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 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
1496 enum isl_dim_type type);
1498 #include <isl/local_space.h>
1499 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1500 __isl_take isl_local_space *ls,
1501 enum isl_dim_type type, __isl_take isl_id *id);
1503 #include <isl/set.h>
1504 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1505 __isl_take isl_basic_set *bset,
1506 __isl_take isl_id *id);
1507 __isl_give isl_set *isl_set_set_tuple_id(
1508 __isl_take isl_set *set, __isl_take isl_id *id);
1509 __isl_give isl_set *isl_set_reset_tuple_id(
1510 __isl_take isl_set *set);
1511 isl_bool isl_set_has_tuple_id(__isl_keep isl_set *set);
1512 __isl_give isl_id *isl_set_get_tuple_id(
1513 __isl_keep isl_set *set);
1514 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1515 __isl_take isl_basic_set *set, const char *s);
1516 __isl_give isl_set *isl_set_set_tuple_name(
1517 __isl_take isl_set *set, const char *s);
1518 const char *isl_basic_set_get_tuple_name(
1519 __isl_keep isl_basic_set *bset);
1520 isl_bool isl_set_has_tuple_name(__isl_keep isl_set *set);
1521 const char *isl_set_get_tuple_name(
1522 __isl_keep isl_set *set);
1524 #include <isl/map.h>
1525 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1526 __isl_take isl_basic_map *bmap,
1527 enum isl_dim_type type, __isl_take isl_id *id);
1528 __isl_give isl_map *isl_map_set_tuple_id(
1529 __isl_take isl_map *map, enum isl_dim_type type,
1530 __isl_take isl_id *id);
1531 __isl_give isl_map *isl_map_reset_tuple_id(
1532 __isl_take isl_map *map, enum isl_dim_type type);
1533 isl_bool isl_map_has_tuple_id(__isl_keep isl_map *map,
1534 enum isl_dim_type type);
1535 __isl_give isl_id *isl_map_get_tuple_id(
1536 __isl_keep isl_map *map, enum isl_dim_type type);
1537 __isl_give isl_map *isl_map_set_tuple_name(
1538 __isl_take isl_map *map,
1539 enum isl_dim_type type, const char *s);
1540 const char *isl_basic_map_get_tuple_name(
1541 __isl_keep isl_basic_map *bmap,
1542 enum isl_dim_type type);
1543 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1544 __isl_take isl_basic_map *bmap,
1545 enum isl_dim_type type, const char *s);
1546 isl_bool isl_map_has_tuple_name(__isl_keep isl_map *map,
1547 enum isl_dim_type type);
1548 const char *isl_map_get_tuple_name(
1549 __isl_keep isl_map *map,
1550 enum isl_dim_type type);
1552 #include <isl/val.h>
1553 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1554 __isl_take isl_multi_val *mv,
1555 enum isl_dim_type type, __isl_take isl_id *id);
1556 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1557 __isl_take isl_multi_val *mv,
1558 enum isl_dim_type type);
1559 isl_bool isl_multi_val_has_tuple_id(
1560 __isl_keep isl_multi_val *mv,
1561 enum isl_dim_type type);
1562 __isl_give isl_id *isl_multi_val_get_tuple_id(
1563 __isl_keep isl_multi_val *mv,
1564 enum isl_dim_type type);
1565 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1566 __isl_take isl_multi_val *mv,
1567 enum isl_dim_type type, const char *s);
1568 const char *isl_multi_val_get_tuple_name(
1569 __isl_keep isl_multi_val *mv,
1570 enum isl_dim_type type);
1572 #include <isl/aff.h>
1573 __isl_give isl_aff *isl_aff_set_tuple_id(
1574 __isl_take isl_aff *aff,
1575 enum isl_dim_type type, __isl_take isl_id *id);
1576 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1577 __isl_take isl_multi_aff *maff,
1578 enum isl_dim_type type, __isl_take isl_id *id);
1579 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1580 __isl_take isl_pw_aff *pwaff,
1581 enum isl_dim_type type, __isl_take isl_id *id);
1582 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1583 __isl_take isl_pw_multi_aff *pma,
1584 enum isl_dim_type type, __isl_take isl_id *id);
1585 __isl_give isl_multi_union_pw_aff *
1586 isl_multi_union_pw_aff_set_tuple_id(
1587 __isl_take isl_multi_union_pw_aff *mupa,
1588 enum isl_dim_type type, __isl_take isl_id *id);
1589 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1590 __isl_take isl_multi_aff *ma,
1591 enum isl_dim_type type);
1592 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1593 __isl_take isl_pw_aff *pa,
1594 enum isl_dim_type type);
1595 __isl_give isl_multi_pw_aff *
1596 isl_multi_pw_aff_reset_tuple_id(
1597 __isl_take isl_multi_pw_aff *mpa,
1598 enum isl_dim_type type);
1599 __isl_give isl_pw_multi_aff *
1600 isl_pw_multi_aff_reset_tuple_id(
1601 __isl_take isl_pw_multi_aff *pma,
1602 enum isl_dim_type type);
1603 __isl_give isl_multi_union_pw_aff *
1604 isl_multi_union_pw_aff_reset_tuple_id(
1605 __isl_take isl_multi_union_pw_aff *mupa,
1606 enum isl_dim_type type);
1607 isl_bool isl_multi_aff_has_tuple_id(
1608 __isl_keep isl_multi_aff *ma,
1609 enum isl_dim_type type);
1610 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1611 __isl_keep isl_multi_aff *ma,
1612 enum isl_dim_type type);
1613 isl_bool isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1614 enum isl_dim_type type);
1615 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1616 __isl_keep isl_pw_aff *pa,
1617 enum isl_dim_type type);
1618 isl_bool isl_pw_multi_aff_has_tuple_id(
1619 __isl_keep isl_pw_multi_aff *pma,
1620 enum isl_dim_type type);
1621 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1622 __isl_keep isl_pw_multi_aff *pma,
1623 enum isl_dim_type type);
1624 isl_bool isl_multi_pw_aff_has_tuple_id(
1625 __isl_keep isl_multi_pw_aff *mpa,
1626 enum isl_dim_type type);
1627 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1628 __isl_keep isl_multi_pw_aff *mpa,
1629 enum isl_dim_type type);
1630 isl_bool isl_multi_union_pw_aff_has_tuple_id(
1631 __isl_keep isl_multi_union_pw_aff *mupa,
1632 enum isl_dim_type type);
1633 __isl_give isl_id *isl_multi_union_pw_aff_get_tuple_id(
1634 __isl_keep isl_multi_union_pw_aff *mupa,
1635 enum isl_dim_type type);
1636 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1637 __isl_take isl_multi_aff *maff,
1638 enum isl_dim_type type, const char *s);
1639 __isl_give isl_multi_pw_aff *
1640 isl_multi_pw_aff_set_tuple_name(
1641 __isl_take isl_multi_pw_aff *mpa,
1642 enum isl_dim_type type, const char *s);
1643 __isl_give isl_multi_union_pw_aff *
1644 isl_multi_union_pw_aff_set_tuple_name(
1645 __isl_take isl_multi_union_pw_aff *mupa,
1646 enum isl_dim_type type, const char *s);
1647 const char *isl_multi_aff_get_tuple_name(
1648 __isl_keep isl_multi_aff *multi,
1649 enum isl_dim_type type);
1650 isl_bool isl_pw_multi_aff_has_tuple_name(
1651 __isl_keep isl_pw_multi_aff *pma,
1652 enum isl_dim_type type);
1653 const char *isl_pw_multi_aff_get_tuple_name(
1654 __isl_keep isl_pw_multi_aff *pma,
1655 enum isl_dim_type type);
1656 const char *isl_multi_union_pw_aff_get_tuple_name(
1657 __isl_keep isl_multi_union_pw_aff *mupa,
1658 enum isl_dim_type type);
1660 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1661 or C<isl_dim_set>. As with C<isl_space_get_name>,
1662 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1664 Binary operations require the corresponding spaces of their arguments
1665 to have the same name.
1667 To keep the names of all parameters and tuples, but reset the user pointers
1668 of all the corresponding identifiers, use the following function.
1670 #include <isl/space.h>
1671 __isl_give isl_space *isl_space_reset_user(
1672 __isl_take isl_space *space);
1674 #include <isl/set.h>
1675 __isl_give isl_set *isl_set_reset_user(
1676 __isl_take isl_set *set);
1678 #include <isl/map.h>
1679 __isl_give isl_map *isl_map_reset_user(
1680 __isl_take isl_map *map);
1682 #include <isl/union_set.h>
1683 __isl_give isl_union_set *isl_union_set_reset_user(
1684 __isl_take isl_union_set *uset);
1686 #include <isl/union_map.h>
1687 __isl_give isl_union_map *isl_union_map_reset_user(
1688 __isl_take isl_union_map *umap);
1690 #include <isl/val.h>
1691 __isl_give isl_multi_val *isl_multi_val_reset_user(
1692 __isl_take isl_multi_val *mv);
1694 #include <isl/aff.h>
1695 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1696 __isl_take isl_multi_aff *ma);
1697 __isl_give isl_pw_aff *isl_pw_aff_reset_user(
1698 __isl_take isl_pw_aff *pa);
1699 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1700 __isl_take isl_multi_pw_aff *mpa);
1701 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_reset_user(
1702 __isl_take isl_pw_multi_aff *pma);
1703 __isl_give isl_union_pw_aff *isl_union_pw_aff_reset_user(
1704 __isl_take isl_union_pw_aff *upa);
1705 __isl_give isl_multi_union_pw_aff *
1706 isl_multi_union_pw_aff_reset_user(
1707 __isl_take isl_multi_union_pw_aff *mupa);
1708 __isl_give isl_union_pw_multi_aff *
1709 isl_union_pw_multi_aff_reset_user(
1710 __isl_take isl_union_pw_multi_aff *upma);
1712 #include <isl/polynomial.h>
1713 __isl_give isl_pw_qpolynomial *
1714 isl_pw_qpolynomial_reset_user(
1715 __isl_take isl_pw_qpolynomial *pwqp);
1716 __isl_give isl_union_pw_qpolynomial *
1717 isl_union_pw_qpolynomial_reset_user(
1718 __isl_take isl_union_pw_qpolynomial *upwqp);
1719 __isl_give isl_pw_qpolynomial_fold *
1720 isl_pw_qpolynomial_fold_reset_user(
1721 __isl_take isl_pw_qpolynomial_fold *pwf);
1722 __isl_give isl_union_pw_qpolynomial_fold *
1723 isl_union_pw_qpolynomial_fold_reset_user(
1724 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1726 Spaces can be nested. In particular, the domain of a set or
1727 the domain or range of a relation can be a nested relation.
1728 This process is also called I<wrapping>.
1729 The functions for detecting, constructing and deconstructing
1730 such nested spaces can be found in the wrapping properties
1731 of L</"Unary Properties">, the wrapping operations
1732 of L</"Unary Operations"> and the Cartesian product operations
1733 of L</"Basic Operations">.
1735 Spaces can be created from other spaces
1736 using the functions described in L</"Unary Operations">
1737 and L</"Binary Operations">.
1741 A local space is essentially a space with
1742 zero or more existentially quantified variables.
1743 The local space of various objects can be obtained
1744 using the following functions.
1746 #include <isl/constraint.h>
1747 __isl_give isl_local_space *isl_constraint_get_local_space(
1748 __isl_keep isl_constraint *constraint);
1750 #include <isl/set.h>
1751 __isl_give isl_local_space *isl_basic_set_get_local_space(
1752 __isl_keep isl_basic_set *bset);
1754 #include <isl/map.h>
1755 __isl_give isl_local_space *isl_basic_map_get_local_space(
1756 __isl_keep isl_basic_map *bmap);
1758 #include <isl/aff.h>
1759 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1760 __isl_keep isl_aff *aff);
1761 __isl_give isl_local_space *isl_aff_get_local_space(
1762 __isl_keep isl_aff *aff);
1764 A new local space can be created from a space using
1766 #include <isl/local_space.h>
1767 __isl_give isl_local_space *isl_local_space_from_space(
1768 __isl_take isl_space *space);
1770 They can be inspected, modified, copied and freed using the following functions.
1772 #include <isl/local_space.h>
1773 isl_bool isl_local_space_is_params(
1774 __isl_keep isl_local_space *ls);
1775 isl_bool isl_local_space_is_set(
1776 __isl_keep isl_local_space *ls);
1777 __isl_give isl_space *isl_local_space_get_space(
1778 __isl_keep isl_local_space *ls);
1779 __isl_give isl_aff *isl_local_space_get_div(
1780 __isl_keep isl_local_space *ls, int pos);
1781 __isl_give isl_local_space *isl_local_space_copy(
1782 __isl_keep isl_local_space *ls);
1783 __isl_null isl_local_space *isl_local_space_free(
1784 __isl_take isl_local_space *ls);
1786 Note that C<isl_local_space_get_div> can only be used on local spaces
1789 Two local spaces can be compared using
1791 isl_bool isl_local_space_is_equal(
1792 __isl_keep isl_local_space *ls1,
1793 __isl_keep isl_local_space *ls2);
1795 Local spaces can be created from other local spaces
1796 using the functions described in L</"Unary Operations">
1797 and L</"Binary Operations">.
1799 =head2 Creating New Sets and Relations
1801 C<isl> has functions for creating some standard sets and relations.
1805 =item * Empty sets and relations
1807 __isl_give isl_basic_set *isl_basic_set_empty(
1808 __isl_take isl_space *space);
1809 __isl_give isl_basic_map *isl_basic_map_empty(
1810 __isl_take isl_space *space);
1811 __isl_give isl_set *isl_set_empty(
1812 __isl_take isl_space *space);
1813 __isl_give isl_map *isl_map_empty(
1814 __isl_take isl_space *space);
1815 __isl_give isl_union_set *isl_union_set_empty(
1816 __isl_take isl_space *space);
1817 __isl_give isl_union_map *isl_union_map_empty(
1818 __isl_take isl_space *space);
1820 For C<isl_union_set>s and C<isl_union_map>s, the space
1821 is only used to specify the parameters.
1823 =item * Universe sets and relations
1825 __isl_give isl_basic_set *isl_basic_set_universe(
1826 __isl_take isl_space *space);
1827 __isl_give isl_basic_map *isl_basic_map_universe(
1828 __isl_take isl_space *space);
1829 __isl_give isl_set *isl_set_universe(
1830 __isl_take isl_space *space);
1831 __isl_give isl_map *isl_map_universe(
1832 __isl_take isl_space *space);
1833 __isl_give isl_union_set *isl_union_set_universe(
1834 __isl_take isl_union_set *uset);
1835 __isl_give isl_union_map *isl_union_map_universe(
1836 __isl_take isl_union_map *umap);
1838 The sets and relations constructed by the functions above
1839 contain all integer values, while those constructed by the
1840 functions below only contain non-negative values.
1842 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1843 __isl_take isl_space *space);
1844 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1845 __isl_take isl_space *space);
1846 __isl_give isl_set *isl_set_nat_universe(
1847 __isl_take isl_space *space);
1848 __isl_give isl_map *isl_map_nat_universe(
1849 __isl_take isl_space *space);
1851 =item * Identity relations
1853 __isl_give isl_basic_map *isl_basic_map_identity(
1854 __isl_take isl_space *space);
1855 __isl_give isl_map *isl_map_identity(
1856 __isl_take isl_space *space);
1858 The number of input and output dimensions in C<space> needs
1861 =item * Lexicographic order
1863 __isl_give isl_map *isl_map_lex_lt(
1864 __isl_take isl_space *set_space);
1865 __isl_give isl_map *isl_map_lex_le(
1866 __isl_take isl_space *set_space);
1867 __isl_give isl_map *isl_map_lex_gt(
1868 __isl_take isl_space *set_space);
1869 __isl_give isl_map *isl_map_lex_ge(
1870 __isl_take isl_space *set_space);
1871 __isl_give isl_map *isl_map_lex_lt_first(
1872 __isl_take isl_space *space, unsigned n);
1873 __isl_give isl_map *isl_map_lex_le_first(
1874 __isl_take isl_space *space, unsigned n);
1875 __isl_give isl_map *isl_map_lex_gt_first(
1876 __isl_take isl_space *space, unsigned n);
1877 __isl_give isl_map *isl_map_lex_ge_first(
1878 __isl_take isl_space *space, unsigned n);
1880 The first four functions take a space for a B<set>
1881 and return relations that express that the elements in the domain
1882 are lexicographically less
1883 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1884 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1885 than the elements in the range.
1886 The last four functions take a space for a map
1887 and return relations that express that the first C<n> dimensions
1888 in the domain are lexicographically less
1889 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1890 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1891 than the first C<n> dimensions in the range.
1895 A basic set or relation can be converted to a set or relation
1896 using the following functions.
1898 __isl_give isl_set *isl_set_from_basic_set(
1899 __isl_take isl_basic_set *bset);
1900 __isl_give isl_map *isl_map_from_basic_map(
1901 __isl_take isl_basic_map *bmap);
1903 Sets and relations can be converted to union sets and relations
1904 using the following functions.
1906 __isl_give isl_union_set *isl_union_set_from_basic_set(
1907 __isl_take isl_basic_set *bset);
1908 __isl_give isl_union_map *isl_union_map_from_basic_map(
1909 __isl_take isl_basic_map *bmap);
1910 __isl_give isl_union_set *isl_union_set_from_set(
1911 __isl_take isl_set *set);
1912 __isl_give isl_union_map *isl_union_map_from_map(
1913 __isl_take isl_map *map);
1915 The inverse conversions below can only be used if the input
1916 union set or relation is known to contain elements in exactly one
1919 __isl_give isl_set *isl_set_from_union_set(
1920 __isl_take isl_union_set *uset);
1921 __isl_give isl_map *isl_map_from_union_map(
1922 __isl_take isl_union_map *umap);
1924 Sets and relations can be copied and freed again using the following
1927 __isl_give isl_basic_set *isl_basic_set_copy(
1928 __isl_keep isl_basic_set *bset);
1929 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1930 __isl_give isl_union_set *isl_union_set_copy(
1931 __isl_keep isl_union_set *uset);
1932 __isl_give isl_basic_map *isl_basic_map_copy(
1933 __isl_keep isl_basic_map *bmap);
1934 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1935 __isl_give isl_union_map *isl_union_map_copy(
1936 __isl_keep isl_union_map *umap);
1937 __isl_null isl_basic_set *isl_basic_set_free(
1938 __isl_take isl_basic_set *bset);
1939 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1940 __isl_null isl_union_set *isl_union_set_free(
1941 __isl_take isl_union_set *uset);
1942 __isl_null isl_basic_map *isl_basic_map_free(
1943 __isl_take isl_basic_map *bmap);
1944 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1945 __isl_null isl_union_map *isl_union_map_free(
1946 __isl_take isl_union_map *umap);
1948 Other sets and relations can be constructed by starting
1949 from a universe set or relation, adding equality and/or
1950 inequality constraints and then projecting out the
1951 existentially quantified variables, if any.
1952 Constraints can be constructed, manipulated and
1953 added to (or removed from) (basic) sets and relations
1954 using the following functions.
1956 #include <isl/constraint.h>
1957 __isl_give isl_constraint *isl_constraint_alloc_equality(
1958 __isl_take isl_local_space *ls);
1959 __isl_give isl_constraint *isl_constraint_alloc_inequality(
1960 __isl_take isl_local_space *ls);
1961 __isl_give isl_constraint *isl_constraint_set_constant_si(
1962 __isl_take isl_constraint *constraint, int v);
1963 __isl_give isl_constraint *isl_constraint_set_constant_val(
1964 __isl_take isl_constraint *constraint,
1965 __isl_take isl_val *v);
1966 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1967 __isl_take isl_constraint *constraint,
1968 enum isl_dim_type type, int pos, int v);
1969 __isl_give isl_constraint *
1970 isl_constraint_set_coefficient_val(
1971 __isl_take isl_constraint *constraint,
1972 enum isl_dim_type type, int pos,
1973 __isl_take isl_val *v);
1974 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1975 __isl_take isl_basic_map *bmap,
1976 __isl_take isl_constraint *constraint);
1977 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1978 __isl_take isl_basic_set *bset,
1979 __isl_take isl_constraint *constraint);
1980 __isl_give isl_map *isl_map_add_constraint(
1981 __isl_take isl_map *map,
1982 __isl_take isl_constraint *constraint);
1983 __isl_give isl_set *isl_set_add_constraint(
1984 __isl_take isl_set *set,
1985 __isl_take isl_constraint *constraint);
1987 For example, to create a set containing the even integers
1988 between 10 and 42, you would use the following code.
1991 isl_local_space *ls;
1993 isl_basic_set *bset;
1995 space = isl_space_set_alloc(ctx, 0, 2);
1996 bset = isl_basic_set_universe(isl_space_copy(space));
1997 ls = isl_local_space_from_space(space);
1999 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
2000 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2001 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
2002 bset = isl_basic_set_add_constraint(bset, c);
2004 c = isl_constraint_alloc_inequality(isl_local_space_copy(ls));
2005 c = isl_constraint_set_constant_si(c, -10);
2006 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
2007 bset = isl_basic_set_add_constraint(bset, c);
2009 c = isl_constraint_alloc_inequality(ls);
2010 c = isl_constraint_set_constant_si(c, 42);
2011 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2012 bset = isl_basic_set_add_constraint(bset, c);
2014 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
2018 isl_basic_set *bset;
2019 bset = isl_basic_set_read_from_str(ctx,
2020 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
2022 A basic set or relation can also be constructed from two matrices
2023 describing the equalities and the inequalities.
2025 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
2026 __isl_take isl_space *space,
2027 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2028 enum isl_dim_type c1,
2029 enum isl_dim_type c2, enum isl_dim_type c3,
2030 enum isl_dim_type c4);
2031 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
2032 __isl_take isl_space *space,
2033 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2034 enum isl_dim_type c1,
2035 enum isl_dim_type c2, enum isl_dim_type c3,
2036 enum isl_dim_type c4, enum isl_dim_type c5);
2038 The C<isl_dim_type> arguments indicate the order in which
2039 different kinds of variables appear in the input matrices
2040 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
2041 C<isl_dim_set> and C<isl_dim_div> for sets and
2042 of C<isl_dim_cst>, C<isl_dim_param>,
2043 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
2045 A (basic or union) set or relation can also be constructed from a
2046 (union) (piecewise) (multiple) affine expression
2047 or a list of affine expressions
2048 (See L</"Functions">), provided these affine expressions do not
2051 __isl_give isl_basic_map *isl_basic_map_from_aff(
2052 __isl_take isl_aff *aff);
2053 __isl_give isl_map *isl_map_from_aff(
2054 __isl_take isl_aff *aff);
2055 __isl_give isl_set *isl_set_from_pw_aff(
2056 __isl_take isl_pw_aff *pwaff);
2057 __isl_give isl_map *isl_map_from_pw_aff(
2058 __isl_take isl_pw_aff *pwaff);
2059 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
2060 __isl_take isl_space *domain_space,
2061 __isl_take isl_aff_list *list);
2062 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
2063 __isl_take isl_multi_aff *maff)
2064 __isl_give isl_map *isl_map_from_multi_aff(
2065 __isl_take isl_multi_aff *maff)
2066 __isl_give isl_set *isl_set_from_pw_multi_aff(
2067 __isl_take isl_pw_multi_aff *pma);
2068 __isl_give isl_map *isl_map_from_pw_multi_aff(
2069 __isl_take isl_pw_multi_aff *pma);
2070 __isl_give isl_set *isl_set_from_multi_pw_aff(
2071 __isl_take isl_multi_pw_aff *mpa);
2072 __isl_give isl_map *isl_map_from_multi_pw_aff(
2073 __isl_take isl_multi_pw_aff *mpa);
2074 __isl_give isl_union_map *isl_union_map_from_union_pw_aff(
2075 __isl_take isl_union_pw_aff *upa);
2076 __isl_give isl_union_map *
2077 isl_union_map_from_union_pw_multi_aff(
2078 __isl_take isl_union_pw_multi_aff *upma);
2079 __isl_give isl_union_map *
2080 isl_union_map_from_multi_union_pw_aff(
2081 __isl_take isl_multi_union_pw_aff *mupa);
2083 The C<domain_space> argument describes the domain of the resulting
2084 basic relation. It is required because the C<list> may consist
2085 of zero affine expressions.
2086 The C<mupa> passed to C<isl_union_map_from_multi_union_pw_aff>
2087 is not allowed to be zero-dimensional. The domain of the result
2088 is the shared domain of the union piecewise affine elements.
2090 =head2 Inspecting Sets and Relations
2092 Usually, the user should not have to care about the actual constraints
2093 of the sets and maps, but should instead apply the abstract operations
2094 explained in the following sections.
2095 Occasionally, however, it may be required to inspect the individual
2096 coefficients of the constraints. This section explains how to do so.
2097 In these cases, it may also be useful to have C<isl> compute
2098 an explicit representation of the existentially quantified variables.
2100 __isl_give isl_set *isl_set_compute_divs(
2101 __isl_take isl_set *set);
2102 __isl_give isl_map *isl_map_compute_divs(
2103 __isl_take isl_map *map);
2104 __isl_give isl_union_set *isl_union_set_compute_divs(
2105 __isl_take isl_union_set *uset);
2106 __isl_give isl_union_map *isl_union_map_compute_divs(
2107 __isl_take isl_union_map *umap);
2109 This explicit representation defines the existentially quantified
2110 variables as integer divisions of the other variables, possibly
2111 including earlier existentially quantified variables.
2112 An explicitly represented existentially quantified variable therefore
2113 has a unique value when the values of the other variables are known.
2115 Alternatively, the existentially quantified variables can be removed
2116 using the following functions, which compute an overapproximation.
2118 __isl_give isl_basic_set *isl_basic_set_remove_divs(
2119 __isl_take isl_basic_set *bset);
2120 __isl_give isl_basic_map *isl_basic_map_remove_divs(
2121 __isl_take isl_basic_map *bmap);
2122 __isl_give isl_set *isl_set_remove_divs(
2123 __isl_take isl_set *set);
2124 __isl_give isl_map *isl_map_remove_divs(
2125 __isl_take isl_map *map);
2127 It is also possible to only remove those divs that are defined
2128 in terms of a given range of dimensions or only those for which
2129 no explicit representation is known.
2131 __isl_give isl_basic_set *
2132 isl_basic_set_remove_divs_involving_dims(
2133 __isl_take isl_basic_set *bset,
2134 enum isl_dim_type type,
2135 unsigned first, unsigned n);
2136 __isl_give isl_basic_map *
2137 isl_basic_map_remove_divs_involving_dims(
2138 __isl_take isl_basic_map *bmap,
2139 enum isl_dim_type type,
2140 unsigned first, unsigned n);
2141 __isl_give isl_set *isl_set_remove_divs_involving_dims(
2142 __isl_take isl_set *set, enum isl_dim_type type,
2143 unsigned first, unsigned n);
2144 __isl_give isl_map *isl_map_remove_divs_involving_dims(
2145 __isl_take isl_map *map, enum isl_dim_type type,
2146 unsigned first, unsigned n);
2148 __isl_give isl_basic_set *
2149 isl_basic_set_remove_unknown_divs(
2150 __isl_take isl_basic_set *bset);
2151 __isl_give isl_set *isl_set_remove_unknown_divs(
2152 __isl_take isl_set *set);
2153 __isl_give isl_map *isl_map_remove_unknown_divs(
2154 __isl_take isl_map *map);
2156 To iterate over all the sets or maps in a union set or map, use
2158 isl_stat isl_union_set_foreach_set(
2159 __isl_keep isl_union_set *uset,
2160 isl_stat (*fn)(__isl_take isl_set *set, void *user),
2162 isl_stat isl_union_map_foreach_map(
2163 __isl_keep isl_union_map *umap,
2164 isl_stat (*fn)(__isl_take isl_map *map, void *user),
2167 These functions call the callback function once for each
2168 (pair of) space(s) for which there are elements in the input.
2169 The argument to the callback contains all elements in the input
2170 with that (pair of) space(s).
2172 The number of sets or maps in a union set or map can be obtained
2175 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
2176 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
2178 To extract the set or map in a given space from a union, use
2180 __isl_give isl_set *isl_union_set_extract_set(
2181 __isl_keep isl_union_set *uset,
2182 __isl_take isl_space *space);
2183 __isl_give isl_map *isl_union_map_extract_map(
2184 __isl_keep isl_union_map *umap,
2185 __isl_take isl_space *space);
2187 To iterate over all the basic sets or maps in a set or map, use
2189 isl_stat isl_set_foreach_basic_set(__isl_keep isl_set *set,
2190 isl_stat (*fn)(__isl_take isl_basic_set *bset,
2193 isl_stat isl_map_foreach_basic_map(__isl_keep isl_map *map,
2194 isl_stat (*fn)(__isl_take isl_basic_map *bmap,
2198 The callback function C<fn> should return 0 if successful and
2199 -1 if an error occurs. In the latter case, or if any other error
2200 occurs, the above functions will return -1.
2202 It should be noted that C<isl> does not guarantee that
2203 the basic sets or maps passed to C<fn> are disjoint.
2204 If this is required, then the user should call one of
2205 the following functions first.
2207 __isl_give isl_set *isl_set_make_disjoint(
2208 __isl_take isl_set *set);
2209 __isl_give isl_map *isl_map_make_disjoint(
2210 __isl_take isl_map *map);
2212 The number of basic sets in a set can be obtained
2213 or the number of basic maps in a map can be obtained
2216 #include <isl/set.h>
2217 int isl_set_n_basic_set(__isl_keep isl_set *set);
2219 #include <isl/map.h>
2220 int isl_map_n_basic_map(__isl_keep isl_map *map);
2222 It is also possible to obtain a list of basic sets from a set
2224 #include <isl/set.h>
2225 __isl_give isl_basic_set_list *isl_set_get_basic_set_list(
2226 __isl_keep isl_set *set);
2228 The returned list can be manipulated using the functions in L<"Lists">.
2230 To iterate over the constraints of a basic set or map, use
2232 #include <isl/constraint.h>
2234 int isl_basic_set_n_constraint(
2235 __isl_keep isl_basic_set *bset);
2236 isl_stat isl_basic_set_foreach_constraint(
2237 __isl_keep isl_basic_set *bset,
2238 isl_stat (*fn)(__isl_take isl_constraint *c,
2241 int isl_basic_map_n_constraint(
2242 __isl_keep isl_basic_map *bmap);
2243 isl_stat isl_basic_map_foreach_constraint(
2244 __isl_keep isl_basic_map *bmap,
2245 isl_stat (*fn)(__isl_take isl_constraint *c,
2248 __isl_null isl_constraint *isl_constraint_free(
2249 __isl_take isl_constraint *c);
2251 Again, the callback function C<fn> should return 0 if successful and
2252 -1 if an error occurs. In the latter case, or if any other error
2253 occurs, the above functions will return -1.
2254 The constraint C<c> represents either an equality or an inequality.
2255 Use the following function to find out whether a constraint
2256 represents an equality. If not, it represents an inequality.
2258 isl_bool isl_constraint_is_equality(
2259 __isl_keep isl_constraint *constraint);
2261 It is also possible to obtain a list of constraints from a basic
2264 #include <isl/constraint.h>
2265 __isl_give isl_constraint_list *
2266 isl_basic_map_get_constraint_list(
2267 __isl_keep isl_basic_map *bmap);
2268 __isl_give isl_constraint_list *
2269 isl_basic_set_get_constraint_list(
2270 __isl_keep isl_basic_set *bset);
2272 These functions require that all existentially quantified variables
2273 have an explicit representation.
2274 The returned list can be manipulated using the functions in L<"Lists">.
2276 The coefficients of the constraints can be inspected using
2277 the following functions.
2279 isl_bool isl_constraint_is_lower_bound(
2280 __isl_keep isl_constraint *constraint,
2281 enum isl_dim_type type, unsigned pos);
2282 isl_bool isl_constraint_is_upper_bound(
2283 __isl_keep isl_constraint *constraint,
2284 enum isl_dim_type type, unsigned pos);
2285 __isl_give isl_val *isl_constraint_get_constant_val(
2286 __isl_keep isl_constraint *constraint);
2287 __isl_give isl_val *isl_constraint_get_coefficient_val(
2288 __isl_keep isl_constraint *constraint,
2289 enum isl_dim_type type, int pos);
2291 The explicit representations of the existentially quantified
2292 variables can be inspected using the following function.
2293 Note that the user is only allowed to use this function
2294 if the inspected set or map is the result of a call
2295 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2296 The existentially quantified variable is equal to the floor
2297 of the returned affine expression. The affine expression
2298 itself can be inspected using the functions in
2301 __isl_give isl_aff *isl_constraint_get_div(
2302 __isl_keep isl_constraint *constraint, int pos);
2304 To obtain the constraints of a basic set or map in matrix
2305 form, use the following functions.
2307 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2308 __isl_keep isl_basic_set *bset,
2309 enum isl_dim_type c1, enum isl_dim_type c2,
2310 enum isl_dim_type c3, enum isl_dim_type c4);
2311 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2312 __isl_keep isl_basic_set *bset,
2313 enum isl_dim_type c1, enum isl_dim_type c2,
2314 enum isl_dim_type c3, enum isl_dim_type c4);
2315 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2316 __isl_keep isl_basic_map *bmap,
2317 enum isl_dim_type c1,
2318 enum isl_dim_type c2, enum isl_dim_type c3,
2319 enum isl_dim_type c4, enum isl_dim_type c5);
2320 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2321 __isl_keep isl_basic_map *bmap,
2322 enum isl_dim_type c1,
2323 enum isl_dim_type c2, enum isl_dim_type c3,
2324 enum isl_dim_type c4, enum isl_dim_type c5);
2326 The C<isl_dim_type> arguments dictate the order in which
2327 different kinds of variables appear in the resulting matrix.
2328 For set inputs, they should be a permutation of
2329 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
2330 For map inputs, they should be a permutation of
2331 C<isl_dim_cst>, C<isl_dim_param>,
2332 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2336 Points are elements of a set. They can be used to construct
2337 simple sets (boxes) or they can be used to represent the
2338 individual elements of a set.
2339 The zero point (the origin) can be created using
2341 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2343 The coordinates of a point can be inspected, set and changed
2346 __isl_give isl_val *isl_point_get_coordinate_val(
2347 __isl_keep isl_point *pnt,
2348 enum isl_dim_type type, int pos);
2349 __isl_give isl_point *isl_point_set_coordinate_val(
2350 __isl_take isl_point *pnt,
2351 enum isl_dim_type type, int pos,
2352 __isl_take isl_val *v);
2354 __isl_give isl_point *isl_point_add_ui(
2355 __isl_take isl_point *pnt,
2356 enum isl_dim_type type, int pos, unsigned val);
2357 __isl_give isl_point *isl_point_sub_ui(
2358 __isl_take isl_point *pnt,
2359 enum isl_dim_type type, int pos, unsigned val);
2361 Points can be copied or freed using
2363 __isl_give isl_point *isl_point_copy(
2364 __isl_keep isl_point *pnt);
2365 __isl_null isl_point *isl_point_free(
2366 __isl_take isl_point *pnt);
2368 A singleton set can be created from a point using
2370 __isl_give isl_basic_set *isl_basic_set_from_point(
2371 __isl_take isl_point *pnt);
2372 __isl_give isl_set *isl_set_from_point(
2373 __isl_take isl_point *pnt);
2374 __isl_give isl_union_set *isl_union_set_from_point(
2375 __isl_take isl_point *pnt);
2377 and a box can be created from two opposite extremal points using
2379 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2380 __isl_take isl_point *pnt1,
2381 __isl_take isl_point *pnt2);
2382 __isl_give isl_set *isl_set_box_from_points(
2383 __isl_take isl_point *pnt1,
2384 __isl_take isl_point *pnt2);
2386 All elements of a B<bounded> (union) set can be enumerated using
2387 the following functions.
2389 isl_stat isl_set_foreach_point(__isl_keep isl_set *set,
2390 isl_stat (*fn)(__isl_take isl_point *pnt,
2393 isl_stat isl_union_set_foreach_point(
2394 __isl_keep isl_union_set *uset,
2395 isl_stat (*fn)(__isl_take isl_point *pnt,
2399 The function C<fn> is called for each integer point in
2400 C<set> with as second argument the last argument of
2401 the C<isl_set_foreach_point> call. The function C<fn>
2402 should return C<0> on success and C<-1> on failure.
2403 In the latter case, C<isl_set_foreach_point> will stop
2404 enumerating and return C<-1> as well.
2405 If the enumeration is performed successfully and to completion,
2406 then C<isl_set_foreach_point> returns C<0>.
2408 To obtain a single point of a (basic or union) set, use
2410 __isl_give isl_point *isl_basic_set_sample_point(
2411 __isl_take isl_basic_set *bset);
2412 __isl_give isl_point *isl_set_sample_point(
2413 __isl_take isl_set *set);
2414 __isl_give isl_point *isl_union_set_sample_point(
2415 __isl_take isl_union_set *uset);
2417 If C<set> does not contain any (integer) points, then the
2418 resulting point will be ``void'', a property that can be
2421 isl_bool isl_point_is_void(__isl_keep isl_point *pnt);
2425 Besides sets and relation, C<isl> also supports various types of functions.
2426 Each of these types is derived from the value type (see L</"Values">)
2427 or from one of two primitive function types
2428 through the application of zero or more type constructors.
2429 We first describe the primitive type and then we describe
2430 the types derived from these primitive types.
2432 =head3 Primitive Functions
2434 C<isl> support two primitive function types, quasi-affine
2435 expressions and quasipolynomials.
2436 A quasi-affine expression is defined either over a parameter
2437 space or over a set and is composed of integer constants,
2438 parameters and set variables, addition, subtraction and
2439 integer division by an integer constant.
2440 For example, the quasi-affine expression
2442 [n] -> { [x] -> [2*floor((4 n + x)/9] }
2444 maps C<x> to C<2*floor((4 n + x)/9>.
2445 A quasipolynomial is a polynomial expression in quasi-affine
2446 expression. That is, it additionally allows for multiplication.
2447 Note, though, that it is not allowed to construct an integer
2448 division of an expression involving multiplications.
2449 Here is an example of a quasipolynomial that is not
2450 quasi-affine expression
2452 [n] -> { [x] -> (n*floor((4 n + x)/9) }
2454 Note that the external representations of quasi-affine expressions
2455 and quasipolynomials are different. Quasi-affine expressions
2456 use a notation with square brackets just like binary relations,
2457 while quasipolynomials do not. This might change at some point.
2459 If a primitive function is defined over a parameter space,
2460 then the space of the function itself is that of a set.
2461 If it is defined over a set, then the space of the function
2462 is that of a relation. In both cases, the set space (or
2463 the output space) is single-dimensional, anonymous and unstructured.
2464 To create functions with multiple dimensions or with other kinds
2465 of set or output spaces, use multiple expressions
2466 (see L</"Multiple Expressions">).
2470 =item * Quasi-affine Expressions
2472 Besides the expressions described above, a quasi-affine
2473 expression can also be set to NaN. Such expressions
2474 typically represent a failure to represent a result
2475 as a quasi-affine expression.
2477 The zero quasi affine expression or the quasi affine expression
2478 that is equal to a given value or
2479 a specified dimension on a given domain can be created using
2481 #include <isl/aff.h>
2482 __isl_give isl_aff *isl_aff_zero_on_domain(
2483 __isl_take isl_local_space *ls);
2484 __isl_give isl_aff *isl_aff_val_on_domain(
2485 __isl_take isl_local_space *ls,
2486 __isl_take isl_val *val);
2487 __isl_give isl_aff *isl_aff_var_on_domain(
2488 __isl_take isl_local_space *ls,
2489 enum isl_dim_type type, unsigned pos);
2490 __isl_give isl_aff *isl_aff_nan_on_domain(
2491 __isl_take isl_local_space *ls);
2493 Quasi affine expressions can be copied and freed using
2495 #include <isl/aff.h>
2496 __isl_give isl_aff *isl_aff_copy(
2497 __isl_keep isl_aff *aff);
2498 __isl_null isl_aff *isl_aff_free(
2499 __isl_take isl_aff *aff);
2501 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2502 using the following function. The constraint is required to have
2503 a non-zero coefficient for the specified dimension.
2505 #include <isl/constraint.h>
2506 __isl_give isl_aff *isl_constraint_get_bound(
2507 __isl_keep isl_constraint *constraint,
2508 enum isl_dim_type type, int pos);
2510 The entire affine expression of the constraint can also be extracted
2511 using the following function.
2513 #include <isl/constraint.h>
2514 __isl_give isl_aff *isl_constraint_get_aff(
2515 __isl_keep isl_constraint *constraint);
2517 Conversely, an equality constraint equating
2518 the affine expression to zero or an inequality constraint enforcing
2519 the affine expression to be non-negative, can be constructed using
2521 __isl_give isl_constraint *isl_equality_from_aff(
2522 __isl_take isl_aff *aff);
2523 __isl_give isl_constraint *isl_inequality_from_aff(
2524 __isl_take isl_aff *aff);
2526 The coefficients and the integer divisions of an affine expression
2527 can be inspected using the following functions.
2529 #include <isl/aff.h>
2530 __isl_give isl_val *isl_aff_get_constant_val(
2531 __isl_keep isl_aff *aff);
2532 __isl_give isl_val *isl_aff_get_coefficient_val(
2533 __isl_keep isl_aff *aff,
2534 enum isl_dim_type type, int pos);
2535 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2536 enum isl_dim_type type, int pos);
2537 __isl_give isl_val *isl_aff_get_denominator_val(
2538 __isl_keep isl_aff *aff);
2539 __isl_give isl_aff *isl_aff_get_div(
2540 __isl_keep isl_aff *aff, int pos);
2542 They can be modified using the following functions.
2544 #include <isl/aff.h>
2545 __isl_give isl_aff *isl_aff_set_constant_si(
2546 __isl_take isl_aff *aff, int v);
2547 __isl_give isl_aff *isl_aff_set_constant_val(
2548 __isl_take isl_aff *aff, __isl_take isl_val *v);
2549 __isl_give isl_aff *isl_aff_set_coefficient_si(
2550 __isl_take isl_aff *aff,
2551 enum isl_dim_type type, int pos, int v);
2552 __isl_give isl_aff *isl_aff_set_coefficient_val(
2553 __isl_take isl_aff *aff,
2554 enum isl_dim_type type, int pos,
2555 __isl_take isl_val *v);
2557 __isl_give isl_aff *isl_aff_add_constant_si(
2558 __isl_take isl_aff *aff, int v);
2559 __isl_give isl_aff *isl_aff_add_constant_val(
2560 __isl_take isl_aff *aff, __isl_take isl_val *v);
2561 __isl_give isl_aff *isl_aff_add_constant_num_si(
2562 __isl_take isl_aff *aff, int v);
2563 __isl_give isl_aff *isl_aff_add_coefficient_si(
2564 __isl_take isl_aff *aff,
2565 enum isl_dim_type type, int pos, int v);
2566 __isl_give isl_aff *isl_aff_add_coefficient_val(
2567 __isl_take isl_aff *aff,
2568 enum isl_dim_type type, int pos,
2569 __isl_take isl_val *v);
2571 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
2572 set the I<numerator> of the constant or coefficient, while
2573 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
2574 the constant or coefficient as a whole.
2575 The C<add_constant> and C<add_coefficient> functions add an integer
2576 or rational value to
2577 the possibly rational constant or coefficient.
2578 The C<add_constant_num> functions add an integer value to
2581 =item * Quasipolynomials
2583 Some simple quasipolynomials can be created using the following functions.
2585 #include <isl/polynomial.h>
2586 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2587 __isl_take isl_space *domain);
2588 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2589 __isl_take isl_space *domain);
2590 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2591 __isl_take isl_space *domain);
2592 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2593 __isl_take isl_space *domain);
2594 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2595 __isl_take isl_space *domain);
2596 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2597 __isl_take isl_space *domain,
2598 __isl_take isl_val *val);
2599 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2600 __isl_take isl_space *domain,
2601 enum isl_dim_type type, unsigned pos);
2602 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2603 __isl_take isl_aff *aff);
2605 Recall that the space in which a quasipolynomial lives is a map space
2606 with a one-dimensional range. The C<domain> argument in some of
2607 the functions above corresponds to the domain of this map space.
2609 Quasipolynomials can be copied and freed again using the following
2612 #include <isl/polynomial.h>
2613 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2614 __isl_keep isl_qpolynomial *qp);
2615 __isl_null isl_qpolynomial *isl_qpolynomial_free(
2616 __isl_take isl_qpolynomial *qp);
2618 The constant term of a quasipolynomial can be extracted using
2620 __isl_give isl_val *isl_qpolynomial_get_constant_val(
2621 __isl_keep isl_qpolynomial *qp);
2623 To iterate over all terms in a quasipolynomial,
2626 isl_stat isl_qpolynomial_foreach_term(
2627 __isl_keep isl_qpolynomial *qp,
2628 isl_stat (*fn)(__isl_take isl_term *term,
2629 void *user), void *user);
2631 The terms themselves can be inspected and freed using
2634 unsigned isl_term_dim(__isl_keep isl_term *term,
2635 enum isl_dim_type type);
2636 __isl_give isl_val *isl_term_get_coefficient_val(
2637 __isl_keep isl_term *term);
2638 int isl_term_get_exp(__isl_keep isl_term *term,
2639 enum isl_dim_type type, unsigned pos);
2640 __isl_give isl_aff *isl_term_get_div(
2641 __isl_keep isl_term *term, unsigned pos);
2642 void isl_term_free(__isl_take isl_term *term);
2644 Each term is a product of parameters, set variables and
2645 integer divisions. The function C<isl_term_get_exp>
2646 returns the exponent of a given dimensions in the given term.
2652 A reduction represents a maximum or a minimum of its
2654 The only reduction type defined by C<isl> is
2655 C<isl_qpolynomial_fold>.
2657 There are currently no functions to directly create such
2658 objects, but they do appear in the piecewise quasipolynomial
2659 reductions returned by the C<isl_pw_qpolynomial_bound> function.
2661 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
2663 Reductions can be copied and freed using
2664 the following functions.
2666 #include <isl/polynomial.h>
2667 __isl_give isl_qpolynomial_fold *
2668 isl_qpolynomial_fold_copy(
2669 __isl_keep isl_qpolynomial_fold *fold);
2670 void isl_qpolynomial_fold_free(
2671 __isl_take isl_qpolynomial_fold *fold);
2673 To iterate over all quasipolynomials in a reduction, use
2675 isl_stat isl_qpolynomial_fold_foreach_qpolynomial(
2676 __isl_keep isl_qpolynomial_fold *fold,
2677 isl_stat (*fn)(__isl_take isl_qpolynomial *qp,
2678 void *user), void *user);
2680 =head3 Multiple Expressions
2682 A multiple expression represents a sequence of zero or
2683 more base expressions, all defined on the same domain space.
2684 The domain space of the multiple expression is the same
2685 as that of the base expressions, but the range space
2686 can be any space. In case the base expressions have
2687 a set space, the corresponding multiple expression
2688 also has a set space.
2689 Objects of the value type do not have an associated space.
2690 The space of a multiple value is therefore always a set space.
2691 Similarly, the space of a multiple union piecewise
2692 affine expression is always a set space.
2694 The multiple expression types defined by C<isl>
2695 are C<isl_multi_val>, C<isl_multi_aff>, C<isl_multi_pw_aff>,
2696 C<isl_multi_union_pw_aff>.
2698 A multiple expression with the value zero for
2699 each output (or set) dimension can be created
2700 using the following functions.
2702 #include <isl/val.h>
2703 __isl_give isl_multi_val *isl_multi_val_zero(
2704 __isl_take isl_space *space);
2706 #include <isl/aff.h>
2707 __isl_give isl_multi_aff *isl_multi_aff_zero(
2708 __isl_take isl_space *space);
2709 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
2710 __isl_take isl_space *space);
2711 __isl_give isl_multi_union_pw_aff *
2712 isl_multi_union_pw_aff_zero(
2713 __isl_take isl_space *space);
2715 Since there is no canonical way of representing a zero
2716 value of type C<isl_union_pw_aff>, the space passed
2717 to C<isl_multi_union_pw_aff_zero> needs to be zero-dimensional.
2719 An identity function can be created using the following
2720 functions. The space needs to be that of a relation
2721 with the same number of input and output dimensions.
2723 #include <isl/aff.h>
2724 __isl_give isl_multi_aff *isl_multi_aff_identity(
2725 __isl_take isl_space *space);
2726 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
2727 __isl_take isl_space *space);
2729 A function that performs a projection on a universe
2730 relation or set can be created using the following functions.
2731 See also the corresponding
2732 projection operations in L</"Unary Operations">.
2734 #include <isl/aff.h>
2735 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
2736 __isl_take isl_space *space);
2737 __isl_give isl_multi_aff *isl_multi_aff_range_map(
2738 __isl_take isl_space *space);
2739 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
2740 __isl_take isl_space *space,
2741 enum isl_dim_type type,
2742 unsigned first, unsigned n);
2744 A multiple expression can be created from a single
2745 base expression using the following functions.
2746 The space of the created multiple expression is the same
2747 as that of the base expression, except for
2748 C<isl_multi_union_pw_aff_from_union_pw_aff> where the input
2749 lives in a parameter space and the output lives
2750 in a single-dimensional set space.
2752 #include <isl/aff.h>
2753 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
2754 __isl_take isl_aff *aff);
2755 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
2756 __isl_take isl_pw_aff *pa);
2757 __isl_give isl_multi_union_pw_aff *
2758 isl_multi_union_pw_aff_from_union_pw_aff(
2759 __isl_take isl_union_pw_aff *upa);
2761 A multiple expression can be created from a list
2762 of base expression in a specified space.
2763 The domain of this space needs to be the same
2764 as the domains of the base expressions in the list.
2765 If the base expressions have a set space (or no associated space),
2766 then this space also needs to be a set space.
2768 #include <isl/val.h>
2769 __isl_give isl_multi_val *isl_multi_val_from_val_list(
2770 __isl_take isl_space *space,
2771 __isl_take isl_val_list *list);
2773 #include <isl/aff.h>
2774 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2775 __isl_take isl_space *space,
2776 __isl_take isl_aff_list *list);
2777 __isl_give isl_multi_pw_aff *
2778 isl_multi_pw_aff_from_pw_aff_list(
2779 __isl_take isl_space *space,
2780 __isl_take isl_pw_aff_list *list);
2781 __isl_give isl_multi_union_pw_aff *
2782 isl_multi_union_pw_aff_from_union_pw_aff_list(
2783 __isl_take isl_space *space,
2784 __isl_take isl_union_pw_aff_list *list);
2786 As a convenience, a multiple piecewise expression can
2787 also be created from a multiple expression.
2788 Each piecewise expression in the result has a single
2791 #include <isl/aff.h>
2792 __isl_give isl_multi_pw_aff *
2793 isl_multi_pw_aff_from_multi_aff(
2794 __isl_take isl_multi_aff *ma);
2796 Similarly, a multiple union expression can be
2797 created from a multiple expression.
2799 #include <isl/aff.h>
2800 __isl_give isl_multi_union_pw_aff *
2801 isl_multi_union_pw_aff_from_multi_aff(
2802 __isl_take isl_multi_aff *ma);
2803 __isl_give isl_multi_union_pw_aff *
2804 isl_multi_union_pw_aff_from_multi_pw_aff(
2805 __isl_take isl_multi_pw_aff *mpa);
2807 A multiple quasi-affine expression can be created from
2808 a multiple value with a given domain space using the following
2811 #include <isl/aff.h>
2812 __isl_give isl_multi_aff *
2813 isl_multi_aff_multi_val_on_space(
2814 __isl_take isl_space *space,
2815 __isl_take isl_multi_val *mv);
2818 a multiple union piecewise affine expression can be created from
2819 a multiple value with a given domain or
2820 a multiple affine expression with a given domain
2821 using the following functions.
2823 #include <isl/aff.h>
2824 __isl_give isl_multi_union_pw_aff *
2825 isl_multi_union_pw_aff_multi_val_on_domain(
2826 __isl_take isl_union_set *domain,
2827 __isl_take isl_multi_val *mv);
2828 __isl_give isl_multi_union_pw_aff *
2829 isl_multi_union_pw_aff_multi_aff_on_domain(
2830 __isl_take isl_union_set *domain,
2831 __isl_take isl_multi_aff *ma);
2833 Multiple expressions can be copied and freed using
2834 the following functions.
2836 #include <isl/val.h>
2837 __isl_give isl_multi_val *isl_multi_val_copy(
2838 __isl_keep isl_multi_val *mv);
2839 __isl_null isl_multi_val *isl_multi_val_free(
2840 __isl_take isl_multi_val *mv);
2842 #include <isl/aff.h>
2843 __isl_give isl_multi_aff *isl_multi_aff_copy(
2844 __isl_keep isl_multi_aff *maff);
2845 __isl_null isl_multi_aff *isl_multi_aff_free(
2846 __isl_take isl_multi_aff *maff);
2847 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
2848 __isl_keep isl_multi_pw_aff *mpa);
2849 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
2850 __isl_take isl_multi_pw_aff *mpa);
2851 __isl_give isl_multi_union_pw_aff *
2852 isl_multi_union_pw_aff_copy(
2853 __isl_keep isl_multi_union_pw_aff *mupa);
2854 __isl_null isl_multi_union_pw_aff *
2855 isl_multi_union_pw_aff_free(
2856 __isl_take isl_multi_union_pw_aff *mupa);
2858 The base expression at a given position of a multiple
2859 expression can be extracted using the following functions.
2861 #include <isl/val.h>
2862 __isl_give isl_val *isl_multi_val_get_val(
2863 __isl_keep isl_multi_val *mv, int pos);
2865 #include <isl/aff.h>
2866 __isl_give isl_aff *isl_multi_aff_get_aff(
2867 __isl_keep isl_multi_aff *multi, int pos);
2868 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
2869 __isl_keep isl_multi_pw_aff *mpa, int pos);
2870 __isl_give isl_union_pw_aff *
2871 isl_multi_union_pw_aff_get_union_pw_aff(
2872 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
2874 It can be replaced using the following functions.
2876 #include <isl/val.h>
2877 __isl_give isl_multi_val *isl_multi_val_set_val(
2878 __isl_take isl_multi_val *mv, int pos,
2879 __isl_take isl_val *val);
2881 #include <isl/aff.h>
2882 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
2883 __isl_take isl_multi_aff *multi, int pos,
2884 __isl_take isl_aff *aff);
2885 __isl_give isl_multi_union_pw_aff *
2886 isl_multi_union_pw_aff_set_union_pw_aff(
2887 __isl_take isl_multi_union_pw_aff *mupa, int pos,
2888 __isl_take isl_union_pw_aff *upa);
2890 As a convenience, a sequence of base expressions that have
2891 their domains in a given space can be extracted from a sequence
2892 of union expressions using the following function.
2894 #include <isl/aff.h>
2895 __isl_give isl_multi_pw_aff *
2896 isl_multi_union_pw_aff_extract_multi_pw_aff(
2897 __isl_keep isl_multi_union_pw_aff *mupa,
2898 __isl_take isl_space *space);
2900 Note that there is a difference between C<isl_multi_union_pw_aff>
2901 and C<isl_union_pw_multi_aff> objects. The first is a sequence
2902 of unions of piecewise expressions, while the second is a union
2903 of piecewise sequences. In particular, multiple affine expressions
2904 in an C<isl_union_pw_multi_aff> may live in different spaces,
2905 while there is only a single multiple expression in
2906 an C<isl_multi_union_pw_aff>, which can therefore only live
2907 in a single space. This means that not every
2908 C<isl_union_pw_multi_aff> can be converted to
2909 an C<isl_multi_union_pw_aff>. Conversely, a zero-dimensional
2910 C<isl_multi_union_pw_aff> carries no information
2911 about any possible domain and therefore cannot be converted
2912 to an C<isl_union_pw_multi_aff>. Moreover, the elements
2913 of an C<isl_multi_union_pw_aff> may be defined over different domains,
2914 while each multiple expression inside an C<isl_union_pw_multi_aff>
2915 has a single domain. The conversion of an C<isl_union_pw_multi_aff>
2916 of dimension greater than one may therefore not be exact.
2917 The following functions can
2918 be used to perform these conversions when they are possible.
2920 #include <isl/aff.h>
2921 __isl_give isl_multi_union_pw_aff *
2922 isl_multi_union_pw_aff_from_union_pw_multi_aff(
2923 __isl_take isl_union_pw_multi_aff *upma);
2924 __isl_give isl_union_pw_multi_aff *
2925 isl_union_pw_multi_aff_from_multi_union_pw_aff(
2926 __isl_take isl_multi_union_pw_aff *mupa);
2928 =head3 Piecewise Expressions
2930 A piecewise expression is an expression that is described
2931 using zero or more base expression defined over the same
2932 number of cells in the domain space of the base expressions.
2933 All base expressions are defined over the same
2934 domain space and the cells are disjoint.
2935 The space of a piecewise expression is the same as
2936 that of the base expressions.
2937 If the union of the cells is a strict subset of the domain
2938 space, then the value of the piecewise expression outside
2939 this union is different for types derived from quasi-affine
2940 expressions and those derived from quasipolynomials.
2941 Piecewise expressions derived from quasi-affine expressions
2942 are considered to be undefined outside the union of their cells.
2943 Piecewise expressions derived from quasipolynomials
2944 are considered to be zero outside the union of their cells.
2946 Piecewise quasipolynomials are mainly used by the C<barvinok>
2947 library for representing the number of elements in a parametric set or map.
2948 For example, the piecewise quasipolynomial
2950 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2952 represents the number of points in the map
2954 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2956 The piecewise expression types defined by C<isl>
2957 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
2958 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
2960 A piecewise expression with no cells can be created using
2961 the following functions.
2963 #include <isl/aff.h>
2964 __isl_give isl_pw_aff *isl_pw_aff_empty(
2965 __isl_take isl_space *space);
2966 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
2967 __isl_take isl_space *space);
2969 A piecewise expression with a single universe cell can be
2970 created using the following functions.
2972 #include <isl/aff.h>
2973 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2974 __isl_take isl_aff *aff);
2975 __isl_give isl_pw_multi_aff *
2976 isl_pw_multi_aff_from_multi_aff(
2977 __isl_take isl_multi_aff *ma);
2979 #include <isl/polynomial.h>
2980 __isl_give isl_pw_qpolynomial *
2981 isl_pw_qpolynomial_from_qpolynomial(
2982 __isl_take isl_qpolynomial *qp);
2984 A piecewise expression with a single specified cell can be
2985 created using the following functions.
2987 #include <isl/aff.h>
2988 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2989 __isl_take isl_set *set, __isl_take isl_aff *aff);
2990 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
2991 __isl_take isl_set *set,
2992 __isl_take isl_multi_aff *maff);
2994 #include <isl/polynomial.h>
2995 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2996 __isl_take isl_set *set,
2997 __isl_take isl_qpolynomial *qp);
2999 The following convenience functions first create a base expression and
3000 then create a piecewise expression over a universe domain.
3002 #include <isl/aff.h>
3003 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3004 __isl_take isl_local_space *ls);
3005 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3006 __isl_take isl_local_space *ls,
3007 enum isl_dim_type type, unsigned pos);
3008 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3009 __isl_take isl_local_space *ls);
3010 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
3011 __isl_take isl_space *space);
3012 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3013 __isl_take isl_space *space);
3014 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
3015 __isl_take isl_space *space);
3016 __isl_give isl_pw_multi_aff *
3017 isl_pw_multi_aff_project_out_map(
3018 __isl_take isl_space *space,
3019 enum isl_dim_type type,
3020 unsigned first, unsigned n);
3022 #include <isl/polynomial.h>
3023 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3024 __isl_take isl_space *space);
3026 The following convenience functions first create a base expression and
3027 then create a piecewise expression over a given domain.
3029 #include <isl/aff.h>
3030 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
3031 __isl_take isl_set *domain,
3032 __isl_take isl_val *v);
3033 __isl_give isl_pw_multi_aff *
3034 isl_pw_multi_aff_multi_val_on_domain(
3035 __isl_take isl_set *domain,
3036 __isl_take isl_multi_val *mv);
3038 As a convenience, a piecewise multiple expression can
3039 also be created from a piecewise expression.
3040 Each multiple expression in the result is derived
3041 from the corresponding base expression.
3043 #include <isl/aff.h>
3044 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
3045 __isl_take isl_pw_aff *pa);
3047 Similarly, a piecewise quasipolynomial can be
3048 created from a piecewise quasi-affine expression using
3049 the following function.
3051 #include <isl/polynomial.h>
3052 __isl_give isl_pw_qpolynomial *
3053 isl_pw_qpolynomial_from_pw_aff(
3054 __isl_take isl_pw_aff *pwaff);
3056 Piecewise expressions can be copied and freed using the following functions.
3058 #include <isl/aff.h>
3059 __isl_give isl_pw_aff *isl_pw_aff_copy(
3060 __isl_keep isl_pw_aff *pwaff);
3061 __isl_null isl_pw_aff *isl_pw_aff_free(
3062 __isl_take isl_pw_aff *pwaff);
3063 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3064 __isl_keep isl_pw_multi_aff *pma);
3065 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
3066 __isl_take isl_pw_multi_aff *pma);
3068 #include <isl/polynomial.h>
3069 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3070 __isl_keep isl_pw_qpolynomial *pwqp);
3071 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
3072 __isl_take isl_pw_qpolynomial *pwqp);
3073 __isl_give isl_pw_qpolynomial_fold *
3074 isl_pw_qpolynomial_fold_copy(
3075 __isl_keep isl_pw_qpolynomial_fold *pwf);
3076 __isl_null isl_pw_qpolynomial_fold *
3077 isl_pw_qpolynomial_fold_free(
3078 __isl_take isl_pw_qpolynomial_fold *pwf);
3080 To iterate over the different cells of a piecewise expression,
3081 use the following functions.
3083 #include <isl/aff.h>
3084 isl_bool isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3085 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3086 isl_stat isl_pw_aff_foreach_piece(
3087 __isl_keep isl_pw_aff *pwaff,
3088 isl_stat (*fn)(__isl_take isl_set *set,
3089 __isl_take isl_aff *aff,
3090 void *user), void *user);
3091 int isl_pw_multi_aff_n_piece(
3092 __isl_keep isl_pw_multi_aff *pma);
3093 isl_stat isl_pw_multi_aff_foreach_piece(
3094 __isl_keep isl_pw_multi_aff *pma,
3095 isl_stat (*fn)(__isl_take isl_set *set,
3096 __isl_take isl_multi_aff *maff,
3097 void *user), void *user);
3099 #include <isl/polynomial.h>
3100 int isl_pw_qpolynomial_n_piece(
3101 __isl_keep isl_pw_qpolynomial *pwqp);
3102 isl_stat isl_pw_qpolynomial_foreach_piece(
3103 __isl_keep isl_pw_qpolynomial *pwqp,
3104 isl_stat (*fn)(__isl_take isl_set *set,
3105 __isl_take isl_qpolynomial *qp,
3106 void *user), void *user);
3107 isl_stat isl_pw_qpolynomial_foreach_lifted_piece(
3108 __isl_keep isl_pw_qpolynomial *pwqp,
3109 isl_stat (*fn)(__isl_take isl_set *set,
3110 __isl_take isl_qpolynomial *qp,
3111 void *user), void *user);
3112 int isl_pw_qpolynomial_fold_n_piece(
3113 __isl_keep isl_pw_qpolynomial_fold *pwf);
3114 isl_stat isl_pw_qpolynomial_fold_foreach_piece(
3115 __isl_keep isl_pw_qpolynomial_fold *pwf,
3116 isl_stat (*fn)(__isl_take isl_set *set,
3117 __isl_take isl_qpolynomial_fold *fold,
3118 void *user), void *user);
3119 isl_stat isl_pw_qpolynomial_fold_foreach_lifted_piece(
3120 __isl_keep isl_pw_qpolynomial_fold *pwf,
3121 isl_stat (*fn)(__isl_take isl_set *set,
3122 __isl_take isl_qpolynomial_fold *fold,
3123 void *user), void *user);
3125 As usual, the function C<fn> should return C<0> on success
3126 and C<-1> on failure. The difference between
3127 C<isl_pw_qpolynomial_foreach_piece> and
3128 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3129 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3130 compute unique representations for all existentially quantified
3131 variables and then turn these existentially quantified variables
3132 into extra set variables, adapting the associated quasipolynomial
3133 accordingly. This means that the C<set> passed to C<fn>
3134 will not have any existentially quantified variables, but that
3135 the dimensions of the sets may be different for different
3136 invocations of C<fn>.
3137 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
3138 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
3140 A piecewise expression consisting of the expressions at a given
3141 position of a piecewise multiple expression can be extracted
3142 using the following function.
3144 #include <isl/aff.h>
3145 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3146 __isl_keep isl_pw_multi_aff *pma, int pos);
3148 These expressions can be replaced using the following function.
3150 #include <isl/aff.h>
3151 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3152 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3153 __isl_take isl_pw_aff *pa);
3155 Note that there is a difference between C<isl_multi_pw_aff> and
3156 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
3157 affine expressions, while the second is a piecewise sequence
3158 of affine expressions. In particular, each of the piecewise
3159 affine expressions in an C<isl_multi_pw_aff> may have a different
3160 domain, while all multiple expressions associated to a cell
3161 in an C<isl_pw_multi_aff> have the same domain.
3162 It is possible to convert between the two, but when converting
3163 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
3164 of the result is the intersection of the domains of the input.
3165 The reverse conversion is exact.
3167 #include <isl/aff.h>
3168 __isl_give isl_pw_multi_aff *
3169 isl_pw_multi_aff_from_multi_pw_aff(
3170 __isl_take isl_multi_pw_aff *mpa);
3171 __isl_give isl_multi_pw_aff *
3172 isl_multi_pw_aff_from_pw_multi_aff(
3173 __isl_take isl_pw_multi_aff *pma);
3175 =head3 Union Expressions
3177 A union expression collects base expressions defined
3178 over different domains. The space of a union expression
3179 is that of the shared parameter space.
3181 The union expression types defined by C<isl>
3182 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
3183 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
3185 C<isl_union_pw_aff>,
3186 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>,
3187 there can be at most one base expression for a given domain space.
3189 C<isl_union_pw_multi_aff>,
3190 there can be multiple such expressions for a given domain space,
3191 but the domains of these expressions need to be disjoint.
3193 An empty union expression can be created using the following functions.
3195 #include <isl/aff.h>
3196 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
3197 __isl_take isl_space *space);
3198 __isl_give isl_union_pw_multi_aff *
3199 isl_union_pw_multi_aff_empty(
3200 __isl_take isl_space *space);
3202 #include <isl/polynomial.h>
3203 __isl_give isl_union_pw_qpolynomial *
3204 isl_union_pw_qpolynomial_zero(
3205 __isl_take isl_space *space);
3207 A union expression containing a single base expression
3208 can be created using the following functions.
3210 #include <isl/aff.h>
3211 __isl_give isl_union_pw_aff *
3212 isl_union_pw_aff_from_pw_aff(
3213 __isl_take isl_pw_aff *pa);
3214 __isl_give isl_union_pw_multi_aff *
3215 isl_union_pw_multi_aff_from_aff(
3216 __isl_take isl_aff *aff);
3217 __isl_give isl_union_pw_multi_aff *
3218 isl_union_pw_multi_aff_from_pw_multi_aff(
3219 __isl_take isl_pw_multi_aff *pma);
3221 #include <isl/polynomial.h>
3222 __isl_give isl_union_pw_qpolynomial *
3223 isl_union_pw_qpolynomial_from_pw_qpolynomial(
3224 __isl_take isl_pw_qpolynomial *pwqp);
3226 The following functions create a base expression on each
3227 of the sets in the union set and collect the results.
3229 #include <isl/aff.h>
3230 __isl_give isl_union_pw_multi_aff *
3231 isl_union_pw_multi_aff_from_union_pw_aff(
3232 __isl_take isl_union_pw_aff *upa);
3233 __isl_give isl_union_pw_aff *
3234 isl_union_pw_multi_aff_get_union_pw_aff(
3235 __isl_keep isl_union_pw_multi_aff *upma, int pos);
3236 __isl_give isl_union_pw_aff *
3237 isl_union_pw_aff_val_on_domain(
3238 __isl_take isl_union_set *domain,
3239 __isl_take isl_val *v);
3240 __isl_give isl_union_pw_multi_aff *
3241 isl_union_pw_multi_aff_multi_val_on_domain(
3242 __isl_take isl_union_set *domain,
3243 __isl_take isl_multi_val *mv);
3245 An C<isl_union_pw_aff> that is equal to a (parametric) affine
3246 expression on a given domain can be created using the following
3249 #include <isl/aff.h>
3250 __isl_give isl_union_pw_aff *
3251 isl_union_pw_aff_aff_on_domain(
3252 __isl_take isl_union_set *domain,
3253 __isl_take isl_aff *aff);
3255 A base expression can be added to a union expression using
3256 the following functions.
3258 #include <isl/aff.h>
3259 __isl_give isl_union_pw_aff *
3260 isl_union_pw_aff_add_pw_aff(
3261 __isl_take isl_union_pw_aff *upa,
3262 __isl_take isl_pw_aff *pa);
3263 __isl_give isl_union_pw_multi_aff *
3264 isl_union_pw_multi_aff_add_pw_multi_aff(
3265 __isl_take isl_union_pw_multi_aff *upma,
3266 __isl_take isl_pw_multi_aff *pma);
3268 #include <isl/polynomial.h>
3269 __isl_give isl_union_pw_qpolynomial *
3270 isl_union_pw_qpolynomial_add_pw_qpolynomial(
3271 __isl_take isl_union_pw_qpolynomial *upwqp,
3272 __isl_take isl_pw_qpolynomial *pwqp);
3274 Union expressions can be copied and freed using
3275 the following functions.
3277 #include <isl/aff.h>
3278 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
3279 __isl_keep isl_union_pw_aff *upa);
3280 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
3281 __isl_take isl_union_pw_aff *upa);
3282 __isl_give isl_union_pw_multi_aff *
3283 isl_union_pw_multi_aff_copy(
3284 __isl_keep isl_union_pw_multi_aff *upma);
3285 __isl_null isl_union_pw_multi_aff *
3286 isl_union_pw_multi_aff_free(
3287 __isl_take isl_union_pw_multi_aff *upma);
3289 #include <isl/polynomial.h>
3290 __isl_give isl_union_pw_qpolynomial *
3291 isl_union_pw_qpolynomial_copy(
3292 __isl_keep isl_union_pw_qpolynomial *upwqp);
3293 __isl_null isl_union_pw_qpolynomial *
3294 isl_union_pw_qpolynomial_free(
3295 __isl_take isl_union_pw_qpolynomial *upwqp);
3296 __isl_give isl_union_pw_qpolynomial_fold *
3297 isl_union_pw_qpolynomial_fold_copy(
3298 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3299 __isl_null isl_union_pw_qpolynomial_fold *
3300 isl_union_pw_qpolynomial_fold_free(
3301 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3303 To iterate over the base expressions in a union expression,
3304 use the following functions.
3306 #include <isl/aff.h>
3307 int isl_union_pw_aff_n_pw_aff(
3308 __isl_keep isl_union_pw_aff *upa);
3309 isl_stat isl_union_pw_aff_foreach_pw_aff(
3310 __isl_keep isl_union_pw_aff *upa,
3311 isl_stat (*fn)(__isl_take isl_pw_aff *pa,
3312 void *user), void *user);
3313 int isl_union_pw_multi_aff_n_pw_multi_aff(
3314 __isl_keep isl_union_pw_multi_aff *upma);
3315 isl_stat isl_union_pw_multi_aff_foreach_pw_multi_aff(
3316 __isl_keep isl_union_pw_multi_aff *upma,
3317 isl_stat (*fn)(__isl_take isl_pw_multi_aff *pma,
3318 void *user), void *user);
3320 #include <isl/polynomial.h>
3321 int isl_union_pw_qpolynomial_n_pw_qpolynomial(
3322 __isl_keep isl_union_pw_qpolynomial *upwqp);
3323 isl_stat isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3324 __isl_keep isl_union_pw_qpolynomial *upwqp,
3325 isl_stat (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
3326 void *user), void *user);
3327 int isl_union_pw_qpolynomial_fold_n_pw_qpolynomial_fold(
3328 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3329 isl_stat isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3330 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3331 isl_stat (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3332 void *user), void *user);
3334 To extract the base expression in a given space from a union, use
3335 the following functions.
3337 #include <isl/aff.h>
3338 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
3339 __isl_keep isl_union_pw_aff *upa,
3340 __isl_take isl_space *space);
3341 __isl_give isl_pw_multi_aff *
3342 isl_union_pw_multi_aff_extract_pw_multi_aff(
3343 __isl_keep isl_union_pw_multi_aff *upma,
3344 __isl_take isl_space *space);
3346 #include <isl/polynomial.h>
3347 __isl_give isl_pw_qpolynomial *
3348 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3349 __isl_keep isl_union_pw_qpolynomial *upwqp,
3350 __isl_take isl_space *space);
3352 =head2 Input and Output
3354 For set and relation,
3355 C<isl> supports its own input/output format, which is similar
3356 to the C<Omega> format, but also supports the C<PolyLib> format
3358 For other object types, typically only an C<isl> format is supported.
3360 =head3 C<isl> format
3362 The C<isl> format is similar to that of C<Omega>, but has a different
3363 syntax for describing the parameters and allows for the definition
3364 of an existentially quantified variable as the integer division
3365 of an affine expression.
3366 For example, the set of integers C<i> between C<0> and C<n>
3367 such that C<i % 10 <= 6> can be described as
3369 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
3372 A set or relation can have several disjuncts, separated
3373 by the keyword C<or>. Each disjunct is either a conjunction
3374 of constraints or a projection (C<exists>) of a conjunction
3375 of constraints. The constraints are separated by the keyword
3378 =head3 C<PolyLib> format
3380 If the represented set is a union, then the first line
3381 contains a single number representing the number of disjuncts.
3382 Otherwise, a line containing the number C<1> is optional.
3384 Each disjunct is represented by a matrix of constraints.
3385 The first line contains two numbers representing
3386 the number of rows and columns,
3387 where the number of rows is equal to the number of constraints
3388 and the number of columns is equal to two plus the number of variables.
3389 The following lines contain the actual rows of the constraint matrix.
3390 In each row, the first column indicates whether the constraint
3391 is an equality (C<0>) or inequality (C<1>). The final column
3392 corresponds to the constant term.
3394 If the set is parametric, then the coefficients of the parameters
3395 appear in the last columns before the constant column.
3396 The coefficients of any existentially quantified variables appear
3397 between those of the set variables and those of the parameters.
3399 =head3 Extended C<PolyLib> format
3401 The extended C<PolyLib> format is nearly identical to the
3402 C<PolyLib> format. The only difference is that the line
3403 containing the number of rows and columns of a constraint matrix
3404 also contains four additional numbers:
3405 the number of output dimensions, the number of input dimensions,
3406 the number of local dimensions (i.e., the number of existentially
3407 quantified variables) and the number of parameters.
3408 For sets, the number of ``output'' dimensions is equal
3409 to the number of set dimensions, while the number of ``input''
3414 Objects can be read from input using the following functions.
3416 #include <isl/val.h>
3417 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
3419 __isl_give isl_multi_val *isl_multi_val_read_from_str(
3420 isl_ctx *ctx, const char *str);
3422 #include <isl/set.h>
3423 __isl_give isl_basic_set *isl_basic_set_read_from_file(
3424 isl_ctx *ctx, FILE *input);
3425 __isl_give isl_basic_set *isl_basic_set_read_from_str(
3426 isl_ctx *ctx, const char *str);
3427 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
3429 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
3432 #include <isl/map.h>
3433 __isl_give isl_basic_map *isl_basic_map_read_from_file(
3434 isl_ctx *ctx, FILE *input);
3435 __isl_give isl_basic_map *isl_basic_map_read_from_str(
3436 isl_ctx *ctx, const char *str);
3437 __isl_give isl_map *isl_map_read_from_file(
3438 isl_ctx *ctx, FILE *input);
3439 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
3442 #include <isl/union_set.h>
3443 __isl_give isl_union_set *isl_union_set_read_from_file(
3444 isl_ctx *ctx, FILE *input);
3445 __isl_give isl_union_set *isl_union_set_read_from_str(
3446 isl_ctx *ctx, const char *str);
3448 #include <isl/union_map.h>
3449 __isl_give isl_union_map *isl_union_map_read_from_file(
3450 isl_ctx *ctx, FILE *input);
3451 __isl_give isl_union_map *isl_union_map_read_from_str(
3452 isl_ctx *ctx, const char *str);
3454 #include <isl/aff.h>
3455 __isl_give isl_aff *isl_aff_read_from_str(
3456 isl_ctx *ctx, const char *str);
3457 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3458 isl_ctx *ctx, const char *str);
3459 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3460 isl_ctx *ctx, const char *str);
3461 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3462 isl_ctx *ctx, const char *str);
3463 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
3464 isl_ctx *ctx, const char *str);
3465 __isl_give isl_union_pw_aff *
3466 isl_union_pw_aff_read_from_str(
3467 isl_ctx *ctx, const char *str);
3468 __isl_give isl_union_pw_multi_aff *
3469 isl_union_pw_multi_aff_read_from_str(
3470 isl_ctx *ctx, const char *str);
3471 __isl_give isl_multi_union_pw_aff *
3472 isl_multi_union_pw_aff_read_from_str(
3473 isl_ctx *ctx, const char *str);
3475 #include <isl/polynomial.h>
3476 __isl_give isl_union_pw_qpolynomial *
3477 isl_union_pw_qpolynomial_read_from_str(
3478 isl_ctx *ctx, const char *str);
3480 For sets and relations,
3481 the input format is autodetected and may be either the C<PolyLib> format
3482 or the C<isl> format.
3486 Before anything can be printed, an C<isl_printer> needs to
3489 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
3491 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
3492 __isl_null isl_printer *isl_printer_free(
3493 __isl_take isl_printer *printer);
3495 C<isl_printer_to_file> prints to the given file, while
3496 C<isl_printer_to_str> prints to a string that can be extracted
3497 using the following function.
3499 #include <isl/printer.h>
3500 __isl_give char *isl_printer_get_str(
3501 __isl_keep isl_printer *printer);
3503 The printer can be inspected using the following functions.
3505 FILE *isl_printer_get_file(
3506 __isl_keep isl_printer *printer);
3507 int isl_printer_get_output_format(
3508 __isl_keep isl_printer *p);
3509 int isl_printer_get_yaml_style(__isl_keep isl_printer *p);
3511 The behavior of the printer can be modified in various ways
3513 __isl_give isl_printer *isl_printer_set_output_format(
3514 __isl_take isl_printer *p, int output_format);
3515 __isl_give isl_printer *isl_printer_set_indent(
3516 __isl_take isl_printer *p, int indent);
3517 __isl_give isl_printer *isl_printer_set_indent_prefix(
3518 __isl_take isl_printer *p, const char *prefix);
3519 __isl_give isl_printer *isl_printer_indent(
3520 __isl_take isl_printer *p, int indent);
3521 __isl_give isl_printer *isl_printer_set_prefix(
3522 __isl_take isl_printer *p, const char *prefix);
3523 __isl_give isl_printer *isl_printer_set_suffix(
3524 __isl_take isl_printer *p, const char *suffix);
3525 __isl_give isl_printer *isl_printer_set_yaml_style(
3526 __isl_take isl_printer *p, int yaml_style);
3528 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
3529 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
3530 and defaults to C<ISL_FORMAT_ISL>.
3531 Each line in the output is prefixed by C<indent_prefix>,
3532 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
3533 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
3534 In the C<PolyLib> format output,
3535 the coefficients of the existentially quantified variables
3536 appear between those of the set variables and those
3538 The function C<isl_printer_indent> increases the indentation
3539 by the specified amount (which may be negative).
3540 The YAML style may be either C<ISL_YAML_STYLE_BLOCK> or
3541 C<ISL_YAML_STYLE_FLOW> and when we are printing something
3544 To actually print something, use
3546 #include <isl/printer.h>
3547 __isl_give isl_printer *isl_printer_print_double(
3548 __isl_take isl_printer *p, double d);
3550 #include <isl/val.h>
3551 __isl_give isl_printer *isl_printer_print_val(
3552 __isl_take isl_printer *p, __isl_keep isl_val *v);
3554 #include <isl/set.h>
3555 __isl_give isl_printer *isl_printer_print_basic_set(
3556 __isl_take isl_printer *printer,
3557 __isl_keep isl_basic_set *bset);
3558 __isl_give isl_printer *isl_printer_print_set(
3559 __isl_take isl_printer *printer,
3560 __isl_keep isl_set *set);
3562 #include <isl/map.h>
3563 __isl_give isl_printer *isl_printer_print_basic_map(
3564 __isl_take isl_printer *printer,
3565 __isl_keep isl_basic_map *bmap);
3566 __isl_give isl_printer *isl_printer_print_map(
3567 __isl_take isl_printer *printer,
3568 __isl_keep isl_map *map);
3570 #include <isl/union_set.h>
3571 __isl_give isl_printer *isl_printer_print_union_set(
3572 __isl_take isl_printer *p,
3573 __isl_keep isl_union_set *uset);
3575 #include <isl/union_map.h>
3576 __isl_give isl_printer *isl_printer_print_union_map(
3577 __isl_take isl_printer *p,
3578 __isl_keep isl_union_map *umap);
3580 #include <isl/val.h>
3581 __isl_give isl_printer *isl_printer_print_multi_val(
3582 __isl_take isl_printer *p,
3583 __isl_keep isl_multi_val *mv);
3585 #include <isl/aff.h>
3586 __isl_give isl_printer *isl_printer_print_aff(
3587 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3588 __isl_give isl_printer *isl_printer_print_multi_aff(
3589 __isl_take isl_printer *p,
3590 __isl_keep isl_multi_aff *maff);
3591 __isl_give isl_printer *isl_printer_print_pw_aff(
3592 __isl_take isl_printer *p,
3593 __isl_keep isl_pw_aff *pwaff);
3594 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3595 __isl_take isl_printer *p,
3596 __isl_keep isl_pw_multi_aff *pma);
3597 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3598 __isl_take isl_printer *p,
3599 __isl_keep isl_multi_pw_aff *mpa);
3600 __isl_give isl_printer *isl_printer_print_union_pw_aff(
3601 __isl_take isl_printer *p,
3602 __isl_keep isl_union_pw_aff *upa);
3603 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3604 __isl_take isl_printer *p,
3605 __isl_keep isl_union_pw_multi_aff *upma);
3606 __isl_give isl_printer *
3607 isl_printer_print_multi_union_pw_aff(
3608 __isl_take isl_printer *p,
3609 __isl_keep isl_multi_union_pw_aff *mupa);
3611 #include <isl/polynomial.h>
3612 __isl_give isl_printer *isl_printer_print_qpolynomial(
3613 __isl_take isl_printer *p,
3614 __isl_keep isl_qpolynomial *qp);
3615 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3616 __isl_take isl_printer *p,
3617 __isl_keep isl_pw_qpolynomial *pwqp);
3618 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3619 __isl_take isl_printer *p,
3620 __isl_keep isl_union_pw_qpolynomial *upwqp);
3622 __isl_give isl_printer *
3623 isl_printer_print_pw_qpolynomial_fold(
3624 __isl_take isl_printer *p,
3625 __isl_keep isl_pw_qpolynomial_fold *pwf);
3626 __isl_give isl_printer *
3627 isl_printer_print_union_pw_qpolynomial_fold(
3628 __isl_take isl_printer *p,
3629 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3631 For C<isl_printer_print_qpolynomial>,
3632 C<isl_printer_print_pw_qpolynomial> and
3633 C<isl_printer_print_pw_qpolynomial_fold>,
3634 the output format of the printer
3635 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3636 For C<isl_printer_print_union_pw_qpolynomial> and
3637 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
3639 In case of printing in C<ISL_FORMAT_C>, the user may want
3640 to set the names of all dimensions first.
3642 C<isl> also provides limited support for printing YAML documents,
3643 just enough for the internal use for printing such documents.
3645 #include <isl/printer.h>
3646 __isl_give isl_printer *isl_printer_yaml_start_mapping(
3647 __isl_take isl_printer *p);
3648 __isl_give isl_printer *isl_printer_yaml_end_mapping(
3649 __isl_take isl_printer *p);
3650 __isl_give isl_printer *isl_printer_yaml_start_sequence(
3651 __isl_take isl_printer *p);
3652 __isl_give isl_printer *isl_printer_yaml_end_sequence(
3653 __isl_take isl_printer *p);
3654 __isl_give isl_printer *isl_printer_yaml_next(
3655 __isl_take isl_printer *p);
3657 A document is started by a call to either
3658 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3659 Anything printed to the printer after such a call belong to the
3660 first key of the mapping or the first element in the sequence.
3661 The function C<isl_printer_yaml_next> moves to the value if
3662 we are currently printing a mapping key, the next key if we
3663 are printing a value or the next element if we are printing
3664 an element in a sequence.
3665 Nested mappings and sequences are initiated by the same
3666 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3667 Each call to these functions needs to have a corresponding call to
3668 C<isl_printer_yaml_end_mapping> or C<isl_printer_yaml_end_sequence>.
3670 When called on a file printer, the following function flushes
3671 the file. When called on a string printer, the buffer is cleared.
3673 __isl_give isl_printer *isl_printer_flush(
3674 __isl_take isl_printer *p);
3676 The following functions allow the user to attach
3677 notes to a printer in order to keep track of additional state.
3679 #include <isl/printer.h>
3680 isl_bool isl_printer_has_note(__isl_keep isl_printer *p,
3681 __isl_keep isl_id *id);
3682 __isl_give isl_id *isl_printer_get_note(
3683 __isl_keep isl_printer *p, __isl_take isl_id *id);
3684 __isl_give isl_printer *isl_printer_set_note(
3685 __isl_take isl_printer *p,
3686 __isl_take isl_id *id, __isl_take isl_id *note);
3688 C<isl_printer_set_note> associates the given note to the given
3689 identifier in the printer.
3690 C<isl_printer_get_note> retrieves a note associated to an
3692 C<isl_printer_has_note> checks if there is such a note.
3693 C<isl_printer_get_note> fails if the requested note does not exist.
3695 Alternatively, a string representation can be obtained
3696 directly using the following functions, which always print
3700 __isl_give char *isl_id_to_str(
3701 __isl_keep isl_id *id);
3703 #include <isl/space.h>
3704 __isl_give char *isl_space_to_str(
3705 __isl_keep isl_space *space);
3707 #include <isl/val.h>
3708 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
3709 __isl_give char *isl_multi_val_to_str(
3710 __isl_keep isl_multi_val *mv);
3712 #include <isl/set.h>
3713 __isl_give char *isl_basic_set_to_str(
3714 __isl_keep isl_basic_set *bset);
3715 __isl_give char *isl_set_to_str(
3716 __isl_keep isl_set *set);
3718 #include <isl/union_set.h>
3719 __isl_give char *isl_union_set_to_str(
3720 __isl_keep isl_union_set *uset);
3722 #include <isl/map.h>
3723 __isl_give char *isl_basic_map_to_str(
3724 __isl_keep isl_basic_map *bmap);
3725 __isl_give char *isl_map_to_str(
3726 __isl_keep isl_map *map);
3728 #include <isl/union_map.h>
3729 __isl_give char *isl_union_map_to_str(
3730 __isl_keep isl_union_map *umap);
3732 #include <isl/aff.h>
3733 __isl_give char *isl_aff_to_str(__isl_keep isl_aff *aff);
3734 __isl_give char *isl_pw_aff_to_str(
3735 __isl_keep isl_pw_aff *pa);
3736 __isl_give char *isl_multi_aff_to_str(
3737 __isl_keep isl_multi_aff *ma);
3738 __isl_give char *isl_pw_multi_aff_to_str(
3739 __isl_keep isl_pw_multi_aff *pma);
3740 __isl_give char *isl_multi_pw_aff_to_str(
3741 __isl_keep isl_multi_pw_aff *mpa);
3742 __isl_give char *isl_union_pw_aff_to_str(
3743 __isl_keep isl_union_pw_aff *upa);
3744 __isl_give char *isl_union_pw_multi_aff_to_str(
3745 __isl_keep isl_union_pw_multi_aff *upma);
3746 __isl_give char *isl_multi_union_pw_aff_to_str(
3747 __isl_keep isl_multi_union_pw_aff *mupa);
3749 #include <isl/point.h>
3750 __isl_give char *isl_point_to_str(
3751 __isl_keep isl_point *pnt);
3753 #include <isl/polynomial.h>
3754 __isl_give char *isl_pw_qpolynomial_to_str(
3755 __isl_keep isl_pw_qpolynomial *pwqp);
3756 __isl_give char *isl_union_pw_qpolynomial_to_str(
3757 __isl_keep isl_union_pw_qpolynomial *upwqp);
3761 =head3 Unary Properties
3767 The following functions test whether the given set or relation
3768 contains any integer points. The ``plain'' variants do not perform
3769 any computations, but simply check if the given set or relation
3770 is already known to be empty.
3772 isl_bool isl_basic_set_plain_is_empty(
3773 __isl_keep isl_basic_set *bset);
3774 isl_bool isl_basic_set_is_empty(
3775 __isl_keep isl_basic_set *bset);
3776 isl_bool isl_set_plain_is_empty(
3777 __isl_keep isl_set *set);
3778 isl_bool isl_set_is_empty(__isl_keep isl_set *set);
3779 isl_bool isl_union_set_is_empty(
3780 __isl_keep isl_union_set *uset);
3781 isl_bool isl_basic_map_plain_is_empty(
3782 __isl_keep isl_basic_map *bmap);
3783 isl_bool isl_basic_map_is_empty(
3784 __isl_keep isl_basic_map *bmap);
3785 isl_bool isl_map_plain_is_empty(
3786 __isl_keep isl_map *map);
3787 isl_bool isl_map_is_empty(__isl_keep isl_map *map);
3788 isl_bool isl_union_map_is_empty(
3789 __isl_keep isl_union_map *umap);
3791 =item * Universality
3793 isl_bool isl_basic_set_plain_is_universe(
3794 __isl_keep isl_basic_set *bset);
3795 isl_bool isl_basic_set_is_universe(
3796 __isl_keep isl_basic_set *bset);
3797 isl_bool isl_basic_map_plain_is_universe(
3798 __isl_keep isl_basic_map *bmap);
3799 isl_bool isl_basic_map_is_universe(
3800 __isl_keep isl_basic_map *bmap);
3801 isl_bool isl_set_plain_is_universe(
3802 __isl_keep isl_set *set);
3803 isl_bool isl_map_plain_is_universe(
3804 __isl_keep isl_map *map);
3806 =item * Single-valuedness
3808 #include <isl/set.h>
3809 isl_bool isl_set_is_singleton(__isl_keep isl_set *set);
3811 #include <isl/map.h>
3812 isl_bool isl_basic_map_is_single_valued(
3813 __isl_keep isl_basic_map *bmap);
3814 isl_bool isl_map_plain_is_single_valued(
3815 __isl_keep isl_map *map);
3816 isl_bool isl_map_is_single_valued(__isl_keep isl_map *map);
3818 #include <isl/union_map.h>
3819 isl_bool isl_union_map_is_single_valued(
3820 __isl_keep isl_union_map *umap);
3824 isl_bool isl_map_plain_is_injective(
3825 __isl_keep isl_map *map);
3826 isl_bool isl_map_is_injective(
3827 __isl_keep isl_map *map);
3828 isl_bool isl_union_map_plain_is_injective(
3829 __isl_keep isl_union_map *umap);
3830 isl_bool isl_union_map_is_injective(
3831 __isl_keep isl_union_map *umap);
3835 isl_bool isl_map_is_bijective(
3836 __isl_keep isl_map *map);
3837 isl_bool isl_union_map_is_bijective(
3838 __isl_keep isl_union_map *umap);
3842 The following functions test whether the given relation
3843 only maps elements to themselves.
3845 #include <isl/map.h>
3846 isl_bool isl_map_is_identity(
3847 __isl_keep isl_map *map);
3849 #include <isl/union_map.h>
3850 isl_bool isl_union_map_is_identity(
3851 __isl_keep isl_union_map *umap);
3855 __isl_give isl_val *
3856 isl_basic_map_plain_get_val_if_fixed(
3857 __isl_keep isl_basic_map *bmap,
3858 enum isl_dim_type type, unsigned pos);
3859 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
3860 __isl_keep isl_set *set,
3861 enum isl_dim_type type, unsigned pos);
3862 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
3863 __isl_keep isl_map *map,
3864 enum isl_dim_type type, unsigned pos);
3866 If the set or relation obviously lies on a hyperplane where the given dimension
3867 has a fixed value, then return that value.
3868 Otherwise return NaN.
3872 isl_stat isl_set_dim_residue_class_val(
3873 __isl_keep isl_set *set,
3874 int pos, __isl_give isl_val **modulo,
3875 __isl_give isl_val **residue);
3877 Check if the values of the given set dimension are equal to a fixed
3878 value modulo some integer value. If so, assign the modulo to C<*modulo>
3879 and the fixed value to C<*residue>. If the given dimension attains only
3880 a single value, then assign C<0> to C<*modulo> and the fixed value to
3882 If the dimension does not attain only a single value and if no modulo
3883 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
3887 To check whether the description of a set, relation or function depends
3888 on one or more given dimensions,
3889 the following functions can be used.
3891 #include <isl/constraint.h>
3892 isl_bool isl_constraint_involves_dims(
3893 __isl_keep isl_constraint *constraint,
3894 enum isl_dim_type type, unsigned first, unsigned n);
3896 #include <isl/set.h>
3897 isl_bool isl_basic_set_involves_dims(
3898 __isl_keep isl_basic_set *bset,
3899 enum isl_dim_type type, unsigned first, unsigned n);
3900 isl_bool isl_set_involves_dims(__isl_keep isl_set *set,
3901 enum isl_dim_type type, unsigned first, unsigned n);
3903 #include <isl/map.h>
3904 isl_bool isl_basic_map_involves_dims(
3905 __isl_keep isl_basic_map *bmap,
3906 enum isl_dim_type type, unsigned first, unsigned n);
3907 isl_bool isl_map_involves_dims(__isl_keep isl_map *map,
3908 enum isl_dim_type type, unsigned first, unsigned n);
3910 #include <isl/union_map.h>
3911 isl_bool isl_union_map_involves_dims(
3912 __isl_keep isl_union_map *umap,
3913 enum isl_dim_type type, unsigned first, unsigned n);
3915 #include <isl/aff.h>
3916 isl_bool isl_aff_involves_dims(__isl_keep isl_aff *aff,
3917 enum isl_dim_type type, unsigned first, unsigned n);
3918 isl_bool isl_pw_aff_involves_dims(
3919 __isl_keep isl_pw_aff *pwaff,
3920 enum isl_dim_type type, unsigned first, unsigned n);
3921 isl_bool isl_multi_aff_involves_dims(
3922 __isl_keep isl_multi_aff *ma,
3923 enum isl_dim_type type, unsigned first, unsigned n);
3924 isl_bool isl_multi_pw_aff_involves_dims(
3925 __isl_keep isl_multi_pw_aff *mpa,
3926 enum isl_dim_type type, unsigned first, unsigned n);
3928 #include <isl/polynomial.h>
3929 isl_bool isl_qpolynomial_involves_dims(
3930 __isl_keep isl_qpolynomial *qp,
3931 enum isl_dim_type type, unsigned first, unsigned n);
3933 Similarly, the following functions can be used to check whether
3934 a given dimension is involved in any lower or upper bound.
3936 #include <isl/set.h>
3937 isl_bool isl_set_dim_has_any_lower_bound(
3938 __isl_keep isl_set *set,
3939 enum isl_dim_type type, unsigned pos);
3940 isl_bool isl_set_dim_has_any_upper_bound(
3941 __isl_keep isl_set *set,
3942 enum isl_dim_type type, unsigned pos);
3944 Note that these functions return true even if there is a bound on
3945 the dimension on only some of the basic sets of C<set>.
3946 To check if they have a bound for all of the basic sets in C<set>,
3947 use the following functions instead.
3949 #include <isl/set.h>
3950 isl_bool isl_set_dim_has_lower_bound(
3951 __isl_keep isl_set *set,
3952 enum isl_dim_type type, unsigned pos);
3953 isl_bool isl_set_dim_has_upper_bound(
3954 __isl_keep isl_set *set,
3955 enum isl_dim_type type, unsigned pos);
3959 To check whether a set is a parameter domain, use this function:
3961 isl_bool isl_set_is_params(__isl_keep isl_set *set);
3962 isl_bool isl_union_set_is_params(
3963 __isl_keep isl_union_set *uset);
3967 The following functions check whether the space of the given
3968 (basic) set or relation range is a wrapped relation.
3970 #include <isl/space.h>
3971 isl_bool isl_space_is_wrapping(
3972 __isl_keep isl_space *space);
3973 isl_bool isl_space_domain_is_wrapping(
3974 __isl_keep isl_space *space);
3975 isl_bool isl_space_range_is_wrapping(
3976 __isl_keep isl_space *space);
3978 #include <isl/set.h>
3979 isl_bool isl_basic_set_is_wrapping(
3980 __isl_keep isl_basic_set *bset);
3981 isl_bool isl_set_is_wrapping(__isl_keep isl_set *set);
3983 #include <isl/map.h>
3984 isl_bool isl_map_domain_is_wrapping(
3985 __isl_keep isl_map *map);
3986 isl_bool isl_map_range_is_wrapping(
3987 __isl_keep isl_map *map);
3989 #include <isl/val.h>
3990 isl_bool isl_multi_val_range_is_wrapping(
3991 __isl_keep isl_multi_val *mv);
3993 #include <isl/aff.h>
3994 isl_bool isl_multi_aff_range_is_wrapping(
3995 __isl_keep isl_multi_aff *ma);
3996 isl_bool isl_multi_pw_aff_range_is_wrapping(
3997 __isl_keep isl_multi_pw_aff *mpa);
3998 isl_bool isl_multi_union_pw_aff_range_is_wrapping(
3999 __isl_keep isl_multi_union_pw_aff *mupa);
4001 The input to C<isl_space_is_wrapping> should
4002 be the space of a set, while that of
4003 C<isl_space_domain_is_wrapping> and
4004 C<isl_space_range_is_wrapping> should be the space of a relation.
4006 =item * Internal Product
4008 isl_bool isl_basic_map_can_zip(
4009 __isl_keep isl_basic_map *bmap);
4010 isl_bool isl_map_can_zip(__isl_keep isl_map *map);
4012 Check whether the product of domain and range of the given relation
4014 i.e., whether both domain and range are nested relations.
4018 #include <isl/space.h>
4019 isl_bool isl_space_can_curry(
4020 __isl_keep isl_space *space);
4022 #include <isl/map.h>
4023 isl_bool isl_basic_map_can_curry(
4024 __isl_keep isl_basic_map *bmap);
4025 isl_bool isl_map_can_curry(__isl_keep isl_map *map);
4027 Check whether the domain of the (basic) relation is a wrapped relation.
4029 #include <isl/space.h>
4030 __isl_give isl_space *isl_space_uncurry(
4031 __isl_take isl_space *space);
4033 #include <isl/map.h>
4034 isl_bool isl_basic_map_can_uncurry(
4035 __isl_keep isl_basic_map *bmap);
4036 isl_bool isl_map_can_uncurry(__isl_keep isl_map *map);
4038 Check whether the range of the (basic) relation is a wrapped relation.
4040 #include <isl/space.h>
4041 isl_bool isl_space_can_range_curry(
4042 __isl_keep isl_space *space);
4044 #include <isl/map.h>
4045 isl_bool isl_map_can_range_curry(
4046 __isl_keep isl_map *map);
4048 Check whether the domain of the relation wrapped in the range of
4049 the input is itself a wrapped relation.
4051 =item * Special Values
4053 #include <isl/aff.h>
4054 isl_bool isl_aff_is_cst(__isl_keep isl_aff *aff);
4055 isl_bool isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
4056 isl_bool isl_multi_pw_aff_is_cst(
4057 __isl_keep isl_multi_pw_aff *mpa);
4059 Check whether the given expression is a constant.
4061 #include <isl/val.h>
4062 isl_bool isl_multi_val_involves_nan(
4063 __isl_keep isl_multi_val *mv);
4065 #include <isl/aff.h>
4066 isl_bool isl_aff_is_nan(__isl_keep isl_aff *aff);
4067 isl_bool isl_multi_aff_involves_nan(
4068 __isl_keep isl_multi_aff *ma);
4069 isl_bool isl_pw_aff_involves_nan(
4070 __isl_keep isl_pw_aff *pa);
4071 isl_bool isl_pw_multi_aff_involves_nan(
4072 __isl_keep isl_pw_multi_aff *pma);
4073 isl_bool isl_multi_pw_aff_involves_nan(
4074 __isl_keep isl_multi_pw_aff *mpa);
4075 isl_bool isl_union_pw_aff_involves_nan(
4076 __isl_keep isl_union_pw_aff *upa);
4077 isl_bool isl_union_pw_multi_aff_involves_nan(
4078 __isl_keep isl_union_pw_multi_aff *upma);
4079 isl_bool isl_multi_union_pw_aff_involves_nan(
4080 __isl_keep isl_multi_union_pw_aff *mupa);
4082 #include <isl/polynomial.h>
4083 isl_bool isl_qpolynomial_is_nan(
4084 __isl_keep isl_qpolynomial *qp);
4085 isl_bool isl_qpolynomial_fold_is_nan(
4086 __isl_keep isl_qpolynomial_fold *fold);
4087 isl_bool isl_pw_qpolynomial_involves_nan(
4088 __isl_keep isl_pw_qpolynomial *pwqp);
4089 isl_bool isl_pw_qpolynomial_fold_involves_nan(
4090 __isl_keep isl_pw_qpolynomial_fold *pwf);
4091 isl_bool isl_union_pw_qpolynomial_involves_nan(
4092 __isl_keep isl_union_pw_qpolynomial *upwqp);
4093 isl_bool isl_union_pw_qpolynomial_fold_involves_nan(
4094 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4096 Check whether the given expression is equal to or involves NaN.
4098 #include <isl/aff.h>
4099 isl_bool isl_aff_plain_is_zero(
4100 __isl_keep isl_aff *aff);
4102 Check whether the affine expression is obviously zero.
4106 =head3 Binary Properties
4112 The following functions check whether two objects
4113 represent the same set, relation or function.
4114 The C<plain> variants only return true if the objects
4115 are obviously the same. That is, they may return false
4116 even if the objects are the same, but they will never
4117 return true if the objects are not the same.
4119 #include <isl/set.h>
4120 isl_bool isl_basic_set_plain_is_equal(
4121 __isl_keep isl_basic_set *bset1,
4122 __isl_keep isl_basic_set *bset2);
4123 isl_bool isl_basic_set_is_equal(
4124 __isl_keep isl_basic_set *bset1,
4125 __isl_keep isl_basic_set *bset2);
4126 isl_bool isl_set_plain_is_equal(
4127 __isl_keep isl_set *set1,
4128 __isl_keep isl_set *set2);
4129 isl_bool isl_set_is_equal(__isl_keep isl_set *set1,
4130 __isl_keep isl_set *set2);
4132 #include <isl/map.h>
4133 isl_bool isl_basic_map_is_equal(
4134 __isl_keep isl_basic_map *bmap1,
4135 __isl_keep isl_basic_map *bmap2);
4136 isl_bool isl_map_is_equal(__isl_keep isl_map *map1,
4137 __isl_keep isl_map *map2);
4138 isl_bool isl_map_plain_is_equal(
4139 __isl_keep isl_map *map1,
4140 __isl_keep isl_map *map2);
4142 #include <isl/union_set.h>
4143 isl_bool isl_union_set_is_equal(
4144 __isl_keep isl_union_set *uset1,
4145 __isl_keep isl_union_set *uset2);
4147 #include <isl/union_map.h>
4148 isl_bool isl_union_map_is_equal(
4149 __isl_keep isl_union_map *umap1,
4150 __isl_keep isl_union_map *umap2);
4152 #include <isl/aff.h>
4153 isl_bool isl_aff_plain_is_equal(
4154 __isl_keep isl_aff *aff1,
4155 __isl_keep isl_aff *aff2);
4156 isl_bool isl_multi_aff_plain_is_equal(
4157 __isl_keep isl_multi_aff *maff1,
4158 __isl_keep isl_multi_aff *maff2);
4159 isl_bool isl_pw_aff_plain_is_equal(
4160 __isl_keep isl_pw_aff *pwaff1,
4161 __isl_keep isl_pw_aff *pwaff2);
4162 isl_bool isl_pw_aff_is_equal(
4163 __isl_keep isl_pw_aff *pa1,
4164 __isl_keep isl_pw_aff *pa2);
4165 isl_bool isl_pw_multi_aff_plain_is_equal(
4166 __isl_keep isl_pw_multi_aff *pma1,
4167 __isl_keep isl_pw_multi_aff *pma2);
4168 isl_bool isl_pw_multi_aff_is_equal(
4169 __isl_keep isl_pw_multi_aff *pma1,
4170 __isl_keep isl_pw_multi_aff *pma2);
4171 isl_bool isl_multi_pw_aff_plain_is_equal(
4172 __isl_keep isl_multi_pw_aff *mpa1,
4173 __isl_keep isl_multi_pw_aff *mpa2);
4174 isl_bool isl_multi_pw_aff_is_equal(
4175 __isl_keep isl_multi_pw_aff *mpa1,
4176 __isl_keep isl_multi_pw_aff *mpa2);
4177 isl_bool isl_union_pw_aff_plain_is_equal(
4178 __isl_keep isl_union_pw_aff *upa1,
4179 __isl_keep isl_union_pw_aff *upa2);
4180 isl_bool isl_union_pw_multi_aff_plain_is_equal(
4181 __isl_keep isl_union_pw_multi_aff *upma1,
4182 __isl_keep isl_union_pw_multi_aff *upma2);
4183 isl_bool isl_multi_union_pw_aff_plain_is_equal(
4184 __isl_keep isl_multi_union_pw_aff *mupa1,
4185 __isl_keep isl_multi_union_pw_aff *mupa2);
4187 #include <isl/polynomial.h>
4188 isl_bool isl_union_pw_qpolynomial_plain_is_equal(
4189 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4190 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4191 isl_bool isl_union_pw_qpolynomial_fold_plain_is_equal(
4192 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4193 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4195 =item * Disjointness
4197 #include <isl/set.h>
4198 isl_bool isl_basic_set_is_disjoint(
4199 __isl_keep isl_basic_set *bset1,
4200 __isl_keep isl_basic_set *bset2);
4201 isl_bool isl_set_plain_is_disjoint(
4202 __isl_keep isl_set *set1,
4203 __isl_keep isl_set *set2);
4204 isl_bool isl_set_is_disjoint(__isl_keep isl_set *set1,
4205 __isl_keep isl_set *set2);
4207 #include <isl/map.h>
4208 isl_bool isl_basic_map_is_disjoint(
4209 __isl_keep isl_basic_map *bmap1,
4210 __isl_keep isl_basic_map *bmap2);
4211 isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1,
4212 __isl_keep isl_map *map2);
4214 #include <isl/union_set.h>
4215 isl_bool isl_union_set_is_disjoint(
4216 __isl_keep isl_union_set *uset1,
4217 __isl_keep isl_union_set *uset2);
4219 #include <isl/union_map.h>
4220 isl_bool isl_union_map_is_disjoint(
4221 __isl_keep isl_union_map *umap1,
4222 __isl_keep isl_union_map *umap2);
4226 isl_bool isl_basic_set_is_subset(
4227 __isl_keep isl_basic_set *bset1,
4228 __isl_keep isl_basic_set *bset2);
4229 isl_bool isl_set_is_subset(__isl_keep isl_set *set1,
4230 __isl_keep isl_set *set2);
4231 isl_bool isl_set_is_strict_subset(
4232 __isl_keep isl_set *set1,
4233 __isl_keep isl_set *set2);
4234 isl_bool isl_union_set_is_subset(
4235 __isl_keep isl_union_set *uset1,
4236 __isl_keep isl_union_set *uset2);
4237 isl_bool isl_union_set_is_strict_subset(
4238 __isl_keep isl_union_set *uset1,
4239 __isl_keep isl_union_set *uset2);
4240 isl_bool isl_basic_map_is_subset(
4241 __isl_keep isl_basic_map *bmap1,
4242 __isl_keep isl_basic_map *bmap2);
4243 isl_bool isl_basic_map_is_strict_subset(
4244 __isl_keep isl_basic_map *bmap1,
4245 __isl_keep isl_basic_map *bmap2);
4246 isl_bool isl_map_is_subset(
4247 __isl_keep isl_map *map1,
4248 __isl_keep isl_map *map2);
4249 isl_bool isl_map_is_strict_subset(
4250 __isl_keep isl_map *map1,
4251 __isl_keep isl_map *map2);
4252 isl_bool isl_union_map_is_subset(
4253 __isl_keep isl_union_map *umap1,
4254 __isl_keep isl_union_map *umap2);
4255 isl_bool isl_union_map_is_strict_subset(
4256 __isl_keep isl_union_map *umap1,
4257 __isl_keep isl_union_map *umap2);
4259 Check whether the first argument is a (strict) subset of the
4264 Every comparison function returns a negative value if the first
4265 argument is considered smaller than the second, a positive value
4266 if the first argument is considered greater and zero if the two
4267 constraints are considered the same by the comparison criterion.
4269 #include <isl/constraint.h>
4270 int isl_constraint_plain_cmp(
4271 __isl_keep isl_constraint *c1,
4272 __isl_keep isl_constraint *c2);
4274 This function is useful for sorting C<isl_constraint>s.
4275 The order depends on the internal representation of the inputs.
4276 The order is fixed over different calls to the function (assuming
4277 the internal representation of the inputs has not changed), but may
4278 change over different versions of C<isl>.
4280 #include <isl/constraint.h>
4281 int isl_constraint_cmp_last_non_zero(
4282 __isl_keep isl_constraint *c1,
4283 __isl_keep isl_constraint *c2);
4285 This function can be used to sort constraints that live in the same
4286 local space. Constraints that involve ``earlier'' dimensions or
4287 that have a smaller coefficient for the shared latest dimension
4288 are considered smaller than other constraints.
4289 This function only defines a B<partial> order.
4291 #include <isl/set.h>
4292 int isl_set_plain_cmp(__isl_keep isl_set *set1,
4293 __isl_keep isl_set *set2);
4295 This function is useful for sorting C<isl_set>s.
4296 The order depends on the internal representation of the inputs.
4297 The order is fixed over different calls to the function (assuming
4298 the internal representation of the inputs has not changed), but may
4299 change over different versions of C<isl>.
4301 #include <isl/aff.h>
4302 int isl_multi_aff_plain_cmp(
4303 __isl_keep isl_multi_aff *ma1,
4304 __isl_keep isl_multi_aff *ma2);
4305 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4306 __isl_keep isl_pw_aff *pa2);
4308 The functions C<isl_multi_aff_plain_cmp> and
4309 C<isl_pw_aff_plain_cmp> can be used to sort C<isl_multi_aff>s and
4310 C<isl_pw_aff>s. The order is not strictly defined.
4311 The current order sorts expressions that only involve
4312 earlier dimensions before those that involve later dimensions.
4316 =head2 Unary Operations
4322 __isl_give isl_set *isl_set_complement(
4323 __isl_take isl_set *set);
4324 __isl_give isl_map *isl_map_complement(
4325 __isl_take isl_map *map);
4329 #include <isl/space.h>
4330 __isl_give isl_space *isl_space_reverse(
4331 __isl_take isl_space *space);
4333 #include <isl/map.h>
4334 __isl_give isl_basic_map *isl_basic_map_reverse(
4335 __isl_take isl_basic_map *bmap);
4336 __isl_give isl_map *isl_map_reverse(
4337 __isl_take isl_map *map);
4339 #include <isl/union_map.h>
4340 __isl_give isl_union_map *isl_union_map_reverse(
4341 __isl_take isl_union_map *umap);
4345 #include <isl/space.h>
4346 __isl_give isl_space *isl_space_domain(
4347 __isl_take isl_space *space);
4348 __isl_give isl_space *isl_space_range(
4349 __isl_take isl_space *space);
4350 __isl_give isl_space *isl_space_params(
4351 __isl_take isl_space *space);
4353 #include <isl/local_space.h>
4354 __isl_give isl_local_space *isl_local_space_domain(
4355 __isl_take isl_local_space *ls);
4356 __isl_give isl_local_space *isl_local_space_range(
4357 __isl_take isl_local_space *ls);
4359 #include <isl/set.h>
4360 __isl_give isl_basic_set *isl_basic_set_project_out(
4361 __isl_take isl_basic_set *bset,
4362 enum isl_dim_type type, unsigned first, unsigned n);
4363 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
4364 enum isl_dim_type type, unsigned first, unsigned n);
4365 __isl_give isl_map *isl_set_project_onto_map(
4366 __isl_take isl_set *set,
4367 enum isl_dim_type type, unsigned first,
4369 __isl_give isl_basic_set *isl_basic_set_params(
4370 __isl_take isl_basic_set *bset);
4371 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
4373 The function C<isl_set_project_onto_map> returns a relation
4374 that projects the input set onto the given set dimensions.
4376 #include <isl/map.h>
4377 __isl_give isl_basic_map *isl_basic_map_project_out(
4378 __isl_take isl_basic_map *bmap,
4379 enum isl_dim_type type, unsigned first, unsigned n);
4380 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
4381 enum isl_dim_type type, unsigned first, unsigned n);
4382 __isl_give isl_basic_set *isl_basic_map_domain(
4383 __isl_take isl_basic_map *bmap);
4384 __isl_give isl_basic_set *isl_basic_map_range(
4385 __isl_take isl_basic_map *bmap);
4386 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
4387 __isl_give isl_set *isl_map_domain(
4388 __isl_take isl_map *bmap);
4389 __isl_give isl_set *isl_map_range(
4390 __isl_take isl_map *map);
4392 #include <isl/union_set.h>
4393 __isl_give isl_union_set *isl_union_set_project_out(
4394 __isl_take isl_union_set *uset,
4395 enum isl_dim_type type,
4396 unsigned first, unsigned n);
4397 __isl_give isl_set *isl_union_set_params(
4398 __isl_take isl_union_set *uset);
4400 The function C<isl_union_set_project_out> can only project out
4403 #include <isl/union_map.h>
4404 __isl_give isl_union_map *isl_union_map_project_out(
4405 __isl_take isl_union_map *umap,
4406 enum isl_dim_type type, unsigned first, unsigned n);
4407 __isl_give isl_set *isl_union_map_params(
4408 __isl_take isl_union_map *umap);
4409 __isl_give isl_union_set *isl_union_map_domain(
4410 __isl_take isl_union_map *umap);
4411 __isl_give isl_union_set *isl_union_map_range(
4412 __isl_take isl_union_map *umap);
4414 The function C<isl_union_map_project_out> can only project out
4417 #include <isl/aff.h>
4418 __isl_give isl_aff *isl_aff_project_domain_on_params(
4419 __isl_take isl_aff *aff);
4420 __isl_give isl_pw_aff *
4421 isl_pw_aff_project_domain_on_params(
4422 __isl_take isl_pw_aff *pa);
4423 __isl_give isl_pw_multi_aff *
4424 isl_pw_multi_aff_project_domain_on_params(
4425 __isl_take isl_pw_multi_aff *pma);
4426 __isl_give isl_set *isl_pw_aff_domain(
4427 __isl_take isl_pw_aff *pwaff);
4428 __isl_give isl_set *isl_pw_multi_aff_domain(
4429 __isl_take isl_pw_multi_aff *pma);
4430 __isl_give isl_set *isl_multi_pw_aff_domain(
4431 __isl_take isl_multi_pw_aff *mpa);
4432 __isl_give isl_union_set *isl_union_pw_aff_domain(
4433 __isl_take isl_union_pw_aff *upa);
4434 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4435 __isl_take isl_union_pw_multi_aff *upma);
4436 __isl_give isl_union_set *
4437 isl_multi_union_pw_aff_domain(
4438 __isl_take isl_multi_union_pw_aff *mupa);
4439 __isl_give isl_set *isl_pw_aff_params(
4440 __isl_take isl_pw_aff *pwa);
4442 The function C<isl_multi_union_pw_aff_domain> requires its
4443 input to have at least one set dimension.
4445 #include <isl/polynomial.h>
4446 __isl_give isl_qpolynomial *
4447 isl_qpolynomial_project_domain_on_params(
4448 __isl_take isl_qpolynomial *qp);
4449 __isl_give isl_pw_qpolynomial *
4450 isl_pw_qpolynomial_project_domain_on_params(
4451 __isl_take isl_pw_qpolynomial *pwqp);
4452 __isl_give isl_pw_qpolynomial_fold *
4453 isl_pw_qpolynomial_fold_project_domain_on_params(
4454 __isl_take isl_pw_qpolynomial_fold *pwf);
4455 __isl_give isl_set *isl_pw_qpolynomial_domain(
4456 __isl_take isl_pw_qpolynomial *pwqp);
4457 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4458 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4459 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4460 __isl_take isl_union_pw_qpolynomial *upwqp);
4462 #include <isl/space.h>
4463 __isl_give isl_space *isl_space_domain_map(
4464 __isl_take isl_space *space);
4465 __isl_give isl_space *isl_space_range_map(
4466 __isl_take isl_space *space);
4468 #include <isl/map.h>
4469 __isl_give isl_map *isl_set_wrapped_domain_map(
4470 __isl_take isl_set *set);
4471 __isl_give isl_basic_map *isl_basic_map_domain_map(
4472 __isl_take isl_basic_map *bmap);
4473 __isl_give isl_basic_map *isl_basic_map_range_map(
4474 __isl_take isl_basic_map *bmap);
4475 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
4476 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
4478 #include <isl/union_map.h>
4479 __isl_give isl_union_map *isl_union_map_domain_map(
4480 __isl_take isl_union_map *umap);
4481 __isl_give isl_union_pw_multi_aff *
4482 isl_union_map_domain_map_union_pw_multi_aff(
4483 __isl_take isl_union_map *umap);
4484 __isl_give isl_union_map *isl_union_map_range_map(
4485 __isl_take isl_union_map *umap);
4486 __isl_give isl_union_map *
4487 isl_union_set_wrapped_domain_map(
4488 __isl_take isl_union_set *uset);
4490 The functions above construct a (basic, regular or union) relation
4491 that maps (a wrapped version of) the input relation to its domain or range.
4492 C<isl_set_wrapped_domain_map> maps the input set to the domain
4493 of its wrapped relation.
4497 __isl_give isl_basic_set *isl_basic_set_eliminate(
4498 __isl_take isl_basic_set *bset,
4499 enum isl_dim_type type,
4500 unsigned first, unsigned n);
4501 __isl_give isl_set *isl_set_eliminate(
4502 __isl_take isl_set *set, enum isl_dim_type type,
4503 unsigned first, unsigned n);
4504 __isl_give isl_basic_map *isl_basic_map_eliminate(
4505 __isl_take isl_basic_map *bmap,
4506 enum isl_dim_type type,
4507 unsigned first, unsigned n);
4508 __isl_give isl_map *isl_map_eliminate(
4509 __isl_take isl_map *map, enum isl_dim_type type,
4510 unsigned first, unsigned n);
4512 Eliminate the coefficients for the given dimensions from the constraints,
4513 without removing the dimensions.
4515 =item * Constructing a set from a parameter domain
4517 A zero-dimensional space or (basic) set can be constructed
4518 on a given parameter domain using the following functions.
4520 #include <isl/space.h>
4521 __isl_give isl_space *isl_space_set_from_params(
4522 __isl_take isl_space *space);
4524 #include <isl/set.h>
4525 __isl_give isl_basic_set *isl_basic_set_from_params(
4526 __isl_take isl_basic_set *bset);
4527 __isl_give isl_set *isl_set_from_params(
4528 __isl_take isl_set *set);
4530 =item * Constructing a relation from one or two sets
4532 Create a relation with the given set(s) as domain and/or range.
4533 If only the domain or the range is specified, then
4534 the range or domain of the created relation is a zero-dimensional
4535 flat anonymous space.
4537 #include <isl/space.h>
4538 __isl_give isl_space *isl_space_from_domain(
4539 __isl_take isl_space *space);
4540 __isl_give isl_space *isl_space_from_range(
4541 __isl_take isl_space *space);
4542 __isl_give isl_space *isl_space_map_from_set(
4543 __isl_take isl_space *space);
4544 __isl_give isl_space *isl_space_map_from_domain_and_range(
4545 __isl_take isl_space *domain,
4546 __isl_take isl_space *range);
4548 #include <isl/local_space.h>
4549 __isl_give isl_local_space *isl_local_space_from_domain(
4550 __isl_take isl_local_space *ls);
4552 #include <isl/map.h>
4553 __isl_give isl_map *isl_map_from_domain(
4554 __isl_take isl_set *set);
4555 __isl_give isl_map *isl_map_from_range(
4556 __isl_take isl_set *set);
4558 #include <isl/union_map.h>
4559 __isl_give isl_union_map *
4560 isl_union_map_from_domain_and_range(
4561 __isl_take isl_union_set *domain,
4562 __isl_take isl_union_set *range);
4564 #include <isl/val.h>
4565 __isl_give isl_multi_val *isl_multi_val_from_range(
4566 __isl_take isl_multi_val *mv);
4568 #include <isl/aff.h>
4569 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4570 __isl_take isl_multi_aff *ma);
4571 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4572 __isl_take isl_pw_aff *pwa);
4573 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4574 __isl_take isl_multi_pw_aff *mpa);
4575 __isl_give isl_multi_union_pw_aff *
4576 isl_multi_union_pw_aff_from_range(
4577 __isl_take isl_multi_union_pw_aff *mupa);
4578 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4579 __isl_take isl_set *set);
4580 __isl_give isl_union_pw_multi_aff *
4581 isl_union_pw_multi_aff_from_domain(
4582 __isl_take isl_union_set *uset);
4584 #include <isl/polynomial.h>
4585 __isl_give isl_pw_qpolynomial *
4586 isl_pw_qpolynomial_from_range(
4587 __isl_take isl_pw_qpolynomial *pwqp);
4588 __isl_give isl_pw_qpolynomial_fold *
4589 isl_pw_qpolynomial_fold_from_range(
4590 __isl_take isl_pw_qpolynomial_fold *pwf);
4594 #include <isl/set.h>
4595 __isl_give isl_basic_set *isl_basic_set_fix_si(
4596 __isl_take isl_basic_set *bset,
4597 enum isl_dim_type type, unsigned pos, int value);
4598 __isl_give isl_basic_set *isl_basic_set_fix_val(
4599 __isl_take isl_basic_set *bset,
4600 enum isl_dim_type type, unsigned pos,
4601 __isl_take isl_val *v);
4602 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
4603 enum isl_dim_type type, unsigned pos, int value);
4604 __isl_give isl_set *isl_set_fix_val(
4605 __isl_take isl_set *set,
4606 enum isl_dim_type type, unsigned pos,
4607 __isl_take isl_val *v);
4609 #include <isl/map.h>
4610 __isl_give isl_basic_map *isl_basic_map_fix_si(
4611 __isl_take isl_basic_map *bmap,
4612 enum isl_dim_type type, unsigned pos, int value);
4613 __isl_give isl_basic_map *isl_basic_map_fix_val(
4614 __isl_take isl_basic_map *bmap,
4615 enum isl_dim_type type, unsigned pos,
4616 __isl_take isl_val *v);
4617 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
4618 enum isl_dim_type type, unsigned pos, int value);
4619 __isl_give isl_map *isl_map_fix_val(
4620 __isl_take isl_map *map,
4621 enum isl_dim_type type, unsigned pos,
4622 __isl_take isl_val *v);
4624 #include <isl/aff.h>
4625 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4626 __isl_take isl_pw_multi_aff *pma,
4627 enum isl_dim_type type, unsigned pos, int value);
4629 #include <isl/polynomial.h>
4630 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4631 __isl_take isl_pw_qpolynomial *pwqp,
4632 enum isl_dim_type type, unsigned n,
4633 __isl_take isl_val *v);
4635 Intersect the set, relation or function domain
4636 with the hyperplane where the given
4637 dimension has the fixed given value.
4639 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
4640 __isl_take isl_basic_map *bmap,
4641 enum isl_dim_type type, unsigned pos, int value);
4642 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
4643 __isl_take isl_basic_map *bmap,
4644 enum isl_dim_type type, unsigned pos, int value);
4645 __isl_give isl_set *isl_set_lower_bound_si(
4646 __isl_take isl_set *set,
4647 enum isl_dim_type type, unsigned pos, int value);
4648 __isl_give isl_set *isl_set_lower_bound_val(
4649 __isl_take isl_set *set,
4650 enum isl_dim_type type, unsigned pos,
4651 __isl_take isl_val *value);
4652 __isl_give isl_map *isl_map_lower_bound_si(
4653 __isl_take isl_map *map,
4654 enum isl_dim_type type, unsigned pos, int value);
4655 __isl_give isl_set *isl_set_upper_bound_si(
4656 __isl_take isl_set *set,
4657 enum isl_dim_type type, unsigned pos, int value);
4658 __isl_give isl_set *isl_set_upper_bound_val(
4659 __isl_take isl_set *set,
4660 enum isl_dim_type type, unsigned pos,
4661 __isl_take isl_val *value);
4662 __isl_give isl_map *isl_map_upper_bound_si(
4663 __isl_take isl_map *map,
4664 enum isl_dim_type type, unsigned pos, int value);
4666 Intersect the set or relation with the half-space where the given
4667 dimension has a value bounded by the fixed given integer value.
4669 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
4670 enum isl_dim_type type1, int pos1,
4671 enum isl_dim_type type2, int pos2);
4672 __isl_give isl_basic_map *isl_basic_map_equate(
4673 __isl_take isl_basic_map *bmap,
4674 enum isl_dim_type type1, int pos1,
4675 enum isl_dim_type type2, int pos2);
4676 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
4677 enum isl_dim_type type1, int pos1,
4678 enum isl_dim_type type2, int pos2);
4680 Intersect the set or relation with the hyperplane where the given
4681 dimensions are equal to each other.
4683 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
4684 enum isl_dim_type type1, int pos1,
4685 enum isl_dim_type type2, int pos2);
4687 Intersect the relation with the hyperplane where the given
4688 dimensions have opposite values.
4690 __isl_give isl_map *isl_map_order_le(
4691 __isl_take isl_map *map,
4692 enum isl_dim_type type1, int pos1,
4693 enum isl_dim_type type2, int pos2);
4694 __isl_give isl_basic_map *isl_basic_map_order_ge(
4695 __isl_take isl_basic_map *bmap,
4696 enum isl_dim_type type1, int pos1,
4697 enum isl_dim_type type2, int pos2);
4698 __isl_give isl_map *isl_map_order_ge(
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_map *isl_map_order_lt(__isl_take isl_map *map,
4703 enum isl_dim_type type1, int pos1,
4704 enum isl_dim_type type2, int pos2);
4705 __isl_give isl_basic_map *isl_basic_map_order_gt(
4706 __isl_take isl_basic_map *bmap,
4707 enum isl_dim_type type1, int pos1,
4708 enum isl_dim_type type2, int pos2);
4709 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
4710 enum isl_dim_type type1, int pos1,
4711 enum isl_dim_type type2, int pos2);
4713 Intersect the relation with the half-space where the given
4714 dimensions satisfy the given ordering.
4718 #include <isl/aff.h>
4719 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4720 __isl_take isl_aff *aff);
4721 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4722 __isl_take isl_aff *aff);
4723 __isl_give isl_set *isl_pw_aff_pos_set(
4724 __isl_take isl_pw_aff *pa);
4725 __isl_give isl_set *isl_pw_aff_nonneg_set(
4726 __isl_take isl_pw_aff *pwaff);
4727 __isl_give isl_set *isl_pw_aff_zero_set(
4728 __isl_take isl_pw_aff *pwaff);
4729 __isl_give isl_set *isl_pw_aff_non_zero_set(
4730 __isl_take isl_pw_aff *pwaff);
4731 __isl_give isl_union_set *
4732 isl_union_pw_aff_zero_union_set(
4733 __isl_take isl_union_pw_aff *upa);
4734 __isl_give isl_union_set *
4735 isl_multi_union_pw_aff_zero_union_set(
4736 __isl_take isl_multi_union_pw_aff *mupa);
4738 The function C<isl_aff_neg_basic_set> returns a basic set
4739 containing those elements in the domain space
4740 of C<aff> where C<aff> is negative.
4741 The function C<isl_pw_aff_nonneg_set> returns a set
4742 containing those elements in the domain
4743 of C<pwaff> where C<pwaff> is non-negative.
4744 The function C<isl_multi_union_pw_aff_zero_union_set>
4745 returns a union set containing those elements
4746 in the domains of its elements where they are all zero.
4750 __isl_give isl_map *isl_set_identity(
4751 __isl_take isl_set *set);
4752 __isl_give isl_union_map *isl_union_set_identity(
4753 __isl_take isl_union_set *uset);
4754 __isl_give isl_union_pw_multi_aff *
4755 isl_union_set_identity_union_pw_multi_aff(
4756 __isl_take isl_union_set *uset);
4758 Construct an identity relation on the given (union) set.
4760 =item * Function Extraction
4762 A piecewise quasi affine expression that is equal to 1 on a set
4763 and 0 outside the set can be created using the following function.
4765 #include <isl/aff.h>
4766 __isl_give isl_pw_aff *isl_set_indicator_function(
4767 __isl_take isl_set *set);
4769 A piecewise multiple quasi affine expression can be extracted
4770 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4771 and the C<isl_map> is single-valued.
4772 In case of a conversion from an C<isl_union_map>
4773 to an C<isl_union_pw_multi_aff>, these properties need to hold
4774 in each domain space.
4775 A conversion to a C<isl_multi_union_pw_aff> additionally
4776 requires that the input is non-empty and involves only a single
4779 #include <isl/aff.h>
4780 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4781 __isl_take isl_set *set);
4782 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4783 __isl_take isl_map *map);
4785 __isl_give isl_union_pw_multi_aff *
4786 isl_union_pw_multi_aff_from_union_set(
4787 __isl_take isl_union_set *uset);
4788 __isl_give isl_union_pw_multi_aff *
4789 isl_union_pw_multi_aff_from_union_map(
4790 __isl_take isl_union_map *umap);
4792 __isl_give isl_multi_union_pw_aff *
4793 isl_multi_union_pw_aff_from_union_map(
4794 __isl_take isl_union_map *umap);
4798 __isl_give isl_basic_set *isl_basic_map_deltas(
4799 __isl_take isl_basic_map *bmap);
4800 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
4801 __isl_give isl_union_set *isl_union_map_deltas(
4802 __isl_take isl_union_map *umap);
4804 These functions return a (basic) set containing the differences
4805 between image elements and corresponding domain elements in the input.
4807 __isl_give isl_basic_map *isl_basic_map_deltas_map(
4808 __isl_take isl_basic_map *bmap);
4809 __isl_give isl_map *isl_map_deltas_map(
4810 __isl_take isl_map *map);
4811 __isl_give isl_union_map *isl_union_map_deltas_map(
4812 __isl_take isl_union_map *umap);
4814 The functions above construct a (basic, regular or union) relation
4815 that maps (a wrapped version of) the input relation to its delta set.
4819 Simplify the representation of a set, relation or functions by trying
4820 to combine pairs of basic sets or relations into a single
4821 basic set or relation.
4823 #include <isl/set.h>
4824 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
4826 #include <isl/map.h>
4827 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
4829 #include <isl/union_set.h>
4830 __isl_give isl_union_set *isl_union_set_coalesce(
4831 __isl_take isl_union_set *uset);
4833 #include <isl/union_map.h>
4834 __isl_give isl_union_map *isl_union_map_coalesce(
4835 __isl_take isl_union_map *umap);
4837 #include <isl/aff.h>
4838 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4839 __isl_take isl_pw_aff *pwqp);
4840 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4841 __isl_take isl_pw_multi_aff *pma);
4842 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4843 __isl_take isl_multi_pw_aff *mpa);
4844 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
4845 __isl_take isl_union_pw_aff *upa);
4846 __isl_give isl_union_pw_multi_aff *
4847 isl_union_pw_multi_aff_coalesce(
4848 __isl_take isl_union_pw_multi_aff *upma);
4849 __isl_give isl_multi_union_pw_aff *
4850 isl_multi_union_pw_aff_coalesce(
4851 __isl_take isl_multi_union_pw_aff *aff);
4853 #include <isl/polynomial.h>
4854 __isl_give isl_pw_qpolynomial_fold *
4855 isl_pw_qpolynomial_fold_coalesce(
4856 __isl_take isl_pw_qpolynomial_fold *pwf);
4857 __isl_give isl_union_pw_qpolynomial *
4858 isl_union_pw_qpolynomial_coalesce(
4859 __isl_take isl_union_pw_qpolynomial *upwqp);
4860 __isl_give isl_union_pw_qpolynomial_fold *
4861 isl_union_pw_qpolynomial_fold_coalesce(
4862 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4864 One of the methods for combining pairs of basic sets or relations
4865 can result in coefficients that are much larger than those that appear
4866 in the constraints of the input. By default, the coefficients are
4867 not allowed to grow larger, but this can be changed by unsetting
4868 the following option.
4870 isl_stat isl_options_set_coalesce_bounded_wrapping(
4871 isl_ctx *ctx, int val);
4872 int isl_options_get_coalesce_bounded_wrapping(
4875 =item * Detecting equalities
4877 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
4878 __isl_take isl_basic_set *bset);
4879 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
4880 __isl_take isl_basic_map *bmap);
4881 __isl_give isl_set *isl_set_detect_equalities(
4882 __isl_take isl_set *set);
4883 __isl_give isl_map *isl_map_detect_equalities(
4884 __isl_take isl_map *map);
4885 __isl_give isl_union_set *isl_union_set_detect_equalities(
4886 __isl_take isl_union_set *uset);
4887 __isl_give isl_union_map *isl_union_map_detect_equalities(
4888 __isl_take isl_union_map *umap);
4890 Simplify the representation of a set or relation by detecting implicit
4893 =item * Removing redundant constraints
4895 #include <isl/set.h>
4896 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
4897 __isl_take isl_basic_set *bset);
4898 __isl_give isl_set *isl_set_remove_redundancies(
4899 __isl_take isl_set *set);
4901 #include <isl/union_set.h>
4902 __isl_give isl_union_set *
4903 isl_union_set_remove_redundancies(
4904 __isl_take isl_union_set *uset);
4906 #include <isl/map.h>
4907 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
4908 __isl_take isl_basic_map *bmap);
4909 __isl_give isl_map *isl_map_remove_redundancies(
4910 __isl_take isl_map *map);
4912 #include <isl/union_map.h>
4913 __isl_give isl_union_map *
4914 isl_union_map_remove_redundancies(
4915 __isl_take isl_union_map *umap);
4919 __isl_give isl_basic_set *isl_set_convex_hull(
4920 __isl_take isl_set *set);
4921 __isl_give isl_basic_map *isl_map_convex_hull(
4922 __isl_take isl_map *map);
4924 If the input set or relation has any existentially quantified
4925 variables, then the result of these operations is currently undefined.
4929 #include <isl/set.h>
4930 __isl_give isl_basic_set *
4931 isl_set_unshifted_simple_hull(
4932 __isl_take isl_set *set);
4933 __isl_give isl_basic_set *isl_set_simple_hull(
4934 __isl_take isl_set *set);
4935 __isl_give isl_basic_set *
4936 isl_set_plain_unshifted_simple_hull(
4937 __isl_take isl_set *set);
4938 __isl_give isl_basic_set *
4939 isl_set_unshifted_simple_hull_from_set_list(
4940 __isl_take isl_set *set,
4941 __isl_take isl_set_list *list);
4943 #include <isl/map.h>
4944 __isl_give isl_basic_map *
4945 isl_map_unshifted_simple_hull(
4946 __isl_take isl_map *map);
4947 __isl_give isl_basic_map *isl_map_simple_hull(
4948 __isl_take isl_map *map);
4949 __isl_give isl_basic_map *
4950 isl_map_plain_unshifted_simple_hull(
4951 __isl_take isl_map *map);
4952 __isl_give isl_basic_map *
4953 isl_map_unshifted_simple_hull_from_map_list(
4954 __isl_take isl_map *map,
4955 __isl_take isl_map_list *list);
4957 #include <isl/union_map.h>
4958 __isl_give isl_union_map *isl_union_map_simple_hull(
4959 __isl_take isl_union_map *umap);
4961 These functions compute a single basic set or relation
4962 that contains the whole input set or relation.
4963 In particular, the output is described by translates
4964 of the constraints describing the basic sets or relations in the input.
4965 In case of C<isl_set_unshifted_simple_hull>, only the original
4966 constraints are used, without any translation.
4967 In case of C<isl_set_plain_unshifted_simple_hull> and
4968 C<isl_map_plain_unshifted_simple_hull>, the result is described
4969 by original constraints that are obviously satisfied
4970 by the entire input set or relation.
4971 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
4972 C<isl_map_unshifted_simple_hull_from_map_list>, the
4973 constraints are taken from the elements of the second argument.
4977 (See \autoref{s:simple hull}.)
4983 __isl_give isl_basic_set *isl_basic_set_affine_hull(
4984 __isl_take isl_basic_set *bset);
4985 __isl_give isl_basic_set *isl_set_affine_hull(
4986 __isl_take isl_set *set);
4987 __isl_give isl_union_set *isl_union_set_affine_hull(
4988 __isl_take isl_union_set *uset);
4989 __isl_give isl_basic_map *isl_basic_map_affine_hull(
4990 __isl_take isl_basic_map *bmap);
4991 __isl_give isl_basic_map *isl_map_affine_hull(
4992 __isl_take isl_map *map);
4993 __isl_give isl_union_map *isl_union_map_affine_hull(
4994 __isl_take isl_union_map *umap);
4996 In case of union sets and relations, the affine hull is computed
4999 =item * Polyhedral hull
5001 __isl_give isl_basic_set *isl_set_polyhedral_hull(
5002 __isl_take isl_set *set);
5003 __isl_give isl_basic_map *isl_map_polyhedral_hull(
5004 __isl_take isl_map *map);
5005 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
5006 __isl_take isl_union_set *uset);
5007 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
5008 __isl_take isl_union_map *umap);
5010 These functions compute a single basic set or relation
5011 not involving any existentially quantified variables
5012 that contains the whole input set or relation.
5013 In case of union sets and relations, the polyhedral hull is computed
5016 =item * Other approximations
5018 #include <isl/set.h>
5019 __isl_give isl_basic_set *
5020 isl_basic_set_drop_constraints_involving_dims(
5021 __isl_take isl_basic_set *bset,
5022 enum isl_dim_type type,
5023 unsigned first, unsigned n);
5024 __isl_give isl_basic_set *
5025 isl_basic_set_drop_constraints_not_involving_dims(
5026 __isl_take isl_basic_set *bset,
5027 enum isl_dim_type type,
5028 unsigned first, unsigned n);
5029 __isl_give isl_set *
5030 isl_set_drop_constraints_involving_dims(
5031 __isl_take isl_set *set,
5032 enum isl_dim_type type,
5033 unsigned first, unsigned n);
5034 __isl_give isl_set *
5035 isl_set_drop_constraints_not_involving_dims(
5036 __isl_take isl_set *set,
5037 enum isl_dim_type type,
5038 unsigned first, unsigned n);
5040 #include <isl/map.h>
5041 __isl_give isl_basic_map *
5042 isl_basic_map_drop_constraints_involving_dims(
5043 __isl_take isl_basic_map *bmap,
5044 enum isl_dim_type type,
5045 unsigned first, unsigned n);
5046 __isl_give isl_basic_map *
5047 isl_basic_map_drop_constraints_not_involving_dims(
5048 __isl_take isl_basic_map *bmap,
5049 enum isl_dim_type type,
5050 unsigned first, unsigned n);
5051 __isl_give isl_map *
5052 isl_map_drop_constraints_involving_dims(
5053 __isl_take isl_map *map,
5054 enum isl_dim_type type,
5055 unsigned first, unsigned n);
5056 __isl_give isl_map *
5057 isl_map_drop_constraints_not_involving_dims(
5058 __isl_take isl_map *map,
5059 enum isl_dim_type type,
5060 unsigned first, unsigned n);
5062 These functions drop any constraints (not) involving the specified dimensions.
5063 Note that the result depends on the representation of the input.
5065 #include <isl/polynomial.h>
5066 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5067 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5068 __isl_give isl_union_pw_qpolynomial *
5069 isl_union_pw_qpolynomial_to_polynomial(
5070 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5072 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5073 the polynomial will be an overapproximation. If C<sign> is negative,
5074 it will be an underapproximation. If C<sign> is zero, the approximation
5075 will lie somewhere in between.
5079 __isl_give isl_basic_set *isl_basic_set_sample(
5080 __isl_take isl_basic_set *bset);
5081 __isl_give isl_basic_set *isl_set_sample(
5082 __isl_take isl_set *set);
5083 __isl_give isl_basic_map *isl_basic_map_sample(
5084 __isl_take isl_basic_map *bmap);
5085 __isl_give isl_basic_map *isl_map_sample(
5086 __isl_take isl_map *map);
5088 If the input (basic) set or relation is non-empty, then return
5089 a singleton subset of the input. Otherwise, return an empty set.
5091 =item * Optimization
5093 #include <isl/ilp.h>
5094 __isl_give isl_val *isl_basic_set_max_val(
5095 __isl_keep isl_basic_set *bset,
5096 __isl_keep isl_aff *obj);
5097 __isl_give isl_val *isl_set_min_val(
5098 __isl_keep isl_set *set,
5099 __isl_keep isl_aff *obj);
5100 __isl_give isl_val *isl_set_max_val(
5101 __isl_keep isl_set *set,
5102 __isl_keep isl_aff *obj);
5103 __isl_give isl_multi_val *
5104 isl_union_set_min_multi_union_pw_aff(
5105 __isl_keep isl_union_set *set,
5106 __isl_keep isl_multi_union_pw_aff *obj);
5108 Compute the minimum or maximum of the integer affine expression C<obj>
5109 over the points in C<set>, returning the result in C<opt>.
5110 The result is C<NULL> in case of an error, the optimal value in case
5111 there is one, negative infinity or infinity if the problem is unbounded and
5112 NaN if the problem is empty.
5114 =item * Parametric optimization
5116 __isl_give isl_pw_aff *isl_set_dim_min(
5117 __isl_take isl_set *set, int pos);
5118 __isl_give isl_pw_aff *isl_set_dim_max(
5119 __isl_take isl_set *set, int pos);
5120 __isl_give isl_pw_aff *isl_map_dim_min(
5121 __isl_take isl_map *map, int pos);
5122 __isl_give isl_pw_aff *isl_map_dim_max(
5123 __isl_take isl_map *map, int pos);
5125 Compute the minimum or maximum of the given set or output dimension
5126 as a function of the parameters (and input dimensions), but independently
5127 of the other set or output dimensions.
5128 For lexicographic optimization, see L<"Lexicographic Optimization">.
5132 The following functions compute either the set of (rational) coefficient
5133 values of valid constraints for the given set or the set of (rational)
5134 values satisfying the constraints with coefficients from the given set.
5135 Internally, these two sets of functions perform essentially the
5136 same operations, except that the set of coefficients is assumed to
5137 be a cone, while the set of values may be any polyhedron.
5138 The current implementation is based on the Farkas lemma and
5139 Fourier-Motzkin elimination, but this may change or be made optional
5140 in future. In particular, future implementations may use different
5141 dualization algorithms or skip the elimination step.
5143 __isl_give isl_basic_set *isl_basic_set_coefficients(
5144 __isl_take isl_basic_set *bset);
5145 __isl_give isl_basic_set *isl_set_coefficients(
5146 __isl_take isl_set *set);
5147 __isl_give isl_union_set *isl_union_set_coefficients(
5148 __isl_take isl_union_set *bset);
5149 __isl_give isl_basic_set *isl_basic_set_solutions(
5150 __isl_take isl_basic_set *bset);
5151 __isl_give isl_basic_set *isl_set_solutions(
5152 __isl_take isl_set *set);
5153 __isl_give isl_union_set *isl_union_set_solutions(
5154 __isl_take isl_union_set *bset);
5158 __isl_give isl_map *isl_map_fixed_power_val(
5159 __isl_take isl_map *map,
5160 __isl_take isl_val *exp);
5161 __isl_give isl_union_map *
5162 isl_union_map_fixed_power_val(
5163 __isl_take isl_union_map *umap,
5164 __isl_take isl_val *exp);
5166 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
5167 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
5168 of C<map> is computed.
5170 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
5172 __isl_give isl_union_map *isl_union_map_power(
5173 __isl_take isl_union_map *umap, int *exact);
5175 Compute a parametric representation for all positive powers I<k> of C<map>.
5176 The result maps I<k> to a nested relation corresponding to the
5177 I<k>th power of C<map>.
5178 The result may be an overapproximation. If the result is known to be exact,
5179 then C<*exact> is set to C<1>.
5181 =item * Transitive closure
5183 __isl_give isl_map *isl_map_transitive_closure(
5184 __isl_take isl_map *map, int *exact);
5185 __isl_give isl_union_map *isl_union_map_transitive_closure(
5186 __isl_take isl_union_map *umap, int *exact);
5188 Compute the transitive closure of C<map>.
5189 The result may be an overapproximation. If the result is known to be exact,
5190 then C<*exact> is set to C<1>.
5192 =item * Reaching path lengths
5194 __isl_give isl_map *isl_map_reaching_path_lengths(
5195 __isl_take isl_map *map, int *exact);
5197 Compute a relation that maps each element in the range of C<map>
5198 to the lengths of all paths composed of edges in C<map> that
5199 end up in the given element.
5200 The result may be an overapproximation. If the result is known to be exact,
5201 then C<*exact> is set to C<1>.
5202 To compute the I<maximal> path length, the resulting relation
5203 should be postprocessed by C<isl_map_lexmax>.
5204 In particular, if the input relation is a dependence relation
5205 (mapping sources to sinks), then the maximal path length corresponds
5206 to the free schedule.
5207 Note, however, that C<isl_map_lexmax> expects the maximum to be
5208 finite, so if the path lengths are unbounded (possibly due to
5209 the overapproximation), then you will get an error message.
5213 #include <isl/space.h>
5214 __isl_give isl_space *isl_space_wrap(
5215 __isl_take isl_space *space);
5216 __isl_give isl_space *isl_space_unwrap(
5217 __isl_take isl_space *space);
5219 #include <isl/local_space.h>
5220 __isl_give isl_local_space *isl_local_space_wrap(
5221 __isl_take isl_local_space *ls);
5223 #include <isl/set.h>
5224 __isl_give isl_basic_map *isl_basic_set_unwrap(
5225 __isl_take isl_basic_set *bset);
5226 __isl_give isl_map *isl_set_unwrap(
5227 __isl_take isl_set *set);
5229 #include <isl/map.h>
5230 __isl_give isl_basic_set *isl_basic_map_wrap(
5231 __isl_take isl_basic_map *bmap);
5232 __isl_give isl_set *isl_map_wrap(
5233 __isl_take isl_map *map);
5235 #include <isl/union_set.h>
5236 __isl_give isl_union_map *isl_union_set_unwrap(
5237 __isl_take isl_union_set *uset);
5239 #include <isl/union_map.h>
5240 __isl_give isl_union_set *isl_union_map_wrap(
5241 __isl_take isl_union_map *umap);
5243 The input to C<isl_space_unwrap> should
5244 be the space of a set, while that of
5245 C<isl_space_wrap> should be the space of a relation.
5246 Conversely, the output of C<isl_space_unwrap> is the space
5247 of a relation, while that of C<isl_space_wrap> is the space of a set.
5251 Remove any internal structure of domain (and range) of the given
5252 set or relation. If there is any such internal structure in the input,
5253 then the name of the space is also removed.
5255 #include <isl/local_space.h>
5256 __isl_give isl_local_space *
5257 isl_local_space_flatten_domain(
5258 __isl_take isl_local_space *ls);
5259 __isl_give isl_local_space *
5260 isl_local_space_flatten_range(
5261 __isl_take isl_local_space *ls);
5263 #include <isl/set.h>
5264 __isl_give isl_basic_set *isl_basic_set_flatten(
5265 __isl_take isl_basic_set *bset);
5266 __isl_give isl_set *isl_set_flatten(
5267 __isl_take isl_set *set);
5269 #include <isl/map.h>
5270 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
5271 __isl_take isl_basic_map *bmap);
5272 __isl_give isl_basic_map *isl_basic_map_flatten_range(
5273 __isl_take isl_basic_map *bmap);
5274 __isl_give isl_map *isl_map_flatten_range(
5275 __isl_take isl_map *map);
5276 __isl_give isl_map *isl_map_flatten_domain(
5277 __isl_take isl_map *map);
5278 __isl_give isl_basic_map *isl_basic_map_flatten(
5279 __isl_take isl_basic_map *bmap);
5280 __isl_give isl_map *isl_map_flatten(
5281 __isl_take isl_map *map);
5283 #include <isl/val.h>
5284 __isl_give isl_multi_val *isl_multi_val_flatten_range(
5285 __isl_take isl_multi_val *mv);
5287 #include <isl/aff.h>
5288 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
5289 __isl_take isl_multi_aff *ma);
5290 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
5291 __isl_take isl_multi_aff *ma);
5292 __isl_give isl_multi_pw_aff *
5293 isl_multi_pw_aff_flatten_range(
5294 __isl_take isl_multi_pw_aff *mpa);
5295 __isl_give isl_multi_union_pw_aff *
5296 isl_multi_union_pw_aff_flatten_range(
5297 __isl_take isl_multi_union_pw_aff *mupa);
5299 #include <isl/map.h>
5300 __isl_give isl_map *isl_set_flatten_map(
5301 __isl_take isl_set *set);
5303 The function above constructs a relation
5304 that maps the input set to a flattened version of the set.
5308 Lift the input set to a space with extra dimensions corresponding
5309 to the existentially quantified variables in the input.
5310 In particular, the result lives in a wrapped map where the domain
5311 is the original space and the range corresponds to the original
5312 existentially quantified variables.
5314 #include <isl/set.h>
5315 __isl_give isl_basic_set *isl_basic_set_lift(
5316 __isl_take isl_basic_set *bset);
5317 __isl_give isl_set *isl_set_lift(
5318 __isl_take isl_set *set);
5319 __isl_give isl_union_set *isl_union_set_lift(
5320 __isl_take isl_union_set *uset);
5322 Given a local space that contains the existentially quantified
5323 variables of a set, a basic relation that, when applied to
5324 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
5325 can be constructed using the following function.
5327 #include <isl/local_space.h>
5328 __isl_give isl_basic_map *isl_local_space_lifting(
5329 __isl_take isl_local_space *ls);
5331 #include <isl/aff.h>
5332 __isl_give isl_multi_aff *isl_multi_aff_lift(
5333 __isl_take isl_multi_aff *maff,
5334 __isl_give isl_local_space **ls);
5336 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
5337 then it is assigned the local space that lies at the basis of
5338 the lifting applied.
5340 =item * Internal Product
5342 #include <isl/space.h>
5343 __isl_give isl_space *isl_space_zip(
5344 __isl_take isl_space *space);
5346 #include <isl/map.h>
5347 __isl_give isl_basic_map *isl_basic_map_zip(
5348 __isl_take isl_basic_map *bmap);
5349 __isl_give isl_map *isl_map_zip(
5350 __isl_take isl_map *map);
5352 #include <isl/union_map.h>
5353 __isl_give isl_union_map *isl_union_map_zip(
5354 __isl_take isl_union_map *umap);
5356 Given a relation with nested relations for domain and range,
5357 interchange the range of the domain with the domain of the range.
5361 #include <isl/space.h>
5362 __isl_give isl_space *isl_space_curry(
5363 __isl_take isl_space *space);
5364 __isl_give isl_space *isl_space_uncurry(
5365 __isl_take isl_space *space);
5367 #include <isl/map.h>
5368 __isl_give isl_basic_map *isl_basic_map_curry(
5369 __isl_take isl_basic_map *bmap);
5370 __isl_give isl_basic_map *isl_basic_map_uncurry(
5371 __isl_take isl_basic_map *bmap);
5372 __isl_give isl_map *isl_map_curry(
5373 __isl_take isl_map *map);
5374 __isl_give isl_map *isl_map_uncurry(
5375 __isl_take isl_map *map);
5377 #include <isl/union_map.h>
5378 __isl_give isl_union_map *isl_union_map_curry(
5379 __isl_take isl_union_map *umap);
5380 __isl_give isl_union_map *isl_union_map_uncurry(
5381 __isl_take isl_union_map *umap);
5383 Given a relation with a nested relation for domain,
5384 the C<curry> functions
5385 move the range of the nested relation out of the domain
5386 and use it as the domain of a nested relation in the range,
5387 with the original range as range of this nested relation.
5388 The C<uncurry> functions perform the inverse operation.
5390 #include <isl/space.h>
5391 __isl_give isl_space *isl_space_range_curry(
5392 __isl_take isl_space *space);
5394 #include <isl/map.h>
5395 __isl_give isl_map *isl_map_range_curry(
5396 __isl_take isl_map *map);
5398 #include <isl/union_map.h>
5399 __isl_give isl_union_map *isl_union_map_range_curry(
5400 __isl_take isl_union_map *umap);
5402 These functions apply the currying to the relation that
5403 is nested inside the range of the input.
5405 =item * Aligning parameters
5407 Change the order of the parameters of the given set, relation
5409 such that the first parameters match those of C<model>.
5410 This may involve the introduction of extra parameters.
5411 All parameters need to be named.
5413 #include <isl/space.h>
5414 __isl_give isl_space *isl_space_align_params(
5415 __isl_take isl_space *space1,
5416 __isl_take isl_space *space2)
5418 #include <isl/set.h>
5419 __isl_give isl_basic_set *isl_basic_set_align_params(
5420 __isl_take isl_basic_set *bset,
5421 __isl_take isl_space *model);
5422 __isl_give isl_set *isl_set_align_params(
5423 __isl_take isl_set *set,
5424 __isl_take isl_space *model);
5426 #include <isl/map.h>
5427 __isl_give isl_basic_map *isl_basic_map_align_params(
5428 __isl_take isl_basic_map *bmap,
5429 __isl_take isl_space *model);
5430 __isl_give isl_map *isl_map_align_params(
5431 __isl_take isl_map *map,
5432 __isl_take isl_space *model);
5434 #include <isl/val.h>
5435 __isl_give isl_multi_val *isl_multi_val_align_params(
5436 __isl_take isl_multi_val *mv,
5437 __isl_take isl_space *model);
5439 #include <isl/aff.h>
5440 __isl_give isl_aff *isl_aff_align_params(
5441 __isl_take isl_aff *aff,
5442 __isl_take isl_space *model);
5443 __isl_give isl_multi_aff *isl_multi_aff_align_params(
5444 __isl_take isl_multi_aff *multi,
5445 __isl_take isl_space *model);
5446 __isl_give isl_pw_aff *isl_pw_aff_align_params(
5447 __isl_take isl_pw_aff *pwaff,
5448 __isl_take isl_space *model);
5449 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
5450 __isl_take isl_pw_multi_aff *pma,
5451 __isl_take isl_space *model);
5452 __isl_give isl_union_pw_aff *
5453 isl_union_pw_aff_align_params(
5454 __isl_take isl_union_pw_aff *upa,
5455 __isl_take isl_space *model);
5456 __isl_give isl_union_pw_multi_aff *
5457 isl_union_pw_multi_aff_align_params(
5458 __isl_take isl_union_pw_multi_aff *upma,
5459 __isl_take isl_space *model);
5460 __isl_give isl_multi_union_pw_aff *
5461 isl_multi_union_pw_aff_align_params(
5462 __isl_take isl_multi_union_pw_aff *mupa,
5463 __isl_take isl_space *model);
5465 #include <isl/polynomial.h>
5466 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5467 __isl_take isl_qpolynomial *qp,
5468 __isl_take isl_space *model);
5470 =item * Unary Arithmetic Operations
5472 #include <isl/set.h>
5473 __isl_give isl_set *isl_set_neg(
5474 __isl_take isl_set *set);
5475 #include <isl/map.h>
5476 __isl_give isl_map *isl_map_neg(
5477 __isl_take isl_map *map);
5479 C<isl_set_neg> constructs a set containing the opposites of
5480 the elements in its argument.
5481 The domain of the result of C<isl_map_neg> is the same
5482 as the domain of its argument. The corresponding range
5483 elements are the opposites of the corresponding range
5484 elements in the argument.
5486 #include <isl/val.h>
5487 __isl_give isl_multi_val *isl_multi_val_neg(
5488 __isl_take isl_multi_val *mv);
5490 #include <isl/aff.h>
5491 __isl_give isl_aff *isl_aff_neg(
5492 __isl_take isl_aff *aff);
5493 __isl_give isl_multi_aff *isl_multi_aff_neg(
5494 __isl_take isl_multi_aff *ma);
5495 __isl_give isl_pw_aff *isl_pw_aff_neg(
5496 __isl_take isl_pw_aff *pwaff);
5497 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
5498 __isl_take isl_pw_multi_aff *pma);
5499 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
5500 __isl_take isl_multi_pw_aff *mpa);
5501 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
5502 __isl_take isl_union_pw_aff *upa);
5503 __isl_give isl_union_pw_multi_aff *
5504 isl_union_pw_multi_aff_neg(
5505 __isl_take isl_union_pw_multi_aff *upma);
5506 __isl_give isl_multi_union_pw_aff *
5507 isl_multi_union_pw_aff_neg(
5508 __isl_take isl_multi_union_pw_aff *mupa);
5509 __isl_give isl_aff *isl_aff_ceil(
5510 __isl_take isl_aff *aff);
5511 __isl_give isl_pw_aff *isl_pw_aff_ceil(
5512 __isl_take isl_pw_aff *pwaff);
5513 __isl_give isl_aff *isl_aff_floor(
5514 __isl_take isl_aff *aff);
5515 __isl_give isl_multi_aff *isl_multi_aff_floor(
5516 __isl_take isl_multi_aff *ma);
5517 __isl_give isl_pw_aff *isl_pw_aff_floor(
5518 __isl_take isl_pw_aff *pwaff);
5519 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
5520 __isl_take isl_union_pw_aff *upa);
5521 __isl_give isl_multi_union_pw_aff *
5522 isl_multi_union_pw_aff_floor(
5523 __isl_take isl_multi_union_pw_aff *mupa);
5525 #include <isl/aff.h>
5526 __isl_give isl_pw_aff *isl_pw_aff_list_min(
5527 __isl_take isl_pw_aff_list *list);
5528 __isl_give isl_pw_aff *isl_pw_aff_list_max(
5529 __isl_take isl_pw_aff_list *list);
5531 #include <isl/polynomial.h>
5532 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5533 __isl_take isl_qpolynomial *qp);
5534 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5535 __isl_take isl_pw_qpolynomial *pwqp);
5536 __isl_give isl_union_pw_qpolynomial *
5537 isl_union_pw_qpolynomial_neg(
5538 __isl_take isl_union_pw_qpolynomial *upwqp);
5539 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5540 __isl_take isl_qpolynomial *qp,
5542 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5543 __isl_take isl_pw_qpolynomial *pwqp,
5548 The following functions evaluate a function in a point.
5550 #include <isl/polynomial.h>
5551 __isl_give isl_val *isl_pw_qpolynomial_eval(
5552 __isl_take isl_pw_qpolynomial *pwqp,
5553 __isl_take isl_point *pnt);
5554 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5555 __isl_take isl_pw_qpolynomial_fold *pwf,
5556 __isl_take isl_point *pnt);
5557 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5558 __isl_take isl_union_pw_qpolynomial *upwqp,
5559 __isl_take isl_point *pnt);
5560 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5561 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5562 __isl_take isl_point *pnt);
5564 =item * Dimension manipulation
5566 It is usually not advisable to directly change the (input or output)
5567 space of a set or a relation as this removes the name and the internal
5568 structure of the space. However, the functions below can be useful
5569 to add new parameters, assuming
5570 C<isl_set_align_params> and C<isl_map_align_params>
5573 #include <isl/space.h>
5574 __isl_give isl_space *isl_space_add_dims(
5575 __isl_take isl_space *space,
5576 enum isl_dim_type type, unsigned n);
5577 __isl_give isl_space *isl_space_insert_dims(
5578 __isl_take isl_space *space,
5579 enum isl_dim_type type, unsigned pos, unsigned n);
5580 __isl_give isl_space *isl_space_drop_dims(
5581 __isl_take isl_space *space,
5582 enum isl_dim_type type, unsigned first, unsigned n);
5583 __isl_give isl_space *isl_space_move_dims(
5584 __isl_take isl_space *space,
5585 enum isl_dim_type dst_type, unsigned dst_pos,
5586 enum isl_dim_type src_type, unsigned src_pos,
5589 #include <isl/local_space.h>
5590 __isl_give isl_local_space *isl_local_space_add_dims(
5591 __isl_take isl_local_space *ls,
5592 enum isl_dim_type type, unsigned n);
5593 __isl_give isl_local_space *isl_local_space_insert_dims(
5594 __isl_take isl_local_space *ls,
5595 enum isl_dim_type type, unsigned first, unsigned n);
5596 __isl_give isl_local_space *isl_local_space_drop_dims(
5597 __isl_take isl_local_space *ls,
5598 enum isl_dim_type type, unsigned first, unsigned n);
5600 #include <isl/set.h>
5601 __isl_give isl_basic_set *isl_basic_set_add_dims(
5602 __isl_take isl_basic_set *bset,
5603 enum isl_dim_type type, unsigned n);
5604 __isl_give isl_set *isl_set_add_dims(
5605 __isl_take isl_set *set,
5606 enum isl_dim_type type, unsigned n);
5607 __isl_give isl_basic_set *isl_basic_set_insert_dims(
5608 __isl_take isl_basic_set *bset,
5609 enum isl_dim_type type, unsigned pos,
5611 __isl_give isl_set *isl_set_insert_dims(
5612 __isl_take isl_set *set,
5613 enum isl_dim_type type, unsigned pos, unsigned n);
5614 __isl_give isl_basic_set *isl_basic_set_move_dims(
5615 __isl_take isl_basic_set *bset,
5616 enum isl_dim_type dst_type, unsigned dst_pos,
5617 enum isl_dim_type src_type, unsigned src_pos,
5619 __isl_give isl_set *isl_set_move_dims(
5620 __isl_take isl_set *set,
5621 enum isl_dim_type dst_type, unsigned dst_pos,
5622 enum isl_dim_type src_type, unsigned src_pos,
5625 #include <isl/map.h>
5626 __isl_give isl_basic_map *isl_basic_map_add_dims(
5627 __isl_take isl_basic_map *bmap,
5628 enum isl_dim_type type, unsigned n);
5629 __isl_give isl_map *isl_map_add_dims(
5630 __isl_take isl_map *map,
5631 enum isl_dim_type type, unsigned n);
5632 __isl_give isl_basic_map *isl_basic_map_insert_dims(
5633 __isl_take isl_basic_map *bmap,
5634 enum isl_dim_type type, unsigned pos,
5636 __isl_give isl_map *isl_map_insert_dims(
5637 __isl_take isl_map *map,
5638 enum isl_dim_type type, unsigned pos, unsigned n);
5639 __isl_give isl_basic_map *isl_basic_map_move_dims(
5640 __isl_take isl_basic_map *bmap,
5641 enum isl_dim_type dst_type, unsigned dst_pos,
5642 enum isl_dim_type src_type, unsigned src_pos,
5644 __isl_give isl_map *isl_map_move_dims(
5645 __isl_take isl_map *map,
5646 enum isl_dim_type dst_type, unsigned dst_pos,
5647 enum isl_dim_type src_type, unsigned src_pos,
5650 #include <isl/val.h>
5651 __isl_give isl_multi_val *isl_multi_val_insert_dims(
5652 __isl_take isl_multi_val *mv,
5653 enum isl_dim_type type, unsigned first, unsigned n);
5654 __isl_give isl_multi_val *isl_multi_val_add_dims(
5655 __isl_take isl_multi_val *mv,
5656 enum isl_dim_type type, unsigned n);
5657 __isl_give isl_multi_val *isl_multi_val_drop_dims(
5658 __isl_take isl_multi_val *mv,
5659 enum isl_dim_type type, unsigned first, unsigned n);
5661 #include <isl/aff.h>
5662 __isl_give isl_aff *isl_aff_insert_dims(
5663 __isl_take isl_aff *aff,
5664 enum isl_dim_type type, unsigned first, unsigned n);
5665 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
5666 __isl_take isl_multi_aff *ma,
5667 enum isl_dim_type type, unsigned first, unsigned n);
5668 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
5669 __isl_take isl_pw_aff *pwaff,
5670 enum isl_dim_type type, unsigned first, unsigned n);
5671 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
5672 __isl_take isl_multi_pw_aff *mpa,
5673 enum isl_dim_type type, unsigned first, unsigned n);
5674 __isl_give isl_aff *isl_aff_add_dims(
5675 __isl_take isl_aff *aff,
5676 enum isl_dim_type type, unsigned n);
5677 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
5678 __isl_take isl_multi_aff *ma,
5679 enum isl_dim_type type, unsigned n);
5680 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
5681 __isl_take isl_pw_aff *pwaff,
5682 enum isl_dim_type type, unsigned n);
5683 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
5684 __isl_take isl_multi_pw_aff *mpa,
5685 enum isl_dim_type type, unsigned n);
5686 __isl_give isl_aff *isl_aff_drop_dims(
5687 __isl_take isl_aff *aff,
5688 enum isl_dim_type type, unsigned first, unsigned n);
5689 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
5690 __isl_take isl_multi_aff *maff,
5691 enum isl_dim_type type, unsigned first, unsigned n);
5692 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
5693 __isl_take isl_pw_aff *pwaff,
5694 enum isl_dim_type type, unsigned first, unsigned n);
5695 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
5696 __isl_take isl_pw_multi_aff *pma,
5697 enum isl_dim_type type, unsigned first, unsigned n);
5698 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
5699 __isl_take isl_union_pw_aff *upa,
5700 enum isl_dim_type type, unsigned first, unsigned n);
5701 __isl_give isl_union_pw_multi_aff *
5702 isl_union_pw_multi_aff_drop_dims(
5703 __isl_take isl_union_pw_multi_aff *upma,
5704 enum isl_dim_type type,
5705 unsigned first, unsigned n);
5706 __isl_give isl_multi_union_pw_aff *
5707 isl_multi_union_pw_aff_drop_dims(
5708 __isl_take isl_multi_union_pw_aff *mupa,
5709 enum isl_dim_type type, unsigned first,
5711 __isl_give isl_aff *isl_aff_move_dims(
5712 __isl_take isl_aff *aff,
5713 enum isl_dim_type dst_type, unsigned dst_pos,
5714 enum isl_dim_type src_type, unsigned src_pos,
5716 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
5717 __isl_take isl_multi_aff *ma,
5718 enum isl_dim_type dst_type, unsigned dst_pos,
5719 enum isl_dim_type src_type, unsigned src_pos,
5721 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
5722 __isl_take isl_pw_aff *pa,
5723 enum isl_dim_type dst_type, unsigned dst_pos,
5724 enum isl_dim_type src_type, unsigned src_pos,
5726 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
5727 __isl_take isl_multi_pw_aff *pma,
5728 enum isl_dim_type dst_type, unsigned dst_pos,
5729 enum isl_dim_type src_type, unsigned src_pos,
5732 #include <isl/polynomial.h>
5733 __isl_give isl_union_pw_qpolynomial *
5734 isl_union_pw_qpolynomial_drop_dims(
5735 __isl_take isl_union_pw_qpolynomial *upwqp,
5736 enum isl_dim_type type,
5737 unsigned first, unsigned n);
5738 __isl_give isl_union_pw_qpolynomial_fold *
5739 isl_union_pw_qpolynomial_fold_drop_dims(
5740 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5741 enum isl_dim_type type,
5742 unsigned first, unsigned n);
5744 The operations on union expressions can only manipulate parameters.
5748 =head2 Binary Operations
5750 The two arguments of a binary operation not only need to live
5751 in the same C<isl_ctx>, they currently also need to have
5752 the same (number of) parameters.
5754 =head3 Basic Operations
5758 =item * Intersection
5760 #include <isl/local_space.h>
5761 __isl_give isl_local_space *isl_local_space_intersect(
5762 __isl_take isl_local_space *ls1,
5763 __isl_take isl_local_space *ls2);
5765 #include <isl/set.h>
5766 __isl_give isl_basic_set *isl_basic_set_intersect_params(
5767 __isl_take isl_basic_set *bset1,
5768 __isl_take isl_basic_set *bset2);
5769 __isl_give isl_basic_set *isl_basic_set_intersect(
5770 __isl_take isl_basic_set *bset1,
5771 __isl_take isl_basic_set *bset2);
5772 __isl_give isl_basic_set *isl_basic_set_list_intersect(
5773 __isl_take struct isl_basic_set_list *list);
5774 __isl_give isl_set *isl_set_intersect_params(
5775 __isl_take isl_set *set,
5776 __isl_take isl_set *params);
5777 __isl_give isl_set *isl_set_intersect(
5778 __isl_take isl_set *set1,
5779 __isl_take isl_set *set2);
5781 #include <isl/map.h>
5782 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
5783 __isl_take isl_basic_map *bmap,
5784 __isl_take isl_basic_set *bset);
5785 __isl_give isl_basic_map *isl_basic_map_intersect_range(
5786 __isl_take isl_basic_map *bmap,
5787 __isl_take isl_basic_set *bset);
5788 __isl_give isl_basic_map *isl_basic_map_intersect(
5789 __isl_take isl_basic_map *bmap1,
5790 __isl_take isl_basic_map *bmap2);
5791 __isl_give isl_basic_map *isl_basic_map_list_intersect(
5792 __isl_take isl_basic_map_list *list);
5793 __isl_give isl_map *isl_map_intersect_params(
5794 __isl_take isl_map *map,
5795 __isl_take isl_set *params);
5796 __isl_give isl_map *isl_map_intersect_domain(
5797 __isl_take isl_map *map,
5798 __isl_take isl_set *set);
5799 __isl_give isl_map *isl_map_intersect_range(
5800 __isl_take isl_map *map,
5801 __isl_take isl_set *set);
5802 __isl_give isl_map *isl_map_intersect(
5803 __isl_take isl_map *map1,
5804 __isl_take isl_map *map2);
5806 #include <isl/union_set.h>
5807 __isl_give isl_union_set *isl_union_set_intersect_params(
5808 __isl_take isl_union_set *uset,
5809 __isl_take isl_set *set);
5810 __isl_give isl_union_set *isl_union_set_intersect(
5811 __isl_take isl_union_set *uset1,
5812 __isl_take isl_union_set *uset2);
5814 #include <isl/union_map.h>
5815 __isl_give isl_union_map *isl_union_map_intersect_params(
5816 __isl_take isl_union_map *umap,
5817 __isl_take isl_set *set);
5818 __isl_give isl_union_map *isl_union_map_intersect_domain(
5819 __isl_take isl_union_map *umap,
5820 __isl_take isl_union_set *uset);
5821 __isl_give isl_union_map *isl_union_map_intersect_range(
5822 __isl_take isl_union_map *umap,
5823 __isl_take isl_union_set *uset);
5824 __isl_give isl_union_map *isl_union_map_intersect(
5825 __isl_take isl_union_map *umap1,
5826 __isl_take isl_union_map *umap2);
5828 #include <isl/aff.h>
5829 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
5830 __isl_take isl_pw_aff *pa,
5831 __isl_take isl_set *set);
5832 __isl_give isl_multi_pw_aff *
5833 isl_multi_pw_aff_intersect_domain(
5834 __isl_take isl_multi_pw_aff *mpa,
5835 __isl_take isl_set *domain);
5836 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
5837 __isl_take isl_pw_multi_aff *pma,
5838 __isl_take isl_set *set);
5839 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
5840 __isl_take isl_union_pw_aff *upa,
5841 __isl_take isl_union_set *uset);
5842 __isl_give isl_union_pw_multi_aff *
5843 isl_union_pw_multi_aff_intersect_domain(
5844 __isl_take isl_union_pw_multi_aff *upma,
5845 __isl_take isl_union_set *uset);
5846 __isl_give isl_multi_union_pw_aff *
5847 isl_multi_union_pw_aff_intersect_domain(
5848 __isl_take isl_multi_union_pw_aff *mupa,
5849 __isl_take isl_union_set *uset);
5850 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
5851 __isl_take isl_pw_aff *pa,
5852 __isl_take isl_set *set);
5853 __isl_give isl_multi_pw_aff *
5854 isl_multi_pw_aff_intersect_params(
5855 __isl_take isl_multi_pw_aff *mpa,
5856 __isl_take isl_set *set);
5857 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
5858 __isl_take isl_pw_multi_aff *pma,
5859 __isl_take isl_set *set);
5860 __isl_give isl_union_pw_aff *
5861 isl_union_pw_aff_intersect_params(
5862 __isl_take isl_union_pw_aff *upa,
5863 __isl_give isl_union_pw_multi_aff *
5864 isl_union_pw_multi_aff_intersect_params(
5865 __isl_take isl_union_pw_multi_aff *upma,
5866 __isl_take isl_set *set);
5867 __isl_give isl_multi_union_pw_aff *
5868 isl_multi_union_pw_aff_intersect_params(
5869 __isl_take isl_multi_union_pw_aff *mupa,
5870 __isl_take isl_set *params);
5871 isl_multi_union_pw_aff_intersect_range(
5872 __isl_take isl_multi_union_pw_aff *mupa,
5873 __isl_take isl_set *set);
5875 #include <isl/polynomial.h>
5876 __isl_give isl_pw_qpolynomial *
5877 isl_pw_qpolynomial_intersect_domain(
5878 __isl_take isl_pw_qpolynomial *pwpq,
5879 __isl_take isl_set *set);
5880 __isl_give isl_union_pw_qpolynomial *
5881 isl_union_pw_qpolynomial_intersect_domain(
5882 __isl_take isl_union_pw_qpolynomial *upwpq,
5883 __isl_take isl_union_set *uset);
5884 __isl_give isl_union_pw_qpolynomial_fold *
5885 isl_union_pw_qpolynomial_fold_intersect_domain(
5886 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5887 __isl_take isl_union_set *uset);
5888 __isl_give isl_pw_qpolynomial *
5889 isl_pw_qpolynomial_intersect_params(
5890 __isl_take isl_pw_qpolynomial *pwpq,
5891 __isl_take isl_set *set);
5892 __isl_give isl_pw_qpolynomial_fold *
5893 isl_pw_qpolynomial_fold_intersect_params(
5894 __isl_take isl_pw_qpolynomial_fold *pwf,
5895 __isl_take isl_set *set);
5896 __isl_give isl_union_pw_qpolynomial *
5897 isl_union_pw_qpolynomial_intersect_params(
5898 __isl_take isl_union_pw_qpolynomial *upwpq,
5899 __isl_take isl_set *set);
5900 __isl_give isl_union_pw_qpolynomial_fold *
5901 isl_union_pw_qpolynomial_fold_intersect_params(
5902 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5903 __isl_take isl_set *set);
5905 The second argument to the C<_params> functions needs to be
5906 a parametric (basic) set. For the other functions, a parametric set
5907 for either argument is only allowed if the other argument is
5908 a parametric set as well.
5909 The list passed to C<isl_basic_set_list_intersect> needs to have
5910 at least one element and all elements need to live in the same space.
5911 The function C<isl_multi_union_pw_aff_intersect_range>
5912 restricts the input function to those shared domain elements
5913 that map to the specified range.
5917 #include <isl/set.h>
5918 __isl_give isl_set *isl_basic_set_union(
5919 __isl_take isl_basic_set *bset1,
5920 __isl_take isl_basic_set *bset2);
5921 __isl_give isl_set *isl_set_union(
5922 __isl_take isl_set *set1,
5923 __isl_take isl_set *set2);
5924 __isl_give isl_set *isl_set_list_union(
5925 __isl_take isl_set_list *list);
5927 #include <isl/map.h>
5928 __isl_give isl_map *isl_basic_map_union(
5929 __isl_take isl_basic_map *bmap1,
5930 __isl_take isl_basic_map *bmap2);
5931 __isl_give isl_map *isl_map_union(
5932 __isl_take isl_map *map1,
5933 __isl_take isl_map *map2);
5935 #include <isl/union_set.h>
5936 __isl_give isl_union_set *isl_union_set_union(
5937 __isl_take isl_union_set *uset1,
5938 __isl_take isl_union_set *uset2);
5939 __isl_give isl_union_set *isl_union_set_list_union(
5940 __isl_take isl_union_set_list *list);
5942 #include <isl/union_map.h>
5943 __isl_give isl_union_map *isl_union_map_union(
5944 __isl_take isl_union_map *umap1,
5945 __isl_take isl_union_map *umap2);
5947 The list passed to C<isl_set_list_union> needs to have
5948 at least one element and all elements need to live in the same space.
5950 =item * Set difference
5952 #include <isl/set.h>
5953 __isl_give isl_set *isl_set_subtract(
5954 __isl_take isl_set *set1,
5955 __isl_take isl_set *set2);
5957 #include <isl/map.h>
5958 __isl_give isl_map *isl_map_subtract(
5959 __isl_take isl_map *map1,
5960 __isl_take isl_map *map2);
5961 __isl_give isl_map *isl_map_subtract_domain(
5962 __isl_take isl_map *map,
5963 __isl_take isl_set *dom);
5964 __isl_give isl_map *isl_map_subtract_range(
5965 __isl_take isl_map *map,
5966 __isl_take isl_set *dom);
5968 #include <isl/union_set.h>
5969 __isl_give isl_union_set *isl_union_set_subtract(
5970 __isl_take isl_union_set *uset1,
5971 __isl_take isl_union_set *uset2);
5973 #include <isl/union_map.h>
5974 __isl_give isl_union_map *isl_union_map_subtract(
5975 __isl_take isl_union_map *umap1,
5976 __isl_take isl_union_map *umap2);
5977 __isl_give isl_union_map *isl_union_map_subtract_domain(
5978 __isl_take isl_union_map *umap,
5979 __isl_take isl_union_set *dom);
5980 __isl_give isl_union_map *isl_union_map_subtract_range(
5981 __isl_take isl_union_map *umap,
5982 __isl_take isl_union_set *dom);
5984 #include <isl/aff.h>
5985 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
5986 __isl_take isl_pw_aff *pa,
5987 __isl_take isl_set *set);
5988 __isl_give isl_pw_multi_aff *
5989 isl_pw_multi_aff_subtract_domain(
5990 __isl_take isl_pw_multi_aff *pma,
5991 __isl_take isl_set *set);
5992 __isl_give isl_union_pw_aff *
5993 isl_union_pw_aff_subtract_domain(
5994 __isl_take isl_union_pw_aff *upa,
5995 __isl_take isl_union_set *uset);
5996 __isl_give isl_union_pw_multi_aff *
5997 isl_union_pw_multi_aff_subtract_domain(
5998 __isl_take isl_union_pw_multi_aff *upma,
5999 __isl_take isl_set *set);
6001 #include <isl/polynomial.h>
6002 __isl_give isl_pw_qpolynomial *
6003 isl_pw_qpolynomial_subtract_domain(
6004 __isl_take isl_pw_qpolynomial *pwpq,
6005 __isl_take isl_set *set);
6006 __isl_give isl_pw_qpolynomial_fold *
6007 isl_pw_qpolynomial_fold_subtract_domain(
6008 __isl_take isl_pw_qpolynomial_fold *pwf,
6009 __isl_take isl_set *set);
6010 __isl_give isl_union_pw_qpolynomial *
6011 isl_union_pw_qpolynomial_subtract_domain(
6012 __isl_take isl_union_pw_qpolynomial *upwpq,
6013 __isl_take isl_union_set *uset);
6014 __isl_give isl_union_pw_qpolynomial_fold *
6015 isl_union_pw_qpolynomial_fold_subtract_domain(
6016 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6017 __isl_take isl_union_set *uset);
6021 #include <isl/space.h>
6022 __isl_give isl_space *isl_space_join(
6023 __isl_take isl_space *left,
6024 __isl_take isl_space *right);
6026 #include <isl/map.h>
6027 __isl_give isl_basic_set *isl_basic_set_apply(
6028 __isl_take isl_basic_set *bset,
6029 __isl_take isl_basic_map *bmap);
6030 __isl_give isl_set *isl_set_apply(
6031 __isl_take isl_set *set,
6032 __isl_take isl_map *map);
6033 __isl_give isl_union_set *isl_union_set_apply(
6034 __isl_take isl_union_set *uset,
6035 __isl_take isl_union_map *umap);
6036 __isl_give isl_basic_map *isl_basic_map_apply_domain(
6037 __isl_take isl_basic_map *bmap1,
6038 __isl_take isl_basic_map *bmap2);
6039 __isl_give isl_basic_map *isl_basic_map_apply_range(
6040 __isl_take isl_basic_map *bmap1,
6041 __isl_take isl_basic_map *bmap2);
6042 __isl_give isl_map *isl_map_apply_domain(
6043 __isl_take isl_map *map1,
6044 __isl_take isl_map *map2);
6045 __isl_give isl_map *isl_map_apply_range(
6046 __isl_take isl_map *map1,
6047 __isl_take isl_map *map2);
6049 #include <isl/union_map.h>
6050 __isl_give isl_union_map *isl_union_map_apply_domain(
6051 __isl_take isl_union_map *umap1,
6052 __isl_take isl_union_map *umap2);
6053 __isl_give isl_union_map *isl_union_map_apply_range(
6054 __isl_take isl_union_map *umap1,
6055 __isl_take isl_union_map *umap2);
6057 #include <isl/aff.h>
6058 __isl_give isl_union_pw_aff *
6059 isl_multi_union_pw_aff_apply_aff(
6060 __isl_take isl_multi_union_pw_aff *mupa,
6061 __isl_take isl_aff *aff);
6062 __isl_give isl_union_pw_aff *
6063 isl_multi_union_pw_aff_apply_pw_aff(
6064 __isl_take isl_multi_union_pw_aff *mupa,
6065 __isl_take isl_pw_aff *pa);
6066 __isl_give isl_multi_union_pw_aff *
6067 isl_multi_union_pw_aff_apply_multi_aff(
6068 __isl_take isl_multi_union_pw_aff *mupa,
6069 __isl_take isl_multi_aff *ma);
6070 __isl_give isl_multi_union_pw_aff *
6071 isl_multi_union_pw_aff_apply_pw_multi_aff(
6072 __isl_take isl_multi_union_pw_aff *mupa,
6073 __isl_take isl_pw_multi_aff *pma);
6075 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
6076 over the shared domain of the elements of the input. The dimension is
6077 required to be greater than zero.
6078 The C<isl_multi_union_pw_aff> argument of
6079 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
6080 but only if the range of the C<isl_multi_aff> argument
6081 is also zero-dimensional.
6082 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
6084 #include <isl/polynomial.h>
6085 __isl_give isl_pw_qpolynomial_fold *
6086 isl_set_apply_pw_qpolynomial_fold(
6087 __isl_take isl_set *set,
6088 __isl_take isl_pw_qpolynomial_fold *pwf,
6090 __isl_give isl_pw_qpolynomial_fold *
6091 isl_map_apply_pw_qpolynomial_fold(
6092 __isl_take isl_map *map,
6093 __isl_take isl_pw_qpolynomial_fold *pwf,
6095 __isl_give isl_union_pw_qpolynomial_fold *
6096 isl_union_set_apply_union_pw_qpolynomial_fold(
6097 __isl_take isl_union_set *uset,
6098 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6100 __isl_give isl_union_pw_qpolynomial_fold *
6101 isl_union_map_apply_union_pw_qpolynomial_fold(
6102 __isl_take isl_union_map *umap,
6103 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6106 The functions taking a map
6107 compose the given map with the given piecewise quasipolynomial reduction.
6108 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
6109 over all elements in the intersection of the range of the map
6110 and the domain of the piecewise quasipolynomial reduction
6111 as a function of an element in the domain of the map.
6112 The functions taking a set compute a bound over all elements in the
6113 intersection of the set and the domain of the
6114 piecewise quasipolynomial reduction.
6118 #include <isl/set.h>
6119 __isl_give isl_basic_set *
6120 isl_basic_set_preimage_multi_aff(
6121 __isl_take isl_basic_set *bset,
6122 __isl_take isl_multi_aff *ma);
6123 __isl_give isl_set *isl_set_preimage_multi_aff(
6124 __isl_take isl_set *set,
6125 __isl_take isl_multi_aff *ma);
6126 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
6127 __isl_take isl_set *set,
6128 __isl_take isl_pw_multi_aff *pma);
6129 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
6130 __isl_take isl_set *set,
6131 __isl_take isl_multi_pw_aff *mpa);
6133 #include <isl/union_set.h>
6134 __isl_give isl_union_set *
6135 isl_union_set_preimage_multi_aff(
6136 __isl_take isl_union_set *uset,
6137 __isl_take isl_multi_aff *ma);
6138 __isl_give isl_union_set *
6139 isl_union_set_preimage_pw_multi_aff(
6140 __isl_take isl_union_set *uset,
6141 __isl_take isl_pw_multi_aff *pma);
6142 __isl_give isl_union_set *
6143 isl_union_set_preimage_union_pw_multi_aff(
6144 __isl_take isl_union_set *uset,
6145 __isl_take isl_union_pw_multi_aff *upma);
6147 #include <isl/map.h>
6148 __isl_give isl_basic_map *
6149 isl_basic_map_preimage_domain_multi_aff(
6150 __isl_take isl_basic_map *bmap,
6151 __isl_take isl_multi_aff *ma);
6152 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
6153 __isl_take isl_map *map,
6154 __isl_take isl_multi_aff *ma);
6155 __isl_give isl_map *isl_map_preimage_range_multi_aff(
6156 __isl_take isl_map *map,
6157 __isl_take isl_multi_aff *ma);
6158 __isl_give isl_map *
6159 isl_map_preimage_domain_pw_multi_aff(
6160 __isl_take isl_map *map,
6161 __isl_take isl_pw_multi_aff *pma);
6162 __isl_give isl_map *
6163 isl_map_preimage_range_pw_multi_aff(
6164 __isl_take isl_map *map,
6165 __isl_take isl_pw_multi_aff *pma);
6166 __isl_give isl_map *
6167 isl_map_preimage_domain_multi_pw_aff(
6168 __isl_take isl_map *map,
6169 __isl_take isl_multi_pw_aff *mpa);
6170 __isl_give isl_basic_map *
6171 isl_basic_map_preimage_range_multi_aff(
6172 __isl_take isl_basic_map *bmap,
6173 __isl_take isl_multi_aff *ma);
6175 #include <isl/union_map.h>
6176 __isl_give isl_union_map *
6177 isl_union_map_preimage_domain_multi_aff(
6178 __isl_take isl_union_map *umap,
6179 __isl_take isl_multi_aff *ma);
6180 __isl_give isl_union_map *
6181 isl_union_map_preimage_range_multi_aff(
6182 __isl_take isl_union_map *umap,
6183 __isl_take isl_multi_aff *ma);
6184 __isl_give isl_union_map *
6185 isl_union_map_preimage_domain_pw_multi_aff(
6186 __isl_take isl_union_map *umap,
6187 __isl_take isl_pw_multi_aff *pma);
6188 __isl_give isl_union_map *
6189 isl_union_map_preimage_range_pw_multi_aff(
6190 __isl_take isl_union_map *umap,
6191 __isl_take isl_pw_multi_aff *pma);
6192 __isl_give isl_union_map *
6193 isl_union_map_preimage_domain_union_pw_multi_aff(
6194 __isl_take isl_union_map *umap,
6195 __isl_take isl_union_pw_multi_aff *upma);
6196 __isl_give isl_union_map *
6197 isl_union_map_preimage_range_union_pw_multi_aff(
6198 __isl_take isl_union_map *umap,
6199 __isl_take isl_union_pw_multi_aff *upma);
6201 These functions compute the preimage of the given set or map domain/range under
6202 the given function. In other words, the expression is plugged
6203 into the set description or into the domain/range of the map.
6207 #include <isl/aff.h>
6208 __isl_give isl_aff *isl_aff_pullback_aff(
6209 __isl_take isl_aff *aff1,
6210 __isl_take isl_aff *aff2);
6211 __isl_give isl_aff *isl_aff_pullback_multi_aff(
6212 __isl_take isl_aff *aff,
6213 __isl_take isl_multi_aff *ma);
6214 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
6215 __isl_take isl_pw_aff *pa,
6216 __isl_take isl_multi_aff *ma);
6217 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
6218 __isl_take isl_pw_aff *pa,
6219 __isl_take isl_pw_multi_aff *pma);
6220 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
6221 __isl_take isl_pw_aff *pa,
6222 __isl_take isl_multi_pw_aff *mpa);
6223 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
6224 __isl_take isl_multi_aff *ma1,
6225 __isl_take isl_multi_aff *ma2);
6226 __isl_give isl_pw_multi_aff *
6227 isl_pw_multi_aff_pullback_multi_aff(
6228 __isl_take isl_pw_multi_aff *pma,
6229 __isl_take isl_multi_aff *ma);
6230 __isl_give isl_multi_pw_aff *
6231 isl_multi_pw_aff_pullback_multi_aff(
6232 __isl_take isl_multi_pw_aff *mpa,
6233 __isl_take isl_multi_aff *ma);
6234 __isl_give isl_pw_multi_aff *
6235 isl_pw_multi_aff_pullback_pw_multi_aff(
6236 __isl_take isl_pw_multi_aff *pma1,
6237 __isl_take isl_pw_multi_aff *pma2);
6238 __isl_give isl_multi_pw_aff *
6239 isl_multi_pw_aff_pullback_pw_multi_aff(
6240 __isl_take isl_multi_pw_aff *mpa,
6241 __isl_take isl_pw_multi_aff *pma);
6242 __isl_give isl_multi_pw_aff *
6243 isl_multi_pw_aff_pullback_multi_pw_aff(
6244 __isl_take isl_multi_pw_aff *mpa1,
6245 __isl_take isl_multi_pw_aff *mpa2);
6246 __isl_give isl_union_pw_aff *
6247 isl_union_pw_aff_pullback_union_pw_multi_aff(
6248 __isl_take isl_union_pw_aff *upa,
6249 __isl_take isl_union_pw_multi_aff *upma);
6250 __isl_give isl_union_pw_multi_aff *
6251 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
6252 __isl_take isl_union_pw_multi_aff *upma1,
6253 __isl_take isl_union_pw_multi_aff *upma2);
6254 __isl_give isl_multi_union_pw_aff *
6255 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
6256 __isl_take isl_multi_union_pw_aff *mupa,
6257 __isl_take isl_union_pw_multi_aff *upma);
6259 These functions precompose the first expression by the second function.
6260 In other words, the second function is plugged
6261 into the first expression.
6265 #include <isl/aff.h>
6266 __isl_give isl_basic_set *isl_aff_eq_basic_set(
6267 __isl_take isl_aff *aff1,
6268 __isl_take isl_aff *aff2);
6269 __isl_give isl_set *isl_aff_eq_set(
6270 __isl_take isl_aff *aff1,
6271 __isl_take isl_aff *aff2);
6272 __isl_give isl_basic_set *isl_aff_le_basic_set(
6273 __isl_take isl_aff *aff1,
6274 __isl_take isl_aff *aff2);
6275 __isl_give isl_set *isl_aff_le_set(
6276 __isl_take isl_aff *aff1,
6277 __isl_take isl_aff *aff2);
6278 __isl_give isl_basic_set *isl_aff_lt_basic_set(
6279 __isl_take isl_aff *aff1,
6280 __isl_take isl_aff *aff2);
6281 __isl_give isl_set *isl_aff_lt_set(
6282 __isl_take isl_aff *aff1,
6283 __isl_take isl_aff *aff2);
6284 __isl_give isl_basic_set *isl_aff_ge_basic_set(
6285 __isl_take isl_aff *aff1,
6286 __isl_take isl_aff *aff2);
6287 __isl_give isl_set *isl_aff_ge_set(
6288 __isl_take isl_aff *aff1,
6289 __isl_take isl_aff *aff2);
6290 __isl_give isl_basic_set *isl_aff_gt_basic_set(
6291 __isl_take isl_aff *aff1,
6292 __isl_take isl_aff *aff2);
6293 __isl_give isl_set *isl_pw_aff_eq_set(
6294 __isl_take isl_pw_aff *pwaff1,
6295 __isl_take isl_pw_aff *pwaff2);
6296 __isl_give isl_set *isl_pw_aff_ne_set(
6297 __isl_take isl_pw_aff *pwaff1,
6298 __isl_take isl_pw_aff *pwaff2);
6299 __isl_give isl_set *isl_pw_aff_le_set(
6300 __isl_take isl_pw_aff *pwaff1,
6301 __isl_take isl_pw_aff *pwaff2);
6302 __isl_give isl_set *isl_pw_aff_lt_set(
6303 __isl_take isl_pw_aff *pwaff1,
6304 __isl_take isl_pw_aff *pwaff2);
6305 __isl_give isl_set *isl_pw_aff_ge_set(
6306 __isl_take isl_pw_aff *pwaff1,
6307 __isl_take isl_pw_aff *pwaff2);
6308 __isl_give isl_set *isl_pw_aff_gt_set(
6309 __isl_take isl_pw_aff *pwaff1,
6310 __isl_take isl_pw_aff *pwaff2);
6312 __isl_give isl_set *isl_multi_aff_lex_le_set(
6313 __isl_take isl_multi_aff *ma1,
6314 __isl_take isl_multi_aff *ma2);
6315 __isl_give isl_set *isl_multi_aff_lex_lt_set(
6316 __isl_take isl_multi_aff *ma1,
6317 __isl_take isl_multi_aff *ma2);
6318 __isl_give isl_set *isl_multi_aff_lex_ge_set(
6319 __isl_take isl_multi_aff *ma1,
6320 __isl_take isl_multi_aff *ma2);
6321 __isl_give isl_set *isl_multi_aff_lex_gt_set(
6322 __isl_take isl_multi_aff *ma1,
6323 __isl_take isl_multi_aff *ma2);
6325 __isl_give isl_set *isl_pw_aff_list_eq_set(
6326 __isl_take isl_pw_aff_list *list1,
6327 __isl_take isl_pw_aff_list *list2);
6328 __isl_give isl_set *isl_pw_aff_list_ne_set(
6329 __isl_take isl_pw_aff_list *list1,
6330 __isl_take isl_pw_aff_list *list2);
6331 __isl_give isl_set *isl_pw_aff_list_le_set(
6332 __isl_take isl_pw_aff_list *list1,
6333 __isl_take isl_pw_aff_list *list2);
6334 __isl_give isl_set *isl_pw_aff_list_lt_set(
6335 __isl_take isl_pw_aff_list *list1,
6336 __isl_take isl_pw_aff_list *list2);
6337 __isl_give isl_set *isl_pw_aff_list_ge_set(
6338 __isl_take isl_pw_aff_list *list1,
6339 __isl_take isl_pw_aff_list *list2);
6340 __isl_give isl_set *isl_pw_aff_list_gt_set(
6341 __isl_take isl_pw_aff_list *list1,
6342 __isl_take isl_pw_aff_list *list2);
6344 The function C<isl_aff_ge_basic_set> returns a basic set
6345 containing those elements in the shared space
6346 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
6347 The function C<isl_pw_aff_ge_set> returns a set
6348 containing those elements in the shared domain
6349 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
6350 greater than or equal to C<pwaff2>.
6351 The function C<isl_multi_aff_lex_le_set> returns a set
6352 containing those elements in the shared domain space
6353 where C<ma1> is lexicographically smaller than or
6355 The functions operating on C<isl_pw_aff_list> apply the corresponding
6356 C<isl_pw_aff> function to each pair of elements in the two lists.
6358 #include <isl/aff.h>
6359 __isl_give isl_map *isl_pw_aff_eq_map(
6360 __isl_take isl_pw_aff *pa1,
6361 __isl_take isl_pw_aff *pa2);
6362 __isl_give isl_map *isl_pw_aff_lt_map(
6363 __isl_take isl_pw_aff *pa1,
6364 __isl_take isl_pw_aff *pa2);
6365 __isl_give isl_map *isl_pw_aff_gt_map(
6366 __isl_take isl_pw_aff *pa1,
6367 __isl_take isl_pw_aff *pa2);
6369 __isl_give isl_map *isl_multi_pw_aff_eq_map(
6370 __isl_take isl_multi_pw_aff *mpa1,
6371 __isl_take isl_multi_pw_aff *mpa2);
6372 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
6373 __isl_take isl_multi_pw_aff *mpa1,
6374 __isl_take isl_multi_pw_aff *mpa2);
6375 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
6376 __isl_take isl_multi_pw_aff *mpa1,
6377 __isl_take isl_multi_pw_aff *mpa2);
6379 These functions return a map between domain elements of the arguments
6380 where the function values satisfy the given relation.
6382 #include <isl/union_map.h>
6383 __isl_give isl_union_map *
6384 isl_union_map_eq_at_multi_union_pw_aff(
6385 __isl_take isl_union_map *umap,
6386 __isl_take isl_multi_union_pw_aff *mupa);
6387 __isl_give isl_union_map *
6388 isl_union_map_lex_lt_at_multi_union_pw_aff(
6389 __isl_take isl_union_map *umap,
6390 __isl_take isl_multi_union_pw_aff *mupa);
6391 __isl_give isl_union_map *
6392 isl_union_map_lex_gt_at_multi_union_pw_aff(
6393 __isl_take isl_union_map *umap,
6394 __isl_take isl_multi_union_pw_aff *mupa);
6396 These functions select the subset of elements in the union map
6397 that have an equal or lexicographically smaller function value.
6399 =item * Cartesian Product
6401 #include <isl/space.h>
6402 __isl_give isl_space *isl_space_product(
6403 __isl_take isl_space *space1,
6404 __isl_take isl_space *space2);
6405 __isl_give isl_space *isl_space_domain_product(
6406 __isl_take isl_space *space1,
6407 __isl_take isl_space *space2);
6408 __isl_give isl_space *isl_space_range_product(
6409 __isl_take isl_space *space1,
6410 __isl_take isl_space *space2);
6413 C<isl_space_product>, C<isl_space_domain_product>
6414 and C<isl_space_range_product> take pairs or relation spaces and
6415 produce a single relations space, where either the domain, the range
6416 or both domain and range are wrapped spaces of relations between
6417 the domains and/or ranges of the input spaces.
6418 If the product is only constructed over the domain or the range
6419 then the ranges or the domains of the inputs should be the same.
6420 The function C<isl_space_product> also accepts a pair of set spaces,
6421 in which case it returns a wrapped space of a relation between the
6424 #include <isl/set.h>
6425 __isl_give isl_set *isl_set_product(
6426 __isl_take isl_set *set1,
6427 __isl_take isl_set *set2);
6429 #include <isl/map.h>
6430 __isl_give isl_basic_map *isl_basic_map_domain_product(
6431 __isl_take isl_basic_map *bmap1,
6432 __isl_take isl_basic_map *bmap2);
6433 __isl_give isl_basic_map *isl_basic_map_range_product(
6434 __isl_take isl_basic_map *bmap1,
6435 __isl_take isl_basic_map *bmap2);
6436 __isl_give isl_basic_map *isl_basic_map_product(
6437 __isl_take isl_basic_map *bmap1,
6438 __isl_take isl_basic_map *bmap2);
6439 __isl_give isl_map *isl_map_domain_product(
6440 __isl_take isl_map *map1,
6441 __isl_take isl_map *map2);
6442 __isl_give isl_map *isl_map_range_product(
6443 __isl_take isl_map *map1,
6444 __isl_take isl_map *map2);
6445 __isl_give isl_map *isl_map_product(
6446 __isl_take isl_map *map1,
6447 __isl_take isl_map *map2);
6449 #include <isl/union_set.h>
6450 __isl_give isl_union_set *isl_union_set_product(
6451 __isl_take isl_union_set *uset1,
6452 __isl_take isl_union_set *uset2);
6454 #include <isl/union_map.h>
6455 __isl_give isl_union_map *isl_union_map_domain_product(
6456 __isl_take isl_union_map *umap1,
6457 __isl_take isl_union_map *umap2);
6458 __isl_give isl_union_map *isl_union_map_range_product(
6459 __isl_take isl_union_map *umap1,
6460 __isl_take isl_union_map *umap2);
6461 __isl_give isl_union_map *isl_union_map_product(
6462 __isl_take isl_union_map *umap1,
6463 __isl_take isl_union_map *umap2);
6465 #include <isl/val.h>
6466 __isl_give isl_multi_val *isl_multi_val_range_product(
6467 __isl_take isl_multi_val *mv1,
6468 __isl_take isl_multi_val *mv2);
6469 __isl_give isl_multi_val *isl_multi_val_product(
6470 __isl_take isl_multi_val *mv1,
6471 __isl_take isl_multi_val *mv2);
6473 #include <isl/aff.h>
6474 __isl_give isl_multi_aff *isl_multi_aff_range_product(
6475 __isl_take isl_multi_aff *ma1,
6476 __isl_take isl_multi_aff *ma2);
6477 __isl_give isl_multi_aff *isl_multi_aff_product(
6478 __isl_take isl_multi_aff *ma1,
6479 __isl_take isl_multi_aff *ma2);
6480 __isl_give isl_multi_pw_aff *
6481 isl_multi_pw_aff_range_product(
6482 __isl_take isl_multi_pw_aff *mpa1,
6483 __isl_take isl_multi_pw_aff *mpa2);
6484 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
6485 __isl_take isl_multi_pw_aff *mpa1,
6486 __isl_take isl_multi_pw_aff *mpa2);
6487 __isl_give isl_pw_multi_aff *
6488 isl_pw_multi_aff_range_product(
6489 __isl_take isl_pw_multi_aff *pma1,
6490 __isl_take isl_pw_multi_aff *pma2);
6491 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
6492 __isl_take isl_pw_multi_aff *pma1,
6493 __isl_take isl_pw_multi_aff *pma2);
6494 __isl_give isl_multi_union_pw_aff *
6495 isl_multi_union_pw_aff_range_product(
6496 __isl_take isl_multi_union_pw_aff *mupa1,
6497 __isl_take isl_multi_union_pw_aff *mupa2);
6499 The above functions compute the cross product of the given
6500 sets, relations or functions. The domains and ranges of the results
6501 are wrapped maps between domains and ranges of the inputs.
6502 To obtain a ``flat'' product, use the following functions
6505 #include <isl/set.h>
6506 __isl_give isl_basic_set *isl_basic_set_flat_product(
6507 __isl_take isl_basic_set *bset1,
6508 __isl_take isl_basic_set *bset2);
6509 __isl_give isl_set *isl_set_flat_product(
6510 __isl_take isl_set *set1,
6511 __isl_take isl_set *set2);
6513 #include <isl/map.h>
6514 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
6515 __isl_take isl_basic_map *bmap1,
6516 __isl_take isl_basic_map *bmap2);
6517 __isl_give isl_map *isl_map_flat_domain_product(
6518 __isl_take isl_map *map1,
6519 __isl_take isl_map *map2);
6520 __isl_give isl_map *isl_map_flat_range_product(
6521 __isl_take isl_map *map1,
6522 __isl_take isl_map *map2);
6523 __isl_give isl_basic_map *isl_basic_map_flat_product(
6524 __isl_take isl_basic_map *bmap1,
6525 __isl_take isl_basic_map *bmap2);
6526 __isl_give isl_map *isl_map_flat_product(
6527 __isl_take isl_map *map1,
6528 __isl_take isl_map *map2);
6530 #include <isl/union_map.h>
6531 __isl_give isl_union_map *
6532 isl_union_map_flat_domain_product(
6533 __isl_take isl_union_map *umap1,
6534 __isl_take isl_union_map *umap2);
6535 __isl_give isl_union_map *
6536 isl_union_map_flat_range_product(
6537 __isl_take isl_union_map *umap1,
6538 __isl_take isl_union_map *umap2);
6540 #include <isl/val.h>
6541 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
6542 __isl_take isl_multi_val *mv1,
6543 __isl_take isl_multi_aff *mv2);
6545 #include <isl/aff.h>
6546 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
6547 __isl_take isl_multi_aff *ma1,
6548 __isl_take isl_multi_aff *ma2);
6549 __isl_give isl_pw_multi_aff *
6550 isl_pw_multi_aff_flat_range_product(
6551 __isl_take isl_pw_multi_aff *pma1,
6552 __isl_take isl_pw_multi_aff *pma2);
6553 __isl_give isl_multi_pw_aff *
6554 isl_multi_pw_aff_flat_range_product(
6555 __isl_take isl_multi_pw_aff *mpa1,
6556 __isl_take isl_multi_pw_aff *mpa2);
6557 __isl_give isl_union_pw_multi_aff *
6558 isl_union_pw_multi_aff_flat_range_product(
6559 __isl_take isl_union_pw_multi_aff *upma1,
6560 __isl_take isl_union_pw_multi_aff *upma2);
6561 __isl_give isl_multi_union_pw_aff *
6562 isl_multi_union_pw_aff_flat_range_product(
6563 __isl_take isl_multi_union_pw_aff *mupa1,
6564 __isl_take isl_multi_union_pw_aff *mupa2);
6566 #include <isl/space.h>
6567 __isl_give isl_space *isl_space_factor_domain(
6568 __isl_take isl_space *space);
6569 __isl_give isl_space *isl_space_factor_range(
6570 __isl_take isl_space *space);
6571 __isl_give isl_space *isl_space_domain_factor_domain(
6572 __isl_take isl_space *space);
6573 __isl_give isl_space *isl_space_domain_factor_range(
6574 __isl_take isl_space *space);
6575 __isl_give isl_space *isl_space_range_factor_domain(
6576 __isl_take isl_space *space);
6577 __isl_give isl_space *isl_space_range_factor_range(
6578 __isl_take isl_space *space);
6580 The functions C<isl_space_range_factor_domain> and
6581 C<isl_space_range_factor_range> extract the two arguments from
6582 the result of a call to C<isl_space_range_product>.
6584 The arguments of a call to a product can be extracted
6585 from the result using the following functions.
6587 #include <isl/map.h>
6588 __isl_give isl_map *isl_map_factor_domain(
6589 __isl_take isl_map *map);
6590 __isl_give isl_map *isl_map_factor_range(
6591 __isl_take isl_map *map);
6592 __isl_give isl_map *isl_map_domain_factor_domain(
6593 __isl_take isl_map *map);
6594 __isl_give isl_map *isl_map_domain_factor_range(
6595 __isl_take isl_map *map);
6596 __isl_give isl_map *isl_map_range_factor_domain(
6597 __isl_take isl_map *map);
6598 __isl_give isl_map *isl_map_range_factor_range(
6599 __isl_take isl_map *map);
6601 #include <isl/union_map.h>
6602 __isl_give isl_union_map *isl_union_map_factor_domain(
6603 __isl_take isl_union_map *umap);
6604 __isl_give isl_union_map *isl_union_map_factor_range(
6605 __isl_take isl_union_map *umap);
6606 __isl_give isl_union_map *
6607 isl_union_map_domain_factor_domain(
6608 __isl_take isl_union_map *umap);
6609 __isl_give isl_union_map *
6610 isl_union_map_domain_factor_range(
6611 __isl_take isl_union_map *umap);
6612 __isl_give isl_union_map *
6613 isl_union_map_range_factor_domain(
6614 __isl_take isl_union_map *umap);
6615 __isl_give isl_union_map *
6616 isl_union_map_range_factor_range(
6617 __isl_take isl_union_map *umap);
6619 #include <isl/val.h>
6620 __isl_give isl_multi_val *isl_multi_val_factor_range(
6621 __isl_take isl_multi_val *mv);
6622 __isl_give isl_multi_val *
6623 isl_multi_val_range_factor_domain(
6624 __isl_take isl_multi_val *mv);
6625 __isl_give isl_multi_val *
6626 isl_multi_val_range_factor_range(
6627 __isl_take isl_multi_val *mv);
6629 #include <isl/aff.h>
6630 __isl_give isl_multi_aff *isl_multi_aff_factor_range(
6631 __isl_take isl_multi_aff *ma);
6632 __isl_give isl_multi_aff *
6633 isl_multi_aff_range_factor_domain(
6634 __isl_take isl_multi_aff *ma);
6635 __isl_give isl_multi_aff *
6636 isl_multi_aff_range_factor_range(
6637 __isl_take isl_multi_aff *ma);
6638 __isl_give isl_multi_pw_aff *
6639 isl_multi_pw_aff_factor_range(
6640 __isl_take isl_multi_pw_aff *mpa);
6641 __isl_give isl_multi_pw_aff *
6642 isl_multi_pw_aff_range_factor_domain(
6643 __isl_take isl_multi_pw_aff *mpa);
6644 __isl_give isl_multi_pw_aff *
6645 isl_multi_pw_aff_range_factor_range(
6646 __isl_take isl_multi_pw_aff *mpa);
6647 __isl_give isl_multi_union_pw_aff *
6648 isl_multi_union_pw_aff_factor_range(
6649 __isl_take isl_multi_union_pw_aff *mupa);
6650 __isl_give isl_multi_union_pw_aff *
6651 isl_multi_union_pw_aff_range_factor_domain(
6652 __isl_take isl_multi_union_pw_aff *mupa);
6653 __isl_give isl_multi_union_pw_aff *
6654 isl_multi_union_pw_aff_range_factor_range(
6655 __isl_take isl_multi_union_pw_aff *mupa);
6657 The splice functions are a generalization of the flat product functions,
6658 where the second argument may be inserted at any position inside
6659 the first argument rather than being placed at the end.
6660 The functions C<isl_multi_val_factor_range>,
6661 C<isl_multi_aff_factor_range>,
6662 C<isl_multi_pw_aff_factor_range> and
6663 C<isl_multi_union_pw_aff_factor_range>
6664 take functions that live in a set space.
6666 #include <isl/val.h>
6667 __isl_give isl_multi_val *isl_multi_val_range_splice(
6668 __isl_take isl_multi_val *mv1, unsigned pos,
6669 __isl_take isl_multi_val *mv2);
6671 #include <isl/aff.h>
6672 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
6673 __isl_take isl_multi_aff *ma1, unsigned pos,
6674 __isl_take isl_multi_aff *ma2);
6675 __isl_give isl_multi_aff *isl_multi_aff_splice(
6676 __isl_take isl_multi_aff *ma1,
6677 unsigned in_pos, unsigned out_pos,
6678 __isl_take isl_multi_aff *ma2);
6679 __isl_give isl_multi_pw_aff *
6680 isl_multi_pw_aff_range_splice(
6681 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
6682 __isl_take isl_multi_pw_aff *mpa2);
6683 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
6684 __isl_take isl_multi_pw_aff *mpa1,
6685 unsigned in_pos, unsigned out_pos,
6686 __isl_take isl_multi_pw_aff *mpa2);
6687 __isl_give isl_multi_union_pw_aff *
6688 isl_multi_union_pw_aff_range_splice(
6689 __isl_take isl_multi_union_pw_aff *mupa1,
6691 __isl_take isl_multi_union_pw_aff *mupa2);
6693 =item * Simplification
6695 When applied to a set or relation,
6696 the gist operation returns a set or relation that has the
6697 same intersection with the context as the input set or relation.
6698 Any implicit equality in the intersection is made explicit in the result,
6699 while all inequalities that are redundant with respect to the intersection
6701 In case of union sets and relations, the gist operation is performed
6704 When applied to a function,
6705 the gist operation applies the set gist operation to each of
6706 the cells in the domain of the input piecewise expression.
6707 The context is also exploited
6708 to simplify the expression associated to each cell.
6710 #include <isl/set.h>
6711 __isl_give isl_basic_set *isl_basic_set_gist(
6712 __isl_take isl_basic_set *bset,
6713 __isl_take isl_basic_set *context);
6714 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
6715 __isl_take isl_set *context);
6716 __isl_give isl_set *isl_set_gist_params(
6717 __isl_take isl_set *set,
6718 __isl_take isl_set *context);
6720 #include <isl/map.h>
6721 __isl_give isl_basic_map *isl_basic_map_gist(
6722 __isl_take isl_basic_map *bmap,
6723 __isl_take isl_basic_map *context);
6724 __isl_give isl_basic_map *isl_basic_map_gist_domain(
6725 __isl_take isl_basic_map *bmap,
6726 __isl_take isl_basic_set *context);
6727 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
6728 __isl_take isl_map *context);
6729 __isl_give isl_map *isl_map_gist_params(
6730 __isl_take isl_map *map,
6731 __isl_take isl_set *context);
6732 __isl_give isl_map *isl_map_gist_domain(
6733 __isl_take isl_map *map,
6734 __isl_take isl_set *context);
6735 __isl_give isl_map *isl_map_gist_range(
6736 __isl_take isl_map *map,
6737 __isl_take isl_set *context);
6739 #include <isl/union_set.h>
6740 __isl_give isl_union_set *isl_union_set_gist(
6741 __isl_take isl_union_set *uset,
6742 __isl_take isl_union_set *context);
6743 __isl_give isl_union_set *isl_union_set_gist_params(
6744 __isl_take isl_union_set *uset,
6745 __isl_take isl_set *set);
6747 #include <isl/union_map.h>
6748 __isl_give isl_union_map *isl_union_map_gist(
6749 __isl_take isl_union_map *umap,
6750 __isl_take isl_union_map *context);
6751 __isl_give isl_union_map *isl_union_map_gist_params(
6752 __isl_take isl_union_map *umap,
6753 __isl_take isl_set *set);
6754 __isl_give isl_union_map *isl_union_map_gist_domain(
6755 __isl_take isl_union_map *umap,
6756 __isl_take isl_union_set *uset);
6757 __isl_give isl_union_map *isl_union_map_gist_range(
6758 __isl_take isl_union_map *umap,
6759 __isl_take isl_union_set *uset);
6761 #include <isl/aff.h>
6762 __isl_give isl_aff *isl_aff_gist_params(
6763 __isl_take isl_aff *aff,
6764 __isl_take isl_set *context);
6765 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
6766 __isl_take isl_set *context);
6767 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
6768 __isl_take isl_multi_aff *maff,
6769 __isl_take isl_set *context);
6770 __isl_give isl_multi_aff *isl_multi_aff_gist(
6771 __isl_take isl_multi_aff *maff,
6772 __isl_take isl_set *context);
6773 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
6774 __isl_take isl_pw_aff *pwaff,
6775 __isl_take isl_set *context);
6776 __isl_give isl_pw_aff *isl_pw_aff_gist(
6777 __isl_take isl_pw_aff *pwaff,
6778 __isl_take isl_set *context);
6779 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
6780 __isl_take isl_pw_multi_aff *pma,
6781 __isl_take isl_set *set);
6782 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
6783 __isl_take isl_pw_multi_aff *pma,
6784 __isl_take isl_set *set);
6785 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
6786 __isl_take isl_multi_pw_aff *mpa,
6787 __isl_take isl_set *set);
6788 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
6789 __isl_take isl_multi_pw_aff *mpa,
6790 __isl_take isl_set *set);
6791 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
6792 __isl_take isl_union_pw_aff *upa,
6793 __isl_take isl_union_set *context);
6794 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
6795 __isl_take isl_union_pw_aff *upa,
6796 __isl_take isl_set *context);
6797 __isl_give isl_union_pw_multi_aff *
6798 isl_union_pw_multi_aff_gist_params(
6799 __isl_take isl_union_pw_multi_aff *upma,
6800 __isl_take isl_set *context);
6801 __isl_give isl_union_pw_multi_aff *
6802 isl_union_pw_multi_aff_gist(
6803 __isl_take isl_union_pw_multi_aff *upma,
6804 __isl_take isl_union_set *context);
6805 __isl_give isl_multi_union_pw_aff *
6806 isl_multi_union_pw_aff_gist_params(
6807 __isl_take isl_multi_union_pw_aff *aff,
6808 __isl_take isl_set *context);
6809 __isl_give isl_multi_union_pw_aff *
6810 isl_multi_union_pw_aff_gist(
6811 __isl_take isl_multi_union_pw_aff *aff,
6812 __isl_take isl_union_set *context);
6814 #include <isl/polynomial.h>
6815 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
6816 __isl_take isl_qpolynomial *qp,
6817 __isl_take isl_set *context);
6818 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
6819 __isl_take isl_qpolynomial *qp,
6820 __isl_take isl_set *context);
6821 __isl_give isl_qpolynomial_fold *
6822 isl_qpolynomial_fold_gist_params(
6823 __isl_take isl_qpolynomial_fold *fold,
6824 __isl_take isl_set *context);
6825 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
6826 __isl_take isl_qpolynomial_fold *fold,
6827 __isl_take isl_set *context);
6828 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
6829 __isl_take isl_pw_qpolynomial *pwqp,
6830 __isl_take isl_set *context);
6831 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
6832 __isl_take isl_pw_qpolynomial *pwqp,
6833 __isl_take isl_set *context);
6834 __isl_give isl_pw_qpolynomial_fold *
6835 isl_pw_qpolynomial_fold_gist(
6836 __isl_take isl_pw_qpolynomial_fold *pwf,
6837 __isl_take isl_set *context);
6838 __isl_give isl_pw_qpolynomial_fold *
6839 isl_pw_qpolynomial_fold_gist_params(
6840 __isl_take isl_pw_qpolynomial_fold *pwf,
6841 __isl_take isl_set *context);
6842 __isl_give isl_union_pw_qpolynomial *
6843 isl_union_pw_qpolynomial_gist_params(
6844 __isl_take isl_union_pw_qpolynomial *upwqp,
6845 __isl_take isl_set *context);
6846 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
6847 __isl_take isl_union_pw_qpolynomial *upwqp,
6848 __isl_take isl_union_set *context);
6849 __isl_give isl_union_pw_qpolynomial_fold *
6850 isl_union_pw_qpolynomial_fold_gist(
6851 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6852 __isl_take isl_union_set *context);
6853 __isl_give isl_union_pw_qpolynomial_fold *
6854 isl_union_pw_qpolynomial_fold_gist_params(
6855 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6856 __isl_take isl_set *context);
6858 =item * Binary Arithmetic Operations
6860 #include <isl/set.h>
6861 __isl_give isl_set *isl_set_sum(
6862 __isl_take isl_set *set1,
6863 __isl_take isl_set *set2);
6864 #include <isl/map.h>
6865 __isl_give isl_map *isl_map_sum(
6866 __isl_take isl_map *map1,
6867 __isl_take isl_map *map2);
6869 C<isl_set_sum> computes the Minkowski sum of its two arguments,
6870 i.e., the set containing the sums of pairs of elements from
6871 C<set1> and C<set2>.
6872 The domain of the result of C<isl_map_sum> is the intersection
6873 of the domains of its two arguments. The corresponding range
6874 elements are the sums of the corresponding range elements
6875 in the two arguments.
6877 #include <isl/val.h>
6878 __isl_give isl_multi_val *isl_multi_val_add(
6879 __isl_take isl_multi_val *mv1,
6880 __isl_take isl_multi_val *mv2);
6881 __isl_give isl_multi_val *isl_multi_val_sub(
6882 __isl_take isl_multi_val *mv1,
6883 __isl_take isl_multi_val *mv2);
6885 #include <isl/aff.h>
6886 __isl_give isl_aff *isl_aff_add(
6887 __isl_take isl_aff *aff1,
6888 __isl_take isl_aff *aff2);
6889 __isl_give isl_multi_aff *isl_multi_aff_add(
6890 __isl_take isl_multi_aff *maff1,
6891 __isl_take isl_multi_aff *maff2);
6892 __isl_give isl_pw_aff *isl_pw_aff_add(
6893 __isl_take isl_pw_aff *pwaff1,
6894 __isl_take isl_pw_aff *pwaff2);
6895 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add(
6896 __isl_take isl_multi_pw_aff *mpa1,
6897 __isl_take isl_multi_pw_aff *mpa2);
6898 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
6899 __isl_take isl_pw_multi_aff *pma1,
6900 __isl_take isl_pw_multi_aff *pma2);
6901 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
6902 __isl_take isl_union_pw_aff *upa1,
6903 __isl_take isl_union_pw_aff *upa2);
6904 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
6905 __isl_take isl_union_pw_multi_aff *upma1,
6906 __isl_take isl_union_pw_multi_aff *upma2);
6907 __isl_give isl_multi_union_pw_aff *
6908 isl_multi_union_pw_aff_add(
6909 __isl_take isl_multi_union_pw_aff *mupa1,
6910 __isl_take isl_multi_union_pw_aff *mupa2);
6911 __isl_give isl_pw_aff *isl_pw_aff_min(
6912 __isl_take isl_pw_aff *pwaff1,
6913 __isl_take isl_pw_aff *pwaff2);
6914 __isl_give isl_pw_aff *isl_pw_aff_max(
6915 __isl_take isl_pw_aff *pwaff1,
6916 __isl_take isl_pw_aff *pwaff2);
6917 __isl_give isl_aff *isl_aff_sub(
6918 __isl_take isl_aff *aff1,
6919 __isl_take isl_aff *aff2);
6920 __isl_give isl_multi_aff *isl_multi_aff_sub(
6921 __isl_take isl_multi_aff *ma1,
6922 __isl_take isl_multi_aff *ma2);
6923 __isl_give isl_pw_aff *isl_pw_aff_sub(
6924 __isl_take isl_pw_aff *pwaff1,
6925 __isl_take isl_pw_aff *pwaff2);
6926 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
6927 __isl_take isl_multi_pw_aff *mpa1,
6928 __isl_take isl_multi_pw_aff *mpa2);
6929 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
6930 __isl_take isl_pw_multi_aff *pma1,
6931 __isl_take isl_pw_multi_aff *pma2);
6932 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
6933 __isl_take isl_union_pw_aff *upa1,
6934 __isl_take isl_union_pw_aff *upa2);
6935 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
6936 __isl_take isl_union_pw_multi_aff *upma1,
6937 __isl_take isl_union_pw_multi_aff *upma2);
6938 __isl_give isl_multi_union_pw_aff *
6939 isl_multi_union_pw_aff_sub(
6940 __isl_take isl_multi_union_pw_aff *mupa1,
6941 __isl_take isl_multi_union_pw_aff *mupa2);
6943 C<isl_aff_sub> subtracts the second argument from the first.
6945 #include <isl/polynomial.h>
6946 __isl_give isl_qpolynomial *isl_qpolynomial_add(
6947 __isl_take isl_qpolynomial *qp1,
6948 __isl_take isl_qpolynomial *qp2);
6949 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
6950 __isl_take isl_pw_qpolynomial *pwqp1,
6951 __isl_take isl_pw_qpolynomial *pwqp2);
6952 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
6953 __isl_take isl_pw_qpolynomial *pwqp1,
6954 __isl_take isl_pw_qpolynomial *pwqp2);
6955 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
6956 __isl_take isl_pw_qpolynomial_fold *pwf1,
6957 __isl_take isl_pw_qpolynomial_fold *pwf2);
6958 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
6959 __isl_take isl_union_pw_qpolynomial *upwqp1,
6960 __isl_take isl_union_pw_qpolynomial *upwqp2);
6961 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
6962 __isl_take isl_qpolynomial *qp1,
6963 __isl_take isl_qpolynomial *qp2);
6964 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
6965 __isl_take isl_pw_qpolynomial *pwqp1,
6966 __isl_take isl_pw_qpolynomial *pwqp2);
6967 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
6968 __isl_take isl_union_pw_qpolynomial *upwqp1,
6969 __isl_take isl_union_pw_qpolynomial *upwqp2);
6970 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
6971 __isl_take isl_pw_qpolynomial_fold *pwf1,
6972 __isl_take isl_pw_qpolynomial_fold *pwf2);
6973 __isl_give isl_union_pw_qpolynomial_fold *
6974 isl_union_pw_qpolynomial_fold_fold(
6975 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
6976 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
6978 #include <isl/aff.h>
6979 __isl_give isl_pw_aff *isl_pw_aff_union_add(
6980 __isl_take isl_pw_aff *pwaff1,
6981 __isl_take isl_pw_aff *pwaff2);
6982 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
6983 __isl_take isl_pw_multi_aff *pma1,
6984 __isl_take isl_pw_multi_aff *pma2);
6985 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
6986 __isl_take isl_union_pw_aff *upa1,
6987 __isl_take isl_union_pw_aff *upa2);
6988 __isl_give isl_union_pw_multi_aff *
6989 isl_union_pw_multi_aff_union_add(
6990 __isl_take isl_union_pw_multi_aff *upma1,
6991 __isl_take isl_union_pw_multi_aff *upma2);
6992 __isl_give isl_multi_union_pw_aff *
6993 isl_multi_union_pw_aff_union_add(
6994 __isl_take isl_multi_union_pw_aff *mupa1,
6995 __isl_take isl_multi_union_pw_aff *mupa2);
6996 __isl_give isl_pw_aff *isl_pw_aff_union_min(
6997 __isl_take isl_pw_aff *pwaff1,
6998 __isl_take isl_pw_aff *pwaff2);
6999 __isl_give isl_pw_aff *isl_pw_aff_union_max(
7000 __isl_take isl_pw_aff *pwaff1,
7001 __isl_take isl_pw_aff *pwaff2);
7003 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
7004 expression with a domain that is the union of those of C<pwaff1> and
7005 C<pwaff2> and such that on each cell, the quasi-affine expression is
7006 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
7007 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
7008 associated expression is the defined one.
7009 This in contrast to the C<isl_pw_aff_max> function, which is
7010 only defined on the shared definition domain of the arguments.
7012 #include <isl/val.h>
7013 __isl_give isl_multi_val *isl_multi_val_add_val(
7014 __isl_take isl_multi_val *mv,
7015 __isl_take isl_val *v);
7016 __isl_give isl_multi_val *isl_multi_val_mod_val(
7017 __isl_take isl_multi_val *mv,
7018 __isl_take isl_val *v);
7019 __isl_give isl_multi_val *isl_multi_val_scale_val(
7020 __isl_take isl_multi_val *mv,
7021 __isl_take isl_val *v);
7022 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
7023 __isl_take isl_multi_val *mv,
7024 __isl_take isl_val *v);
7026 #include <isl/aff.h>
7027 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
7028 __isl_take isl_val *mod);
7029 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
7030 __isl_take isl_pw_aff *pa,
7031 __isl_take isl_val *mod);
7032 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
7033 __isl_take isl_union_pw_aff *upa,
7034 __isl_take isl_val *f);
7035 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
7036 __isl_take isl_val *v);
7037 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
7038 __isl_take isl_multi_aff *ma,
7039 __isl_take isl_val *v);
7040 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
7041 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
7042 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
7043 __isl_take isl_multi_pw_aff *mpa,
7044 __isl_take isl_val *v);
7045 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
7046 __isl_take isl_pw_multi_aff *pma,
7047 __isl_take isl_val *v);
7048 __isl_give isl_union_pw_multi_aff *
7049 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
7050 __isl_take isl_union_pw_aff *upa,
7051 __isl_take isl_val *f);
7052 isl_union_pw_multi_aff_scale_val(
7053 __isl_take isl_union_pw_multi_aff *upma,
7054 __isl_take isl_val *val);
7055 __isl_give isl_multi_union_pw_aff *
7056 isl_multi_union_pw_aff_scale_val(
7057 __isl_take isl_multi_union_pw_aff *mupa,
7058 __isl_take isl_val *v);
7059 __isl_give isl_aff *isl_aff_scale_down_ui(
7060 __isl_take isl_aff *aff, unsigned f);
7061 __isl_give isl_aff *isl_aff_scale_down_val(
7062 __isl_take isl_aff *aff, __isl_take isl_val *v);
7063 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
7064 __isl_take isl_multi_aff *ma,
7065 __isl_take isl_val *v);
7066 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
7067 __isl_take isl_pw_aff *pa,
7068 __isl_take isl_val *f);
7069 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
7070 __isl_take isl_multi_pw_aff *mpa,
7071 __isl_take isl_val *v);
7072 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
7073 __isl_take isl_pw_multi_aff *pma,
7074 __isl_take isl_val *v);
7075 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
7076 __isl_take isl_union_pw_aff *upa,
7077 __isl_take isl_val *v);
7078 __isl_give isl_union_pw_multi_aff *
7079 isl_union_pw_multi_aff_scale_down_val(
7080 __isl_take isl_union_pw_multi_aff *upma,
7081 __isl_take isl_val *val);
7082 __isl_give isl_multi_union_pw_aff *
7083 isl_multi_union_pw_aff_scale_down_val(
7084 __isl_take isl_multi_union_pw_aff *mupa,
7085 __isl_take isl_val *v);
7087 #include <isl/polynomial.h>
7088 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
7089 __isl_take isl_qpolynomial *qp,
7090 __isl_take isl_val *v);
7091 __isl_give isl_qpolynomial_fold *
7092 isl_qpolynomial_fold_scale_val(
7093 __isl_take isl_qpolynomial_fold *fold,
7094 __isl_take isl_val *v);
7095 __isl_give isl_pw_qpolynomial *
7096 isl_pw_qpolynomial_scale_val(
7097 __isl_take isl_pw_qpolynomial *pwqp,
7098 __isl_take isl_val *v);
7099 __isl_give isl_pw_qpolynomial_fold *
7100 isl_pw_qpolynomial_fold_scale_val(
7101 __isl_take isl_pw_qpolynomial_fold *pwf,
7102 __isl_take isl_val *v);
7103 __isl_give isl_union_pw_qpolynomial *
7104 isl_union_pw_qpolynomial_scale_val(
7105 __isl_take isl_union_pw_qpolynomial *upwqp,
7106 __isl_take isl_val *v);
7107 __isl_give isl_union_pw_qpolynomial_fold *
7108 isl_union_pw_qpolynomial_fold_scale_val(
7109 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7110 __isl_take isl_val *v);
7111 __isl_give isl_qpolynomial *
7112 isl_qpolynomial_scale_down_val(
7113 __isl_take isl_qpolynomial *qp,
7114 __isl_take isl_val *v);
7115 __isl_give isl_qpolynomial_fold *
7116 isl_qpolynomial_fold_scale_down_val(
7117 __isl_take isl_qpolynomial_fold *fold,
7118 __isl_take isl_val *v);
7119 __isl_give isl_pw_qpolynomial *
7120 isl_pw_qpolynomial_scale_down_val(
7121 __isl_take isl_pw_qpolynomial *pwqp,
7122 __isl_take isl_val *v);
7123 __isl_give isl_pw_qpolynomial_fold *
7124 isl_pw_qpolynomial_fold_scale_down_val(
7125 __isl_take isl_pw_qpolynomial_fold *pwf,
7126 __isl_take isl_val *v);
7127 __isl_give isl_union_pw_qpolynomial *
7128 isl_union_pw_qpolynomial_scale_down_val(
7129 __isl_take isl_union_pw_qpolynomial *upwqp,
7130 __isl_take isl_val *v);
7131 __isl_give isl_union_pw_qpolynomial_fold *
7132 isl_union_pw_qpolynomial_fold_scale_down_val(
7133 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7134 __isl_take isl_val *v);
7136 #include <isl/val.h>
7137 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
7138 __isl_take isl_multi_val *mv1,
7139 __isl_take isl_multi_val *mv2);
7140 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
7141 __isl_take isl_multi_val *mv1,
7142 __isl_take isl_multi_val *mv2);
7143 __isl_give isl_multi_val *
7144 isl_multi_val_scale_down_multi_val(
7145 __isl_take isl_multi_val *mv1,
7146 __isl_take isl_multi_val *mv2);
7148 #include <isl/aff.h>
7149 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
7150 __isl_take isl_multi_aff *ma,
7151 __isl_take isl_multi_val *mv);
7152 __isl_give isl_multi_union_pw_aff *
7153 isl_multi_union_pw_aff_mod_multi_val(
7154 __isl_take isl_multi_union_pw_aff *upma,
7155 __isl_take isl_multi_val *mv);
7156 __isl_give isl_multi_pw_aff *
7157 isl_multi_pw_aff_mod_multi_val(
7158 __isl_take isl_multi_pw_aff *mpa,
7159 __isl_take isl_multi_val *mv);
7160 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
7161 __isl_take isl_multi_aff *ma,
7162 __isl_take isl_multi_val *mv);
7163 __isl_give isl_pw_multi_aff *
7164 isl_pw_multi_aff_scale_multi_val(
7165 __isl_take isl_pw_multi_aff *pma,
7166 __isl_take isl_multi_val *mv);
7167 __isl_give isl_multi_pw_aff *
7168 isl_multi_pw_aff_scale_multi_val(
7169 __isl_take isl_multi_pw_aff *mpa,
7170 __isl_take isl_multi_val *mv);
7171 __isl_give isl_multi_union_pw_aff *
7172 isl_multi_union_pw_aff_scale_multi_val(
7173 __isl_take isl_multi_union_pw_aff *mupa,
7174 __isl_take isl_multi_val *mv);
7175 __isl_give isl_union_pw_multi_aff *
7176 isl_union_pw_multi_aff_scale_multi_val(
7177 __isl_take isl_union_pw_multi_aff *upma,
7178 __isl_take isl_multi_val *mv);
7179 __isl_give isl_multi_aff *
7180 isl_multi_aff_scale_down_multi_val(
7181 __isl_take isl_multi_aff *ma,
7182 __isl_take isl_multi_val *mv);
7183 __isl_give isl_multi_pw_aff *
7184 isl_multi_pw_aff_scale_down_multi_val(
7185 __isl_take isl_multi_pw_aff *mpa,
7186 __isl_take isl_multi_val *mv);
7187 __isl_give isl_multi_union_pw_aff *
7188 isl_multi_union_pw_aff_scale_down_multi_val(
7189 __isl_take isl_multi_union_pw_aff *mupa,
7190 __isl_take isl_multi_val *mv);
7192 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
7193 by the corresponding elements of C<mv>.
7195 #include <isl/aff.h>
7196 __isl_give isl_aff *isl_aff_mul(
7197 __isl_take isl_aff *aff1,
7198 __isl_take isl_aff *aff2);
7199 __isl_give isl_aff *isl_aff_div(
7200 __isl_take isl_aff *aff1,
7201 __isl_take isl_aff *aff2);
7202 __isl_give isl_pw_aff *isl_pw_aff_mul(
7203 __isl_take isl_pw_aff *pwaff1,
7204 __isl_take isl_pw_aff *pwaff2);
7205 __isl_give isl_pw_aff *isl_pw_aff_div(
7206 __isl_take isl_pw_aff *pa1,
7207 __isl_take isl_pw_aff *pa2);
7208 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
7209 __isl_take isl_pw_aff *pa1,
7210 __isl_take isl_pw_aff *pa2);
7211 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
7212 __isl_take isl_pw_aff *pa1,
7213 __isl_take isl_pw_aff *pa2);
7215 When multiplying two affine expressions, at least one of the two needs
7216 to be a constant. Similarly, when dividing an affine expression by another,
7217 the second expression needs to be a constant.
7218 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
7219 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
7222 #include <isl/polynomial.h>
7223 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
7224 __isl_take isl_qpolynomial *qp1,
7225 __isl_take isl_qpolynomial *qp2);
7226 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
7227 __isl_take isl_pw_qpolynomial *pwqp1,
7228 __isl_take isl_pw_qpolynomial *pwqp2);
7229 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
7230 __isl_take isl_union_pw_qpolynomial *upwqp1,
7231 __isl_take isl_union_pw_qpolynomial *upwqp2);
7235 =head3 Lexicographic Optimization
7237 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
7238 the following functions
7239 compute a set that contains the lexicographic minimum or maximum
7240 of the elements in C<set> (or C<bset>) for those values of the parameters
7241 that satisfy C<dom>.
7242 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7243 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
7245 In other words, the union of the parameter values
7246 for which the result is non-empty and of C<*empty>
7249 #include <isl/set.h>
7250 __isl_give isl_set *isl_basic_set_partial_lexmin(
7251 __isl_take isl_basic_set *bset,
7252 __isl_take isl_basic_set *dom,
7253 __isl_give isl_set **empty);
7254 __isl_give isl_set *isl_basic_set_partial_lexmax(
7255 __isl_take isl_basic_set *bset,
7256 __isl_take isl_basic_set *dom,
7257 __isl_give isl_set **empty);
7258 __isl_give isl_set *isl_set_partial_lexmin(
7259 __isl_take isl_set *set, __isl_take isl_set *dom,
7260 __isl_give isl_set **empty);
7261 __isl_give isl_set *isl_set_partial_lexmax(
7262 __isl_take isl_set *set, __isl_take isl_set *dom,
7263 __isl_give isl_set **empty);
7265 Given a (basic) set C<set> (or C<bset>), the following functions simply
7266 return a set containing the lexicographic minimum or maximum
7267 of the elements in C<set> (or C<bset>).
7268 In case of union sets, the optimum is computed per space.
7270 #include <isl/set.h>
7271 __isl_give isl_set *isl_basic_set_lexmin(
7272 __isl_take isl_basic_set *bset);
7273 __isl_give isl_set *isl_basic_set_lexmax(
7274 __isl_take isl_basic_set *bset);
7275 __isl_give isl_set *isl_set_lexmin(
7276 __isl_take isl_set *set);
7277 __isl_give isl_set *isl_set_lexmax(
7278 __isl_take isl_set *set);
7279 __isl_give isl_union_set *isl_union_set_lexmin(
7280 __isl_take isl_union_set *uset);
7281 __isl_give isl_union_set *isl_union_set_lexmax(
7282 __isl_take isl_union_set *uset);
7284 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
7285 the following functions
7286 compute a relation that maps each element of C<dom>
7287 to the single lexicographic minimum or maximum
7288 of the elements that are associated to that same
7289 element in C<map> (or C<bmap>).
7290 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7291 that contains the elements in C<dom> that do not map
7292 to any elements in C<map> (or C<bmap>).
7293 In other words, the union of the domain of the result and of C<*empty>
7296 #include <isl/map.h>
7297 __isl_give isl_map *isl_basic_map_partial_lexmax(
7298 __isl_take isl_basic_map *bmap,
7299 __isl_take isl_basic_set *dom,
7300 __isl_give isl_set **empty);
7301 __isl_give isl_map *isl_basic_map_partial_lexmin(
7302 __isl_take isl_basic_map *bmap,
7303 __isl_take isl_basic_set *dom,
7304 __isl_give isl_set **empty);
7305 __isl_give isl_map *isl_map_partial_lexmax(
7306 __isl_take isl_map *map, __isl_take isl_set *dom,
7307 __isl_give isl_set **empty);
7308 __isl_give isl_map *isl_map_partial_lexmin(
7309 __isl_take isl_map *map, __isl_take isl_set *dom,
7310 __isl_give isl_set **empty);
7312 Given a (basic) map C<map> (or C<bmap>), the following functions simply
7313 return a map mapping each element in the domain of
7314 C<map> (or C<bmap>) to the lexicographic minimum or maximum
7315 of all elements associated to that element.
7316 In case of union relations, the optimum is computed per space.
7318 #include <isl/map.h>
7319 __isl_give isl_map *isl_basic_map_lexmin(
7320 __isl_take isl_basic_map *bmap);
7321 __isl_give isl_map *isl_basic_map_lexmax(
7322 __isl_take isl_basic_map *bmap);
7323 __isl_give isl_map *isl_map_lexmin(
7324 __isl_take isl_map *map);
7325 __isl_give isl_map *isl_map_lexmax(
7326 __isl_take isl_map *map);
7327 __isl_give isl_union_map *isl_union_map_lexmin(
7328 __isl_take isl_union_map *umap);
7329 __isl_give isl_union_map *isl_union_map_lexmax(
7330 __isl_take isl_union_map *umap);
7332 The following functions return their result in the form of
7333 a piecewise multi-affine expression,
7334 but are otherwise equivalent to the corresponding functions
7335 returning a basic set or relation.
7337 #include <isl/set.h>
7338 __isl_give isl_pw_multi_aff *
7339 isl_basic_set_partial_lexmin_pw_multi_aff(
7340 __isl_take isl_basic_set *bset,
7341 __isl_take isl_basic_set *dom,
7342 __isl_give isl_set **empty);
7343 __isl_give isl_pw_multi_aff *
7344 isl_basic_set_partial_lexmax_pw_multi_aff(
7345 __isl_take isl_basic_set *bset,
7346 __isl_take isl_basic_set *dom,
7347 __isl_give isl_set **empty);
7348 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
7349 __isl_take isl_set *set);
7350 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
7351 __isl_take isl_set *set);
7353 #include <isl/map.h>
7354 __isl_give isl_pw_multi_aff *
7355 isl_basic_map_lexmin_pw_multi_aff(
7356 __isl_take isl_basic_map *bmap);
7357 __isl_give isl_pw_multi_aff *
7358 isl_basic_map_partial_lexmin_pw_multi_aff(
7359 __isl_take isl_basic_map *bmap,
7360 __isl_take isl_basic_set *dom,
7361 __isl_give isl_set **empty);
7362 __isl_give isl_pw_multi_aff *
7363 isl_basic_map_partial_lexmax_pw_multi_aff(
7364 __isl_take isl_basic_map *bmap,
7365 __isl_take isl_basic_set *dom,
7366 __isl_give isl_set **empty);
7367 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
7368 __isl_take isl_map *map);
7369 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
7370 __isl_take isl_map *map);
7372 The following functions return the lexicographic minimum or maximum
7373 on the shared domain of the inputs and the single defined function
7374 on those parts of the domain where only a single function is defined.
7376 #include <isl/aff.h>
7377 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
7378 __isl_take isl_pw_multi_aff *pma1,
7379 __isl_take isl_pw_multi_aff *pma2);
7380 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
7381 __isl_take isl_pw_multi_aff *pma1,
7382 __isl_take isl_pw_multi_aff *pma2);
7384 If the input to a lexicographic optimization problem has
7385 multiple constraints with the same coefficients for the optimized
7386 variables, then, by default, this symmetry is exploited by
7387 replacing those constraints by a single constraint with
7388 an abstract bound, which is in turn bounded by the corresponding terms
7389 in the original constraints.
7390 Without this optimization, the solver would typically consider
7391 all possible orderings of those original bounds, resulting in a needless
7392 decomposition of the domain.
7393 However, the optimization can also result in slowdowns since
7394 an extra parameter is introduced that may get used in additional
7396 The following option determines whether symmetry detection is applied
7397 during lexicographic optimization.
7399 #include <isl/options.h>
7400 isl_stat isl_options_set_pip_symmetry(isl_ctx *ctx,
7402 int isl_options_get_pip_symmetry(isl_ctx *ctx);
7406 See also \autoref{s:offline}.
7410 =head2 Ternary Operations
7412 #include <isl/aff.h>
7413 __isl_give isl_pw_aff *isl_pw_aff_cond(
7414 __isl_take isl_pw_aff *cond,
7415 __isl_take isl_pw_aff *pwaff_true,
7416 __isl_take isl_pw_aff *pwaff_false);
7418 The function C<isl_pw_aff_cond> performs a conditional operator
7419 and returns an expression that is equal to C<pwaff_true>
7420 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
7421 where C<cond> is zero.
7425 Lists are defined over several element types, including
7426 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_union_pw_aff>,
7427 C<isl_union_pw_multi_aff>, C<isl_constraint>,
7428 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
7429 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
7430 Here we take lists of C<isl_set>s as an example.
7431 Lists can be created, copied, modified and freed using the following functions.
7433 #include <isl/set.h>
7434 __isl_give isl_set_list *isl_set_list_from_set(
7435 __isl_take isl_set *el);
7436 __isl_give isl_set_list *isl_set_list_alloc(
7437 isl_ctx *ctx, int n);
7438 __isl_give isl_set_list *isl_set_list_copy(
7439 __isl_keep isl_set_list *list);
7440 __isl_give isl_set_list *isl_set_list_insert(
7441 __isl_take isl_set_list *list, unsigned pos,
7442 __isl_take isl_set *el);
7443 __isl_give isl_set_list *isl_set_list_add(
7444 __isl_take isl_set_list *list,
7445 __isl_take isl_set *el);
7446 __isl_give isl_set_list *isl_set_list_drop(
7447 __isl_take isl_set_list *list,
7448 unsigned first, unsigned n);
7449 __isl_give isl_set_list *isl_set_list_set_set(
7450 __isl_take isl_set_list *list, int index,
7451 __isl_take isl_set *set);
7452 __isl_give isl_set_list *isl_set_list_concat(
7453 __isl_take isl_set_list *list1,
7454 __isl_take isl_set_list *list2);
7455 __isl_give isl_set_list *isl_set_list_sort(
7456 __isl_take isl_set_list *list,
7457 int (*cmp)(__isl_keep isl_set *a,
7458 __isl_keep isl_set *b, void *user),
7460 __isl_null isl_set_list *isl_set_list_free(
7461 __isl_take isl_set_list *list);
7463 C<isl_set_list_alloc> creates an empty list with an initial capacity
7464 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
7465 add elements to a list, increasing its capacity as needed.
7466 C<isl_set_list_from_set> creates a list with a single element.
7468 Lists can be inspected using the following functions.
7470 #include <isl/set.h>
7471 int isl_set_list_n_set(__isl_keep isl_set_list *list);
7472 __isl_give isl_set *isl_set_list_get_set(
7473 __isl_keep isl_set_list *list, int index);
7474 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list,
7475 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7477 isl_stat isl_set_list_foreach_scc(
7478 __isl_keep isl_set_list *list,
7479 isl_bool (*follows)(__isl_keep isl_set *a,
7480 __isl_keep isl_set *b, void *user),
7482 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7485 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
7486 strongly connected components of the graph with as vertices the elements
7487 of C<list> and a directed edge from vertex C<b> to vertex C<a>
7488 iff C<follows(a, b)> returns C<isl_bool_true>. The callbacks C<follows> and
7489 C<fn> should return C<isl_bool_error> or C<isl_stat_error> on error.
7491 Lists can be printed using
7493 #include <isl/set.h>
7494 __isl_give isl_printer *isl_printer_print_set_list(
7495 __isl_take isl_printer *p,
7496 __isl_keep isl_set_list *list);
7498 =head2 Associative arrays
7500 Associative arrays map isl objects of a specific type to isl objects
7501 of some (other) specific type. They are defined for several pairs
7502 of types, including (C<isl_map>, C<isl_basic_set>),
7503 (C<isl_id>, C<isl_ast_expr>),
7504 (C<isl_id>, C<isl_id>) and
7505 (C<isl_id>, C<isl_pw_aff>).
7506 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
7509 Associative arrays can be created, copied and freed using
7510 the following functions.
7512 #include <isl/id_to_ast_expr.h>
7513 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
7514 isl_ctx *ctx, int min_size);
7515 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
7516 __isl_keep isl_id_to_ast_expr *id2expr);
7517 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
7518 __isl_take isl_id_to_ast_expr *id2expr);
7520 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
7521 to specify the expected size of the associative array.
7522 The associative array will be grown automatically as needed.
7524 Associative arrays can be inspected using the following functions.
7526 #include <isl/id_to_ast_expr.h>
7527 __isl_give isl_maybe_isl_ast_expr
7528 isl_id_to_ast_expr_try_get(
7529 __isl_keep isl_id_to_ast_expr *id2expr,
7530 __isl_keep isl_id *key);
7531 isl_bool isl_id_to_ast_expr_has(
7532 __isl_keep isl_id_to_ast_expr *id2expr,
7533 __isl_keep isl_id *key);
7534 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
7535 __isl_keep isl_id_to_ast_expr *id2expr,
7536 __isl_take isl_id *key);
7537 isl_stat isl_id_to_ast_expr_foreach(
7538 __isl_keep isl_id_to_ast_expr *id2expr,
7539 isl_stat (*fn)(__isl_take isl_id *key,
7540 __isl_take isl_ast_expr *val, void *user),
7543 The function C<isl_id_to_ast_expr_try_get> returns a structure
7544 containing two elements, C<valid> and C<value>.
7545 If there is a value associated to the key, then C<valid>
7546 is set to C<isl_bool_true> and C<value> contains a copy of
7547 the associated value. Otherwise C<value> is C<NULL> and
7548 C<valid> may be C<isl_bool_error> or C<isl_bool_false> depending
7549 on whether some error has occurred or there simply is no associated value.
7550 The function C<isl_id_to_ast_expr_has> returns the C<valid> field
7551 in the structure and
7552 the function C<isl_id_to_ast_expr_get> returns the C<value> field.
7554 Associative arrays can be modified using the following functions.
7556 #include <isl/id_to_ast_expr.h>
7557 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
7558 __isl_take isl_id_to_ast_expr *id2expr,
7559 __isl_take isl_id *key,
7560 __isl_take isl_ast_expr *val);
7561 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
7562 __isl_take isl_id_to_ast_expr *id2expr,
7563 __isl_take isl_id *key);
7565 Associative arrays can be printed using the following function.
7567 #include <isl/id_to_ast_expr.h>
7568 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
7569 __isl_take isl_printer *p,
7570 __isl_keep isl_id_to_ast_expr *id2expr);
7574 Vectors can be created, copied and freed using the following functions.
7576 #include <isl/vec.h>
7577 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
7579 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
7580 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
7582 Note that the elements of a newly created vector may have arbitrary values.
7583 The elements can be changed and inspected using the following functions.
7585 int isl_vec_size(__isl_keep isl_vec *vec);
7586 __isl_give isl_val *isl_vec_get_element_val(
7587 __isl_keep isl_vec *vec, int pos);
7588 __isl_give isl_vec *isl_vec_set_element_si(
7589 __isl_take isl_vec *vec, int pos, int v);
7590 __isl_give isl_vec *isl_vec_set_element_val(
7591 __isl_take isl_vec *vec, int pos,
7592 __isl_take isl_val *v);
7593 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
7595 __isl_give isl_vec *isl_vec_set_val(
7596 __isl_take isl_vec *vec, __isl_take isl_val *v);
7597 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
7598 __isl_keep isl_vec *vec2, int pos);
7600 C<isl_vec_get_element> will return a negative value if anything went wrong.
7601 In that case, the value of C<*v> is undefined.
7603 The following function can be used to concatenate two vectors.
7605 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
7606 __isl_take isl_vec *vec2);
7610 Matrices can be created, copied and freed using the following functions.
7612 #include <isl/mat.h>
7613 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
7614 unsigned n_row, unsigned n_col);
7615 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
7616 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
7618 Note that the elements of a newly created matrix may have arbitrary values.
7619 The elements can be changed and inspected using the following functions.
7621 int isl_mat_rows(__isl_keep isl_mat *mat);
7622 int isl_mat_cols(__isl_keep isl_mat *mat);
7623 __isl_give isl_val *isl_mat_get_element_val(
7624 __isl_keep isl_mat *mat, int row, int col);
7625 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
7626 int row, int col, int v);
7627 __isl_give isl_mat *isl_mat_set_element_val(
7628 __isl_take isl_mat *mat, int row, int col,
7629 __isl_take isl_val *v);
7631 C<isl_mat_get_element> will return a negative value if anything went wrong.
7632 In that case, the value of C<*v> is undefined.
7634 The following function can be used to compute the (right) inverse
7635 of a matrix, i.e., a matrix such that the product of the original
7636 and the inverse (in that order) is a multiple of the identity matrix.
7637 The input matrix is assumed to be of full row-rank.
7639 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
7641 The following function can be used to compute the (right) kernel
7642 (or null space) of a matrix, i.e., a matrix such that the product of
7643 the original and the kernel (in that order) is the zero matrix.
7645 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
7647 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
7649 The following functions determine
7650 an upper or lower bound on a quasipolynomial over its domain.
7652 __isl_give isl_pw_qpolynomial_fold *
7653 isl_pw_qpolynomial_bound(
7654 __isl_take isl_pw_qpolynomial *pwqp,
7655 enum isl_fold type, int *tight);
7657 __isl_give isl_union_pw_qpolynomial_fold *
7658 isl_union_pw_qpolynomial_bound(
7659 __isl_take isl_union_pw_qpolynomial *upwqp,
7660 enum isl_fold type, int *tight);
7662 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
7663 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
7664 is the returned bound is known be tight, i.e., for each value
7665 of the parameters there is at least
7666 one element in the domain that reaches the bound.
7667 If the domain of C<pwqp> is not wrapping, then the bound is computed
7668 over all elements in that domain and the result has a purely parametric
7669 domain. If the domain of C<pwqp> is wrapping, then the bound is
7670 computed over the range of the wrapped relation. The domain of the
7671 wrapped relation becomes the domain of the result.
7673 =head2 Parametric Vertex Enumeration
7675 The parametric vertex enumeration described in this section
7676 is mainly intended to be used internally and by the C<barvinok>
7679 #include <isl/vertices.h>
7680 __isl_give isl_vertices *isl_basic_set_compute_vertices(
7681 __isl_keep isl_basic_set *bset);
7683 The function C<isl_basic_set_compute_vertices> performs the
7684 actual computation of the parametric vertices and the chamber
7685 decomposition and stores the result in an C<isl_vertices> object.
7686 This information can be queried by either iterating over all
7687 the vertices or iterating over all the chambers or cells
7688 and then iterating over all vertices that are active on the chamber.
7690 isl_stat isl_vertices_foreach_vertex(
7691 __isl_keep isl_vertices *vertices,
7692 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7693 void *user), void *user);
7695 isl_stat isl_vertices_foreach_cell(
7696 __isl_keep isl_vertices *vertices,
7697 isl_stat (*fn)(__isl_take isl_cell *cell,
7698 void *user), void *user);
7699 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
7700 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7701 void *user), void *user);
7703 Other operations that can be performed on an C<isl_vertices> object are
7706 int isl_vertices_get_n_vertices(
7707 __isl_keep isl_vertices *vertices);
7708 __isl_null isl_vertices *isl_vertices_free(
7709 __isl_take isl_vertices *vertices);
7711 Vertices can be inspected and destroyed using the following functions.
7713 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
7714 __isl_give isl_basic_set *isl_vertex_get_domain(
7715 __isl_keep isl_vertex *vertex);
7716 __isl_give isl_multi_aff *isl_vertex_get_expr(
7717 __isl_keep isl_vertex *vertex);
7718 void isl_vertex_free(__isl_take isl_vertex *vertex);
7720 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
7721 describing the vertex in terms of the parameters,
7722 while C<isl_vertex_get_domain> returns the activity domain
7725 Chambers can be inspected and destroyed using the following functions.
7727 __isl_give isl_basic_set *isl_cell_get_domain(
7728 __isl_keep isl_cell *cell);
7729 void isl_cell_free(__isl_take isl_cell *cell);
7731 =head1 Polyhedral Compilation Library
7733 This section collects functionality in C<isl> that has been specifically
7734 designed for use during polyhedral compilation.
7736 =head2 Schedule Trees
7738 A schedule tree is a structured representation of a schedule,
7739 assigning a relative order to a set of domain elements.
7740 The relative order expressed by the schedule tree is
7741 defined recursively. In particular, the order between
7742 two domain elements is determined by the node that is closest
7743 to the root that refers to both elements and that orders them apart.
7744 Each node in the tree is of one of several types.
7745 The root node is always of type C<isl_schedule_node_domain>
7746 (or C<isl_schedule_node_extension>)
7747 and it describes the (extra) domain elements to which the schedule applies.
7748 The other types of nodes are as follows.
7752 =item C<isl_schedule_node_band>
7754 A band of schedule dimensions. Each schedule dimension is represented
7755 by a union piecewise quasi-affine expression. If this expression
7756 assigns a different value to two domain elements, while all previous
7757 schedule dimensions in the same band assign them the same value,
7758 then the two domain elements are ordered according to these two
7760 Each expression is required to be total in the domain elements
7761 that reach the band node.
7763 =item C<isl_schedule_node_expansion>
7765 An expansion node maps each of the domain elements that reach the node
7766 to one or more domain elements. The image of this mapping forms
7767 the set of domain elements that reach the child of the expansion node.
7768 The function that maps each of the expanded domain elements
7769 to the original domain element from which it was expanded
7770 is called the contraction.
7772 =item C<isl_schedule_node_filter>
7774 A filter node does not impose any ordering, but rather intersects
7775 the set of domain elements that the current subtree refers to
7776 with a given union set. The subtree of the filter node only
7777 refers to domain elements in the intersection.
7778 A filter node is typically only used as a child of a sequence or
7781 =item C<isl_schedule_node_leaf>
7783 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
7785 =item C<isl_schedule_node_mark>
7787 A mark node can be used to attach any kind of information to a subtree
7788 of the schedule tree.
7790 =item C<isl_schedule_node_sequence>
7792 A sequence node has one or more children, each of which is a filter node.
7793 The filters on these filter nodes form a partition of
7794 the domain elements that the current subtree refers to.
7795 If two domain elements appear in distinct filters then the sequence
7796 node orders them according to the child positions of the corresponding
7799 =item C<isl_schedule_node_set>
7801 A set node is similar to a sequence node, except that
7802 it expresses that domain elements appearing in distinct filters
7803 may have any order. The order of the children of a set node
7804 is therefore also immaterial.
7808 The following node types are only supported by the AST generator.
7812 =item C<isl_schedule_node_context>
7814 The context describes constraints on the parameters and
7815 the schedule dimensions of outer
7816 bands that the AST generator may assume to hold. It is also the only
7817 kind of node that may introduce additional parameters.
7818 The space of the context is that of the flat product of the outer
7819 band nodes. In particular, if there are no outer band nodes, then
7820 this space is the unnamed zero-dimensional space.
7821 Since a context node references the outer band nodes, any tree
7822 containing a context node is considered to be anchored.
7824 =item C<isl_schedule_node_extension>
7826 An extension node instructs the AST generator to add additional
7827 domain elements that need to be scheduled.
7828 The additional domain elements are described by the range of
7829 the extension map in terms of the outer schedule dimensions,
7830 i.e., the flat product of the outer band nodes.
7831 Note that domain elements are added whenever the AST generator
7832 reaches the extension node, meaning that there are still some
7833 active domain elements for which an AST needs to be generated.
7834 The conditions under which some domain elements are still active
7835 may however not be completely described by the outer AST nodes
7836 generated at that point.
7838 An extension node may also appear as the root of a schedule tree,
7839 when it is intended to be inserted into another tree
7840 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
7841 In this case, the domain of the extension node should
7842 correspond to the flat product of the outer band nodes
7843 in this other schedule tree at the point where the extension tree
7846 =item C<isl_schedule_node_guard>
7848 The guard describes constraints on the parameters and
7849 the schedule dimensions of outer
7850 bands that need to be enforced by the outer nodes
7851 in the generated AST.
7852 The space of the guard is that of the flat product of the outer
7853 band nodes. In particular, if there are no outer band nodes, then
7854 this space is the unnamed zero-dimensional space.
7855 Since a guard node references the outer band nodes, any tree
7856 containing a guard node is considered to be anchored.
7860 Except for the C<isl_schedule_node_context> nodes,
7861 none of the nodes may introduce any parameters that were not
7862 already present in the root domain node.
7864 A schedule tree is encapsulated in an C<isl_schedule> object.
7865 The simplest such objects, those with a tree consisting of single domain node,
7866 can be created using the following functions with either an empty
7867 domain or a given domain.
7869 #include <isl/schedule.h>
7870 __isl_give isl_schedule *isl_schedule_empty(
7871 __isl_take isl_space *space);
7872 __isl_give isl_schedule *isl_schedule_from_domain(
7873 __isl_take isl_union_set *domain);
7875 The function C<isl_schedule_constraints_compute_schedule> described
7876 in L</"Scheduling"> can also be used to construct schedules.
7878 C<isl_schedule> objects may be copied and freed using the following functions.
7880 #include <isl/schedule.h>
7881 __isl_give isl_schedule *isl_schedule_copy(
7882 __isl_keep isl_schedule *sched);
7883 __isl_null isl_schedule *isl_schedule_free(
7884 __isl_take isl_schedule *sched);
7886 The following functions checks whether two C<isl_schedule> objects
7887 are obviously the same.
7889 #include <isl/schedule.h>
7890 isl_bool isl_schedule_plain_is_equal(
7891 __isl_keep isl_schedule *schedule1,
7892 __isl_keep isl_schedule *schedule2);
7894 The domain of the schedule, i.e., the domain described by the root node,
7895 can be obtained using the following function.
7897 #include <isl/schedule.h>
7898 __isl_give isl_union_set *isl_schedule_get_domain(
7899 __isl_keep isl_schedule *schedule);
7901 An extra top-level band node (right underneath the domain node) can
7902 be introduced into the schedule using the following function.
7903 The schedule tree is assumed not to have any anchored nodes.
7905 #include <isl/schedule.h>
7906 __isl_give isl_schedule *
7907 isl_schedule_insert_partial_schedule(
7908 __isl_take isl_schedule *schedule,
7909 __isl_take isl_multi_union_pw_aff *partial);
7911 A top-level context node (right underneath the domain node) can
7912 be introduced into the schedule using the following function.
7914 #include <isl/schedule.h>
7915 __isl_give isl_schedule *isl_schedule_insert_context(
7916 __isl_take isl_schedule *schedule,
7917 __isl_take isl_set *context)
7919 A top-level guard 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_guard(
7924 __isl_take isl_schedule *schedule,
7925 __isl_take isl_set *guard)
7927 A schedule that combines two schedules either in the given
7928 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
7929 or an C<isl_schedule_node_set> node,
7930 can be created using the following functions.
7932 #include <isl/schedule.h>
7933 __isl_give isl_schedule *isl_schedule_sequence(
7934 __isl_take isl_schedule *schedule1,
7935 __isl_take isl_schedule *schedule2);
7936 __isl_give isl_schedule *isl_schedule_set(
7937 __isl_take isl_schedule *schedule1,
7938 __isl_take isl_schedule *schedule2);
7940 The domains of the two input schedules need to be disjoint.
7942 The following function can be used to restrict the domain
7943 of a schedule with a domain node as root to be a subset of the given union set.
7944 This operation may remove nodes in the tree that have become
7947 #include <isl/schedule.h>
7948 __isl_give isl_schedule *isl_schedule_intersect_domain(
7949 __isl_take isl_schedule *schedule,
7950 __isl_take isl_union_set *domain);
7952 The following function can be used to simplify the domain
7953 of a schedule with a domain node as root with respect to the given
7956 #include <isl/schedule.h>
7957 __isl_give isl_schedule *isl_schedule_gist_domain_params(
7958 __isl_take isl_schedule *schedule,
7959 __isl_take isl_set *context);
7961 The following function resets the user pointers on all parameter
7962 and tuple identifiers referenced by the nodes of the given schedule.
7964 #include <isl/schedule.h>
7965 __isl_give isl_schedule *isl_schedule_reset_user(
7966 __isl_take isl_schedule *schedule);
7968 The following function aligns the parameters of all nodes
7969 in the given schedule to the given space.
7971 #include <isl/schedule.h>
7972 __isl_give isl_schedule *isl_schedule_align_params(
7973 __isl_take isl_schedule *schedule,
7974 __isl_take isl_space *space);
7976 The following function allows the user to plug in a given function
7977 in the iteration domains. The input schedule is not allowed to contain
7978 any expansion nodes.
7980 #include <isl/schedule.h>
7981 __isl_give isl_schedule *
7982 isl_schedule_pullback_union_pw_multi_aff(
7983 __isl_take isl_schedule *schedule,
7984 __isl_take isl_union_pw_multi_aff *upma);
7986 The following function can be used to plug in the schedule C<expansion>
7987 in the leaves of C<schedule>, where C<contraction> describes how
7988 the domain elements of C<expansion> map to the domain elements
7989 at the original leaves of C<schedule>.
7990 The resulting schedule will contain expansion nodes, unless
7991 C<contraction> is an identity function.
7993 #include <isl/schedule.h>
7994 __isl_give isl_schedule *isl_schedule_expand(
7995 __isl_take isl_schedule *schedule,
7996 __isl_take isl_union_pw_multi_aff *contraction,
7997 __isl_take isl_schedule *expansion);
7999 An C<isl_union_map> representation of the schedule can be obtained
8000 from an C<isl_schedule> using the following function.
8002 #include <isl/schedule.h>
8003 __isl_give isl_union_map *isl_schedule_get_map(
8004 __isl_keep isl_schedule *sched);
8006 The resulting relation encodes the same relative ordering as
8007 the schedule by mapping the domain elements to a common schedule space.
8008 If the schedule_separate_components option is set, then the order
8009 of the children of a set node is explicitly encoded in the result.
8010 If the tree contains any expansion nodes, then the relation
8011 is formulated in terms of the expanded domain elements.
8013 Schedules can be read from input using the following functions.
8015 #include <isl/schedule.h>
8016 __isl_give isl_schedule *isl_schedule_read_from_file(
8017 isl_ctx *ctx, FILE *input);
8018 __isl_give isl_schedule *isl_schedule_read_from_str(
8019 isl_ctx *ctx, const char *str);
8021 A representation of the schedule can be printed using
8023 #include <isl/schedule.h>
8024 __isl_give isl_printer *isl_printer_print_schedule(
8025 __isl_take isl_printer *p,
8026 __isl_keep isl_schedule *schedule);
8027 __isl_give char *isl_schedule_to_str(
8028 __isl_keep isl_schedule *schedule);
8030 C<isl_schedule_to_str> prints the schedule in flow format.
8032 The schedule tree can be traversed through the use of
8033 C<isl_schedule_node> objects that point to a particular
8034 position in the schedule tree. Whenever a C<isl_schedule_node>
8035 is use to modify a node in the schedule tree, the original schedule
8036 tree is left untouched and the modifications are performed to a copy
8037 of the tree. The returned C<isl_schedule_node> then points to
8038 this modified copy of the tree.
8040 The root of the schedule tree can be obtained using the following function.
8042 #include <isl/schedule.h>
8043 __isl_give isl_schedule_node *isl_schedule_get_root(
8044 __isl_keep isl_schedule *schedule);
8046 A pointer to a newly created schedule tree with a single domain
8047 node can be created using the following functions.
8049 #include <isl/schedule_node.h>
8050 __isl_give isl_schedule_node *
8051 isl_schedule_node_from_domain(
8052 __isl_take isl_union_set *domain);
8053 __isl_give isl_schedule_node *
8054 isl_schedule_node_from_extension(
8055 __isl_take isl_union_map *extension);
8057 C<isl_schedule_node_from_extension> creates a tree with an extension
8060 Schedule nodes can be copied and freed using the following functions.
8062 #include <isl/schedule_node.h>
8063 __isl_give isl_schedule_node *isl_schedule_node_copy(
8064 __isl_keep isl_schedule_node *node);
8065 __isl_null isl_schedule_node *isl_schedule_node_free(
8066 __isl_take isl_schedule_node *node);
8068 The following functions can be used to check if two schedule
8069 nodes point to the same position in the same schedule.
8071 #include <isl/schedule_node.h>
8072 isl_bool isl_schedule_node_is_equal(
8073 __isl_keep isl_schedule_node *node1,
8074 __isl_keep isl_schedule_node *node2);
8076 The following properties can be obtained from a schedule node.
8078 #include <isl/schedule_node.h>
8079 enum isl_schedule_node_type isl_schedule_node_get_type(
8080 __isl_keep isl_schedule_node *node);
8081 enum isl_schedule_node_type
8082 isl_schedule_node_get_parent_type(
8083 __isl_keep isl_schedule_node *node);
8084 __isl_give isl_schedule *isl_schedule_node_get_schedule(
8085 __isl_keep isl_schedule_node *node);
8087 The function C<isl_schedule_node_get_type> returns the type of
8088 the node, while C<isl_schedule_node_get_parent_type> returns
8089 type of the parent of the node, which is required to exist.
8090 The function C<isl_schedule_node_get_schedule> returns a copy
8091 to the schedule to which the node belongs.
8093 The following functions can be used to move the schedule node
8094 to a different position in the tree or to check if such a position
8097 #include <isl/schedule_node.h>
8098 isl_bool isl_schedule_node_has_parent(
8099 __isl_keep isl_schedule_node *node);
8100 __isl_give isl_schedule_node *isl_schedule_node_parent(
8101 __isl_take isl_schedule_node *node);
8102 __isl_give isl_schedule_node *isl_schedule_node_root(
8103 __isl_take isl_schedule_node *node);
8104 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
8105 __isl_take isl_schedule_node *node,
8107 int isl_schedule_node_n_children(
8108 __isl_keep isl_schedule_node *node);
8109 __isl_give isl_schedule_node *isl_schedule_node_child(
8110 __isl_take isl_schedule_node *node, int pos);
8111 isl_bool isl_schedule_node_has_children(
8112 __isl_keep isl_schedule_node *node);
8113 __isl_give isl_schedule_node *isl_schedule_node_first_child(
8114 __isl_take isl_schedule_node *node);
8115 isl_bool isl_schedule_node_has_previous_sibling(
8116 __isl_keep isl_schedule_node *node);
8117 __isl_give isl_schedule_node *
8118 isl_schedule_node_previous_sibling(
8119 __isl_take isl_schedule_node *node);
8120 isl_bool isl_schedule_node_has_next_sibling(
8121 __isl_keep isl_schedule_node *node);
8122 __isl_give isl_schedule_node *
8123 isl_schedule_node_next_sibling(
8124 __isl_take isl_schedule_node *node);
8126 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
8127 is the node itself, the ancestor of generation 1 is its parent and so on.
8129 It is also possible to query the number of ancestors of a node,
8130 the position of the current node
8131 within the children of its parent, the position of the subtree
8132 containing a node within the children of an ancestor
8133 or to obtain a copy of a given
8134 child without destroying the current node.
8135 Given two nodes that point to the same schedule, their closest
8136 shared ancestor can be obtained using
8137 C<isl_schedule_node_get_shared_ancestor>.
8139 #include <isl/schedule_node.h>
8140 int isl_schedule_node_get_tree_depth(
8141 __isl_keep isl_schedule_node *node);
8142 int isl_schedule_node_get_child_position(
8143 __isl_keep isl_schedule_node *node);
8144 int isl_schedule_node_get_ancestor_child_position(
8145 __isl_keep isl_schedule_node *node,
8146 __isl_keep isl_schedule_node *ancestor);
8147 __isl_give isl_schedule_node *isl_schedule_node_get_child(
8148 __isl_keep isl_schedule_node *node, int pos);
8149 __isl_give isl_schedule_node *
8150 isl_schedule_node_get_shared_ancestor(
8151 __isl_keep isl_schedule_node *node1,
8152 __isl_keep isl_schedule_node *node2);
8154 All nodes in a schedule tree or
8155 all descendants of a specific node (including the node) can be visited
8156 in depth-first pre-order using the following functions.
8158 #include <isl/schedule.h>
8159 isl_stat isl_schedule_foreach_schedule_node_top_down(
8160 __isl_keep isl_schedule *sched,
8161 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8162 void *user), void *user);
8164 #include <isl/schedule_node.h>
8165 isl_stat isl_schedule_node_foreach_descendant_top_down(
8166 __isl_keep isl_schedule_node *node,
8167 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8168 void *user), void *user);
8170 The callback function is slightly different from the usual
8171 callbacks in that it not only indicates success (non-negative result)
8172 or failure (negative result), but also indicates whether the children
8173 of the given node should be visited. In particular, if the callback
8174 returns a positive value, then the children are visited, but if
8175 the callback returns zero, then the children are not visited.
8177 The ancestors of a node in a schedule tree can be visited from
8178 the root down to and including the parent of the node using
8179 the following function.
8181 #include <isl/schedule_node.h>
8182 isl_stat isl_schedule_node_foreach_ancestor_top_down(
8183 __isl_keep isl_schedule_node *node,
8184 isl_stat (*fn)(__isl_keep isl_schedule_node *node,
8185 void *user), void *user);
8187 The following functions allows for a depth-first post-order
8188 traversal of the nodes in a schedule tree or
8189 of the descendants of a specific node (including the node
8190 itself), where the user callback is allowed to modify the
8193 #include <isl/schedule.h>
8194 __isl_give isl_schedule *
8195 isl_schedule_map_schedule_node_bottom_up(
8196 __isl_take isl_schedule *schedule,
8197 __isl_give isl_schedule_node *(*fn)(
8198 __isl_take isl_schedule_node *node,
8199 void *user), void *user);
8201 #include <isl/schedule_node.h>
8202 __isl_give isl_schedule_node *
8203 isl_schedule_node_map_descendant_bottom_up(
8204 __isl_take isl_schedule_node *node,
8205 __isl_give isl_schedule_node *(*fn)(
8206 __isl_take isl_schedule_node *node,
8207 void *user), void *user);
8209 The traversal continues from the node returned by the callback function.
8210 It is the responsibility of the user to ensure that this does not
8211 lead to an infinite loop. It is safest to always return a pointer
8212 to the same position (same ancestors and child positions) as the input node.
8214 The following function removes a node (along with its descendants)
8215 from a schedule tree and returns a pointer to the leaf at the
8216 same position in the updated tree.
8217 It is not allowed to remove the root of a schedule tree or
8218 a child of a set or sequence node.
8220 #include <isl/schedule_node.h>
8221 __isl_give isl_schedule_node *isl_schedule_node_cut(
8222 __isl_take isl_schedule_node *node);
8224 The following function removes a single node
8225 from a schedule tree and returns a pointer to the child
8226 of the node, now located at the position of the original node
8227 or to a leaf node at that position if there was no child.
8228 It is not allowed to remove the root of a schedule tree,
8229 a set or sequence node, a child of a set or sequence node or
8230 a band node with an anchored subtree.
8232 #include <isl/schedule_node.h>
8233 __isl_give isl_schedule_node *isl_schedule_node_delete(
8234 __isl_take isl_schedule_node *node);
8236 Most nodes in a schedule tree only contain local information.
8237 In some cases, however, a node may also refer to the schedule dimensions
8238 of its outer band nodes.
8239 This means that the position of the node within the tree should
8240 not be changed, or at least that no changes are performed to the
8241 outer band nodes. The following function can be used to test
8242 whether the subtree rooted at a given node contains any such nodes.
8244 #include <isl/schedule_node.h>
8245 isl_bool isl_schedule_node_is_subtree_anchored(
8246 __isl_keep isl_schedule_node *node);
8248 The following function resets the user pointers on all parameter
8249 and tuple identifiers referenced by the given schedule node.
8251 #include <isl/schedule_node.h>
8252 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
8253 __isl_take isl_schedule_node *node);
8255 The following function aligns the parameters of the given schedule
8256 node to the given space.
8258 #include <isl/schedule_node.h>
8259 __isl_give isl_schedule_node *
8260 isl_schedule_node_align_params(
8261 __isl_take isl_schedule_node *node,
8262 __isl_take isl_space *space);
8264 Several node types have their own functions for querying
8265 (and in some cases setting) some node type specific properties.
8267 #include <isl/schedule_node.h>
8268 __isl_give isl_space *isl_schedule_node_band_get_space(
8269 __isl_keep isl_schedule_node *node);
8270 __isl_give isl_multi_union_pw_aff *
8271 isl_schedule_node_band_get_partial_schedule(
8272 __isl_keep isl_schedule_node *node);
8273 __isl_give isl_union_map *
8274 isl_schedule_node_band_get_partial_schedule_union_map(
8275 __isl_keep isl_schedule_node *node);
8276 unsigned isl_schedule_node_band_n_member(
8277 __isl_keep isl_schedule_node *node);
8278 isl_bool isl_schedule_node_band_member_get_coincident(
8279 __isl_keep isl_schedule_node *node, int pos);
8280 __isl_give isl_schedule_node *
8281 isl_schedule_node_band_member_set_coincident(
8282 __isl_take isl_schedule_node *node, int pos,
8284 isl_bool isl_schedule_node_band_get_permutable(
8285 __isl_keep isl_schedule_node *node);
8286 __isl_give isl_schedule_node *
8287 isl_schedule_node_band_set_permutable(
8288 __isl_take isl_schedule_node *node, int permutable);
8289 enum isl_ast_loop_type
8290 isl_schedule_node_band_member_get_ast_loop_type(
8291 __isl_keep isl_schedule_node *node, int pos);
8292 __isl_give isl_schedule_node *
8293 isl_schedule_node_band_member_set_ast_loop_type(
8294 __isl_take isl_schedule_node *node, int pos,
8295 enum isl_ast_loop_type type);
8296 __isl_give isl_union_set *
8297 enum isl_ast_loop_type
8298 isl_schedule_node_band_member_get_isolate_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_isolate_ast_loop_type(
8302 __isl_take isl_schedule_node *node, int pos,
8303 enum isl_ast_loop_type type);
8304 isl_schedule_node_band_get_ast_build_options(
8305 __isl_keep isl_schedule_node *node);
8306 __isl_give isl_schedule_node *
8307 isl_schedule_node_band_set_ast_build_options(
8308 __isl_take isl_schedule_node *node,
8309 __isl_take isl_union_set *options);
8310 __isl_give isl_set *
8311 isl_schedule_node_band_get_ast_isolate_option(
8312 __isl_keep isl_schedule_node *node);
8314 The function C<isl_schedule_node_band_get_space> returns the space
8315 of the partial schedule of the band.
8316 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
8317 returns a representation of the partial schedule of the band node
8318 in the form of an C<isl_union_map>.
8319 The coincident and permutable properties are set by
8320 C<isl_schedule_constraints_compute_schedule> on the schedule tree
8322 A scheduling dimension is considered to be ``coincident''
8323 if it satisfies the coincidence constraints within its band.
8324 That is, if the dependence distances of the coincidence
8325 constraints are all zero in that direction (for fixed
8326 iterations of outer bands).
8327 A band is marked permutable if it was produced using the Pluto-like scheduler.
8328 Note that the scheduler may have to resort to a Feautrier style scheduling
8329 step even if the default scheduler is used.
8330 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
8331 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
8332 For the meaning of these loop AST generation types and the difference
8333 between the regular loop AST generation type and the isolate
8334 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
8335 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
8336 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
8337 may return C<isl_ast_loop_error> if an error occurs.
8338 The AST build options govern how an AST is generated for
8339 the individual schedule dimensions during AST generation.
8340 See L</"AST Generation Options (Schedule Tree)">.
8341 The isolate option for the given node can be extracted from these
8342 AST build options using the function
8343 C<isl_schedule_node_band_get_ast_isolate_option>.
8345 #include <isl/schedule_node.h>
8346 __isl_give isl_set *
8347 isl_schedule_node_context_get_context(
8348 __isl_keep isl_schedule_node *node);
8350 #include <isl/schedule_node.h>
8351 __isl_give isl_union_set *
8352 isl_schedule_node_domain_get_domain(
8353 __isl_keep isl_schedule_node *node);
8355 #include <isl/schedule_node.h>
8356 __isl_give isl_union_map *
8357 isl_schedule_node_expansion_get_expansion(
8358 __isl_keep isl_schedule_node *node);
8359 __isl_give isl_union_pw_multi_aff *
8360 isl_schedule_node_expansion_get_contraction(
8361 __isl_keep isl_schedule_node *node);
8363 #include <isl/schedule_node.h>
8364 __isl_give isl_union_map *
8365 isl_schedule_node_extension_get_extension(
8366 __isl_keep isl_schedule_node *node);
8368 #include <isl/schedule_node.h>
8369 __isl_give isl_union_set *
8370 isl_schedule_node_filter_get_filter(
8371 __isl_keep isl_schedule_node *node);
8373 #include <isl/schedule_node.h>
8374 __isl_give isl_set *isl_schedule_node_guard_get_guard(
8375 __isl_keep isl_schedule_node *node);
8377 #include <isl/schedule_node.h>
8378 __isl_give isl_id *isl_schedule_node_mark_get_id(
8379 __isl_keep isl_schedule_node *node);
8381 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
8382 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
8383 partial schedules related to the node.
8385 #include <isl/schedule_node.h>
8386 __isl_give isl_multi_union_pw_aff *
8387 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
8388 __isl_keep isl_schedule_node *node);
8389 __isl_give isl_union_pw_multi_aff *
8390 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
8391 __isl_keep isl_schedule_node *node);
8392 __isl_give isl_union_map *
8393 isl_schedule_node_get_prefix_schedule_union_map(
8394 __isl_keep isl_schedule_node *node);
8395 __isl_give isl_union_map *
8396 isl_schedule_node_get_prefix_schedule_relation(
8397 __isl_keep isl_schedule_node *node);
8398 __isl_give isl_union_map *
8399 isl_schedule_node_get_subtree_schedule_union_map(
8400 __isl_keep isl_schedule_node *node);
8402 In particular, the functions
8403 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
8404 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
8405 and C<isl_schedule_node_get_prefix_schedule_union_map>
8406 return a relative ordering on the domain elements that reach the given
8407 node determined by its ancestors.
8408 The function C<isl_schedule_node_get_prefix_schedule_relation>
8409 additionally includes the domain constraints in the result.
8410 The function C<isl_schedule_node_get_subtree_schedule_union_map>
8411 returns a representation of the partial schedule defined by the
8412 subtree rooted at the given node.
8413 If the tree contains any expansion nodes, then the subtree schedule
8414 is formulated in terms of the expanded domain elements.
8415 The tree passed to functions returning a prefix schedule
8416 may only contain extension nodes if these would not affect
8417 the result of these functions. That is, if one of the ancestors
8418 is an extension node, then all of the domain elements that were
8419 added by the extension node need to have been filtered out
8420 by filter nodes between the extension node and the input node.
8421 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
8422 may not contain in extension nodes in the selected subtree.
8424 The expansion/contraction defined by an entire subtree, combining
8425 the expansions/contractions
8426 on the expansion nodes in the subtree, can be obtained using
8427 the following functions.
8429 #include <isl/schedule_node.h>
8430 __isl_give isl_union_map *
8431 isl_schedule_node_get_subtree_expansion(
8432 __isl_keep isl_schedule_node *node);
8433 __isl_give isl_union_pw_multi_aff *
8434 isl_schedule_node_get_subtree_contraction(
8435 __isl_keep isl_schedule_node *node);
8437 The total number of outer band members of given node, i.e.,
8438 the shared output dimension of the maps in the result
8439 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
8440 using the following function.
8442 #include <isl/schedule_node.h>
8443 int isl_schedule_node_get_schedule_depth(
8444 __isl_keep isl_schedule_node *node);
8446 The following functions return the elements that reach the given node
8447 or the union of universes in the spaces that contain these elements.
8449 #include <isl/schedule_node.h>
8450 __isl_give isl_union_set *
8451 isl_schedule_node_get_domain(
8452 __isl_keep isl_schedule_node *node);
8453 __isl_give isl_union_set *
8454 isl_schedule_node_get_universe_domain(
8455 __isl_keep isl_schedule_node *node);
8457 The input tree of C<isl_schedule_node_get_domain>
8458 may only contain extension nodes if these would not affect
8459 the result of this function. That is, if one of the ancestors
8460 is an extension node, then all of the domain elements that were
8461 added by the extension node need to have been filtered out
8462 by filter nodes between the extension node and the input node.
8464 The following functions can be used to introduce additional nodes
8465 in the schedule tree. The new node is introduced at the point
8466 in the tree where the C<isl_schedule_node> points to and
8467 the results points to the new node.
8469 #include <isl/schedule_node.h>
8470 __isl_give isl_schedule_node *
8471 isl_schedule_node_insert_partial_schedule(
8472 __isl_take isl_schedule_node *node,
8473 __isl_take isl_multi_union_pw_aff *schedule);
8475 This function inserts a new band node with (the greatest integer
8476 part of) the given partial schedule.
8477 The subtree rooted at the given node is assumed not to have
8480 #include <isl/schedule_node.h>
8481 __isl_give isl_schedule_node *
8482 isl_schedule_node_insert_context(
8483 __isl_take isl_schedule_node *node,
8484 __isl_take isl_set *context);
8486 This function inserts a new context node with the given context constraints.
8488 #include <isl/schedule_node.h>
8489 __isl_give isl_schedule_node *
8490 isl_schedule_node_insert_filter(
8491 __isl_take isl_schedule_node *node,
8492 __isl_take isl_union_set *filter);
8494 This function inserts a new filter node with the given filter.
8495 If the original node already pointed to a filter node, then the
8496 two filter nodes are merged into one.
8498 #include <isl/schedule_node.h>
8499 __isl_give isl_schedule_node *
8500 isl_schedule_node_insert_guard(
8501 __isl_take isl_schedule_node *node,
8502 __isl_take isl_set *guard);
8504 This function inserts a new guard node with the given guard constraints.
8506 #include <isl/schedule_node.h>
8507 __isl_give isl_schedule_node *
8508 isl_schedule_node_insert_mark(
8509 __isl_take isl_schedule_node *node,
8510 __isl_take isl_id *mark);
8512 This function inserts a new mark node with the give mark identifier.
8514 #include <isl/schedule_node.h>
8515 __isl_give isl_schedule_node *
8516 isl_schedule_node_insert_sequence(
8517 __isl_take isl_schedule_node *node,
8518 __isl_take isl_union_set_list *filters);
8519 __isl_give isl_schedule_node *
8520 isl_schedule_node_insert_set(
8521 __isl_take isl_schedule_node *node,
8522 __isl_take isl_union_set_list *filters);
8524 These functions insert a new sequence or set node with the given
8525 filters as children.
8527 #include <isl/schedule_node.h>
8528 __isl_give isl_schedule_node *isl_schedule_node_group(
8529 __isl_take isl_schedule_node *node,
8530 __isl_take isl_id *group_id);
8532 This function introduces an expansion node in between the current
8533 node and its parent that expands instances of a space with tuple
8534 identifier C<group_id> to the original domain elements that reach
8535 the node. The group instances are identified by the prefix schedule
8536 of those domain elements. The ancestors of the node are adjusted
8537 to refer to the group instances instead of the original domain
8538 elements. The return value points to the same node in the updated
8539 schedule tree as the input node, i.e., to the child of the newly
8540 introduced expansion node. Grouping instances of different statements
8541 ensures that they will be treated as a single statement by the
8542 AST generator up to the point of the expansion node.
8544 The following function can be used to flatten a nested
8547 #include <isl/schedule_node.h>
8548 __isl_give isl_schedule_node *
8549 isl_schedule_node_sequence_splice_child(
8550 __isl_take isl_schedule_node *node, int pos);
8552 That is, given a sequence node C<node> that has another sequence node
8553 in its child at position C<pos> (in particular, the child of that filter
8554 node is a sequence node), attach the children of that other sequence
8555 node as children of C<node>, replacing the original child at position
8558 The partial schedule of a band node can be scaled (down) or reduced using
8559 the following functions.
8561 #include <isl/schedule_node.h>
8562 __isl_give isl_schedule_node *
8563 isl_schedule_node_band_scale(
8564 __isl_take isl_schedule_node *node,
8565 __isl_take isl_multi_val *mv);
8566 __isl_give isl_schedule_node *
8567 isl_schedule_node_band_scale_down(
8568 __isl_take isl_schedule_node *node,
8569 __isl_take isl_multi_val *mv);
8570 __isl_give isl_schedule_node *
8571 isl_schedule_node_band_mod(
8572 __isl_take isl_schedule_node *node,
8573 __isl_take isl_multi_val *mv);
8575 The spaces of the two arguments need to match.
8576 After scaling, the partial schedule is replaced by its greatest
8577 integer part to ensure that the schedule remains integral.
8579 The partial schedule of a band node can be shifted by an
8580 C<isl_multi_union_pw_aff> with a domain that is a superset
8581 of the domain of the partial schedule using
8582 the following function.
8584 #include <isl/schedule_node.h>
8585 __isl_give isl_schedule_node *
8586 isl_schedule_node_band_shift(
8587 __isl_take isl_schedule_node *node,
8588 __isl_take isl_multi_union_pw_aff *shift);
8590 A band node can be tiled using the following function.
8592 #include <isl/schedule_node.h>
8593 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
8594 __isl_take isl_schedule_node *node,
8595 __isl_take isl_multi_val *sizes);
8597 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
8599 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
8600 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
8602 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
8604 The C<isl_schedule_node_band_tile> function tiles
8605 the band using the given tile sizes inside its schedule.
8606 A new child band node is created to represent the point loops and it is
8607 inserted between the modified band and its children.
8608 The subtree rooted at the given node is assumed not to have
8610 The C<tile_scale_tile_loops> option specifies whether the tile
8611 loops iterators should be scaled by the tile sizes.
8612 If the C<tile_shift_point_loops> option is set, then the point loops
8613 are shifted to start at zero.
8615 A band node can be split into two nested band nodes
8616 using the following function.
8618 #include <isl/schedule_node.h>
8619 __isl_give isl_schedule_node *isl_schedule_node_band_split(
8620 __isl_take isl_schedule_node *node, int pos);
8622 The resulting outer band node contains the first C<pos> dimensions of
8623 the schedule of C<node> while the inner band contains the remaining dimensions.
8624 The schedules of the two band nodes live in anonymous spaces.
8625 The loop AST generation type options and the isolate option
8626 are split over the the two band nodes.
8628 A band node can be moved down to the leaves of the subtree rooted
8629 at the band node using the following function.
8631 #include <isl/schedule_node.h>
8632 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
8633 __isl_take isl_schedule_node *node);
8635 The subtree rooted at the given node is assumed not to have
8637 The result points to the node in the resulting tree that is in the same
8638 position as the node pointed to by C<node> in the original tree.
8640 #include <isl/schedule_node.h>
8641 __isl_give isl_schedule_node *
8642 isl_schedule_node_order_before(
8643 __isl_take isl_schedule_node *node,
8644 __isl_take isl_union_set *filter);
8645 __isl_give isl_schedule_node *
8646 isl_schedule_node_order_after(
8647 __isl_take isl_schedule_node *node,
8648 __isl_take isl_union_set *filter);
8650 These functions split the domain elements that reach C<node>
8651 into those that satisfy C<filter> and those that do not and
8652 arranges for the elements that do satisfy the filter to be
8653 executed before (in case of C<isl_schedule_node_order_before>)
8654 or after (in case of C<isl_schedule_node_order_after>)
8655 those that do not. The order is imposed by
8656 a sequence node, possibly reusing the grandparent of C<node>
8657 on two copies of the subtree attached to the original C<node>.
8658 Both copies are simplified with respect to their filter.
8660 Return a pointer to the copy of the subtree that does not
8661 satisfy C<filter>. If there is no such copy (because all
8662 reaching domain elements satisfy the filter), then return
8663 the original pointer.
8665 #include <isl/schedule_node.h>
8666 __isl_give isl_schedule_node *
8667 isl_schedule_node_graft_before(
8668 __isl_take isl_schedule_node *node,
8669 __isl_take isl_schedule_node *graft);
8670 __isl_give isl_schedule_node *
8671 isl_schedule_node_graft_after(
8672 __isl_take isl_schedule_node *node,
8673 __isl_take isl_schedule_node *graft);
8675 This function inserts the C<graft> tree into the tree containing C<node>
8676 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
8677 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
8678 The root node of C<graft>
8679 should be an extension node where the domain of the extension
8680 is the flat product of all outer band nodes of C<node>.
8681 The root node may also be a domain node.
8682 The elements of the domain or the range of the extension may not
8683 intersect with the domain elements that reach "node".
8684 The schedule tree of C<graft> may not be anchored.
8686 The schedule tree of C<node> is modified to include an extension node
8687 corresponding to the root node of C<graft> as a child of the original
8688 parent of C<node>. The original node that C<node> points to and the
8689 child of the root node of C<graft> are attached to this extension node
8690 through a sequence, with appropriate filters and with the child
8691 of C<graft> appearing before or after the original C<node>.
8693 If C<node> already appears inside a sequence that is the child of
8694 an extension node and if the spaces of the new domain elements
8695 do not overlap with those of the original domain elements,
8696 then that extension node is extended with the new extension
8697 rather than introducing a new segment of extension and sequence nodes.
8699 Return a pointer to the same node in the modified tree that
8700 C<node> pointed to in the original tree.
8702 A representation of the schedule node can be printed using
8704 #include <isl/schedule_node.h>
8705 __isl_give isl_printer *isl_printer_print_schedule_node(
8706 __isl_take isl_printer *p,
8707 __isl_keep isl_schedule_node *node);
8708 __isl_give char *isl_schedule_node_to_str(
8709 __isl_keep isl_schedule_node *node);
8711 C<isl_schedule_node_to_str> prints the schedule node in block format.
8713 =head2 Dependence Analysis
8715 C<isl> contains specialized functionality for performing
8716 array dataflow analysis. That is, given a I<sink> access relation
8717 and a collection of possible I<source> access relations,
8718 C<isl> can compute relations that describe
8719 for each iteration of the sink access, which iteration
8720 of which of the source access relations was the last
8721 to access the same data element before the given iteration
8723 The resulting dependence relations map source iterations
8724 to either the corresponding sink iterations or
8725 pairs of corresponding sink iterations and accessed data elements.
8726 To compute standard flow dependences, the sink should be
8727 a read, while the sources should be writes.
8728 If any of the source accesses are marked as being I<may>
8729 accesses, then there will be a dependence from the last
8730 I<must> access B<and> from any I<may> access that follows
8731 this last I<must> access.
8732 In particular, if I<all> sources are I<may> accesses,
8733 then memory based dependence analysis is performed.
8734 If, on the other hand, all sources are I<must> accesses,
8735 then value based dependence analysis is performed.
8737 =head3 High-level Interface
8739 A high-level interface to dependence analysis is provided
8740 by the following function.
8742 #include <isl/flow.h>
8743 __isl_give isl_union_flow *
8744 isl_union_access_info_compute_flow(
8745 __isl_take isl_union_access_info *access);
8747 The input C<isl_union_access_info> object describes the sink
8748 access relations, the source access relations and a schedule,
8749 while the output C<isl_union_flow> object describes
8750 the resulting dependence relations and the subsets of the
8751 sink relations for which no source was found.
8753 An C<isl_union_access_info> is created, modified, copied and freed using
8754 the following functions.
8756 #include <isl/flow.h>
8757 __isl_give isl_union_access_info *
8758 isl_union_access_info_from_sink(
8759 __isl_take isl_union_map *sink);
8760 __isl_give isl_union_access_info *
8761 isl_union_access_info_set_must_source(
8762 __isl_take isl_union_access_info *access,
8763 __isl_take isl_union_map *must_source);
8764 __isl_give isl_union_access_info *
8765 isl_union_access_info_set_may_source(
8766 __isl_take isl_union_access_info *access,
8767 __isl_take isl_union_map *may_source);
8768 __isl_give isl_union_access_info *
8769 isl_union_access_info_set_schedule(
8770 __isl_take isl_union_access_info *access,
8771 __isl_take isl_schedule *schedule);
8772 __isl_give isl_union_access_info *
8773 isl_union_access_info_set_schedule_map(
8774 __isl_take isl_union_access_info *access,
8775 __isl_take isl_union_map *schedule_map);
8776 __isl_give isl_union_access_info *
8777 isl_union_access_info_copy(
8778 __isl_keep isl_union_access_info *access);
8779 __isl_null isl_union_access_info *
8780 isl_union_access_info_free(
8781 __isl_take isl_union_access_info *access);
8783 The may sources set by C<isl_union_access_info_set_may_source>
8784 do not need to include the must sources set by
8785 C<isl_union_access_info_set_must_source> as a subset.
8786 The user is free not to call one (or both) of these functions,
8787 in which case the corresponding set is kept to its empty default.
8788 Similarly, the default schedule initialized by
8789 C<isl_union_access_info_from_sink> is empty.
8790 The current schedule is determined by the last call to either
8791 C<isl_union_access_info_set_schedule> or
8792 C<isl_union_access_info_set_schedule_map>.
8793 The domain of the schedule corresponds to the domains of
8794 the access relations. In particular, the domains of the access
8795 relations are effectively intersected with the domain of the schedule
8796 and only the resulting accesses are considered by the dependence analysis.
8798 A representation of the information contained in an object
8799 of type C<isl_union_access_info> can be obtained using
8801 #include <isl/flow.h>
8802 __isl_give isl_printer *
8803 isl_printer_print_union_access_info(
8804 __isl_take isl_printer *p,
8805 __isl_keep isl_union_access_info *access);
8806 __isl_give char *isl_union_access_info_to_str(
8807 __isl_keep isl_union_access_info *access);
8809 C<isl_union_access_info_to_str> prints the information in flow format.
8811 The output of C<isl_union_access_info_compute_flow> can be examined,
8812 copied, and freed using the following functions.
8814 #include <isl/flow.h>
8815 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
8816 __isl_keep isl_union_flow *flow);
8817 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
8818 __isl_keep isl_union_flow *flow);
8819 __isl_give isl_union_map *
8820 isl_union_flow_get_full_must_dependence(
8821 __isl_keep isl_union_flow *flow);
8822 __isl_give isl_union_map *
8823 isl_union_flow_get_full_may_dependence(
8824 __isl_keep isl_union_flow *flow);
8825 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
8826 __isl_keep isl_union_flow *flow);
8827 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
8828 __isl_keep isl_union_flow *flow);
8829 __isl_give isl_union_flow *isl_union_flow_copy(
8830 __isl_keep isl_union_flow *flow);
8831 __isl_null isl_union_flow *isl_union_flow_free(
8832 __isl_take isl_union_flow *flow);
8834 The relation returned by C<isl_union_flow_get_must_dependence>
8835 relates domain elements of must sources to domain elements of the sink.
8836 The relation returned by C<isl_union_flow_get_may_dependence>
8837 relates domain elements of must or may sources to domain elements of the sink
8838 and includes the previous relation as a subset.
8839 The relation returned by C<isl_union_flow_get_full_must_dependence>
8840 relates domain elements of must sources to pairs of domain elements of the sink
8841 and accessed data elements.
8842 The relation returned by C<isl_union_flow_get_full_may_dependence>
8843 relates domain elements of must or may sources to pairs of
8844 domain elements of the sink and accessed data elements.
8845 This relation includes the previous relation as a subset.
8846 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
8847 of the sink relation for which no dependences have been found.
8848 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
8849 of the sink relation for which no definite dependences have been found.
8850 That is, it contains those sink access that do not contribute to any
8851 of the elements in the relation returned
8852 by C<isl_union_flow_get_must_dependence>.
8854 A representation of the information contained in an object
8855 of type C<isl_union_flow> can be obtained using
8857 #include <isl/flow.h>
8858 __isl_give isl_printer *isl_printer_print_union_flow(
8859 __isl_take isl_printer *p,
8860 __isl_keep isl_union_flow *flow);
8861 __isl_give char *isl_union_flow_to_str(
8862 __isl_keep isl_union_flow *flow);
8864 C<isl_union_flow_to_str> prints the information in flow format.
8866 =head3 Low-level Interface
8868 A lower-level interface is provided by the following functions.
8870 #include <isl/flow.h>
8872 typedef int (*isl_access_level_before)(void *first, void *second);
8874 __isl_give isl_access_info *isl_access_info_alloc(
8875 __isl_take isl_map *sink,
8876 void *sink_user, isl_access_level_before fn,
8878 __isl_give isl_access_info *isl_access_info_add_source(
8879 __isl_take isl_access_info *acc,
8880 __isl_take isl_map *source, int must,
8882 __isl_null isl_access_info *isl_access_info_free(
8883 __isl_take isl_access_info *acc);
8885 __isl_give isl_flow *isl_access_info_compute_flow(
8886 __isl_take isl_access_info *acc);
8888 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,
8889 isl_stat (*fn)(__isl_take isl_map *dep, int must,
8890 void *dep_user, void *user),
8892 __isl_give isl_map *isl_flow_get_no_source(
8893 __isl_keep isl_flow *deps, int must);
8894 void isl_flow_free(__isl_take isl_flow *deps);
8896 The function C<isl_access_info_compute_flow> performs the actual
8897 dependence analysis. The other functions are used to construct
8898 the input for this function or to read off the output.
8900 The input is collected in an C<isl_access_info>, which can
8901 be created through a call to C<isl_access_info_alloc>.
8902 The arguments to this functions are the sink access relation
8903 C<sink>, a token C<sink_user> used to identify the sink
8904 access to the user, a callback function for specifying the
8905 relative order of source and sink accesses, and the number
8906 of source access relations that will be added.
8907 The callback function has type C<int (*)(void *first, void *second)>.
8908 The function is called with two user supplied tokens identifying
8909 either a source or the sink and it should return the shared nesting
8910 level and the relative order of the two accesses.
8911 In particular, let I<n> be the number of loops shared by
8912 the two accesses. If C<first> precedes C<second> textually,
8913 then the function should return I<2 * n + 1>; otherwise,
8914 it should return I<2 * n>.
8915 The sources can be added to the C<isl_access_info> by performing
8916 (at most) C<max_source> calls to C<isl_access_info_add_source>.
8917 C<must> indicates whether the source is a I<must> access
8918 or a I<may> access. Note that a multi-valued access relation
8919 should only be marked I<must> if every iteration in the domain
8920 of the relation accesses I<all> elements in its image.
8921 The C<source_user> token is again used to identify
8922 the source access. The range of the source access relation
8923 C<source> should have the same dimension as the range
8924 of the sink access relation.
8925 The C<isl_access_info_free> function should usually not be
8926 called explicitly, because it is called implicitly by
8927 C<isl_access_info_compute_flow>.
8929 The result of the dependence analysis is collected in an
8930 C<isl_flow>. There may be elements of
8931 the sink access for which no preceding source access could be
8932 found or for which all preceding sources are I<may> accesses.
8933 The relations containing these elements can be obtained through
8934 calls to C<isl_flow_get_no_source>, the first with C<must> set
8935 and the second with C<must> unset.
8936 In the case of standard flow dependence analysis,
8937 with the sink a read and the sources I<must> writes,
8938 the first relation corresponds to the reads from uninitialized
8939 array elements and the second relation is empty.
8940 The actual flow dependences can be extracted using
8941 C<isl_flow_foreach>. This function will call the user-specified
8942 callback function C<fn> for each B<non-empty> dependence between
8943 a source and the sink. The callback function is called
8944 with four arguments, the actual flow dependence relation
8945 mapping source iterations to sink iterations, a boolean that
8946 indicates whether it is a I<must> or I<may> dependence, a token
8947 identifying the source and an additional C<void *> with value
8948 equal to the third argument of the C<isl_flow_foreach> call.
8949 A dependence is marked I<must> if it originates from a I<must>
8950 source and if it is not followed by any I<may> sources.
8952 After finishing with an C<isl_flow>, the user should call
8953 C<isl_flow_free> to free all associated memory.
8955 =head3 Interaction with the Low-level Interface
8957 During the dependence analysis, we frequently need to perform
8958 the following operation. Given a relation between sink iterations
8959 and potential source iterations from a particular source domain,
8960 what is the last potential source iteration corresponding to each
8961 sink iteration. It can sometimes be convenient to adjust
8962 the set of potential source iterations before or after each such operation.
8963 The prototypical example is fuzzy array dataflow analysis,
8964 where we need to analyze if, based on data-dependent constraints,
8965 the sink iteration can ever be executed without one or more of
8966 the corresponding potential source iterations being executed.
8967 If so, we can introduce extra parameters and select an unknown
8968 but fixed source iteration from the potential source iterations.
8969 To be able to perform such manipulations, C<isl> provides the following
8972 #include <isl/flow.h>
8974 typedef __isl_give isl_restriction *(*isl_access_restrict)(
8975 __isl_keep isl_map *source_map,
8976 __isl_keep isl_set *sink, void *source_user,
8978 __isl_give isl_access_info *isl_access_info_set_restrict(
8979 __isl_take isl_access_info *acc,
8980 isl_access_restrict fn, void *user);
8982 The function C<isl_access_info_set_restrict> should be called
8983 before calling C<isl_access_info_compute_flow> and registers a callback function
8984 that will be called any time C<isl> is about to compute the last
8985 potential source. The first argument is the (reverse) proto-dependence,
8986 mapping sink iterations to potential source iterations.
8987 The second argument represents the sink iterations for which
8988 we want to compute the last source iteration.
8989 The third argument is the token corresponding to the source
8990 and the final argument is the token passed to C<isl_access_info_set_restrict>.
8991 The callback is expected to return a restriction on either the input or
8992 the output of the operation computing the last potential source.
8993 If the input needs to be restricted then restrictions are needed
8994 for both the source and the sink iterations. The sink iterations
8995 and the potential source iterations will be intersected with these sets.
8996 If the output needs to be restricted then only a restriction on the source
8997 iterations is required.
8998 If any error occurs, the callback should return C<NULL>.
8999 An C<isl_restriction> object can be created, freed and inspected
9000 using the following functions.
9002 #include <isl/flow.h>
9004 __isl_give isl_restriction *isl_restriction_input(
9005 __isl_take isl_set *source_restr,
9006 __isl_take isl_set *sink_restr);
9007 __isl_give isl_restriction *isl_restriction_output(
9008 __isl_take isl_set *source_restr);
9009 __isl_give isl_restriction *isl_restriction_none(
9010 __isl_take isl_map *source_map);
9011 __isl_give isl_restriction *isl_restriction_empty(
9012 __isl_take isl_map *source_map);
9013 __isl_null isl_restriction *isl_restriction_free(
9014 __isl_take isl_restriction *restr);
9016 C<isl_restriction_none> and C<isl_restriction_empty> are special
9017 cases of C<isl_restriction_input>. C<isl_restriction_none>
9018 is essentially equivalent to
9020 isl_restriction_input(isl_set_universe(
9021 isl_space_range(isl_map_get_space(source_map))),
9023 isl_space_domain(isl_map_get_space(source_map))));
9025 whereas C<isl_restriction_empty> is essentially equivalent to
9027 isl_restriction_input(isl_set_empty(
9028 isl_space_range(isl_map_get_space(source_map))),
9030 isl_space_domain(isl_map_get_space(source_map))));
9034 #include <isl/schedule.h>
9035 __isl_give isl_schedule *
9036 isl_schedule_constraints_compute_schedule(
9037 __isl_take isl_schedule_constraints *sc);
9039 The function C<isl_schedule_constraints_compute_schedule> can be
9040 used to compute a schedule that satisfies the given schedule constraints.
9041 These schedule constraints include the iteration domain for which
9042 a schedule should be computed and dependences between pairs of
9043 iterations. In particular, these dependences include
9044 I<validity> dependences and I<proximity> dependences.
9045 By default, the algorithm used to construct the schedule is similar
9046 to that of C<Pluto>.
9047 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
9049 The generated schedule respects all validity dependences.
9050 That is, all dependence distances over these dependences in the
9051 scheduled space are lexicographically positive.
9053 The default algorithm tries to ensure that the dependence distances
9054 over coincidence constraints are zero and to minimize the
9055 dependence distances over proximity dependences.
9056 Moreover, it tries to obtain sequences (bands) of schedule dimensions
9057 for groups of domains where the dependence distances over validity
9058 dependences have only non-negative values.
9059 Note that when minimizing the maximal dependence distance
9060 over proximity dependences, a single affine expression in the parameters
9061 is constructed that bounds all dependence distances. If no such expression
9062 exists, then the algorithm will fail and resort to an alternative
9063 scheduling algorithm. In particular, this means that adding proximity
9064 dependences may eliminate valid solutions. A typical example where this
9065 phenomenon may occur is when some subset of the proximity dependences
9066 has no restriction on some parameter, forcing the coefficient of that
9067 parameter to be zero, while some other subset forces the dependence
9068 distance to depend on that parameter, requiring the same coefficient
9070 When using Feautrier's algorithm, the coincidence and proximity constraints
9071 are only taken into account during the extension to a
9072 full-dimensional schedule.
9074 An C<isl_schedule_constraints> object can be constructed
9075 and manipulated using the following functions.
9077 #include <isl/schedule.h>
9078 __isl_give isl_schedule_constraints *
9079 isl_schedule_constraints_copy(
9080 __isl_keep isl_schedule_constraints *sc);
9081 __isl_give isl_schedule_constraints *
9082 isl_schedule_constraints_on_domain(
9083 __isl_take isl_union_set *domain);
9084 __isl_give isl_schedule_constraints *
9085 isl_schedule_constraints_set_context(
9086 __isl_take isl_schedule_constraints *sc,
9087 __isl_take isl_set *context);
9088 __isl_give isl_schedule_constraints *
9089 isl_schedule_constraints_set_validity(
9090 __isl_take isl_schedule_constraints *sc,
9091 __isl_take isl_union_map *validity);
9092 __isl_give isl_schedule_constraints *
9093 isl_schedule_constraints_set_coincidence(
9094 __isl_take isl_schedule_constraints *sc,
9095 __isl_take isl_union_map *coincidence);
9096 __isl_give isl_schedule_constraints *
9097 isl_schedule_constraints_set_proximity(
9098 __isl_take isl_schedule_constraints *sc,
9099 __isl_take isl_union_map *proximity);
9100 __isl_give isl_schedule_constraints *
9101 isl_schedule_constraints_set_conditional_validity(
9102 __isl_take isl_schedule_constraints *sc,
9103 __isl_take isl_union_map *condition,
9104 __isl_take isl_union_map *validity);
9105 __isl_give isl_schedule_constraints *
9106 isl_schedule_constraints_apply(
9107 __isl_take isl_schedule_constraints *sc,
9108 __isl_take isl_union_map *umap);
9109 __isl_null isl_schedule_constraints *
9110 isl_schedule_constraints_free(
9111 __isl_take isl_schedule_constraints *sc);
9113 The initial C<isl_schedule_constraints> object created by
9114 C<isl_schedule_constraints_on_domain> does not impose any constraints.
9115 That is, it has an empty set of dependences.
9116 The function C<isl_schedule_constraints_set_context> allows the user
9117 to specify additional constraints on the parameters that may
9118 be assumed to hold during the construction of the schedule.
9119 The function C<isl_schedule_constraints_set_validity> replaces the
9120 validity dependences, mapping domain elements I<i> to domain
9121 elements that should be scheduled after I<i>.
9122 The function C<isl_schedule_constraints_set_coincidence> replaces the
9123 coincidence dependences, mapping domain elements I<i> to domain
9124 elements that should be scheduled together with I<I>, if possible.
9125 The function C<isl_schedule_constraints_set_proximity> replaces the
9126 proximity dependences, mapping domain elements I<i> to domain
9127 elements that should be scheduled either before I<I>
9128 or as early as possible after I<i>.
9130 The function C<isl_schedule_constraints_set_conditional_validity>
9131 replaces the conditional validity constraints.
9132 A conditional validity constraint is only imposed when any of the corresponding
9133 conditions is satisfied, i.e., when any of them is non-zero.
9134 That is, the scheduler ensures that within each band if the dependence
9135 distances over the condition constraints are not all zero
9136 then all corresponding conditional validity constraints are respected.
9137 A conditional validity constraint corresponds to a condition
9138 if the two are adjacent, i.e., if the domain of one relation intersect
9139 the range of the other relation.
9140 The typical use case of conditional validity constraints is
9141 to allow order constraints between live ranges to be violated
9142 as long as the live ranges themselves are local to the band.
9143 To allow more fine-grained control over which conditions correspond
9144 to which conditional validity constraints, the domains and ranges
9145 of these relations may include I<tags>. That is, the domains and
9146 ranges of those relation may themselves be wrapped relations
9147 where the iteration domain appears in the domain of those wrapped relations
9148 and the range of the wrapped relations can be arbitrarily chosen
9149 by the user. Conditions and conditional validity constraints are only
9150 considered adjacent to each other if the entire wrapped relation matches.
9151 In particular, a relation with a tag will never be considered adjacent
9152 to a relation without a tag.
9154 The function C<isl_schedule_constraints_compute_schedule> takes
9155 schedule constraints that are defined on some set of domain elements
9156 and transforms them to schedule constraints on the elements
9157 to which these domain elements are mapped by the given transformation.
9159 An C<isl_schedule_constraints> object can be inspected
9160 using the following functions.
9162 #include <isl/schedule.h>
9163 __isl_give isl_union_set *
9164 isl_schedule_constraints_get_domain(
9165 __isl_keep isl_schedule_constraints *sc);
9166 __isl_give isl_set *isl_schedule_constraints_get_context(
9167 __isl_keep isl_schedule_constraints *sc);
9168 __isl_give isl_union_map *
9169 isl_schedule_constraints_get_validity(
9170 __isl_keep isl_schedule_constraints *sc);
9171 __isl_give isl_union_map *
9172 isl_schedule_constraints_get_coincidence(
9173 __isl_keep isl_schedule_constraints *sc);
9174 __isl_give isl_union_map *
9175 isl_schedule_constraints_get_proximity(
9176 __isl_keep isl_schedule_constraints *sc);
9177 __isl_give isl_union_map *
9178 isl_schedule_constraints_get_conditional_validity(
9179 __isl_keep isl_schedule_constraints *sc);
9180 __isl_give isl_union_map *
9181 isl_schedule_constraints_get_conditional_validity_condition(
9182 __isl_keep isl_schedule_constraints *sc);
9184 An C<isl_schedule_constraints> object can be read from input
9185 using the following functions.
9187 #include <isl/schedule.h>
9188 __isl_give isl_schedule_constraints *
9189 isl_schedule_constraints_read_from_str(isl_ctx *ctx,
9191 __isl_give isl_schedule_constraints *
9192 isl_schedule_constraints_read_from_file(isl_ctx *ctx,
9195 The contents of an C<isl_schedule_constraints> object can be printed
9196 using the following functions.
9198 #include <isl/schedule.h>
9199 __isl_give isl_printer *
9200 isl_printer_print_schedule_constraints(
9201 __isl_take isl_printer *p,
9202 __isl_keep isl_schedule_constraints *sc);
9203 __isl_give char *isl_schedule_constraints_to_str(
9204 __isl_keep isl_schedule_constraints *sc);
9206 The following function computes a schedule directly from
9207 an iteration domain and validity and proximity dependences
9208 and is implemented in terms of the functions described above.
9209 The use of C<isl_union_set_compute_schedule> is discouraged.
9211 #include <isl/schedule.h>
9212 __isl_give isl_schedule *isl_union_set_compute_schedule(
9213 __isl_take isl_union_set *domain,
9214 __isl_take isl_union_map *validity,
9215 __isl_take isl_union_map *proximity);
9217 The generated schedule represents a schedule tree.
9218 For more information on schedule trees, see
9219 L</"Schedule Trees">.
9223 #include <isl/schedule.h>
9224 isl_stat isl_options_set_schedule_max_coefficient(
9225 isl_ctx *ctx, int val);
9226 int isl_options_get_schedule_max_coefficient(
9228 isl_stat isl_options_set_schedule_max_constant_term(
9229 isl_ctx *ctx, int val);
9230 int isl_options_get_schedule_max_constant_term(
9232 isl_stat isl_options_set_schedule_serialize_sccs(
9233 isl_ctx *ctx, int val);
9234 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx);
9235 isl_stat isl_options_set_schedule_whole_component(
9236 isl_ctx *ctx, int val);
9237 int isl_options_get_schedule_whole_component(
9239 isl_stat isl_options_set_schedule_maximize_band_depth(
9240 isl_ctx *ctx, int val);
9241 int isl_options_get_schedule_maximize_band_depth(
9243 isl_stat isl_options_set_schedule_maximize_coincidence(
9244 isl_ctx *ctx, int val);
9245 int isl_options_get_schedule_maximize_coincidence(
9247 isl_stat isl_options_set_schedule_outer_coincidence(
9248 isl_ctx *ctx, int val);
9249 int isl_options_get_schedule_outer_coincidence(
9251 isl_stat isl_options_set_schedule_split_scaled(
9252 isl_ctx *ctx, int val);
9253 int isl_options_get_schedule_split_scaled(
9255 isl_stat isl_options_set_schedule_treat_coalescing(
9256 isl_ctx *ctx, int val);
9257 int isl_options_get_schedule_treat_coalescing(
9259 isl_stat isl_options_set_schedule_algorithm(
9260 isl_ctx *ctx, int val);
9261 int isl_options_get_schedule_algorithm(
9263 isl_stat isl_options_set_schedule_separate_components(
9264 isl_ctx *ctx, int val);
9265 int isl_options_get_schedule_separate_components(
9270 =item * schedule_max_coefficient
9272 This option enforces that the coefficients for variable and parameter
9273 dimensions in the calculated schedule are not larger than the specified value.
9274 This option can significantly increase the speed of the scheduling calculation
9275 and may also prevent fusing of unrelated dimensions. A value of -1 means that
9276 this option does not introduce bounds on the variable or parameter
9279 =item * schedule_max_constant_term
9281 This option enforces that the constant coefficients in the calculated schedule
9282 are not larger than the maximal constant term. This option can significantly
9283 increase the speed of the scheduling calculation and may also prevent fusing of
9284 unrelated dimensions. A value of -1 means that this option does not introduce
9285 bounds on the constant coefficients.
9287 =item * schedule_serialize_sccs
9289 If this option is set, then all strongly connected components
9290 in the dependence graph are serialized as soon as they are detected.
9291 This means in particular that instances of statements will only
9292 appear in the same band node if these statements belong
9293 to the same strongly connected component at the point where
9294 the band node is constructed.
9296 =item * schedule_whole_component
9298 If this option is set, then entire (weakly) connected
9299 components in the dependence graph are scheduled together
9301 Otherwise, each strongly connected component within
9302 such a weakly connected component is first scheduled separately
9303 and then combined with other strongly connected components.
9304 This option has no effect if C<schedule_serialize_sccs> is set.
9306 =item * schedule_maximize_band_depth
9308 If this option is set, then the scheduler tries to maximize
9309 the width of the bands. Wider bands give more possibilities for tiling.
9310 In particular, if the C<schedule_whole_component> option is set,
9311 then bands are split if this might result in wider bands.
9312 Otherwise, the effect of this option is to only allow
9313 strongly connected components to be combined if this does
9314 not reduce the width of the bands.
9315 Note that if the C<schedule_serialize_sccs> options is set, then
9316 the C<schedule_maximize_band_depth> option therefore has no effect.
9318 =item * schedule_maximize_coincidence
9320 This option is only effective if the C<schedule_whole_component>
9321 option is turned off.
9322 If the C<schedule_maximize_coincidence> option is set, then (clusters of)
9323 strongly connected components are only combined with each other
9324 if this does not reduce the number of coincident band members.
9326 =item * schedule_outer_coincidence
9328 If this option is set, then we try to construct schedules
9329 where the outermost scheduling dimension in each band
9330 satisfies the coincidence constraints.
9332 =item * schedule_algorithm
9334 Selects the scheduling algorithm to be used.
9335 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
9336 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
9338 =item * schedule_split_scaled
9340 If this option is set, then we try to construct schedules in which the
9341 constant term is split off from the linear part if the linear parts of
9342 the scheduling rows for all nodes in the graphs have a common non-trivial
9344 The constant term is then placed in a separate band and the linear
9346 This option is only effective when the Feautrier style scheduler is
9347 being used, either as the main scheduler or as a fallback for the
9348 Pluto-like scheduler.
9350 =item * schedule_treat_coalescing
9352 If this option is set, then the scheduler will try and avoid
9353 producing schedules that perform loop coalescing.
9354 In particular, for the Pluto-like scheduler, this option places
9355 bounds on the schedule coefficients based on the sizes of the instance sets.
9356 For the Feautrier style scheduler, this option detects potentially
9357 coalescing schedules and then tries to adjust the schedule to avoid
9360 =item * schedule_separate_components
9362 If this option is set then the function C<isl_schedule_get_map>
9363 will treat set nodes in the same way as sequence nodes.
9367 =head2 AST Generation
9369 This section describes the C<isl> functionality for generating
9370 ASTs that visit all the elements
9371 in a domain in an order specified by a schedule tree or
9373 In case the schedule given as a C<isl_union_map>, an AST is generated
9374 that visits all the elements in the domain of the C<isl_union_map>
9375 according to the lexicographic order of the corresponding image
9376 element(s). If the range of the C<isl_union_map> consists of
9377 elements in more than one space, then each of these spaces is handled
9378 separately in an arbitrary order.
9379 It should be noted that the schedule tree or the image elements
9380 in a schedule map only specify the I<order>
9381 in which the corresponding domain elements should be visited.
9382 No direct relation between the partial schedule values
9383 or the image elements on the one hand and the loop iterators
9384 in the generated AST on the other hand should be assumed.
9386 Each AST is generated within a build. The initial build
9387 simply specifies the constraints on the parameters (if any)
9388 and can be created, inspected, copied and freed using the following functions.
9390 #include <isl/ast_build.h>
9391 __isl_give isl_ast_build *isl_ast_build_alloc(
9393 __isl_give isl_ast_build *isl_ast_build_from_context(
9394 __isl_take isl_set *set);
9395 __isl_give isl_ast_build *isl_ast_build_copy(
9396 __isl_keep isl_ast_build *build);
9397 __isl_null isl_ast_build *isl_ast_build_free(
9398 __isl_take isl_ast_build *build);
9400 The C<set> argument is usually a parameter set with zero or more parameters.
9401 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
9402 this set is required to be a parameter set.
9403 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
9404 specify any parameter constraints.
9405 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
9406 and L</"Fine-grained Control over AST Generation">.
9407 Finally, the AST itself can be constructed using one of the following
9410 #include <isl/ast_build.h>
9411 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
9412 __isl_keep isl_ast_build *build,
9413 __isl_take isl_schedule *schedule);
9414 __isl_give isl_ast_node *
9415 isl_ast_build_node_from_schedule_map(
9416 __isl_keep isl_ast_build *build,
9417 __isl_take isl_union_map *schedule);
9419 =head3 Inspecting the AST
9421 The basic properties of an AST node can be obtained as follows.
9423 #include <isl/ast.h>
9424 enum isl_ast_node_type isl_ast_node_get_type(
9425 __isl_keep isl_ast_node *node);
9427 The type of an AST node is one of
9428 C<isl_ast_node_for>,
9430 C<isl_ast_node_block>,
9431 C<isl_ast_node_mark> or
9432 C<isl_ast_node_user>.
9433 An C<isl_ast_node_for> represents a for node.
9434 An C<isl_ast_node_if> represents an if node.
9435 An C<isl_ast_node_block> represents a compound node.
9436 An C<isl_ast_node_mark> introduces a mark in the AST.
9437 An C<isl_ast_node_user> represents an expression statement.
9438 An expression statement typically corresponds to a domain element, i.e.,
9439 one of the elements that is visited by the AST.
9441 Each type of node has its own additional properties.
9443 #include <isl/ast.h>
9444 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
9445 __isl_keep isl_ast_node *node);
9446 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
9447 __isl_keep isl_ast_node *node);
9448 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
9449 __isl_keep isl_ast_node *node);
9450 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
9451 __isl_keep isl_ast_node *node);
9452 __isl_give isl_ast_node *isl_ast_node_for_get_body(
9453 __isl_keep isl_ast_node *node);
9454 isl_bool isl_ast_node_for_is_degenerate(
9455 __isl_keep isl_ast_node *node);
9457 An C<isl_ast_for> is considered degenerate if it is known to execute
9460 #include <isl/ast.h>
9461 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
9462 __isl_keep isl_ast_node *node);
9463 __isl_give isl_ast_node *isl_ast_node_if_get_then(
9464 __isl_keep isl_ast_node *node);
9465 isl_bool isl_ast_node_if_has_else(
9466 __isl_keep isl_ast_node *node);
9467 __isl_give isl_ast_node *isl_ast_node_if_get_else(
9468 __isl_keep isl_ast_node *node);
9470 __isl_give isl_ast_node_list *
9471 isl_ast_node_block_get_children(
9472 __isl_keep isl_ast_node *node);
9474 __isl_give isl_id *isl_ast_node_mark_get_id(
9475 __isl_keep isl_ast_node *node);
9476 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
9477 __isl_keep isl_ast_node *node);
9479 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
9480 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
9482 #include <isl/ast.h>
9483 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
9484 __isl_keep isl_ast_node *node);
9486 All descendants of a specific node in the AST (including the node itself)
9488 in depth-first pre-order using the following function.
9490 #include <isl/ast.h>
9491 isl_stat isl_ast_node_foreach_descendant_top_down(
9492 __isl_keep isl_ast_node *node,
9493 isl_bool (*fn)(__isl_keep isl_ast_node *node,
9494 void *user), void *user);
9496 The callback function should return C<isl_bool_true> if the children
9497 of the given node should be visited and C<isl_bool_false> if they should not.
9498 It should return C<isl_bool_error> in case of failure, in which case
9499 the entire traversal is aborted.
9501 Each of the returned C<isl_ast_expr>s can in turn be inspected using
9502 the following functions.
9504 #include <isl/ast.h>
9505 enum isl_ast_expr_type isl_ast_expr_get_type(
9506 __isl_keep isl_ast_expr *expr);
9508 The type of an AST expression is one of
9510 C<isl_ast_expr_id> or
9511 C<isl_ast_expr_int>.
9512 An C<isl_ast_expr_op> represents the result of an operation.
9513 An C<isl_ast_expr_id> represents an identifier.
9514 An C<isl_ast_expr_int> represents an integer value.
9516 Each type of expression has its own additional properties.
9518 #include <isl/ast.h>
9519 enum isl_ast_op_type isl_ast_expr_get_op_type(
9520 __isl_keep isl_ast_expr *expr);
9521 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
9522 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
9523 __isl_keep isl_ast_expr *expr, int pos);
9524 isl_stat isl_ast_expr_foreach_ast_op_type(
9525 __isl_keep isl_ast_expr *expr,
9526 isl_stat (*fn)(enum isl_ast_op_type type,
9527 void *user), void *user);
9528 isl_stat isl_ast_node_foreach_ast_op_type(
9529 __isl_keep isl_ast_node *node,
9530 isl_stat (*fn)(enum isl_ast_op_type type,
9531 void *user), void *user);
9533 C<isl_ast_expr_get_op_type> returns the type of the operation
9534 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
9535 arguments. C<isl_ast_expr_get_op_arg> returns the specified
9537 C<isl_ast_expr_foreach_ast_op_type> calls C<fn> for each distinct
9538 C<isl_ast_op_type> that appears in C<expr>.
9539 C<isl_ast_node_foreach_ast_op_type> does the same for each distinct
9540 C<isl_ast_op_type> that appears in C<node>.
9541 The operation type is one of the following.
9545 =item C<isl_ast_op_and>
9547 Logical I<and> of two arguments.
9548 Both arguments can be evaluated.
9550 =item C<isl_ast_op_and_then>
9552 Logical I<and> of two arguments.
9553 The second argument can only be evaluated if the first evaluates to true.
9555 =item C<isl_ast_op_or>
9557 Logical I<or> of two arguments.
9558 Both arguments can be evaluated.
9560 =item C<isl_ast_op_or_else>
9562 Logical I<or> of two arguments.
9563 The second argument can only be evaluated if the first evaluates to false.
9565 =item C<isl_ast_op_max>
9567 Maximum of two or more arguments.
9569 =item C<isl_ast_op_min>
9571 Minimum of two or more arguments.
9573 =item C<isl_ast_op_minus>
9577 =item C<isl_ast_op_add>
9579 Sum of two arguments.
9581 =item C<isl_ast_op_sub>
9583 Difference of two arguments.
9585 =item C<isl_ast_op_mul>
9587 Product of two arguments.
9589 =item C<isl_ast_op_div>
9591 Exact division. That is, the result is known to be an integer.
9593 =item C<isl_ast_op_fdiv_q>
9595 Result of integer division, rounded towards negative
9598 =item C<isl_ast_op_pdiv_q>
9600 Result of integer division, where dividend is known to be non-negative.
9602 =item C<isl_ast_op_pdiv_r>
9604 Remainder of integer division, where dividend is known to be non-negative.
9606 =item C<isl_ast_op_zdiv_r>
9608 Equal to zero iff the remainder on integer division is zero.
9610 =item C<isl_ast_op_cond>
9612 Conditional operator defined on three arguments.
9613 If the first argument evaluates to true, then the result
9614 is equal to the second argument. Otherwise, the result
9615 is equal to the third argument.
9616 The second and third argument may only be evaluated if
9617 the first argument evaluates to true and false, respectively.
9618 Corresponds to C<a ? b : c> in C.
9620 =item C<isl_ast_op_select>
9622 Conditional operator defined on three arguments.
9623 If the first argument evaluates to true, then the result
9624 is equal to the second argument. Otherwise, the result
9625 is equal to the third argument.
9626 The second and third argument may be evaluated independently
9627 of the value of the first argument.
9628 Corresponds to C<a * b + (1 - a) * c> in C.
9630 =item C<isl_ast_op_eq>
9634 =item C<isl_ast_op_le>
9636 Less than or equal relation.
9638 =item C<isl_ast_op_lt>
9642 =item C<isl_ast_op_ge>
9644 Greater than or equal relation.
9646 =item C<isl_ast_op_gt>
9648 Greater than relation.
9650 =item C<isl_ast_op_call>
9653 The number of arguments of the C<isl_ast_expr> is one more than
9654 the number of arguments in the function call, the first argument
9655 representing the function being called.
9657 =item C<isl_ast_op_access>
9660 The number of arguments of the C<isl_ast_expr> is one more than
9661 the number of index expressions in the array access, the first argument
9662 representing the array being accessed.
9664 =item C<isl_ast_op_member>
9667 This operation has two arguments, a structure and the name of
9668 the member of the structure being accessed.
9672 #include <isl/ast.h>
9673 __isl_give isl_id *isl_ast_expr_get_id(
9674 __isl_keep isl_ast_expr *expr);
9676 Return the identifier represented by the AST expression.
9678 #include <isl/ast.h>
9679 __isl_give isl_val *isl_ast_expr_get_val(
9680 __isl_keep isl_ast_expr *expr);
9682 Return the integer represented by the AST expression.
9684 =head3 Properties of ASTs
9686 #include <isl/ast.h>
9687 isl_bool isl_ast_expr_is_equal(
9688 __isl_keep isl_ast_expr *expr1,
9689 __isl_keep isl_ast_expr *expr2);
9691 Check if two C<isl_ast_expr>s are equal to each other.
9693 =head3 Manipulating and printing the AST
9695 AST nodes can be copied and freed using the following functions.
9697 #include <isl/ast.h>
9698 __isl_give isl_ast_node *isl_ast_node_copy(
9699 __isl_keep isl_ast_node *node);
9700 __isl_null isl_ast_node *isl_ast_node_free(
9701 __isl_take isl_ast_node *node);
9703 AST expressions can be copied and freed using the following functions.
9705 #include <isl/ast.h>
9706 __isl_give isl_ast_expr *isl_ast_expr_copy(
9707 __isl_keep isl_ast_expr *expr);
9708 __isl_null isl_ast_expr *isl_ast_expr_free(
9709 __isl_take isl_ast_expr *expr);
9711 New AST expressions can be created either directly or within
9712 the context of an C<isl_ast_build>.
9714 #include <isl/ast.h>
9715 __isl_give isl_ast_expr *isl_ast_expr_from_val(
9716 __isl_take isl_val *v);
9717 __isl_give isl_ast_expr *isl_ast_expr_from_id(
9718 __isl_take isl_id *id);
9719 __isl_give isl_ast_expr *isl_ast_expr_neg(
9720 __isl_take isl_ast_expr *expr);
9721 __isl_give isl_ast_expr *isl_ast_expr_address_of(
9722 __isl_take isl_ast_expr *expr);
9723 __isl_give isl_ast_expr *isl_ast_expr_add(
9724 __isl_take isl_ast_expr *expr1,
9725 __isl_take isl_ast_expr *expr2);
9726 __isl_give isl_ast_expr *isl_ast_expr_sub(
9727 __isl_take isl_ast_expr *expr1,
9728 __isl_take isl_ast_expr *expr2);
9729 __isl_give isl_ast_expr *isl_ast_expr_mul(
9730 __isl_take isl_ast_expr *expr1,
9731 __isl_take isl_ast_expr *expr2);
9732 __isl_give isl_ast_expr *isl_ast_expr_div(
9733 __isl_take isl_ast_expr *expr1,
9734 __isl_take isl_ast_expr *expr2);
9735 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
9736 __isl_take isl_ast_expr *expr1,
9737 __isl_take isl_ast_expr *expr2);
9738 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
9739 __isl_take isl_ast_expr *expr1,
9740 __isl_take isl_ast_expr *expr2);
9741 __isl_give isl_ast_expr *isl_ast_expr_and(
9742 __isl_take isl_ast_expr *expr1,
9743 __isl_take isl_ast_expr *expr2)
9744 __isl_give isl_ast_expr *isl_ast_expr_and_then(
9745 __isl_take isl_ast_expr *expr1,
9746 __isl_take isl_ast_expr *expr2)
9747 __isl_give isl_ast_expr *isl_ast_expr_or(
9748 __isl_take isl_ast_expr *expr1,
9749 __isl_take isl_ast_expr *expr2)
9750 __isl_give isl_ast_expr *isl_ast_expr_or_else(
9751 __isl_take isl_ast_expr *expr1,
9752 __isl_take isl_ast_expr *expr2)
9753 __isl_give isl_ast_expr *isl_ast_expr_eq(
9754 __isl_take isl_ast_expr *expr1,
9755 __isl_take isl_ast_expr *expr2);
9756 __isl_give isl_ast_expr *isl_ast_expr_le(
9757 __isl_take isl_ast_expr *expr1,
9758 __isl_take isl_ast_expr *expr2);
9759 __isl_give isl_ast_expr *isl_ast_expr_lt(
9760 __isl_take isl_ast_expr *expr1,
9761 __isl_take isl_ast_expr *expr2);
9762 __isl_give isl_ast_expr *isl_ast_expr_ge(
9763 __isl_take isl_ast_expr *expr1,
9764 __isl_take isl_ast_expr *expr2);
9765 __isl_give isl_ast_expr *isl_ast_expr_gt(
9766 __isl_take isl_ast_expr *expr1,
9767 __isl_take isl_ast_expr *expr2);
9768 __isl_give isl_ast_expr *isl_ast_expr_access(
9769 __isl_take isl_ast_expr *array,
9770 __isl_take isl_ast_expr_list *indices);
9771 __isl_give isl_ast_expr *isl_ast_expr_call(
9772 __isl_take isl_ast_expr *function,
9773 __isl_take isl_ast_expr_list *arguments);
9775 The function C<isl_ast_expr_address_of> can be applied to an
9776 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
9777 to represent the address of the C<isl_ast_expr_access>. The function
9778 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
9779 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
9781 #include <isl/ast_build.h>
9782 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
9783 __isl_keep isl_ast_build *build,
9784 __isl_take isl_set *set);
9785 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
9786 __isl_keep isl_ast_build *build,
9787 __isl_take isl_pw_aff *pa);
9788 __isl_give isl_ast_expr *
9789 isl_ast_build_access_from_pw_multi_aff(
9790 __isl_keep isl_ast_build *build,
9791 __isl_take isl_pw_multi_aff *pma);
9792 __isl_give isl_ast_expr *
9793 isl_ast_build_access_from_multi_pw_aff(
9794 __isl_keep isl_ast_build *build,
9795 __isl_take isl_multi_pw_aff *mpa);
9796 __isl_give isl_ast_expr *
9797 isl_ast_build_call_from_pw_multi_aff(
9798 __isl_keep isl_ast_build *build,
9799 __isl_take isl_pw_multi_aff *pma);
9800 __isl_give isl_ast_expr *
9801 isl_ast_build_call_from_multi_pw_aff(
9802 __isl_keep isl_ast_build *build,
9803 __isl_take isl_multi_pw_aff *mpa);
9806 the domains of C<pa>, C<mpa> and C<pma> should correspond
9807 to the schedule space of C<build>.
9808 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
9809 the function being called.
9810 If the accessed space is a nested relation, then it is taken
9811 to represent an access of the member specified by the range
9812 of this nested relation of the structure specified by the domain
9813 of the nested relation.
9815 The following functions can be used to modify an C<isl_ast_expr>.
9817 #include <isl/ast.h>
9818 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
9819 __isl_take isl_ast_expr *expr, int pos,
9820 __isl_take isl_ast_expr *arg);
9822 Replace the argument of C<expr> at position C<pos> by C<arg>.
9824 #include <isl/ast.h>
9825 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
9826 __isl_take isl_ast_expr *expr,
9827 __isl_take isl_id_to_ast_expr *id2expr);
9829 The function C<isl_ast_expr_substitute_ids> replaces the
9830 subexpressions of C<expr> of type C<isl_ast_expr_id>
9831 by the corresponding expression in C<id2expr>, if there is any.
9834 User specified data can be attached to an C<isl_ast_node> and obtained
9835 from the same C<isl_ast_node> using the following functions.
9837 #include <isl/ast.h>
9838 __isl_give isl_ast_node *isl_ast_node_set_annotation(
9839 __isl_take isl_ast_node *node,
9840 __isl_take isl_id *annotation);
9841 __isl_give isl_id *isl_ast_node_get_annotation(
9842 __isl_keep isl_ast_node *node);
9844 Basic printing can be performed using the following functions.
9846 #include <isl/ast.h>
9847 __isl_give isl_printer *isl_printer_print_ast_expr(
9848 __isl_take isl_printer *p,
9849 __isl_keep isl_ast_expr *expr);
9850 __isl_give isl_printer *isl_printer_print_ast_node(
9851 __isl_take isl_printer *p,
9852 __isl_keep isl_ast_node *node);
9853 __isl_give char *isl_ast_expr_to_str(
9854 __isl_keep isl_ast_expr *expr);
9855 __isl_give char *isl_ast_node_to_str(
9856 __isl_keep isl_ast_node *node);
9857 __isl_give char *isl_ast_expr_to_C_str(
9858 __isl_keep isl_ast_expr *expr);
9859 __isl_give char *isl_ast_node_to_C_str(
9860 __isl_keep isl_ast_node *node);
9862 The functions C<isl_ast_expr_to_C_str> and
9863 C<isl_ast_node_to_C_str> are convenience functions
9864 that return a string representation of the input in C format.
9866 More advanced printing can be performed using the following functions.
9868 #include <isl/ast.h>
9869 __isl_give isl_printer *isl_ast_op_type_set_print_name(
9870 __isl_take isl_printer *p,
9871 enum isl_ast_op_type type,
9872 __isl_keep const char *name);
9873 isl_stat isl_options_set_ast_print_macro_once(
9874 isl_ctx *ctx, int val);
9875 int isl_options_get_ast_print_macro_once(isl_ctx *ctx);
9876 __isl_give isl_printer *isl_ast_op_type_print_macro(
9877 enum isl_ast_op_type type,
9878 __isl_take isl_printer *p);
9879 __isl_give isl_printer *isl_ast_expr_print_macros(
9880 __isl_keep isl_ast_expr *expr,
9881 __isl_take isl_printer *p);
9882 __isl_give isl_printer *isl_ast_node_print_macros(
9883 __isl_keep isl_ast_node *node,
9884 __isl_take isl_printer *p);
9885 __isl_give isl_printer *isl_ast_node_print(
9886 __isl_keep isl_ast_node *node,
9887 __isl_take isl_printer *p,
9888 __isl_take isl_ast_print_options *options);
9889 __isl_give isl_printer *isl_ast_node_for_print(
9890 __isl_keep isl_ast_node *node,
9891 __isl_take isl_printer *p,
9892 __isl_take isl_ast_print_options *options);
9893 __isl_give isl_printer *isl_ast_node_if_print(
9894 __isl_keep isl_ast_node *node,
9895 __isl_take isl_printer *p,
9896 __isl_take isl_ast_print_options *options);
9898 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
9899 C<isl> may print out an AST that makes use of macros such
9900 as C<floord>, C<min> and C<max>.
9901 The names of these macros may be modified by a call
9902 to C<isl_ast_op_type_set_print_name>. The user-specified
9903 names are associated to the printer object.
9904 C<isl_ast_op_type_print_macro> prints out the macro
9905 corresponding to a specific C<isl_ast_op_type>.
9906 If the print-macro-once option is set, then a given macro definition
9907 is only printed once to any given printer object.
9908 C<isl_ast_expr_print_macros> scans the C<isl_ast_expr>
9909 for subexpressions where these macros would be used and prints
9910 out the required macro definitions.
9911 Essentially, C<isl_ast_expr_print_macros> calls
9912 C<isl_ast_expr_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
9913 as function argument.
9914 C<isl_ast_node_print_macros> does the same
9915 for expressions in its C<isl_ast_node> argument.
9916 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
9917 C<isl_ast_node_if_print> print an C<isl_ast_node>
9918 in C<ISL_FORMAT_C>, but allow for some extra control
9919 through an C<isl_ast_print_options> object.
9920 This object can be created using the following functions.
9922 #include <isl/ast.h>
9923 __isl_give isl_ast_print_options *
9924 isl_ast_print_options_alloc(isl_ctx *ctx);
9925 __isl_give isl_ast_print_options *
9926 isl_ast_print_options_copy(
9927 __isl_keep isl_ast_print_options *options);
9928 __isl_null isl_ast_print_options *
9929 isl_ast_print_options_free(
9930 __isl_take isl_ast_print_options *options);
9932 __isl_give isl_ast_print_options *
9933 isl_ast_print_options_set_print_user(
9934 __isl_take isl_ast_print_options *options,
9935 __isl_give isl_printer *(*print_user)(
9936 __isl_take isl_printer *p,
9937 __isl_take isl_ast_print_options *options,
9938 __isl_keep isl_ast_node *node, void *user),
9940 __isl_give isl_ast_print_options *
9941 isl_ast_print_options_set_print_for(
9942 __isl_take isl_ast_print_options *options,
9943 __isl_give isl_printer *(*print_for)(
9944 __isl_take isl_printer *p,
9945 __isl_take isl_ast_print_options *options,
9946 __isl_keep isl_ast_node *node, void *user),
9949 The callback set by C<isl_ast_print_options_set_print_user>
9950 is called whenever a node of type C<isl_ast_node_user> needs to
9952 The callback set by C<isl_ast_print_options_set_print_for>
9953 is called whenever a node of type C<isl_ast_node_for> needs to
9955 Note that C<isl_ast_node_for_print> will I<not> call the
9956 callback set by C<isl_ast_print_options_set_print_for> on the node
9957 on which C<isl_ast_node_for_print> is called, but only on nested
9958 nodes of type C<isl_ast_node_for>. It is therefore safe to
9959 call C<isl_ast_node_for_print> from within the callback set by
9960 C<isl_ast_print_options_set_print_for>.
9962 The following option determines the type to be used for iterators
9963 while printing the AST.
9965 isl_stat isl_options_set_ast_iterator_type(
9966 isl_ctx *ctx, const char *val);
9967 const char *isl_options_get_ast_iterator_type(
9970 The AST printer only prints body nodes as blocks if these
9971 blocks cannot be safely omitted.
9972 For example, a C<for> node with one body node will not be
9973 surrounded with braces in C<ISL_FORMAT_C>.
9974 A block will always be printed by setting the following option.
9976 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx,
9978 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
9982 #include <isl/ast_build.h>
9983 isl_stat isl_options_set_ast_build_atomic_upper_bound(
9984 isl_ctx *ctx, int val);
9985 int isl_options_get_ast_build_atomic_upper_bound(
9987 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
9989 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
9990 isl_stat isl_options_set_ast_build_detect_min_max(
9991 isl_ctx *ctx, int val);
9992 int isl_options_get_ast_build_detect_min_max(
9994 isl_stat isl_options_set_ast_build_exploit_nested_bounds(
9995 isl_ctx *ctx, int val);
9996 int isl_options_get_ast_build_exploit_nested_bounds(
9998 isl_stat isl_options_set_ast_build_group_coscheduled(
9999 isl_ctx *ctx, int val);
10000 int isl_options_get_ast_build_group_coscheduled(
10002 isl_stat isl_options_set_ast_build_scale_strides(
10003 isl_ctx *ctx, int val);
10004 int isl_options_get_ast_build_scale_strides(
10006 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx,
10008 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
10009 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx,
10011 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
10015 =item * ast_build_atomic_upper_bound
10017 Generate loop upper bounds that consist of the current loop iterator,
10018 an operator and an expression not involving the iterator.
10019 If this option is not set, then the current loop iterator may appear
10020 several times in the upper bound.
10021 For example, when this option is turned off, AST generation
10024 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
10028 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
10031 When the option is turned on, the following AST is generated
10033 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
10036 =item * ast_build_prefer_pdiv
10038 If this option is turned off, then the AST generation will
10039 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
10040 operators, but no C<isl_ast_op_pdiv_q> or
10041 C<isl_ast_op_pdiv_r> operators.
10042 If this option is turned on, then C<isl> will try to convert
10043 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
10044 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
10046 =item * ast_build_detect_min_max
10048 If this option is turned on, then C<isl> will try and detect
10049 min or max-expressions when building AST expressions from
10050 piecewise affine expressions.
10052 =item * ast_build_exploit_nested_bounds
10054 Simplify conditions based on bounds of nested for loops.
10055 In particular, remove conditions that are implied by the fact
10056 that one or more nested loops have at least one iteration,
10057 meaning that the upper bound is at least as large as the lower bound.
10058 For example, when this option is turned off, AST generation
10061 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
10067 for (int c0 = 0; c0 <= N; c0 += 1)
10068 for (int c1 = 0; c1 <= M; c1 += 1)
10071 When the option is turned on, the following AST is generated
10073 for (int c0 = 0; c0 <= N; c0 += 1)
10074 for (int c1 = 0; c1 <= M; c1 += 1)
10077 =item * ast_build_group_coscheduled
10079 If two domain elements are assigned the same schedule point, then
10080 they may be executed in any order and they may even appear in different
10081 loops. If this options is set, then the AST generator will make
10082 sure that coscheduled domain elements do not appear in separate parts
10083 of the AST. This is useful in case of nested AST generation
10084 if the outer AST generation is given only part of a schedule
10085 and the inner AST generation should handle the domains that are
10086 coscheduled by this initial part of the schedule together.
10087 For example if an AST is generated for a schedule
10089 { A[i] -> [0]; B[i] -> [0] }
10091 then the C<isl_ast_build_set_create_leaf> callback described
10092 below may get called twice, once for each domain.
10093 Setting this option ensures that the callback is only called once
10094 on both domains together.
10096 =item * ast_build_separation_bounds
10098 This option specifies which bounds to use during separation.
10099 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
10100 then all (possibly implicit) bounds on the current dimension will
10101 be used during separation.
10102 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
10103 then only those bounds that are explicitly available will
10104 be used during separation.
10106 =item * ast_build_scale_strides
10108 This option specifies whether the AST generator is allowed
10109 to scale down iterators of strided loops.
10111 =item * ast_build_allow_else
10113 This option specifies whether the AST generator is allowed
10114 to construct if statements with else branches.
10116 =item * ast_build_allow_or
10118 This option specifies whether the AST generator is allowed
10119 to construct if conditions with disjunctions.
10123 =head3 AST Generation Options (Schedule Tree)
10125 In case of AST construction from a schedule tree, the options
10126 that control how an AST is created from the individual schedule
10127 dimensions are stored in the band nodes of the tree
10128 (see L</"Schedule Trees">).
10130 In particular, a schedule dimension can be handled in four
10131 different ways, atomic, separate, unroll or the default.
10132 This loop AST generation type can be set using
10133 C<isl_schedule_node_band_member_set_ast_loop_type>.
10135 the first three can be selected by including a one-dimensional
10136 element with as value the position of the schedule dimension
10137 within the band and as name one of C<atomic>, C<separate>
10138 or C<unroll> in the options
10139 set by C<isl_schedule_node_band_set_ast_build_options>.
10140 Only one of these three may be specified for
10141 any given schedule dimension within a band node.
10142 If none of these is specified, then the default
10143 is used. The meaning of the options is as follows.
10149 When this option is specified, the AST generator will make
10150 sure that a given domains space only appears in a single
10151 loop at the specified level.
10153 For example, for the schedule tree
10155 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10157 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10158 options: "{ atomic[x] }"
10160 the following AST will be generated
10162 for (int c0 = 0; c0 <= 10; c0 += 1) {
10169 On the other hand, for the schedule tree
10171 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10173 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10174 options: "{ separate[x] }"
10176 the following AST will be generated
10180 for (int c0 = 1; c0 <= 9; c0 += 1) {
10187 If neither C<atomic> nor C<separate> is specified, then the AST generator
10188 may produce either of these two results or some intermediate form.
10192 When this option is specified, the AST generator will
10193 split the domain of the specified schedule dimension
10194 into pieces with a fixed set of statements for which
10195 instances need to be executed by the iterations in
10196 the schedule domain part. This option tends to avoid
10197 the generation of guards inside the corresponding loops.
10198 See also the C<atomic> option.
10202 When this option is specified, the AST generator will
10203 I<completely> unroll the corresponding schedule dimension.
10204 It is the responsibility of the user to ensure that such
10205 unrolling is possible.
10206 To obtain a partial unrolling, the user should apply an additional
10207 strip-mining to the schedule and fully unroll the inner schedule
10212 The C<isolate> option is a bit more involved. It allows the user
10213 to isolate a range of schedule dimension values from smaller and
10214 greater values. Additionally, the user may specify a different
10215 atomic/separate/unroll choice for the isolated part and the remaining
10216 parts. The typical use case of the C<isolate> option is to isolate
10217 full tiles from partial tiles.
10218 The part that needs to be isolated may depend on outer schedule dimensions.
10219 The option therefore needs to be able to reference those outer schedule
10220 dimensions. In particular, the space of the C<isolate> option is that
10221 of a wrapped map with as domain the flat product of all outer band nodes
10222 and as range the space of the current band node.
10223 The atomic/separate/unroll choice for the isolated part is determined
10224 by an option that lives in an unnamed wrapped space with as domain
10225 a zero-dimensional C<isolate> space and as range the regular
10226 C<atomic>, C<separate> or C<unroll> space.
10227 This option may also be set directly using
10228 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
10229 The atomic/separate/unroll choice for the remaining part is determined
10230 by the regular C<atomic>, C<separate> or C<unroll> option.
10231 Since the C<isolate> option references outer schedule dimensions,
10232 its use in a band node causes any tree containing the node
10233 to be considered anchored.
10235 As an example, consider the isolation of full tiles from partial tiles
10236 in a tiling of a triangular domain. The original schedule is as follows.
10238 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10240 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10241 { A[i,j] -> [floor(j/10)] }, \
10242 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10246 for (int c0 = 0; c0 <= 10; c0 += 1)
10247 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10248 for (int c2 = 10 * c0;
10249 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10250 for (int c3 = 10 * c1;
10251 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10254 Isolating the full tiles, we have the following input
10256 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10258 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10259 { A[i,j] -> [floor(j/10)] }, \
10260 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10261 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10262 10a+9+10b+9 <= 100 }"
10267 for (int c0 = 0; c0 <= 8; c0 += 1) {
10268 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10269 for (int c2 = 10 * c0;
10270 c2 <= 10 * c0 + 9; c2 += 1)
10271 for (int c3 = 10 * c1;
10272 c3 <= 10 * c1 + 9; c3 += 1)
10274 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10275 for (int c2 = 10 * c0;
10276 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10277 for (int c3 = 10 * c1;
10278 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10281 for (int c0 = 9; c0 <= 10; c0 += 1)
10282 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10283 for (int c2 = 10 * c0;
10284 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10285 for (int c3 = 10 * c1;
10286 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10290 We may then additionally unroll the innermost loop of the isolated part
10292 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10294 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10295 { A[i,j] -> [floor(j/10)] }, \
10296 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10297 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10298 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
10303 for (int c0 = 0; c0 <= 8; c0 += 1) {
10304 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10305 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
10307 A(c2, 10 * c1 + 1);
10308 A(c2, 10 * c1 + 2);
10309 A(c2, 10 * c1 + 3);
10310 A(c2, 10 * c1 + 4);
10311 A(c2, 10 * c1 + 5);
10312 A(c2, 10 * c1 + 6);
10313 A(c2, 10 * c1 + 7);
10314 A(c2, 10 * c1 + 8);
10315 A(c2, 10 * c1 + 9);
10317 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10318 for (int c2 = 10 * c0;
10319 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10320 for (int c3 = 10 * c1;
10321 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10324 for (int c0 = 9; c0 <= 10; c0 += 1)
10325 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10326 for (int c2 = 10 * c0;
10327 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10328 for (int c3 = 10 * c1;
10329 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10334 =head3 AST Generation Options (Schedule Map)
10336 In case of AST construction using
10337 C<isl_ast_build_node_from_schedule_map>, the options
10338 that control how an AST is created from the individual schedule
10339 dimensions are stored in the C<isl_ast_build>.
10340 They can be set using the following function.
10342 #include <isl/ast_build.h>
10343 __isl_give isl_ast_build *
10344 isl_ast_build_set_options(
10345 __isl_take isl_ast_build *control,
10346 __isl_take isl_union_map *options);
10348 The options are encoded in an C<isl_union_map>.
10349 The domain of this union relation refers to the schedule domain,
10350 i.e., the range of the schedule passed
10351 to C<isl_ast_build_node_from_schedule_map>.
10352 In the case of nested AST generation (see L</"Nested AST Generation">),
10353 the domain of C<options> should refer to the extra piece of the schedule.
10354 That is, it should be equal to the range of the wrapped relation in the
10355 range of the schedule.
10356 The range of the options can consist of elements in one or more spaces,
10357 the names of which determine the effect of the option.
10358 The values of the range typically also refer to the schedule dimension
10359 to which the option applies. In case of nested AST generation
10360 (see L</"Nested AST Generation">), these values refer to the position
10361 of the schedule dimension within the innermost AST generation.
10362 The constraints on the domain elements of
10363 the option should only refer to this dimension and earlier dimensions.
10364 We consider the following spaces.
10368 =item C<separation_class>
10370 B<This option has been deprecated. Use the isolate option on
10371 schedule trees instead.>
10373 This space is a wrapped relation between two one dimensional spaces.
10374 The input space represents the schedule dimension to which the option
10375 applies and the output space represents the separation class.
10376 While constructing a loop corresponding to the specified schedule
10377 dimension(s), the AST generator will try to generate separate loops
10378 for domain elements that are assigned different classes.
10379 If only some of the elements are assigned a class, then those elements
10380 that are not assigned any class will be treated as belonging to a class
10381 that is separate from the explicitly assigned classes.
10382 The typical use case for this option is to separate full tiles from
10384 The other options, described below, are applied after the separation
10387 As an example, consider the separation into full and partial tiles
10388 of a tiling of a triangular domain.
10389 Take, for example, the domain
10391 { A[i,j] : 0 <= i,j and i + j <= 100 }
10393 and a tiling into tiles of 10 by 10. The input to the AST generator
10394 is then the schedule
10396 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
10399 Without any options, the following AST is generated
10401 for (int c0 = 0; c0 <= 10; c0 += 1)
10402 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10403 for (int c2 = 10 * c0;
10404 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10406 for (int c3 = 10 * c1;
10407 c3 <= min(10 * c1 + 9, -c2 + 100);
10411 Separation into full and partial tiles can be obtained by assigning
10412 a class, say C<0>, to the full tiles. The full tiles are represented by those
10413 values of the first and second schedule dimensions for which there are
10414 values of the third and fourth dimensions to cover an entire tile.
10415 That is, we need to specify the following option
10417 { [a,b,c,d] -> separation_class[[0]->[0]] :
10418 exists b': 0 <= 10a,10b' and
10419 10a+9+10b'+9 <= 100;
10420 [a,b,c,d] -> separation_class[[1]->[0]] :
10421 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
10423 which simplifies to
10425 { [a, b, c, d] -> separation_class[[1] -> [0]] :
10426 a >= 0 and b >= 0 and b <= 8 - a;
10427 [a, b, c, d] -> separation_class[[0] -> [0]] :
10428 a >= 0 and a <= 8 }
10430 With this option, the generated AST is as follows
10433 for (int c0 = 0; c0 <= 8; c0 += 1) {
10434 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10435 for (int c2 = 10 * c0;
10436 c2 <= 10 * c0 + 9; c2 += 1)
10437 for (int c3 = 10 * c1;
10438 c3 <= 10 * c1 + 9; c3 += 1)
10440 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10441 for (int c2 = 10 * c0;
10442 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10444 for (int c3 = 10 * c1;
10445 c3 <= min(-c2 + 100, 10 * c1 + 9);
10449 for (int c0 = 9; c0 <= 10; c0 += 1)
10450 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10451 for (int c2 = 10 * c0;
10452 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10454 for (int c3 = 10 * c1;
10455 c3 <= min(10 * c1 + 9, -c2 + 100);
10462 This is a single-dimensional space representing the schedule dimension(s)
10463 to which ``separation'' should be applied. Separation tries to split
10464 a loop into several pieces if this can avoid the generation of guards
10466 See also the C<atomic> option.
10470 This is a single-dimensional space representing the schedule dimension(s)
10471 for which the domains should be considered ``atomic''. That is, the
10472 AST generator will make sure that any given domain space will only appear
10473 in a single loop at the specified level.
10475 Consider the following schedule
10477 { a[i] -> [i] : 0 <= i < 10;
10478 b[i] -> [i+1] : 0 <= i < 10 }
10480 If the following option is specified
10482 { [i] -> separate[x] }
10484 then the following AST will be generated
10488 for (int c0 = 1; c0 <= 9; c0 += 1) {
10495 If, on the other hand, the following option is specified
10497 { [i] -> atomic[x] }
10499 then the following AST will be generated
10501 for (int c0 = 0; c0 <= 10; c0 += 1) {
10508 If neither C<atomic> nor C<separate> is specified, then the AST generator
10509 may produce either of these two results or some intermediate form.
10513 This is a single-dimensional space representing the schedule dimension(s)
10514 that should be I<completely> unrolled.
10515 To obtain a partial unrolling, the user should apply an additional
10516 strip-mining to the schedule and fully unroll the inner loop.
10520 =head3 Fine-grained Control over AST Generation
10522 Besides specifying the constraints on the parameters,
10523 an C<isl_ast_build> object can be used to control
10524 various aspects of the AST generation process.
10525 In case of AST construction using
10526 C<isl_ast_build_node_from_schedule_map>,
10527 the most prominent way of control is through ``options'',
10528 as explained above.
10530 Additional control is available through the following functions.
10532 #include <isl/ast_build.h>
10533 __isl_give isl_ast_build *
10534 isl_ast_build_set_iterators(
10535 __isl_take isl_ast_build *control,
10536 __isl_take isl_id_list *iterators);
10538 The function C<isl_ast_build_set_iterators> allows the user to
10539 specify a list of iterator C<isl_id>s to be used as iterators.
10540 If the input schedule is injective, then
10541 the number of elements in this list should be as large as the dimension
10542 of the schedule space, but no direct correspondence should be assumed
10543 between dimensions and elements.
10544 If the input schedule is not injective, then an additional number
10545 of C<isl_id>s equal to the largest dimension of the input domains
10547 If the number of provided C<isl_id>s is insufficient, then additional
10548 names are automatically generated.
10550 #include <isl/ast_build.h>
10551 __isl_give isl_ast_build *
10552 isl_ast_build_set_create_leaf(
10553 __isl_take isl_ast_build *control,
10554 __isl_give isl_ast_node *(*fn)(
10555 __isl_take isl_ast_build *build,
10556 void *user), void *user);
10559 C<isl_ast_build_set_create_leaf> function allows for the
10560 specification of a callback that should be called whenever the AST
10561 generator arrives at an element of the schedule domain.
10562 The callback should return an AST node that should be inserted
10563 at the corresponding position of the AST. The default action (when
10564 the callback is not set) is to continue generating parts of the AST to scan
10565 all the domain elements associated to the schedule domain element
10566 and to insert user nodes, ``calling'' the domain element, for each of them.
10567 The C<build> argument contains the current state of the C<isl_ast_build>.
10568 To ease nested AST generation (see L</"Nested AST Generation">),
10569 all control information that is
10570 specific to the current AST generation such as the options and
10571 the callbacks has been removed from this C<isl_ast_build>.
10572 The callback would typically return the result of a nested
10573 AST generation or a
10574 user defined node created using the following function.
10576 #include <isl/ast.h>
10577 __isl_give isl_ast_node *isl_ast_node_alloc_user(
10578 __isl_take isl_ast_expr *expr);
10580 #include <isl/ast_build.h>
10581 __isl_give isl_ast_build *
10582 isl_ast_build_set_at_each_domain(
10583 __isl_take isl_ast_build *build,
10584 __isl_give isl_ast_node *(*fn)(
10585 __isl_take isl_ast_node *node,
10586 __isl_keep isl_ast_build *build,
10587 void *user), void *user);
10588 __isl_give isl_ast_build *
10589 isl_ast_build_set_before_each_for(
10590 __isl_take isl_ast_build *build,
10591 __isl_give isl_id *(*fn)(
10592 __isl_keep isl_ast_build *build,
10593 void *user), void *user);
10594 __isl_give isl_ast_build *
10595 isl_ast_build_set_after_each_for(
10596 __isl_take isl_ast_build *build,
10597 __isl_give isl_ast_node *(*fn)(
10598 __isl_take isl_ast_node *node,
10599 __isl_keep isl_ast_build *build,
10600 void *user), void *user);
10601 __isl_give isl_ast_build *
10602 isl_ast_build_set_before_each_mark(
10603 __isl_take isl_ast_build *build,
10604 isl_stat (*fn)(__isl_keep isl_id *mark,
10605 __isl_keep isl_ast_build *build,
10606 void *user), void *user);
10607 __isl_give isl_ast_build *
10608 isl_ast_build_set_after_each_mark(
10609 __isl_take isl_ast_build *build,
10610 __isl_give isl_ast_node *(*fn)(
10611 __isl_take isl_ast_node *node,
10612 __isl_keep isl_ast_build *build,
10613 void *user), void *user);
10615 The callback set by C<isl_ast_build_set_at_each_domain> will
10616 be called for each domain AST node.
10617 The callbacks set by C<isl_ast_build_set_before_each_for>
10618 and C<isl_ast_build_set_after_each_for> will be called
10619 for each for AST node. The first will be called in depth-first
10620 pre-order, while the second will be called in depth-first post-order.
10621 Since C<isl_ast_build_set_before_each_for> is called before the for
10622 node is actually constructed, it is only passed an C<isl_ast_build>.
10623 The returned C<isl_id> will be added as an annotation (using
10624 C<isl_ast_node_set_annotation>) to the constructed for node.
10625 In particular, if the user has also specified an C<after_each_for>
10626 callback, then the annotation can be retrieved from the node passed to
10627 that callback using C<isl_ast_node_get_annotation>.
10628 The callbacks set by C<isl_ast_build_set_before_each_mark>
10629 and C<isl_ast_build_set_after_each_mark> will be called for each
10630 mark AST node that is created, i.e., for each mark schedule node
10631 in the input schedule tree. The first will be called in depth-first
10632 pre-order, while the second will be called in depth-first post-order.
10633 Since the callback set by C<isl_ast_build_set_before_each_mark>
10634 is called before the mark AST node is actually constructed, it is passed
10635 the identifier of the mark node.
10636 All callbacks should C<NULL> (or -1) on failure.
10637 The given C<isl_ast_build> can be used to create new
10638 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
10639 or C<isl_ast_build_call_from_pw_multi_aff>.
10641 =head3 Nested AST Generation
10643 C<isl> allows the user to create an AST within the context
10644 of another AST. These nested ASTs are created using the
10645 same C<isl_ast_build_node_from_schedule_map> function that is used to create
10646 the outer AST. The C<build> argument should be an C<isl_ast_build>
10647 passed to a callback set by
10648 C<isl_ast_build_set_create_leaf>.
10649 The space of the range of the C<schedule> argument should refer
10650 to this build. In particular, the space should be a wrapped
10651 relation and the domain of this wrapped relation should be the
10652 same as that of the range of the schedule returned by
10653 C<isl_ast_build_get_schedule> below.
10654 In practice, the new schedule is typically
10655 created by calling C<isl_union_map_range_product> on the old schedule
10656 and some extra piece of the schedule.
10657 The space of the schedule domain is also available from
10658 the C<isl_ast_build>.
10660 #include <isl/ast_build.h>
10661 __isl_give isl_union_map *isl_ast_build_get_schedule(
10662 __isl_keep isl_ast_build *build);
10663 __isl_give isl_space *isl_ast_build_get_schedule_space(
10664 __isl_keep isl_ast_build *build);
10665 __isl_give isl_ast_build *isl_ast_build_restrict(
10666 __isl_take isl_ast_build *build,
10667 __isl_take isl_set *set);
10669 The C<isl_ast_build_get_schedule> function returns a (partial)
10670 schedule for the domains elements for which part of the AST still needs to
10671 be generated in the current build.
10672 In particular, the domain elements are mapped to those iterations of the loops
10673 enclosing the current point of the AST generation inside which
10674 the domain elements are executed.
10675 No direct correspondence between
10676 the input schedule and this schedule should be assumed.
10677 The space obtained from C<isl_ast_build_get_schedule_space> can be used
10678 to create a set for C<isl_ast_build_restrict> to intersect
10679 with the current build. In particular, the set passed to
10680 C<isl_ast_build_restrict> can have additional parameters.
10681 The ids of the set dimensions in the space returned by
10682 C<isl_ast_build_get_schedule_space> correspond to the
10683 iterators of the already generated loops.
10684 The user should not rely on the ids of the output dimensions
10685 of the relations in the union relation returned by
10686 C<isl_ast_build_get_schedule> having any particular value.
10688 =head1 Applications
10690 Although C<isl> is mainly meant to be used as a library,
10691 it also contains some basic applications that use some
10692 of the functionality of C<isl>.
10693 For applications that take one or more polytopes or polyhedra
10694 as input, this input may be specified in either the L<isl format>
10695 or the L<PolyLib format>.
10697 =head2 C<isl_polyhedron_sample>
10699 C<isl_polyhedron_sample> takes a polyhedron as input and prints
10700 an integer element of the polyhedron, if there is any.
10701 The first column in the output is the denominator and is always
10702 equal to 1. If the polyhedron contains no integer points,
10703 then a vector of length zero is printed.
10707 C<isl_pip> takes the same input as the C<example> program
10708 from the C<piplib> distribution, i.e., a set of constraints
10709 on the parameters, a line containing only -1 and finally a set
10710 of constraints on a parametric polyhedron.
10711 The coefficients of the parameters appear in the last columns
10712 (but before the final constant column).
10713 The output is the lexicographic minimum of the parametric polyhedron.
10714 As C<isl> currently does not have its own output format, the output
10715 is just a dump of the internal state.
10717 =head2 C<isl_polyhedron_minimize>
10719 C<isl_polyhedron_minimize> computes the minimum of some linear
10720 or affine objective function over the integer points in a polyhedron.
10721 If an affine objective function
10722 is given, then the constant should appear in the last column.
10724 =head2 C<isl_polytope_scan>
10726 Given a polytope, C<isl_polytope_scan> prints
10727 all integer points in the polytope.
10729 =head2 C<isl_codegen>
10731 Given either a schedule tree or a sequence consisting of
10732 a schedule map, a context set and an options relation,
10733 C<isl_codegen> prints out an AST that scans the domain elements
10734 of the schedule in the order of their image(s) taking into account
10735 the constraints in the context set.
10737 =head2 C<isl_schedule>
10739 Given an C<isl_schedule_constraints> object as input,
10740 C<isl_schedule> prints out a schedule that satisfies the given