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_params(
961 __isl_keep isl_space *space1,
962 __isl_keep isl_space *space2);
963 isl_bool isl_space_has_equal_tuples(
964 __isl_keep isl_space *space1,
965 __isl_keep isl_space *space2);
966 isl_bool isl_space_is_domain(__isl_keep isl_space *space1,
967 __isl_keep isl_space *space2);
968 isl_bool isl_space_is_range(__isl_keep isl_space *space1,
969 __isl_keep isl_space *space2);
970 isl_bool isl_space_tuple_is_equal(
971 __isl_keep isl_space *space1,
972 enum isl_dim_type type1,
973 __isl_keep isl_space *space2,
974 enum isl_dim_type type2);
976 C<isl_space_is_domain> checks whether the first argument is equal
977 to the domain of the second argument. This requires in particular that
978 the first argument is a set space and that the second argument
979 is a map space. C<isl_space_tuple_is_equal> checks whether the given
980 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
981 spaces are the same. That is, it checks if they have the same
982 identifier (if any), the same dimension and the same internal structure
985 C<isl_space_has_equal_params> checks whether two spaces
986 have the same parameters in the same order.
987 C<isl_space_has_equal_tuples> check whether two spaces have
988 the same tuples. In contrast to C<isl_space_is_equal> below,
989 it does not check the
990 parameters. This is useful because many C<isl> functions align the
991 parameters before they perform their operations, such that equivalence
993 C<isl_space_is_equal> checks whether two spaces are identical,
994 meaning that they have the same parameters and the same tuples.
995 That is, it checks whether both C<isl_space_has_equal_params> and
996 C<isl_space_has_equal_tuples> hold.
998 It is often useful to create objects that live in the
999 same space as some other object. This can be accomplished
1000 by creating the new objects
1001 (see L</"Creating New Sets and Relations"> or
1002 L</"Functions">) based on the space
1003 of the original object.
1005 #include <isl/set.h>
1006 __isl_give isl_space *isl_basic_set_get_space(
1007 __isl_keep isl_basic_set *bset);
1008 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
1010 #include <isl/union_set.h>
1011 __isl_give isl_space *isl_union_set_get_space(
1012 __isl_keep isl_union_set *uset);
1014 #include <isl/map.h>
1015 __isl_give isl_space *isl_basic_map_get_space(
1016 __isl_keep isl_basic_map *bmap);
1017 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
1019 #include <isl/union_map.h>
1020 __isl_give isl_space *isl_union_map_get_space(
1021 __isl_keep isl_union_map *umap);
1023 #include <isl/constraint.h>
1024 __isl_give isl_space *isl_constraint_get_space(
1025 __isl_keep isl_constraint *constraint);
1027 #include <isl/polynomial.h>
1028 __isl_give isl_space *isl_qpolynomial_get_domain_space(
1029 __isl_keep isl_qpolynomial *qp);
1030 __isl_give isl_space *isl_qpolynomial_get_space(
1031 __isl_keep isl_qpolynomial *qp);
1032 __isl_give isl_space *
1033 isl_qpolynomial_fold_get_domain_space(
1034 __isl_keep isl_qpolynomial_fold *fold);
1035 __isl_give isl_space *isl_qpolynomial_fold_get_space(
1036 __isl_keep isl_qpolynomial_fold *fold);
1037 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
1038 __isl_keep isl_pw_qpolynomial *pwqp);
1039 __isl_give isl_space *isl_pw_qpolynomial_get_space(
1040 __isl_keep isl_pw_qpolynomial *pwqp);
1041 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
1042 __isl_keep isl_pw_qpolynomial_fold *pwf);
1043 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
1044 __isl_keep isl_pw_qpolynomial_fold *pwf);
1045 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
1046 __isl_keep isl_union_pw_qpolynomial *upwqp);
1047 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
1048 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1050 #include <isl/val.h>
1051 __isl_give isl_space *isl_multi_val_get_space(
1052 __isl_keep isl_multi_val *mv);
1054 #include <isl/aff.h>
1055 __isl_give isl_space *isl_aff_get_domain_space(
1056 __isl_keep isl_aff *aff);
1057 __isl_give isl_space *isl_aff_get_space(
1058 __isl_keep isl_aff *aff);
1059 __isl_give isl_space *isl_pw_aff_get_domain_space(
1060 __isl_keep isl_pw_aff *pwaff);
1061 __isl_give isl_space *isl_pw_aff_get_space(
1062 __isl_keep isl_pw_aff *pwaff);
1063 __isl_give isl_space *isl_multi_aff_get_domain_space(
1064 __isl_keep isl_multi_aff *maff);
1065 __isl_give isl_space *isl_multi_aff_get_space(
1066 __isl_keep isl_multi_aff *maff);
1067 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
1068 __isl_keep isl_pw_multi_aff *pma);
1069 __isl_give isl_space *isl_pw_multi_aff_get_space(
1070 __isl_keep isl_pw_multi_aff *pma);
1071 __isl_give isl_space *isl_union_pw_aff_get_space(
1072 __isl_keep isl_union_pw_aff *upa);
1073 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
1074 __isl_keep isl_union_pw_multi_aff *upma);
1075 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
1076 __isl_keep isl_multi_pw_aff *mpa);
1077 __isl_give isl_space *isl_multi_pw_aff_get_space(
1078 __isl_keep isl_multi_pw_aff *mpa);
1079 __isl_give isl_space *
1080 isl_multi_union_pw_aff_get_domain_space(
1081 __isl_keep isl_multi_union_pw_aff *mupa);
1082 __isl_give isl_space *
1083 isl_multi_union_pw_aff_get_space(
1084 __isl_keep isl_multi_union_pw_aff *mupa);
1086 #include <isl/point.h>
1087 __isl_give isl_space *isl_point_get_space(
1088 __isl_keep isl_point *pnt);
1090 The number of dimensions of a given type of space
1091 may be read off from a space or an object that lives
1092 in a space using the following functions.
1093 In case of C<isl_space_dim>, type may be
1094 C<isl_dim_param>, C<isl_dim_in> (only for relations),
1095 C<isl_dim_out> (only for relations), C<isl_dim_set>
1096 (only for sets) or C<isl_dim_all>.
1098 #include <isl/space.h>
1099 unsigned isl_space_dim(__isl_keep isl_space *space,
1100 enum isl_dim_type type);
1102 #include <isl/local_space.h>
1103 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1104 enum isl_dim_type type);
1106 #include <isl/set.h>
1107 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1108 enum isl_dim_type type);
1109 unsigned isl_set_dim(__isl_keep isl_set *set,
1110 enum isl_dim_type type);
1112 #include <isl/union_set.h>
1113 unsigned isl_union_set_dim(__isl_keep isl_union_set *uset,
1114 enum isl_dim_type type);
1116 #include <isl/map.h>
1117 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1118 enum isl_dim_type type);
1119 unsigned isl_map_dim(__isl_keep isl_map *map,
1120 enum isl_dim_type type);
1122 #include <isl/union_map.h>
1123 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1124 enum isl_dim_type type);
1126 #include <isl/val.h>
1127 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
1128 enum isl_dim_type type);
1130 #include <isl/aff.h>
1131 int isl_aff_dim(__isl_keep isl_aff *aff,
1132 enum isl_dim_type type);
1133 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1134 enum isl_dim_type type);
1135 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1136 enum isl_dim_type type);
1137 unsigned isl_pw_multi_aff_dim(
1138 __isl_keep isl_pw_multi_aff *pma,
1139 enum isl_dim_type type);
1140 unsigned isl_multi_pw_aff_dim(
1141 __isl_keep isl_multi_pw_aff *mpa,
1142 enum isl_dim_type type);
1143 unsigned isl_union_pw_aff_dim(
1144 __isl_keep isl_union_pw_aff *upa,
1145 enum isl_dim_type type);
1146 unsigned isl_union_pw_multi_aff_dim(
1147 __isl_keep isl_union_pw_multi_aff *upma,
1148 enum isl_dim_type type);
1149 unsigned isl_multi_union_pw_aff_dim(
1150 __isl_keep isl_multi_union_pw_aff *mupa,
1151 enum isl_dim_type type);
1153 #include <isl/polynomial.h>
1154 unsigned isl_union_pw_qpolynomial_dim(
1155 __isl_keep isl_union_pw_qpolynomial *upwqp,
1156 enum isl_dim_type type);
1157 unsigned isl_union_pw_qpolynomial_fold_dim(
1158 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1159 enum isl_dim_type type);
1161 Note that an C<isl_union_set>, an C<isl_union_map>,
1162 an C<isl_union_pw_multi_aff>,
1163 an C<isl_union_pw_qpolynomial> and
1164 an C<isl_union_pw_qpolynomial_fold>
1165 only have parameters.
1167 The identifiers or names of the individual dimensions of spaces
1168 may be set or read off using the following functions on spaces
1169 or objects that live in spaces.
1170 These functions are mostly useful to obtain the identifiers, positions
1171 or names of the parameters. Identifiers of individual dimensions are
1172 essentially only useful for printing. They are ignored by all other
1173 operations and may not be preserved across those operations.
1175 #include <isl/space.h>
1176 __isl_give isl_space *isl_space_set_dim_id(
1177 __isl_take isl_space *space,
1178 enum isl_dim_type type, unsigned pos,
1179 __isl_take isl_id *id);
1180 isl_bool isl_space_has_dim_id(__isl_keep isl_space *space,
1181 enum isl_dim_type type, unsigned pos);
1182 __isl_give isl_id *isl_space_get_dim_id(
1183 __isl_keep isl_space *space,
1184 enum isl_dim_type type, unsigned pos);
1185 __isl_give isl_space *isl_space_set_dim_name(
1186 __isl_take isl_space *space,
1187 enum isl_dim_type type, unsigned pos,
1188 __isl_keep const char *name);
1189 isl_bool isl_space_has_dim_name(__isl_keep isl_space *space,
1190 enum isl_dim_type type, unsigned pos);
1191 __isl_keep const char *isl_space_get_dim_name(
1192 __isl_keep isl_space *space,
1193 enum isl_dim_type type, unsigned pos);
1195 #include <isl/local_space.h>
1196 __isl_give isl_local_space *isl_local_space_set_dim_id(
1197 __isl_take isl_local_space *ls,
1198 enum isl_dim_type type, unsigned pos,
1199 __isl_take isl_id *id);
1200 isl_bool isl_local_space_has_dim_id(
1201 __isl_keep isl_local_space *ls,
1202 enum isl_dim_type type, unsigned pos);
1203 __isl_give isl_id *isl_local_space_get_dim_id(
1204 __isl_keep isl_local_space *ls,
1205 enum isl_dim_type type, unsigned pos);
1206 __isl_give isl_local_space *isl_local_space_set_dim_name(
1207 __isl_take isl_local_space *ls,
1208 enum isl_dim_type type, unsigned pos, const char *s);
1209 isl_bool isl_local_space_has_dim_name(
1210 __isl_keep isl_local_space *ls,
1211 enum isl_dim_type type, unsigned pos)
1212 const char *isl_local_space_get_dim_name(
1213 __isl_keep isl_local_space *ls,
1214 enum isl_dim_type type, unsigned pos);
1216 #include <isl/constraint.h>
1217 const char *isl_constraint_get_dim_name(
1218 __isl_keep isl_constraint *constraint,
1219 enum isl_dim_type type, unsigned pos);
1221 #include <isl/set.h>
1222 __isl_give isl_id *isl_basic_set_get_dim_id(
1223 __isl_keep isl_basic_set *bset,
1224 enum isl_dim_type type, unsigned pos);
1225 __isl_give isl_set *isl_set_set_dim_id(
1226 __isl_take isl_set *set, enum isl_dim_type type,
1227 unsigned pos, __isl_take isl_id *id);
1228 isl_bool isl_set_has_dim_id(__isl_keep isl_set *set,
1229 enum isl_dim_type type, unsigned pos);
1230 __isl_give isl_id *isl_set_get_dim_id(
1231 __isl_keep isl_set *set, enum isl_dim_type type,
1233 const char *isl_basic_set_get_dim_name(
1234 __isl_keep isl_basic_set *bset,
1235 enum isl_dim_type type, unsigned pos);
1236 isl_bool isl_set_has_dim_name(__isl_keep isl_set *set,
1237 enum isl_dim_type type, unsigned pos);
1238 const char *isl_set_get_dim_name(
1239 __isl_keep isl_set *set,
1240 enum isl_dim_type type, unsigned pos);
1242 #include <isl/map.h>
1243 __isl_give isl_map *isl_map_set_dim_id(
1244 __isl_take isl_map *map, enum isl_dim_type type,
1245 unsigned pos, __isl_take isl_id *id);
1246 isl_bool isl_basic_map_has_dim_id(
1247 __isl_keep isl_basic_map *bmap,
1248 enum isl_dim_type type, unsigned pos);
1249 isl_bool isl_map_has_dim_id(__isl_keep isl_map *map,
1250 enum isl_dim_type type, unsigned pos);
1251 __isl_give isl_id *isl_map_get_dim_id(
1252 __isl_keep isl_map *map, enum isl_dim_type type,
1254 __isl_give isl_id *isl_union_map_get_dim_id(
1255 __isl_keep isl_union_map *umap,
1256 enum isl_dim_type type, unsigned pos);
1257 const char *isl_basic_map_get_dim_name(
1258 __isl_keep isl_basic_map *bmap,
1259 enum isl_dim_type type, unsigned pos);
1260 isl_bool isl_map_has_dim_name(__isl_keep isl_map *map,
1261 enum isl_dim_type type, unsigned pos);
1262 const char *isl_map_get_dim_name(
1263 __isl_keep isl_map *map,
1264 enum isl_dim_type type, unsigned pos);
1266 #include <isl/val.h>
1267 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1268 __isl_take isl_multi_val *mv,
1269 enum isl_dim_type type, unsigned pos,
1270 __isl_take isl_id *id);
1271 __isl_give isl_id *isl_multi_val_get_dim_id(
1272 __isl_keep isl_multi_val *mv,
1273 enum isl_dim_type type, unsigned pos);
1274 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1275 __isl_take isl_multi_val *mv,
1276 enum isl_dim_type type, unsigned pos, const char *s);
1278 #include <isl/aff.h>
1279 __isl_give isl_aff *isl_aff_set_dim_id(
1280 __isl_take isl_aff *aff, enum isl_dim_type type,
1281 unsigned pos, __isl_take isl_id *id);
1282 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1283 __isl_take isl_multi_aff *maff,
1284 enum isl_dim_type type, unsigned pos,
1285 __isl_take isl_id *id);
1286 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1287 __isl_take isl_pw_aff *pma,
1288 enum isl_dim_type type, unsigned pos,
1289 __isl_take isl_id *id);
1290 __isl_give isl_multi_pw_aff *
1291 isl_multi_pw_aff_set_dim_id(
1292 __isl_take isl_multi_pw_aff *mpa,
1293 enum isl_dim_type type, unsigned pos,
1294 __isl_take isl_id *id);
1295 __isl_give isl_multi_union_pw_aff *
1296 isl_multi_union_pw_aff_set_dim_id(
1297 __isl_take isl_multi_union_pw_aff *mupa,
1298 enum isl_dim_type type, unsigned pos,
1299 __isl_take isl_id *id);
1300 __isl_give isl_id *isl_multi_aff_get_dim_id(
1301 __isl_keep isl_multi_aff *ma,
1302 enum isl_dim_type type, unsigned pos);
1303 isl_bool isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1304 enum isl_dim_type type, unsigned pos);
1305 __isl_give isl_id *isl_pw_aff_get_dim_id(
1306 __isl_keep isl_pw_aff *pa,
1307 enum isl_dim_type type, unsigned pos);
1308 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1309 __isl_keep isl_pw_multi_aff *pma,
1310 enum isl_dim_type type, unsigned pos);
1311 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1312 __isl_keep isl_multi_pw_aff *mpa,
1313 enum isl_dim_type type, unsigned pos);
1314 __isl_give isl_id *isl_multi_union_pw_aff_get_dim_id(
1315 __isl_keep isl_multi_union_pw_aff *mupa,
1316 enum isl_dim_type type, unsigned pos);
1317 __isl_give isl_aff *isl_aff_set_dim_name(
1318 __isl_take isl_aff *aff, enum isl_dim_type type,
1319 unsigned pos, const char *s);
1320 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1321 __isl_take isl_multi_aff *maff,
1322 enum isl_dim_type type, unsigned pos, const char *s);
1323 __isl_give isl_multi_pw_aff *
1324 isl_multi_pw_aff_set_dim_name(
1325 __isl_take isl_multi_pw_aff *mpa,
1326 enum isl_dim_type type, unsigned pos, const char *s);
1327 __isl_give isl_union_pw_aff *
1328 isl_union_pw_aff_set_dim_name(
1329 __isl_take isl_union_pw_aff *upa,
1330 enum isl_dim_type type, unsigned pos,
1332 __isl_give isl_union_pw_multi_aff *
1333 isl_union_pw_multi_aff_set_dim_name(
1334 __isl_take isl_union_pw_multi_aff *upma,
1335 enum isl_dim_type type, unsigned pos,
1337 __isl_give isl_multi_union_pw_aff *
1338 isl_multi_union_pw_aff_set_dim_name(
1339 __isl_take isl_multi_union_pw_aff *mupa,
1340 enum isl_dim_type type, unsigned pos,
1341 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1342 enum isl_dim_type type, unsigned pos);
1343 const char *isl_pw_aff_get_dim_name(
1344 __isl_keep isl_pw_aff *pa,
1345 enum isl_dim_type type, unsigned pos);
1346 const char *isl_pw_multi_aff_get_dim_name(
1347 __isl_keep isl_pw_multi_aff *pma,
1348 enum isl_dim_type type, unsigned pos);
1350 #include <isl/polynomial.h>
1351 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1352 __isl_take isl_qpolynomial *qp,
1353 enum isl_dim_type type, unsigned pos,
1355 __isl_give isl_pw_qpolynomial *
1356 isl_pw_qpolynomial_set_dim_name(
1357 __isl_take isl_pw_qpolynomial *pwqp,
1358 enum isl_dim_type type, unsigned pos,
1360 __isl_give isl_pw_qpolynomial_fold *
1361 isl_pw_qpolynomial_fold_set_dim_name(
1362 __isl_take isl_pw_qpolynomial_fold *pwf,
1363 enum isl_dim_type type, unsigned pos,
1365 __isl_give isl_union_pw_qpolynomial *
1366 isl_union_pw_qpolynomial_set_dim_name(
1367 __isl_take isl_union_pw_qpolynomial *upwqp,
1368 enum isl_dim_type type, unsigned pos,
1370 __isl_give isl_union_pw_qpolynomial_fold *
1371 isl_union_pw_qpolynomial_fold_set_dim_name(
1372 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1373 enum isl_dim_type type, unsigned pos,
1376 Note that C<isl_space_get_name> returns a pointer to some internal
1377 data structure, so the result can only be used while the
1378 corresponding C<isl_space> is alive.
1379 Also note that every function that operates on two sets or relations
1380 requires that both arguments have the same parameters. This also
1381 means that if one of the arguments has named parameters, then the
1382 other needs to have named parameters too and the names need to match.
1383 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1384 arguments may have different parameters (as long as they are named),
1385 in which case the result will have as parameters the union of the parameters of
1388 Given the identifier or name of a dimension (typically a parameter),
1389 its position can be obtained from the following functions.
1391 #include <isl/space.h>
1392 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1393 enum isl_dim_type type, __isl_keep isl_id *id);
1394 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1395 enum isl_dim_type type, const char *name);
1397 #include <isl/local_space.h>
1398 int isl_local_space_find_dim_by_name(
1399 __isl_keep isl_local_space *ls,
1400 enum isl_dim_type type, const char *name);
1402 #include <isl/val.h>
1403 int isl_multi_val_find_dim_by_id(
1404 __isl_keep isl_multi_val *mv,
1405 enum isl_dim_type type, __isl_keep isl_id *id);
1406 int isl_multi_val_find_dim_by_name(
1407 __isl_keep isl_multi_val *mv,
1408 enum isl_dim_type type, const char *name);
1410 #include <isl/set.h>
1411 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1412 enum isl_dim_type type, __isl_keep isl_id *id);
1413 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1414 enum isl_dim_type type, const char *name);
1416 #include <isl/map.h>
1417 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1418 enum isl_dim_type type, __isl_keep isl_id *id);
1419 int isl_basic_map_find_dim_by_name(
1420 __isl_keep isl_basic_map *bmap,
1421 enum isl_dim_type type, const char *name);
1422 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1423 enum isl_dim_type type, const char *name);
1424 int isl_union_map_find_dim_by_name(
1425 __isl_keep isl_union_map *umap,
1426 enum isl_dim_type type, const char *name);
1428 #include <isl/aff.h>
1429 int isl_multi_aff_find_dim_by_id(
1430 __isl_keep isl_multi_aff *ma,
1431 enum isl_dim_type type, __isl_keep isl_id *id);
1432 int isl_multi_pw_aff_find_dim_by_id(
1433 __isl_keep isl_multi_pw_aff *mpa,
1434 enum isl_dim_type type, __isl_keep isl_id *id);
1435 int isl_multi_union_pw_aff_find_dim_by_id(
1436 __isl_keep isl_union_multi_pw_aff *mupa,
1437 enum isl_dim_type type, __isl_keep isl_id *id);
1438 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff,
1439 enum isl_dim_type type, const char *name);
1440 int isl_multi_aff_find_dim_by_name(
1441 __isl_keep isl_multi_aff *ma,
1442 enum isl_dim_type type, const char *name);
1443 int isl_pw_aff_find_dim_by_name(__isl_keep isl_pw_aff *pa,
1444 enum isl_dim_type type, const char *name);
1445 int isl_multi_pw_aff_find_dim_by_name(
1446 __isl_keep isl_multi_pw_aff *mpa,
1447 enum isl_dim_type type, const char *name);
1448 int isl_pw_multi_aff_find_dim_by_name(
1449 __isl_keep isl_pw_multi_aff *pma,
1450 enum isl_dim_type type, const char *name);
1451 int isl_union_pw_aff_find_dim_by_name(
1452 __isl_keep isl_union_pw_aff *upa,
1453 enum isl_dim_type type, const char *name);
1454 int isl_union_pw_multi_aff_find_dim_by_name(
1455 __isl_keep isl_union_pw_multi_aff *upma,
1456 enum isl_dim_type type, const char *name);
1457 int isl_multi_union_pw_aff_find_dim_by_name(
1458 __isl_keep isl_multi_union_pw_aff *mupa,
1459 enum isl_dim_type type, const char *name);
1461 #include <isl/polynomial.h>
1462 int isl_pw_qpolynomial_find_dim_by_name(
1463 __isl_keep isl_pw_qpolynomial *pwqp,
1464 enum isl_dim_type type, const char *name);
1465 int isl_pw_qpolynomial_fold_find_dim_by_name(
1466 __isl_keep isl_pw_qpolynomial_fold *pwf,
1467 enum isl_dim_type type, const char *name);
1468 int isl_union_pw_qpolynomial_find_dim_by_name(
1469 __isl_keep isl_union_pw_qpolynomial *upwqp,
1470 enum isl_dim_type type, const char *name);
1471 int isl_union_pw_qpolynomial_fold_find_dim_by_name(
1472 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1473 enum isl_dim_type type, const char *name);
1475 The identifiers or names of entire spaces may be set or read off
1476 using the following functions.
1478 #include <isl/space.h>
1479 __isl_give isl_space *isl_space_set_tuple_id(
1480 __isl_take isl_space *space,
1481 enum isl_dim_type type, __isl_take isl_id *id);
1482 __isl_give isl_space *isl_space_reset_tuple_id(
1483 __isl_take isl_space *space, enum isl_dim_type type);
1484 isl_bool isl_space_has_tuple_id(
1485 __isl_keep isl_space *space,
1486 enum isl_dim_type type);
1487 __isl_give isl_id *isl_space_get_tuple_id(
1488 __isl_keep isl_space *space, enum isl_dim_type type);
1489 __isl_give isl_space *isl_space_set_tuple_name(
1490 __isl_take isl_space *space,
1491 enum isl_dim_type type, const char *s);
1492 isl_bool isl_space_has_tuple_name(
1493 __isl_keep isl_space *space,
1494 enum isl_dim_type type);
1495 __isl_keep const char *isl_space_get_tuple_name(
1496 __isl_keep isl_space *space,
1497 enum isl_dim_type type);
1499 #include <isl/local_space.h>
1500 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1501 __isl_take isl_local_space *ls,
1502 enum isl_dim_type type, __isl_take isl_id *id);
1504 #include <isl/set.h>
1505 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1506 __isl_take isl_basic_set *bset,
1507 __isl_take isl_id *id);
1508 __isl_give isl_set *isl_set_set_tuple_id(
1509 __isl_take isl_set *set, __isl_take isl_id *id);
1510 __isl_give isl_set *isl_set_reset_tuple_id(
1511 __isl_take isl_set *set);
1512 isl_bool isl_set_has_tuple_id(__isl_keep isl_set *set);
1513 __isl_give isl_id *isl_set_get_tuple_id(
1514 __isl_keep isl_set *set);
1515 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1516 __isl_take isl_basic_set *set, const char *s);
1517 __isl_give isl_set *isl_set_set_tuple_name(
1518 __isl_take isl_set *set, const char *s);
1519 const char *isl_basic_set_get_tuple_name(
1520 __isl_keep isl_basic_set *bset);
1521 isl_bool isl_set_has_tuple_name(__isl_keep isl_set *set);
1522 const char *isl_set_get_tuple_name(
1523 __isl_keep isl_set *set);
1525 #include <isl/map.h>
1526 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1527 __isl_take isl_basic_map *bmap,
1528 enum isl_dim_type type, __isl_take isl_id *id);
1529 __isl_give isl_map *isl_map_set_tuple_id(
1530 __isl_take isl_map *map, enum isl_dim_type type,
1531 __isl_take isl_id *id);
1532 __isl_give isl_map *isl_map_reset_tuple_id(
1533 __isl_take isl_map *map, enum isl_dim_type type);
1534 isl_bool isl_map_has_tuple_id(__isl_keep isl_map *map,
1535 enum isl_dim_type type);
1536 __isl_give isl_id *isl_map_get_tuple_id(
1537 __isl_keep isl_map *map, enum isl_dim_type type);
1538 __isl_give isl_map *isl_map_set_tuple_name(
1539 __isl_take isl_map *map,
1540 enum isl_dim_type type, const char *s);
1541 const char *isl_basic_map_get_tuple_name(
1542 __isl_keep isl_basic_map *bmap,
1543 enum isl_dim_type type);
1544 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1545 __isl_take isl_basic_map *bmap,
1546 enum isl_dim_type type, const char *s);
1547 isl_bool isl_map_has_tuple_name(__isl_keep isl_map *map,
1548 enum isl_dim_type type);
1549 const char *isl_map_get_tuple_name(
1550 __isl_keep isl_map *map,
1551 enum isl_dim_type type);
1553 #include <isl/val.h>
1554 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1555 __isl_take isl_multi_val *mv,
1556 enum isl_dim_type type, __isl_take isl_id *id);
1557 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1558 __isl_take isl_multi_val *mv,
1559 enum isl_dim_type type);
1560 isl_bool isl_multi_val_has_tuple_id(
1561 __isl_keep isl_multi_val *mv,
1562 enum isl_dim_type type);
1563 __isl_give isl_id *isl_multi_val_get_tuple_id(
1564 __isl_keep isl_multi_val *mv,
1565 enum isl_dim_type type);
1566 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1567 __isl_take isl_multi_val *mv,
1568 enum isl_dim_type type, const char *s);
1569 const char *isl_multi_val_get_tuple_name(
1570 __isl_keep isl_multi_val *mv,
1571 enum isl_dim_type type);
1573 #include <isl/aff.h>
1574 __isl_give isl_aff *isl_aff_set_tuple_id(
1575 __isl_take isl_aff *aff,
1576 enum isl_dim_type type, __isl_take isl_id *id);
1577 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1578 __isl_take isl_multi_aff *maff,
1579 enum isl_dim_type type, __isl_take isl_id *id);
1580 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1581 __isl_take isl_pw_aff *pwaff,
1582 enum isl_dim_type type, __isl_take isl_id *id);
1583 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1584 __isl_take isl_pw_multi_aff *pma,
1585 enum isl_dim_type type, __isl_take isl_id *id);
1586 __isl_give isl_multi_union_pw_aff *
1587 isl_multi_union_pw_aff_set_tuple_id(
1588 __isl_take isl_multi_union_pw_aff *mupa,
1589 enum isl_dim_type type, __isl_take isl_id *id);
1590 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1591 __isl_take isl_multi_aff *ma,
1592 enum isl_dim_type type);
1593 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1594 __isl_take isl_pw_aff *pa,
1595 enum isl_dim_type type);
1596 __isl_give isl_multi_pw_aff *
1597 isl_multi_pw_aff_reset_tuple_id(
1598 __isl_take isl_multi_pw_aff *mpa,
1599 enum isl_dim_type type);
1600 __isl_give isl_pw_multi_aff *
1601 isl_pw_multi_aff_reset_tuple_id(
1602 __isl_take isl_pw_multi_aff *pma,
1603 enum isl_dim_type type);
1604 __isl_give isl_multi_union_pw_aff *
1605 isl_multi_union_pw_aff_reset_tuple_id(
1606 __isl_take isl_multi_union_pw_aff *mupa,
1607 enum isl_dim_type type);
1608 isl_bool isl_multi_aff_has_tuple_id(
1609 __isl_keep isl_multi_aff *ma,
1610 enum isl_dim_type type);
1611 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1612 __isl_keep isl_multi_aff *ma,
1613 enum isl_dim_type type);
1614 isl_bool isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1615 enum isl_dim_type type);
1616 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1617 __isl_keep isl_pw_aff *pa,
1618 enum isl_dim_type type);
1619 isl_bool isl_pw_multi_aff_has_tuple_id(
1620 __isl_keep isl_pw_multi_aff *pma,
1621 enum isl_dim_type type);
1622 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1623 __isl_keep isl_pw_multi_aff *pma,
1624 enum isl_dim_type type);
1625 isl_bool isl_multi_pw_aff_has_tuple_id(
1626 __isl_keep isl_multi_pw_aff *mpa,
1627 enum isl_dim_type type);
1628 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1629 __isl_keep isl_multi_pw_aff *mpa,
1630 enum isl_dim_type type);
1631 isl_bool isl_multi_union_pw_aff_has_tuple_id(
1632 __isl_keep isl_multi_union_pw_aff *mupa,
1633 enum isl_dim_type type);
1634 __isl_give isl_id *isl_multi_union_pw_aff_get_tuple_id(
1635 __isl_keep isl_multi_union_pw_aff *mupa,
1636 enum isl_dim_type type);
1637 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1638 __isl_take isl_multi_aff *maff,
1639 enum isl_dim_type type, const char *s);
1640 __isl_give isl_multi_pw_aff *
1641 isl_multi_pw_aff_set_tuple_name(
1642 __isl_take isl_multi_pw_aff *mpa,
1643 enum isl_dim_type type, const char *s);
1644 __isl_give isl_multi_union_pw_aff *
1645 isl_multi_union_pw_aff_set_tuple_name(
1646 __isl_take isl_multi_union_pw_aff *mupa,
1647 enum isl_dim_type type, const char *s);
1648 const char *isl_multi_aff_get_tuple_name(
1649 __isl_keep isl_multi_aff *multi,
1650 enum isl_dim_type type);
1651 isl_bool isl_pw_multi_aff_has_tuple_name(
1652 __isl_keep isl_pw_multi_aff *pma,
1653 enum isl_dim_type type);
1654 const char *isl_pw_multi_aff_get_tuple_name(
1655 __isl_keep isl_pw_multi_aff *pma,
1656 enum isl_dim_type type);
1657 const char *isl_multi_union_pw_aff_get_tuple_name(
1658 __isl_keep isl_multi_union_pw_aff *mupa,
1659 enum isl_dim_type type);
1661 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1662 or C<isl_dim_set>. As with C<isl_space_get_name>,
1663 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1665 Binary operations require the corresponding spaces of their arguments
1666 to have the same name.
1668 To keep the names of all parameters and tuples, but reset the user pointers
1669 of all the corresponding identifiers, use the following function.
1671 #include <isl/space.h>
1672 __isl_give isl_space *isl_space_reset_user(
1673 __isl_take isl_space *space);
1675 #include <isl/set.h>
1676 __isl_give isl_set *isl_set_reset_user(
1677 __isl_take isl_set *set);
1679 #include <isl/map.h>
1680 __isl_give isl_map *isl_map_reset_user(
1681 __isl_take isl_map *map);
1683 #include <isl/union_set.h>
1684 __isl_give isl_union_set *isl_union_set_reset_user(
1685 __isl_take isl_union_set *uset);
1687 #include <isl/union_map.h>
1688 __isl_give isl_union_map *isl_union_map_reset_user(
1689 __isl_take isl_union_map *umap);
1691 #include <isl/val.h>
1692 __isl_give isl_multi_val *isl_multi_val_reset_user(
1693 __isl_take isl_multi_val *mv);
1695 #include <isl/aff.h>
1696 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1697 __isl_take isl_multi_aff *ma);
1698 __isl_give isl_pw_aff *isl_pw_aff_reset_user(
1699 __isl_take isl_pw_aff *pa);
1700 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1701 __isl_take isl_multi_pw_aff *mpa);
1702 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_reset_user(
1703 __isl_take isl_pw_multi_aff *pma);
1704 __isl_give isl_union_pw_aff *isl_union_pw_aff_reset_user(
1705 __isl_take isl_union_pw_aff *upa);
1706 __isl_give isl_multi_union_pw_aff *
1707 isl_multi_union_pw_aff_reset_user(
1708 __isl_take isl_multi_union_pw_aff *mupa);
1709 __isl_give isl_union_pw_multi_aff *
1710 isl_union_pw_multi_aff_reset_user(
1711 __isl_take isl_union_pw_multi_aff *upma);
1713 #include <isl/polynomial.h>
1714 __isl_give isl_pw_qpolynomial *
1715 isl_pw_qpolynomial_reset_user(
1716 __isl_take isl_pw_qpolynomial *pwqp);
1717 __isl_give isl_union_pw_qpolynomial *
1718 isl_union_pw_qpolynomial_reset_user(
1719 __isl_take isl_union_pw_qpolynomial *upwqp);
1720 __isl_give isl_pw_qpolynomial_fold *
1721 isl_pw_qpolynomial_fold_reset_user(
1722 __isl_take isl_pw_qpolynomial_fold *pwf);
1723 __isl_give isl_union_pw_qpolynomial_fold *
1724 isl_union_pw_qpolynomial_fold_reset_user(
1725 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1727 Spaces can be nested. In particular, the domain of a set or
1728 the domain or range of a relation can be a nested relation.
1729 This process is also called I<wrapping>.
1730 The functions for detecting, constructing and deconstructing
1731 such nested spaces can be found in the wrapping properties
1732 of L</"Unary Properties">, the wrapping operations
1733 of L</"Unary Operations"> and the Cartesian product operations
1734 of L</"Basic Operations">.
1736 Spaces can be created from other spaces
1737 using the functions described in L</"Unary Operations">
1738 and L</"Binary Operations">.
1742 A local space is essentially a space with
1743 zero or more existentially quantified variables.
1744 The local space of various objects can be obtained
1745 using the following functions.
1747 #include <isl/constraint.h>
1748 __isl_give isl_local_space *isl_constraint_get_local_space(
1749 __isl_keep isl_constraint *constraint);
1751 #include <isl/set.h>
1752 __isl_give isl_local_space *isl_basic_set_get_local_space(
1753 __isl_keep isl_basic_set *bset);
1755 #include <isl/map.h>
1756 __isl_give isl_local_space *isl_basic_map_get_local_space(
1757 __isl_keep isl_basic_map *bmap);
1759 #include <isl/aff.h>
1760 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1761 __isl_keep isl_aff *aff);
1762 __isl_give isl_local_space *isl_aff_get_local_space(
1763 __isl_keep isl_aff *aff);
1765 A new local space can be created from a space using
1767 #include <isl/local_space.h>
1768 __isl_give isl_local_space *isl_local_space_from_space(
1769 __isl_take isl_space *space);
1771 They can be inspected, modified, copied and freed using the following functions.
1773 #include <isl/local_space.h>
1774 isl_bool isl_local_space_is_params(
1775 __isl_keep isl_local_space *ls);
1776 isl_bool isl_local_space_is_set(
1777 __isl_keep isl_local_space *ls);
1778 __isl_give isl_space *isl_local_space_get_space(
1779 __isl_keep isl_local_space *ls);
1780 __isl_give isl_aff *isl_local_space_get_div(
1781 __isl_keep isl_local_space *ls, int pos);
1782 __isl_give isl_local_space *isl_local_space_copy(
1783 __isl_keep isl_local_space *ls);
1784 __isl_null isl_local_space *isl_local_space_free(
1785 __isl_take isl_local_space *ls);
1787 Note that C<isl_local_space_get_div> can only be used on local spaces
1790 Two local spaces can be compared using
1792 isl_bool isl_local_space_is_equal(
1793 __isl_keep isl_local_space *ls1,
1794 __isl_keep isl_local_space *ls2);
1796 Local spaces can be created from other local spaces
1797 using the functions described in L</"Unary Operations">
1798 and L</"Binary Operations">.
1800 =head2 Creating New Sets and Relations
1802 C<isl> has functions for creating some standard sets and relations.
1806 =item * Empty sets and relations
1808 __isl_give isl_basic_set *isl_basic_set_empty(
1809 __isl_take isl_space *space);
1810 __isl_give isl_basic_map *isl_basic_map_empty(
1811 __isl_take isl_space *space);
1812 __isl_give isl_set *isl_set_empty(
1813 __isl_take isl_space *space);
1814 __isl_give isl_map *isl_map_empty(
1815 __isl_take isl_space *space);
1816 __isl_give isl_union_set *isl_union_set_empty(
1817 __isl_take isl_space *space);
1818 __isl_give isl_union_map *isl_union_map_empty(
1819 __isl_take isl_space *space);
1821 For C<isl_union_set>s and C<isl_union_map>s, the space
1822 is only used to specify the parameters.
1824 =item * Universe sets and relations
1826 __isl_give isl_basic_set *isl_basic_set_universe(
1827 __isl_take isl_space *space);
1828 __isl_give isl_basic_map *isl_basic_map_universe(
1829 __isl_take isl_space *space);
1830 __isl_give isl_set *isl_set_universe(
1831 __isl_take isl_space *space);
1832 __isl_give isl_map *isl_map_universe(
1833 __isl_take isl_space *space);
1834 __isl_give isl_union_set *isl_union_set_universe(
1835 __isl_take isl_union_set *uset);
1836 __isl_give isl_union_map *isl_union_map_universe(
1837 __isl_take isl_union_map *umap);
1839 The sets and relations constructed by the functions above
1840 contain all integer values, while those constructed by the
1841 functions below only contain non-negative values.
1843 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1844 __isl_take isl_space *space);
1845 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1846 __isl_take isl_space *space);
1847 __isl_give isl_set *isl_set_nat_universe(
1848 __isl_take isl_space *space);
1849 __isl_give isl_map *isl_map_nat_universe(
1850 __isl_take isl_space *space);
1852 =item * Identity relations
1854 __isl_give isl_basic_map *isl_basic_map_identity(
1855 __isl_take isl_space *space);
1856 __isl_give isl_map *isl_map_identity(
1857 __isl_take isl_space *space);
1859 The number of input and output dimensions in C<space> needs
1862 =item * Lexicographic order
1864 __isl_give isl_map *isl_map_lex_lt(
1865 __isl_take isl_space *set_space);
1866 __isl_give isl_map *isl_map_lex_le(
1867 __isl_take isl_space *set_space);
1868 __isl_give isl_map *isl_map_lex_gt(
1869 __isl_take isl_space *set_space);
1870 __isl_give isl_map *isl_map_lex_ge(
1871 __isl_take isl_space *set_space);
1872 __isl_give isl_map *isl_map_lex_lt_first(
1873 __isl_take isl_space *space, unsigned n);
1874 __isl_give isl_map *isl_map_lex_le_first(
1875 __isl_take isl_space *space, unsigned n);
1876 __isl_give isl_map *isl_map_lex_gt_first(
1877 __isl_take isl_space *space, unsigned n);
1878 __isl_give isl_map *isl_map_lex_ge_first(
1879 __isl_take isl_space *space, unsigned n);
1881 The first four functions take a space for a B<set>
1882 and return relations that express that the elements in the domain
1883 are lexicographically less
1884 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1885 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1886 than the elements in the range.
1887 The last four functions take a space for a map
1888 and return relations that express that the first C<n> dimensions
1889 in the domain are lexicographically less
1890 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1891 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1892 than the first C<n> dimensions in the range.
1896 A basic set or relation can be converted to a set or relation
1897 using the following functions.
1899 __isl_give isl_set *isl_set_from_basic_set(
1900 __isl_take isl_basic_set *bset);
1901 __isl_give isl_map *isl_map_from_basic_map(
1902 __isl_take isl_basic_map *bmap);
1904 Sets and relations can be converted to union sets and relations
1905 using the following functions.
1907 __isl_give isl_union_set *isl_union_set_from_basic_set(
1908 __isl_take isl_basic_set *bset);
1909 __isl_give isl_union_map *isl_union_map_from_basic_map(
1910 __isl_take isl_basic_map *bmap);
1911 __isl_give isl_union_set *isl_union_set_from_set(
1912 __isl_take isl_set *set);
1913 __isl_give isl_union_map *isl_union_map_from_map(
1914 __isl_take isl_map *map);
1916 The inverse conversions below can only be used if the input
1917 union set or relation is known to contain elements in exactly one
1920 __isl_give isl_set *isl_set_from_union_set(
1921 __isl_take isl_union_set *uset);
1922 __isl_give isl_map *isl_map_from_union_map(
1923 __isl_take isl_union_map *umap);
1925 Sets and relations can be copied and freed again using the following
1928 __isl_give isl_basic_set *isl_basic_set_copy(
1929 __isl_keep isl_basic_set *bset);
1930 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1931 __isl_give isl_union_set *isl_union_set_copy(
1932 __isl_keep isl_union_set *uset);
1933 __isl_give isl_basic_map *isl_basic_map_copy(
1934 __isl_keep isl_basic_map *bmap);
1935 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1936 __isl_give isl_union_map *isl_union_map_copy(
1937 __isl_keep isl_union_map *umap);
1938 __isl_null isl_basic_set *isl_basic_set_free(
1939 __isl_take isl_basic_set *bset);
1940 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1941 __isl_null isl_union_set *isl_union_set_free(
1942 __isl_take isl_union_set *uset);
1943 __isl_null isl_basic_map *isl_basic_map_free(
1944 __isl_take isl_basic_map *bmap);
1945 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1946 __isl_null isl_union_map *isl_union_map_free(
1947 __isl_take isl_union_map *umap);
1949 Other sets and relations can be constructed by starting
1950 from a universe set or relation, adding equality and/or
1951 inequality constraints and then projecting out the
1952 existentially quantified variables, if any.
1953 Constraints can be constructed, manipulated and
1954 added to (or removed from) (basic) sets and relations
1955 using the following functions.
1957 #include <isl/constraint.h>
1958 __isl_give isl_constraint *isl_constraint_alloc_equality(
1959 __isl_take isl_local_space *ls);
1960 __isl_give isl_constraint *isl_constraint_alloc_inequality(
1961 __isl_take isl_local_space *ls);
1962 __isl_give isl_constraint *isl_constraint_set_constant_si(
1963 __isl_take isl_constraint *constraint, int v);
1964 __isl_give isl_constraint *isl_constraint_set_constant_val(
1965 __isl_take isl_constraint *constraint,
1966 __isl_take isl_val *v);
1967 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1968 __isl_take isl_constraint *constraint,
1969 enum isl_dim_type type, int pos, int v);
1970 __isl_give isl_constraint *
1971 isl_constraint_set_coefficient_val(
1972 __isl_take isl_constraint *constraint,
1973 enum isl_dim_type type, int pos,
1974 __isl_take isl_val *v);
1975 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1976 __isl_take isl_basic_map *bmap,
1977 __isl_take isl_constraint *constraint);
1978 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1979 __isl_take isl_basic_set *bset,
1980 __isl_take isl_constraint *constraint);
1981 __isl_give isl_map *isl_map_add_constraint(
1982 __isl_take isl_map *map,
1983 __isl_take isl_constraint *constraint);
1984 __isl_give isl_set *isl_set_add_constraint(
1985 __isl_take isl_set *set,
1986 __isl_take isl_constraint *constraint);
1988 For example, to create a set containing the even integers
1989 between 10 and 42, you would use the following code.
1992 isl_local_space *ls;
1994 isl_basic_set *bset;
1996 space = isl_space_set_alloc(ctx, 0, 2);
1997 bset = isl_basic_set_universe(isl_space_copy(space));
1998 ls = isl_local_space_from_space(space);
2000 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
2001 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2002 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
2003 bset = isl_basic_set_add_constraint(bset, c);
2005 c = isl_constraint_alloc_inequality(isl_local_space_copy(ls));
2006 c = isl_constraint_set_constant_si(c, -10);
2007 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
2008 bset = isl_basic_set_add_constraint(bset, c);
2010 c = isl_constraint_alloc_inequality(ls);
2011 c = isl_constraint_set_constant_si(c, 42);
2012 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2013 bset = isl_basic_set_add_constraint(bset, c);
2015 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
2019 isl_basic_set *bset;
2020 bset = isl_basic_set_read_from_str(ctx,
2021 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
2023 A basic set or relation can also be constructed from two matrices
2024 describing the equalities and the inequalities.
2026 __isl_give isl_basic_set *isl_basic_set_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);
2032 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
2033 __isl_take isl_space *space,
2034 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2035 enum isl_dim_type c1,
2036 enum isl_dim_type c2, enum isl_dim_type c3,
2037 enum isl_dim_type c4, enum isl_dim_type c5);
2039 The C<isl_dim_type> arguments indicate the order in which
2040 different kinds of variables appear in the input matrices
2041 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
2042 C<isl_dim_set> and C<isl_dim_div> for sets and
2043 of C<isl_dim_cst>, C<isl_dim_param>,
2044 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
2046 A (basic or union) set or relation can also be constructed from a
2047 (union) (piecewise) (multiple) affine expression
2048 or a list of affine expressions
2049 (See L</"Functions">), provided these affine expressions do not
2052 __isl_give isl_basic_map *isl_basic_map_from_aff(
2053 __isl_take isl_aff *aff);
2054 __isl_give isl_map *isl_map_from_aff(
2055 __isl_take isl_aff *aff);
2056 __isl_give isl_set *isl_set_from_pw_aff(
2057 __isl_take isl_pw_aff *pwaff);
2058 __isl_give isl_map *isl_map_from_pw_aff(
2059 __isl_take isl_pw_aff *pwaff);
2060 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
2061 __isl_take isl_space *domain_space,
2062 __isl_take isl_aff_list *list);
2063 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
2064 __isl_take isl_multi_aff *maff)
2065 __isl_give isl_map *isl_map_from_multi_aff(
2066 __isl_take isl_multi_aff *maff)
2067 __isl_give isl_set *isl_set_from_pw_multi_aff(
2068 __isl_take isl_pw_multi_aff *pma);
2069 __isl_give isl_map *isl_map_from_pw_multi_aff(
2070 __isl_take isl_pw_multi_aff *pma);
2071 __isl_give isl_set *isl_set_from_multi_pw_aff(
2072 __isl_take isl_multi_pw_aff *mpa);
2073 __isl_give isl_map *isl_map_from_multi_pw_aff(
2074 __isl_take isl_multi_pw_aff *mpa);
2075 __isl_give isl_union_map *isl_union_map_from_union_pw_aff(
2076 __isl_take isl_union_pw_aff *upa);
2077 __isl_give isl_union_map *
2078 isl_union_map_from_union_pw_multi_aff(
2079 __isl_take isl_union_pw_multi_aff *upma);
2080 __isl_give isl_union_map *
2081 isl_union_map_from_multi_union_pw_aff(
2082 __isl_take isl_multi_union_pw_aff *mupa);
2084 The C<domain_space> argument describes the domain of the resulting
2085 basic relation. It is required because the C<list> may consist
2086 of zero affine expressions.
2087 The C<mupa> passed to C<isl_union_map_from_multi_union_pw_aff>
2088 is not allowed to be zero-dimensional. The domain of the result
2089 is the shared domain of the union piecewise affine elements.
2091 =head2 Inspecting Sets and Relations
2093 Usually, the user should not have to care about the actual constraints
2094 of the sets and maps, but should instead apply the abstract operations
2095 explained in the following sections.
2096 Occasionally, however, it may be required to inspect the individual
2097 coefficients of the constraints. This section explains how to do so.
2098 In these cases, it may also be useful to have C<isl> compute
2099 an explicit representation of the existentially quantified variables.
2101 __isl_give isl_set *isl_set_compute_divs(
2102 __isl_take isl_set *set);
2103 __isl_give isl_map *isl_map_compute_divs(
2104 __isl_take isl_map *map);
2105 __isl_give isl_union_set *isl_union_set_compute_divs(
2106 __isl_take isl_union_set *uset);
2107 __isl_give isl_union_map *isl_union_map_compute_divs(
2108 __isl_take isl_union_map *umap);
2110 This explicit representation defines the existentially quantified
2111 variables as integer divisions of the other variables, possibly
2112 including earlier existentially quantified variables.
2113 An explicitly represented existentially quantified variable therefore
2114 has a unique value when the values of the other variables are known.
2116 Alternatively, the existentially quantified variables can be removed
2117 using the following functions, which compute an overapproximation.
2119 __isl_give isl_basic_set *isl_basic_set_remove_divs(
2120 __isl_take isl_basic_set *bset);
2121 __isl_give isl_basic_map *isl_basic_map_remove_divs(
2122 __isl_take isl_basic_map *bmap);
2123 __isl_give isl_set *isl_set_remove_divs(
2124 __isl_take isl_set *set);
2125 __isl_give isl_map *isl_map_remove_divs(
2126 __isl_take isl_map *map);
2128 It is also possible to only remove those divs that are defined
2129 in terms of a given range of dimensions or only those for which
2130 no explicit representation is known.
2132 __isl_give isl_basic_set *
2133 isl_basic_set_remove_divs_involving_dims(
2134 __isl_take isl_basic_set *bset,
2135 enum isl_dim_type type,
2136 unsigned first, unsigned n);
2137 __isl_give isl_basic_map *
2138 isl_basic_map_remove_divs_involving_dims(
2139 __isl_take isl_basic_map *bmap,
2140 enum isl_dim_type type,
2141 unsigned first, unsigned n);
2142 __isl_give isl_set *isl_set_remove_divs_involving_dims(
2143 __isl_take isl_set *set, enum isl_dim_type type,
2144 unsigned first, unsigned n);
2145 __isl_give isl_map *isl_map_remove_divs_involving_dims(
2146 __isl_take isl_map *map, enum isl_dim_type type,
2147 unsigned first, unsigned n);
2149 __isl_give isl_basic_set *
2150 isl_basic_set_remove_unknown_divs(
2151 __isl_take isl_basic_set *bset);
2152 __isl_give isl_set *isl_set_remove_unknown_divs(
2153 __isl_take isl_set *set);
2154 __isl_give isl_map *isl_map_remove_unknown_divs(
2155 __isl_take isl_map *map);
2157 To iterate over all the sets or maps in a union set or map, use
2159 isl_stat isl_union_set_foreach_set(
2160 __isl_keep isl_union_set *uset,
2161 isl_stat (*fn)(__isl_take isl_set *set, void *user),
2163 isl_stat isl_union_map_foreach_map(
2164 __isl_keep isl_union_map *umap,
2165 isl_stat (*fn)(__isl_take isl_map *map, void *user),
2168 These functions call the callback function once for each
2169 (pair of) space(s) for which there are elements in the input.
2170 The argument to the callback contains all elements in the input
2171 with that (pair of) space(s).
2173 The number of sets or maps in a union set or map can be obtained
2176 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
2177 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
2179 To extract the set or map in a given space from a union, use
2181 __isl_give isl_set *isl_union_set_extract_set(
2182 __isl_keep isl_union_set *uset,
2183 __isl_take isl_space *space);
2184 __isl_give isl_map *isl_union_map_extract_map(
2185 __isl_keep isl_union_map *umap,
2186 __isl_take isl_space *space);
2188 To iterate over all the basic sets or maps in a set or map, use
2190 isl_stat isl_set_foreach_basic_set(__isl_keep isl_set *set,
2191 isl_stat (*fn)(__isl_take isl_basic_set *bset,
2194 isl_stat isl_map_foreach_basic_map(__isl_keep isl_map *map,
2195 isl_stat (*fn)(__isl_take isl_basic_map *bmap,
2199 The callback function C<fn> should return 0 if successful and
2200 -1 if an error occurs. In the latter case, or if any other error
2201 occurs, the above functions will return -1.
2203 It should be noted that C<isl> does not guarantee that
2204 the basic sets or maps passed to C<fn> are disjoint.
2205 If this is required, then the user should call one of
2206 the following functions first.
2208 __isl_give isl_set *isl_set_make_disjoint(
2209 __isl_take isl_set *set);
2210 __isl_give isl_map *isl_map_make_disjoint(
2211 __isl_take isl_map *map);
2213 The number of basic sets in a set can be obtained
2214 or the number of basic maps in a map can be obtained
2217 #include <isl/set.h>
2218 int isl_set_n_basic_set(__isl_keep isl_set *set);
2220 #include <isl/map.h>
2221 int isl_map_n_basic_map(__isl_keep isl_map *map);
2223 It is also possible to obtain a list of basic sets from a set
2225 #include <isl/set.h>
2226 __isl_give isl_basic_set_list *isl_set_get_basic_set_list(
2227 __isl_keep isl_set *set);
2229 The returned list can be manipulated using the functions in L<"Lists">.
2231 To iterate over the constraints of a basic set or map, use
2233 #include <isl/constraint.h>
2235 int isl_basic_set_n_constraint(
2236 __isl_keep isl_basic_set *bset);
2237 isl_stat isl_basic_set_foreach_constraint(
2238 __isl_keep isl_basic_set *bset,
2239 isl_stat (*fn)(__isl_take isl_constraint *c,
2242 int isl_basic_map_n_constraint(
2243 __isl_keep isl_basic_map *bmap);
2244 isl_stat isl_basic_map_foreach_constraint(
2245 __isl_keep isl_basic_map *bmap,
2246 isl_stat (*fn)(__isl_take isl_constraint *c,
2249 __isl_null isl_constraint *isl_constraint_free(
2250 __isl_take isl_constraint *c);
2252 Again, the callback function C<fn> should return 0 if successful and
2253 -1 if an error occurs. In the latter case, or if any other error
2254 occurs, the above functions will return -1.
2255 The constraint C<c> represents either an equality or an inequality.
2256 Use the following function to find out whether a constraint
2257 represents an equality. If not, it represents an inequality.
2259 isl_bool isl_constraint_is_equality(
2260 __isl_keep isl_constraint *constraint);
2262 It is also possible to obtain a list of constraints from a basic
2265 #include <isl/constraint.h>
2266 __isl_give isl_constraint_list *
2267 isl_basic_map_get_constraint_list(
2268 __isl_keep isl_basic_map *bmap);
2269 __isl_give isl_constraint_list *
2270 isl_basic_set_get_constraint_list(
2271 __isl_keep isl_basic_set *bset);
2273 These functions require that all existentially quantified variables
2274 have an explicit representation.
2275 The returned list can be manipulated using the functions in L<"Lists">.
2277 The coefficients of the constraints can be inspected using
2278 the following functions.
2280 isl_bool isl_constraint_is_lower_bound(
2281 __isl_keep isl_constraint *constraint,
2282 enum isl_dim_type type, unsigned pos);
2283 isl_bool isl_constraint_is_upper_bound(
2284 __isl_keep isl_constraint *constraint,
2285 enum isl_dim_type type, unsigned pos);
2286 __isl_give isl_val *isl_constraint_get_constant_val(
2287 __isl_keep isl_constraint *constraint);
2288 __isl_give isl_val *isl_constraint_get_coefficient_val(
2289 __isl_keep isl_constraint *constraint,
2290 enum isl_dim_type type, int pos);
2292 The explicit representations of the existentially quantified
2293 variables can be inspected using the following function.
2294 Note that the user is only allowed to use this function
2295 if the inspected set or map is the result of a call
2296 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2297 The existentially quantified variable is equal to the floor
2298 of the returned affine expression. The affine expression
2299 itself can be inspected using the functions in
2302 __isl_give isl_aff *isl_constraint_get_div(
2303 __isl_keep isl_constraint *constraint, int pos);
2305 To obtain the constraints of a basic set or map in matrix
2306 form, use the following functions.
2308 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2309 __isl_keep isl_basic_set *bset,
2310 enum isl_dim_type c1, enum isl_dim_type c2,
2311 enum isl_dim_type c3, enum isl_dim_type c4);
2312 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2313 __isl_keep isl_basic_set *bset,
2314 enum isl_dim_type c1, enum isl_dim_type c2,
2315 enum isl_dim_type c3, enum isl_dim_type c4);
2316 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2317 __isl_keep isl_basic_map *bmap,
2318 enum isl_dim_type c1,
2319 enum isl_dim_type c2, enum isl_dim_type c3,
2320 enum isl_dim_type c4, enum isl_dim_type c5);
2321 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2322 __isl_keep isl_basic_map *bmap,
2323 enum isl_dim_type c1,
2324 enum isl_dim_type c2, enum isl_dim_type c3,
2325 enum isl_dim_type c4, enum isl_dim_type c5);
2327 The C<isl_dim_type> arguments dictate the order in which
2328 different kinds of variables appear in the resulting matrix.
2329 For set inputs, they should be a permutation of
2330 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
2331 For map inputs, they should be a permutation of
2332 C<isl_dim_cst>, C<isl_dim_param>,
2333 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2337 Points are elements of a set. They can be used to construct
2338 simple sets (boxes) or they can be used to represent the
2339 individual elements of a set.
2340 The zero point (the origin) can be created using
2342 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2344 The coordinates of a point can be inspected, set and changed
2347 __isl_give isl_val *isl_point_get_coordinate_val(
2348 __isl_keep isl_point *pnt,
2349 enum isl_dim_type type, int pos);
2350 __isl_give isl_point *isl_point_set_coordinate_val(
2351 __isl_take isl_point *pnt,
2352 enum isl_dim_type type, int pos,
2353 __isl_take isl_val *v);
2355 __isl_give isl_point *isl_point_add_ui(
2356 __isl_take isl_point *pnt,
2357 enum isl_dim_type type, int pos, unsigned val);
2358 __isl_give isl_point *isl_point_sub_ui(
2359 __isl_take isl_point *pnt,
2360 enum isl_dim_type type, int pos, unsigned val);
2362 Points can be copied or freed using
2364 __isl_give isl_point *isl_point_copy(
2365 __isl_keep isl_point *pnt);
2366 __isl_null isl_point *isl_point_free(
2367 __isl_take isl_point *pnt);
2369 A singleton set can be created from a point using
2371 __isl_give isl_basic_set *isl_basic_set_from_point(
2372 __isl_take isl_point *pnt);
2373 __isl_give isl_set *isl_set_from_point(
2374 __isl_take isl_point *pnt);
2375 __isl_give isl_union_set *isl_union_set_from_point(
2376 __isl_take isl_point *pnt);
2378 and a box can be created from two opposite extremal points using
2380 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2381 __isl_take isl_point *pnt1,
2382 __isl_take isl_point *pnt2);
2383 __isl_give isl_set *isl_set_box_from_points(
2384 __isl_take isl_point *pnt1,
2385 __isl_take isl_point *pnt2);
2387 All elements of a B<bounded> (union) set can be enumerated using
2388 the following functions.
2390 isl_stat isl_set_foreach_point(__isl_keep isl_set *set,
2391 isl_stat (*fn)(__isl_take isl_point *pnt,
2394 isl_stat isl_union_set_foreach_point(
2395 __isl_keep isl_union_set *uset,
2396 isl_stat (*fn)(__isl_take isl_point *pnt,
2400 The function C<fn> is called for each integer point in
2401 C<set> with as second argument the last argument of
2402 the C<isl_set_foreach_point> call. The function C<fn>
2403 should return C<0> on success and C<-1> on failure.
2404 In the latter case, C<isl_set_foreach_point> will stop
2405 enumerating and return C<-1> as well.
2406 If the enumeration is performed successfully and to completion,
2407 then C<isl_set_foreach_point> returns C<0>.
2409 To obtain a single point of a (basic or union) set, use
2411 __isl_give isl_point *isl_basic_set_sample_point(
2412 __isl_take isl_basic_set *bset);
2413 __isl_give isl_point *isl_set_sample_point(
2414 __isl_take isl_set *set);
2415 __isl_give isl_point *isl_union_set_sample_point(
2416 __isl_take isl_union_set *uset);
2418 If C<set> does not contain any (integer) points, then the
2419 resulting point will be ``void'', a property that can be
2422 isl_bool isl_point_is_void(__isl_keep isl_point *pnt);
2426 Besides sets and relation, C<isl> also supports various types of functions.
2427 Each of these types is derived from the value type (see L</"Values">)
2428 or from one of two primitive function types
2429 through the application of zero or more type constructors.
2430 We first describe the primitive type and then we describe
2431 the types derived from these primitive types.
2433 =head3 Primitive Functions
2435 C<isl> support two primitive function types, quasi-affine
2436 expressions and quasipolynomials.
2437 A quasi-affine expression is defined either over a parameter
2438 space or over a set and is composed of integer constants,
2439 parameters and set variables, addition, subtraction and
2440 integer division by an integer constant.
2441 For example, the quasi-affine expression
2443 [n] -> { [x] -> [2*floor((4 n + x)/9] }
2445 maps C<x> to C<2*floor((4 n + x)/9>.
2446 A quasipolynomial is a polynomial expression in quasi-affine
2447 expression. That is, it additionally allows for multiplication.
2448 Note, though, that it is not allowed to construct an integer
2449 division of an expression involving multiplications.
2450 Here is an example of a quasipolynomial that is not
2451 quasi-affine expression
2453 [n] -> { [x] -> (n*floor((4 n + x)/9) }
2455 Note that the external representations of quasi-affine expressions
2456 and quasipolynomials are different. Quasi-affine expressions
2457 use a notation with square brackets just like binary relations,
2458 while quasipolynomials do not. This might change at some point.
2460 If a primitive function is defined over a parameter space,
2461 then the space of the function itself is that of a set.
2462 If it is defined over a set, then the space of the function
2463 is that of a relation. In both cases, the set space (or
2464 the output space) is single-dimensional, anonymous and unstructured.
2465 To create functions with multiple dimensions or with other kinds
2466 of set or output spaces, use multiple expressions
2467 (see L</"Multiple Expressions">).
2471 =item * Quasi-affine Expressions
2473 Besides the expressions described above, a quasi-affine
2474 expression can also be set to NaN. Such expressions
2475 typically represent a failure to represent a result
2476 as a quasi-affine expression.
2478 The zero quasi affine expression or the quasi affine expression
2479 that is equal to a given value or
2480 a specified dimension on a given domain can be created using
2482 #include <isl/aff.h>
2483 __isl_give isl_aff *isl_aff_zero_on_domain(
2484 __isl_take isl_local_space *ls);
2485 __isl_give isl_aff *isl_aff_val_on_domain(
2486 __isl_take isl_local_space *ls,
2487 __isl_take isl_val *val);
2488 __isl_give isl_aff *isl_aff_var_on_domain(
2489 __isl_take isl_local_space *ls,
2490 enum isl_dim_type type, unsigned pos);
2491 __isl_give isl_aff *isl_aff_nan_on_domain(
2492 __isl_take isl_local_space *ls);
2494 Quasi affine expressions can be copied and freed using
2496 #include <isl/aff.h>
2497 __isl_give isl_aff *isl_aff_copy(
2498 __isl_keep isl_aff *aff);
2499 __isl_null isl_aff *isl_aff_free(
2500 __isl_take isl_aff *aff);
2502 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2503 using the following function. The constraint is required to have
2504 a non-zero coefficient for the specified dimension.
2506 #include <isl/constraint.h>
2507 __isl_give isl_aff *isl_constraint_get_bound(
2508 __isl_keep isl_constraint *constraint,
2509 enum isl_dim_type type, int pos);
2511 The entire affine expression of the constraint can also be extracted
2512 using the following function.
2514 #include <isl/constraint.h>
2515 __isl_give isl_aff *isl_constraint_get_aff(
2516 __isl_keep isl_constraint *constraint);
2518 Conversely, an equality constraint equating
2519 the affine expression to zero or an inequality constraint enforcing
2520 the affine expression to be non-negative, can be constructed using
2522 __isl_give isl_constraint *isl_equality_from_aff(
2523 __isl_take isl_aff *aff);
2524 __isl_give isl_constraint *isl_inequality_from_aff(
2525 __isl_take isl_aff *aff);
2527 The coefficients and the integer divisions of an affine expression
2528 can be inspected using the following functions.
2530 #include <isl/aff.h>
2531 __isl_give isl_val *isl_aff_get_constant_val(
2532 __isl_keep isl_aff *aff);
2533 __isl_give isl_val *isl_aff_get_coefficient_val(
2534 __isl_keep isl_aff *aff,
2535 enum isl_dim_type type, int pos);
2536 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2537 enum isl_dim_type type, int pos);
2538 __isl_give isl_val *isl_aff_get_denominator_val(
2539 __isl_keep isl_aff *aff);
2540 __isl_give isl_aff *isl_aff_get_div(
2541 __isl_keep isl_aff *aff, int pos);
2543 They can be modified using the following functions.
2545 #include <isl/aff.h>
2546 __isl_give isl_aff *isl_aff_set_constant_si(
2547 __isl_take isl_aff *aff, int v);
2548 __isl_give isl_aff *isl_aff_set_constant_val(
2549 __isl_take isl_aff *aff, __isl_take isl_val *v);
2550 __isl_give isl_aff *isl_aff_set_coefficient_si(
2551 __isl_take isl_aff *aff,
2552 enum isl_dim_type type, int pos, int v);
2553 __isl_give isl_aff *isl_aff_set_coefficient_val(
2554 __isl_take isl_aff *aff,
2555 enum isl_dim_type type, int pos,
2556 __isl_take isl_val *v);
2558 __isl_give isl_aff *isl_aff_add_constant_si(
2559 __isl_take isl_aff *aff, int v);
2560 __isl_give isl_aff *isl_aff_add_constant_val(
2561 __isl_take isl_aff *aff, __isl_take isl_val *v);
2562 __isl_give isl_aff *isl_aff_add_constant_num_si(
2563 __isl_take isl_aff *aff, int v);
2564 __isl_give isl_aff *isl_aff_add_coefficient_si(
2565 __isl_take isl_aff *aff,
2566 enum isl_dim_type type, int pos, int v);
2567 __isl_give isl_aff *isl_aff_add_coefficient_val(
2568 __isl_take isl_aff *aff,
2569 enum isl_dim_type type, int pos,
2570 __isl_take isl_val *v);
2572 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
2573 set the I<numerator> of the constant or coefficient, while
2574 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
2575 the constant or coefficient as a whole.
2576 The C<add_constant> and C<add_coefficient> functions add an integer
2577 or rational value to
2578 the possibly rational constant or coefficient.
2579 The C<add_constant_num> functions add an integer value to
2582 =item * Quasipolynomials
2584 Some simple quasipolynomials can be created using the following functions.
2586 #include <isl/polynomial.h>
2587 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2588 __isl_take isl_space *domain);
2589 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2590 __isl_take isl_space *domain);
2591 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2592 __isl_take isl_space *domain);
2593 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2594 __isl_take isl_space *domain);
2595 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2596 __isl_take isl_space *domain);
2597 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2598 __isl_take isl_space *domain,
2599 __isl_take isl_val *val);
2600 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2601 __isl_take isl_space *domain,
2602 enum isl_dim_type type, unsigned pos);
2603 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2604 __isl_take isl_aff *aff);
2606 Recall that the space in which a quasipolynomial lives is a map space
2607 with a one-dimensional range. The C<domain> argument in some of
2608 the functions above corresponds to the domain of this map space.
2610 Quasipolynomials can be copied and freed again using the following
2613 #include <isl/polynomial.h>
2614 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2615 __isl_keep isl_qpolynomial *qp);
2616 __isl_null isl_qpolynomial *isl_qpolynomial_free(
2617 __isl_take isl_qpolynomial *qp);
2619 The constant term of a quasipolynomial can be extracted using
2621 __isl_give isl_val *isl_qpolynomial_get_constant_val(
2622 __isl_keep isl_qpolynomial *qp);
2624 To iterate over all terms in a quasipolynomial,
2627 isl_stat isl_qpolynomial_foreach_term(
2628 __isl_keep isl_qpolynomial *qp,
2629 isl_stat (*fn)(__isl_take isl_term *term,
2630 void *user), void *user);
2632 The terms themselves can be inspected and freed using
2635 unsigned isl_term_dim(__isl_keep isl_term *term,
2636 enum isl_dim_type type);
2637 __isl_give isl_val *isl_term_get_coefficient_val(
2638 __isl_keep isl_term *term);
2639 int isl_term_get_exp(__isl_keep isl_term *term,
2640 enum isl_dim_type type, unsigned pos);
2641 __isl_give isl_aff *isl_term_get_div(
2642 __isl_keep isl_term *term, unsigned pos);
2643 void isl_term_free(__isl_take isl_term *term);
2645 Each term is a product of parameters, set variables and
2646 integer divisions. The function C<isl_term_get_exp>
2647 returns the exponent of a given dimensions in the given term.
2653 A reduction represents a maximum or a minimum of its
2655 The only reduction type defined by C<isl> is
2656 C<isl_qpolynomial_fold>.
2658 There are currently no functions to directly create such
2659 objects, but they do appear in the piecewise quasipolynomial
2660 reductions returned by the C<isl_pw_qpolynomial_bound> function.
2662 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
2664 Reductions can be copied and freed using
2665 the following functions.
2667 #include <isl/polynomial.h>
2668 __isl_give isl_qpolynomial_fold *
2669 isl_qpolynomial_fold_copy(
2670 __isl_keep isl_qpolynomial_fold *fold);
2671 void isl_qpolynomial_fold_free(
2672 __isl_take isl_qpolynomial_fold *fold);
2674 To iterate over all quasipolynomials in a reduction, use
2676 isl_stat isl_qpolynomial_fold_foreach_qpolynomial(
2677 __isl_keep isl_qpolynomial_fold *fold,
2678 isl_stat (*fn)(__isl_take isl_qpolynomial *qp,
2679 void *user), void *user);
2681 =head3 Multiple Expressions
2683 A multiple expression represents a sequence of zero or
2684 more base expressions, all defined on the same domain space.
2685 The domain space of the multiple expression is the same
2686 as that of the base expressions, but the range space
2687 can be any space. In case the base expressions have
2688 a set space, the corresponding multiple expression
2689 also has a set space.
2690 Objects of the value type do not have an associated space.
2691 The space of a multiple value is therefore always a set space.
2692 Similarly, the space of a multiple union piecewise
2693 affine expression is always a set space.
2695 The multiple expression types defined by C<isl>
2696 are C<isl_multi_val>, C<isl_multi_aff>, C<isl_multi_pw_aff>,
2697 C<isl_multi_union_pw_aff>.
2699 A multiple expression with the value zero for
2700 each output (or set) dimension can be created
2701 using the following functions.
2703 #include <isl/val.h>
2704 __isl_give isl_multi_val *isl_multi_val_zero(
2705 __isl_take isl_space *space);
2707 #include <isl/aff.h>
2708 __isl_give isl_multi_aff *isl_multi_aff_zero(
2709 __isl_take isl_space *space);
2710 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
2711 __isl_take isl_space *space);
2712 __isl_give isl_multi_union_pw_aff *
2713 isl_multi_union_pw_aff_zero(
2714 __isl_take isl_space *space);
2716 Since there is no canonical way of representing a zero
2717 value of type C<isl_union_pw_aff>, the space passed
2718 to C<isl_multi_union_pw_aff_zero> needs to be zero-dimensional.
2720 An identity function can be created using the following
2721 functions. The space needs to be that of a relation
2722 with the same number of input and output dimensions.
2724 #include <isl/aff.h>
2725 __isl_give isl_multi_aff *isl_multi_aff_identity(
2726 __isl_take isl_space *space);
2727 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
2728 __isl_take isl_space *space);
2730 A function that performs a projection on a universe
2731 relation or set can be created using the following functions.
2732 See also the corresponding
2733 projection operations in L</"Unary Operations">.
2735 #include <isl/aff.h>
2736 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
2737 __isl_take isl_space *space);
2738 __isl_give isl_multi_aff *isl_multi_aff_range_map(
2739 __isl_take isl_space *space);
2740 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
2741 __isl_take isl_space *space,
2742 enum isl_dim_type type,
2743 unsigned first, unsigned n);
2745 A multiple expression can be created from a single
2746 base expression using the following functions.
2747 The space of the created multiple expression is the same
2748 as that of the base expression, except for
2749 C<isl_multi_union_pw_aff_from_union_pw_aff> where the input
2750 lives in a parameter space and the output lives
2751 in a single-dimensional set space.
2753 #include <isl/aff.h>
2754 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
2755 __isl_take isl_aff *aff);
2756 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
2757 __isl_take isl_pw_aff *pa);
2758 __isl_give isl_multi_union_pw_aff *
2759 isl_multi_union_pw_aff_from_union_pw_aff(
2760 __isl_take isl_union_pw_aff *upa);
2762 A multiple expression can be created from a list
2763 of base expression in a specified space.
2764 The domain of this space needs to be the same
2765 as the domains of the base expressions in the list.
2766 If the base expressions have a set space (or no associated space),
2767 then this space also needs to be a set space.
2769 #include <isl/val.h>
2770 __isl_give isl_multi_val *isl_multi_val_from_val_list(
2771 __isl_take isl_space *space,
2772 __isl_take isl_val_list *list);
2774 #include <isl/aff.h>
2775 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2776 __isl_take isl_space *space,
2777 __isl_take isl_aff_list *list);
2778 __isl_give isl_multi_pw_aff *
2779 isl_multi_pw_aff_from_pw_aff_list(
2780 __isl_take isl_space *space,
2781 __isl_take isl_pw_aff_list *list);
2782 __isl_give isl_multi_union_pw_aff *
2783 isl_multi_union_pw_aff_from_union_pw_aff_list(
2784 __isl_take isl_space *space,
2785 __isl_take isl_union_pw_aff_list *list);
2787 As a convenience, a multiple piecewise expression can
2788 also be created from a multiple expression.
2789 Each piecewise expression in the result has a single
2792 #include <isl/aff.h>
2793 __isl_give isl_multi_pw_aff *
2794 isl_multi_pw_aff_from_multi_aff(
2795 __isl_take isl_multi_aff *ma);
2797 Similarly, a multiple union expression can be
2798 created from a multiple expression.
2800 #include <isl/aff.h>
2801 __isl_give isl_multi_union_pw_aff *
2802 isl_multi_union_pw_aff_from_multi_aff(
2803 __isl_take isl_multi_aff *ma);
2804 __isl_give isl_multi_union_pw_aff *
2805 isl_multi_union_pw_aff_from_multi_pw_aff(
2806 __isl_take isl_multi_pw_aff *mpa);
2808 A multiple quasi-affine expression can be created from
2809 a multiple value with a given domain space using the following
2812 #include <isl/aff.h>
2813 __isl_give isl_multi_aff *
2814 isl_multi_aff_multi_val_on_space(
2815 __isl_take isl_space *space,
2816 __isl_take isl_multi_val *mv);
2819 a multiple union piecewise affine expression can be created from
2820 a multiple value with a given domain or
2821 a multiple affine expression with a given domain
2822 using the following functions.
2824 #include <isl/aff.h>
2825 __isl_give isl_multi_union_pw_aff *
2826 isl_multi_union_pw_aff_multi_val_on_domain(
2827 __isl_take isl_union_set *domain,
2828 __isl_take isl_multi_val *mv);
2829 __isl_give isl_multi_union_pw_aff *
2830 isl_multi_union_pw_aff_multi_aff_on_domain(
2831 __isl_take isl_union_set *domain,
2832 __isl_take isl_multi_aff *ma);
2834 Multiple expressions can be copied and freed using
2835 the following functions.
2837 #include <isl/val.h>
2838 __isl_give isl_multi_val *isl_multi_val_copy(
2839 __isl_keep isl_multi_val *mv);
2840 __isl_null isl_multi_val *isl_multi_val_free(
2841 __isl_take isl_multi_val *mv);
2843 #include <isl/aff.h>
2844 __isl_give isl_multi_aff *isl_multi_aff_copy(
2845 __isl_keep isl_multi_aff *maff);
2846 __isl_null isl_multi_aff *isl_multi_aff_free(
2847 __isl_take isl_multi_aff *maff);
2848 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
2849 __isl_keep isl_multi_pw_aff *mpa);
2850 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
2851 __isl_take isl_multi_pw_aff *mpa);
2852 __isl_give isl_multi_union_pw_aff *
2853 isl_multi_union_pw_aff_copy(
2854 __isl_keep isl_multi_union_pw_aff *mupa);
2855 __isl_null isl_multi_union_pw_aff *
2856 isl_multi_union_pw_aff_free(
2857 __isl_take isl_multi_union_pw_aff *mupa);
2859 The base expression at a given position of a multiple
2860 expression can be extracted using the following functions.
2862 #include <isl/val.h>
2863 __isl_give isl_val *isl_multi_val_get_val(
2864 __isl_keep isl_multi_val *mv, int pos);
2866 #include <isl/aff.h>
2867 __isl_give isl_aff *isl_multi_aff_get_aff(
2868 __isl_keep isl_multi_aff *multi, int pos);
2869 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
2870 __isl_keep isl_multi_pw_aff *mpa, int pos);
2871 __isl_give isl_union_pw_aff *
2872 isl_multi_union_pw_aff_get_union_pw_aff(
2873 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
2875 It can be replaced using the following functions.
2877 #include <isl/val.h>
2878 __isl_give isl_multi_val *isl_multi_val_set_val(
2879 __isl_take isl_multi_val *mv, int pos,
2880 __isl_take isl_val *val);
2882 #include <isl/aff.h>
2883 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
2884 __isl_take isl_multi_aff *multi, int pos,
2885 __isl_take isl_aff *aff);
2886 __isl_give isl_multi_union_pw_aff *
2887 isl_multi_union_pw_aff_set_union_pw_aff(
2888 __isl_take isl_multi_union_pw_aff *mupa, int pos,
2889 __isl_take isl_union_pw_aff *upa);
2891 As a convenience, a sequence of base expressions that have
2892 their domains in a given space can be extracted from a sequence
2893 of union expressions using the following function.
2895 #include <isl/aff.h>
2896 __isl_give isl_multi_pw_aff *
2897 isl_multi_union_pw_aff_extract_multi_pw_aff(
2898 __isl_keep isl_multi_union_pw_aff *mupa,
2899 __isl_take isl_space *space);
2901 Note that there is a difference between C<isl_multi_union_pw_aff>
2902 and C<isl_union_pw_multi_aff> objects. The first is a sequence
2903 of unions of piecewise expressions, while the second is a union
2904 of piecewise sequences. In particular, multiple affine expressions
2905 in an C<isl_union_pw_multi_aff> may live in different spaces,
2906 while there is only a single multiple expression in
2907 an C<isl_multi_union_pw_aff>, which can therefore only live
2908 in a single space. This means that not every
2909 C<isl_union_pw_multi_aff> can be converted to
2910 an C<isl_multi_union_pw_aff>. Conversely, a zero-dimensional
2911 C<isl_multi_union_pw_aff> carries no information
2912 about any possible domain and therefore cannot be converted
2913 to an C<isl_union_pw_multi_aff>. Moreover, the elements
2914 of an C<isl_multi_union_pw_aff> may be defined over different domains,
2915 while each multiple expression inside an C<isl_union_pw_multi_aff>
2916 has a single domain. The conversion of an C<isl_union_pw_multi_aff>
2917 of dimension greater than one may therefore not be exact.
2918 The following functions can
2919 be used to perform these conversions when they are possible.
2921 #include <isl/aff.h>
2922 __isl_give isl_multi_union_pw_aff *
2923 isl_multi_union_pw_aff_from_union_pw_multi_aff(
2924 __isl_take isl_union_pw_multi_aff *upma);
2925 __isl_give isl_union_pw_multi_aff *
2926 isl_union_pw_multi_aff_from_multi_union_pw_aff(
2927 __isl_take isl_multi_union_pw_aff *mupa);
2929 =head3 Piecewise Expressions
2931 A piecewise expression is an expression that is described
2932 using zero or more base expression defined over the same
2933 number of cells in the domain space of the base expressions.
2934 All base expressions are defined over the same
2935 domain space and the cells are disjoint.
2936 The space of a piecewise expression is the same as
2937 that of the base expressions.
2938 If the union of the cells is a strict subset of the domain
2939 space, then the value of the piecewise expression outside
2940 this union is different for types derived from quasi-affine
2941 expressions and those derived from quasipolynomials.
2942 Piecewise expressions derived from quasi-affine expressions
2943 are considered to be undefined outside the union of their cells.
2944 Piecewise expressions derived from quasipolynomials
2945 are considered to be zero outside the union of their cells.
2947 Piecewise quasipolynomials are mainly used by the C<barvinok>
2948 library for representing the number of elements in a parametric set or map.
2949 For example, the piecewise quasipolynomial
2951 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2953 represents the number of points in the map
2955 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2957 The piecewise expression types defined by C<isl>
2958 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
2959 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
2961 A piecewise expression with no cells can be created using
2962 the following functions.
2964 #include <isl/aff.h>
2965 __isl_give isl_pw_aff *isl_pw_aff_empty(
2966 __isl_take isl_space *space);
2967 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
2968 __isl_take isl_space *space);
2970 A piecewise expression with a single universe cell can be
2971 created using the following functions.
2973 #include <isl/aff.h>
2974 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2975 __isl_take isl_aff *aff);
2976 __isl_give isl_pw_multi_aff *
2977 isl_pw_multi_aff_from_multi_aff(
2978 __isl_take isl_multi_aff *ma);
2980 #include <isl/polynomial.h>
2981 __isl_give isl_pw_qpolynomial *
2982 isl_pw_qpolynomial_from_qpolynomial(
2983 __isl_take isl_qpolynomial *qp);
2985 A piecewise expression with a single specified cell can be
2986 created using the following functions.
2988 #include <isl/aff.h>
2989 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2990 __isl_take isl_set *set, __isl_take isl_aff *aff);
2991 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
2992 __isl_take isl_set *set,
2993 __isl_take isl_multi_aff *maff);
2995 #include <isl/polynomial.h>
2996 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2997 __isl_take isl_set *set,
2998 __isl_take isl_qpolynomial *qp);
3000 The following convenience functions first create a base expression and
3001 then create a piecewise expression over a universe domain.
3003 #include <isl/aff.h>
3004 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3005 __isl_take isl_local_space *ls);
3006 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3007 __isl_take isl_local_space *ls,
3008 enum isl_dim_type type, unsigned pos);
3009 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3010 __isl_take isl_local_space *ls);
3011 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
3012 __isl_take isl_space *space);
3013 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3014 __isl_take isl_space *space);
3015 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
3016 __isl_take isl_space *space);
3017 __isl_give isl_pw_multi_aff *
3018 isl_pw_multi_aff_project_out_map(
3019 __isl_take isl_space *space,
3020 enum isl_dim_type type,
3021 unsigned first, unsigned n);
3023 #include <isl/polynomial.h>
3024 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3025 __isl_take isl_space *space);
3027 The following convenience functions first create a base expression and
3028 then create a piecewise expression over a given domain.
3030 #include <isl/aff.h>
3031 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
3032 __isl_take isl_set *domain,
3033 __isl_take isl_val *v);
3034 __isl_give isl_pw_multi_aff *
3035 isl_pw_multi_aff_multi_val_on_domain(
3036 __isl_take isl_set *domain,
3037 __isl_take isl_multi_val *mv);
3039 As a convenience, a piecewise multiple expression can
3040 also be created from a piecewise expression.
3041 Each multiple expression in the result is derived
3042 from the corresponding base expression.
3044 #include <isl/aff.h>
3045 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
3046 __isl_take isl_pw_aff *pa);
3048 Similarly, a piecewise quasipolynomial can be
3049 created from a piecewise quasi-affine expression using
3050 the following function.
3052 #include <isl/polynomial.h>
3053 __isl_give isl_pw_qpolynomial *
3054 isl_pw_qpolynomial_from_pw_aff(
3055 __isl_take isl_pw_aff *pwaff);
3057 Piecewise expressions can be copied and freed using the following functions.
3059 #include <isl/aff.h>
3060 __isl_give isl_pw_aff *isl_pw_aff_copy(
3061 __isl_keep isl_pw_aff *pwaff);
3062 __isl_null isl_pw_aff *isl_pw_aff_free(
3063 __isl_take isl_pw_aff *pwaff);
3064 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3065 __isl_keep isl_pw_multi_aff *pma);
3066 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
3067 __isl_take isl_pw_multi_aff *pma);
3069 #include <isl/polynomial.h>
3070 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3071 __isl_keep isl_pw_qpolynomial *pwqp);
3072 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
3073 __isl_take isl_pw_qpolynomial *pwqp);
3074 __isl_give isl_pw_qpolynomial_fold *
3075 isl_pw_qpolynomial_fold_copy(
3076 __isl_keep isl_pw_qpolynomial_fold *pwf);
3077 __isl_null isl_pw_qpolynomial_fold *
3078 isl_pw_qpolynomial_fold_free(
3079 __isl_take isl_pw_qpolynomial_fold *pwf);
3081 To iterate over the different cells of a piecewise expression,
3082 use the following functions.
3084 #include <isl/aff.h>
3085 isl_bool isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3086 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3087 isl_stat isl_pw_aff_foreach_piece(
3088 __isl_keep isl_pw_aff *pwaff,
3089 isl_stat (*fn)(__isl_take isl_set *set,
3090 __isl_take isl_aff *aff,
3091 void *user), void *user);
3092 int isl_pw_multi_aff_n_piece(
3093 __isl_keep isl_pw_multi_aff *pma);
3094 isl_stat isl_pw_multi_aff_foreach_piece(
3095 __isl_keep isl_pw_multi_aff *pma,
3096 isl_stat (*fn)(__isl_take isl_set *set,
3097 __isl_take isl_multi_aff *maff,
3098 void *user), void *user);
3100 #include <isl/polynomial.h>
3101 int isl_pw_qpolynomial_n_piece(
3102 __isl_keep isl_pw_qpolynomial *pwqp);
3103 isl_stat isl_pw_qpolynomial_foreach_piece(
3104 __isl_keep isl_pw_qpolynomial *pwqp,
3105 isl_stat (*fn)(__isl_take isl_set *set,
3106 __isl_take isl_qpolynomial *qp,
3107 void *user), void *user);
3108 isl_stat isl_pw_qpolynomial_foreach_lifted_piece(
3109 __isl_keep isl_pw_qpolynomial *pwqp,
3110 isl_stat (*fn)(__isl_take isl_set *set,
3111 __isl_take isl_qpolynomial *qp,
3112 void *user), void *user);
3113 int isl_pw_qpolynomial_fold_n_piece(
3114 __isl_keep isl_pw_qpolynomial_fold *pwf);
3115 isl_stat isl_pw_qpolynomial_fold_foreach_piece(
3116 __isl_keep isl_pw_qpolynomial_fold *pwf,
3117 isl_stat (*fn)(__isl_take isl_set *set,
3118 __isl_take isl_qpolynomial_fold *fold,
3119 void *user), void *user);
3120 isl_stat isl_pw_qpolynomial_fold_foreach_lifted_piece(
3121 __isl_keep isl_pw_qpolynomial_fold *pwf,
3122 isl_stat (*fn)(__isl_take isl_set *set,
3123 __isl_take isl_qpolynomial_fold *fold,
3124 void *user), void *user);
3126 As usual, the function C<fn> should return C<0> on success
3127 and C<-1> on failure. The difference between
3128 C<isl_pw_qpolynomial_foreach_piece> and
3129 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3130 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3131 compute unique representations for all existentially quantified
3132 variables and then turn these existentially quantified variables
3133 into extra set variables, adapting the associated quasipolynomial
3134 accordingly. This means that the C<set> passed to C<fn>
3135 will not have any existentially quantified variables, but that
3136 the dimensions of the sets may be different for different
3137 invocations of C<fn>.
3138 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
3139 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
3141 A piecewise expression consisting of the expressions at a given
3142 position of a piecewise multiple expression can be extracted
3143 using the following function.
3145 #include <isl/aff.h>
3146 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3147 __isl_keep isl_pw_multi_aff *pma, int pos);
3149 These expressions can be replaced using the following function.
3151 #include <isl/aff.h>
3152 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3153 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3154 __isl_take isl_pw_aff *pa);
3156 Note that there is a difference between C<isl_multi_pw_aff> and
3157 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
3158 affine expressions, while the second is a piecewise sequence
3159 of affine expressions. In particular, each of the piecewise
3160 affine expressions in an C<isl_multi_pw_aff> may have a different
3161 domain, while all multiple expressions associated to a cell
3162 in an C<isl_pw_multi_aff> have the same domain.
3163 It is possible to convert between the two, but when converting
3164 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
3165 of the result is the intersection of the domains of the input.
3166 The reverse conversion is exact.
3168 #include <isl/aff.h>
3169 __isl_give isl_pw_multi_aff *
3170 isl_pw_multi_aff_from_multi_pw_aff(
3171 __isl_take isl_multi_pw_aff *mpa);
3172 __isl_give isl_multi_pw_aff *
3173 isl_multi_pw_aff_from_pw_multi_aff(
3174 __isl_take isl_pw_multi_aff *pma);
3176 =head3 Union Expressions
3178 A union expression collects base expressions defined
3179 over different domains. The space of a union expression
3180 is that of the shared parameter space.
3182 The union expression types defined by C<isl>
3183 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
3184 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
3186 C<isl_union_pw_aff>,
3187 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>,
3188 there can be at most one base expression for a given domain space.
3190 C<isl_union_pw_multi_aff>,
3191 there can be multiple such expressions for a given domain space,
3192 but the domains of these expressions need to be disjoint.
3194 An empty union expression can be created using the following functions.
3196 #include <isl/aff.h>
3197 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
3198 __isl_take isl_space *space);
3199 __isl_give isl_union_pw_multi_aff *
3200 isl_union_pw_multi_aff_empty(
3201 __isl_take isl_space *space);
3203 #include <isl/polynomial.h>
3204 __isl_give isl_union_pw_qpolynomial *
3205 isl_union_pw_qpolynomial_zero(
3206 __isl_take isl_space *space);
3208 A union expression containing a single base expression
3209 can be created using the following functions.
3211 #include <isl/aff.h>
3212 __isl_give isl_union_pw_aff *
3213 isl_union_pw_aff_from_pw_aff(
3214 __isl_take isl_pw_aff *pa);
3215 __isl_give isl_union_pw_multi_aff *
3216 isl_union_pw_multi_aff_from_aff(
3217 __isl_take isl_aff *aff);
3218 __isl_give isl_union_pw_multi_aff *
3219 isl_union_pw_multi_aff_from_pw_multi_aff(
3220 __isl_take isl_pw_multi_aff *pma);
3222 #include <isl/polynomial.h>
3223 __isl_give isl_union_pw_qpolynomial *
3224 isl_union_pw_qpolynomial_from_pw_qpolynomial(
3225 __isl_take isl_pw_qpolynomial *pwqp);
3227 The following functions create a base expression on each
3228 of the sets in the union set and collect the results.
3230 #include <isl/aff.h>
3231 __isl_give isl_union_pw_multi_aff *
3232 isl_union_pw_multi_aff_from_union_pw_aff(
3233 __isl_take isl_union_pw_aff *upa);
3234 __isl_give isl_union_pw_aff *
3235 isl_union_pw_multi_aff_get_union_pw_aff(
3236 __isl_keep isl_union_pw_multi_aff *upma, int pos);
3237 __isl_give isl_union_pw_aff *
3238 isl_union_pw_aff_val_on_domain(
3239 __isl_take isl_union_set *domain,
3240 __isl_take isl_val *v);
3241 __isl_give isl_union_pw_multi_aff *
3242 isl_union_pw_multi_aff_multi_val_on_domain(
3243 __isl_take isl_union_set *domain,
3244 __isl_take isl_multi_val *mv);
3246 An C<isl_union_pw_aff> that is equal to a (parametric) affine
3247 expression on a given domain can be created using the following
3250 #include <isl/aff.h>
3251 __isl_give isl_union_pw_aff *
3252 isl_union_pw_aff_aff_on_domain(
3253 __isl_take isl_union_set *domain,
3254 __isl_take isl_aff *aff);
3256 A base expression can be added to a union expression using
3257 the following functions.
3259 #include <isl/aff.h>
3260 __isl_give isl_union_pw_aff *
3261 isl_union_pw_aff_add_pw_aff(
3262 __isl_take isl_union_pw_aff *upa,
3263 __isl_take isl_pw_aff *pa);
3264 __isl_give isl_union_pw_multi_aff *
3265 isl_union_pw_multi_aff_add_pw_multi_aff(
3266 __isl_take isl_union_pw_multi_aff *upma,
3267 __isl_take isl_pw_multi_aff *pma);
3269 #include <isl/polynomial.h>
3270 __isl_give isl_union_pw_qpolynomial *
3271 isl_union_pw_qpolynomial_add_pw_qpolynomial(
3272 __isl_take isl_union_pw_qpolynomial *upwqp,
3273 __isl_take isl_pw_qpolynomial *pwqp);
3275 Union expressions can be copied and freed using
3276 the following functions.
3278 #include <isl/aff.h>
3279 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
3280 __isl_keep isl_union_pw_aff *upa);
3281 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
3282 __isl_take isl_union_pw_aff *upa);
3283 __isl_give isl_union_pw_multi_aff *
3284 isl_union_pw_multi_aff_copy(
3285 __isl_keep isl_union_pw_multi_aff *upma);
3286 __isl_null isl_union_pw_multi_aff *
3287 isl_union_pw_multi_aff_free(
3288 __isl_take isl_union_pw_multi_aff *upma);
3290 #include <isl/polynomial.h>
3291 __isl_give isl_union_pw_qpolynomial *
3292 isl_union_pw_qpolynomial_copy(
3293 __isl_keep isl_union_pw_qpolynomial *upwqp);
3294 __isl_null isl_union_pw_qpolynomial *
3295 isl_union_pw_qpolynomial_free(
3296 __isl_take isl_union_pw_qpolynomial *upwqp);
3297 __isl_give isl_union_pw_qpolynomial_fold *
3298 isl_union_pw_qpolynomial_fold_copy(
3299 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3300 __isl_null isl_union_pw_qpolynomial_fold *
3301 isl_union_pw_qpolynomial_fold_free(
3302 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3304 To iterate over the base expressions in a union expression,
3305 use the following functions.
3307 #include <isl/aff.h>
3308 int isl_union_pw_aff_n_pw_aff(
3309 __isl_keep isl_union_pw_aff *upa);
3310 isl_stat isl_union_pw_aff_foreach_pw_aff(
3311 __isl_keep isl_union_pw_aff *upa,
3312 isl_stat (*fn)(__isl_take isl_pw_aff *pa,
3313 void *user), void *user);
3314 int isl_union_pw_multi_aff_n_pw_multi_aff(
3315 __isl_keep isl_union_pw_multi_aff *upma);
3316 isl_stat isl_union_pw_multi_aff_foreach_pw_multi_aff(
3317 __isl_keep isl_union_pw_multi_aff *upma,
3318 isl_stat (*fn)(__isl_take isl_pw_multi_aff *pma,
3319 void *user), void *user);
3321 #include <isl/polynomial.h>
3322 int isl_union_pw_qpolynomial_n_pw_qpolynomial(
3323 __isl_keep isl_union_pw_qpolynomial *upwqp);
3324 isl_stat isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3325 __isl_keep isl_union_pw_qpolynomial *upwqp,
3326 isl_stat (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
3327 void *user), void *user);
3328 int isl_union_pw_qpolynomial_fold_n_pw_qpolynomial_fold(
3329 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3330 isl_stat isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3331 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3332 isl_stat (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3333 void *user), void *user);
3335 To extract the base expression in a given space from a union, use
3336 the following functions.
3338 #include <isl/aff.h>
3339 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
3340 __isl_keep isl_union_pw_aff *upa,
3341 __isl_take isl_space *space);
3342 __isl_give isl_pw_multi_aff *
3343 isl_union_pw_multi_aff_extract_pw_multi_aff(
3344 __isl_keep isl_union_pw_multi_aff *upma,
3345 __isl_take isl_space *space);
3347 #include <isl/polynomial.h>
3348 __isl_give isl_pw_qpolynomial *
3349 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3350 __isl_keep isl_union_pw_qpolynomial *upwqp,
3351 __isl_take isl_space *space);
3353 =head2 Input and Output
3355 For set and relation,
3356 C<isl> supports its own input/output format, which is similar
3357 to the C<Omega> format, but also supports the C<PolyLib> format
3359 For other object types, typically only an C<isl> format is supported.
3361 =head3 C<isl> format
3363 The C<isl> format is similar to that of C<Omega>, but has a different
3364 syntax for describing the parameters and allows for the definition
3365 of an existentially quantified variable as the integer division
3366 of an affine expression.
3367 For example, the set of integers C<i> between C<0> and C<n>
3368 such that C<i % 10 <= 6> can be described as
3370 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
3373 A set or relation can have several disjuncts, separated
3374 by the keyword C<or>. Each disjunct is either a conjunction
3375 of constraints or a projection (C<exists>) of a conjunction
3376 of constraints. The constraints are separated by the keyword
3379 =head3 C<PolyLib> format
3381 If the represented set is a union, then the first line
3382 contains a single number representing the number of disjuncts.
3383 Otherwise, a line containing the number C<1> is optional.
3385 Each disjunct is represented by a matrix of constraints.
3386 The first line contains two numbers representing
3387 the number of rows and columns,
3388 where the number of rows is equal to the number of constraints
3389 and the number of columns is equal to two plus the number of variables.
3390 The following lines contain the actual rows of the constraint matrix.
3391 In each row, the first column indicates whether the constraint
3392 is an equality (C<0>) or inequality (C<1>). The final column
3393 corresponds to the constant term.
3395 If the set is parametric, then the coefficients of the parameters
3396 appear in the last columns before the constant column.
3397 The coefficients of any existentially quantified variables appear
3398 between those of the set variables and those of the parameters.
3400 =head3 Extended C<PolyLib> format
3402 The extended C<PolyLib> format is nearly identical to the
3403 C<PolyLib> format. The only difference is that the line
3404 containing the number of rows and columns of a constraint matrix
3405 also contains four additional numbers:
3406 the number of output dimensions, the number of input dimensions,
3407 the number of local dimensions (i.e., the number of existentially
3408 quantified variables) and the number of parameters.
3409 For sets, the number of ``output'' dimensions is equal
3410 to the number of set dimensions, while the number of ``input''
3415 Objects can be read from input using the following functions.
3417 #include <isl/val.h>
3418 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
3420 __isl_give isl_multi_val *isl_multi_val_read_from_str(
3421 isl_ctx *ctx, const char *str);
3423 #include <isl/set.h>
3424 __isl_give isl_basic_set *isl_basic_set_read_from_file(
3425 isl_ctx *ctx, FILE *input);
3426 __isl_give isl_basic_set *isl_basic_set_read_from_str(
3427 isl_ctx *ctx, const char *str);
3428 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
3430 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
3433 #include <isl/map.h>
3434 __isl_give isl_basic_map *isl_basic_map_read_from_file(
3435 isl_ctx *ctx, FILE *input);
3436 __isl_give isl_basic_map *isl_basic_map_read_from_str(
3437 isl_ctx *ctx, const char *str);
3438 __isl_give isl_map *isl_map_read_from_file(
3439 isl_ctx *ctx, FILE *input);
3440 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
3443 #include <isl/union_set.h>
3444 __isl_give isl_union_set *isl_union_set_read_from_file(
3445 isl_ctx *ctx, FILE *input);
3446 __isl_give isl_union_set *isl_union_set_read_from_str(
3447 isl_ctx *ctx, const char *str);
3449 #include <isl/union_map.h>
3450 __isl_give isl_union_map *isl_union_map_read_from_file(
3451 isl_ctx *ctx, FILE *input);
3452 __isl_give isl_union_map *isl_union_map_read_from_str(
3453 isl_ctx *ctx, const char *str);
3455 #include <isl/aff.h>
3456 __isl_give isl_aff *isl_aff_read_from_str(
3457 isl_ctx *ctx, const char *str);
3458 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3459 isl_ctx *ctx, const char *str);
3460 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3461 isl_ctx *ctx, const char *str);
3462 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3463 isl_ctx *ctx, const char *str);
3464 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
3465 isl_ctx *ctx, const char *str);
3466 __isl_give isl_union_pw_aff *
3467 isl_union_pw_aff_read_from_str(
3468 isl_ctx *ctx, const char *str);
3469 __isl_give isl_union_pw_multi_aff *
3470 isl_union_pw_multi_aff_read_from_str(
3471 isl_ctx *ctx, const char *str);
3472 __isl_give isl_multi_union_pw_aff *
3473 isl_multi_union_pw_aff_read_from_str(
3474 isl_ctx *ctx, const char *str);
3476 #include <isl/polynomial.h>
3477 __isl_give isl_union_pw_qpolynomial *
3478 isl_union_pw_qpolynomial_read_from_str(
3479 isl_ctx *ctx, const char *str);
3481 For sets and relations,
3482 the input format is autodetected and may be either the C<PolyLib> format
3483 or the C<isl> format.
3487 Before anything can be printed, an C<isl_printer> needs to
3490 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
3492 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
3493 __isl_null isl_printer *isl_printer_free(
3494 __isl_take isl_printer *printer);
3496 C<isl_printer_to_file> prints to the given file, while
3497 C<isl_printer_to_str> prints to a string that can be extracted
3498 using the following function.
3500 #include <isl/printer.h>
3501 __isl_give char *isl_printer_get_str(
3502 __isl_keep isl_printer *printer);
3504 The printer can be inspected using the following functions.
3506 FILE *isl_printer_get_file(
3507 __isl_keep isl_printer *printer);
3508 int isl_printer_get_output_format(
3509 __isl_keep isl_printer *p);
3510 int isl_printer_get_yaml_style(__isl_keep isl_printer *p);
3512 The behavior of the printer can be modified in various ways
3514 __isl_give isl_printer *isl_printer_set_output_format(
3515 __isl_take isl_printer *p, int output_format);
3516 __isl_give isl_printer *isl_printer_set_indent(
3517 __isl_take isl_printer *p, int indent);
3518 __isl_give isl_printer *isl_printer_set_indent_prefix(
3519 __isl_take isl_printer *p, const char *prefix);
3520 __isl_give isl_printer *isl_printer_indent(
3521 __isl_take isl_printer *p, int indent);
3522 __isl_give isl_printer *isl_printer_set_prefix(
3523 __isl_take isl_printer *p, const char *prefix);
3524 __isl_give isl_printer *isl_printer_set_suffix(
3525 __isl_take isl_printer *p, const char *suffix);
3526 __isl_give isl_printer *isl_printer_set_yaml_style(
3527 __isl_take isl_printer *p, int yaml_style);
3529 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
3530 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
3531 and defaults to C<ISL_FORMAT_ISL>.
3532 Each line in the output is prefixed by C<indent_prefix>,
3533 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
3534 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
3535 In the C<PolyLib> format output,
3536 the coefficients of the existentially quantified variables
3537 appear between those of the set variables and those
3539 The function C<isl_printer_indent> increases the indentation
3540 by the specified amount (which may be negative).
3541 The YAML style may be either C<ISL_YAML_STYLE_BLOCK> or
3542 C<ISL_YAML_STYLE_FLOW> and when we are printing something
3545 To actually print something, use
3547 #include <isl/printer.h>
3548 __isl_give isl_printer *isl_printer_print_double(
3549 __isl_take isl_printer *p, double d);
3551 #include <isl/val.h>
3552 __isl_give isl_printer *isl_printer_print_val(
3553 __isl_take isl_printer *p, __isl_keep isl_val *v);
3555 #include <isl/set.h>
3556 __isl_give isl_printer *isl_printer_print_basic_set(
3557 __isl_take isl_printer *printer,
3558 __isl_keep isl_basic_set *bset);
3559 __isl_give isl_printer *isl_printer_print_set(
3560 __isl_take isl_printer *printer,
3561 __isl_keep isl_set *set);
3563 #include <isl/map.h>
3564 __isl_give isl_printer *isl_printer_print_basic_map(
3565 __isl_take isl_printer *printer,
3566 __isl_keep isl_basic_map *bmap);
3567 __isl_give isl_printer *isl_printer_print_map(
3568 __isl_take isl_printer *printer,
3569 __isl_keep isl_map *map);
3571 #include <isl/union_set.h>
3572 __isl_give isl_printer *isl_printer_print_union_set(
3573 __isl_take isl_printer *p,
3574 __isl_keep isl_union_set *uset);
3576 #include <isl/union_map.h>
3577 __isl_give isl_printer *isl_printer_print_union_map(
3578 __isl_take isl_printer *p,
3579 __isl_keep isl_union_map *umap);
3581 #include <isl/val.h>
3582 __isl_give isl_printer *isl_printer_print_multi_val(
3583 __isl_take isl_printer *p,
3584 __isl_keep isl_multi_val *mv);
3586 #include <isl/aff.h>
3587 __isl_give isl_printer *isl_printer_print_aff(
3588 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3589 __isl_give isl_printer *isl_printer_print_multi_aff(
3590 __isl_take isl_printer *p,
3591 __isl_keep isl_multi_aff *maff);
3592 __isl_give isl_printer *isl_printer_print_pw_aff(
3593 __isl_take isl_printer *p,
3594 __isl_keep isl_pw_aff *pwaff);
3595 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3596 __isl_take isl_printer *p,
3597 __isl_keep isl_pw_multi_aff *pma);
3598 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3599 __isl_take isl_printer *p,
3600 __isl_keep isl_multi_pw_aff *mpa);
3601 __isl_give isl_printer *isl_printer_print_union_pw_aff(
3602 __isl_take isl_printer *p,
3603 __isl_keep isl_union_pw_aff *upa);
3604 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3605 __isl_take isl_printer *p,
3606 __isl_keep isl_union_pw_multi_aff *upma);
3607 __isl_give isl_printer *
3608 isl_printer_print_multi_union_pw_aff(
3609 __isl_take isl_printer *p,
3610 __isl_keep isl_multi_union_pw_aff *mupa);
3612 #include <isl/polynomial.h>
3613 __isl_give isl_printer *isl_printer_print_qpolynomial(
3614 __isl_take isl_printer *p,
3615 __isl_keep isl_qpolynomial *qp);
3616 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3617 __isl_take isl_printer *p,
3618 __isl_keep isl_pw_qpolynomial *pwqp);
3619 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3620 __isl_take isl_printer *p,
3621 __isl_keep isl_union_pw_qpolynomial *upwqp);
3623 __isl_give isl_printer *
3624 isl_printer_print_pw_qpolynomial_fold(
3625 __isl_take isl_printer *p,
3626 __isl_keep isl_pw_qpolynomial_fold *pwf);
3627 __isl_give isl_printer *
3628 isl_printer_print_union_pw_qpolynomial_fold(
3629 __isl_take isl_printer *p,
3630 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3632 For C<isl_printer_print_qpolynomial>,
3633 C<isl_printer_print_pw_qpolynomial> and
3634 C<isl_printer_print_pw_qpolynomial_fold>,
3635 the output format of the printer
3636 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3637 For C<isl_printer_print_union_pw_qpolynomial> and
3638 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
3640 In case of printing in C<ISL_FORMAT_C>, the user may want
3641 to set the names of all dimensions first.
3643 C<isl> also provides limited support for printing YAML documents,
3644 just enough for the internal use for printing such documents.
3646 #include <isl/printer.h>
3647 __isl_give isl_printer *isl_printer_yaml_start_mapping(
3648 __isl_take isl_printer *p);
3649 __isl_give isl_printer *isl_printer_yaml_end_mapping(
3650 __isl_take isl_printer *p);
3651 __isl_give isl_printer *isl_printer_yaml_start_sequence(
3652 __isl_take isl_printer *p);
3653 __isl_give isl_printer *isl_printer_yaml_end_sequence(
3654 __isl_take isl_printer *p);
3655 __isl_give isl_printer *isl_printer_yaml_next(
3656 __isl_take isl_printer *p);
3658 A document is started by a call to either
3659 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3660 Anything printed to the printer after such a call belong to the
3661 first key of the mapping or the first element in the sequence.
3662 The function C<isl_printer_yaml_next> moves to the value if
3663 we are currently printing a mapping key, the next key if we
3664 are printing a value or the next element if we are printing
3665 an element in a sequence.
3666 Nested mappings and sequences are initiated by the same
3667 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3668 Each call to these functions needs to have a corresponding call to
3669 C<isl_printer_yaml_end_mapping> or C<isl_printer_yaml_end_sequence>.
3671 When called on a file printer, the following function flushes
3672 the file. When called on a string printer, the buffer is cleared.
3674 __isl_give isl_printer *isl_printer_flush(
3675 __isl_take isl_printer *p);
3677 The following functions allow the user to attach
3678 notes to a printer in order to keep track of additional state.
3680 #include <isl/printer.h>
3681 isl_bool isl_printer_has_note(__isl_keep isl_printer *p,
3682 __isl_keep isl_id *id);
3683 __isl_give isl_id *isl_printer_get_note(
3684 __isl_keep isl_printer *p, __isl_take isl_id *id);
3685 __isl_give isl_printer *isl_printer_set_note(
3686 __isl_take isl_printer *p,
3687 __isl_take isl_id *id, __isl_take isl_id *note);
3689 C<isl_printer_set_note> associates the given note to the given
3690 identifier in the printer.
3691 C<isl_printer_get_note> retrieves a note associated to an
3693 C<isl_printer_has_note> checks if there is such a note.
3694 C<isl_printer_get_note> fails if the requested note does not exist.
3696 Alternatively, a string representation can be obtained
3697 directly using the following functions, which always print
3701 __isl_give char *isl_id_to_str(
3702 __isl_keep isl_id *id);
3704 #include <isl/space.h>
3705 __isl_give char *isl_space_to_str(
3706 __isl_keep isl_space *space);
3708 #include <isl/val.h>
3709 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
3710 __isl_give char *isl_multi_val_to_str(
3711 __isl_keep isl_multi_val *mv);
3713 #include <isl/set.h>
3714 __isl_give char *isl_basic_set_to_str(
3715 __isl_keep isl_basic_set *bset);
3716 __isl_give char *isl_set_to_str(
3717 __isl_keep isl_set *set);
3719 #include <isl/union_set.h>
3720 __isl_give char *isl_union_set_to_str(
3721 __isl_keep isl_union_set *uset);
3723 #include <isl/map.h>
3724 __isl_give char *isl_basic_map_to_str(
3725 __isl_keep isl_basic_map *bmap);
3726 __isl_give char *isl_map_to_str(
3727 __isl_keep isl_map *map);
3729 #include <isl/union_map.h>
3730 __isl_give char *isl_union_map_to_str(
3731 __isl_keep isl_union_map *umap);
3733 #include <isl/aff.h>
3734 __isl_give char *isl_aff_to_str(__isl_keep isl_aff *aff);
3735 __isl_give char *isl_pw_aff_to_str(
3736 __isl_keep isl_pw_aff *pa);
3737 __isl_give char *isl_multi_aff_to_str(
3738 __isl_keep isl_multi_aff *ma);
3739 __isl_give char *isl_pw_multi_aff_to_str(
3740 __isl_keep isl_pw_multi_aff *pma);
3741 __isl_give char *isl_multi_pw_aff_to_str(
3742 __isl_keep isl_multi_pw_aff *mpa);
3743 __isl_give char *isl_union_pw_aff_to_str(
3744 __isl_keep isl_union_pw_aff *upa);
3745 __isl_give char *isl_union_pw_multi_aff_to_str(
3746 __isl_keep isl_union_pw_multi_aff *upma);
3747 __isl_give char *isl_multi_union_pw_aff_to_str(
3748 __isl_keep isl_multi_union_pw_aff *mupa);
3750 #include <isl/point.h>
3751 __isl_give char *isl_point_to_str(
3752 __isl_keep isl_point *pnt);
3754 #include <isl/polynomial.h>
3755 __isl_give char *isl_pw_qpolynomial_to_str(
3756 __isl_keep isl_pw_qpolynomial *pwqp);
3757 __isl_give char *isl_union_pw_qpolynomial_to_str(
3758 __isl_keep isl_union_pw_qpolynomial *upwqp);
3762 =head3 Unary Properties
3768 The following functions test whether the given set or relation
3769 contains any integer points. The ``plain'' variants do not perform
3770 any computations, but simply check if the given set or relation
3771 is already known to be empty.
3773 isl_bool isl_basic_set_plain_is_empty(
3774 __isl_keep isl_basic_set *bset);
3775 isl_bool isl_basic_set_is_empty(
3776 __isl_keep isl_basic_set *bset);
3777 isl_bool isl_set_plain_is_empty(
3778 __isl_keep isl_set *set);
3779 isl_bool isl_set_is_empty(__isl_keep isl_set *set);
3780 isl_bool isl_union_set_is_empty(
3781 __isl_keep isl_union_set *uset);
3782 isl_bool isl_basic_map_plain_is_empty(
3783 __isl_keep isl_basic_map *bmap);
3784 isl_bool isl_basic_map_is_empty(
3785 __isl_keep isl_basic_map *bmap);
3786 isl_bool isl_map_plain_is_empty(
3787 __isl_keep isl_map *map);
3788 isl_bool isl_map_is_empty(__isl_keep isl_map *map);
3789 isl_bool isl_union_map_is_empty(
3790 __isl_keep isl_union_map *umap);
3792 =item * Universality
3794 isl_bool isl_basic_set_plain_is_universe(
3795 __isl_keep isl_basic_set *bset);
3796 isl_bool isl_basic_set_is_universe(
3797 __isl_keep isl_basic_set *bset);
3798 isl_bool isl_basic_map_plain_is_universe(
3799 __isl_keep isl_basic_map *bmap);
3800 isl_bool isl_basic_map_is_universe(
3801 __isl_keep isl_basic_map *bmap);
3802 isl_bool isl_set_plain_is_universe(
3803 __isl_keep isl_set *set);
3804 isl_bool isl_map_plain_is_universe(
3805 __isl_keep isl_map *map);
3807 =item * Single-valuedness
3809 #include <isl/set.h>
3810 isl_bool isl_set_is_singleton(__isl_keep isl_set *set);
3812 #include <isl/map.h>
3813 isl_bool isl_basic_map_is_single_valued(
3814 __isl_keep isl_basic_map *bmap);
3815 isl_bool isl_map_plain_is_single_valued(
3816 __isl_keep isl_map *map);
3817 isl_bool isl_map_is_single_valued(__isl_keep isl_map *map);
3819 #include <isl/union_map.h>
3820 isl_bool isl_union_map_is_single_valued(
3821 __isl_keep isl_union_map *umap);
3825 isl_bool isl_map_plain_is_injective(
3826 __isl_keep isl_map *map);
3827 isl_bool isl_map_is_injective(
3828 __isl_keep isl_map *map);
3829 isl_bool isl_union_map_plain_is_injective(
3830 __isl_keep isl_union_map *umap);
3831 isl_bool isl_union_map_is_injective(
3832 __isl_keep isl_union_map *umap);
3836 isl_bool isl_map_is_bijective(
3837 __isl_keep isl_map *map);
3838 isl_bool isl_union_map_is_bijective(
3839 __isl_keep isl_union_map *umap);
3843 The following functions test whether the given relation
3844 only maps elements to themselves.
3846 #include <isl/map.h>
3847 isl_bool isl_map_is_identity(
3848 __isl_keep isl_map *map);
3850 #include <isl/union_map.h>
3851 isl_bool isl_union_map_is_identity(
3852 __isl_keep isl_union_map *umap);
3856 __isl_give isl_val *
3857 isl_basic_map_plain_get_val_if_fixed(
3858 __isl_keep isl_basic_map *bmap,
3859 enum isl_dim_type type, unsigned pos);
3860 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
3861 __isl_keep isl_set *set,
3862 enum isl_dim_type type, unsigned pos);
3863 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
3864 __isl_keep isl_map *map,
3865 enum isl_dim_type type, unsigned pos);
3867 If the set or relation obviously lies on a hyperplane where the given dimension
3868 has a fixed value, then return that value.
3869 Otherwise return NaN.
3873 isl_stat isl_set_dim_residue_class_val(
3874 __isl_keep isl_set *set,
3875 int pos, __isl_give isl_val **modulo,
3876 __isl_give isl_val **residue);
3878 Check if the values of the given set dimension are equal to a fixed
3879 value modulo some integer value. If so, assign the modulo to C<*modulo>
3880 and the fixed value to C<*residue>. If the given dimension attains only
3881 a single value, then assign C<0> to C<*modulo> and the fixed value to
3883 If the dimension does not attain only a single value and if no modulo
3884 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
3888 To check whether the description of a set, relation or function depends
3889 on one or more given dimensions,
3890 the following functions can be used.
3892 #include <isl/constraint.h>
3893 isl_bool isl_constraint_involves_dims(
3894 __isl_keep isl_constraint *constraint,
3895 enum isl_dim_type type, unsigned first, unsigned n);
3897 #include <isl/set.h>
3898 isl_bool isl_basic_set_involves_dims(
3899 __isl_keep isl_basic_set *bset,
3900 enum isl_dim_type type, unsigned first, unsigned n);
3901 isl_bool isl_set_involves_dims(__isl_keep isl_set *set,
3902 enum isl_dim_type type, unsigned first, unsigned n);
3904 #include <isl/map.h>
3905 isl_bool isl_basic_map_involves_dims(
3906 __isl_keep isl_basic_map *bmap,
3907 enum isl_dim_type type, unsigned first, unsigned n);
3908 isl_bool isl_map_involves_dims(__isl_keep isl_map *map,
3909 enum isl_dim_type type, unsigned first, unsigned n);
3911 #include <isl/union_map.h>
3912 isl_bool isl_union_map_involves_dims(
3913 __isl_keep isl_union_map *umap,
3914 enum isl_dim_type type, unsigned first, unsigned n);
3916 #include <isl/aff.h>
3917 isl_bool isl_aff_involves_dims(__isl_keep isl_aff *aff,
3918 enum isl_dim_type type, unsigned first, unsigned n);
3919 isl_bool isl_pw_aff_involves_dims(
3920 __isl_keep isl_pw_aff *pwaff,
3921 enum isl_dim_type type, unsigned first, unsigned n);
3922 isl_bool isl_multi_aff_involves_dims(
3923 __isl_keep isl_multi_aff *ma,
3924 enum isl_dim_type type, unsigned first, unsigned n);
3925 isl_bool isl_multi_pw_aff_involves_dims(
3926 __isl_keep isl_multi_pw_aff *mpa,
3927 enum isl_dim_type type, unsigned first, unsigned n);
3929 #include <isl/polynomial.h>
3930 isl_bool isl_qpolynomial_involves_dims(
3931 __isl_keep isl_qpolynomial *qp,
3932 enum isl_dim_type type, unsigned first, unsigned n);
3934 Similarly, the following functions can be used to check whether
3935 a given dimension is involved in any lower or upper bound.
3937 #include <isl/set.h>
3938 isl_bool isl_set_dim_has_any_lower_bound(
3939 __isl_keep isl_set *set,
3940 enum isl_dim_type type, unsigned pos);
3941 isl_bool isl_set_dim_has_any_upper_bound(
3942 __isl_keep isl_set *set,
3943 enum isl_dim_type type, unsigned pos);
3945 Note that these functions return true even if there is a bound on
3946 the dimension on only some of the basic sets of C<set>.
3947 To check if they have a bound for all of the basic sets in C<set>,
3948 use the following functions instead.
3950 #include <isl/set.h>
3951 isl_bool isl_set_dim_has_lower_bound(
3952 __isl_keep isl_set *set,
3953 enum isl_dim_type type, unsigned pos);
3954 isl_bool isl_set_dim_has_upper_bound(
3955 __isl_keep isl_set *set,
3956 enum isl_dim_type type, unsigned pos);
3960 To check whether a set is a parameter domain, use this function:
3962 isl_bool isl_set_is_params(__isl_keep isl_set *set);
3963 isl_bool isl_union_set_is_params(
3964 __isl_keep isl_union_set *uset);
3968 The following functions check whether the space of the given
3969 (basic) set or relation domain and/or range is a wrapped relation.
3971 #include <isl/space.h>
3972 isl_bool isl_space_is_wrapping(
3973 __isl_keep isl_space *space);
3974 isl_bool isl_space_domain_is_wrapping(
3975 __isl_keep isl_space *space);
3976 isl_bool isl_space_range_is_wrapping(
3977 __isl_keep isl_space *space);
3978 isl_bool isl_space_is_product(
3979 __isl_keep isl_space *space);
3981 #include <isl/set.h>
3982 isl_bool isl_basic_set_is_wrapping(
3983 __isl_keep isl_basic_set *bset);
3984 isl_bool isl_set_is_wrapping(__isl_keep isl_set *set);
3986 #include <isl/map.h>
3987 isl_bool isl_map_domain_is_wrapping(
3988 __isl_keep isl_map *map);
3989 isl_bool isl_map_range_is_wrapping(
3990 __isl_keep isl_map *map);
3991 isl_bool isl_map_is_product(__isl_keep isl_map *map);
3993 #include <isl/val.h>
3994 isl_bool isl_multi_val_range_is_wrapping(
3995 __isl_keep isl_multi_val *mv);
3997 #include <isl/aff.h>
3998 isl_bool isl_multi_aff_range_is_wrapping(
3999 __isl_keep isl_multi_aff *ma);
4000 isl_bool isl_multi_pw_aff_range_is_wrapping(
4001 __isl_keep isl_multi_pw_aff *mpa);
4002 isl_bool isl_multi_union_pw_aff_range_is_wrapping(
4003 __isl_keep isl_multi_union_pw_aff *mupa);
4005 The input to C<isl_space_is_wrapping> should
4006 be the space of a set, while that of
4007 C<isl_space_domain_is_wrapping> and
4008 C<isl_space_range_is_wrapping> should be the space of a relation.
4009 The input to C<isl_space_is_product> can be either the space
4010 of a set or that of a binary relation.
4011 In case the input is the space of a binary relation, it checks
4012 whether both domain and range are wrapping.
4014 =item * Internal Product
4016 isl_bool isl_basic_map_can_zip(
4017 __isl_keep isl_basic_map *bmap);
4018 isl_bool isl_map_can_zip(__isl_keep isl_map *map);
4020 Check whether the product of domain and range of the given relation
4022 i.e., whether both domain and range are nested relations.
4026 #include <isl/space.h>
4027 isl_bool isl_space_can_curry(
4028 __isl_keep isl_space *space);
4030 #include <isl/map.h>
4031 isl_bool isl_basic_map_can_curry(
4032 __isl_keep isl_basic_map *bmap);
4033 isl_bool isl_map_can_curry(__isl_keep isl_map *map);
4035 Check whether the domain of the (basic) relation is a wrapped relation.
4037 #include <isl/space.h>
4038 __isl_give isl_space *isl_space_uncurry(
4039 __isl_take isl_space *space);
4041 #include <isl/map.h>
4042 isl_bool isl_basic_map_can_uncurry(
4043 __isl_keep isl_basic_map *bmap);
4044 isl_bool isl_map_can_uncurry(__isl_keep isl_map *map);
4046 Check whether the range of the (basic) relation is a wrapped relation.
4048 #include <isl/space.h>
4049 isl_bool isl_space_can_range_curry(
4050 __isl_keep isl_space *space);
4052 #include <isl/map.h>
4053 isl_bool isl_map_can_range_curry(
4054 __isl_keep isl_map *map);
4056 Check whether the domain of the relation wrapped in the range of
4057 the input is itself a wrapped relation.
4059 =item * Special Values
4061 #include <isl/aff.h>
4062 isl_bool isl_aff_is_cst(__isl_keep isl_aff *aff);
4063 isl_bool isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
4064 isl_bool isl_multi_pw_aff_is_cst(
4065 __isl_keep isl_multi_pw_aff *mpa);
4067 Check whether the given expression is a constant.
4069 #include <isl/val.h>
4070 isl_bool isl_multi_val_involves_nan(
4071 __isl_keep isl_multi_val *mv);
4073 #include <isl/aff.h>
4074 isl_bool isl_aff_is_nan(__isl_keep isl_aff *aff);
4075 isl_bool isl_multi_aff_involves_nan(
4076 __isl_keep isl_multi_aff *ma);
4077 isl_bool isl_pw_aff_involves_nan(
4078 __isl_keep isl_pw_aff *pa);
4079 isl_bool isl_pw_multi_aff_involves_nan(
4080 __isl_keep isl_pw_multi_aff *pma);
4081 isl_bool isl_multi_pw_aff_involves_nan(
4082 __isl_keep isl_multi_pw_aff *mpa);
4083 isl_bool isl_union_pw_aff_involves_nan(
4084 __isl_keep isl_union_pw_aff *upa);
4085 isl_bool isl_union_pw_multi_aff_involves_nan(
4086 __isl_keep isl_union_pw_multi_aff *upma);
4087 isl_bool isl_multi_union_pw_aff_involves_nan(
4088 __isl_keep isl_multi_union_pw_aff *mupa);
4090 #include <isl/polynomial.h>
4091 isl_bool isl_qpolynomial_is_nan(
4092 __isl_keep isl_qpolynomial *qp);
4093 isl_bool isl_qpolynomial_fold_is_nan(
4094 __isl_keep isl_qpolynomial_fold *fold);
4095 isl_bool isl_pw_qpolynomial_involves_nan(
4096 __isl_keep isl_pw_qpolynomial *pwqp);
4097 isl_bool isl_pw_qpolynomial_fold_involves_nan(
4098 __isl_keep isl_pw_qpolynomial_fold *pwf);
4099 isl_bool isl_union_pw_qpolynomial_involves_nan(
4100 __isl_keep isl_union_pw_qpolynomial *upwqp);
4101 isl_bool isl_union_pw_qpolynomial_fold_involves_nan(
4102 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4104 Check whether the given expression is equal to or involves NaN.
4106 #include <isl/aff.h>
4107 isl_bool isl_aff_plain_is_zero(
4108 __isl_keep isl_aff *aff);
4110 Check whether the affine expression is obviously zero.
4114 =head3 Binary Properties
4120 The following functions check whether two objects
4121 represent the same set, relation or function.
4122 The C<plain> variants only return true if the objects
4123 are obviously the same. That is, they may return false
4124 even if the objects are the same, but they will never
4125 return true if the objects are not the same.
4127 #include <isl/set.h>
4128 isl_bool isl_basic_set_plain_is_equal(
4129 __isl_keep isl_basic_set *bset1,
4130 __isl_keep isl_basic_set *bset2);
4131 isl_bool isl_basic_set_is_equal(
4132 __isl_keep isl_basic_set *bset1,
4133 __isl_keep isl_basic_set *bset2);
4134 isl_bool isl_set_plain_is_equal(
4135 __isl_keep isl_set *set1,
4136 __isl_keep isl_set *set2);
4137 isl_bool isl_set_is_equal(__isl_keep isl_set *set1,
4138 __isl_keep isl_set *set2);
4140 #include <isl/map.h>
4141 isl_bool isl_basic_map_is_equal(
4142 __isl_keep isl_basic_map *bmap1,
4143 __isl_keep isl_basic_map *bmap2);
4144 isl_bool isl_map_is_equal(__isl_keep isl_map *map1,
4145 __isl_keep isl_map *map2);
4146 isl_bool isl_map_plain_is_equal(
4147 __isl_keep isl_map *map1,
4148 __isl_keep isl_map *map2);
4150 #include <isl/union_set.h>
4151 isl_bool isl_union_set_is_equal(
4152 __isl_keep isl_union_set *uset1,
4153 __isl_keep isl_union_set *uset2);
4155 #include <isl/union_map.h>
4156 isl_bool isl_union_map_is_equal(
4157 __isl_keep isl_union_map *umap1,
4158 __isl_keep isl_union_map *umap2);
4160 #include <isl/aff.h>
4161 isl_bool isl_aff_plain_is_equal(
4162 __isl_keep isl_aff *aff1,
4163 __isl_keep isl_aff *aff2);
4164 isl_bool isl_multi_aff_plain_is_equal(
4165 __isl_keep isl_multi_aff *maff1,
4166 __isl_keep isl_multi_aff *maff2);
4167 isl_bool isl_pw_aff_plain_is_equal(
4168 __isl_keep isl_pw_aff *pwaff1,
4169 __isl_keep isl_pw_aff *pwaff2);
4170 isl_bool isl_pw_aff_is_equal(
4171 __isl_keep isl_pw_aff *pa1,
4172 __isl_keep isl_pw_aff *pa2);
4173 isl_bool isl_pw_multi_aff_plain_is_equal(
4174 __isl_keep isl_pw_multi_aff *pma1,
4175 __isl_keep isl_pw_multi_aff *pma2);
4176 isl_bool isl_pw_multi_aff_is_equal(
4177 __isl_keep isl_pw_multi_aff *pma1,
4178 __isl_keep isl_pw_multi_aff *pma2);
4179 isl_bool isl_multi_pw_aff_plain_is_equal(
4180 __isl_keep isl_multi_pw_aff *mpa1,
4181 __isl_keep isl_multi_pw_aff *mpa2);
4182 isl_bool isl_multi_pw_aff_is_equal(
4183 __isl_keep isl_multi_pw_aff *mpa1,
4184 __isl_keep isl_multi_pw_aff *mpa2);
4185 isl_bool isl_union_pw_aff_plain_is_equal(
4186 __isl_keep isl_union_pw_aff *upa1,
4187 __isl_keep isl_union_pw_aff *upa2);
4188 isl_bool isl_union_pw_multi_aff_plain_is_equal(
4189 __isl_keep isl_union_pw_multi_aff *upma1,
4190 __isl_keep isl_union_pw_multi_aff *upma2);
4191 isl_bool isl_multi_union_pw_aff_plain_is_equal(
4192 __isl_keep isl_multi_union_pw_aff *mupa1,
4193 __isl_keep isl_multi_union_pw_aff *mupa2);
4195 #include <isl/polynomial.h>
4196 isl_bool isl_union_pw_qpolynomial_plain_is_equal(
4197 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4198 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4199 isl_bool isl_union_pw_qpolynomial_fold_plain_is_equal(
4200 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4201 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4203 =item * Disjointness
4205 #include <isl/set.h>
4206 isl_bool isl_basic_set_is_disjoint(
4207 __isl_keep isl_basic_set *bset1,
4208 __isl_keep isl_basic_set *bset2);
4209 isl_bool isl_set_plain_is_disjoint(
4210 __isl_keep isl_set *set1,
4211 __isl_keep isl_set *set2);
4212 isl_bool isl_set_is_disjoint(__isl_keep isl_set *set1,
4213 __isl_keep isl_set *set2);
4215 #include <isl/map.h>
4216 isl_bool isl_basic_map_is_disjoint(
4217 __isl_keep isl_basic_map *bmap1,
4218 __isl_keep isl_basic_map *bmap2);
4219 isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1,
4220 __isl_keep isl_map *map2);
4222 #include <isl/union_set.h>
4223 isl_bool isl_union_set_is_disjoint(
4224 __isl_keep isl_union_set *uset1,
4225 __isl_keep isl_union_set *uset2);
4227 #include <isl/union_map.h>
4228 isl_bool isl_union_map_is_disjoint(
4229 __isl_keep isl_union_map *umap1,
4230 __isl_keep isl_union_map *umap2);
4234 isl_bool isl_basic_set_is_subset(
4235 __isl_keep isl_basic_set *bset1,
4236 __isl_keep isl_basic_set *bset2);
4237 isl_bool isl_set_is_subset(__isl_keep isl_set *set1,
4238 __isl_keep isl_set *set2);
4239 isl_bool isl_set_is_strict_subset(
4240 __isl_keep isl_set *set1,
4241 __isl_keep isl_set *set2);
4242 isl_bool isl_union_set_is_subset(
4243 __isl_keep isl_union_set *uset1,
4244 __isl_keep isl_union_set *uset2);
4245 isl_bool isl_union_set_is_strict_subset(
4246 __isl_keep isl_union_set *uset1,
4247 __isl_keep isl_union_set *uset2);
4248 isl_bool isl_basic_map_is_subset(
4249 __isl_keep isl_basic_map *bmap1,
4250 __isl_keep isl_basic_map *bmap2);
4251 isl_bool isl_basic_map_is_strict_subset(
4252 __isl_keep isl_basic_map *bmap1,
4253 __isl_keep isl_basic_map *bmap2);
4254 isl_bool isl_map_is_subset(
4255 __isl_keep isl_map *map1,
4256 __isl_keep isl_map *map2);
4257 isl_bool isl_map_is_strict_subset(
4258 __isl_keep isl_map *map1,
4259 __isl_keep isl_map *map2);
4260 isl_bool isl_union_map_is_subset(
4261 __isl_keep isl_union_map *umap1,
4262 __isl_keep isl_union_map *umap2);
4263 isl_bool isl_union_map_is_strict_subset(
4264 __isl_keep isl_union_map *umap1,
4265 __isl_keep isl_union_map *umap2);
4267 Check whether the first argument is a (strict) subset of the
4272 Every comparison function returns a negative value if the first
4273 argument is considered smaller than the second, a positive value
4274 if the first argument is considered greater and zero if the two
4275 constraints are considered the same by the comparison criterion.
4277 #include <isl/constraint.h>
4278 int isl_constraint_plain_cmp(
4279 __isl_keep isl_constraint *c1,
4280 __isl_keep isl_constraint *c2);
4282 This function is useful for sorting C<isl_constraint>s.
4283 The order depends on the internal representation of the inputs.
4284 The order is fixed over different calls to the function (assuming
4285 the internal representation of the inputs has not changed), but may
4286 change over different versions of C<isl>.
4288 #include <isl/constraint.h>
4289 int isl_constraint_cmp_last_non_zero(
4290 __isl_keep isl_constraint *c1,
4291 __isl_keep isl_constraint *c2);
4293 This function can be used to sort constraints that live in the same
4294 local space. Constraints that involve ``earlier'' dimensions or
4295 that have a smaller coefficient for the shared latest dimension
4296 are considered smaller than other constraints.
4297 This function only defines a B<partial> order.
4299 #include <isl/set.h>
4300 int isl_set_plain_cmp(__isl_keep isl_set *set1,
4301 __isl_keep isl_set *set2);
4303 This function is useful for sorting C<isl_set>s.
4304 The order depends on the internal representation of the inputs.
4305 The order is fixed over different calls to the function (assuming
4306 the internal representation of the inputs has not changed), but may
4307 change over different versions of C<isl>.
4309 #include <isl/aff.h>
4310 int isl_multi_aff_plain_cmp(
4311 __isl_keep isl_multi_aff *ma1,
4312 __isl_keep isl_multi_aff *ma2);
4313 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4314 __isl_keep isl_pw_aff *pa2);
4316 The functions C<isl_multi_aff_plain_cmp> and
4317 C<isl_pw_aff_plain_cmp> can be used to sort C<isl_multi_aff>s and
4318 C<isl_pw_aff>s. The order is not strictly defined.
4319 The current order sorts expressions that only involve
4320 earlier dimensions before those that involve later dimensions.
4324 =head2 Unary Operations
4330 __isl_give isl_set *isl_set_complement(
4331 __isl_take isl_set *set);
4332 __isl_give isl_map *isl_map_complement(
4333 __isl_take isl_map *map);
4337 #include <isl/space.h>
4338 __isl_give isl_space *isl_space_reverse(
4339 __isl_take isl_space *space);
4341 #include <isl/map.h>
4342 __isl_give isl_basic_map *isl_basic_map_reverse(
4343 __isl_take isl_basic_map *bmap);
4344 __isl_give isl_map *isl_map_reverse(
4345 __isl_take isl_map *map);
4347 #include <isl/union_map.h>
4348 __isl_give isl_union_map *isl_union_map_reverse(
4349 __isl_take isl_union_map *umap);
4353 #include <isl/space.h>
4354 __isl_give isl_space *isl_space_domain(
4355 __isl_take isl_space *space);
4356 __isl_give isl_space *isl_space_range(
4357 __isl_take isl_space *space);
4358 __isl_give isl_space *isl_space_params(
4359 __isl_take isl_space *space);
4361 #include <isl/local_space.h>
4362 __isl_give isl_local_space *isl_local_space_domain(
4363 __isl_take isl_local_space *ls);
4364 __isl_give isl_local_space *isl_local_space_range(
4365 __isl_take isl_local_space *ls);
4367 #include <isl/set.h>
4368 __isl_give isl_basic_set *isl_basic_set_project_out(
4369 __isl_take isl_basic_set *bset,
4370 enum isl_dim_type type, unsigned first, unsigned n);
4371 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
4372 enum isl_dim_type type, unsigned first, unsigned n);
4373 __isl_give isl_map *isl_set_project_onto_map(
4374 __isl_take isl_set *set,
4375 enum isl_dim_type type, unsigned first,
4377 __isl_give isl_basic_set *isl_basic_set_params(
4378 __isl_take isl_basic_set *bset);
4379 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
4381 The function C<isl_set_project_onto_map> returns a relation
4382 that projects the input set onto the given set dimensions.
4384 #include <isl/map.h>
4385 __isl_give isl_basic_map *isl_basic_map_project_out(
4386 __isl_take isl_basic_map *bmap,
4387 enum isl_dim_type type, unsigned first, unsigned n);
4388 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
4389 enum isl_dim_type type, unsigned first, unsigned n);
4390 __isl_give isl_basic_set *isl_basic_map_domain(
4391 __isl_take isl_basic_map *bmap);
4392 __isl_give isl_basic_set *isl_basic_map_range(
4393 __isl_take isl_basic_map *bmap);
4394 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
4395 __isl_give isl_set *isl_map_domain(
4396 __isl_take isl_map *bmap);
4397 __isl_give isl_set *isl_map_range(
4398 __isl_take isl_map *map);
4400 #include <isl/union_set.h>
4401 __isl_give isl_union_set *isl_union_set_project_out(
4402 __isl_take isl_union_set *uset,
4403 enum isl_dim_type type,
4404 unsigned first, unsigned n);
4405 __isl_give isl_set *isl_union_set_params(
4406 __isl_take isl_union_set *uset);
4408 The function C<isl_union_set_project_out> can only project out
4411 #include <isl/union_map.h>
4412 __isl_give isl_union_map *isl_union_map_project_out(
4413 __isl_take isl_union_map *umap,
4414 enum isl_dim_type type, unsigned first, unsigned n);
4415 __isl_give isl_set *isl_union_map_params(
4416 __isl_take isl_union_map *umap);
4417 __isl_give isl_union_set *isl_union_map_domain(
4418 __isl_take isl_union_map *umap);
4419 __isl_give isl_union_set *isl_union_map_range(
4420 __isl_take isl_union_map *umap);
4422 The function C<isl_union_map_project_out> can only project out
4425 #include <isl/aff.h>
4426 __isl_give isl_aff *isl_aff_project_domain_on_params(
4427 __isl_take isl_aff *aff);
4428 __isl_give isl_pw_aff *
4429 isl_pw_aff_project_domain_on_params(
4430 __isl_take isl_pw_aff *pa);
4431 __isl_give isl_pw_multi_aff *
4432 isl_pw_multi_aff_project_domain_on_params(
4433 __isl_take isl_pw_multi_aff *pma);
4434 __isl_give isl_set *isl_pw_aff_domain(
4435 __isl_take isl_pw_aff *pwaff);
4436 __isl_give isl_set *isl_pw_multi_aff_domain(
4437 __isl_take isl_pw_multi_aff *pma);
4438 __isl_give isl_set *isl_multi_pw_aff_domain(
4439 __isl_take isl_multi_pw_aff *mpa);
4440 __isl_give isl_union_set *isl_union_pw_aff_domain(
4441 __isl_take isl_union_pw_aff *upa);
4442 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4443 __isl_take isl_union_pw_multi_aff *upma);
4444 __isl_give isl_union_set *
4445 isl_multi_union_pw_aff_domain(
4446 __isl_take isl_multi_union_pw_aff *mupa);
4447 __isl_give isl_set *isl_pw_aff_params(
4448 __isl_take isl_pw_aff *pwa);
4450 The function C<isl_multi_union_pw_aff_domain> requires its
4451 input to have at least one set dimension.
4453 #include <isl/polynomial.h>
4454 __isl_give isl_qpolynomial *
4455 isl_qpolynomial_project_domain_on_params(
4456 __isl_take isl_qpolynomial *qp);
4457 __isl_give isl_pw_qpolynomial *
4458 isl_pw_qpolynomial_project_domain_on_params(
4459 __isl_take isl_pw_qpolynomial *pwqp);
4460 __isl_give isl_pw_qpolynomial_fold *
4461 isl_pw_qpolynomial_fold_project_domain_on_params(
4462 __isl_take isl_pw_qpolynomial_fold *pwf);
4463 __isl_give isl_set *isl_pw_qpolynomial_domain(
4464 __isl_take isl_pw_qpolynomial *pwqp);
4465 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4466 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4467 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4468 __isl_take isl_union_pw_qpolynomial *upwqp);
4470 #include <isl/space.h>
4471 __isl_give isl_space *isl_space_domain_map(
4472 __isl_take isl_space *space);
4473 __isl_give isl_space *isl_space_range_map(
4474 __isl_take isl_space *space);
4476 #include <isl/map.h>
4477 __isl_give isl_map *isl_set_wrapped_domain_map(
4478 __isl_take isl_set *set);
4479 __isl_give isl_basic_map *isl_basic_map_domain_map(
4480 __isl_take isl_basic_map *bmap);
4481 __isl_give isl_basic_map *isl_basic_map_range_map(
4482 __isl_take isl_basic_map *bmap);
4483 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
4484 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
4486 #include <isl/union_map.h>
4487 __isl_give isl_union_map *isl_union_map_domain_map(
4488 __isl_take isl_union_map *umap);
4489 __isl_give isl_union_pw_multi_aff *
4490 isl_union_map_domain_map_union_pw_multi_aff(
4491 __isl_take isl_union_map *umap);
4492 __isl_give isl_union_map *isl_union_map_range_map(
4493 __isl_take isl_union_map *umap);
4494 __isl_give isl_union_map *
4495 isl_union_set_wrapped_domain_map(
4496 __isl_take isl_union_set *uset);
4498 The functions above construct a (basic, regular or union) relation
4499 that maps (a wrapped version of) the input relation to its domain or range.
4500 C<isl_set_wrapped_domain_map> maps the input set to the domain
4501 of its wrapped relation.
4505 __isl_give isl_basic_set *isl_basic_set_eliminate(
4506 __isl_take isl_basic_set *bset,
4507 enum isl_dim_type type,
4508 unsigned first, unsigned n);
4509 __isl_give isl_set *isl_set_eliminate(
4510 __isl_take isl_set *set, enum isl_dim_type type,
4511 unsigned first, unsigned n);
4512 __isl_give isl_basic_map *isl_basic_map_eliminate(
4513 __isl_take isl_basic_map *bmap,
4514 enum isl_dim_type type,
4515 unsigned first, unsigned n);
4516 __isl_give isl_map *isl_map_eliminate(
4517 __isl_take isl_map *map, enum isl_dim_type type,
4518 unsigned first, unsigned n);
4520 Eliminate the coefficients for the given dimensions from the constraints,
4521 without removing the dimensions.
4523 =item * Constructing a set from a parameter domain
4525 A zero-dimensional space or (basic) set can be constructed
4526 on a given parameter domain using the following functions.
4528 #include <isl/space.h>
4529 __isl_give isl_space *isl_space_set_from_params(
4530 __isl_take isl_space *space);
4532 #include <isl/set.h>
4533 __isl_give isl_basic_set *isl_basic_set_from_params(
4534 __isl_take isl_basic_set *bset);
4535 __isl_give isl_set *isl_set_from_params(
4536 __isl_take isl_set *set);
4538 =item * Constructing a relation from one or two sets
4540 Create a relation with the given set(s) as domain and/or range.
4541 If only the domain or the range is specified, then
4542 the range or domain of the created relation is a zero-dimensional
4543 flat anonymous space.
4545 #include <isl/space.h>
4546 __isl_give isl_space *isl_space_from_domain(
4547 __isl_take isl_space *space);
4548 __isl_give isl_space *isl_space_from_range(
4549 __isl_take isl_space *space);
4550 __isl_give isl_space *isl_space_map_from_set(
4551 __isl_take isl_space *space);
4552 __isl_give isl_space *isl_space_map_from_domain_and_range(
4553 __isl_take isl_space *domain,
4554 __isl_take isl_space *range);
4556 #include <isl/local_space.h>
4557 __isl_give isl_local_space *isl_local_space_from_domain(
4558 __isl_take isl_local_space *ls);
4560 #include <isl/map.h>
4561 __isl_give isl_map *isl_map_from_domain(
4562 __isl_take isl_set *set);
4563 __isl_give isl_map *isl_map_from_range(
4564 __isl_take isl_set *set);
4566 #include <isl/union_map.h>
4567 __isl_give isl_union_map *
4568 isl_union_map_from_domain_and_range(
4569 __isl_take isl_union_set *domain,
4570 __isl_take isl_union_set *range);
4572 #include <isl/val.h>
4573 __isl_give isl_multi_val *isl_multi_val_from_range(
4574 __isl_take isl_multi_val *mv);
4576 #include <isl/aff.h>
4577 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4578 __isl_take isl_multi_aff *ma);
4579 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4580 __isl_take isl_pw_aff *pwa);
4581 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4582 __isl_take isl_multi_pw_aff *mpa);
4583 __isl_give isl_multi_union_pw_aff *
4584 isl_multi_union_pw_aff_from_range(
4585 __isl_take isl_multi_union_pw_aff *mupa);
4586 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4587 __isl_take isl_set *set);
4588 __isl_give isl_union_pw_multi_aff *
4589 isl_union_pw_multi_aff_from_domain(
4590 __isl_take isl_union_set *uset);
4592 #include <isl/polynomial.h>
4593 __isl_give isl_pw_qpolynomial *
4594 isl_pw_qpolynomial_from_range(
4595 __isl_take isl_pw_qpolynomial *pwqp);
4596 __isl_give isl_pw_qpolynomial_fold *
4597 isl_pw_qpolynomial_fold_from_range(
4598 __isl_take isl_pw_qpolynomial_fold *pwf);
4602 #include <isl/set.h>
4603 __isl_give isl_basic_set *isl_basic_set_fix_si(
4604 __isl_take isl_basic_set *bset,
4605 enum isl_dim_type type, unsigned pos, int value);
4606 __isl_give isl_basic_set *isl_basic_set_fix_val(
4607 __isl_take isl_basic_set *bset,
4608 enum isl_dim_type type, unsigned pos,
4609 __isl_take isl_val *v);
4610 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
4611 enum isl_dim_type type, unsigned pos, int value);
4612 __isl_give isl_set *isl_set_fix_val(
4613 __isl_take isl_set *set,
4614 enum isl_dim_type type, unsigned pos,
4615 __isl_take isl_val *v);
4617 #include <isl/map.h>
4618 __isl_give isl_basic_map *isl_basic_map_fix_si(
4619 __isl_take isl_basic_map *bmap,
4620 enum isl_dim_type type, unsigned pos, int value);
4621 __isl_give isl_basic_map *isl_basic_map_fix_val(
4622 __isl_take isl_basic_map *bmap,
4623 enum isl_dim_type type, unsigned pos,
4624 __isl_take isl_val *v);
4625 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
4626 enum isl_dim_type type, unsigned pos, int value);
4627 __isl_give isl_map *isl_map_fix_val(
4628 __isl_take isl_map *map,
4629 enum isl_dim_type type, unsigned pos,
4630 __isl_take isl_val *v);
4632 #include <isl/aff.h>
4633 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4634 __isl_take isl_pw_multi_aff *pma,
4635 enum isl_dim_type type, unsigned pos, int value);
4637 #include <isl/polynomial.h>
4638 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4639 __isl_take isl_pw_qpolynomial *pwqp,
4640 enum isl_dim_type type, unsigned n,
4641 __isl_take isl_val *v);
4643 Intersect the set, relation or function domain
4644 with the hyperplane where the given
4645 dimension has the fixed given value.
4647 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
4648 __isl_take isl_basic_map *bmap,
4649 enum isl_dim_type type, unsigned pos, int value);
4650 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
4651 __isl_take isl_basic_map *bmap,
4652 enum isl_dim_type type, unsigned pos, int value);
4653 __isl_give isl_set *isl_set_lower_bound_si(
4654 __isl_take isl_set *set,
4655 enum isl_dim_type type, unsigned pos, int value);
4656 __isl_give isl_set *isl_set_lower_bound_val(
4657 __isl_take isl_set *set,
4658 enum isl_dim_type type, unsigned pos,
4659 __isl_take isl_val *value);
4660 __isl_give isl_map *isl_map_lower_bound_si(
4661 __isl_take isl_map *map,
4662 enum isl_dim_type type, unsigned pos, int value);
4663 __isl_give isl_set *isl_set_upper_bound_si(
4664 __isl_take isl_set *set,
4665 enum isl_dim_type type, unsigned pos, int value);
4666 __isl_give isl_set *isl_set_upper_bound_val(
4667 __isl_take isl_set *set,
4668 enum isl_dim_type type, unsigned pos,
4669 __isl_take isl_val *value);
4670 __isl_give isl_map *isl_map_upper_bound_si(
4671 __isl_take isl_map *map,
4672 enum isl_dim_type type, unsigned pos, int value);
4674 Intersect the set or relation with the half-space where the given
4675 dimension has a value bounded by the fixed given integer value.
4677 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
4678 enum isl_dim_type type1, int pos1,
4679 enum isl_dim_type type2, int pos2);
4680 __isl_give isl_basic_map *isl_basic_map_equate(
4681 __isl_take isl_basic_map *bmap,
4682 enum isl_dim_type type1, int pos1,
4683 enum isl_dim_type type2, int pos2);
4684 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
4685 enum isl_dim_type type1, int pos1,
4686 enum isl_dim_type type2, int pos2);
4688 Intersect the set or relation with the hyperplane where the given
4689 dimensions are equal to each other.
4691 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
4692 enum isl_dim_type type1, int pos1,
4693 enum isl_dim_type type2, int pos2);
4695 Intersect the relation with the hyperplane where the given
4696 dimensions have opposite values.
4698 __isl_give isl_map *isl_map_order_le(
4699 __isl_take isl_map *map,
4700 enum isl_dim_type type1, int pos1,
4701 enum isl_dim_type type2, int pos2);
4702 __isl_give isl_basic_map *isl_basic_map_order_ge(
4703 __isl_take isl_basic_map *bmap,
4704 enum isl_dim_type type1, int pos1,
4705 enum isl_dim_type type2, int pos2);
4706 __isl_give isl_map *isl_map_order_ge(
4707 __isl_take isl_map *map,
4708 enum isl_dim_type type1, int pos1,
4709 enum isl_dim_type type2, int pos2);
4710 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
4711 enum isl_dim_type type1, int pos1,
4712 enum isl_dim_type type2, int pos2);
4713 __isl_give isl_basic_map *isl_basic_map_order_gt(
4714 __isl_take isl_basic_map *bmap,
4715 enum isl_dim_type type1, int pos1,
4716 enum isl_dim_type type2, int pos2);
4717 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
4718 enum isl_dim_type type1, int pos1,
4719 enum isl_dim_type type2, int pos2);
4721 Intersect the relation with the half-space where the given
4722 dimensions satisfy the given ordering.
4726 #include <isl/aff.h>
4727 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4728 __isl_take isl_aff *aff);
4729 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4730 __isl_take isl_aff *aff);
4731 __isl_give isl_set *isl_pw_aff_pos_set(
4732 __isl_take isl_pw_aff *pa);
4733 __isl_give isl_set *isl_pw_aff_nonneg_set(
4734 __isl_take isl_pw_aff *pwaff);
4735 __isl_give isl_set *isl_pw_aff_zero_set(
4736 __isl_take isl_pw_aff *pwaff);
4737 __isl_give isl_set *isl_pw_aff_non_zero_set(
4738 __isl_take isl_pw_aff *pwaff);
4739 __isl_give isl_union_set *
4740 isl_union_pw_aff_zero_union_set(
4741 __isl_take isl_union_pw_aff *upa);
4742 __isl_give isl_union_set *
4743 isl_multi_union_pw_aff_zero_union_set(
4744 __isl_take isl_multi_union_pw_aff *mupa);
4746 The function C<isl_aff_neg_basic_set> returns a basic set
4747 containing those elements in the domain space
4748 of C<aff> where C<aff> is negative.
4749 The function C<isl_pw_aff_nonneg_set> returns a set
4750 containing those elements in the domain
4751 of C<pwaff> where C<pwaff> is non-negative.
4752 The function C<isl_multi_union_pw_aff_zero_union_set>
4753 returns a union set containing those elements
4754 in the domains of its elements where they are all zero.
4758 __isl_give isl_map *isl_set_identity(
4759 __isl_take isl_set *set);
4760 __isl_give isl_union_map *isl_union_set_identity(
4761 __isl_take isl_union_set *uset);
4762 __isl_give isl_union_pw_multi_aff *
4763 isl_union_set_identity_union_pw_multi_aff(
4764 __isl_take isl_union_set *uset);
4766 Construct an identity relation on the given (union) set.
4768 =item * Function Extraction
4770 A piecewise quasi affine expression that is equal to 1 on a set
4771 and 0 outside the set can be created using the following function.
4773 #include <isl/aff.h>
4774 __isl_give isl_pw_aff *isl_set_indicator_function(
4775 __isl_take isl_set *set);
4777 A piecewise multiple quasi affine expression can be extracted
4778 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4779 and the C<isl_map> is single-valued.
4780 In case of a conversion from an C<isl_union_map>
4781 to an C<isl_union_pw_multi_aff>, these properties need to hold
4782 in each domain space.
4783 A conversion to a C<isl_multi_union_pw_aff> additionally
4784 requires that the input is non-empty and involves only a single
4787 #include <isl/aff.h>
4788 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4789 __isl_take isl_set *set);
4790 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4791 __isl_take isl_map *map);
4793 __isl_give isl_union_pw_multi_aff *
4794 isl_union_pw_multi_aff_from_union_set(
4795 __isl_take isl_union_set *uset);
4796 __isl_give isl_union_pw_multi_aff *
4797 isl_union_pw_multi_aff_from_union_map(
4798 __isl_take isl_union_map *umap);
4800 __isl_give isl_multi_union_pw_aff *
4801 isl_multi_union_pw_aff_from_union_map(
4802 __isl_take isl_union_map *umap);
4806 __isl_give isl_basic_set *isl_basic_map_deltas(
4807 __isl_take isl_basic_map *bmap);
4808 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
4809 __isl_give isl_union_set *isl_union_map_deltas(
4810 __isl_take isl_union_map *umap);
4812 These functions return a (basic) set containing the differences
4813 between image elements and corresponding domain elements in the input.
4815 __isl_give isl_basic_map *isl_basic_map_deltas_map(
4816 __isl_take isl_basic_map *bmap);
4817 __isl_give isl_map *isl_map_deltas_map(
4818 __isl_take isl_map *map);
4819 __isl_give isl_union_map *isl_union_map_deltas_map(
4820 __isl_take isl_union_map *umap);
4822 The functions above construct a (basic, regular or union) relation
4823 that maps (a wrapped version of) the input relation to its delta set.
4827 Simplify the representation of a set, relation or functions by trying
4828 to combine pairs of basic sets or relations into a single
4829 basic set or relation.
4831 #include <isl/set.h>
4832 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
4834 #include <isl/map.h>
4835 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
4837 #include <isl/union_set.h>
4838 __isl_give isl_union_set *isl_union_set_coalesce(
4839 __isl_take isl_union_set *uset);
4841 #include <isl/union_map.h>
4842 __isl_give isl_union_map *isl_union_map_coalesce(
4843 __isl_take isl_union_map *umap);
4845 #include <isl/aff.h>
4846 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4847 __isl_take isl_pw_aff *pwqp);
4848 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4849 __isl_take isl_pw_multi_aff *pma);
4850 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4851 __isl_take isl_multi_pw_aff *mpa);
4852 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
4853 __isl_take isl_union_pw_aff *upa);
4854 __isl_give isl_union_pw_multi_aff *
4855 isl_union_pw_multi_aff_coalesce(
4856 __isl_take isl_union_pw_multi_aff *upma);
4857 __isl_give isl_multi_union_pw_aff *
4858 isl_multi_union_pw_aff_coalesce(
4859 __isl_take isl_multi_union_pw_aff *aff);
4861 #include <isl/polynomial.h>
4862 __isl_give isl_pw_qpolynomial_fold *
4863 isl_pw_qpolynomial_fold_coalesce(
4864 __isl_take isl_pw_qpolynomial_fold *pwf);
4865 __isl_give isl_union_pw_qpolynomial *
4866 isl_union_pw_qpolynomial_coalesce(
4867 __isl_take isl_union_pw_qpolynomial *upwqp);
4868 __isl_give isl_union_pw_qpolynomial_fold *
4869 isl_union_pw_qpolynomial_fold_coalesce(
4870 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4872 One of the methods for combining pairs of basic sets or relations
4873 can result in coefficients that are much larger than those that appear
4874 in the constraints of the input. By default, the coefficients are
4875 not allowed to grow larger, but this can be changed by unsetting
4876 the following option.
4878 isl_stat isl_options_set_coalesce_bounded_wrapping(
4879 isl_ctx *ctx, int val);
4880 int isl_options_get_coalesce_bounded_wrapping(
4883 =item * Detecting equalities
4885 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
4886 __isl_take isl_basic_set *bset);
4887 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
4888 __isl_take isl_basic_map *bmap);
4889 __isl_give isl_set *isl_set_detect_equalities(
4890 __isl_take isl_set *set);
4891 __isl_give isl_map *isl_map_detect_equalities(
4892 __isl_take isl_map *map);
4893 __isl_give isl_union_set *isl_union_set_detect_equalities(
4894 __isl_take isl_union_set *uset);
4895 __isl_give isl_union_map *isl_union_map_detect_equalities(
4896 __isl_take isl_union_map *umap);
4898 Simplify the representation of a set or relation by detecting implicit
4901 =item * Removing redundant constraints
4903 #include <isl/set.h>
4904 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
4905 __isl_take isl_basic_set *bset);
4906 __isl_give isl_set *isl_set_remove_redundancies(
4907 __isl_take isl_set *set);
4909 #include <isl/union_set.h>
4910 __isl_give isl_union_set *
4911 isl_union_set_remove_redundancies(
4912 __isl_take isl_union_set *uset);
4914 #include <isl/map.h>
4915 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
4916 __isl_take isl_basic_map *bmap);
4917 __isl_give isl_map *isl_map_remove_redundancies(
4918 __isl_take isl_map *map);
4920 #include <isl/union_map.h>
4921 __isl_give isl_union_map *
4922 isl_union_map_remove_redundancies(
4923 __isl_take isl_union_map *umap);
4927 __isl_give isl_basic_set *isl_set_convex_hull(
4928 __isl_take isl_set *set);
4929 __isl_give isl_basic_map *isl_map_convex_hull(
4930 __isl_take isl_map *map);
4932 If the input set or relation has any existentially quantified
4933 variables, then the result of these operations is currently undefined.
4937 #include <isl/set.h>
4938 __isl_give isl_basic_set *
4939 isl_set_unshifted_simple_hull(
4940 __isl_take isl_set *set);
4941 __isl_give isl_basic_set *isl_set_simple_hull(
4942 __isl_take isl_set *set);
4943 __isl_give isl_basic_set *
4944 isl_set_plain_unshifted_simple_hull(
4945 __isl_take isl_set *set);
4946 __isl_give isl_basic_set *
4947 isl_set_unshifted_simple_hull_from_set_list(
4948 __isl_take isl_set *set,
4949 __isl_take isl_set_list *list);
4951 #include <isl/map.h>
4952 __isl_give isl_basic_map *
4953 isl_map_unshifted_simple_hull(
4954 __isl_take isl_map *map);
4955 __isl_give isl_basic_map *isl_map_simple_hull(
4956 __isl_take isl_map *map);
4957 __isl_give isl_basic_map *
4958 isl_map_plain_unshifted_simple_hull(
4959 __isl_take isl_map *map);
4960 __isl_give isl_basic_map *
4961 isl_map_unshifted_simple_hull_from_map_list(
4962 __isl_take isl_map *map,
4963 __isl_take isl_map_list *list);
4965 #include <isl/union_map.h>
4966 __isl_give isl_union_map *isl_union_map_simple_hull(
4967 __isl_take isl_union_map *umap);
4969 These functions compute a single basic set or relation
4970 that contains the whole input set or relation.
4971 In particular, the output is described by translates
4972 of the constraints describing the basic sets or relations in the input.
4973 In case of C<isl_set_unshifted_simple_hull>, only the original
4974 constraints are used, without any translation.
4975 In case of C<isl_set_plain_unshifted_simple_hull> and
4976 C<isl_map_plain_unshifted_simple_hull>, the result is described
4977 by original constraints that are obviously satisfied
4978 by the entire input set or relation.
4979 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
4980 C<isl_map_unshifted_simple_hull_from_map_list>, the
4981 constraints are taken from the elements of the second argument.
4985 (See \autoref{s:simple hull}.)
4991 __isl_give isl_basic_set *isl_basic_set_affine_hull(
4992 __isl_take isl_basic_set *bset);
4993 __isl_give isl_basic_set *isl_set_affine_hull(
4994 __isl_take isl_set *set);
4995 __isl_give isl_union_set *isl_union_set_affine_hull(
4996 __isl_take isl_union_set *uset);
4997 __isl_give isl_basic_map *isl_basic_map_affine_hull(
4998 __isl_take isl_basic_map *bmap);
4999 __isl_give isl_basic_map *isl_map_affine_hull(
5000 __isl_take isl_map *map);
5001 __isl_give isl_union_map *isl_union_map_affine_hull(
5002 __isl_take isl_union_map *umap);
5004 In case of union sets and relations, the affine hull is computed
5007 =item * Polyhedral hull
5009 __isl_give isl_basic_set *isl_set_polyhedral_hull(
5010 __isl_take isl_set *set);
5011 __isl_give isl_basic_map *isl_map_polyhedral_hull(
5012 __isl_take isl_map *map);
5013 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
5014 __isl_take isl_union_set *uset);
5015 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
5016 __isl_take isl_union_map *umap);
5018 These functions compute a single basic set or relation
5019 not involving any existentially quantified variables
5020 that contains the whole input set or relation.
5021 In case of union sets and relations, the polyhedral hull is computed
5024 =item * Other approximations
5026 #include <isl/set.h>
5027 __isl_give isl_basic_set *
5028 isl_basic_set_drop_constraints_involving_dims(
5029 __isl_take isl_basic_set *bset,
5030 enum isl_dim_type type,
5031 unsigned first, unsigned n);
5032 __isl_give isl_basic_set *
5033 isl_basic_set_drop_constraints_not_involving_dims(
5034 __isl_take isl_basic_set *bset,
5035 enum isl_dim_type type,
5036 unsigned first, unsigned n);
5037 __isl_give isl_set *
5038 isl_set_drop_constraints_involving_dims(
5039 __isl_take isl_set *set,
5040 enum isl_dim_type type,
5041 unsigned first, unsigned n);
5042 __isl_give isl_set *
5043 isl_set_drop_constraints_not_involving_dims(
5044 __isl_take isl_set *set,
5045 enum isl_dim_type type,
5046 unsigned first, unsigned n);
5048 #include <isl/map.h>
5049 __isl_give isl_basic_map *
5050 isl_basic_map_drop_constraints_involving_dims(
5051 __isl_take isl_basic_map *bmap,
5052 enum isl_dim_type type,
5053 unsigned first, unsigned n);
5054 __isl_give isl_basic_map *
5055 isl_basic_map_drop_constraints_not_involving_dims(
5056 __isl_take isl_basic_map *bmap,
5057 enum isl_dim_type type,
5058 unsigned first, unsigned n);
5059 __isl_give isl_map *
5060 isl_map_drop_constraints_involving_dims(
5061 __isl_take isl_map *map,
5062 enum isl_dim_type type,
5063 unsigned first, unsigned n);
5064 __isl_give isl_map *
5065 isl_map_drop_constraints_not_involving_dims(
5066 __isl_take isl_map *map,
5067 enum isl_dim_type type,
5068 unsigned first, unsigned n);
5070 These functions drop any constraints (not) involving the specified dimensions.
5071 Note that the result depends on the representation of the input.
5073 #include <isl/polynomial.h>
5074 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5075 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5076 __isl_give isl_union_pw_qpolynomial *
5077 isl_union_pw_qpolynomial_to_polynomial(
5078 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5080 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5081 the polynomial will be an overapproximation. If C<sign> is negative,
5082 it will be an underapproximation. If C<sign> is zero, the approximation
5083 will lie somewhere in between.
5087 __isl_give isl_basic_set *isl_basic_set_sample(
5088 __isl_take isl_basic_set *bset);
5089 __isl_give isl_basic_set *isl_set_sample(
5090 __isl_take isl_set *set);
5091 __isl_give isl_basic_map *isl_basic_map_sample(
5092 __isl_take isl_basic_map *bmap);
5093 __isl_give isl_basic_map *isl_map_sample(
5094 __isl_take isl_map *map);
5096 If the input (basic) set or relation is non-empty, then return
5097 a singleton subset of the input. Otherwise, return an empty set.
5099 =item * Optimization
5101 #include <isl/ilp.h>
5102 __isl_give isl_val *isl_basic_set_max_val(
5103 __isl_keep isl_basic_set *bset,
5104 __isl_keep isl_aff *obj);
5105 __isl_give isl_val *isl_set_min_val(
5106 __isl_keep isl_set *set,
5107 __isl_keep isl_aff *obj);
5108 __isl_give isl_val *isl_set_max_val(
5109 __isl_keep isl_set *set,
5110 __isl_keep isl_aff *obj);
5111 __isl_give isl_multi_val *
5112 isl_union_set_min_multi_union_pw_aff(
5113 __isl_keep isl_union_set *set,
5114 __isl_keep isl_multi_union_pw_aff *obj);
5116 Compute the minimum or maximum of the integer affine expression C<obj>
5117 over the points in C<set>, returning the result in C<opt>.
5118 The result is C<NULL> in case of an error, the optimal value in case
5119 there is one, negative infinity or infinity if the problem is unbounded and
5120 NaN if the problem is empty.
5122 =item * Parametric optimization
5124 __isl_give isl_pw_aff *isl_set_dim_min(
5125 __isl_take isl_set *set, int pos);
5126 __isl_give isl_pw_aff *isl_set_dim_max(
5127 __isl_take isl_set *set, int pos);
5128 __isl_give isl_pw_aff *isl_map_dim_min(
5129 __isl_take isl_map *map, int pos);
5130 __isl_give isl_pw_aff *isl_map_dim_max(
5131 __isl_take isl_map *map, int pos);
5133 Compute the minimum or maximum of the given set or output dimension
5134 as a function of the parameters (and input dimensions), but independently
5135 of the other set or output dimensions.
5136 For lexicographic optimization, see L<"Lexicographic Optimization">.
5140 The following functions compute either the set of (rational) coefficient
5141 values of valid constraints for the given set or the set of (rational)
5142 values satisfying the constraints with coefficients from the given set.
5143 Internally, these two sets of functions perform essentially the
5144 same operations, except that the set of coefficients is assumed to
5145 be a cone, while the set of values may be any polyhedron.
5146 The current implementation is based on the Farkas lemma and
5147 Fourier-Motzkin elimination, but this may change or be made optional
5148 in future. In particular, future implementations may use different
5149 dualization algorithms or skip the elimination step.
5151 __isl_give isl_basic_set *isl_basic_set_coefficients(
5152 __isl_take isl_basic_set *bset);
5153 __isl_give isl_basic_set *isl_set_coefficients(
5154 __isl_take isl_set *set);
5155 __isl_give isl_union_set *isl_union_set_coefficients(
5156 __isl_take isl_union_set *bset);
5157 __isl_give isl_basic_set *isl_basic_set_solutions(
5158 __isl_take isl_basic_set *bset);
5159 __isl_give isl_basic_set *isl_set_solutions(
5160 __isl_take isl_set *set);
5161 __isl_give isl_union_set *isl_union_set_solutions(
5162 __isl_take isl_union_set *bset);
5166 __isl_give isl_map *isl_map_fixed_power_val(
5167 __isl_take isl_map *map,
5168 __isl_take isl_val *exp);
5169 __isl_give isl_union_map *
5170 isl_union_map_fixed_power_val(
5171 __isl_take isl_union_map *umap,
5172 __isl_take isl_val *exp);
5174 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
5175 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
5176 of C<map> is computed.
5178 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
5180 __isl_give isl_union_map *isl_union_map_power(
5181 __isl_take isl_union_map *umap, int *exact);
5183 Compute a parametric representation for all positive powers I<k> of C<map>.
5184 The result maps I<k> to a nested relation corresponding to the
5185 I<k>th power of C<map>.
5186 The result may be an overapproximation. If the result is known to be exact,
5187 then C<*exact> is set to C<1>.
5189 =item * Transitive closure
5191 __isl_give isl_map *isl_map_transitive_closure(
5192 __isl_take isl_map *map, int *exact);
5193 __isl_give isl_union_map *isl_union_map_transitive_closure(
5194 __isl_take isl_union_map *umap, int *exact);
5196 Compute the transitive closure of C<map>.
5197 The result may be an overapproximation. If the result is known to be exact,
5198 then C<*exact> is set to C<1>.
5200 =item * Reaching path lengths
5202 __isl_give isl_map *isl_map_reaching_path_lengths(
5203 __isl_take isl_map *map, int *exact);
5205 Compute a relation that maps each element in the range of C<map>
5206 to the lengths of all paths composed of edges in C<map> that
5207 end up in the given element.
5208 The result may be an overapproximation. If the result is known to be exact,
5209 then C<*exact> is set to C<1>.
5210 To compute the I<maximal> path length, the resulting relation
5211 should be postprocessed by C<isl_map_lexmax>.
5212 In particular, if the input relation is a dependence relation
5213 (mapping sources to sinks), then the maximal path length corresponds
5214 to the free schedule.
5215 Note, however, that C<isl_map_lexmax> expects the maximum to be
5216 finite, so if the path lengths are unbounded (possibly due to
5217 the overapproximation), then you will get an error message.
5221 #include <isl/space.h>
5222 __isl_give isl_space *isl_space_wrap(
5223 __isl_take isl_space *space);
5224 __isl_give isl_space *isl_space_unwrap(
5225 __isl_take isl_space *space);
5227 #include <isl/local_space.h>
5228 __isl_give isl_local_space *isl_local_space_wrap(
5229 __isl_take isl_local_space *ls);
5231 #include <isl/set.h>
5232 __isl_give isl_basic_map *isl_basic_set_unwrap(
5233 __isl_take isl_basic_set *bset);
5234 __isl_give isl_map *isl_set_unwrap(
5235 __isl_take isl_set *set);
5237 #include <isl/map.h>
5238 __isl_give isl_basic_set *isl_basic_map_wrap(
5239 __isl_take isl_basic_map *bmap);
5240 __isl_give isl_set *isl_map_wrap(
5241 __isl_take isl_map *map);
5243 #include <isl/union_set.h>
5244 __isl_give isl_union_map *isl_union_set_unwrap(
5245 __isl_take isl_union_set *uset);
5247 #include <isl/union_map.h>
5248 __isl_give isl_union_set *isl_union_map_wrap(
5249 __isl_take isl_union_map *umap);
5251 The input to C<isl_space_unwrap> should
5252 be the space of a set, while that of
5253 C<isl_space_wrap> should be the space of a relation.
5254 Conversely, the output of C<isl_space_unwrap> is the space
5255 of a relation, while that of C<isl_space_wrap> is the space of a set.
5259 Remove any internal structure of domain (and range) of the given
5260 set or relation. If there is any such internal structure in the input,
5261 then the name of the space is also removed.
5263 #include <isl/local_space.h>
5264 __isl_give isl_local_space *
5265 isl_local_space_flatten_domain(
5266 __isl_take isl_local_space *ls);
5267 __isl_give isl_local_space *
5268 isl_local_space_flatten_range(
5269 __isl_take isl_local_space *ls);
5271 #include <isl/set.h>
5272 __isl_give isl_basic_set *isl_basic_set_flatten(
5273 __isl_take isl_basic_set *bset);
5274 __isl_give isl_set *isl_set_flatten(
5275 __isl_take isl_set *set);
5277 #include <isl/map.h>
5278 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
5279 __isl_take isl_basic_map *bmap);
5280 __isl_give isl_basic_map *isl_basic_map_flatten_range(
5281 __isl_take isl_basic_map *bmap);
5282 __isl_give isl_map *isl_map_flatten_range(
5283 __isl_take isl_map *map);
5284 __isl_give isl_map *isl_map_flatten_domain(
5285 __isl_take isl_map *map);
5286 __isl_give isl_basic_map *isl_basic_map_flatten(
5287 __isl_take isl_basic_map *bmap);
5288 __isl_give isl_map *isl_map_flatten(
5289 __isl_take isl_map *map);
5291 #include <isl/val.h>
5292 __isl_give isl_multi_val *isl_multi_val_flatten_range(
5293 __isl_take isl_multi_val *mv);
5295 #include <isl/aff.h>
5296 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
5297 __isl_take isl_multi_aff *ma);
5298 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
5299 __isl_take isl_multi_aff *ma);
5300 __isl_give isl_multi_pw_aff *
5301 isl_multi_pw_aff_flatten_range(
5302 __isl_take isl_multi_pw_aff *mpa);
5303 __isl_give isl_multi_union_pw_aff *
5304 isl_multi_union_pw_aff_flatten_range(
5305 __isl_take isl_multi_union_pw_aff *mupa);
5307 #include <isl/map.h>
5308 __isl_give isl_map *isl_set_flatten_map(
5309 __isl_take isl_set *set);
5311 The function above constructs a relation
5312 that maps the input set to a flattened version of the set.
5316 Lift the input set to a space with extra dimensions corresponding
5317 to the existentially quantified variables in the input.
5318 In particular, the result lives in a wrapped map where the domain
5319 is the original space and the range corresponds to the original
5320 existentially quantified variables.
5322 #include <isl/set.h>
5323 __isl_give isl_basic_set *isl_basic_set_lift(
5324 __isl_take isl_basic_set *bset);
5325 __isl_give isl_set *isl_set_lift(
5326 __isl_take isl_set *set);
5327 __isl_give isl_union_set *isl_union_set_lift(
5328 __isl_take isl_union_set *uset);
5330 Given a local space that contains the existentially quantified
5331 variables of a set, a basic relation that, when applied to
5332 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
5333 can be constructed using the following function.
5335 #include <isl/local_space.h>
5336 __isl_give isl_basic_map *isl_local_space_lifting(
5337 __isl_take isl_local_space *ls);
5339 #include <isl/aff.h>
5340 __isl_give isl_multi_aff *isl_multi_aff_lift(
5341 __isl_take isl_multi_aff *maff,
5342 __isl_give isl_local_space **ls);
5344 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
5345 then it is assigned the local space that lies at the basis of
5346 the lifting applied.
5348 =item * Internal Product
5350 #include <isl/space.h>
5351 __isl_give isl_space *isl_space_zip(
5352 __isl_take isl_space *space);
5354 #include <isl/map.h>
5355 __isl_give isl_basic_map *isl_basic_map_zip(
5356 __isl_take isl_basic_map *bmap);
5357 __isl_give isl_map *isl_map_zip(
5358 __isl_take isl_map *map);
5360 #include <isl/union_map.h>
5361 __isl_give isl_union_map *isl_union_map_zip(
5362 __isl_take isl_union_map *umap);
5364 Given a relation with nested relations for domain and range,
5365 interchange the range of the domain with the domain of the range.
5369 #include <isl/space.h>
5370 __isl_give isl_space *isl_space_curry(
5371 __isl_take isl_space *space);
5372 __isl_give isl_space *isl_space_uncurry(
5373 __isl_take isl_space *space);
5375 #include <isl/map.h>
5376 __isl_give isl_basic_map *isl_basic_map_curry(
5377 __isl_take isl_basic_map *bmap);
5378 __isl_give isl_basic_map *isl_basic_map_uncurry(
5379 __isl_take isl_basic_map *bmap);
5380 __isl_give isl_map *isl_map_curry(
5381 __isl_take isl_map *map);
5382 __isl_give isl_map *isl_map_uncurry(
5383 __isl_take isl_map *map);
5385 #include <isl/union_map.h>
5386 __isl_give isl_union_map *isl_union_map_curry(
5387 __isl_take isl_union_map *umap);
5388 __isl_give isl_union_map *isl_union_map_uncurry(
5389 __isl_take isl_union_map *umap);
5391 Given a relation with a nested relation for domain,
5392 the C<curry> functions
5393 move the range of the nested relation out of the domain
5394 and use it as the domain of a nested relation in the range,
5395 with the original range as range of this nested relation.
5396 The C<uncurry> functions perform the inverse operation.
5398 #include <isl/space.h>
5399 __isl_give isl_space *isl_space_range_curry(
5400 __isl_take isl_space *space);
5402 #include <isl/map.h>
5403 __isl_give isl_map *isl_map_range_curry(
5404 __isl_take isl_map *map);
5406 #include <isl/union_map.h>
5407 __isl_give isl_union_map *isl_union_map_range_curry(
5408 __isl_take isl_union_map *umap);
5410 These functions apply the currying to the relation that
5411 is nested inside the range of the input.
5413 =item * Aligning parameters
5415 Change the order of the parameters of the given set, relation
5417 such that the first parameters match those of C<model>.
5418 This may involve the introduction of extra parameters.
5419 All parameters need to be named.
5421 #include <isl/space.h>
5422 __isl_give isl_space *isl_space_align_params(
5423 __isl_take isl_space *space1,
5424 __isl_take isl_space *space2)
5426 #include <isl/set.h>
5427 __isl_give isl_basic_set *isl_basic_set_align_params(
5428 __isl_take isl_basic_set *bset,
5429 __isl_take isl_space *model);
5430 __isl_give isl_set *isl_set_align_params(
5431 __isl_take isl_set *set,
5432 __isl_take isl_space *model);
5434 #include <isl/map.h>
5435 __isl_give isl_basic_map *isl_basic_map_align_params(
5436 __isl_take isl_basic_map *bmap,
5437 __isl_take isl_space *model);
5438 __isl_give isl_map *isl_map_align_params(
5439 __isl_take isl_map *map,
5440 __isl_take isl_space *model);
5442 #include <isl/val.h>
5443 __isl_give isl_multi_val *isl_multi_val_align_params(
5444 __isl_take isl_multi_val *mv,
5445 __isl_take isl_space *model);
5447 #include <isl/aff.h>
5448 __isl_give isl_aff *isl_aff_align_params(
5449 __isl_take isl_aff *aff,
5450 __isl_take isl_space *model);
5451 __isl_give isl_multi_aff *isl_multi_aff_align_params(
5452 __isl_take isl_multi_aff *multi,
5453 __isl_take isl_space *model);
5454 __isl_give isl_pw_aff *isl_pw_aff_align_params(
5455 __isl_take isl_pw_aff *pwaff,
5456 __isl_take isl_space *model);
5457 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
5458 __isl_take isl_pw_multi_aff *pma,
5459 __isl_take isl_space *model);
5460 __isl_give isl_union_pw_aff *
5461 isl_union_pw_aff_align_params(
5462 __isl_take isl_union_pw_aff *upa,
5463 __isl_take isl_space *model);
5464 __isl_give isl_union_pw_multi_aff *
5465 isl_union_pw_multi_aff_align_params(
5466 __isl_take isl_union_pw_multi_aff *upma,
5467 __isl_take isl_space *model);
5468 __isl_give isl_multi_union_pw_aff *
5469 isl_multi_union_pw_aff_align_params(
5470 __isl_take isl_multi_union_pw_aff *mupa,
5471 __isl_take isl_space *model);
5473 #include <isl/polynomial.h>
5474 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5475 __isl_take isl_qpolynomial *qp,
5476 __isl_take isl_space *model);
5478 =item * Unary Arithmetic Operations
5480 #include <isl/set.h>
5481 __isl_give isl_set *isl_set_neg(
5482 __isl_take isl_set *set);
5483 #include <isl/map.h>
5484 __isl_give isl_map *isl_map_neg(
5485 __isl_take isl_map *map);
5487 C<isl_set_neg> constructs a set containing the opposites of
5488 the elements in its argument.
5489 The domain of the result of C<isl_map_neg> is the same
5490 as the domain of its argument. The corresponding range
5491 elements are the opposites of the corresponding range
5492 elements in the argument.
5494 #include <isl/val.h>
5495 __isl_give isl_multi_val *isl_multi_val_neg(
5496 __isl_take isl_multi_val *mv);
5498 #include <isl/aff.h>
5499 __isl_give isl_aff *isl_aff_neg(
5500 __isl_take isl_aff *aff);
5501 __isl_give isl_multi_aff *isl_multi_aff_neg(
5502 __isl_take isl_multi_aff *ma);
5503 __isl_give isl_pw_aff *isl_pw_aff_neg(
5504 __isl_take isl_pw_aff *pwaff);
5505 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
5506 __isl_take isl_pw_multi_aff *pma);
5507 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
5508 __isl_take isl_multi_pw_aff *mpa);
5509 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
5510 __isl_take isl_union_pw_aff *upa);
5511 __isl_give isl_union_pw_multi_aff *
5512 isl_union_pw_multi_aff_neg(
5513 __isl_take isl_union_pw_multi_aff *upma);
5514 __isl_give isl_multi_union_pw_aff *
5515 isl_multi_union_pw_aff_neg(
5516 __isl_take isl_multi_union_pw_aff *mupa);
5517 __isl_give isl_aff *isl_aff_ceil(
5518 __isl_take isl_aff *aff);
5519 __isl_give isl_pw_aff *isl_pw_aff_ceil(
5520 __isl_take isl_pw_aff *pwaff);
5521 __isl_give isl_aff *isl_aff_floor(
5522 __isl_take isl_aff *aff);
5523 __isl_give isl_multi_aff *isl_multi_aff_floor(
5524 __isl_take isl_multi_aff *ma);
5525 __isl_give isl_pw_aff *isl_pw_aff_floor(
5526 __isl_take isl_pw_aff *pwaff);
5527 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
5528 __isl_take isl_union_pw_aff *upa);
5529 __isl_give isl_multi_union_pw_aff *
5530 isl_multi_union_pw_aff_floor(
5531 __isl_take isl_multi_union_pw_aff *mupa);
5533 #include <isl/aff.h>
5534 __isl_give isl_pw_aff *isl_pw_aff_list_min(
5535 __isl_take isl_pw_aff_list *list);
5536 __isl_give isl_pw_aff *isl_pw_aff_list_max(
5537 __isl_take isl_pw_aff_list *list);
5539 #include <isl/polynomial.h>
5540 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5541 __isl_take isl_qpolynomial *qp);
5542 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5543 __isl_take isl_pw_qpolynomial *pwqp);
5544 __isl_give isl_union_pw_qpolynomial *
5545 isl_union_pw_qpolynomial_neg(
5546 __isl_take isl_union_pw_qpolynomial *upwqp);
5547 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5548 __isl_take isl_qpolynomial *qp,
5550 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5551 __isl_take isl_pw_qpolynomial *pwqp,
5556 The following functions evaluate a function in a point.
5558 #include <isl/polynomial.h>
5559 __isl_give isl_val *isl_pw_qpolynomial_eval(
5560 __isl_take isl_pw_qpolynomial *pwqp,
5561 __isl_take isl_point *pnt);
5562 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5563 __isl_take isl_pw_qpolynomial_fold *pwf,
5564 __isl_take isl_point *pnt);
5565 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5566 __isl_take isl_union_pw_qpolynomial *upwqp,
5567 __isl_take isl_point *pnt);
5568 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5569 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5570 __isl_take isl_point *pnt);
5572 =item * Dimension manipulation
5574 It is usually not advisable to directly change the (input or output)
5575 space of a set or a relation as this removes the name and the internal
5576 structure of the space. However, the functions below can be useful
5577 to add new parameters, assuming
5578 C<isl_set_align_params> and C<isl_map_align_params>
5581 #include <isl/space.h>
5582 __isl_give isl_space *isl_space_add_dims(
5583 __isl_take isl_space *space,
5584 enum isl_dim_type type, unsigned n);
5585 __isl_give isl_space *isl_space_insert_dims(
5586 __isl_take isl_space *space,
5587 enum isl_dim_type type, unsigned pos, unsigned n);
5588 __isl_give isl_space *isl_space_drop_dims(
5589 __isl_take isl_space *space,
5590 enum isl_dim_type type, unsigned first, unsigned n);
5591 __isl_give isl_space *isl_space_move_dims(
5592 __isl_take isl_space *space,
5593 enum isl_dim_type dst_type, unsigned dst_pos,
5594 enum isl_dim_type src_type, unsigned src_pos,
5597 #include <isl/local_space.h>
5598 __isl_give isl_local_space *isl_local_space_add_dims(
5599 __isl_take isl_local_space *ls,
5600 enum isl_dim_type type, unsigned n);
5601 __isl_give isl_local_space *isl_local_space_insert_dims(
5602 __isl_take isl_local_space *ls,
5603 enum isl_dim_type type, unsigned first, unsigned n);
5604 __isl_give isl_local_space *isl_local_space_drop_dims(
5605 __isl_take isl_local_space *ls,
5606 enum isl_dim_type type, unsigned first, unsigned n);
5608 #include <isl/set.h>
5609 __isl_give isl_basic_set *isl_basic_set_add_dims(
5610 __isl_take isl_basic_set *bset,
5611 enum isl_dim_type type, unsigned n);
5612 __isl_give isl_set *isl_set_add_dims(
5613 __isl_take isl_set *set,
5614 enum isl_dim_type type, unsigned n);
5615 __isl_give isl_basic_set *isl_basic_set_insert_dims(
5616 __isl_take isl_basic_set *bset,
5617 enum isl_dim_type type, unsigned pos,
5619 __isl_give isl_set *isl_set_insert_dims(
5620 __isl_take isl_set *set,
5621 enum isl_dim_type type, unsigned pos, unsigned n);
5622 __isl_give isl_basic_set *isl_basic_set_move_dims(
5623 __isl_take isl_basic_set *bset,
5624 enum isl_dim_type dst_type, unsigned dst_pos,
5625 enum isl_dim_type src_type, unsigned src_pos,
5627 __isl_give isl_set *isl_set_move_dims(
5628 __isl_take isl_set *set,
5629 enum isl_dim_type dst_type, unsigned dst_pos,
5630 enum isl_dim_type src_type, unsigned src_pos,
5633 #include <isl/map.h>
5634 __isl_give isl_basic_map *isl_basic_map_add_dims(
5635 __isl_take isl_basic_map *bmap,
5636 enum isl_dim_type type, unsigned n);
5637 __isl_give isl_map *isl_map_add_dims(
5638 __isl_take isl_map *map,
5639 enum isl_dim_type type, unsigned n);
5640 __isl_give isl_basic_map *isl_basic_map_insert_dims(
5641 __isl_take isl_basic_map *bmap,
5642 enum isl_dim_type type, unsigned pos,
5644 __isl_give isl_map *isl_map_insert_dims(
5645 __isl_take isl_map *map,
5646 enum isl_dim_type type, unsigned pos, unsigned n);
5647 __isl_give isl_basic_map *isl_basic_map_move_dims(
5648 __isl_take isl_basic_map *bmap,
5649 enum isl_dim_type dst_type, unsigned dst_pos,
5650 enum isl_dim_type src_type, unsigned src_pos,
5652 __isl_give isl_map *isl_map_move_dims(
5653 __isl_take isl_map *map,
5654 enum isl_dim_type dst_type, unsigned dst_pos,
5655 enum isl_dim_type src_type, unsigned src_pos,
5658 #include <isl/val.h>
5659 __isl_give isl_multi_val *isl_multi_val_insert_dims(
5660 __isl_take isl_multi_val *mv,
5661 enum isl_dim_type type, unsigned first, unsigned n);
5662 __isl_give isl_multi_val *isl_multi_val_add_dims(
5663 __isl_take isl_multi_val *mv,
5664 enum isl_dim_type type, unsigned n);
5665 __isl_give isl_multi_val *isl_multi_val_drop_dims(
5666 __isl_take isl_multi_val *mv,
5667 enum isl_dim_type type, unsigned first, unsigned n);
5669 #include <isl/aff.h>
5670 __isl_give isl_aff *isl_aff_insert_dims(
5671 __isl_take isl_aff *aff,
5672 enum isl_dim_type type, unsigned first, unsigned n);
5673 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
5674 __isl_take isl_multi_aff *ma,
5675 enum isl_dim_type type, unsigned first, unsigned n);
5676 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
5677 __isl_take isl_pw_aff *pwaff,
5678 enum isl_dim_type type, unsigned first, unsigned n);
5679 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
5680 __isl_take isl_multi_pw_aff *mpa,
5681 enum isl_dim_type type, unsigned first, unsigned n);
5682 __isl_give isl_aff *isl_aff_add_dims(
5683 __isl_take isl_aff *aff,
5684 enum isl_dim_type type, unsigned n);
5685 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
5686 __isl_take isl_multi_aff *ma,
5687 enum isl_dim_type type, unsigned n);
5688 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
5689 __isl_take isl_pw_aff *pwaff,
5690 enum isl_dim_type type, unsigned n);
5691 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
5692 __isl_take isl_multi_pw_aff *mpa,
5693 enum isl_dim_type type, unsigned n);
5694 __isl_give isl_aff *isl_aff_drop_dims(
5695 __isl_take isl_aff *aff,
5696 enum isl_dim_type type, unsigned first, unsigned n);
5697 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
5698 __isl_take isl_multi_aff *maff,
5699 enum isl_dim_type type, unsigned first, unsigned n);
5700 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
5701 __isl_take isl_pw_aff *pwaff,
5702 enum isl_dim_type type, unsigned first, unsigned n);
5703 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
5704 __isl_take isl_pw_multi_aff *pma,
5705 enum isl_dim_type type, unsigned first, unsigned n);
5706 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
5707 __isl_take isl_union_pw_aff *upa,
5708 enum isl_dim_type type, unsigned first, unsigned n);
5709 __isl_give isl_union_pw_multi_aff *
5710 isl_union_pw_multi_aff_drop_dims(
5711 __isl_take isl_union_pw_multi_aff *upma,
5712 enum isl_dim_type type,
5713 unsigned first, unsigned n);
5714 __isl_give isl_multi_union_pw_aff *
5715 isl_multi_union_pw_aff_drop_dims(
5716 __isl_take isl_multi_union_pw_aff *mupa,
5717 enum isl_dim_type type, unsigned first,
5719 __isl_give isl_aff *isl_aff_move_dims(
5720 __isl_take isl_aff *aff,
5721 enum isl_dim_type dst_type, unsigned dst_pos,
5722 enum isl_dim_type src_type, unsigned src_pos,
5724 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
5725 __isl_take isl_multi_aff *ma,
5726 enum isl_dim_type dst_type, unsigned dst_pos,
5727 enum isl_dim_type src_type, unsigned src_pos,
5729 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
5730 __isl_take isl_pw_aff *pa,
5731 enum isl_dim_type dst_type, unsigned dst_pos,
5732 enum isl_dim_type src_type, unsigned src_pos,
5734 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
5735 __isl_take isl_multi_pw_aff *pma,
5736 enum isl_dim_type dst_type, unsigned dst_pos,
5737 enum isl_dim_type src_type, unsigned src_pos,
5740 #include <isl/polynomial.h>
5741 __isl_give isl_union_pw_qpolynomial *
5742 isl_union_pw_qpolynomial_drop_dims(
5743 __isl_take isl_union_pw_qpolynomial *upwqp,
5744 enum isl_dim_type type,
5745 unsigned first, unsigned n);
5746 __isl_give isl_union_pw_qpolynomial_fold *
5747 isl_union_pw_qpolynomial_fold_drop_dims(
5748 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5749 enum isl_dim_type type,
5750 unsigned first, unsigned n);
5752 The operations on union expressions can only manipulate parameters.
5756 =head2 Binary Operations
5758 The two arguments of a binary operation not only need to live
5759 in the same C<isl_ctx>, they currently also need to have
5760 the same (number of) parameters.
5762 =head3 Basic Operations
5766 =item * Intersection
5768 #include <isl/local_space.h>
5769 __isl_give isl_local_space *isl_local_space_intersect(
5770 __isl_take isl_local_space *ls1,
5771 __isl_take isl_local_space *ls2);
5773 #include <isl/set.h>
5774 __isl_give isl_basic_set *isl_basic_set_intersect_params(
5775 __isl_take isl_basic_set *bset1,
5776 __isl_take isl_basic_set *bset2);
5777 __isl_give isl_basic_set *isl_basic_set_intersect(
5778 __isl_take isl_basic_set *bset1,
5779 __isl_take isl_basic_set *bset2);
5780 __isl_give isl_basic_set *isl_basic_set_list_intersect(
5781 __isl_take struct isl_basic_set_list *list);
5782 __isl_give isl_set *isl_set_intersect_params(
5783 __isl_take isl_set *set,
5784 __isl_take isl_set *params);
5785 __isl_give isl_set *isl_set_intersect(
5786 __isl_take isl_set *set1,
5787 __isl_take isl_set *set2);
5789 #include <isl/map.h>
5790 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
5791 __isl_take isl_basic_map *bmap,
5792 __isl_take isl_basic_set *bset);
5793 __isl_give isl_basic_map *isl_basic_map_intersect_range(
5794 __isl_take isl_basic_map *bmap,
5795 __isl_take isl_basic_set *bset);
5796 __isl_give isl_basic_map *isl_basic_map_intersect(
5797 __isl_take isl_basic_map *bmap1,
5798 __isl_take isl_basic_map *bmap2);
5799 __isl_give isl_basic_map *isl_basic_map_list_intersect(
5800 __isl_take isl_basic_map_list *list);
5801 __isl_give isl_map *isl_map_intersect_params(
5802 __isl_take isl_map *map,
5803 __isl_take isl_set *params);
5804 __isl_give isl_map *isl_map_intersect_domain(
5805 __isl_take isl_map *map,
5806 __isl_take isl_set *set);
5807 __isl_give isl_map *isl_map_intersect_range(
5808 __isl_take isl_map *map,
5809 __isl_take isl_set *set);
5810 __isl_give isl_map *isl_map_intersect(
5811 __isl_take isl_map *map1,
5812 __isl_take isl_map *map2);
5814 #include <isl/union_set.h>
5815 __isl_give isl_union_set *isl_union_set_intersect_params(
5816 __isl_take isl_union_set *uset,
5817 __isl_take isl_set *set);
5818 __isl_give isl_union_set *isl_union_set_intersect(
5819 __isl_take isl_union_set *uset1,
5820 __isl_take isl_union_set *uset2);
5822 #include <isl/union_map.h>
5823 __isl_give isl_union_map *isl_union_map_intersect_params(
5824 __isl_take isl_union_map *umap,
5825 __isl_take isl_set *set);
5826 __isl_give isl_union_map *isl_union_map_intersect_domain(
5827 __isl_take isl_union_map *umap,
5828 __isl_take isl_union_set *uset);
5829 __isl_give isl_union_map *isl_union_map_intersect_range(
5830 __isl_take isl_union_map *umap,
5831 __isl_take isl_union_set *uset);
5832 __isl_give isl_union_map *isl_union_map_intersect(
5833 __isl_take isl_union_map *umap1,
5834 __isl_take isl_union_map *umap2);
5836 #include <isl/aff.h>
5837 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
5838 __isl_take isl_pw_aff *pa,
5839 __isl_take isl_set *set);
5840 __isl_give isl_multi_pw_aff *
5841 isl_multi_pw_aff_intersect_domain(
5842 __isl_take isl_multi_pw_aff *mpa,
5843 __isl_take isl_set *domain);
5844 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
5845 __isl_take isl_pw_multi_aff *pma,
5846 __isl_take isl_set *set);
5847 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
5848 __isl_take isl_union_pw_aff *upa,
5849 __isl_take isl_union_set *uset);
5850 __isl_give isl_union_pw_multi_aff *
5851 isl_union_pw_multi_aff_intersect_domain(
5852 __isl_take isl_union_pw_multi_aff *upma,
5853 __isl_take isl_union_set *uset);
5854 __isl_give isl_multi_union_pw_aff *
5855 isl_multi_union_pw_aff_intersect_domain(
5856 __isl_take isl_multi_union_pw_aff *mupa,
5857 __isl_take isl_union_set *uset);
5858 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
5859 __isl_take isl_pw_aff *pa,
5860 __isl_take isl_set *set);
5861 __isl_give isl_multi_pw_aff *
5862 isl_multi_pw_aff_intersect_params(
5863 __isl_take isl_multi_pw_aff *mpa,
5864 __isl_take isl_set *set);
5865 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
5866 __isl_take isl_pw_multi_aff *pma,
5867 __isl_take isl_set *set);
5868 __isl_give isl_union_pw_aff *
5869 isl_union_pw_aff_intersect_params(
5870 __isl_take isl_union_pw_aff *upa,
5871 __isl_give isl_union_pw_multi_aff *
5872 isl_union_pw_multi_aff_intersect_params(
5873 __isl_take isl_union_pw_multi_aff *upma,
5874 __isl_take isl_set *set);
5875 __isl_give isl_multi_union_pw_aff *
5876 isl_multi_union_pw_aff_intersect_params(
5877 __isl_take isl_multi_union_pw_aff *mupa,
5878 __isl_take isl_set *params);
5879 isl_multi_union_pw_aff_intersect_range(
5880 __isl_take isl_multi_union_pw_aff *mupa,
5881 __isl_take isl_set *set);
5883 #include <isl/polynomial.h>
5884 __isl_give isl_pw_qpolynomial *
5885 isl_pw_qpolynomial_intersect_domain(
5886 __isl_take isl_pw_qpolynomial *pwpq,
5887 __isl_take isl_set *set);
5888 __isl_give isl_union_pw_qpolynomial *
5889 isl_union_pw_qpolynomial_intersect_domain(
5890 __isl_take isl_union_pw_qpolynomial *upwpq,
5891 __isl_take isl_union_set *uset);
5892 __isl_give isl_union_pw_qpolynomial_fold *
5893 isl_union_pw_qpolynomial_fold_intersect_domain(
5894 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5895 __isl_take isl_union_set *uset);
5896 __isl_give isl_pw_qpolynomial *
5897 isl_pw_qpolynomial_intersect_params(
5898 __isl_take isl_pw_qpolynomial *pwpq,
5899 __isl_take isl_set *set);
5900 __isl_give isl_pw_qpolynomial_fold *
5901 isl_pw_qpolynomial_fold_intersect_params(
5902 __isl_take isl_pw_qpolynomial_fold *pwf,
5903 __isl_take isl_set *set);
5904 __isl_give isl_union_pw_qpolynomial *
5905 isl_union_pw_qpolynomial_intersect_params(
5906 __isl_take isl_union_pw_qpolynomial *upwpq,
5907 __isl_take isl_set *set);
5908 __isl_give isl_union_pw_qpolynomial_fold *
5909 isl_union_pw_qpolynomial_fold_intersect_params(
5910 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5911 __isl_take isl_set *set);
5913 The second argument to the C<_params> functions needs to be
5914 a parametric (basic) set. For the other functions, a parametric set
5915 for either argument is only allowed if the other argument is
5916 a parametric set as well.
5917 The list passed to C<isl_basic_set_list_intersect> needs to have
5918 at least one element and all elements need to live in the same space.
5919 The function C<isl_multi_union_pw_aff_intersect_range>
5920 restricts the input function to those shared domain elements
5921 that map to the specified range.
5925 #include <isl/set.h>
5926 __isl_give isl_set *isl_basic_set_union(
5927 __isl_take isl_basic_set *bset1,
5928 __isl_take isl_basic_set *bset2);
5929 __isl_give isl_set *isl_set_union(
5930 __isl_take isl_set *set1,
5931 __isl_take isl_set *set2);
5932 __isl_give isl_set *isl_set_list_union(
5933 __isl_take isl_set_list *list);
5935 #include <isl/map.h>
5936 __isl_give isl_map *isl_basic_map_union(
5937 __isl_take isl_basic_map *bmap1,
5938 __isl_take isl_basic_map *bmap2);
5939 __isl_give isl_map *isl_map_union(
5940 __isl_take isl_map *map1,
5941 __isl_take isl_map *map2);
5943 #include <isl/union_set.h>
5944 __isl_give isl_union_set *isl_union_set_union(
5945 __isl_take isl_union_set *uset1,
5946 __isl_take isl_union_set *uset2);
5947 __isl_give isl_union_set *isl_union_set_list_union(
5948 __isl_take isl_union_set_list *list);
5950 #include <isl/union_map.h>
5951 __isl_give isl_union_map *isl_union_map_union(
5952 __isl_take isl_union_map *umap1,
5953 __isl_take isl_union_map *umap2);
5955 The list passed to C<isl_set_list_union> needs to have
5956 at least one element and all elements need to live in the same space.
5958 =item * Set difference
5960 #include <isl/set.h>
5961 __isl_give isl_set *isl_set_subtract(
5962 __isl_take isl_set *set1,
5963 __isl_take isl_set *set2);
5965 #include <isl/map.h>
5966 __isl_give isl_map *isl_map_subtract(
5967 __isl_take isl_map *map1,
5968 __isl_take isl_map *map2);
5969 __isl_give isl_map *isl_map_subtract_domain(
5970 __isl_take isl_map *map,
5971 __isl_take isl_set *dom);
5972 __isl_give isl_map *isl_map_subtract_range(
5973 __isl_take isl_map *map,
5974 __isl_take isl_set *dom);
5976 #include <isl/union_set.h>
5977 __isl_give isl_union_set *isl_union_set_subtract(
5978 __isl_take isl_union_set *uset1,
5979 __isl_take isl_union_set *uset2);
5981 #include <isl/union_map.h>
5982 __isl_give isl_union_map *isl_union_map_subtract(
5983 __isl_take isl_union_map *umap1,
5984 __isl_take isl_union_map *umap2);
5985 __isl_give isl_union_map *isl_union_map_subtract_domain(
5986 __isl_take isl_union_map *umap,
5987 __isl_take isl_union_set *dom);
5988 __isl_give isl_union_map *isl_union_map_subtract_range(
5989 __isl_take isl_union_map *umap,
5990 __isl_take isl_union_set *dom);
5992 #include <isl/aff.h>
5993 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
5994 __isl_take isl_pw_aff *pa,
5995 __isl_take isl_set *set);
5996 __isl_give isl_pw_multi_aff *
5997 isl_pw_multi_aff_subtract_domain(
5998 __isl_take isl_pw_multi_aff *pma,
5999 __isl_take isl_set *set);
6000 __isl_give isl_union_pw_aff *
6001 isl_union_pw_aff_subtract_domain(
6002 __isl_take isl_union_pw_aff *upa,
6003 __isl_take isl_union_set *uset);
6004 __isl_give isl_union_pw_multi_aff *
6005 isl_union_pw_multi_aff_subtract_domain(
6006 __isl_take isl_union_pw_multi_aff *upma,
6007 __isl_take isl_set *set);
6009 #include <isl/polynomial.h>
6010 __isl_give isl_pw_qpolynomial *
6011 isl_pw_qpolynomial_subtract_domain(
6012 __isl_take isl_pw_qpolynomial *pwpq,
6013 __isl_take isl_set *set);
6014 __isl_give isl_pw_qpolynomial_fold *
6015 isl_pw_qpolynomial_fold_subtract_domain(
6016 __isl_take isl_pw_qpolynomial_fold *pwf,
6017 __isl_take isl_set *set);
6018 __isl_give isl_union_pw_qpolynomial *
6019 isl_union_pw_qpolynomial_subtract_domain(
6020 __isl_take isl_union_pw_qpolynomial *upwpq,
6021 __isl_take isl_union_set *uset);
6022 __isl_give isl_union_pw_qpolynomial_fold *
6023 isl_union_pw_qpolynomial_fold_subtract_domain(
6024 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6025 __isl_take isl_union_set *uset);
6029 #include <isl/space.h>
6030 __isl_give isl_space *isl_space_join(
6031 __isl_take isl_space *left,
6032 __isl_take isl_space *right);
6034 #include <isl/map.h>
6035 __isl_give isl_basic_set *isl_basic_set_apply(
6036 __isl_take isl_basic_set *bset,
6037 __isl_take isl_basic_map *bmap);
6038 __isl_give isl_set *isl_set_apply(
6039 __isl_take isl_set *set,
6040 __isl_take isl_map *map);
6041 __isl_give isl_union_set *isl_union_set_apply(
6042 __isl_take isl_union_set *uset,
6043 __isl_take isl_union_map *umap);
6044 __isl_give isl_basic_map *isl_basic_map_apply_domain(
6045 __isl_take isl_basic_map *bmap1,
6046 __isl_take isl_basic_map *bmap2);
6047 __isl_give isl_basic_map *isl_basic_map_apply_range(
6048 __isl_take isl_basic_map *bmap1,
6049 __isl_take isl_basic_map *bmap2);
6050 __isl_give isl_map *isl_map_apply_domain(
6051 __isl_take isl_map *map1,
6052 __isl_take isl_map *map2);
6053 __isl_give isl_map *isl_map_apply_range(
6054 __isl_take isl_map *map1,
6055 __isl_take isl_map *map2);
6057 #include <isl/union_map.h>
6058 __isl_give isl_union_map *isl_union_map_apply_domain(
6059 __isl_take isl_union_map *umap1,
6060 __isl_take isl_union_map *umap2);
6061 __isl_give isl_union_map *isl_union_map_apply_range(
6062 __isl_take isl_union_map *umap1,
6063 __isl_take isl_union_map *umap2);
6065 #include <isl/aff.h>
6066 __isl_give isl_union_pw_aff *
6067 isl_multi_union_pw_aff_apply_aff(
6068 __isl_take isl_multi_union_pw_aff *mupa,
6069 __isl_take isl_aff *aff);
6070 __isl_give isl_union_pw_aff *
6071 isl_multi_union_pw_aff_apply_pw_aff(
6072 __isl_take isl_multi_union_pw_aff *mupa,
6073 __isl_take isl_pw_aff *pa);
6074 __isl_give isl_multi_union_pw_aff *
6075 isl_multi_union_pw_aff_apply_multi_aff(
6076 __isl_take isl_multi_union_pw_aff *mupa,
6077 __isl_take isl_multi_aff *ma);
6078 __isl_give isl_multi_union_pw_aff *
6079 isl_multi_union_pw_aff_apply_pw_multi_aff(
6080 __isl_take isl_multi_union_pw_aff *mupa,
6081 __isl_take isl_pw_multi_aff *pma);
6083 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
6084 over the shared domain of the elements of the input. The dimension is
6085 required to be greater than zero.
6086 The C<isl_multi_union_pw_aff> argument of
6087 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
6088 but only if the range of the C<isl_multi_aff> argument
6089 is also zero-dimensional.
6090 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
6092 #include <isl/polynomial.h>
6093 __isl_give isl_pw_qpolynomial_fold *
6094 isl_set_apply_pw_qpolynomial_fold(
6095 __isl_take isl_set *set,
6096 __isl_take isl_pw_qpolynomial_fold *pwf,
6098 __isl_give isl_pw_qpolynomial_fold *
6099 isl_map_apply_pw_qpolynomial_fold(
6100 __isl_take isl_map *map,
6101 __isl_take isl_pw_qpolynomial_fold *pwf,
6103 __isl_give isl_union_pw_qpolynomial_fold *
6104 isl_union_set_apply_union_pw_qpolynomial_fold(
6105 __isl_take isl_union_set *uset,
6106 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6108 __isl_give isl_union_pw_qpolynomial_fold *
6109 isl_union_map_apply_union_pw_qpolynomial_fold(
6110 __isl_take isl_union_map *umap,
6111 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6114 The functions taking a map
6115 compose the given map with the given piecewise quasipolynomial reduction.
6116 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
6117 over all elements in the intersection of the range of the map
6118 and the domain of the piecewise quasipolynomial reduction
6119 as a function of an element in the domain of the map.
6120 The functions taking a set compute a bound over all elements in the
6121 intersection of the set and the domain of the
6122 piecewise quasipolynomial reduction.
6126 #include <isl/set.h>
6127 __isl_give isl_basic_set *
6128 isl_basic_set_preimage_multi_aff(
6129 __isl_take isl_basic_set *bset,
6130 __isl_take isl_multi_aff *ma);
6131 __isl_give isl_set *isl_set_preimage_multi_aff(
6132 __isl_take isl_set *set,
6133 __isl_take isl_multi_aff *ma);
6134 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
6135 __isl_take isl_set *set,
6136 __isl_take isl_pw_multi_aff *pma);
6137 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
6138 __isl_take isl_set *set,
6139 __isl_take isl_multi_pw_aff *mpa);
6141 #include <isl/union_set.h>
6142 __isl_give isl_union_set *
6143 isl_union_set_preimage_multi_aff(
6144 __isl_take isl_union_set *uset,
6145 __isl_take isl_multi_aff *ma);
6146 __isl_give isl_union_set *
6147 isl_union_set_preimage_pw_multi_aff(
6148 __isl_take isl_union_set *uset,
6149 __isl_take isl_pw_multi_aff *pma);
6150 __isl_give isl_union_set *
6151 isl_union_set_preimage_union_pw_multi_aff(
6152 __isl_take isl_union_set *uset,
6153 __isl_take isl_union_pw_multi_aff *upma);
6155 #include <isl/map.h>
6156 __isl_give isl_basic_map *
6157 isl_basic_map_preimage_domain_multi_aff(
6158 __isl_take isl_basic_map *bmap,
6159 __isl_take isl_multi_aff *ma);
6160 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
6161 __isl_take isl_map *map,
6162 __isl_take isl_multi_aff *ma);
6163 __isl_give isl_map *isl_map_preimage_range_multi_aff(
6164 __isl_take isl_map *map,
6165 __isl_take isl_multi_aff *ma);
6166 __isl_give isl_map *
6167 isl_map_preimage_domain_pw_multi_aff(
6168 __isl_take isl_map *map,
6169 __isl_take isl_pw_multi_aff *pma);
6170 __isl_give isl_map *
6171 isl_map_preimage_range_pw_multi_aff(
6172 __isl_take isl_map *map,
6173 __isl_take isl_pw_multi_aff *pma);
6174 __isl_give isl_map *
6175 isl_map_preimage_domain_multi_pw_aff(
6176 __isl_take isl_map *map,
6177 __isl_take isl_multi_pw_aff *mpa);
6178 __isl_give isl_basic_map *
6179 isl_basic_map_preimage_range_multi_aff(
6180 __isl_take isl_basic_map *bmap,
6181 __isl_take isl_multi_aff *ma);
6183 #include <isl/union_map.h>
6184 __isl_give isl_union_map *
6185 isl_union_map_preimage_domain_multi_aff(
6186 __isl_take isl_union_map *umap,
6187 __isl_take isl_multi_aff *ma);
6188 __isl_give isl_union_map *
6189 isl_union_map_preimage_range_multi_aff(
6190 __isl_take isl_union_map *umap,
6191 __isl_take isl_multi_aff *ma);
6192 __isl_give isl_union_map *
6193 isl_union_map_preimage_domain_pw_multi_aff(
6194 __isl_take isl_union_map *umap,
6195 __isl_take isl_pw_multi_aff *pma);
6196 __isl_give isl_union_map *
6197 isl_union_map_preimage_range_pw_multi_aff(
6198 __isl_take isl_union_map *umap,
6199 __isl_take isl_pw_multi_aff *pma);
6200 __isl_give isl_union_map *
6201 isl_union_map_preimage_domain_union_pw_multi_aff(
6202 __isl_take isl_union_map *umap,
6203 __isl_take isl_union_pw_multi_aff *upma);
6204 __isl_give isl_union_map *
6205 isl_union_map_preimage_range_union_pw_multi_aff(
6206 __isl_take isl_union_map *umap,
6207 __isl_take isl_union_pw_multi_aff *upma);
6209 These functions compute the preimage of the given set or map domain/range under
6210 the given function. In other words, the expression is plugged
6211 into the set description or into the domain/range of the map.
6215 #include <isl/aff.h>
6216 __isl_give isl_aff *isl_aff_pullback_aff(
6217 __isl_take isl_aff *aff1,
6218 __isl_take isl_aff *aff2);
6219 __isl_give isl_aff *isl_aff_pullback_multi_aff(
6220 __isl_take isl_aff *aff,
6221 __isl_take isl_multi_aff *ma);
6222 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
6223 __isl_take isl_pw_aff *pa,
6224 __isl_take isl_multi_aff *ma);
6225 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
6226 __isl_take isl_pw_aff *pa,
6227 __isl_take isl_pw_multi_aff *pma);
6228 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
6229 __isl_take isl_pw_aff *pa,
6230 __isl_take isl_multi_pw_aff *mpa);
6231 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
6232 __isl_take isl_multi_aff *ma1,
6233 __isl_take isl_multi_aff *ma2);
6234 __isl_give isl_pw_multi_aff *
6235 isl_pw_multi_aff_pullback_multi_aff(
6236 __isl_take isl_pw_multi_aff *pma,
6237 __isl_take isl_multi_aff *ma);
6238 __isl_give isl_multi_pw_aff *
6239 isl_multi_pw_aff_pullback_multi_aff(
6240 __isl_take isl_multi_pw_aff *mpa,
6241 __isl_take isl_multi_aff *ma);
6242 __isl_give isl_pw_multi_aff *
6243 isl_pw_multi_aff_pullback_pw_multi_aff(
6244 __isl_take isl_pw_multi_aff *pma1,
6245 __isl_take isl_pw_multi_aff *pma2);
6246 __isl_give isl_multi_pw_aff *
6247 isl_multi_pw_aff_pullback_pw_multi_aff(
6248 __isl_take isl_multi_pw_aff *mpa,
6249 __isl_take isl_pw_multi_aff *pma);
6250 __isl_give isl_multi_pw_aff *
6251 isl_multi_pw_aff_pullback_multi_pw_aff(
6252 __isl_take isl_multi_pw_aff *mpa1,
6253 __isl_take isl_multi_pw_aff *mpa2);
6254 __isl_give isl_union_pw_aff *
6255 isl_union_pw_aff_pullback_union_pw_multi_aff(
6256 __isl_take isl_union_pw_aff *upa,
6257 __isl_take isl_union_pw_multi_aff *upma);
6258 __isl_give isl_union_pw_multi_aff *
6259 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
6260 __isl_take isl_union_pw_multi_aff *upma1,
6261 __isl_take isl_union_pw_multi_aff *upma2);
6262 __isl_give isl_multi_union_pw_aff *
6263 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
6264 __isl_take isl_multi_union_pw_aff *mupa,
6265 __isl_take isl_union_pw_multi_aff *upma);
6267 These functions precompose the first expression by the second function.
6268 In other words, the second function is plugged
6269 into the first expression.
6273 #include <isl/aff.h>
6274 __isl_give isl_basic_set *isl_aff_eq_basic_set(
6275 __isl_take isl_aff *aff1,
6276 __isl_take isl_aff *aff2);
6277 __isl_give isl_set *isl_aff_eq_set(
6278 __isl_take isl_aff *aff1,
6279 __isl_take isl_aff *aff2);
6280 __isl_give isl_basic_set *isl_aff_le_basic_set(
6281 __isl_take isl_aff *aff1,
6282 __isl_take isl_aff *aff2);
6283 __isl_give isl_set *isl_aff_le_set(
6284 __isl_take isl_aff *aff1,
6285 __isl_take isl_aff *aff2);
6286 __isl_give isl_basic_set *isl_aff_lt_basic_set(
6287 __isl_take isl_aff *aff1,
6288 __isl_take isl_aff *aff2);
6289 __isl_give isl_set *isl_aff_lt_set(
6290 __isl_take isl_aff *aff1,
6291 __isl_take isl_aff *aff2);
6292 __isl_give isl_basic_set *isl_aff_ge_basic_set(
6293 __isl_take isl_aff *aff1,
6294 __isl_take isl_aff *aff2);
6295 __isl_give isl_set *isl_aff_ge_set(
6296 __isl_take isl_aff *aff1,
6297 __isl_take isl_aff *aff2);
6298 __isl_give isl_basic_set *isl_aff_gt_basic_set(
6299 __isl_take isl_aff *aff1,
6300 __isl_take isl_aff *aff2);
6301 __isl_give isl_set *isl_pw_aff_eq_set(
6302 __isl_take isl_pw_aff *pwaff1,
6303 __isl_take isl_pw_aff *pwaff2);
6304 __isl_give isl_set *isl_pw_aff_ne_set(
6305 __isl_take isl_pw_aff *pwaff1,
6306 __isl_take isl_pw_aff *pwaff2);
6307 __isl_give isl_set *isl_pw_aff_le_set(
6308 __isl_take isl_pw_aff *pwaff1,
6309 __isl_take isl_pw_aff *pwaff2);
6310 __isl_give isl_set *isl_pw_aff_lt_set(
6311 __isl_take isl_pw_aff *pwaff1,
6312 __isl_take isl_pw_aff *pwaff2);
6313 __isl_give isl_set *isl_pw_aff_ge_set(
6314 __isl_take isl_pw_aff *pwaff1,
6315 __isl_take isl_pw_aff *pwaff2);
6316 __isl_give isl_set *isl_pw_aff_gt_set(
6317 __isl_take isl_pw_aff *pwaff1,
6318 __isl_take isl_pw_aff *pwaff2);
6320 __isl_give isl_set *isl_multi_aff_lex_le_set(
6321 __isl_take isl_multi_aff *ma1,
6322 __isl_take isl_multi_aff *ma2);
6323 __isl_give isl_set *isl_multi_aff_lex_lt_set(
6324 __isl_take isl_multi_aff *ma1,
6325 __isl_take isl_multi_aff *ma2);
6326 __isl_give isl_set *isl_multi_aff_lex_ge_set(
6327 __isl_take isl_multi_aff *ma1,
6328 __isl_take isl_multi_aff *ma2);
6329 __isl_give isl_set *isl_multi_aff_lex_gt_set(
6330 __isl_take isl_multi_aff *ma1,
6331 __isl_take isl_multi_aff *ma2);
6333 __isl_give isl_set *isl_pw_aff_list_eq_set(
6334 __isl_take isl_pw_aff_list *list1,
6335 __isl_take isl_pw_aff_list *list2);
6336 __isl_give isl_set *isl_pw_aff_list_ne_set(
6337 __isl_take isl_pw_aff_list *list1,
6338 __isl_take isl_pw_aff_list *list2);
6339 __isl_give isl_set *isl_pw_aff_list_le_set(
6340 __isl_take isl_pw_aff_list *list1,
6341 __isl_take isl_pw_aff_list *list2);
6342 __isl_give isl_set *isl_pw_aff_list_lt_set(
6343 __isl_take isl_pw_aff_list *list1,
6344 __isl_take isl_pw_aff_list *list2);
6345 __isl_give isl_set *isl_pw_aff_list_ge_set(
6346 __isl_take isl_pw_aff_list *list1,
6347 __isl_take isl_pw_aff_list *list2);
6348 __isl_give isl_set *isl_pw_aff_list_gt_set(
6349 __isl_take isl_pw_aff_list *list1,
6350 __isl_take isl_pw_aff_list *list2);
6352 The function C<isl_aff_ge_basic_set> returns a basic set
6353 containing those elements in the shared space
6354 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
6355 The function C<isl_pw_aff_ge_set> returns a set
6356 containing those elements in the shared domain
6357 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
6358 greater than or equal to C<pwaff2>.
6359 The function C<isl_multi_aff_lex_le_set> returns a set
6360 containing those elements in the shared domain space
6361 where C<ma1> is lexicographically smaller than or
6363 The functions operating on C<isl_pw_aff_list> apply the corresponding
6364 C<isl_pw_aff> function to each pair of elements in the two lists.
6366 #include <isl/aff.h>
6367 __isl_give isl_map *isl_pw_aff_eq_map(
6368 __isl_take isl_pw_aff *pa1,
6369 __isl_take isl_pw_aff *pa2);
6370 __isl_give isl_map *isl_pw_aff_lt_map(
6371 __isl_take isl_pw_aff *pa1,
6372 __isl_take isl_pw_aff *pa2);
6373 __isl_give isl_map *isl_pw_aff_gt_map(
6374 __isl_take isl_pw_aff *pa1,
6375 __isl_take isl_pw_aff *pa2);
6377 __isl_give isl_map *isl_multi_pw_aff_eq_map(
6378 __isl_take isl_multi_pw_aff *mpa1,
6379 __isl_take isl_multi_pw_aff *mpa2);
6380 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
6381 __isl_take isl_multi_pw_aff *mpa1,
6382 __isl_take isl_multi_pw_aff *mpa2);
6383 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
6384 __isl_take isl_multi_pw_aff *mpa1,
6385 __isl_take isl_multi_pw_aff *mpa2);
6387 These functions return a map between domain elements of the arguments
6388 where the function values satisfy the given relation.
6390 #include <isl/union_map.h>
6391 __isl_give isl_union_map *
6392 isl_union_map_eq_at_multi_union_pw_aff(
6393 __isl_take isl_union_map *umap,
6394 __isl_take isl_multi_union_pw_aff *mupa);
6395 __isl_give isl_union_map *
6396 isl_union_map_lex_lt_at_multi_union_pw_aff(
6397 __isl_take isl_union_map *umap,
6398 __isl_take isl_multi_union_pw_aff *mupa);
6399 __isl_give isl_union_map *
6400 isl_union_map_lex_gt_at_multi_union_pw_aff(
6401 __isl_take isl_union_map *umap,
6402 __isl_take isl_multi_union_pw_aff *mupa);
6404 These functions select the subset of elements in the union map
6405 that have an equal or lexicographically smaller function value.
6407 =item * Cartesian Product
6409 #include <isl/space.h>
6410 __isl_give isl_space *isl_space_product(
6411 __isl_take isl_space *space1,
6412 __isl_take isl_space *space2);
6413 __isl_give isl_space *isl_space_domain_product(
6414 __isl_take isl_space *space1,
6415 __isl_take isl_space *space2);
6416 __isl_give isl_space *isl_space_range_product(
6417 __isl_take isl_space *space1,
6418 __isl_take isl_space *space2);
6421 C<isl_space_product>, C<isl_space_domain_product>
6422 and C<isl_space_range_product> take pairs or relation spaces and
6423 produce a single relations space, where either the domain, the range
6424 or both domain and range are wrapped spaces of relations between
6425 the domains and/or ranges of the input spaces.
6426 If the product is only constructed over the domain or the range
6427 then the ranges or the domains of the inputs should be the same.
6428 The function C<isl_space_product> also accepts a pair of set spaces,
6429 in which case it returns a wrapped space of a relation between the
6432 #include <isl/set.h>
6433 __isl_give isl_set *isl_set_product(
6434 __isl_take isl_set *set1,
6435 __isl_take isl_set *set2);
6437 #include <isl/map.h>
6438 __isl_give isl_basic_map *isl_basic_map_domain_product(
6439 __isl_take isl_basic_map *bmap1,
6440 __isl_take isl_basic_map *bmap2);
6441 __isl_give isl_basic_map *isl_basic_map_range_product(
6442 __isl_take isl_basic_map *bmap1,
6443 __isl_take isl_basic_map *bmap2);
6444 __isl_give isl_basic_map *isl_basic_map_product(
6445 __isl_take isl_basic_map *bmap1,
6446 __isl_take isl_basic_map *bmap2);
6447 __isl_give isl_map *isl_map_domain_product(
6448 __isl_take isl_map *map1,
6449 __isl_take isl_map *map2);
6450 __isl_give isl_map *isl_map_range_product(
6451 __isl_take isl_map *map1,
6452 __isl_take isl_map *map2);
6453 __isl_give isl_map *isl_map_product(
6454 __isl_take isl_map *map1,
6455 __isl_take isl_map *map2);
6457 #include <isl/union_set.h>
6458 __isl_give isl_union_set *isl_union_set_product(
6459 __isl_take isl_union_set *uset1,
6460 __isl_take isl_union_set *uset2);
6462 #include <isl/union_map.h>
6463 __isl_give isl_union_map *isl_union_map_domain_product(
6464 __isl_take isl_union_map *umap1,
6465 __isl_take isl_union_map *umap2);
6466 __isl_give isl_union_map *isl_union_map_range_product(
6467 __isl_take isl_union_map *umap1,
6468 __isl_take isl_union_map *umap2);
6469 __isl_give isl_union_map *isl_union_map_product(
6470 __isl_take isl_union_map *umap1,
6471 __isl_take isl_union_map *umap2);
6473 #include <isl/val.h>
6474 __isl_give isl_multi_val *isl_multi_val_range_product(
6475 __isl_take isl_multi_val *mv1,
6476 __isl_take isl_multi_val *mv2);
6477 __isl_give isl_multi_val *isl_multi_val_product(
6478 __isl_take isl_multi_val *mv1,
6479 __isl_take isl_multi_val *mv2);
6481 #include <isl/aff.h>
6482 __isl_give isl_multi_aff *isl_multi_aff_range_product(
6483 __isl_take isl_multi_aff *ma1,
6484 __isl_take isl_multi_aff *ma2);
6485 __isl_give isl_multi_aff *isl_multi_aff_product(
6486 __isl_take isl_multi_aff *ma1,
6487 __isl_take isl_multi_aff *ma2);
6488 __isl_give isl_multi_pw_aff *
6489 isl_multi_pw_aff_range_product(
6490 __isl_take isl_multi_pw_aff *mpa1,
6491 __isl_take isl_multi_pw_aff *mpa2);
6492 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
6493 __isl_take isl_multi_pw_aff *mpa1,
6494 __isl_take isl_multi_pw_aff *mpa2);
6495 __isl_give isl_pw_multi_aff *
6496 isl_pw_multi_aff_range_product(
6497 __isl_take isl_pw_multi_aff *pma1,
6498 __isl_take isl_pw_multi_aff *pma2);
6499 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
6500 __isl_take isl_pw_multi_aff *pma1,
6501 __isl_take isl_pw_multi_aff *pma2);
6502 __isl_give isl_multi_union_pw_aff *
6503 isl_multi_union_pw_aff_range_product(
6504 __isl_take isl_multi_union_pw_aff *mupa1,
6505 __isl_take isl_multi_union_pw_aff *mupa2);
6507 The above functions compute the cross product of the given
6508 sets, relations or functions. The domains and ranges of the results
6509 are wrapped maps between domains and ranges of the inputs.
6510 To obtain a ``flat'' product, use the following functions
6513 #include <isl/set.h>
6514 __isl_give isl_basic_set *isl_basic_set_flat_product(
6515 __isl_take isl_basic_set *bset1,
6516 __isl_take isl_basic_set *bset2);
6517 __isl_give isl_set *isl_set_flat_product(
6518 __isl_take isl_set *set1,
6519 __isl_take isl_set *set2);
6521 #include <isl/map.h>
6522 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
6523 __isl_take isl_basic_map *bmap1,
6524 __isl_take isl_basic_map *bmap2);
6525 __isl_give isl_map *isl_map_flat_domain_product(
6526 __isl_take isl_map *map1,
6527 __isl_take isl_map *map2);
6528 __isl_give isl_map *isl_map_flat_range_product(
6529 __isl_take isl_map *map1,
6530 __isl_take isl_map *map2);
6531 __isl_give isl_basic_map *isl_basic_map_flat_product(
6532 __isl_take isl_basic_map *bmap1,
6533 __isl_take isl_basic_map *bmap2);
6534 __isl_give isl_map *isl_map_flat_product(
6535 __isl_take isl_map *map1,
6536 __isl_take isl_map *map2);
6538 #include <isl/union_map.h>
6539 __isl_give isl_union_map *
6540 isl_union_map_flat_domain_product(
6541 __isl_take isl_union_map *umap1,
6542 __isl_take isl_union_map *umap2);
6543 __isl_give isl_union_map *
6544 isl_union_map_flat_range_product(
6545 __isl_take isl_union_map *umap1,
6546 __isl_take isl_union_map *umap2);
6548 #include <isl/val.h>
6549 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
6550 __isl_take isl_multi_val *mv1,
6551 __isl_take isl_multi_aff *mv2);
6553 #include <isl/aff.h>
6554 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
6555 __isl_take isl_multi_aff *ma1,
6556 __isl_take isl_multi_aff *ma2);
6557 __isl_give isl_pw_multi_aff *
6558 isl_pw_multi_aff_flat_range_product(
6559 __isl_take isl_pw_multi_aff *pma1,
6560 __isl_take isl_pw_multi_aff *pma2);
6561 __isl_give isl_multi_pw_aff *
6562 isl_multi_pw_aff_flat_range_product(
6563 __isl_take isl_multi_pw_aff *mpa1,
6564 __isl_take isl_multi_pw_aff *mpa2);
6565 __isl_give isl_union_pw_multi_aff *
6566 isl_union_pw_multi_aff_flat_range_product(
6567 __isl_take isl_union_pw_multi_aff *upma1,
6568 __isl_take isl_union_pw_multi_aff *upma2);
6569 __isl_give isl_multi_union_pw_aff *
6570 isl_multi_union_pw_aff_flat_range_product(
6571 __isl_take isl_multi_union_pw_aff *mupa1,
6572 __isl_take isl_multi_union_pw_aff *mupa2);
6574 #include <isl/space.h>
6575 __isl_give isl_space *isl_space_factor_domain(
6576 __isl_take isl_space *space);
6577 __isl_give isl_space *isl_space_factor_range(
6578 __isl_take isl_space *space);
6579 __isl_give isl_space *isl_space_domain_factor_domain(
6580 __isl_take isl_space *space);
6581 __isl_give isl_space *isl_space_domain_factor_range(
6582 __isl_take isl_space *space);
6583 __isl_give isl_space *isl_space_range_factor_domain(
6584 __isl_take isl_space *space);
6585 __isl_give isl_space *isl_space_range_factor_range(
6586 __isl_take isl_space *space);
6588 The functions C<isl_space_range_factor_domain> and
6589 C<isl_space_range_factor_range> extract the two arguments from
6590 the result of a call to C<isl_space_range_product>.
6592 The arguments of a call to a product can be extracted
6593 from the result using the following functions.
6595 #include <isl/map.h>
6596 __isl_give isl_map *isl_map_factor_domain(
6597 __isl_take isl_map *map);
6598 __isl_give isl_map *isl_map_factor_range(
6599 __isl_take isl_map *map);
6600 __isl_give isl_map *isl_map_domain_factor_domain(
6601 __isl_take isl_map *map);
6602 __isl_give isl_map *isl_map_domain_factor_range(
6603 __isl_take isl_map *map);
6604 __isl_give isl_map *isl_map_range_factor_domain(
6605 __isl_take isl_map *map);
6606 __isl_give isl_map *isl_map_range_factor_range(
6607 __isl_take isl_map *map);
6609 #include <isl/union_map.h>
6610 __isl_give isl_union_map *isl_union_map_factor_domain(
6611 __isl_take isl_union_map *umap);
6612 __isl_give isl_union_map *isl_union_map_factor_range(
6613 __isl_take isl_union_map *umap);
6614 __isl_give isl_union_map *
6615 isl_union_map_domain_factor_domain(
6616 __isl_take isl_union_map *umap);
6617 __isl_give isl_union_map *
6618 isl_union_map_domain_factor_range(
6619 __isl_take isl_union_map *umap);
6620 __isl_give isl_union_map *
6621 isl_union_map_range_factor_domain(
6622 __isl_take isl_union_map *umap);
6623 __isl_give isl_union_map *
6624 isl_union_map_range_factor_range(
6625 __isl_take isl_union_map *umap);
6627 #include <isl/val.h>
6628 __isl_give isl_multi_val *isl_multi_val_factor_range(
6629 __isl_take isl_multi_val *mv);
6630 __isl_give isl_multi_val *
6631 isl_multi_val_range_factor_domain(
6632 __isl_take isl_multi_val *mv);
6633 __isl_give isl_multi_val *
6634 isl_multi_val_range_factor_range(
6635 __isl_take isl_multi_val *mv);
6637 #include <isl/aff.h>
6638 __isl_give isl_multi_aff *isl_multi_aff_factor_range(
6639 __isl_take isl_multi_aff *ma);
6640 __isl_give isl_multi_aff *
6641 isl_multi_aff_range_factor_domain(
6642 __isl_take isl_multi_aff *ma);
6643 __isl_give isl_multi_aff *
6644 isl_multi_aff_range_factor_range(
6645 __isl_take isl_multi_aff *ma);
6646 __isl_give isl_multi_pw_aff *
6647 isl_multi_pw_aff_factor_range(
6648 __isl_take isl_multi_pw_aff *mpa);
6649 __isl_give isl_multi_pw_aff *
6650 isl_multi_pw_aff_range_factor_domain(
6651 __isl_take isl_multi_pw_aff *mpa);
6652 __isl_give isl_multi_pw_aff *
6653 isl_multi_pw_aff_range_factor_range(
6654 __isl_take isl_multi_pw_aff *mpa);
6655 __isl_give isl_multi_union_pw_aff *
6656 isl_multi_union_pw_aff_factor_range(
6657 __isl_take isl_multi_union_pw_aff *mupa);
6658 __isl_give isl_multi_union_pw_aff *
6659 isl_multi_union_pw_aff_range_factor_domain(
6660 __isl_take isl_multi_union_pw_aff *mupa);
6661 __isl_give isl_multi_union_pw_aff *
6662 isl_multi_union_pw_aff_range_factor_range(
6663 __isl_take isl_multi_union_pw_aff *mupa);
6665 The splice functions are a generalization of the flat product functions,
6666 where the second argument may be inserted at any position inside
6667 the first argument rather than being placed at the end.
6668 The functions C<isl_multi_val_factor_range>,
6669 C<isl_multi_aff_factor_range>,
6670 C<isl_multi_pw_aff_factor_range> and
6671 C<isl_multi_union_pw_aff_factor_range>
6672 take functions that live in a set space.
6674 #include <isl/val.h>
6675 __isl_give isl_multi_val *isl_multi_val_range_splice(
6676 __isl_take isl_multi_val *mv1, unsigned pos,
6677 __isl_take isl_multi_val *mv2);
6679 #include <isl/aff.h>
6680 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
6681 __isl_take isl_multi_aff *ma1, unsigned pos,
6682 __isl_take isl_multi_aff *ma2);
6683 __isl_give isl_multi_aff *isl_multi_aff_splice(
6684 __isl_take isl_multi_aff *ma1,
6685 unsigned in_pos, unsigned out_pos,
6686 __isl_take isl_multi_aff *ma2);
6687 __isl_give isl_multi_pw_aff *
6688 isl_multi_pw_aff_range_splice(
6689 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
6690 __isl_take isl_multi_pw_aff *mpa2);
6691 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
6692 __isl_take isl_multi_pw_aff *mpa1,
6693 unsigned in_pos, unsigned out_pos,
6694 __isl_take isl_multi_pw_aff *mpa2);
6695 __isl_give isl_multi_union_pw_aff *
6696 isl_multi_union_pw_aff_range_splice(
6697 __isl_take isl_multi_union_pw_aff *mupa1,
6699 __isl_take isl_multi_union_pw_aff *mupa2);
6701 =item * Simplification
6703 When applied to a set or relation,
6704 the gist operation returns a set or relation that has the
6705 same intersection with the context as the input set or relation.
6706 Any implicit equality in the intersection is made explicit in the result,
6707 while all inequalities that are redundant with respect to the intersection
6709 In case of union sets and relations, the gist operation is performed
6712 When applied to a function,
6713 the gist operation applies the set gist operation to each of
6714 the cells in the domain of the input piecewise expression.
6715 The context is also exploited
6716 to simplify the expression associated to each cell.
6718 #include <isl/set.h>
6719 __isl_give isl_basic_set *isl_basic_set_gist(
6720 __isl_take isl_basic_set *bset,
6721 __isl_take isl_basic_set *context);
6722 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
6723 __isl_take isl_set *context);
6724 __isl_give isl_set *isl_set_gist_params(
6725 __isl_take isl_set *set,
6726 __isl_take isl_set *context);
6728 #include <isl/map.h>
6729 __isl_give isl_basic_map *isl_basic_map_gist(
6730 __isl_take isl_basic_map *bmap,
6731 __isl_take isl_basic_map *context);
6732 __isl_give isl_basic_map *isl_basic_map_gist_domain(
6733 __isl_take isl_basic_map *bmap,
6734 __isl_take isl_basic_set *context);
6735 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
6736 __isl_take isl_map *context);
6737 __isl_give isl_map *isl_map_gist_params(
6738 __isl_take isl_map *map,
6739 __isl_take isl_set *context);
6740 __isl_give isl_map *isl_map_gist_domain(
6741 __isl_take isl_map *map,
6742 __isl_take isl_set *context);
6743 __isl_give isl_map *isl_map_gist_range(
6744 __isl_take isl_map *map,
6745 __isl_take isl_set *context);
6747 #include <isl/union_set.h>
6748 __isl_give isl_union_set *isl_union_set_gist(
6749 __isl_take isl_union_set *uset,
6750 __isl_take isl_union_set *context);
6751 __isl_give isl_union_set *isl_union_set_gist_params(
6752 __isl_take isl_union_set *uset,
6753 __isl_take isl_set *set);
6755 #include <isl/union_map.h>
6756 __isl_give isl_union_map *isl_union_map_gist(
6757 __isl_take isl_union_map *umap,
6758 __isl_take isl_union_map *context);
6759 __isl_give isl_union_map *isl_union_map_gist_params(
6760 __isl_take isl_union_map *umap,
6761 __isl_take isl_set *set);
6762 __isl_give isl_union_map *isl_union_map_gist_domain(
6763 __isl_take isl_union_map *umap,
6764 __isl_take isl_union_set *uset);
6765 __isl_give isl_union_map *isl_union_map_gist_range(
6766 __isl_take isl_union_map *umap,
6767 __isl_take isl_union_set *uset);
6769 #include <isl/aff.h>
6770 __isl_give isl_aff *isl_aff_gist_params(
6771 __isl_take isl_aff *aff,
6772 __isl_take isl_set *context);
6773 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
6774 __isl_take isl_set *context);
6775 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
6776 __isl_take isl_multi_aff *maff,
6777 __isl_take isl_set *context);
6778 __isl_give isl_multi_aff *isl_multi_aff_gist(
6779 __isl_take isl_multi_aff *maff,
6780 __isl_take isl_set *context);
6781 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
6782 __isl_take isl_pw_aff *pwaff,
6783 __isl_take isl_set *context);
6784 __isl_give isl_pw_aff *isl_pw_aff_gist(
6785 __isl_take isl_pw_aff *pwaff,
6786 __isl_take isl_set *context);
6787 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
6788 __isl_take isl_pw_multi_aff *pma,
6789 __isl_take isl_set *set);
6790 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
6791 __isl_take isl_pw_multi_aff *pma,
6792 __isl_take isl_set *set);
6793 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
6794 __isl_take isl_multi_pw_aff *mpa,
6795 __isl_take isl_set *set);
6796 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
6797 __isl_take isl_multi_pw_aff *mpa,
6798 __isl_take isl_set *set);
6799 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
6800 __isl_take isl_union_pw_aff *upa,
6801 __isl_take isl_union_set *context);
6802 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
6803 __isl_take isl_union_pw_aff *upa,
6804 __isl_take isl_set *context);
6805 __isl_give isl_union_pw_multi_aff *
6806 isl_union_pw_multi_aff_gist_params(
6807 __isl_take isl_union_pw_multi_aff *upma,
6808 __isl_take isl_set *context);
6809 __isl_give isl_union_pw_multi_aff *
6810 isl_union_pw_multi_aff_gist(
6811 __isl_take isl_union_pw_multi_aff *upma,
6812 __isl_take isl_union_set *context);
6813 __isl_give isl_multi_union_pw_aff *
6814 isl_multi_union_pw_aff_gist_params(
6815 __isl_take isl_multi_union_pw_aff *aff,
6816 __isl_take isl_set *context);
6817 __isl_give isl_multi_union_pw_aff *
6818 isl_multi_union_pw_aff_gist(
6819 __isl_take isl_multi_union_pw_aff *aff,
6820 __isl_take isl_union_set *context);
6822 #include <isl/polynomial.h>
6823 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
6824 __isl_take isl_qpolynomial *qp,
6825 __isl_take isl_set *context);
6826 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
6827 __isl_take isl_qpolynomial *qp,
6828 __isl_take isl_set *context);
6829 __isl_give isl_qpolynomial_fold *
6830 isl_qpolynomial_fold_gist_params(
6831 __isl_take isl_qpolynomial_fold *fold,
6832 __isl_take isl_set *context);
6833 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
6834 __isl_take isl_qpolynomial_fold *fold,
6835 __isl_take isl_set *context);
6836 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
6837 __isl_take isl_pw_qpolynomial *pwqp,
6838 __isl_take isl_set *context);
6839 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
6840 __isl_take isl_pw_qpolynomial *pwqp,
6841 __isl_take isl_set *context);
6842 __isl_give isl_pw_qpolynomial_fold *
6843 isl_pw_qpolynomial_fold_gist(
6844 __isl_take isl_pw_qpolynomial_fold *pwf,
6845 __isl_take isl_set *context);
6846 __isl_give isl_pw_qpolynomial_fold *
6847 isl_pw_qpolynomial_fold_gist_params(
6848 __isl_take isl_pw_qpolynomial_fold *pwf,
6849 __isl_take isl_set *context);
6850 __isl_give isl_union_pw_qpolynomial *
6851 isl_union_pw_qpolynomial_gist_params(
6852 __isl_take isl_union_pw_qpolynomial *upwqp,
6853 __isl_take isl_set *context);
6854 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
6855 __isl_take isl_union_pw_qpolynomial *upwqp,
6856 __isl_take isl_union_set *context);
6857 __isl_give isl_union_pw_qpolynomial_fold *
6858 isl_union_pw_qpolynomial_fold_gist(
6859 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6860 __isl_take isl_union_set *context);
6861 __isl_give isl_union_pw_qpolynomial_fold *
6862 isl_union_pw_qpolynomial_fold_gist_params(
6863 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6864 __isl_take isl_set *context);
6866 =item * Binary Arithmetic Operations
6868 #include <isl/set.h>
6869 __isl_give isl_set *isl_set_sum(
6870 __isl_take isl_set *set1,
6871 __isl_take isl_set *set2);
6872 #include <isl/map.h>
6873 __isl_give isl_map *isl_map_sum(
6874 __isl_take isl_map *map1,
6875 __isl_take isl_map *map2);
6877 C<isl_set_sum> computes the Minkowski sum of its two arguments,
6878 i.e., the set containing the sums of pairs of elements from
6879 C<set1> and C<set2>.
6880 The domain of the result of C<isl_map_sum> is the intersection
6881 of the domains of its two arguments. The corresponding range
6882 elements are the sums of the corresponding range elements
6883 in the two arguments.
6885 #include <isl/val.h>
6886 __isl_give isl_multi_val *isl_multi_val_add(
6887 __isl_take isl_multi_val *mv1,
6888 __isl_take isl_multi_val *mv2);
6889 __isl_give isl_multi_val *isl_multi_val_sub(
6890 __isl_take isl_multi_val *mv1,
6891 __isl_take isl_multi_val *mv2);
6893 #include <isl/aff.h>
6894 __isl_give isl_aff *isl_aff_add(
6895 __isl_take isl_aff *aff1,
6896 __isl_take isl_aff *aff2);
6897 __isl_give isl_multi_aff *isl_multi_aff_add(
6898 __isl_take isl_multi_aff *maff1,
6899 __isl_take isl_multi_aff *maff2);
6900 __isl_give isl_pw_aff *isl_pw_aff_add(
6901 __isl_take isl_pw_aff *pwaff1,
6902 __isl_take isl_pw_aff *pwaff2);
6903 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add(
6904 __isl_take isl_multi_pw_aff *mpa1,
6905 __isl_take isl_multi_pw_aff *mpa2);
6906 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
6907 __isl_take isl_pw_multi_aff *pma1,
6908 __isl_take isl_pw_multi_aff *pma2);
6909 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
6910 __isl_take isl_union_pw_aff *upa1,
6911 __isl_take isl_union_pw_aff *upa2);
6912 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
6913 __isl_take isl_union_pw_multi_aff *upma1,
6914 __isl_take isl_union_pw_multi_aff *upma2);
6915 __isl_give isl_multi_union_pw_aff *
6916 isl_multi_union_pw_aff_add(
6917 __isl_take isl_multi_union_pw_aff *mupa1,
6918 __isl_take isl_multi_union_pw_aff *mupa2);
6919 __isl_give isl_pw_aff *isl_pw_aff_min(
6920 __isl_take isl_pw_aff *pwaff1,
6921 __isl_take isl_pw_aff *pwaff2);
6922 __isl_give isl_pw_aff *isl_pw_aff_max(
6923 __isl_take isl_pw_aff *pwaff1,
6924 __isl_take isl_pw_aff *pwaff2);
6925 __isl_give isl_aff *isl_aff_sub(
6926 __isl_take isl_aff *aff1,
6927 __isl_take isl_aff *aff2);
6928 __isl_give isl_multi_aff *isl_multi_aff_sub(
6929 __isl_take isl_multi_aff *ma1,
6930 __isl_take isl_multi_aff *ma2);
6931 __isl_give isl_pw_aff *isl_pw_aff_sub(
6932 __isl_take isl_pw_aff *pwaff1,
6933 __isl_take isl_pw_aff *pwaff2);
6934 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
6935 __isl_take isl_multi_pw_aff *mpa1,
6936 __isl_take isl_multi_pw_aff *mpa2);
6937 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
6938 __isl_take isl_pw_multi_aff *pma1,
6939 __isl_take isl_pw_multi_aff *pma2);
6940 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
6941 __isl_take isl_union_pw_aff *upa1,
6942 __isl_take isl_union_pw_aff *upa2);
6943 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
6944 __isl_take isl_union_pw_multi_aff *upma1,
6945 __isl_take isl_union_pw_multi_aff *upma2);
6946 __isl_give isl_multi_union_pw_aff *
6947 isl_multi_union_pw_aff_sub(
6948 __isl_take isl_multi_union_pw_aff *mupa1,
6949 __isl_take isl_multi_union_pw_aff *mupa2);
6951 C<isl_aff_sub> subtracts the second argument from the first.
6953 #include <isl/polynomial.h>
6954 __isl_give isl_qpolynomial *isl_qpolynomial_add(
6955 __isl_take isl_qpolynomial *qp1,
6956 __isl_take isl_qpolynomial *qp2);
6957 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
6958 __isl_take isl_pw_qpolynomial *pwqp1,
6959 __isl_take isl_pw_qpolynomial *pwqp2);
6960 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
6961 __isl_take isl_pw_qpolynomial *pwqp1,
6962 __isl_take isl_pw_qpolynomial *pwqp2);
6963 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
6964 __isl_take isl_pw_qpolynomial_fold *pwf1,
6965 __isl_take isl_pw_qpolynomial_fold *pwf2);
6966 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
6967 __isl_take isl_union_pw_qpolynomial *upwqp1,
6968 __isl_take isl_union_pw_qpolynomial *upwqp2);
6969 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
6970 __isl_take isl_qpolynomial *qp1,
6971 __isl_take isl_qpolynomial *qp2);
6972 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
6973 __isl_take isl_pw_qpolynomial *pwqp1,
6974 __isl_take isl_pw_qpolynomial *pwqp2);
6975 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
6976 __isl_take isl_union_pw_qpolynomial *upwqp1,
6977 __isl_take isl_union_pw_qpolynomial *upwqp2);
6978 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
6979 __isl_take isl_pw_qpolynomial_fold *pwf1,
6980 __isl_take isl_pw_qpolynomial_fold *pwf2);
6981 __isl_give isl_union_pw_qpolynomial_fold *
6982 isl_union_pw_qpolynomial_fold_fold(
6983 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
6984 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
6986 #include <isl/aff.h>
6987 __isl_give isl_pw_aff *isl_pw_aff_union_add(
6988 __isl_take isl_pw_aff *pwaff1,
6989 __isl_take isl_pw_aff *pwaff2);
6990 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
6991 __isl_take isl_pw_multi_aff *pma1,
6992 __isl_take isl_pw_multi_aff *pma2);
6993 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
6994 __isl_take isl_union_pw_aff *upa1,
6995 __isl_take isl_union_pw_aff *upa2);
6996 __isl_give isl_union_pw_multi_aff *
6997 isl_union_pw_multi_aff_union_add(
6998 __isl_take isl_union_pw_multi_aff *upma1,
6999 __isl_take isl_union_pw_multi_aff *upma2);
7000 __isl_give isl_multi_union_pw_aff *
7001 isl_multi_union_pw_aff_union_add(
7002 __isl_take isl_multi_union_pw_aff *mupa1,
7003 __isl_take isl_multi_union_pw_aff *mupa2);
7004 __isl_give isl_pw_aff *isl_pw_aff_union_min(
7005 __isl_take isl_pw_aff *pwaff1,
7006 __isl_take isl_pw_aff *pwaff2);
7007 __isl_give isl_pw_aff *isl_pw_aff_union_max(
7008 __isl_take isl_pw_aff *pwaff1,
7009 __isl_take isl_pw_aff *pwaff2);
7011 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
7012 expression with a domain that is the union of those of C<pwaff1> and
7013 C<pwaff2> and such that on each cell, the quasi-affine expression is
7014 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
7015 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
7016 associated expression is the defined one.
7017 This in contrast to the C<isl_pw_aff_max> function, which is
7018 only defined on the shared definition domain of the arguments.
7020 #include <isl/val.h>
7021 __isl_give isl_multi_val *isl_multi_val_add_val(
7022 __isl_take isl_multi_val *mv,
7023 __isl_take isl_val *v);
7024 __isl_give isl_multi_val *isl_multi_val_mod_val(
7025 __isl_take isl_multi_val *mv,
7026 __isl_take isl_val *v);
7027 __isl_give isl_multi_val *isl_multi_val_scale_val(
7028 __isl_take isl_multi_val *mv,
7029 __isl_take isl_val *v);
7030 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
7031 __isl_take isl_multi_val *mv,
7032 __isl_take isl_val *v);
7034 #include <isl/aff.h>
7035 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
7036 __isl_take isl_val *mod);
7037 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
7038 __isl_take isl_pw_aff *pa,
7039 __isl_take isl_val *mod);
7040 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
7041 __isl_take isl_union_pw_aff *upa,
7042 __isl_take isl_val *f);
7043 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
7044 __isl_take isl_val *v);
7045 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
7046 __isl_take isl_multi_aff *ma,
7047 __isl_take isl_val *v);
7048 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
7049 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
7050 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
7051 __isl_take isl_multi_pw_aff *mpa,
7052 __isl_take isl_val *v);
7053 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
7054 __isl_take isl_pw_multi_aff *pma,
7055 __isl_take isl_val *v);
7056 __isl_give isl_union_pw_multi_aff *
7057 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
7058 __isl_take isl_union_pw_aff *upa,
7059 __isl_take isl_val *f);
7060 isl_union_pw_multi_aff_scale_val(
7061 __isl_take isl_union_pw_multi_aff *upma,
7062 __isl_take isl_val *val);
7063 __isl_give isl_multi_union_pw_aff *
7064 isl_multi_union_pw_aff_scale_val(
7065 __isl_take isl_multi_union_pw_aff *mupa,
7066 __isl_take isl_val *v);
7067 __isl_give isl_aff *isl_aff_scale_down_ui(
7068 __isl_take isl_aff *aff, unsigned f);
7069 __isl_give isl_aff *isl_aff_scale_down_val(
7070 __isl_take isl_aff *aff, __isl_take isl_val *v);
7071 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
7072 __isl_take isl_multi_aff *ma,
7073 __isl_take isl_val *v);
7074 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
7075 __isl_take isl_pw_aff *pa,
7076 __isl_take isl_val *f);
7077 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
7078 __isl_take isl_multi_pw_aff *mpa,
7079 __isl_take isl_val *v);
7080 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
7081 __isl_take isl_pw_multi_aff *pma,
7082 __isl_take isl_val *v);
7083 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
7084 __isl_take isl_union_pw_aff *upa,
7085 __isl_take isl_val *v);
7086 __isl_give isl_union_pw_multi_aff *
7087 isl_union_pw_multi_aff_scale_down_val(
7088 __isl_take isl_union_pw_multi_aff *upma,
7089 __isl_take isl_val *val);
7090 __isl_give isl_multi_union_pw_aff *
7091 isl_multi_union_pw_aff_scale_down_val(
7092 __isl_take isl_multi_union_pw_aff *mupa,
7093 __isl_take isl_val *v);
7095 #include <isl/polynomial.h>
7096 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
7097 __isl_take isl_qpolynomial *qp,
7098 __isl_take isl_val *v);
7099 __isl_give isl_qpolynomial_fold *
7100 isl_qpolynomial_fold_scale_val(
7101 __isl_take isl_qpolynomial_fold *fold,
7102 __isl_take isl_val *v);
7103 __isl_give isl_pw_qpolynomial *
7104 isl_pw_qpolynomial_scale_val(
7105 __isl_take isl_pw_qpolynomial *pwqp,
7106 __isl_take isl_val *v);
7107 __isl_give isl_pw_qpolynomial_fold *
7108 isl_pw_qpolynomial_fold_scale_val(
7109 __isl_take isl_pw_qpolynomial_fold *pwf,
7110 __isl_take isl_val *v);
7111 __isl_give isl_union_pw_qpolynomial *
7112 isl_union_pw_qpolynomial_scale_val(
7113 __isl_take isl_union_pw_qpolynomial *upwqp,
7114 __isl_take isl_val *v);
7115 __isl_give isl_union_pw_qpolynomial_fold *
7116 isl_union_pw_qpolynomial_fold_scale_val(
7117 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7118 __isl_take isl_val *v);
7119 __isl_give isl_qpolynomial *
7120 isl_qpolynomial_scale_down_val(
7121 __isl_take isl_qpolynomial *qp,
7122 __isl_take isl_val *v);
7123 __isl_give isl_qpolynomial_fold *
7124 isl_qpolynomial_fold_scale_down_val(
7125 __isl_take isl_qpolynomial_fold *fold,
7126 __isl_take isl_val *v);
7127 __isl_give isl_pw_qpolynomial *
7128 isl_pw_qpolynomial_scale_down_val(
7129 __isl_take isl_pw_qpolynomial *pwqp,
7130 __isl_take isl_val *v);
7131 __isl_give isl_pw_qpolynomial_fold *
7132 isl_pw_qpolynomial_fold_scale_down_val(
7133 __isl_take isl_pw_qpolynomial_fold *pwf,
7134 __isl_take isl_val *v);
7135 __isl_give isl_union_pw_qpolynomial *
7136 isl_union_pw_qpolynomial_scale_down_val(
7137 __isl_take isl_union_pw_qpolynomial *upwqp,
7138 __isl_take isl_val *v);
7139 __isl_give isl_union_pw_qpolynomial_fold *
7140 isl_union_pw_qpolynomial_fold_scale_down_val(
7141 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7142 __isl_take isl_val *v);
7144 #include <isl/val.h>
7145 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
7146 __isl_take isl_multi_val *mv1,
7147 __isl_take isl_multi_val *mv2);
7148 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
7149 __isl_take isl_multi_val *mv1,
7150 __isl_take isl_multi_val *mv2);
7151 __isl_give isl_multi_val *
7152 isl_multi_val_scale_down_multi_val(
7153 __isl_take isl_multi_val *mv1,
7154 __isl_take isl_multi_val *mv2);
7156 #include <isl/aff.h>
7157 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
7158 __isl_take isl_multi_aff *ma,
7159 __isl_take isl_multi_val *mv);
7160 __isl_give isl_multi_union_pw_aff *
7161 isl_multi_union_pw_aff_mod_multi_val(
7162 __isl_take isl_multi_union_pw_aff *upma,
7163 __isl_take isl_multi_val *mv);
7164 __isl_give isl_multi_pw_aff *
7165 isl_multi_pw_aff_mod_multi_val(
7166 __isl_take isl_multi_pw_aff *mpa,
7167 __isl_take isl_multi_val *mv);
7168 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
7169 __isl_take isl_multi_aff *ma,
7170 __isl_take isl_multi_val *mv);
7171 __isl_give isl_pw_multi_aff *
7172 isl_pw_multi_aff_scale_multi_val(
7173 __isl_take isl_pw_multi_aff *pma,
7174 __isl_take isl_multi_val *mv);
7175 __isl_give isl_multi_pw_aff *
7176 isl_multi_pw_aff_scale_multi_val(
7177 __isl_take isl_multi_pw_aff *mpa,
7178 __isl_take isl_multi_val *mv);
7179 __isl_give isl_multi_union_pw_aff *
7180 isl_multi_union_pw_aff_scale_multi_val(
7181 __isl_take isl_multi_union_pw_aff *mupa,
7182 __isl_take isl_multi_val *mv);
7183 __isl_give isl_union_pw_multi_aff *
7184 isl_union_pw_multi_aff_scale_multi_val(
7185 __isl_take isl_union_pw_multi_aff *upma,
7186 __isl_take isl_multi_val *mv);
7187 __isl_give isl_multi_aff *
7188 isl_multi_aff_scale_down_multi_val(
7189 __isl_take isl_multi_aff *ma,
7190 __isl_take isl_multi_val *mv);
7191 __isl_give isl_multi_pw_aff *
7192 isl_multi_pw_aff_scale_down_multi_val(
7193 __isl_take isl_multi_pw_aff *mpa,
7194 __isl_take isl_multi_val *mv);
7195 __isl_give isl_multi_union_pw_aff *
7196 isl_multi_union_pw_aff_scale_down_multi_val(
7197 __isl_take isl_multi_union_pw_aff *mupa,
7198 __isl_take isl_multi_val *mv);
7200 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
7201 by the corresponding elements of C<mv>.
7203 #include <isl/aff.h>
7204 __isl_give isl_aff *isl_aff_mul(
7205 __isl_take isl_aff *aff1,
7206 __isl_take isl_aff *aff2);
7207 __isl_give isl_aff *isl_aff_div(
7208 __isl_take isl_aff *aff1,
7209 __isl_take isl_aff *aff2);
7210 __isl_give isl_pw_aff *isl_pw_aff_mul(
7211 __isl_take isl_pw_aff *pwaff1,
7212 __isl_take isl_pw_aff *pwaff2);
7213 __isl_give isl_pw_aff *isl_pw_aff_div(
7214 __isl_take isl_pw_aff *pa1,
7215 __isl_take isl_pw_aff *pa2);
7216 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
7217 __isl_take isl_pw_aff *pa1,
7218 __isl_take isl_pw_aff *pa2);
7219 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
7220 __isl_take isl_pw_aff *pa1,
7221 __isl_take isl_pw_aff *pa2);
7223 When multiplying two affine expressions, at least one of the two needs
7224 to be a constant. Similarly, when dividing an affine expression by another,
7225 the second expression needs to be a constant.
7226 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
7227 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
7230 #include <isl/polynomial.h>
7231 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
7232 __isl_take isl_qpolynomial *qp1,
7233 __isl_take isl_qpolynomial *qp2);
7234 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
7235 __isl_take isl_pw_qpolynomial *pwqp1,
7236 __isl_take isl_pw_qpolynomial *pwqp2);
7237 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
7238 __isl_take isl_union_pw_qpolynomial *upwqp1,
7239 __isl_take isl_union_pw_qpolynomial *upwqp2);
7243 =head3 Lexicographic Optimization
7245 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
7246 the following functions
7247 compute a set that contains the lexicographic minimum or maximum
7248 of the elements in C<set> (or C<bset>) for those values of the parameters
7249 that satisfy C<dom>.
7250 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7251 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
7253 In other words, the union of the parameter values
7254 for which the result is non-empty and of C<*empty>
7257 #include <isl/set.h>
7258 __isl_give isl_set *isl_basic_set_partial_lexmin(
7259 __isl_take isl_basic_set *bset,
7260 __isl_take isl_basic_set *dom,
7261 __isl_give isl_set **empty);
7262 __isl_give isl_set *isl_basic_set_partial_lexmax(
7263 __isl_take isl_basic_set *bset,
7264 __isl_take isl_basic_set *dom,
7265 __isl_give isl_set **empty);
7266 __isl_give isl_set *isl_set_partial_lexmin(
7267 __isl_take isl_set *set, __isl_take isl_set *dom,
7268 __isl_give isl_set **empty);
7269 __isl_give isl_set *isl_set_partial_lexmax(
7270 __isl_take isl_set *set, __isl_take isl_set *dom,
7271 __isl_give isl_set **empty);
7273 Given a (basic) set C<set> (or C<bset>), the following functions simply
7274 return a set containing the lexicographic minimum or maximum
7275 of the elements in C<set> (or C<bset>).
7276 In case of union sets, the optimum is computed per space.
7278 #include <isl/set.h>
7279 __isl_give isl_set *isl_basic_set_lexmin(
7280 __isl_take isl_basic_set *bset);
7281 __isl_give isl_set *isl_basic_set_lexmax(
7282 __isl_take isl_basic_set *bset);
7283 __isl_give isl_set *isl_set_lexmin(
7284 __isl_take isl_set *set);
7285 __isl_give isl_set *isl_set_lexmax(
7286 __isl_take isl_set *set);
7287 __isl_give isl_union_set *isl_union_set_lexmin(
7288 __isl_take isl_union_set *uset);
7289 __isl_give isl_union_set *isl_union_set_lexmax(
7290 __isl_take isl_union_set *uset);
7292 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
7293 the following functions
7294 compute a relation that maps each element of C<dom>
7295 to the single lexicographic minimum or maximum
7296 of the elements that are associated to that same
7297 element in C<map> (or C<bmap>).
7298 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7299 that contains the elements in C<dom> that do not map
7300 to any elements in C<map> (or C<bmap>).
7301 In other words, the union of the domain of the result and of C<*empty>
7304 #include <isl/map.h>
7305 __isl_give isl_map *isl_basic_map_partial_lexmax(
7306 __isl_take isl_basic_map *bmap,
7307 __isl_take isl_basic_set *dom,
7308 __isl_give isl_set **empty);
7309 __isl_give isl_map *isl_basic_map_partial_lexmin(
7310 __isl_take isl_basic_map *bmap,
7311 __isl_take isl_basic_set *dom,
7312 __isl_give isl_set **empty);
7313 __isl_give isl_map *isl_map_partial_lexmax(
7314 __isl_take isl_map *map, __isl_take isl_set *dom,
7315 __isl_give isl_set **empty);
7316 __isl_give isl_map *isl_map_partial_lexmin(
7317 __isl_take isl_map *map, __isl_take isl_set *dom,
7318 __isl_give isl_set **empty);
7320 Given a (basic) map C<map> (or C<bmap>), the following functions simply
7321 return a map mapping each element in the domain of
7322 C<map> (or C<bmap>) to the lexicographic minimum or maximum
7323 of all elements associated to that element.
7324 In case of union relations, the optimum is computed per space.
7326 #include <isl/map.h>
7327 __isl_give isl_map *isl_basic_map_lexmin(
7328 __isl_take isl_basic_map *bmap);
7329 __isl_give isl_map *isl_basic_map_lexmax(
7330 __isl_take isl_basic_map *bmap);
7331 __isl_give isl_map *isl_map_lexmin(
7332 __isl_take isl_map *map);
7333 __isl_give isl_map *isl_map_lexmax(
7334 __isl_take isl_map *map);
7335 __isl_give isl_union_map *isl_union_map_lexmin(
7336 __isl_take isl_union_map *umap);
7337 __isl_give isl_union_map *isl_union_map_lexmax(
7338 __isl_take isl_union_map *umap);
7340 The following functions return their result in the form of
7341 a piecewise multi-affine expression,
7342 but are otherwise equivalent to the corresponding functions
7343 returning a basic set or relation.
7345 #include <isl/set.h>
7346 __isl_give isl_pw_multi_aff *
7347 isl_basic_set_partial_lexmin_pw_multi_aff(
7348 __isl_take isl_basic_set *bset,
7349 __isl_take isl_basic_set *dom,
7350 __isl_give isl_set **empty);
7351 __isl_give isl_pw_multi_aff *
7352 isl_basic_set_partial_lexmax_pw_multi_aff(
7353 __isl_take isl_basic_set *bset,
7354 __isl_take isl_basic_set *dom,
7355 __isl_give isl_set **empty);
7356 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
7357 __isl_take isl_set *set);
7358 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
7359 __isl_take isl_set *set);
7361 #include <isl/map.h>
7362 __isl_give isl_pw_multi_aff *
7363 isl_basic_map_lexmin_pw_multi_aff(
7364 __isl_take isl_basic_map *bmap);
7365 __isl_give isl_pw_multi_aff *
7366 isl_basic_map_partial_lexmin_pw_multi_aff(
7367 __isl_take isl_basic_map *bmap,
7368 __isl_take isl_basic_set *dom,
7369 __isl_give isl_set **empty);
7370 __isl_give isl_pw_multi_aff *
7371 isl_basic_map_partial_lexmax_pw_multi_aff(
7372 __isl_take isl_basic_map *bmap,
7373 __isl_take isl_basic_set *dom,
7374 __isl_give isl_set **empty);
7375 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
7376 __isl_take isl_map *map);
7377 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
7378 __isl_take isl_map *map);
7380 The following functions return the lexicographic minimum or maximum
7381 on the shared domain of the inputs and the single defined function
7382 on those parts of the domain where only a single function is defined.
7384 #include <isl/aff.h>
7385 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
7386 __isl_take isl_pw_multi_aff *pma1,
7387 __isl_take isl_pw_multi_aff *pma2);
7388 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
7389 __isl_take isl_pw_multi_aff *pma1,
7390 __isl_take isl_pw_multi_aff *pma2);
7392 If the input to a lexicographic optimization problem has
7393 multiple constraints with the same coefficients for the optimized
7394 variables, then, by default, this symmetry is exploited by
7395 replacing those constraints by a single constraint with
7396 an abstract bound, which is in turn bounded by the corresponding terms
7397 in the original constraints.
7398 Without this optimization, the solver would typically consider
7399 all possible orderings of those original bounds, resulting in a needless
7400 decomposition of the domain.
7401 However, the optimization can also result in slowdowns since
7402 an extra parameter is introduced that may get used in additional
7404 The following option determines whether symmetry detection is applied
7405 during lexicographic optimization.
7407 #include <isl/options.h>
7408 isl_stat isl_options_set_pip_symmetry(isl_ctx *ctx,
7410 int isl_options_get_pip_symmetry(isl_ctx *ctx);
7414 See also \autoref{s:offline}.
7418 =head2 Ternary Operations
7420 #include <isl/aff.h>
7421 __isl_give isl_pw_aff *isl_pw_aff_cond(
7422 __isl_take isl_pw_aff *cond,
7423 __isl_take isl_pw_aff *pwaff_true,
7424 __isl_take isl_pw_aff *pwaff_false);
7426 The function C<isl_pw_aff_cond> performs a conditional operator
7427 and returns an expression that is equal to C<pwaff_true>
7428 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
7429 where C<cond> is zero.
7433 Lists are defined over several element types, including
7434 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_union_pw_aff>,
7435 C<isl_union_pw_multi_aff>, C<isl_constraint>,
7436 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
7437 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
7438 Here we take lists of C<isl_set>s as an example.
7439 Lists can be created, copied, modified and freed using the following functions.
7441 #include <isl/set.h>
7442 __isl_give isl_set_list *isl_set_list_from_set(
7443 __isl_take isl_set *el);
7444 __isl_give isl_set_list *isl_set_list_alloc(
7445 isl_ctx *ctx, int n);
7446 __isl_give isl_set_list *isl_set_list_copy(
7447 __isl_keep isl_set_list *list);
7448 __isl_give isl_set_list *isl_set_list_insert(
7449 __isl_take isl_set_list *list, unsigned pos,
7450 __isl_take isl_set *el);
7451 __isl_give isl_set_list *isl_set_list_add(
7452 __isl_take isl_set_list *list,
7453 __isl_take isl_set *el);
7454 __isl_give isl_set_list *isl_set_list_drop(
7455 __isl_take isl_set_list *list,
7456 unsigned first, unsigned n);
7457 __isl_give isl_set_list *isl_set_list_set_set(
7458 __isl_take isl_set_list *list, int index,
7459 __isl_take isl_set *set);
7460 __isl_give isl_set_list *isl_set_list_concat(
7461 __isl_take isl_set_list *list1,
7462 __isl_take isl_set_list *list2);
7463 __isl_give isl_set_list *isl_set_list_sort(
7464 __isl_take isl_set_list *list,
7465 int (*cmp)(__isl_keep isl_set *a,
7466 __isl_keep isl_set *b, void *user),
7468 __isl_null isl_set_list *isl_set_list_free(
7469 __isl_take isl_set_list *list);
7471 C<isl_set_list_alloc> creates an empty list with an initial capacity
7472 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
7473 add elements to a list, increasing its capacity as needed.
7474 C<isl_set_list_from_set> creates a list with a single element.
7476 Lists can be inspected using the following functions.
7478 #include <isl/set.h>
7479 int isl_set_list_n_set(__isl_keep isl_set_list *list);
7480 __isl_give isl_set *isl_set_list_get_set(
7481 __isl_keep isl_set_list *list, int index);
7482 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list,
7483 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7485 isl_stat isl_set_list_foreach_scc(
7486 __isl_keep isl_set_list *list,
7487 isl_bool (*follows)(__isl_keep isl_set *a,
7488 __isl_keep isl_set *b, void *user),
7490 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7493 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
7494 strongly connected components of the graph with as vertices the elements
7495 of C<list> and a directed edge from vertex C<b> to vertex C<a>
7496 iff C<follows(a, b)> returns C<isl_bool_true>. The callbacks C<follows> and
7497 C<fn> should return C<isl_bool_error> or C<isl_stat_error> on error.
7499 Lists can be printed using
7501 #include <isl/set.h>
7502 __isl_give isl_printer *isl_printer_print_set_list(
7503 __isl_take isl_printer *p,
7504 __isl_keep isl_set_list *list);
7506 =head2 Associative arrays
7508 Associative arrays map isl objects of a specific type to isl objects
7509 of some (other) specific type. They are defined for several pairs
7510 of types, including (C<isl_map>, C<isl_basic_set>),
7511 (C<isl_id>, C<isl_ast_expr>),
7512 (C<isl_id>, C<isl_id>) and
7513 (C<isl_id>, C<isl_pw_aff>).
7514 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
7517 Associative arrays can be created, copied and freed using
7518 the following functions.
7520 #include <isl/id_to_ast_expr.h>
7521 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
7522 isl_ctx *ctx, int min_size);
7523 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
7524 __isl_keep isl_id_to_ast_expr *id2expr);
7525 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
7526 __isl_take isl_id_to_ast_expr *id2expr);
7528 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
7529 to specify the expected size of the associative array.
7530 The associative array will be grown automatically as needed.
7532 Associative arrays can be inspected using the following functions.
7534 #include <isl/id_to_ast_expr.h>
7535 __isl_give isl_maybe_isl_ast_expr
7536 isl_id_to_ast_expr_try_get(
7537 __isl_keep isl_id_to_ast_expr *id2expr,
7538 __isl_keep isl_id *key);
7539 isl_bool isl_id_to_ast_expr_has(
7540 __isl_keep isl_id_to_ast_expr *id2expr,
7541 __isl_keep isl_id *key);
7542 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
7543 __isl_keep isl_id_to_ast_expr *id2expr,
7544 __isl_take isl_id *key);
7545 isl_stat isl_id_to_ast_expr_foreach(
7546 __isl_keep isl_id_to_ast_expr *id2expr,
7547 isl_stat (*fn)(__isl_take isl_id *key,
7548 __isl_take isl_ast_expr *val, void *user),
7551 The function C<isl_id_to_ast_expr_try_get> returns a structure
7552 containing two elements, C<valid> and C<value>.
7553 If there is a value associated to the key, then C<valid>
7554 is set to C<isl_bool_true> and C<value> contains a copy of
7555 the associated value. Otherwise C<value> is C<NULL> and
7556 C<valid> may be C<isl_bool_error> or C<isl_bool_false> depending
7557 on whether some error has occurred or there simply is no associated value.
7558 The function C<isl_id_to_ast_expr_has> returns the C<valid> field
7559 in the structure and
7560 the function C<isl_id_to_ast_expr_get> returns the C<value> field.
7562 Associative arrays can be modified using the following functions.
7564 #include <isl/id_to_ast_expr.h>
7565 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
7566 __isl_take isl_id_to_ast_expr *id2expr,
7567 __isl_take isl_id *key,
7568 __isl_take isl_ast_expr *val);
7569 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
7570 __isl_take isl_id_to_ast_expr *id2expr,
7571 __isl_take isl_id *key);
7573 Associative arrays can be printed using the following function.
7575 #include <isl/id_to_ast_expr.h>
7576 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
7577 __isl_take isl_printer *p,
7578 __isl_keep isl_id_to_ast_expr *id2expr);
7582 Vectors can be created, copied and freed using the following functions.
7584 #include <isl/vec.h>
7585 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
7587 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
7588 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
7590 Note that the elements of a newly created vector may have arbitrary values.
7591 The elements can be changed and inspected using the following functions.
7593 int isl_vec_size(__isl_keep isl_vec *vec);
7594 __isl_give isl_val *isl_vec_get_element_val(
7595 __isl_keep isl_vec *vec, int pos);
7596 __isl_give isl_vec *isl_vec_set_element_si(
7597 __isl_take isl_vec *vec, int pos, int v);
7598 __isl_give isl_vec *isl_vec_set_element_val(
7599 __isl_take isl_vec *vec, int pos,
7600 __isl_take isl_val *v);
7601 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
7603 __isl_give isl_vec *isl_vec_set_val(
7604 __isl_take isl_vec *vec, __isl_take isl_val *v);
7605 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
7606 __isl_keep isl_vec *vec2, int pos);
7608 C<isl_vec_get_element> will return a negative value if anything went wrong.
7609 In that case, the value of C<*v> is undefined.
7611 The following function can be used to concatenate two vectors.
7613 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
7614 __isl_take isl_vec *vec2);
7618 Matrices can be created, copied and freed using the following functions.
7620 #include <isl/mat.h>
7621 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
7622 unsigned n_row, unsigned n_col);
7623 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
7624 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
7626 Note that the elements of a newly created matrix may have arbitrary values.
7627 The elements can be changed and inspected using the following functions.
7629 int isl_mat_rows(__isl_keep isl_mat *mat);
7630 int isl_mat_cols(__isl_keep isl_mat *mat);
7631 __isl_give isl_val *isl_mat_get_element_val(
7632 __isl_keep isl_mat *mat, int row, int col);
7633 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
7634 int row, int col, int v);
7635 __isl_give isl_mat *isl_mat_set_element_val(
7636 __isl_take isl_mat *mat, int row, int col,
7637 __isl_take isl_val *v);
7639 C<isl_mat_get_element> will return a negative value if anything went wrong.
7640 In that case, the value of C<*v> is undefined.
7642 The following function can be used to compute the (right) inverse
7643 of a matrix, i.e., a matrix such that the product of the original
7644 and the inverse (in that order) is a multiple of the identity matrix.
7645 The input matrix is assumed to be of full row-rank.
7647 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
7649 The following function can be used to compute the (right) kernel
7650 (or null space) of a matrix, i.e., a matrix such that the product of
7651 the original and the kernel (in that order) is the zero matrix.
7653 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
7655 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
7657 The following functions determine
7658 an upper or lower bound on a quasipolynomial over its domain.
7660 __isl_give isl_pw_qpolynomial_fold *
7661 isl_pw_qpolynomial_bound(
7662 __isl_take isl_pw_qpolynomial *pwqp,
7663 enum isl_fold type, int *tight);
7665 __isl_give isl_union_pw_qpolynomial_fold *
7666 isl_union_pw_qpolynomial_bound(
7667 __isl_take isl_union_pw_qpolynomial *upwqp,
7668 enum isl_fold type, int *tight);
7670 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
7671 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
7672 is the returned bound is known be tight, i.e., for each value
7673 of the parameters there is at least
7674 one element in the domain that reaches the bound.
7675 If the domain of C<pwqp> is not wrapping, then the bound is computed
7676 over all elements in that domain and the result has a purely parametric
7677 domain. If the domain of C<pwqp> is wrapping, then the bound is
7678 computed over the range of the wrapped relation. The domain of the
7679 wrapped relation becomes the domain of the result.
7681 =head2 Parametric Vertex Enumeration
7683 The parametric vertex enumeration described in this section
7684 is mainly intended to be used internally and by the C<barvinok>
7687 #include <isl/vertices.h>
7688 __isl_give isl_vertices *isl_basic_set_compute_vertices(
7689 __isl_keep isl_basic_set *bset);
7691 The function C<isl_basic_set_compute_vertices> performs the
7692 actual computation of the parametric vertices and the chamber
7693 decomposition and stores the result in an C<isl_vertices> object.
7694 This information can be queried by either iterating over all
7695 the vertices or iterating over all the chambers or cells
7696 and then iterating over all vertices that are active on the chamber.
7698 isl_stat isl_vertices_foreach_vertex(
7699 __isl_keep isl_vertices *vertices,
7700 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7701 void *user), void *user);
7703 isl_stat isl_vertices_foreach_cell(
7704 __isl_keep isl_vertices *vertices,
7705 isl_stat (*fn)(__isl_take isl_cell *cell,
7706 void *user), void *user);
7707 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
7708 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7709 void *user), void *user);
7711 Other operations that can be performed on an C<isl_vertices> object are
7714 int isl_vertices_get_n_vertices(
7715 __isl_keep isl_vertices *vertices);
7716 __isl_null isl_vertices *isl_vertices_free(
7717 __isl_take isl_vertices *vertices);
7719 Vertices can be inspected and destroyed using the following functions.
7721 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
7722 __isl_give isl_basic_set *isl_vertex_get_domain(
7723 __isl_keep isl_vertex *vertex);
7724 __isl_give isl_multi_aff *isl_vertex_get_expr(
7725 __isl_keep isl_vertex *vertex);
7726 void isl_vertex_free(__isl_take isl_vertex *vertex);
7728 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
7729 describing the vertex in terms of the parameters,
7730 while C<isl_vertex_get_domain> returns the activity domain
7733 Chambers can be inspected and destroyed using the following functions.
7735 __isl_give isl_basic_set *isl_cell_get_domain(
7736 __isl_keep isl_cell *cell);
7737 void isl_cell_free(__isl_take isl_cell *cell);
7739 =head1 Polyhedral Compilation Library
7741 This section collects functionality in C<isl> that has been specifically
7742 designed for use during polyhedral compilation.
7744 =head2 Schedule Trees
7746 A schedule tree is a structured representation of a schedule,
7747 assigning a relative order to a set of domain elements.
7748 The relative order expressed by the schedule tree is
7749 defined recursively. In particular, the order between
7750 two domain elements is determined by the node that is closest
7751 to the root that refers to both elements and that orders them apart.
7752 Each node in the tree is of one of several types.
7753 The root node is always of type C<isl_schedule_node_domain>
7754 (or C<isl_schedule_node_extension>)
7755 and it describes the (extra) domain elements to which the schedule applies.
7756 The other types of nodes are as follows.
7760 =item C<isl_schedule_node_band>
7762 A band of schedule dimensions. Each schedule dimension is represented
7763 by a union piecewise quasi-affine expression. If this expression
7764 assigns a different value to two domain elements, while all previous
7765 schedule dimensions in the same band assign them the same value,
7766 then the two domain elements are ordered according to these two
7768 Each expression is required to be total in the domain elements
7769 that reach the band node.
7771 =item C<isl_schedule_node_expansion>
7773 An expansion node maps each of the domain elements that reach the node
7774 to one or more domain elements. The image of this mapping forms
7775 the set of domain elements that reach the child of the expansion node.
7776 The function that maps each of the expanded domain elements
7777 to the original domain element from which it was expanded
7778 is called the contraction.
7780 =item C<isl_schedule_node_filter>
7782 A filter node does not impose any ordering, but rather intersects
7783 the set of domain elements that the current subtree refers to
7784 with a given union set. The subtree of the filter node only
7785 refers to domain elements in the intersection.
7786 A filter node is typically only used as a child of a sequence or
7789 =item C<isl_schedule_node_leaf>
7791 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
7793 =item C<isl_schedule_node_mark>
7795 A mark node can be used to attach any kind of information to a subtree
7796 of the schedule tree.
7798 =item C<isl_schedule_node_sequence>
7800 A sequence node has one or more children, each of which is a filter node.
7801 The filters on these filter nodes form a partition of
7802 the domain elements that the current subtree refers to.
7803 If two domain elements appear in distinct filters then the sequence
7804 node orders them according to the child positions of the corresponding
7807 =item C<isl_schedule_node_set>
7809 A set node is similar to a sequence node, except that
7810 it expresses that domain elements appearing in distinct filters
7811 may have any order. The order of the children of a set node
7812 is therefore also immaterial.
7816 The following node types are only supported by the AST generator.
7820 =item C<isl_schedule_node_context>
7822 The context describes constraints on the parameters and
7823 the schedule dimensions of outer
7824 bands that the AST generator may assume to hold. It is also the only
7825 kind of node that may introduce additional parameters.
7826 The space of the context is that of the flat product of the outer
7827 band nodes. In particular, if there are no outer band nodes, then
7828 this space is the unnamed zero-dimensional space.
7829 Since a context node references the outer band nodes, any tree
7830 containing a context node is considered to be anchored.
7832 =item C<isl_schedule_node_extension>
7834 An extension node instructs the AST generator to add additional
7835 domain elements that need to be scheduled.
7836 The additional domain elements are described by the range of
7837 the extension map in terms of the outer schedule dimensions,
7838 i.e., the flat product of the outer band nodes.
7839 Note that domain elements are added whenever the AST generator
7840 reaches the extension node, meaning that there are still some
7841 active domain elements for which an AST needs to be generated.
7842 The conditions under which some domain elements are still active
7843 may however not be completely described by the outer AST nodes
7844 generated at that point.
7846 An extension node may also appear as the root of a schedule tree,
7847 when it is intended to be inserted into another tree
7848 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
7849 In this case, the domain of the extension node should
7850 correspond to the flat product of the outer band nodes
7851 in this other schedule tree at the point where the extension tree
7854 =item C<isl_schedule_node_guard>
7856 The guard describes constraints on the parameters and
7857 the schedule dimensions of outer
7858 bands that need to be enforced by the outer nodes
7859 in the generated AST.
7860 The space of the guard is that of the flat product of the outer
7861 band nodes. In particular, if there are no outer band nodes, then
7862 this space is the unnamed zero-dimensional space.
7863 Since a guard node references the outer band nodes, any tree
7864 containing a guard node is considered to be anchored.
7868 Except for the C<isl_schedule_node_context> nodes,
7869 none of the nodes may introduce any parameters that were not
7870 already present in the root domain node.
7872 A schedule tree is encapsulated in an C<isl_schedule> object.
7873 The simplest such objects, those with a tree consisting of single domain node,
7874 can be created using the following functions with either an empty
7875 domain or a given domain.
7877 #include <isl/schedule.h>
7878 __isl_give isl_schedule *isl_schedule_empty(
7879 __isl_take isl_space *space);
7880 __isl_give isl_schedule *isl_schedule_from_domain(
7881 __isl_take isl_union_set *domain);
7883 The function C<isl_schedule_constraints_compute_schedule> described
7884 in L</"Scheduling"> can also be used to construct schedules.
7886 C<isl_schedule> objects may be copied and freed using the following functions.
7888 #include <isl/schedule.h>
7889 __isl_give isl_schedule *isl_schedule_copy(
7890 __isl_keep isl_schedule *sched);
7891 __isl_null isl_schedule *isl_schedule_free(
7892 __isl_take isl_schedule *sched);
7894 The following functions checks whether two C<isl_schedule> objects
7895 are obviously the same.
7897 #include <isl/schedule.h>
7898 isl_bool isl_schedule_plain_is_equal(
7899 __isl_keep isl_schedule *schedule1,
7900 __isl_keep isl_schedule *schedule2);
7902 The domain of the schedule, i.e., the domain described by the root node,
7903 can be obtained using the following function.
7905 #include <isl/schedule.h>
7906 __isl_give isl_union_set *isl_schedule_get_domain(
7907 __isl_keep isl_schedule *schedule);
7909 An extra top-level band node (right underneath the domain node) can
7910 be introduced into the schedule using the following function.
7911 The schedule tree is assumed not to have any anchored nodes.
7913 #include <isl/schedule.h>
7914 __isl_give isl_schedule *
7915 isl_schedule_insert_partial_schedule(
7916 __isl_take isl_schedule *schedule,
7917 __isl_take isl_multi_union_pw_aff *partial);
7919 A top-level context node (right underneath the domain node) can
7920 be introduced into the schedule using the following function.
7922 #include <isl/schedule.h>
7923 __isl_give isl_schedule *isl_schedule_insert_context(
7924 __isl_take isl_schedule *schedule,
7925 __isl_take isl_set *context)
7927 A top-level guard node (right underneath the domain node) can
7928 be introduced into the schedule using the following function.
7930 #include <isl/schedule.h>
7931 __isl_give isl_schedule *isl_schedule_insert_guard(
7932 __isl_take isl_schedule *schedule,
7933 __isl_take isl_set *guard)
7935 A schedule that combines two schedules either in the given
7936 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
7937 or an C<isl_schedule_node_set> node,
7938 can be created using the following functions.
7940 #include <isl/schedule.h>
7941 __isl_give isl_schedule *isl_schedule_sequence(
7942 __isl_take isl_schedule *schedule1,
7943 __isl_take isl_schedule *schedule2);
7944 __isl_give isl_schedule *isl_schedule_set(
7945 __isl_take isl_schedule *schedule1,
7946 __isl_take isl_schedule *schedule2);
7948 The domains of the two input schedules need to be disjoint.
7950 The following function can be used to restrict the domain
7951 of a schedule with a domain node as root to be a subset of the given union set.
7952 This operation may remove nodes in the tree that have become
7955 #include <isl/schedule.h>
7956 __isl_give isl_schedule *isl_schedule_intersect_domain(
7957 __isl_take isl_schedule *schedule,
7958 __isl_take isl_union_set *domain);
7960 The following function can be used to simplify the domain
7961 of a schedule with a domain node as root with respect to the given
7964 #include <isl/schedule.h>
7965 __isl_give isl_schedule *isl_schedule_gist_domain_params(
7966 __isl_take isl_schedule *schedule,
7967 __isl_take isl_set *context);
7969 The following function resets the user pointers on all parameter
7970 and tuple identifiers referenced by the nodes of the given schedule.
7972 #include <isl/schedule.h>
7973 __isl_give isl_schedule *isl_schedule_reset_user(
7974 __isl_take isl_schedule *schedule);
7976 The following function aligns the parameters of all nodes
7977 in the given schedule to the given space.
7979 #include <isl/schedule.h>
7980 __isl_give isl_schedule *isl_schedule_align_params(
7981 __isl_take isl_schedule *schedule,
7982 __isl_take isl_space *space);
7984 The following function allows the user to plug in a given function
7985 in the iteration domains. The input schedule is not allowed to contain
7986 any expansion nodes.
7988 #include <isl/schedule.h>
7989 __isl_give isl_schedule *
7990 isl_schedule_pullback_union_pw_multi_aff(
7991 __isl_take isl_schedule *schedule,
7992 __isl_take isl_union_pw_multi_aff *upma);
7994 The following function can be used to plug in the schedule C<expansion>
7995 in the leaves of C<schedule>, where C<contraction> describes how
7996 the domain elements of C<expansion> map to the domain elements
7997 at the original leaves of C<schedule>.
7998 The resulting schedule will contain expansion nodes, unless
7999 C<contraction> is an identity function.
8001 #include <isl/schedule.h>
8002 __isl_give isl_schedule *isl_schedule_expand(
8003 __isl_take isl_schedule *schedule,
8004 __isl_take isl_union_pw_multi_aff *contraction,
8005 __isl_take isl_schedule *expansion);
8007 An C<isl_union_map> representation of the schedule can be obtained
8008 from an C<isl_schedule> using the following function.
8010 #include <isl/schedule.h>
8011 __isl_give isl_union_map *isl_schedule_get_map(
8012 __isl_keep isl_schedule *sched);
8014 The resulting relation encodes the same relative ordering as
8015 the schedule by mapping the domain elements to a common schedule space.
8016 If the schedule_separate_components option is set, then the order
8017 of the children of a set node is explicitly encoded in the result.
8018 If the tree contains any expansion nodes, then the relation
8019 is formulated in terms of the expanded domain elements.
8021 Schedules can be read from input using the following functions.
8023 #include <isl/schedule.h>
8024 __isl_give isl_schedule *isl_schedule_read_from_file(
8025 isl_ctx *ctx, FILE *input);
8026 __isl_give isl_schedule *isl_schedule_read_from_str(
8027 isl_ctx *ctx, const char *str);
8029 A representation of the schedule can be printed using
8031 #include <isl/schedule.h>
8032 __isl_give isl_printer *isl_printer_print_schedule(
8033 __isl_take isl_printer *p,
8034 __isl_keep isl_schedule *schedule);
8035 __isl_give char *isl_schedule_to_str(
8036 __isl_keep isl_schedule *schedule);
8038 C<isl_schedule_to_str> prints the schedule in flow format.
8040 The schedule tree can be traversed through the use of
8041 C<isl_schedule_node> objects that point to a particular
8042 position in the schedule tree. Whenever a C<isl_schedule_node>
8043 is use to modify a node in the schedule tree, the original schedule
8044 tree is left untouched and the modifications are performed to a copy
8045 of the tree. The returned C<isl_schedule_node> then points to
8046 this modified copy of the tree.
8048 The root of the schedule tree can be obtained using the following function.
8050 #include <isl/schedule.h>
8051 __isl_give isl_schedule_node *isl_schedule_get_root(
8052 __isl_keep isl_schedule *schedule);
8054 A pointer to a newly created schedule tree with a single domain
8055 node can be created using the following functions.
8057 #include <isl/schedule_node.h>
8058 __isl_give isl_schedule_node *
8059 isl_schedule_node_from_domain(
8060 __isl_take isl_union_set *domain);
8061 __isl_give isl_schedule_node *
8062 isl_schedule_node_from_extension(
8063 __isl_take isl_union_map *extension);
8065 C<isl_schedule_node_from_extension> creates a tree with an extension
8068 Schedule nodes can be copied and freed using the following functions.
8070 #include <isl/schedule_node.h>
8071 __isl_give isl_schedule_node *isl_schedule_node_copy(
8072 __isl_keep isl_schedule_node *node);
8073 __isl_null isl_schedule_node *isl_schedule_node_free(
8074 __isl_take isl_schedule_node *node);
8076 The following functions can be used to check if two schedule
8077 nodes point to the same position in the same schedule.
8079 #include <isl/schedule_node.h>
8080 isl_bool isl_schedule_node_is_equal(
8081 __isl_keep isl_schedule_node *node1,
8082 __isl_keep isl_schedule_node *node2);
8084 The following properties can be obtained from a schedule node.
8086 #include <isl/schedule_node.h>
8087 enum isl_schedule_node_type isl_schedule_node_get_type(
8088 __isl_keep isl_schedule_node *node);
8089 enum isl_schedule_node_type
8090 isl_schedule_node_get_parent_type(
8091 __isl_keep isl_schedule_node *node);
8092 __isl_give isl_schedule *isl_schedule_node_get_schedule(
8093 __isl_keep isl_schedule_node *node);
8095 The function C<isl_schedule_node_get_type> returns the type of
8096 the node, while C<isl_schedule_node_get_parent_type> returns
8097 type of the parent of the node, which is required to exist.
8098 The function C<isl_schedule_node_get_schedule> returns a copy
8099 to the schedule to which the node belongs.
8101 The following functions can be used to move the schedule node
8102 to a different position in the tree or to check if such a position
8105 #include <isl/schedule_node.h>
8106 isl_bool isl_schedule_node_has_parent(
8107 __isl_keep isl_schedule_node *node);
8108 __isl_give isl_schedule_node *isl_schedule_node_parent(
8109 __isl_take isl_schedule_node *node);
8110 __isl_give isl_schedule_node *isl_schedule_node_root(
8111 __isl_take isl_schedule_node *node);
8112 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
8113 __isl_take isl_schedule_node *node,
8115 int isl_schedule_node_n_children(
8116 __isl_keep isl_schedule_node *node);
8117 __isl_give isl_schedule_node *isl_schedule_node_child(
8118 __isl_take isl_schedule_node *node, int pos);
8119 isl_bool isl_schedule_node_has_children(
8120 __isl_keep isl_schedule_node *node);
8121 __isl_give isl_schedule_node *isl_schedule_node_first_child(
8122 __isl_take isl_schedule_node *node);
8123 isl_bool isl_schedule_node_has_previous_sibling(
8124 __isl_keep isl_schedule_node *node);
8125 __isl_give isl_schedule_node *
8126 isl_schedule_node_previous_sibling(
8127 __isl_take isl_schedule_node *node);
8128 isl_bool isl_schedule_node_has_next_sibling(
8129 __isl_keep isl_schedule_node *node);
8130 __isl_give isl_schedule_node *
8131 isl_schedule_node_next_sibling(
8132 __isl_take isl_schedule_node *node);
8134 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
8135 is the node itself, the ancestor of generation 1 is its parent and so on.
8137 It is also possible to query the number of ancestors of a node,
8138 the position of the current node
8139 within the children of its parent, the position of the subtree
8140 containing a node within the children of an ancestor
8141 or to obtain a copy of a given
8142 child without destroying the current node.
8143 Given two nodes that point to the same schedule, their closest
8144 shared ancestor can be obtained using
8145 C<isl_schedule_node_get_shared_ancestor>.
8147 #include <isl/schedule_node.h>
8148 int isl_schedule_node_get_tree_depth(
8149 __isl_keep isl_schedule_node *node);
8150 int isl_schedule_node_get_child_position(
8151 __isl_keep isl_schedule_node *node);
8152 int isl_schedule_node_get_ancestor_child_position(
8153 __isl_keep isl_schedule_node *node,
8154 __isl_keep isl_schedule_node *ancestor);
8155 __isl_give isl_schedule_node *isl_schedule_node_get_child(
8156 __isl_keep isl_schedule_node *node, int pos);
8157 __isl_give isl_schedule_node *
8158 isl_schedule_node_get_shared_ancestor(
8159 __isl_keep isl_schedule_node *node1,
8160 __isl_keep isl_schedule_node *node2);
8162 All nodes in a schedule tree or
8163 all descendants of a specific node (including the node) can be visited
8164 in depth-first pre-order using the following functions.
8166 #include <isl/schedule.h>
8167 isl_stat isl_schedule_foreach_schedule_node_top_down(
8168 __isl_keep isl_schedule *sched,
8169 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8170 void *user), void *user);
8172 #include <isl/schedule_node.h>
8173 isl_stat isl_schedule_node_foreach_descendant_top_down(
8174 __isl_keep isl_schedule_node *node,
8175 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8176 void *user), void *user);
8178 The callback function is slightly different from the usual
8179 callbacks in that it not only indicates success (non-negative result)
8180 or failure (negative result), but also indicates whether the children
8181 of the given node should be visited. In particular, if the callback
8182 returns a positive value, then the children are visited, but if
8183 the callback returns zero, then the children are not visited.
8185 The ancestors of a node in a schedule tree can be visited from
8186 the root down to and including the parent of the node using
8187 the following function.
8189 #include <isl/schedule_node.h>
8190 isl_stat isl_schedule_node_foreach_ancestor_top_down(
8191 __isl_keep isl_schedule_node *node,
8192 isl_stat (*fn)(__isl_keep isl_schedule_node *node,
8193 void *user), void *user);
8195 The following functions allows for a depth-first post-order
8196 traversal of the nodes in a schedule tree or
8197 of the descendants of a specific node (including the node
8198 itself), where the user callback is allowed to modify the
8201 #include <isl/schedule.h>
8202 __isl_give isl_schedule *
8203 isl_schedule_map_schedule_node_bottom_up(
8204 __isl_take isl_schedule *schedule,
8205 __isl_give isl_schedule_node *(*fn)(
8206 __isl_take isl_schedule_node *node,
8207 void *user), void *user);
8209 #include <isl/schedule_node.h>
8210 __isl_give isl_schedule_node *
8211 isl_schedule_node_map_descendant_bottom_up(
8212 __isl_take isl_schedule_node *node,
8213 __isl_give isl_schedule_node *(*fn)(
8214 __isl_take isl_schedule_node *node,
8215 void *user), void *user);
8217 The traversal continues from the node returned by the callback function.
8218 It is the responsibility of the user to ensure that this does not
8219 lead to an infinite loop. It is safest to always return a pointer
8220 to the same position (same ancestors and child positions) as the input node.
8222 The following function removes a node (along with its descendants)
8223 from a schedule tree and returns a pointer to the leaf at the
8224 same position in the updated tree.
8225 It is not allowed to remove the root of a schedule tree or
8226 a child of a set or sequence node.
8228 #include <isl/schedule_node.h>
8229 __isl_give isl_schedule_node *isl_schedule_node_cut(
8230 __isl_take isl_schedule_node *node);
8232 The following function removes a single node
8233 from a schedule tree and returns a pointer to the child
8234 of the node, now located at the position of the original node
8235 or to a leaf node at that position if there was no child.
8236 It is not allowed to remove the root of a schedule tree,
8237 a set or sequence node, a child of a set or sequence node or
8238 a band node with an anchored subtree.
8240 #include <isl/schedule_node.h>
8241 __isl_give isl_schedule_node *isl_schedule_node_delete(
8242 __isl_take isl_schedule_node *node);
8244 Most nodes in a schedule tree only contain local information.
8245 In some cases, however, a node may also refer to the schedule dimensions
8246 of its outer band nodes.
8247 This means that the position of the node within the tree should
8248 not be changed, or at least that no changes are performed to the
8249 outer band nodes. The following function can be used to test
8250 whether the subtree rooted at a given node contains any such nodes.
8252 #include <isl/schedule_node.h>
8253 isl_bool isl_schedule_node_is_subtree_anchored(
8254 __isl_keep isl_schedule_node *node);
8256 The following function resets the user pointers on all parameter
8257 and tuple identifiers referenced by the given schedule node.
8259 #include <isl/schedule_node.h>
8260 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
8261 __isl_take isl_schedule_node *node);
8263 The following function aligns the parameters of the given schedule
8264 node to the given space.
8266 #include <isl/schedule_node.h>
8267 __isl_give isl_schedule_node *
8268 isl_schedule_node_align_params(
8269 __isl_take isl_schedule_node *node,
8270 __isl_take isl_space *space);
8272 Several node types have their own functions for querying
8273 (and in some cases setting) some node type specific properties.
8275 #include <isl/schedule_node.h>
8276 __isl_give isl_space *isl_schedule_node_band_get_space(
8277 __isl_keep isl_schedule_node *node);
8278 __isl_give isl_multi_union_pw_aff *
8279 isl_schedule_node_band_get_partial_schedule(
8280 __isl_keep isl_schedule_node *node);
8281 __isl_give isl_union_map *
8282 isl_schedule_node_band_get_partial_schedule_union_map(
8283 __isl_keep isl_schedule_node *node);
8284 unsigned isl_schedule_node_band_n_member(
8285 __isl_keep isl_schedule_node *node);
8286 isl_bool isl_schedule_node_band_member_get_coincident(
8287 __isl_keep isl_schedule_node *node, int pos);
8288 __isl_give isl_schedule_node *
8289 isl_schedule_node_band_member_set_coincident(
8290 __isl_take isl_schedule_node *node, int pos,
8292 isl_bool isl_schedule_node_band_get_permutable(
8293 __isl_keep isl_schedule_node *node);
8294 __isl_give isl_schedule_node *
8295 isl_schedule_node_band_set_permutable(
8296 __isl_take isl_schedule_node *node, int permutable);
8297 enum isl_ast_loop_type
8298 isl_schedule_node_band_member_get_ast_loop_type(
8299 __isl_keep isl_schedule_node *node, int pos);
8300 __isl_give isl_schedule_node *
8301 isl_schedule_node_band_member_set_ast_loop_type(
8302 __isl_take isl_schedule_node *node, int pos,
8303 enum isl_ast_loop_type type);
8304 __isl_give isl_union_set *
8305 enum isl_ast_loop_type
8306 isl_schedule_node_band_member_get_isolate_ast_loop_type(
8307 __isl_keep isl_schedule_node *node, int pos);
8308 __isl_give isl_schedule_node *
8309 isl_schedule_node_band_member_set_isolate_ast_loop_type(
8310 __isl_take isl_schedule_node *node, int pos,
8311 enum isl_ast_loop_type type);
8312 isl_schedule_node_band_get_ast_build_options(
8313 __isl_keep isl_schedule_node *node);
8314 __isl_give isl_schedule_node *
8315 isl_schedule_node_band_set_ast_build_options(
8316 __isl_take isl_schedule_node *node,
8317 __isl_take isl_union_set *options);
8318 __isl_give isl_set *
8319 isl_schedule_node_band_get_ast_isolate_option(
8320 __isl_keep isl_schedule_node *node);
8322 The function C<isl_schedule_node_band_get_space> returns the space
8323 of the partial schedule of the band.
8324 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
8325 returns a representation of the partial schedule of the band node
8326 in the form of an C<isl_union_map>.
8327 The coincident and permutable properties are set by
8328 C<isl_schedule_constraints_compute_schedule> on the schedule tree
8330 A scheduling dimension is considered to be ``coincident''
8331 if it satisfies the coincidence constraints within its band.
8332 That is, if the dependence distances of the coincidence
8333 constraints are all zero in that direction (for fixed
8334 iterations of outer bands).
8335 A band is marked permutable if it was produced using the Pluto-like scheduler.
8336 Note that the scheduler may have to resort to a Feautrier style scheduling
8337 step even if the default scheduler is used.
8338 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
8339 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
8340 For the meaning of these loop AST generation types and the difference
8341 between the regular loop AST generation type and the isolate
8342 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
8343 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
8344 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
8345 may return C<isl_ast_loop_error> if an error occurs.
8346 The AST build options govern how an AST is generated for
8347 the individual schedule dimensions during AST generation.
8348 See L</"AST Generation Options (Schedule Tree)">.
8349 The isolate option for the given node can be extracted from these
8350 AST build options using the function
8351 C<isl_schedule_node_band_get_ast_isolate_option>.
8353 #include <isl/schedule_node.h>
8354 __isl_give isl_set *
8355 isl_schedule_node_context_get_context(
8356 __isl_keep isl_schedule_node *node);
8358 #include <isl/schedule_node.h>
8359 __isl_give isl_union_set *
8360 isl_schedule_node_domain_get_domain(
8361 __isl_keep isl_schedule_node *node);
8363 #include <isl/schedule_node.h>
8364 __isl_give isl_union_map *
8365 isl_schedule_node_expansion_get_expansion(
8366 __isl_keep isl_schedule_node *node);
8367 __isl_give isl_union_pw_multi_aff *
8368 isl_schedule_node_expansion_get_contraction(
8369 __isl_keep isl_schedule_node *node);
8371 #include <isl/schedule_node.h>
8372 __isl_give isl_union_map *
8373 isl_schedule_node_extension_get_extension(
8374 __isl_keep isl_schedule_node *node);
8376 #include <isl/schedule_node.h>
8377 __isl_give isl_union_set *
8378 isl_schedule_node_filter_get_filter(
8379 __isl_keep isl_schedule_node *node);
8381 #include <isl/schedule_node.h>
8382 __isl_give isl_set *isl_schedule_node_guard_get_guard(
8383 __isl_keep isl_schedule_node *node);
8385 #include <isl/schedule_node.h>
8386 __isl_give isl_id *isl_schedule_node_mark_get_id(
8387 __isl_keep isl_schedule_node *node);
8389 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
8390 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
8391 partial schedules related to the node.
8393 #include <isl/schedule_node.h>
8394 __isl_give isl_multi_union_pw_aff *
8395 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
8396 __isl_keep isl_schedule_node *node);
8397 __isl_give isl_union_pw_multi_aff *
8398 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
8399 __isl_keep isl_schedule_node *node);
8400 __isl_give isl_union_map *
8401 isl_schedule_node_get_prefix_schedule_union_map(
8402 __isl_keep isl_schedule_node *node);
8403 __isl_give isl_union_map *
8404 isl_schedule_node_get_prefix_schedule_relation(
8405 __isl_keep isl_schedule_node *node);
8406 __isl_give isl_union_map *
8407 isl_schedule_node_get_subtree_schedule_union_map(
8408 __isl_keep isl_schedule_node *node);
8410 In particular, the functions
8411 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
8412 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
8413 and C<isl_schedule_node_get_prefix_schedule_union_map>
8414 return a relative ordering on the domain elements that reach the given
8415 node determined by its ancestors.
8416 The function C<isl_schedule_node_get_prefix_schedule_relation>
8417 additionally includes the domain constraints in the result.
8418 The function C<isl_schedule_node_get_subtree_schedule_union_map>
8419 returns a representation of the partial schedule defined by the
8420 subtree rooted at the given node.
8421 If the tree contains any expansion nodes, then the subtree schedule
8422 is formulated in terms of the expanded domain elements.
8423 The tree passed to functions returning a prefix schedule
8424 may only contain extension nodes if these would not affect
8425 the result of these functions. That is, if one of the ancestors
8426 is an extension node, then all of the domain elements that were
8427 added by the extension node need to have been filtered out
8428 by filter nodes between the extension node and the input node.
8429 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
8430 may not contain in extension nodes in the selected subtree.
8432 The expansion/contraction defined by an entire subtree, combining
8433 the expansions/contractions
8434 on the expansion nodes in the subtree, can be obtained using
8435 the following functions.
8437 #include <isl/schedule_node.h>
8438 __isl_give isl_union_map *
8439 isl_schedule_node_get_subtree_expansion(
8440 __isl_keep isl_schedule_node *node);
8441 __isl_give isl_union_pw_multi_aff *
8442 isl_schedule_node_get_subtree_contraction(
8443 __isl_keep isl_schedule_node *node);
8445 The total number of outer band members of given node, i.e.,
8446 the shared output dimension of the maps in the result
8447 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
8448 using the following function.
8450 #include <isl/schedule_node.h>
8451 int isl_schedule_node_get_schedule_depth(
8452 __isl_keep isl_schedule_node *node);
8454 The following functions return the elements that reach the given node
8455 or the union of universes in the spaces that contain these elements.
8457 #include <isl/schedule_node.h>
8458 __isl_give isl_union_set *
8459 isl_schedule_node_get_domain(
8460 __isl_keep isl_schedule_node *node);
8461 __isl_give isl_union_set *
8462 isl_schedule_node_get_universe_domain(
8463 __isl_keep isl_schedule_node *node);
8465 The input tree of C<isl_schedule_node_get_domain>
8466 may only contain extension nodes if these would not affect
8467 the result of this function. That is, if one of the ancestors
8468 is an extension node, then all of the domain elements that were
8469 added by the extension node need to have been filtered out
8470 by filter nodes between the extension node and the input node.
8472 The following functions can be used to introduce additional nodes
8473 in the schedule tree. The new node is introduced at the point
8474 in the tree where the C<isl_schedule_node> points to and
8475 the results points to the new node.
8477 #include <isl/schedule_node.h>
8478 __isl_give isl_schedule_node *
8479 isl_schedule_node_insert_partial_schedule(
8480 __isl_take isl_schedule_node *node,
8481 __isl_take isl_multi_union_pw_aff *schedule);
8483 This function inserts a new band node with (the greatest integer
8484 part of) the given partial schedule.
8485 The subtree rooted at the given node is assumed not to have
8488 #include <isl/schedule_node.h>
8489 __isl_give isl_schedule_node *
8490 isl_schedule_node_insert_context(
8491 __isl_take isl_schedule_node *node,
8492 __isl_take isl_set *context);
8494 This function inserts a new context node with the given context constraints.
8496 #include <isl/schedule_node.h>
8497 __isl_give isl_schedule_node *
8498 isl_schedule_node_insert_filter(
8499 __isl_take isl_schedule_node *node,
8500 __isl_take isl_union_set *filter);
8502 This function inserts a new filter node with the given filter.
8503 If the original node already pointed to a filter node, then the
8504 two filter nodes are merged into one.
8506 #include <isl/schedule_node.h>
8507 __isl_give isl_schedule_node *
8508 isl_schedule_node_insert_guard(
8509 __isl_take isl_schedule_node *node,
8510 __isl_take isl_set *guard);
8512 This function inserts a new guard node with the given guard constraints.
8514 #include <isl/schedule_node.h>
8515 __isl_give isl_schedule_node *
8516 isl_schedule_node_insert_mark(
8517 __isl_take isl_schedule_node *node,
8518 __isl_take isl_id *mark);
8520 This function inserts a new mark node with the give mark identifier.
8522 #include <isl/schedule_node.h>
8523 __isl_give isl_schedule_node *
8524 isl_schedule_node_insert_sequence(
8525 __isl_take isl_schedule_node *node,
8526 __isl_take isl_union_set_list *filters);
8527 __isl_give isl_schedule_node *
8528 isl_schedule_node_insert_set(
8529 __isl_take isl_schedule_node *node,
8530 __isl_take isl_union_set_list *filters);
8532 These functions insert a new sequence or set node with the given
8533 filters as children.
8535 #include <isl/schedule_node.h>
8536 __isl_give isl_schedule_node *isl_schedule_node_group(
8537 __isl_take isl_schedule_node *node,
8538 __isl_take isl_id *group_id);
8540 This function introduces an expansion node in between the current
8541 node and its parent that expands instances of a space with tuple
8542 identifier C<group_id> to the original domain elements that reach
8543 the node. The group instances are identified by the prefix schedule
8544 of those domain elements. The ancestors of the node are adjusted
8545 to refer to the group instances instead of the original domain
8546 elements. The return value points to the same node in the updated
8547 schedule tree as the input node, i.e., to the child of the newly
8548 introduced expansion node. Grouping instances of different statements
8549 ensures that they will be treated as a single statement by the
8550 AST generator up to the point of the expansion node.
8552 The following function can be used to flatten a nested
8555 #include <isl/schedule_node.h>
8556 __isl_give isl_schedule_node *
8557 isl_schedule_node_sequence_splice_child(
8558 __isl_take isl_schedule_node *node, int pos);
8560 That is, given a sequence node C<node> that has another sequence node
8561 in its child at position C<pos> (in particular, the child of that filter
8562 node is a sequence node), attach the children of that other sequence
8563 node as children of C<node>, replacing the original child at position
8566 The partial schedule of a band node can be scaled (down) or reduced using
8567 the following functions.
8569 #include <isl/schedule_node.h>
8570 __isl_give isl_schedule_node *
8571 isl_schedule_node_band_scale(
8572 __isl_take isl_schedule_node *node,
8573 __isl_take isl_multi_val *mv);
8574 __isl_give isl_schedule_node *
8575 isl_schedule_node_band_scale_down(
8576 __isl_take isl_schedule_node *node,
8577 __isl_take isl_multi_val *mv);
8578 __isl_give isl_schedule_node *
8579 isl_schedule_node_band_mod(
8580 __isl_take isl_schedule_node *node,
8581 __isl_take isl_multi_val *mv);
8583 The spaces of the two arguments need to match.
8584 After scaling, the partial schedule is replaced by its greatest
8585 integer part to ensure that the schedule remains integral.
8587 The partial schedule of a band node can be shifted by an
8588 C<isl_multi_union_pw_aff> with a domain that is a superset
8589 of the domain of the partial schedule using
8590 the following function.
8592 #include <isl/schedule_node.h>
8593 __isl_give isl_schedule_node *
8594 isl_schedule_node_band_shift(
8595 __isl_take isl_schedule_node *node,
8596 __isl_take isl_multi_union_pw_aff *shift);
8598 A band node can be tiled using the following function.
8600 #include <isl/schedule_node.h>
8601 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
8602 __isl_take isl_schedule_node *node,
8603 __isl_take isl_multi_val *sizes);
8605 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
8607 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
8608 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
8610 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
8612 The C<isl_schedule_node_band_tile> function tiles
8613 the band using the given tile sizes inside its schedule.
8614 A new child band node is created to represent the point loops and it is
8615 inserted between the modified band and its children.
8616 The subtree rooted at the given node is assumed not to have
8618 The C<tile_scale_tile_loops> option specifies whether the tile
8619 loops iterators should be scaled by the tile sizes.
8620 If the C<tile_shift_point_loops> option is set, then the point loops
8621 are shifted to start at zero.
8623 A band node can be split into two nested band nodes
8624 using the following function.
8626 #include <isl/schedule_node.h>
8627 __isl_give isl_schedule_node *isl_schedule_node_band_split(
8628 __isl_take isl_schedule_node *node, int pos);
8630 The resulting outer band node contains the first C<pos> dimensions of
8631 the schedule of C<node> while the inner band contains the remaining dimensions.
8632 The schedules of the two band nodes live in anonymous spaces.
8633 The loop AST generation type options and the isolate option
8634 are split over the the two band nodes.
8636 A band node can be moved down to the leaves of the subtree rooted
8637 at the band node using the following function.
8639 #include <isl/schedule_node.h>
8640 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
8641 __isl_take isl_schedule_node *node);
8643 The subtree rooted at the given node is assumed not to have
8645 The result points to the node in the resulting tree that is in the same
8646 position as the node pointed to by C<node> in the original tree.
8648 #include <isl/schedule_node.h>
8649 __isl_give isl_schedule_node *
8650 isl_schedule_node_order_before(
8651 __isl_take isl_schedule_node *node,
8652 __isl_take isl_union_set *filter);
8653 __isl_give isl_schedule_node *
8654 isl_schedule_node_order_after(
8655 __isl_take isl_schedule_node *node,
8656 __isl_take isl_union_set *filter);
8658 These functions split the domain elements that reach C<node>
8659 into those that satisfy C<filter> and those that do not and
8660 arranges for the elements that do satisfy the filter to be
8661 executed before (in case of C<isl_schedule_node_order_before>)
8662 or after (in case of C<isl_schedule_node_order_after>)
8663 those that do not. The order is imposed by
8664 a sequence node, possibly reusing the grandparent of C<node>
8665 on two copies of the subtree attached to the original C<node>.
8666 Both copies are simplified with respect to their filter.
8668 Return a pointer to the copy of the subtree that does not
8669 satisfy C<filter>. If there is no such copy (because all
8670 reaching domain elements satisfy the filter), then return
8671 the original pointer.
8673 #include <isl/schedule_node.h>
8674 __isl_give isl_schedule_node *
8675 isl_schedule_node_graft_before(
8676 __isl_take isl_schedule_node *node,
8677 __isl_take isl_schedule_node *graft);
8678 __isl_give isl_schedule_node *
8679 isl_schedule_node_graft_after(
8680 __isl_take isl_schedule_node *node,
8681 __isl_take isl_schedule_node *graft);
8683 This function inserts the C<graft> tree into the tree containing C<node>
8684 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
8685 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
8686 The root node of C<graft>
8687 should be an extension node where the domain of the extension
8688 is the flat product of all outer band nodes of C<node>.
8689 The root node may also be a domain node.
8690 The elements of the domain or the range of the extension may not
8691 intersect with the domain elements that reach "node".
8692 The schedule tree of C<graft> may not be anchored.
8694 The schedule tree of C<node> is modified to include an extension node
8695 corresponding to the root node of C<graft> as a child of the original
8696 parent of C<node>. The original node that C<node> points to and the
8697 child of the root node of C<graft> are attached to this extension node
8698 through a sequence, with appropriate filters and with the child
8699 of C<graft> appearing before or after the original C<node>.
8701 If C<node> already appears inside a sequence that is the child of
8702 an extension node and if the spaces of the new domain elements
8703 do not overlap with those of the original domain elements,
8704 then that extension node is extended with the new extension
8705 rather than introducing a new segment of extension and sequence nodes.
8707 Return a pointer to the same node in the modified tree that
8708 C<node> pointed to in the original tree.
8710 A representation of the schedule node can be printed using
8712 #include <isl/schedule_node.h>
8713 __isl_give isl_printer *isl_printer_print_schedule_node(
8714 __isl_take isl_printer *p,
8715 __isl_keep isl_schedule_node *node);
8716 __isl_give char *isl_schedule_node_to_str(
8717 __isl_keep isl_schedule_node *node);
8719 C<isl_schedule_node_to_str> prints the schedule node in block format.
8721 =head2 Dependence Analysis
8723 C<isl> contains specialized functionality for performing
8724 array dataflow analysis. That is, given a I<sink> access relation
8725 and a collection of possible I<source> access relations,
8726 C<isl> can compute relations that describe
8727 for each iteration of the sink access, which iteration
8728 of which of the source access relations was the last
8729 to access the same data element before the given iteration
8731 The resulting dependence relations map source iterations
8732 to either the corresponding sink iterations or
8733 pairs of corresponding sink iterations and accessed data elements.
8734 To compute standard flow dependences, the sink should be
8735 a read, while the sources should be writes.
8736 If any of the source accesses are marked as being I<may>
8737 accesses, then there will be a (may) dependence from the last
8738 I<must> access B<and> from any I<may> access that follows
8739 this last I<must> access, but still precedes the sink access.
8740 Only dependences originating in a must access and without
8741 any may accesses between the must access and the sink access
8742 are considered to be must dependences.
8743 In particular, if I<all> sources are I<may> accesses,
8744 then memory based dependence analysis is performed.
8745 If, on the other hand, all sources are I<must> accesses,
8746 then value based dependence analysis is performed.
8748 =head3 High-level Interface
8750 A high-level interface to dependence analysis is provided
8751 by the following function.
8753 #include <isl/flow.h>
8754 __isl_give isl_union_flow *
8755 isl_union_access_info_compute_flow(
8756 __isl_take isl_union_access_info *access);
8758 The input C<isl_union_access_info> object describes the sink
8759 access relations, the source access relations and a schedule,
8760 while the output C<isl_union_flow> object describes
8761 the resulting dependence relations and the subsets of the
8762 sink relations for which no source was found.
8764 An C<isl_union_access_info> is created, modified, copied and freed using
8765 the following functions.
8767 #include <isl/flow.h>
8768 __isl_give isl_union_access_info *
8769 isl_union_access_info_from_sink(
8770 __isl_take isl_union_map *sink);
8771 __isl_give isl_union_access_info *
8772 isl_union_access_info_set_must_source(
8773 __isl_take isl_union_access_info *access,
8774 __isl_take isl_union_map *must_source);
8775 __isl_give isl_union_access_info *
8776 isl_union_access_info_set_may_source(
8777 __isl_take isl_union_access_info *access,
8778 __isl_take isl_union_map *may_source);
8779 __isl_give isl_union_access_info *
8780 isl_union_access_info_set_schedule(
8781 __isl_take isl_union_access_info *access,
8782 __isl_take isl_schedule *schedule);
8783 __isl_give isl_union_access_info *
8784 isl_union_access_info_set_schedule_map(
8785 __isl_take isl_union_access_info *access,
8786 __isl_take isl_union_map *schedule_map);
8787 __isl_give isl_union_access_info *
8788 isl_union_access_info_copy(
8789 __isl_keep isl_union_access_info *access);
8790 __isl_null isl_union_access_info *
8791 isl_union_access_info_free(
8792 __isl_take isl_union_access_info *access);
8794 The may sources set by C<isl_union_access_info_set_may_source>
8795 do not need to include the must sources set by
8796 C<isl_union_access_info_set_must_source> as a subset.
8797 The user is free not to call one (or both) of these functions,
8798 in which case the corresponding set is kept to its empty default.
8799 Similarly, the default schedule initialized by
8800 C<isl_union_access_info_from_sink> is empty.
8801 The current schedule is determined by the last call to either
8802 C<isl_union_access_info_set_schedule> or
8803 C<isl_union_access_info_set_schedule_map>.
8804 The domain of the schedule corresponds to the domains of
8805 the access relations. In particular, the domains of the access
8806 relations are effectively intersected with the domain of the schedule
8807 and only the resulting accesses are considered by the dependence analysis.
8809 A representation of the information contained in an object
8810 of type C<isl_union_access_info> can be obtained using
8812 #include <isl/flow.h>
8813 __isl_give isl_printer *
8814 isl_printer_print_union_access_info(
8815 __isl_take isl_printer *p,
8816 __isl_keep isl_union_access_info *access);
8817 __isl_give char *isl_union_access_info_to_str(
8818 __isl_keep isl_union_access_info *access);
8820 C<isl_union_access_info_to_str> prints the information in flow format.
8822 The output of C<isl_union_access_info_compute_flow> can be examined,
8823 copied, and freed using the following functions.
8825 #include <isl/flow.h>
8826 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
8827 __isl_keep isl_union_flow *flow);
8828 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
8829 __isl_keep isl_union_flow *flow);
8830 __isl_give isl_union_map *
8831 isl_union_flow_get_full_must_dependence(
8832 __isl_keep isl_union_flow *flow);
8833 __isl_give isl_union_map *
8834 isl_union_flow_get_full_may_dependence(
8835 __isl_keep isl_union_flow *flow);
8836 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
8837 __isl_keep isl_union_flow *flow);
8838 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
8839 __isl_keep isl_union_flow *flow);
8840 __isl_give isl_union_flow *isl_union_flow_copy(
8841 __isl_keep isl_union_flow *flow);
8842 __isl_null isl_union_flow *isl_union_flow_free(
8843 __isl_take isl_union_flow *flow);
8845 The relation returned by C<isl_union_flow_get_must_dependence>
8846 relates domain elements of must sources to domain elements of the sink.
8847 The relation returned by C<isl_union_flow_get_may_dependence>
8848 relates domain elements of must or may sources to domain elements of the sink
8849 and includes the previous relation as a subset.
8850 The relation returned by C<isl_union_flow_get_full_must_dependence>
8851 relates domain elements of must sources to pairs of domain elements of the sink
8852 and accessed data elements.
8853 The relation returned by C<isl_union_flow_get_full_may_dependence>
8854 relates domain elements of must or may sources to pairs of
8855 domain elements of the sink and accessed data elements.
8856 This relation includes the previous relation as a subset.
8857 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
8858 of the sink relation for which no dependences have been found.
8859 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
8860 of the sink relation for which no definite dependences have been found.
8861 That is, it contains those sink access that do not contribute to any
8862 of the elements in the relation returned
8863 by C<isl_union_flow_get_must_dependence>.
8865 A representation of the information contained in an object
8866 of type C<isl_union_flow> can be obtained using
8868 #include <isl/flow.h>
8869 __isl_give isl_printer *isl_printer_print_union_flow(
8870 __isl_take isl_printer *p,
8871 __isl_keep isl_union_flow *flow);
8872 __isl_give char *isl_union_flow_to_str(
8873 __isl_keep isl_union_flow *flow);
8875 C<isl_union_flow_to_str> prints the information in flow format.
8877 =head3 Low-level Interface
8879 A lower-level interface is provided by the following functions.
8881 #include <isl/flow.h>
8883 typedef int (*isl_access_level_before)(void *first, void *second);
8885 __isl_give isl_access_info *isl_access_info_alloc(
8886 __isl_take isl_map *sink,
8887 void *sink_user, isl_access_level_before fn,
8889 __isl_give isl_access_info *isl_access_info_add_source(
8890 __isl_take isl_access_info *acc,
8891 __isl_take isl_map *source, int must,
8893 __isl_null isl_access_info *isl_access_info_free(
8894 __isl_take isl_access_info *acc);
8896 __isl_give isl_flow *isl_access_info_compute_flow(
8897 __isl_take isl_access_info *acc);
8899 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,
8900 isl_stat (*fn)(__isl_take isl_map *dep, int must,
8901 void *dep_user, void *user),
8903 __isl_give isl_map *isl_flow_get_no_source(
8904 __isl_keep isl_flow *deps, int must);
8905 void isl_flow_free(__isl_take isl_flow *deps);
8907 The function C<isl_access_info_compute_flow> performs the actual
8908 dependence analysis. The other functions are used to construct
8909 the input for this function or to read off the output.
8911 The input is collected in an C<isl_access_info>, which can
8912 be created through a call to C<isl_access_info_alloc>.
8913 The arguments to this functions are the sink access relation
8914 C<sink>, a token C<sink_user> used to identify the sink
8915 access to the user, a callback function for specifying the
8916 relative order of source and sink accesses, and the number
8917 of source access relations that will be added.
8918 The callback function has type C<int (*)(void *first, void *second)>.
8919 The function is called with two user supplied tokens identifying
8920 either a source or the sink and it should return the shared nesting
8921 level and the relative order of the two accesses.
8922 In particular, let I<n> be the number of loops shared by
8923 the two accesses. If C<first> precedes C<second> textually,
8924 then the function should return I<2 * n + 1>; otherwise,
8925 it should return I<2 * n>.
8926 The sources can be added to the C<isl_access_info> by performing
8927 (at most) C<max_source> calls to C<isl_access_info_add_source>.
8928 C<must> indicates whether the source is a I<must> access
8929 or a I<may> access. Note that a multi-valued access relation
8930 should only be marked I<must> if every iteration in the domain
8931 of the relation accesses I<all> elements in its image.
8932 The C<source_user> token is again used to identify
8933 the source access. The range of the source access relation
8934 C<source> should have the same dimension as the range
8935 of the sink access relation.
8936 The C<isl_access_info_free> function should usually not be
8937 called explicitly, because it is called implicitly by
8938 C<isl_access_info_compute_flow>.
8940 The result of the dependence analysis is collected in an
8941 C<isl_flow>. There may be elements of
8942 the sink access for which no preceding source access could be
8943 found or for which all preceding sources are I<may> accesses.
8944 The relations containing these elements can be obtained through
8945 calls to C<isl_flow_get_no_source>, the first with C<must> set
8946 and the second with C<must> unset.
8947 In the case of standard flow dependence analysis,
8948 with the sink a read and the sources I<must> writes,
8949 the first relation corresponds to the reads from uninitialized
8950 array elements and the second relation is empty.
8951 The actual flow dependences can be extracted using
8952 C<isl_flow_foreach>. This function will call the user-specified
8953 callback function C<fn> for each B<non-empty> dependence between
8954 a source and the sink. The callback function is called
8955 with four arguments, the actual flow dependence relation
8956 mapping source iterations to sink iterations, a boolean that
8957 indicates whether it is a I<must> or I<may> dependence, a token
8958 identifying the source and an additional C<void *> with value
8959 equal to the third argument of the C<isl_flow_foreach> call.
8960 A dependence is marked I<must> if it originates from a I<must>
8961 source and if it is not followed by any I<may> sources.
8963 After finishing with an C<isl_flow>, the user should call
8964 C<isl_flow_free> to free all associated memory.
8966 =head3 Interaction with the Low-level Interface
8968 During the dependence analysis, we frequently need to perform
8969 the following operation. Given a relation between sink iterations
8970 and potential source iterations from a particular source domain,
8971 what is the last potential source iteration corresponding to each
8972 sink iteration. It can sometimes be convenient to adjust
8973 the set of potential source iterations before or after each such operation.
8974 The prototypical example is fuzzy array dataflow analysis,
8975 where we need to analyze if, based on data-dependent constraints,
8976 the sink iteration can ever be executed without one or more of
8977 the corresponding potential source iterations being executed.
8978 If so, we can introduce extra parameters and select an unknown
8979 but fixed source iteration from the potential source iterations.
8980 To be able to perform such manipulations, C<isl> provides the following
8983 #include <isl/flow.h>
8985 typedef __isl_give isl_restriction *(*isl_access_restrict)(
8986 __isl_keep isl_map *source_map,
8987 __isl_keep isl_set *sink, void *source_user,
8989 __isl_give isl_access_info *isl_access_info_set_restrict(
8990 __isl_take isl_access_info *acc,
8991 isl_access_restrict fn, void *user);
8993 The function C<isl_access_info_set_restrict> should be called
8994 before calling C<isl_access_info_compute_flow> and registers a callback function
8995 that will be called any time C<isl> is about to compute the last
8996 potential source. The first argument is the (reverse) proto-dependence,
8997 mapping sink iterations to potential source iterations.
8998 The second argument represents the sink iterations for which
8999 we want to compute the last source iteration.
9000 The third argument is the token corresponding to the source
9001 and the final argument is the token passed to C<isl_access_info_set_restrict>.
9002 The callback is expected to return a restriction on either the input or
9003 the output of the operation computing the last potential source.
9004 If the input needs to be restricted then restrictions are needed
9005 for both the source and the sink iterations. The sink iterations
9006 and the potential source iterations will be intersected with these sets.
9007 If the output needs to be restricted then only a restriction on the source
9008 iterations is required.
9009 If any error occurs, the callback should return C<NULL>.
9010 An C<isl_restriction> object can be created, freed and inspected
9011 using the following functions.
9013 #include <isl/flow.h>
9015 __isl_give isl_restriction *isl_restriction_input(
9016 __isl_take isl_set *source_restr,
9017 __isl_take isl_set *sink_restr);
9018 __isl_give isl_restriction *isl_restriction_output(
9019 __isl_take isl_set *source_restr);
9020 __isl_give isl_restriction *isl_restriction_none(
9021 __isl_take isl_map *source_map);
9022 __isl_give isl_restriction *isl_restriction_empty(
9023 __isl_take isl_map *source_map);
9024 __isl_null isl_restriction *isl_restriction_free(
9025 __isl_take isl_restriction *restr);
9027 C<isl_restriction_none> and C<isl_restriction_empty> are special
9028 cases of C<isl_restriction_input>. C<isl_restriction_none>
9029 is essentially equivalent to
9031 isl_restriction_input(isl_set_universe(
9032 isl_space_range(isl_map_get_space(source_map))),
9034 isl_space_domain(isl_map_get_space(source_map))));
9036 whereas C<isl_restriction_empty> is essentially equivalent to
9038 isl_restriction_input(isl_set_empty(
9039 isl_space_range(isl_map_get_space(source_map))),
9041 isl_space_domain(isl_map_get_space(source_map))));
9045 #include <isl/schedule.h>
9046 __isl_give isl_schedule *
9047 isl_schedule_constraints_compute_schedule(
9048 __isl_take isl_schedule_constraints *sc);
9050 The function C<isl_schedule_constraints_compute_schedule> can be
9051 used to compute a schedule that satisfies the given schedule constraints.
9052 These schedule constraints include the iteration domain for which
9053 a schedule should be computed and dependences between pairs of
9054 iterations. In particular, these dependences include
9055 I<validity> dependences and I<proximity> dependences.
9056 By default, the algorithm used to construct the schedule is similar
9057 to that of C<Pluto>.
9058 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
9060 The generated schedule respects all validity dependences.
9061 That is, all dependence distances over these dependences in the
9062 scheduled space are lexicographically positive.
9064 The default algorithm tries to ensure that the dependence distances
9065 over coincidence constraints are zero and to minimize the
9066 dependence distances over proximity dependences.
9067 Moreover, it tries to obtain sequences (bands) of schedule dimensions
9068 for groups of domains where the dependence distances over validity
9069 dependences have only non-negative values.
9070 Note that when minimizing the maximal dependence distance
9071 over proximity dependences, a single affine expression in the parameters
9072 is constructed that bounds all dependence distances. If no such expression
9073 exists, then the algorithm will fail and resort to an alternative
9074 scheduling algorithm. In particular, this means that adding proximity
9075 dependences may eliminate valid solutions. A typical example where this
9076 phenomenon may occur is when some subset of the proximity dependences
9077 has no restriction on some parameter, forcing the coefficient of that
9078 parameter to be zero, while some other subset forces the dependence
9079 distance to depend on that parameter, requiring the same coefficient
9081 When using Feautrier's algorithm, the coincidence and proximity constraints
9082 are only taken into account during the extension to a
9083 full-dimensional schedule.
9085 An C<isl_schedule_constraints> object can be constructed
9086 and manipulated using the following functions.
9088 #include <isl/schedule.h>
9089 __isl_give isl_schedule_constraints *
9090 isl_schedule_constraints_copy(
9091 __isl_keep isl_schedule_constraints *sc);
9092 __isl_give isl_schedule_constraints *
9093 isl_schedule_constraints_on_domain(
9094 __isl_take isl_union_set *domain);
9095 __isl_give isl_schedule_constraints *
9096 isl_schedule_constraints_set_context(
9097 __isl_take isl_schedule_constraints *sc,
9098 __isl_take isl_set *context);
9099 __isl_give isl_schedule_constraints *
9100 isl_schedule_constraints_set_validity(
9101 __isl_take isl_schedule_constraints *sc,
9102 __isl_take isl_union_map *validity);
9103 __isl_give isl_schedule_constraints *
9104 isl_schedule_constraints_set_coincidence(
9105 __isl_take isl_schedule_constraints *sc,
9106 __isl_take isl_union_map *coincidence);
9107 __isl_give isl_schedule_constraints *
9108 isl_schedule_constraints_set_proximity(
9109 __isl_take isl_schedule_constraints *sc,
9110 __isl_take isl_union_map *proximity);
9111 __isl_give isl_schedule_constraints *
9112 isl_schedule_constraints_set_conditional_validity(
9113 __isl_take isl_schedule_constraints *sc,
9114 __isl_take isl_union_map *condition,
9115 __isl_take isl_union_map *validity);
9116 __isl_give isl_schedule_constraints *
9117 isl_schedule_constraints_apply(
9118 __isl_take isl_schedule_constraints *sc,
9119 __isl_take isl_union_map *umap);
9120 __isl_null isl_schedule_constraints *
9121 isl_schedule_constraints_free(
9122 __isl_take isl_schedule_constraints *sc);
9124 The initial C<isl_schedule_constraints> object created by
9125 C<isl_schedule_constraints_on_domain> does not impose any constraints.
9126 That is, it has an empty set of dependences.
9127 The function C<isl_schedule_constraints_set_context> allows the user
9128 to specify additional constraints on the parameters that may
9129 be assumed to hold during the construction of the schedule.
9130 The function C<isl_schedule_constraints_set_validity> replaces the
9131 validity dependences, mapping domain elements I<i> to domain
9132 elements that should be scheduled after I<i>.
9133 The function C<isl_schedule_constraints_set_coincidence> replaces the
9134 coincidence dependences, mapping domain elements I<i> to domain
9135 elements that should be scheduled together with I<I>, if possible.
9136 The function C<isl_schedule_constraints_set_proximity> replaces the
9137 proximity dependences, mapping domain elements I<i> to domain
9138 elements that should be scheduled either before I<I>
9139 or as early as possible after I<i>.
9141 The function C<isl_schedule_constraints_set_conditional_validity>
9142 replaces the conditional validity constraints.
9143 A conditional validity constraint is only imposed when any of the corresponding
9144 conditions is satisfied, i.e., when any of them is non-zero.
9145 That is, the scheduler ensures that within each band if the dependence
9146 distances over the condition constraints are not all zero
9147 then all corresponding conditional validity constraints are respected.
9148 A conditional validity constraint corresponds to a condition
9149 if the two are adjacent, i.e., if the domain of one relation intersect
9150 the range of the other relation.
9151 The typical use case of conditional validity constraints is
9152 to allow order constraints between live ranges to be violated
9153 as long as the live ranges themselves are local to the band.
9154 To allow more fine-grained control over which conditions correspond
9155 to which conditional validity constraints, the domains and ranges
9156 of these relations may include I<tags>. That is, the domains and
9157 ranges of those relation may themselves be wrapped relations
9158 where the iteration domain appears in the domain of those wrapped relations
9159 and the range of the wrapped relations can be arbitrarily chosen
9160 by the user. Conditions and conditional validity constraints are only
9161 considered adjacent to each other if the entire wrapped relation matches.
9162 In particular, a relation with a tag will never be considered adjacent
9163 to a relation without a tag.
9165 The function C<isl_schedule_constraints_compute_schedule> takes
9166 schedule constraints that are defined on some set of domain elements
9167 and transforms them to schedule constraints on the elements
9168 to which these domain elements are mapped by the given transformation.
9170 An C<isl_schedule_constraints> object can be inspected
9171 using the following functions.
9173 #include <isl/schedule.h>
9174 __isl_give isl_union_set *
9175 isl_schedule_constraints_get_domain(
9176 __isl_keep isl_schedule_constraints *sc);
9177 __isl_give isl_set *isl_schedule_constraints_get_context(
9178 __isl_keep isl_schedule_constraints *sc);
9179 __isl_give isl_union_map *
9180 isl_schedule_constraints_get_validity(
9181 __isl_keep isl_schedule_constraints *sc);
9182 __isl_give isl_union_map *
9183 isl_schedule_constraints_get_coincidence(
9184 __isl_keep isl_schedule_constraints *sc);
9185 __isl_give isl_union_map *
9186 isl_schedule_constraints_get_proximity(
9187 __isl_keep isl_schedule_constraints *sc);
9188 __isl_give isl_union_map *
9189 isl_schedule_constraints_get_conditional_validity(
9190 __isl_keep isl_schedule_constraints *sc);
9191 __isl_give isl_union_map *
9192 isl_schedule_constraints_get_conditional_validity_condition(
9193 __isl_keep isl_schedule_constraints *sc);
9195 An C<isl_schedule_constraints> object can be read from input
9196 using the following functions.
9198 #include <isl/schedule.h>
9199 __isl_give isl_schedule_constraints *
9200 isl_schedule_constraints_read_from_str(isl_ctx *ctx,
9202 __isl_give isl_schedule_constraints *
9203 isl_schedule_constraints_read_from_file(isl_ctx *ctx,
9206 The contents of an C<isl_schedule_constraints> object can be printed
9207 using the following functions.
9209 #include <isl/schedule.h>
9210 __isl_give isl_printer *
9211 isl_printer_print_schedule_constraints(
9212 __isl_take isl_printer *p,
9213 __isl_keep isl_schedule_constraints *sc);
9214 __isl_give char *isl_schedule_constraints_to_str(
9215 __isl_keep isl_schedule_constraints *sc);
9217 The following function computes a schedule directly from
9218 an iteration domain and validity and proximity dependences
9219 and is implemented in terms of the functions described above.
9220 The use of C<isl_union_set_compute_schedule> is discouraged.
9222 #include <isl/schedule.h>
9223 __isl_give isl_schedule *isl_union_set_compute_schedule(
9224 __isl_take isl_union_set *domain,
9225 __isl_take isl_union_map *validity,
9226 __isl_take isl_union_map *proximity);
9228 The generated schedule represents a schedule tree.
9229 For more information on schedule trees, see
9230 L</"Schedule Trees">.
9234 #include <isl/schedule.h>
9235 isl_stat isl_options_set_schedule_max_coefficient(
9236 isl_ctx *ctx, int val);
9237 int isl_options_get_schedule_max_coefficient(
9239 isl_stat isl_options_set_schedule_max_constant_term(
9240 isl_ctx *ctx, int val);
9241 int isl_options_get_schedule_max_constant_term(
9243 isl_stat isl_options_set_schedule_serialize_sccs(
9244 isl_ctx *ctx, int val);
9245 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx);
9246 isl_stat isl_options_set_schedule_whole_component(
9247 isl_ctx *ctx, int val);
9248 int isl_options_get_schedule_whole_component(
9250 isl_stat isl_options_set_schedule_maximize_band_depth(
9251 isl_ctx *ctx, int val);
9252 int isl_options_get_schedule_maximize_band_depth(
9254 isl_stat isl_options_set_schedule_maximize_coincidence(
9255 isl_ctx *ctx, int val);
9256 int isl_options_get_schedule_maximize_coincidence(
9258 isl_stat isl_options_set_schedule_outer_coincidence(
9259 isl_ctx *ctx, int val);
9260 int isl_options_get_schedule_outer_coincidence(
9262 isl_stat isl_options_set_schedule_split_scaled(
9263 isl_ctx *ctx, int val);
9264 int isl_options_get_schedule_split_scaled(
9266 isl_stat isl_options_set_schedule_treat_coalescing(
9267 isl_ctx *ctx, int val);
9268 int isl_options_get_schedule_treat_coalescing(
9270 isl_stat isl_options_set_schedule_algorithm(
9271 isl_ctx *ctx, int val);
9272 int isl_options_get_schedule_algorithm(
9274 isl_stat isl_options_set_schedule_separate_components(
9275 isl_ctx *ctx, int val);
9276 int isl_options_get_schedule_separate_components(
9281 =item * schedule_max_coefficient
9283 This option enforces that the coefficients for variable and parameter
9284 dimensions in the calculated schedule are not larger than the specified value.
9285 This option can significantly increase the speed of the scheduling calculation
9286 and may also prevent fusing of unrelated dimensions. A value of -1 means that
9287 this option does not introduce bounds on the variable or parameter
9290 =item * schedule_max_constant_term
9292 This option enforces that the constant coefficients in the calculated schedule
9293 are not larger than the maximal constant term. This option can significantly
9294 increase the speed of the scheduling calculation and may also prevent fusing of
9295 unrelated dimensions. A value of -1 means that this option does not introduce
9296 bounds on the constant coefficients.
9298 =item * schedule_serialize_sccs
9300 If this option is set, then all strongly connected components
9301 in the dependence graph are serialized as soon as they are detected.
9302 This means in particular that instances of statements will only
9303 appear in the same band node if these statements belong
9304 to the same strongly connected component at the point where
9305 the band node is constructed.
9307 =item * schedule_whole_component
9309 If this option is set, then entire (weakly) connected
9310 components in the dependence graph are scheduled together
9312 Otherwise, each strongly connected component within
9313 such a weakly connected component is first scheduled separately
9314 and then combined with other strongly connected components.
9315 This option has no effect if C<schedule_serialize_sccs> is set.
9317 =item * schedule_maximize_band_depth
9319 If this option is set, then the scheduler tries to maximize
9320 the width of the bands. Wider bands give more possibilities for tiling.
9321 In particular, if the C<schedule_whole_component> option is set,
9322 then bands are split if this might result in wider bands.
9323 Otherwise, the effect of this option is to only allow
9324 strongly connected components to be combined if this does
9325 not reduce the width of the bands.
9326 Note that if the C<schedule_serialize_sccs> options is set, then
9327 the C<schedule_maximize_band_depth> option therefore has no effect.
9329 =item * schedule_maximize_coincidence
9331 This option is only effective if the C<schedule_whole_component>
9332 option is turned off.
9333 If the C<schedule_maximize_coincidence> option is set, then (clusters of)
9334 strongly connected components are only combined with each other
9335 if this does not reduce the number of coincident band members.
9337 =item * schedule_outer_coincidence
9339 If this option is set, then we try to construct schedules
9340 where the outermost scheduling dimension in each band
9341 satisfies the coincidence constraints.
9343 =item * schedule_algorithm
9345 Selects the scheduling algorithm to be used.
9346 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
9347 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
9349 =item * schedule_split_scaled
9351 If this option is set, then we try to construct schedules in which the
9352 constant term is split off from the linear part if the linear parts of
9353 the scheduling rows for all nodes in the graph have a common non-trivial
9355 The constant term is then placed in a separate band and the linear
9357 This option is only effective when the Feautrier style scheduler is
9358 being used, either as the main scheduler or as a fallback for the
9359 Pluto-like scheduler.
9361 =item * schedule_treat_coalescing
9363 If this option is set, then the scheduler will try and avoid
9364 producing schedules that perform loop coalescing.
9365 In particular, for the Pluto-like scheduler, this option places
9366 bounds on the schedule coefficients based on the sizes of the instance sets.
9367 For the Feautrier style scheduler, this option detects potentially
9368 coalescing schedules and then tries to adjust the schedule to avoid
9371 =item * schedule_separate_components
9373 If this option is set then the function C<isl_schedule_get_map>
9374 will treat set nodes in the same way as sequence nodes.
9378 =head2 AST Generation
9380 This section describes the C<isl> functionality for generating
9381 ASTs that visit all the elements
9382 in a domain in an order specified by a schedule tree or
9384 In case the schedule given as a C<isl_union_map>, an AST is generated
9385 that visits all the elements in the domain of the C<isl_union_map>
9386 according to the lexicographic order of the corresponding image
9387 element(s). If the range of the C<isl_union_map> consists of
9388 elements in more than one space, then each of these spaces is handled
9389 separately in an arbitrary order.
9390 It should be noted that the schedule tree or the image elements
9391 in a schedule map only specify the I<order>
9392 in which the corresponding domain elements should be visited.
9393 No direct relation between the partial schedule values
9394 or the image elements on the one hand and the loop iterators
9395 in the generated AST on the other hand should be assumed.
9397 Each AST is generated within a build. The initial build
9398 simply specifies the constraints on the parameters (if any)
9399 and can be created, inspected, copied and freed using the following functions.
9401 #include <isl/ast_build.h>
9402 __isl_give isl_ast_build *isl_ast_build_alloc(
9404 __isl_give isl_ast_build *isl_ast_build_from_context(
9405 __isl_take isl_set *set);
9406 __isl_give isl_ast_build *isl_ast_build_copy(
9407 __isl_keep isl_ast_build *build);
9408 __isl_null isl_ast_build *isl_ast_build_free(
9409 __isl_take isl_ast_build *build);
9411 The C<set> argument is usually a parameter set with zero or more parameters.
9412 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
9413 this set is required to be a parameter set.
9414 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
9415 specify any parameter constraints.
9416 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
9417 and L</"Fine-grained Control over AST Generation">.
9418 Finally, the AST itself can be constructed using one of the following
9421 #include <isl/ast_build.h>
9422 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
9423 __isl_keep isl_ast_build *build,
9424 __isl_take isl_schedule *schedule);
9425 __isl_give isl_ast_node *
9426 isl_ast_build_node_from_schedule_map(
9427 __isl_keep isl_ast_build *build,
9428 __isl_take isl_union_map *schedule);
9430 =head3 Inspecting the AST
9432 The basic properties of an AST node can be obtained as follows.
9434 #include <isl/ast.h>
9435 enum isl_ast_node_type isl_ast_node_get_type(
9436 __isl_keep isl_ast_node *node);
9438 The type of an AST node is one of
9439 C<isl_ast_node_for>,
9441 C<isl_ast_node_block>,
9442 C<isl_ast_node_mark> or
9443 C<isl_ast_node_user>.
9444 An C<isl_ast_node_for> represents a for node.
9445 An C<isl_ast_node_if> represents an if node.
9446 An C<isl_ast_node_block> represents a compound node.
9447 An C<isl_ast_node_mark> introduces a mark in the AST.
9448 An C<isl_ast_node_user> represents an expression statement.
9449 An expression statement typically corresponds to a domain element, i.e.,
9450 one of the elements that is visited by the AST.
9452 Each type of node has its own additional properties.
9454 #include <isl/ast.h>
9455 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
9456 __isl_keep isl_ast_node *node);
9457 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
9458 __isl_keep isl_ast_node *node);
9459 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
9460 __isl_keep isl_ast_node *node);
9461 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
9462 __isl_keep isl_ast_node *node);
9463 __isl_give isl_ast_node *isl_ast_node_for_get_body(
9464 __isl_keep isl_ast_node *node);
9465 isl_bool isl_ast_node_for_is_degenerate(
9466 __isl_keep isl_ast_node *node);
9468 An C<isl_ast_for> is considered degenerate if it is known to execute
9471 #include <isl/ast.h>
9472 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
9473 __isl_keep isl_ast_node *node);
9474 __isl_give isl_ast_node *isl_ast_node_if_get_then(
9475 __isl_keep isl_ast_node *node);
9476 isl_bool isl_ast_node_if_has_else(
9477 __isl_keep isl_ast_node *node);
9478 __isl_give isl_ast_node *isl_ast_node_if_get_else(
9479 __isl_keep isl_ast_node *node);
9481 __isl_give isl_ast_node_list *
9482 isl_ast_node_block_get_children(
9483 __isl_keep isl_ast_node *node);
9485 __isl_give isl_id *isl_ast_node_mark_get_id(
9486 __isl_keep isl_ast_node *node);
9487 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
9488 __isl_keep isl_ast_node *node);
9490 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
9491 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
9493 #include <isl/ast.h>
9494 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
9495 __isl_keep isl_ast_node *node);
9497 All descendants of a specific node in the AST (including the node itself)
9499 in depth-first pre-order using the following function.
9501 #include <isl/ast.h>
9502 isl_stat isl_ast_node_foreach_descendant_top_down(
9503 __isl_keep isl_ast_node *node,
9504 isl_bool (*fn)(__isl_keep isl_ast_node *node,
9505 void *user), void *user);
9507 The callback function should return C<isl_bool_true> if the children
9508 of the given node should be visited and C<isl_bool_false> if they should not.
9509 It should return C<isl_bool_error> in case of failure, in which case
9510 the entire traversal is aborted.
9512 Each of the returned C<isl_ast_expr>s can in turn be inspected using
9513 the following functions.
9515 #include <isl/ast.h>
9516 enum isl_ast_expr_type isl_ast_expr_get_type(
9517 __isl_keep isl_ast_expr *expr);
9519 The type of an AST expression is one of
9521 C<isl_ast_expr_id> or
9522 C<isl_ast_expr_int>.
9523 An C<isl_ast_expr_op> represents the result of an operation.
9524 An C<isl_ast_expr_id> represents an identifier.
9525 An C<isl_ast_expr_int> represents an integer value.
9527 Each type of expression has its own additional properties.
9529 #include <isl/ast.h>
9530 enum isl_ast_op_type isl_ast_expr_get_op_type(
9531 __isl_keep isl_ast_expr *expr);
9532 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
9533 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
9534 __isl_keep isl_ast_expr *expr, int pos);
9535 isl_stat isl_ast_expr_foreach_ast_op_type(
9536 __isl_keep isl_ast_expr *expr,
9537 isl_stat (*fn)(enum isl_ast_op_type type,
9538 void *user), void *user);
9539 isl_stat isl_ast_node_foreach_ast_op_type(
9540 __isl_keep isl_ast_node *node,
9541 isl_stat (*fn)(enum isl_ast_op_type type,
9542 void *user), void *user);
9544 C<isl_ast_expr_get_op_type> returns the type of the operation
9545 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
9546 arguments. C<isl_ast_expr_get_op_arg> returns the specified
9548 C<isl_ast_expr_foreach_ast_op_type> calls C<fn> for each distinct
9549 C<isl_ast_op_type> that appears in C<expr>.
9550 C<isl_ast_node_foreach_ast_op_type> does the same for each distinct
9551 C<isl_ast_op_type> that appears in C<node>.
9552 The operation type is one of the following.
9556 =item C<isl_ast_op_and>
9558 Logical I<and> of two arguments.
9559 Both arguments can be evaluated.
9561 =item C<isl_ast_op_and_then>
9563 Logical I<and> of two arguments.
9564 The second argument can only be evaluated if the first evaluates to true.
9566 =item C<isl_ast_op_or>
9568 Logical I<or> of two arguments.
9569 Both arguments can be evaluated.
9571 =item C<isl_ast_op_or_else>
9573 Logical I<or> of two arguments.
9574 The second argument can only be evaluated if the first evaluates to false.
9576 =item C<isl_ast_op_max>
9578 Maximum of two or more arguments.
9580 =item C<isl_ast_op_min>
9582 Minimum of two or more arguments.
9584 =item C<isl_ast_op_minus>
9588 =item C<isl_ast_op_add>
9590 Sum of two arguments.
9592 =item C<isl_ast_op_sub>
9594 Difference of two arguments.
9596 =item C<isl_ast_op_mul>
9598 Product of two arguments.
9600 =item C<isl_ast_op_div>
9602 Exact division. That is, the result is known to be an integer.
9604 =item C<isl_ast_op_fdiv_q>
9606 Result of integer division, rounded towards negative
9609 =item C<isl_ast_op_pdiv_q>
9611 Result of integer division, where dividend is known to be non-negative.
9613 =item C<isl_ast_op_pdiv_r>
9615 Remainder of integer division, where dividend is known to be non-negative.
9617 =item C<isl_ast_op_zdiv_r>
9619 Equal to zero iff the remainder on integer division is zero.
9621 =item C<isl_ast_op_cond>
9623 Conditional operator defined on three arguments.
9624 If the first argument evaluates to true, then the result
9625 is equal to the second argument. Otherwise, the result
9626 is equal to the third argument.
9627 The second and third argument may only be evaluated if
9628 the first argument evaluates to true and false, respectively.
9629 Corresponds to C<a ? b : c> in C.
9631 =item C<isl_ast_op_select>
9633 Conditional operator defined on three arguments.
9634 If the first argument evaluates to true, then the result
9635 is equal to the second argument. Otherwise, the result
9636 is equal to the third argument.
9637 The second and third argument may be evaluated independently
9638 of the value of the first argument.
9639 Corresponds to C<a * b + (1 - a) * c> in C.
9641 =item C<isl_ast_op_eq>
9645 =item C<isl_ast_op_le>
9647 Less than or equal relation.
9649 =item C<isl_ast_op_lt>
9653 =item C<isl_ast_op_ge>
9655 Greater than or equal relation.
9657 =item C<isl_ast_op_gt>
9659 Greater than relation.
9661 =item C<isl_ast_op_call>
9664 The number of arguments of the C<isl_ast_expr> is one more than
9665 the number of arguments in the function call, the first argument
9666 representing the function being called.
9668 =item C<isl_ast_op_access>
9671 The number of arguments of the C<isl_ast_expr> is one more than
9672 the number of index expressions in the array access, the first argument
9673 representing the array being accessed.
9675 =item C<isl_ast_op_member>
9678 This operation has two arguments, a structure and the name of
9679 the member of the structure being accessed.
9683 #include <isl/ast.h>
9684 __isl_give isl_id *isl_ast_expr_get_id(
9685 __isl_keep isl_ast_expr *expr);
9687 Return the identifier represented by the AST expression.
9689 #include <isl/ast.h>
9690 __isl_give isl_val *isl_ast_expr_get_val(
9691 __isl_keep isl_ast_expr *expr);
9693 Return the integer represented by the AST expression.
9695 =head3 Properties of ASTs
9697 #include <isl/ast.h>
9698 isl_bool isl_ast_expr_is_equal(
9699 __isl_keep isl_ast_expr *expr1,
9700 __isl_keep isl_ast_expr *expr2);
9702 Check if two C<isl_ast_expr>s are equal to each other.
9704 =head3 Manipulating and printing the AST
9706 AST nodes can be copied and freed using the following functions.
9708 #include <isl/ast.h>
9709 __isl_give isl_ast_node *isl_ast_node_copy(
9710 __isl_keep isl_ast_node *node);
9711 __isl_null isl_ast_node *isl_ast_node_free(
9712 __isl_take isl_ast_node *node);
9714 AST expressions can be copied and freed using the following functions.
9716 #include <isl/ast.h>
9717 __isl_give isl_ast_expr *isl_ast_expr_copy(
9718 __isl_keep isl_ast_expr *expr);
9719 __isl_null isl_ast_expr *isl_ast_expr_free(
9720 __isl_take isl_ast_expr *expr);
9722 New AST expressions can be created either directly or within
9723 the context of an C<isl_ast_build>.
9725 #include <isl/ast.h>
9726 __isl_give isl_ast_expr *isl_ast_expr_from_val(
9727 __isl_take isl_val *v);
9728 __isl_give isl_ast_expr *isl_ast_expr_from_id(
9729 __isl_take isl_id *id);
9730 __isl_give isl_ast_expr *isl_ast_expr_neg(
9731 __isl_take isl_ast_expr *expr);
9732 __isl_give isl_ast_expr *isl_ast_expr_address_of(
9733 __isl_take isl_ast_expr *expr);
9734 __isl_give isl_ast_expr *isl_ast_expr_add(
9735 __isl_take isl_ast_expr *expr1,
9736 __isl_take isl_ast_expr *expr2);
9737 __isl_give isl_ast_expr *isl_ast_expr_sub(
9738 __isl_take isl_ast_expr *expr1,
9739 __isl_take isl_ast_expr *expr2);
9740 __isl_give isl_ast_expr *isl_ast_expr_mul(
9741 __isl_take isl_ast_expr *expr1,
9742 __isl_take isl_ast_expr *expr2);
9743 __isl_give isl_ast_expr *isl_ast_expr_div(
9744 __isl_take isl_ast_expr *expr1,
9745 __isl_take isl_ast_expr *expr2);
9746 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
9747 __isl_take isl_ast_expr *expr1,
9748 __isl_take isl_ast_expr *expr2);
9749 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
9750 __isl_take isl_ast_expr *expr1,
9751 __isl_take isl_ast_expr *expr2);
9752 __isl_give isl_ast_expr *isl_ast_expr_and(
9753 __isl_take isl_ast_expr *expr1,
9754 __isl_take isl_ast_expr *expr2)
9755 __isl_give isl_ast_expr *isl_ast_expr_and_then(
9756 __isl_take isl_ast_expr *expr1,
9757 __isl_take isl_ast_expr *expr2)
9758 __isl_give isl_ast_expr *isl_ast_expr_or(
9759 __isl_take isl_ast_expr *expr1,
9760 __isl_take isl_ast_expr *expr2)
9761 __isl_give isl_ast_expr *isl_ast_expr_or_else(
9762 __isl_take isl_ast_expr *expr1,
9763 __isl_take isl_ast_expr *expr2)
9764 __isl_give isl_ast_expr *isl_ast_expr_eq(
9765 __isl_take isl_ast_expr *expr1,
9766 __isl_take isl_ast_expr *expr2);
9767 __isl_give isl_ast_expr *isl_ast_expr_le(
9768 __isl_take isl_ast_expr *expr1,
9769 __isl_take isl_ast_expr *expr2);
9770 __isl_give isl_ast_expr *isl_ast_expr_lt(
9771 __isl_take isl_ast_expr *expr1,
9772 __isl_take isl_ast_expr *expr2);
9773 __isl_give isl_ast_expr *isl_ast_expr_ge(
9774 __isl_take isl_ast_expr *expr1,
9775 __isl_take isl_ast_expr *expr2);
9776 __isl_give isl_ast_expr *isl_ast_expr_gt(
9777 __isl_take isl_ast_expr *expr1,
9778 __isl_take isl_ast_expr *expr2);
9779 __isl_give isl_ast_expr *isl_ast_expr_access(
9780 __isl_take isl_ast_expr *array,
9781 __isl_take isl_ast_expr_list *indices);
9782 __isl_give isl_ast_expr *isl_ast_expr_call(
9783 __isl_take isl_ast_expr *function,
9784 __isl_take isl_ast_expr_list *arguments);
9786 The function C<isl_ast_expr_address_of> can be applied to an
9787 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
9788 to represent the address of the C<isl_ast_expr_access>. The function
9789 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
9790 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
9792 #include <isl/ast_build.h>
9793 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
9794 __isl_keep isl_ast_build *build,
9795 __isl_take isl_set *set);
9796 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
9797 __isl_keep isl_ast_build *build,
9798 __isl_take isl_pw_aff *pa);
9799 __isl_give isl_ast_expr *
9800 isl_ast_build_access_from_pw_multi_aff(
9801 __isl_keep isl_ast_build *build,
9802 __isl_take isl_pw_multi_aff *pma);
9803 __isl_give isl_ast_expr *
9804 isl_ast_build_access_from_multi_pw_aff(
9805 __isl_keep isl_ast_build *build,
9806 __isl_take isl_multi_pw_aff *mpa);
9807 __isl_give isl_ast_expr *
9808 isl_ast_build_call_from_pw_multi_aff(
9809 __isl_keep isl_ast_build *build,
9810 __isl_take isl_pw_multi_aff *pma);
9811 __isl_give isl_ast_expr *
9812 isl_ast_build_call_from_multi_pw_aff(
9813 __isl_keep isl_ast_build *build,
9814 __isl_take isl_multi_pw_aff *mpa);
9817 the domains of C<pa>, C<mpa> and C<pma> should correspond
9818 to the schedule space of C<build>.
9819 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
9820 the function being called.
9821 If the accessed space is a nested relation, then it is taken
9822 to represent an access of the member specified by the range
9823 of this nested relation of the structure specified by the domain
9824 of the nested relation.
9826 The following functions can be used to modify an C<isl_ast_expr>.
9828 #include <isl/ast.h>
9829 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
9830 __isl_take isl_ast_expr *expr, int pos,
9831 __isl_take isl_ast_expr *arg);
9833 Replace the argument of C<expr> at position C<pos> by C<arg>.
9835 #include <isl/ast.h>
9836 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
9837 __isl_take isl_ast_expr *expr,
9838 __isl_take isl_id_to_ast_expr *id2expr);
9840 The function C<isl_ast_expr_substitute_ids> replaces the
9841 subexpressions of C<expr> of type C<isl_ast_expr_id>
9842 by the corresponding expression in C<id2expr>, if there is any.
9845 User specified data can be attached to an C<isl_ast_node> and obtained
9846 from the same C<isl_ast_node> using the following functions.
9848 #include <isl/ast.h>
9849 __isl_give isl_ast_node *isl_ast_node_set_annotation(
9850 __isl_take isl_ast_node *node,
9851 __isl_take isl_id *annotation);
9852 __isl_give isl_id *isl_ast_node_get_annotation(
9853 __isl_keep isl_ast_node *node);
9855 Basic printing can be performed using the following functions.
9857 #include <isl/ast.h>
9858 __isl_give isl_printer *isl_printer_print_ast_expr(
9859 __isl_take isl_printer *p,
9860 __isl_keep isl_ast_expr *expr);
9861 __isl_give isl_printer *isl_printer_print_ast_node(
9862 __isl_take isl_printer *p,
9863 __isl_keep isl_ast_node *node);
9864 __isl_give char *isl_ast_expr_to_str(
9865 __isl_keep isl_ast_expr *expr);
9866 __isl_give char *isl_ast_node_to_str(
9867 __isl_keep isl_ast_node *node);
9868 __isl_give char *isl_ast_expr_to_C_str(
9869 __isl_keep isl_ast_expr *expr);
9870 __isl_give char *isl_ast_node_to_C_str(
9871 __isl_keep isl_ast_node *node);
9873 The functions C<isl_ast_expr_to_C_str> and
9874 C<isl_ast_node_to_C_str> are convenience functions
9875 that return a string representation of the input in C format.
9877 More advanced printing can be performed using the following functions.
9879 #include <isl/ast.h>
9880 __isl_give isl_printer *isl_ast_op_type_set_print_name(
9881 __isl_take isl_printer *p,
9882 enum isl_ast_op_type type,
9883 __isl_keep const char *name);
9884 isl_stat isl_options_set_ast_print_macro_once(
9885 isl_ctx *ctx, int val);
9886 int isl_options_get_ast_print_macro_once(isl_ctx *ctx);
9887 __isl_give isl_printer *isl_ast_op_type_print_macro(
9888 enum isl_ast_op_type type,
9889 __isl_take isl_printer *p);
9890 __isl_give isl_printer *isl_ast_expr_print_macros(
9891 __isl_keep isl_ast_expr *expr,
9892 __isl_take isl_printer *p);
9893 __isl_give isl_printer *isl_ast_node_print_macros(
9894 __isl_keep isl_ast_node *node,
9895 __isl_take isl_printer *p);
9896 __isl_give isl_printer *isl_ast_node_print(
9897 __isl_keep isl_ast_node *node,
9898 __isl_take isl_printer *p,
9899 __isl_take isl_ast_print_options *options);
9900 __isl_give isl_printer *isl_ast_node_for_print(
9901 __isl_keep isl_ast_node *node,
9902 __isl_take isl_printer *p,
9903 __isl_take isl_ast_print_options *options);
9904 __isl_give isl_printer *isl_ast_node_if_print(
9905 __isl_keep isl_ast_node *node,
9906 __isl_take isl_printer *p,
9907 __isl_take isl_ast_print_options *options);
9909 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
9910 C<isl> may print out an AST that makes use of macros such
9911 as C<floord>, C<min> and C<max>.
9912 The names of these macros may be modified by a call
9913 to C<isl_ast_op_type_set_print_name>. The user-specified
9914 names are associated to the printer object.
9915 C<isl_ast_op_type_print_macro> prints out the macro
9916 corresponding to a specific C<isl_ast_op_type>.
9917 If the print-macro-once option is set, then a given macro definition
9918 is only printed once to any given printer object.
9919 C<isl_ast_expr_print_macros> scans the C<isl_ast_expr>
9920 for subexpressions where these macros would be used and prints
9921 out the required macro definitions.
9922 Essentially, C<isl_ast_expr_print_macros> calls
9923 C<isl_ast_expr_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
9924 as function argument.
9925 C<isl_ast_node_print_macros> does the same
9926 for expressions in its C<isl_ast_node> argument.
9927 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
9928 C<isl_ast_node_if_print> print an C<isl_ast_node>
9929 in C<ISL_FORMAT_C>, but allow for some extra control
9930 through an C<isl_ast_print_options> object.
9931 This object can be created using the following functions.
9933 #include <isl/ast.h>
9934 __isl_give isl_ast_print_options *
9935 isl_ast_print_options_alloc(isl_ctx *ctx);
9936 __isl_give isl_ast_print_options *
9937 isl_ast_print_options_copy(
9938 __isl_keep isl_ast_print_options *options);
9939 __isl_null isl_ast_print_options *
9940 isl_ast_print_options_free(
9941 __isl_take isl_ast_print_options *options);
9943 __isl_give isl_ast_print_options *
9944 isl_ast_print_options_set_print_user(
9945 __isl_take isl_ast_print_options *options,
9946 __isl_give isl_printer *(*print_user)(
9947 __isl_take isl_printer *p,
9948 __isl_take isl_ast_print_options *options,
9949 __isl_keep isl_ast_node *node, void *user),
9951 __isl_give isl_ast_print_options *
9952 isl_ast_print_options_set_print_for(
9953 __isl_take isl_ast_print_options *options,
9954 __isl_give isl_printer *(*print_for)(
9955 __isl_take isl_printer *p,
9956 __isl_take isl_ast_print_options *options,
9957 __isl_keep isl_ast_node *node, void *user),
9960 The callback set by C<isl_ast_print_options_set_print_user>
9961 is called whenever a node of type C<isl_ast_node_user> needs to
9963 The callback set by C<isl_ast_print_options_set_print_for>
9964 is called whenever a node of type C<isl_ast_node_for> needs to
9966 Note that C<isl_ast_node_for_print> will I<not> call the
9967 callback set by C<isl_ast_print_options_set_print_for> on the node
9968 on which C<isl_ast_node_for_print> is called, but only on nested
9969 nodes of type C<isl_ast_node_for>. It is therefore safe to
9970 call C<isl_ast_node_for_print> from within the callback set by
9971 C<isl_ast_print_options_set_print_for>.
9973 The following option determines the type to be used for iterators
9974 while printing the AST.
9976 isl_stat isl_options_set_ast_iterator_type(
9977 isl_ctx *ctx, const char *val);
9978 const char *isl_options_get_ast_iterator_type(
9981 The AST printer only prints body nodes as blocks if these
9982 blocks cannot be safely omitted.
9983 For example, a C<for> node with one body node will not be
9984 surrounded with braces in C<ISL_FORMAT_C>.
9985 A block will always be printed by setting the following option.
9987 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx,
9989 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
9993 #include <isl/ast_build.h>
9994 isl_stat isl_options_set_ast_build_atomic_upper_bound(
9995 isl_ctx *ctx, int val);
9996 int isl_options_get_ast_build_atomic_upper_bound(
9998 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
10000 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
10001 isl_stat isl_options_set_ast_build_detect_min_max(
10002 isl_ctx *ctx, int val);
10003 int isl_options_get_ast_build_detect_min_max(
10005 isl_stat isl_options_set_ast_build_exploit_nested_bounds(
10006 isl_ctx *ctx, int val);
10007 int isl_options_get_ast_build_exploit_nested_bounds(
10009 isl_stat isl_options_set_ast_build_group_coscheduled(
10010 isl_ctx *ctx, int val);
10011 int isl_options_get_ast_build_group_coscheduled(
10013 isl_stat isl_options_set_ast_build_scale_strides(
10014 isl_ctx *ctx, int val);
10015 int isl_options_get_ast_build_scale_strides(
10017 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx,
10019 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
10020 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx,
10022 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
10026 =item * ast_build_atomic_upper_bound
10028 Generate loop upper bounds that consist of the current loop iterator,
10029 an operator and an expression not involving the iterator.
10030 If this option is not set, then the current loop iterator may appear
10031 several times in the upper bound.
10032 For example, when this option is turned off, AST generation
10035 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
10039 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
10042 When the option is turned on, the following AST is generated
10044 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
10047 =item * ast_build_prefer_pdiv
10049 If this option is turned off, then the AST generation will
10050 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
10051 operators, but no C<isl_ast_op_pdiv_q> or
10052 C<isl_ast_op_pdiv_r> operators.
10053 If this option is turned on, then C<isl> will try to convert
10054 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
10055 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
10057 =item * ast_build_detect_min_max
10059 If this option is turned on, then C<isl> will try and detect
10060 min or max-expressions when building AST expressions from
10061 piecewise affine expressions.
10063 =item * ast_build_exploit_nested_bounds
10065 Simplify conditions based on bounds of nested for loops.
10066 In particular, remove conditions that are implied by the fact
10067 that one or more nested loops have at least one iteration,
10068 meaning that the upper bound is at least as large as the lower bound.
10069 For example, when this option is turned off, AST generation
10072 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
10078 for (int c0 = 0; c0 <= N; c0 += 1)
10079 for (int c1 = 0; c1 <= M; c1 += 1)
10082 When the option is turned on, the following AST is generated
10084 for (int c0 = 0; c0 <= N; c0 += 1)
10085 for (int c1 = 0; c1 <= M; c1 += 1)
10088 =item * ast_build_group_coscheduled
10090 If two domain elements are assigned the same schedule point, then
10091 they may be executed in any order and they may even appear in different
10092 loops. If this options is set, then the AST generator will make
10093 sure that coscheduled domain elements do not appear in separate parts
10094 of the AST. This is useful in case of nested AST generation
10095 if the outer AST generation is given only part of a schedule
10096 and the inner AST generation should handle the domains that are
10097 coscheduled by this initial part of the schedule together.
10098 For example if an AST is generated for a schedule
10100 { A[i] -> [0]; B[i] -> [0] }
10102 then the C<isl_ast_build_set_create_leaf> callback described
10103 below may get called twice, once for each domain.
10104 Setting this option ensures that the callback is only called once
10105 on both domains together.
10107 =item * ast_build_separation_bounds
10109 This option specifies which bounds to use during separation.
10110 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
10111 then all (possibly implicit) bounds on the current dimension will
10112 be used during separation.
10113 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
10114 then only those bounds that are explicitly available will
10115 be used during separation.
10117 =item * ast_build_scale_strides
10119 This option specifies whether the AST generator is allowed
10120 to scale down iterators of strided loops.
10122 =item * ast_build_allow_else
10124 This option specifies whether the AST generator is allowed
10125 to construct if statements with else branches.
10127 =item * ast_build_allow_or
10129 This option specifies whether the AST generator is allowed
10130 to construct if conditions with disjunctions.
10134 =head3 AST Generation Options (Schedule Tree)
10136 In case of AST construction from a schedule tree, the options
10137 that control how an AST is created from the individual schedule
10138 dimensions are stored in the band nodes of the tree
10139 (see L</"Schedule Trees">).
10141 In particular, a schedule dimension can be handled in four
10142 different ways, atomic, separate, unroll or the default.
10143 This loop AST generation type can be set using
10144 C<isl_schedule_node_band_member_set_ast_loop_type>.
10146 the first three can be selected by including a one-dimensional
10147 element with as value the position of the schedule dimension
10148 within the band and as name one of C<atomic>, C<separate>
10149 or C<unroll> in the options
10150 set by C<isl_schedule_node_band_set_ast_build_options>.
10151 Only one of these three may be specified for
10152 any given schedule dimension within a band node.
10153 If none of these is specified, then the default
10154 is used. The meaning of the options is as follows.
10160 When this option is specified, the AST generator will make
10161 sure that a given domains space only appears in a single
10162 loop at the specified level.
10164 For example, for the schedule tree
10166 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10168 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10169 options: "{ atomic[x] }"
10171 the following AST will be generated
10173 for (int c0 = 0; c0 <= 10; c0 += 1) {
10180 On the other hand, for the schedule tree
10182 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10184 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10185 options: "{ separate[x] }"
10187 the following AST will be generated
10191 for (int c0 = 1; c0 <= 9; c0 += 1) {
10198 If neither C<atomic> nor C<separate> is specified, then the AST generator
10199 may produce either of these two results or some intermediate form.
10203 When this option is specified, the AST generator will
10204 split the domain of the specified schedule dimension
10205 into pieces with a fixed set of statements for which
10206 instances need to be executed by the iterations in
10207 the schedule domain part. This option tends to avoid
10208 the generation of guards inside the corresponding loops.
10209 See also the C<atomic> option.
10213 When this option is specified, the AST generator will
10214 I<completely> unroll the corresponding schedule dimension.
10215 It is the responsibility of the user to ensure that such
10216 unrolling is possible.
10217 To obtain a partial unrolling, the user should apply an additional
10218 strip-mining to the schedule and fully unroll the inner schedule
10223 The C<isolate> option is a bit more involved. It allows the user
10224 to isolate a range of schedule dimension values from smaller and
10225 greater values. Additionally, the user may specify a different
10226 atomic/separate/unroll choice for the isolated part and the remaining
10227 parts. The typical use case of the C<isolate> option is to isolate
10228 full tiles from partial tiles.
10229 The part that needs to be isolated may depend on outer schedule dimensions.
10230 The option therefore needs to be able to reference those outer schedule
10231 dimensions. In particular, the space of the C<isolate> option is that
10232 of a wrapped map with as domain the flat product of all outer band nodes
10233 and as range the space of the current band node.
10234 The atomic/separate/unroll choice for the isolated part is determined
10235 by an option that lives in an unnamed wrapped space with as domain
10236 a zero-dimensional C<isolate> space and as range the regular
10237 C<atomic>, C<separate> or C<unroll> space.
10238 This option may also be set directly using
10239 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
10240 The atomic/separate/unroll choice for the remaining part is determined
10241 by the regular C<atomic>, C<separate> or C<unroll> option.
10242 Since the C<isolate> option references outer schedule dimensions,
10243 its use in a band node causes any tree containing the node
10244 to be considered anchored.
10246 As an example, consider the isolation of full tiles from partial tiles
10247 in a tiling of a triangular domain. The original schedule is as follows.
10249 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10251 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10252 { A[i,j] -> [floor(j/10)] }, \
10253 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10257 for (int c0 = 0; c0 <= 10; c0 += 1)
10258 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10259 for (int c2 = 10 * c0;
10260 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10261 for (int c3 = 10 * c1;
10262 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10265 Isolating the full tiles, we have the following input
10267 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10269 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10270 { A[i,j] -> [floor(j/10)] }, \
10271 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10272 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10273 10a+9+10b+9 <= 100 }"
10278 for (int c0 = 0; c0 <= 8; c0 += 1) {
10279 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10280 for (int c2 = 10 * c0;
10281 c2 <= 10 * c0 + 9; c2 += 1)
10282 for (int c3 = 10 * c1;
10283 c3 <= 10 * c1 + 9; c3 += 1)
10285 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10286 for (int c2 = 10 * c0;
10287 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10288 for (int c3 = 10 * c1;
10289 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10292 for (int c0 = 9; c0 <= 10; c0 += 1)
10293 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10294 for (int c2 = 10 * c0;
10295 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10296 for (int c3 = 10 * c1;
10297 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10301 We may then additionally unroll the innermost loop of the isolated part
10303 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10305 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10306 { A[i,j] -> [floor(j/10)] }, \
10307 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10308 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10309 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
10314 for (int c0 = 0; c0 <= 8; c0 += 1) {
10315 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10316 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
10318 A(c2, 10 * c1 + 1);
10319 A(c2, 10 * c1 + 2);
10320 A(c2, 10 * c1 + 3);
10321 A(c2, 10 * c1 + 4);
10322 A(c2, 10 * c1 + 5);
10323 A(c2, 10 * c1 + 6);
10324 A(c2, 10 * c1 + 7);
10325 A(c2, 10 * c1 + 8);
10326 A(c2, 10 * c1 + 9);
10328 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10329 for (int c2 = 10 * c0;
10330 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10331 for (int c3 = 10 * c1;
10332 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10335 for (int c0 = 9; c0 <= 10; c0 += 1)
10336 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10337 for (int c2 = 10 * c0;
10338 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10339 for (int c3 = 10 * c1;
10340 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10345 =head3 AST Generation Options (Schedule Map)
10347 In case of AST construction using
10348 C<isl_ast_build_node_from_schedule_map>, the options
10349 that control how an AST is created from the individual schedule
10350 dimensions are stored in the C<isl_ast_build>.
10351 They can be set using the following function.
10353 #include <isl/ast_build.h>
10354 __isl_give isl_ast_build *
10355 isl_ast_build_set_options(
10356 __isl_take isl_ast_build *control,
10357 __isl_take isl_union_map *options);
10359 The options are encoded in an C<isl_union_map>.
10360 The domain of this union relation refers to the schedule domain,
10361 i.e., the range of the schedule passed
10362 to C<isl_ast_build_node_from_schedule_map>.
10363 In the case of nested AST generation (see L</"Nested AST Generation">),
10364 the domain of C<options> should refer to the extra piece of the schedule.
10365 That is, it should be equal to the range of the wrapped relation in the
10366 range of the schedule.
10367 The range of the options can consist of elements in one or more spaces,
10368 the names of which determine the effect of the option.
10369 The values of the range typically also refer to the schedule dimension
10370 to which the option applies. In case of nested AST generation
10371 (see L</"Nested AST Generation">), these values refer to the position
10372 of the schedule dimension within the innermost AST generation.
10373 The constraints on the domain elements of
10374 the option should only refer to this dimension and earlier dimensions.
10375 We consider the following spaces.
10379 =item C<separation_class>
10381 B<This option has been deprecated. Use the isolate option on
10382 schedule trees instead.>
10384 This space is a wrapped relation between two one dimensional spaces.
10385 The input space represents the schedule dimension to which the option
10386 applies and the output space represents the separation class.
10387 While constructing a loop corresponding to the specified schedule
10388 dimension(s), the AST generator will try to generate separate loops
10389 for domain elements that are assigned different classes.
10390 If only some of the elements are assigned a class, then those elements
10391 that are not assigned any class will be treated as belonging to a class
10392 that is separate from the explicitly assigned classes.
10393 The typical use case for this option is to separate full tiles from
10395 The other options, described below, are applied after the separation
10398 As an example, consider the separation into full and partial tiles
10399 of a tiling of a triangular domain.
10400 Take, for example, the domain
10402 { A[i,j] : 0 <= i,j and i + j <= 100 }
10404 and a tiling into tiles of 10 by 10. The input to the AST generator
10405 is then the schedule
10407 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
10410 Without any options, the following AST is generated
10412 for (int c0 = 0; 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);
10422 Separation into full and partial tiles can be obtained by assigning
10423 a class, say C<0>, to the full tiles. The full tiles are represented by those
10424 values of the first and second schedule dimensions for which there are
10425 values of the third and fourth dimensions to cover an entire tile.
10426 That is, we need to specify the following option
10428 { [a,b,c,d] -> separation_class[[0]->[0]] :
10429 exists b': 0 <= 10a,10b' and
10430 10a+9+10b'+9 <= 100;
10431 [a,b,c,d] -> separation_class[[1]->[0]] :
10432 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
10434 which simplifies to
10436 { [a, b, c, d] -> separation_class[[1] -> [0]] :
10437 a >= 0 and b >= 0 and b <= 8 - a;
10438 [a, b, c, d] -> separation_class[[0] -> [0]] :
10439 a >= 0 and a <= 8 }
10441 With this option, the generated AST is as follows
10444 for (int c0 = 0; c0 <= 8; c0 += 1) {
10445 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10446 for (int c2 = 10 * c0;
10447 c2 <= 10 * c0 + 9; c2 += 1)
10448 for (int c3 = 10 * c1;
10449 c3 <= 10 * c1 + 9; c3 += 1)
10451 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10452 for (int c2 = 10 * c0;
10453 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10455 for (int c3 = 10 * c1;
10456 c3 <= min(-c2 + 100, 10 * c1 + 9);
10460 for (int c0 = 9; c0 <= 10; c0 += 1)
10461 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10462 for (int c2 = 10 * c0;
10463 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10465 for (int c3 = 10 * c1;
10466 c3 <= min(10 * c1 + 9, -c2 + 100);
10473 This is a single-dimensional space representing the schedule dimension(s)
10474 to which ``separation'' should be applied. Separation tries to split
10475 a loop into several pieces if this can avoid the generation of guards
10477 See also the C<atomic> option.
10481 This is a single-dimensional space representing the schedule dimension(s)
10482 for which the domains should be considered ``atomic''. That is, the
10483 AST generator will make sure that any given domain space will only appear
10484 in a single loop at the specified level.
10486 Consider the following schedule
10488 { a[i] -> [i] : 0 <= i < 10;
10489 b[i] -> [i+1] : 0 <= i < 10 }
10491 If the following option is specified
10493 { [i] -> separate[x] }
10495 then the following AST will be generated
10499 for (int c0 = 1; c0 <= 9; c0 += 1) {
10506 If, on the other hand, the following option is specified
10508 { [i] -> atomic[x] }
10510 then the following AST will be generated
10512 for (int c0 = 0; c0 <= 10; c0 += 1) {
10519 If neither C<atomic> nor C<separate> is specified, then the AST generator
10520 may produce either of these two results or some intermediate form.
10524 This is a single-dimensional space representing the schedule dimension(s)
10525 that should be I<completely> unrolled.
10526 To obtain a partial unrolling, the user should apply an additional
10527 strip-mining to the schedule and fully unroll the inner loop.
10531 =head3 Fine-grained Control over AST Generation
10533 Besides specifying the constraints on the parameters,
10534 an C<isl_ast_build> object can be used to control
10535 various aspects of the AST generation process.
10536 In case of AST construction using
10537 C<isl_ast_build_node_from_schedule_map>,
10538 the most prominent way of control is through ``options'',
10539 as explained above.
10541 Additional control is available through the following functions.
10543 #include <isl/ast_build.h>
10544 __isl_give isl_ast_build *
10545 isl_ast_build_set_iterators(
10546 __isl_take isl_ast_build *control,
10547 __isl_take isl_id_list *iterators);
10549 The function C<isl_ast_build_set_iterators> allows the user to
10550 specify a list of iterator C<isl_id>s to be used as iterators.
10551 If the input schedule is injective, then
10552 the number of elements in this list should be as large as the dimension
10553 of the schedule space, but no direct correspondence should be assumed
10554 between dimensions and elements.
10555 If the input schedule is not injective, then an additional number
10556 of C<isl_id>s equal to the largest dimension of the input domains
10558 If the number of provided C<isl_id>s is insufficient, then additional
10559 names are automatically generated.
10561 #include <isl/ast_build.h>
10562 __isl_give isl_ast_build *
10563 isl_ast_build_set_create_leaf(
10564 __isl_take isl_ast_build *control,
10565 __isl_give isl_ast_node *(*fn)(
10566 __isl_take isl_ast_build *build,
10567 void *user), void *user);
10570 C<isl_ast_build_set_create_leaf> function allows for the
10571 specification of a callback that should be called whenever the AST
10572 generator arrives at an element of the schedule domain.
10573 The callback should return an AST node that should be inserted
10574 at the corresponding position of the AST. The default action (when
10575 the callback is not set) is to continue generating parts of the AST to scan
10576 all the domain elements associated to the schedule domain element
10577 and to insert user nodes, ``calling'' the domain element, for each of them.
10578 The C<build> argument contains the current state of the C<isl_ast_build>.
10579 To ease nested AST generation (see L</"Nested AST Generation">),
10580 all control information that is
10581 specific to the current AST generation such as the options and
10582 the callbacks has been removed from this C<isl_ast_build>.
10583 The callback would typically return the result of a nested
10584 AST generation or a
10585 user defined node created using the following function.
10587 #include <isl/ast.h>
10588 __isl_give isl_ast_node *isl_ast_node_alloc_user(
10589 __isl_take isl_ast_expr *expr);
10591 #include <isl/ast_build.h>
10592 __isl_give isl_ast_build *
10593 isl_ast_build_set_at_each_domain(
10594 __isl_take isl_ast_build *build,
10595 __isl_give isl_ast_node *(*fn)(
10596 __isl_take isl_ast_node *node,
10597 __isl_keep isl_ast_build *build,
10598 void *user), void *user);
10599 __isl_give isl_ast_build *
10600 isl_ast_build_set_before_each_for(
10601 __isl_take isl_ast_build *build,
10602 __isl_give isl_id *(*fn)(
10603 __isl_keep isl_ast_build *build,
10604 void *user), void *user);
10605 __isl_give isl_ast_build *
10606 isl_ast_build_set_after_each_for(
10607 __isl_take isl_ast_build *build,
10608 __isl_give isl_ast_node *(*fn)(
10609 __isl_take isl_ast_node *node,
10610 __isl_keep isl_ast_build *build,
10611 void *user), void *user);
10612 __isl_give isl_ast_build *
10613 isl_ast_build_set_before_each_mark(
10614 __isl_take isl_ast_build *build,
10615 isl_stat (*fn)(__isl_keep isl_id *mark,
10616 __isl_keep isl_ast_build *build,
10617 void *user), void *user);
10618 __isl_give isl_ast_build *
10619 isl_ast_build_set_after_each_mark(
10620 __isl_take isl_ast_build *build,
10621 __isl_give isl_ast_node *(*fn)(
10622 __isl_take isl_ast_node *node,
10623 __isl_keep isl_ast_build *build,
10624 void *user), void *user);
10626 The callback set by C<isl_ast_build_set_at_each_domain> will
10627 be called for each domain AST node.
10628 The callbacks set by C<isl_ast_build_set_before_each_for>
10629 and C<isl_ast_build_set_after_each_for> will be called
10630 for each for AST node. The first will be called in depth-first
10631 pre-order, while the second will be called in depth-first post-order.
10632 Since C<isl_ast_build_set_before_each_for> is called before the for
10633 node is actually constructed, it is only passed an C<isl_ast_build>.
10634 The returned C<isl_id> will be added as an annotation (using
10635 C<isl_ast_node_set_annotation>) to the constructed for node.
10636 In particular, if the user has also specified an C<after_each_for>
10637 callback, then the annotation can be retrieved from the node passed to
10638 that callback using C<isl_ast_node_get_annotation>.
10639 The callbacks set by C<isl_ast_build_set_before_each_mark>
10640 and C<isl_ast_build_set_after_each_mark> will be called for each
10641 mark AST node that is created, i.e., for each mark schedule node
10642 in the input schedule tree. The first will be called in depth-first
10643 pre-order, while the second will be called in depth-first post-order.
10644 Since the callback set by C<isl_ast_build_set_before_each_mark>
10645 is called before the mark AST node is actually constructed, it is passed
10646 the identifier of the mark node.
10647 All callbacks should C<NULL> (or -1) on failure.
10648 The given C<isl_ast_build> can be used to create new
10649 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
10650 or C<isl_ast_build_call_from_pw_multi_aff>.
10652 =head3 Nested AST Generation
10654 C<isl> allows the user to create an AST within the context
10655 of another AST. These nested ASTs are created using the
10656 same C<isl_ast_build_node_from_schedule_map> function that is used to create
10657 the outer AST. The C<build> argument should be an C<isl_ast_build>
10658 passed to a callback set by
10659 C<isl_ast_build_set_create_leaf>.
10660 The space of the range of the C<schedule> argument should refer
10661 to this build. In particular, the space should be a wrapped
10662 relation and the domain of this wrapped relation should be the
10663 same as that of the range of the schedule returned by
10664 C<isl_ast_build_get_schedule> below.
10665 In practice, the new schedule is typically
10666 created by calling C<isl_union_map_range_product> on the old schedule
10667 and some extra piece of the schedule.
10668 The space of the schedule domain is also available from
10669 the C<isl_ast_build>.
10671 #include <isl/ast_build.h>
10672 __isl_give isl_union_map *isl_ast_build_get_schedule(
10673 __isl_keep isl_ast_build *build);
10674 __isl_give isl_space *isl_ast_build_get_schedule_space(
10675 __isl_keep isl_ast_build *build);
10676 __isl_give isl_ast_build *isl_ast_build_restrict(
10677 __isl_take isl_ast_build *build,
10678 __isl_take isl_set *set);
10680 The C<isl_ast_build_get_schedule> function returns a (partial)
10681 schedule for the domains elements for which part of the AST still needs to
10682 be generated in the current build.
10683 In particular, the domain elements are mapped to those iterations of the loops
10684 enclosing the current point of the AST generation inside which
10685 the domain elements are executed.
10686 No direct correspondence between
10687 the input schedule and this schedule should be assumed.
10688 The space obtained from C<isl_ast_build_get_schedule_space> can be used
10689 to create a set for C<isl_ast_build_restrict> to intersect
10690 with the current build. In particular, the set passed to
10691 C<isl_ast_build_restrict> can have additional parameters.
10692 The ids of the set dimensions in the space returned by
10693 C<isl_ast_build_get_schedule_space> correspond to the
10694 iterators of the already generated loops.
10695 The user should not rely on the ids of the output dimensions
10696 of the relations in the union relation returned by
10697 C<isl_ast_build_get_schedule> having any particular value.
10699 =head1 Applications
10701 Although C<isl> is mainly meant to be used as a library,
10702 it also contains some basic applications that use some
10703 of the functionality of C<isl>.
10704 For applications that take one or more polytopes or polyhedra
10705 as input, this input may be specified in either the L<isl format>
10706 or the L<PolyLib format>.
10708 =head2 C<isl_polyhedron_sample>
10710 C<isl_polyhedron_sample> takes a polyhedron as input and prints
10711 an integer element of the polyhedron, if there is any.
10712 The first column in the output is the denominator and is always
10713 equal to 1. If the polyhedron contains no integer points,
10714 then a vector of length zero is printed.
10718 C<isl_pip> takes the same input as the C<example> program
10719 from the C<piplib> distribution, i.e., a set of constraints
10720 on the parameters, a line containing only -1 and finally a set
10721 of constraints on a parametric polyhedron.
10722 The coefficients of the parameters appear in the last columns
10723 (but before the final constant column).
10724 The output is the lexicographic minimum of the parametric polyhedron.
10725 As C<isl> currently does not have its own output format, the output
10726 is just a dump of the internal state.
10728 =head2 C<isl_polyhedron_minimize>
10730 C<isl_polyhedron_minimize> computes the minimum of some linear
10731 or affine objective function over the integer points in a polyhedron.
10732 If an affine objective function
10733 is given, then the constant should appear in the last column.
10735 =head2 C<isl_polytope_scan>
10737 Given a polytope, C<isl_polytope_scan> prints
10738 all integer points in the polytope.
10740 =head2 C<isl_codegen>
10742 Given either a schedule tree or a sequence consisting of
10743 a schedule map, a context set and an options relation,
10744 C<isl_codegen> prints out an AST that scans the domain elements
10745 of the schedule in the order of their image(s) taking into account
10746 the constraints in the context set.
10748 =head2 C<isl_schedule>
10750 Given an C<isl_schedule_constraints> object as input,
10751 C<isl_schedule> prints out a schedule that satisfies the given