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.
275 C<isl> is released under the MIT license.
279 Permission is hereby granted, free of charge, to any person obtaining a copy of
280 this software and associated documentation files (the "Software"), to deal in
281 the Software without restriction, including without limitation the rights to
282 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
283 of the Software, and to permit persons to whom the Software is furnished to do
284 so, subject to the following conditions:
286 The above copyright notice and this permission notice shall be included in all
287 copies or substantial portions of the Software.
289 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
290 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
291 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
292 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
293 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
294 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
299 Note that by default C<isl> requires C<GMP>, which is released
300 under the GNU Lesser General Public License (LGPL). This means
301 that code linked against C<isl> is also linked against LGPL code.
303 When configuring with C<--with-int=imath> or C<--with-int=imath-32>, C<isl>
304 will link against C<imath>, a library for exact integer arithmetic released
305 under the MIT license.
309 The source of C<isl> can be obtained either as a tarball
310 or from the git repository. Both are available from
311 L<http://isl.gforge.inria.fr/>.
312 The installation process depends on how you obtained
315 =head2 Installation from the git repository
319 =item 1 Clone or update the repository
321 The first time the source is obtained, you need to clone
324 git clone git://repo.or.cz/isl.git
326 To obtain updates, you need to pull in the latest changes
330 =item 2 Optionally get C<imath> submodule
332 To build C<isl> with C<imath>, you need to obtain the C<imath>
333 submodule by running in the git source tree of C<isl>
338 This will fetch the required version of C<imath> in a subdirectory of C<isl>.
340 =item 2 Generate C<configure>
346 After performing the above steps, continue
347 with the L<Common installation instructions>.
349 =head2 Common installation instructions
353 =item 1 Obtain C<GMP>
355 By default, building C<isl> requires C<GMP>, including its headers files.
356 Your distribution may not provide these header files by default
357 and you may need to install a package called C<gmp-devel> or something
358 similar. Alternatively, C<GMP> can be built from
359 source, available from L<http://gmplib.org/>.
360 C<GMP> is not needed if you build C<isl> with C<imath>.
364 C<isl> uses the standard C<autoconf> C<configure> script.
369 optionally followed by some configure options.
370 A complete list of options can be obtained by running
374 Below we discuss some of the more common options.
380 Installation prefix for C<isl>
382 =item C<--with-int=[gmp|imath|imath-32]>
384 Select the integer library to be used by C<isl>, the default is C<gmp>.
385 With C<imath-32>, C<isl> will use 32 bit integers, but fall back to C<imath>
386 for values out of the 32 bit range. In most applications, C<isl> will run
387 fastest with the C<imath-32> option, followed by C<gmp> and C<imath>, the
390 =item C<--with-gmp-prefix>
392 Installation prefix for C<GMP> (architecture-independent files).
394 =item C<--with-gmp-exec-prefix>
396 Installation prefix for C<GMP> (architecture-dependent files).
404 =item 4 Install (optional)
410 =head1 Integer Set Library
412 =head2 Memory Management
414 Since a high-level operation on isl objects usually involves
415 several substeps and since the user is usually not interested in
416 the intermediate results, most functions that return a new object
417 will also release all the objects passed as arguments.
418 If the user still wants to use one or more of these arguments
419 after the function call, she should pass along a copy of the
420 object rather than the object itself.
421 The user is then responsible for making sure that the original
422 object gets used somewhere else or is explicitly freed.
424 The arguments and return values of all documented functions are
425 annotated to make clear which arguments are released and which
426 arguments are preserved. In particular, the following annotations
433 C<__isl_give> means that a new object is returned.
434 The user should make sure that the returned pointer is
435 used exactly once as a value for an C<__isl_take> argument.
436 In between, it can be used as a value for as many
437 C<__isl_keep> arguments as the user likes.
438 There is one exception, and that is the case where the
439 pointer returned is C<NULL>. Is this case, the user
440 is free to use it as an C<__isl_take> argument or not.
441 When applied to a C<char *>, the returned pointer needs to be
446 C<__isl_null> means that a C<NULL> value is returned.
450 C<__isl_take> means that the object the argument points to
451 is taken over by the function and may no longer be used
452 by the user as an argument to any other function.
453 The pointer value must be one returned by a function
454 returning an C<__isl_give> pointer.
455 If the user passes in a C<NULL> value, then this will
456 be treated as an error in the sense that the function will
457 not perform its usual operation. However, it will still
458 make sure that all the other C<__isl_take> arguments
463 C<__isl_keep> means that the function will only use the object
464 temporarily. After the function has finished, the user
465 can still use it as an argument to other functions.
466 A C<NULL> value will be treated in the same way as
467 a C<NULL> value for an C<__isl_take> argument.
468 This annotation may also be used on return values of
469 type C<const char *>, in which case the returned pointer should
470 not be freed by the user and is only valid until the object
471 from which it was derived is updated or freed.
475 =head2 Initialization
477 All manipulations of integer sets and relations occur within
478 the context of an C<isl_ctx>.
479 A given C<isl_ctx> can only be used within a single thread.
480 All arguments of a function are required to have been allocated
481 within the same context.
482 There are currently no functions available for moving an object
483 from one C<isl_ctx> to another C<isl_ctx>. This means that
484 there is currently no way of safely moving an object from one
485 thread to another, unless the whole C<isl_ctx> is moved.
487 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
488 freed using C<isl_ctx_free>.
489 All objects allocated within an C<isl_ctx> should be freed
490 before the C<isl_ctx> itself is freed.
492 isl_ctx *isl_ctx_alloc();
493 void isl_ctx_free(isl_ctx *ctx);
495 The user can impose a bound on the number of low-level I<operations>
496 that can be performed by an C<isl_ctx>. This bound can be set and
497 retrieved using the following functions. A bound of zero means that
498 no bound is imposed. The number of operations performed can be
499 reset using C<isl_ctx_reset_operations>. Note that the number
500 of low-level operations needed to perform a high-level computation
501 may differ significantly across different versions
502 of C<isl>, but it should be the same across different platforms
503 for the same version of C<isl>.
505 Warning: This feature is experimental. C<isl> has good support to abort and
506 bail out during the computation, but this feature may exercise error code paths
507 that are normally not used that much. Consequently, it is not unlikely that
508 hidden bugs will be exposed.
510 void isl_ctx_set_max_operations(isl_ctx *ctx,
511 unsigned long max_operations);
512 unsigned long isl_ctx_get_max_operations(isl_ctx *ctx);
513 void isl_ctx_reset_operations(isl_ctx *ctx);
515 In order to be able to create an object in the same context
516 as another object, most object types (described later in
517 this document) provide a function to obtain the context
518 in which the object was created.
521 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
522 isl_ctx *isl_multi_val_get_ctx(
523 __isl_keep isl_multi_val *mv);
526 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
528 #include <isl/local_space.h>
529 isl_ctx *isl_local_space_get_ctx(
530 __isl_keep isl_local_space *ls);
533 isl_ctx *isl_set_list_get_ctx(
534 __isl_keep isl_set_list *list);
537 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
538 isl_ctx *isl_multi_aff_get_ctx(
539 __isl_keep isl_multi_aff *maff);
540 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pa);
541 isl_ctx *isl_pw_multi_aff_get_ctx(
542 __isl_keep isl_pw_multi_aff *pma);
543 isl_ctx *isl_multi_pw_aff_get_ctx(
544 __isl_keep isl_multi_pw_aff *mpa);
545 isl_ctx *isl_union_pw_aff_get_ctx(
546 __isl_keep isl_union_pw_aff *upa);
547 isl_ctx *isl_union_pw_multi_aff_get_ctx(
548 __isl_keep isl_union_pw_multi_aff *upma);
549 isl_ctx *isl_multi_union_pw_aff_get_ctx(
550 __isl_keep isl_multi_union_pw_aff *mupa);
552 #include <isl/id_to_ast_expr.h>
553 isl_ctx *isl_id_to_ast_expr_get_ctx(
554 __isl_keep isl_id_to_ast_expr *id2expr);
556 #include <isl/point.h>
557 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
560 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
563 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
565 #include <isl/vertices.h>
566 isl_ctx *isl_vertices_get_ctx(
567 __isl_keep isl_vertices *vertices);
568 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
569 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
571 #include <isl/flow.h>
572 isl_ctx *isl_restriction_get_ctx(
573 __isl_keep isl_restriction *restr);
574 isl_ctx *isl_union_access_info_get_ctx(
575 __isl_keep isl_union_access_info *access);
576 isl_ctx *isl_union_flow_get_ctx(
577 __isl_keep isl_union_flow *flow);
579 #include <isl/schedule.h>
580 isl_ctx *isl_schedule_get_ctx(
581 __isl_keep isl_schedule *sched);
582 isl_ctx *isl_schedule_constraints_get_ctx(
583 __isl_keep isl_schedule_constraints *sc);
585 #include <isl/schedule_node.h>
586 isl_ctx *isl_schedule_node_get_ctx(
587 __isl_keep isl_schedule_node *node);
589 #include <isl/band.h>
590 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
592 #include <isl/ast_build.h>
593 isl_ctx *isl_ast_build_get_ctx(
594 __isl_keep isl_ast_build *build);
597 isl_ctx *isl_ast_expr_get_ctx(
598 __isl_keep isl_ast_expr *expr);
599 isl_ctx *isl_ast_node_get_ctx(
600 __isl_keep isl_ast_node *node);
604 C<isl> uses two special return types for functions that either return
605 a boolean or that in principle do not return anything.
606 In particular, the C<isl_bool> type has three possible values:
607 C<isl_bool_true> (a positive integer value), indicating I<true> or I<yes>;
608 C<isl_bool_false> (the integer value zero), indicating I<false> or I<no>; and
609 C<isl_bool_error> (a negative integer value), indicating that something
610 went wrong. The following function can be used to negate an C<isl_bool>,
611 where the negation of C<isl_bool_error> is C<isl_bool_error> again.
614 isl_bool isl_bool_not(isl_bool b);
616 The C<isl_stat> type has two possible values:
617 C<isl_stat_ok> (the integer value zero), indicating a successful
619 C<isl_stat_error> (a negative integer value), indicating that something
621 See L</"Error Handling"> for more information on
622 C<isl_bool_error> and C<isl_stat_error>.
626 An C<isl_val> represents an integer value, a rational value
627 or one of three special values, infinity, negative infinity and NaN.
628 Some predefined values can be created using the following functions.
631 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
632 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
633 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
634 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
635 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
636 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
638 Specific integer values can be created using the following functions.
641 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
643 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
645 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
646 size_t n, size_t size, const void *chunks);
648 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
649 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
650 The least significant digit is assumed to be stored first.
652 Value objects can be copied and freed using the following functions.
655 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
656 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
658 They can be inspected using the following functions.
661 long isl_val_get_num_si(__isl_keep isl_val *v);
662 long isl_val_get_den_si(__isl_keep isl_val *v);
663 __isl_give isl_val *isl_val_get_den_val(
664 __isl_keep isl_val *v);
665 double isl_val_get_d(__isl_keep isl_val *v);
666 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
668 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
669 size_t size, void *chunks);
671 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
672 of C<size> bytes needed to store the absolute value of the
674 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
675 which is assumed to have been preallocated by the caller.
676 The least significant digit is stored first.
677 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
678 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
679 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
681 An C<isl_val> can be modified using the following function.
684 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
687 The following unary properties are defined on C<isl_val>s.
690 int isl_val_sgn(__isl_keep isl_val *v);
691 isl_bool isl_val_is_zero(__isl_keep isl_val *v);
692 isl_bool isl_val_is_one(__isl_keep isl_val *v);
693 isl_bool isl_val_is_negone(__isl_keep isl_val *v);
694 isl_bool isl_val_is_nonneg(__isl_keep isl_val *v);
695 isl_bool isl_val_is_nonpos(__isl_keep isl_val *v);
696 isl_bool isl_val_is_pos(__isl_keep isl_val *v);
697 isl_bool isl_val_is_neg(__isl_keep isl_val *v);
698 isl_bool isl_val_is_int(__isl_keep isl_val *v);
699 isl_bool isl_val_is_rat(__isl_keep isl_val *v);
700 isl_bool isl_val_is_nan(__isl_keep isl_val *v);
701 isl_bool isl_val_is_infty(__isl_keep isl_val *v);
702 isl_bool isl_val_is_neginfty(__isl_keep isl_val *v);
704 Note that the sign of NaN is undefined.
706 The following binary properties are defined on pairs of C<isl_val>s.
709 isl_bool isl_val_lt(__isl_keep isl_val *v1,
710 __isl_keep isl_val *v2);
711 isl_bool isl_val_le(__isl_keep isl_val *v1,
712 __isl_keep isl_val *v2);
713 isl_bool isl_val_gt(__isl_keep isl_val *v1,
714 __isl_keep isl_val *v2);
715 isl_bool isl_val_ge(__isl_keep isl_val *v1,
716 __isl_keep isl_val *v2);
717 isl_bool isl_val_eq(__isl_keep isl_val *v1,
718 __isl_keep isl_val *v2);
719 isl_bool isl_val_ne(__isl_keep isl_val *v1,
720 __isl_keep isl_val *v2);
721 isl_bool isl_val_abs_eq(__isl_keep isl_val *v1,
722 __isl_keep isl_val *v2);
724 The function C<isl_val_abs_eq> checks whether its two arguments
725 are equal in absolute value.
727 For integer C<isl_val>s we additionally have the following binary property.
730 isl_bool isl_val_is_divisible_by(__isl_keep isl_val *v1,
731 __isl_keep isl_val *v2);
733 An C<isl_val> can also be compared to an integer using the following
734 function. The result is undefined for NaN.
737 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
739 The following unary operations are available on C<isl_val>s.
742 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
743 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
744 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
745 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
746 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
747 __isl_give isl_val *isl_val_inv(__isl_take isl_val *v);
748 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
750 The following binary operations are available on C<isl_val>s.
753 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
754 __isl_take isl_val *v2);
755 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
756 __isl_take isl_val *v2);
757 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
758 __isl_take isl_val *v2);
759 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
761 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
762 __isl_take isl_val *v2);
763 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
765 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
766 __isl_take isl_val *v2);
767 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
769 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
770 __isl_take isl_val *v2);
772 On integer values, we additionally have the following operations.
775 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
776 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
777 __isl_take isl_val *v2);
778 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
779 __isl_take isl_val *v2);
780 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
781 __isl_take isl_val *v2, __isl_give isl_val **x,
782 __isl_give isl_val **y);
784 The function C<isl_val_gcdext> returns the greatest common divisor g
785 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
786 that C<*x> * C<v1> + C<*y> * C<v2> = g.
788 =head3 GMP specific functions
790 These functions are only available if C<isl> has been compiled with C<GMP>
793 Specific integer and rational values can be created from C<GMP> values using
794 the following functions.
796 #include <isl/val_gmp.h>
797 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
799 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
800 const mpz_t n, const mpz_t d);
802 The numerator and denominator of a rational value can be extracted as
803 C<GMP> values using the following functions.
805 #include <isl/val_gmp.h>
806 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
807 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
809 =head2 Sets and Relations
811 C<isl> uses six types of objects for representing sets and relations,
812 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
813 C<isl_union_set> and C<isl_union_map>.
814 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
815 can be described as a conjunction of affine constraints, while
816 C<isl_set> and C<isl_map> represent unions of
817 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
818 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
819 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
820 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
821 where spaces are considered different if they have a different number
822 of dimensions and/or different names (see L<"Spaces">).
823 The difference between sets and relations (maps) is that sets have
824 one set of variables, while relations have two sets of variables,
825 input variables and output variables.
827 =head2 Error Handling
829 C<isl> supports different ways to react in case a runtime error is triggered.
830 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
831 with two maps that have incompatible spaces. There are three possible ways
832 to react on error: to warn, to continue or to abort.
834 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
835 the last error in the corresponding C<isl_ctx> and the function in which the
836 error was triggered returns a value indicating that some error has
837 occurred. In case of functions returning a pointer, this value is
838 C<NULL>. In case of functions returning an C<isl_bool> or an
839 C<isl_stat>, this valus is C<isl_bool_error> or C<isl_stat_error>.
840 An error does not corrupt internal state,
841 such that isl can continue to be used. C<isl> also provides functions to
842 read the last error and to reset the memory that stores the last error. The
843 last error is only stored for information purposes. Its presence does not
844 change the behavior of C<isl>. Hence, resetting an error is not required to
845 continue to use isl, but only to observe new errors.
848 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
849 void isl_ctx_reset_error(isl_ctx *ctx);
851 Another option is to continue on error. This is similar to warn on error mode,
852 except that C<isl> does not print any warning. This allows a program to
853 implement its own error reporting.
855 The last option is to directly abort the execution of the program from within
856 the isl library. This makes it obviously impossible to recover from an error,
857 but it allows to directly spot the error location. By aborting on error,
858 debuggers break at the location the error occurred and can provide a stack
859 trace. Other tools that automatically provide stack traces on abort or that do
860 not want to continue execution after an error was triggered may also prefer to
863 The on error behavior of isl can be specified by calling
864 C<isl_options_set_on_error> or by setting the command line option
865 C<--isl-on-error>. Valid arguments for the function call are
866 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
867 choices for the command line option are C<warn>, C<continue> and C<abort>.
868 It is also possible to query the current error mode.
870 #include <isl/options.h>
871 isl_stat isl_options_set_on_error(isl_ctx *ctx, int val);
872 int isl_options_get_on_error(isl_ctx *ctx);
876 Identifiers are used to identify both individual dimensions
877 and tuples of dimensions. They consist of an optional name and an optional
878 user pointer. The name and the user pointer cannot both be C<NULL>, however.
879 Identifiers with the same name but different pointer values
880 are considered to be distinct.
881 Similarly, identifiers with different names but the same pointer value
882 are also considered to be distinct.
883 Equal identifiers are represented using the same object.
884 Pairs of identifiers can therefore be tested for equality using the
886 Identifiers can be constructed, copied, freed, inspected and printed
887 using the following functions.
890 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
891 __isl_keep const char *name, void *user);
892 __isl_give isl_id *isl_id_set_free_user(
893 __isl_take isl_id *id,
894 void (*free_user)(void *user));
895 __isl_give isl_id *isl_id_copy(isl_id *id);
896 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
898 void *isl_id_get_user(__isl_keep isl_id *id);
899 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
901 __isl_give isl_printer *isl_printer_print_id(
902 __isl_take isl_printer *p, __isl_keep isl_id *id);
904 The callback set by C<isl_id_set_free_user> is called on the user
905 pointer when the last reference to the C<isl_id> is freed.
906 Note that C<isl_id_get_name> returns a pointer to some internal
907 data structure, so the result can only be used while the
908 corresponding C<isl_id> is alive.
912 Whenever a new set, relation or similar object is created from scratch,
913 the space in which it lives needs to be specified using an C<isl_space>.
914 Each space involves zero or more parameters and zero, one or two
915 tuples of set or input/output dimensions. The parameters and dimensions
916 are identified by an C<isl_dim_type> and a position.
917 The type C<isl_dim_param> refers to parameters,
918 the type C<isl_dim_set> refers to set dimensions (for spaces
919 with a single tuple of dimensions) and the types C<isl_dim_in>
920 and C<isl_dim_out> refer to input and output dimensions
921 (for spaces with two tuples of dimensions).
922 Local spaces (see L</"Local Spaces">) also contain dimensions
923 of type C<isl_dim_div>.
924 Note that parameters are only identified by their position within
925 a given object. Across different objects, parameters are (usually)
926 identified by their names or identifiers. Only unnamed parameters
927 are identified by their positions across objects. The use of unnamed
928 parameters is discouraged.
930 #include <isl/space.h>
931 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
932 unsigned nparam, unsigned n_in, unsigned n_out);
933 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
935 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
936 unsigned nparam, unsigned dim);
937 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
938 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
940 The space used for creating a parameter domain
941 needs to be created using C<isl_space_params_alloc>.
942 For other sets, the space
943 needs to be created using C<isl_space_set_alloc>, while
944 for a relation, the space
945 needs to be created using C<isl_space_alloc>.
947 To check whether a given space is that of a set or a map
948 or whether it is a parameter space, use these functions:
950 #include <isl/space.h>
951 isl_bool isl_space_is_params(__isl_keep isl_space *space);
952 isl_bool isl_space_is_set(__isl_keep isl_space *space);
953 isl_bool isl_space_is_map(__isl_keep isl_space *space);
955 Spaces can be compared using the following functions:
957 #include <isl/space.h>
958 isl_bool isl_space_is_equal(__isl_keep isl_space *space1,
959 __isl_keep isl_space *space2);
960 isl_bool isl_space_has_equal_tuples(
961 __isl_keep isl_space *space1,
962 __isl_keep isl_space *space2);
963 isl_bool isl_space_is_domain(__isl_keep isl_space *space1,
964 __isl_keep isl_space *space2);
965 isl_bool isl_space_is_range(__isl_keep isl_space *space1,
966 __isl_keep isl_space *space2);
967 isl_bool isl_space_tuple_is_equal(
968 __isl_keep isl_space *space1,
969 enum isl_dim_type type1,
970 __isl_keep isl_space *space2,
971 enum isl_dim_type type2);
973 C<isl_space_is_domain> checks whether the first argument is equal
974 to the domain of the second argument. This requires in particular that
975 the first argument is a set space and that the second argument
976 is a map space. C<isl_space_tuple_is_equal> checks whether the given
977 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
978 spaces are the same. That is, it checks if they have the same
979 identifier (if any), the same dimension and the same internal structure
981 C<isl_space_is_equal> checks whether two spaces are identical.
982 In particular, it checks whether they have the same type
983 (parameter, set or map space), the same tuples
984 (if they are not parameter spaces) in the sense
985 of C<isl_space_tuple_is_equal> and the same parameters
987 C<isl_space_has_equal_tuples> check whether two spaces have
988 the same tuples. In contrast to C<isl_space_is_equal>, it does not check the
989 parameters. This is useful because many C<isl> functions align the
990 parameters before they perform their operations, such that equivalence
993 It is often useful to create objects that live in the
994 same space as some other object. This can be accomplished
995 by creating the new objects
996 (see L</"Creating New Sets and Relations"> or
997 L</"Functions">) based on the space
998 of the original object.
1000 #include <isl/set.h>
1001 __isl_give isl_space *isl_basic_set_get_space(
1002 __isl_keep isl_basic_set *bset);
1003 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
1005 #include <isl/union_set.h>
1006 __isl_give isl_space *isl_union_set_get_space(
1007 __isl_keep isl_union_set *uset);
1009 #include <isl/map.h>
1010 __isl_give isl_space *isl_basic_map_get_space(
1011 __isl_keep isl_basic_map *bmap);
1012 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
1014 #include <isl/union_map.h>
1015 __isl_give isl_space *isl_union_map_get_space(
1016 __isl_keep isl_union_map *umap);
1018 #include <isl/constraint.h>
1019 __isl_give isl_space *isl_constraint_get_space(
1020 __isl_keep isl_constraint *constraint);
1022 #include <isl/polynomial.h>
1023 __isl_give isl_space *isl_qpolynomial_get_domain_space(
1024 __isl_keep isl_qpolynomial *qp);
1025 __isl_give isl_space *isl_qpolynomial_get_space(
1026 __isl_keep isl_qpolynomial *qp);
1027 __isl_give isl_space *
1028 isl_qpolynomial_fold_get_domain_space(
1029 __isl_keep isl_qpolynomial_fold *fold);
1030 __isl_give isl_space *isl_qpolynomial_fold_get_space(
1031 __isl_keep isl_qpolynomial_fold *fold);
1032 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
1033 __isl_keep isl_pw_qpolynomial *pwqp);
1034 __isl_give isl_space *isl_pw_qpolynomial_get_space(
1035 __isl_keep isl_pw_qpolynomial *pwqp);
1036 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
1037 __isl_keep isl_pw_qpolynomial_fold *pwf);
1038 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
1039 __isl_keep isl_pw_qpolynomial_fold *pwf);
1040 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
1041 __isl_keep isl_union_pw_qpolynomial *upwqp);
1042 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
1043 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1045 #include <isl/val.h>
1046 __isl_give isl_space *isl_multi_val_get_space(
1047 __isl_keep isl_multi_val *mv);
1049 #include <isl/aff.h>
1050 __isl_give isl_space *isl_aff_get_domain_space(
1051 __isl_keep isl_aff *aff);
1052 __isl_give isl_space *isl_aff_get_space(
1053 __isl_keep isl_aff *aff);
1054 __isl_give isl_space *isl_pw_aff_get_domain_space(
1055 __isl_keep isl_pw_aff *pwaff);
1056 __isl_give isl_space *isl_pw_aff_get_space(
1057 __isl_keep isl_pw_aff *pwaff);
1058 __isl_give isl_space *isl_multi_aff_get_domain_space(
1059 __isl_keep isl_multi_aff *maff);
1060 __isl_give isl_space *isl_multi_aff_get_space(
1061 __isl_keep isl_multi_aff *maff);
1062 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
1063 __isl_keep isl_pw_multi_aff *pma);
1064 __isl_give isl_space *isl_pw_multi_aff_get_space(
1065 __isl_keep isl_pw_multi_aff *pma);
1066 __isl_give isl_space *isl_union_pw_aff_get_space(
1067 __isl_keep isl_union_pw_aff *upa);
1068 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
1069 __isl_keep isl_union_pw_multi_aff *upma);
1070 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
1071 __isl_keep isl_multi_pw_aff *mpa);
1072 __isl_give isl_space *isl_multi_pw_aff_get_space(
1073 __isl_keep isl_multi_pw_aff *mpa);
1074 __isl_give isl_space *
1075 isl_multi_union_pw_aff_get_domain_space(
1076 __isl_keep isl_multi_union_pw_aff *mupa);
1077 __isl_give isl_space *
1078 isl_multi_union_pw_aff_get_space(
1079 __isl_keep isl_multi_union_pw_aff *mupa);
1081 #include <isl/point.h>
1082 __isl_give isl_space *isl_point_get_space(
1083 __isl_keep isl_point *pnt);
1085 The number of dimensions of a given type of space
1086 may be read off from a space or an object that lives
1087 in a space using the following functions.
1088 In case of C<isl_space_dim>, type may be
1089 C<isl_dim_param>, C<isl_dim_in> (only for relations),
1090 C<isl_dim_out> (only for relations), C<isl_dim_set>
1091 (only for sets) or C<isl_dim_all>.
1093 #include <isl/space.h>
1094 unsigned isl_space_dim(__isl_keep isl_space *space,
1095 enum isl_dim_type type);
1097 #include <isl/local_space.h>
1098 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1099 enum isl_dim_type type);
1101 #include <isl/set.h>
1102 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1103 enum isl_dim_type type);
1104 unsigned isl_set_dim(__isl_keep isl_set *set,
1105 enum isl_dim_type type);
1107 #include <isl/union_set.h>
1108 unsigned isl_union_set_dim(__isl_keep isl_union_set *uset,
1109 enum isl_dim_type type);
1111 #include <isl/map.h>
1112 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1113 enum isl_dim_type type);
1114 unsigned isl_map_dim(__isl_keep isl_map *map,
1115 enum isl_dim_type type);
1117 #include <isl/union_map.h>
1118 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1119 enum isl_dim_type type);
1121 #include <isl/val.h>
1122 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
1123 enum isl_dim_type type);
1125 #include <isl/aff.h>
1126 int isl_aff_dim(__isl_keep isl_aff *aff,
1127 enum isl_dim_type type);
1128 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1129 enum isl_dim_type type);
1130 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1131 enum isl_dim_type type);
1132 unsigned isl_pw_multi_aff_dim(
1133 __isl_keep isl_pw_multi_aff *pma,
1134 enum isl_dim_type type);
1135 unsigned isl_multi_pw_aff_dim(
1136 __isl_keep isl_multi_pw_aff *mpa,
1137 enum isl_dim_type type);
1138 unsigned isl_union_pw_aff_dim(
1139 __isl_keep isl_union_pw_aff *upa,
1140 enum isl_dim_type type);
1141 unsigned isl_union_pw_multi_aff_dim(
1142 __isl_keep isl_union_pw_multi_aff *upma,
1143 enum isl_dim_type type);
1144 unsigned isl_multi_union_pw_aff_dim(
1145 __isl_keep isl_multi_union_pw_aff *mupa,
1146 enum isl_dim_type type);
1148 #include <isl/polynomial.h>
1149 unsigned isl_union_pw_qpolynomial_dim(
1150 __isl_keep isl_union_pw_qpolynomial *upwqp,
1151 enum isl_dim_type type);
1152 unsigned isl_union_pw_qpolynomial_fold_dim(
1153 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1154 enum isl_dim_type type);
1156 Note that an C<isl_union_set>, an C<isl_union_map>,
1157 an C<isl_union_pw_multi_aff>,
1158 an C<isl_union_pw_qpolynomial> and
1159 an C<isl_union_pw_qpolynomial_fold>
1160 only have parameters.
1162 The identifiers or names of the individual dimensions of spaces
1163 may be set or read off using the following functions on spaces
1164 or objects that live in spaces.
1165 These functions are mostly useful to obtain the identifiers, positions
1166 or names of the parameters. Identifiers of individual dimensions are
1167 essentially only useful for printing. They are ignored by all other
1168 operations and may not be preserved across those operations.
1170 #include <isl/space.h>
1171 __isl_give isl_space *isl_space_set_dim_id(
1172 __isl_take isl_space *space,
1173 enum isl_dim_type type, unsigned pos,
1174 __isl_take isl_id *id);
1175 isl_bool isl_space_has_dim_id(__isl_keep isl_space *space,
1176 enum isl_dim_type type, unsigned pos);
1177 __isl_give isl_id *isl_space_get_dim_id(
1178 __isl_keep isl_space *space,
1179 enum isl_dim_type type, unsigned pos);
1180 __isl_give isl_space *isl_space_set_dim_name(
1181 __isl_take isl_space *space,
1182 enum isl_dim_type type, unsigned pos,
1183 __isl_keep const char *name);
1184 isl_bool isl_space_has_dim_name(__isl_keep isl_space *space,
1185 enum isl_dim_type type, unsigned pos);
1186 __isl_keep const char *isl_space_get_dim_name(
1187 __isl_keep isl_space *space,
1188 enum isl_dim_type type, unsigned pos);
1190 #include <isl/local_space.h>
1191 __isl_give isl_local_space *isl_local_space_set_dim_id(
1192 __isl_take isl_local_space *ls,
1193 enum isl_dim_type type, unsigned pos,
1194 __isl_take isl_id *id);
1195 isl_bool isl_local_space_has_dim_id(
1196 __isl_keep isl_local_space *ls,
1197 enum isl_dim_type type, unsigned pos);
1198 __isl_give isl_id *isl_local_space_get_dim_id(
1199 __isl_keep isl_local_space *ls,
1200 enum isl_dim_type type, unsigned pos);
1201 __isl_give isl_local_space *isl_local_space_set_dim_name(
1202 __isl_take isl_local_space *ls,
1203 enum isl_dim_type type, unsigned pos, const char *s);
1204 isl_bool isl_local_space_has_dim_name(
1205 __isl_keep isl_local_space *ls,
1206 enum isl_dim_type type, unsigned pos)
1207 const char *isl_local_space_get_dim_name(
1208 __isl_keep isl_local_space *ls,
1209 enum isl_dim_type type, unsigned pos);
1211 #include <isl/constraint.h>
1212 const char *isl_constraint_get_dim_name(
1213 __isl_keep isl_constraint *constraint,
1214 enum isl_dim_type type, unsigned pos);
1216 #include <isl/set.h>
1217 __isl_give isl_id *isl_basic_set_get_dim_id(
1218 __isl_keep isl_basic_set *bset,
1219 enum isl_dim_type type, unsigned pos);
1220 __isl_give isl_set *isl_set_set_dim_id(
1221 __isl_take isl_set *set, enum isl_dim_type type,
1222 unsigned pos, __isl_take isl_id *id);
1223 isl_bool isl_set_has_dim_id(__isl_keep isl_set *set,
1224 enum isl_dim_type type, unsigned pos);
1225 __isl_give isl_id *isl_set_get_dim_id(
1226 __isl_keep isl_set *set, enum isl_dim_type type,
1228 const char *isl_basic_set_get_dim_name(
1229 __isl_keep isl_basic_set *bset,
1230 enum isl_dim_type type, unsigned pos);
1231 isl_bool isl_set_has_dim_name(__isl_keep isl_set *set,
1232 enum isl_dim_type type, unsigned pos);
1233 const char *isl_set_get_dim_name(
1234 __isl_keep isl_set *set,
1235 enum isl_dim_type type, unsigned pos);
1237 #include <isl/map.h>
1238 __isl_give isl_map *isl_map_set_dim_id(
1239 __isl_take isl_map *map, enum isl_dim_type type,
1240 unsigned pos, __isl_take isl_id *id);
1241 isl_bool isl_basic_map_has_dim_id(
1242 __isl_keep isl_basic_map *bmap,
1243 enum isl_dim_type type, unsigned pos);
1244 isl_bool isl_map_has_dim_id(__isl_keep isl_map *map,
1245 enum isl_dim_type type, unsigned pos);
1246 __isl_give isl_id *isl_map_get_dim_id(
1247 __isl_keep isl_map *map, enum isl_dim_type type,
1249 __isl_give isl_id *isl_union_map_get_dim_id(
1250 __isl_keep isl_union_map *umap,
1251 enum isl_dim_type type, unsigned pos);
1252 const char *isl_basic_map_get_dim_name(
1253 __isl_keep isl_basic_map *bmap,
1254 enum isl_dim_type type, unsigned pos);
1255 isl_bool isl_map_has_dim_name(__isl_keep isl_map *map,
1256 enum isl_dim_type type, unsigned pos);
1257 const char *isl_map_get_dim_name(
1258 __isl_keep isl_map *map,
1259 enum isl_dim_type type, unsigned pos);
1261 #include <isl/val.h>
1262 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1263 __isl_take isl_multi_val *mv,
1264 enum isl_dim_type type, unsigned pos,
1265 __isl_take isl_id *id);
1266 __isl_give isl_id *isl_multi_val_get_dim_id(
1267 __isl_keep isl_multi_val *mv,
1268 enum isl_dim_type type, unsigned pos);
1269 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1270 __isl_take isl_multi_val *mv,
1271 enum isl_dim_type type, unsigned pos, const char *s);
1273 #include <isl/aff.h>
1274 __isl_give isl_aff *isl_aff_set_dim_id(
1275 __isl_take isl_aff *aff, enum isl_dim_type type,
1276 unsigned pos, __isl_take isl_id *id);
1277 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1278 __isl_take isl_multi_aff *maff,
1279 enum isl_dim_type type, unsigned pos,
1280 __isl_take isl_id *id);
1281 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1282 __isl_take isl_pw_aff *pma,
1283 enum isl_dim_type type, unsigned pos,
1284 __isl_take isl_id *id);
1285 __isl_give isl_multi_pw_aff *
1286 isl_multi_pw_aff_set_dim_id(
1287 __isl_take isl_multi_pw_aff *mpa,
1288 enum isl_dim_type type, unsigned pos,
1289 __isl_take isl_id *id);
1290 __isl_give isl_multi_union_pw_aff *
1291 isl_multi_union_pw_aff_set_dim_id(
1292 __isl_take isl_multi_union_pw_aff *mupa,
1293 enum isl_dim_type type, unsigned pos,
1294 __isl_take isl_id *id);
1295 __isl_give isl_id *isl_multi_aff_get_dim_id(
1296 __isl_keep isl_multi_aff *ma,
1297 enum isl_dim_type type, unsigned pos);
1298 isl_bool isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1299 enum isl_dim_type type, unsigned pos);
1300 __isl_give isl_id *isl_pw_aff_get_dim_id(
1301 __isl_keep isl_pw_aff *pa,
1302 enum isl_dim_type type, unsigned pos);
1303 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1304 __isl_keep isl_pw_multi_aff *pma,
1305 enum isl_dim_type type, unsigned pos);
1306 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1307 __isl_keep isl_multi_pw_aff *mpa,
1308 enum isl_dim_type type, unsigned pos);
1309 __isl_give isl_id *isl_multi_union_pw_aff_get_dim_id(
1310 __isl_keep isl_multi_union_pw_aff *mupa,
1311 enum isl_dim_type type, unsigned pos);
1312 __isl_give isl_aff *isl_aff_set_dim_name(
1313 __isl_take isl_aff *aff, enum isl_dim_type type,
1314 unsigned pos, const char *s);
1315 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1316 __isl_take isl_multi_aff *maff,
1317 enum isl_dim_type type, unsigned pos, const char *s);
1318 __isl_give isl_multi_pw_aff *
1319 isl_multi_pw_aff_set_dim_name(
1320 __isl_take isl_multi_pw_aff *mpa,
1321 enum isl_dim_type type, unsigned pos, const char *s);
1322 __isl_give isl_union_pw_aff *
1323 isl_union_pw_aff_set_dim_name(
1324 __isl_take isl_union_pw_aff *upa,
1325 enum isl_dim_type type, unsigned pos,
1327 __isl_give isl_union_pw_multi_aff *
1328 isl_union_pw_multi_aff_set_dim_name(
1329 __isl_take isl_union_pw_multi_aff *upma,
1330 enum isl_dim_type type, unsigned pos,
1332 __isl_give isl_multi_union_pw_aff *
1333 isl_multi_union_pw_aff_set_dim_name(
1334 __isl_take isl_multi_union_pw_aff *mupa,
1335 enum isl_dim_type type, unsigned pos,
1336 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1337 enum isl_dim_type type, unsigned pos);
1338 const char *isl_pw_aff_get_dim_name(
1339 __isl_keep isl_pw_aff *pa,
1340 enum isl_dim_type type, unsigned pos);
1341 const char *isl_pw_multi_aff_get_dim_name(
1342 __isl_keep isl_pw_multi_aff *pma,
1343 enum isl_dim_type type, unsigned pos);
1345 #include <isl/polynomial.h>
1346 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1347 __isl_take isl_qpolynomial *qp,
1348 enum isl_dim_type type, unsigned pos,
1350 __isl_give isl_pw_qpolynomial *
1351 isl_pw_qpolynomial_set_dim_name(
1352 __isl_take isl_pw_qpolynomial *pwqp,
1353 enum isl_dim_type type, unsigned pos,
1355 __isl_give isl_pw_qpolynomial_fold *
1356 isl_pw_qpolynomial_fold_set_dim_name(
1357 __isl_take isl_pw_qpolynomial_fold *pwf,
1358 enum isl_dim_type type, unsigned pos,
1360 __isl_give isl_union_pw_qpolynomial *
1361 isl_union_pw_qpolynomial_set_dim_name(
1362 __isl_take isl_union_pw_qpolynomial *upwqp,
1363 enum isl_dim_type type, unsigned pos,
1365 __isl_give isl_union_pw_qpolynomial_fold *
1366 isl_union_pw_qpolynomial_fold_set_dim_name(
1367 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1368 enum isl_dim_type type, unsigned pos,
1371 Note that C<isl_space_get_name> returns a pointer to some internal
1372 data structure, so the result can only be used while the
1373 corresponding C<isl_space> is alive.
1374 Also note that every function that operates on two sets or relations
1375 requires that both arguments have the same parameters. This also
1376 means that if one of the arguments has named parameters, then the
1377 other needs to have named parameters too and the names need to match.
1378 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1379 arguments may have different parameters (as long as they are named),
1380 in which case the result will have as parameters the union of the parameters of
1383 Given the identifier or name of a dimension (typically a parameter),
1384 its position can be obtained from the following functions.
1386 #include <isl/space.h>
1387 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1388 enum isl_dim_type type, __isl_keep isl_id *id);
1389 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1390 enum isl_dim_type type, const char *name);
1392 #include <isl/local_space.h>
1393 int isl_local_space_find_dim_by_name(
1394 __isl_keep isl_local_space *ls,
1395 enum isl_dim_type type, const char *name);
1397 #include <isl/val.h>
1398 int isl_multi_val_find_dim_by_id(
1399 __isl_keep isl_multi_val *mv,
1400 enum isl_dim_type type, __isl_keep isl_id *id);
1401 int isl_multi_val_find_dim_by_name(
1402 __isl_keep isl_multi_val *mv,
1403 enum isl_dim_type type, const char *name);
1405 #include <isl/set.h>
1406 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1407 enum isl_dim_type type, __isl_keep isl_id *id);
1408 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1409 enum isl_dim_type type, const char *name);
1411 #include <isl/map.h>
1412 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1413 enum isl_dim_type type, __isl_keep isl_id *id);
1414 int isl_basic_map_find_dim_by_name(
1415 __isl_keep isl_basic_map *bmap,
1416 enum isl_dim_type type, const char *name);
1417 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1418 enum isl_dim_type type, const char *name);
1419 int isl_union_map_find_dim_by_name(
1420 __isl_keep isl_union_map *umap,
1421 enum isl_dim_type type, const char *name);
1423 #include <isl/aff.h>
1424 int isl_multi_aff_find_dim_by_id(
1425 __isl_keep isl_multi_aff *ma,
1426 enum isl_dim_type type, __isl_keep isl_id *id);
1427 int isl_multi_pw_aff_find_dim_by_id(
1428 __isl_keep isl_multi_pw_aff *mpa,
1429 enum isl_dim_type type, __isl_keep isl_id *id);
1430 int isl_multi_union_pw_aff_find_dim_by_id(
1431 __isl_keep isl_union_multi_pw_aff *mupa,
1432 enum isl_dim_type type, __isl_keep isl_id *id);
1433 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff,
1434 enum isl_dim_type type, const char *name);
1435 int isl_multi_aff_find_dim_by_name(
1436 __isl_keep isl_multi_aff *ma,
1437 enum isl_dim_type type, const char *name);
1438 int isl_pw_aff_find_dim_by_name(__isl_keep isl_pw_aff *pa,
1439 enum isl_dim_type type, const char *name);
1440 int isl_multi_pw_aff_find_dim_by_name(
1441 __isl_keep isl_multi_pw_aff *mpa,
1442 enum isl_dim_type type, const char *name);
1443 int isl_pw_multi_aff_find_dim_by_name(
1444 __isl_keep isl_pw_multi_aff *pma,
1445 enum isl_dim_type type, const char *name);
1446 int isl_union_pw_aff_find_dim_by_name(
1447 __isl_keep isl_union_pw_aff *upa,
1448 enum isl_dim_type type, const char *name);
1449 int isl_union_pw_multi_aff_find_dim_by_name(
1450 __isl_keep isl_union_pw_multi_aff *upma,
1451 enum isl_dim_type type, const char *name);
1452 int isl_multi_union_pw_aff_find_dim_by_name(
1453 __isl_keep isl_multi_union_pw_aff *mupa,
1454 enum isl_dim_type type, const char *name);
1456 #include <isl/polynomial.h>
1457 int isl_pw_qpolynomial_find_dim_by_name(
1458 __isl_keep isl_pw_qpolynomial *pwqp,
1459 enum isl_dim_type type, const char *name);
1460 int isl_pw_qpolynomial_fold_find_dim_by_name(
1461 __isl_keep isl_pw_qpolynomial_fold *pwf,
1462 enum isl_dim_type type, const char *name);
1463 int isl_union_pw_qpolynomial_find_dim_by_name(
1464 __isl_keep isl_union_pw_qpolynomial *upwqp,
1465 enum isl_dim_type type, const char *name);
1466 int isl_union_pw_qpolynomial_fold_find_dim_by_name(
1467 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1468 enum isl_dim_type type, const char *name);
1470 The identifiers or names of entire spaces may be set or read off
1471 using the following functions.
1473 #include <isl/space.h>
1474 __isl_give isl_space *isl_space_set_tuple_id(
1475 __isl_take isl_space *space,
1476 enum isl_dim_type type, __isl_take isl_id *id);
1477 __isl_give isl_space *isl_space_reset_tuple_id(
1478 __isl_take isl_space *space, enum isl_dim_type type);
1479 isl_bool isl_space_has_tuple_id(
1480 __isl_keep isl_space *space,
1481 enum isl_dim_type type);
1482 __isl_give isl_id *isl_space_get_tuple_id(
1483 __isl_keep isl_space *space, enum isl_dim_type type);
1484 __isl_give isl_space *isl_space_set_tuple_name(
1485 __isl_take isl_space *space,
1486 enum isl_dim_type type, const char *s);
1487 isl_bool isl_space_has_tuple_name(
1488 __isl_keep isl_space *space,
1489 enum isl_dim_type type);
1490 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
1491 enum isl_dim_type type);
1493 #include <isl/local_space.h>
1494 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1495 __isl_take isl_local_space *ls,
1496 enum isl_dim_type type, __isl_take isl_id *id);
1498 #include <isl/set.h>
1499 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1500 __isl_take isl_basic_set *bset,
1501 __isl_take isl_id *id);
1502 __isl_give isl_set *isl_set_set_tuple_id(
1503 __isl_take isl_set *set, __isl_take isl_id *id);
1504 __isl_give isl_set *isl_set_reset_tuple_id(
1505 __isl_take isl_set *set);
1506 isl_bool isl_set_has_tuple_id(__isl_keep isl_set *set);
1507 __isl_give isl_id *isl_set_get_tuple_id(
1508 __isl_keep isl_set *set);
1509 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1510 __isl_take isl_basic_set *set, const char *s);
1511 __isl_give isl_set *isl_set_set_tuple_name(
1512 __isl_take isl_set *set, const char *s);
1513 const char *isl_basic_set_get_tuple_name(
1514 __isl_keep isl_basic_set *bset);
1515 isl_bool isl_set_has_tuple_name(__isl_keep isl_set *set);
1516 const char *isl_set_get_tuple_name(
1517 __isl_keep isl_set *set);
1519 #include <isl/map.h>
1520 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1521 __isl_take isl_basic_map *bmap,
1522 enum isl_dim_type type, __isl_take isl_id *id);
1523 __isl_give isl_map *isl_map_set_tuple_id(
1524 __isl_take isl_map *map, enum isl_dim_type type,
1525 __isl_take isl_id *id);
1526 __isl_give isl_map *isl_map_reset_tuple_id(
1527 __isl_take isl_map *map, enum isl_dim_type type);
1528 isl_bool isl_map_has_tuple_id(__isl_keep isl_map *map,
1529 enum isl_dim_type type);
1530 __isl_give isl_id *isl_map_get_tuple_id(
1531 __isl_keep isl_map *map, enum isl_dim_type type);
1532 __isl_give isl_map *isl_map_set_tuple_name(
1533 __isl_take isl_map *map,
1534 enum isl_dim_type type, const char *s);
1535 const char *isl_basic_map_get_tuple_name(
1536 __isl_keep isl_basic_map *bmap,
1537 enum isl_dim_type type);
1538 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1539 __isl_take isl_basic_map *bmap,
1540 enum isl_dim_type type, const char *s);
1541 isl_bool isl_map_has_tuple_name(__isl_keep isl_map *map,
1542 enum isl_dim_type type);
1543 const char *isl_map_get_tuple_name(
1544 __isl_keep isl_map *map,
1545 enum isl_dim_type type);
1547 #include <isl/val.h>
1548 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1549 __isl_take isl_multi_val *mv,
1550 enum isl_dim_type type, __isl_take isl_id *id);
1551 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1552 __isl_take isl_multi_val *mv,
1553 enum isl_dim_type type);
1554 isl_bool isl_multi_val_has_tuple_id(
1555 __isl_keep isl_multi_val *mv,
1556 enum isl_dim_type type);
1557 __isl_give isl_id *isl_multi_val_get_tuple_id(
1558 __isl_keep isl_multi_val *mv,
1559 enum isl_dim_type type);
1560 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1561 __isl_take isl_multi_val *mv,
1562 enum isl_dim_type type, const char *s);
1563 const char *isl_multi_val_get_tuple_name(
1564 __isl_keep isl_multi_val *mv,
1565 enum isl_dim_type type);
1567 #include <isl/aff.h>
1568 __isl_give isl_aff *isl_aff_set_tuple_id(
1569 __isl_take isl_aff *aff,
1570 enum isl_dim_type type, __isl_take isl_id *id);
1571 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1572 __isl_take isl_multi_aff *maff,
1573 enum isl_dim_type type, __isl_take isl_id *id);
1574 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1575 __isl_take isl_pw_aff *pwaff,
1576 enum isl_dim_type type, __isl_take isl_id *id);
1577 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1578 __isl_take isl_pw_multi_aff *pma,
1579 enum isl_dim_type type, __isl_take isl_id *id);
1580 __isl_give isl_multi_union_pw_aff *
1581 isl_multi_union_pw_aff_set_tuple_id(
1582 __isl_take isl_multi_union_pw_aff *mupa,
1583 enum isl_dim_type type, __isl_take isl_id *id);
1584 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1585 __isl_take isl_multi_aff *ma,
1586 enum isl_dim_type type);
1587 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1588 __isl_take isl_pw_aff *pa,
1589 enum isl_dim_type type);
1590 __isl_give isl_multi_pw_aff *
1591 isl_multi_pw_aff_reset_tuple_id(
1592 __isl_take isl_multi_pw_aff *mpa,
1593 enum isl_dim_type type);
1594 __isl_give isl_pw_multi_aff *
1595 isl_pw_multi_aff_reset_tuple_id(
1596 __isl_take isl_pw_multi_aff *pma,
1597 enum isl_dim_type type);
1598 __isl_give isl_multi_union_pw_aff *
1599 isl_multi_union_pw_aff_reset_tuple_id(
1600 __isl_take isl_multi_union_pw_aff *mupa,
1601 enum isl_dim_type type);
1602 isl_bool isl_multi_aff_has_tuple_id(
1603 __isl_keep isl_multi_aff *ma,
1604 enum isl_dim_type type);
1605 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1606 __isl_keep isl_multi_aff *ma,
1607 enum isl_dim_type type);
1608 isl_bool isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1609 enum isl_dim_type type);
1610 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1611 __isl_keep isl_pw_aff *pa,
1612 enum isl_dim_type type);
1613 isl_bool isl_pw_multi_aff_has_tuple_id(
1614 __isl_keep isl_pw_multi_aff *pma,
1615 enum isl_dim_type type);
1616 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1617 __isl_keep isl_pw_multi_aff *pma,
1618 enum isl_dim_type type);
1619 isl_bool isl_multi_pw_aff_has_tuple_id(
1620 __isl_keep isl_multi_pw_aff *mpa,
1621 enum isl_dim_type type);
1622 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1623 __isl_keep isl_multi_pw_aff *mpa,
1624 enum isl_dim_type type);
1625 isl_bool isl_multi_union_pw_aff_has_tuple_id(
1626 __isl_keep isl_multi_union_pw_aff *mupa,
1627 enum isl_dim_type type);
1628 __isl_give isl_id *isl_multi_union_pw_aff_get_tuple_id(
1629 __isl_keep isl_multi_union_pw_aff *mupa,
1630 enum isl_dim_type type);
1631 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1632 __isl_take isl_multi_aff *maff,
1633 enum isl_dim_type type, const char *s);
1634 __isl_give isl_multi_pw_aff *
1635 isl_multi_pw_aff_set_tuple_name(
1636 __isl_take isl_multi_pw_aff *mpa,
1637 enum isl_dim_type type, const char *s);
1638 __isl_give isl_multi_union_pw_aff *
1639 isl_multi_union_pw_aff_set_tuple_name(
1640 __isl_take isl_multi_union_pw_aff *mupa,
1641 enum isl_dim_type type, const char *s);
1642 const char *isl_multi_aff_get_tuple_name(
1643 __isl_keep isl_multi_aff *multi,
1644 enum isl_dim_type type);
1645 isl_bool isl_pw_multi_aff_has_tuple_name(
1646 __isl_keep isl_pw_multi_aff *pma,
1647 enum isl_dim_type type);
1648 const char *isl_pw_multi_aff_get_tuple_name(
1649 __isl_keep isl_pw_multi_aff *pma,
1650 enum isl_dim_type type);
1651 const char *isl_multi_union_pw_aff_get_tuple_name(
1652 __isl_keep isl_multi_union_pw_aff *mupa,
1653 enum isl_dim_type type);
1655 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1656 or C<isl_dim_set>. As with C<isl_space_get_name>,
1657 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1659 Binary operations require the corresponding spaces of their arguments
1660 to have the same name.
1662 To keep the names of all parameters and tuples, but reset the user pointers
1663 of all the corresponding identifiers, use the following function.
1665 #include <isl/space.h>
1666 __isl_give isl_space *isl_space_reset_user(
1667 __isl_take isl_space *space);
1669 #include <isl/set.h>
1670 __isl_give isl_set *isl_set_reset_user(
1671 __isl_take isl_set *set);
1673 #include <isl/map.h>
1674 __isl_give isl_map *isl_map_reset_user(
1675 __isl_take isl_map *map);
1677 #include <isl/union_set.h>
1678 __isl_give isl_union_set *isl_union_set_reset_user(
1679 __isl_take isl_union_set *uset);
1681 #include <isl/union_map.h>
1682 __isl_give isl_union_map *isl_union_map_reset_user(
1683 __isl_take isl_union_map *umap);
1685 #include <isl/val.h>
1686 __isl_give isl_multi_val *isl_multi_val_reset_user(
1687 __isl_take isl_multi_val *mv);
1689 #include <isl/aff.h>
1690 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1691 __isl_take isl_multi_aff *ma);
1692 __isl_give isl_pw_aff *isl_pw_aff_reset_user(
1693 __isl_take isl_pw_aff *pa);
1694 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1695 __isl_take isl_multi_pw_aff *mpa);
1696 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_reset_user(
1697 __isl_take isl_pw_multi_aff *pma);
1698 __isl_give isl_union_pw_aff *isl_union_pw_aff_reset_user(
1699 __isl_take isl_union_pw_aff *upa);
1700 __isl_give isl_multi_union_pw_aff *
1701 isl_multi_union_pw_aff_reset_user(
1702 __isl_take isl_multi_union_pw_aff *mupa);
1703 __isl_give isl_union_pw_multi_aff *
1704 isl_union_pw_multi_aff_reset_user(
1705 __isl_take isl_union_pw_multi_aff *upma);
1707 #include <isl/polynomial.h>
1708 __isl_give isl_pw_qpolynomial *
1709 isl_pw_qpolynomial_reset_user(
1710 __isl_take isl_pw_qpolynomial *pwqp);
1711 __isl_give isl_union_pw_qpolynomial *
1712 isl_union_pw_qpolynomial_reset_user(
1713 __isl_take isl_union_pw_qpolynomial *upwqp);
1714 __isl_give isl_pw_qpolynomial_fold *
1715 isl_pw_qpolynomial_fold_reset_user(
1716 __isl_take isl_pw_qpolynomial_fold *pwf);
1717 __isl_give isl_union_pw_qpolynomial_fold *
1718 isl_union_pw_qpolynomial_fold_reset_user(
1719 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1721 Spaces can be nested. In particular, the domain of a set or
1722 the domain or range of a relation can be a nested relation.
1723 This process is also called I<wrapping>.
1724 The functions for detecting, constructing and deconstructing
1725 such nested spaces can be found in the wrapping properties
1726 of L</"Unary Properties">, the wrapping operations
1727 of L</"Unary Operations"> and the Cartesian product operations
1728 of L</"Basic Operations">.
1730 Spaces can be created from other spaces
1731 using the functions described in L</"Unary Operations">
1732 and L</"Binary Operations">.
1736 A local space is essentially a space with
1737 zero or more existentially quantified variables.
1738 The local space of various objects can be obtained
1739 using the following functions.
1741 #include <isl/constraint.h>
1742 __isl_give isl_local_space *isl_constraint_get_local_space(
1743 __isl_keep isl_constraint *constraint);
1745 #include <isl/set.h>
1746 __isl_give isl_local_space *isl_basic_set_get_local_space(
1747 __isl_keep isl_basic_set *bset);
1749 #include <isl/map.h>
1750 __isl_give isl_local_space *isl_basic_map_get_local_space(
1751 __isl_keep isl_basic_map *bmap);
1753 #include <isl/aff.h>
1754 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1755 __isl_keep isl_aff *aff);
1756 __isl_give isl_local_space *isl_aff_get_local_space(
1757 __isl_keep isl_aff *aff);
1759 A new local space can be created from a space using
1761 #include <isl/local_space.h>
1762 __isl_give isl_local_space *isl_local_space_from_space(
1763 __isl_take isl_space *space);
1765 They can be inspected, modified, copied and freed using the following functions.
1767 #include <isl/local_space.h>
1768 isl_bool isl_local_space_is_params(
1769 __isl_keep isl_local_space *ls);
1770 isl_bool isl_local_space_is_set(
1771 __isl_keep isl_local_space *ls);
1772 __isl_give isl_space *isl_local_space_get_space(
1773 __isl_keep isl_local_space *ls);
1774 __isl_give isl_aff *isl_local_space_get_div(
1775 __isl_keep isl_local_space *ls, int pos);
1776 __isl_give isl_local_space *isl_local_space_copy(
1777 __isl_keep isl_local_space *ls);
1778 __isl_null isl_local_space *isl_local_space_free(
1779 __isl_take isl_local_space *ls);
1781 Note that C<isl_local_space_get_div> can only be used on local spaces
1784 Two local spaces can be compared using
1786 isl_bool isl_local_space_is_equal(
1787 __isl_keep isl_local_space *ls1,
1788 __isl_keep isl_local_space *ls2);
1790 Local spaces can be created from other local spaces
1791 using the functions described in L</"Unary Operations">
1792 and L</"Binary Operations">.
1794 =head2 Creating New Sets and Relations
1796 C<isl> has functions for creating some standard sets and relations.
1800 =item * Empty sets and relations
1802 __isl_give isl_basic_set *isl_basic_set_empty(
1803 __isl_take isl_space *space);
1804 __isl_give isl_basic_map *isl_basic_map_empty(
1805 __isl_take isl_space *space);
1806 __isl_give isl_set *isl_set_empty(
1807 __isl_take isl_space *space);
1808 __isl_give isl_map *isl_map_empty(
1809 __isl_take isl_space *space);
1810 __isl_give isl_union_set *isl_union_set_empty(
1811 __isl_take isl_space *space);
1812 __isl_give isl_union_map *isl_union_map_empty(
1813 __isl_take isl_space *space);
1815 For C<isl_union_set>s and C<isl_union_map>s, the space
1816 is only used to specify the parameters.
1818 =item * Universe sets and relations
1820 __isl_give isl_basic_set *isl_basic_set_universe(
1821 __isl_take isl_space *space);
1822 __isl_give isl_basic_map *isl_basic_map_universe(
1823 __isl_take isl_space *space);
1824 __isl_give isl_set *isl_set_universe(
1825 __isl_take isl_space *space);
1826 __isl_give isl_map *isl_map_universe(
1827 __isl_take isl_space *space);
1828 __isl_give isl_union_set *isl_union_set_universe(
1829 __isl_take isl_union_set *uset);
1830 __isl_give isl_union_map *isl_union_map_universe(
1831 __isl_take isl_union_map *umap);
1833 The sets and relations constructed by the functions above
1834 contain all integer values, while those constructed by the
1835 functions below only contain non-negative values.
1837 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1838 __isl_take isl_space *space);
1839 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1840 __isl_take isl_space *space);
1841 __isl_give isl_set *isl_set_nat_universe(
1842 __isl_take isl_space *space);
1843 __isl_give isl_map *isl_map_nat_universe(
1844 __isl_take isl_space *space);
1846 =item * Identity relations
1848 __isl_give isl_basic_map *isl_basic_map_identity(
1849 __isl_take isl_space *space);
1850 __isl_give isl_map *isl_map_identity(
1851 __isl_take isl_space *space);
1853 The number of input and output dimensions in C<space> needs
1856 =item * Lexicographic order
1858 __isl_give isl_map *isl_map_lex_lt(
1859 __isl_take isl_space *set_space);
1860 __isl_give isl_map *isl_map_lex_le(
1861 __isl_take isl_space *set_space);
1862 __isl_give isl_map *isl_map_lex_gt(
1863 __isl_take isl_space *set_space);
1864 __isl_give isl_map *isl_map_lex_ge(
1865 __isl_take isl_space *set_space);
1866 __isl_give isl_map *isl_map_lex_lt_first(
1867 __isl_take isl_space *space, unsigned n);
1868 __isl_give isl_map *isl_map_lex_le_first(
1869 __isl_take isl_space *space, unsigned n);
1870 __isl_give isl_map *isl_map_lex_gt_first(
1871 __isl_take isl_space *space, unsigned n);
1872 __isl_give isl_map *isl_map_lex_ge_first(
1873 __isl_take isl_space *space, unsigned n);
1875 The first four functions take a space for a B<set>
1876 and return relations that express that the elements in the domain
1877 are lexicographically less
1878 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1879 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1880 than the elements in the range.
1881 The last four functions take a space for a map
1882 and return relations that express that the first C<n> dimensions
1883 in the domain are lexicographically less
1884 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1885 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1886 than the first C<n> dimensions in the range.
1890 A basic set or relation can be converted to a set or relation
1891 using the following functions.
1893 __isl_give isl_set *isl_set_from_basic_set(
1894 __isl_take isl_basic_set *bset);
1895 __isl_give isl_map *isl_map_from_basic_map(
1896 __isl_take isl_basic_map *bmap);
1898 Sets and relations can be converted to union sets and relations
1899 using the following functions.
1901 __isl_give isl_union_set *isl_union_set_from_basic_set(
1902 __isl_take isl_basic_set *bset);
1903 __isl_give isl_union_map *isl_union_map_from_basic_map(
1904 __isl_take isl_basic_map *bmap);
1905 __isl_give isl_union_set *isl_union_set_from_set(
1906 __isl_take isl_set *set);
1907 __isl_give isl_union_map *isl_union_map_from_map(
1908 __isl_take isl_map *map);
1910 The inverse conversions below can only be used if the input
1911 union set or relation is known to contain elements in exactly one
1914 __isl_give isl_set *isl_set_from_union_set(
1915 __isl_take isl_union_set *uset);
1916 __isl_give isl_map *isl_map_from_union_map(
1917 __isl_take isl_union_map *umap);
1919 Sets and relations can be copied and freed again using the following
1922 __isl_give isl_basic_set *isl_basic_set_copy(
1923 __isl_keep isl_basic_set *bset);
1924 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1925 __isl_give isl_union_set *isl_union_set_copy(
1926 __isl_keep isl_union_set *uset);
1927 __isl_give isl_basic_map *isl_basic_map_copy(
1928 __isl_keep isl_basic_map *bmap);
1929 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1930 __isl_give isl_union_map *isl_union_map_copy(
1931 __isl_keep isl_union_map *umap);
1932 __isl_null isl_basic_set *isl_basic_set_free(
1933 __isl_take isl_basic_set *bset);
1934 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1935 __isl_null isl_union_set *isl_union_set_free(
1936 __isl_take isl_union_set *uset);
1937 __isl_null isl_basic_map *isl_basic_map_free(
1938 __isl_take isl_basic_map *bmap);
1939 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1940 __isl_null isl_union_map *isl_union_map_free(
1941 __isl_take isl_union_map *umap);
1943 Other sets and relations can be constructed by starting
1944 from a universe set or relation, adding equality and/or
1945 inequality constraints and then projecting out the
1946 existentially quantified variables, if any.
1947 Constraints can be constructed, manipulated and
1948 added to (or removed from) (basic) sets and relations
1949 using the following functions.
1951 #include <isl/constraint.h>
1952 __isl_give isl_constraint *isl_constraint_alloc_equality(
1953 __isl_take isl_local_space *ls);
1954 __isl_give isl_constraint *isl_constraint_alloc_inequality(
1955 __isl_take isl_local_space *ls);
1956 __isl_give isl_constraint *isl_constraint_set_constant_si(
1957 __isl_take isl_constraint *constraint, int v);
1958 __isl_give isl_constraint *isl_constraint_set_constant_val(
1959 __isl_take isl_constraint *constraint,
1960 __isl_take isl_val *v);
1961 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1962 __isl_take isl_constraint *constraint,
1963 enum isl_dim_type type, int pos, int v);
1964 __isl_give isl_constraint *
1965 isl_constraint_set_coefficient_val(
1966 __isl_take isl_constraint *constraint,
1967 enum isl_dim_type type, int pos,
1968 __isl_take isl_val *v);
1969 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1970 __isl_take isl_basic_map *bmap,
1971 __isl_take isl_constraint *constraint);
1972 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1973 __isl_take isl_basic_set *bset,
1974 __isl_take isl_constraint *constraint);
1975 __isl_give isl_map *isl_map_add_constraint(
1976 __isl_take isl_map *map,
1977 __isl_take isl_constraint *constraint);
1978 __isl_give isl_set *isl_set_add_constraint(
1979 __isl_take isl_set *set,
1980 __isl_take isl_constraint *constraint);
1982 For example, to create a set containing the even integers
1983 between 10 and 42, you would use the following code.
1986 isl_local_space *ls;
1988 isl_basic_set *bset;
1990 space = isl_space_set_alloc(ctx, 0, 2);
1991 bset = isl_basic_set_universe(isl_space_copy(space));
1992 ls = isl_local_space_from_space(space);
1994 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
1995 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1996 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1997 bset = isl_basic_set_add_constraint(bset, c);
1999 c = isl_constraint_alloc_inequality(isl_local_space_copy(ls));
2000 c = isl_constraint_set_constant_si(c, -10);
2001 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
2002 bset = isl_basic_set_add_constraint(bset, c);
2004 c = isl_constraint_alloc_inequality(ls);
2005 c = isl_constraint_set_constant_si(c, 42);
2006 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2007 bset = isl_basic_set_add_constraint(bset, c);
2009 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
2013 isl_basic_set *bset;
2014 bset = isl_basic_set_read_from_str(ctx,
2015 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
2017 A basic set or relation can also be constructed from two matrices
2018 describing the equalities and the inequalities.
2020 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
2021 __isl_take isl_space *space,
2022 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2023 enum isl_dim_type c1,
2024 enum isl_dim_type c2, enum isl_dim_type c3,
2025 enum isl_dim_type c4);
2026 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
2027 __isl_take isl_space *space,
2028 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2029 enum isl_dim_type c1,
2030 enum isl_dim_type c2, enum isl_dim_type c3,
2031 enum isl_dim_type c4, enum isl_dim_type c5);
2033 The C<isl_dim_type> arguments indicate the order in which
2034 different kinds of variables appear in the input matrices
2035 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
2036 C<isl_dim_set> and C<isl_dim_div> for sets and
2037 of C<isl_dim_cst>, C<isl_dim_param>,
2038 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
2040 A (basic or union) set or relation can also be constructed from a
2041 (union) (piecewise) (multiple) affine expression
2042 or a list of affine expressions
2043 (See L</"Functions">), provided these affine expressions do not
2046 __isl_give isl_basic_map *isl_basic_map_from_aff(
2047 __isl_take isl_aff *aff);
2048 __isl_give isl_map *isl_map_from_aff(
2049 __isl_take isl_aff *aff);
2050 __isl_give isl_set *isl_set_from_pw_aff(
2051 __isl_take isl_pw_aff *pwaff);
2052 __isl_give isl_map *isl_map_from_pw_aff(
2053 __isl_take isl_pw_aff *pwaff);
2054 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
2055 __isl_take isl_space *domain_space,
2056 __isl_take isl_aff_list *list);
2057 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
2058 __isl_take isl_multi_aff *maff)
2059 __isl_give isl_map *isl_map_from_multi_aff(
2060 __isl_take isl_multi_aff *maff)
2061 __isl_give isl_set *isl_set_from_pw_multi_aff(
2062 __isl_take isl_pw_multi_aff *pma);
2063 __isl_give isl_map *isl_map_from_pw_multi_aff(
2064 __isl_take isl_pw_multi_aff *pma);
2065 __isl_give isl_set *isl_set_from_multi_pw_aff(
2066 __isl_take isl_multi_pw_aff *mpa);
2067 __isl_give isl_map *isl_map_from_multi_pw_aff(
2068 __isl_take isl_multi_pw_aff *mpa);
2069 __isl_give isl_union_map *isl_union_map_from_union_pw_aff(
2070 __isl_take isl_union_pw_aff *upa);
2071 __isl_give isl_union_map *
2072 isl_union_map_from_union_pw_multi_aff(
2073 __isl_take isl_union_pw_multi_aff *upma);
2074 __isl_give isl_union_map *
2075 isl_union_map_from_multi_union_pw_aff(
2076 __isl_take isl_multi_union_pw_aff *mupa);
2078 The C<domain_space> argument describes the domain of the resulting
2079 basic relation. It is required because the C<list> may consist
2080 of zero affine expressions.
2081 The C<mupa> passed to C<isl_union_map_from_multi_union_pw_aff>
2082 is not allowed to be zero-dimensional. The domain of the result
2083 is the shared domain of the union piecewise affine elements.
2085 =head2 Inspecting Sets and Relations
2087 Usually, the user should not have to care about the actual constraints
2088 of the sets and maps, but should instead apply the abstract operations
2089 explained in the following sections.
2090 Occasionally, however, it may be required to inspect the individual
2091 coefficients of the constraints. This section explains how to do so.
2092 In these cases, it may also be useful to have C<isl> compute
2093 an explicit representation of the existentially quantified variables.
2095 __isl_give isl_set *isl_set_compute_divs(
2096 __isl_take isl_set *set);
2097 __isl_give isl_map *isl_map_compute_divs(
2098 __isl_take isl_map *map);
2099 __isl_give isl_union_set *isl_union_set_compute_divs(
2100 __isl_take isl_union_set *uset);
2101 __isl_give isl_union_map *isl_union_map_compute_divs(
2102 __isl_take isl_union_map *umap);
2104 This explicit representation defines the existentially quantified
2105 variables as integer divisions of the other variables, possibly
2106 including earlier existentially quantified variables.
2107 An explicitly represented existentially quantified variable therefore
2108 has a unique value when the values of the other variables are known.
2110 Alternatively, the existentially quantified variables can be removed
2111 using the following functions, which compute an overapproximation.
2113 __isl_give isl_basic_set *isl_basic_set_remove_divs(
2114 __isl_take isl_basic_set *bset);
2115 __isl_give isl_basic_map *isl_basic_map_remove_divs(
2116 __isl_take isl_basic_map *bmap);
2117 __isl_give isl_set *isl_set_remove_divs(
2118 __isl_take isl_set *set);
2119 __isl_give isl_map *isl_map_remove_divs(
2120 __isl_take isl_map *map);
2122 It is also possible to only remove those divs that are defined
2123 in terms of a given range of dimensions or only those for which
2124 no explicit representation is known.
2126 __isl_give isl_basic_set *
2127 isl_basic_set_remove_divs_involving_dims(
2128 __isl_take isl_basic_set *bset,
2129 enum isl_dim_type type,
2130 unsigned first, unsigned n);
2131 __isl_give isl_basic_map *
2132 isl_basic_map_remove_divs_involving_dims(
2133 __isl_take isl_basic_map *bmap,
2134 enum isl_dim_type type,
2135 unsigned first, unsigned n);
2136 __isl_give isl_set *isl_set_remove_divs_involving_dims(
2137 __isl_take isl_set *set, enum isl_dim_type type,
2138 unsigned first, unsigned n);
2139 __isl_give isl_map *isl_map_remove_divs_involving_dims(
2140 __isl_take isl_map *map, enum isl_dim_type type,
2141 unsigned first, unsigned n);
2143 __isl_give isl_basic_set *
2144 isl_basic_set_remove_unknown_divs(
2145 __isl_take isl_basic_set *bset);
2146 __isl_give isl_set *isl_set_remove_unknown_divs(
2147 __isl_take isl_set *set);
2148 __isl_give isl_map *isl_map_remove_unknown_divs(
2149 __isl_take isl_map *map);
2151 To iterate over all the sets or maps in a union set or map, use
2153 isl_stat isl_union_set_foreach_set(
2154 __isl_keep isl_union_set *uset,
2155 isl_stat (*fn)(__isl_take isl_set *set, void *user),
2157 isl_stat isl_union_map_foreach_map(
2158 __isl_keep isl_union_map *umap,
2159 isl_stat (*fn)(__isl_take isl_map *map, void *user),
2162 These functions call the callback function once for each
2163 (pair of) space(s) for which there are elements in the input.
2164 The argument to the callback contains all elements in the input
2165 with that (pair of) space(s).
2167 The number of sets or maps in a union set or map can be obtained
2170 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
2171 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
2173 To extract the set or map in a given space from a union, use
2175 __isl_give isl_set *isl_union_set_extract_set(
2176 __isl_keep isl_union_set *uset,
2177 __isl_take isl_space *space);
2178 __isl_give isl_map *isl_union_map_extract_map(
2179 __isl_keep isl_union_map *umap,
2180 __isl_take isl_space *space);
2182 To iterate over all the basic sets or maps in a set or map, use
2184 isl_stat isl_set_foreach_basic_set(__isl_keep isl_set *set,
2185 isl_stat (*fn)(__isl_take isl_basic_set *bset,
2188 isl_stat isl_map_foreach_basic_map(__isl_keep isl_map *map,
2189 isl_stat (*fn)(__isl_take isl_basic_map *bmap,
2193 The callback function C<fn> should return 0 if successful and
2194 -1 if an error occurs. In the latter case, or if any other error
2195 occurs, the above functions will return -1.
2197 It should be noted that C<isl> does not guarantee that
2198 the basic sets or maps passed to C<fn> are disjoint.
2199 If this is required, then the user should call one of
2200 the following functions first.
2202 __isl_give isl_set *isl_set_make_disjoint(
2203 __isl_take isl_set *set);
2204 __isl_give isl_map *isl_map_make_disjoint(
2205 __isl_take isl_map *map);
2207 The number of basic sets in a set can be obtained
2208 or the number of basic maps in a map can be obtained
2211 #include <isl/set.h>
2212 int isl_set_n_basic_set(__isl_keep isl_set *set);
2214 #include <isl/map.h>
2215 int isl_map_n_basic_map(__isl_keep isl_map *map);
2217 It is also possible to obtain a list of basic sets from a set
2219 #include <isl/set.h>
2220 __isl_give isl_basic_set_list *isl_set_get_basic_set_list(
2221 __isl_keep isl_set *set);
2223 The returned list can be manipulated using the functions in L<"Lists">.
2225 To iterate over the constraints of a basic set or map, use
2227 #include <isl/constraint.h>
2229 int isl_basic_set_n_constraint(
2230 __isl_keep isl_basic_set *bset);
2231 isl_stat isl_basic_set_foreach_constraint(
2232 __isl_keep isl_basic_set *bset,
2233 isl_stat (*fn)(__isl_take isl_constraint *c,
2236 int isl_basic_map_n_constraint(
2237 __isl_keep isl_basic_map *bmap);
2238 isl_stat isl_basic_map_foreach_constraint(
2239 __isl_keep isl_basic_map *bmap,
2240 isl_stat (*fn)(__isl_take isl_constraint *c,
2243 __isl_null isl_constraint *isl_constraint_free(
2244 __isl_take isl_constraint *c);
2246 Again, the callback function C<fn> should return 0 if successful and
2247 -1 if an error occurs. In the latter case, or if any other error
2248 occurs, the above functions will return -1.
2249 The constraint C<c> represents either an equality or an inequality.
2250 Use the following function to find out whether a constraint
2251 represents an equality. If not, it represents an inequality.
2253 isl_bool isl_constraint_is_equality(
2254 __isl_keep isl_constraint *constraint);
2256 It is also possible to obtain a list of constraints from a basic
2259 #include <isl/constraint.h>
2260 __isl_give isl_constraint_list *
2261 isl_basic_map_get_constraint_list(
2262 __isl_keep isl_basic_map *bmap);
2263 __isl_give isl_constraint_list *
2264 isl_basic_set_get_constraint_list(
2265 __isl_keep isl_basic_set *bset);
2267 These functions require that all existentially quantified variables
2268 have an explicit representation.
2269 The returned list can be manipulated using the functions in L<"Lists">.
2271 The coefficients of the constraints can be inspected using
2272 the following functions.
2274 isl_bool isl_constraint_is_lower_bound(
2275 __isl_keep isl_constraint *constraint,
2276 enum isl_dim_type type, unsigned pos);
2277 isl_bool isl_constraint_is_upper_bound(
2278 __isl_keep isl_constraint *constraint,
2279 enum isl_dim_type type, unsigned pos);
2280 __isl_give isl_val *isl_constraint_get_constant_val(
2281 __isl_keep isl_constraint *constraint);
2282 __isl_give isl_val *isl_constraint_get_coefficient_val(
2283 __isl_keep isl_constraint *constraint,
2284 enum isl_dim_type type, int pos);
2286 The explicit representations of the existentially quantified
2287 variables can be inspected using the following function.
2288 Note that the user is only allowed to use this function
2289 if the inspected set or map is the result of a call
2290 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2291 The existentially quantified variable is equal to the floor
2292 of the returned affine expression. The affine expression
2293 itself can be inspected using the functions in
2296 __isl_give isl_aff *isl_constraint_get_div(
2297 __isl_keep isl_constraint *constraint, int pos);
2299 To obtain the constraints of a basic set or map in matrix
2300 form, use the following functions.
2302 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2303 __isl_keep isl_basic_set *bset,
2304 enum isl_dim_type c1, enum isl_dim_type c2,
2305 enum isl_dim_type c3, enum isl_dim_type c4);
2306 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2307 __isl_keep isl_basic_set *bset,
2308 enum isl_dim_type c1, enum isl_dim_type c2,
2309 enum isl_dim_type c3, enum isl_dim_type c4);
2310 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2311 __isl_keep isl_basic_map *bmap,
2312 enum isl_dim_type c1,
2313 enum isl_dim_type c2, enum isl_dim_type c3,
2314 enum isl_dim_type c4, enum isl_dim_type c5);
2315 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2316 __isl_keep isl_basic_map *bmap,
2317 enum isl_dim_type c1,
2318 enum isl_dim_type c2, enum isl_dim_type c3,
2319 enum isl_dim_type c4, enum isl_dim_type c5);
2321 The C<isl_dim_type> arguments dictate the order in which
2322 different kinds of variables appear in the resulting matrix.
2323 For set inputs, they should be a permutation of
2324 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
2325 For map inputs, they should be a permutation of
2326 C<isl_dim_cst>, C<isl_dim_param>,
2327 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2331 Points are elements of a set. They can be used to construct
2332 simple sets (boxes) or they can be used to represent the
2333 individual elements of a set.
2334 The zero point (the origin) can be created using
2336 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2338 The coordinates of a point can be inspected, set and changed
2341 __isl_give isl_val *isl_point_get_coordinate_val(
2342 __isl_keep isl_point *pnt,
2343 enum isl_dim_type type, int pos);
2344 __isl_give isl_point *isl_point_set_coordinate_val(
2345 __isl_take isl_point *pnt,
2346 enum isl_dim_type type, int pos,
2347 __isl_take isl_val *v);
2349 __isl_give isl_point *isl_point_add_ui(
2350 __isl_take isl_point *pnt,
2351 enum isl_dim_type type, int pos, unsigned val);
2352 __isl_give isl_point *isl_point_sub_ui(
2353 __isl_take isl_point *pnt,
2354 enum isl_dim_type type, int pos, unsigned val);
2356 Points can be copied or freed using
2358 __isl_give isl_point *isl_point_copy(
2359 __isl_keep isl_point *pnt);
2360 void isl_point_free(__isl_take isl_point *pnt);
2362 A singleton set can be created from a point using
2364 __isl_give isl_basic_set *isl_basic_set_from_point(
2365 __isl_take isl_point *pnt);
2366 __isl_give isl_set *isl_set_from_point(
2367 __isl_take isl_point *pnt);
2368 __isl_give isl_union_set *isl_union_set_from_point(
2369 __isl_take isl_point *pnt);
2371 and a box can be created from two opposite extremal points using
2373 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2374 __isl_take isl_point *pnt1,
2375 __isl_take isl_point *pnt2);
2376 __isl_give isl_set *isl_set_box_from_points(
2377 __isl_take isl_point *pnt1,
2378 __isl_take isl_point *pnt2);
2380 All elements of a B<bounded> (union) set can be enumerated using
2381 the following functions.
2383 isl_stat isl_set_foreach_point(__isl_keep isl_set *set,
2384 isl_stat (*fn)(__isl_take isl_point *pnt,
2387 isl_stat isl_union_set_foreach_point(
2388 __isl_keep isl_union_set *uset,
2389 isl_stat (*fn)(__isl_take isl_point *pnt,
2393 The function C<fn> is called for each integer point in
2394 C<set> with as second argument the last argument of
2395 the C<isl_set_foreach_point> call. The function C<fn>
2396 should return C<0> on success and C<-1> on failure.
2397 In the latter case, C<isl_set_foreach_point> will stop
2398 enumerating and return C<-1> as well.
2399 If the enumeration is performed successfully and to completion,
2400 then C<isl_set_foreach_point> returns C<0>.
2402 To obtain a single point of a (basic or union) set, use
2404 __isl_give isl_point *isl_basic_set_sample_point(
2405 __isl_take isl_basic_set *bset);
2406 __isl_give isl_point *isl_set_sample_point(
2407 __isl_take isl_set *set);
2408 __isl_give isl_point *isl_union_set_sample_point(
2409 __isl_take isl_union_set *uset);
2411 If C<set> does not contain any (integer) points, then the
2412 resulting point will be ``void'', a property that can be
2415 isl_bool isl_point_is_void(__isl_keep isl_point *pnt);
2419 Besides sets and relation, C<isl> also supports various types of functions.
2420 Each of these types is derived from the value type (see L</"Values">)
2421 or from one of two primitive function types
2422 through the application of zero or more type constructors.
2423 We first describe the primitive type and then we describe
2424 the types derived from these primitive types.
2426 =head3 Primitive Functions
2428 C<isl> support two primitive function types, quasi-affine
2429 expressions and quasipolynomials.
2430 A quasi-affine expression is defined either over a parameter
2431 space or over a set and is composed of integer constants,
2432 parameters and set variables, addition, subtraction and
2433 integer division by an integer constant.
2434 For example, the quasi-affine expression
2436 [n] -> { [x] -> [2*floor((4 n + x)/9] }
2438 maps C<x> to C<2*floor((4 n + x)/9>.
2439 A quasipolynomial is a polynomial expression in quasi-affine
2440 expression. That is, it additionally allows for multiplication.
2441 Note, though, that it is not allowed to construct an integer
2442 division of an expression involving multiplications.
2443 Here is an example of a quasipolynomial that is not
2444 quasi-affine expression
2446 [n] -> { [x] -> (n*floor((4 n + x)/9) }
2448 Note that the external representations of quasi-affine expressions
2449 and quasipolynomials are different. Quasi-affine expressions
2450 use a notation with square brackets just like binary relations,
2451 while quasipolynomials do not. This might change at some point.
2453 If a primitive function is defined over a parameter space,
2454 then the space of the function itself is that of a set.
2455 If it is defined over a set, then the space of the function
2456 is that of a relation. In both cases, the set space (or
2457 the output space) is single-dimensional, anonymous and unstructured.
2458 To create functions with multiple dimensions or with other kinds
2459 of set or output spaces, use multiple expressions
2460 (see L</"Multiple Expressions">).
2464 =item * Quasi-affine Expressions
2466 Besides the expressions described above, a quasi-affine
2467 expression can also be set to NaN. Such expressions
2468 typically represent a failure to represent a result
2469 as a quasi-affine expression.
2471 The zero quasi affine expression or the quasi affine expression
2472 that is equal to a given value or
2473 a specified dimension on a given domain can be created using
2475 #include <isl/aff.h>
2476 __isl_give isl_aff *isl_aff_zero_on_domain(
2477 __isl_take isl_local_space *ls);
2478 __isl_give isl_aff *isl_aff_val_on_domain(
2479 __isl_take isl_local_space *ls,
2480 __isl_take isl_val *val);
2481 __isl_give isl_aff *isl_aff_var_on_domain(
2482 __isl_take isl_local_space *ls,
2483 enum isl_dim_type type, unsigned pos);
2484 __isl_give isl_aff *isl_aff_nan_on_domain(
2485 __isl_take isl_local_space *ls);
2487 Quasi affine expressions can be copied and freed using
2489 #include <isl/aff.h>
2490 __isl_give isl_aff *isl_aff_copy(
2491 __isl_keep isl_aff *aff);
2492 __isl_null isl_aff *isl_aff_free(
2493 __isl_take isl_aff *aff);
2495 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2496 using the following function. The constraint is required to have
2497 a non-zero coefficient for the specified dimension.
2499 #include <isl/constraint.h>
2500 __isl_give isl_aff *isl_constraint_get_bound(
2501 __isl_keep isl_constraint *constraint,
2502 enum isl_dim_type type, int pos);
2504 The entire affine expression of the constraint can also be extracted
2505 using the following function.
2507 #include <isl/constraint.h>
2508 __isl_give isl_aff *isl_constraint_get_aff(
2509 __isl_keep isl_constraint *constraint);
2511 Conversely, an equality constraint equating
2512 the affine expression to zero or an inequality constraint enforcing
2513 the affine expression to be non-negative, can be constructed using
2515 __isl_give isl_constraint *isl_equality_from_aff(
2516 __isl_take isl_aff *aff);
2517 __isl_give isl_constraint *isl_inequality_from_aff(
2518 __isl_take isl_aff *aff);
2520 The coefficients and the integer divisions of an affine expression
2521 can be inspected using the following functions.
2523 #include <isl/aff.h>
2524 __isl_give isl_val *isl_aff_get_constant_val(
2525 __isl_keep isl_aff *aff);
2526 __isl_give isl_val *isl_aff_get_coefficient_val(
2527 __isl_keep isl_aff *aff,
2528 enum isl_dim_type type, int pos);
2529 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2530 enum isl_dim_type type, int pos);
2531 __isl_give isl_val *isl_aff_get_denominator_val(
2532 __isl_keep isl_aff *aff);
2533 __isl_give isl_aff *isl_aff_get_div(
2534 __isl_keep isl_aff *aff, int pos);
2536 They can be modified using the following functions.
2538 #include <isl/aff.h>
2539 __isl_give isl_aff *isl_aff_set_constant_si(
2540 __isl_take isl_aff *aff, int v);
2541 __isl_give isl_aff *isl_aff_set_constant_val(
2542 __isl_take isl_aff *aff, __isl_take isl_val *v);
2543 __isl_give isl_aff *isl_aff_set_coefficient_si(
2544 __isl_take isl_aff *aff,
2545 enum isl_dim_type type, int pos, int v);
2546 __isl_give isl_aff *isl_aff_set_coefficient_val(
2547 __isl_take isl_aff *aff,
2548 enum isl_dim_type type, int pos,
2549 __isl_take isl_val *v);
2551 __isl_give isl_aff *isl_aff_add_constant_si(
2552 __isl_take isl_aff *aff, int v);
2553 __isl_give isl_aff *isl_aff_add_constant_val(
2554 __isl_take isl_aff *aff, __isl_take isl_val *v);
2555 __isl_give isl_aff *isl_aff_add_constant_num_si(
2556 __isl_take isl_aff *aff, int v);
2557 __isl_give isl_aff *isl_aff_add_coefficient_si(
2558 __isl_take isl_aff *aff,
2559 enum isl_dim_type type, int pos, int v);
2560 __isl_give isl_aff *isl_aff_add_coefficient_val(
2561 __isl_take isl_aff *aff,
2562 enum isl_dim_type type, int pos,
2563 __isl_take isl_val *v);
2565 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
2566 set the I<numerator> of the constant or coefficient, while
2567 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
2568 the constant or coefficient as a whole.
2569 The C<add_constant> and C<add_coefficient> functions add an integer
2570 or rational value to
2571 the possibly rational constant or coefficient.
2572 The C<add_constant_num> functions add an integer value to
2575 =item * Quasipolynomials
2577 Some simple quasipolynomials can be created using the following functions.
2579 #include <isl/polynomial.h>
2580 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2581 __isl_take isl_space *domain);
2582 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2583 __isl_take isl_space *domain);
2584 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2585 __isl_take isl_space *domain);
2586 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2587 __isl_take isl_space *domain);
2588 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2589 __isl_take isl_space *domain);
2590 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2591 __isl_take isl_space *domain,
2592 __isl_take isl_val *val);
2593 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2594 __isl_take isl_space *domain,
2595 enum isl_dim_type type, unsigned pos);
2596 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2597 __isl_take isl_aff *aff);
2599 Recall that the space in which a quasipolynomial lives is a map space
2600 with a one-dimensional range. The C<domain> argument in some of
2601 the functions above corresponds to the domain of this map space.
2603 Quasipolynomials can be copied and freed again using the following
2606 #include <isl/polynomial.h>
2607 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2608 __isl_keep isl_qpolynomial *qp);
2609 __isl_null isl_qpolynomial *isl_qpolynomial_free(
2610 __isl_take isl_qpolynomial *qp);
2612 The constant term of a quasipolynomial can be extracted using
2614 __isl_give isl_val *isl_qpolynomial_get_constant_val(
2615 __isl_keep isl_qpolynomial *qp);
2617 To iterate over all terms in a quasipolynomial,
2620 isl_stat isl_qpolynomial_foreach_term(
2621 __isl_keep isl_qpolynomial *qp,
2622 isl_stat (*fn)(__isl_take isl_term *term,
2623 void *user), void *user);
2625 The terms themselves can be inspected and freed using
2628 unsigned isl_term_dim(__isl_keep isl_term *term,
2629 enum isl_dim_type type);
2630 __isl_give isl_val *isl_term_get_coefficient_val(
2631 __isl_keep isl_term *term);
2632 int isl_term_get_exp(__isl_keep isl_term *term,
2633 enum isl_dim_type type, unsigned pos);
2634 __isl_give isl_aff *isl_term_get_div(
2635 __isl_keep isl_term *term, unsigned pos);
2636 void isl_term_free(__isl_take isl_term *term);
2638 Each term is a product of parameters, set variables and
2639 integer divisions. The function C<isl_term_get_exp>
2640 returns the exponent of a given dimensions in the given term.
2646 A reduction represents a maximum or a minimum of its
2648 The only reduction type defined by C<isl> is
2649 C<isl_qpolynomial_fold>.
2651 There are currently no functions to directly create such
2652 objects, but they do appear in the piecewise quasipolynomial
2653 reductions returned by the C<isl_pw_qpolynomial_bound> function.
2655 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
2657 Reductions can be copied and freed using
2658 the following functions.
2660 #include <isl/polynomial.h>
2661 __isl_give isl_qpolynomial_fold *
2662 isl_qpolynomial_fold_copy(
2663 __isl_keep isl_qpolynomial_fold *fold);
2664 void isl_qpolynomial_fold_free(
2665 __isl_take isl_qpolynomial_fold *fold);
2667 To iterate over all quasipolynomials in a reduction, use
2669 isl_stat isl_qpolynomial_fold_foreach_qpolynomial(
2670 __isl_keep isl_qpolynomial_fold *fold,
2671 isl_stat (*fn)(__isl_take isl_qpolynomial *qp,
2672 void *user), void *user);
2674 =head3 Multiple Expressions
2676 A multiple expression represents a sequence of zero or
2677 more base expressions, all defined on the same domain space.
2678 The domain space of the multiple expression is the same
2679 as that of the base expressions, but the range space
2680 can be any space. In case the base expressions have
2681 a set space, the corresponding multiple expression
2682 also has a set space.
2683 Objects of the value type do not have an associated space.
2684 The space of a multiple value is therefore always a set space.
2685 Similarly, the space of a multiple union piecewise
2686 affine expression is always a set space.
2688 The multiple expression types defined by C<isl>
2689 are C<isl_multi_val>, C<isl_multi_aff>, C<isl_multi_pw_aff>,
2690 C<isl_multi_union_pw_aff>.
2692 A multiple expression with the value zero for
2693 each output (or set) dimension can be created
2694 using the following functions.
2696 #include <isl/val.h>
2697 __isl_give isl_multi_val *isl_multi_val_zero(
2698 __isl_take isl_space *space);
2700 #include <isl/aff.h>
2701 __isl_give isl_multi_aff *isl_multi_aff_zero(
2702 __isl_take isl_space *space);
2703 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
2704 __isl_take isl_space *space);
2705 __isl_give isl_multi_union_pw_aff *
2706 isl_multi_union_pw_aff_zero(
2707 __isl_take isl_space *space);
2709 Since there is no canonical way of representing a zero
2710 value of type C<isl_union_pw_aff>, the space passed
2711 to C<isl_multi_union_pw_aff_zero> needs to be zero-dimensional.
2713 An identity function can be created using the following
2714 functions. The space needs to be that of a relation
2715 with the same number of input and output dimensions.
2717 #include <isl/aff.h>
2718 __isl_give isl_multi_aff *isl_multi_aff_identity(
2719 __isl_take isl_space *space);
2720 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
2721 __isl_take isl_space *space);
2723 A function that performs a projection on a universe
2724 relation or set can be created using the following functions.
2725 See also the corresponding
2726 projection operations in L</"Unary Operations">.
2728 #include <isl/aff.h>
2729 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
2730 __isl_take isl_space *space);
2731 __isl_give isl_multi_aff *isl_multi_aff_range_map(
2732 __isl_take isl_space *space);
2733 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
2734 __isl_take isl_space *space,
2735 enum isl_dim_type type,
2736 unsigned first, unsigned n);
2738 A multiple expression can be created from a single
2739 base expression using the following functions.
2740 The space of the created multiple expression is the same
2741 as that of the base expression, except for
2742 C<isl_multi_union_pw_aff_from_union_pw_aff> where the input
2743 lives in a parameter space and the output lives
2744 in a single-dimensional set space.
2746 #include <isl/aff.h>
2747 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
2748 __isl_take isl_aff *aff);
2749 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
2750 __isl_take isl_pw_aff *pa);
2751 __isl_give isl_multi_union_pw_aff *
2752 isl_multi_union_pw_aff_from_union_pw_aff(
2753 __isl_take isl_union_pw_aff *upa);
2755 A multiple expression can be created from a list
2756 of base expression in a specified space.
2757 The domain of this space needs to be the same
2758 as the domains of the base expressions in the list.
2759 If the base expressions have a set space (or no associated space),
2760 then this space also needs to be a set space.
2762 #include <isl/val.h>
2763 __isl_give isl_multi_val *isl_multi_val_from_val_list(
2764 __isl_take isl_space *space,
2765 __isl_take isl_val_list *list);
2767 #include <isl/aff.h>
2768 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2769 __isl_take isl_space *space,
2770 __isl_take isl_aff_list *list);
2771 __isl_give isl_multi_pw_aff *
2772 isl_multi_pw_aff_from_pw_aff_list(
2773 __isl_take isl_space *space,
2774 __isl_take isl_pw_aff_list *list);
2775 __isl_give isl_multi_union_pw_aff *
2776 isl_multi_union_pw_aff_from_union_pw_aff_list(
2777 __isl_take isl_space *space,
2778 __isl_take isl_union_pw_aff_list *list);
2780 As a convenience, a multiple piecewise expression can
2781 also be created from a multiple expression.
2782 Each piecewise expression in the result has a single
2785 #include <isl/aff.h>
2786 __isl_give isl_multi_pw_aff *
2787 isl_multi_pw_aff_from_multi_aff(
2788 __isl_take isl_multi_aff *ma);
2790 Similarly, a multiple union expression can be
2791 created from a multiple expression.
2793 #include <isl/aff.h>
2794 __isl_give isl_multi_union_pw_aff *
2795 isl_multi_union_pw_aff_from_multi_aff(
2796 __isl_take isl_multi_aff *ma);
2797 __isl_give isl_multi_union_pw_aff *
2798 isl_multi_union_pw_aff_from_multi_pw_aff(
2799 __isl_take isl_multi_pw_aff *mpa);
2801 A multiple quasi-affine expression can be created from
2802 a multiple value with a given domain space using the following
2805 #include <isl/aff.h>
2806 __isl_give isl_multi_aff *
2807 isl_multi_aff_multi_val_on_space(
2808 __isl_take isl_space *space,
2809 __isl_take isl_multi_val *mv);
2812 a multiple union piecewise affine expression can be created from
2813 a multiple value with a given domain or
2814 a multiple affine expression with a given domain
2815 using the following functions.
2817 #include <isl/aff.h>
2818 __isl_give isl_multi_union_pw_aff *
2819 isl_multi_union_pw_aff_multi_val_on_domain(
2820 __isl_take isl_union_set *domain,
2821 __isl_take isl_multi_val *mv);
2822 __isl_give isl_multi_union_pw_aff *
2823 isl_multi_union_pw_aff_multi_aff_on_domain(
2824 __isl_take isl_union_set *domain,
2825 __isl_take isl_multi_aff *ma);
2827 Multiple expressions can be copied and freed using
2828 the following functions.
2830 #include <isl/val.h>
2831 __isl_give isl_multi_val *isl_multi_val_copy(
2832 __isl_keep isl_multi_val *mv);
2833 __isl_null isl_multi_val *isl_multi_val_free(
2834 __isl_take isl_multi_val *mv);
2836 #include <isl/aff.h>
2837 __isl_give isl_multi_aff *isl_multi_aff_copy(
2838 __isl_keep isl_multi_aff *maff);
2839 __isl_null isl_multi_aff *isl_multi_aff_free(
2840 __isl_take isl_multi_aff *maff);
2841 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
2842 __isl_keep isl_multi_pw_aff *mpa);
2843 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
2844 __isl_take isl_multi_pw_aff *mpa);
2845 __isl_give isl_multi_union_pw_aff *
2846 isl_multi_union_pw_aff_copy(
2847 __isl_keep isl_multi_union_pw_aff *mupa);
2848 __isl_null isl_multi_union_pw_aff *
2849 isl_multi_union_pw_aff_free(
2850 __isl_take isl_multi_union_pw_aff *mupa);
2852 The base expression at a given position of a multiple
2853 expression can be extracted using the following functions.
2855 #include <isl/val.h>
2856 __isl_give isl_val *isl_multi_val_get_val(
2857 __isl_keep isl_multi_val *mv, int pos);
2859 #include <isl/aff.h>
2860 __isl_give isl_aff *isl_multi_aff_get_aff(
2861 __isl_keep isl_multi_aff *multi, int pos);
2862 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
2863 __isl_keep isl_multi_pw_aff *mpa, int pos);
2864 __isl_give isl_union_pw_aff *
2865 isl_multi_union_pw_aff_get_union_pw_aff(
2866 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
2868 It can be replaced using the following functions.
2870 #include <isl/val.h>
2871 __isl_give isl_multi_val *isl_multi_val_set_val(
2872 __isl_take isl_multi_val *mv, int pos,
2873 __isl_take isl_val *val);
2875 #include <isl/aff.h>
2876 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
2877 __isl_take isl_multi_aff *multi, int pos,
2878 __isl_take isl_aff *aff);
2879 __isl_give isl_multi_union_pw_aff *
2880 isl_multi_union_pw_aff_set_union_pw_aff(
2881 __isl_take isl_multi_union_pw_aff *mupa, int pos,
2882 __isl_take isl_union_pw_aff *upa);
2884 As a convenience, a sequence of base expressions that have
2885 their domains in a given space can be extracted from a sequence
2886 of union expressions using the following function.
2888 #include <isl/aff.h>
2889 __isl_give isl_multi_pw_aff *
2890 isl_multi_union_pw_aff_extract_multi_pw_aff(
2891 __isl_keep isl_multi_union_pw_aff *mupa,
2892 __isl_take isl_space *space);
2894 Note that there is a difference between C<isl_multi_union_pw_aff>
2895 and C<isl_union_pw_multi_aff> objects. The first is a sequence
2896 of unions of piecewise expressions, while the second is a union
2897 of piecewise sequences. In particular, multiple affine expressions
2898 in an C<isl_union_pw_multi_aff> may live in different spaces,
2899 while there is only a single multiple expression in
2900 an C<isl_multi_union_pw_aff>, which can therefore only live
2901 in a single space. This means that not every
2902 C<isl_union_pw_multi_aff> can be converted to
2903 an C<isl_multi_union_pw_aff>. Conversely, a zero-dimensional
2904 C<isl_multi_union_pw_aff> carries no information
2905 about any possible domain and therefore cannot be converted
2906 to an C<isl_union_pw_multi_aff>. Moreover, the elements
2907 of an C<isl_multi_union_pw_aff> may be defined over different domains,
2908 while each multiple expression inside an C<isl_union_pw_multi_aff>
2909 has a single domain. The conversion of an C<isl_union_pw_multi_aff>
2910 of dimension greater than one may therefore not be exact.
2911 The following functions can
2912 be used to perform these conversions when they are possible.
2914 #include <isl/aff.h>
2915 __isl_give isl_multi_union_pw_aff *
2916 isl_multi_union_pw_aff_from_union_pw_multi_aff(
2917 __isl_take isl_union_pw_multi_aff *upma);
2918 __isl_give isl_union_pw_multi_aff *
2919 isl_union_pw_multi_aff_from_multi_union_pw_aff(
2920 __isl_take isl_multi_union_pw_aff *mupa);
2922 =head3 Piecewise Expressions
2924 A piecewise expression is an expression that is described
2925 using zero or more base expression defined over the same
2926 number of cells in the domain space of the base expressions.
2927 All base expressions are defined over the same
2928 domain space and the cells are disjoint.
2929 The space of a piecewise expression is the same as
2930 that of the base expressions.
2931 If the union of the cells is a strict subset of the domain
2932 space, then the value of the piecewise expression outside
2933 this union is different for types derived from quasi-affine
2934 expressions and those derived from quasipolynomials.
2935 Piecewise expressions derived from quasi-affine expressions
2936 are considered to be undefined outside the union of their cells.
2937 Piecewise expressions derived from quasipolynomials
2938 are considered to be zero outside the union of their cells.
2940 Piecewise quasipolynomials are mainly used by the C<barvinok>
2941 library for representing the number of elements in a parametric set or map.
2942 For example, the piecewise quasipolynomial
2944 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2946 represents the number of points in the map
2948 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2950 The piecewise expression types defined by C<isl>
2951 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
2952 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
2954 A piecewise expression with no cells can be created using
2955 the following functions.
2957 #include <isl/aff.h>
2958 __isl_give isl_pw_aff *isl_pw_aff_empty(
2959 __isl_take isl_space *space);
2960 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
2961 __isl_take isl_space *space);
2963 A piecewise expression with a single universe cell can be
2964 created using the following functions.
2966 #include <isl/aff.h>
2967 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2968 __isl_take isl_aff *aff);
2969 __isl_give isl_pw_multi_aff *
2970 isl_pw_multi_aff_from_multi_aff(
2971 __isl_take isl_multi_aff *ma);
2973 #include <isl/polynomial.h>
2974 __isl_give isl_pw_qpolynomial *
2975 isl_pw_qpolynomial_from_qpolynomial(
2976 __isl_take isl_qpolynomial *qp);
2978 A piecewise expression with a single specified cell can be
2979 created using the following functions.
2981 #include <isl/aff.h>
2982 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2983 __isl_take isl_set *set, __isl_take isl_aff *aff);
2984 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
2985 __isl_take isl_set *set,
2986 __isl_take isl_multi_aff *maff);
2988 #include <isl/polynomial.h>
2989 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2990 __isl_take isl_set *set,
2991 __isl_take isl_qpolynomial *qp);
2993 The following convenience functions first create a base expression and
2994 then create a piecewise expression over a universe domain.
2996 #include <isl/aff.h>
2997 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
2998 __isl_take isl_local_space *ls);
2999 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3000 __isl_take isl_local_space *ls,
3001 enum isl_dim_type type, unsigned pos);
3002 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3003 __isl_take isl_local_space *ls);
3004 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
3005 __isl_take isl_space *space);
3006 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3007 __isl_take isl_space *space);
3008 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
3009 __isl_take isl_space *space);
3010 __isl_give isl_pw_multi_aff *
3011 isl_pw_multi_aff_project_out_map(
3012 __isl_take isl_space *space,
3013 enum isl_dim_type type,
3014 unsigned first, unsigned n);
3016 #include <isl/polynomial.h>
3017 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3018 __isl_take isl_space *space);
3020 The following convenience functions first create a base expression and
3021 then create a piecewise expression over a given domain.
3023 #include <isl/aff.h>
3024 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
3025 __isl_take isl_set *domain,
3026 __isl_take isl_val *v);
3027 __isl_give isl_pw_multi_aff *
3028 isl_pw_multi_aff_multi_val_on_domain(
3029 __isl_take isl_set *domain,
3030 __isl_take isl_multi_val *mv);
3032 As a convenience, a piecewise multiple expression can
3033 also be created from a piecewise expression.
3034 Each multiple expression in the result is derived
3035 from the corresponding base expression.
3037 #include <isl/aff.h>
3038 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
3039 __isl_take isl_pw_aff *pa);
3041 Similarly, a piecewise quasipolynomial can be
3042 created from a piecewise quasi-affine expression using
3043 the following function.
3045 #include <isl/polynomial.h>
3046 __isl_give isl_pw_qpolynomial *
3047 isl_pw_qpolynomial_from_pw_aff(
3048 __isl_take isl_pw_aff *pwaff);
3050 Piecewise expressions can be copied and freed using the following functions.
3052 #include <isl/aff.h>
3053 __isl_give isl_pw_aff *isl_pw_aff_copy(
3054 __isl_keep isl_pw_aff *pwaff);
3055 __isl_null isl_pw_aff *isl_pw_aff_free(
3056 __isl_take isl_pw_aff *pwaff);
3057 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3058 __isl_keep isl_pw_multi_aff *pma);
3059 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
3060 __isl_take isl_pw_multi_aff *pma);
3062 #include <isl/polynomial.h>
3063 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3064 __isl_keep isl_pw_qpolynomial *pwqp);
3065 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
3066 __isl_take isl_pw_qpolynomial *pwqp);
3067 __isl_give isl_pw_qpolynomial_fold *
3068 isl_pw_qpolynomial_fold_copy(
3069 __isl_keep isl_pw_qpolynomial_fold *pwf);
3070 __isl_null isl_pw_qpolynomial_fold *
3071 isl_pw_qpolynomial_fold_free(
3072 __isl_take isl_pw_qpolynomial_fold *pwf);
3074 To iterate over the different cells of a piecewise expression,
3075 use the following functions.
3077 #include <isl/aff.h>
3078 isl_bool isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3079 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3080 isl_stat isl_pw_aff_foreach_piece(
3081 __isl_keep isl_pw_aff *pwaff,
3082 isl_stat (*fn)(__isl_take isl_set *set,
3083 __isl_take isl_aff *aff,
3084 void *user), void *user);
3085 isl_stat isl_pw_multi_aff_foreach_piece(
3086 __isl_keep isl_pw_multi_aff *pma,
3087 isl_stat (*fn)(__isl_take isl_set *set,
3088 __isl_take isl_multi_aff *maff,
3089 void *user), void *user);
3091 #include <isl/polynomial.h>
3092 isl_stat isl_pw_qpolynomial_foreach_piece(
3093 __isl_keep isl_pw_qpolynomial *pwqp,
3094 isl_stat (*fn)(__isl_take isl_set *set,
3095 __isl_take isl_qpolynomial *qp,
3096 void *user), void *user);
3097 isl_stat isl_pw_qpolynomial_foreach_lifted_piece(
3098 __isl_keep isl_pw_qpolynomial *pwqp,
3099 isl_stat (*fn)(__isl_take isl_set *set,
3100 __isl_take isl_qpolynomial *qp,
3101 void *user), void *user);
3102 isl_stat isl_pw_qpolynomial_fold_foreach_piece(
3103 __isl_keep isl_pw_qpolynomial_fold *pwf,
3104 isl_stat (*fn)(__isl_take isl_set *set,
3105 __isl_take isl_qpolynomial_fold *fold,
3106 void *user), void *user);
3107 isl_stat isl_pw_qpolynomial_fold_foreach_lifted_piece(
3108 __isl_keep isl_pw_qpolynomial_fold *pwf,
3109 isl_stat (*fn)(__isl_take isl_set *set,
3110 __isl_take isl_qpolynomial_fold *fold,
3111 void *user), void *user);
3113 As usual, the function C<fn> should return C<0> on success
3114 and C<-1> on failure. The difference between
3115 C<isl_pw_qpolynomial_foreach_piece> and
3116 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3117 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3118 compute unique representations for all existentially quantified
3119 variables and then turn these existentially quantified variables
3120 into extra set variables, adapting the associated quasipolynomial
3121 accordingly. This means that the C<set> passed to C<fn>
3122 will not have any existentially quantified variables, but that
3123 the dimensions of the sets may be different for different
3124 invocations of C<fn>.
3125 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
3126 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
3128 A piecewise expression consisting of the expressions at a given
3129 position of a piecewise multiple expression can be extracted
3130 using the following function.
3132 #include <isl/aff.h>
3133 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3134 __isl_keep isl_pw_multi_aff *pma, int pos);
3136 These expressions can be replaced using the following function.
3138 #include <isl/aff.h>
3139 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3140 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3141 __isl_take isl_pw_aff *pa);
3143 Note that there is a difference between C<isl_multi_pw_aff> and
3144 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
3145 affine expressions, while the second is a piecewise sequence
3146 of affine expressions. In particular, each of the piecewise
3147 affine expressions in an C<isl_multi_pw_aff> may have a different
3148 domain, while all multiple expressions associated to a cell
3149 in an C<isl_pw_multi_aff> have the same domain.
3150 It is possible to convert between the two, but when converting
3151 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
3152 of the result is the intersection of the domains of the input.
3153 The reverse conversion is exact.
3155 #include <isl/aff.h>
3156 __isl_give isl_pw_multi_aff *
3157 isl_pw_multi_aff_from_multi_pw_aff(
3158 __isl_take isl_multi_pw_aff *mpa);
3159 __isl_give isl_multi_pw_aff *
3160 isl_multi_pw_aff_from_pw_multi_aff(
3161 __isl_take isl_pw_multi_aff *pma);
3163 =head3 Union Expressions
3165 A union expression collects base expressions defined
3166 over different domains. The space of a union expression
3167 is that of the shared parameter space.
3169 The union expression types defined by C<isl>
3170 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
3171 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
3173 C<isl_union_pw_aff>,
3174 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>,
3175 there can be at most one base expression for a given domain space.
3177 C<isl_union_pw_multi_aff>,
3178 there can be multiple such expressions for a given domain space,
3179 but the domains of these expressions need to be disjoint.
3181 An empty union expression can be created using the following functions.
3183 #include <isl/aff.h>
3184 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
3185 __isl_take isl_space *space);
3186 __isl_give isl_union_pw_multi_aff *
3187 isl_union_pw_multi_aff_empty(
3188 __isl_take isl_space *space);
3190 #include <isl/polynomial.h>
3191 __isl_give isl_union_pw_qpolynomial *
3192 isl_union_pw_qpolynomial_zero(
3193 __isl_take isl_space *space);
3195 A union expression containing a single base expression
3196 can be created using the following functions.
3198 #include <isl/aff.h>
3199 __isl_give isl_union_pw_aff *
3200 isl_union_pw_aff_from_pw_aff(
3201 __isl_take isl_pw_aff *pa);
3202 __isl_give isl_union_pw_multi_aff *
3203 isl_union_pw_multi_aff_from_aff(
3204 __isl_take isl_aff *aff);
3205 __isl_give isl_union_pw_multi_aff *
3206 isl_union_pw_multi_aff_from_pw_multi_aff(
3207 __isl_take isl_pw_multi_aff *pma);
3209 #include <isl/polynomial.h>
3210 __isl_give isl_union_pw_qpolynomial *
3211 isl_union_pw_qpolynomial_from_pw_qpolynomial(
3212 __isl_take isl_pw_qpolynomial *pwqp);
3214 The following functions create a base expression on each
3215 of the sets in the union set and collect the results.
3217 #include <isl/aff.h>
3218 __isl_give isl_union_pw_multi_aff *
3219 isl_union_pw_multi_aff_from_union_pw_aff(
3220 __isl_take isl_union_pw_aff *upa);
3221 __isl_give isl_union_pw_aff *
3222 isl_union_pw_multi_aff_get_union_pw_aff(
3223 __isl_keep isl_union_pw_multi_aff *upma, int pos);
3224 __isl_give isl_union_pw_aff *
3225 isl_union_pw_aff_val_on_domain(
3226 __isl_take isl_union_set *domain,
3227 __isl_take isl_val *v);
3228 __isl_give isl_union_pw_multi_aff *
3229 isl_union_pw_multi_aff_multi_val_on_domain(
3230 __isl_take isl_union_set *domain,
3231 __isl_take isl_multi_val *mv);
3233 An C<isl_union_pw_aff> that is equal to a (parametric) affine
3234 expression on a given domain can be created using the following
3237 #include <isl/aff.h>
3238 __isl_give isl_union_pw_aff *
3239 isl_union_pw_aff_aff_on_domain(
3240 __isl_take isl_union_set *domain,
3241 __isl_take isl_aff *aff);
3243 A base expression can be added to a union expression using
3244 the following functions.
3246 #include <isl/aff.h>
3247 __isl_give isl_union_pw_aff *
3248 isl_union_pw_aff_add_pw_aff(
3249 __isl_take isl_union_pw_aff *upa,
3250 __isl_take isl_pw_aff *pa);
3251 __isl_give isl_union_pw_multi_aff *
3252 isl_union_pw_multi_aff_add_pw_multi_aff(
3253 __isl_take isl_union_pw_multi_aff *upma,
3254 __isl_take isl_pw_multi_aff *pma);
3256 #include <isl/polynomial.h>
3257 __isl_give isl_union_pw_qpolynomial *
3258 isl_union_pw_qpolynomial_add_pw_qpolynomial(
3259 __isl_take isl_union_pw_qpolynomial *upwqp,
3260 __isl_take isl_pw_qpolynomial *pwqp);
3262 Union expressions can be copied and freed using
3263 the following functions.
3265 #include <isl/aff.h>
3266 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
3267 __isl_keep isl_union_pw_aff *upa);
3268 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
3269 __isl_take isl_union_pw_aff *upa);
3270 __isl_give isl_union_pw_multi_aff *
3271 isl_union_pw_multi_aff_copy(
3272 __isl_keep isl_union_pw_multi_aff *upma);
3273 __isl_null isl_union_pw_multi_aff *
3274 isl_union_pw_multi_aff_free(
3275 __isl_take isl_union_pw_multi_aff *upma);
3277 #include <isl/polynomial.h>
3278 __isl_give isl_union_pw_qpolynomial *
3279 isl_union_pw_qpolynomial_copy(
3280 __isl_keep isl_union_pw_qpolynomial *upwqp);
3281 __isl_null isl_union_pw_qpolynomial *
3282 isl_union_pw_qpolynomial_free(
3283 __isl_take isl_union_pw_qpolynomial *upwqp);
3284 __isl_give isl_union_pw_qpolynomial_fold *
3285 isl_union_pw_qpolynomial_fold_copy(
3286 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3287 __isl_null isl_union_pw_qpolynomial_fold *
3288 isl_union_pw_qpolynomial_fold_free(
3289 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3291 To iterate over the base expressions in a union expression,
3292 use the following functions.
3294 #include <isl/aff.h>
3295 int isl_union_pw_aff_n_pw_aff(
3296 __isl_keep isl_union_pw_aff *upa);
3297 isl_stat isl_union_pw_aff_foreach_pw_aff(
3298 __isl_keep isl_union_pw_aff *upa,
3299 isl_stat (*fn)(__isl_take isl_pw_aff *pa,
3300 void *user), void *user);
3301 int isl_union_pw_multi_aff_n_pw_multi_aff(
3302 __isl_keep isl_union_pw_multi_aff *upma);
3303 isl_stat isl_union_pw_multi_aff_foreach_pw_multi_aff(
3304 __isl_keep isl_union_pw_multi_aff *upma,
3305 isl_stat (*fn)(__isl_take isl_pw_multi_aff *pma,
3306 void *user), void *user);
3308 #include <isl/polynomial.h>
3309 int isl_union_pw_qpolynomial_n_pw_qpolynomial(
3310 __isl_keep isl_union_pw_qpolynomial *upwqp);
3311 isl_stat isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3312 __isl_keep isl_union_pw_qpolynomial *upwqp,
3313 isl_stat (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
3314 void *user), void *user);
3315 int isl_union_pw_qpolynomial_fold_n_pw_qpolynomial_fold(
3316 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3317 isl_stat isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3318 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3319 isl_stat (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3320 void *user), void *user);
3322 To extract the base expression in a given space from a union, use
3323 the following functions.
3325 #include <isl/aff.h>
3326 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
3327 __isl_keep isl_union_pw_aff *upa,
3328 __isl_take isl_space *space);
3329 __isl_give isl_pw_multi_aff *
3330 isl_union_pw_multi_aff_extract_pw_multi_aff(
3331 __isl_keep isl_union_pw_multi_aff *upma,
3332 __isl_take isl_space *space);
3334 #include <isl/polynomial.h>
3335 __isl_give isl_pw_qpolynomial *
3336 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3337 __isl_keep isl_union_pw_qpolynomial *upwqp,
3338 __isl_take isl_space *space);
3340 =head2 Input and Output
3342 For set and relation,
3343 C<isl> supports its own input/output format, which is similar
3344 to the C<Omega> format, but also supports the C<PolyLib> format
3346 For other object types, typically only an C<isl> format is supported.
3348 =head3 C<isl> format
3350 The C<isl> format is similar to that of C<Omega>, but has a different
3351 syntax for describing the parameters and allows for the definition
3352 of an existentially quantified variable as the integer division
3353 of an affine expression.
3354 For example, the set of integers C<i> between C<0> and C<n>
3355 such that C<i % 10 <= 6> can be described as
3357 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
3360 A set or relation can have several disjuncts, separated
3361 by the keyword C<or>. Each disjunct is either a conjunction
3362 of constraints or a projection (C<exists>) of a conjunction
3363 of constraints. The constraints are separated by the keyword
3366 =head3 C<PolyLib> format
3368 If the represented set is a union, then the first line
3369 contains a single number representing the number of disjuncts.
3370 Otherwise, a line containing the number C<1> is optional.
3372 Each disjunct is represented by a matrix of constraints.
3373 The first line contains two numbers representing
3374 the number of rows and columns,
3375 where the number of rows is equal to the number of constraints
3376 and the number of columns is equal to two plus the number of variables.
3377 The following lines contain the actual rows of the constraint matrix.
3378 In each row, the first column indicates whether the constraint
3379 is an equality (C<0>) or inequality (C<1>). The final column
3380 corresponds to the constant term.
3382 If the set is parametric, then the coefficients of the parameters
3383 appear in the last columns before the constant column.
3384 The coefficients of any existentially quantified variables appear
3385 between those of the set variables and those of the parameters.
3387 =head3 Extended C<PolyLib> format
3389 The extended C<PolyLib> format is nearly identical to the
3390 C<PolyLib> format. The only difference is that the line
3391 containing the number of rows and columns of a constraint matrix
3392 also contains four additional numbers:
3393 the number of output dimensions, the number of input dimensions,
3394 the number of local dimensions (i.e., the number of existentially
3395 quantified variables) and the number of parameters.
3396 For sets, the number of ``output'' dimensions is equal
3397 to the number of set dimensions, while the number of ``input''
3402 Objects can be read from input using the following functions.
3404 #include <isl/val.h>
3405 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
3407 __isl_give isl_multi_val *isl_multi_val_read_from_str(
3408 isl_ctx *ctx, const char *str);
3410 #include <isl/set.h>
3411 __isl_give isl_basic_set *isl_basic_set_read_from_file(
3412 isl_ctx *ctx, FILE *input);
3413 __isl_give isl_basic_set *isl_basic_set_read_from_str(
3414 isl_ctx *ctx, const char *str);
3415 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
3417 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
3420 #include <isl/map.h>
3421 __isl_give isl_basic_map *isl_basic_map_read_from_file(
3422 isl_ctx *ctx, FILE *input);
3423 __isl_give isl_basic_map *isl_basic_map_read_from_str(
3424 isl_ctx *ctx, const char *str);
3425 __isl_give isl_map *isl_map_read_from_file(
3426 isl_ctx *ctx, FILE *input);
3427 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
3430 #include <isl/union_set.h>
3431 __isl_give isl_union_set *isl_union_set_read_from_file(
3432 isl_ctx *ctx, FILE *input);
3433 __isl_give isl_union_set *isl_union_set_read_from_str(
3434 isl_ctx *ctx, const char *str);
3436 #include <isl/union_map.h>
3437 __isl_give isl_union_map *isl_union_map_read_from_file(
3438 isl_ctx *ctx, FILE *input);
3439 __isl_give isl_union_map *isl_union_map_read_from_str(
3440 isl_ctx *ctx, const char *str);
3442 #include <isl/aff.h>
3443 __isl_give isl_aff *isl_aff_read_from_str(
3444 isl_ctx *ctx, const char *str);
3445 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3446 isl_ctx *ctx, const char *str);
3447 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3448 isl_ctx *ctx, const char *str);
3449 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3450 isl_ctx *ctx, const char *str);
3451 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
3452 isl_ctx *ctx, const char *str);
3453 __isl_give isl_union_pw_aff *
3454 isl_union_pw_aff_read_from_str(
3455 isl_ctx *ctx, const char *str);
3456 __isl_give isl_union_pw_multi_aff *
3457 isl_union_pw_multi_aff_read_from_str(
3458 isl_ctx *ctx, const char *str);
3459 __isl_give isl_multi_union_pw_aff *
3460 isl_multi_union_pw_aff_read_from_str(
3461 isl_ctx *ctx, const char *str);
3463 #include <isl/polynomial.h>
3464 __isl_give isl_union_pw_qpolynomial *
3465 isl_union_pw_qpolynomial_read_from_str(
3466 isl_ctx *ctx, const char *str);
3468 For sets and relations,
3469 the input format is autodetected and may be either the C<PolyLib> format
3470 or the C<isl> format.
3474 Before anything can be printed, an C<isl_printer> needs to
3477 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
3479 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
3480 __isl_null isl_printer *isl_printer_free(
3481 __isl_take isl_printer *printer);
3483 C<isl_printer_to_file> prints to the given file, while
3484 C<isl_printer_to_str> prints to a string that can be extracted
3485 using the following function.
3487 #include <isl/printer.h>
3488 __isl_give char *isl_printer_get_str(
3489 __isl_keep isl_printer *printer);
3491 The printer can be inspected using the following functions.
3493 FILE *isl_printer_get_file(
3494 __isl_keep isl_printer *printer);
3495 int isl_printer_get_output_format(
3496 __isl_keep isl_printer *p);
3497 int isl_printer_get_yaml_style(__isl_keep isl_printer *p);
3499 The behavior of the printer can be modified in various ways
3501 __isl_give isl_printer *isl_printer_set_output_format(
3502 __isl_take isl_printer *p, int output_format);
3503 __isl_give isl_printer *isl_printer_set_indent(
3504 __isl_take isl_printer *p, int indent);
3505 __isl_give isl_printer *isl_printer_set_indent_prefix(
3506 __isl_take isl_printer *p, const char *prefix);
3507 __isl_give isl_printer *isl_printer_indent(
3508 __isl_take isl_printer *p, int indent);
3509 __isl_give isl_printer *isl_printer_set_prefix(
3510 __isl_take isl_printer *p, const char *prefix);
3511 __isl_give isl_printer *isl_printer_set_suffix(
3512 __isl_take isl_printer *p, const char *suffix);
3513 __isl_give isl_printer *isl_printer_set_yaml_style(
3514 __isl_take isl_printer *p, int yaml_style);
3516 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
3517 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
3518 and defaults to C<ISL_FORMAT_ISL>.
3519 Each line in the output is prefixed by C<indent_prefix>,
3520 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
3521 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
3522 In the C<PolyLib> format output,
3523 the coefficients of the existentially quantified variables
3524 appear between those of the set variables and those
3526 The function C<isl_printer_indent> increases the indentation
3527 by the specified amount (which may be negative).
3528 The YAML style may be either C<ISL_YAML_STYLE_BLOCK> or
3529 C<ISL_YAML_STYLE_FLOW> and when we are printing something
3532 To actually print something, use
3534 #include <isl/printer.h>
3535 __isl_give isl_printer *isl_printer_print_double(
3536 __isl_take isl_printer *p, double d);
3538 #include <isl/val.h>
3539 __isl_give isl_printer *isl_printer_print_val(
3540 __isl_take isl_printer *p, __isl_keep isl_val *v);
3542 #include <isl/set.h>
3543 __isl_give isl_printer *isl_printer_print_basic_set(
3544 __isl_take isl_printer *printer,
3545 __isl_keep isl_basic_set *bset);
3546 __isl_give isl_printer *isl_printer_print_set(
3547 __isl_take isl_printer *printer,
3548 __isl_keep isl_set *set);
3550 #include <isl/map.h>
3551 __isl_give isl_printer *isl_printer_print_basic_map(
3552 __isl_take isl_printer *printer,
3553 __isl_keep isl_basic_map *bmap);
3554 __isl_give isl_printer *isl_printer_print_map(
3555 __isl_take isl_printer *printer,
3556 __isl_keep isl_map *map);
3558 #include <isl/union_set.h>
3559 __isl_give isl_printer *isl_printer_print_union_set(
3560 __isl_take isl_printer *p,
3561 __isl_keep isl_union_set *uset);
3563 #include <isl/union_map.h>
3564 __isl_give isl_printer *isl_printer_print_union_map(
3565 __isl_take isl_printer *p,
3566 __isl_keep isl_union_map *umap);
3568 #include <isl/val.h>
3569 __isl_give isl_printer *isl_printer_print_multi_val(
3570 __isl_take isl_printer *p,
3571 __isl_keep isl_multi_val *mv);
3573 #include <isl/aff.h>
3574 __isl_give isl_printer *isl_printer_print_aff(
3575 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3576 __isl_give isl_printer *isl_printer_print_multi_aff(
3577 __isl_take isl_printer *p,
3578 __isl_keep isl_multi_aff *maff);
3579 __isl_give isl_printer *isl_printer_print_pw_aff(
3580 __isl_take isl_printer *p,
3581 __isl_keep isl_pw_aff *pwaff);
3582 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3583 __isl_take isl_printer *p,
3584 __isl_keep isl_pw_multi_aff *pma);
3585 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3586 __isl_take isl_printer *p,
3587 __isl_keep isl_multi_pw_aff *mpa);
3588 __isl_give isl_printer *isl_printer_print_union_pw_aff(
3589 __isl_take isl_printer *p,
3590 __isl_keep isl_union_pw_aff *upa);
3591 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3592 __isl_take isl_printer *p,
3593 __isl_keep isl_union_pw_multi_aff *upma);
3594 __isl_give isl_printer *
3595 isl_printer_print_multi_union_pw_aff(
3596 __isl_take isl_printer *p,
3597 __isl_keep isl_multi_union_pw_aff *mupa);
3599 #include <isl/polynomial.h>
3600 __isl_give isl_printer *isl_printer_print_qpolynomial(
3601 __isl_take isl_printer *p,
3602 __isl_keep isl_qpolynomial *qp);
3603 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3604 __isl_take isl_printer *p,
3605 __isl_keep isl_pw_qpolynomial *pwqp);
3606 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3607 __isl_take isl_printer *p,
3608 __isl_keep isl_union_pw_qpolynomial *upwqp);
3610 __isl_give isl_printer *
3611 isl_printer_print_pw_qpolynomial_fold(
3612 __isl_take isl_printer *p,
3613 __isl_keep isl_pw_qpolynomial_fold *pwf);
3614 __isl_give isl_printer *
3615 isl_printer_print_union_pw_qpolynomial_fold(
3616 __isl_take isl_printer *p,
3617 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3619 For C<isl_printer_print_qpolynomial>,
3620 C<isl_printer_print_pw_qpolynomial> and
3621 C<isl_printer_print_pw_qpolynomial_fold>,
3622 the output format of the printer
3623 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3624 For C<isl_printer_print_union_pw_qpolynomial> and
3625 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
3627 In case of printing in C<ISL_FORMAT_C>, the user may want
3628 to set the names of all dimensions first.
3630 C<isl> also provides limited support for printing YAML documents,
3631 just enough for the internal use for printing such documents.
3633 #include <isl/printer.h>
3634 __isl_give isl_printer *isl_printer_yaml_start_mapping(
3635 __isl_take isl_printer *p);
3636 __isl_give isl_printer *isl_printer_yaml_end_mapping(
3637 __isl_take isl_printer *p);
3638 __isl_give isl_printer *isl_printer_yaml_start_sequence(
3639 __isl_take isl_printer *p);
3640 __isl_give isl_printer *isl_printer_yaml_end_sequence(
3641 __isl_take isl_printer *p);
3642 __isl_give isl_printer *isl_printer_yaml_next(
3643 __isl_take isl_printer *p);
3645 A document is started by a call to either
3646 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3647 Anything printed to the printer after such a call belong to the
3648 first key of the mapping or the first element in the sequence.
3649 The function C<isl_printer_yaml_next> moves to the value if
3650 we are currently printing a mapping key, the next key if we
3651 are printing a value or the next element if we are printing
3652 an element in a sequence.
3653 Nested mappings and sequences are initiated by the same
3654 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3655 Each call to these functions needs to have a corresponding call to
3656 C<isl_printer_yaml_end_mapping> or C<isl_printer_yaml_end_sequence>.
3658 When called on a file printer, the following function flushes
3659 the file. When called on a string printer, the buffer is cleared.
3661 __isl_give isl_printer *isl_printer_flush(
3662 __isl_take isl_printer *p);
3664 The following functions allow the user to attach
3665 notes to a printer in order to keep track of additional state.
3667 #include <isl/printer.h>
3668 isl_bool isl_printer_has_note(__isl_keep isl_printer *p,
3669 __isl_keep isl_id *id);
3670 __isl_give isl_id *isl_printer_get_note(
3671 __isl_keep isl_printer *p, __isl_take isl_id *id);
3672 __isl_give isl_printer *isl_printer_set_note(
3673 __isl_take isl_printer *p,
3674 __isl_take isl_id *id, __isl_take isl_id *note);
3676 C<isl_printer_set_note> associates the given note to the given
3677 identifier in the printer.
3678 C<isl_printer_get_note> retrieves a note associated to an
3680 C<isl_printer_has_note> checks if there is such a note.
3681 C<isl_printer_get_note> fails if the requested note does not exist.
3683 Alternatively, a string representation can be obtained
3684 directly using the following functions, which always print
3688 __isl_give char *isl_id_to_str(
3689 __isl_keep isl_id *id);
3691 #include <isl/space.h>
3692 __isl_give char *isl_space_to_str(
3693 __isl_keep isl_space *space);
3695 #include <isl/val.h>
3696 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
3697 __isl_give char *isl_multi_val_to_str(
3698 __isl_keep isl_multi_val *mv);
3700 #include <isl/set.h>
3701 __isl_give char *isl_basic_set_to_str(
3702 __isl_keep isl_basic_set *bset);
3703 __isl_give char *isl_set_to_str(
3704 __isl_keep isl_set *set);
3706 #include <isl/union_set.h>
3707 __isl_give char *isl_union_set_to_str(
3708 __isl_keep isl_union_set *uset);
3710 #include <isl/map.h>
3711 __isl_give char *isl_basic_map_to_str(
3712 __isl_keep isl_basic_map *bmap);
3713 __isl_give char *isl_map_to_str(
3714 __isl_keep isl_map *map);
3716 #include <isl/union_map.h>
3717 __isl_give char *isl_union_map_to_str(
3718 __isl_keep isl_union_map *umap);
3720 #include <isl/aff.h>
3721 __isl_give char *isl_aff_to_str(__isl_keep isl_aff *aff);
3722 __isl_give char *isl_pw_aff_to_str(
3723 __isl_keep isl_pw_aff *pa);
3724 __isl_give char *isl_multi_aff_to_str(
3725 __isl_keep isl_multi_aff *ma);
3726 __isl_give char *isl_pw_multi_aff_to_str(
3727 __isl_keep isl_pw_multi_aff *pma);
3728 __isl_give char *isl_multi_pw_aff_to_str(
3729 __isl_keep isl_multi_pw_aff *mpa);
3730 __isl_give char *isl_union_pw_aff_to_str(
3731 __isl_keep isl_union_pw_aff *upa);
3732 __isl_give char *isl_union_pw_multi_aff_to_str(
3733 __isl_keep isl_union_pw_multi_aff *upma);
3734 __isl_give char *isl_multi_union_pw_aff_to_str(
3735 __isl_keep isl_multi_union_pw_aff *mupa);
3737 #include <isl/point.h>
3738 __isl_give char *isl_point_to_str(
3739 __isl_keep isl_point *pnt);
3741 #include <isl/polynomial.h>
3742 __isl_give char *isl_pw_qpolynomial_to_str(
3743 __isl_keep isl_pw_qpolynomial *pwqp);
3744 __isl_give char *isl_union_pw_qpolynomial_to_str(
3745 __isl_keep isl_union_pw_qpolynomial *upwqp);
3749 =head3 Unary Properties
3755 The following functions test whether the given set or relation
3756 contains any integer points. The ``plain'' variants do not perform
3757 any computations, but simply check if the given set or relation
3758 is already known to be empty.
3760 isl_bool isl_basic_set_plain_is_empty(
3761 __isl_keep isl_basic_set *bset);
3762 isl_bool isl_basic_set_is_empty(
3763 __isl_keep isl_basic_set *bset);
3764 isl_bool isl_set_plain_is_empty(
3765 __isl_keep isl_set *set);
3766 isl_bool isl_set_is_empty(__isl_keep isl_set *set);
3767 isl_bool isl_union_set_is_empty(
3768 __isl_keep isl_union_set *uset);
3769 isl_bool isl_basic_map_plain_is_empty(
3770 __isl_keep isl_basic_map *bmap);
3771 isl_bool isl_basic_map_is_empty(
3772 __isl_keep isl_basic_map *bmap);
3773 isl_bool isl_map_plain_is_empty(
3774 __isl_keep isl_map *map);
3775 isl_bool isl_map_is_empty(__isl_keep isl_map *map);
3776 isl_bool isl_union_map_is_empty(
3777 __isl_keep isl_union_map *umap);
3779 =item * Universality
3781 isl_bool isl_basic_set_plain_is_universe(
3782 __isl_keep isl_basic_set *bset);
3783 isl_bool isl_basic_set_is_universe(
3784 __isl_keep isl_basic_set *bset);
3785 isl_bool isl_basic_map_plain_is_universe(
3786 __isl_keep isl_basic_map *bmap);
3787 isl_bool isl_basic_map_is_universe(
3788 __isl_keep isl_basic_map *bmap);
3789 isl_bool isl_set_plain_is_universe(
3790 __isl_keep isl_set *set);
3791 isl_bool isl_map_plain_is_universe(
3792 __isl_keep isl_map *map);
3794 =item * Single-valuedness
3796 #include <isl/set.h>
3797 isl_bool isl_set_is_singleton(__isl_keep isl_set *set);
3799 #include <isl/map.h>
3800 isl_bool isl_basic_map_is_single_valued(
3801 __isl_keep isl_basic_map *bmap);
3802 isl_bool isl_map_plain_is_single_valued(
3803 __isl_keep isl_map *map);
3804 isl_bool isl_map_is_single_valued(__isl_keep isl_map *map);
3806 #include <isl/union_map.h>
3807 isl_bool isl_union_map_is_single_valued(
3808 __isl_keep isl_union_map *umap);
3812 isl_bool isl_map_plain_is_injective(
3813 __isl_keep isl_map *map);
3814 isl_bool isl_map_is_injective(
3815 __isl_keep isl_map *map);
3816 isl_bool isl_union_map_plain_is_injective(
3817 __isl_keep isl_union_map *umap);
3818 isl_bool isl_union_map_is_injective(
3819 __isl_keep isl_union_map *umap);
3823 isl_bool isl_map_is_bijective(
3824 __isl_keep isl_map *map);
3825 isl_bool isl_union_map_is_bijective(
3826 __isl_keep isl_union_map *umap);
3830 The following functions test whether the given relation
3831 only maps elements to themselves.
3833 #include <isl/map.h>
3834 isl_bool isl_map_is_identity(
3835 __isl_keep isl_map *map);
3837 #include <isl/union_map.h>
3838 isl_bool isl_union_map_is_identity(
3839 __isl_keep isl_union_map *umap);
3843 __isl_give isl_val *
3844 isl_basic_map_plain_get_val_if_fixed(
3845 __isl_keep isl_basic_map *bmap,
3846 enum isl_dim_type type, unsigned pos);
3847 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
3848 __isl_keep isl_set *set,
3849 enum isl_dim_type type, unsigned pos);
3850 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
3851 __isl_keep isl_map *map,
3852 enum isl_dim_type type, unsigned pos);
3854 If the set or relation obviously lies on a hyperplane where the given dimension
3855 has a fixed value, then return that value.
3856 Otherwise return NaN.
3860 isl_stat isl_set_dim_residue_class_val(
3861 __isl_keep isl_set *set,
3862 int pos, __isl_give isl_val **modulo,
3863 __isl_give isl_val **residue);
3865 Check if the values of the given set dimension are equal to a fixed
3866 value modulo some integer value. If so, assign the modulo to C<*modulo>
3867 and the fixed value to C<*residue>. If the given dimension attains only
3868 a single value, then assign C<0> to C<*modulo> and the fixed value to
3870 If the dimension does not attain only a single value and if no modulo
3871 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
3875 To check whether the description of a set, relation or function depends
3876 on one or more given dimensions,
3877 the following functions can be used.
3879 #include <isl/constraint.h>
3880 isl_bool isl_constraint_involves_dims(
3881 __isl_keep isl_constraint *constraint,
3882 enum isl_dim_type type, unsigned first, unsigned n);
3884 #include <isl/set.h>
3885 isl_bool isl_basic_set_involves_dims(
3886 __isl_keep isl_basic_set *bset,
3887 enum isl_dim_type type, unsigned first, unsigned n);
3888 isl_bool isl_set_involves_dims(__isl_keep isl_set *set,
3889 enum isl_dim_type type, unsigned first, unsigned n);
3891 #include <isl/map.h>
3892 isl_bool isl_basic_map_involves_dims(
3893 __isl_keep isl_basic_map *bmap,
3894 enum isl_dim_type type, unsigned first, unsigned n);
3895 isl_bool isl_map_involves_dims(__isl_keep isl_map *map,
3896 enum isl_dim_type type, unsigned first, unsigned n);
3898 #include <isl/union_map.h>
3899 isl_bool isl_union_map_involves_dims(
3900 __isl_keep isl_union_map *umap,
3901 enum isl_dim_type type, unsigned first, unsigned n);
3903 #include <isl/aff.h>
3904 isl_bool isl_aff_involves_dims(__isl_keep isl_aff *aff,
3905 enum isl_dim_type type, unsigned first, unsigned n);
3906 isl_bool isl_pw_aff_involves_dims(
3907 __isl_keep isl_pw_aff *pwaff,
3908 enum isl_dim_type type, unsigned first, unsigned n);
3909 isl_bool isl_multi_aff_involves_dims(
3910 __isl_keep isl_multi_aff *ma,
3911 enum isl_dim_type type, unsigned first, unsigned n);
3912 isl_bool isl_multi_pw_aff_involves_dims(
3913 __isl_keep isl_multi_pw_aff *mpa,
3914 enum isl_dim_type type, unsigned first, unsigned n);
3916 #include <isl/polynomial.h>
3917 isl_bool isl_qpolynomial_involves_dims(
3918 __isl_keep isl_qpolynomial *qp,
3919 enum isl_dim_type type, unsigned first, unsigned n);
3921 Similarly, the following functions can be used to check whether
3922 a given dimension is involved in any lower or upper bound.
3924 #include <isl/set.h>
3925 isl_bool isl_set_dim_has_any_lower_bound(
3926 __isl_keep isl_set *set,
3927 enum isl_dim_type type, unsigned pos);
3928 isl_bool isl_set_dim_has_any_upper_bound(
3929 __isl_keep isl_set *set,
3930 enum isl_dim_type type, unsigned pos);
3932 Note that these functions return true even if there is a bound on
3933 the dimension on only some of the basic sets of C<set>.
3934 To check if they have a bound for all of the basic sets in C<set>,
3935 use the following functions instead.
3937 #include <isl/set.h>
3938 isl_bool isl_set_dim_has_lower_bound(
3939 __isl_keep isl_set *set,
3940 enum isl_dim_type type, unsigned pos);
3941 isl_bool isl_set_dim_has_upper_bound(
3942 __isl_keep isl_set *set,
3943 enum isl_dim_type type, unsigned pos);
3947 To check whether a set is a parameter domain, use this function:
3949 isl_bool isl_set_is_params(__isl_keep isl_set *set);
3950 isl_bool isl_union_set_is_params(
3951 __isl_keep isl_union_set *uset);
3955 The following functions check whether the space of the given
3956 (basic) set or relation range is a wrapped relation.
3958 #include <isl/space.h>
3959 isl_bool isl_space_is_wrapping(
3960 __isl_keep isl_space *space);
3961 isl_bool isl_space_domain_is_wrapping(
3962 __isl_keep isl_space *space);
3963 isl_bool isl_space_range_is_wrapping(
3964 __isl_keep isl_space *space);
3966 #include <isl/set.h>
3967 isl_bool isl_basic_set_is_wrapping(
3968 __isl_keep isl_basic_set *bset);
3969 isl_bool isl_set_is_wrapping(__isl_keep isl_set *set);
3971 #include <isl/map.h>
3972 isl_bool isl_map_domain_is_wrapping(
3973 __isl_keep isl_map *map);
3974 isl_bool isl_map_range_is_wrapping(
3975 __isl_keep isl_map *map);
3977 #include <isl/val.h>
3978 isl_bool isl_multi_val_range_is_wrapping(
3979 __isl_keep isl_multi_val *mv);
3981 #include <isl/aff.h>
3982 isl_bool isl_multi_aff_range_is_wrapping(
3983 __isl_keep isl_multi_aff *ma);
3984 isl_bool isl_multi_pw_aff_range_is_wrapping(
3985 __isl_keep isl_multi_pw_aff *mpa);
3986 isl_bool isl_multi_union_pw_aff_range_is_wrapping(
3987 __isl_keep isl_multi_union_pw_aff *mupa);
3989 The input to C<isl_space_is_wrapping> should
3990 be the space of a set, while that of
3991 C<isl_space_domain_is_wrapping> and
3992 C<isl_space_range_is_wrapping> should be the space of a relation.
3994 =item * Internal Product
3996 isl_bool isl_basic_map_can_zip(
3997 __isl_keep isl_basic_map *bmap);
3998 isl_bool isl_map_can_zip(__isl_keep isl_map *map);
4000 Check whether the product of domain and range of the given relation
4002 i.e., whether both domain and range are nested relations.
4006 #include <isl/space.h>
4007 isl_bool isl_space_can_curry(
4008 __isl_keep isl_space *space);
4010 #include <isl/map.h>
4011 isl_bool isl_basic_map_can_curry(
4012 __isl_keep isl_basic_map *bmap);
4013 isl_bool isl_map_can_curry(__isl_keep isl_map *map);
4015 Check whether the domain of the (basic) relation is a wrapped relation.
4017 #include <isl/space.h>
4018 __isl_give isl_space *isl_space_uncurry(
4019 __isl_take isl_space *space);
4021 #include <isl/map.h>
4022 isl_bool isl_basic_map_can_uncurry(
4023 __isl_keep isl_basic_map *bmap);
4024 isl_bool isl_map_can_uncurry(__isl_keep isl_map *map);
4026 Check whether the range of the (basic) relation is a wrapped relation.
4028 #include <isl/space.h>
4029 isl_bool isl_space_can_range_curry(
4030 __isl_keep isl_space *space);
4032 #include <isl/map.h>
4033 isl_bool isl_map_can_range_curry(
4034 __isl_keep isl_map *map);
4036 Check whether the domain of the relation wrapped in the range of
4037 the input is itself a wrapped relation.
4039 =item * Special Values
4041 #include <isl/aff.h>
4042 isl_bool isl_aff_is_cst(__isl_keep isl_aff *aff);
4043 isl_bool isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
4044 isl_bool isl_multi_pw_aff_is_cst(
4045 __isl_keep isl_multi_pw_aff *mpa);
4047 Check whether the given expression is a constant.
4049 #include <isl/val.h>
4050 isl_bool isl_multi_val_involves_nan(
4051 __isl_keep isl_multi_val *mv);
4053 #include <isl/aff.h>
4054 isl_bool isl_aff_is_nan(__isl_keep isl_aff *aff);
4055 isl_bool isl_multi_aff_involves_nan(
4056 __isl_keep isl_multi_aff *ma);
4057 isl_bool isl_pw_aff_involves_nan(
4058 __isl_keep isl_pw_aff *pa);
4059 isl_bool isl_pw_multi_aff_involves_nan(
4060 __isl_keep isl_pw_multi_aff *pma);
4061 isl_bool isl_multi_pw_aff_involves_nan(
4062 __isl_keep isl_multi_pw_aff *mpa);
4063 isl_bool isl_union_pw_aff_involves_nan(
4064 __isl_keep isl_union_pw_aff *upa);
4065 isl_bool isl_union_pw_multi_aff_involves_nan(
4066 __isl_keep isl_union_pw_multi_aff *upma);
4067 isl_bool isl_multi_union_pw_aff_involves_nan(
4068 __isl_keep isl_multi_union_pw_aff *mupa);
4070 #include <isl/polynomial.h>
4071 isl_bool isl_qpolynomial_is_nan(
4072 __isl_keep isl_qpolynomial *qp);
4073 isl_bool isl_qpolynomial_fold_is_nan(
4074 __isl_keep isl_qpolynomial_fold *fold);
4075 isl_bool isl_pw_qpolynomial_involves_nan(
4076 __isl_keep isl_pw_qpolynomial *pwqp);
4077 isl_bool isl_pw_qpolynomial_fold_involves_nan(
4078 __isl_keep isl_pw_qpolynomial_fold *pwf);
4079 isl_bool isl_union_pw_qpolynomial_involves_nan(
4080 __isl_keep isl_union_pw_qpolynomial *upwqp);
4081 isl_bool isl_union_pw_qpolynomial_fold_involves_nan(
4082 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4084 Check whether the given expression is equal to or involves NaN.
4086 #include <isl/aff.h>
4087 isl_bool isl_aff_plain_is_zero(
4088 __isl_keep isl_aff *aff);
4090 Check whether the affine expression is obviously zero.
4094 =head3 Binary Properties
4100 The following functions check whether two objects
4101 represent the same set, relation or function.
4102 The C<plain> variants only return true if the objects
4103 are obviously the same. That is, they may return false
4104 even if the objects are the same, but they will never
4105 return true if the objects are not the same.
4107 #include <isl/set.h>
4108 isl_bool isl_basic_set_plain_is_equal(
4109 __isl_keep isl_basic_set *bset1,
4110 __isl_keep isl_basic_set *bset2);
4111 isl_bool isl_basic_set_is_equal(
4112 __isl_keep isl_basic_set *bset1,
4113 __isl_keep isl_basic_set *bset2);
4114 isl_bool isl_set_plain_is_equal(
4115 __isl_keep isl_set *set1,
4116 __isl_keep isl_set *set2);
4117 isl_bool isl_set_is_equal(__isl_keep isl_set *set1,
4118 __isl_keep isl_set *set2);
4120 #include <isl/map.h>
4121 isl_bool isl_basic_map_is_equal(
4122 __isl_keep isl_basic_map *bmap1,
4123 __isl_keep isl_basic_map *bmap2);
4124 isl_bool isl_map_is_equal(__isl_keep isl_map *map1,
4125 __isl_keep isl_map *map2);
4126 isl_bool isl_map_plain_is_equal(
4127 __isl_keep isl_map *map1,
4128 __isl_keep isl_map *map2);
4130 #include <isl/union_set.h>
4131 isl_bool isl_union_set_is_equal(
4132 __isl_keep isl_union_set *uset1,
4133 __isl_keep isl_union_set *uset2);
4135 #include <isl/union_map.h>
4136 isl_bool isl_union_map_is_equal(
4137 __isl_keep isl_union_map *umap1,
4138 __isl_keep isl_union_map *umap2);
4140 #include <isl/aff.h>
4141 isl_bool isl_aff_plain_is_equal(
4142 __isl_keep isl_aff *aff1,
4143 __isl_keep isl_aff *aff2);
4144 isl_bool isl_multi_aff_plain_is_equal(
4145 __isl_keep isl_multi_aff *maff1,
4146 __isl_keep isl_multi_aff *maff2);
4147 isl_bool isl_pw_aff_plain_is_equal(
4148 __isl_keep isl_pw_aff *pwaff1,
4149 __isl_keep isl_pw_aff *pwaff2);
4150 isl_bool isl_pw_aff_is_equal(
4151 __isl_keep isl_pw_aff *pa1,
4152 __isl_keep isl_pw_aff *pa2);
4153 isl_bool isl_pw_multi_aff_plain_is_equal(
4154 __isl_keep isl_pw_multi_aff *pma1,
4155 __isl_keep isl_pw_multi_aff *pma2);
4156 isl_bool isl_pw_multi_aff_is_equal(
4157 __isl_keep isl_pw_multi_aff *pma1,
4158 __isl_keep isl_pw_multi_aff *pma2);
4159 isl_bool isl_multi_pw_aff_plain_is_equal(
4160 __isl_keep isl_multi_pw_aff *mpa1,
4161 __isl_keep isl_multi_pw_aff *mpa2);
4162 isl_bool isl_multi_pw_aff_is_equal(
4163 __isl_keep isl_multi_pw_aff *mpa1,
4164 __isl_keep isl_multi_pw_aff *mpa2);
4165 isl_bool isl_union_pw_aff_plain_is_equal(
4166 __isl_keep isl_union_pw_aff *upa1,
4167 __isl_keep isl_union_pw_aff *upa2);
4168 isl_bool isl_union_pw_multi_aff_plain_is_equal(
4169 __isl_keep isl_union_pw_multi_aff *upma1,
4170 __isl_keep isl_union_pw_multi_aff *upma2);
4171 isl_bool isl_multi_union_pw_aff_plain_is_equal(
4172 __isl_keep isl_multi_union_pw_aff *mupa1,
4173 __isl_keep isl_multi_union_pw_aff *mupa2);
4175 #include <isl/polynomial.h>
4176 isl_bool isl_union_pw_qpolynomial_plain_is_equal(
4177 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4178 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4179 isl_bool isl_union_pw_qpolynomial_fold_plain_is_equal(
4180 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4181 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4183 =item * Disjointness
4185 #include <isl/set.h>
4186 isl_bool isl_basic_set_is_disjoint(
4187 __isl_keep isl_basic_set *bset1,
4188 __isl_keep isl_basic_set *bset2);
4189 isl_bool isl_set_plain_is_disjoint(
4190 __isl_keep isl_set *set1,
4191 __isl_keep isl_set *set2);
4192 isl_bool isl_set_is_disjoint(__isl_keep isl_set *set1,
4193 __isl_keep isl_set *set2);
4195 #include <isl/map.h>
4196 isl_bool isl_basic_map_is_disjoint(
4197 __isl_keep isl_basic_map *bmap1,
4198 __isl_keep isl_basic_map *bmap2);
4199 isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1,
4200 __isl_keep isl_map *map2);
4202 #include <isl/union_set.h>
4203 isl_bool isl_union_set_is_disjoint(
4204 __isl_keep isl_union_set *uset1,
4205 __isl_keep isl_union_set *uset2);
4207 #include <isl/union_map.h>
4208 isl_bool isl_union_map_is_disjoint(
4209 __isl_keep isl_union_map *umap1,
4210 __isl_keep isl_union_map *umap2);
4214 isl_bool isl_basic_set_is_subset(
4215 __isl_keep isl_basic_set *bset1,
4216 __isl_keep isl_basic_set *bset2);
4217 isl_bool isl_set_is_subset(__isl_keep isl_set *set1,
4218 __isl_keep isl_set *set2);
4219 isl_bool isl_set_is_strict_subset(
4220 __isl_keep isl_set *set1,
4221 __isl_keep isl_set *set2);
4222 isl_bool isl_union_set_is_subset(
4223 __isl_keep isl_union_set *uset1,
4224 __isl_keep isl_union_set *uset2);
4225 isl_bool isl_union_set_is_strict_subset(
4226 __isl_keep isl_union_set *uset1,
4227 __isl_keep isl_union_set *uset2);
4228 isl_bool isl_basic_map_is_subset(
4229 __isl_keep isl_basic_map *bmap1,
4230 __isl_keep isl_basic_map *bmap2);
4231 isl_bool isl_basic_map_is_strict_subset(
4232 __isl_keep isl_basic_map *bmap1,
4233 __isl_keep isl_basic_map *bmap2);
4234 isl_bool isl_map_is_subset(
4235 __isl_keep isl_map *map1,
4236 __isl_keep isl_map *map2);
4237 isl_bool isl_map_is_strict_subset(
4238 __isl_keep isl_map *map1,
4239 __isl_keep isl_map *map2);
4240 isl_bool isl_union_map_is_subset(
4241 __isl_keep isl_union_map *umap1,
4242 __isl_keep isl_union_map *umap2);
4243 isl_bool isl_union_map_is_strict_subset(
4244 __isl_keep isl_union_map *umap1,
4245 __isl_keep isl_union_map *umap2);
4247 Check whether the first argument is a (strict) subset of the
4252 Every comparison function returns a negative value if the first
4253 argument is considered smaller than the second, a positive value
4254 if the first argument is considered greater and zero if the two
4255 constraints are considered the same by the comparison criterion.
4257 #include <isl/constraint.h>
4258 int isl_constraint_plain_cmp(
4259 __isl_keep isl_constraint *c1,
4260 __isl_keep isl_constraint *c2);
4262 This function is useful for sorting C<isl_constraint>s.
4263 The order depends on the internal representation of the inputs.
4264 The order is fixed over different calls to the function (assuming
4265 the internal representation of the inputs has not changed), but may
4266 change over different versions of C<isl>.
4268 #include <isl/constraint.h>
4269 int isl_constraint_cmp_last_non_zero(
4270 __isl_keep isl_constraint *c1,
4271 __isl_keep isl_constraint *c2);
4273 This function can be used to sort constraints that live in the same
4274 local space. Constraints that involve ``earlier'' dimensions or
4275 that have a smaller coefficient for the shared latest dimension
4276 are considered smaller than other constraints.
4277 This function only defines a B<partial> order.
4279 #include <isl/set.h>
4280 int isl_set_plain_cmp(__isl_keep isl_set *set1,
4281 __isl_keep isl_set *set2);
4283 This function is useful for sorting C<isl_set>s.
4284 The order depends on the internal representation of the inputs.
4285 The order is fixed over different calls to the function (assuming
4286 the internal representation of the inputs has not changed), but may
4287 change over different versions of C<isl>.
4289 #include <isl/aff.h>
4290 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4291 __isl_keep isl_pw_aff *pa2);
4293 The function C<isl_pw_aff_plain_cmp> can be used to sort
4294 C<isl_pw_aff>s. The order is not strictly defined.
4295 The current order sorts expressions that only involve
4296 earlier dimensions before those that involve later dimensions.
4300 =head2 Unary Operations
4306 __isl_give isl_set *isl_set_complement(
4307 __isl_take isl_set *set);
4308 __isl_give isl_map *isl_map_complement(
4309 __isl_take isl_map *map);
4313 #include <isl/space.h>
4314 __isl_give isl_space *isl_space_reverse(
4315 __isl_take isl_space *space);
4317 #include <isl/map.h>
4318 __isl_give isl_basic_map *isl_basic_map_reverse(
4319 __isl_take isl_basic_map *bmap);
4320 __isl_give isl_map *isl_map_reverse(
4321 __isl_take isl_map *map);
4323 #include <isl/union_map.h>
4324 __isl_give isl_union_map *isl_union_map_reverse(
4325 __isl_take isl_union_map *umap);
4329 #include <isl/space.h>
4330 __isl_give isl_space *isl_space_domain(
4331 __isl_take isl_space *space);
4332 __isl_give isl_space *isl_space_range(
4333 __isl_take isl_space *space);
4334 __isl_give isl_space *isl_space_params(
4335 __isl_take isl_space *space);
4337 #include <isl/local_space.h>
4338 __isl_give isl_local_space *isl_local_space_domain(
4339 __isl_take isl_local_space *ls);
4340 __isl_give isl_local_space *isl_local_space_range(
4341 __isl_take isl_local_space *ls);
4343 #include <isl/set.h>
4344 __isl_give isl_basic_set *isl_basic_set_project_out(
4345 __isl_take isl_basic_set *bset,
4346 enum isl_dim_type type, unsigned first, unsigned n);
4347 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
4348 enum isl_dim_type type, unsigned first, unsigned n);
4349 __isl_give isl_map *isl_set_project_onto_map(
4350 __isl_take isl_set *set,
4351 enum isl_dim_type type, unsigned first,
4353 __isl_give isl_basic_set *isl_basic_set_params(
4354 __isl_take isl_basic_set *bset);
4355 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
4357 The function C<isl_set_project_onto_map> returns a relation
4358 that projects the input set onto the given set dimensions.
4360 #include <isl/map.h>
4361 __isl_give isl_basic_map *isl_basic_map_project_out(
4362 __isl_take isl_basic_map *bmap,
4363 enum isl_dim_type type, unsigned first, unsigned n);
4364 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
4365 enum isl_dim_type type, unsigned first, unsigned n);
4366 __isl_give isl_basic_set *isl_basic_map_domain(
4367 __isl_take isl_basic_map *bmap);
4368 __isl_give isl_basic_set *isl_basic_map_range(
4369 __isl_take isl_basic_map *bmap);
4370 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
4371 __isl_give isl_set *isl_map_domain(
4372 __isl_take isl_map *bmap);
4373 __isl_give isl_set *isl_map_range(
4374 __isl_take isl_map *map);
4376 #include <isl/union_set.h>
4377 __isl_give isl_union_set *isl_union_set_project_out(
4378 __isl_take isl_union_set *uset,
4379 enum isl_dim_type type,
4380 unsigned first, unsigned n);
4381 __isl_give isl_set *isl_union_set_params(
4382 __isl_take isl_union_set *uset);
4384 The function C<isl_union_set_project_out> can only project out
4387 #include <isl/union_map.h>
4388 __isl_give isl_union_map *isl_union_map_project_out(
4389 __isl_take isl_union_map *umap,
4390 enum isl_dim_type type, unsigned first, unsigned n);
4391 __isl_give isl_set *isl_union_map_params(
4392 __isl_take isl_union_map *umap);
4393 __isl_give isl_union_set *isl_union_map_domain(
4394 __isl_take isl_union_map *umap);
4395 __isl_give isl_union_set *isl_union_map_range(
4396 __isl_take isl_union_map *umap);
4398 The function C<isl_union_map_project_out> can only project out
4401 #include <isl/aff.h>
4402 __isl_give isl_aff *isl_aff_project_domain_on_params(
4403 __isl_take isl_aff *aff);
4404 __isl_give isl_pw_multi_aff *
4405 isl_pw_multi_aff_project_domain_on_params(
4406 __isl_take isl_pw_multi_aff *pma);
4407 __isl_give isl_set *isl_pw_aff_domain(
4408 __isl_take isl_pw_aff *pwaff);
4409 __isl_give isl_set *isl_pw_multi_aff_domain(
4410 __isl_take isl_pw_multi_aff *pma);
4411 __isl_give isl_set *isl_multi_pw_aff_domain(
4412 __isl_take isl_multi_pw_aff *mpa);
4413 __isl_give isl_union_set *isl_union_pw_aff_domain(
4414 __isl_take isl_union_pw_aff *upa);
4415 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4416 __isl_take isl_union_pw_multi_aff *upma);
4417 __isl_give isl_union_set *
4418 isl_multi_union_pw_aff_domain(
4419 __isl_take isl_multi_union_pw_aff *mupa);
4420 __isl_give isl_set *isl_pw_aff_params(
4421 __isl_take isl_pw_aff *pwa);
4423 The function C<isl_multi_union_pw_aff_domain> requires its
4424 input to have at least one set dimension.
4426 #include <isl/polynomial.h>
4427 __isl_give isl_qpolynomial *
4428 isl_qpolynomial_project_domain_on_params(
4429 __isl_take isl_qpolynomial *qp);
4430 __isl_give isl_pw_qpolynomial *
4431 isl_pw_qpolynomial_project_domain_on_params(
4432 __isl_take isl_pw_qpolynomial *pwqp);
4433 __isl_give isl_pw_qpolynomial_fold *
4434 isl_pw_qpolynomial_fold_project_domain_on_params(
4435 __isl_take isl_pw_qpolynomial_fold *pwf);
4436 __isl_give isl_set *isl_pw_qpolynomial_domain(
4437 __isl_take isl_pw_qpolynomial *pwqp);
4438 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4439 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4440 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4441 __isl_take isl_union_pw_qpolynomial *upwqp);
4443 #include <isl/space.h>
4444 __isl_give isl_space *isl_space_domain_map(
4445 __isl_take isl_space *space);
4446 __isl_give isl_space *isl_space_range_map(
4447 __isl_take isl_space *space);
4449 #include <isl/map.h>
4450 __isl_give isl_map *isl_set_wrapped_domain_map(
4451 __isl_take isl_set *set);
4452 __isl_give isl_basic_map *isl_basic_map_domain_map(
4453 __isl_take isl_basic_map *bmap);
4454 __isl_give isl_basic_map *isl_basic_map_range_map(
4455 __isl_take isl_basic_map *bmap);
4456 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
4457 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
4459 #include <isl/union_map.h>
4460 __isl_give isl_union_map *isl_union_map_domain_map(
4461 __isl_take isl_union_map *umap);
4462 __isl_give isl_union_pw_multi_aff *
4463 isl_union_map_domain_map_union_pw_multi_aff(
4464 __isl_take isl_union_map *umap);
4465 __isl_give isl_union_map *isl_union_map_range_map(
4466 __isl_take isl_union_map *umap);
4467 __isl_give isl_union_map *
4468 isl_union_set_wrapped_domain_map(
4469 __isl_take isl_union_set *uset);
4471 The functions above construct a (basic, regular or union) relation
4472 that maps (a wrapped version of) the input relation to its domain or range.
4473 C<isl_set_wrapped_domain_map> maps the input set to the domain
4474 of its wrapped relation.
4478 __isl_give isl_basic_set *isl_basic_set_eliminate(
4479 __isl_take isl_basic_set *bset,
4480 enum isl_dim_type type,
4481 unsigned first, unsigned n);
4482 __isl_give isl_set *isl_set_eliminate(
4483 __isl_take isl_set *set, enum isl_dim_type type,
4484 unsigned first, unsigned n);
4485 __isl_give isl_basic_map *isl_basic_map_eliminate(
4486 __isl_take isl_basic_map *bmap,
4487 enum isl_dim_type type,
4488 unsigned first, unsigned n);
4489 __isl_give isl_map *isl_map_eliminate(
4490 __isl_take isl_map *map, enum isl_dim_type type,
4491 unsigned first, unsigned n);
4493 Eliminate the coefficients for the given dimensions from the constraints,
4494 without removing the dimensions.
4496 =item * Constructing a set from a parameter domain
4498 A zero-dimensional space or (basic) set can be constructed
4499 on a given parameter domain using the following functions.
4501 #include <isl/space.h>
4502 __isl_give isl_space *isl_space_set_from_params(
4503 __isl_take isl_space *space);
4505 #include <isl/set.h>
4506 __isl_give isl_basic_set *isl_basic_set_from_params(
4507 __isl_take isl_basic_set *bset);
4508 __isl_give isl_set *isl_set_from_params(
4509 __isl_take isl_set *set);
4511 =item * Constructing a relation from one or two sets
4513 Create a relation with the given set(s) as domain and/or range.
4514 If only the domain or the range is specified, then
4515 the range or domain of the created relation is a zero-dimensional
4516 flat anonymous space.
4518 #include <isl/space.h>
4519 __isl_give isl_space *isl_space_from_domain(
4520 __isl_take isl_space *space);
4521 __isl_give isl_space *isl_space_from_range(
4522 __isl_take isl_space *space);
4523 __isl_give isl_space *isl_space_map_from_set(
4524 __isl_take isl_space *space);
4525 __isl_give isl_space *isl_space_map_from_domain_and_range(
4526 __isl_take isl_space *domain,
4527 __isl_take isl_space *range);
4529 #include <isl/local_space.h>
4530 __isl_give isl_local_space *isl_local_space_from_domain(
4531 __isl_take isl_local_space *ls);
4533 #include <isl/map.h>
4534 __isl_give isl_map *isl_map_from_domain(
4535 __isl_take isl_set *set);
4536 __isl_give isl_map *isl_map_from_range(
4537 __isl_take isl_set *set);
4539 #include <isl/union_map.h>
4540 __isl_give isl_union_map *
4541 isl_union_map_from_domain_and_range(
4542 __isl_take isl_union_set *domain,
4543 __isl_take isl_union_set *range);
4545 #include <isl/val.h>
4546 __isl_give isl_multi_val *isl_multi_val_from_range(
4547 __isl_take isl_multi_val *mv);
4549 #include <isl/aff.h>
4550 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4551 __isl_take isl_multi_aff *ma);
4552 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4553 __isl_take isl_pw_aff *pwa);
4554 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4555 __isl_take isl_multi_pw_aff *mpa);
4556 __isl_give isl_multi_union_pw_aff *
4557 isl_multi_union_pw_aff_from_range(
4558 __isl_take isl_multi_union_pw_aff *mupa);
4559 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4560 __isl_take isl_set *set);
4561 __isl_give isl_union_pw_multi_aff *
4562 isl_union_pw_multi_aff_from_domain(
4563 __isl_take isl_union_set *uset);
4567 #include <isl/set.h>
4568 __isl_give isl_basic_set *isl_basic_set_fix_si(
4569 __isl_take isl_basic_set *bset,
4570 enum isl_dim_type type, unsigned pos, int value);
4571 __isl_give isl_basic_set *isl_basic_set_fix_val(
4572 __isl_take isl_basic_set *bset,
4573 enum isl_dim_type type, unsigned pos,
4574 __isl_take isl_val *v);
4575 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
4576 enum isl_dim_type type, unsigned pos, int value);
4577 __isl_give isl_set *isl_set_fix_val(
4578 __isl_take isl_set *set,
4579 enum isl_dim_type type, unsigned pos,
4580 __isl_take isl_val *v);
4582 #include <isl/map.h>
4583 __isl_give isl_basic_map *isl_basic_map_fix_si(
4584 __isl_take isl_basic_map *bmap,
4585 enum isl_dim_type type, unsigned pos, int value);
4586 __isl_give isl_basic_map *isl_basic_map_fix_val(
4587 __isl_take isl_basic_map *bmap,
4588 enum isl_dim_type type, unsigned pos,
4589 __isl_take isl_val *v);
4590 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
4591 enum isl_dim_type type, unsigned pos, int value);
4592 __isl_give isl_map *isl_map_fix_val(
4593 __isl_take isl_map *map,
4594 enum isl_dim_type type, unsigned pos,
4595 __isl_take isl_val *v);
4597 #include <isl/aff.h>
4598 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4599 __isl_take isl_pw_multi_aff *pma,
4600 enum isl_dim_type type, unsigned pos, int value);
4602 #include <isl/polynomial.h>
4603 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4604 __isl_take isl_pw_qpolynomial *pwqp,
4605 enum isl_dim_type type, unsigned n,
4606 __isl_take isl_val *v);
4608 Intersect the set, relation or function domain
4609 with the hyperplane where the given
4610 dimension has the fixed given value.
4612 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
4613 __isl_take isl_basic_map *bmap,
4614 enum isl_dim_type type, unsigned pos, int value);
4615 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
4616 __isl_take isl_basic_map *bmap,
4617 enum isl_dim_type type, unsigned pos, int value);
4618 __isl_give isl_set *isl_set_lower_bound_si(
4619 __isl_take isl_set *set,
4620 enum isl_dim_type type, unsigned pos, int value);
4621 __isl_give isl_set *isl_set_lower_bound_val(
4622 __isl_take isl_set *set,
4623 enum isl_dim_type type, unsigned pos,
4624 __isl_take isl_val *value);
4625 __isl_give isl_map *isl_map_lower_bound_si(
4626 __isl_take isl_map *map,
4627 enum isl_dim_type type, unsigned pos, int value);
4628 __isl_give isl_set *isl_set_upper_bound_si(
4629 __isl_take isl_set *set,
4630 enum isl_dim_type type, unsigned pos, int value);
4631 __isl_give isl_set *isl_set_upper_bound_val(
4632 __isl_take isl_set *set,
4633 enum isl_dim_type type, unsigned pos,
4634 __isl_take isl_val *value);
4635 __isl_give isl_map *isl_map_upper_bound_si(
4636 __isl_take isl_map *map,
4637 enum isl_dim_type type, unsigned pos, int value);
4639 Intersect the set or relation with the half-space where the given
4640 dimension has a value bounded by the fixed given integer value.
4642 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
4643 enum isl_dim_type type1, int pos1,
4644 enum isl_dim_type type2, int pos2);
4645 __isl_give isl_basic_map *isl_basic_map_equate(
4646 __isl_take isl_basic_map *bmap,
4647 enum isl_dim_type type1, int pos1,
4648 enum isl_dim_type type2, int pos2);
4649 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
4650 enum isl_dim_type type1, int pos1,
4651 enum isl_dim_type type2, int pos2);
4653 Intersect the set or relation with the hyperplane where the given
4654 dimensions are equal to each other.
4656 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
4657 enum isl_dim_type type1, int pos1,
4658 enum isl_dim_type type2, int pos2);
4660 Intersect the relation with the hyperplane where the given
4661 dimensions have opposite values.
4663 __isl_give isl_map *isl_map_order_le(
4664 __isl_take isl_map *map,
4665 enum isl_dim_type type1, int pos1,
4666 enum isl_dim_type type2, int pos2);
4667 __isl_give isl_basic_map *isl_basic_map_order_ge(
4668 __isl_take isl_basic_map *bmap,
4669 enum isl_dim_type type1, int pos1,
4670 enum isl_dim_type type2, int pos2);
4671 __isl_give isl_map *isl_map_order_ge(
4672 __isl_take isl_map *map,
4673 enum isl_dim_type type1, int pos1,
4674 enum isl_dim_type type2, int pos2);
4675 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
4676 enum isl_dim_type type1, int pos1,
4677 enum isl_dim_type type2, int pos2);
4678 __isl_give isl_basic_map *isl_basic_map_order_gt(
4679 __isl_take isl_basic_map *bmap,
4680 enum isl_dim_type type1, int pos1,
4681 enum isl_dim_type type2, int pos2);
4682 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
4683 enum isl_dim_type type1, int pos1,
4684 enum isl_dim_type type2, int pos2);
4686 Intersect the relation with the half-space where the given
4687 dimensions satisfy the given ordering.
4691 #include <isl/aff.h>
4692 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4693 __isl_take isl_aff *aff);
4694 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4695 __isl_take isl_aff *aff);
4696 __isl_give isl_set *isl_pw_aff_pos_set(
4697 __isl_take isl_pw_aff *pa);
4698 __isl_give isl_set *isl_pw_aff_nonneg_set(
4699 __isl_take isl_pw_aff *pwaff);
4700 __isl_give isl_set *isl_pw_aff_zero_set(
4701 __isl_take isl_pw_aff *pwaff);
4702 __isl_give isl_set *isl_pw_aff_non_zero_set(
4703 __isl_take isl_pw_aff *pwaff);
4704 __isl_give isl_union_set *
4705 isl_union_pw_aff_zero_union_set(
4706 __isl_take isl_union_pw_aff *upa);
4707 __isl_give isl_union_set *
4708 isl_multi_union_pw_aff_zero_union_set(
4709 __isl_take isl_multi_union_pw_aff *mupa);
4711 The function C<isl_aff_neg_basic_set> returns a basic set
4712 containing those elements in the domain space
4713 of C<aff> where C<aff> is negative.
4714 The function C<isl_pw_aff_nonneg_set> returns a set
4715 containing those elements in the domain
4716 of C<pwaff> where C<pwaff> is non-negative.
4717 The function C<isl_multi_union_pw_aff_zero_union_set>
4718 returns a union set containing those elements
4719 in the domains of its elements where they are all zero.
4723 __isl_give isl_map *isl_set_identity(
4724 __isl_take isl_set *set);
4725 __isl_give isl_union_map *isl_union_set_identity(
4726 __isl_take isl_union_set *uset);
4727 __isl_give isl_union_pw_multi_aff *
4728 isl_union_set_identity_union_pw_multi_aff(
4729 __isl_take isl_union_set *uset);
4731 Construct an identity relation on the given (union) set.
4733 =item * Function Extraction
4735 A piecewise quasi affine expression that is equal to 1 on a set
4736 and 0 outside the set can be created using the following function.
4738 #include <isl/aff.h>
4739 __isl_give isl_pw_aff *isl_set_indicator_function(
4740 __isl_take isl_set *set);
4742 A piecewise multiple quasi affine expression can be extracted
4743 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4744 and the C<isl_map> is single-valued.
4745 In case of a conversion from an C<isl_union_map>
4746 to an C<isl_union_pw_multi_aff>, these properties need to hold
4747 in each domain space.
4748 A conversion to a C<isl_multi_union_pw_aff> additionally
4749 requires that the input is non-empty and involves only a single
4752 #include <isl/aff.h>
4753 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4754 __isl_take isl_set *set);
4755 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4756 __isl_take isl_map *map);
4758 __isl_give isl_union_pw_multi_aff *
4759 isl_union_pw_multi_aff_from_union_set(
4760 __isl_take isl_union_set *uset);
4761 __isl_give isl_union_pw_multi_aff *
4762 isl_union_pw_multi_aff_from_union_map(
4763 __isl_take isl_union_map *umap);
4765 __isl_give isl_multi_union_pw_aff *
4766 isl_multi_union_pw_aff_from_union_map(
4767 __isl_take isl_union_map *umap);
4771 __isl_give isl_basic_set *isl_basic_map_deltas(
4772 __isl_take isl_basic_map *bmap);
4773 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
4774 __isl_give isl_union_set *isl_union_map_deltas(
4775 __isl_take isl_union_map *umap);
4777 These functions return a (basic) set containing the differences
4778 between image elements and corresponding domain elements in the input.
4780 __isl_give isl_basic_map *isl_basic_map_deltas_map(
4781 __isl_take isl_basic_map *bmap);
4782 __isl_give isl_map *isl_map_deltas_map(
4783 __isl_take isl_map *map);
4784 __isl_give isl_union_map *isl_union_map_deltas_map(
4785 __isl_take isl_union_map *umap);
4787 The functions above construct a (basic, regular or union) relation
4788 that maps (a wrapped version of) the input relation to its delta set.
4792 Simplify the representation of a set, relation or functions by trying
4793 to combine pairs of basic sets or relations into a single
4794 basic set or relation.
4796 #include <isl/set.h>
4797 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
4799 #include <isl/map.h>
4800 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
4802 #include <isl/union_set.h>
4803 __isl_give isl_union_set *isl_union_set_coalesce(
4804 __isl_take isl_union_set *uset);
4806 #include <isl/union_map.h>
4807 __isl_give isl_union_map *isl_union_map_coalesce(
4808 __isl_take isl_union_map *umap);
4810 #include <isl/aff.h>
4811 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4812 __isl_take isl_pw_aff *pwqp);
4813 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4814 __isl_take isl_pw_multi_aff *pma);
4815 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4816 __isl_take isl_multi_pw_aff *mpa);
4817 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
4818 __isl_take isl_union_pw_aff *upa);
4819 __isl_give isl_union_pw_multi_aff *
4820 isl_union_pw_multi_aff_coalesce(
4821 __isl_take isl_union_pw_multi_aff *upma);
4822 __isl_give isl_multi_union_pw_aff *
4823 isl_multi_union_pw_aff_coalesce(
4824 __isl_take isl_multi_union_pw_aff *aff);
4826 #include <isl/polynomial.h>
4827 __isl_give isl_pw_qpolynomial_fold *
4828 isl_pw_qpolynomial_fold_coalesce(
4829 __isl_take isl_pw_qpolynomial_fold *pwf);
4830 __isl_give isl_union_pw_qpolynomial *
4831 isl_union_pw_qpolynomial_coalesce(
4832 __isl_take isl_union_pw_qpolynomial *upwqp);
4833 __isl_give isl_union_pw_qpolynomial_fold *
4834 isl_union_pw_qpolynomial_fold_coalesce(
4835 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4837 One of the methods for combining pairs of basic sets or relations
4838 can result in coefficients that are much larger than those that appear
4839 in the constraints of the input. By default, the coefficients are
4840 not allowed to grow larger, but this can be changed by unsetting
4841 the following option.
4843 isl_stat isl_options_set_coalesce_bounded_wrapping(
4844 isl_ctx *ctx, int val);
4845 int isl_options_get_coalesce_bounded_wrapping(
4848 =item * Detecting equalities
4850 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
4851 __isl_take isl_basic_set *bset);
4852 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
4853 __isl_take isl_basic_map *bmap);
4854 __isl_give isl_set *isl_set_detect_equalities(
4855 __isl_take isl_set *set);
4856 __isl_give isl_map *isl_map_detect_equalities(
4857 __isl_take isl_map *map);
4858 __isl_give isl_union_set *isl_union_set_detect_equalities(
4859 __isl_take isl_union_set *uset);
4860 __isl_give isl_union_map *isl_union_map_detect_equalities(
4861 __isl_take isl_union_map *umap);
4863 Simplify the representation of a set or relation by detecting implicit
4866 =item * Removing redundant constraints
4868 #include <isl/set.h>
4869 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
4870 __isl_take isl_basic_set *bset);
4871 __isl_give isl_set *isl_set_remove_redundancies(
4872 __isl_take isl_set *set);
4874 #include <isl/union_set.h>
4875 __isl_give isl_union_set *
4876 isl_union_set_remove_redundancies(
4877 __isl_take isl_union_set *uset);
4879 #include <isl/map.h>
4880 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
4881 __isl_take isl_basic_map *bmap);
4882 __isl_give isl_map *isl_map_remove_redundancies(
4883 __isl_take isl_map *map);
4885 #include <isl/union_map.h>
4886 __isl_give isl_union_map *
4887 isl_union_map_remove_redundancies(
4888 __isl_take isl_union_map *umap);
4892 __isl_give isl_basic_set *isl_set_convex_hull(
4893 __isl_take isl_set *set);
4894 __isl_give isl_basic_map *isl_map_convex_hull(
4895 __isl_take isl_map *map);
4897 If the input set or relation has any existentially quantified
4898 variables, then the result of these operations is currently undefined.
4902 #include <isl/set.h>
4903 __isl_give isl_basic_set *
4904 isl_set_unshifted_simple_hull(
4905 __isl_take isl_set *set);
4906 __isl_give isl_basic_set *isl_set_simple_hull(
4907 __isl_take isl_set *set);
4908 __isl_give isl_basic_set *
4909 isl_set_plain_unshifted_simple_hull(
4910 __isl_take isl_set *set);
4911 __isl_give isl_basic_set *
4912 isl_set_unshifted_simple_hull_from_set_list(
4913 __isl_take isl_set *set,
4914 __isl_take isl_set_list *list);
4916 #include <isl/map.h>
4917 __isl_give isl_basic_map *
4918 isl_map_unshifted_simple_hull(
4919 __isl_take isl_map *map);
4920 __isl_give isl_basic_map *isl_map_simple_hull(
4921 __isl_take isl_map *map);
4922 __isl_give isl_basic_map *
4923 isl_map_plain_unshifted_simple_hull(
4924 __isl_take isl_map *map);
4925 __isl_give isl_basic_map *
4926 isl_map_unshifted_simple_hull_from_map_list(
4927 __isl_take isl_map *map,
4928 __isl_take isl_map_list *list);
4930 #include <isl/union_map.h>
4931 __isl_give isl_union_map *isl_union_map_simple_hull(
4932 __isl_take isl_union_map *umap);
4934 These functions compute a single basic set or relation
4935 that contains the whole input set or relation.
4936 In particular, the output is described by translates
4937 of the constraints describing the basic sets or relations in the input.
4938 In case of C<isl_set_unshifted_simple_hull>, only the original
4939 constraints are used, without any translation.
4940 In case of C<isl_set_plain_unshifted_simple_hull> and
4941 C<isl_map_plain_unshifted_simple_hull>, the result is described
4942 by original constraints that are obviously satisfied
4943 by the entire input set or relation.
4944 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
4945 C<isl_map_unshifted_simple_hull_from_map_list>, the
4946 constraints are taken from the elements of the second argument.
4950 (See \autoref{s:simple hull}.)
4956 __isl_give isl_basic_set *isl_basic_set_affine_hull(
4957 __isl_take isl_basic_set *bset);
4958 __isl_give isl_basic_set *isl_set_affine_hull(
4959 __isl_take isl_set *set);
4960 __isl_give isl_union_set *isl_union_set_affine_hull(
4961 __isl_take isl_union_set *uset);
4962 __isl_give isl_basic_map *isl_basic_map_affine_hull(
4963 __isl_take isl_basic_map *bmap);
4964 __isl_give isl_basic_map *isl_map_affine_hull(
4965 __isl_take isl_map *map);
4966 __isl_give isl_union_map *isl_union_map_affine_hull(
4967 __isl_take isl_union_map *umap);
4969 In case of union sets and relations, the affine hull is computed
4972 =item * Polyhedral hull
4974 __isl_give isl_basic_set *isl_set_polyhedral_hull(
4975 __isl_take isl_set *set);
4976 __isl_give isl_basic_map *isl_map_polyhedral_hull(
4977 __isl_take isl_map *map);
4978 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
4979 __isl_take isl_union_set *uset);
4980 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
4981 __isl_take isl_union_map *umap);
4983 These functions compute a single basic set or relation
4984 not involving any existentially quantified variables
4985 that contains the whole input set or relation.
4986 In case of union sets and relations, the polyhedral hull is computed
4989 =item * Other approximations
4991 #include <isl/set.h>
4992 __isl_give isl_basic_set *
4993 isl_basic_set_drop_constraints_involving_dims(
4994 __isl_take isl_basic_set *bset,
4995 enum isl_dim_type type,
4996 unsigned first, unsigned n);
4997 __isl_give isl_basic_set *
4998 isl_basic_set_drop_constraints_not_involving_dims(
4999 __isl_take isl_basic_set *bset,
5000 enum isl_dim_type type,
5001 unsigned first, unsigned n);
5002 __isl_give isl_set *
5003 isl_set_drop_constraints_involving_dims(
5004 __isl_take isl_set *set,
5005 enum isl_dim_type type,
5006 unsigned first, unsigned n);
5007 __isl_give isl_set *
5008 isl_set_drop_constraints_not_involving_dims(
5009 __isl_take isl_set *set,
5010 enum isl_dim_type type,
5011 unsigned first, unsigned n);
5013 #include <isl/map.h>
5014 __isl_give isl_basic_map *
5015 isl_basic_map_drop_constraints_involving_dims(
5016 __isl_take isl_basic_map *bmap,
5017 enum isl_dim_type type,
5018 unsigned first, unsigned n);
5019 __isl_give isl_basic_map *
5020 isl_basic_map_drop_constraints_not_involving_dims(
5021 __isl_take isl_basic_map *bmap,
5022 enum isl_dim_type type,
5023 unsigned first, unsigned n);
5024 __isl_give isl_map *
5025 isl_map_drop_constraints_involving_dims(
5026 __isl_take isl_map *map,
5027 enum isl_dim_type type,
5028 unsigned first, unsigned n);
5029 __isl_give isl_map *
5030 isl_map_drop_constraints_not_involving_dims(
5031 __isl_take isl_map *map,
5032 enum isl_dim_type type,
5033 unsigned first, unsigned n);
5035 These functions drop any constraints (not) involving the specified dimensions.
5036 Note that the result depends on the representation of the input.
5038 #include <isl/polynomial.h>
5039 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5040 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5041 __isl_give isl_union_pw_qpolynomial *
5042 isl_union_pw_qpolynomial_to_polynomial(
5043 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5045 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5046 the polynomial will be an overapproximation. If C<sign> is negative,
5047 it will be an underapproximation. If C<sign> is zero, the approximation
5048 will lie somewhere in between.
5052 __isl_give isl_basic_set *isl_basic_set_sample(
5053 __isl_take isl_basic_set *bset);
5054 __isl_give isl_basic_set *isl_set_sample(
5055 __isl_take isl_set *set);
5056 __isl_give isl_basic_map *isl_basic_map_sample(
5057 __isl_take isl_basic_map *bmap);
5058 __isl_give isl_basic_map *isl_map_sample(
5059 __isl_take isl_map *map);
5061 If the input (basic) set or relation is non-empty, then return
5062 a singleton subset of the input. Otherwise, return an empty set.
5064 =item * Optimization
5066 #include <isl/ilp.h>
5067 __isl_give isl_val *isl_basic_set_max_val(
5068 __isl_keep isl_basic_set *bset,
5069 __isl_keep isl_aff *obj);
5070 __isl_give isl_val *isl_set_min_val(
5071 __isl_keep isl_set *set,
5072 __isl_keep isl_aff *obj);
5073 __isl_give isl_val *isl_set_max_val(
5074 __isl_keep isl_set *set,
5075 __isl_keep isl_aff *obj);
5076 __isl_give isl_multi_val *
5077 isl_union_set_min_multi_union_pw_aff(
5078 __isl_keep isl_union_set *set,
5079 __isl_keep isl_multi_union_pw_aff *obj);
5081 Compute the minimum or maximum of the integer affine expression C<obj>
5082 over the points in C<set>, returning the result in C<opt>.
5083 The result is C<NULL> in case of an error, the optimal value in case
5084 there is one, negative infinity or infinity if the problem is unbounded and
5085 NaN if the problem is empty.
5087 =item * Parametric optimization
5089 __isl_give isl_pw_aff *isl_set_dim_min(
5090 __isl_take isl_set *set, int pos);
5091 __isl_give isl_pw_aff *isl_set_dim_max(
5092 __isl_take isl_set *set, int pos);
5093 __isl_give isl_pw_aff *isl_map_dim_min(
5094 __isl_take isl_map *map, int pos);
5095 __isl_give isl_pw_aff *isl_map_dim_max(
5096 __isl_take isl_map *map, int pos);
5098 Compute the minimum or maximum of the given set or output dimension
5099 as a function of the parameters (and input dimensions), but independently
5100 of the other set or output dimensions.
5101 For lexicographic optimization, see L<"Lexicographic Optimization">.
5105 The following functions compute either the set of (rational) coefficient
5106 values of valid constraints for the given set or the set of (rational)
5107 values satisfying the constraints with coefficients from the given set.
5108 Internally, these two sets of functions perform essentially the
5109 same operations, except that the set of coefficients is assumed to
5110 be a cone, while the set of values may be any polyhedron.
5111 The current implementation is based on the Farkas lemma and
5112 Fourier-Motzkin elimination, but this may change or be made optional
5113 in future. In particular, future implementations may use different
5114 dualization algorithms or skip the elimination step.
5116 __isl_give isl_basic_set *isl_basic_set_coefficients(
5117 __isl_take isl_basic_set *bset);
5118 __isl_give isl_basic_set *isl_set_coefficients(
5119 __isl_take isl_set *set);
5120 __isl_give isl_union_set *isl_union_set_coefficients(
5121 __isl_take isl_union_set *bset);
5122 __isl_give isl_basic_set *isl_basic_set_solutions(
5123 __isl_take isl_basic_set *bset);
5124 __isl_give isl_basic_set *isl_set_solutions(
5125 __isl_take isl_set *set);
5126 __isl_give isl_union_set *isl_union_set_solutions(
5127 __isl_take isl_union_set *bset);
5131 __isl_give isl_map *isl_map_fixed_power_val(
5132 __isl_take isl_map *map,
5133 __isl_take isl_val *exp);
5134 __isl_give isl_union_map *
5135 isl_union_map_fixed_power_val(
5136 __isl_take isl_union_map *umap,
5137 __isl_take isl_val *exp);
5139 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
5140 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
5141 of C<map> is computed.
5143 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
5145 __isl_give isl_union_map *isl_union_map_power(
5146 __isl_take isl_union_map *umap, int *exact);
5148 Compute a parametric representation for all positive powers I<k> of C<map>.
5149 The result maps I<k> to a nested relation corresponding to the
5150 I<k>th power of C<map>.
5151 The result may be an overapproximation. If the result is known to be exact,
5152 then C<*exact> is set to C<1>.
5154 =item * Transitive closure
5156 __isl_give isl_map *isl_map_transitive_closure(
5157 __isl_take isl_map *map, int *exact);
5158 __isl_give isl_union_map *isl_union_map_transitive_closure(
5159 __isl_take isl_union_map *umap, int *exact);
5161 Compute the transitive closure of C<map>.
5162 The result may be an overapproximation. If the result is known to be exact,
5163 then C<*exact> is set to C<1>.
5165 =item * Reaching path lengths
5167 __isl_give isl_map *isl_map_reaching_path_lengths(
5168 __isl_take isl_map *map, int *exact);
5170 Compute a relation that maps each element in the range of C<map>
5171 to the lengths of all paths composed of edges in C<map> that
5172 end up in the given element.
5173 The result may be an overapproximation. If the result is known to be exact,
5174 then C<*exact> is set to C<1>.
5175 To compute the I<maximal> path length, the resulting relation
5176 should be postprocessed by C<isl_map_lexmax>.
5177 In particular, if the input relation is a dependence relation
5178 (mapping sources to sinks), then the maximal path length corresponds
5179 to the free schedule.
5180 Note, however, that C<isl_map_lexmax> expects the maximum to be
5181 finite, so if the path lengths are unbounded (possibly due to
5182 the overapproximation), then you will get an error message.
5186 #include <isl/space.h>
5187 __isl_give isl_space *isl_space_wrap(
5188 __isl_take isl_space *space);
5189 __isl_give isl_space *isl_space_unwrap(
5190 __isl_take isl_space *space);
5192 #include <isl/local_space.h>
5193 __isl_give isl_local_space *isl_local_space_wrap(
5194 __isl_take isl_local_space *ls);
5196 #include <isl/set.h>
5197 __isl_give isl_basic_map *isl_basic_set_unwrap(
5198 __isl_take isl_basic_set *bset);
5199 __isl_give isl_map *isl_set_unwrap(
5200 __isl_take isl_set *set);
5202 #include <isl/map.h>
5203 __isl_give isl_basic_set *isl_basic_map_wrap(
5204 __isl_take isl_basic_map *bmap);
5205 __isl_give isl_set *isl_map_wrap(
5206 __isl_take isl_map *map);
5208 #include <isl/union_set.h>
5209 __isl_give isl_union_map *isl_union_set_unwrap(
5210 __isl_take isl_union_set *uset);
5212 #include <isl/union_map.h>
5213 __isl_give isl_union_set *isl_union_map_wrap(
5214 __isl_take isl_union_map *umap);
5216 The input to C<isl_space_unwrap> should
5217 be the space of a set, while that of
5218 C<isl_space_wrap> should be the space of a relation.
5219 Conversely, the output of C<isl_space_unwrap> is the space
5220 of a relation, while that of C<isl_space_wrap> is the space of a set.
5224 Remove any internal structure of domain (and range) of the given
5225 set or relation. If there is any such internal structure in the input,
5226 then the name of the space is also removed.
5228 #include <isl/local_space.h>
5229 __isl_give isl_local_space *
5230 isl_local_space_flatten_domain(
5231 __isl_take isl_local_space *ls);
5232 __isl_give isl_local_space *
5233 isl_local_space_flatten_range(
5234 __isl_take isl_local_space *ls);
5236 #include <isl/set.h>
5237 __isl_give isl_basic_set *isl_basic_set_flatten(
5238 __isl_take isl_basic_set *bset);
5239 __isl_give isl_set *isl_set_flatten(
5240 __isl_take isl_set *set);
5242 #include <isl/map.h>
5243 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
5244 __isl_take isl_basic_map *bmap);
5245 __isl_give isl_basic_map *isl_basic_map_flatten_range(
5246 __isl_take isl_basic_map *bmap);
5247 __isl_give isl_map *isl_map_flatten_range(
5248 __isl_take isl_map *map);
5249 __isl_give isl_map *isl_map_flatten_domain(
5250 __isl_take isl_map *map);
5251 __isl_give isl_basic_map *isl_basic_map_flatten(
5252 __isl_take isl_basic_map *bmap);
5253 __isl_give isl_map *isl_map_flatten(
5254 __isl_take isl_map *map);
5256 #include <isl/val.h>
5257 __isl_give isl_multi_val *isl_multi_val_flatten_range(
5258 __isl_take isl_multi_val *mv);
5260 #include <isl/aff.h>
5261 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
5262 __isl_take isl_multi_aff *ma);
5263 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
5264 __isl_take isl_multi_aff *ma);
5265 __isl_give isl_multi_pw_aff *
5266 isl_multi_pw_aff_flatten_range(
5267 __isl_take isl_multi_pw_aff *mpa);
5268 __isl_give isl_multi_union_pw_aff *
5269 isl_multi_union_pw_aff_flatten_range(
5270 __isl_take isl_multi_union_pw_aff *mupa);
5272 #include <isl/map.h>
5273 __isl_give isl_map *isl_set_flatten_map(
5274 __isl_take isl_set *set);
5276 The function above constructs a relation
5277 that maps the input set to a flattened version of the set.
5281 Lift the input set to a space with extra dimensions corresponding
5282 to the existentially quantified variables in the input.
5283 In particular, the result lives in a wrapped map where the domain
5284 is the original space and the range corresponds to the original
5285 existentially quantified variables.
5287 #include <isl/set.h>
5288 __isl_give isl_basic_set *isl_basic_set_lift(
5289 __isl_take isl_basic_set *bset);
5290 __isl_give isl_set *isl_set_lift(
5291 __isl_take isl_set *set);
5292 __isl_give isl_union_set *isl_union_set_lift(
5293 __isl_take isl_union_set *uset);
5295 Given a local space that contains the existentially quantified
5296 variables of a set, a basic relation that, when applied to
5297 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
5298 can be constructed using the following function.
5300 #include <isl/local_space.h>
5301 __isl_give isl_basic_map *isl_local_space_lifting(
5302 __isl_take isl_local_space *ls);
5304 #include <isl/aff.h>
5305 __isl_give isl_multi_aff *isl_multi_aff_lift(
5306 __isl_take isl_multi_aff *maff,
5307 __isl_give isl_local_space **ls);
5309 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
5310 then it is assigned the local space that lies at the basis of
5311 the lifting applied.
5313 =item * Internal Product
5315 #include <isl/space.h>
5316 __isl_give isl_space *isl_space_zip(
5317 __isl_take isl_space *space);
5319 #include <isl/map.h>
5320 __isl_give isl_basic_map *isl_basic_map_zip(
5321 __isl_take isl_basic_map *bmap);
5322 __isl_give isl_map *isl_map_zip(
5323 __isl_take isl_map *map);
5325 #include <isl/union_map.h>
5326 __isl_give isl_union_map *isl_union_map_zip(
5327 __isl_take isl_union_map *umap);
5329 Given a relation with nested relations for domain and range,
5330 interchange the range of the domain with the domain of the range.
5334 #include <isl/space.h>
5335 __isl_give isl_space *isl_space_curry(
5336 __isl_take isl_space *space);
5337 __isl_give isl_space *isl_space_uncurry(
5338 __isl_take isl_space *space);
5340 #include <isl/map.h>
5341 __isl_give isl_basic_map *isl_basic_map_curry(
5342 __isl_take isl_basic_map *bmap);
5343 __isl_give isl_basic_map *isl_basic_map_uncurry(
5344 __isl_take isl_basic_map *bmap);
5345 __isl_give isl_map *isl_map_curry(
5346 __isl_take isl_map *map);
5347 __isl_give isl_map *isl_map_uncurry(
5348 __isl_take isl_map *map);
5350 #include <isl/union_map.h>
5351 __isl_give isl_union_map *isl_union_map_curry(
5352 __isl_take isl_union_map *umap);
5353 __isl_give isl_union_map *isl_union_map_uncurry(
5354 __isl_take isl_union_map *umap);
5356 Given a relation with a nested relation for domain,
5357 the C<curry> functions
5358 move the range of the nested relation out of the domain
5359 and use it as the domain of a nested relation in the range,
5360 with the original range as range of this nested relation.
5361 The C<uncurry> functions perform the inverse operation.
5363 #include <isl/space.h>
5364 __isl_give isl_space *isl_space_range_curry(
5365 __isl_take isl_space *space);
5367 #include <isl/map.h>
5368 __isl_give isl_map *isl_map_range_curry(
5369 __isl_take isl_map *map);
5371 #include <isl/union_map.h>
5372 __isl_give isl_union_map *isl_union_map_range_curry(
5373 __isl_take isl_union_map *umap);
5375 These functions apply the currying to the relation that
5376 is nested inside the range of the input.
5378 =item * Aligning parameters
5380 Change the order of the parameters of the given set, relation
5382 such that the first parameters match those of C<model>.
5383 This may involve the introduction of extra parameters.
5384 All parameters need to be named.
5386 #include <isl/space.h>
5387 __isl_give isl_space *isl_space_align_params(
5388 __isl_take isl_space *space1,
5389 __isl_take isl_space *space2)
5391 #include <isl/set.h>
5392 __isl_give isl_basic_set *isl_basic_set_align_params(
5393 __isl_take isl_basic_set *bset,
5394 __isl_take isl_space *model);
5395 __isl_give isl_set *isl_set_align_params(
5396 __isl_take isl_set *set,
5397 __isl_take isl_space *model);
5399 #include <isl/map.h>
5400 __isl_give isl_basic_map *isl_basic_map_align_params(
5401 __isl_take isl_basic_map *bmap,
5402 __isl_take isl_space *model);
5403 __isl_give isl_map *isl_map_align_params(
5404 __isl_take isl_map *map,
5405 __isl_take isl_space *model);
5407 #include <isl/val.h>
5408 __isl_give isl_multi_val *isl_multi_val_align_params(
5409 __isl_take isl_multi_val *mv,
5410 __isl_take isl_space *model);
5412 #include <isl/aff.h>
5413 __isl_give isl_aff *isl_aff_align_params(
5414 __isl_take isl_aff *aff,
5415 __isl_take isl_space *model);
5416 __isl_give isl_multi_aff *isl_multi_aff_align_params(
5417 __isl_take isl_multi_aff *multi,
5418 __isl_take isl_space *model);
5419 __isl_give isl_pw_aff *isl_pw_aff_align_params(
5420 __isl_take isl_pw_aff *pwaff,
5421 __isl_take isl_space *model);
5422 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
5423 __isl_take isl_pw_multi_aff *pma,
5424 __isl_take isl_space *model);
5425 __isl_give isl_union_pw_aff *
5426 isl_union_pw_aff_align_params(
5427 __isl_take isl_union_pw_aff *upa,
5428 __isl_take isl_space *model);
5429 __isl_give isl_union_pw_multi_aff *
5430 isl_union_pw_multi_aff_align_params(
5431 __isl_take isl_union_pw_multi_aff *upma,
5432 __isl_take isl_space *model);
5433 __isl_give isl_multi_union_pw_aff *
5434 isl_multi_union_pw_aff_align_params(
5435 __isl_take isl_multi_union_pw_aff *mupa,
5436 __isl_take isl_space *model);
5438 #include <isl/polynomial.h>
5439 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5440 __isl_take isl_qpolynomial *qp,
5441 __isl_take isl_space *model);
5443 =item * Unary Arithmetic Operations
5445 #include <isl/set.h>
5446 __isl_give isl_set *isl_set_neg(
5447 __isl_take isl_set *set);
5448 #include <isl/map.h>
5449 __isl_give isl_map *isl_map_neg(
5450 __isl_take isl_map *map);
5452 C<isl_set_neg> constructs a set containing the opposites of
5453 the elements in its argument.
5454 The domain of the result of C<isl_map_neg> is the same
5455 as the domain of its argument. The corresponding range
5456 elements are the opposites of the corresponding range
5457 elements in the argument.
5459 #include <isl/val.h>
5460 __isl_give isl_multi_val *isl_multi_val_neg(
5461 __isl_take isl_multi_val *mv);
5463 #include <isl/aff.h>
5464 __isl_give isl_aff *isl_aff_neg(
5465 __isl_take isl_aff *aff);
5466 __isl_give isl_multi_aff *isl_multi_aff_neg(
5467 __isl_take isl_multi_aff *ma);
5468 __isl_give isl_pw_aff *isl_pw_aff_neg(
5469 __isl_take isl_pw_aff *pwaff);
5470 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
5471 __isl_take isl_pw_multi_aff *pma);
5472 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
5473 __isl_take isl_multi_pw_aff *mpa);
5474 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
5475 __isl_take isl_union_pw_aff *upa);
5476 __isl_give isl_union_pw_multi_aff *
5477 isl_union_pw_multi_aff_neg(
5478 __isl_take isl_union_pw_multi_aff *upma);
5479 __isl_give isl_multi_union_pw_aff *
5480 isl_multi_union_pw_aff_neg(
5481 __isl_take isl_multi_union_pw_aff *mupa);
5482 __isl_give isl_aff *isl_aff_ceil(
5483 __isl_take isl_aff *aff);
5484 __isl_give isl_pw_aff *isl_pw_aff_ceil(
5485 __isl_take isl_pw_aff *pwaff);
5486 __isl_give isl_aff *isl_aff_floor(
5487 __isl_take isl_aff *aff);
5488 __isl_give isl_multi_aff *isl_multi_aff_floor(
5489 __isl_take isl_multi_aff *ma);
5490 __isl_give isl_pw_aff *isl_pw_aff_floor(
5491 __isl_take isl_pw_aff *pwaff);
5492 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
5493 __isl_take isl_union_pw_aff *upa);
5494 __isl_give isl_multi_union_pw_aff *
5495 isl_multi_union_pw_aff_floor(
5496 __isl_take isl_multi_union_pw_aff *mupa);
5498 #include <isl/aff.h>
5499 __isl_give isl_pw_aff *isl_pw_aff_list_min(
5500 __isl_take isl_pw_aff_list *list);
5501 __isl_give isl_pw_aff *isl_pw_aff_list_max(
5502 __isl_take isl_pw_aff_list *list);
5504 #include <isl/polynomial.h>
5505 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5506 __isl_take isl_qpolynomial *qp);
5507 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5508 __isl_take isl_pw_qpolynomial *pwqp);
5509 __isl_give isl_union_pw_qpolynomial *
5510 isl_union_pw_qpolynomial_neg(
5511 __isl_take isl_union_pw_qpolynomial *upwqp);
5512 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5513 __isl_take isl_qpolynomial *qp,
5515 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5516 __isl_take isl_pw_qpolynomial *pwqp,
5521 The following functions evaluate a function in a point.
5523 #include <isl/polynomial.h>
5524 __isl_give isl_val *isl_pw_qpolynomial_eval(
5525 __isl_take isl_pw_qpolynomial *pwqp,
5526 __isl_take isl_point *pnt);
5527 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5528 __isl_take isl_pw_qpolynomial_fold *pwf,
5529 __isl_take isl_point *pnt);
5530 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5531 __isl_take isl_union_pw_qpolynomial *upwqp,
5532 __isl_take isl_point *pnt);
5533 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5534 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5535 __isl_take isl_point *pnt);
5537 =item * Dimension manipulation
5539 It is usually not advisable to directly change the (input or output)
5540 space of a set or a relation as this removes the name and the internal
5541 structure of the space. However, the functions below can be useful
5542 to add new parameters, assuming
5543 C<isl_set_align_params> and C<isl_map_align_params>
5546 #include <isl/space.h>
5547 __isl_give isl_space *isl_space_add_dims(
5548 __isl_take isl_space *space,
5549 enum isl_dim_type type, unsigned n);
5550 __isl_give isl_space *isl_space_insert_dims(
5551 __isl_take isl_space *space,
5552 enum isl_dim_type type, unsigned pos, unsigned n);
5553 __isl_give isl_space *isl_space_drop_dims(
5554 __isl_take isl_space *space,
5555 enum isl_dim_type type, unsigned first, unsigned n);
5556 __isl_give isl_space *isl_space_move_dims(
5557 __isl_take isl_space *space,
5558 enum isl_dim_type dst_type, unsigned dst_pos,
5559 enum isl_dim_type src_type, unsigned src_pos,
5562 #include <isl/local_space.h>
5563 __isl_give isl_local_space *isl_local_space_add_dims(
5564 __isl_take isl_local_space *ls,
5565 enum isl_dim_type type, unsigned n);
5566 __isl_give isl_local_space *isl_local_space_insert_dims(
5567 __isl_take isl_local_space *ls,
5568 enum isl_dim_type type, unsigned first, unsigned n);
5569 __isl_give isl_local_space *isl_local_space_drop_dims(
5570 __isl_take isl_local_space *ls,
5571 enum isl_dim_type type, unsigned first, unsigned n);
5573 #include <isl/set.h>
5574 __isl_give isl_basic_set *isl_basic_set_add_dims(
5575 __isl_take isl_basic_set *bset,
5576 enum isl_dim_type type, unsigned n);
5577 __isl_give isl_set *isl_set_add_dims(
5578 __isl_take isl_set *set,
5579 enum isl_dim_type type, unsigned n);
5580 __isl_give isl_basic_set *isl_basic_set_insert_dims(
5581 __isl_take isl_basic_set *bset,
5582 enum isl_dim_type type, unsigned pos,
5584 __isl_give isl_set *isl_set_insert_dims(
5585 __isl_take isl_set *set,
5586 enum isl_dim_type type, unsigned pos, unsigned n);
5587 __isl_give isl_basic_set *isl_basic_set_move_dims(
5588 __isl_take isl_basic_set *bset,
5589 enum isl_dim_type dst_type, unsigned dst_pos,
5590 enum isl_dim_type src_type, unsigned src_pos,
5592 __isl_give isl_set *isl_set_move_dims(
5593 __isl_take isl_set *set,
5594 enum isl_dim_type dst_type, unsigned dst_pos,
5595 enum isl_dim_type src_type, unsigned src_pos,
5598 #include <isl/map.h>
5599 __isl_give isl_basic_map *isl_basic_map_add_dims(
5600 __isl_take isl_basic_map *bmap,
5601 enum isl_dim_type type, unsigned n);
5602 __isl_give isl_map *isl_map_add_dims(
5603 __isl_take isl_map *map,
5604 enum isl_dim_type type, unsigned n);
5605 __isl_give isl_basic_map *isl_basic_map_insert_dims(
5606 __isl_take isl_basic_map *bmap,
5607 enum isl_dim_type type, unsigned pos,
5609 __isl_give isl_map *isl_map_insert_dims(
5610 __isl_take isl_map *map,
5611 enum isl_dim_type type, unsigned pos, unsigned n);
5612 __isl_give isl_basic_map *isl_basic_map_move_dims(
5613 __isl_take isl_basic_map *bmap,
5614 enum isl_dim_type dst_type, unsigned dst_pos,
5615 enum isl_dim_type src_type, unsigned src_pos,
5617 __isl_give isl_map *isl_map_move_dims(
5618 __isl_take isl_map *map,
5619 enum isl_dim_type dst_type, unsigned dst_pos,
5620 enum isl_dim_type src_type, unsigned src_pos,
5623 #include <isl/val.h>
5624 __isl_give isl_multi_val *isl_multi_val_insert_dims(
5625 __isl_take isl_multi_val *mv,
5626 enum isl_dim_type type, unsigned first, unsigned n);
5627 __isl_give isl_multi_val *isl_multi_val_add_dims(
5628 __isl_take isl_multi_val *mv,
5629 enum isl_dim_type type, unsigned n);
5630 __isl_give isl_multi_val *isl_multi_val_drop_dims(
5631 __isl_take isl_multi_val *mv,
5632 enum isl_dim_type type, unsigned first, unsigned n);
5634 #include <isl/aff.h>
5635 __isl_give isl_aff *isl_aff_insert_dims(
5636 __isl_take isl_aff *aff,
5637 enum isl_dim_type type, unsigned first, unsigned n);
5638 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
5639 __isl_take isl_multi_aff *ma,
5640 enum isl_dim_type type, unsigned first, unsigned n);
5641 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
5642 __isl_take isl_pw_aff *pwaff,
5643 enum isl_dim_type type, unsigned first, unsigned n);
5644 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
5645 __isl_take isl_multi_pw_aff *mpa,
5646 enum isl_dim_type type, unsigned first, unsigned n);
5647 __isl_give isl_aff *isl_aff_add_dims(
5648 __isl_take isl_aff *aff,
5649 enum isl_dim_type type, unsigned n);
5650 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
5651 __isl_take isl_multi_aff *ma,
5652 enum isl_dim_type type, unsigned n);
5653 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
5654 __isl_take isl_pw_aff *pwaff,
5655 enum isl_dim_type type, unsigned n);
5656 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
5657 __isl_take isl_multi_pw_aff *mpa,
5658 enum isl_dim_type type, unsigned n);
5659 __isl_give isl_aff *isl_aff_drop_dims(
5660 __isl_take isl_aff *aff,
5661 enum isl_dim_type type, unsigned first, unsigned n);
5662 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
5663 __isl_take isl_multi_aff *maff,
5664 enum isl_dim_type type, unsigned first, unsigned n);
5665 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
5666 __isl_take isl_pw_aff *pwaff,
5667 enum isl_dim_type type, unsigned first, unsigned n);
5668 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
5669 __isl_take isl_pw_multi_aff *pma,
5670 enum isl_dim_type type, unsigned first, unsigned n);
5671 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
5672 __isl_take isl_union_pw_aff *upa,
5673 enum isl_dim_type type, unsigned first, unsigned n);
5674 __isl_give isl_union_pw_multi_aff *
5675 isl_union_pw_multi_aff_drop_dims(
5676 __isl_take isl_union_pw_multi_aff *upma,
5677 enum isl_dim_type type,
5678 unsigned first, unsigned n);
5679 __isl_give isl_multi_union_pw_aff *
5680 isl_multi_union_pw_aff_drop_dims(
5681 __isl_take isl_multi_union_pw_aff *mupa,
5682 enum isl_dim_type type, unsigned first,
5684 __isl_give isl_aff *isl_aff_move_dims(
5685 __isl_take isl_aff *aff,
5686 enum isl_dim_type dst_type, unsigned dst_pos,
5687 enum isl_dim_type src_type, unsigned src_pos,
5689 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
5690 __isl_take isl_multi_aff *ma,
5691 enum isl_dim_type dst_type, unsigned dst_pos,
5692 enum isl_dim_type src_type, unsigned src_pos,
5694 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
5695 __isl_take isl_pw_aff *pa,
5696 enum isl_dim_type dst_type, unsigned dst_pos,
5697 enum isl_dim_type src_type, unsigned src_pos,
5699 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
5700 __isl_take isl_multi_pw_aff *pma,
5701 enum isl_dim_type dst_type, unsigned dst_pos,
5702 enum isl_dim_type src_type, unsigned src_pos,
5705 #include <isl/polynomial.h>
5706 __isl_give isl_union_pw_qpolynomial *
5707 isl_union_pw_qpolynomial_drop_dims(
5708 __isl_take isl_union_pw_qpolynomial *upwqp,
5709 enum isl_dim_type type,
5710 unsigned first, unsigned n);
5711 __isl_give isl_union_pw_qpolynomial_fold *
5712 isl_union_pw_qpolynomial_fold_drop_dims(
5713 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5714 enum isl_dim_type type,
5715 unsigned first, unsigned n);
5717 The operations on union expressions can only manipulate parameters.
5721 =head2 Binary Operations
5723 The two arguments of a binary operation not only need to live
5724 in the same C<isl_ctx>, they currently also need to have
5725 the same (number of) parameters.
5727 =head3 Basic Operations
5731 =item * Intersection
5733 #include <isl/local_space.h>
5734 __isl_give isl_local_space *isl_local_space_intersect(
5735 __isl_take isl_local_space *ls1,
5736 __isl_take isl_local_space *ls2);
5738 #include <isl/set.h>
5739 __isl_give isl_basic_set *isl_basic_set_intersect_params(
5740 __isl_take isl_basic_set *bset1,
5741 __isl_take isl_basic_set *bset2);
5742 __isl_give isl_basic_set *isl_basic_set_intersect(
5743 __isl_take isl_basic_set *bset1,
5744 __isl_take isl_basic_set *bset2);
5745 __isl_give isl_basic_set *isl_basic_set_list_intersect(
5746 __isl_take struct isl_basic_set_list *list);
5747 __isl_give isl_set *isl_set_intersect_params(
5748 __isl_take isl_set *set,
5749 __isl_take isl_set *params);
5750 __isl_give isl_set *isl_set_intersect(
5751 __isl_take isl_set *set1,
5752 __isl_take isl_set *set2);
5754 #include <isl/map.h>
5755 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
5756 __isl_take isl_basic_map *bmap,
5757 __isl_take isl_basic_set *bset);
5758 __isl_give isl_basic_map *isl_basic_map_intersect_range(
5759 __isl_take isl_basic_map *bmap,
5760 __isl_take isl_basic_set *bset);
5761 __isl_give isl_basic_map *isl_basic_map_intersect(
5762 __isl_take isl_basic_map *bmap1,
5763 __isl_take isl_basic_map *bmap2);
5764 __isl_give isl_basic_map *isl_basic_map_list_intersect(
5765 __isl_take isl_basic_map_list *list);
5766 __isl_give isl_map *isl_map_intersect_params(
5767 __isl_take isl_map *map,
5768 __isl_take isl_set *params);
5769 __isl_give isl_map *isl_map_intersect_domain(
5770 __isl_take isl_map *map,
5771 __isl_take isl_set *set);
5772 __isl_give isl_map *isl_map_intersect_range(
5773 __isl_take isl_map *map,
5774 __isl_take isl_set *set);
5775 __isl_give isl_map *isl_map_intersect(
5776 __isl_take isl_map *map1,
5777 __isl_take isl_map *map2);
5779 #include <isl/union_set.h>
5780 __isl_give isl_union_set *isl_union_set_intersect_params(
5781 __isl_take isl_union_set *uset,
5782 __isl_take isl_set *set);
5783 __isl_give isl_union_set *isl_union_set_intersect(
5784 __isl_take isl_union_set *uset1,
5785 __isl_take isl_union_set *uset2);
5787 #include <isl/union_map.h>
5788 __isl_give isl_union_map *isl_union_map_intersect_params(
5789 __isl_take isl_union_map *umap,
5790 __isl_take isl_set *set);
5791 __isl_give isl_union_map *isl_union_map_intersect_domain(
5792 __isl_take isl_union_map *umap,
5793 __isl_take isl_union_set *uset);
5794 __isl_give isl_union_map *isl_union_map_intersect_range(
5795 __isl_take isl_union_map *umap,
5796 __isl_take isl_union_set *uset);
5797 __isl_give isl_union_map *isl_union_map_intersect(
5798 __isl_take isl_union_map *umap1,
5799 __isl_take isl_union_map *umap2);
5801 #include <isl/aff.h>
5802 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
5803 __isl_take isl_pw_aff *pa,
5804 __isl_take isl_set *set);
5805 __isl_give isl_multi_pw_aff *
5806 isl_multi_pw_aff_intersect_domain(
5807 __isl_take isl_multi_pw_aff *mpa,
5808 __isl_take isl_set *domain);
5809 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
5810 __isl_take isl_pw_multi_aff *pma,
5811 __isl_take isl_set *set);
5812 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
5813 __isl_take isl_union_pw_aff *upa,
5814 __isl_take isl_union_set *uset);
5815 __isl_give isl_union_pw_multi_aff *
5816 isl_union_pw_multi_aff_intersect_domain(
5817 __isl_take isl_union_pw_multi_aff *upma,
5818 __isl_take isl_union_set *uset);
5819 __isl_give isl_multi_union_pw_aff *
5820 isl_multi_union_pw_aff_intersect_domain(
5821 __isl_take isl_multi_union_pw_aff *mupa,
5822 __isl_take isl_union_set *uset);
5823 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
5824 __isl_take isl_pw_aff *pa,
5825 __isl_take isl_set *set);
5826 __isl_give isl_multi_pw_aff *
5827 isl_multi_pw_aff_intersect_params(
5828 __isl_take isl_multi_pw_aff *mpa,
5829 __isl_take isl_set *set);
5830 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
5831 __isl_take isl_pw_multi_aff *pma,
5832 __isl_take isl_set *set);
5833 __isl_give isl_union_pw_aff *
5834 isl_union_pw_aff_intersect_params(
5835 __isl_take isl_union_pw_aff *upa,
5836 __isl_give isl_union_pw_multi_aff *
5837 isl_union_pw_multi_aff_intersect_params(
5838 __isl_take isl_union_pw_multi_aff *upma,
5839 __isl_take isl_set *set);
5840 __isl_give isl_multi_union_pw_aff *
5841 isl_multi_union_pw_aff_intersect_params(
5842 __isl_take isl_multi_union_pw_aff *mupa,
5843 __isl_take isl_set *params);
5844 isl_multi_union_pw_aff_intersect_range(
5845 __isl_take isl_multi_union_pw_aff *mupa,
5846 __isl_take isl_set *set);
5848 #include <isl/polynomial.h>
5849 __isl_give isl_pw_qpolynomial *
5850 isl_pw_qpolynomial_intersect_domain(
5851 __isl_take isl_pw_qpolynomial *pwpq,
5852 __isl_take isl_set *set);
5853 __isl_give isl_union_pw_qpolynomial *
5854 isl_union_pw_qpolynomial_intersect_domain(
5855 __isl_take isl_union_pw_qpolynomial *upwpq,
5856 __isl_take isl_union_set *uset);
5857 __isl_give isl_union_pw_qpolynomial_fold *
5858 isl_union_pw_qpolynomial_fold_intersect_domain(
5859 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5860 __isl_take isl_union_set *uset);
5861 __isl_give isl_pw_qpolynomial *
5862 isl_pw_qpolynomial_intersect_params(
5863 __isl_take isl_pw_qpolynomial *pwpq,
5864 __isl_take isl_set *set);
5865 __isl_give isl_pw_qpolynomial_fold *
5866 isl_pw_qpolynomial_fold_intersect_params(
5867 __isl_take isl_pw_qpolynomial_fold *pwf,
5868 __isl_take isl_set *set);
5869 __isl_give isl_union_pw_qpolynomial *
5870 isl_union_pw_qpolynomial_intersect_params(
5871 __isl_take isl_union_pw_qpolynomial *upwpq,
5872 __isl_take isl_set *set);
5873 __isl_give isl_union_pw_qpolynomial_fold *
5874 isl_union_pw_qpolynomial_fold_intersect_params(
5875 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5876 __isl_take isl_set *set);
5878 The second argument to the C<_params> functions needs to be
5879 a parametric (basic) set. For the other functions, a parametric set
5880 for either argument is only allowed if the other argument is
5881 a parametric set as well.
5882 The list passed to C<isl_basic_set_list_intersect> needs to have
5883 at least one element and all elements need to live in the same space.
5884 The function C<isl_multi_union_pw_aff_intersect_range>
5885 restricts the input function to those shared domain elements
5886 that map to the specified range.
5890 #include <isl/set.h>
5891 __isl_give isl_set *isl_basic_set_union(
5892 __isl_take isl_basic_set *bset1,
5893 __isl_take isl_basic_set *bset2);
5894 __isl_give isl_set *isl_set_union(
5895 __isl_take isl_set *set1,
5896 __isl_take isl_set *set2);
5897 __isl_give isl_set *isl_set_list_union(
5898 __isl_take isl_set_list *list);
5900 #include <isl/map.h>
5901 __isl_give isl_map *isl_basic_map_union(
5902 __isl_take isl_basic_map *bmap1,
5903 __isl_take isl_basic_map *bmap2);
5904 __isl_give isl_map *isl_map_union(
5905 __isl_take isl_map *map1,
5906 __isl_take isl_map *map2);
5908 #include <isl/union_set.h>
5909 __isl_give isl_union_set *isl_union_set_union(
5910 __isl_take isl_union_set *uset1,
5911 __isl_take isl_union_set *uset2);
5912 __isl_give isl_union_set *isl_union_set_list_union(
5913 __isl_take isl_union_set_list *list);
5915 #include <isl/union_map.h>
5916 __isl_give isl_union_map *isl_union_map_union(
5917 __isl_take isl_union_map *umap1,
5918 __isl_take isl_union_map *umap2);
5920 The list passed to C<isl_set_list_union> needs to have
5921 at least one element and all elements need to live in the same space.
5923 =item * Set difference
5925 #include <isl/set.h>
5926 __isl_give isl_set *isl_set_subtract(
5927 __isl_take isl_set *set1,
5928 __isl_take isl_set *set2);
5930 #include <isl/map.h>
5931 __isl_give isl_map *isl_map_subtract(
5932 __isl_take isl_map *map1,
5933 __isl_take isl_map *map2);
5934 __isl_give isl_map *isl_map_subtract_domain(
5935 __isl_take isl_map *map,
5936 __isl_take isl_set *dom);
5937 __isl_give isl_map *isl_map_subtract_range(
5938 __isl_take isl_map *map,
5939 __isl_take isl_set *dom);
5941 #include <isl/union_set.h>
5942 __isl_give isl_union_set *isl_union_set_subtract(
5943 __isl_take isl_union_set *uset1,
5944 __isl_take isl_union_set *uset2);
5946 #include <isl/union_map.h>
5947 __isl_give isl_union_map *isl_union_map_subtract(
5948 __isl_take isl_union_map *umap1,
5949 __isl_take isl_union_map *umap2);
5950 __isl_give isl_union_map *isl_union_map_subtract_domain(
5951 __isl_take isl_union_map *umap,
5952 __isl_take isl_union_set *dom);
5953 __isl_give isl_union_map *isl_union_map_subtract_range(
5954 __isl_take isl_union_map *umap,
5955 __isl_take isl_union_set *dom);
5957 #include <isl/aff.h>
5958 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
5959 __isl_take isl_pw_aff *pa,
5960 __isl_take isl_set *set);
5961 __isl_give isl_pw_multi_aff *
5962 isl_pw_multi_aff_subtract_domain(
5963 __isl_take isl_pw_multi_aff *pma,
5964 __isl_take isl_set *set);
5965 __isl_give isl_union_pw_aff *
5966 isl_union_pw_aff_subtract_domain(
5967 __isl_take isl_union_pw_aff *upa,
5968 __isl_take isl_union_set *uset);
5969 __isl_give isl_union_pw_multi_aff *
5970 isl_union_pw_multi_aff_subtract_domain(
5971 __isl_take isl_union_pw_multi_aff *upma,
5972 __isl_take isl_set *set);
5974 #include <isl/polynomial.h>
5975 __isl_give isl_pw_qpolynomial *
5976 isl_pw_qpolynomial_subtract_domain(
5977 __isl_take isl_pw_qpolynomial *pwpq,
5978 __isl_take isl_set *set);
5979 __isl_give isl_pw_qpolynomial_fold *
5980 isl_pw_qpolynomial_fold_subtract_domain(
5981 __isl_take isl_pw_qpolynomial_fold *pwf,
5982 __isl_take isl_set *set);
5983 __isl_give isl_union_pw_qpolynomial *
5984 isl_union_pw_qpolynomial_subtract_domain(
5985 __isl_take isl_union_pw_qpolynomial *upwpq,
5986 __isl_take isl_union_set *uset);
5987 __isl_give isl_union_pw_qpolynomial_fold *
5988 isl_union_pw_qpolynomial_fold_subtract_domain(
5989 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5990 __isl_take isl_union_set *uset);
5994 #include <isl/space.h>
5995 __isl_give isl_space *isl_space_join(
5996 __isl_take isl_space *left,
5997 __isl_take isl_space *right);
5999 #include <isl/map.h>
6000 __isl_give isl_basic_set *isl_basic_set_apply(
6001 __isl_take isl_basic_set *bset,
6002 __isl_take isl_basic_map *bmap);
6003 __isl_give isl_set *isl_set_apply(
6004 __isl_take isl_set *set,
6005 __isl_take isl_map *map);
6006 __isl_give isl_union_set *isl_union_set_apply(
6007 __isl_take isl_union_set *uset,
6008 __isl_take isl_union_map *umap);
6009 __isl_give isl_basic_map *isl_basic_map_apply_domain(
6010 __isl_take isl_basic_map *bmap1,
6011 __isl_take isl_basic_map *bmap2);
6012 __isl_give isl_basic_map *isl_basic_map_apply_range(
6013 __isl_take isl_basic_map *bmap1,
6014 __isl_take isl_basic_map *bmap2);
6015 __isl_give isl_map *isl_map_apply_domain(
6016 __isl_take isl_map *map1,
6017 __isl_take isl_map *map2);
6018 __isl_give isl_map *isl_map_apply_range(
6019 __isl_take isl_map *map1,
6020 __isl_take isl_map *map2);
6022 #include <isl/union_map.h>
6023 __isl_give isl_union_map *isl_union_map_apply_domain(
6024 __isl_take isl_union_map *umap1,
6025 __isl_take isl_union_map *umap2);
6026 __isl_give isl_union_map *isl_union_map_apply_range(
6027 __isl_take isl_union_map *umap1,
6028 __isl_take isl_union_map *umap2);
6030 #include <isl/aff.h>
6031 __isl_give isl_union_pw_aff *
6032 isl_multi_union_pw_aff_apply_aff(
6033 __isl_take isl_multi_union_pw_aff *mupa,
6034 __isl_take isl_aff *aff);
6035 __isl_give isl_union_pw_aff *
6036 isl_multi_union_pw_aff_apply_pw_aff(
6037 __isl_take isl_multi_union_pw_aff *mupa,
6038 __isl_take isl_pw_aff *pa);
6039 __isl_give isl_multi_union_pw_aff *
6040 isl_multi_union_pw_aff_apply_multi_aff(
6041 __isl_take isl_multi_union_pw_aff *mupa,
6042 __isl_take isl_multi_aff *ma);
6043 __isl_give isl_multi_union_pw_aff *
6044 isl_multi_union_pw_aff_apply_pw_multi_aff(
6045 __isl_take isl_multi_union_pw_aff *mupa,
6046 __isl_take isl_pw_multi_aff *pma);
6048 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
6049 over the shared domain of the elements of the input. The dimension is
6050 required to be greater than zero.
6051 The C<isl_multi_union_pw_aff> argument of
6052 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
6053 but only if the range of the C<isl_multi_aff> argument
6054 is also zero-dimensional.
6055 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
6057 #include <isl/polynomial.h>
6058 __isl_give isl_pw_qpolynomial_fold *
6059 isl_set_apply_pw_qpolynomial_fold(
6060 __isl_take isl_set *set,
6061 __isl_take isl_pw_qpolynomial_fold *pwf,
6063 __isl_give isl_pw_qpolynomial_fold *
6064 isl_map_apply_pw_qpolynomial_fold(
6065 __isl_take isl_map *map,
6066 __isl_take isl_pw_qpolynomial_fold *pwf,
6068 __isl_give isl_union_pw_qpolynomial_fold *
6069 isl_union_set_apply_union_pw_qpolynomial_fold(
6070 __isl_take isl_union_set *uset,
6071 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6073 __isl_give isl_union_pw_qpolynomial_fold *
6074 isl_union_map_apply_union_pw_qpolynomial_fold(
6075 __isl_take isl_union_map *umap,
6076 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6079 The functions taking a map
6080 compose the given map with the given piecewise quasipolynomial reduction.
6081 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
6082 over all elements in the intersection of the range of the map
6083 and the domain of the piecewise quasipolynomial reduction
6084 as a function of an element in the domain of the map.
6085 The functions taking a set compute a bound over all elements in the
6086 intersection of the set and the domain of the
6087 piecewise quasipolynomial reduction.
6091 #include <isl/set.h>
6092 __isl_give isl_basic_set *
6093 isl_basic_set_preimage_multi_aff(
6094 __isl_take isl_basic_set *bset,
6095 __isl_take isl_multi_aff *ma);
6096 __isl_give isl_set *isl_set_preimage_multi_aff(
6097 __isl_take isl_set *set,
6098 __isl_take isl_multi_aff *ma);
6099 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
6100 __isl_take isl_set *set,
6101 __isl_take isl_pw_multi_aff *pma);
6102 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
6103 __isl_take isl_set *set,
6104 __isl_take isl_multi_pw_aff *mpa);
6106 #include <isl/union_set.h>
6107 __isl_give isl_union_set *
6108 isl_union_set_preimage_multi_aff(
6109 __isl_take isl_union_set *uset,
6110 __isl_take isl_multi_aff *ma);
6111 __isl_give isl_union_set *
6112 isl_union_set_preimage_pw_multi_aff(
6113 __isl_take isl_union_set *uset,
6114 __isl_take isl_pw_multi_aff *pma);
6115 __isl_give isl_union_set *
6116 isl_union_set_preimage_union_pw_multi_aff(
6117 __isl_take isl_union_set *uset,
6118 __isl_take isl_union_pw_multi_aff *upma);
6120 #include <isl/map.h>
6121 __isl_give isl_basic_map *
6122 isl_basic_map_preimage_domain_multi_aff(
6123 __isl_take isl_basic_map *bmap,
6124 __isl_take isl_multi_aff *ma);
6125 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
6126 __isl_take isl_map *map,
6127 __isl_take isl_multi_aff *ma);
6128 __isl_give isl_map *isl_map_preimage_range_multi_aff(
6129 __isl_take isl_map *map,
6130 __isl_take isl_multi_aff *ma);
6131 __isl_give isl_map *
6132 isl_map_preimage_domain_pw_multi_aff(
6133 __isl_take isl_map *map,
6134 __isl_take isl_pw_multi_aff *pma);
6135 __isl_give isl_map *
6136 isl_map_preimage_range_pw_multi_aff(
6137 __isl_take isl_map *map,
6138 __isl_take isl_pw_multi_aff *pma);
6139 __isl_give isl_map *
6140 isl_map_preimage_domain_multi_pw_aff(
6141 __isl_take isl_map *map,
6142 __isl_take isl_multi_pw_aff *mpa);
6143 __isl_give isl_basic_map *
6144 isl_basic_map_preimage_range_multi_aff(
6145 __isl_take isl_basic_map *bmap,
6146 __isl_take isl_multi_aff *ma);
6148 #include <isl/union_map.h>
6149 __isl_give isl_union_map *
6150 isl_union_map_preimage_domain_multi_aff(
6151 __isl_take isl_union_map *umap,
6152 __isl_take isl_multi_aff *ma);
6153 __isl_give isl_union_map *
6154 isl_union_map_preimage_range_multi_aff(
6155 __isl_take isl_union_map *umap,
6156 __isl_take isl_multi_aff *ma);
6157 __isl_give isl_union_map *
6158 isl_union_map_preimage_domain_pw_multi_aff(
6159 __isl_take isl_union_map *umap,
6160 __isl_take isl_pw_multi_aff *pma);
6161 __isl_give isl_union_map *
6162 isl_union_map_preimage_range_pw_multi_aff(
6163 __isl_take isl_union_map *umap,
6164 __isl_take isl_pw_multi_aff *pma);
6165 __isl_give isl_union_map *
6166 isl_union_map_preimage_domain_union_pw_multi_aff(
6167 __isl_take isl_union_map *umap,
6168 __isl_take isl_union_pw_multi_aff *upma);
6169 __isl_give isl_union_map *
6170 isl_union_map_preimage_range_union_pw_multi_aff(
6171 __isl_take isl_union_map *umap,
6172 __isl_take isl_union_pw_multi_aff *upma);
6174 These functions compute the preimage of the given set or map domain/range under
6175 the given function. In other words, the expression is plugged
6176 into the set description or into the domain/range of the map.
6180 #include <isl/aff.h>
6181 __isl_give isl_aff *isl_aff_pullback_aff(
6182 __isl_take isl_aff *aff1,
6183 __isl_take isl_aff *aff2);
6184 __isl_give isl_aff *isl_aff_pullback_multi_aff(
6185 __isl_take isl_aff *aff,
6186 __isl_take isl_multi_aff *ma);
6187 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
6188 __isl_take isl_pw_aff *pa,
6189 __isl_take isl_multi_aff *ma);
6190 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
6191 __isl_take isl_pw_aff *pa,
6192 __isl_take isl_pw_multi_aff *pma);
6193 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
6194 __isl_take isl_pw_aff *pa,
6195 __isl_take isl_multi_pw_aff *mpa);
6196 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
6197 __isl_take isl_multi_aff *ma1,
6198 __isl_take isl_multi_aff *ma2);
6199 __isl_give isl_pw_multi_aff *
6200 isl_pw_multi_aff_pullback_multi_aff(
6201 __isl_take isl_pw_multi_aff *pma,
6202 __isl_take isl_multi_aff *ma);
6203 __isl_give isl_multi_pw_aff *
6204 isl_multi_pw_aff_pullback_multi_aff(
6205 __isl_take isl_multi_pw_aff *mpa,
6206 __isl_take isl_multi_aff *ma);
6207 __isl_give isl_pw_multi_aff *
6208 isl_pw_multi_aff_pullback_pw_multi_aff(
6209 __isl_take isl_pw_multi_aff *pma1,
6210 __isl_take isl_pw_multi_aff *pma2);
6211 __isl_give isl_multi_pw_aff *
6212 isl_multi_pw_aff_pullback_pw_multi_aff(
6213 __isl_take isl_multi_pw_aff *mpa,
6214 __isl_take isl_pw_multi_aff *pma);
6215 __isl_give isl_multi_pw_aff *
6216 isl_multi_pw_aff_pullback_multi_pw_aff(
6217 __isl_take isl_multi_pw_aff *mpa1,
6218 __isl_take isl_multi_pw_aff *mpa2);
6219 __isl_give isl_union_pw_aff *
6220 isl_union_pw_aff_pullback_union_pw_multi_aff(
6221 __isl_take isl_union_pw_aff *upa,
6222 __isl_take isl_union_pw_multi_aff *upma);
6223 __isl_give isl_union_pw_multi_aff *
6224 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
6225 __isl_take isl_union_pw_multi_aff *upma1,
6226 __isl_take isl_union_pw_multi_aff *upma2);
6227 __isl_give isl_multi_union_pw_aff *
6228 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
6229 __isl_take isl_multi_union_pw_aff *mupa,
6230 __isl_take isl_union_pw_multi_aff *upma);
6232 These functions precompose the first expression by the second function.
6233 In other words, the second function is plugged
6234 into the first expression.
6238 #include <isl/aff.h>
6239 __isl_give isl_basic_set *isl_aff_eq_basic_set(
6240 __isl_take isl_aff *aff1,
6241 __isl_take isl_aff *aff2);
6242 __isl_give isl_set *isl_aff_eq_set(
6243 __isl_take isl_aff *aff1,
6244 __isl_take isl_aff *aff2);
6245 __isl_give isl_basic_set *isl_aff_le_basic_set(
6246 __isl_take isl_aff *aff1,
6247 __isl_take isl_aff *aff2);
6248 __isl_give isl_set *isl_aff_le_set(
6249 __isl_take isl_aff *aff1,
6250 __isl_take isl_aff *aff2);
6251 __isl_give isl_basic_set *isl_aff_ge_basic_set(
6252 __isl_take isl_aff *aff1,
6253 __isl_take isl_aff *aff2);
6254 __isl_give isl_set *isl_aff_ge_set(
6255 __isl_take isl_aff *aff1,
6256 __isl_take isl_aff *aff2);
6257 __isl_give isl_set *isl_pw_aff_eq_set(
6258 __isl_take isl_pw_aff *pwaff1,
6259 __isl_take isl_pw_aff *pwaff2);
6260 __isl_give isl_set *isl_pw_aff_ne_set(
6261 __isl_take isl_pw_aff *pwaff1,
6262 __isl_take isl_pw_aff *pwaff2);
6263 __isl_give isl_set *isl_pw_aff_le_set(
6264 __isl_take isl_pw_aff *pwaff1,
6265 __isl_take isl_pw_aff *pwaff2);
6266 __isl_give isl_set *isl_pw_aff_lt_set(
6267 __isl_take isl_pw_aff *pwaff1,
6268 __isl_take isl_pw_aff *pwaff2);
6269 __isl_give isl_set *isl_pw_aff_ge_set(
6270 __isl_take isl_pw_aff *pwaff1,
6271 __isl_take isl_pw_aff *pwaff2);
6272 __isl_give isl_set *isl_pw_aff_gt_set(
6273 __isl_take isl_pw_aff *pwaff1,
6274 __isl_take isl_pw_aff *pwaff2);
6276 __isl_give isl_set *isl_multi_aff_lex_le_set(
6277 __isl_take isl_multi_aff *ma1,
6278 __isl_take isl_multi_aff *ma2);
6279 __isl_give isl_set *isl_multi_aff_lex_lt_set(
6280 __isl_take isl_multi_aff *ma1,
6281 __isl_take isl_multi_aff *ma2);
6282 __isl_give isl_set *isl_multi_aff_lex_ge_set(
6283 __isl_take isl_multi_aff *ma1,
6284 __isl_take isl_multi_aff *ma2);
6285 __isl_give isl_set *isl_multi_aff_lex_gt_set(
6286 __isl_take isl_multi_aff *ma1,
6287 __isl_take isl_multi_aff *ma2);
6289 __isl_give isl_set *isl_pw_aff_list_eq_set(
6290 __isl_take isl_pw_aff_list *list1,
6291 __isl_take isl_pw_aff_list *list2);
6292 __isl_give isl_set *isl_pw_aff_list_ne_set(
6293 __isl_take isl_pw_aff_list *list1,
6294 __isl_take isl_pw_aff_list *list2);
6295 __isl_give isl_set *isl_pw_aff_list_le_set(
6296 __isl_take isl_pw_aff_list *list1,
6297 __isl_take isl_pw_aff_list *list2);
6298 __isl_give isl_set *isl_pw_aff_list_lt_set(
6299 __isl_take isl_pw_aff_list *list1,
6300 __isl_take isl_pw_aff_list *list2);
6301 __isl_give isl_set *isl_pw_aff_list_ge_set(
6302 __isl_take isl_pw_aff_list *list1,
6303 __isl_take isl_pw_aff_list *list2);
6304 __isl_give isl_set *isl_pw_aff_list_gt_set(
6305 __isl_take isl_pw_aff_list *list1,
6306 __isl_take isl_pw_aff_list *list2);
6308 The function C<isl_aff_ge_basic_set> returns a basic set
6309 containing those elements in the shared space
6310 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
6311 The function C<isl_pw_aff_ge_set> returns a set
6312 containing those elements in the shared domain
6313 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
6314 greater than or equal to C<pwaff2>.
6315 The function C<isl_multi_aff_lex_le_set> returns a set
6316 containing those elements in the shared domain space
6317 where C<ma1> is lexicographically smaller than or
6319 The functions operating on C<isl_pw_aff_list> apply the corresponding
6320 C<isl_pw_aff> function to each pair of elements in the two lists.
6322 #include <isl/aff.h>
6323 __isl_give isl_map *isl_pw_aff_eq_map(
6324 __isl_take isl_pw_aff *pa1,
6325 __isl_take isl_pw_aff *pa2);
6326 __isl_give isl_map *isl_pw_aff_lt_map(
6327 __isl_take isl_pw_aff *pa1,
6328 __isl_take isl_pw_aff *pa2);
6329 __isl_give isl_map *isl_pw_aff_gt_map(
6330 __isl_take isl_pw_aff *pa1,
6331 __isl_take isl_pw_aff *pa2);
6333 __isl_give isl_map *isl_multi_pw_aff_eq_map(
6334 __isl_take isl_multi_pw_aff *mpa1,
6335 __isl_take isl_multi_pw_aff *mpa2);
6336 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
6337 __isl_take isl_multi_pw_aff *mpa1,
6338 __isl_take isl_multi_pw_aff *mpa2);
6339 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
6340 __isl_take isl_multi_pw_aff *mpa1,
6341 __isl_take isl_multi_pw_aff *mpa2);
6343 These functions return a map between domain elements of the arguments
6344 where the function values satisfy the given relation.
6346 #include <isl/union_map.h>
6347 __isl_give isl_union_map *
6348 isl_union_map_eq_at_multi_union_pw_aff(
6349 __isl_take isl_union_map *umap,
6350 __isl_take isl_multi_union_pw_aff *mupa);
6351 __isl_give isl_union_map *
6352 isl_union_map_lex_lt_at_multi_union_pw_aff(
6353 __isl_take isl_union_map *umap,
6354 __isl_take isl_multi_union_pw_aff *mupa);
6355 __isl_give isl_union_map *
6356 isl_union_map_lex_gt_at_multi_union_pw_aff(
6357 __isl_take isl_union_map *umap,
6358 __isl_take isl_multi_union_pw_aff *mupa);
6360 These functions select the subset of elements in the union map
6361 that have an equal or lexicographically smaller function value.
6363 =item * Cartesian Product
6365 #include <isl/space.h>
6366 __isl_give isl_space *isl_space_product(
6367 __isl_take isl_space *space1,
6368 __isl_take isl_space *space2);
6369 __isl_give isl_space *isl_space_domain_product(
6370 __isl_take isl_space *space1,
6371 __isl_take isl_space *space2);
6372 __isl_give isl_space *isl_space_range_product(
6373 __isl_take isl_space *space1,
6374 __isl_take isl_space *space2);
6377 C<isl_space_product>, C<isl_space_domain_product>
6378 and C<isl_space_range_product> take pairs or relation spaces and
6379 produce a single relations space, where either the domain, the range
6380 or both domain and range are wrapped spaces of relations between
6381 the domains and/or ranges of the input spaces.
6382 If the product is only constructed over the domain or the range
6383 then the ranges or the domains of the inputs should be the same.
6384 The function C<isl_space_product> also accepts a pair of set spaces,
6385 in which case it returns a wrapped space of a relation between the
6388 #include <isl/set.h>
6389 __isl_give isl_set *isl_set_product(
6390 __isl_take isl_set *set1,
6391 __isl_take isl_set *set2);
6393 #include <isl/map.h>
6394 __isl_give isl_basic_map *isl_basic_map_domain_product(
6395 __isl_take isl_basic_map *bmap1,
6396 __isl_take isl_basic_map *bmap2);
6397 __isl_give isl_basic_map *isl_basic_map_range_product(
6398 __isl_take isl_basic_map *bmap1,
6399 __isl_take isl_basic_map *bmap2);
6400 __isl_give isl_basic_map *isl_basic_map_product(
6401 __isl_take isl_basic_map *bmap1,
6402 __isl_take isl_basic_map *bmap2);
6403 __isl_give isl_map *isl_map_domain_product(
6404 __isl_take isl_map *map1,
6405 __isl_take isl_map *map2);
6406 __isl_give isl_map *isl_map_range_product(
6407 __isl_take isl_map *map1,
6408 __isl_take isl_map *map2);
6409 __isl_give isl_map *isl_map_product(
6410 __isl_take isl_map *map1,
6411 __isl_take isl_map *map2);
6413 #include <isl/union_set.h>
6414 __isl_give isl_union_set *isl_union_set_product(
6415 __isl_take isl_union_set *uset1,
6416 __isl_take isl_union_set *uset2);
6418 #include <isl/union_map.h>
6419 __isl_give isl_union_map *isl_union_map_domain_product(
6420 __isl_take isl_union_map *umap1,
6421 __isl_take isl_union_map *umap2);
6422 __isl_give isl_union_map *isl_union_map_range_product(
6423 __isl_take isl_union_map *umap1,
6424 __isl_take isl_union_map *umap2);
6425 __isl_give isl_union_map *isl_union_map_product(
6426 __isl_take isl_union_map *umap1,
6427 __isl_take isl_union_map *umap2);
6429 #include <isl/val.h>
6430 __isl_give isl_multi_val *isl_multi_val_range_product(
6431 __isl_take isl_multi_val *mv1,
6432 __isl_take isl_multi_val *mv2);
6433 __isl_give isl_multi_val *isl_multi_val_product(
6434 __isl_take isl_multi_val *mv1,
6435 __isl_take isl_multi_val *mv2);
6437 #include <isl/aff.h>
6438 __isl_give isl_multi_aff *isl_multi_aff_range_product(
6439 __isl_take isl_multi_aff *ma1,
6440 __isl_take isl_multi_aff *ma2);
6441 __isl_give isl_multi_aff *isl_multi_aff_product(
6442 __isl_take isl_multi_aff *ma1,
6443 __isl_take isl_multi_aff *ma2);
6444 __isl_give isl_multi_pw_aff *
6445 isl_multi_pw_aff_range_product(
6446 __isl_take isl_multi_pw_aff *mpa1,
6447 __isl_take isl_multi_pw_aff *mpa2);
6448 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
6449 __isl_take isl_multi_pw_aff *mpa1,
6450 __isl_take isl_multi_pw_aff *mpa2);
6451 __isl_give isl_pw_multi_aff *
6452 isl_pw_multi_aff_range_product(
6453 __isl_take isl_pw_multi_aff *pma1,
6454 __isl_take isl_pw_multi_aff *pma2);
6455 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
6456 __isl_take isl_pw_multi_aff *pma1,
6457 __isl_take isl_pw_multi_aff *pma2);
6458 __isl_give isl_multi_union_pw_aff *
6459 isl_multi_union_pw_aff_range_product(
6460 __isl_take isl_multi_union_pw_aff *mupa1,
6461 __isl_take isl_multi_union_pw_aff *mupa2);
6463 The above functions compute the cross product of the given
6464 sets, relations or functions. The domains and ranges of the results
6465 are wrapped maps between domains and ranges of the inputs.
6466 To obtain a ``flat'' product, use the following functions
6469 #include <isl/set.h>
6470 __isl_give isl_basic_set *isl_basic_set_flat_product(
6471 __isl_take isl_basic_set *bset1,
6472 __isl_take isl_basic_set *bset2);
6473 __isl_give isl_set *isl_set_flat_product(
6474 __isl_take isl_set *set1,
6475 __isl_take isl_set *set2);
6477 #include <isl/map.h>
6478 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
6479 __isl_take isl_basic_map *bmap1,
6480 __isl_take isl_basic_map *bmap2);
6481 __isl_give isl_map *isl_map_flat_domain_product(
6482 __isl_take isl_map *map1,
6483 __isl_take isl_map *map2);
6484 __isl_give isl_map *isl_map_flat_range_product(
6485 __isl_take isl_map *map1,
6486 __isl_take isl_map *map2);
6487 __isl_give isl_basic_map *isl_basic_map_flat_product(
6488 __isl_take isl_basic_map *bmap1,
6489 __isl_take isl_basic_map *bmap2);
6490 __isl_give isl_map *isl_map_flat_product(
6491 __isl_take isl_map *map1,
6492 __isl_take isl_map *map2);
6494 #include <isl/union_map.h>
6495 __isl_give isl_union_map *
6496 isl_union_map_flat_domain_product(
6497 __isl_take isl_union_map *umap1,
6498 __isl_take isl_union_map *umap2);
6499 __isl_give isl_union_map *
6500 isl_union_map_flat_range_product(
6501 __isl_take isl_union_map *umap1,
6502 __isl_take isl_union_map *umap2);
6504 #include <isl/val.h>
6505 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
6506 __isl_take isl_multi_val *mv1,
6507 __isl_take isl_multi_aff *mv2);
6509 #include <isl/aff.h>
6510 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
6511 __isl_take isl_multi_aff *ma1,
6512 __isl_take isl_multi_aff *ma2);
6513 __isl_give isl_pw_multi_aff *
6514 isl_pw_multi_aff_flat_range_product(
6515 __isl_take isl_pw_multi_aff *pma1,
6516 __isl_take isl_pw_multi_aff *pma2);
6517 __isl_give isl_multi_pw_aff *
6518 isl_multi_pw_aff_flat_range_product(
6519 __isl_take isl_multi_pw_aff *mpa1,
6520 __isl_take isl_multi_pw_aff *mpa2);
6521 __isl_give isl_union_pw_multi_aff *
6522 isl_union_pw_multi_aff_flat_range_product(
6523 __isl_take isl_union_pw_multi_aff *upma1,
6524 __isl_take isl_union_pw_multi_aff *upma2);
6525 __isl_give isl_multi_union_pw_aff *
6526 isl_multi_union_pw_aff_flat_range_product(
6527 __isl_take isl_multi_union_pw_aff *mupa1,
6528 __isl_take isl_multi_union_pw_aff *mupa2);
6530 #include <isl/space.h>
6531 __isl_give isl_space *isl_space_factor_domain(
6532 __isl_take isl_space *space);
6533 __isl_give isl_space *isl_space_factor_range(
6534 __isl_take isl_space *space);
6535 __isl_give isl_space *isl_space_domain_factor_domain(
6536 __isl_take isl_space *space);
6537 __isl_give isl_space *isl_space_domain_factor_range(
6538 __isl_take isl_space *space);
6539 __isl_give isl_space *isl_space_range_factor_domain(
6540 __isl_take isl_space *space);
6541 __isl_give isl_space *isl_space_range_factor_range(
6542 __isl_take isl_space *space);
6544 The functions C<isl_space_range_factor_domain> and
6545 C<isl_space_range_factor_range> extract the two arguments from
6546 the result of a call to C<isl_space_range_product>.
6548 The arguments of a call to a product can be extracted
6549 from the result using the following functions.
6551 #include <isl/map.h>
6552 __isl_give isl_map *isl_map_factor_domain(
6553 __isl_take isl_map *map);
6554 __isl_give isl_map *isl_map_factor_range(
6555 __isl_take isl_map *map);
6556 __isl_give isl_map *isl_map_domain_factor_domain(
6557 __isl_take isl_map *map);
6558 __isl_give isl_map *isl_map_domain_factor_range(
6559 __isl_take isl_map *map);
6560 __isl_give isl_map *isl_map_range_factor_domain(
6561 __isl_take isl_map *map);
6562 __isl_give isl_map *isl_map_range_factor_range(
6563 __isl_take isl_map *map);
6565 #include <isl/union_map.h>
6566 __isl_give isl_union_map *isl_union_map_factor_domain(
6567 __isl_take isl_union_map *umap);
6568 __isl_give isl_union_map *isl_union_map_factor_range(
6569 __isl_take isl_union_map *umap);
6570 __isl_give isl_union_map *
6571 isl_union_map_domain_factor_domain(
6572 __isl_take isl_union_map *umap);
6573 __isl_give isl_union_map *
6574 isl_union_map_domain_factor_range(
6575 __isl_take isl_union_map *umap);
6576 __isl_give isl_union_map *
6577 isl_union_map_range_factor_domain(
6578 __isl_take isl_union_map *umap);
6579 __isl_give isl_union_map *
6580 isl_union_map_range_factor_range(
6581 __isl_take isl_union_map *umap);
6583 #include <isl/val.h>
6584 __isl_give isl_multi_val *isl_multi_val_factor_range(
6585 __isl_take isl_multi_val *mv);
6586 __isl_give isl_multi_val *
6587 isl_multi_val_range_factor_domain(
6588 __isl_take isl_multi_val *mv);
6589 __isl_give isl_multi_val *
6590 isl_multi_val_range_factor_range(
6591 __isl_take isl_multi_val *mv);
6593 #include <isl/aff.h>
6594 __isl_give isl_multi_aff *isl_multi_aff_factor_range(
6595 __isl_take isl_multi_aff *ma);
6596 __isl_give isl_multi_aff *
6597 isl_multi_aff_range_factor_domain(
6598 __isl_take isl_multi_aff *ma);
6599 __isl_give isl_multi_aff *
6600 isl_multi_aff_range_factor_range(
6601 __isl_take isl_multi_aff *ma);
6602 __isl_give isl_multi_pw_aff *
6603 isl_multi_pw_aff_factor_range(
6604 __isl_take isl_multi_pw_aff *mpa);
6605 __isl_give isl_multi_pw_aff *
6606 isl_multi_pw_aff_range_factor_domain(
6607 __isl_take isl_multi_pw_aff *mpa);
6608 __isl_give isl_multi_pw_aff *
6609 isl_multi_pw_aff_range_factor_range(
6610 __isl_take isl_multi_pw_aff *mpa);
6611 __isl_give isl_multi_union_pw_aff *
6612 isl_multi_union_pw_aff_factor_range(
6613 __isl_take isl_multi_union_pw_aff *mupa);
6614 __isl_give isl_multi_union_pw_aff *
6615 isl_multi_union_pw_aff_range_factor_domain(
6616 __isl_take isl_multi_union_pw_aff *mupa);
6617 __isl_give isl_multi_union_pw_aff *
6618 isl_multi_union_pw_aff_range_factor_range(
6619 __isl_take isl_multi_union_pw_aff *mupa);
6621 The splice functions are a generalization of the flat product functions,
6622 where the second argument may be inserted at any position inside
6623 the first argument rather than being placed at the end.
6624 The functions C<isl_multi_val_factor_range>,
6625 C<isl_multi_aff_factor_range>,
6626 C<isl_multi_pw_aff_factor_range> and
6627 C<isl_multi_union_pw_aff_factor_range>
6628 take functions that live in a set space.
6630 #include <isl/val.h>
6631 __isl_give isl_multi_val *isl_multi_val_range_splice(
6632 __isl_take isl_multi_val *mv1, unsigned pos,
6633 __isl_take isl_multi_val *mv2);
6635 #include <isl/aff.h>
6636 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
6637 __isl_take isl_multi_aff *ma1, unsigned pos,
6638 __isl_take isl_multi_aff *ma2);
6639 __isl_give isl_multi_aff *isl_multi_aff_splice(
6640 __isl_take isl_multi_aff *ma1,
6641 unsigned in_pos, unsigned out_pos,
6642 __isl_take isl_multi_aff *ma2);
6643 __isl_give isl_multi_pw_aff *
6644 isl_multi_pw_aff_range_splice(
6645 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
6646 __isl_take isl_multi_pw_aff *mpa2);
6647 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
6648 __isl_take isl_multi_pw_aff *mpa1,
6649 unsigned in_pos, unsigned out_pos,
6650 __isl_take isl_multi_pw_aff *mpa2);
6651 __isl_give isl_multi_union_pw_aff *
6652 isl_multi_union_pw_aff_range_splice(
6653 __isl_take isl_multi_union_pw_aff *mupa1,
6655 __isl_take isl_multi_union_pw_aff *mupa2);
6657 =item * Simplification
6659 When applied to a set or relation,
6660 the gist operation returns a set or relation that has the
6661 same intersection with the context as the input set or relation.
6662 Any implicit equality in the intersection is made explicit in the result,
6663 while all inequalities that are redundant with respect to the intersection
6665 In case of union sets and relations, the gist operation is performed
6668 When applied to a function,
6669 the gist operation applies the set gist operation to each of
6670 the cells in the domain of the input piecewise expression.
6671 The context is also exploited
6672 to simplify the expression associated to each cell.
6674 #include <isl/set.h>
6675 __isl_give isl_basic_set *isl_basic_set_gist(
6676 __isl_take isl_basic_set *bset,
6677 __isl_take isl_basic_set *context);
6678 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
6679 __isl_take isl_set *context);
6680 __isl_give isl_set *isl_set_gist_params(
6681 __isl_take isl_set *set,
6682 __isl_take isl_set *context);
6684 #include <isl/map.h>
6685 __isl_give isl_basic_map *isl_basic_map_gist(
6686 __isl_take isl_basic_map *bmap,
6687 __isl_take isl_basic_map *context);
6688 __isl_give isl_basic_map *isl_basic_map_gist_domain(
6689 __isl_take isl_basic_map *bmap,
6690 __isl_take isl_basic_set *context);
6691 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
6692 __isl_take isl_map *context);
6693 __isl_give isl_map *isl_map_gist_params(
6694 __isl_take isl_map *map,
6695 __isl_take isl_set *context);
6696 __isl_give isl_map *isl_map_gist_domain(
6697 __isl_take isl_map *map,
6698 __isl_take isl_set *context);
6699 __isl_give isl_map *isl_map_gist_range(
6700 __isl_take isl_map *map,
6701 __isl_take isl_set *context);
6703 #include <isl/union_set.h>
6704 __isl_give isl_union_set *isl_union_set_gist(
6705 __isl_take isl_union_set *uset,
6706 __isl_take isl_union_set *context);
6707 __isl_give isl_union_set *isl_union_set_gist_params(
6708 __isl_take isl_union_set *uset,
6709 __isl_take isl_set *set);
6711 #include <isl/union_map.h>
6712 __isl_give isl_union_map *isl_union_map_gist(
6713 __isl_take isl_union_map *umap,
6714 __isl_take isl_union_map *context);
6715 __isl_give isl_union_map *isl_union_map_gist_params(
6716 __isl_take isl_union_map *umap,
6717 __isl_take isl_set *set);
6718 __isl_give isl_union_map *isl_union_map_gist_domain(
6719 __isl_take isl_union_map *umap,
6720 __isl_take isl_union_set *uset);
6721 __isl_give isl_union_map *isl_union_map_gist_range(
6722 __isl_take isl_union_map *umap,
6723 __isl_take isl_union_set *uset);
6725 #include <isl/aff.h>
6726 __isl_give isl_aff *isl_aff_gist_params(
6727 __isl_take isl_aff *aff,
6728 __isl_take isl_set *context);
6729 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
6730 __isl_take isl_set *context);
6731 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
6732 __isl_take isl_multi_aff *maff,
6733 __isl_take isl_set *context);
6734 __isl_give isl_multi_aff *isl_multi_aff_gist(
6735 __isl_take isl_multi_aff *maff,
6736 __isl_take isl_set *context);
6737 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
6738 __isl_take isl_pw_aff *pwaff,
6739 __isl_take isl_set *context);
6740 __isl_give isl_pw_aff *isl_pw_aff_gist(
6741 __isl_take isl_pw_aff *pwaff,
6742 __isl_take isl_set *context);
6743 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
6744 __isl_take isl_pw_multi_aff *pma,
6745 __isl_take isl_set *set);
6746 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
6747 __isl_take isl_pw_multi_aff *pma,
6748 __isl_take isl_set *set);
6749 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
6750 __isl_take isl_multi_pw_aff *mpa,
6751 __isl_take isl_set *set);
6752 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
6753 __isl_take isl_multi_pw_aff *mpa,
6754 __isl_take isl_set *set);
6755 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
6756 __isl_take isl_union_pw_aff *upa,
6757 __isl_take isl_union_set *context);
6758 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
6759 __isl_take isl_union_pw_aff *upa,
6760 __isl_take isl_set *context);
6761 __isl_give isl_union_pw_multi_aff *
6762 isl_union_pw_multi_aff_gist_params(
6763 __isl_take isl_union_pw_multi_aff *upma,
6764 __isl_take isl_set *context);
6765 __isl_give isl_union_pw_multi_aff *
6766 isl_union_pw_multi_aff_gist(
6767 __isl_take isl_union_pw_multi_aff *upma,
6768 __isl_take isl_union_set *context);
6769 __isl_give isl_multi_union_pw_aff *
6770 isl_multi_union_pw_aff_gist_params(
6771 __isl_take isl_multi_union_pw_aff *aff,
6772 __isl_take isl_set *context);
6773 __isl_give isl_multi_union_pw_aff *
6774 isl_multi_union_pw_aff_gist(
6775 __isl_take isl_multi_union_pw_aff *aff,
6776 __isl_take isl_union_set *context);
6778 #include <isl/polynomial.h>
6779 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
6780 __isl_take isl_qpolynomial *qp,
6781 __isl_take isl_set *context);
6782 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
6783 __isl_take isl_qpolynomial *qp,
6784 __isl_take isl_set *context);
6785 __isl_give isl_qpolynomial_fold *
6786 isl_qpolynomial_fold_gist_params(
6787 __isl_take isl_qpolynomial_fold *fold,
6788 __isl_take isl_set *context);
6789 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
6790 __isl_take isl_qpolynomial_fold *fold,
6791 __isl_take isl_set *context);
6792 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
6793 __isl_take isl_pw_qpolynomial *pwqp,
6794 __isl_take isl_set *context);
6795 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
6796 __isl_take isl_pw_qpolynomial *pwqp,
6797 __isl_take isl_set *context);
6798 __isl_give isl_pw_qpolynomial_fold *
6799 isl_pw_qpolynomial_fold_gist(
6800 __isl_take isl_pw_qpolynomial_fold *pwf,
6801 __isl_take isl_set *context);
6802 __isl_give isl_pw_qpolynomial_fold *
6803 isl_pw_qpolynomial_fold_gist_params(
6804 __isl_take isl_pw_qpolynomial_fold *pwf,
6805 __isl_take isl_set *context);
6806 __isl_give isl_union_pw_qpolynomial *
6807 isl_union_pw_qpolynomial_gist_params(
6808 __isl_take isl_union_pw_qpolynomial *upwqp,
6809 __isl_take isl_set *context);
6810 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
6811 __isl_take isl_union_pw_qpolynomial *upwqp,
6812 __isl_take isl_union_set *context);
6813 __isl_give isl_union_pw_qpolynomial_fold *
6814 isl_union_pw_qpolynomial_fold_gist(
6815 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6816 __isl_take isl_union_set *context);
6817 __isl_give isl_union_pw_qpolynomial_fold *
6818 isl_union_pw_qpolynomial_fold_gist_params(
6819 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6820 __isl_take isl_set *context);
6822 =item * Binary Arithmetic Operations
6824 #include <isl/set.h>
6825 __isl_give isl_set *isl_set_sum(
6826 __isl_take isl_set *set1,
6827 __isl_take isl_set *set2);
6828 #include <isl/map.h>
6829 __isl_give isl_map *isl_map_sum(
6830 __isl_take isl_map *map1,
6831 __isl_take isl_map *map2);
6833 C<isl_set_sum> computes the Minkowski sum of its two arguments,
6834 i.e., the set containing the sums of pairs of elements from
6835 C<set1> and C<set2>.
6836 The domain of the result of C<isl_map_sum> is the intersection
6837 of the domains of its two arguments. The corresponding range
6838 elements are the sums of the corresponding range elements
6839 in the two arguments.
6841 #include <isl/val.h>
6842 __isl_give isl_multi_val *isl_multi_val_add(
6843 __isl_take isl_multi_val *mv1,
6844 __isl_take isl_multi_val *mv2);
6845 __isl_give isl_multi_val *isl_multi_val_sub(
6846 __isl_take isl_multi_val *mv1,
6847 __isl_take isl_multi_val *mv2);
6849 #include <isl/aff.h>
6850 __isl_give isl_aff *isl_aff_add(
6851 __isl_take isl_aff *aff1,
6852 __isl_take isl_aff *aff2);
6853 __isl_give isl_multi_aff *isl_multi_aff_add(
6854 __isl_take isl_multi_aff *maff1,
6855 __isl_take isl_multi_aff *maff2);
6856 __isl_give isl_pw_aff *isl_pw_aff_add(
6857 __isl_take isl_pw_aff *pwaff1,
6858 __isl_take isl_pw_aff *pwaff2);
6859 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add(
6860 __isl_take isl_multi_pw_aff *mpa1,
6861 __isl_take isl_multi_pw_aff *mpa2);
6862 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
6863 __isl_take isl_pw_multi_aff *pma1,
6864 __isl_take isl_pw_multi_aff *pma2);
6865 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
6866 __isl_take isl_union_pw_aff *upa1,
6867 __isl_take isl_union_pw_aff *upa2);
6868 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
6869 __isl_take isl_union_pw_multi_aff *upma1,
6870 __isl_take isl_union_pw_multi_aff *upma2);
6871 __isl_give isl_multi_union_pw_aff *
6872 isl_multi_union_pw_aff_add(
6873 __isl_take isl_multi_union_pw_aff *mupa1,
6874 __isl_take isl_multi_union_pw_aff *mupa2);
6875 __isl_give isl_pw_aff *isl_pw_aff_min(
6876 __isl_take isl_pw_aff *pwaff1,
6877 __isl_take isl_pw_aff *pwaff2);
6878 __isl_give isl_pw_aff *isl_pw_aff_max(
6879 __isl_take isl_pw_aff *pwaff1,
6880 __isl_take isl_pw_aff *pwaff2);
6881 __isl_give isl_aff *isl_aff_sub(
6882 __isl_take isl_aff *aff1,
6883 __isl_take isl_aff *aff2);
6884 __isl_give isl_multi_aff *isl_multi_aff_sub(
6885 __isl_take isl_multi_aff *ma1,
6886 __isl_take isl_multi_aff *ma2);
6887 __isl_give isl_pw_aff *isl_pw_aff_sub(
6888 __isl_take isl_pw_aff *pwaff1,
6889 __isl_take isl_pw_aff *pwaff2);
6890 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
6891 __isl_take isl_multi_pw_aff *mpa1,
6892 __isl_take isl_multi_pw_aff *mpa2);
6893 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
6894 __isl_take isl_pw_multi_aff *pma1,
6895 __isl_take isl_pw_multi_aff *pma2);
6896 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
6897 __isl_take isl_union_pw_aff *upa1,
6898 __isl_take isl_union_pw_aff *upa2);
6899 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
6900 __isl_take isl_union_pw_multi_aff *upma1,
6901 __isl_take isl_union_pw_multi_aff *upma2);
6902 __isl_give isl_multi_union_pw_aff *
6903 isl_multi_union_pw_aff_sub(
6904 __isl_take isl_multi_union_pw_aff *mupa1,
6905 __isl_take isl_multi_union_pw_aff *mupa2);
6907 C<isl_aff_sub> subtracts the second argument from the first.
6909 #include <isl/polynomial.h>
6910 __isl_give isl_qpolynomial *isl_qpolynomial_add(
6911 __isl_take isl_qpolynomial *qp1,
6912 __isl_take isl_qpolynomial *qp2);
6913 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
6914 __isl_take isl_pw_qpolynomial *pwqp1,
6915 __isl_take isl_pw_qpolynomial *pwqp2);
6916 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
6917 __isl_take isl_pw_qpolynomial *pwqp1,
6918 __isl_take isl_pw_qpolynomial *pwqp2);
6919 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
6920 __isl_take isl_pw_qpolynomial_fold *pwf1,
6921 __isl_take isl_pw_qpolynomial_fold *pwf2);
6922 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
6923 __isl_take isl_union_pw_qpolynomial *upwqp1,
6924 __isl_take isl_union_pw_qpolynomial *upwqp2);
6925 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
6926 __isl_take isl_qpolynomial *qp1,
6927 __isl_take isl_qpolynomial *qp2);
6928 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
6929 __isl_take isl_pw_qpolynomial *pwqp1,
6930 __isl_take isl_pw_qpolynomial *pwqp2);
6931 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
6932 __isl_take isl_union_pw_qpolynomial *upwqp1,
6933 __isl_take isl_union_pw_qpolynomial *upwqp2);
6934 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
6935 __isl_take isl_pw_qpolynomial_fold *pwf1,
6936 __isl_take isl_pw_qpolynomial_fold *pwf2);
6937 __isl_give isl_union_pw_qpolynomial_fold *
6938 isl_union_pw_qpolynomial_fold_fold(
6939 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
6940 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
6942 #include <isl/aff.h>
6943 __isl_give isl_pw_aff *isl_pw_aff_union_add(
6944 __isl_take isl_pw_aff *pwaff1,
6945 __isl_take isl_pw_aff *pwaff2);
6946 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
6947 __isl_take isl_pw_multi_aff *pma1,
6948 __isl_take isl_pw_multi_aff *pma2);
6949 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
6950 __isl_take isl_union_pw_aff *upa1,
6951 __isl_take isl_union_pw_aff *upa2);
6952 __isl_give isl_union_pw_multi_aff *
6953 isl_union_pw_multi_aff_union_add(
6954 __isl_take isl_union_pw_multi_aff *upma1,
6955 __isl_take isl_union_pw_multi_aff *upma2);
6956 __isl_give isl_multi_union_pw_aff *
6957 isl_multi_union_pw_aff_union_add(
6958 __isl_take isl_multi_union_pw_aff *mupa1,
6959 __isl_take isl_multi_union_pw_aff *mupa2);
6960 __isl_give isl_pw_aff *isl_pw_aff_union_min(
6961 __isl_take isl_pw_aff *pwaff1,
6962 __isl_take isl_pw_aff *pwaff2);
6963 __isl_give isl_pw_aff *isl_pw_aff_union_max(
6964 __isl_take isl_pw_aff *pwaff1,
6965 __isl_take isl_pw_aff *pwaff2);
6967 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
6968 expression with a domain that is the union of those of C<pwaff1> and
6969 C<pwaff2> and such that on each cell, the quasi-affine expression is
6970 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
6971 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
6972 associated expression is the defined one.
6973 This in contrast to the C<isl_pw_aff_max> function, which is
6974 only defined on the shared definition domain of the arguments.
6976 #include <isl/val.h>
6977 __isl_give isl_multi_val *isl_multi_val_add_val(
6978 __isl_take isl_multi_val *mv,
6979 __isl_take isl_val *v);
6980 __isl_give isl_multi_val *isl_multi_val_mod_val(
6981 __isl_take isl_multi_val *mv,
6982 __isl_take isl_val *v);
6983 __isl_give isl_multi_val *isl_multi_val_scale_val(
6984 __isl_take isl_multi_val *mv,
6985 __isl_take isl_val *v);
6986 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
6987 __isl_take isl_multi_val *mv,
6988 __isl_take isl_val *v);
6990 #include <isl/aff.h>
6991 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
6992 __isl_take isl_val *mod);
6993 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
6994 __isl_take isl_pw_aff *pa,
6995 __isl_take isl_val *mod);
6996 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
6997 __isl_take isl_union_pw_aff *upa,
6998 __isl_take isl_val *f);
6999 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
7000 __isl_take isl_val *v);
7001 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
7002 __isl_take isl_multi_aff *ma,
7003 __isl_take isl_val *v);
7004 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
7005 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
7006 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
7007 __isl_take isl_multi_pw_aff *mpa,
7008 __isl_take isl_val *v);
7009 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
7010 __isl_take isl_pw_multi_aff *pma,
7011 __isl_take isl_val *v);
7012 __isl_give isl_union_pw_multi_aff *
7013 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
7014 __isl_take isl_union_pw_aff *upa,
7015 __isl_take isl_val *f);
7016 isl_union_pw_multi_aff_scale_val(
7017 __isl_take isl_union_pw_multi_aff *upma,
7018 __isl_take isl_val *val);
7019 __isl_give isl_multi_union_pw_aff *
7020 isl_multi_union_pw_aff_scale_val(
7021 __isl_take isl_multi_union_pw_aff *mupa,
7022 __isl_take isl_val *v);
7023 __isl_give isl_aff *isl_aff_scale_down_ui(
7024 __isl_take isl_aff *aff, unsigned f);
7025 __isl_give isl_aff *isl_aff_scale_down_val(
7026 __isl_take isl_aff *aff, __isl_take isl_val *v);
7027 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
7028 __isl_take isl_multi_aff *ma,
7029 __isl_take isl_val *v);
7030 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
7031 __isl_take isl_pw_aff *pa,
7032 __isl_take isl_val *f);
7033 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
7034 __isl_take isl_multi_pw_aff *mpa,
7035 __isl_take isl_val *v);
7036 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
7037 __isl_take isl_pw_multi_aff *pma,
7038 __isl_take isl_val *v);
7039 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
7040 __isl_take isl_union_pw_aff *upa,
7041 __isl_take isl_val *v);
7042 __isl_give isl_union_pw_multi_aff *
7043 isl_union_pw_multi_aff_scale_down_val(
7044 __isl_take isl_union_pw_multi_aff *upma,
7045 __isl_take isl_val *val);
7046 __isl_give isl_multi_union_pw_aff *
7047 isl_multi_union_pw_aff_scale_down_val(
7048 __isl_take isl_multi_union_pw_aff *mupa,
7049 __isl_take isl_val *v);
7051 #include <isl/polynomial.h>
7052 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
7053 __isl_take isl_qpolynomial *qp,
7054 __isl_take isl_val *v);
7055 __isl_give isl_qpolynomial_fold *
7056 isl_qpolynomial_fold_scale_val(
7057 __isl_take isl_qpolynomial_fold *fold,
7058 __isl_take isl_val *v);
7059 __isl_give isl_pw_qpolynomial *
7060 isl_pw_qpolynomial_scale_val(
7061 __isl_take isl_pw_qpolynomial *pwqp,
7062 __isl_take isl_val *v);
7063 __isl_give isl_pw_qpolynomial_fold *
7064 isl_pw_qpolynomial_fold_scale_val(
7065 __isl_take isl_pw_qpolynomial_fold *pwf,
7066 __isl_take isl_val *v);
7067 __isl_give isl_union_pw_qpolynomial *
7068 isl_union_pw_qpolynomial_scale_val(
7069 __isl_take isl_union_pw_qpolynomial *upwqp,
7070 __isl_take isl_val *v);
7071 __isl_give isl_union_pw_qpolynomial_fold *
7072 isl_union_pw_qpolynomial_fold_scale_val(
7073 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7074 __isl_take isl_val *v);
7075 __isl_give isl_qpolynomial *
7076 isl_qpolynomial_scale_down_val(
7077 __isl_take isl_qpolynomial *qp,
7078 __isl_take isl_val *v);
7079 __isl_give isl_qpolynomial_fold *
7080 isl_qpolynomial_fold_scale_down_val(
7081 __isl_take isl_qpolynomial_fold *fold,
7082 __isl_take isl_val *v);
7083 __isl_give isl_pw_qpolynomial *
7084 isl_pw_qpolynomial_scale_down_val(
7085 __isl_take isl_pw_qpolynomial *pwqp,
7086 __isl_take isl_val *v);
7087 __isl_give isl_pw_qpolynomial_fold *
7088 isl_pw_qpolynomial_fold_scale_down_val(
7089 __isl_take isl_pw_qpolynomial_fold *pwf,
7090 __isl_take isl_val *v);
7091 __isl_give isl_union_pw_qpolynomial *
7092 isl_union_pw_qpolynomial_scale_down_val(
7093 __isl_take isl_union_pw_qpolynomial *upwqp,
7094 __isl_take isl_val *v);
7095 __isl_give isl_union_pw_qpolynomial_fold *
7096 isl_union_pw_qpolynomial_fold_scale_down_val(
7097 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7098 __isl_take isl_val *v);
7100 #include <isl/val.h>
7101 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
7102 __isl_take isl_multi_val *mv1,
7103 __isl_take isl_multi_val *mv2);
7104 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
7105 __isl_take isl_multi_val *mv1,
7106 __isl_take isl_multi_val *mv2);
7107 __isl_give isl_multi_val *
7108 isl_multi_val_scale_down_multi_val(
7109 __isl_take isl_multi_val *mv1,
7110 __isl_take isl_multi_val *mv2);
7112 #include <isl/aff.h>
7113 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
7114 __isl_take isl_multi_aff *ma,
7115 __isl_take isl_multi_val *mv);
7116 __isl_give isl_multi_union_pw_aff *
7117 isl_multi_union_pw_aff_mod_multi_val(
7118 __isl_take isl_multi_union_pw_aff *upma,
7119 __isl_take isl_multi_val *mv);
7120 __isl_give isl_multi_pw_aff *
7121 isl_multi_pw_aff_mod_multi_val(
7122 __isl_take isl_multi_pw_aff *mpa,
7123 __isl_take isl_multi_val *mv);
7124 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
7125 __isl_take isl_multi_aff *ma,
7126 __isl_take isl_multi_val *mv);
7127 __isl_give isl_pw_multi_aff *
7128 isl_pw_multi_aff_scale_multi_val(
7129 __isl_take isl_pw_multi_aff *pma,
7130 __isl_take isl_multi_val *mv);
7131 __isl_give isl_multi_pw_aff *
7132 isl_multi_pw_aff_scale_multi_val(
7133 __isl_take isl_multi_pw_aff *mpa,
7134 __isl_take isl_multi_val *mv);
7135 __isl_give isl_multi_union_pw_aff *
7136 isl_multi_union_pw_aff_scale_multi_val(
7137 __isl_take isl_multi_union_pw_aff *mupa,
7138 __isl_take isl_multi_val *mv);
7139 __isl_give isl_union_pw_multi_aff *
7140 isl_union_pw_multi_aff_scale_multi_val(
7141 __isl_take isl_union_pw_multi_aff *upma,
7142 __isl_take isl_multi_val *mv);
7143 __isl_give isl_multi_aff *
7144 isl_multi_aff_scale_down_multi_val(
7145 __isl_take isl_multi_aff *ma,
7146 __isl_take isl_multi_val *mv);
7147 __isl_give isl_multi_pw_aff *
7148 isl_multi_pw_aff_scale_down_multi_val(
7149 __isl_take isl_multi_pw_aff *mpa,
7150 __isl_take isl_multi_val *mv);
7151 __isl_give isl_multi_union_pw_aff *
7152 isl_multi_union_pw_aff_scale_down_multi_val(
7153 __isl_take isl_multi_union_pw_aff *mupa,
7154 __isl_take isl_multi_val *mv);
7156 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
7157 by the corresponding elements of C<mv>.
7159 #include <isl/aff.h>
7160 __isl_give isl_aff *isl_aff_mul(
7161 __isl_take isl_aff *aff1,
7162 __isl_take isl_aff *aff2);
7163 __isl_give isl_aff *isl_aff_div(
7164 __isl_take isl_aff *aff1,
7165 __isl_take isl_aff *aff2);
7166 __isl_give isl_pw_aff *isl_pw_aff_mul(
7167 __isl_take isl_pw_aff *pwaff1,
7168 __isl_take isl_pw_aff *pwaff2);
7169 __isl_give isl_pw_aff *isl_pw_aff_div(
7170 __isl_take isl_pw_aff *pa1,
7171 __isl_take isl_pw_aff *pa2);
7172 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
7173 __isl_take isl_pw_aff *pa1,
7174 __isl_take isl_pw_aff *pa2);
7175 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
7176 __isl_take isl_pw_aff *pa1,
7177 __isl_take isl_pw_aff *pa2);
7179 When multiplying two affine expressions, at least one of the two needs
7180 to be a constant. Similarly, when dividing an affine expression by another,
7181 the second expression needs to be a constant.
7182 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
7183 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
7186 #include <isl/polynomial.h>
7187 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
7188 __isl_take isl_qpolynomial *qp1,
7189 __isl_take isl_qpolynomial *qp2);
7190 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
7191 __isl_take isl_pw_qpolynomial *pwqp1,
7192 __isl_take isl_pw_qpolynomial *pwqp2);
7193 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
7194 __isl_take isl_union_pw_qpolynomial *upwqp1,
7195 __isl_take isl_union_pw_qpolynomial *upwqp2);
7199 =head3 Lexicographic Optimization
7201 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
7202 the following functions
7203 compute a set that contains the lexicographic minimum or maximum
7204 of the elements in C<set> (or C<bset>) for those values of the parameters
7205 that satisfy C<dom>.
7206 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7207 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
7209 In other words, the union of the parameter values
7210 for which the result is non-empty and of C<*empty>
7213 #include <isl/set.h>
7214 __isl_give isl_set *isl_basic_set_partial_lexmin(
7215 __isl_take isl_basic_set *bset,
7216 __isl_take isl_basic_set *dom,
7217 __isl_give isl_set **empty);
7218 __isl_give isl_set *isl_basic_set_partial_lexmax(
7219 __isl_take isl_basic_set *bset,
7220 __isl_take isl_basic_set *dom,
7221 __isl_give isl_set **empty);
7222 __isl_give isl_set *isl_set_partial_lexmin(
7223 __isl_take isl_set *set, __isl_take isl_set *dom,
7224 __isl_give isl_set **empty);
7225 __isl_give isl_set *isl_set_partial_lexmax(
7226 __isl_take isl_set *set, __isl_take isl_set *dom,
7227 __isl_give isl_set **empty);
7229 Given a (basic) set C<set> (or C<bset>), the following functions simply
7230 return a set containing the lexicographic minimum or maximum
7231 of the elements in C<set> (or C<bset>).
7232 In case of union sets, the optimum is computed per space.
7234 #include <isl/set.h>
7235 __isl_give isl_set *isl_basic_set_lexmin(
7236 __isl_take isl_basic_set *bset);
7237 __isl_give isl_set *isl_basic_set_lexmax(
7238 __isl_take isl_basic_set *bset);
7239 __isl_give isl_set *isl_set_lexmin(
7240 __isl_take isl_set *set);
7241 __isl_give isl_set *isl_set_lexmax(
7242 __isl_take isl_set *set);
7243 __isl_give isl_union_set *isl_union_set_lexmin(
7244 __isl_take isl_union_set *uset);
7245 __isl_give isl_union_set *isl_union_set_lexmax(
7246 __isl_take isl_union_set *uset);
7248 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
7249 the following functions
7250 compute a relation that maps each element of C<dom>
7251 to the single lexicographic minimum or maximum
7252 of the elements that are associated to that same
7253 element in C<map> (or C<bmap>).
7254 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7255 that contains the elements in C<dom> that do not map
7256 to any elements in C<map> (or C<bmap>).
7257 In other words, the union of the domain of the result and of C<*empty>
7260 #include <isl/map.h>
7261 __isl_give isl_map *isl_basic_map_partial_lexmax(
7262 __isl_take isl_basic_map *bmap,
7263 __isl_take isl_basic_set *dom,
7264 __isl_give isl_set **empty);
7265 __isl_give isl_map *isl_basic_map_partial_lexmin(
7266 __isl_take isl_basic_map *bmap,
7267 __isl_take isl_basic_set *dom,
7268 __isl_give isl_set **empty);
7269 __isl_give isl_map *isl_map_partial_lexmax(
7270 __isl_take isl_map *map, __isl_take isl_set *dom,
7271 __isl_give isl_set **empty);
7272 __isl_give isl_map *isl_map_partial_lexmin(
7273 __isl_take isl_map *map, __isl_take isl_set *dom,
7274 __isl_give isl_set **empty);
7276 Given a (basic) map C<map> (or C<bmap>), the following functions simply
7277 return a map mapping each element in the domain of
7278 C<map> (or C<bmap>) to the lexicographic minimum or maximum
7279 of all elements associated to that element.
7280 In case of union relations, the optimum is computed per space.
7282 #include <isl/map.h>
7283 __isl_give isl_map *isl_basic_map_lexmin(
7284 __isl_take isl_basic_map *bmap);
7285 __isl_give isl_map *isl_basic_map_lexmax(
7286 __isl_take isl_basic_map *bmap);
7287 __isl_give isl_map *isl_map_lexmin(
7288 __isl_take isl_map *map);
7289 __isl_give isl_map *isl_map_lexmax(
7290 __isl_take isl_map *map);
7291 __isl_give isl_union_map *isl_union_map_lexmin(
7292 __isl_take isl_union_map *umap);
7293 __isl_give isl_union_map *isl_union_map_lexmax(
7294 __isl_take isl_union_map *umap);
7296 The following functions return their result in the form of
7297 a piecewise multi-affine expression,
7298 but are otherwise equivalent to the corresponding functions
7299 returning a basic set or relation.
7301 #include <isl/set.h>
7302 __isl_give isl_pw_multi_aff *
7303 isl_basic_set_partial_lexmin_pw_multi_aff(
7304 __isl_take isl_basic_set *bset,
7305 __isl_take isl_basic_set *dom,
7306 __isl_give isl_set **empty);
7307 __isl_give isl_pw_multi_aff *
7308 isl_basic_set_partial_lexmax_pw_multi_aff(
7309 __isl_take isl_basic_set *bset,
7310 __isl_take isl_basic_set *dom,
7311 __isl_give isl_set **empty);
7312 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
7313 __isl_take isl_set *set);
7314 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
7315 __isl_take isl_set *set);
7317 #include <isl/map.h>
7318 __isl_give isl_pw_multi_aff *
7319 isl_basic_map_lexmin_pw_multi_aff(
7320 __isl_take isl_basic_map *bmap);
7321 __isl_give isl_pw_multi_aff *
7322 isl_basic_map_partial_lexmin_pw_multi_aff(
7323 __isl_take isl_basic_map *bmap,
7324 __isl_take isl_basic_set *dom,
7325 __isl_give isl_set **empty);
7326 __isl_give isl_pw_multi_aff *
7327 isl_basic_map_partial_lexmax_pw_multi_aff(
7328 __isl_take isl_basic_map *bmap,
7329 __isl_take isl_basic_set *dom,
7330 __isl_give isl_set **empty);
7331 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
7332 __isl_take isl_map *map);
7333 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
7334 __isl_take isl_map *map);
7336 The following functions return the lexicographic minimum or maximum
7337 on the shared domain of the inputs and the single defined function
7338 on those parts of the domain where only a single function is defined.
7340 #include <isl/aff.h>
7341 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
7342 __isl_take isl_pw_multi_aff *pma1,
7343 __isl_take isl_pw_multi_aff *pma2);
7344 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
7345 __isl_take isl_pw_multi_aff *pma1,
7346 __isl_take isl_pw_multi_aff *pma2);
7348 If the input to a lexicographic optimization problem has
7349 multiple constraints with the same coefficients for the optimized
7350 variables, then, by default, this symmetry is exploited by
7351 replacing those constraints by a single constraint with
7352 an abstract bound, which is in turn bounded by the corresponding terms
7353 in the original constraints.
7354 Without this optimization, the solver would typically consider
7355 all possible orderings of those original bounds, resulting in a needless
7356 decomposition of the domain.
7357 However, the optimization can also result in slowdowns since
7358 an extra parameter is introduced that may get used in additional
7360 The following option determines whether symmetry detection is applied
7361 during lexicographic optimization.
7363 #include <isl/options.h>
7364 isl_stat isl_options_set_pip_symmetry(isl_ctx *ctx,
7366 int isl_options_get_pip_symmetry(isl_ctx *ctx);
7370 See also \autoref{s:offline}.
7374 =head2 Ternary Operations
7376 #include <isl/aff.h>
7377 __isl_give isl_pw_aff *isl_pw_aff_cond(
7378 __isl_take isl_pw_aff *cond,
7379 __isl_take isl_pw_aff *pwaff_true,
7380 __isl_take isl_pw_aff *pwaff_false);
7382 The function C<isl_pw_aff_cond> performs a conditional operator
7383 and returns an expression that is equal to C<pwaff_true>
7384 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
7385 where C<cond> is zero.
7389 Lists are defined over several element types, including
7390 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_union_pw_aff>,
7391 C<isl_union_pw_multi_aff>, C<isl_constraint>,
7392 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
7393 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
7394 Here we take lists of C<isl_set>s as an example.
7395 Lists can be created, copied, modified and freed using the following functions.
7397 #include <isl/set.h>
7398 __isl_give isl_set_list *isl_set_list_from_set(
7399 __isl_take isl_set *el);
7400 __isl_give isl_set_list *isl_set_list_alloc(
7401 isl_ctx *ctx, int n);
7402 __isl_give isl_set_list *isl_set_list_copy(
7403 __isl_keep isl_set_list *list);
7404 __isl_give isl_set_list *isl_set_list_insert(
7405 __isl_take isl_set_list *list, unsigned pos,
7406 __isl_take isl_set *el);
7407 __isl_give isl_set_list *isl_set_list_add(
7408 __isl_take isl_set_list *list,
7409 __isl_take isl_set *el);
7410 __isl_give isl_set_list *isl_set_list_drop(
7411 __isl_take isl_set_list *list,
7412 unsigned first, unsigned n);
7413 __isl_give isl_set_list *isl_set_list_set_set(
7414 __isl_take isl_set_list *list, int index,
7415 __isl_take isl_set *set);
7416 __isl_give isl_set_list *isl_set_list_concat(
7417 __isl_take isl_set_list *list1,
7418 __isl_take isl_set_list *list2);
7419 __isl_give isl_set_list *isl_set_list_sort(
7420 __isl_take isl_set_list *list,
7421 int (*cmp)(__isl_keep isl_set *a,
7422 __isl_keep isl_set *b, void *user),
7424 __isl_null isl_set_list *isl_set_list_free(
7425 __isl_take isl_set_list *list);
7427 C<isl_set_list_alloc> creates an empty list with an initial capacity
7428 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
7429 add elements to a list, increasing its capacity as needed.
7430 C<isl_set_list_from_set> creates a list with a single element.
7432 Lists can be inspected using the following functions.
7434 #include <isl/set.h>
7435 int isl_set_list_n_set(__isl_keep isl_set_list *list);
7436 __isl_give isl_set *isl_set_list_get_set(
7437 __isl_keep isl_set_list *list, int index);
7438 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list,
7439 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7441 isl_stat isl_set_list_foreach_scc(
7442 __isl_keep isl_set_list *list,
7443 isl_bool (*follows)(__isl_keep isl_set *a,
7444 __isl_keep isl_set *b, void *user),
7446 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7449 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
7450 strongly connected components of the graph with as vertices the elements
7451 of C<list> and a directed edge from vertex C<b> to vertex C<a>
7452 iff C<follows(a, b)> returns C<isl_bool_true>. The callbacks C<follows> and
7453 C<fn> should return C<isl_bool_error> or C<isl_stat_error> on error.
7455 Lists can be printed using
7457 #include <isl/set.h>
7458 __isl_give isl_printer *isl_printer_print_set_list(
7459 __isl_take isl_printer *p,
7460 __isl_keep isl_set_list *list);
7462 =head2 Associative arrays
7464 Associative arrays map isl objects of a specific type to isl objects
7465 of some (other) specific type. They are defined for several pairs
7466 of types, including (C<isl_map>, C<isl_basic_set>),
7467 (C<isl_id>, C<isl_ast_expr>),
7468 (C<isl_id>, C<isl_id>) and
7469 (C<isl_id>, C<isl_pw_aff>).
7470 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
7473 Associative arrays can be created, copied and freed using
7474 the following functions.
7476 #include <isl/id_to_ast_expr.h>
7477 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
7478 isl_ctx *ctx, int min_size);
7479 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
7480 __isl_keep isl_id_to_ast_expr *id2expr);
7481 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
7482 __isl_take isl_id_to_ast_expr *id2expr);
7484 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
7485 to specify the expected size of the associative array.
7486 The associative array will be grown automatically as needed.
7488 Associative arrays can be inspected using the following functions.
7490 #include <isl/id_to_ast_expr.h>
7491 __isl_give isl_maybe_isl_ast_expr
7492 isl_id_to_ast_expr_try_get(
7493 __isl_keep isl_id_to_ast_expr *id2expr,
7494 __isl_keep isl_id *key);
7495 isl_bool isl_id_to_ast_expr_has(
7496 __isl_keep isl_id_to_ast_expr *id2expr,
7497 __isl_keep isl_id *key);
7498 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
7499 __isl_keep isl_id_to_ast_expr *id2expr,
7500 __isl_take isl_id *key);
7501 isl_stat isl_id_to_ast_expr_foreach(
7502 __isl_keep isl_id_to_ast_expr *id2expr,
7503 isl_stat (*fn)(__isl_take isl_id *key,
7504 __isl_take isl_ast_expr *val, void *user),
7507 The function C<isl_id_to_ast_expr_try_get> returns a structure
7508 containing two elements, C<valid> and C<value>.
7509 If there is a value associated to the key, then C<valid>
7510 is set to C<isl_bool_true> and C<value> contains a copy of
7511 the associated value. Otherwise C<value> is C<NULL> and
7512 C<valid> may be C<isl_bool_error> or C<isl_bool_false> depending
7513 on whether some error has occurred or there simply is no associated value.
7514 The function C<isl_id_to_ast_expr_has> returns the C<valid> field
7515 in the structure and
7516 the function C<isl_id_to_ast_expr_get> returns the C<value> field.
7518 Associative arrays can be modified using the following functions.
7520 #include <isl/id_to_ast_expr.h>
7521 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
7522 __isl_take isl_id_to_ast_expr *id2expr,
7523 __isl_take isl_id *key,
7524 __isl_take isl_ast_expr *val);
7525 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
7526 __isl_take isl_id_to_ast_expr *id2expr,
7527 __isl_take isl_id *key);
7529 Associative arrays can be printed using the following function.
7531 #include <isl/id_to_ast_expr.h>
7532 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
7533 __isl_take isl_printer *p,
7534 __isl_keep isl_id_to_ast_expr *id2expr);
7538 Vectors can be created, copied and freed using the following functions.
7540 #include <isl/vec.h>
7541 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
7543 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
7544 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
7546 Note that the elements of a newly created vector may have arbitrary values.
7547 The elements can be changed and inspected using the following functions.
7549 int isl_vec_size(__isl_keep isl_vec *vec);
7550 __isl_give isl_val *isl_vec_get_element_val(
7551 __isl_keep isl_vec *vec, int pos);
7552 __isl_give isl_vec *isl_vec_set_element_si(
7553 __isl_take isl_vec *vec, int pos, int v);
7554 __isl_give isl_vec *isl_vec_set_element_val(
7555 __isl_take isl_vec *vec, int pos,
7556 __isl_take isl_val *v);
7557 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
7559 __isl_give isl_vec *isl_vec_set_val(
7560 __isl_take isl_vec *vec, __isl_take isl_val *v);
7561 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
7562 __isl_keep isl_vec *vec2, int pos);
7564 C<isl_vec_get_element> will return a negative value if anything went wrong.
7565 In that case, the value of C<*v> is undefined.
7567 The following function can be used to concatenate two vectors.
7569 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
7570 __isl_take isl_vec *vec2);
7574 Matrices can be created, copied and freed using the following functions.
7576 #include <isl/mat.h>
7577 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
7578 unsigned n_row, unsigned n_col);
7579 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
7580 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
7582 Note that the elements of a newly created matrix may have arbitrary values.
7583 The elements can be changed and inspected using the following functions.
7585 int isl_mat_rows(__isl_keep isl_mat *mat);
7586 int isl_mat_cols(__isl_keep isl_mat *mat);
7587 __isl_give isl_val *isl_mat_get_element_val(
7588 __isl_keep isl_mat *mat, int row, int col);
7589 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
7590 int row, int col, int v);
7591 __isl_give isl_mat *isl_mat_set_element_val(
7592 __isl_take isl_mat *mat, int row, int col,
7593 __isl_take isl_val *v);
7595 C<isl_mat_get_element> will return a negative value if anything went wrong.
7596 In that case, the value of C<*v> is undefined.
7598 The following function can be used to compute the (right) inverse
7599 of a matrix, i.e., a matrix such that the product of the original
7600 and the inverse (in that order) is a multiple of the identity matrix.
7601 The input matrix is assumed to be of full row-rank.
7603 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
7605 The following function can be used to compute the (right) kernel
7606 (or null space) of a matrix, i.e., a matrix such that the product of
7607 the original and the kernel (in that order) is the zero matrix.
7609 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
7611 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
7613 The following functions determine
7614 an upper or lower bound on a quasipolynomial over its domain.
7616 __isl_give isl_pw_qpolynomial_fold *
7617 isl_pw_qpolynomial_bound(
7618 __isl_take isl_pw_qpolynomial *pwqp,
7619 enum isl_fold type, int *tight);
7621 __isl_give isl_union_pw_qpolynomial_fold *
7622 isl_union_pw_qpolynomial_bound(
7623 __isl_take isl_union_pw_qpolynomial *upwqp,
7624 enum isl_fold type, int *tight);
7626 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
7627 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
7628 is the returned bound is known be tight, i.e., for each value
7629 of the parameters there is at least
7630 one element in the domain that reaches the bound.
7631 If the domain of C<pwqp> is not wrapping, then the bound is computed
7632 over all elements in that domain and the result has a purely parametric
7633 domain. If the domain of C<pwqp> is wrapping, then the bound is
7634 computed over the range of the wrapped relation. The domain of the
7635 wrapped relation becomes the domain of the result.
7637 =head2 Parametric Vertex Enumeration
7639 The parametric vertex enumeration described in this section
7640 is mainly intended to be used internally and by the C<barvinok>
7643 #include <isl/vertices.h>
7644 __isl_give isl_vertices *isl_basic_set_compute_vertices(
7645 __isl_keep isl_basic_set *bset);
7647 The function C<isl_basic_set_compute_vertices> performs the
7648 actual computation of the parametric vertices and the chamber
7649 decomposition and stores the result in an C<isl_vertices> object.
7650 This information can be queried by either iterating over all
7651 the vertices or iterating over all the chambers or cells
7652 and then iterating over all vertices that are active on the chamber.
7654 isl_stat isl_vertices_foreach_vertex(
7655 __isl_keep isl_vertices *vertices,
7656 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7657 void *user), void *user);
7659 isl_stat isl_vertices_foreach_cell(
7660 __isl_keep isl_vertices *vertices,
7661 isl_stat (*fn)(__isl_take isl_cell *cell,
7662 void *user), void *user);
7663 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
7664 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7665 void *user), void *user);
7667 Other operations that can be performed on an C<isl_vertices> object are
7670 int isl_vertices_get_n_vertices(
7671 __isl_keep isl_vertices *vertices);
7672 void isl_vertices_free(__isl_take isl_vertices *vertices);
7674 Vertices can be inspected and destroyed using the following functions.
7676 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
7677 __isl_give isl_basic_set *isl_vertex_get_domain(
7678 __isl_keep isl_vertex *vertex);
7679 __isl_give isl_multi_aff *isl_vertex_get_expr(
7680 __isl_keep isl_vertex *vertex);
7681 void isl_vertex_free(__isl_take isl_vertex *vertex);
7683 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
7684 describing the vertex in terms of the parameters,
7685 while C<isl_vertex_get_domain> returns the activity domain
7688 Chambers can be inspected and destroyed using the following functions.
7690 __isl_give isl_basic_set *isl_cell_get_domain(
7691 __isl_keep isl_cell *cell);
7692 void isl_cell_free(__isl_take isl_cell *cell);
7694 =head1 Polyhedral Compilation Library
7696 This section collects functionality in C<isl> that has been specifically
7697 designed for use during polyhedral compilation.
7699 =head2 Schedule Trees
7701 A schedule tree is a structured representation of a schedule,
7702 assigning a relative order to a set of domain elements.
7703 The relative order expressed by the schedule tree is
7704 defined recursively. In particular, the order between
7705 two domain elements is determined by the node that is closest
7706 to the root that refers to both elements and that orders them apart.
7707 Each node in the tree is of one of several types.
7708 The root node is always of type C<isl_schedule_node_domain>
7709 (or C<isl_schedule_node_extension>)
7710 and it describes the (extra) domain elements to which the schedule applies.
7711 The other types of nodes are as follows.
7715 =item C<isl_schedule_node_band>
7717 A band of schedule dimensions. Each schedule dimension is represented
7718 by a union piecewise quasi-affine expression. If this expression
7719 assigns a different value to two domain elements, while all previous
7720 schedule dimensions in the same band assign them the same value,
7721 then the two domain elements are ordered according to these two
7723 Each expression is required to be total in the domain elements
7724 that reach the band node.
7726 =item C<isl_schedule_node_expansion>
7728 An expansion node maps each of the domain elements that reach the node
7729 to one or more domain elements. The image of this mapping forms
7730 the set of domain elements that reach the child of the expansion node.
7731 The function that maps each of the expanded domain elements
7732 to the original domain element from which it was expanded
7733 is called the contraction.
7735 =item C<isl_schedule_node_filter>
7737 A filter node does not impose any ordering, but rather intersects
7738 the set of domain elements that the current subtree refers to
7739 with a given union set. The subtree of the filter node only
7740 refers to domain elements in the intersection.
7741 A filter node is typically only used as a child of a sequence or
7744 =item C<isl_schedule_node_leaf>
7746 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
7748 =item C<isl_schedule_node_mark>
7750 A mark node can be used to attach any kind of information to a subtree
7751 of the schedule tree.
7753 =item C<isl_schedule_node_sequence>
7755 A sequence node has one or more children, each of which is a filter node.
7756 The filters on these filter nodes form a partition of
7757 the domain elements that the current subtree refers to.
7758 If two domain elements appear in distinct filters then the sequence
7759 node orders them according to the child positions of the corresponding
7762 =item C<isl_schedule_node_set>
7764 A set node is similar to a sequence node, except that
7765 it expresses that domain elements appearing in distinct filters
7766 may have any order. The order of the children of a set node
7767 is therefore also immaterial.
7771 The following node types are only supported by the AST generator.
7775 =item C<isl_schedule_node_context>
7777 The context describes constraints on the parameters and
7778 the schedule dimensions of outer
7779 bands that the AST generator may assume to hold. It is also the only
7780 kind of node that may introduce additional parameters.
7781 The space of the context is that of the flat product of the outer
7782 band nodes. In particular, if there are no outer band nodes, then
7783 this space is the unnamed zero-dimensional space.
7784 Since a context node references the outer band nodes, any tree
7785 containing a context node is considered to be anchored.
7787 =item C<isl_schedule_node_extension>
7789 An extension node instructs the AST generator to add additional
7790 domain elements that need to be scheduled.
7791 The additional domain elements are described by the range of
7792 the extension map in terms of the outer schedule dimensions,
7793 i.e., the flat product of the outer band nodes.
7794 Note that domain elements are added whenever the AST generator
7795 reaches the extension node, meaning that there are still some
7796 active domain elements for which an AST needs to be generated.
7797 The conditions under which some domain elements are still active
7798 may however not be completely described by the outer AST nodes
7799 generated at that point.
7801 An extension node may also appear as the root of a schedule tree,
7802 when it is intended to be inserted into another tree
7803 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
7804 In this case, the domain of the extension node should
7805 correspond to the flat product of the outer band nodes
7806 in this other schedule tree at the point where the extension tree
7809 =item C<isl_schedule_node_guard>
7811 The guard describes constraints on the parameters and
7812 the schedule dimensions of outer
7813 bands that need to be enforced by the outer nodes
7814 in the generated AST.
7815 The space of the guard is that of the flat product of the outer
7816 band nodes. In particular, if there are no outer band nodes, then
7817 this space is the unnamed zero-dimensional space.
7818 Since a guard node references the outer band nodes, any tree
7819 containing a guard node is considered to be anchored.
7823 Except for the C<isl_schedule_node_context> nodes,
7824 none of the nodes may introduce any parameters that were not
7825 already present in the root domain node.
7827 A schedule tree is encapsulated in an C<isl_schedule> object.
7828 The simplest such objects, those with a tree consisting of single domain node,
7829 can be created using the following functions with either an empty
7830 domain or a given domain.
7832 #include <isl/schedule.h>
7833 __isl_give isl_schedule *isl_schedule_empty(
7834 __isl_take isl_space *space);
7835 __isl_give isl_schedule *isl_schedule_from_domain(
7836 __isl_take isl_union_set *domain);
7838 The function C<isl_schedule_constraints_compute_schedule> described
7839 in L</"Scheduling"> can also be used to construct schedules.
7841 C<isl_schedule> objects may be copied and freed using the following functions.
7843 #include <isl/schedule.h>
7844 __isl_give isl_schedule *isl_schedule_copy(
7845 __isl_keep isl_schedule *sched);
7846 __isl_null isl_schedule *isl_schedule_free(
7847 __isl_take isl_schedule *sched);
7849 The following functions checks whether two C<isl_schedule> objects
7850 are obviously the same.
7852 #include <isl/schedule.h>
7853 isl_bool isl_schedule_plain_is_equal(
7854 __isl_keep isl_schedule *schedule1,
7855 __isl_keep isl_schedule *schedule2);
7857 The domain of the schedule, i.e., the domain described by the root node,
7858 can be obtained using the following function.
7860 #include <isl/schedule.h>
7861 __isl_give isl_union_set *isl_schedule_get_domain(
7862 __isl_keep isl_schedule *schedule);
7864 An extra top-level band node (right underneath the domain node) can
7865 be introduced into the schedule using the following function.
7866 The schedule tree is assumed not to have any anchored nodes.
7868 #include <isl/schedule.h>
7869 __isl_give isl_schedule *
7870 isl_schedule_insert_partial_schedule(
7871 __isl_take isl_schedule *schedule,
7872 __isl_take isl_multi_union_pw_aff *partial);
7874 A top-level context node (right underneath the domain node) can
7875 be introduced into the schedule using the following function.
7877 #include <isl/schedule.h>
7878 __isl_give isl_schedule *isl_schedule_insert_context(
7879 __isl_take isl_schedule *schedule,
7880 __isl_take isl_set *context)
7882 A top-level guard node (right underneath the domain node) can
7883 be introduced into the schedule using the following function.
7885 #include <isl/schedule.h>
7886 __isl_give isl_schedule *isl_schedule_insert_guard(
7887 __isl_take isl_schedule *schedule,
7888 __isl_take isl_set *guard)
7890 A schedule that combines two schedules either in the given
7891 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
7892 or an C<isl_schedule_node_set> node,
7893 can be created using the following functions.
7895 #include <isl/schedule.h>
7896 __isl_give isl_schedule *isl_schedule_sequence(
7897 __isl_take isl_schedule *schedule1,
7898 __isl_take isl_schedule *schedule2);
7899 __isl_give isl_schedule *isl_schedule_set(
7900 __isl_take isl_schedule *schedule1,
7901 __isl_take isl_schedule *schedule2);
7903 The domains of the two input schedules need to be disjoint.
7905 The following function can be used to restrict the domain
7906 of a schedule with a domain node as root to be a subset of the given union set.
7907 This operation may remove nodes in the tree that have become
7910 #include <isl/schedule.h>
7911 __isl_give isl_schedule *isl_schedule_intersect_domain(
7912 __isl_take isl_schedule *schedule,
7913 __isl_take isl_union_set *domain);
7915 The following function can be used to simplify the domain
7916 of a schedule with a domain node as root with respect to the given
7919 #include <isl/schedule.h>
7920 __isl_give isl_schedule *isl_schedule_gist_domain_params(
7921 __isl_take isl_schedule *schedule,
7922 __isl_take isl_set *context);
7924 The following function resets the user pointers on all parameter
7925 and tuple identifiers referenced by the nodes of the given schedule.
7927 #include <isl/schedule.h>
7928 __isl_give isl_schedule *isl_schedule_reset_user(
7929 __isl_take isl_schedule *schedule);
7931 The following function aligns the parameters of all nodes
7932 in the given schedule to the given space.
7934 #include <isl/schedule.h>
7935 __isl_give isl_schedule *isl_schedule_align_params(
7936 __isl_take isl_schedule *schedule,
7937 __isl_take isl_space *space);
7939 The following function allows the user to plug in a given function
7940 in the iteration domains. The input schedule is not allowed to contain
7941 any expansion nodes.
7943 #include <isl/schedule.h>
7944 __isl_give isl_schedule *
7945 isl_schedule_pullback_union_pw_multi_aff(
7946 __isl_take isl_schedule *schedule,
7947 __isl_take isl_union_pw_multi_aff *upma);
7949 The following function can be used to plug in the schedule C<expansion>
7950 in the leaves of C<schedule>, where C<contraction> describes how
7951 the domain elements of C<expansion> map to the domain elements
7952 at the original leaves of C<schedule>.
7953 The resulting schedule will contain expansion nodes, unless
7954 C<contraction> is an identity function.
7956 #include <isl/schedule.h>
7957 __isl_give isl_schedule *isl_schedule_expand(
7958 __isl_take isl_schedule *schedule,
7959 __isl_take isl_union_pw_multi_aff *contraction,
7960 __isl_take isl_schedule *expansion);
7962 An C<isl_union_map> representation of the schedule can be obtained
7963 from an C<isl_schedule> using the following function.
7965 #include <isl/schedule.h>
7966 __isl_give isl_union_map *isl_schedule_get_map(
7967 __isl_keep isl_schedule *sched);
7969 The resulting relation encodes the same relative ordering as
7970 the schedule by mapping the domain elements to a common schedule space.
7971 If the schedule_separate_components option is set, then the order
7972 of the children of a set node is explicitly encoded in the result.
7973 If the tree contains any expansion nodes, then the relation
7974 is formulated in terms of the expanded domain elements.
7976 Schedules can be read from input using the following functions.
7978 #include <isl/schedule.h>
7979 __isl_give isl_schedule *isl_schedule_read_from_file(
7980 isl_ctx *ctx, FILE *input);
7981 __isl_give isl_schedule *isl_schedule_read_from_str(
7982 isl_ctx *ctx, const char *str);
7984 A representation of the schedule can be printed using
7986 #include <isl/schedule.h>
7987 __isl_give isl_printer *isl_printer_print_schedule(
7988 __isl_take isl_printer *p,
7989 __isl_keep isl_schedule *schedule);
7990 __isl_give char *isl_schedule_to_str(
7991 __isl_keep isl_schedule *schedule);
7993 C<isl_schedule_to_str> prints the schedule in flow format.
7995 The schedule tree can be traversed through the use of
7996 C<isl_schedule_node> objects that point to a particular
7997 position in the schedule tree. Whenever a C<isl_schedule_node>
7998 is use to modify a node in the schedule tree, the original schedule
7999 tree is left untouched and the modifications are performed to a copy
8000 of the tree. The returned C<isl_schedule_node> then points to
8001 this modified copy of the tree.
8003 The root of the schedule tree can be obtained using the following function.
8005 #include <isl/schedule.h>
8006 __isl_give isl_schedule_node *isl_schedule_get_root(
8007 __isl_keep isl_schedule *schedule);
8009 A pointer to a newly created schedule tree with a single domain
8010 node can be created using the following functions.
8012 #include <isl/schedule_node.h>
8013 __isl_give isl_schedule_node *
8014 isl_schedule_node_from_domain(
8015 __isl_take isl_union_set *domain);
8016 __isl_give isl_schedule_node *
8017 isl_schedule_node_from_extension(
8018 __isl_take isl_union_map *extension);
8020 C<isl_schedule_node_from_extension> creates a tree with an extension
8023 Schedule nodes can be copied and freed using the following functions.
8025 #include <isl/schedule_node.h>
8026 __isl_give isl_schedule_node *isl_schedule_node_copy(
8027 __isl_keep isl_schedule_node *node);
8028 __isl_null isl_schedule_node *isl_schedule_node_free(
8029 __isl_take isl_schedule_node *node);
8031 The following functions can be used to check if two schedule
8032 nodes point to the same position in the same schedule.
8034 #include <isl/schedule_node.h>
8035 isl_bool isl_schedule_node_is_equal(
8036 __isl_keep isl_schedule_node *node1,
8037 __isl_keep isl_schedule_node *node2);
8039 The following properties can be obtained from a schedule node.
8041 #include <isl/schedule_node.h>
8042 enum isl_schedule_node_type isl_schedule_node_get_type(
8043 __isl_keep isl_schedule_node *node);
8044 enum isl_schedule_node_type
8045 isl_schedule_node_get_parent_type(
8046 __isl_keep isl_schedule_node *node);
8047 __isl_give isl_schedule *isl_schedule_node_get_schedule(
8048 __isl_keep isl_schedule_node *node);
8050 The function C<isl_schedule_node_get_type> returns the type of
8051 the node, while C<isl_schedule_node_get_parent_type> returns
8052 type of the parent of the node, which is required to exist.
8053 The function C<isl_schedule_node_get_schedule> returns a copy
8054 to the schedule to which the node belongs.
8056 The following functions can be used to move the schedule node
8057 to a different position in the tree or to check if such a position
8060 #include <isl/schedule_node.h>
8061 isl_bool isl_schedule_node_has_parent(
8062 __isl_keep isl_schedule_node *node);
8063 __isl_give isl_schedule_node *isl_schedule_node_parent(
8064 __isl_take isl_schedule_node *node);
8065 __isl_give isl_schedule_node *isl_schedule_node_root(
8066 __isl_take isl_schedule_node *node);
8067 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
8068 __isl_take isl_schedule_node *node,
8070 int isl_schedule_node_n_children(
8071 __isl_keep isl_schedule_node *node);
8072 __isl_give isl_schedule_node *isl_schedule_node_child(
8073 __isl_take isl_schedule_node *node, int pos);
8074 isl_bool isl_schedule_node_has_children(
8075 __isl_keep isl_schedule_node *node);
8076 __isl_give isl_schedule_node *isl_schedule_node_first_child(
8077 __isl_take isl_schedule_node *node);
8078 isl_bool isl_schedule_node_has_previous_sibling(
8079 __isl_keep isl_schedule_node *node);
8080 __isl_give isl_schedule_node *
8081 isl_schedule_node_previous_sibling(
8082 __isl_take isl_schedule_node *node);
8083 isl_bool isl_schedule_node_has_next_sibling(
8084 __isl_keep isl_schedule_node *node);
8085 __isl_give isl_schedule_node *
8086 isl_schedule_node_next_sibling(
8087 __isl_take isl_schedule_node *node);
8089 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
8090 is the node itself, the ancestor of generation 1 is its parent and so on.
8092 It is also possible to query the number of ancestors of a node,
8093 the position of the current node
8094 within the children of its parent, the position of the subtree
8095 containing a node within the children of an ancestor
8096 or to obtain a copy of a given
8097 child without destroying the current node.
8098 Given two nodes that point to the same schedule, their closest
8099 shared ancestor can be obtained using
8100 C<isl_schedule_node_get_shared_ancestor>.
8102 #include <isl/schedule_node.h>
8103 int isl_schedule_node_get_tree_depth(
8104 __isl_keep isl_schedule_node *node);
8105 int isl_schedule_node_get_child_position(
8106 __isl_keep isl_schedule_node *node);
8107 int isl_schedule_node_get_ancestor_child_position(
8108 __isl_keep isl_schedule_node *node,
8109 __isl_keep isl_schedule_node *ancestor);
8110 __isl_give isl_schedule_node *isl_schedule_node_get_child(
8111 __isl_keep isl_schedule_node *node, int pos);
8112 __isl_give isl_schedule_node *
8113 isl_schedule_node_get_shared_ancestor(
8114 __isl_keep isl_schedule_node *node1,
8115 __isl_keep isl_schedule_node *node2);
8117 All nodes in a schedule tree or
8118 all descendants of a specific node (including the node) can be visited
8119 in depth-first pre-order using the following functions.
8121 #include <isl/schedule.h>
8122 isl_stat isl_schedule_foreach_schedule_node_top_down(
8123 __isl_keep isl_schedule *sched,
8124 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8125 void *user), void *user);
8127 #include <isl/schedule_node.h>
8128 isl_stat isl_schedule_node_foreach_descendant_top_down(
8129 __isl_keep isl_schedule_node *node,
8130 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8131 void *user), void *user);
8133 The callback function is slightly different from the usual
8134 callbacks in that it not only indicates success (non-negative result)
8135 or failure (negative result), but also indicates whether the children
8136 of the given node should be visited. In particular, if the callback
8137 returns a positive value, then the children are visited, but if
8138 the callback returns zero, then the children are not visited.
8140 The ancestors of a node in a schedule tree can be visited from
8141 the root down to and including the parent of the node using
8142 the following function.
8144 #include <isl/schedule_node.h>
8145 isl_stat isl_schedule_node_foreach_ancestor_top_down(
8146 __isl_keep isl_schedule_node *node,
8147 isl_stat (*fn)(__isl_keep isl_schedule_node *node,
8148 void *user), void *user);
8150 The following functions allows for a depth-first post-order
8151 traversal of the nodes in a schedule tree or
8152 of the descendants of a specific node (including the node
8153 itself), where the user callback is allowed to modify the
8156 #include <isl/schedule.h>
8157 __isl_give isl_schedule *
8158 isl_schedule_map_schedule_node_bottom_up(
8159 __isl_take isl_schedule *schedule,
8160 __isl_give isl_schedule_node *(*fn)(
8161 __isl_take isl_schedule_node *node,
8162 void *user), void *user);
8164 #include <isl/schedule_node.h>
8165 __isl_give isl_schedule_node *
8166 isl_schedule_node_map_descendant_bottom_up(
8167 __isl_take isl_schedule_node *node,
8168 __isl_give isl_schedule_node *(*fn)(
8169 __isl_take isl_schedule_node *node,
8170 void *user), void *user);
8172 The traversal continues from the node returned by the callback function.
8173 It is the responsibility of the user to ensure that this does not
8174 lead to an infinite loop. It is safest to always return a pointer
8175 to the same position (same ancestors and child positions) as the input node.
8177 The following function removes a node (along with its descendants)
8178 from a schedule tree and returns a pointer to the leaf at the
8179 same position in the updated tree.
8180 It is not allowed to remove the root of a schedule tree or
8181 a child of a set or sequence node.
8183 #include <isl/schedule_node.h>
8184 __isl_give isl_schedule_node *isl_schedule_node_cut(
8185 __isl_take isl_schedule_node *node);
8187 The following function removes a single node
8188 from a schedule tree and returns a pointer to the child
8189 of the node, now located at the position of the original node
8190 or to a leaf node at that position if there was no child.
8191 It is not allowed to remove the root of a schedule tree,
8192 a set or sequence node, a child of a set or sequence node or
8193 a band node with an anchored subtree.
8195 #include <isl/schedule_node.h>
8196 __isl_give isl_schedule_node *isl_schedule_node_delete(
8197 __isl_take isl_schedule_node *node);
8199 Most nodes in a schedule tree only contain local information.
8200 In some cases, however, a node may also refer to the schedule dimensions
8201 of its outer band nodes.
8202 This means that the position of the node within the tree should
8203 not be changed, or at least that no changes are performed to the
8204 outer band nodes. The following function can be used to test
8205 whether the subtree rooted at a given node contains any such nodes.
8207 #include <isl/schedule_node.h>
8208 isl_bool isl_schedule_node_is_subtree_anchored(
8209 __isl_keep isl_schedule_node *node);
8211 The following function resets the user pointers on all parameter
8212 and tuple identifiers referenced by the given schedule node.
8214 #include <isl/schedule_node.h>
8215 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
8216 __isl_take isl_schedule_node *node);
8218 The following function aligns the parameters of the given schedule
8219 node to the given space.
8221 #include <isl/schedule_node.h>
8222 __isl_give isl_schedule_node *
8223 isl_schedule_node_align_params(
8224 __isl_take isl_schedule_node *node,
8225 __isl_take isl_space *space);
8227 Several node types have their own functions for querying
8228 (and in some cases setting) some node type specific properties.
8230 #include <isl/schedule_node.h>
8231 __isl_give isl_space *isl_schedule_node_band_get_space(
8232 __isl_keep isl_schedule_node *node);
8233 __isl_give isl_multi_union_pw_aff *
8234 isl_schedule_node_band_get_partial_schedule(
8235 __isl_keep isl_schedule_node *node);
8236 __isl_give isl_union_map *
8237 isl_schedule_node_band_get_partial_schedule_union_map(
8238 __isl_keep isl_schedule_node *node);
8239 unsigned isl_schedule_node_band_n_member(
8240 __isl_keep isl_schedule_node *node);
8241 isl_bool isl_schedule_node_band_member_get_coincident(
8242 __isl_keep isl_schedule_node *node, int pos);
8243 __isl_give isl_schedule_node *
8244 isl_schedule_node_band_member_set_coincident(
8245 __isl_take isl_schedule_node *node, int pos,
8247 isl_bool isl_schedule_node_band_get_permutable(
8248 __isl_keep isl_schedule_node *node);
8249 __isl_give isl_schedule_node *
8250 isl_schedule_node_band_set_permutable(
8251 __isl_take isl_schedule_node *node, int permutable);
8252 enum isl_ast_loop_type
8253 isl_schedule_node_band_member_get_ast_loop_type(
8254 __isl_keep isl_schedule_node *node, int pos);
8255 __isl_give isl_schedule_node *
8256 isl_schedule_node_band_member_set_ast_loop_type(
8257 __isl_take isl_schedule_node *node, int pos,
8258 enum isl_ast_loop_type type);
8259 __isl_give isl_union_set *
8260 enum isl_ast_loop_type
8261 isl_schedule_node_band_member_get_isolate_ast_loop_type(
8262 __isl_keep isl_schedule_node *node, int pos);
8263 __isl_give isl_schedule_node *
8264 isl_schedule_node_band_member_set_isolate_ast_loop_type(
8265 __isl_take isl_schedule_node *node, int pos,
8266 enum isl_ast_loop_type type);
8267 isl_schedule_node_band_get_ast_build_options(
8268 __isl_keep isl_schedule_node *node);
8269 __isl_give isl_schedule_node *
8270 isl_schedule_node_band_set_ast_build_options(
8271 __isl_take isl_schedule_node *node,
8272 __isl_take isl_union_set *options);
8273 __isl_give isl_set *
8274 isl_schedule_node_band_get_ast_isolate_option(
8275 __isl_keep isl_schedule_node *node);
8277 The function C<isl_schedule_node_band_get_space> returns the space
8278 of the partial schedule of the band.
8279 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
8280 returns a representation of the partial schedule of the band node
8281 in the form of an C<isl_union_map>.
8282 The coincident and permutable properties are set by
8283 C<isl_schedule_constraints_compute_schedule> on the schedule tree
8285 A scheduling dimension is considered to be ``coincident''
8286 if it satisfies the coincidence constraints within its band.
8287 That is, if the dependence distances of the coincidence
8288 constraints are all zero in that direction (for fixed
8289 iterations of outer bands).
8290 A band is marked permutable if it was produced using the Pluto-like scheduler.
8291 Note that the scheduler may have to resort to a Feautrier style scheduling
8292 step even if the default scheduler is used.
8293 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
8294 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
8295 For the meaning of these loop AST generation types and the difference
8296 between the regular loop AST generation type and the isolate
8297 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
8298 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
8299 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
8300 may return C<isl_ast_loop_error> if an error occurs.
8301 The AST build options govern how an AST is generated for
8302 the individual schedule dimensions during AST generation.
8303 See L</"AST Generation Options (Schedule Tree)">.
8304 The isolate option for the given node can be extracted from these
8305 AST build options using the function
8306 C<isl_schedule_node_band_get_ast_isolate_option>.
8308 #include <isl/schedule_node.h>
8309 __isl_give isl_set *
8310 isl_schedule_node_context_get_context(
8311 __isl_keep isl_schedule_node *node);
8313 #include <isl/schedule_node.h>
8314 __isl_give isl_union_set *
8315 isl_schedule_node_domain_get_domain(
8316 __isl_keep isl_schedule_node *node);
8318 #include <isl/schedule_node.h>
8319 __isl_give isl_union_map *
8320 isl_schedule_node_expansion_get_expansion(
8321 __isl_keep isl_schedule_node *node);
8322 __isl_give isl_union_pw_multi_aff *
8323 isl_schedule_node_expansion_get_contraction(
8324 __isl_keep isl_schedule_node *node);
8326 #include <isl/schedule_node.h>
8327 __isl_give isl_union_map *
8328 isl_schedule_node_extension_get_extension(
8329 __isl_keep isl_schedule_node *node);
8331 #include <isl/schedule_node.h>
8332 __isl_give isl_union_set *
8333 isl_schedule_node_filter_get_filter(
8334 __isl_keep isl_schedule_node *node);
8336 #include <isl/schedule_node.h>
8337 __isl_give isl_set *isl_schedule_node_guard_get_guard(
8338 __isl_keep isl_schedule_node *node);
8340 #include <isl/schedule_node.h>
8341 __isl_give isl_id *isl_schedule_node_mark_get_id(
8342 __isl_keep isl_schedule_node *node);
8344 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
8345 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
8346 partial schedules related to the node.
8348 #include <isl/schedule_node.h>
8349 __isl_give isl_multi_union_pw_aff *
8350 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
8351 __isl_keep isl_schedule_node *node);
8352 __isl_give isl_union_pw_multi_aff *
8353 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
8354 __isl_keep isl_schedule_node *node);
8355 __isl_give isl_union_map *
8356 isl_schedule_node_get_prefix_schedule_union_map(
8357 __isl_keep isl_schedule_node *node);
8358 __isl_give isl_union_map *
8359 isl_schedule_node_get_prefix_schedule_relation(
8360 __isl_keep isl_schedule_node *node);
8361 __isl_give isl_union_map *
8362 isl_schedule_node_get_subtree_schedule_union_map(
8363 __isl_keep isl_schedule_node *node);
8365 In particular, the functions
8366 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
8367 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
8368 and C<isl_schedule_node_get_prefix_schedule_union_map>
8369 return a relative ordering on the domain elements that reach the given
8370 node determined by its ancestors.
8371 The function C<isl_schedule_node_get_prefix_schedule_relation>
8372 additionally includes the domain constraints in the result.
8373 The function C<isl_schedule_node_get_subtree_schedule_union_map>
8374 returns a representation of the partial schedule defined by the
8375 subtree rooted at the given node.
8376 If the tree contains any expansion nodes, then the subtree schedule
8377 is formulated in terms of the expanded domain elements.
8378 The tree passed to functions returning a prefix schedule
8379 may only contain extension nodes if these would not affect
8380 the result of these functions. That is, if one of the ancestors
8381 is an extension node, then all of the domain elements that were
8382 added by the extension node need to have been filtered out
8383 by filter nodes between the extension node and the input node.
8384 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
8385 may not contain in extension nodes in the selected subtree.
8387 The expansion/contraction defined by an entire subtree, combining
8388 the expansions/contractions
8389 on the expansion nodes in the subtree, can be obtained using
8390 the following functions.
8392 #include <isl/schedule_node.h>
8393 __isl_give isl_union_map *
8394 isl_schedule_node_get_subtree_expansion(
8395 __isl_keep isl_schedule_node *node);
8396 __isl_give isl_union_pw_multi_aff *
8397 isl_schedule_node_get_subtree_contraction(
8398 __isl_keep isl_schedule_node *node);
8400 The total number of outer band members of given node, i.e.,
8401 the shared output dimension of the maps in the result
8402 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
8403 using the following function.
8405 #include <isl/schedule_node.h>
8406 int isl_schedule_node_get_schedule_depth(
8407 __isl_keep isl_schedule_node *node);
8409 The following functions return the elements that reach the given node
8410 or the union of universes in the spaces that contain these elements.
8412 #include <isl/schedule_node.h>
8413 __isl_give isl_union_set *
8414 isl_schedule_node_get_domain(
8415 __isl_keep isl_schedule_node *node);
8416 __isl_give isl_union_set *
8417 isl_schedule_node_get_universe_domain(
8418 __isl_keep isl_schedule_node *node);
8420 The input tree of C<isl_schedule_node_get_domain>
8421 may only contain extension nodes if these would not affect
8422 the result of this function. That is, if one of the ancestors
8423 is an extension node, then all of the domain elements that were
8424 added by the extension node need to have been filtered out
8425 by filter nodes between the extension node and the input node.
8427 The following functions can be used to introduce additional nodes
8428 in the schedule tree. The new node is introduced at the point
8429 in the tree where the C<isl_schedule_node> points to and
8430 the results points to the new node.
8432 #include <isl/schedule_node.h>
8433 __isl_give isl_schedule_node *
8434 isl_schedule_node_insert_partial_schedule(
8435 __isl_take isl_schedule_node *node,
8436 __isl_take isl_multi_union_pw_aff *schedule);
8438 This function inserts a new band node with (the greatest integer
8439 part of) the given partial schedule.
8440 The subtree rooted at the given node is assumed not to have
8443 #include <isl/schedule_node.h>
8444 __isl_give isl_schedule_node *
8445 isl_schedule_node_insert_context(
8446 __isl_take isl_schedule_node *node,
8447 __isl_take isl_set *context);
8449 This function inserts a new context node with the given context constraints.
8451 #include <isl/schedule_node.h>
8452 __isl_give isl_schedule_node *
8453 isl_schedule_node_insert_filter(
8454 __isl_take isl_schedule_node *node,
8455 __isl_take isl_union_set *filter);
8457 This function inserts a new filter node with the given filter.
8458 If the original node already pointed to a filter node, then the
8459 two filter nodes are merged into one.
8461 #include <isl/schedule_node.h>
8462 __isl_give isl_schedule_node *
8463 isl_schedule_node_insert_guard(
8464 __isl_take isl_schedule_node *node,
8465 __isl_take isl_set *guard);
8467 This function inserts a new guard node with the given guard constraints.
8469 #include <isl/schedule_node.h>
8470 __isl_give isl_schedule_node *
8471 isl_schedule_node_insert_mark(
8472 __isl_take isl_schedule_node *node,
8473 __isl_take isl_id *mark);
8475 This function inserts a new mark node with the give mark identifier.
8477 #include <isl/schedule_node.h>
8478 __isl_give isl_schedule_node *
8479 isl_schedule_node_insert_sequence(
8480 __isl_take isl_schedule_node *node,
8481 __isl_take isl_union_set_list *filters);
8482 __isl_give isl_schedule_node *
8483 isl_schedule_node_insert_set(
8484 __isl_take isl_schedule_node *node,
8485 __isl_take isl_union_set_list *filters);
8487 These functions insert a new sequence or set node with the given
8488 filters as children.
8490 #include <isl/schedule_node.h>
8491 __isl_give isl_schedule_node *isl_schedule_node_group(
8492 __isl_take isl_schedule_node *node,
8493 __isl_take isl_id *group_id);
8495 This function introduces an expansion node in between the current
8496 node and its parent that expands instances of a space with tuple
8497 identifier C<group_id> to the original domain elements that reach
8498 the node. The group instances are identified by the prefix schedule
8499 of those domain elements. The ancestors of the node are adjusted
8500 to refer to the group instances instead of the original domain
8501 elements. The return value points to the same node in the updated
8502 schedule tree as the input node, i.e., to the child of the newly
8503 introduced expansion node. Grouping instances of different statements
8504 ensures that they will be treated as a single statement by the
8505 AST generator up to the point of the expansion node.
8507 The following function can be used to flatten a nested
8510 #include <isl/schedule_node.h>
8511 __isl_give isl_schedule_node *
8512 isl_schedule_node_sequence_splice_child(
8513 __isl_take isl_schedule_node *node, int pos);
8515 That is, given a sequence node C<node> that has another sequence node
8516 in its child at position C<pos> (in particular, the child of that filter
8517 node is a sequence node), attach the children of that other sequence
8518 node as children of C<node>, replacing the original child at position
8521 The partial schedule of a band node can be scaled (down) or reduced using
8522 the following functions.
8524 #include <isl/schedule_node.h>
8525 __isl_give isl_schedule_node *
8526 isl_schedule_node_band_scale(
8527 __isl_take isl_schedule_node *node,
8528 __isl_take isl_multi_val *mv);
8529 __isl_give isl_schedule_node *
8530 isl_schedule_node_band_scale_down(
8531 __isl_take isl_schedule_node *node,
8532 __isl_take isl_multi_val *mv);
8533 __isl_give isl_schedule_node *
8534 isl_schedule_node_band_mod(
8535 __isl_take isl_schedule_node *node,
8536 __isl_take isl_multi_val *mv);
8538 The spaces of the two arguments need to match.
8539 After scaling, the partial schedule is replaced by its greatest
8540 integer part to ensure that the schedule remains integral.
8542 The partial schedule of a band node can be shifted by an
8543 C<isl_multi_union_pw_aff> with a domain that is a superset
8544 of the domain of the partial schedule using
8545 the following function.
8547 #include <isl/schedule_node.h>
8548 __isl_give isl_schedule_node *
8549 isl_schedule_node_band_shift(
8550 __isl_take isl_schedule_node *node,
8551 __isl_take isl_multi_union_pw_aff *shift);
8553 A band node can be tiled using the following function.
8555 #include <isl/schedule_node.h>
8556 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
8557 __isl_take isl_schedule_node *node,
8558 __isl_take isl_multi_val *sizes);
8560 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
8562 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
8563 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
8565 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
8567 The C<isl_schedule_node_band_tile> function tiles
8568 the band using the given tile sizes inside its schedule.
8569 A new child band node is created to represent the point loops and it is
8570 inserted between the modified band and its children.
8571 The subtree rooted at the given node is assumed not to have
8573 The C<tile_scale_tile_loops> option specifies whether the tile
8574 loops iterators should be scaled by the tile sizes.
8575 If the C<tile_shift_point_loops> option is set, then the point loops
8576 are shifted to start at zero.
8578 A band node can be split into two nested band nodes
8579 using the following function.
8581 #include <isl/schedule_node.h>
8582 __isl_give isl_schedule_node *isl_schedule_node_band_split(
8583 __isl_take isl_schedule_node *node, int pos);
8585 The resulting outer band node contains the first C<pos> dimensions of
8586 the schedule of C<node> while the inner band contains the remaining dimensions.
8587 The schedules of the two band nodes live in anonymous spaces.
8588 The loop AST generation type options and the isolate option
8589 are split over the the two band nodes.
8591 A band node can be moved down to the leaves of the subtree rooted
8592 at the band node using the following function.
8594 #include <isl/schedule_node.h>
8595 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
8596 __isl_take isl_schedule_node *node);
8598 The subtree rooted at the given node is assumed not to have
8600 The result points to the node in the resulting tree that is in the same
8601 position as the node pointed to by C<node> in the original tree.
8603 #include <isl/schedule_node.h>
8604 __isl_give isl_schedule_node *
8605 isl_schedule_node_order_before(
8606 __isl_take isl_schedule_node *node,
8607 __isl_take isl_union_set *filter);
8608 __isl_give isl_schedule_node *
8609 isl_schedule_node_order_after(
8610 __isl_take isl_schedule_node *node,
8611 __isl_take isl_union_set *filter);
8613 These functions split the domain elements that reach C<node>
8614 into those that satisfy C<filter> and those that do not and
8615 arranges for the elements that do satisfy the filter to be
8616 executed before (in case of C<isl_schedule_node_order_before>)
8617 or after (in case of C<isl_schedule_node_order_after>)
8618 those that do not. The order is imposed by
8619 a sequence node, possibly reusing the grandparent of C<node>
8620 on two copies of the subtree attached to the original C<node>.
8621 Both copies are simplified with respect to their filter.
8623 Return a pointer to the copy of the subtree that does not
8624 satisfy C<filter>. If there is no such copy (because all
8625 reaching domain elements satisfy the filter), then return
8626 the original pointer.
8628 #include <isl/schedule_node.h>
8629 __isl_give isl_schedule_node *
8630 isl_schedule_node_graft_before(
8631 __isl_take isl_schedule_node *node,
8632 __isl_take isl_schedule_node *graft);
8633 __isl_give isl_schedule_node *
8634 isl_schedule_node_graft_after(
8635 __isl_take isl_schedule_node *node,
8636 __isl_take isl_schedule_node *graft);
8638 This function inserts the C<graft> tree into the tree containing C<node>
8639 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
8640 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
8641 The root node of C<graft>
8642 should be an extension node where the domain of the extension
8643 is the flat product of all outer band nodes of C<node>.
8644 The root node may also be a domain node.
8645 The elements of the domain or the range of the extension may not
8646 intersect with the domain elements that reach "node".
8647 The schedule tree of C<graft> may not be anchored.
8649 The schedule tree of C<node> is modified to include an extension node
8650 corresponding to the root node of C<graft> as a child of the original
8651 parent of C<node>. The original node that C<node> points to and the
8652 child of the root node of C<graft> are attached to this extension node
8653 through a sequence, with appropriate filters and with the child
8654 of C<graft> appearing before or after the original C<node>.
8656 If C<node> already appears inside a sequence that is the child of
8657 an extension node and if the spaces of the new domain elements
8658 do not overlap with those of the original domain elements,
8659 then that extension node is extended with the new extension
8660 rather than introducing a new segment of extension and sequence nodes.
8662 Return a pointer to the same node in the modified tree that
8663 C<node> pointed to in the original tree.
8665 A representation of the schedule node can be printed using
8667 #include <isl/schedule_node.h>
8668 __isl_give isl_printer *isl_printer_print_schedule_node(
8669 __isl_take isl_printer *p,
8670 __isl_keep isl_schedule_node *node);
8671 __isl_give char *isl_schedule_node_to_str(
8672 __isl_keep isl_schedule_node *node);
8674 C<isl_schedule_node_to_str> prints the schedule node in block format.
8676 =head2 Dependence Analysis
8678 C<isl> contains specialized functionality for performing
8679 array dataflow analysis. That is, given a I<sink> access relation
8680 and a collection of possible I<source> access relations,
8681 C<isl> can compute relations that describe
8682 for each iteration of the sink access, which iteration
8683 of which of the source access relations was the last
8684 to access the same data element before the given iteration
8686 The resulting dependence relations map source iterations
8687 to either the corresponding sink iterations or
8688 pairs of corresponding sink iterations and accessed data elements.
8689 To compute standard flow dependences, the sink should be
8690 a read, while the sources should be writes.
8691 If any of the source accesses are marked as being I<may>
8692 accesses, then there will be a dependence from the last
8693 I<must> access B<and> from any I<may> access that follows
8694 this last I<must> access.
8695 In particular, if I<all> sources are I<may> accesses,
8696 then memory based dependence analysis is performed.
8697 If, on the other hand, all sources are I<must> accesses,
8698 then value based dependence analysis is performed.
8700 =head3 High-level Interface
8702 A high-level interface to dependence analysis is provided
8703 by the following function.
8705 #include <isl/flow.h>
8706 __isl_give isl_union_flow *
8707 isl_union_access_info_compute_flow(
8708 __isl_take isl_union_access_info *access);
8710 The input C<isl_union_access_info> object describes the sink
8711 access relations, the source access relations and a schedule,
8712 while the output C<isl_union_flow> object describes
8713 the resulting dependence relations and the subsets of the
8714 sink relations for which no source was found.
8716 An C<isl_union_access_info> is created, modified, copied and freed using
8717 the following functions.
8719 #include <isl/flow.h>
8720 __isl_give isl_union_access_info *
8721 isl_union_access_info_from_sink(
8722 __isl_take isl_union_map *sink);
8723 __isl_give isl_union_access_info *
8724 isl_union_access_info_set_must_source(
8725 __isl_take isl_union_access_info *access,
8726 __isl_take isl_union_map *must_source);
8727 __isl_give isl_union_access_info *
8728 isl_union_access_info_set_may_source(
8729 __isl_take isl_union_access_info *access,
8730 __isl_take isl_union_map *may_source);
8731 __isl_give isl_union_access_info *
8732 isl_union_access_info_set_schedule(
8733 __isl_take isl_union_access_info *access,
8734 __isl_take isl_schedule *schedule);
8735 __isl_give isl_union_access_info *
8736 isl_union_access_info_set_schedule_map(
8737 __isl_take isl_union_access_info *access,
8738 __isl_take isl_union_map *schedule_map);
8739 __isl_give isl_union_access_info *
8740 isl_union_access_info_copy(
8741 __isl_keep isl_union_access_info *access);
8742 __isl_null isl_union_access_info *
8743 isl_union_access_info_free(
8744 __isl_take isl_union_access_info *access);
8746 The may sources set by C<isl_union_access_info_set_may_source>
8747 do not need to include the must sources set by
8748 C<isl_union_access_info_set_must_source> as a subset.
8749 The user is free not to call one (or both) of these functions,
8750 in which case the corresponding set is kept to its empty default.
8751 Similarly, the default schedule initialized by
8752 C<isl_union_access_info_from_sink> is empty.
8753 The current schedule is determined by the last call to either
8754 C<isl_union_access_info_set_schedule> or
8755 C<isl_union_access_info_set_schedule_map>.
8756 The domain of the schedule corresponds to the domains of
8757 the access relations. In particular, the domains of the access
8758 relations are effectively intersected with the domain of the schedule
8759 and only the resulting accesses are considered by the dependence analysis.
8761 A representation of the information contained in an object
8762 of type C<isl_union_access_info> can be obtained using
8764 #include <isl/flow.h>
8765 __isl_give isl_printer *
8766 isl_printer_print_union_access_info(
8767 __isl_take isl_printer *p,
8768 __isl_keep isl_union_access_info *access);
8769 __isl_give char *isl_union_access_info_to_str(
8770 __isl_keep isl_union_access_info *access);
8772 C<isl_union_access_info_to_str> prints the information in flow format.
8774 The output of C<isl_union_access_info_compute_flow> can be examined,
8775 copied, and freed using the following functions.
8777 #include <isl/flow.h>
8778 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
8779 __isl_keep isl_union_flow *flow);
8780 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
8781 __isl_keep isl_union_flow *flow);
8782 __isl_give isl_union_map *
8783 isl_union_flow_get_full_must_dependence(
8784 __isl_keep isl_union_flow *flow);
8785 __isl_give isl_union_map *
8786 isl_union_flow_get_full_may_dependence(
8787 __isl_keep isl_union_flow *flow);
8788 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
8789 __isl_keep isl_union_flow *flow);
8790 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
8791 __isl_keep isl_union_flow *flow);
8792 __isl_give isl_union_flow *isl_union_flow_copy(
8793 __isl_keep isl_union_flow *flow);
8794 __isl_null isl_union_flow *isl_union_flow_free(
8795 __isl_take isl_union_flow *flow);
8797 The relation returned by C<isl_union_flow_get_must_dependence>
8798 relates domain elements of must sources to domain elements of the sink.
8799 The relation returned by C<isl_union_flow_get_may_dependence>
8800 relates domain elements of must or may sources to domain elements of the sink
8801 and includes the previous relation as a subset.
8802 The relation returned by C<isl_union_flow_get_full_must_dependence>
8803 relates domain elements of must sources to pairs of domain elements of the sink
8804 and accessed data elements.
8805 The relation returned by C<isl_union_flow_get_full_may_dependence>
8806 relates domain elements of must or may sources to pairs of
8807 domain elements of the sink and accessed data elements.
8808 This relation includes the previous relation as a subset.
8809 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
8810 of the sink relation for which no dependences have been found.
8811 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
8812 of the sink relation for which no definite dependences have been found.
8813 That is, it contains those sink access that do not contribute to any
8814 of the elements in the relation returned
8815 by C<isl_union_flow_get_must_dependence>.
8817 A representation of the information contained in an object
8818 of type C<isl_union_flow> can be obtained using
8820 #include <isl/flow.h>
8821 __isl_give isl_printer *isl_printer_print_union_flow(
8822 __isl_take isl_printer *p,
8823 __isl_keep isl_union_flow *flow);
8824 __isl_give char *isl_union_flow_to_str(
8825 __isl_keep isl_union_flow *flow);
8827 C<isl_union_flow_to_str> prints the information in flow format.
8829 =head3 Low-level Interface
8831 A lower-level interface is provided by the following functions.
8833 #include <isl/flow.h>
8835 typedef int (*isl_access_level_before)(void *first, void *second);
8837 __isl_give isl_access_info *isl_access_info_alloc(
8838 __isl_take isl_map *sink,
8839 void *sink_user, isl_access_level_before fn,
8841 __isl_give isl_access_info *isl_access_info_add_source(
8842 __isl_take isl_access_info *acc,
8843 __isl_take isl_map *source, int must,
8845 __isl_null isl_access_info *isl_access_info_free(
8846 __isl_take isl_access_info *acc);
8848 __isl_give isl_flow *isl_access_info_compute_flow(
8849 __isl_take isl_access_info *acc);
8851 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,
8852 isl_stat (*fn)(__isl_take isl_map *dep, int must,
8853 void *dep_user, void *user),
8855 __isl_give isl_map *isl_flow_get_no_source(
8856 __isl_keep isl_flow *deps, int must);
8857 void isl_flow_free(__isl_take isl_flow *deps);
8859 The function C<isl_access_info_compute_flow> performs the actual
8860 dependence analysis. The other functions are used to construct
8861 the input for this function or to read off the output.
8863 The input is collected in an C<isl_access_info>, which can
8864 be created through a call to C<isl_access_info_alloc>.
8865 The arguments to this functions are the sink access relation
8866 C<sink>, a token C<sink_user> used to identify the sink
8867 access to the user, a callback function for specifying the
8868 relative order of source and sink accesses, and the number
8869 of source access relations that will be added.
8870 The callback function has type C<int (*)(void *first, void *second)>.
8871 The function is called with two user supplied tokens identifying
8872 either a source or the sink and it should return the shared nesting
8873 level and the relative order of the two accesses.
8874 In particular, let I<n> be the number of loops shared by
8875 the two accesses. If C<first> precedes C<second> textually,
8876 then the function should return I<2 * n + 1>; otherwise,
8877 it should return I<2 * n>.
8878 The sources can be added to the C<isl_access_info> by performing
8879 (at most) C<max_source> calls to C<isl_access_info_add_source>.
8880 C<must> indicates whether the source is a I<must> access
8881 or a I<may> access. Note that a multi-valued access relation
8882 should only be marked I<must> if every iteration in the domain
8883 of the relation accesses I<all> elements in its image.
8884 The C<source_user> token is again used to identify
8885 the source access. The range of the source access relation
8886 C<source> should have the same dimension as the range
8887 of the sink access relation.
8888 The C<isl_access_info_free> function should usually not be
8889 called explicitly, because it is called implicitly by
8890 C<isl_access_info_compute_flow>.
8892 The result of the dependence analysis is collected in an
8893 C<isl_flow>. There may be elements of
8894 the sink access for which no preceding source access could be
8895 found or for which all preceding sources are I<may> accesses.
8896 The relations containing these elements can be obtained through
8897 calls to C<isl_flow_get_no_source>, the first with C<must> set
8898 and the second with C<must> unset.
8899 In the case of standard flow dependence analysis,
8900 with the sink a read and the sources I<must> writes,
8901 the first relation corresponds to the reads from uninitialized
8902 array elements and the second relation is empty.
8903 The actual flow dependences can be extracted using
8904 C<isl_flow_foreach>. This function will call the user-specified
8905 callback function C<fn> for each B<non-empty> dependence between
8906 a source and the sink. The callback function is called
8907 with four arguments, the actual flow dependence relation
8908 mapping source iterations to sink iterations, a boolean that
8909 indicates whether it is a I<must> or I<may> dependence, a token
8910 identifying the source and an additional C<void *> with value
8911 equal to the third argument of the C<isl_flow_foreach> call.
8912 A dependence is marked I<must> if it originates from a I<must>
8913 source and if it is not followed by any I<may> sources.
8915 After finishing with an C<isl_flow>, the user should call
8916 C<isl_flow_free> to free all associated memory.
8918 =head3 Interaction with the Low-level Interface
8920 During the dependence analysis, we frequently need to perform
8921 the following operation. Given a relation between sink iterations
8922 and potential source iterations from a particular source domain,
8923 what is the last potential source iteration corresponding to each
8924 sink iteration. It can sometimes be convenient to adjust
8925 the set of potential source iterations before or after each such operation.
8926 The prototypical example is fuzzy array dataflow analysis,
8927 where we need to analyze if, based on data-dependent constraints,
8928 the sink iteration can ever be executed without one or more of
8929 the corresponding potential source iterations being executed.
8930 If so, we can introduce extra parameters and select an unknown
8931 but fixed source iteration from the potential source iterations.
8932 To be able to perform such manipulations, C<isl> provides the following
8935 #include <isl/flow.h>
8937 typedef __isl_give isl_restriction *(*isl_access_restrict)(
8938 __isl_keep isl_map *source_map,
8939 __isl_keep isl_set *sink, void *source_user,
8941 __isl_give isl_access_info *isl_access_info_set_restrict(
8942 __isl_take isl_access_info *acc,
8943 isl_access_restrict fn, void *user);
8945 The function C<isl_access_info_set_restrict> should be called
8946 before calling C<isl_access_info_compute_flow> and registers a callback function
8947 that will be called any time C<isl> is about to compute the last
8948 potential source. The first argument is the (reverse) proto-dependence,
8949 mapping sink iterations to potential source iterations.
8950 The second argument represents the sink iterations for which
8951 we want to compute the last source iteration.
8952 The third argument is the token corresponding to the source
8953 and the final argument is the token passed to C<isl_access_info_set_restrict>.
8954 The callback is expected to return a restriction on either the input or
8955 the output of the operation computing the last potential source.
8956 If the input needs to be restricted then restrictions are needed
8957 for both the source and the sink iterations. The sink iterations
8958 and the potential source iterations will be intersected with these sets.
8959 If the output needs to be restricted then only a restriction on the source
8960 iterations is required.
8961 If any error occurs, the callback should return C<NULL>.
8962 An C<isl_restriction> object can be created, freed and inspected
8963 using the following functions.
8965 #include <isl/flow.h>
8967 __isl_give isl_restriction *isl_restriction_input(
8968 __isl_take isl_set *source_restr,
8969 __isl_take isl_set *sink_restr);
8970 __isl_give isl_restriction *isl_restriction_output(
8971 __isl_take isl_set *source_restr);
8972 __isl_give isl_restriction *isl_restriction_none(
8973 __isl_take isl_map *source_map);
8974 __isl_give isl_restriction *isl_restriction_empty(
8975 __isl_take isl_map *source_map);
8976 __isl_null isl_restriction *isl_restriction_free(
8977 __isl_take isl_restriction *restr);
8979 C<isl_restriction_none> and C<isl_restriction_empty> are special
8980 cases of C<isl_restriction_input>. C<isl_restriction_none>
8981 is essentially equivalent to
8983 isl_restriction_input(isl_set_universe(
8984 isl_space_range(isl_map_get_space(source_map))),
8986 isl_space_domain(isl_map_get_space(source_map))));
8988 whereas C<isl_restriction_empty> is essentially equivalent to
8990 isl_restriction_input(isl_set_empty(
8991 isl_space_range(isl_map_get_space(source_map))),
8993 isl_space_domain(isl_map_get_space(source_map))));
8997 #include <isl/schedule.h>
8998 __isl_give isl_schedule *
8999 isl_schedule_constraints_compute_schedule(
9000 __isl_take isl_schedule_constraints *sc);
9002 The function C<isl_schedule_constraints_compute_schedule> can be
9003 used to compute a schedule that satisfies the given schedule constraints.
9004 These schedule constraints include the iteration domain for which
9005 a schedule should be computed and dependences between pairs of
9006 iterations. In particular, these dependences include
9007 I<validity> dependences and I<proximity> dependences.
9008 By default, the algorithm used to construct the schedule is similar
9009 to that of C<Pluto>.
9010 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
9012 The generated schedule respects all validity dependences.
9013 That is, all dependence distances over these dependences in the
9014 scheduled space are lexicographically positive.
9016 The default algorithm tries to ensure that the dependence distances
9017 over coincidence constraints are zero and to minimize the
9018 dependence distances over proximity dependences.
9019 Moreover, it tries to obtain sequences (bands) of schedule dimensions
9020 for groups of domains where the dependence distances over validity
9021 dependences have only non-negative values.
9022 Note that when minimizing the maximal dependence distance
9023 over proximity dependences, a single affine expression in the parameters
9024 is constructed that bounds all dependence distances. If no such expression
9025 exists, then the algorithm will fail and resort to an alternative
9026 scheduling algorithm. In particular, this means that adding proximity
9027 dependences may eliminate valid solutions. A typical example where this
9028 phenomenon may occur is when some subset of the proximity dependences
9029 has no restriction on some parameter, forcing the coefficient of that
9030 parameter to be zero, while some other subset forces the dependence
9031 distance to depend on that parameter, requiring the same coefficient
9033 When using Feautrier's algorithm, the coincidence and proximity constraints
9034 are only taken into account during the extension to a
9035 full-dimensional schedule.
9037 An C<isl_schedule_constraints> object can be constructed
9038 and manipulated using the following functions.
9040 #include <isl/schedule.h>
9041 __isl_give isl_schedule_constraints *
9042 isl_schedule_constraints_copy(
9043 __isl_keep isl_schedule_constraints *sc);
9044 __isl_give isl_schedule_constraints *
9045 isl_schedule_constraints_on_domain(
9046 __isl_take isl_union_set *domain);
9047 __isl_give isl_schedule_constraints *
9048 isl_schedule_constraints_set_context(
9049 __isl_take isl_schedule_constraints *sc,
9050 __isl_take isl_set *context);
9051 __isl_give isl_schedule_constraints *
9052 isl_schedule_constraints_set_validity(
9053 __isl_take isl_schedule_constraints *sc,
9054 __isl_take isl_union_map *validity);
9055 __isl_give isl_schedule_constraints *
9056 isl_schedule_constraints_set_coincidence(
9057 __isl_take isl_schedule_constraints *sc,
9058 __isl_take isl_union_map *coincidence);
9059 __isl_give isl_schedule_constraints *
9060 isl_schedule_constraints_set_proximity(
9061 __isl_take isl_schedule_constraints *sc,
9062 __isl_take isl_union_map *proximity);
9063 __isl_give isl_schedule_constraints *
9064 isl_schedule_constraints_set_conditional_validity(
9065 __isl_take isl_schedule_constraints *sc,
9066 __isl_take isl_union_map *condition,
9067 __isl_take isl_union_map *validity);
9068 __isl_give isl_schedule_constraints *
9069 isl_schedule_constraints_apply(
9070 __isl_take isl_schedule_constraints *sc,
9071 __isl_take isl_union_map *umap);
9072 __isl_null isl_schedule_constraints *
9073 isl_schedule_constraints_free(
9074 __isl_take isl_schedule_constraints *sc);
9076 The initial C<isl_schedule_constraints> object created by
9077 C<isl_schedule_constraints_on_domain> does not impose any constraints.
9078 That is, it has an empty set of dependences.
9079 The function C<isl_schedule_constraints_set_context> allows the user
9080 to specify additional constraints on the parameters that may
9081 be assumed to hold during the construction of the schedule.
9082 The function C<isl_schedule_constraints_set_validity> replaces the
9083 validity dependences, mapping domain elements I<i> to domain
9084 elements that should be scheduled after I<i>.
9085 The function C<isl_schedule_constraints_set_coincidence> replaces the
9086 coincidence dependences, mapping domain elements I<i> to domain
9087 elements that should be scheduled together with I<I>, if possible.
9088 The function C<isl_schedule_constraints_set_proximity> replaces the
9089 proximity dependences, mapping domain elements I<i> to domain
9090 elements that should be scheduled either before I<I>
9091 or as early as possible after I<i>.
9093 The function C<isl_schedule_constraints_set_conditional_validity>
9094 replaces the conditional validity constraints.
9095 A conditional validity constraint is only imposed when any of the corresponding
9096 conditions is satisfied, i.e., when any of them is non-zero.
9097 That is, the scheduler ensures that within each band if the dependence
9098 distances over the condition constraints are not all zero
9099 then all corresponding conditional validity constraints are respected.
9100 A conditional validity constraint corresponds to a condition
9101 if the two are adjacent, i.e., if the domain of one relation intersect
9102 the range of the other relation.
9103 The typical use case of conditional validity constraints is
9104 to allow order constraints between live ranges to be violated
9105 as long as the live ranges themselves are local to the band.
9106 To allow more fine-grained control over which conditions correspond
9107 to which conditional validity constraints, the domains and ranges
9108 of these relations may include I<tags>. That is, the domains and
9109 ranges of those relation may themselves be wrapped relations
9110 where the iteration domain appears in the domain of those wrapped relations
9111 and the range of the wrapped relations can be arbitrarily chosen
9112 by the user. Conditions and conditional validity constraints are only
9113 considered adjacent to each other if the entire wrapped relation matches.
9114 In particular, a relation with a tag will never be considered adjacent
9115 to a relation without a tag.
9117 The function C<isl_schedule_constraints_compute_schedule> takes
9118 schedule constraints that are defined on some set of domain elements
9119 and transforms them to schedule constraints on the elements
9120 to which these domain elements are mapped by the given transformation.
9122 An C<isl_schedule_constraints> object can be inspected
9123 using the following functions.
9125 #include <isl/schedule.h>
9126 __isl_give isl_union_set *
9127 isl_schedule_constraints_get_domain(
9128 __isl_keep isl_schedule_constraints *sc);
9129 __isl_give isl_set *isl_schedule_constraints_get_context(
9130 __isl_keep isl_schedule_constraints *sc);
9131 __isl_give isl_union_map *
9132 isl_schedule_constraints_get_validity(
9133 __isl_keep isl_schedule_constraints *sc);
9134 __isl_give isl_union_map *
9135 isl_schedule_constraints_get_coincidence(
9136 __isl_keep isl_schedule_constraints *sc);
9137 __isl_give isl_union_map *
9138 isl_schedule_constraints_get_proximity(
9139 __isl_keep isl_schedule_constraints *sc);
9140 __isl_give isl_union_map *
9141 isl_schedule_constraints_get_conditional_validity(
9142 __isl_keep isl_schedule_constraints *sc);
9143 __isl_give isl_union_map *
9144 isl_schedule_constraints_get_conditional_validity_condition(
9145 __isl_keep isl_schedule_constraints *sc);
9147 An C<isl_schedule_constraints> object can be read from input
9148 using the following functions.
9150 #include <isl/schedule.h>
9151 __isl_give isl_schedule_constraints *
9152 isl_schedule_constraints_read_from_str(isl_ctx *ctx,
9154 __isl_give isl_schedule_constraints *
9155 isl_schedule_constraints_read_from_file(isl_ctx *ctx,
9158 The contents of an C<isl_schedule_constraints> object can be printed
9159 using the following functions.
9161 #include <isl/schedule.h>
9162 __isl_give isl_printer *
9163 isl_printer_print_schedule_constraints(
9164 __isl_take isl_printer *p,
9165 __isl_keep isl_schedule_constraints *sc);
9166 __isl_give char *isl_schedule_constraints_to_str(
9167 __isl_keep isl_schedule_constraints *sc);
9169 The following function computes a schedule directly from
9170 an iteration domain and validity and proximity dependences
9171 and is implemented in terms of the functions described above.
9172 The use of C<isl_union_set_compute_schedule> is discouraged.
9174 #include <isl/schedule.h>
9175 __isl_give isl_schedule *isl_union_set_compute_schedule(
9176 __isl_take isl_union_set *domain,
9177 __isl_take isl_union_map *validity,
9178 __isl_take isl_union_map *proximity);
9180 The generated schedule represents a schedule tree.
9181 For more information on schedule trees, see
9182 L</"Schedule Trees">.
9186 #include <isl/schedule.h>
9187 isl_stat isl_options_set_schedule_max_coefficient(
9188 isl_ctx *ctx, int val);
9189 int isl_options_get_schedule_max_coefficient(
9191 isl_stat isl_options_set_schedule_max_constant_term(
9192 isl_ctx *ctx, int val);
9193 int isl_options_get_schedule_max_constant_term(
9195 isl_stat isl_options_set_schedule_serialize_sccs(
9196 isl_ctx *ctx, int val);
9197 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx);
9198 isl_stat isl_options_set_schedule_whole_component(
9199 isl_ctx *ctx, int val);
9200 int isl_options_get_schedule_whole_component(
9202 isl_stat isl_options_set_schedule_maximize_band_depth(
9203 isl_ctx *ctx, int val);
9204 int isl_options_get_schedule_maximize_band_depth(
9206 isl_stat isl_options_set_schedule_maximize_coincidence(
9207 isl_ctx *ctx, int val);
9208 int isl_options_get_schedule_maximize_coincidence(
9210 isl_stat isl_options_set_schedule_outer_coincidence(
9211 isl_ctx *ctx, int val);
9212 int isl_options_get_schedule_outer_coincidence(
9214 isl_stat isl_options_set_schedule_split_scaled(
9215 isl_ctx *ctx, int val);
9216 int isl_options_get_schedule_split_scaled(
9218 isl_stat isl_options_set_schedule_treat_coalescing(
9219 isl_ctx *ctx, int val);
9220 int isl_options_get_schedule_treat_coalescing(
9222 isl_stat isl_options_set_schedule_algorithm(
9223 isl_ctx *ctx, int val);
9224 int isl_options_get_schedule_algorithm(
9226 isl_stat isl_options_set_schedule_separate_components(
9227 isl_ctx *ctx, int val);
9228 int isl_options_get_schedule_separate_components(
9233 =item * schedule_max_coefficient
9235 This option enforces that the coefficients for variable and parameter
9236 dimensions in the calculated schedule are not larger than the specified value.
9237 This option can significantly increase the speed of the scheduling calculation
9238 and may also prevent fusing of unrelated dimensions. A value of -1 means that
9239 this option does not introduce bounds on the variable or parameter
9242 =item * schedule_max_constant_term
9244 This option enforces that the constant coefficients in the calculated schedule
9245 are not larger than the maximal constant term. This option can significantly
9246 increase the speed of the scheduling calculation and may also prevent fusing of
9247 unrelated dimensions. A value of -1 means that this option does not introduce
9248 bounds on the constant coefficients.
9250 =item * schedule_serialize_sccs
9252 If this option is set, then all strongly connected components
9253 in the dependence graph are serialized as soon as they are detected.
9254 This means in particular that instances of statements will only
9255 appear in the same band node if these statements belong
9256 to the same strongly connected component at the point where
9257 the band node is constructed.
9259 =item * schedule_whole_component
9261 If this option is set, then entire (weakly) connected
9262 components in the dependence graph are scheduled together
9264 Otherwise, each strongly connected component within
9265 such a weakly connected component is first scheduled separately
9266 and then combined with other strongly connected components.
9267 This option has no effect if C<schedule_serialize_sccs> is set.
9269 =item * schedule_maximize_band_depth
9271 If this option is set, then the scheduler tries to maximize
9272 the width of the bands. Wider bands give more possibilities for tiling.
9273 In particular, if the C<schedule_whole_component> option is set,
9274 then bands are split if this might result in wider bands.
9275 Otherwise, the effect of this option is to only allow
9276 strongly connected components to be combined if this does
9277 not reduce the width of the bands.
9278 Note that if the C<schedule_serialize_sccs> options is set, then
9279 the C<schedule_maximize_band_depth> option therefore has no effect.
9281 =item * schedule_maximize_coincidence
9283 This option is only effective if the C<schedule_whole_component>
9284 option is turned off.
9285 If the C<schedule_maximize_coincidence> option is set, then (clusters of)
9286 strongly connected components are only combined with each other
9287 if this does not reduce the number of coincident band members.
9289 =item * schedule_outer_coincidence
9291 If this option is set, then we try to construct schedules
9292 where the outermost scheduling dimension in each band
9293 satisfies the coincidence constraints.
9295 =item * schedule_algorithm
9297 Selects the scheduling algorithm to be used.
9298 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
9299 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
9301 =item * schedule_split_scaled
9303 If this option is set, then we try to construct schedules in which the
9304 constant term is split off from the linear part if the linear parts of
9305 the scheduling rows for all nodes in the graphs have a common non-trivial
9307 The constant term is then placed in a separate band and the linear
9309 This option is only effective when the Feautrier style scheduler is
9310 being used, either as the main scheduler or as a fallback for the
9311 Pluto-like scheduler.
9313 =item * schedule_treat_coalescing
9315 If this option is set, then the scheduler will try and avoid
9316 producing schedules that perform loop coalescing.
9317 In particular, for the Pluto-like scheduler, this option places
9318 bounds on the schedule coefficients based on the sizes of the instance sets.
9319 For the Feautrier style scheduler, this option detects potentially
9320 coalescing schedules and then tries to adjust the schedule to avoid
9323 =item * schedule_separate_components
9325 If this option is set then the function C<isl_schedule_get_map>
9326 will treat set nodes in the same way as sequence nodes.
9330 =head2 AST Generation
9332 This section describes the C<isl> functionality for generating
9333 ASTs that visit all the elements
9334 in a domain in an order specified by a schedule tree or
9336 In case the schedule given as a C<isl_union_map>, an AST is generated
9337 that visits all the elements in the domain of the C<isl_union_map>
9338 according to the lexicographic order of the corresponding image
9339 element(s). If the range of the C<isl_union_map> consists of
9340 elements in more than one space, then each of these spaces is handled
9341 separately in an arbitrary order.
9342 It should be noted that the schedule tree or the image elements
9343 in a schedule map only specify the I<order>
9344 in which the corresponding domain elements should be visited.
9345 No direct relation between the partial schedule values
9346 or the image elements on the one hand and the loop iterators
9347 in the generated AST on the other hand should be assumed.
9349 Each AST is generated within a build. The initial build
9350 simply specifies the constraints on the parameters (if any)
9351 and can be created, inspected, copied and freed using the following functions.
9353 #include <isl/ast_build.h>
9354 __isl_give isl_ast_build *isl_ast_build_alloc(
9356 __isl_give isl_ast_build *isl_ast_build_from_context(
9357 __isl_take isl_set *set);
9358 __isl_give isl_ast_build *isl_ast_build_copy(
9359 __isl_keep isl_ast_build *build);
9360 __isl_null isl_ast_build *isl_ast_build_free(
9361 __isl_take isl_ast_build *build);
9363 The C<set> argument is usually a parameter set with zero or more parameters.
9364 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
9365 this set is required to be a parameter set.
9366 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
9367 specify any parameter constraints.
9368 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
9369 and L</"Fine-grained Control over AST Generation">.
9370 Finally, the AST itself can be constructed using one of the following
9373 #include <isl/ast_build.h>
9374 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
9375 __isl_keep isl_ast_build *build,
9376 __isl_take isl_schedule *schedule);
9377 __isl_give isl_ast_node *
9378 isl_ast_build_node_from_schedule_map(
9379 __isl_keep isl_ast_build *build,
9380 __isl_take isl_union_map *schedule);
9382 =head3 Inspecting the AST
9384 The basic properties of an AST node can be obtained as follows.
9386 #include <isl/ast.h>
9387 enum isl_ast_node_type isl_ast_node_get_type(
9388 __isl_keep isl_ast_node *node);
9390 The type of an AST node is one of
9391 C<isl_ast_node_for>,
9393 C<isl_ast_node_block>,
9394 C<isl_ast_node_mark> or
9395 C<isl_ast_node_user>.
9396 An C<isl_ast_node_for> represents a for node.
9397 An C<isl_ast_node_if> represents an if node.
9398 An C<isl_ast_node_block> represents a compound node.
9399 An C<isl_ast_node_mark> introduces a mark in the AST.
9400 An C<isl_ast_node_user> represents an expression statement.
9401 An expression statement typically corresponds to a domain element, i.e.,
9402 one of the elements that is visited by the AST.
9404 Each type of node has its own additional properties.
9406 #include <isl/ast.h>
9407 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
9408 __isl_keep isl_ast_node *node);
9409 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
9410 __isl_keep isl_ast_node *node);
9411 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
9412 __isl_keep isl_ast_node *node);
9413 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
9414 __isl_keep isl_ast_node *node);
9415 __isl_give isl_ast_node *isl_ast_node_for_get_body(
9416 __isl_keep isl_ast_node *node);
9417 isl_bool isl_ast_node_for_is_degenerate(
9418 __isl_keep isl_ast_node *node);
9420 An C<isl_ast_for> is considered degenerate if it is known to execute
9423 #include <isl/ast.h>
9424 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
9425 __isl_keep isl_ast_node *node);
9426 __isl_give isl_ast_node *isl_ast_node_if_get_then(
9427 __isl_keep isl_ast_node *node);
9428 isl_bool isl_ast_node_if_has_else(
9429 __isl_keep isl_ast_node *node);
9430 __isl_give isl_ast_node *isl_ast_node_if_get_else(
9431 __isl_keep isl_ast_node *node);
9433 __isl_give isl_ast_node_list *
9434 isl_ast_node_block_get_children(
9435 __isl_keep isl_ast_node *node);
9437 __isl_give isl_id *isl_ast_node_mark_get_id(
9438 __isl_keep isl_ast_node *node);
9439 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
9440 __isl_keep isl_ast_node *node);
9442 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
9443 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
9445 #include <isl/ast.h>
9446 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
9447 __isl_keep isl_ast_node *node);
9449 All descendants of a specific node in the AST (including the node itself)
9451 in depth-first pre-order using the following function.
9453 #include <isl/ast.h>
9454 isl_stat isl_ast_node_foreach_descendant_top_down(
9455 __isl_keep isl_ast_node *node,
9456 isl_bool (*fn)(__isl_keep isl_ast_node *node,
9457 void *user), void *user);
9459 The callback function should return C<isl_bool_true> if the children
9460 of the given node should be visited and C<isl_bool_false> if they should not.
9461 It should return C<isl_bool_error> in case of failure, in which case
9462 the entire traversal is aborted.
9464 Each of the returned C<isl_ast_expr>s can in turn be inspected using
9465 the following functions.
9467 #include <isl/ast.h>
9468 enum isl_ast_expr_type isl_ast_expr_get_type(
9469 __isl_keep isl_ast_expr *expr);
9471 The type of an AST expression is one of
9473 C<isl_ast_expr_id> or
9474 C<isl_ast_expr_int>.
9475 An C<isl_ast_expr_op> represents the result of an operation.
9476 An C<isl_ast_expr_id> represents an identifier.
9477 An C<isl_ast_expr_int> represents an integer value.
9479 Each type of expression has its own additional properties.
9481 #include <isl/ast.h>
9482 enum isl_ast_op_type isl_ast_expr_get_op_type(
9483 __isl_keep isl_ast_expr *expr);
9484 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
9485 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
9486 __isl_keep isl_ast_expr *expr, int pos);
9487 isl_stat isl_ast_expr_foreach_ast_op_type(
9488 __isl_keep isl_ast_expr *expr,
9489 isl_stat (*fn)(enum isl_ast_op_type type,
9490 void *user), void *user);
9491 isl_stat isl_ast_node_foreach_ast_op_type(
9492 __isl_keep isl_ast_node *node,
9493 isl_stat (*fn)(enum isl_ast_op_type type,
9494 void *user), void *user);
9496 C<isl_ast_expr_get_op_type> returns the type of the operation
9497 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
9498 arguments. C<isl_ast_expr_get_op_arg> returns the specified
9500 C<isl_ast_expr_foreach_ast_op_type> calls C<fn> for each distinct
9501 C<isl_ast_op_type> that appears in C<expr>.
9502 C<isl_ast_node_foreach_ast_op_type> does the same for each distinct
9503 C<isl_ast_op_type> that appears in C<node>.
9504 The operation type is one of the following.
9508 =item C<isl_ast_op_and>
9510 Logical I<and> of two arguments.
9511 Both arguments can be evaluated.
9513 =item C<isl_ast_op_and_then>
9515 Logical I<and> of two arguments.
9516 The second argument can only be evaluated if the first evaluates to true.
9518 =item C<isl_ast_op_or>
9520 Logical I<or> of two arguments.
9521 Both arguments can be evaluated.
9523 =item C<isl_ast_op_or_else>
9525 Logical I<or> of two arguments.
9526 The second argument can only be evaluated if the first evaluates to false.
9528 =item C<isl_ast_op_max>
9530 Maximum of two or more arguments.
9532 =item C<isl_ast_op_min>
9534 Minimum of two or more arguments.
9536 =item C<isl_ast_op_minus>
9540 =item C<isl_ast_op_add>
9542 Sum of two arguments.
9544 =item C<isl_ast_op_sub>
9546 Difference of two arguments.
9548 =item C<isl_ast_op_mul>
9550 Product of two arguments.
9552 =item C<isl_ast_op_div>
9554 Exact division. That is, the result is known to be an integer.
9556 =item C<isl_ast_op_fdiv_q>
9558 Result of integer division, rounded towards negative
9561 =item C<isl_ast_op_pdiv_q>
9563 Result of integer division, where dividend is known to be non-negative.
9565 =item C<isl_ast_op_pdiv_r>
9567 Remainder of integer division, where dividend is known to be non-negative.
9569 =item C<isl_ast_op_zdiv_r>
9571 Equal to zero iff the remainder on integer division is zero.
9573 =item C<isl_ast_op_cond>
9575 Conditional operator defined on three arguments.
9576 If the first argument evaluates to true, then the result
9577 is equal to the second argument. Otherwise, the result
9578 is equal to the third argument.
9579 The second and third argument may only be evaluated if
9580 the first argument evaluates to true and false, respectively.
9581 Corresponds to C<a ? b : c> in C.
9583 =item C<isl_ast_op_select>
9585 Conditional operator defined on three arguments.
9586 If the first argument evaluates to true, then the result
9587 is equal to the second argument. Otherwise, the result
9588 is equal to the third argument.
9589 The second and third argument may be evaluated independently
9590 of the value of the first argument.
9591 Corresponds to C<a * b + (1 - a) * c> in C.
9593 =item C<isl_ast_op_eq>
9597 =item C<isl_ast_op_le>
9599 Less than or equal relation.
9601 =item C<isl_ast_op_lt>
9605 =item C<isl_ast_op_ge>
9607 Greater than or equal relation.
9609 =item C<isl_ast_op_gt>
9611 Greater than relation.
9613 =item C<isl_ast_op_call>
9616 The number of arguments of the C<isl_ast_expr> is one more than
9617 the number of arguments in the function call, the first argument
9618 representing the function being called.
9620 =item C<isl_ast_op_access>
9623 The number of arguments of the C<isl_ast_expr> is one more than
9624 the number of index expressions in the array access, the first argument
9625 representing the array being accessed.
9627 =item C<isl_ast_op_member>
9630 This operation has two arguments, a structure and the name of
9631 the member of the structure being accessed.
9635 #include <isl/ast.h>
9636 __isl_give isl_id *isl_ast_expr_get_id(
9637 __isl_keep isl_ast_expr *expr);
9639 Return the identifier represented by the AST expression.
9641 #include <isl/ast.h>
9642 __isl_give isl_val *isl_ast_expr_get_val(
9643 __isl_keep isl_ast_expr *expr);
9645 Return the integer represented by the AST expression.
9647 =head3 Properties of ASTs
9649 #include <isl/ast.h>
9650 isl_bool isl_ast_expr_is_equal(
9651 __isl_keep isl_ast_expr *expr1,
9652 __isl_keep isl_ast_expr *expr2);
9654 Check if two C<isl_ast_expr>s are equal to each other.
9656 =head3 Manipulating and printing the AST
9658 AST nodes can be copied and freed using the following functions.
9660 #include <isl/ast.h>
9661 __isl_give isl_ast_node *isl_ast_node_copy(
9662 __isl_keep isl_ast_node *node);
9663 __isl_null isl_ast_node *isl_ast_node_free(
9664 __isl_take isl_ast_node *node);
9666 AST expressions can be copied and freed using the following functions.
9668 #include <isl/ast.h>
9669 __isl_give isl_ast_expr *isl_ast_expr_copy(
9670 __isl_keep isl_ast_expr *expr);
9671 __isl_null isl_ast_expr *isl_ast_expr_free(
9672 __isl_take isl_ast_expr *expr);
9674 New AST expressions can be created either directly or within
9675 the context of an C<isl_ast_build>.
9677 #include <isl/ast.h>
9678 __isl_give isl_ast_expr *isl_ast_expr_from_val(
9679 __isl_take isl_val *v);
9680 __isl_give isl_ast_expr *isl_ast_expr_from_id(
9681 __isl_take isl_id *id);
9682 __isl_give isl_ast_expr *isl_ast_expr_neg(
9683 __isl_take isl_ast_expr *expr);
9684 __isl_give isl_ast_expr *isl_ast_expr_address_of(
9685 __isl_take isl_ast_expr *expr);
9686 __isl_give isl_ast_expr *isl_ast_expr_add(
9687 __isl_take isl_ast_expr *expr1,
9688 __isl_take isl_ast_expr *expr2);
9689 __isl_give isl_ast_expr *isl_ast_expr_sub(
9690 __isl_take isl_ast_expr *expr1,
9691 __isl_take isl_ast_expr *expr2);
9692 __isl_give isl_ast_expr *isl_ast_expr_mul(
9693 __isl_take isl_ast_expr *expr1,
9694 __isl_take isl_ast_expr *expr2);
9695 __isl_give isl_ast_expr *isl_ast_expr_div(
9696 __isl_take isl_ast_expr *expr1,
9697 __isl_take isl_ast_expr *expr2);
9698 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
9699 __isl_take isl_ast_expr *expr1,
9700 __isl_take isl_ast_expr *expr2);
9701 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
9702 __isl_take isl_ast_expr *expr1,
9703 __isl_take isl_ast_expr *expr2);
9704 __isl_give isl_ast_expr *isl_ast_expr_and(
9705 __isl_take isl_ast_expr *expr1,
9706 __isl_take isl_ast_expr *expr2)
9707 __isl_give isl_ast_expr *isl_ast_expr_and_then(
9708 __isl_take isl_ast_expr *expr1,
9709 __isl_take isl_ast_expr *expr2)
9710 __isl_give isl_ast_expr *isl_ast_expr_or(
9711 __isl_take isl_ast_expr *expr1,
9712 __isl_take isl_ast_expr *expr2)
9713 __isl_give isl_ast_expr *isl_ast_expr_or_else(
9714 __isl_take isl_ast_expr *expr1,
9715 __isl_take isl_ast_expr *expr2)
9716 __isl_give isl_ast_expr *isl_ast_expr_eq(
9717 __isl_take isl_ast_expr *expr1,
9718 __isl_take isl_ast_expr *expr2);
9719 __isl_give isl_ast_expr *isl_ast_expr_le(
9720 __isl_take isl_ast_expr *expr1,
9721 __isl_take isl_ast_expr *expr2);
9722 __isl_give isl_ast_expr *isl_ast_expr_lt(
9723 __isl_take isl_ast_expr *expr1,
9724 __isl_take isl_ast_expr *expr2);
9725 __isl_give isl_ast_expr *isl_ast_expr_ge(
9726 __isl_take isl_ast_expr *expr1,
9727 __isl_take isl_ast_expr *expr2);
9728 __isl_give isl_ast_expr *isl_ast_expr_gt(
9729 __isl_take isl_ast_expr *expr1,
9730 __isl_take isl_ast_expr *expr2);
9731 __isl_give isl_ast_expr *isl_ast_expr_access(
9732 __isl_take isl_ast_expr *array,
9733 __isl_take isl_ast_expr_list *indices);
9734 __isl_give isl_ast_expr *isl_ast_expr_call(
9735 __isl_take isl_ast_expr *function,
9736 __isl_take isl_ast_expr_list *arguments);
9738 The function C<isl_ast_expr_address_of> can be applied to an
9739 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
9740 to represent the address of the C<isl_ast_expr_access>. The function
9741 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
9742 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
9744 #include <isl/ast_build.h>
9745 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
9746 __isl_keep isl_ast_build *build,
9747 __isl_take isl_set *set);
9748 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
9749 __isl_keep isl_ast_build *build,
9750 __isl_take isl_pw_aff *pa);
9751 __isl_give isl_ast_expr *
9752 isl_ast_build_access_from_pw_multi_aff(
9753 __isl_keep isl_ast_build *build,
9754 __isl_take isl_pw_multi_aff *pma);
9755 __isl_give isl_ast_expr *
9756 isl_ast_build_access_from_multi_pw_aff(
9757 __isl_keep isl_ast_build *build,
9758 __isl_take isl_multi_pw_aff *mpa);
9759 __isl_give isl_ast_expr *
9760 isl_ast_build_call_from_pw_multi_aff(
9761 __isl_keep isl_ast_build *build,
9762 __isl_take isl_pw_multi_aff *pma);
9763 __isl_give isl_ast_expr *
9764 isl_ast_build_call_from_multi_pw_aff(
9765 __isl_keep isl_ast_build *build,
9766 __isl_take isl_multi_pw_aff *mpa);
9769 the domains of C<pa>, C<mpa> and C<pma> should correspond
9770 to the schedule space of C<build>.
9771 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
9772 the function being called.
9773 If the accessed space is a nested relation, then it is taken
9774 to represent an access of the member specified by the range
9775 of this nested relation of the structure specified by the domain
9776 of the nested relation.
9778 The following functions can be used to modify an C<isl_ast_expr>.
9780 #include <isl/ast.h>
9781 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
9782 __isl_take isl_ast_expr *expr, int pos,
9783 __isl_take isl_ast_expr *arg);
9785 Replace the argument of C<expr> at position C<pos> by C<arg>.
9787 #include <isl/ast.h>
9788 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
9789 __isl_take isl_ast_expr *expr,
9790 __isl_take isl_id_to_ast_expr *id2expr);
9792 The function C<isl_ast_expr_substitute_ids> replaces the
9793 subexpressions of C<expr> of type C<isl_ast_expr_id>
9794 by the corresponding expression in C<id2expr>, if there is any.
9797 User specified data can be attached to an C<isl_ast_node> and obtained
9798 from the same C<isl_ast_node> using the following functions.
9800 #include <isl/ast.h>
9801 __isl_give isl_ast_node *isl_ast_node_set_annotation(
9802 __isl_take isl_ast_node *node,
9803 __isl_take isl_id *annotation);
9804 __isl_give isl_id *isl_ast_node_get_annotation(
9805 __isl_keep isl_ast_node *node);
9807 Basic printing can be performed using the following functions.
9809 #include <isl/ast.h>
9810 __isl_give isl_printer *isl_printer_print_ast_expr(
9811 __isl_take isl_printer *p,
9812 __isl_keep isl_ast_expr *expr);
9813 __isl_give isl_printer *isl_printer_print_ast_node(
9814 __isl_take isl_printer *p,
9815 __isl_keep isl_ast_node *node);
9816 __isl_give char *isl_ast_expr_to_str(
9817 __isl_keep isl_ast_expr *expr);
9818 __isl_give char *isl_ast_node_to_str(
9819 __isl_keep isl_ast_node *node);
9820 __isl_give char *isl_ast_expr_to_C_str(
9821 __isl_keep isl_ast_expr *expr);
9822 __isl_give char *isl_ast_node_to_C_str(
9823 __isl_keep isl_ast_node *node);
9825 The functions C<isl_ast_expr_to_C_str> and
9826 C<isl_ast_node_to_C_str> are convenience functions
9827 that return a string representation of the input in C format.
9829 More advanced printing can be performed using the following functions.
9831 #include <isl/ast.h>
9832 __isl_give isl_printer *isl_ast_op_type_set_print_name(
9833 __isl_take isl_printer *p,
9834 enum isl_ast_op_type type,
9835 __isl_keep const char *name);
9836 isl_stat isl_options_set_ast_print_macro_once(
9837 isl_ctx *ctx, int val);
9838 int isl_options_get_ast_print_macro_once(isl_ctx *ctx);
9839 __isl_give isl_printer *isl_ast_op_type_print_macro(
9840 enum isl_ast_op_type type,
9841 __isl_take isl_printer *p);
9842 __isl_give isl_printer *isl_ast_expr_print_macros(
9843 __isl_keep isl_ast_expr *expr,
9844 __isl_take isl_printer *p);
9845 __isl_give isl_printer *isl_ast_node_print_macros(
9846 __isl_keep isl_ast_node *node,
9847 __isl_take isl_printer *p);
9848 __isl_give isl_printer *isl_ast_node_print(
9849 __isl_keep isl_ast_node *node,
9850 __isl_take isl_printer *p,
9851 __isl_take isl_ast_print_options *options);
9852 __isl_give isl_printer *isl_ast_node_for_print(
9853 __isl_keep isl_ast_node *node,
9854 __isl_take isl_printer *p,
9855 __isl_take isl_ast_print_options *options);
9856 __isl_give isl_printer *isl_ast_node_if_print(
9857 __isl_keep isl_ast_node *node,
9858 __isl_take isl_printer *p,
9859 __isl_take isl_ast_print_options *options);
9861 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
9862 C<isl> may print out an AST that makes use of macros such
9863 as C<floord>, C<min> and C<max>.
9864 The names of these macros may be modified by a call
9865 to C<isl_ast_op_type_set_print_name>. The user-specified
9866 names are associated to the printer object.
9867 C<isl_ast_op_type_print_macro> prints out the macro
9868 corresponding to a specific C<isl_ast_op_type>.
9869 If the print-macro-once option is set, then a given macro definition
9870 is only printed once to any given printer object.
9871 C<isl_ast_expr_print_macros> scans the C<isl_ast_expr>
9872 for subexpressions where these macros would be used and prints
9873 out the required macro definitions.
9874 Essentially, C<isl_ast_expr_print_macros> calls
9875 C<isl_ast_expr_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
9876 as function argument.
9877 C<isl_ast_node_print_macros> does the same
9878 for expressions in its C<isl_ast_node> argument.
9879 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
9880 C<isl_ast_node_if_print> print an C<isl_ast_node>
9881 in C<ISL_FORMAT_C>, but allow for some extra control
9882 through an C<isl_ast_print_options> object.
9883 This object can be created using the following functions.
9885 #include <isl/ast.h>
9886 __isl_give isl_ast_print_options *
9887 isl_ast_print_options_alloc(isl_ctx *ctx);
9888 __isl_give isl_ast_print_options *
9889 isl_ast_print_options_copy(
9890 __isl_keep isl_ast_print_options *options);
9891 __isl_null isl_ast_print_options *
9892 isl_ast_print_options_free(
9893 __isl_take isl_ast_print_options *options);
9895 __isl_give isl_ast_print_options *
9896 isl_ast_print_options_set_print_user(
9897 __isl_take isl_ast_print_options *options,
9898 __isl_give isl_printer *(*print_user)(
9899 __isl_take isl_printer *p,
9900 __isl_take isl_ast_print_options *options,
9901 __isl_keep isl_ast_node *node, void *user),
9903 __isl_give isl_ast_print_options *
9904 isl_ast_print_options_set_print_for(
9905 __isl_take isl_ast_print_options *options,
9906 __isl_give isl_printer *(*print_for)(
9907 __isl_take isl_printer *p,
9908 __isl_take isl_ast_print_options *options,
9909 __isl_keep isl_ast_node *node, void *user),
9912 The callback set by C<isl_ast_print_options_set_print_user>
9913 is called whenever a node of type C<isl_ast_node_user> needs to
9915 The callback set by C<isl_ast_print_options_set_print_for>
9916 is called whenever a node of type C<isl_ast_node_for> needs to
9918 Note that C<isl_ast_node_for_print> will I<not> call the
9919 callback set by C<isl_ast_print_options_set_print_for> on the node
9920 on which C<isl_ast_node_for_print> is called, but only on nested
9921 nodes of type C<isl_ast_node_for>. It is therefore safe to
9922 call C<isl_ast_node_for_print> from within the callback set by
9923 C<isl_ast_print_options_set_print_for>.
9925 The following option determines the type to be used for iterators
9926 while printing the AST.
9928 isl_stat isl_options_set_ast_iterator_type(
9929 isl_ctx *ctx, const char *val);
9930 const char *isl_options_get_ast_iterator_type(
9933 The AST printer only prints body nodes as blocks if these
9934 blocks cannot be safely omitted.
9935 For example, a C<for> node with one body node will not be
9936 surrounded with braces in C<ISL_FORMAT_C>.
9937 A block will always be printed by setting the following option.
9939 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx,
9941 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
9945 #include <isl/ast_build.h>
9946 isl_stat isl_options_set_ast_build_atomic_upper_bound(
9947 isl_ctx *ctx, int val);
9948 int isl_options_get_ast_build_atomic_upper_bound(
9950 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
9952 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
9953 isl_stat isl_options_set_ast_build_detect_min_max(
9954 isl_ctx *ctx, int val);
9955 int isl_options_get_ast_build_detect_min_max(
9957 isl_stat isl_options_set_ast_build_exploit_nested_bounds(
9958 isl_ctx *ctx, int val);
9959 int isl_options_get_ast_build_exploit_nested_bounds(
9961 isl_stat isl_options_set_ast_build_group_coscheduled(
9962 isl_ctx *ctx, int val);
9963 int isl_options_get_ast_build_group_coscheduled(
9965 isl_stat isl_options_set_ast_build_scale_strides(
9966 isl_ctx *ctx, int val);
9967 int isl_options_get_ast_build_scale_strides(
9969 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx,
9971 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
9972 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx,
9974 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
9978 =item * ast_build_atomic_upper_bound
9980 Generate loop upper bounds that consist of the current loop iterator,
9981 an operator and an expression not involving the iterator.
9982 If this option is not set, then the current loop iterator may appear
9983 several times in the upper bound.
9984 For example, when this option is turned off, AST generation
9987 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
9991 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
9994 When the option is turned on, the following AST is generated
9996 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
9999 =item * ast_build_prefer_pdiv
10001 If this option is turned off, then the AST generation will
10002 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
10003 operators, but no C<isl_ast_op_pdiv_q> or
10004 C<isl_ast_op_pdiv_r> operators.
10005 If this option is turned on, then C<isl> will try to convert
10006 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
10007 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
10009 =item * ast_build_detect_min_max
10011 If this option is turned on, then C<isl> will try and detect
10012 min or max-expressions when building AST expressions from
10013 piecewise affine expressions.
10015 =item * ast_build_exploit_nested_bounds
10017 Simplify conditions based on bounds of nested for loops.
10018 In particular, remove conditions that are implied by the fact
10019 that one or more nested loops have at least one iteration,
10020 meaning that the upper bound is at least as large as the lower bound.
10021 For example, when this option is turned off, AST generation
10024 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
10030 for (int c0 = 0; c0 <= N; c0 += 1)
10031 for (int c1 = 0; c1 <= M; c1 += 1)
10034 When the option is turned on, the following AST is generated
10036 for (int c0 = 0; c0 <= N; c0 += 1)
10037 for (int c1 = 0; c1 <= M; c1 += 1)
10040 =item * ast_build_group_coscheduled
10042 If two domain elements are assigned the same schedule point, then
10043 they may be executed in any order and they may even appear in different
10044 loops. If this options is set, then the AST generator will make
10045 sure that coscheduled domain elements do not appear in separate parts
10046 of the AST. This is useful in case of nested AST generation
10047 if the outer AST generation is given only part of a schedule
10048 and the inner AST generation should handle the domains that are
10049 coscheduled by this initial part of the schedule together.
10050 For example if an AST is generated for a schedule
10052 { A[i] -> [0]; B[i] -> [0] }
10054 then the C<isl_ast_build_set_create_leaf> callback described
10055 below may get called twice, once for each domain.
10056 Setting this option ensures that the callback is only called once
10057 on both domains together.
10059 =item * ast_build_separation_bounds
10061 This option specifies which bounds to use during separation.
10062 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
10063 then all (possibly implicit) bounds on the current dimension will
10064 be used during separation.
10065 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
10066 then only those bounds that are explicitly available will
10067 be used during separation.
10069 =item * ast_build_scale_strides
10071 This option specifies whether the AST generator is allowed
10072 to scale down iterators of strided loops.
10074 =item * ast_build_allow_else
10076 This option specifies whether the AST generator is allowed
10077 to construct if statements with else branches.
10079 =item * ast_build_allow_or
10081 This option specifies whether the AST generator is allowed
10082 to construct if conditions with disjunctions.
10086 =head3 AST Generation Options (Schedule Tree)
10088 In case of AST construction from a schedule tree, the options
10089 that control how an AST is created from the individual schedule
10090 dimensions are stored in the band nodes of the tree
10091 (see L</"Schedule Trees">).
10093 In particular, a schedule dimension can be handled in four
10094 different ways, atomic, separate, unroll or the default.
10095 This loop AST generation type can be set using
10096 C<isl_schedule_node_band_member_set_ast_loop_type>.
10098 the first three can be selected by including a one-dimensional
10099 element with as value the position of the schedule dimension
10100 within the band and as name one of C<atomic>, C<separate>
10101 or C<unroll> in the options
10102 set by C<isl_schedule_node_band_set_ast_build_options>.
10103 Only one of these three may be specified for
10104 any given schedule dimension within a band node.
10105 If none of these is specified, then the default
10106 is used. The meaning of the options is as follows.
10112 When this option is specified, the AST generator will make
10113 sure that a given domains space only appears in a single
10114 loop at the specified level.
10116 For example, for the schedule tree
10118 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10120 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10121 options: "{ atomic[x] }"
10123 the following AST will be generated
10125 for (int c0 = 0; c0 <= 10; c0 += 1) {
10132 On the other hand, for the schedule tree
10134 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10136 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10137 options: "{ separate[x] }"
10139 the following AST will be generated
10143 for (int c0 = 1; c0 <= 9; c0 += 1) {
10150 If neither C<atomic> nor C<separate> is specified, then the AST generator
10151 may produce either of these two results or some intermediate form.
10155 When this option is specified, the AST generator will
10156 split the domain of the specified schedule dimension
10157 into pieces with a fixed set of statements for which
10158 instances need to be executed by the iterations in
10159 the schedule domain part. This option tends to avoid
10160 the generation of guards inside the corresponding loops.
10161 See also the C<atomic> option.
10165 When this option is specified, the AST generator will
10166 I<completely> unroll the corresponding schedule dimension.
10167 It is the responsibility of the user to ensure that such
10168 unrolling is possible.
10169 To obtain a partial unrolling, the user should apply an additional
10170 strip-mining to the schedule and fully unroll the inner schedule
10175 The C<isolate> option is a bit more involved. It allows the user
10176 to isolate a range of schedule dimension values from smaller and
10177 greater values. Additionally, the user may specify a different
10178 atomic/separate/unroll choice for the isolated part and the remaining
10179 parts. The typical use case of the C<isolate> option is to isolate
10180 full tiles from partial tiles.
10181 The part that needs to be isolated may depend on outer schedule dimensions.
10182 The option therefore needs to be able to reference those outer schedule
10183 dimensions. In particular, the space of the C<isolate> option is that
10184 of a wrapped map with as domain the flat product of all outer band nodes
10185 and as range the space of the current band node.
10186 The atomic/separate/unroll choice for the isolated part is determined
10187 by an option that lives in an unnamed wrapped space with as domain
10188 a zero-dimensional C<isolate> space and as range the regular
10189 C<atomic>, C<separate> or C<unroll> space.
10190 This option may also be set directly using
10191 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
10192 The atomic/separate/unroll choice for the remaining part is determined
10193 by the regular C<atomic>, C<separate> or C<unroll> option.
10194 Since the C<isolate> option references outer schedule dimensions,
10195 its use in a band node causes any tree containing the node
10196 to be considered anchored.
10198 As an example, consider the isolation of full tiles from partial tiles
10199 in a tiling of a triangular domain. The original schedule is as follows.
10201 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10203 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10204 { A[i,j] -> [floor(j/10)] }, \
10205 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10209 for (int c0 = 0; c0 <= 10; c0 += 1)
10210 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10211 for (int c2 = 10 * c0;
10212 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10213 for (int c3 = 10 * c1;
10214 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10217 Isolating the full tiles, we have the following input
10219 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10221 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10222 { A[i,j] -> [floor(j/10)] }, \
10223 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10224 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10225 10a+9+10b+9 <= 100 }"
10230 for (int c0 = 0; c0 <= 8; c0 += 1) {
10231 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10232 for (int c2 = 10 * c0;
10233 c2 <= 10 * c0 + 9; c2 += 1)
10234 for (int c3 = 10 * c1;
10235 c3 <= 10 * c1 + 9; c3 += 1)
10237 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10238 for (int c2 = 10 * c0;
10239 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10240 for (int c3 = 10 * c1;
10241 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10244 for (int c0 = 9; c0 <= 10; c0 += 1)
10245 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10246 for (int c2 = 10 * c0;
10247 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10248 for (int c3 = 10 * c1;
10249 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10253 We may then additionally unroll the innermost loop of the isolated part
10255 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10257 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10258 { A[i,j] -> [floor(j/10)] }, \
10259 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10260 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10261 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
10266 for (int c0 = 0; c0 <= 8; c0 += 1) {
10267 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10268 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
10270 A(c2, 10 * c1 + 1);
10271 A(c2, 10 * c1 + 2);
10272 A(c2, 10 * c1 + 3);
10273 A(c2, 10 * c1 + 4);
10274 A(c2, 10 * c1 + 5);
10275 A(c2, 10 * c1 + 6);
10276 A(c2, 10 * c1 + 7);
10277 A(c2, 10 * c1 + 8);
10278 A(c2, 10 * c1 + 9);
10280 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10281 for (int c2 = 10 * c0;
10282 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10283 for (int c3 = 10 * c1;
10284 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10287 for (int c0 = 9; c0 <= 10; c0 += 1)
10288 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10289 for (int c2 = 10 * c0;
10290 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10291 for (int c3 = 10 * c1;
10292 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10297 =head3 AST Generation Options (Schedule Map)
10299 In case of AST construction using
10300 C<isl_ast_build_node_from_schedule_map>, the options
10301 that control how an AST is created from the individual schedule
10302 dimensions are stored in the C<isl_ast_build>.
10303 They can be set using the following function.
10305 #include <isl/ast_build.h>
10306 __isl_give isl_ast_build *
10307 isl_ast_build_set_options(
10308 __isl_take isl_ast_build *control,
10309 __isl_take isl_union_map *options);
10311 The options are encoded in an C<isl_union_map>.
10312 The domain of this union relation refers to the schedule domain,
10313 i.e., the range of the schedule passed
10314 to C<isl_ast_build_node_from_schedule_map>.
10315 In the case of nested AST generation (see L</"Nested AST Generation">),
10316 the domain of C<options> should refer to the extra piece of the schedule.
10317 That is, it should be equal to the range of the wrapped relation in the
10318 range of the schedule.
10319 The range of the options can consist of elements in one or more spaces,
10320 the names of which determine the effect of the option.
10321 The values of the range typically also refer to the schedule dimension
10322 to which the option applies. In case of nested AST generation
10323 (see L</"Nested AST Generation">), these values refer to the position
10324 of the schedule dimension within the innermost AST generation.
10325 The constraints on the domain elements of
10326 the option should only refer to this dimension and earlier dimensions.
10327 We consider the following spaces.
10331 =item C<separation_class>
10333 B<This option has been deprecated. Use the isolate option on
10334 schedule trees instead.>
10336 This space is a wrapped relation between two one dimensional spaces.
10337 The input space represents the schedule dimension to which the option
10338 applies and the output space represents the separation class.
10339 While constructing a loop corresponding to the specified schedule
10340 dimension(s), the AST generator will try to generate separate loops
10341 for domain elements that are assigned different classes.
10342 If only some of the elements are assigned a class, then those elements
10343 that are not assigned any class will be treated as belonging to a class
10344 that is separate from the explicitly assigned classes.
10345 The typical use case for this option is to separate full tiles from
10347 The other options, described below, are applied after the separation
10350 As an example, consider the separation into full and partial tiles
10351 of a tiling of a triangular domain.
10352 Take, for example, the domain
10354 { A[i,j] : 0 <= i,j and i + j <= 100 }
10356 and a tiling into tiles of 10 by 10. The input to the AST generator
10357 is then the schedule
10359 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
10362 Without any options, the following AST is generated
10364 for (int c0 = 0; c0 <= 10; c0 += 1)
10365 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10366 for (int c2 = 10 * c0;
10367 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10369 for (int c3 = 10 * c1;
10370 c3 <= min(10 * c1 + 9, -c2 + 100);
10374 Separation into full and partial tiles can be obtained by assigning
10375 a class, say C<0>, to the full tiles. The full tiles are represented by those
10376 values of the first and second schedule dimensions for which there are
10377 values of the third and fourth dimensions to cover an entire tile.
10378 That is, we need to specify the following option
10380 { [a,b,c,d] -> separation_class[[0]->[0]] :
10381 exists b': 0 <= 10a,10b' and
10382 10a+9+10b'+9 <= 100;
10383 [a,b,c,d] -> separation_class[[1]->[0]] :
10384 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
10386 which simplifies to
10388 { [a, b, c, d] -> separation_class[[1] -> [0]] :
10389 a >= 0 and b >= 0 and b <= 8 - a;
10390 [a, b, c, d] -> separation_class[[0] -> [0]] :
10391 a >= 0 and a <= 8 }
10393 With this option, the generated AST is as follows
10396 for (int c0 = 0; c0 <= 8; c0 += 1) {
10397 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10398 for (int c2 = 10 * c0;
10399 c2 <= 10 * c0 + 9; c2 += 1)
10400 for (int c3 = 10 * c1;
10401 c3 <= 10 * c1 + 9; c3 += 1)
10403 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10404 for (int c2 = 10 * c0;
10405 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10407 for (int c3 = 10 * c1;
10408 c3 <= min(-c2 + 100, 10 * c1 + 9);
10412 for (int c0 = 9; c0 <= 10; c0 += 1)
10413 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10414 for (int c2 = 10 * c0;
10415 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10417 for (int c3 = 10 * c1;
10418 c3 <= min(10 * c1 + 9, -c2 + 100);
10425 This is a single-dimensional space representing the schedule dimension(s)
10426 to which ``separation'' should be applied. Separation tries to split
10427 a loop into several pieces if this can avoid the generation of guards
10429 See also the C<atomic> option.
10433 This is a single-dimensional space representing the schedule dimension(s)
10434 for which the domains should be considered ``atomic''. That is, the
10435 AST generator will make sure that any given domain space will only appear
10436 in a single loop at the specified level.
10438 Consider the following schedule
10440 { a[i] -> [i] : 0 <= i < 10;
10441 b[i] -> [i+1] : 0 <= i < 10 }
10443 If the following option is specified
10445 { [i] -> separate[x] }
10447 then the following AST will be generated
10451 for (int c0 = 1; c0 <= 9; c0 += 1) {
10458 If, on the other hand, the following option is specified
10460 { [i] -> atomic[x] }
10462 then the following AST will be generated
10464 for (int c0 = 0; c0 <= 10; c0 += 1) {
10471 If neither C<atomic> nor C<separate> is specified, then the AST generator
10472 may produce either of these two results or some intermediate form.
10476 This is a single-dimensional space representing the schedule dimension(s)
10477 that should be I<completely> unrolled.
10478 To obtain a partial unrolling, the user should apply an additional
10479 strip-mining to the schedule and fully unroll the inner loop.
10483 =head3 Fine-grained Control over AST Generation
10485 Besides specifying the constraints on the parameters,
10486 an C<isl_ast_build> object can be used to control
10487 various aspects of the AST generation process.
10488 In case of AST construction using
10489 C<isl_ast_build_node_from_schedule_map>,
10490 the most prominent way of control is through ``options'',
10491 as explained above.
10493 Additional control is available through the following functions.
10495 #include <isl/ast_build.h>
10496 __isl_give isl_ast_build *
10497 isl_ast_build_set_iterators(
10498 __isl_take isl_ast_build *control,
10499 __isl_take isl_id_list *iterators);
10501 The function C<isl_ast_build_set_iterators> allows the user to
10502 specify a list of iterator C<isl_id>s to be used as iterators.
10503 If the input schedule is injective, then
10504 the number of elements in this list should be as large as the dimension
10505 of the schedule space, but no direct correspondence should be assumed
10506 between dimensions and elements.
10507 If the input schedule is not injective, then an additional number
10508 of C<isl_id>s equal to the largest dimension of the input domains
10510 If the number of provided C<isl_id>s is insufficient, then additional
10511 names are automatically generated.
10513 #include <isl/ast_build.h>
10514 __isl_give isl_ast_build *
10515 isl_ast_build_set_create_leaf(
10516 __isl_take isl_ast_build *control,
10517 __isl_give isl_ast_node *(*fn)(
10518 __isl_take isl_ast_build *build,
10519 void *user), void *user);
10522 C<isl_ast_build_set_create_leaf> function allows for the
10523 specification of a callback that should be called whenever the AST
10524 generator arrives at an element of the schedule domain.
10525 The callback should return an AST node that should be inserted
10526 at the corresponding position of the AST. The default action (when
10527 the callback is not set) is to continue generating parts of the AST to scan
10528 all the domain elements associated to the schedule domain element
10529 and to insert user nodes, ``calling'' the domain element, for each of them.
10530 The C<build> argument contains the current state of the C<isl_ast_build>.
10531 To ease nested AST generation (see L</"Nested AST Generation">),
10532 all control information that is
10533 specific to the current AST generation such as the options and
10534 the callbacks has been removed from this C<isl_ast_build>.
10535 The callback would typically return the result of a nested
10536 AST generation or a
10537 user defined node created using the following function.
10539 #include <isl/ast.h>
10540 __isl_give isl_ast_node *isl_ast_node_alloc_user(
10541 __isl_take isl_ast_expr *expr);
10543 #include <isl/ast_build.h>
10544 __isl_give isl_ast_build *
10545 isl_ast_build_set_at_each_domain(
10546 __isl_take isl_ast_build *build,
10547 __isl_give isl_ast_node *(*fn)(
10548 __isl_take isl_ast_node *node,
10549 __isl_keep isl_ast_build *build,
10550 void *user), void *user);
10551 __isl_give isl_ast_build *
10552 isl_ast_build_set_before_each_for(
10553 __isl_take isl_ast_build *build,
10554 __isl_give isl_id *(*fn)(
10555 __isl_keep isl_ast_build *build,
10556 void *user), void *user);
10557 __isl_give isl_ast_build *
10558 isl_ast_build_set_after_each_for(
10559 __isl_take isl_ast_build *build,
10560 __isl_give isl_ast_node *(*fn)(
10561 __isl_take isl_ast_node *node,
10562 __isl_keep isl_ast_build *build,
10563 void *user), void *user);
10564 __isl_give isl_ast_build *
10565 isl_ast_build_set_before_each_mark(
10566 __isl_take isl_ast_build *build,
10567 isl_stat (*fn)(__isl_keep isl_id *mark,
10568 __isl_keep isl_ast_build *build,
10569 void *user), void *user);
10570 __isl_give isl_ast_build *
10571 isl_ast_build_set_after_each_mark(
10572 __isl_take isl_ast_build *build,
10573 __isl_give isl_ast_node *(*fn)(
10574 __isl_take isl_ast_node *node,
10575 __isl_keep isl_ast_build *build,
10576 void *user), void *user);
10578 The callback set by C<isl_ast_build_set_at_each_domain> will
10579 be called for each domain AST node.
10580 The callbacks set by C<isl_ast_build_set_before_each_for>
10581 and C<isl_ast_build_set_after_each_for> will be called
10582 for each for AST node. The first will be called in depth-first
10583 pre-order, while the second will be called in depth-first post-order.
10584 Since C<isl_ast_build_set_before_each_for> is called before the for
10585 node is actually constructed, it is only passed an C<isl_ast_build>.
10586 The returned C<isl_id> will be added as an annotation (using
10587 C<isl_ast_node_set_annotation>) to the constructed for node.
10588 In particular, if the user has also specified an C<after_each_for>
10589 callback, then the annotation can be retrieved from the node passed to
10590 that callback using C<isl_ast_node_get_annotation>.
10591 The callbacks set by C<isl_ast_build_set_before_each_mark>
10592 and C<isl_ast_build_set_after_each_mark> will be called for each
10593 mark AST node that is created, i.e., for each mark schedule node
10594 in the input schedule tree. The first will be called in depth-first
10595 pre-order, while the second will be called in depth-first post-order.
10596 Since the callback set by C<isl_ast_build_set_before_each_mark>
10597 is called before the mark AST node is actually constructed, it is passed
10598 the identifier of the mark node.
10599 All callbacks should C<NULL> (or -1) on failure.
10600 The given C<isl_ast_build> can be used to create new
10601 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
10602 or C<isl_ast_build_call_from_pw_multi_aff>.
10604 =head3 Nested AST Generation
10606 C<isl> allows the user to create an AST within the context
10607 of another AST. These nested ASTs are created using the
10608 same C<isl_ast_build_node_from_schedule_map> function that is used to create
10609 the outer AST. The C<build> argument should be an C<isl_ast_build>
10610 passed to a callback set by
10611 C<isl_ast_build_set_create_leaf>.
10612 The space of the range of the C<schedule> argument should refer
10613 to this build. In particular, the space should be a wrapped
10614 relation and the domain of this wrapped relation should be the
10615 same as that of the range of the schedule returned by
10616 C<isl_ast_build_get_schedule> below.
10617 In practice, the new schedule is typically
10618 created by calling C<isl_union_map_range_product> on the old schedule
10619 and some extra piece of the schedule.
10620 The space of the schedule domain is also available from
10621 the C<isl_ast_build>.
10623 #include <isl/ast_build.h>
10624 __isl_give isl_union_map *isl_ast_build_get_schedule(
10625 __isl_keep isl_ast_build *build);
10626 __isl_give isl_space *isl_ast_build_get_schedule_space(
10627 __isl_keep isl_ast_build *build);
10628 __isl_give isl_ast_build *isl_ast_build_restrict(
10629 __isl_take isl_ast_build *build,
10630 __isl_take isl_set *set);
10632 The C<isl_ast_build_get_schedule> function returns a (partial)
10633 schedule for the domains elements for which part of the AST still needs to
10634 be generated in the current build.
10635 In particular, the domain elements are mapped to those iterations of the loops
10636 enclosing the current point of the AST generation inside which
10637 the domain elements are executed.
10638 No direct correspondence between
10639 the input schedule and this schedule should be assumed.
10640 The space obtained from C<isl_ast_build_get_schedule_space> can be used
10641 to create a set for C<isl_ast_build_restrict> to intersect
10642 with the current build. In particular, the set passed to
10643 C<isl_ast_build_restrict> can have additional parameters.
10644 The ids of the set dimensions in the space returned by
10645 C<isl_ast_build_get_schedule_space> correspond to the
10646 iterators of the already generated loops.
10647 The user should not rely on the ids of the output dimensions
10648 of the relations in the union relation returned by
10649 C<isl_ast_build_get_schedule> having any particular value.
10651 =head1 Applications
10653 Although C<isl> is mainly meant to be used as a library,
10654 it also contains some basic applications that use some
10655 of the functionality of C<isl>.
10656 For applications that take one or more polytopes or polyhedra
10657 as input, this input may be specified in either the L<isl format>
10658 or the L<PolyLib format>.
10660 =head2 C<isl_polyhedron_sample>
10662 C<isl_polyhedron_sample> takes a polyhedron as input and prints
10663 an integer element of the polyhedron, if there is any.
10664 The first column in the output is the denominator and is always
10665 equal to 1. If the polyhedron contains no integer points,
10666 then a vector of length zero is printed.
10670 C<isl_pip> takes the same input as the C<example> program
10671 from the C<piplib> distribution, i.e., a set of constraints
10672 on the parameters, a line containing only -1 and finally a set
10673 of constraints on a parametric polyhedron.
10674 The coefficients of the parameters appear in the last columns
10675 (but before the final constant column).
10676 The output is the lexicographic minimum of the parametric polyhedron.
10677 As C<isl> currently does not have its own output format, the output
10678 is just a dump of the internal state.
10680 =head2 C<isl_polyhedron_minimize>
10682 C<isl_polyhedron_minimize> computes the minimum of some linear
10683 or affine objective function over the integer points in a polyhedron.
10684 If an affine objective function
10685 is given, then the constant should appear in the last column.
10687 =head2 C<isl_polytope_scan>
10689 Given a polytope, C<isl_polytope_scan> prints
10690 all integer points in the polytope.
10692 =head2 C<isl_codegen>
10694 Given either a schedule tree or a sequence consisting of
10695 a schedule map, a context set and an options relation,
10696 C<isl_codegen> prints out an AST that scans the domain elements
10697 of the schedule in the order of their image(s) taking into account
10698 the constraints in the context set.
10700 =head2 C<isl_schedule>
10702 Given an C<isl_schedule_constraints> object as input,
10703 C<isl_schedule> prints out a schedule that satisfies the given