qpolynomial_fold *
7698 isl_union_pw_qpolynomial_fold_intersect_domain_wrapped_domain(
7699 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7700 __isl_take isl_union_set *uset);
7701 __isl_give isl_pw_qpolynomial *
7702 isl_pw_qpolynomial_intersect_domain_wrapped_range(
7703 __isl_take isl_pw_qpolynomial *pwpq,
7704 __isl_take isl_set *set);
7705 __isl_give isl_pw_qpolynomial_fold *
7706 isl_pw_qpolynomial_fold_intersect_domain_wrapped_range(
7707 __isl_take isl_pw_qpolynomial_fold *pwf,
7708 __isl_take isl_set *set);
7709 __isl_give isl_union_pw_qpolynomial *
7710 isl_union_pw_qpolynomial_intersect_domain_wrapped_range(
7711 __isl_take isl_union_pw_qpolynomial *upwpq,
7712 __isl_take isl_union_set *uset);
7713 __isl_give isl_union_pw_qpolynomial_fold *
7714 isl_union_pw_qpolynomial_fold_intersect_domain_wrapped_range(
7715 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7716 __isl_take isl_union_set *uset);
7717 __isl_give isl_pw_qpolynomial *
7718 isl_pw_qpolynomial_intersect_params(
7719 __isl_take isl_pw_qpolynomial *pwpq,
7720 __isl_take isl_set *set);
7721 __isl_give isl_pw_qpolynomial_fold *
7722 isl_pw_qpolynomial_fold_intersect_params(
7723 __isl_take isl_pw_qpolynomial_fold *pwf,
7724 __isl_take isl_set *set);
7725 __isl_give isl_union_pw_qpolynomial *
7726 isl_union_pw_qpolynomial_intersect_params(
7727 __isl_take isl_union_pw_qpolynomial *upwpq,
7728 __isl_take isl_set *set);
7729 __isl_give isl_union_pw_qpolynomial_fold *
7730 isl_union_pw_qpolynomial_fold_intersect_params(
7731 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7732 __isl_take isl_set *set);
7734 The second argument to the C<_params> functions needs to be
7735 a parametric (basic) set. For the other functions, a parametric set
7736 for either argument is only allowed if the other argument is
7737 a parametric set as well.
7738 The list passed to C<isl_basic_set_list_intersect> needs to have
7739 at least one element and all elements need to live in the same space.
7740 The function C<isl_multi_union_pw_aff_intersect_range>
7741 restricts the input function to those shared domain elements
7742 that map to the specified range.
7743 C<isl_union_map_intersect_domain> is an alternative name for
7744 C<isl_union_map_intersect_domain_union_set>.
7745 Similarly for the other pairs of functions.
7749 #include <isl/set.h>
7750 __isl_give isl_set *isl_basic_set_union(
7751 __isl_take isl_basic_set *bset1,
7752 __isl_take isl_basic_set *bset2);
7753 __isl_give isl_set *isl_set_union(
7754 __isl_take isl_set *set1,
7755 __isl_take isl_set *set2);
7756 __isl_give isl_set *isl_set_list_union(
7757 __isl_take isl_set_list *list);
7759 #include <isl/map.h>
7760 __isl_give isl_map *isl_basic_map_union(
7761 __isl_take isl_basic_map *bmap1,
7762 __isl_take isl_basic_map *bmap2);
7763 __isl_give isl_map *isl_map_union(
7764 __isl_take isl_map *map1,
7765 __isl_take isl_map *map2);
7767 #include <isl/union_set.h>
7768 __isl_give isl_union_set *isl_union_set_union(
7769 __isl_take isl_union_set *uset1,
7770 __isl_take isl_union_set *uset2);
7771 __isl_give isl_union_set *isl_union_set_list_union(
7772 __isl_take isl_union_set_list *list);
7774 #include <isl/union_map.h>
7775 __isl_give isl_union_map *isl_union_map_union(
7776 __isl_take isl_union_map *umap1,
7777 __isl_take isl_union_map *umap2);
7779 The list passed to C<isl_set_list_union> needs to have
7780 at least one element and all elements need to live in the same space.
7782 =item * Set difference
7784 #include <isl/set.h>
7785 __isl_give isl_set *isl_set_subtract(
7786 __isl_take isl_set *set1,
7787 __isl_take isl_set *set2);
7789 #include <isl/map.h>
7790 __isl_give isl_map *isl_map_subtract(
7791 __isl_take isl_map *map1,
7792 __isl_take isl_map *map2);
7793 __isl_give isl_map *isl_map_subtract_domain(
7794 __isl_take isl_map *map,
7795 __isl_take isl_set *dom);
7796 __isl_give isl_map *isl_map_subtract_range(
7797 __isl_take isl_map *map,
7798 __isl_take isl_set *dom);
7800 #include <isl/union_set.h>
7801 __isl_give isl_union_set *isl_union_set_subtract(
7802 __isl_take isl_union_set *uset1,
7803 __isl_take isl_union_set *uset2);
7805 #include <isl/union_map.h>
7806 __isl_give isl_union_map *isl_union_map_subtract(
7807 __isl_take isl_union_map *umap1,
7808 __isl_take isl_union_map *umap2);
7809 __isl_give isl_union_map *isl_union_map_subtract_domain(
7810 __isl_take isl_union_map *umap,
7811 __isl_take isl_union_set *dom);
7812 __isl_give isl_union_map *isl_union_map_subtract_range(
7813 __isl_take isl_union_map *umap,
7814 __isl_take isl_union_set *dom);
7816 #include <isl/aff.h>
7817 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
7818 __isl_take isl_pw_aff *pa,
7819 __isl_take isl_set *set);
7820 __isl_give isl_pw_multi_aff *
7821 isl_pw_multi_aff_subtract_domain(
7822 __isl_take isl_pw_multi_aff *pma,
7823 __isl_take isl_set *set);
7824 __isl_give isl_union_pw_aff *
7825 isl_union_pw_aff_subtract_domain_union_set(
7826 __isl_take isl_union_pw_aff *upa,
7827 __isl_take isl_union_set *uset);
7828 __isl_give isl_union_pw_aff *
7829 isl_union_pw_aff_subtract_domain_space(
7830 __isl_take isl_union_pw_aff *upa,
7831 __isl_take isl_space *space);
7832 __isl_give isl_union_pw_aff *
7833 isl_union_pw_aff_subtract_domain(
7834 __isl_take isl_union_pw_aff *upa,
7835 __isl_take isl_union_set *uset);
7836 __isl_give isl_union_pw_multi_aff *
7837 isl_union_pw_multi_aff_subtract_domain_union_set(
7838 __isl_take isl_union_pw_multi_aff *upma,
7839 __isl_take isl_set *set);
7840 __isl_give isl_union_pw_multi_aff *
7841 isl_union_pw_multi_aff_subtract_domain_space(
7842 __isl_take isl_union_pw_multi_aff *upma,
7843 __isl_take isl_space *space);
7844 __isl_give isl_union_pw_multi_aff *
7845 isl_union_pw_multi_aff_subtract_domain(
7846 __isl_take isl_union_pw_multi_aff *upma,
7847 __isl_take isl_union_set *uset);
7849 #include <isl/polynomial.h>
7850 __isl_give isl_pw_qpolynomial *
7851 isl_pw_qpolynomial_subtract_domain(
7852 __isl_take isl_pw_qpolynomial *pwpq,
7853 __isl_take isl_set *set);
7854 __isl_give isl_pw_qpolynomial_fold *
7855 isl_pw_qpolynomial_fold_subtract_domain(
7856 __isl_take isl_pw_qpolynomial_fold *pwf,
7857 __isl_take isl_set *set);
7858 __isl_give isl_union_pw_qpolynomial *
7859 isl_union_pw_qpolynomial_subtract_domain_union_set(
7860 __isl_take isl_union_pw_qpolynomial *upwpq,
7861 __isl_take isl_union_set *uset);
7862 __isl_give isl_union_pw_qpolynomial *
7863 isl_union_pw_qpolynomial_subtract_domain_space(
7864 __isl_take isl_union_pw_qpolynomial *upwpq,
7865 __isl_take isl_space *space);
7866 __isl_give isl_union_pw_qpolynomial *
7867 isl_union_pw_qpolynomial_subtract_domain(
7868 __isl_take isl_union_pw_qpolynomial *upwpq,
7869 __isl_take isl_union_set *uset);
7870 __isl_give isl_union_pw_qpolynomial_fold *
7871 isl_union_pw_qpolynomial_fold_subtract_domain_union_set(
7872 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7873 __isl_take isl_union_set *uset);
7874 __isl_give isl_union_pw_qpolynomial_fold *
7875 isl_union_pw_qpolynomial_fold_subtract_domain_space(
7876 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7877 __isl_take isl_space *space);
7878 __isl_give isl_union_pw_qpolynomial_fold *
7879 isl_union_pw_qpolynomial_fold_subtract_domain(
7880 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7881 __isl_take isl_union_set *uset);
7883 C<isl_union_pw_aff_subtract_domain> is an alternative name for
7884 C<isl_union_pw_aff_subtract_domain_union_set>.
7885 Similarly for the other pairs of functions.
7889 #include <isl/space.h>
7890 __isl_give isl_space *isl_space_join(
7891 __isl_take isl_space *left,
7892 __isl_take isl_space *right);
7894 #include <isl/set.h>
7895 __isl_give isl_basic_set *isl_basic_set_apply(
7896 __isl_take isl_basic_set *bset,
7897 __isl_take isl_basic_map *bmap);
7898 __isl_give isl_set *isl_set_apply(
7899 __isl_take isl_set *set,
7900 __isl_take isl_map *map);
7902 #include <isl/union_set.h>
7903 __isl_give isl_union_set *isl_union_set_apply(
7904 __isl_take isl_union_set *uset,
7905 __isl_take isl_union_map *umap);
7907 #include <isl/map.h>
7908 __isl_give isl_basic_map *isl_basic_map_apply_domain(
7909 __isl_take isl_basic_map *bmap1,
7910 __isl_take isl_basic_map *bmap2);
7911 __isl_give isl_basic_map *isl_basic_map_apply_range(
7912 __isl_take isl_basic_map *bmap1,
7913 __isl_take isl_basic_map *bmap2);
7914 __isl_give isl_map *isl_map_apply_domain(
7915 __isl_take isl_map *map1,
7916 __isl_take isl_map *map2);
7917 __isl_give isl_map *isl_map_apply_range(
7918 __isl_take isl_map *map1,
7919 __isl_take isl_map *map2);
7921 #include <isl/union_map.h>
7922 __isl_give isl_union_map *isl_union_map_apply_domain(
7923 __isl_take isl_union_map *umap1,
7924 __isl_take isl_union_map *umap2);
7925 __isl_give isl_union_map *isl_union_map_apply_range(
7926 __isl_take isl_union_map *umap1,
7927 __isl_take isl_union_map *umap2);
7929 #include <isl/aff.h>
7930 __isl_give isl_union_pw_multi_aff *
7931 isl_union_pw_multi_aff_apply_union_pw_multi_aff(
7932 __isl_take isl_union_pw_multi_aff *upma1,
7933 __isl_take isl_union_pw_multi_aff *upma2);
7934 __isl_give isl_union_pw_aff *
7935 isl_multi_union_pw_aff_apply_aff(
7936 __isl_take isl_multi_union_pw_aff *mupa,
7937 __isl_take isl_aff *aff);
7938 __isl_give isl_union_pw_aff *
7939 isl_multi_union_pw_aff_apply_pw_aff(
7940 __isl_take isl_multi_union_pw_aff *mupa,
7941 __isl_take isl_pw_aff *pa);
7942 __isl_give isl_multi_union_pw_aff *
7943 isl_multi_union_pw_aff_apply_multi_aff(
7944 __isl_take isl_multi_union_pw_aff *mupa,
7945 __isl_take isl_multi_aff *ma);
7946 __isl_give isl_multi_union_pw_aff *
7947 isl_multi_union_pw_aff_apply_pw_multi_aff(
7948 __isl_take isl_multi_union_pw_aff *mupa,
7949 __isl_take isl_pw_multi_aff *pma);
7951 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
7952 over the shared domain of the elements of the input. The dimension is
7953 required to be greater than zero.
7954 The C<isl_multi_union_pw_aff> argument of
7955 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
7956 but only if the range of the C<isl_multi_aff> argument
7957 is also zero-dimensional.
7958 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
7960 #include <isl/polynomial.h>
7961 __isl_give isl_pw_qpolynomial_fold *
7962 isl_set_apply_pw_qpolynomial_fold(
7963 __isl_take isl_set *set,
7964 __isl_take isl_pw_qpolynomial_fold *pwf,
7966 __isl_give isl_pw_qpolynomial_fold *
7967 isl_map_apply_pw_qpolynomial_fold(
7968 __isl_take isl_map *map,
7969 __isl_take isl_pw_qpolynomial_fold *pwf,
7971 __isl_give isl_union_pw_qpolynomial_fold *
7972 isl_union_set_apply_union_pw_qpolynomial_fold(
7973 __isl_take isl_union_set *uset,
7974 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7976 __isl_give isl_union_pw_qpolynomial_fold *
7977 isl_union_map_apply_union_pw_qpolynomial_fold(
7978 __isl_take isl_union_map *umap,
7979 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7982 The functions taking a map
7983 compose the given map with the given piecewise quasipolynomial reduction.
7984 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
7985 over all elements in the intersection of the range of the map
7986 and the domain of the piecewise quasipolynomial reduction
7987 as a function of an element in the domain of the map.
7988 The functions taking a set compute a bound over all elements in the
7989 intersection of the set and the domain of the
7990 piecewise quasipolynomial reduction.
7994 #include <isl/set.h>
7995 __isl_give isl_basic_set *
7996 isl_basic_set_preimage_multi_aff(
7997 __isl_take isl_basic_set *bset,
7998 __isl_take isl_multi_aff *ma);
7999 __isl_give isl_set *isl_set_preimage_multi_aff(
8000 __isl_take isl_set *set,
8001 __isl_take isl_multi_aff *ma);
8002 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
8003 __isl_take isl_set *set,
8004 __isl_take isl_pw_multi_aff *pma);
8005 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
8006 __isl_take isl_set *set,
8007 __isl_take isl_multi_pw_aff *mpa);
8009 #include <isl/union_set.h>
8010 __isl_give isl_union_set *
8011 isl_union_set_preimage_multi_aff(
8012 __isl_take isl_union_set *uset,
8013 __isl_take isl_multi_aff *ma);
8014 __isl_give isl_union_set *
8015 isl_union_set_preimage_pw_multi_aff(
8016 __isl_take isl_union_set *uset,
8017 __isl_take isl_pw_multi_aff *pma);
8018 __isl_give isl_union_set *
8019 isl_union_set_preimage_union_pw_multi_aff(
8020 __isl_take isl_union_set *uset,
8021 __isl_take isl_union_pw_multi_aff *upma);
8023 #include <isl/map.h>
8024 __isl_give isl_basic_map *
8025 isl_basic_map_preimage_domain_multi_aff(
8026 __isl_take isl_basic_map *bmap,
8027 __isl_take isl_multi_aff *ma);
8028 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
8029 __isl_take isl_map *map,
8030 __isl_take isl_multi_aff *ma);
8031 __isl_give isl_map *isl_map_preimage_range_multi_aff(
8032 __isl_take isl_map *map,
8033 __isl_take isl_multi_aff *ma);
8034 __isl_give isl_map *
8035 isl_map_preimage_domain_pw_multi_aff(
8036 __isl_take isl_map *map,
8037 __isl_take isl_pw_multi_aff *pma);
8038 __isl_give isl_map *
8039 isl_map_preimage_range_pw_multi_aff(
8040 __isl_take isl_map *map,
8041 __isl_take isl_pw_multi_aff *pma);
8042 __isl_give isl_map *
8043 isl_map_preimage_domain_multi_pw_aff(
8044 __isl_take isl_map *map,
8045 __isl_take isl_multi_pw_aff *mpa);
8046 __isl_give isl_basic_map *
8047 isl_basic_map_preimage_range_multi_aff(
8048 __isl_take isl_basic_map *bmap,
8049 __isl_take isl_multi_aff *ma);
8051 #include <isl/union_map.h>
8052 __isl_give isl_union_map *
8053 isl_union_map_preimage_domain_multi_aff(
8054 __isl_take isl_union_map *umap,
8055 __isl_take isl_multi_aff *ma);
8056 __isl_give isl_union_map *
8057 isl_union_map_preimage_range_multi_aff(
8058 __isl_take isl_union_map *umap,
8059 __isl_take isl_multi_aff *ma);
8060 __isl_give isl_union_map *
8061 isl_union_map_preimage_domain_pw_multi_aff(
8062 __isl_take isl_union_map *umap,
8063 __isl_take isl_pw_multi_aff *pma);
8064 __isl_give isl_union_map *
8065 isl_union_map_preimage_range_pw_multi_aff(
8066 __isl_take isl_union_map *umap,
8067 __isl_take isl_pw_multi_aff *pma);
8068 __isl_give isl_union_map *
8069 isl_union_map_preimage_domain_union_pw_multi_aff(
8070 __isl_take isl_union_map *umap,
8071 __isl_take isl_union_pw_multi_aff *upma);
8072 __isl_give isl_union_map *
8073 isl_union_map_preimage_range_union_pw_multi_aff(
8074 __isl_take isl_union_map *umap,
8075 __isl_take isl_union_pw_multi_aff *upma);
8077 #include <isl/aff.h>
8078 __isl_give isl_pw_multi_aff *
8079 isl_pw_multi_aff_preimage_domain_wrapped_domain_pw_multi_aff(
8080 __isl_take isl_pw_multi_aff *pma1,
8081 __isl_take isl_pw_multi_aff *pma2);
8082 __isl_give isl_union_pw_multi_aff *
8083 isl_union_pw_multi_aff_preimage_domain_wrapped_domain_union_pw_multi_aff(
8084 __isl_take isl_union_pw_multi_aff *upma1,
8085 __isl_take isl_union_pw_multi_aff *upma2);
8087 These functions compute the preimage of the given set or map domain/range under
8088 the given function. In other words, the expression is plugged
8089 into the set description or into the domain/range of the map or function.
8093 #include <isl/aff.h>
8094 __isl_give isl_aff *isl_aff_pullback_aff(
8095 __isl_take isl_aff *aff1,
8096 __isl_take isl_aff *aff2);
8097 __isl_give isl_aff *isl_aff_pullback_multi_aff(
8098 __isl_take isl_aff *aff,
8099 __isl_take isl_multi_aff *ma);
8100 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
8101 __isl_take isl_pw_aff *pa,
8102 __isl_take isl_multi_aff *ma);
8103 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
8104 __isl_take isl_pw_aff *pa,
8105 __isl_take isl_pw_multi_aff *pma);
8106 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
8107 __isl_take isl_pw_aff *pa,
8108 __isl_take isl_multi_pw_aff *mpa);
8109 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
8110 __isl_take isl_multi_aff *ma1,
8111 __isl_take isl_multi_aff *ma2);
8112 __isl_give isl_pw_multi_aff *
8113 isl_pw_multi_aff_pullback_multi_aff(
8114 __isl_take isl_pw_multi_aff *pma,
8115 __isl_take isl_multi_aff *ma);
8116 __isl_give isl_multi_pw_aff *
8117 isl_multi_pw_aff_pullback_multi_aff(
8118 __isl_take isl_multi_pw_aff *mpa,
8119 __isl_take isl_multi_aff *ma);
8120 __isl_give isl_pw_multi_aff *
8121 isl_pw_multi_aff_pullback_pw_multi_aff(
8122 __isl_take isl_pw_multi_aff *pma1,
8123 __isl_take isl_pw_multi_aff *pma2);
8124 __isl_give isl_multi_pw_aff *
8125 isl_multi_pw_aff_pullback_pw_multi_aff(
8126 __isl_take isl_multi_pw_aff *mpa,
8127 __isl_take isl_pw_multi_aff *pma);
8128 __isl_give isl_multi_pw_aff *
8129 isl_multi_pw_aff_pullback_multi_pw_aff(
8130 __isl_take isl_multi_pw_aff *mpa1,
8131 __isl_take isl_multi_pw_aff *mpa2);
8132 __isl_give isl_union_pw_aff *
8133 isl_union_pw_aff_pullback_union_pw_multi_aff(
8134 __isl_take isl_union_pw_aff *upa,
8135 __isl_take isl_union_pw_multi_aff *upma);
8136 __isl_give isl_union_pw_multi_aff *
8137 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
8138 __isl_take isl_union_pw_multi_aff *upma1,
8139 __isl_take isl_union_pw_multi_aff *upma2);
8140 __isl_give isl_multi_union_pw_aff *
8141 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
8142 __isl_take isl_multi_union_pw_aff *mupa,
8143 __isl_take isl_union_pw_multi_aff *upma);
8145 These functions precompose the first expression by the second function.
8146 In other words, the second function is plugged
8147 into the first expression.
8151 #include <isl/aff.h>
8152 __isl_give isl_basic_set *isl_aff_eq_basic_set(
8153 __isl_take isl_aff *aff1,
8154 __isl_take isl_aff *aff2);
8155 __isl_give isl_set *isl_aff_eq_set(
8156 __isl_take isl_aff *aff1,
8157 __isl_take isl_aff *aff2);
8158 __isl_give isl_set *isl_aff_ne_set(
8159 __isl_take isl_aff *aff1,
8160 __isl_take isl_aff *aff2);
8161 __isl_give isl_basic_set *isl_aff_le_basic_set(
8162 __isl_take isl_aff *aff1,
8163 __isl_take isl_aff *aff2);
8164 __isl_give isl_set *isl_aff_le_set(
8165 __isl_take isl_aff *aff1,
8166 __isl_take isl_aff *aff2);
8167 __isl_give isl_basic_set *isl_aff_lt_basic_set(
8168 __isl_take isl_aff *aff1,
8169 __isl_take isl_aff *aff2);
8170 __isl_give isl_set *isl_aff_lt_set(
8171 __isl_take isl_aff *aff1,
8172 __isl_take isl_aff *aff2);
8173 __isl_give isl_basic_set *isl_aff_ge_basic_set(
8174 __isl_take isl_aff *aff1,
8175 __isl_take isl_aff *aff2);
8176 __isl_give isl_set *isl_aff_ge_set(
8177 __isl_take isl_aff *aff1,
8178 __isl_take isl_aff *aff2);
8179 __isl_give isl_basic_set *isl_aff_gt_basic_set(
8180 __isl_take isl_aff *aff1,
8181 __isl_take isl_aff *aff2);
8182 __isl_give isl_set *isl_aff_gt_set(
8183 __isl_take isl_aff *aff1,
8184 __isl_take isl_aff *aff2);
8185 __isl_give isl_set *isl_pw_aff_eq_set(
8186 __isl_take isl_pw_aff *pwaff1,
8187 __isl_take isl_pw_aff *pwaff2);
8188 __isl_give isl_set *isl_pw_aff_ne_set(
8189 __isl_take isl_pw_aff *pwaff1,
8190 __isl_take isl_pw_aff *pwaff2);
8191 __isl_give isl_set *isl_pw_aff_le_set(
8192 __isl_take isl_pw_aff *pwaff1,
8193 __isl_take isl_pw_aff *pwaff2);
8194 __isl_give isl_set *isl_pw_aff_lt_set(
8195 __isl_take isl_pw_aff *pwaff1,
8196 __isl_take isl_pw_aff *pwaff2);
8197 __isl_give isl_set *isl_pw_aff_ge_set(
8198 __isl_take isl_pw_aff *pwaff1,
8199 __isl_take isl_pw_aff *pwaff2);
8200 __isl_give isl_set *isl_pw_aff_gt_set(
8201 __isl_take isl_pw_aff *pwaff1,
8202 __isl_take isl_pw_aff *pwaff2);
8204 __isl_give isl_set *isl_multi_aff_lex_le_set(
8205 __isl_take isl_multi_aff *ma1,
8206 __isl_take isl_multi_aff *ma2);
8207 __isl_give isl_set *isl_multi_aff_lex_lt_set(
8208 __isl_take isl_multi_aff *ma1,
8209 __isl_take isl_multi_aff *ma2);
8210 __isl_give isl_set *isl_multi_aff_lex_ge_set(
8211 __isl_take isl_multi_aff *ma1,
8212 __isl_take isl_multi_aff *ma2);
8213 __isl_give isl_set *isl_multi_aff_lex_gt_set(
8214 __isl_take isl_multi_aff *ma1,
8215 __isl_take isl_multi_aff *ma2);
8217 __isl_give isl_set *isl_pw_aff_list_eq_set(
8218 __isl_take isl_pw_aff_list *list1,
8219 __isl_take isl_pw_aff_list *list2);
8220 __isl_give isl_set *isl_pw_aff_list_ne_set(
8221 __isl_take isl_pw_aff_list *list1,
8222 __isl_take isl_pw_aff_list *list2);
8223 __isl_give isl_set *isl_pw_aff_list_le_set(
8224 __isl_take isl_pw_aff_list *list1,
8225 __isl_take isl_pw_aff_list *list2);
8226 __isl_give isl_set *isl_pw_aff_list_lt_set(
8227 __isl_take isl_pw_aff_list *list1,
8228 __isl_take isl_pw_aff_list *list2);
8229 __isl_give isl_set *isl_pw_aff_list_ge_set(
8230 __isl_take isl_pw_aff_list *list1,
8231 __isl_take isl_pw_aff_list *list2);
8232 __isl_give isl_set *isl_pw_aff_list_gt_set(
8233 __isl_take isl_pw_aff_list *list1,
8234 __isl_take isl_pw_aff_list *list2);
8236 The function C<isl_aff_ge_basic_set> returns a basic set
8237 containing those elements in the shared space
8238 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
8239 The function C<isl_pw_aff_ge_set> returns a set
8240 containing those elements in the shared domain
8241 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
8242 greater than or equal to C<pwaff2>.
8243 The function C<isl_multi_aff_lex_le_set> returns a set
8244 containing those elements in the shared domain space
8245 where C<ma1> is lexicographically smaller than or
8247 The functions operating on C<isl_pw_aff_list> apply the corresponding
8248 C<isl_pw_aff> function to each pair of elements in the two lists.
8250 #include <isl/aff.h>
8251 __isl_give isl_map *isl_pw_aff_eq_map(
8252 __isl_take isl_pw_aff *pa1,
8253 __isl_take isl_pw_aff *pa2);
8254 __isl_give isl_map *isl_pw_aff_le_map(
8255 __isl_take isl_pw_aff *pa1,
8256 __isl_take isl_pw_aff *pa2);
8257 __isl_give isl_map *isl_pw_aff_lt_map(
8258 __isl_take isl_pw_aff *pa1,
8259 __isl_take isl_pw_aff *pa2);
8260 __isl_give isl_map *isl_pw_aff_ge_map(
8261 __isl_take isl_pw_aff *pa1,
8262 __isl_take isl_pw_aff *pa2);
8263 __isl_give isl_map *isl_pw_aff_gt_map(
8264 __isl_take isl_pw_aff *pa1,
8265 __isl_take isl_pw_aff *pa2);
8267 __isl_give isl_map *isl_multi_pw_aff_eq_map(
8268 __isl_take isl_multi_pw_aff *mpa1,
8269 __isl_take isl_multi_pw_aff *mpa2);
8270 __isl_give isl_map *isl_multi_pw_aff_lex_le_map(
8271 __isl_take isl_multi_pw_aff *mpa1,
8272 __isl_take isl_multi_pw_aff *mpa2);
8273 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
8274 __isl_take isl_multi_pw_aff *mpa1,
8275 __isl_take isl_multi_pw_aff *mpa2);
8276 __isl_give isl_map *isl_multi_pw_aff_lex_ge_map(
8277 __isl_take isl_multi_pw_aff *mpa1,
8278 __isl_take isl_multi_pw_aff *mpa2);
8279 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
8280 __isl_take isl_multi_pw_aff *mpa1,
8281 __isl_take isl_multi_pw_aff *mpa2);
8283 These functions return a map between domain elements of the arguments
8284 where the function values satisfy the given relation.
8286 #include <isl/map.h>
8287 __isl_give isl_map *isl_map_eq_at_multi_pw_aff(
8288 __isl_take isl_map *map,
8289 __isl_take isl_multi_pw_aff *mpa);
8290 __isl_give isl_map *isl_map_lex_lt_at_multi_pw_aff(
8291 __isl_take isl_map *map,
8292 __isl_take isl_multi_pw_aff *mpa);
8293 __isl_give isl_map *isl_map_lex_le_at_multi_pw_aff(
8294 __isl_take isl_map *map,
8295 __isl_take isl_multi_pw_aff *mpa);
8296 __isl_give isl_map *isl_map_lex_gt_at_multi_pw_aff(
8297 __isl_take isl_map *map,
8298 __isl_take isl_multi_pw_aff *mpa);
8299 __isl_give isl_map *isl_map_lex_ge_at_multi_pw_aff(
8300 __isl_take isl_map *map,
8301 __isl_take isl_multi_pw_aff *mpa);
8303 #include <isl/union_map.h>
8304 __isl_give isl_union_map *
8305 isl_union_map_eq_at_multi_union_pw_aff(
8306 __isl_take isl_union_map *umap,
8307 __isl_take isl_multi_union_pw_aff *mupa);
8308 __isl_give isl_union_map *
8309 isl_union_map_lex_lt_at_multi_union_pw_aff(
8310 __isl_take isl_union_map *umap,
8311 __isl_take isl_multi_union_pw_aff *mupa);
8312 __isl_give isl_union_map *
8313 isl_union_map_lex_le_at_multi_union_pw_aff(
8314 __isl_take isl_union_map *umap,
8315 __isl_take isl_multi_union_pw_aff *mupa);
8316 __isl_give isl_union_map *
8317 isl_union_map_lex_gt_at_multi_union_pw_aff(
8318 __isl_take isl_union_map *umap,
8319 __isl_take isl_multi_union_pw_aff *mupa);
8320 __isl_give isl_union_map *
8321 isl_union_map_lex_ge_at_multi_union_pw_aff(
8322 __isl_take isl_union_map *umap,
8323 __isl_take isl_multi_union_pw_aff *mupa);
8325 These functions select the subset of elements in the union map
8326 that have an equal or lexicographically smaller or greater function value.
8328 =item * Cartesian Product
8330 #include <isl/space.h>
8331 __isl_give isl_space *isl_space_product(
8332 __isl_take isl_space *space1,
8333 __isl_take isl_space *space2);
8334 __isl_give isl_space *isl_space_domain_product(
8335 __isl_take isl_space *space1,
8336 __isl_take isl_space *space2);
8337 __isl_give isl_space *isl_space_range_product(
8338 __isl_take isl_space *space1,
8339 __isl_take isl_space *space2);
8342 C<isl_space_product>, C<isl_space_domain_product>
8343 and C<isl_space_range_product> take pairs or relation spaces and
8344 produce a single relations space, where either the domain, the range
8345 or both domain and range are wrapped spaces of relations between
8346 the domains and/or ranges of the input spaces.
8347 If the product is only constructed over the domain or the range
8348 then the ranges or the domains of the inputs should be the same.
8349 The function C<isl_space_product> also accepts a pair of set spaces,
8350 in which case it returns a wrapped space of a relation between the
8353 #include <isl/set.h>
8354 __isl_give isl_set *isl_set_product(
8355 __isl_take isl_set *set1,
8356 __isl_take isl_set *set2);
8358 #include <isl/map.h>
8359 __isl_give isl_basic_map *isl_basic_map_domain_product(
8360 __isl_take isl_basic_map *bmap1,
8361 __isl_take isl_basic_map *bmap2);
8362 __isl_give isl_basic_map *isl_basic_map_range_product(
8363 __isl_take isl_basic_map *bmap1,
8364 __isl_take isl_basic_map *bmap2);
8365 __isl_give isl_basic_map *isl_basic_map_product(
8366 __isl_take isl_basic_map *bmap1,
8367 __isl_take isl_basic_map *bmap2);
8368 __isl_give isl_map *isl_map_domain_product(
8369 __isl_take isl_map *map1,
8370 __isl_take isl_map *map2);
8371 __isl_give isl_map *isl_map_range_product(
8372 __isl_take isl_map *map1,
8373 __isl_take isl_map *map2);
8374 __isl_give isl_map *isl_map_product(
8375 __isl_take isl_map *map1,
8376 __isl_take isl_map *map2);
8378 #include <isl/union_set.h>
8379 __isl_give isl_union_set *isl_union_set_product(
8380 __isl_take isl_union_set *uset1,
8381 __isl_take isl_union_set *uset2);
8383 #include <isl/union_map.h>
8384 __isl_give isl_union_map *isl_union_map_domain_product(
8385 __isl_take isl_union_map *umap1,
8386 __isl_take isl_union_map *umap2);
8387 __isl_give isl_union_map *isl_union_map_range_product(
8388 __isl_take isl_union_map *umap1,
8389 __isl_take isl_union_map *umap2);
8390 __isl_give isl_union_map *isl_union_map_product(
8391 __isl_take isl_union_map *umap1,
8392 __isl_take isl_union_map *umap2);
8395 __isl_give isl_multi_id *isl_multi_id_range_product(
8396 __isl_take isl_multi_id *mi1,
8397 __isl_take isl_multi_id *mi2);
8399 #include <isl/val.h>
8400 __isl_give isl_multi_val *isl_multi_val_range_product(
8401 __isl_take isl_multi_val *mv1,
8402 __isl_take isl_multi_val *mv2);
8403 __isl_give isl_multi_val *isl_multi_val_product(
8404 __isl_take isl_multi_val *mv1,
8405 __isl_take isl_multi_val *mv2);
8407 #include <isl/aff.h>
8408 __isl_give isl_multi_aff *isl_multi_aff_range_product(
8409 __isl_take isl_multi_aff *ma1,
8410 __isl_take isl_multi_aff *ma2);
8411 __isl_give isl_multi_aff *isl_multi_aff_product(
8412 __isl_take isl_multi_aff *ma1,
8413 __isl_take isl_multi_aff *ma2);
8414 __isl_give isl_multi_pw_aff *
8415 isl_multi_pw_aff_range_product(
8416 __isl_take isl_multi_pw_aff *mpa1,
8417 __isl_take isl_multi_pw_aff *mpa2);
8418 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
8419 __isl_take isl_multi_pw_aff *mpa1,
8420 __isl_take isl_multi_pw_aff *mpa2);
8421 __isl_give isl_pw_multi_aff *
8422 isl_pw_multi_aff_range_product(
8423 __isl_take isl_pw_multi_aff *pma1,
8424 __isl_take isl_pw_multi_aff *pma2);
8425 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
8426 __isl_take isl_pw_multi_aff *pma1,
8427 __isl_take isl_pw_multi_aff *pma2);
8428 __isl_give isl_union_pw_multi_aff *
8429 isl_union_pw_multi_aff_range_product(
8430 __isl_take isl_union_pw_multi_aff *upma1,
8431 __isl_take isl_union_pw_multi_aff *upma2);
8432 __isl_give isl_multi_union_pw_aff *
8433 isl_multi_union_pw_aff_range_product(
8434 __isl_take isl_multi_union_pw_aff *mupa1,
8435 __isl_take isl_multi_union_pw_aff *mupa2);
8437 The above functions compute the cross product of the given
8438 sets, relations or functions. The domains and ranges of the results
8439 are wrapped maps between domains and ranges of the inputs.
8440 To obtain a ``flat'' product, use the following functions
8443 #include <isl/set.h>
8444 __isl_give isl_basic_set *isl_basic_set_flat_product(
8445 __isl_take isl_basic_set *bset1,
8446 __isl_take isl_basic_set *bset2);
8447 __isl_give isl_set *isl_set_flat_product(
8448 __isl_take isl_set *set1,
8449 __isl_take isl_set *set2);
8451 #include <isl/map.h>
8452 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
8453 __isl_take isl_basic_map *bmap1,
8454 __isl_take isl_basic_map *bmap2);
8455 __isl_give isl_map *isl_map_flat_domain_product(
8456 __isl_take isl_map *map1,
8457 __isl_take isl_map *map2);
8458 __isl_give isl_map *isl_map_flat_range_product(
8459 __isl_take isl_map *map1,
8460 __isl_take isl_map *map2);
8461 __isl_give isl_basic_map *isl_basic_map_flat_product(
8462 __isl_take isl_basic_map *bmap1,
8463 __isl_take isl_basic_map *bmap2);
8464 __isl_give isl_map *isl_map_flat_product(
8465 __isl_take isl_map *map1,
8466 __isl_take isl_map *map2);
8468 #include <isl/union_map.h>
8469 __isl_give isl_union_map *
8470 isl_union_map_flat_domain_product(
8471 __isl_take isl_union_map *umap1,
8472 __isl_take isl_union_map *umap2);
8473 __isl_give isl_union_map *
8474 isl_union_map_flat_range_product(
8475 __isl_take isl_union_map *umap1,
8476 __isl_take isl_union_map *umap2);
8479 __isl_give isl_multi_id *
8480 isl_multi_id_flat_range_product(
8481 __isl_take isl_multi_id *mi1,
8482 __isl_take isl_multi_id *mi2);
8484 #include <isl/val.h>
8485 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
8486 __isl_take isl_multi_val *mv1,
8487 __isl_take isl_multi_val *mv2);
8489 #include <isl/aff.h>
8490 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
8491 __isl_take isl_multi_aff *ma1,
8492 __isl_take isl_multi_aff *ma2);
8493 __isl_give isl_pw_multi_aff *
8494 isl_pw_multi_aff_flat_range_product(
8495 __isl_take isl_pw_multi_aff *pma1,
8496 __isl_take isl_pw_multi_aff *pma2);
8497 __isl_give isl_multi_pw_aff *
8498 isl_multi_pw_aff_flat_range_product(
8499 __isl_take isl_multi_pw_aff *mpa1,
8500 __isl_take isl_multi_pw_aff *mpa2);
8501 __isl_give isl_union_pw_multi_aff *
8502 isl_union_pw_multi_aff_flat_range_product(
8503 __isl_take isl_union_pw_multi_aff *upma1,
8504 __isl_take isl_union_pw_multi_aff *upma2);
8505 __isl_give isl_multi_union_pw_aff *
8506 isl_multi_union_pw_aff_flat_range_product(
8507 __isl_take isl_multi_union_pw_aff *mupa1,
8508 __isl_take isl_multi_union_pw_aff *mupa2);
8510 #include <isl/space.h>
8511 __isl_give isl_space *isl_space_factor_domain(
8512 __isl_take isl_space *space);
8513 __isl_give isl_space *isl_space_factor_range(
8514 __isl_take isl_space *space);
8515 __isl_give isl_space *isl_space_domain_factor_domain(
8516 __isl_take isl_space *space);
8517 __isl_give isl_space *isl_space_domain_factor_range(
8518 __isl_take isl_space *space);
8519 __isl_give isl_space *isl_space_range_factor_domain(
8520 __isl_take isl_space *space);
8521 __isl_give isl_space *isl_space_range_factor_range(
8522 __isl_take isl_space *space);
8524 The functions C<isl_space_range_factor_domain> and
8525 C<isl_space_range_factor_range> extract the two arguments from
8526 the result of a call to C<isl_space_range_product>.
8528 The arguments of a call to a product can be extracted
8529 from the result using the following functions.
8531 #include <isl/map.h>
8532 __isl_give isl_map *isl_map_factor_domain(
8533 __isl_take isl_map *map);
8534 __isl_give isl_map *isl_map_factor_range(
8535 __isl_take isl_map *map);
8536 __isl_give isl_map *isl_map_domain_factor_domain(
8537 __isl_take isl_map *map);
8538 __isl_give isl_map *isl_map_domain_factor_range(
8539 __isl_take isl_map *map);
8540 __isl_give isl_map *isl_map_range_factor_domain(
8541 __isl_take isl_map *map);
8542 __isl_give isl_map *isl_map_range_factor_range(
8543 __isl_take isl_map *map);
8545 #include <isl/union_map.h>
8546 __isl_give isl_union_map *isl_union_map_factor_domain(
8547 __isl_take isl_union_map *umap);
8548 __isl_give isl_union_map *isl_union_map_factor_range(
8549 __isl_take isl_union_map *umap);
8550 __isl_give isl_union_map *
8551 isl_union_map_domain_factor_domain(
8552 __isl_take isl_union_map *umap);
8553 __isl_give isl_union_map *
8554 isl_union_map_domain_factor_range(
8555 __isl_take isl_union_map *umap);
8556 __isl_give isl_union_map *
8557 isl_union_map_range_factor_domain(
8558 __isl_take isl_union_map *umap);
8559 __isl_give isl_union_map *
8560 isl_union_map_range_factor_range(
8561 __isl_take isl_union_map *umap);
8564 __isl_give isl_multi_id *isl_multi_id_factor_range(
8565 __isl_take isl_multi_id *mi);
8566 __isl_give isl_multi_id *
8567 isl_multi_id_range_factor_domain(
8568 __isl_take isl_multi_id *mi);
8569 __isl_give isl_multi_id *
8570 isl_multi_id_range_factor_range(
8571 __isl_take isl_multi_id *mi);
8573 #include <isl/val.h>
8574 __isl_give isl_multi_val *isl_multi_val_factor_range(
8575 __isl_take isl_multi_val *mv);
8576 __isl_give isl_multi_val *
8577 isl_multi_val_range_factor_domain(
8578 __isl_take isl_multi_val *mv);
8579 __isl_give isl_multi_val *
8580 isl_multi_val_range_factor_range(
8581 __isl_take isl_multi_val *mv);
8583 #include <isl/aff.h>
8584 __isl_give isl_multi_aff *isl_multi_aff_factor_range(
8585 __isl_take isl_multi_aff *ma);
8586 __isl_give isl_multi_aff *
8587 isl_multi_aff_range_factor_domain(
8588 __isl_take isl_multi_aff *ma);
8589 __isl_give isl_multi_aff *
8590 isl_multi_aff_range_factor_range(
8591 __isl_take isl_multi_aff *ma);
8592 __isl_give isl_multi_pw_aff *
8593 isl_multi_pw_aff_factor_range(
8594 __isl_take isl_multi_pw_aff *mpa);
8595 __isl_give isl_multi_pw_aff *
8596 isl_multi_pw_aff_range_factor_domain(
8597 __isl_take isl_multi_pw_aff *mpa);
8598 __isl_give isl_multi_pw_aff *
8599 isl_multi_pw_aff_range_factor_range(
8600 __isl_take isl_multi_pw_aff *mpa);
8601 __isl_give isl_pw_multi_aff *
8602 isl_pw_multi_aff_range_factor_domain(
8603 __isl_take isl_pw_multi_aff *pma);
8604 __isl_give isl_pw_multi_aff *
8605 isl_pw_multi_aff_range_factor_range(
8606 __isl_take isl_pw_multi_aff *pma);
8607 __isl_give isl_union_pw_multi_aff *
8608 isl_union_pw_multi_aff_range_factor_domain(
8609 __isl_take isl_union_pw_multi_aff *upma);
8610 __isl_give isl_union_pw_multi_aff *
8611 isl_union_pw_multi_aff_range_factor_range(
8612 __isl_take isl_union_pw_multi_aff *upma);
8613 __isl_give isl_multi_union_pw_aff *
8614 isl_multi_union_pw_aff_factor_range(
8615 __isl_take isl_multi_union_pw_aff *mupa);
8616 __isl_give isl_multi_union_pw_aff *
8617 isl_multi_union_pw_aff_range_factor_domain(
8618 __isl_take isl_multi_union_pw_aff *mupa);
8619 __isl_give isl_multi_union_pw_aff *
8620 isl_multi_union_pw_aff_range_factor_range(
8621 __isl_take isl_multi_union_pw_aff *mupa);
8623 The splice functions are a generalization of the flat product functions,
8624 where the second argument may be inserted at any position inside
8625 the first argument rather than being placed at the end.
8626 The functions C<isl_multi_val_factor_range>,
8627 C<isl_multi_aff_factor_range>,
8628 C<isl_multi_pw_aff_factor_range> and
8629 C<isl_multi_union_pw_aff_factor_range>
8630 take functions that live in a set space.
8633 __isl_give isl_multi_id *isl_multi_id_range_splice(
8634 __isl_take isl_multi_id *mi1, unsigned pos,
8635 __isl_take isl_multi_id *mi2);
8637 #include <isl/val.h>
8638 __isl_give isl_multi_val *isl_multi_val_range_splice(
8639 __isl_take isl_multi_val *mv1, unsigned pos,
8640 __isl_take isl_multi_val *mv2);
8642 #include <isl/aff.h>
8643 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
8644 __isl_take isl_multi_aff *ma1, unsigned pos,
8645 __isl_take isl_multi_aff *ma2);
8646 __isl_give isl_multi_aff *isl_multi_aff_splice(
8647 __isl_take isl_multi_aff *ma1,
8648 unsigned in_pos, unsigned out_pos,
8649 __isl_take isl_multi_aff *ma2);
8650 __isl_give isl_multi_pw_aff *
8651 isl_multi_pw_aff_range_splice(
8652 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
8653 __isl_take isl_multi_pw_aff *mpa2);
8654 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
8655 __isl_take isl_multi_pw_aff *mpa1,
8656 unsigned in_pos, unsigned out_pos,
8657 __isl_take isl_multi_pw_aff *mpa2);
8658 __isl_give isl_multi_union_pw_aff *
8659 isl_multi_union_pw_aff_range_splice(
8660 __isl_take isl_multi_union_pw_aff *mupa1,
8662 __isl_take isl_multi_union_pw_aff *mupa2);
8664 =item * Simplification
8666 When applied to a set or relation,
8667 the gist operation returns a set or relation that has the
8668 same intersection with the context as the input set or relation.
8669 Any implicit equality in the intersection is made explicit in the result,
8670 while all inequalities that are redundant with respect to the intersection
8672 In case of union sets and relations, the gist operation is performed
8675 When applied to a function,
8676 the gist operation applies the set gist operation to each of
8677 the cells in the domain of the input piecewise expression.
8678 The context is also exploited
8679 to simplify the expression associated to each cell.
8681 #include <isl/set.h>
8682 __isl_give isl_basic_set *isl_basic_set_gist(
8683 __isl_take isl_basic_set *bset,
8684 __isl_take isl_basic_set *context);
8685 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
8686 __isl_take isl_set *context);
8687 __isl_give isl_set *isl_set_gist_params(
8688 __isl_take isl_set *set,
8689 __isl_take isl_set *context);
8691 #include <isl/map.h>
8692 __isl_give isl_basic_map *isl_basic_map_gist(
8693 __isl_take isl_basic_map *bmap,
8694 __isl_take isl_basic_map *context);
8695 __isl_give isl_basic_map *isl_basic_map_gist_domain(
8696 __isl_take isl_basic_map *bmap,
8697 __isl_take isl_basic_set *context);
8698 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
8699 __isl_take isl_map *context);
8700 __isl_give isl_map *isl_map_gist_params(
8701 __isl_take isl_map *map,
8702 __isl_take isl_set *context);
8703 __isl_give isl_map *isl_map_gist_domain(
8704 __isl_take isl_map *map,
8705 __isl_take isl_set *context);
8706 __isl_give isl_map *isl_map_gist_range(
8707 __isl_take isl_map *map,
8708 __isl_take isl_set *context);
8710 #include <isl/union_set.h>
8711 __isl_give isl_union_set *isl_union_set_gist(
8712 __isl_take isl_union_set *uset,
8713 __isl_take isl_union_set *context);
8714 __isl_give isl_union_set *isl_union_set_gist_params(
8715 __isl_take isl_union_set *uset,
8716 __isl_take isl_set *set);
8718 #include <isl/union_map.h>
8719 __isl_give isl_union_map *isl_union_map_gist(
8720 __isl_take isl_union_map *umap,
8721 __isl_take isl_union_map *context);
8722 __isl_give isl_union_map *isl_union_map_gist_params(
8723 __isl_take isl_union_map *umap,
8724 __isl_take isl_set *set);
8725 __isl_give isl_union_map *isl_union_map_gist_domain(
8726 __isl_take isl_union_map *umap,
8727 __isl_take isl_union_set *uset);
8728 __isl_give isl_union_map *isl_union_map_gist_range(
8729 __isl_take isl_union_map *umap,
8730 __isl_take isl_union_set *uset);
8732 #include <isl/aff.h>
8733 __isl_give isl_aff *isl_aff_gist_params(
8734 __isl_take isl_aff *aff,
8735 __isl_take isl_set *context);
8736 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
8737 __isl_take isl_set *context);
8738 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
8739 __isl_take isl_multi_aff *maff,
8740 __isl_take isl_set *context);
8741 __isl_give isl_multi_aff *isl_multi_aff_gist(
8742 __isl_take isl_multi_aff *maff,
8743 __isl_take isl_set *context);
8744 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
8745 __isl_take isl_pw_aff *pwaff,
8746 __isl_take isl_set *context);
8747 __isl_give isl_pw_aff *isl_pw_aff_gist(
8748 __isl_take isl_pw_aff *pwaff,
8749 __isl_take isl_set *context);
8750 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
8751 __isl_take isl_pw_multi_aff *pma,
8752 __isl_take isl_set *set);
8753 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
8754 __isl_take isl_pw_multi_aff *pma,
8755 __isl_take isl_set *set);
8756 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
8757 __isl_take isl_multi_pw_aff *mpa,
8758 __isl_take isl_set *set);
8759 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
8760 __isl_take isl_multi_pw_aff *mpa,
8761 __isl_take isl_set *set);
8762 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
8763 __isl_take isl_union_pw_aff *upa,
8764 __isl_take isl_union_set *context);
8765 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
8766 __isl_take isl_union_pw_aff *upa,
8767 __isl_take isl_set *context);
8768 __isl_give isl_union_pw_multi_aff *
8769 isl_union_pw_multi_aff_gist_params(
8770 __isl_take isl_union_pw_multi_aff *upma,
8771 __isl_take isl_set *context);
8772 __isl_give isl_union_pw_multi_aff *
8773 isl_union_pw_multi_aff_gist(
8774 __isl_take isl_union_pw_multi_aff *upma,
8775 __isl_take isl_union_set *context);
8776 __isl_give isl_multi_union_pw_aff *
8777 isl_multi_union_pw_aff_gist_params(
8778 __isl_take isl_multi_union_pw_aff *mupa,
8779 __isl_take isl_set *context);
8780 __isl_give isl_multi_union_pw_aff *
8781 isl_multi_union_pw_aff_gist(
8782 __isl_take isl_multi_union_pw_aff *mupa,
8783 __isl_take isl_union_set *context);
8785 #include <isl/polynomial.h>
8786 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
8787 __isl_take isl_qpolynomial *qp,
8788 __isl_take isl_set *context);
8789 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
8790 __isl_take isl_qpolynomial *qp,
8791 __isl_take isl_set *context);
8792 __isl_give isl_qpolynomial_fold *
8793 isl_qpolynomial_fold_gist_params(
8794 __isl_take isl_qpolynomial_fold *fold,
8795 __isl_take isl_set *context);
8796 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
8797 __isl_take isl_qpolynomial_fold *fold,
8798 __isl_take isl_set *context);
8799 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
8800 __isl_take isl_pw_qpolynomial *pwqp,
8801 __isl_take isl_set *context);
8802 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
8803 __isl_take isl_pw_qpolynomial *pwqp,
8804 __isl_take isl_set *context);
8805 __isl_give isl_pw_qpolynomial_fold *
8806 isl_pw_qpolynomial_fold_gist(
8807 __isl_take isl_pw_qpolynomial_fold *pwf,
8808 __isl_take isl_set *context);
8809 __isl_give isl_pw_qpolynomial_fold *
8810 isl_pw_qpolynomial_fold_gist_params(
8811 __isl_take isl_pw_qpolynomial_fold *pwf,
8812 __isl_take isl_set *context);
8813 __isl_give isl_union_pw_qpolynomial *
8814 isl_union_pw_qpolynomial_gist_params(
8815 __isl_take isl_union_pw_qpolynomial *upwqp,
8816 __isl_take isl_set *context);
8817 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
8818 __isl_take isl_union_pw_qpolynomial *upwqp,
8819 __isl_take isl_union_set *context);
8820 __isl_give isl_union_pw_qpolynomial_fold *
8821 isl_union_pw_qpolynomial_fold_gist(
8822 __isl_take isl_union_pw_qpolynomial_fold *upwf,
8823 __isl_take isl_union_set *context);
8824 __isl_give isl_union_pw_qpolynomial_fold *
8825 isl_union_pw_qpolynomial_fold_gist_params(
8826 __isl_take isl_union_pw_qpolynomial_fold *upwf,
8827 __isl_take isl_set *context);
8829 =item * Binary Arithmetic Operations
8831 #include <isl/set.h>
8832 __isl_give isl_set *isl_set_sum(
8833 __isl_take isl_set *set1,
8834 __isl_take isl_set *set2);
8835 #include <isl/map.h>
8836 __isl_give isl_map *isl_map_sum(
8837 __isl_take isl_map *map1,
8838 __isl_take isl_map *map2);
8840 C<isl_set_sum> computes the Minkowski sum of its two arguments,
8841 i.e., the set containing the sums of pairs of elements from
8842 C<set1> and C<set2>.
8843 The domain of the result of C<isl_map_sum> is the intersection
8844 of the domains of its two arguments. The corresponding range
8845 elements are the sums of the corresponding range elements
8846 in the two arguments.
8848 #include <isl/val.h>
8849 __isl_give isl_multi_val *isl_multi_val_add(
8850 __isl_take isl_multi_val *mv1,
8851 __isl_take isl_multi_val *mv2);
8852 __isl_give isl_multi_val *isl_multi_val_sub(
8853 __isl_take isl_multi_val *mv1,
8854 __isl_take isl_multi_val *mv2);
8855 __isl_give isl_multi_val *isl_multi_val_min(
8856 __isl_take isl_multi_val *mv1,
8857 __isl_take isl_multi_val *mv2);
8858 __isl_give isl_multi_val *isl_multi_val_max(
8859 __isl_take isl_multi_val *mv1,
8860 __isl_take isl_multi_val *mv2);
8862 #include <isl/aff.h>
8863 __isl_give isl_aff *isl_aff_add(
8864 __isl_take isl_aff *aff1,
8865 __isl_take isl_aff *aff2);
8866 __isl_give isl_multi_aff *isl_multi_aff_add(
8867 __isl_take isl_multi_aff *maff1,
8868 __isl_take isl_multi_aff *maff2);
8869 __isl_give isl_pw_aff *isl_pw_aff_add(
8870 __isl_take isl_pw_aff *pwaff1,
8871 __isl_take isl_pw_aff *pwaff2);
8872 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add(
8873 __isl_take isl_multi_pw_aff *mpa1,
8874 __isl_take isl_multi_pw_aff *mpa2);
8875 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
8876 __isl_take isl_pw_multi_aff *pma1,
8877 __isl_take isl_pw_multi_aff *pma2);
8878 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
8879 __isl_take isl_union_pw_aff *upa1,
8880 __isl_take isl_union_pw_aff *upa2);
8881 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
8882 __isl_take isl_union_pw_multi_aff *upma1,
8883 __isl_take isl_union_pw_multi_aff *upma2);
8884 __isl_give isl_multi_union_pw_aff *
8885 isl_multi_union_pw_aff_add(
8886 __isl_take isl_multi_union_pw_aff *mupa1,
8887 __isl_take isl_multi_union_pw_aff *mupa2);
8888 __isl_give isl_pw_aff *isl_pw_aff_add_constant_val(
8889 __isl_take isl_pw_aff *pa,
8890 __isl_take isl_val *v);
8891 __isl_give isl_multi_aff *
8892 isl_multi_aff_add_constant_val(
8893 __isl_take isl_multi_aff *pa,
8894 __isl_take isl_val *v);
8895 __isl_give isl_pw_multi_aff *
8896 isl_pw_multi_aff_add_constant_val(
8897 __isl_take isl_pw_multi_aff *pma,
8898 __isl_take isl_val *v);
8899 __isl_give isl_pw_multi_aff *
8900 isl_pw_multi_aff_add_constant_multi_val(
8901 __isl_take isl_pw_multi_aff *pma,
8902 __isl_take isl_multi_val *mv);
8903 __isl_give isl_multi_pw_aff *
8904 isl_multi_pw_aff_add_constant_val(
8905 __isl_take isl_multi_pw_aff *mpa,
8906 __isl_take isl_val *v);
8907 __isl_give isl_multi_aff *
8908 isl_multi_aff_add_constant_multi_val(
8909 __isl_take isl_multi_aff *pa,
8910 __isl_take isl_multi_val *mv);
8911 __isl_give isl_multi_pw_aff *
8912 isl_multi_pw_aff_add_constant_multi_val(
8913 __isl_take isl_multi_pw_aff *mpa,
8914 __isl_take isl_multi_val *mv);
8915 __isl_give isl_pw_aff *isl_pw_aff_min(
8916 __isl_take isl_pw_aff *pwaff1,
8917 __isl_take isl_pw_aff *pwaff2);
8918 __isl_give isl_pw_aff *isl_pw_aff_max(
8919 __isl_take isl_pw_aff *pwaff1,
8920 __isl_take isl_pw_aff *pwaff2);
8921 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_min(
8922 __isl_take isl_multi_pw_aff *mpa1,
8923 __isl_take isl_multi_pw_aff *mpa2);
8924 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_max(
8925 __isl_take isl_multi_pw_aff *mpa1,
8926 __isl_take isl_multi_pw_aff *mpa2);
8927 __isl_give isl_aff *isl_aff_sub(
8928 __isl_take isl_aff *aff1,
8929 __isl_take isl_aff *aff2);
8930 __isl_give isl_multi_aff *isl_multi_aff_sub(
8931 __isl_take isl_multi_aff *ma1,
8932 __isl_take isl_multi_aff *ma2);
8933 __isl_give isl_pw_aff *isl_pw_aff_sub(
8934 __isl_take isl_pw_aff *pwaff1,
8935 __isl_take isl_pw_aff *pwaff2);
8936 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
8937 __isl_take isl_multi_pw_aff *mpa1,
8938 __isl_take isl_multi_pw_aff *mpa2);
8939 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
8940 __isl_take isl_pw_multi_aff *pma1,
8941 __isl_take isl_pw_multi_aff *pma2);
8942 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
8943 __isl_take isl_union_pw_aff *upa1,
8944 __isl_take isl_union_pw_aff *upa2);
8945 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
8946 __isl_take isl_union_pw_multi_aff *upma1,
8947 __isl_take isl_union_pw_multi_aff *upma2);
8948 __isl_give isl_multi_union_pw_aff *
8949 isl_multi_union_pw_aff_sub(
8950 __isl_take isl_multi_union_pw_aff *mupa1,
8951 __isl_take isl_multi_union_pw_aff *mupa2);
8953 C<isl_aff_sub> subtracts the second argument from the first.
8955 #include <isl/polynomial.h>
8956 __isl_give isl_qpolynomial *isl_qpolynomial_add(
8957 __isl_take isl_qpolynomial *qp1,
8958 __isl_take isl_qpolynomial *qp2);
8959 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
8960 __isl_take isl_pw_qpolynomial *pwqp1,
8961 __isl_take isl_pw_qpolynomial *pwqp2);
8962 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
8963 __isl_take isl_pw_qpolynomial *pwqp1,
8964 __isl_take isl_pw_qpolynomial *pwqp2);
8965 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
8966 __isl_take isl_pw_qpolynomial_fold *pwf1,
8967 __isl_take isl_pw_qpolynomial_fold *pwf2);
8968 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
8969 __isl_take isl_union_pw_qpolynomial *upwqp1,
8970 __isl_take isl_union_pw_qpolynomial *upwqp2);
8971 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
8972 __isl_take isl_qpolynomial *qp1,
8973 __isl_take isl_qpolynomial *qp2);
8974 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
8975 __isl_take isl_pw_qpolynomial *pwqp1,
8976 __isl_take isl_pw_qpolynomial *pwqp2);
8977 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
8978 __isl_take isl_union_pw_qpolynomial *upwqp1,
8979 __isl_take isl_union_pw_qpolynomial *upwqp2);
8980 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
8981 __isl_take isl_pw_qpolynomial_fold *pwf1,
8982 __isl_take isl_pw_qpolynomial_fold *pwf2);
8983 __isl_give isl_union_pw_qpolynomial_fold *
8984 isl_union_pw_qpolynomial_fold_fold(
8985 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
8986 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
8988 #include <isl/aff.h>
8989 __isl_give isl_pw_aff *isl_pw_aff_union_add(
8990 __isl_take isl_pw_aff *pwaff1,
8991 __isl_take isl_pw_aff *pwaff2);
8992 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_union_add(
8993 __isl_take isl_multi_pw_aff *mpa1,
8994 __isl_take isl_multi_pw_aff *mpa2);
8995 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
8996 __isl_take isl_pw_multi_aff *pma1,
8997 __isl_take isl_pw_multi_aff *pma2);
8998 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
8999 __isl_take isl_union_pw_aff *upa1,
9000 __isl_take isl_union_pw_aff *upa2);
9001 __isl_give isl_union_pw_multi_aff *
9002 isl_union_pw_multi_aff_union_add(
9003 __isl_take isl_union_pw_multi_aff *upma1,
9004 __isl_take isl_union_pw_multi_aff *upma2);
9005 __isl_give isl_multi_union_pw_aff *
9006 isl_multi_union_pw_aff_union_add(
9007 __isl_take isl_multi_union_pw_aff *mupa1,
9008 __isl_take isl_multi_union_pw_aff *mupa2);
9009 __isl_give isl_pw_aff *isl_pw_aff_union_min(
9010 __isl_take isl_pw_aff *pwaff1,
9011 __isl_take isl_pw_aff *pwaff2);
9012 __isl_give isl_pw_aff *isl_pw_aff_union_max(
9013 __isl_take isl_pw_aff *pwaff1,
9014 __isl_take isl_pw_aff *pwaff2);
9016 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
9017 expression with a domain that is the union of those of C<pwaff1> and
9018 C<pwaff2> and such that on each cell, the quasi-affine expression is
9019 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
9020 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
9021 associated expression is the defined one.
9022 This in contrast to the C<isl_pw_aff_max> function, which is
9023 only defined on the shared definition domain of the arguments.
9025 #include <isl/val.h>
9026 __isl_give isl_multi_val *isl_multi_val_add_val(
9027 __isl_take isl_multi_val *mv,
9028 __isl_take isl_val *v);
9029 __isl_give isl_multi_val *isl_multi_val_mod_val(
9030 __isl_take isl_multi_val *mv,
9031 __isl_take isl_val *v);
9032 __isl_give isl_multi_val *isl_multi_val_scale_val(
9033 __isl_take isl_multi_val *mv,
9034 __isl_take isl_val *v);
9035 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
9036 __isl_take isl_multi_val *mv,
9037 __isl_take isl_val *v);
9039 #include <isl/aff.h>
9040 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
9041 __isl_take isl_val *mod);
9042 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
9043 __isl_take isl_pw_aff *pa,
9044 __isl_take isl_val *mod);
9045 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
9046 __isl_take isl_union_pw_aff *upa,
9047 __isl_take isl_val *f);
9048 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
9049 __isl_take isl_val *v);
9050 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
9051 __isl_take isl_multi_aff *ma,
9052 __isl_take isl_val *v);
9053 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
9054 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
9055 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
9056 __isl_take isl_multi_pw_aff *mpa,
9057 __isl_take isl_val *v);
9058 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
9059 __isl_take isl_pw_multi_aff *pma,
9060 __isl_take isl_val *v);
9061 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
9062 __isl_take isl_union_pw_aff *upa,
9063 __isl_take isl_val *f);
9064 __isl_give isl_union_pw_multi_aff *
9065 isl_union_pw_multi_aff_scale_val(
9066 __isl_take isl_union_pw_multi_aff *upma,
9067 __isl_take isl_val *val);
9068 __isl_give isl_multi_union_pw_aff *
9069 isl_multi_union_pw_aff_scale_val(
9070 __isl_take isl_multi_union_pw_aff *mupa,
9071 __isl_take isl_val *v);
9072 __isl_give isl_aff *isl_aff_scale_down_ui(
9073 __isl_take isl_aff *aff, unsigned f);
9074 __isl_give isl_aff *isl_aff_scale_down_val(
9075 __isl_take isl_aff *aff, __isl_take isl_val *v);
9076 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
9077 __isl_take isl_multi_aff *ma,
9078 __isl_take isl_val *v);
9079 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
9080 __isl_take isl_pw_aff *pa,
9081 __isl_take isl_val *f);
9082 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
9083 __isl_take isl_multi_pw_aff *mpa,
9084 __isl_take isl_val *v);
9085 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
9086 __isl_take isl_pw_multi_aff *pma,
9087 __isl_take isl_val *v);
9088 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
9089 __isl_take isl_union_pw_aff *upa,
9090 __isl_take isl_val *v);
9091 __isl_give isl_union_pw_multi_aff *
9092 isl_union_pw_multi_aff_scale_down_val(
9093 __isl_take isl_union_pw_multi_aff *upma,
9094 __isl_take isl_val *val);
9095 __isl_give isl_multi_union_pw_aff *
9096 isl_multi_union_pw_aff_scale_down_val(
9097 __isl_take isl_multi_union_pw_aff *mupa,
9098 __isl_take isl_val *v);
9100 #include <isl/polynomial.h>
9101 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
9102 __isl_take isl_qpolynomial *qp,
9103 __isl_take isl_val *v);
9104 __isl_give isl_qpolynomial_fold *
9105 isl_qpolynomial_fold_scale_val(
9106 __isl_take isl_qpolynomial_fold *fold,
9107 __isl_take isl_val *v);
9108 __isl_give isl_pw_qpolynomial *
9109 isl_pw_qpolynomial_scale_val(
9110 __isl_take isl_pw_qpolynomial *pwqp,
9111 __isl_take isl_val *v);
9112 __isl_give isl_pw_qpolynomial_fold *
9113 isl_pw_qpolynomial_fold_scale_val(
9114 __isl_take isl_pw_qpolynomial_fold *pwf,
9115 __isl_take isl_val *v);
9116 __isl_give isl_union_pw_qpolynomial *
9117 isl_union_pw_qpolynomial_scale_val(
9118 __isl_take isl_union_pw_qpolynomial *upwqp,
9119 __isl_take isl_val *v);
9120 __isl_give isl_union_pw_qpolynomial_fold *
9121 isl_union_pw_qpolynomial_fold_scale_val(
9122 __isl_take isl_union_pw_qpolynomial_fold *upwf,
9123 __isl_take isl_val *v);
9124 __isl_give isl_qpolynomial *
9125 isl_qpolynomial_scale_down_val(
9126 __isl_take isl_qpolynomial *qp,
9127 __isl_take isl_val *v);
9128 __isl_give isl_qpolynomial_fold *
9129 isl_qpolynomial_fold_scale_down_val(
9130 __isl_take isl_qpolynomial_fold *fold,
9131 __isl_take isl_val *v);
9132 __isl_give isl_pw_qpolynomial *
9133 isl_pw_qpolynomial_scale_down_val(
9134 __isl_take isl_pw_qpolynomial *pwqp,
9135 __isl_take isl_val *v);
9136 __isl_give isl_pw_qpolynomial_fold *
9137 isl_pw_qpolynomial_fold_scale_down_val(
9138 __isl_take isl_pw_qpolynomial_fold *pwf,
9139 __isl_take isl_val *v);
9140 __isl_give isl_union_pw_qpolynomial *
9141 isl_union_pw_qpolynomial_scale_down_val(
9142 __isl_take isl_union_pw_qpolynomial *upwqp,
9143 __isl_take isl_val *v);
9144 __isl_give isl_union_pw_qpolynomial_fold *
9145 isl_union_pw_qpolynomial_fold_scale_down_val(
9146 __isl_take isl_union_pw_qpolynomial_fold *upwf,
9147 __isl_take isl_val *v);
9149 #include <isl/val.h>
9150 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
9151 __isl_take isl_multi_val *mv1,
9152 __isl_take isl_multi_val *mv2);
9153 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
9154 __isl_take isl_multi_val *mv1,
9155 __isl_take isl_multi_val *mv2);
9156 __isl_give isl_multi_val *
9157 isl_multi_val_scale_down_multi_val(
9158 __isl_take isl_multi_val *mv1,
9159 __isl_take isl_multi_val *mv2);
9161 #include <isl/aff.h>
9162 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
9163 __isl_take isl_multi_aff *ma,
9164 __isl_take isl_multi_val *mv);
9165 __isl_give isl_multi_union_pw_aff *
9166 isl_multi_union_pw_aff_mod_multi_val(
9167 __isl_take isl_multi_union_pw_aff *upma,
9168 __isl_take isl_multi_val *mv);
9169 __isl_give isl_multi_pw_aff *
9170 isl_multi_pw_aff_mod_multi_val(
9171 __isl_take isl_multi_pw_aff *mpa,
9172 __isl_take isl_multi_val *mv);
9173 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
9174 __isl_take isl_multi_aff *ma,
9175 __isl_take isl_multi_val *mv);
9176 __isl_give isl_pw_multi_aff *
9177 isl_pw_multi_aff_scale_multi_val(
9178 __isl_take isl_pw_multi_aff *pma,
9179 __isl_take isl_multi_val *mv);
9180 __isl_give isl_multi_pw_aff *
9181 isl_multi_pw_aff_scale_multi_val(
9182 __isl_take isl_multi_pw_aff *mpa,
9183 __isl_take isl_multi_val *mv);
9184 __isl_give isl_multi_union_pw_aff *
9185 isl_multi_union_pw_aff_scale_multi_val(
9186 __isl_take isl_multi_union_pw_aff *mupa,
9187 __isl_take isl_multi_val *mv);
9188 __isl_give isl_union_pw_multi_aff *
9189 isl_union_pw_multi_aff_scale_multi_val(
9190 __isl_take isl_union_pw_multi_aff *upma,
9191 __isl_take isl_multi_val *mv);
9192 __isl_give isl_multi_aff *
9193 isl_multi_aff_scale_down_multi_val(
9194 __isl_take isl_multi_aff *ma,
9195 __isl_take isl_multi_val *mv);
9196 __isl_give isl_pw_multi_aff *
9197 isl_pw_multi_aff_scale_down_multi_val(
9198 __isl_take isl_pw_multi_aff *pma,
9199 __isl_take isl_multi_val *mv);
9200 __isl_give isl_multi_pw_aff *
9201 isl_multi_pw_aff_scale_down_multi_val(
9202 __isl_take isl_multi_pw_aff *mpa,
9203 __isl_take isl_multi_val *mv);
9204 __isl_give isl_multi_union_pw_aff *
9205 isl_multi_union_pw_aff_scale_down_multi_val(
9206 __isl_take isl_multi_union_pw_aff *mupa,
9207 __isl_take isl_multi_val *mv);
9209 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
9210 by the corresponding elements of C<mv>.
9212 #include <isl/aff.h>
9213 __isl_give isl_aff *isl_aff_mul(
9214 __isl_take isl_aff *aff1,
9215 __isl_take isl_aff *aff2);
9216 __isl_give isl_aff *isl_aff_div(
9217 __isl_take isl_aff *aff1,
9218 __isl_take isl_aff *aff2);
9219 __isl_give isl_pw_aff *isl_pw_aff_mul(
9220 __isl_take isl_pw_aff *pwaff1,
9221 __isl_take isl_pw_aff *pwaff2);
9222 __isl_give isl_pw_aff *isl_pw_aff_div(
9223 __isl_take isl_pw_aff *pa1,
9224 __isl_take isl_pw_aff *pa2);
9225 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
9226 __isl_take isl_pw_aff *pa1,
9227 __isl_take isl_pw_aff *pa2);
9228 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
9229 __isl_take isl_pw_aff *pa1,
9230 __isl_take isl_pw_aff *pa2);
9232 When multiplying two affine expressions, at least one of the two needs
9233 to be a constant. Similarly, when dividing an affine expression by another,
9234 the second expression needs to be a constant.
9235 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
9236 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
9239 #include <isl/polynomial.h>
9240 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
9241 __isl_take isl_qpolynomial *qp1,
9242 __isl_take isl_qpolynomial *qp2);
9243 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
9244 __isl_take isl_pw_qpolynomial *pwqp1,
9245 __isl_take isl_pw_qpolynomial *pwqp2);
9246 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
9247 __isl_take isl_union_pw_qpolynomial *upwqp1,
9248 __isl_take isl_union_pw_qpolynomial *upwqp2);
9252 =head3 Lexicographic Optimization
9254 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
9255 the following functions
9256 compute a set that contains the lexicographic minimum or maximum
9257 of the elements in C<set> (or C<bset>) for those values of the parameters
9258 that satisfy C<dom>.
9259 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
9260 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
9262 In other words, the union of the parameter values
9263 for which the result is non-empty and of C<*empty>
9266 #include <isl/set.h>
9267 __isl_give isl_set *isl_basic_set_partial_lexmin(
9268 __isl_take isl_basic_set *bset,
9269 __isl_take isl_basic_set *dom,
9270 __isl_give isl_set **empty);
9271 __isl_give isl_set *isl_basic_set_partial_lexmax(
9272 __isl_take isl_basic_set *bset,
9273 __isl_take isl_basic_set *dom,
9274 __isl_give isl_set **empty);
9275 __isl_give isl_set *isl_set_partial_lexmin(
9276 __isl_take isl_set *set, __isl_take isl_set *dom,
9277 __isl_give isl_set **empty);
9278 __isl_give isl_set *isl_set_partial_lexmax(
9279 __isl_take isl_set *set, __isl_take isl_set *dom,
9280 __isl_give isl_set **empty);
9282 Given a (basic) set C<set> (or C<bset>), the following functions simply
9283 return a set containing the lexicographic minimum or maximum
9284 of the elements in C<set> (or C<bset>).
9285 In case of union sets, the optimum is computed per space.
9287 #include <isl/set.h>
9288 __isl_give isl_set *isl_basic_set_lexmin(
9289 __isl_take isl_basic_set *bset);
9290 __isl_give isl_set *isl_basic_set_lexmax(
9291 __isl_take isl_basic_set *bset);
9292 __isl_give isl_set *isl_set_lexmin(
9293 __isl_take isl_set *set);
9294 __isl_give isl_set *isl_set_lexmax(
9295 __isl_take isl_set *set);
9296 __isl_give isl_union_set *isl_union_set_lexmin(
9297 __isl_take isl_union_set *uset);
9298 __isl_give isl_union_set *isl_union_set_lexmax(
9299 __isl_take isl_union_set *uset);
9301 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
9302 the following functions
9303 compute a relation that maps each element of C<dom>
9304 to the single lexicographic minimum or maximum
9305 of the elements that are associated to that same
9306 element in C<map> (or C<bmap>).
9307 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
9308 that contains the elements in C<dom> that do not map
9309 to any elements in C<map> (or C<bmap>).
9310 In other words, the union of the domain of the result and of C<*empty>
9313 #include <isl/map.h>
9314 __isl_give isl_map *isl_basic_map_partial_lexmax(
9315 __isl_take isl_basic_map *bmap,
9316 __isl_take isl_basic_set *dom,
9317 __isl_give isl_set **empty);
9318 __isl_give isl_map *isl_basic_map_partial_lexmin(
9319 __isl_take isl_basic_map *bmap,
9320 __isl_take isl_basic_set *dom,
9321 __isl_give isl_set **empty);
9322 __isl_give isl_map *isl_map_partial_lexmax(
9323 __isl_take isl_map *map, __isl_take isl_set *dom,
9324 __isl_give isl_set **empty);
9325 __isl_give isl_map *isl_map_partial_lexmin(
9326 __isl_take isl_map *map, __isl_take isl_set *dom,
9327 __isl_give isl_set **empty);
9329 Given a (basic) map C<map> (or C<bmap>), the following functions simply
9330 return a map mapping each element in the domain of
9331 C<map> (or C<bmap>) to the lexicographic minimum or maximum
9332 of all elements associated to that element.
9333 In case of union relations, the optimum is computed per space.
9335 #include <isl/map.h>
9336 __isl_give isl_map *isl_basic_map_lexmin(
9337 __isl_take isl_basic_map *bmap);
9338 __isl_give isl_map *isl_basic_map_lexmax(
9339 __isl_take isl_basic_map *bmap);
9340 __isl_give isl_map *isl_map_lexmin(
9341 __isl_take isl_map *map);
9342 __isl_give isl_map *isl_map_lexmax(
9343 __isl_take isl_map *map);
9344 __isl_give isl_union_map *isl_union_map_lexmin(
9345 __isl_take isl_union_map *umap);
9346 __isl_give isl_union_map *isl_union_map_lexmax(
9347 __isl_take isl_union_map *umap);
9349 The following functions return their result in the form of
9350 a piecewise multi-affine expression,
9351 but are otherwise equivalent to the corresponding functions
9352 returning a basic set or relation.
9354 #include <isl/set.h>
9355 __isl_give isl_pw_multi_aff *
9356 isl_basic_set_partial_lexmin_pw_multi_aff(
9357 __isl_take isl_basic_set *bset,
9358 __isl_take isl_basic_set *dom,
9359 __isl_give isl_set **empty);
9360 __isl_give isl_pw_multi_aff *
9361 isl_basic_set_partial_lexmax_pw_multi_aff(
9362 __isl_take isl_basic_set *bset,
9363 __isl_take isl_basic_set *dom,
9364 __isl_give isl_set **empty);
9365 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
9366 __isl_take isl_set *set);
9367 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
9368 __isl_take isl_set *set);
9370 #include <isl/map.h>
9371 __isl_give isl_pw_multi_aff *
9372 isl_basic_map_lexmin_pw_multi_aff(
9373 __isl_take isl_basic_map *bmap);
9374 __isl_give isl_pw_multi_aff *
9375 isl_basic_map_partial_lexmin_pw_multi_aff(
9376 __isl_take isl_basic_map *bmap,
9377 __isl_take isl_basic_set *dom,
9378 __isl_give isl_set **empty);
9379 __isl_give isl_pw_multi_aff *
9380 isl_basic_map_partial_lexmax_pw_multi_aff(
9381 __isl_take isl_basic_map *bmap,
9382 __isl_take isl_basic_set *dom,
9383 __isl_give isl_set **empty);
9384 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
9385 __isl_take isl_map *map);
9386 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
9387 __isl_take isl_map *map);
9389 The following functions return the lexicographic minimum or maximum
9390 on the shared domain of the inputs and the single defined function
9391 on those parts of the domain where only a single function is defined.
9393 #include <isl/aff.h>
9394 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
9395 __isl_take isl_pw_multi_aff *pma1,
9396 __isl_take isl_pw_multi_aff *pma2);
9397 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
9398 __isl_take isl_pw_multi_aff *pma1,
9399 __isl_take isl_pw_multi_aff *pma2);
9401 If the input to a lexicographic optimization problem has
9402 multiple constraints with the same coefficients for the optimized
9403 variables, then, by default, this symmetry is exploited by
9404 replacing those constraints by a single constraint with
9405 an abstract bound, which is in turn bounded by the corresponding terms
9406 in the original constraints.
9407 Without this optimization, the solver would typically consider
9408 all possible orderings of those original bounds, resulting in a needless
9409 decomposition of the domain.
9410 However, the optimization can also result in slowdowns since
9411 an extra parameter is introduced that may get used in additional
9413 The following option determines whether symmetry detection is applied
9414 during lexicographic optimization.
9416 #include <isl/options.h>
9417 isl_stat isl_options_set_pip_symmetry(isl_ctx *ctx,
9419 int isl_options_get_pip_symmetry(isl_ctx *ctx);
9423 See also \autoref{s:offline}.
9427 =head2 Ternary Operations
9429 #include <isl/aff.h>
9430 __isl_give isl_pw_aff *isl_pw_aff_cond(
9431 __isl_take isl_pw_aff *cond,
9432 __isl_take isl_pw_aff *pwaff_true,
9433 __isl_take isl_pw_aff *pwaff_false);
9435 The function C<isl_pw_aff_cond> performs a conditional operator
9436 and returns an expression that is equal to C<pwaff_true>
9437 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
9438 where C<cond> is zero.
9442 Lists are defined over several element types, including
9443 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_pw_multi_aff>,
9444 C<isl_union_pw_aff>,
9445 C<isl_union_pw_multi_aff>,
9446 C<isl_qpolynomial>, C<isl_pw_qpolynomial>, C<isl_pw_qpolynomial_fold>,
9448 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
9449 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
9450 Here we take lists of C<isl_set>s as an example.
9451 Lists can be created, copied, modified and freed using the following functions.
9453 #include <isl/set.h>
9454 __isl_give isl_set_list *isl_set_to_list(
9455 __isl_take isl_set *el);
9456 __isl_give isl_set_list *isl_set_list_from_set(
9457 __isl_take isl_set *el);
9458 __isl_give isl_set_list *isl_set_list_alloc(
9459 isl_ctx *ctx, int n);
9460 __isl_give isl_set_list *isl_set_list_copy(
9461 __isl_keep isl_set_list *list);
9462 __isl_give isl_set_list *isl_set_list_insert(
9463 __isl_take isl_set_list *list, unsigned pos,
9464 __isl_take isl_set *el);
9465 __isl_give isl_set_list *isl_set_list_add(
9466 __isl_take isl_set_list *list,
9467 __isl_take isl_set *el);
9468 __isl_give isl_set_list *isl_set_list_drop(
9469 __isl_take isl_set_list *list,
9470 unsigned first, unsigned n);
9471 __isl_give isl_set_list *isl_set_list_clear(
9472 __isl_take isl_set_list *list);
9473 __isl_give isl_set_list *isl_set_list_swap(
9474 __isl_take isl_set_list *list,
9475 unsigned pos1, unsigned pos2);
9476 __isl_give isl_set_list *isl_set_list_reverse(
9477 __isl_take isl_set_list *list);
9478 __isl_give isl_set_list *isl_set_list_set_at(
9479 __isl_take isl_set_list *list, int index,
9480 __isl_take isl_set *set);
9481 __isl_give isl_set_list *isl_set_list_set_set(
9482 __isl_take isl_set_list *list, int index,
9483 __isl_take isl_set *set);
9484 __isl_give isl_set_list *isl_set_list_concat(
9485 __isl_take isl_set_list *list1,
9486 __isl_take isl_set_list *list2);
9487 __isl_give isl_set_list *isl_set_list_map(
9488 __isl_take isl_set_list *list,
9489 __isl_give isl_set *(*fn)(__isl_take isl_set *el,
9492 __isl_give isl_set_list *isl_set_list_sort(
9493 __isl_take isl_set_list *list,
9494 int (*cmp)(__isl_keep isl_set *a,
9495 __isl_keep isl_set *b, void *user),
9497 __isl_null isl_set_list *isl_set_list_free(
9498 __isl_take isl_set_list *list);
9500 C<isl_set_list_alloc> creates an empty list with an initial capacity
9501 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
9502 add elements to a list, increasing its capacity as needed.
9503 C<isl_set_to_list> creates a list with a single element.
9504 C<isl_set_list_from_set> performs the same operation.
9505 C<isl_set_list_clear> removes all elements from a list.
9506 C<isl_set_list_swap> swaps the elements at the specified locations.
9507 C<isl_set_list_reverse> reverses the elements in the list.
9508 C<isl_set_list_set_set> is an alternative name for C<isl_set_list_set_at>.
9510 Lists can be inspected using the following functions.
9512 #include <isl/set.h>
9513 isl_size isl_set_list_size(__isl_keep isl_set_list *list);
9514 isl_size isl_set_list_n_set(__isl_keep isl_set_list *list);
9515 __isl_give isl_set *isl_set_list_get_at(
9516 __isl_keep isl_set_list *list, int index);
9517 __isl_give isl_set *isl_set_list_get_set(
9518 __isl_keep isl_set_list *list, int index);
9519 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list,
9520 isl_stat (*fn)(__isl_take isl_set *el, void *user),
9522 isl_bool isl_set_list_every(__isl_keep isl_set_list *list,
9523 isl_bool (*test)(__isl_take isl_set *el,
9526 isl_stat isl_set_list_foreach_scc(
9527 __isl_keep isl_set_list *list,
9528 isl_bool (*follows)(__isl_keep isl_set *a,
9529 __isl_keep isl_set *b, void *user),
9531 isl_stat (*fn)(__isl_take isl_set_list *scc,
9535 C<isl_set_list_n_set> is an alternative name for C<isl_set_list_size>.
9537 C<isl_set_list_get_set> is an alternative name for C<isl_set_list_get_at>.
9538 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
9539 strongly connected components of the graph with as vertices the elements
9540 of C<list> and a directed edge from vertex C<b> to vertex C<a>
9541 iff C<follows(a, b)> returns C<isl_bool_true>. The callbacks C<follows> and
9542 C<fn> should return C<isl_bool_error> or C<isl_stat_error> on error.
9544 Lists can be printed using
9546 #include <isl/set.h>
9547 __isl_give isl_printer *isl_printer_print_set_list(
9548 __isl_take isl_printer *p,
9549 __isl_keep isl_set_list *list);
9551 Alternatively, a string representation can be obtained
9552 directly using the following function, which always prints
9555 #include <isl/set.h>
9556 __isl_give char *isl_set_list_to_str(
9557 __isl_keep isl_set_list *list);
9559 An C<isl_val_list>, C<isl_id_list>,
9560 C<isl_aff_list>, C<isl_pw_aff_list>, C<isl_pw_multi_aff_list>,
9561 C<isl_union_pw_aff_list>,
9562 C<isl_set_list>, C<isl_map_list> or C<isl_union_set_list> object
9563 can also be read from input using the following functions.
9565 #include <isl/val.h>
9566 __isl_give isl_val_list *isl_val_list_read_from_str(
9567 isl_ctx *ctx, const char *str);
9570 __isl_give isl_id_list *isl_id_list_read_from_str(
9571 isl_ctx *ctx, const char *str);
9573 #include <isl/aff.h>
9574 __isl_give isl_aff_list *
9575 isl_aff_list_read_from_str(isl_ctx *ctx,
9577 __isl_give isl_pw_aff_list *
9578 isl_pw_aff_list_read_from_str(isl_ctx *ctx,
9580 __isl_give isl_pw_multi_aff_list *
9581 isl_pw_multi_aff_list_read_from_str(isl_ctx *ctx,
9583 __isl_give isl_union_pw_aff_list *
9584 isl_union_pw_aff_list_read_from_str(isl_ctx *ctx,
9587 #include <isl/set.h>
9588 __isl_give isl_set_list *isl_set_list_read_from_str(
9589 isl_ctx *ctx, const char *str);
9591 #include <isl/map.h>
9592 __isl_give isl_map_list *isl_map_list_read_from_str(
9593 isl_ctx *ctx, const char *str);
9595 #include <isl/union_set.h>
9596 __isl_give isl_union_set_list *
9597 isl_union_set_list_read_from_str(isl_ctx *ctx,
9600 =head2 Associative arrays
9602 Associative arrays map isl objects of a specific type to isl objects
9603 of some (other) specific type. They are defined for several pairs
9604 of types, including (C<isl_map>, C<isl_basic_set>),
9605 (C<isl_id>, C<isl_ast_expr>),
9606 (C<isl_id>, C<isl_id>) and
9607 (C<isl_id>, C<isl_pw_aff>).
9608 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
9611 Associative arrays can be created, copied and freed using
9612 the following functions.
9614 #include <isl/id_to_ast_expr.h>
9615 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
9616 isl_ctx *ctx, int min_size);
9617 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
9618 __isl_keep isl_id_to_ast_expr *id2expr);
9619 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
9620 __isl_take isl_id_to_ast_expr *id2expr);
9622 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
9623 to specify the expected size of the associative array.
9624 The associative array will be grown automatically as needed.
9626 Associative arrays can be inspected using the following functions.
9628 #include <isl/id_to_ast_expr.h>
9629 __isl_give isl_maybe_isl_ast_expr
9630 isl_id_to_ast_expr_try_get(
9631 __isl_keep isl_id_to_ast_expr *id2expr,
9632 __isl_keep isl_id *key);
9633 isl_bool isl_id_to_ast_expr_has(
9634 __isl_keep isl_id_to_ast_expr *id2expr,
9635 __isl_keep isl_id *key);
9636 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
9637 __isl_keep isl_id_to_ast_expr *id2expr,
9638 __isl_take isl_id *key);
9639 isl_stat isl_id_to_ast_expr_foreach(
9640 __isl_keep isl_id_to_ast_expr *id2expr,
9641 isl_stat (*fn)(__isl_take isl_id *key,
9642 __isl_take isl_ast_expr *val, void *user),
9644 isl_bool isl_id_to_ast_expr_every(
9645 __isl_keep isl_id_to_ast_expr *id2expr,
9646 isl_bool (*test)(__isl_keep isl_id *key,
9647 __isl_keep isl_ast_expr *val, void *user),
9650 The function C<isl_id_to_ast_expr_try_get> returns a structure
9651 containing two elements, C<valid> and C<value>.
9652 If there is a value associated to the key, then C<valid>
9653 is set to C<isl_bool_true> and C<value> contains a copy of
9654 the associated value. Otherwise C<value> is C<NULL> and
9655 C<valid> may be C<isl_bool_error> or C<isl_bool_false> depending
9656 on whether some error has occurred or there simply is no associated value.
9657 The function C<isl_id_to_ast_expr_has> returns the C<valid> field
9658 in the structure and
9659 the function C<isl_id_to_ast_expr_get> returns the C<value> field.
9661 Associative arrays can be modified using the following functions.
9663 #include <isl/id_to_ast_expr.h>
9664 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
9665 __isl_take isl_id_to_ast_expr *id2expr,
9666 __isl_take isl_id *key,
9667 __isl_take isl_ast_expr *val);
9668 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
9669 __isl_take isl_id_to_ast_expr *id2expr,
9670 __isl_take isl_id *key);
9672 Associative arrays can be checked for (obvious) equality
9673 using the following function.
9675 #include <isl/id_to_ast_expr.h>
9676 isl_bool isl_id_to_ast_expr_is_equal(
9677 __isl_take isl_id_to_ast_expr *id2expr1,
9678 __isl_take isl_id_to_ast_expr *id2expr2);
9680 Note that depending on how the keys and values are being compared,
9681 for other types of keys and/or values, this function may be called
9682 C<plain_is_equal> rather than C<is_equal>.
9684 Associative arrays can be printed using the following functions.
9686 #include <isl/id_to_ast_expr.h>
9687 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
9688 __isl_take isl_printer *p,
9689 __isl_keep isl_id_to_ast_expr *id2expr);
9690 __isl_give char *isl_id_to_ast_expr_to_str(
9691 __isl_keep isl_id_to_ast_expr *id2expr);
9693 They can be read from input using the following function.
9695 #include <isl/id_to_ast_expr.h>
9696 __isl_give isl_id_to_ast_expr *
9697 isl_id_to_ast_expr_read_from_str(isl_ctx *ctx,
9702 Vectors can be created, copied and freed using the following functions.
9704 #include <isl/vec.h>
9705 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
9707 __isl_give isl_vec *isl_vec_zero(isl_ctx *ctx,
9709 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
9710 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
9712 Note that the elements of a vector created by C<isl_vec_alloc>
9713 may have arbitrary values.
9714 A vector created by C<isl_vec_zero> has elements with value zero.
9715 The elements can be changed and inspected using the following functions.
9717 isl_size isl_vec_size(__isl_keep isl_vec *vec);
9718 __isl_give isl_val *isl_vec_get_element_val(
9719 __isl_keep isl_vec *vec, int pos);
9720 __isl_give isl_vec *isl_vec_set_element_si(
9721 __isl_take isl_vec *vec, int pos, int v);
9722 __isl_give isl_vec *isl_vec_set_element_val(
9723 __isl_take isl_vec *vec, int pos,
9724 __isl_take isl_val *v);
9725 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
9727 __isl_give isl_vec *isl_vec_set_val(
9728 __isl_take isl_vec *vec, __isl_take isl_val *v);
9729 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
9730 __isl_keep isl_vec *vec2, int pos);
9732 C<isl_vec_get_element> will return a negative value if anything went wrong.
9733 In that case, the value of C<*v> is undefined.
9735 The following function can be used to concatenate two vectors.
9737 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
9738 __isl_take isl_vec *vec2);
9742 Matrices can be created, copied and freed using the following functions.
9744 #include <isl/mat.h>
9745 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
9746 unsigned n_row, unsigned n_col);
9747 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
9748 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
9750 Note that the elements of a newly created matrix may have arbitrary values.
9751 The elements can be changed and inspected using the following functions.
9753 isl_size isl_mat_rows(__isl_keep isl_mat *mat);
9754 isl_size isl_mat_cols(__isl_keep isl_mat *mat);
9755 __isl_give isl_val *isl_mat_get_element_val(
9756 __isl_keep isl_mat *mat, int row, int col);
9757 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
9758 int row, int col, int v);
9759 __isl_give isl_mat *isl_mat_set_element_val(
9760 __isl_take isl_mat *mat, int row, int col,
9761 __isl_take isl_val *v);
9763 The following function computes the rank of a matrix.
9764 The return value may be -1 if some error occurred.
9766 #include <isl/mat.h>
9767 isl_size isl_mat_rank(__isl_keep isl_mat *mat);
9769 The following function can be used to compute the (right) inverse
9770 of a matrix, i.e., a matrix such that the product of the original
9771 and the inverse (in that order) is a multiple of the identity matrix.
9772 The input matrix is assumed to be of full row-rank.
9774 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
9776 The following function can be used to compute the (right) kernel
9777 (or null space) of a matrix, i.e., a matrix such that the product of
9778 the original and the kernel (in that order) is the zero matrix.
9780 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
9782 The following function computes a basis for the space spanned
9783 by the rows of a matrix.
9785 __isl_give isl_mat *isl_mat_row_basis(
9786 __isl_take isl_mat *mat);
9788 The following function computes rows that extend a basis of C<mat1>
9789 to a basis that also covers C<mat2>.
9791 __isl_give isl_mat *isl_mat_row_basis_extension(
9792 __isl_take isl_mat *mat1,
9793 __isl_take isl_mat *mat2);
9795 The following function checks whether there is no linear dependence
9796 among the combined rows of "mat1" and "mat2" that is not already present
9797 in "mat1" or "mat2" individually.
9798 If "mat1" and "mat2" have linearly independent rows by themselves,
9799 then this means that there is no linear dependence among all rows together.
9801 isl_bool isl_mat_has_linearly_independent_rows(
9802 __isl_keep isl_mat *mat1,
9803 __isl_keep isl_mat *mat2);
9805 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
9807 The following functions determine
9808 an upper or lower bound on a quasipolynomial over its domain.
9810 __isl_give isl_pw_qpolynomial_fold *
9811 isl_pw_qpolynomial_bound(
9812 __isl_take isl_pw_qpolynomial *pwqp,
9813 enum isl_fold type, isl_bool *tight);
9815 __isl_give isl_union_pw_qpolynomial_fold *
9816 isl_union_pw_qpolynomial_bound(
9817 __isl_take isl_union_pw_qpolynomial *upwqp,
9818 enum isl_fold type, isl_bool *tight);
9820 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
9821 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
9822 is the returned bound is known be tight, i.e., for each value
9823 of the parameters there is at least
9824 one element in the domain that reaches the bound.
9825 If the domain of C<pwqp> is not wrapping, then the bound is computed
9826 over all elements in that domain and the result has a purely parametric
9827 domain. If the domain of C<pwqp> is wrapping, then the bound is
9828 computed over the range of the wrapped relation. The domain of the
9829 wrapped relation becomes the domain of the result.
9831 =head2 Parametric Vertex Enumeration
9833 The parametric vertex enumeration described in this section
9834 is mainly intended to be used internally and by the C<barvinok>
9837 #include <isl/vertices.h>
9838 __isl_give isl_vertices *isl_basic_set_compute_vertices(
9839 __isl_keep isl_basic_set *bset);
9841 The function C<isl_basic_set_compute_vertices> performs the
9842 actual computation of the parametric vertices and the chamber
9843 decomposition and stores the result in an C<isl_vertices> object.
9844 This information can be queried by either iterating over all
9845 the vertices or iterating over all the chambers or cells
9846 and then iterating over all vertices that are active on the chamber.
9848 isl_stat isl_vertices_foreach_vertex(
9849 __isl_keep isl_vertices *vertices,
9850 isl_stat (*fn)(__isl_take isl_vertex *vertex,
9851 void *user), void *user);
9853 isl_stat isl_vertices_foreach_cell(
9854 __isl_keep isl_vertices *vertices,
9855 isl_stat (*fn)(__isl_take isl_cell *cell,
9856 void *user), void *user);
9857 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
9858 isl_stat (*fn)(__isl_take isl_vertex *vertex,
9859 void *user), void *user);
9861 Other operations that can be performed on an C<isl_vertices> object are
9864 isl_size isl_vertices_get_n_vertices(
9865 __isl_keep isl_vertices *vertices);
9866 __isl_null isl_vertices *isl_vertices_free(
9867 __isl_take isl_vertices *vertices);
9869 Vertices can be inspected and destroyed using the following functions.
9871 isl_size isl_vertex_get_id(__isl_keep isl_vertex *vertex);
9872 __isl_give isl_basic_set *isl_vertex_get_domain(
9873 __isl_keep isl_vertex *vertex);
9874 __isl_give isl_multi_aff *isl_vertex_get_expr(
9875 __isl_keep isl_vertex *vertex);
9876 __isl_null isl_vertex *isl_vertex_free(
9877 __isl_take isl_vertex *vertex);
9879 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
9880 describing the vertex in terms of the parameters,
9881 while C<isl_vertex_get_domain> returns the activity domain
9884 Chambers can be inspected and destroyed using the following functions.
9886 __isl_give isl_basic_set *isl_cell_get_domain(
9887 __isl_keep isl_cell *cell);
9888 __isl_null isl_cell *isl_cell_free(
9889 __isl_take isl_cell *cell);
9891 =head1 Polyhedral Compilation Library
9893 This section collects functionality in C<isl> that has been specifically
9894 designed for use during polyhedral compilation.
9896 =head2 Schedule Trees
9898 A schedule tree is a structured representation of a schedule,
9899 assigning a relative order to a set of domain elements.
9900 The relative order expressed by the schedule tree is
9901 defined recursively. In particular, the order between
9902 two domain elements is determined by the node that is closest
9903 to the root that refers to both elements and that orders them apart.
9904 Each node in the tree is of one of several types.
9905 The root node is always of type C<isl_schedule_node_domain>
9906 (or C<isl_schedule_node_extension>)
9907 and it describes the (extra) domain elements to which the schedule applies.
9908 The other types of nodes are as follows.
9912 =item C<isl_schedule_node_band>
9914 A band of schedule dimensions. Each schedule dimension is represented
9915 by a union piecewise quasi-affine expression. If this expression
9916 assigns a different value to two domain elements, while all previous
9917 schedule dimensions in the same band assign them the same value,
9918 then the two domain elements are ordered according to these two
9920 Each expression is required to be total in the domain elements
9921 that reach the band node.
9923 =item C<isl_schedule_node_expansion>
9925 An expansion node maps each of the domain elements that reach the node
9926 to one or more domain elements. The image of this mapping forms
9927 the set of domain elements that reach the child of the expansion node.
9928 The function that maps each of the expanded domain elements
9929 to the original domain element from which it was expanded
9930 is called the contraction.
9932 =item C<isl_schedule_node_filter>
9934 A filter node does not impose any ordering, but rather intersects
9935 the set of domain elements that the current subtree refers to
9936 with a given union set. The subtree of the filter node only
9937 refers to domain elements in the intersection.
9938 A filter node is typically only used as a child of a sequence or
9941 =item C<isl_schedule_node_leaf>
9943 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
9945 =item C<isl_schedule_node_mark>
9947 A mark node can be used to attach any kind of information to a subtree
9948 of the schedule tree.
9950 =item C<isl_schedule_node_sequence>
9952 A sequence node has one or more children, each of which is a filter node.
9953 The filters on these filter nodes form a partition of
9954 the domain elements that the current subtree refers to.
9955 If two domain elements appear in distinct filters then the sequence
9956 node orders them according to the child positions of the corresponding
9959 =item C<isl_schedule_node_set>
9961 A set node is similar to a sequence node, except that
9962 it expresses that domain elements appearing in distinct filters
9963 may have any order. The order of the children of a set node
9964 is therefore also immaterial.
9968 The following node types are only supported by the AST generator.
9972 =item C<isl_schedule_node_context>
9974 The context describes constraints on the parameters and
9975 the schedule dimensions of outer
9976 bands that the AST generator may assume to hold. It is also the only
9977 kind of node that may introduce additional parameters.
9978 The space of the context is that of the flat product of the outer
9979 band nodes. In particular, if there are no outer band nodes, then
9980 this space is the unnamed zero-dimensional space.
9981 Since a context node references the outer band nodes, any tree
9982 containing a context node is considered to be anchored.
9984 =item C<isl_schedule_node_extension>
9986 An extension node instructs the AST generator to add additional
9987 domain elements that need to be scheduled.
9988 The additional domain elements are described by the range of
9989 the extension map in terms of the outer schedule dimensions,
9990 i.e., the flat product of the outer band nodes.
9991 Note that domain elements are added whenever the AST generator
9992 reaches the extension node, meaning that there are still some
9993 active domain elements for which an AST needs to be generated.
9994 The conditions under which some domain elements are still active
9995 may however not be completely described by the outer AST nodes
9996 generated at that point.
9997 Since an extension node references the outer band nodes, any tree
9998 containing an extension node is considered to be anchored.
10000 An extension node may also appear as the root of a schedule tree,
10001 when it is intended to be inserted into another tree
10002 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
10003 In this case, the domain of the extension node should
10004 correspond to the flat product of the outer band nodes
10005 in this other schedule tree at the point where the extension tree
10008 =item C<isl_schedule_node_guard>
10010 The guard describes constraints on the parameters and
10011 the schedule dimensions of outer
10012 bands that need to be enforced by the outer nodes
10013 in the generated AST.
10014 That is, the part of the AST that is generated from descendants
10015 of the guard node can assume that these constraints are satisfied.
10016 The space of the guard is that of the flat product of the outer
10017 band nodes. In particular, if there are no outer band nodes, then
10018 this space is the unnamed zero-dimensional space.
10019 Since a guard node references the outer band nodes, any tree
10020 containing a guard node is considered to be anchored.
10024 Except for the C<isl_schedule_node_context> nodes,
10025 none of the nodes may introduce any parameters that were not
10026 already present in the root domain node.
10028 A schedule tree is encapsulated in an C<isl_schedule> object.
10029 The simplest such objects, those with a tree consisting of single domain node,
10030 can be created using the following functions with either an empty
10031 domain or a given domain.
10033 #include <isl/schedule.h>
10034 __isl_give isl_schedule *isl_schedule_empty(
10035 __isl_take isl_space *space);
10036 __isl_give isl_schedule *isl_schedule_from_domain(
10037 __isl_take isl_union_set *domain);
10039 The function C<isl_schedule_constraints_compute_schedule> described
10040 in L</"Scheduling"> can also be used to construct schedules.
10042 C<isl_schedule> objects may be copied and freed using the following functions.
10044 #include <isl/schedule.h>
10045 __isl_give isl_schedule *isl_schedule_copy(
10046 __isl_keep isl_schedule *sched);
10047 __isl_null isl_schedule *isl_schedule_free(
10048 __isl_take isl_schedule *sched);
10050 The following functions checks whether two C<isl_schedule> objects
10051 are obviously the same.
10053 #include <isl/schedule.h>
10054 isl_bool isl_schedule_plain_is_equal(
10055 __isl_keep isl_schedule *schedule1,
10056 __isl_keep isl_schedule *schedule2);
10058 The domain of the schedule, i.e., the domain described by the root node,
10059 can be obtained using the following function.
10061 #include <isl/schedule.h>
10062 __isl_give isl_union_set *isl_schedule_get_domain(
10063 __isl_keep isl_schedule *schedule);
10065 An extra top-level band node (right underneath the domain node) can
10066 be introduced into the schedule using the following function.
10067 The schedule tree is assumed not to have any anchored nodes.
10069 #include <isl/schedule.h>
10070 __isl_give isl_schedule *
10071 isl_schedule_insert_partial_schedule(
10072 __isl_take isl_schedule *schedule,
10073 __isl_take isl_multi_union_pw_aff *partial);
10075 A top-level context node (right underneath the domain node) can
10076 be introduced into the schedule using the following function.
10078 #include <isl/schedule.h>
10079 __isl_give isl_schedule *isl_schedule_insert_context(
10080 __isl_take isl_schedule *schedule,
10081 __isl_take isl_set *context)
10083 A top-level guard node (right underneath the domain node) can
10084 be introduced into the schedule using the following function.
10086 #include <isl/schedule.h>
10087 __isl_give isl_schedule *isl_schedule_insert_guard(
10088 __isl_take isl_schedule *schedule,
10089 __isl_take isl_set *guard)
10091 A schedule that combines two schedules either in the given
10092 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
10093 or an C<isl_schedule_node_set> node,
10094 can be created using the following functions.
10096 #include <isl/schedule.h>
10097 __isl_give isl_schedule *isl_schedule_sequence(
10098 __isl_take isl_schedule *schedule1,
10099 __isl_take isl_schedule *schedule2);
10100 __isl_give isl_schedule *isl_schedule_set(
10101 __isl_take isl_schedule *schedule1,
10102 __isl_take isl_schedule *schedule2);
10104 The domains of the two input schedules need to be disjoint.
10106 The following function can be used to restrict the domain
10107 of a schedule with a domain node as root to be a subset of the given union set.
10108 This operation may remove nodes in the tree that have become
10111 #include <isl/schedule.h>
10112 __isl_give isl_schedule *isl_schedule_intersect_domain(
10113 __isl_take isl_schedule *schedule,
10114 __isl_take isl_union_set *domain);
10116 The following function can be used to simplify the domain
10117 of a schedule with a domain node as root with respect to the given
10120 #include <isl/schedule.h>
10121 __isl_give isl_schedule *isl_schedule_gist_domain_params(
10122 __isl_take isl_schedule *schedule,
10123 __isl_take isl_set *context);
10125 The following function resets the user pointers on all parameter
10126 and tuple identifiers referenced by the nodes of the given schedule.
10128 #include <isl/schedule.h>
10129 __isl_give isl_schedule *isl_schedule_reset_user(
10130 __isl_take isl_schedule *schedule);
10132 The following function aligns the parameters of all nodes
10133 in the given schedule to the given space.
10135 #include <isl/schedule.h>
10136 __isl_give isl_schedule *isl_schedule_align_params(
10137 __isl_take isl_schedule *schedule,
10138 __isl_take isl_space *space);
10140 The following function allows the user to plug in a given function
10141 in the iteration domains. The input schedule is not allowed to contain
10142 any expansion nodes.
10144 #include <isl/schedule.h>
10145 __isl_give isl_schedule *
10146 isl_schedule_pullback_union_pw_multi_aff(
10147 __isl_take isl_schedule *schedule,
10148 __isl_take isl_union_pw_multi_aff *upma);
10150 The following function can be used to plug in the schedule C<expansion>
10151 in the leaves of C<schedule>, where C<contraction> describes how
10152 the domain elements of C<expansion> map to the domain elements
10153 at the original leaves of C<schedule>.
10154 The resulting schedule will contain expansion nodes, unless
10155 C<contraction> is an identity function.
10157 #include <isl/schedule.h>
10158 __isl_give isl_schedule *isl_schedule_expand(
10159 __isl_take isl_schedule *schedule,
10160 __isl_take isl_union_pw_multi_aff *contraction,
10161 __isl_take isl_schedule *expansion);
10163 An C<isl_union_map> representation of the schedule can be obtained
10164 from an C<isl_schedule> using the following function.
10166 #include <isl/schedule.h>
10167 __isl_give isl_union_map *isl_schedule_get_map(
10168 __isl_keep isl_schedule *sched);
10170 The resulting relation encodes the same relative ordering as
10171 the schedule by mapping the domain elements to a common schedule space.
10172 If the schedule_separate_components option is set, then the order
10173 of the children of a set node is explicitly encoded in the result.
10174 If the tree contains any expansion nodes, then the relation
10175 is formulated in terms of the expanded domain elements.
10177 Schedules can be read from input using the following functions.
10179 #include <isl/schedule.h>
10180 __isl_give isl_schedule *isl_schedule_read_from_file(
10181 isl_ctx *ctx, FILE *input);
10182 __isl_give isl_schedule *isl_schedule_read_from_str(
10183 isl_ctx *ctx, const char *str);
10185 A representation of the schedule can be printed using
10187 #include <isl/schedule.h>
10188 __isl_give isl_printer *isl_printer_print_schedule(
10189 __isl_take isl_printer *p,
10190 __isl_keep isl_schedule *schedule);
10191 __isl_give char *isl_schedule_to_str(
10192 __isl_keep isl_schedule *schedule);
10194 C<isl_schedule_to_str> prints the schedule in flow format.
10196 The schedule tree can be traversed through the use of
10197 C<isl_schedule_node> objects that point to a particular
10198 position in the schedule tree. Whenever a C<isl_schedule_node>
10199 is used to modify a node in the schedule tree, the original schedule
10200 tree is left untouched and the modifications are performed to a copy
10201 of the tree. The returned C<isl_schedule_node> then points to
10202 this modified copy of the tree.
10204 The root of the schedule tree can be obtained using the following function.
10206 #include <isl/schedule.h>
10207 __isl_give isl_schedule_node *isl_schedule_get_root(
10208 __isl_keep isl_schedule *schedule);
10210 A pointer to a newly created schedule tree with a single domain
10211 node can be created using the following functions.
10213 #include <isl/schedule_node.h>
10214 __isl_give isl_schedule_node *
10215 isl_schedule_node_from_domain(
10216 __isl_take isl_union_set *domain);
10217 __isl_give isl_schedule_node *
10218 isl_schedule_node_from_extension(
10219 __isl_take isl_union_map *extension);
10221 C<isl_schedule_node_from_extension> creates a tree with an extension
10224 Schedule nodes can be copied and freed using the following functions.
10226 #include <isl/schedule_node.h>
10227 __isl_give isl_schedule_node *isl_schedule_node_copy(
10228 __isl_keep isl_schedule_node *node);
10229 __isl_null isl_schedule_node *isl_schedule_node_free(
10230 __isl_take isl_schedule_node *node);
10232 The following functions can be used to check if two schedule
10233 nodes point to the same position in the same schedule.
10235 #include <isl/schedule_node.h>
10236 isl_bool isl_schedule_node_is_equal(
10237 __isl_keep isl_schedule_node *node1,
10238 __isl_keep isl_schedule_node *node2);
10240 The following properties can be obtained from a schedule node.
10242 #include <isl/schedule_node.h>
10243 enum isl_schedule_node_type isl_schedule_node_get_type(
10244 __isl_keep isl_schedule_node *node);
10245 enum isl_schedule_node_type
10246 isl_schedule_node_get_parent_type(
10247 __isl_keep isl_schedule_node *node);
10248 __isl_give isl_schedule *isl_schedule_node_get_schedule(
10249 __isl_keep isl_schedule_node *node);
10251 The function C<isl_schedule_node_get_type> returns the type of
10252 the node, while C<isl_schedule_node_get_parent_type> returns
10253 type of the parent of the node, which is required to exist.
10254 The function C<isl_schedule_node_get_schedule> returns a copy
10255 to the schedule to which the node belongs.
10257 The following functions can be used to move the schedule node
10258 to a different position in the tree or to check if such a position
10261 #include <isl/schedule_node.h>
10262 isl_bool isl_schedule_node_has_parent(
10263 __isl_keep isl_schedule_node *node);
10264 __isl_give isl_schedule_node *isl_schedule_node_parent(
10265 __isl_take isl_schedule_node *node);
10266 __isl_give isl_schedule_node *
10267 isl_schedule_node_grandparent(
10268 __isl_take isl_schedule_node *node);
10269 __isl_give isl_schedule_node *isl_schedule_node_root(
10270 __isl_take isl_schedule_node *node);
10271 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
10272 __isl_take isl_schedule_node *node,
10274 isl_size isl_schedule_node_n_children(
10275 __isl_keep isl_schedule_node *node);
10276 __isl_give isl_schedule_node *isl_schedule_node_child(
10277 __isl_take isl_schedule_node *node, int pos);
10278 isl_bool isl_schedule_node_has_children(
10279 __isl_keep isl_schedule_node *node);
10280 __isl_give isl_schedule_node *
10281 isl_schedule_node_grandchild(
10282 __isl_take isl_schedule_node *node,
10283 int pos1, int pos2);
10284 __isl_give isl_schedule_node *isl_schedule_node_first_child(
10285 __isl_take isl_schedule_node *node);
10286 isl_bool isl_schedule_node_has_previous_sibling(
10287 __isl_keep isl_schedule_node *node);
10288 __isl_give isl_schedule_node *
10289 isl_schedule_node_previous_sibling(
10290 __isl_take isl_schedule_node *node);
10291 isl_bool isl_schedule_node_has_next_sibling(
10292 __isl_keep isl_schedule_node *node);
10293 __isl_give isl_schedule_node *
10294 isl_schedule_node_next_sibling(
10295 __isl_take isl_schedule_node *node);
10297 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
10298 is the node itself, the ancestor of generation 1 is its parent and so on.
10300 It is also possible to query the number of ancestors of a node,
10301 the position of the current node
10302 within the children of its parent, the position of the subtree
10303 containing a node within the children of an ancestor
10304 or to obtain a copy of a given
10305 child without destroying the current node.
10306 Given two nodes that point to the same schedule, their closest
10307 shared ancestor can be obtained using
10308 C<isl_schedule_node_get_shared_ancestor>.
10310 #include <isl/schedule_node.h>
10311 isl_size isl_schedule_node_get_tree_depth(
10312 __isl_keep isl_schedule_node *node);
10313 isl_size isl_schedule_node_get_child_position(
10314 __isl_keep isl_schedule_node *node);
10315 isl_size isl_schedule_node_get_ancestor_child_position(
10316 __isl_keep isl_schedule_node *node,
10317 __isl_keep isl_schedule_node *ancestor);
10318 __isl_give isl_schedule_node *isl_schedule_node_get_child(
10319 __isl_keep isl_schedule_node *node, int pos);
10320 __isl_give isl_schedule_node *
10321 isl_schedule_node_get_shared_ancestor(
10322 __isl_keep isl_schedule_node *node1,
10323 __isl_keep isl_schedule_node *node2);
10325 All nodes in a schedule tree or
10326 all descendants of a specific node (including the node) can be visited
10327 in depth-first pre-order using the following functions.
10329 #include <isl/schedule.h>
10330 isl_stat isl_schedule_foreach_schedule_node_top_down(
10331 __isl_keep isl_schedule *sched,
10332 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
10333 void *user), void *user);
10335 #include <isl/schedule_node.h>
10336 isl_stat isl_schedule_node_foreach_descendant_top_down(
10337 __isl_keep isl_schedule_node *node,
10338 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
10339 void *user), void *user);
10341 The callback function is slightly different from the usual
10342 callbacks in that it not only indicates success (non-negative result)
10343 or failure (negative result), but also indicates whether the children
10344 of the given node should be visited. In particular, if the callback
10345 returns a positive value, then the children are visited, but if
10346 the callback returns zero, then the children are not visited.
10348 The following functions checks whether
10349 all descendants of a specific node (including the node itself)
10350 satisfy a user-specified test.
10352 #include <isl/schedule_node.h>
10353 isl_bool isl_schedule_node_every_descendant(
10354 __isl_keep isl_schedule_node *node,
10355 isl_bool (*test)(__isl_keep isl_schedule_node *node,
10356 void *user), void *user)
10358 The ancestors of a node in a schedule tree can be visited from
10359 the root down to and including the parent of the node using
10360 the following function.
10362 #include <isl/schedule_node.h>
10363 isl_stat isl_schedule_node_foreach_ancestor_top_down(
10364 __isl_keep isl_schedule_node *node,
10365 isl_stat (*fn)(__isl_keep isl_schedule_node *node,
10366 void *user), void *user);
10368 The following functions allows for a depth-first post-order
10369 traversal of the nodes in a schedule tree or
10370 of the descendants of a specific node (including the node
10371 itself), where the user callback is allowed to modify the
10374 #include <isl/schedule.h>
10375 __isl_give isl_schedule *
10376 isl_schedule_map_schedule_node_bottom_up(
10377 __isl_take isl_schedule *schedule,
10378 __isl_give isl_schedule_node *(*fn)(
10379 __isl_take isl_schedule_node *node,
10380 void *user), void *user);
10382 #include <isl/schedule_node.h>
10383 __isl_give isl_schedule_node *
10384 isl_schedule_node_map_descendant_bottom_up(
10385 __isl_take isl_schedule_node *node,
10386 __isl_give isl_schedule_node *(*fn)(
10387 __isl_take isl_schedule_node *node,
10388 void *user), void *user);
10390 The traversal continues from the node returned by the callback function.
10391 It is the responsibility of the user to ensure that this does not
10392 lead to an infinite loop. It is safest to always return a pointer
10393 to the same position (same ancestors and child positions) as the input node.
10395 The following function removes a node (along with its descendants)
10396 from a schedule tree and returns a pointer to the leaf at the
10397 same position in the updated tree.
10398 It is not allowed to remove the root of a schedule tree or
10399 a child of a set or sequence node.
10401 #include <isl/schedule_node.h>
10402 __isl_give isl_schedule_node *isl_schedule_node_cut(
10403 __isl_take isl_schedule_node *node);
10405 The following function removes a single node
10406 from a schedule tree and returns a pointer to the child
10407 of the node, now located at the position of the original node
10408 or to a leaf node at that position if there was no child.
10409 It is not allowed to remove the root of a schedule tree,
10410 a set or sequence node, a child of a set or sequence node or
10411 a band node with an anchored subtree.
10413 #include <isl/schedule_node.h>
10414 __isl_give isl_schedule_node *isl_schedule_node_delete(
10415 __isl_take isl_schedule_node *node);
10417 Most nodes in a schedule tree only contain local information.
10418 In some cases, however, a node may also refer to the schedule dimensions
10419 of its outer band nodes.
10420 This means that the position of the node within the tree should
10421 not be changed, or at least that no changes are performed to the
10422 outer band nodes. The following function can be used to test
10423 whether the subtree rooted at a given node contains any such nodes.
10425 #include <isl/schedule_node.h>
10426 isl_bool isl_schedule_node_is_subtree_anchored(
10427 __isl_keep isl_schedule_node *node);
10429 The following function resets the user pointers on all parameter
10430 and tuple identifiers referenced by the given schedule node.
10432 #include <isl/schedule_node.h>
10433 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
10434 __isl_take isl_schedule_node *node);
10436 The following function aligns the parameters of the given schedule
10437 node to the given space.
10439 #include <isl/schedule_node.h>
10440 __isl_give isl_schedule_node *
10441 isl_schedule_node_align_params(
10442 __isl_take isl_schedule_node *node,
10443 __isl_take isl_space *space);
10445 Several node types have their own functions for querying
10446 (and in some cases setting) some node type specific properties.
10448 #include <isl/schedule_node.h>
10449 __isl_give isl_space *isl_schedule_node_band_get_space(
10450 __isl_keep isl_schedule_node *node);
10451 __isl_give isl_multi_union_pw_aff *
10452 isl_schedule_node_band_get_partial_schedule(
10453 __isl_keep isl_schedule_node *node);
10454 __isl_give isl_union_map *
10455 isl_schedule_node_band_get_partial_schedule_union_map(
10456 __isl_keep isl_schedule_node *node);
10457 isl_size isl_schedule_node_band_n_member(
10458 __isl_keep isl_schedule_node *node);
10459 isl_bool isl_schedule_node_band_member_get_coincident(
10460 __isl_keep isl_schedule_node *node, int pos);
10461 __isl_give isl_schedule_node *
10462 isl_schedule_node_band_member_set_coincident(
10463 __isl_take isl_schedule_node *node, int pos,
10465 isl_bool isl_schedule_node_band_get_permutable(
10466 __isl_keep isl_schedule_node *node);
10467 __isl_give isl_schedule_node *
10468 isl_schedule_node_band_set_permutable(
10469 __isl_take isl_schedule_node *node, int permutable);
10470 enum isl_ast_loop_type
10471 isl_schedule_node_band_member_get_ast_loop_type(
10472 __isl_keep isl_schedule_node *node, int pos);
10473 __isl_give isl_schedule_node *
10474 isl_schedule_node_band_member_set_ast_loop_type(
10475 __isl_take isl_schedule_node *node, int pos,
10476 enum isl_ast_loop_type type);
10477 enum isl_ast_loop_type
10478 isl_schedule_node_band_member_get_isolate_ast_loop_type(
10479 __isl_keep isl_schedule_node *node, int pos);
10480 __isl_give isl_schedule_node *
10481 isl_schedule_node_band_member_set_isolate_ast_loop_type(
10482 __isl_take isl_schedule_node *node, int pos,
10483 enum isl_ast_loop_type type);
10484 __isl_give isl_union_set *
10485 isl_schedule_node_band_get_ast_build_options(
10486 __isl_keep isl_schedule_node *node);
10487 __isl_give isl_schedule_node *
10488 isl_schedule_node_band_set_ast_build_options(
10489 __isl_take isl_schedule_node *node,
10490 __isl_take isl_union_set *options);
10491 __isl_give isl_set *
10492 isl_schedule_node_band_get_ast_isolate_option(
10493 __isl_keep isl_schedule_node *node);
10495 The function C<isl_schedule_node_band_get_space> returns the space
10496 of the partial schedule of the band.
10497 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
10498 returns a representation of the partial schedule of the band node
10499 in the form of an C<isl_union_map>.
10500 The coincident and permutable properties are set by
10501 C<isl_schedule_constraints_compute_schedule> on the schedule tree
10503 A scheduling dimension is considered to be ``coincident''
10504 if it satisfies the coincidence constraints within its band.
10505 That is, if the dependence distances of the coincidence
10506 constraints are all zero in that direction (for fixed
10507 iterations of outer bands).
10508 A band is marked permutable if it was produced using the Pluto-like scheduler.
10509 Note that the scheduler may have to resort to a Feautrier style scheduling
10510 step even if the default scheduler is used.
10511 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
10512 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
10513 For the meaning of these loop AST generation types and the difference
10514 between the regular loop AST generation type and the isolate
10515 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
10516 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
10517 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
10518 may return C<isl_ast_loop_error> if an error occurs.
10519 The AST build options govern how an AST is generated for
10520 the individual schedule dimensions during AST generation.
10521 See L</"AST Generation Options (Schedule Tree)">.
10522 The isolate option for the given node can be extracted from these
10523 AST build options using the function
10524 C<isl_schedule_node_band_get_ast_isolate_option>.
10526 #include <isl/schedule_node.h>
10527 __isl_give isl_set *
10528 isl_schedule_node_context_get_context(
10529 __isl_keep isl_schedule_node *node);
10531 #include <isl/schedule_node.h>
10532 __isl_give isl_union_set *
10533 isl_schedule_node_domain_get_domain(
10534 __isl_keep isl_schedule_node *node);
10536 #include <isl/schedule_node.h>
10537 __isl_give isl_union_map *
10538 isl_schedule_node_expansion_get_expansion(
10539 __isl_keep isl_schedule_node *node);
10540 __isl_give isl_union_pw_multi_aff *
10541 isl_schedule_node_expansion_get_contraction(
10542 __isl_keep isl_schedule_node *node);
10544 #include <isl/schedule_node.h>
10545 __isl_give isl_union_map *
10546 isl_schedule_node_extension_get_extension(
10547 __isl_keep isl_schedule_node *node);
10549 #include <isl/schedule_node.h>
10550 __isl_give isl_union_set *
10551 isl_schedule_node_filter_get_filter(
10552 __isl_keep isl_schedule_node *node);
10554 #include <isl/schedule_node.h>
10555 __isl_give isl_set *isl_schedule_node_guard_get_guard(
10556 __isl_keep isl_schedule_node *node);
10558 #include <isl/schedule_node.h>
10559 __isl_give isl_id *isl_schedule_node_mark_get_id(
10560 __isl_keep isl_schedule_node *node);
10562 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
10563 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
10564 partial schedules related to the node.
10566 #include <isl/schedule_node.h>
10567 __isl_give isl_multi_union_pw_aff *
10568 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
10569 __isl_keep isl_schedule_node *node);
10570 __isl_give isl_union_pw_multi_aff *
10571 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
10572 __isl_keep isl_schedule_node *node);
10573 __isl_give isl_union_map *
10574 isl_schedule_node_get_prefix_schedule_union_map(
10575 __isl_keep isl_schedule_node *node);
10576 __isl_give isl_union_map *
10577 isl_schedule_node_get_prefix_schedule_relation(
10578 __isl_keep isl_schedule_node *node);
10579 __isl_give isl_union_map *
10580 isl_schedule_node_get_subtree_schedule_union_map(
10581 __isl_keep isl_schedule_node *node);
10583 In particular, the functions
10584 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
10585 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
10586 and C<isl_schedule_node_get_prefix_schedule_union_map>
10587 return a relative ordering on the domain elements that reach the given
10588 node determined by its ancestors.
10589 The function C<isl_schedule_node_get_prefix_schedule_relation>
10590 additionally includes the domain constraints in the result.
10591 The function C<isl_schedule_node_get_subtree_schedule_union_map>
10592 returns a representation of the partial schedule defined by the
10593 subtree rooted at the given node.
10594 If the tree contains any expansion nodes, then the subtree schedule
10595 is formulated in terms of the expanded domain elements.
10596 The tree passed to functions returning a prefix schedule
10597 may only contain extension nodes if these would not affect
10598 the result of these functions. That is, if one of the ancestors
10599 is an extension node, then all of the domain elements that were
10600 added by the extension node need to have been filtered out
10601 by filter nodes between the extension node and the input node.
10602 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
10603 may not contain in extension nodes in the selected subtree.
10605 The expansion/contraction defined by an entire subtree, combining
10606 the expansions/contractions
10607 on the expansion nodes in the subtree, can be obtained using
10608 the following functions.
10610 #include <isl/schedule_node.h>
10611 __isl_give isl_union_map *
10612 isl_schedule_node_get_subtree_expansion(
10613 __isl_keep isl_schedule_node *node);
10614 __isl_give isl_union_pw_multi_aff *
10615 isl_schedule_node_get_subtree_contraction(
10616 __isl_keep isl_schedule_node *node);
10618 The total number of outer band members of given node, i.e.,
10619 the shared output dimension of the maps in the result
10620 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
10621 using the following function.
10623 #include <isl/schedule_node.h>
10624 isl_size isl_schedule_node_get_schedule_depth(
10625 __isl_keep isl_schedule_node *node);
10627 The following functions return the elements that reach the given node
10628 or the union of universes in the spaces that contain these elements.
10630 #include <isl/schedule_node.h>
10631 __isl_give isl_union_set *
10632 isl_schedule_node_get_domain(
10633 __isl_keep isl_schedule_node *node);
10634 __isl_give isl_union_set *
10635 isl_schedule_node_get_universe_domain(
10636 __isl_keep isl_schedule_node *node);
10638 The input tree of C<isl_schedule_node_get_domain>
10639 may only contain extension nodes if these would not affect
10640 the result of this function. That is, if one of the ancestors
10641 is an extension node, then all of the domain elements that were
10642 added by the extension node need to have been filtered out
10643 by filter nodes between the extension node and the input node.
10645 The following functions can be used to introduce additional nodes
10646 in the schedule tree. The new node is introduced at the point
10647 in the tree where the C<isl_schedule_node> points to and
10648 the results points to the new node.
10650 #include <isl/schedule_node.h>
10651 __isl_give isl_schedule_node *
10652 isl_schedule_node_insert_partial_schedule(
10653 __isl_take isl_schedule_node *node,
10654 __isl_take isl_multi_union_pw_aff *schedule);
10656 This function inserts a new band node with (the greatest integer
10657 part of) the given partial schedule.
10658 The subtree rooted at the given node is assumed not to have
10659 any anchored nodes.
10661 #include <isl/schedule_node.h>
10662 __isl_give isl_schedule_node *
10663 isl_schedule_node_insert_context(
10664 __isl_take isl_schedule_node *node,
10665 __isl_take isl_set *context);
10667 This function inserts a new context node with the given context constraints.
10669 #include <isl/schedule_node.h>
10670 __isl_give isl_schedule_node *
10671 isl_schedule_node_insert_filter(
10672 __isl_take isl_schedule_node *node,
10673 __isl_take isl_union_set *filter);
10675 This function inserts a new filter node with the given filter.
10676 If the original node already pointed to a filter node, then the
10677 two filter nodes are merged into one.
10679 #include <isl/schedule_node.h>
10680 __isl_give isl_schedule_node *
10681 isl_schedule_node_insert_guard(
10682 __isl_take isl_schedule_node *node,
10683 __isl_take isl_set *guard);
10685 This function inserts a new guard node with the given guard constraints.
10687 #include <isl/schedule_node.h>
10688 __isl_give isl_schedule_node *
10689 isl_schedule_node_insert_mark(
10690 __isl_take isl_schedule_node *node,
10691 __isl_take isl_id *mark);
10693 This function inserts a new mark node with the give mark identifier.
10695 #include <isl/schedule_node.h>
10696 __isl_give isl_schedule_node *
10697 isl_schedule_node_insert_sequence(
10698 __isl_take isl_schedule_node *node,
10699 __isl_take isl_union_set_list *filters);
10700 __isl_give isl_schedule_node *
10701 isl_schedule_node_insert_set(
10702 __isl_take isl_schedule_node *node,
10703 __isl_take isl_union_set_list *filters);
10705 These functions insert a new sequence or set node with the given
10706 filters as children.
10708 #include <isl/schedule_node.h>
10709 __isl_give isl_schedule_node *isl_schedule_node_group(
10710 __isl_take isl_schedule_node *node,
10711 __isl_take isl_id *group_id);
10713 This function introduces an expansion node in between the current
10714 node and its parent that expands instances of a space with tuple
10715 identifier C<group_id> to the original domain elements that reach
10716 the node. The group instances are identified by the prefix schedule
10717 of those domain elements. The ancestors of the node are adjusted
10718 to refer to the group instances instead of the original domain
10719 elements. The return value points to the same node in the updated
10720 schedule tree as the input node, i.e., to the child of the newly
10721 introduced expansion node. Grouping instances of different statements
10722 ensures that they will be treated as a single statement by the
10723 AST generator up to the point of the expansion node.
10725 The following functions can be used to flatten a nested
10728 #include <isl/schedule_node.h>
10729 __isl_give isl_schedule_node *
10730 isl_schedule_node_sequence_splice_child(
10731 __isl_take isl_schedule_node *node, int pos);
10732 __isl_give isl_schedule_node *
10733 isl_schedule_node_sequence_splice_children(
10734 __isl_take isl_schedule_node *node);
10736 That is, given a sequence node C<node> that has another sequence node
10737 in its child at position C<pos> (in particular, the child of that filter
10738 node is a sequence node), the function
10739 C<isl_schedule_node_sequence_splice_child>
10740 attaches the children of that other sequence
10741 node as children of C<node>, replacing the original child at position
10743 C<isl_schedule_node_sequence_splice_children> does this for all
10746 The partial schedule of a band node can be scaled (down) or reduced using
10747 the following functions.
10749 #include <isl/schedule_node.h>
10750 __isl_give isl_schedule_node *
10751 isl_schedule_node_band_scale(
10752 __isl_take isl_schedule_node *node,
10753 __isl_take isl_multi_val *mv);
10754 __isl_give isl_schedule_node *
10755 isl_schedule_node_band_scale_down(
10756 __isl_take isl_schedule_node *node,
10757 __isl_take isl_multi_val *mv);
10758 __isl_give isl_schedule_node *
10759 isl_schedule_node_band_mod(
10760 __isl_take isl_schedule_node *node,
10761 __isl_take isl_multi_val *mv);
10763 The spaces of the two arguments need to match.
10764 After scaling, the partial schedule is replaced by its greatest
10765 integer part to ensure that the schedule remains integral.
10767 The partial schedule of a band node can be shifted by an
10768 C<isl_multi_union_pw_aff> with a domain that is a superset
10769 of the domain of the partial schedule using
10770 the following function.
10772 #include <isl/schedule_node.h>
10773 __isl_give isl_schedule_node *
10774 isl_schedule_node_band_shift(
10775 __isl_take isl_schedule_node *node,
10776 __isl_take isl_multi_union_pw_aff *shift);
10778 A band node can be tiled using the following function.
10780 #include <isl/schedule_node.h>
10781 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
10782 __isl_take isl_schedule_node *node,
10783 __isl_take isl_multi_val *sizes);
10785 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
10787 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
10788 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
10790 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
10792 The C<isl_schedule_node_band_tile> function tiles
10793 the band using the given tile sizes inside its schedule.
10794 A new child band node is created to represent the point loops and it is
10795 inserted between the modified band and its children.
10796 The subtree rooted at the given node is assumed not to have
10797 any anchored nodes.
10798 The C<tile_scale_tile_loops> option specifies whether the tile
10799 loops iterators should be scaled by the tile sizes.
10800 If the C<tile_shift_point_loops> option is set, then the point loops
10801 are shifted to start at zero.
10803 A band node can be split into two nested band nodes
10804 using the following function.
10806 #include <isl/schedule_node.h>
10807 __isl_give isl_schedule_node *isl_schedule_node_band_split(
10808 __isl_take isl_schedule_node *node, int pos);
10810 The resulting outer band node contains the first C<pos> dimensions of
10811 the schedule of C<node> while the inner band contains the remaining dimensions.
10812 The schedules of the two band nodes live in anonymous spaces.
10813 The loop AST generation type options and the isolate option
10814 are split over the two band nodes.
10816 A band node can be moved down to the leaves of the subtree rooted
10817 at the band node using the following function.
10819 #include <isl/schedule_node.h>
10820 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
10821 __isl_take isl_schedule_node *node);
10823 The subtree rooted at the given node is assumed not to have
10824 any anchored nodes.
10825 The result points to the node in the resulting tree that is in the same
10826 position as the node pointed to by C<node> in the original tree.
10828 #include <isl/schedule_node.h>
10829 __isl_give isl_schedule_node *
10830 isl_schedule_node_order_before(
10831 __isl_take isl_schedule_node *node,
10832 __isl_take isl_union_set *filter);
10833 __isl_give isl_schedule_node *
10834 isl_schedule_node_order_after(
10835 __isl_take isl_schedule_node *node,
10836 __isl_take isl_union_set *filter);
10838 These functions split the domain elements that reach C<node>
10839 into those that satisfy C<filter> and those that do not and
10840 arranges for the elements that do satisfy the filter to be
10841 executed before (in case of C<isl_schedule_node_order_before>)
10842 or after (in case of C<isl_schedule_node_order_after>)
10843 those that do not. The order is imposed by
10844 a sequence node, possibly reusing the grandparent of C<node>
10845 on two copies of the subtree attached to the original C<node>.
10846 Both copies are simplified with respect to their filter.
10848 Return a pointer to the copy of the subtree that does not
10849 satisfy C<filter>. If there is no such copy (because all
10850 reaching domain elements satisfy the filter), then return
10851 the original pointer.
10853 #include <isl/schedule_node.h>
10854 __isl_give isl_schedule_node *
10855 isl_schedule_node_graft_before(
10856 __isl_take isl_schedule_node *node,
10857 __isl_take isl_schedule_node *graft);
10858 __isl_give isl_schedule_node *
10859 isl_schedule_node_graft_after(
10860 __isl_take isl_schedule_node *node,
10861 __isl_take isl_schedule_node *graft);
10863 This function inserts the C<graft> tree into the tree containing C<node>
10864 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
10865 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
10866 The root node of C<graft>
10867 should be an extension node where the domain of the extension
10868 is the flat product of all outer band nodes of C<node>.
10869 The root node may also be a domain node.
10870 The elements of the domain or the range of the extension may not
10871 intersect with the domain elements that reach "node".
10872 The schedule tree of C<graft> may not be anchored.
10874 The schedule tree of C<node> is modified to include an extension node
10875 corresponding to the root node of C<graft> as a child of the original
10876 parent of C<node>. The original node that C<node> points to and the
10877 child of the root node of C<graft> are attached to this extension node
10878 through a sequence, with appropriate filters and with the child
10879 of C<graft> appearing before or after the original C<node>.
10881 If C<node> already appears inside a sequence that is the child of
10882 an extension node and if the spaces of the new domain elements
10883 do not overlap with those of the original domain elements,
10884 then that extension node is extended with the new extension
10885 rather than introducing a new segment of extension and sequence nodes.
10887 Return a pointer to the same node in the modified tree that
10888 C<node> pointed to in the original tree.
10890 A representation of the schedule node can be printed using
10892 #include <isl/schedule_node.h>
10893 __isl_give isl_printer *isl_printer_print_schedule_node(
10894 __isl_take isl_printer *p,
10895 __isl_keep isl_schedule_node *node);
10896 __isl_give char *isl_schedule_node_to_str(
10897 __isl_keep isl_schedule_node *node);
10899 C<isl_schedule_node_to_str> prints the schedule node in block format.
10901 =head2 Dependence Analysis
10903 C<isl> contains specialized functionality for performing
10904 array dataflow analysis. That is, given a I<sink> access relation,
10905 a collection of possible I<source> accesses and
10906 a collection of I<kill> accesses,
10907 C<isl> can compute relations that describe
10908 for each iteration of the sink access, which iterations
10909 of which of the source access relations may have
10910 accessed the same data element before the given iteration
10911 of the sink access without any intermediate kill of that data element.
10912 The resulting dependence relations map source iterations
10913 to either the corresponding sink iterations or
10914 pairs of corresponding sink iterations and accessed data elements.
10915 To compute standard flow dependences, the sink should be
10916 a read, while the sources should be writes.
10917 If no kills are specified,
10918 then memory based dependence analysis is performed.
10919 If, on the other hand, all sources are also kills,
10920 then value based dependence analysis is performed.
10921 If any of the source accesses are marked as being I<must>
10922 accesses, then they are also treated as kills.
10923 Furthermore, the specification of must-sources results
10924 in the computation of must-dependences.
10925 Only dependences originating in a must access not coscheduled
10926 with any other access to the same element and without
10927 any may accesses between the must access and the sink access
10928 are considered to be must dependences.
10930 =head3 High-level Interface
10932 A high-level interface to dependence analysis is provided
10933 by the following function.
10935 #include <isl/flow.h>
10936 __isl_give isl_union_flow *
10937 isl_union_access_info_compute_flow(
10938 __isl_take isl_union_access_info *access);
10940 The input C<isl_union_access_info> object describes the sink
10941 access relations, the source access relations and a schedule,
10942 while the output C<isl_union_flow> object describes
10943 the resulting dependence relations and the subsets of the
10944 sink relations for which no source was found.
10946 An C<isl_union_access_info> is created, modified, copied and freed using
10947 the following functions.
10949 #include <isl/flow.h>
10950 __isl_give isl_union_access_info *
10951 isl_union_access_info_from_sink(
10952 __isl_take isl_union_map *sink);
10953 __isl_give isl_union_access_info *
10954 isl_union_access_info_set_kill(
10955 __isl_take isl_union_access_info *access,
10956 __isl_take isl_union_map *kill);
10957 __isl_give isl_union_access_info *
10958 isl_union_access_info_set_may_source(
10959 __isl_take isl_union_access_info *access,
10960 __isl_take isl_union_map *may_source);
10961 __isl_give isl_union_access_info *
10962 isl_union_access_info_set_must_source(
10963 __isl_take isl_union_access_info *access,
10964 __isl_take isl_union_map *must_source);
10965 __isl_give isl_union_access_info *
10966 isl_union_access_info_set_schedule(
10967 __isl_take isl_union_access_info *access,
10968 __isl_take isl_schedule *schedule);
10969 __isl_give isl_union_access_info *
10970 isl_union_access_info_set_schedule_map(
10971 __isl_take isl_union_access_info *access,
10972 __isl_take isl_union_map *schedule_map);
10973 __isl_give isl_union_access_info *
10974 isl_union_access_info_copy(
10975 __isl_keep isl_union_access_info *access);
10976 __isl_null isl_union_access_info *
10977 isl_union_access_info_free(
10978 __isl_take isl_union_access_info *access);
10980 The may sources set by C<isl_union_access_info_set_may_source>
10981 do not need to include the must sources set by
10982 C<isl_union_access_info_set_must_source> as a subset.
10983 The kills set by C<isl_union_access_info_set_kill> may overlap
10984 with the may-sources and/or must-sources.
10985 The user is free not to call one (or more) of these functions,
10986 in which case the corresponding set is kept to its empty default.
10987 Similarly, the default schedule initialized by
10988 C<isl_union_access_info_from_sink> is empty.
10989 The current schedule is determined by the last call to either
10990 C<isl_union_access_info_set_schedule> or
10991 C<isl_union_access_info_set_schedule_map>.
10992 The domain of the schedule corresponds to the domains of
10993 the access relations. In particular, the domains of the access
10994 relations are effectively intersected with the domain of the schedule
10995 and only the resulting accesses are considered by the dependence analysis.
10997 An C<isl_union_access_info> object can be read from input
10998 using the following function.
11000 #include <isl/flow.h>
11001 __isl_give isl_union_access_info *
11002 isl_union_access_info_read_from_file(isl_ctx *ctx,
11005 A representation of the information contained in an object
11006 of type C<isl_union_access_info> can be obtained using
11008 #include <isl/flow.h>
11009 __isl_give isl_printer *
11010 isl_printer_print_union_access_info(
11011 __isl_take isl_printer *p,
11012 __isl_keep isl_union_access_info *access);
11013 __isl_give char *isl_union_access_info_to_str(
11014 __isl_keep isl_union_access_info *access);
11016 C<isl_union_access_info_to_str> prints the information in flow format.
11018 The output of C<isl_union_access_info_compute_flow> can be examined,
11019 copied, and freed using the following functions.
11021 #include <isl/flow.h>
11022 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
11023 __isl_keep isl_union_flow *flow);
11024 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
11025 __isl_keep isl_union_flow *flow);
11026 __isl_give isl_union_map *
11027 isl_union_flow_get_full_must_dependence(
11028 __isl_keep isl_union_flow *flow);
11029 __isl_give isl_union_map *
11030 isl_union_flow_get_full_may_dependence(
11031 __isl_keep isl_union_flow *flow);
11032 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
11033 __isl_keep isl_union_flow *flow);
11034 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
11035 __isl_keep isl_union_flow *flow);
11036 __isl_give isl_union_flow *isl_union_flow_copy(
11037 __isl_keep isl_union_flow *flow);
11038 __isl_null isl_union_flow *isl_union_flow_free(
11039 __isl_take isl_union_flow *flow);
11041 The relation returned by C<isl_union_flow_get_must_dependence>
11042 relates domain elements of must sources to domain elements of the sink.
11043 The relation returned by C<isl_union_flow_get_may_dependence>
11044 relates domain elements of must or may sources to domain elements of the sink
11045 and includes the previous relation as a subset.
11046 The relation returned by C<isl_union_flow_get_full_must_dependence>
11047 relates domain elements of must sources to pairs of domain elements of the sink
11048 and accessed data elements.
11049 The relation returned by C<isl_union_flow_get_full_may_dependence>
11050 relates domain elements of must or may sources to pairs of
11051 domain elements of the sink and accessed data elements.
11052 This relation includes the previous relation as a subset.
11053 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
11054 of the sink relation for which no dependences have been found.
11055 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
11056 of the sink relation for which no definite dependences have been found.
11057 That is, it contains those sink access that do not contribute to any
11058 of the elements in the relation returned
11059 by C<isl_union_flow_get_must_dependence>.
11061 A representation of the information contained in an object
11062 of type C<isl_union_flow> can be obtained using
11064 #include <isl/flow.h>
11065 __isl_give isl_printer *isl_printer_print_union_flow(
11066 __isl_take isl_printer *p,
11067 __isl_keep isl_union_flow *flow);
11068 __isl_give char *isl_union_flow_to_str(
11069 __isl_keep isl_union_flow *flow);
11071 C<isl_union_flow_to_str> prints the information in flow format.
11073 =head3 Low-level Interface
11075 A lower-level interface is provided by the following functions.
11077 #include <isl/flow.h>
11079 typedef int (*isl_access_level_before)(void *first, void *second);
11081 __isl_give isl_access_info *isl_access_info_alloc(
11082 __isl_take isl_map *sink,
11083 void *sink_user, isl_access_level_before fn,
11085 __isl_give isl_access_info *isl_access_info_add_source(
11086 __isl_take isl_access_info *acc,
11087 __isl_take isl_map *source, int must,
11088 void *source_user);
11089 __isl_null isl_access_info *isl_access_info_free(
11090 __isl_take isl_access_info *acc);
11092 __isl_give isl_flow *isl_access_info_compute_flow(
11093 __isl_take isl_access_info *acc);
11095 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,
11096 isl_stat (*fn)(__isl_take isl_map *dep, int must,
11097 void *dep_user, void *user),
11099 __isl_give isl_map *isl_flow_get_no_source(
11100 __isl_keep isl_flow *deps, int must);
11101 __isl_null isl_flow *isl_flow_free(
11102 __isl_take isl_flow *deps);
11104 The function C<isl_access_info_compute_flow> performs the actual
11105 dependence analysis. The other functions are used to construct
11106 the input for this function or to read off the output.
11108 The input is collected in an C<isl_access_info>, which can
11109 be created through a call to C<isl_access_info_alloc>.
11110 The arguments to this functions are the sink access relation
11111 C<sink>, a token C<sink_user> used to identify the sink
11112 access to the user, a callback function for specifying the
11113 relative order of source and sink accesses, and the number
11114 of source access relations that will be added.
11116 The callback function has type C<int (*)(void *first, void *second)>.
11117 The function is called with two user supplied tokens identifying
11118 either a source or the sink and it should return the shared nesting
11119 level and the relative order of the two accesses.
11120 In particular, let I<n> be the number of loops shared by
11121 the two accesses. If C<first> precedes C<second> textually,
11122 then the function should return I<2 * n + 1>; otherwise,
11123 it should return I<2 * n>.
11124 The low-level interface assumes that no sources are coscheduled.
11125 If the information returned by the callback does not allow
11126 the relative order to be determined, then one of the sources
11127 is arbitrarily taken to be executed after the other(s).
11129 The sources can be added to the C<isl_access_info> object by performing
11130 (at most) C<max_source> calls to C<isl_access_info_add_source>.
11131 C<must> indicates whether the source is a I<must> access
11132 or a I<may> access. Note that a multi-valued access relation
11133 should only be marked I<must> if every iteration in the domain
11134 of the relation accesses I<all> elements in its image.
11135 The C<source_user> token is again used to identify
11136 the source access. The range of the source access relation
11137 C<source> should have the same dimension as the range
11138 of the sink access relation.
11139 The C<isl_access_info_free> function should usually not be
11140 called explicitly, because it is already called implicitly by
11141 C<isl_access_info_compute_flow>.
11143 The result of the dependence analysis is collected in an
11144 C<isl_flow>. There may be elements of
11145 the sink access for which no preceding source access could be
11146 found or for which all preceding sources are I<may> accesses.
11147 The relations containing these elements can be obtained through
11148 calls to C<isl_flow_get_no_source>, the first with C<must> set
11149 and the second with C<must> unset.
11150 In the case of standard flow dependence analysis,
11151 with the sink a read and the sources I<must> writes,
11152 the first relation corresponds to the reads from uninitialized
11153 array elements and the second relation is empty.
11154 The actual flow dependences can be extracted using
11155 C<isl_flow_foreach>. This function will call the user-specified
11156 callback function C<fn> for each B<non-empty> dependence between
11157 a source and the sink. The callback function is called
11158 with four arguments, the actual flow dependence relation
11159 mapping source iterations to sink iterations, a boolean that
11160 indicates whether it is a I<must> or I<may> dependence, a token
11161 identifying the source and an additional C<void *> with value
11162 equal to the third argument of the C<isl_flow_foreach> call.
11163 A dependence is marked I<must> if it originates from a I<must>
11164 source and if it is not followed by any I<may> sources.
11166 After finishing with an C<isl_flow>, the user should call
11167 C<isl_flow_free> to free all associated memory.
11169 =head3 Interaction with the Low-level Interface
11171 During the dependence analysis, we frequently need to perform
11172 the following operation. Given a relation between sink iterations
11173 and potential source iterations from a particular source domain,
11174 what is the last potential source iteration corresponding to each
11175 sink iteration. It can sometimes be convenient to adjust
11176 the set of potential source iterations before or after each such operation.
11177 The prototypical example is fuzzy array dataflow analysis,
11178 where we need to analyze if, based on data-dependent constraints,
11179 the sink iteration can ever be executed without one or more of
11180 the corresponding potential source iterations being executed.
11181 If so, we can introduce extra parameters and select an unknown
11182 but fixed source iteration from the potential source iterations.
11183 To be able to perform such manipulations, C<isl> provides the following
11186 #include <isl/flow.h>
11188 typedef __isl_give isl_restriction *(*isl_access_restrict)(
11189 __isl_keep isl_map *source_map,
11190 __isl_keep isl_set *sink, void *source_user,
11192 __isl_give isl_access_info *isl_access_info_set_restrict(
11193 __isl_take isl_access_info *acc,
11194 isl_access_restrict fn, void *user);
11196 The function C<isl_access_info_set_restrict> should be called
11197 before calling C<isl_access_info_compute_flow> and registers a callback function
11198 that will be called any time C<isl> is about to compute the last
11199 potential source. The first argument is the (reverse) proto-dependence,
11200 mapping sink iterations to potential source iterations.
11201 The second argument represents the sink iterations for which
11202 we want to compute the last source iteration.
11203 The third argument is the token corresponding to the source
11204 and the final argument is the token passed to C<isl_access_info_set_restrict>.
11205 The callback is expected to return a restriction on either the input or
11206 the output of the operation computing the last potential source.
11207 If the input needs to be restricted then restrictions are needed
11208 for both the source and the sink iterations. The sink iterations
11209 and the potential source iterations will be intersected with these sets.
11210 If the output needs to be restricted then only a restriction on the source
11211 iterations is required.
11212 If any error occurs, the callback should return C<NULL>.
11213 An C<isl_restriction> object can be created, freed and inspected
11214 using the following functions.
11216 #include <isl/flow.h>
11218 __isl_give isl_restriction *isl_restriction_input(
11219 __isl_take isl_set *source_restr,
11220 __isl_take isl_set *sink_restr);
11221 __isl_give isl_restriction *isl_restriction_output(
11222 __isl_take isl_set *source_restr);
11223 __isl_give isl_restriction *isl_restriction_none(
11224 __isl_take isl_map *source_map);
11225 __isl_give isl_restriction *isl_restriction_empty(
11226 __isl_take isl_map *source_map);
11227 __isl_null isl_restriction *isl_restriction_free(
11228 __isl_take isl_restriction *restr);
11230 C<isl_restriction_none> and C<isl_restriction_empty> are special
11231 cases of C<isl_restriction_input>. C<isl_restriction_none>
11232 is essentially equivalent to
11234 isl_restriction_input(isl_set_universe(
11235 isl_space_range(isl_map_get_space(source_map))),
11237 isl_space_domain(isl_map_get_space(source_map))));
11239 whereas C<isl_restriction_empty> is essentially equivalent to
11241 isl_restriction_input(isl_set_empty(
11242 isl_space_range(isl_map_get_space(source_map))),
11244 isl_space_domain(isl_map_get_space(source_map))));
11248 #include <isl/schedule.h>
11249 __isl_give isl_schedule *
11250 isl_schedule_constraints_compute_schedule(
11251 __isl_take isl_schedule_constraints *sc);
11253 The function C<isl_schedule_constraints_compute_schedule> can be
11254 used to compute a schedule that satisfies the given schedule constraints.
11255 These schedule constraints include the iteration domain for which
11256 a schedule should be computed and dependences between pairs of
11257 iterations. In particular, these dependences include
11258 I<validity> dependences and I<proximity> dependences.
11259 By default, the algorithm used to construct the schedule is similar
11260 to that of C<Pluto>.
11261 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
11263 The generated schedule respects all validity dependences.
11264 That is, all dependence distances over these dependences in the
11265 scheduled space are lexicographically positive.
11267 The default algorithm tries to ensure that the dependence distances
11268 over coincidence constraints are zero and to minimize the
11269 dependence distances over proximity dependences.
11270 Moreover, it tries to obtain sequences (bands) of schedule dimensions
11271 for groups of domains where the dependence distances over validity
11272 dependences have only non-negative values.
11273 Note that when minimizing the maximal dependence distance
11274 over proximity dependences, a single affine expression in the parameters
11275 is constructed that bounds all dependence distances. If no such expression
11276 exists, then the algorithm will fail and resort to an alternative
11277 scheduling algorithm. In particular, this means that adding proximity
11278 dependences may eliminate valid solutions. A typical example where this
11279 phenomenon may occur is when some subset of the proximity dependences
11280 has no restriction on some parameter, forcing the coefficient of that
11281 parameter to be zero, while some other subset forces the dependence
11282 distance to depend on that parameter, requiring the same coefficient
11284 When using Feautrier's algorithm, the coincidence and proximity constraints
11285 are only taken into account during the extension to a
11286 full-dimensional schedule.
11288 An C<isl_schedule_constraints> object can be constructed
11289 and manipulated using the following functions.
11291 #include <isl/schedule.h>
11292 __isl_give isl_schedule_constraints *
11293 isl_schedule_constraints_copy(
11294 __isl_keep isl_schedule_constraints *sc);
11295 __isl_give isl_schedule_constraints *
11296 isl_schedule_constraints_on_domain(
11297 __isl_take isl_union_set *domain);
11298 __isl_give isl_schedule_constraints *
11299 isl_schedule_constraints_set_context(
11300 __isl_take isl_schedule_constraints *sc,
11301 __isl_take isl_set *context);
11302 __isl_give isl_schedule_constraints *
11303 isl_schedule_constraints_set_validity(
11304 __isl_take isl_schedule_constraints *sc,
11305 __isl_take isl_union_map *validity);
11306 __isl_give isl_schedule_constraints *
11307 isl_schedule_constraints_set_coincidence(
11308 __isl_take isl_schedule_constraints *sc,
11309 __isl_take isl_union_map *coincidence);
11310 __isl_give isl_schedule_constraints *
11311 isl_schedule_constraints_set_proximity(
11312 __isl_take isl_schedule_constraints *sc,
11313 __isl_take isl_union_map *proximity);
11314 __isl_give isl_schedule_constraints *
11315 isl_schedule_constraints_set_conditional_validity(
11316 __isl_take isl_schedule_constraints *sc,
11317 __isl_take isl_union_map *condition,
11318 __isl_take isl_union_map *validity);
11319 __isl_give isl_schedule_constraints *
11320 isl_schedule_constraints_apply(
11321 __isl_take isl_schedule_constraints *sc,
11322 __isl_take isl_union_map *umap);
11323 __isl_null isl_schedule_constraints *
11324 isl_schedule_constraints_free(
11325 __isl_take isl_schedule_constraints *sc);
11327 The initial C<isl_schedule_constraints> object created by
11328 C<isl_schedule_constraints_on_domain> does not impose any constraints.
11329 That is, it has an empty set of dependences.
11330 The function C<isl_schedule_constraints_set_context> allows the user
11331 to specify additional constraints on the parameters that may
11332 be assumed to hold during the construction of the schedule.
11333 The function C<isl_schedule_constraints_set_validity> replaces the
11334 validity dependences, mapping domain elements I<i> to domain
11335 elements that should be scheduled after I<i>.
11336 The function C<isl_schedule_constraints_set_coincidence> replaces the
11337 coincidence dependences, mapping domain elements I<i> to domain
11338 elements that should be scheduled together with I<I>, if possible.
11339 The function C<isl_schedule_constraints_set_proximity> replaces the
11340 proximity dependences, mapping domain elements I<i> to domain
11341 elements that should be scheduled either before I<I>
11342 or as early as possible after I<i>.
11344 The function C<isl_schedule_constraints_set_conditional_validity>
11345 replaces the conditional validity constraints.
11346 A conditional validity constraint is only imposed when any of the corresponding
11347 conditions is satisfied, i.e., when any of them is non-zero.
11348 That is, the scheduler ensures that within each band if the dependence
11349 distances over the condition constraints are not all zero
11350 then all corresponding conditional validity constraints are respected.
11351 A conditional validity constraint corresponds to a condition
11352 if the two are adjacent, i.e., if the domain of one relation intersect
11353 the range of the other relation.
11354 The typical use case of conditional validity constraints is
11355 to allow order constraints between live ranges to be violated
11356 as long as the live ranges themselves are local to the band.
11357 To allow more fine-grained control over which conditions correspond
11358 to which conditional validity constraints, the domains and ranges
11359 of these relations may include I<tags>. That is, the domains and
11360 ranges of those relation may themselves be wrapped relations
11361 where the iteration domain appears in the domain of those wrapped relations
11362 and the range of the wrapped relations can be arbitrarily chosen
11363 by the user. Conditions and conditional validity constraints are only
11364 considered adjacent to each other if the entire wrapped relation matches.
11365 In particular, a relation with a tag will never be considered adjacent
11366 to a relation without a tag.
11368 The function C<isl_schedule_constraints_apply> takes
11369 schedule constraints that are defined on some set of domain elements
11370 and transforms them to schedule constraints on the elements
11371 to which these domain elements are mapped by the given transformation.
11373 An C<isl_schedule_constraints> object can be inspected
11374 using the following functions.
11376 #include <isl/schedule.h>
11377 __isl_give isl_union_set *
11378 isl_schedule_constraints_get_domain(
11379 __isl_keep isl_schedule_constraints *sc);
11380 __isl_give isl_set *isl_schedule_constraints_get_context(
11381 __isl_keep isl_schedule_constraints *sc);
11382 __isl_give isl_union_map *
11383 isl_schedule_constraints_get_validity(
11384 __isl_keep isl_schedule_constraints *sc);
11385 __isl_give isl_union_map *
11386 isl_schedule_constraints_get_coincidence(
11387 __isl_keep isl_schedule_constraints *sc);
11388 __isl_give isl_union_map *
11389 isl_schedule_constraints_get_proximity(
11390 __isl_keep isl_schedule_constraints *sc);
11391 __isl_give isl_union_map *
11392 isl_schedule_constraints_get_conditional_validity(
11393 __isl_keep isl_schedule_constraints *sc);
11394 __isl_give isl_union_map *
11395 isl_schedule_constraints_get_conditional_validity_condition(
11396 __isl_keep isl_schedule_constraints *sc);
11398 An C<isl_schedule_constraints> object can be read from input
11399 using the following functions.
11401 #include <isl/schedule.h>
11402 __isl_give isl_schedule_constraints *
11403 isl_schedule_constraints_read_from_str(isl_ctx *ctx,
11405 __isl_give isl_schedule_constraints *
11406 isl_schedule_constraints_read_from_file(isl_ctx *ctx,
11409 The contents of an C<isl_schedule_constraints> object can be printed
11410 using the following functions.
11412 #include <isl/schedule.h>
11413 __isl_give isl_printer *
11414 isl_printer_print_schedule_constraints(
11415 __isl_take isl_printer *p,
11416 __isl_keep isl_schedule_constraints *sc);
11417 __isl_give char *isl_schedule_constraints_to_str(
11418 __isl_keep isl_schedule_constraints *sc);
11420 The following function computes a schedule directly from
11421 an iteration domain and validity and proximity dependences
11422 and is implemented in terms of the functions described above.
11423 The use of C<isl_union_set_compute_schedule> is discouraged.
11425 #include <isl/schedule.h>
11426 __isl_give isl_schedule *isl_union_set_compute_schedule(
11427 __isl_take isl_union_set *domain,
11428 __isl_take isl_union_map *validity,
11429 __isl_take isl_union_map *proximity);
11431 The generated schedule represents a schedule tree.
11432 For more information on schedule trees, see
11433 L</"Schedule Trees">.
11437 #include <isl/schedule.h>
11438 isl_stat isl_options_set_schedule_max_coefficient(
11439 isl_ctx *ctx, int val);
11440 int isl_options_get_schedule_max_coefficient(
11442 isl_stat isl_options_set_schedule_max_constant_term(
11443 isl_ctx *ctx, int val);
11444 int isl_options_get_schedule_max_constant_term(
11446 isl_stat isl_options_set_schedule_serialize_sccs(
11447 isl_ctx *ctx, int val);
11448 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx);
11449 isl_stat isl_options_set_schedule_whole_component(
11450 isl_ctx *ctx, int val);
11451 int isl_options_get_schedule_whole_component(
11453 isl_stat isl_options_set_schedule_maximize_band_depth(
11454 isl_ctx *ctx, int val);
11455 int isl_options_get_schedule_maximize_band_depth(
11457 isl_stat isl_options_set_schedule_maximize_coincidence(
11458 isl_ctx *ctx, int val);
11459 int isl_options_get_schedule_maximize_coincidence(
11461 isl_stat isl_options_set_schedule_outer_coincidence(
11462 isl_ctx *ctx, int val);
11463 int isl_options_get_schedule_outer_coincidence(
11465 isl_stat isl_options_set_schedule_split_scaled(
11466 isl_ctx *ctx, int val);
11467 int isl_options_get_schedule_split_scaled(
11469 isl_stat isl_options_set_schedule_treat_coalescing(
11470 isl_ctx *ctx, int val);
11471 int isl_options_get_schedule_treat_coalescing(
11473 isl_stat isl_options_set_schedule_algorithm(
11474 isl_ctx *ctx, int val);
11475 int isl_options_get_schedule_algorithm(
11477 isl_stat isl_options_set_schedule_carry_self_first(
11478 isl_ctx *ctx, int val);
11479 int isl_options_get_schedule_carry_self_first(
11481 isl_stat isl_options_set_schedule_separate_components(
11482 isl_ctx *ctx, int val);
11483 int isl_options_get_schedule_separate_components(
11488 =item * schedule_max_coefficient
11490 This option enforces that the coefficients for variable and parameter
11491 dimensions in the calculated schedule are not larger than the specified value.
11492 This option can significantly increase the speed of the scheduling calculation
11493 and may also prevent fusing of unrelated dimensions. A value of -1 means that
11494 this option does not introduce bounds on the variable or parameter
11496 This option has no effect on the Feautrier style scheduler.
11498 =item * schedule_max_constant_term
11500 This option enforces that the constant coefficients in the calculated schedule
11501 are not larger than the maximal constant term. This option can significantly
11502 increase the speed of the scheduling calculation and may also prevent fusing of
11503 unrelated dimensions. A value of -1 means that this option does not introduce
11504 bounds on the constant coefficients.
11506 =item * schedule_serialize_sccs
11508 If this option is set, then all strongly connected components
11509 in the dependence graph are serialized as soon as they are detected.
11510 This means in particular that instances of statements will only
11511 appear in the same band node if these statements belong
11512 to the same strongly connected component at the point where
11513 the band node is constructed.
11515 =item * schedule_whole_component
11517 If this option is set, then entire (weakly) connected
11518 components in the dependence graph are scheduled together
11520 Otherwise, each strongly connected component within
11521 such a weakly connected component is first scheduled separately
11522 and then combined with other strongly connected components.
11523 This option has no effect if C<schedule_serialize_sccs> is set.
11525 =item * schedule_maximize_band_depth
11527 If this option is set, then the scheduler tries to maximize
11528 the width of the bands. Wider bands give more possibilities for tiling.
11529 In particular, if the C<schedule_whole_component> option is set,
11530 then bands are split if this might result in wider bands.
11531 Otherwise, the effect of this option is to only allow
11532 strongly connected components to be combined if this does
11533 not reduce the width of the bands.
11534 Note that if the C<schedule_serialize_sccs> options is set, then
11535 the C<schedule_maximize_band_depth> option therefore has no effect.
11537 =item * schedule_maximize_coincidence
11539 This option is only effective if the C<schedule_whole_component>
11540 option is turned off.
11541 If the C<schedule_maximize_coincidence> option is set, then (clusters of)
11542 strongly connected components are only combined with each other
11543 if this does not reduce the number of coincident band members.
11545 =item * schedule_outer_coincidence
11547 If this option is set, then we try to construct schedules
11548 where the outermost scheduling dimension in each band
11549 satisfies the coincidence constraints.
11551 =item * schedule_algorithm
11553 Selects the scheduling algorithm to be used.
11554 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
11555 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
11557 =item * schedule_split_scaled
11559 If this option is set, then we try to construct schedules in which the
11560 constant term is split off from the linear part if the linear parts of
11561 the scheduling rows for all nodes in the graph have a common non-trivial
11563 The constant term is then dropped and the linear
11565 This option is only effective when the Feautrier style scheduler is
11566 being used, either as the main scheduler or as a fallback for the
11567 Pluto-like scheduler.
11569 =item * schedule_treat_coalescing
11571 If this option is set, then the scheduler will try and avoid
11572 producing schedules that perform loop coalescing.
11573 In particular, for the Pluto-like scheduler, this option places
11574 bounds on the schedule coefficients based on the sizes of the instance sets.
11575 For the Feautrier style scheduler, this option detects potentially
11576 coalescing schedules and then tries to adjust the schedule to avoid
11579 =item * schedule_carry_self_first
11581 If this option is set, then the Feautrier style scheduler
11582 (when used as a fallback for the Pluto-like scheduler) will
11583 first try to only carry self-dependences.
11585 =item * schedule_separate_components
11587 If this option is set then the function C<isl_schedule_get_map>
11588 will treat set nodes in the same way as sequence nodes.
11592 =head2 AST Generation
11594 This section describes the C<isl> functionality for generating
11595 ASTs that visit all the elements
11596 in a domain in an order specified by a schedule tree or
11598 In case the schedule given as a C<isl_union_map>, an AST is generated
11599 that visits all the elements in the domain of the C<isl_union_map>
11600 according to the lexicographic order of the corresponding image
11601 element(s). If the range of the C<isl_union_map> consists of
11602 elements in more than one space, then each of these spaces is handled
11603 separately in an arbitrary order.
11604 It should be noted that the schedule tree or the image elements
11605 in a schedule map only specify the I<order>
11606 in which the corresponding domain elements should be visited.
11607 No direct relation between the partial schedule values
11608 or the image elements on the one hand and the loop iterators
11609 in the generated AST on the other hand should be assumed.
11611 Each AST is generated within a build. The initial build
11612 simply specifies the constraints on the parameters (if any)
11613 and can be created, inspected, copied and freed using the following functions.
11615 #include <isl/ast_build.h>
11616 __isl_give isl_ast_build *isl_ast_build_alloc(
11618 __isl_give isl_ast_build *isl_ast_build_from_context(
11619 __isl_take isl_set *set);
11620 __isl_give isl_ast_build *isl_ast_build_copy(
11621 __isl_keep isl_ast_build *build);
11622 __isl_null isl_ast_build *isl_ast_build_free(
11623 __isl_take isl_ast_build *build);
11625 The C<set> argument is usually a parameter set with zero or more parameters.
11626 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
11627 this set is required to be a parameter set.
11628 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
11629 specify any parameter constraints.
11630 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
11631 and L</"Fine-grained Control over AST Generation">.
11632 Finally, the AST itself can be constructed using one of the following
11635 #include <isl/ast_build.h>
11636 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
11637 __isl_keep isl_ast_build *build,
11638 __isl_take isl_schedule *schedule);
11639 __isl_give isl_ast_node *
11640 isl_ast_build_node_from_schedule_map(
11641 __isl_keep isl_ast_build *build,
11642 __isl_take isl_union_map *schedule);
11644 =head3 Inspecting the AST
11646 The basic properties of an AST node can be obtained as follows.
11648 #include <isl/ast.h>
11649 enum isl_ast_node_type isl_ast_node_get_type(
11650 __isl_keep isl_ast_node *node);
11652 The type of an AST node is one of
11653 C<isl_ast_node_for>,
11654 C<isl_ast_node_if>,
11655 C<isl_ast_node_block>,
11656 C<isl_ast_node_mark> or
11657 C<isl_ast_node_user>.
11658 An C<isl_ast_node_for> represents a for node.
11659 An C<isl_ast_node_if> represents an if node.
11660 An C<isl_ast_node_block> represents a compound node.
11661 An C<isl_ast_node_mark> introduces a mark in the AST.
11662 An C<isl_ast_node_user> represents an expression statement.
11663 An expression statement typically corresponds to a domain element, i.e.,
11664 one of the elements that is visited by the AST.
11666 Each type of node has its own additional properties.
11668 #include <isl/ast.h>
11669 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
11670 __isl_keep isl_ast_node *node);
11671 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
11672 __isl_keep isl_ast_node *node);
11673 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
11674 __isl_keep isl_ast_node *node);
11675 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
11676 __isl_keep isl_ast_node *node);
11677 __isl_give isl_ast_node *isl_ast_node_for_get_body(
11678 __isl_keep isl_ast_node *node);
11679 isl_bool isl_ast_node_for_is_degenerate(
11680 __isl_keep isl_ast_node *node);
11682 An C<isl_ast_for> is considered degenerate if it is known to execute
11685 #include <isl/ast.h>
11686 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
11687 __isl_keep isl_ast_node *node);
11688 __isl_give isl_ast_node *isl_ast_node_if_get_then_node(
11689 __isl_keep isl_ast_node *node);
11690 __isl_give isl_ast_node *isl_ast_node_if_get_then(
11691 __isl_keep isl_ast_node *node);
11692 isl_bool isl_ast_node_if_has_else_node(
11693 __isl_keep isl_ast_node *node);
11694 isl_bool isl_ast_node_if_has_else(
11695 __isl_keep isl_ast_node *node);
11696 __isl_give isl_ast_node *isl_ast_node_if_get_else_node(
11697 __isl_keep isl_ast_node *node);
11698 __isl_give isl_ast_node *isl_ast_node_if_get_else(
11699 __isl_keep isl_ast_node *node);
11701 C<isl_ast_node_if_get_then>,
11702 C<isl_ast_node_if_has_else> and
11703 C<isl_ast_node_if_get_else>
11704 are alternative names for
11705 C<isl_ast_node_if_get_then_node>,
11706 C<isl_ast_node_if_has_else_node> and
11707 C<isl_ast_node_if_get_else_node>, respectively.
11709 __isl_give isl_ast_node_list *
11710 isl_ast_node_block_get_children(
11711 __isl_keep isl_ast_node *node);
11713 __isl_give isl_id *isl_ast_node_mark_get_id(
11714 __isl_keep isl_ast_node *node);
11715 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
11716 __isl_keep isl_ast_node *node);
11718 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
11719 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
11721 #include <isl/ast.h>
11722 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
11723 __isl_keep isl_ast_node *node);
11725 All descendants of a specific node in the AST (including the node itself)
11727 in depth-first pre-order using the following function.
11729 #include <isl/ast.h>
11730 isl_stat isl_ast_node_foreach_descendant_top_down(
11731 __isl_keep isl_ast_node *node,
11732 isl_bool (*fn)(__isl_keep isl_ast_node *node,
11733 void *user), void *user);
11735 The callback function should return C<isl_bool_true> if the children
11736 of the given node should be visited and C<isl_bool_false> if they should not.
11737 It should return C<isl_bool_error> in case of failure, in which case
11738 the entire traversal is aborted.
11740 Each of the returned C<isl_ast_expr>s can in turn be inspected using
11741 the following functions.
11743 #include <isl/ast.h>
11744 enum isl_ast_expr_type isl_ast_expr_get_type(
11745 __isl_keep isl_ast_expr *expr);
11747 The type of an AST expression is one of
11748 C<isl_ast_expr_op>,
11749 C<isl_ast_expr_id> or
11750 C<isl_ast_expr_int>.
11751 An C<isl_ast_expr_op> represents the result of an operation.
11752 An C<isl_ast_expr_id> represents an identifier.
11753 An C<isl_ast_expr_int> represents an integer value.
11755 Each type of expression has its own additional properties.
11757 #include <isl/ast.h>
11758 enum isl_ast_expr_op_type isl_ast_expr_op_get_type(
11759 __isl_keep isl_ast_expr *expr);
11760 enum isl_ast_expr_op_type isl_ast_expr_get_op_type(
11761 __isl_keep isl_ast_expr *expr);
11762 isl_size isl_ast_expr_op_get_n_arg(__isl_keep isl_ast_expr *expr);
11763 isl_size isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
11764 __isl_give isl_ast_expr *isl_ast_expr_op_get_arg(
11765 __isl_keep isl_ast_expr *expr, int pos);
11766 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
11767 __isl_keep isl_ast_expr *expr, int pos);
11768 isl_stat isl_ast_expr_foreach_ast_expr_op_type(
11769 __isl_keep isl_ast_expr *expr,
11770 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11771 void *user), void *user);
11772 isl_stat isl_ast_expr_foreach_ast_op_type(
11773 __isl_keep isl_ast_expr *expr,
11774 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11775 void *user), void *user);
11776 isl_stat isl_ast_node_foreach_ast_expr_op_type(
11777 __isl_keep isl_ast_node *node,
11778 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11779 void *user), void *user);
11780 isl_stat isl_ast_node_foreach_ast_op_type(
11781 __isl_keep isl_ast_node *node,
11782 isl_stat (*fn)(enum isl_ast_expr_op_type type,
11783 void *user), void *user);
11785 C<isl_ast_expr_op_get_type> returns the type of the operation
11786 performed. C<isl_ast_expr_op_get_n_arg> returns the number of
11787 arguments. C<isl_ast_expr_get_op_arg> returns the specified
11789 C<isl_ast_expr_get_op_type> is an alternative name for
11790 C<isl_ast_expr_op_get_type>.
11792 C<isl_ast_expr_get_op_n_arg> is an alternative name for
11793 C<isl_ast_expr_op_get_n_arg> and
11794 C<isl_ast_expr_get_op_arg> is an alternative name for
11795 C<isl_ast_expr_op_get_arg>.
11797 C<isl_ast_expr_foreach_ast_expr_op_type> calls C<fn> for each distinct
11798 C<isl_ast_expr_op_type> that appears in C<expr>.
11799 C<isl_ast_expr_foreach_ast_op_type> is an alternative name for
11800 C<isl_ast_expr_foreach_ast_expr_op_type>.
11801 C<isl_ast_node_foreach_ast_expr_op_type> does the same for each distinct
11802 C<isl_ast_expr_op_type> that appears in C<node>.
11803 C<isl_ast_node_foreach_ast_op_type> is an alternative name for
11804 C<isl_ast_node_foreach_ast_expr_op_type>.
11805 The operation type is one of the following.
11809 =item C<isl_ast_expr_op_and>
11811 Logical I<and> of two arguments.
11812 Both arguments can be evaluated.
11814 =item C<isl_ast_expr_op_and_then>
11816 Logical I<and> of two arguments.
11817 The second argument can only be evaluated if the first evaluates to true.
11819 =item C<isl_ast_expr_op_or>
11821 Logical I<or> of two arguments.
11822 Both arguments can be evaluated.
11824 =item C<isl_ast_expr_op_or_else>
11826 Logical I<or> of two arguments.
11827 The second argument can only be evaluated if the first evaluates to false.
11829 =item C<isl_ast_expr_op_max>
11831 Maximum of two or more arguments.
11833 =item C<isl_ast_expr_op_min>
11835 Minimum of two or more arguments.
11837 =item C<isl_ast_expr_op_minus>
11841 =item C<isl_ast_expr_op_add>
11843 Sum of two arguments.
11845 =item C<isl_ast_expr_op_sub>
11847 Difference of two arguments.
11849 =item C<isl_ast_expr_op_mul>
11851 Product of two arguments.
11853 =item C<isl_ast_expr_op_div>
11855 Exact division. That is, the result is known to be an integer.
11857 =item C<isl_ast_expr_op_fdiv_q>
11859 Result of integer division, rounded towards negative
11861 The divisor is known to be positive.
11863 =item C<isl_ast_expr_op_pdiv_q>
11865 Result of integer division, where dividend is known to be non-negative.
11866 The divisor is known to be positive.
11868 =item C<isl_ast_expr_op_pdiv_r>
11870 Remainder of integer division, where dividend is known to be non-negative.
11871 The divisor is known to be positive.
11873 =item C<isl_ast_expr_op_zdiv_r>
11875 Equal to zero iff the remainder on integer division is zero.
11876 The divisor is known to be positive.
11878 =item C<isl_ast_expr_op_cond>
11880 Conditional operator defined on three arguments.
11881 If the first argument evaluates to true, then the result
11882 is equal to the second argument. Otherwise, the result
11883 is equal to the third argument.
11884 The second and third argument may only be evaluated if
11885 the first argument evaluates to true and false, respectively.
11886 Corresponds to C<a ? b : c> in C.
11888 =item C<isl_ast_expr_op_select>
11890 Conditional operator defined on three arguments.
11891 If the first argument evaluates to true, then the result
11892 is equal to the second argument. Otherwise, the result
11893 is equal to the third argument.
11894 The second and third argument may be evaluated independently
11895 of the value of the first argument.
11896 Corresponds to C<a * b + (1 - a) * c> in C.
11898 =item C<isl_ast_expr_op_eq>
11902 =item C<isl_ast_expr_op_le>
11904 Less than or equal relation.
11906 =item C<isl_ast_expr_op_lt>
11908 Less than relation.
11910 =item C<isl_ast_expr_op_ge>
11912 Greater than or equal relation.
11914 =item C<isl_ast_expr_op_gt>
11916 Greater than relation.
11918 =item C<isl_ast_expr_op_call>
11921 The number of arguments of the C<isl_ast_expr> is one more than
11922 the number of arguments in the function call, the first argument
11923 representing the function being called.
11925 =item C<isl_ast_expr_op_access>
11928 The number of arguments of the C<isl_ast_expr> is one more than
11929 the number of index expressions in the array access, the first argument
11930 representing the array being accessed.
11932 =item C<isl_ast_expr_op_member>
11935 This operation has two arguments, a structure and the name of
11936 the member of the structure being accessed.
11938 =item C<isl_ast_expr_op_address_of>
11940 The address of its single argument, which is always an array access.
11944 #include <isl/ast.h>
11945 __isl_give isl_id *isl_ast_expr_id_get_id(
11946 __isl_keep isl_ast_expr *expr);
11947 __isl_give isl_id *isl_ast_expr_get_id(
11948 __isl_keep isl_ast_expr *expr);
11950 Return the identifier represented by the AST expression.
11951 C<isl_ast_expr_get_id> is an alternative name for
11952 C<isl_ast_expr_id_get_id>.
11954 #include <isl/ast.h>
11955 __isl_give isl_val *isl_ast_expr_int_get_val(
11956 __isl_keep isl_ast_expr *expr);
11957 __isl_give isl_val *isl_ast_expr_get_val(
11958 __isl_keep isl_ast_expr *expr);
11960 Return the integer represented by the AST expression.
11961 C<isl_ast_expr_get_val> is an alternative name for
11962 C<isl_ast_expr_int_get_val>.
11964 =head3 Properties of ASTs
11966 #include <isl/ast.h>
11967 isl_bool isl_ast_expr_is_equal(
11968 __isl_keep isl_ast_expr *expr1,
11969 __isl_keep isl_ast_expr *expr2);
11971 Check if two C<isl_ast_expr>s are equal to each other.
11973 =head3 Manipulating and printing the AST
11975 AST nodes can be copied and freed using the following functions.
11977 #include <isl/ast.h>
11978 __isl_give isl_ast_node *isl_ast_node_copy(
11979 __isl_keep isl_ast_node *node);
11980 __isl_null isl_ast_node *isl_ast_node_free(
11981 __isl_take isl_ast_node *node);
11983 AST expressions can be copied and freed using the following functions.
11985 #include <isl/ast.h>
11986 __isl_give isl_ast_expr *isl_ast_expr_copy(
11987 __isl_keep isl_ast_expr *expr);
11988 __isl_null isl_ast_expr *isl_ast_expr_free(
11989 __isl_take isl_ast_expr *expr);
11991 New AST expressions can be created either directly or within
11992 the context of an C<isl_ast_build>.
11994 #include <isl/ast.h>
11995 __isl_give isl_ast_expr *isl_ast_expr_from_val(
11996 __isl_take isl_val *v);
11997 __isl_give isl_ast_expr *isl_ast_expr_from_id(
11998 __isl_take isl_id *id);
11999 __isl_give isl_ast_expr *isl_ast_expr_neg(
12000 __isl_take isl_ast_expr *expr);
12001 __isl_give isl_ast_expr *isl_ast_expr_address_of(
12002 __isl_take isl_ast_expr *expr);
12003 __isl_give isl_ast_expr *isl_ast_expr_add(
12004 __isl_take isl_ast_expr *expr1,
12005 __isl_take isl_ast_expr *expr2);
12006 __isl_give isl_ast_expr *isl_ast_expr_sub(
12007 __isl_take isl_ast_expr *expr1,
12008 __isl_take isl_ast_expr *expr2);
12009 __isl_give isl_ast_expr *isl_ast_expr_mul(
12010 __isl_take isl_ast_expr *expr1,
12011 __isl_take isl_ast_expr *expr2);
12012 __isl_give isl_ast_expr *isl_ast_expr_div(
12013 __isl_take isl_ast_expr *expr1,
12014 __isl_take isl_ast_expr *expr2);
12015 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
12016 __isl_take isl_ast_expr *expr1,
12017 __isl_take isl_ast_expr *expr2);
12018 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
12019 __isl_take isl_ast_expr *expr1,
12020 __isl_take isl_ast_expr *expr2);
12021 __isl_give isl_ast_expr *isl_ast_expr_and(
12022 __isl_take isl_ast_expr *expr1,
12023 __isl_take isl_ast_expr *expr2)
12024 __isl_give isl_ast_expr *isl_ast_expr_and_then(
12025 __isl_take isl_ast_expr *expr1,
12026 __isl_take isl_ast_expr *expr2)
12027 __isl_give isl_ast_expr *isl_ast_expr_or(
12028 __isl_take isl_ast_expr *expr1,
12029 __isl_take isl_ast_expr *expr2)
12030 __isl_give isl_ast_expr *isl_ast_expr_or_else(
12031 __isl_take isl_ast_expr *expr1,
12032 __isl_take isl_ast_expr *expr2)
12033 __isl_give isl_ast_expr *isl_ast_expr_eq(
12034 __isl_take isl_ast_expr *expr1,
12035 __isl_take isl_ast_expr *expr2);
12036 __isl_give isl_ast_expr *isl_ast_expr_le(
12037 __isl_take isl_ast_expr *expr1,
12038 __isl_take isl_ast_expr *expr2);
12039 __isl_give isl_ast_expr *isl_ast_expr_lt(
12040 __isl_take isl_ast_expr *expr1,
12041 __isl_take isl_ast_expr *expr2);
12042 __isl_give isl_ast_expr *isl_ast_expr_ge(
12043 __isl_take isl_ast_expr *expr1,
12044 __isl_take isl_ast_expr *expr2);
12045 __isl_give isl_ast_expr *isl_ast_expr_gt(
12046 __isl_take isl_ast_expr *expr1,
12047 __isl_take isl_ast_expr *expr2);
12048 __isl_give isl_ast_expr *isl_ast_expr_access(
12049 __isl_take isl_ast_expr *array,
12050 __isl_take isl_ast_expr_list *indices);
12051 __isl_give isl_ast_expr *isl_ast_expr_call(
12052 __isl_take isl_ast_expr *function,
12053 __isl_take isl_ast_expr_list *arguments);
12055 The function C<isl_ast_expr_address_of> can be applied to an
12056 C<isl_ast_expr> of type C<isl_ast_expr_op_access> only. It is meant
12057 to represent the address of the C<isl_ast_expr_access>.
12058 The second argument of the functions C<isl_ast_expr_pdiv_q> and
12059 C<isl_ast_expr_pdiv_r> should always evaluate to a positive number.
12061 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
12062 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
12064 #include <isl/ast_build.h>
12065 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
12066 __isl_keep isl_ast_build *build,
12067 __isl_take isl_set *set);
12068 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
12069 __isl_keep isl_ast_build *build,
12070 __isl_take isl_pw_aff *pa);
12071 __isl_give isl_ast_expr *
12072 isl_ast_build_access_from_pw_multi_aff(
12073 __isl_keep isl_ast_build *build,
12074 __isl_take isl_pw_multi_aff *pma);
12075 __isl_give isl_ast_expr *
12076 isl_ast_build_access_from_multi_pw_aff(
12077 __isl_keep isl_ast_build *build,
12078 __isl_take isl_multi_pw_aff *mpa);
12079 __isl_give isl_ast_expr *
12080 isl_ast_build_call_from_pw_multi_aff(
12081 __isl_keep isl_ast_build *build,
12082 __isl_take isl_pw_multi_aff *pma);
12083 __isl_give isl_ast_expr *
12084 isl_ast_build_call_from_multi_pw_aff(
12085 __isl_keep isl_ast_build *build,
12086 __isl_take isl_multi_pw_aff *mpa);
12089 the domains of C<pa>, C<mpa> and C<pma> should correspond
12090 to the schedule space of C<build>.
12091 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
12092 the function being called.
12093 If the accessed space is a nested relation, then it is taken
12094 to represent an access of the member specified by the range
12095 of this nested relation of the structure specified by the domain
12096 of the nested relation.
12098 The following functions can be used to modify an C<isl_ast_expr>.
12100 #include <isl/ast.h>
12101 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
12102 __isl_take isl_ast_expr *expr, int pos,
12103 __isl_take isl_ast_expr *arg);
12105 Replace the argument of C<expr> at position C<pos> by C<arg>.
12107 #include <isl/ast.h>
12108 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
12109 __isl_take isl_ast_expr *expr,
12110 __isl_take isl_id_to_ast_expr *id2expr);
12112 The function C<isl_ast_expr_substitute_ids> replaces the
12113 subexpressions of C<expr> of type C<isl_ast_expr_id>
12114 by the corresponding expression in C<id2expr>, if there is any.
12117 The following function can be used to modify the descendants
12118 of a specific node in an AST using a depth-first post-order
12119 traversal of those descendants (including the node itself).
12121 #include <isl/ast.h>
12122 __isl_give isl_ast_node *
12123 isl_ast_node_map_descendant_bottom_up(
12124 __isl_take isl_ast_node *node,
12125 __isl_give isl_ast_node *(*fn)(
12126 __isl_take isl_ast_node *node,
12127 void *user), void *user);
12129 User specified data can be attached to an C<isl_ast_node> and obtained
12130 from the same C<isl_ast_node> using the following functions.
12132 #include <isl/ast.h>
12133 __isl_give isl_ast_node *isl_ast_node_set_annotation(
12134 __isl_take isl_ast_node *node,
12135 __isl_take isl_id *annotation);
12136 __isl_give isl_id *isl_ast_node_get_annotation(
12137 __isl_keep isl_ast_node *node);
12139 Basic printing can be performed using the following functions.
12141 #include <isl/ast.h>
12142 __isl_give isl_printer *isl_printer_print_ast_expr(
12143 __isl_take isl_printer *p,
12144 __isl_keep isl_ast_expr *expr);
12145 __isl_give isl_printer *isl_printer_print_ast_node(
12146 __isl_take isl_printer *p,
12147 __isl_keep isl_ast_node *node);
12148 __isl_give char *isl_ast_expr_to_str(
12149 __isl_keep isl_ast_expr *expr);
12150 __isl_give char *isl_ast_node_to_str(
12151 __isl_keep isl_ast_node *node);
12152 __isl_give char *isl_ast_expr_to_C_str(
12153 __isl_keep isl_ast_expr *expr);
12154 __isl_give char *isl_ast_node_to_C_str(
12155 __isl_keep isl_ast_node *node);
12157 The functions C<isl_ast_expr_to_C_str> and
12158 C<isl_ast_node_to_C_str> are convenience functions
12159 that return a string representation of the input in C format.
12161 More advanced printing can be performed using the following functions.
12163 #include <isl/ast.h>
12164 __isl_give isl_printer *
12165 isl_ast_expr_op_type_set_print_name(
12166 __isl_take isl_printer *p,
12167 enum isl_ast_expr_op_type type,
12168 __isl_keep const char *name);
12169 __isl_give isl_printer *isl_ast_op_type_set_print_name(
12170 __isl_take isl_printer *p,
12171 enum isl_ast_expr_op_type type,
12172 __isl_keep const char *name);
12173 isl_stat isl_options_set_ast_print_macro_once(
12174 isl_ctx *ctx, int val);
12175 int isl_options_get_ast_print_macro_once(isl_ctx *ctx);
12176 __isl_give isl_printer *isl_ast_expr_op_type_print_macro(
12177 enum isl_ast_expr_op_type type,
12178 __isl_take isl_printer *p);
12179 __isl_give isl_printer *isl_ast_op_type_print_macro(
12180 enum isl_ast_expr_op_type type,
12181 __isl_take isl_printer *p);
12182 __isl_give isl_printer *isl_ast_expr_print_macros(
12183 __isl_keep isl_ast_expr *expr,
12184 __isl_take isl_printer *p);
12185 __isl_give isl_printer *isl_ast_node_print_macros(
12186 __isl_keep isl_ast_node *node,
12187 __isl_take isl_printer *p);
12188 __isl_give isl_printer *isl_ast_node_print(
12189 __isl_keep isl_ast_node *node,
12190 __isl_take isl_printer *p,
12191 __isl_take isl_ast_print_options *options);
12192 __isl_give isl_printer *isl_ast_node_for_print(
12193 __isl_keep isl_ast_node *node,
12194 __isl_take isl_printer *p,
12195 __isl_take isl_ast_print_options *options);
12196 __isl_give isl_printer *isl_ast_node_if_print(
12197 __isl_keep isl_ast_node *node,
12198 __isl_take isl_printer *p,
12199 __isl_take isl_ast_print_options *options);
12201 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
12202 C<isl> may print out an AST that makes use of macros such
12203 as C<floord>, C<min> and C<max>.
12204 The names of these macros may be modified by a call
12205 to C<isl_ast_expr_op_type_set_print_name>. The user-specified
12206 names are associated to the printer object.
12207 C<isl_ast_op_type_set_print_name> is an alternative name for
12208 C<isl_ast_expr_op_type_set_print_name>.
12209 C<isl_ast_expr_op_type_print_macro> prints out the macro
12210 corresponding to a specific C<isl_ast_expr_op_type>.
12211 If the print-macro-once option is set, then a given macro definition
12212 is only printed once to any given printer object.
12213 C<isl_ast_op_type_print_macro> is an alternative name for
12214 C<isl_ast_expr_op_type_print_macro>.
12215 C<isl_ast_expr_print_macros> scans the C<isl_ast_expr>
12216 for subexpressions where these macros would be used and prints
12217 out the required macro definitions.
12218 Essentially, C<isl_ast_expr_print_macros> calls
12219 C<isl_ast_expr_foreach_ast_expr_op_type> with
12220 C<isl_ast_expr_op_type_print_macro>
12221 as function argument.
12222 C<isl_ast_node_print_macros> does the same
12223 for expressions in its C<isl_ast_node> argument.
12224 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
12225 C<isl_ast_node_if_print> print an C<isl_ast_node>
12226 in C<ISL_FORMAT_C>, but allow for some extra control
12227 through an C<isl_ast_print_options> object.
12228 This object can be created using the following functions.
12230 #include <isl/ast.h>
12231 __isl_give isl_ast_print_options *
12232 isl_ast_print_options_alloc(isl_ctx *ctx);
12233 __isl_give isl_ast_print_options *
12234 isl_ast_print_options_copy(
12235 __isl_keep isl_ast_print_options *options);
12236 __isl_null isl_ast_print_options *
12237 isl_ast_print_options_free(
12238 __isl_take isl_ast_print_options *options);
12240 __isl_give isl_ast_print_options *
12241 isl_ast_print_options_set_print_user(
12242 __isl_take isl_ast_print_options *options,
12243 __isl_give isl_printer *(*print_user)(
12244 __isl_take isl_printer *p,
12245 __isl_take isl_ast_print_options *options,
12246 __isl_keep isl_ast_node *node, void *user),
12248 __isl_give isl_ast_print_options *
12249 isl_ast_print_options_set_print_for(
12250 __isl_take isl_ast_print_options *options,
12251 __isl_give isl_printer *(*print_for)(
12252 __isl_take isl_printer *p,
12253 __isl_take isl_ast_print_options *options,
12254 __isl_keep isl_ast_node *node, void *user),
12257 The callback set by C<isl_ast_print_options_set_print_user>
12258 is called whenever a node of type C<isl_ast_node_user> needs to
12260 The callback set by C<isl_ast_print_options_set_print_for>
12261 is called whenever a node of type C<isl_ast_node_for> needs to
12263 Note that C<isl_ast_node_for_print> will I<not> call the
12264 callback set by C<isl_ast_print_options_set_print_for> on the node
12265 on which C<isl_ast_node_for_print> is called, but only on nested
12266 nodes of type C<isl_ast_node_for>. It is therefore safe to
12267 call C<isl_ast_node_for_print> from within the callback set by
12268 C<isl_ast_print_options_set_print_for>.
12270 The following option determines the type to be used for iterators
12271 while printing the AST.
12273 isl_stat isl_options_set_ast_iterator_type(
12274 isl_ctx *ctx, const char *val);
12275 const char *isl_options_get_ast_iterator_type(
12278 The AST printer only prints body nodes of C<if> and C<for> nodes
12280 blocks cannot be safely omitted.
12281 For example, a C<for> node with one body node will not be
12282 surrounded with braces in C<ISL_FORMAT_C>.
12283 A block will always be printed by setting the following option.
12285 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx,
12287 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
12289 Explicit block nodes that appear inside the AST are always printed as blocks.
12290 If the block node appears as the outermost node,
12291 then it is only printed if the following option is set.
12293 isl_stat isl_options_set_ast_print_outermost_block(
12294 isl_ctx *ctx, int val);
12295 int isl_options_get_ast_print_outermost_block(
12300 #include <isl/ast_build.h>
12301 isl_stat isl_options_set_ast_build_atomic_upper_bound(
12302 isl_ctx *ctx, int val);
12303 int isl_options_get_ast_build_atomic_upper_bound(
12305 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
12307 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
12308 isl_stat isl_options_set_ast_build_detect_min_max(
12309 isl_ctx *ctx, int val);
12310 int isl_options_get_ast_build_detect_min_max(
12312 isl_stat isl_options_set_ast_build_exploit_nested_bounds(
12313 isl_ctx *ctx, int val);
12314 int isl_options_get_ast_build_exploit_nested_bounds(
12316 isl_stat isl_options_set_ast_build_group_coscheduled(
12317 isl_ctx *ctx, int val);
12318 int isl_options_get_ast_build_group_coscheduled(
12320 isl_stat isl_options_set_ast_build_separation_bounds(
12321 isl_ctx *ctx, int val);
12322 int isl_options_get_ast_build_separation_bounds(
12324 isl_stat isl_options_set_ast_build_scale_strides(
12325 isl_ctx *ctx, int val);
12326 int isl_options_get_ast_build_scale_strides(
12328 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx,
12330 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
12331 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx,
12333 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
12337 =item * ast_build_atomic_upper_bound
12339 Generate loop upper bounds that consist of the current loop iterator,
12340 an operator and an expression not involving the iterator.
12341 If this option is not set, then the current loop iterator may appear
12342 several times in the upper bound.
12343 For example, when this option is turned off, AST generation
12346 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
12350 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
12353 When the option is turned on, the following AST is generated
12355 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
12358 =item * ast_build_prefer_pdiv
12360 If this option is turned off, then the AST generation will
12361 produce ASTs that may only contain C<isl_ast_expr_op_fdiv_q>
12362 operators, but no C<isl_ast_expr_op_pdiv_q> or
12363 C<isl_ast_expr_op_pdiv_r> operators.
12364 If this option is turned on, then C<isl> will try to convert
12365 some of the C<isl_ast_expr_op_fdiv_q> operators to (expressions containing)
12366 C<isl_ast_expr_op_pdiv_q> or C<isl_ast_expr_op_pdiv_r> operators.
12368 =item * ast_build_detect_min_max
12370 If this option is turned on, then C<isl> will try and detect
12371 min or max-expressions when building AST expressions from
12372 piecewise affine expressions.
12374 =item * ast_build_exploit_nested_bounds
12376 Simplify conditions based on bounds of nested for loops.
12377 In particular, remove conditions that are implied by the fact
12378 that one or more nested loops have at least one iteration,
12379 meaning that the upper bound is at least as large as the lower bound.
12380 For example, when this option is turned off, AST generation
12383 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
12389 for (int c0 = 0; c0 <= N; c0 += 1)
12390 for (int c1 = 0; c1 <= M; c1 += 1)
12393 When the option is turned on, the following AST is generated
12395 for (int c0 = 0; c0 <= N; c0 += 1)
12396 for (int c1 = 0; c1 <= M; c1 += 1)
12399 =item * ast_build_group_coscheduled
12401 If two domain elements are assigned the same schedule point, then
12402 they may be executed in any order and they may even appear in different
12403 loops. If this options is set, then the AST generator will make
12404 sure that coscheduled domain elements do not appear in separate parts
12405 of the AST. This is useful in case of nested AST generation
12406 if the outer AST generation is given only part of a schedule
12407 and the inner AST generation should handle the domains that are
12408 coscheduled by this initial part of the schedule together.
12409 For example if an AST is generated for a schedule
12411 { A[i] -> [0]; B[i] -> [0] }
12413 then the C<isl_ast_build_set_create_leaf> callback described
12414 below may get called twice, once for each domain.
12415 Setting this option ensures that the callback is only called once
12416 on both domains together.
12418 =item * ast_build_separation_bounds
12420 This option specifies which bounds to use during separation.
12421 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
12422 then all (possibly implicit) bounds on the current dimension will
12423 be used during separation.
12424 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
12425 then only those bounds that are explicitly available will
12426 be used during separation.
12428 =item * ast_build_scale_strides
12430 This option specifies whether the AST generator is allowed
12431 to scale down iterators of strided loops.
12433 =item * ast_build_allow_else
12435 This option specifies whether the AST generator is allowed
12436 to construct if statements with else branches.
12438 =item * ast_build_allow_or
12440 This option specifies whether the AST generator is allowed
12441 to construct if conditions with disjunctions.
12445 =head3 AST Generation Options (Schedule Tree)
12447 In case of AST construction from a schedule tree, the options
12448 that control how an AST is created from the individual schedule
12449 dimensions are stored in the band nodes of the tree
12450 (see L</"Schedule Trees">).
12452 In particular, a schedule dimension can be handled in four
12453 different ways, atomic, separate, unroll or the default.
12454 This loop AST generation type can be set using
12455 C<isl_schedule_node_band_member_set_ast_loop_type>.
12457 the first three can be selected by including a one-dimensional
12458 element with as value the position of the schedule dimension
12459 within the band and as name one of C<atomic>, C<separate>
12460 or C<unroll> in the options
12461 set by C<isl_schedule_node_band_set_ast_build_options>.
12462 Only one of these three may be specified for
12463 any given schedule dimension within a band node.
12464 If none of these is specified, then the default
12465 is used. The meaning of the options is as follows.
12471 When this option is specified, the AST generator will make
12472 sure that a given domain space only appears in a single
12473 loop at the specified level.
12475 For example, for the schedule tree
12477 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
12479 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
12480 options: "{ atomic[x] }"
12482 the following AST will be generated
12484 for (int c0 = 0; c0 <= 10; c0 += 1) {
12491 On the other hand, for the schedule tree
12493 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
12495 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
12496 options: "{ separate[x] }"
12498 the following AST will be generated
12502 for (int c0 = 1; c0 <= 9; c0 += 1) {
12509 If neither C<atomic> nor C<separate> is specified, then the AST generator
12510 may produce either of these two results or some intermediate form.
12514 When this option is specified, the AST generator will
12515 split the domain of the specified schedule dimension
12516 into pieces with a fixed set of statements for which
12517 instances need to be executed by the iterations in
12518 the schedule domain part. This option tends to avoid
12519 the generation of guards inside the corresponding loops.
12520 See also the C<atomic> option.
12524 When this option is specified, the AST generator will
12525 I<completely> unroll the corresponding schedule dimension.
12526 It is the responsibility of the user to ensure that such
12527 unrolling is possible.
12528 To obtain a partial unrolling, the user should apply an additional
12529 strip-mining to the schedule and fully unroll the inner schedule
12534 The C<isolate> option is a bit more involved. It allows the user
12535 to isolate a range of schedule dimension values from smaller and
12536 greater values. Additionally, the user may specify a different
12537 atomic/separate/unroll choice for the isolated part and the remaining
12538 parts. The typical use case of the C<isolate> option is to isolate
12539 full tiles from partial tiles.
12540 The part that needs to be isolated may depend on outer schedule dimensions.
12541 The option therefore needs to be able to reference those outer schedule
12542 dimensions. In particular, the space of the C<isolate> option is that
12543 of a wrapped map with as domain the flat product of all outer band nodes
12544 and as range the space of the current band node.
12545 The atomic/separate/unroll choice for the isolated part is determined
12546 by an option that lives in an unnamed wrapped space with as domain
12547 a zero-dimensional C<isolate> space and as range the regular
12548 C<atomic>, C<separate> or C<unroll> space.
12549 This option may also be set directly using
12550 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
12551 The atomic/separate/unroll choice for the remaining part is determined
12552 by the regular C<atomic>, C<separate> or C<unroll> option.
12553 Since the C<isolate> option references outer schedule dimensions,
12554 its use in a band node causes any tree containing the node
12555 to be considered anchored.
12557 As an example, consider the isolation of full tiles from partial tiles
12558 in a tiling of a triangular domain. The original schedule is as follows.
12560 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
12562 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
12563 { A[i,j] -> [floor(j/10)] }, \
12564 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
12568 for (int c0 = 0; c0 <= 10; c0 += 1)
12569 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12570 for (int c2 = 10 * c0;
12571 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12572 for (int c3 = 10 * c1;
12573 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12576 Isolating the full tiles, we have the following input
12578 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
12580 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
12581 { A[i,j] -> [floor(j/10)] }, \
12582 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
12583 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
12584 10a+9+10b+9 <= 100 }"
12589 for (int c0 = 0; c0 <= 8; c0 += 1) {
12590 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
12591 for (int c2 = 10 * c0;
12592 c2 <= 10 * c0 + 9; c2 += 1)
12593 for (int c3 = 10 * c1;
12594 c3 <= 10 * c1 + 9; c3 += 1)
12596 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
12597 for (int c2 = 10 * c0;
12598 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12599 for (int c3 = 10 * c1;
12600 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12603 for (int c0 = 9; c0 <= 10; c0 += 1)
12604 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12605 for (int c2 = 10 * c0;
12606 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12607 for (int c3 = 10 * c1;
12608 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12612 We may then additionally unroll the innermost loop of the isolated part
12614 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
12616 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
12617 { A[i,j] -> [floor(j/10)] }, \
12618 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
12619 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
12620 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
12625 for (int c0 = 0; c0 <= 8; c0 += 1) {
12626 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
12627 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
12629 A(c2, 10 * c1 + 1);
12630 A(c2, 10 * c1 + 2);
12631 A(c2, 10 * c1 + 3);
12632 A(c2, 10 * c1 + 4);
12633 A(c2, 10 * c1 + 5);
12634 A(c2, 10 * c1 + 6);
12635 A(c2, 10 * c1 + 7);
12636 A(c2, 10 * c1 + 8);
12637 A(c2, 10 * c1 + 9);
12639 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
12640 for (int c2 = 10 * c0;
12641 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12642 for (int c3 = 10 * c1;
12643 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12646 for (int c0 = 9; c0 <= 10; c0 += 1)
12647 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12648 for (int c2 = 10 * c0;
12649 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
12650 for (int c3 = 10 * c1;
12651 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
12656 =head3 AST Generation Options (Schedule Map)
12658 In case of AST construction using
12659 C<isl_ast_build_node_from_schedule_map>, the options
12660 that control how an AST is created from the individual schedule
12661 dimensions are stored in the C<isl_ast_build>.
12662 They can be set using the following function.
12664 #include <isl/ast_build.h>
12665 __isl_give isl_ast_build *
12666 isl_ast_build_set_options(
12667 __isl_take isl_ast_build *build,
12668 __isl_take isl_union_map *options);
12670 The options are encoded in an C<isl_union_map>.
12671 The domain of this union relation refers to the schedule domain,
12672 i.e., the range of the schedule passed
12673 to C<isl_ast_build_node_from_schedule_map>.
12674 In the case of nested AST generation (see L</"Nested AST Generation">),
12675 the domain of C<options> should refer to the extra piece of the schedule.
12676 That is, it should be equal to the range of the wrapped relation in the
12677 range of the schedule.
12678 The range of the options can consist of elements in one or more spaces,
12679 the names of which determine the effect of the option.
12680 The values of the range typically also refer to the schedule dimension
12681 to which the option applies, with value C<0> representing
12682 the outermost schedule dimension. In case of nested AST generation
12683 (see L</"Nested AST Generation">), these values refer to the position
12684 of the schedule dimension within the innermost AST generation.
12685 The constraints on the domain elements of
12686 the option should only refer to this dimension and earlier dimensions.
12687 We consider the following spaces.
12691 =item C<separation_class>
12693 B<This option has been deprecated. Use the isolate option on
12694 schedule trees instead.>
12696 This space is a wrapped relation between two one dimensional spaces.
12697 The input space represents the schedule dimension to which the option
12698 applies and the output space represents the separation class.
12699 While constructing a loop corresponding to the specified schedule
12700 dimension(s), the AST generator will try to generate separate loops
12701 for domain elements that are assigned different classes.
12702 If only some of the elements are assigned a class, then those elements
12703 that are not assigned any class will be treated as belonging to a class
12704 that is separate from the explicitly assigned classes.
12705 The typical use case for this option is to separate full tiles from
12707 The other options, described below, are applied after the separation
12710 As an example, consider the separation into full and partial tiles
12711 of a tiling of a triangular domain.
12712 Take, for example, the domain
12714 { A[i,j] : 0 <= i,j and i + j <= 100 }
12716 and a tiling into tiles of 10 by 10. The input to the AST generator
12717 is then the schedule
12719 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
12722 Without any options, the following AST is generated
12724 for (int c0 = 0; c0 <= 10; c0 += 1)
12725 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12726 for (int c2 = 10 * c0;
12727 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
12729 for (int c3 = 10 * c1;
12730 c3 <= min(10 * c1 + 9, -c2 + 100);
12734 Separation into full and partial tiles can be obtained by assigning
12735 a class, say C<0>, to the full tiles. The full tiles are represented by those
12736 values of the first and second schedule dimensions for which there are
12737 values of the third and fourth dimensions to cover an entire tile.
12738 That is, we need to specify the following option
12740 { [a,b,c,d] -> separation_class[[0]->[0]] :
12741 exists b': 0 <= 10a,10b' and
12742 10a+9+10b'+9 <= 100;
12743 [a,b,c,d] -> separation_class[[1]->[0]] :
12744 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
12746 which simplifies to
12748 { [a, b, c, d] -> separation_class[[1] -> [0]] :
12749 a >= 0 and b >= 0 and b <= 8 - a;
12750 [a, b, c, d] -> separation_class[[0] -> [0]] :
12751 a >= 0 and a <= 8 }
12753 With this option, the generated AST is as follows
12756 for (int c0 = 0; c0 <= 8; c0 += 1) {
12757 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
12758 for (int c2 = 10 * c0;
12759 c2 <= 10 * c0 + 9; c2 += 1)
12760 for (int c3 = 10 * c1;
12761 c3 <= 10 * c1 + 9; c3 += 1)
12763 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
12764 for (int c2 = 10 * c0;
12765 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
12767 for (int c3 = 10 * c1;
12768 c3 <= min(-c2 + 100, 10 * c1 + 9);
12772 for (int c0 = 9; c0 <= 10; c0 += 1)
12773 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
12774 for (int c2 = 10 * c0;
12775 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
12777 for (int c3 = 10 * c1;
12778 c3 <= min(10 * c1 + 9, -c2 + 100);
12785 This is a single-dimensional space representing the schedule dimension(s)
12786 to which ``separation'' should be applied. Separation tries to split
12787 a loop into several pieces if this can avoid the generation of guards
12789 See also the C<atomic> option.
12793 This is a single-dimensional space representing the schedule dimension(s)
12794 for which the domains should be considered ``atomic''. That is, the
12795 AST generator will make sure that any given domain space will only appear
12796 in a single loop at the specified level.
12798 Consider the following schedule
12800 { a[i] -> [i] : 0 <= i < 10;
12801 b[i] -> [i+1] : 0 <= i < 10 }
12803 If the following option is specified
12805 { [i] -> separate[x] }
12807 then the following AST will be generated
12811 for (int c0 = 1; c0 <= 9; c0 += 1) {
12818 If, on the other hand, the following option is specified
12820 { [i] -> atomic[x] }
12822 then the following AST will be generated
12824 for (int c0 = 0; c0 <= 10; c0 += 1) {
12831 If neither C<atomic> nor C<separate> is specified, then the AST generator
12832 may produce either of these two results or some intermediate form.
12836 This is a single-dimensional space representing the schedule dimension(s)
12837 that should be I<completely> unrolled.
12838 To obtain a partial unrolling, the user should apply an additional
12839 strip-mining to the schedule and fully unroll the inner loop.
12843 =head3 Fine-grained Control over AST Generation
12845 Besides specifying the constraints on the parameters,
12846 an C<isl_ast_build> object can be used to control
12847 various aspects of the AST generation process.
12848 In case of AST construction using
12849 C<isl_ast_build_node_from_schedule_map>,
12850 the most prominent way of control is through ``options'',
12851 as explained above.
12853 Additional control is available through the following functions.
12855 #include <isl/ast_build.h>
12856 __isl_give isl_ast_build *
12857 isl_ast_build_set_iterators(
12858 __isl_take isl_ast_build *build,
12859 __isl_take isl_id_list *iterators);
12861 The function C<isl_ast_build_set_iterators> allows the user to
12862 specify a list of iterator C<isl_id>s to be used as iterators.
12863 If the input schedule is injective, then
12864 the number of elements in this list should be as large as the dimension
12865 of the schedule space, but no direct correspondence should be assumed
12866 between dimensions and elements.
12867 If the input schedule is not injective, then an additional number
12868 of C<isl_id>s equal to the largest dimension of the input domains
12870 If the number of provided C<isl_id>s is insufficient, then additional
12871 names are automatically generated.
12873 #include <isl/ast_build.h>
12874 __isl_give isl_ast_build *
12875 isl_ast_build_set_create_leaf(
12876 __isl_take isl_ast_build *build,
12877 __isl_give isl_ast_node *(*fn)(
12878 __isl_take isl_ast_build *build,
12879 void *user), void *user);
12882 C<isl_ast_build_set_create_leaf> function allows for the
12883 specification of a callback that should be called whenever the AST
12884 generator arrives at an element of the schedule domain.
12885 The callback should return an AST node that should be inserted
12886 at the corresponding position of the AST. The default action (when
12887 the callback is not set) is to continue generating parts of the AST to scan
12888 all the domain elements associated to the schedule domain element
12889 and to insert user nodes, ``calling'' the domain element, for each of them.
12890 The C<build> argument contains the current state of the C<isl_ast_build>.
12891 To ease nested AST generation (see L</"Nested AST Generation">),
12892 all control information that is
12893 specific to the current AST generation such as the options and
12894 the callbacks has been removed from this C<isl_ast_build>.
12895 The callback would typically return the result of a nested
12896 AST generation or a
12897 user defined node created using the following function.
12899 #include <isl/ast.h>
12900 __isl_give isl_ast_node *isl_ast_node_user_from_expr(
12901 __isl_take isl_ast_expr *expr);
12902 __isl_give isl_ast_node *isl_ast_node_alloc_user(
12903 __isl_take isl_ast_expr *expr);
12905 C<isl_ast_node_alloc_user> is an alternative name for
12906 C<isl_ast_node_user_from_expr>.
12908 In some cases, a single user defined node is not enough,
12909 in which case the following function can be used
12910 to create a block node from multiple AST nodes.
12912 #include <isl/ast.h>
12913 __isl_give isl_ast_node *isl_ast_node_block_from_children(
12914 __isl_take isl_ast_node_list *list);
12916 #include <isl/ast_build.h>
12917 __isl_give isl_ast_build *
12918 isl_ast_build_set_at_each_domain(
12919 __isl_take isl_ast_build *build,
12920 __isl_give isl_ast_node *(*fn)(
12921 __isl_take isl_ast_node *node,
12922 __isl_keep isl_ast_build *build,
12923 void *user), void *user);
12924 __isl_give isl_ast_build *
12925 isl_ast_build_set_before_each_for(
12926 __isl_take isl_ast_build *build,
12927 __isl_give isl_id *(*fn)(
12928 __isl_keep isl_ast_build *build,
12929 void *user), void *user);
12930 __isl_give isl_ast_build *
12931 isl_ast_build_set_after_each_for(
12932 __isl_take isl_ast_build *build,
12933 __isl_give isl_ast_node *(*fn)(
12934 __isl_take isl_ast_node *node,
12935 __isl_keep isl_ast_build *build,
12936 void *user), void *user);
12937 __isl_give isl_ast_build *
12938 isl_ast_build_set_before_each_mark(
12939 __isl_take isl_ast_build *build,
12940 isl_stat (*fn)(__isl_keep isl_id *mark,
12941 __isl_keep isl_ast_build *build,
12942 void *user), void *user);
12943 __isl_give isl_ast_build *
12944 isl_ast_build_set_after_each_mark(
12945 __isl_take isl_ast_build *build,
12946 __isl_give isl_ast_node *(*fn)(
12947 __isl_take isl_ast_node *node,
12948 __isl_keep isl_ast_build *build,
12949 void *user), void *user);
12951 The callback set by C<isl_ast_build_set_at_each_domain> will
12952 be called for each domain AST node.
12953 The callbacks set by C<isl_ast_build_set_before_each_for>
12954 and C<isl_ast_build_set_after_each_for> will be called
12955 for each for AST node. The first will be called in depth-first
12956 pre-order, while the second will be called in depth-first post-order.
12957 Since C<isl_ast_build_set_before_each_for> is called before the for
12958 node is actually constructed, it is only passed an C<isl_ast_build>.
12959 The returned C<isl_id> will be added as an annotation (using
12960 C<isl_ast_node_set_annotation>) to the constructed for node.
12961 In particular, if the user has also specified an C<after_each_for>
12962 callback, then the annotation can be retrieved from the node passed to
12963 that callback using C<isl_ast_node_get_annotation>.
12964 The callbacks set by C<isl_ast_build_set_before_each_mark>
12965 and C<isl_ast_build_set_after_each_mark> will be called for each
12966 mark AST node that is created, i.e., for each mark schedule node
12967 in the input schedule tree. The first will be called in depth-first
12968 pre-order, while the second will be called in depth-first post-order.
12969 Since the callback set by C<isl_ast_build_set_before_each_mark>
12970 is called before the mark AST node is actually constructed, it is passed
12971 the identifier of the mark node.
12972 All callbacks should C<NULL> (or C<isl_stat_error>) on failure.
12973 The given C<isl_ast_build> can be used to create new
12974 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
12975 or C<isl_ast_build_call_from_pw_multi_aff>.
12977 =head3 Nested AST Generation
12979 C<isl> allows the user to create an AST within the context
12980 of another AST. These nested ASTs are created using the
12981 same C<isl_ast_build_node_from_schedule_map> function that is used to create
12982 the outer AST. The C<build> argument should be an C<isl_ast_build>
12983 passed to a callback set by
12984 C<isl_ast_build_set_create_leaf>.
12985 The space of the range of the C<schedule> argument should refer
12986 to this build. In particular, the space should be a wrapped
12987 relation and the domain of this wrapped relation should be the
12988 same as that of the range of the schedule returned by
12989 C<isl_ast_build_get_schedule> below.
12990 In practice, the new schedule is typically
12991 created by calling C<isl_union_map_range_product> on the old schedule
12992 and some extra piece of the schedule.
12993 The space of the schedule domain is also available from
12994 the C<isl_ast_build>.
12996 #include <isl/ast_build.h>
12997 __isl_give isl_union_map *isl_ast_build_get_schedule(
12998 __isl_keep isl_ast_build *build);
12999 __isl_give isl_space *isl_ast_build_get_schedule_space(
13000 __isl_keep isl_ast_build *build);
13001 __isl_give isl_ast_build *isl_ast_build_restrict(
13002 __isl_take isl_ast_build *build,
13003 __isl_take isl_set *set);
13005 The C<isl_ast_build_get_schedule> function returns a (partial)
13006 schedule for the domains elements for which part of the AST still needs to
13007 be generated in the current build.
13008 In particular, the domain elements are mapped to those iterations of the loops
13009 enclosing the current point of the AST generation inside which
13010 the domain elements are executed.
13011 No direct correspondence between
13012 the input schedule and this schedule should be assumed.
13013 The space obtained from C<isl_ast_build_get_schedule_space> can be used
13014 to create a set for C<isl_ast_build_restrict> to intersect
13015 with the current build. In particular, the set passed to
13016 C<isl_ast_build_restrict> can have additional parameters.
13017 The ids of the set dimensions in the space returned by
13018 C<isl_ast_build_get_schedule_space> correspond to the
13019 iterators of the already generated loops.
13020 The user should not rely on the ids of the output dimensions
13021 of the relations in the union relation returned by
13022 C<isl_ast_build_get_schedule> having any particular value.
13024 =head1 Applications
13026 Although C<isl> is mainly meant to be used as a library,
13027 it also contains some basic applications that use some
13028 of the functionality of C<isl>.
13029 For applications that take one or more polytopes or polyhedra
13030 as input, this input may be specified in either the L<isl format>
13031 or the L<PolyLib format>.
13033 =head2 C<isl_polyhedron_sample>
13035 C<isl_polyhedron_sample> takes a polyhedron as input and prints
13036 an integer element of the polyhedron, if there is any.
13037 The first column in the output is the denominator and is always
13038 equal to 1. If the polyhedron contains no integer points,
13039 then a vector of length zero is printed.
13043 C<isl_pip> takes the same input as the C<example> program
13044 from the C<piplib> distribution, i.e., a set of constraints
13045 on the parameters, a line containing only -1 and finally a set
13046 of constraints on a parametric polyhedron.
13047 The coefficients of the parameters appear in the last columns
13048 (but before the final constant column).
13049 The output is the lexicographic minimum of the parametric polyhedron.
13050 As C<isl> currently does not have its own output format, the output
13051 is just a dump of the internal state.
13053 =head2 C<isl_polyhedron_minimize>
13055 C<isl_polyhedron_minimize> computes the minimum of some linear
13056 or affine objective function over the integer points in a polyhedron.
13057 If an affine objective function
13058 is given, then the constant should appear in the last column.
13060 =head2 C<isl_polytope_scan>
13062 Given a polytope, C<isl_polytope_scan> prints
13063 all integer points in the polytope.
13067 Given an C<isl_union_access_info> object as input,
13068 C<isl_flow> prints out the corresponding dependences,
13069 as computed by C<isl_union_access_info_compute_flow>.
13071 =head2 C<isl_codegen>
13073 Given either a schedule tree or a sequence consisting of
13074 a schedule map, a context set and an options relation,
13075 C<isl_codegen> prints out an AST that scans the domain elements
13076 of the schedule in the order of their image(s) taking into account
13077 the constraints in the context set.
13079 =head2 C<isl_schedule>
13081 Given an C<isl_schedule_constraints> object as input,
13082 C<isl_schedule> prints out a schedule that satisfies the given