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);
771 __isl_give isl_val *isl_val_div_ui(__isl_take isl_val *v1,
774 On integer values, we additionally have the following operations.
777 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
778 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
779 __isl_take isl_val *v2);
780 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
781 __isl_take isl_val *v2);
782 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
783 __isl_take isl_val *v2, __isl_give isl_val **x,
784 __isl_give isl_val **y);
786 The function C<isl_val_gcdext> returns the greatest common divisor g
787 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
788 that C<*x> * C<v1> + C<*y> * C<v2> = g.
790 =head3 GMP specific functions
792 These functions are only available if C<isl> has been compiled with C<GMP>
795 Specific integer and rational values can be created from C<GMP> values using
796 the following functions.
798 #include <isl/val_gmp.h>
799 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
801 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
802 const mpz_t n, const mpz_t d);
804 The numerator and denominator of a rational value can be extracted as
805 C<GMP> values using the following functions.
807 #include <isl/val_gmp.h>
808 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
809 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
811 =head2 Sets and Relations
813 C<isl> uses six types of objects for representing sets and relations,
814 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
815 C<isl_union_set> and C<isl_union_map>.
816 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
817 can be described as a conjunction of affine constraints, while
818 C<isl_set> and C<isl_map> represent unions of
819 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
820 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
821 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
822 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
823 where spaces are considered different if they have a different number
824 of dimensions and/or different names (see L<"Spaces">).
825 The difference between sets and relations (maps) is that sets have
826 one set of variables, while relations have two sets of variables,
827 input variables and output variables.
829 =head2 Error Handling
831 C<isl> supports different ways to react in case a runtime error is triggered.
832 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
833 with two maps that have incompatible spaces. There are three possible ways
834 to react on error: to warn, to continue or to abort.
836 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
837 the last error in the corresponding C<isl_ctx> and the function in which the
838 error was triggered returns a value indicating that some error has
839 occurred. In case of functions returning a pointer, this value is
840 C<NULL>. In case of functions returning an C<isl_bool> or an
841 C<isl_stat>, this valus is C<isl_bool_error> or C<isl_stat_error>.
842 An error does not corrupt internal state,
843 such that isl can continue to be used. C<isl> also provides functions to
844 read the last error and to reset the memory that stores the last error. The
845 last error is only stored for information purposes. Its presence does not
846 change the behavior of C<isl>. Hence, resetting an error is not required to
847 continue to use isl, but only to observe new errors.
850 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
851 void isl_ctx_reset_error(isl_ctx *ctx);
853 Another option is to continue on error. This is similar to warn on error mode,
854 except that C<isl> does not print any warning. This allows a program to
855 implement its own error reporting.
857 The last option is to directly abort the execution of the program from within
858 the isl library. This makes it obviously impossible to recover from an error,
859 but it allows to directly spot the error location. By aborting on error,
860 debuggers break at the location the error occurred and can provide a stack
861 trace. Other tools that automatically provide stack traces on abort or that do
862 not want to continue execution after an error was triggered may also prefer to
865 The on error behavior of isl can be specified by calling
866 C<isl_options_set_on_error> or by setting the command line option
867 C<--isl-on-error>. Valid arguments for the function call are
868 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
869 choices for the command line option are C<warn>, C<continue> and C<abort>.
870 It is also possible to query the current error mode.
872 #include <isl/options.h>
873 isl_stat isl_options_set_on_error(isl_ctx *ctx, int val);
874 int isl_options_get_on_error(isl_ctx *ctx);
878 Identifiers are used to identify both individual dimensions
879 and tuples of dimensions. They consist of an optional name and an optional
880 user pointer. The name and the user pointer cannot both be C<NULL>, however.
881 Identifiers with the same name but different pointer values
882 are considered to be distinct.
883 Similarly, identifiers with different names but the same pointer value
884 are also considered to be distinct.
885 Equal identifiers are represented using the same object.
886 Pairs of identifiers can therefore be tested for equality using the
888 Identifiers can be constructed, copied, freed, inspected and printed
889 using the following functions.
892 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
893 __isl_keep const char *name, void *user);
894 __isl_give isl_id *isl_id_set_free_user(
895 __isl_take isl_id *id,
896 void (*free_user)(void *user));
897 __isl_give isl_id *isl_id_copy(isl_id *id);
898 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
900 void *isl_id_get_user(__isl_keep isl_id *id);
901 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
903 __isl_give isl_printer *isl_printer_print_id(
904 __isl_take isl_printer *p, __isl_keep isl_id *id);
906 The callback set by C<isl_id_set_free_user> is called on the user
907 pointer when the last reference to the C<isl_id> is freed.
908 Note that C<isl_id_get_name> returns a pointer to some internal
909 data structure, so the result can only be used while the
910 corresponding C<isl_id> is alive.
914 Whenever a new set, relation or similar object is created from scratch,
915 the space in which it lives needs to be specified using an C<isl_space>.
916 Each space involves zero or more parameters and zero, one or two
917 tuples of set or input/output dimensions. The parameters and dimensions
918 are identified by an C<isl_dim_type> and a position.
919 The type C<isl_dim_param> refers to parameters,
920 the type C<isl_dim_set> refers to set dimensions (for spaces
921 with a single tuple of dimensions) and the types C<isl_dim_in>
922 and C<isl_dim_out> refer to input and output dimensions
923 (for spaces with two tuples of dimensions).
924 Local spaces (see L</"Local Spaces">) also contain dimensions
925 of type C<isl_dim_div>.
926 Note that parameters are only identified by their position within
927 a given object. Across different objects, parameters are (usually)
928 identified by their names or identifiers. Only unnamed parameters
929 are identified by their positions across objects. The use of unnamed
930 parameters is discouraged.
932 #include <isl/space.h>
933 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
934 unsigned nparam, unsigned n_in, unsigned n_out);
935 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
937 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
938 unsigned nparam, unsigned dim);
939 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
940 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
942 The space used for creating a parameter domain
943 needs to be created using C<isl_space_params_alloc>.
944 For other sets, the space
945 needs to be created using C<isl_space_set_alloc>, while
946 for a relation, the space
947 needs to be created using C<isl_space_alloc>.
949 To check whether a given space is that of a set or a map
950 or whether it is a parameter space, use these functions:
952 #include <isl/space.h>
953 isl_bool isl_space_is_params(__isl_keep isl_space *space);
954 isl_bool isl_space_is_set(__isl_keep isl_space *space);
955 isl_bool isl_space_is_map(__isl_keep isl_space *space);
957 Spaces can be compared using the following functions:
959 #include <isl/space.h>
960 isl_bool isl_space_is_equal(__isl_keep isl_space *space1,
961 __isl_keep isl_space *space2);
962 isl_bool isl_space_has_equal_params(
963 __isl_keep isl_space *space1,
964 __isl_keep isl_space *space2);
965 isl_bool isl_space_has_equal_tuples(
966 __isl_keep isl_space *space1,
967 __isl_keep isl_space *space2);
968 isl_bool isl_space_is_domain(__isl_keep isl_space *space1,
969 __isl_keep isl_space *space2);
970 isl_bool isl_space_is_range(__isl_keep isl_space *space1,
971 __isl_keep isl_space *space2);
972 isl_bool isl_space_tuple_is_equal(
973 __isl_keep isl_space *space1,
974 enum isl_dim_type type1,
975 __isl_keep isl_space *space2,
976 enum isl_dim_type type2);
978 C<isl_space_is_domain> checks whether the first argument is equal
979 to the domain of the second argument. This requires in particular that
980 the first argument is a set space and that the second argument
981 is a map space. C<isl_space_tuple_is_equal> checks whether the given
982 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
983 spaces are the same. That is, it checks if they have the same
984 identifier (if any), the same dimension and the same internal structure
987 C<isl_space_has_equal_params> checks whether two spaces
988 have the same parameters in the same order.
989 C<isl_space_has_equal_tuples> check whether two spaces have
990 the same tuples. In contrast to C<isl_space_is_equal> below,
991 it does not check the
992 parameters. This is useful because many C<isl> functions align the
993 parameters before they perform their operations, such that equivalence
995 C<isl_space_is_equal> checks whether two spaces are identical,
996 meaning that they have the same parameters and the same tuples.
997 That is, it checks whether both C<isl_space_has_equal_params> and
998 C<isl_space_has_equal_tuples> hold.
1000 It is often useful to create objects that live in the
1001 same space as some other object. This can be accomplished
1002 by creating the new objects
1003 (see L</"Creating New Sets and Relations"> or
1004 L</"Functions">) based on the space
1005 of the original object.
1007 #include <isl/set.h>
1008 __isl_give isl_space *isl_basic_set_get_space(
1009 __isl_keep isl_basic_set *bset);
1010 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
1012 #include <isl/union_set.h>
1013 __isl_give isl_space *isl_union_set_get_space(
1014 __isl_keep isl_union_set *uset);
1016 #include <isl/map.h>
1017 __isl_give isl_space *isl_basic_map_get_space(
1018 __isl_keep isl_basic_map *bmap);
1019 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
1021 #include <isl/union_map.h>
1022 __isl_give isl_space *isl_union_map_get_space(
1023 __isl_keep isl_union_map *umap);
1025 #include <isl/constraint.h>
1026 __isl_give isl_space *isl_constraint_get_space(
1027 __isl_keep isl_constraint *constraint);
1029 #include <isl/polynomial.h>
1030 __isl_give isl_space *isl_qpolynomial_get_domain_space(
1031 __isl_keep isl_qpolynomial *qp);
1032 __isl_give isl_space *isl_qpolynomial_get_space(
1033 __isl_keep isl_qpolynomial *qp);
1034 __isl_give isl_space *
1035 isl_qpolynomial_fold_get_domain_space(
1036 __isl_keep isl_qpolynomial_fold *fold);
1037 __isl_give isl_space *isl_qpolynomial_fold_get_space(
1038 __isl_keep isl_qpolynomial_fold *fold);
1039 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
1040 __isl_keep isl_pw_qpolynomial *pwqp);
1041 __isl_give isl_space *isl_pw_qpolynomial_get_space(
1042 __isl_keep isl_pw_qpolynomial *pwqp);
1043 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
1044 __isl_keep isl_pw_qpolynomial_fold *pwf);
1045 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
1046 __isl_keep isl_pw_qpolynomial_fold *pwf);
1047 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
1048 __isl_keep isl_union_pw_qpolynomial *upwqp);
1049 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
1050 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1052 #include <isl/val.h>
1053 __isl_give isl_space *isl_multi_val_get_space(
1054 __isl_keep isl_multi_val *mv);
1056 #include <isl/aff.h>
1057 __isl_give isl_space *isl_aff_get_domain_space(
1058 __isl_keep isl_aff *aff);
1059 __isl_give isl_space *isl_aff_get_space(
1060 __isl_keep isl_aff *aff);
1061 __isl_give isl_space *isl_pw_aff_get_domain_space(
1062 __isl_keep isl_pw_aff *pwaff);
1063 __isl_give isl_space *isl_pw_aff_get_space(
1064 __isl_keep isl_pw_aff *pwaff);
1065 __isl_give isl_space *isl_multi_aff_get_domain_space(
1066 __isl_keep isl_multi_aff *maff);
1067 __isl_give isl_space *isl_multi_aff_get_space(
1068 __isl_keep isl_multi_aff *maff);
1069 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
1070 __isl_keep isl_pw_multi_aff *pma);
1071 __isl_give isl_space *isl_pw_multi_aff_get_space(
1072 __isl_keep isl_pw_multi_aff *pma);
1073 __isl_give isl_space *isl_union_pw_aff_get_space(
1074 __isl_keep isl_union_pw_aff *upa);
1075 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
1076 __isl_keep isl_union_pw_multi_aff *upma);
1077 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
1078 __isl_keep isl_multi_pw_aff *mpa);
1079 __isl_give isl_space *isl_multi_pw_aff_get_space(
1080 __isl_keep isl_multi_pw_aff *mpa);
1081 __isl_give isl_space *
1082 isl_multi_union_pw_aff_get_domain_space(
1083 __isl_keep isl_multi_union_pw_aff *mupa);
1084 __isl_give isl_space *
1085 isl_multi_union_pw_aff_get_space(
1086 __isl_keep isl_multi_union_pw_aff *mupa);
1088 #include <isl/point.h>
1089 __isl_give isl_space *isl_point_get_space(
1090 __isl_keep isl_point *pnt);
1092 The number of dimensions of a given type of space
1093 may be read off from a space or an object that lives
1094 in a space using the following functions.
1095 In case of C<isl_space_dim>, type may be
1096 C<isl_dim_param>, C<isl_dim_in> (only for relations),
1097 C<isl_dim_out> (only for relations), C<isl_dim_set>
1098 (only for sets) or C<isl_dim_all>.
1100 #include <isl/space.h>
1101 unsigned isl_space_dim(__isl_keep isl_space *space,
1102 enum isl_dim_type type);
1104 #include <isl/local_space.h>
1105 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1106 enum isl_dim_type type);
1108 #include <isl/set.h>
1109 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1110 enum isl_dim_type type);
1111 unsigned isl_set_dim(__isl_keep isl_set *set,
1112 enum isl_dim_type type);
1114 #include <isl/union_set.h>
1115 unsigned isl_union_set_dim(__isl_keep isl_union_set *uset,
1116 enum isl_dim_type type);
1118 #include <isl/map.h>
1119 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1120 enum isl_dim_type type);
1121 unsigned isl_map_dim(__isl_keep isl_map *map,
1122 enum isl_dim_type type);
1124 #include <isl/union_map.h>
1125 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1126 enum isl_dim_type type);
1128 #include <isl/val.h>
1129 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
1130 enum isl_dim_type type);
1132 #include <isl/aff.h>
1133 int isl_aff_dim(__isl_keep isl_aff *aff,
1134 enum isl_dim_type type);
1135 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1136 enum isl_dim_type type);
1137 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1138 enum isl_dim_type type);
1139 unsigned isl_pw_multi_aff_dim(
1140 __isl_keep isl_pw_multi_aff *pma,
1141 enum isl_dim_type type);
1142 unsigned isl_multi_pw_aff_dim(
1143 __isl_keep isl_multi_pw_aff *mpa,
1144 enum isl_dim_type type);
1145 unsigned isl_union_pw_aff_dim(
1146 __isl_keep isl_union_pw_aff *upa,
1147 enum isl_dim_type type);
1148 unsigned isl_union_pw_multi_aff_dim(
1149 __isl_keep isl_union_pw_multi_aff *upma,
1150 enum isl_dim_type type);
1151 unsigned isl_multi_union_pw_aff_dim(
1152 __isl_keep isl_multi_union_pw_aff *mupa,
1153 enum isl_dim_type type);
1155 #include <isl/polynomial.h>
1156 unsigned isl_union_pw_qpolynomial_dim(
1157 __isl_keep isl_union_pw_qpolynomial *upwqp,
1158 enum isl_dim_type type);
1159 unsigned isl_union_pw_qpolynomial_fold_dim(
1160 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1161 enum isl_dim_type type);
1163 Note that an C<isl_union_set>, an C<isl_union_map>,
1164 an C<isl_union_pw_multi_aff>,
1165 an C<isl_union_pw_qpolynomial> and
1166 an C<isl_union_pw_qpolynomial_fold>
1167 only have parameters.
1169 The identifiers or names of the individual dimensions of spaces
1170 may be set or read off using the following functions on spaces
1171 or objects that live in spaces.
1172 These functions are mostly useful to obtain the identifiers, positions
1173 or names of the parameters. Identifiers of individual dimensions are
1174 essentially only useful for printing. They are ignored by all other
1175 operations and may not be preserved across those operations.
1177 #include <isl/space.h>
1178 __isl_give isl_space *isl_space_set_dim_id(
1179 __isl_take isl_space *space,
1180 enum isl_dim_type type, unsigned pos,
1181 __isl_take isl_id *id);
1182 isl_bool isl_space_has_dim_id(__isl_keep isl_space *space,
1183 enum isl_dim_type type, unsigned pos);
1184 __isl_give isl_id *isl_space_get_dim_id(
1185 __isl_keep isl_space *space,
1186 enum isl_dim_type type, unsigned pos);
1187 __isl_give isl_space *isl_space_set_dim_name(
1188 __isl_take isl_space *space,
1189 enum isl_dim_type type, unsigned pos,
1190 __isl_keep const char *name);
1191 isl_bool isl_space_has_dim_name(__isl_keep isl_space *space,
1192 enum isl_dim_type type, unsigned pos);
1193 __isl_keep const char *isl_space_get_dim_name(
1194 __isl_keep isl_space *space,
1195 enum isl_dim_type type, unsigned pos);
1197 #include <isl/local_space.h>
1198 __isl_give isl_local_space *isl_local_space_set_dim_id(
1199 __isl_take isl_local_space *ls,
1200 enum isl_dim_type type, unsigned pos,
1201 __isl_take isl_id *id);
1202 isl_bool isl_local_space_has_dim_id(
1203 __isl_keep isl_local_space *ls,
1204 enum isl_dim_type type, unsigned pos);
1205 __isl_give isl_id *isl_local_space_get_dim_id(
1206 __isl_keep isl_local_space *ls,
1207 enum isl_dim_type type, unsigned pos);
1208 __isl_give isl_local_space *isl_local_space_set_dim_name(
1209 __isl_take isl_local_space *ls,
1210 enum isl_dim_type type, unsigned pos, const char *s);
1211 isl_bool isl_local_space_has_dim_name(
1212 __isl_keep isl_local_space *ls,
1213 enum isl_dim_type type, unsigned pos)
1214 const char *isl_local_space_get_dim_name(
1215 __isl_keep isl_local_space *ls,
1216 enum isl_dim_type type, unsigned pos);
1218 #include <isl/constraint.h>
1219 const char *isl_constraint_get_dim_name(
1220 __isl_keep isl_constraint *constraint,
1221 enum isl_dim_type type, unsigned pos);
1223 #include <isl/set.h>
1224 __isl_give isl_id *isl_basic_set_get_dim_id(
1225 __isl_keep isl_basic_set *bset,
1226 enum isl_dim_type type, unsigned pos);
1227 __isl_give isl_set *isl_set_set_dim_id(
1228 __isl_take isl_set *set, enum isl_dim_type type,
1229 unsigned pos, __isl_take isl_id *id);
1230 isl_bool isl_set_has_dim_id(__isl_keep isl_set *set,
1231 enum isl_dim_type type, unsigned pos);
1232 __isl_give isl_id *isl_set_get_dim_id(
1233 __isl_keep isl_set *set, enum isl_dim_type type,
1235 const char *isl_basic_set_get_dim_name(
1236 __isl_keep isl_basic_set *bset,
1237 enum isl_dim_type type, unsigned pos);
1238 isl_bool isl_set_has_dim_name(__isl_keep isl_set *set,
1239 enum isl_dim_type type, unsigned pos);
1240 const char *isl_set_get_dim_name(
1241 __isl_keep isl_set *set,
1242 enum isl_dim_type type, unsigned pos);
1244 #include <isl/map.h>
1245 __isl_give isl_map *isl_map_set_dim_id(
1246 __isl_take isl_map *map, enum isl_dim_type type,
1247 unsigned pos, __isl_take isl_id *id);
1248 isl_bool isl_basic_map_has_dim_id(
1249 __isl_keep isl_basic_map *bmap,
1250 enum isl_dim_type type, unsigned pos);
1251 isl_bool isl_map_has_dim_id(__isl_keep isl_map *map,
1252 enum isl_dim_type type, unsigned pos);
1253 __isl_give isl_id *isl_map_get_dim_id(
1254 __isl_keep isl_map *map, enum isl_dim_type type,
1256 __isl_give isl_id *isl_union_map_get_dim_id(
1257 __isl_keep isl_union_map *umap,
1258 enum isl_dim_type type, unsigned pos);
1259 const char *isl_basic_map_get_dim_name(
1260 __isl_keep isl_basic_map *bmap,
1261 enum isl_dim_type type, unsigned pos);
1262 isl_bool isl_map_has_dim_name(__isl_keep isl_map *map,
1263 enum isl_dim_type type, unsigned pos);
1264 const char *isl_map_get_dim_name(
1265 __isl_keep isl_map *map,
1266 enum isl_dim_type type, unsigned pos);
1268 #include <isl/val.h>
1269 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1270 __isl_take isl_multi_val *mv,
1271 enum isl_dim_type type, unsigned pos,
1272 __isl_take isl_id *id);
1273 __isl_give isl_id *isl_multi_val_get_dim_id(
1274 __isl_keep isl_multi_val *mv,
1275 enum isl_dim_type type, unsigned pos);
1276 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1277 __isl_take isl_multi_val *mv,
1278 enum isl_dim_type type, unsigned pos, const char *s);
1280 #include <isl/aff.h>
1281 __isl_give isl_aff *isl_aff_set_dim_id(
1282 __isl_take isl_aff *aff, enum isl_dim_type type,
1283 unsigned pos, __isl_take isl_id *id);
1284 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1285 __isl_take isl_multi_aff *maff,
1286 enum isl_dim_type type, unsigned pos,
1287 __isl_take isl_id *id);
1288 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1289 __isl_take isl_pw_aff *pma,
1290 enum isl_dim_type type, unsigned pos,
1291 __isl_take isl_id *id);
1292 __isl_give isl_multi_pw_aff *
1293 isl_multi_pw_aff_set_dim_id(
1294 __isl_take isl_multi_pw_aff *mpa,
1295 enum isl_dim_type type, unsigned pos,
1296 __isl_take isl_id *id);
1297 __isl_give isl_multi_union_pw_aff *
1298 isl_multi_union_pw_aff_set_dim_id(
1299 __isl_take isl_multi_union_pw_aff *mupa,
1300 enum isl_dim_type type, unsigned pos,
1301 __isl_take isl_id *id);
1302 __isl_give isl_id *isl_multi_aff_get_dim_id(
1303 __isl_keep isl_multi_aff *ma,
1304 enum isl_dim_type type, unsigned pos);
1305 isl_bool isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1306 enum isl_dim_type type, unsigned pos);
1307 __isl_give isl_id *isl_pw_aff_get_dim_id(
1308 __isl_keep isl_pw_aff *pa,
1309 enum isl_dim_type type, unsigned pos);
1310 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1311 __isl_keep isl_pw_multi_aff *pma,
1312 enum isl_dim_type type, unsigned pos);
1313 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1314 __isl_keep isl_multi_pw_aff *mpa,
1315 enum isl_dim_type type, unsigned pos);
1316 __isl_give isl_id *isl_multi_union_pw_aff_get_dim_id(
1317 __isl_keep isl_multi_union_pw_aff *mupa,
1318 enum isl_dim_type type, unsigned pos);
1319 __isl_give isl_aff *isl_aff_set_dim_name(
1320 __isl_take isl_aff *aff, enum isl_dim_type type,
1321 unsigned pos, const char *s);
1322 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1323 __isl_take isl_multi_aff *maff,
1324 enum isl_dim_type type, unsigned pos, const char *s);
1325 __isl_give isl_multi_pw_aff *
1326 isl_multi_pw_aff_set_dim_name(
1327 __isl_take isl_multi_pw_aff *mpa,
1328 enum isl_dim_type type, unsigned pos, const char *s);
1329 __isl_give isl_union_pw_aff *
1330 isl_union_pw_aff_set_dim_name(
1331 __isl_take isl_union_pw_aff *upa,
1332 enum isl_dim_type type, unsigned pos,
1334 __isl_give isl_union_pw_multi_aff *
1335 isl_union_pw_multi_aff_set_dim_name(
1336 __isl_take isl_union_pw_multi_aff *upma,
1337 enum isl_dim_type type, unsigned pos,
1339 __isl_give isl_multi_union_pw_aff *
1340 isl_multi_union_pw_aff_set_dim_name(
1341 __isl_take isl_multi_union_pw_aff *mupa,
1342 enum isl_dim_type type, unsigned pos,
1343 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1344 enum isl_dim_type type, unsigned pos);
1345 const char *isl_pw_aff_get_dim_name(
1346 __isl_keep isl_pw_aff *pa,
1347 enum isl_dim_type type, unsigned pos);
1348 const char *isl_pw_multi_aff_get_dim_name(
1349 __isl_keep isl_pw_multi_aff *pma,
1350 enum isl_dim_type type, unsigned pos);
1352 #include <isl/polynomial.h>
1353 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1354 __isl_take isl_qpolynomial *qp,
1355 enum isl_dim_type type, unsigned pos,
1357 __isl_give isl_pw_qpolynomial *
1358 isl_pw_qpolynomial_set_dim_name(
1359 __isl_take isl_pw_qpolynomial *pwqp,
1360 enum isl_dim_type type, unsigned pos,
1362 __isl_give isl_pw_qpolynomial_fold *
1363 isl_pw_qpolynomial_fold_set_dim_name(
1364 __isl_take isl_pw_qpolynomial_fold *pwf,
1365 enum isl_dim_type type, unsigned pos,
1367 __isl_give isl_union_pw_qpolynomial *
1368 isl_union_pw_qpolynomial_set_dim_name(
1369 __isl_take isl_union_pw_qpolynomial *upwqp,
1370 enum isl_dim_type type, unsigned pos,
1372 __isl_give isl_union_pw_qpolynomial_fold *
1373 isl_union_pw_qpolynomial_fold_set_dim_name(
1374 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1375 enum isl_dim_type type, unsigned pos,
1378 Note that C<isl_space_get_name> returns a pointer to some internal
1379 data structure, so the result can only be used while the
1380 corresponding C<isl_space> is alive.
1381 Also note that every function that operates on two sets or relations
1382 requires that both arguments have the same parameters. This also
1383 means that if one of the arguments has named parameters, then the
1384 other needs to have named parameters too and the names need to match.
1385 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1386 arguments may have different parameters (as long as they are named),
1387 in which case the result will have as parameters the union of the parameters of
1390 Given the identifier or name of a dimension (typically a parameter),
1391 its position can be obtained from the following functions.
1393 #include <isl/space.h>
1394 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1395 enum isl_dim_type type, __isl_keep isl_id *id);
1396 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1397 enum isl_dim_type type, const char *name);
1399 #include <isl/local_space.h>
1400 int isl_local_space_find_dim_by_name(
1401 __isl_keep isl_local_space *ls,
1402 enum isl_dim_type type, const char *name);
1404 #include <isl/val.h>
1405 int isl_multi_val_find_dim_by_id(
1406 __isl_keep isl_multi_val *mv,
1407 enum isl_dim_type type, __isl_keep isl_id *id);
1408 int isl_multi_val_find_dim_by_name(
1409 __isl_keep isl_multi_val *mv,
1410 enum isl_dim_type type, const char *name);
1412 #include <isl/set.h>
1413 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1414 enum isl_dim_type type, __isl_keep isl_id *id);
1415 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1416 enum isl_dim_type type, const char *name);
1418 #include <isl/map.h>
1419 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1420 enum isl_dim_type type, __isl_keep isl_id *id);
1421 int isl_basic_map_find_dim_by_name(
1422 __isl_keep isl_basic_map *bmap,
1423 enum isl_dim_type type, const char *name);
1424 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1425 enum isl_dim_type type, const char *name);
1426 int isl_union_map_find_dim_by_name(
1427 __isl_keep isl_union_map *umap,
1428 enum isl_dim_type type, const char *name);
1430 #include <isl/aff.h>
1431 int isl_multi_aff_find_dim_by_id(
1432 __isl_keep isl_multi_aff *ma,
1433 enum isl_dim_type type, __isl_keep isl_id *id);
1434 int isl_multi_pw_aff_find_dim_by_id(
1435 __isl_keep isl_multi_pw_aff *mpa,
1436 enum isl_dim_type type, __isl_keep isl_id *id);
1437 int isl_multi_union_pw_aff_find_dim_by_id(
1438 __isl_keep isl_union_multi_pw_aff *mupa,
1439 enum isl_dim_type type, __isl_keep isl_id *id);
1440 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff,
1441 enum isl_dim_type type, const char *name);
1442 int isl_multi_aff_find_dim_by_name(
1443 __isl_keep isl_multi_aff *ma,
1444 enum isl_dim_type type, const char *name);
1445 int isl_pw_aff_find_dim_by_name(__isl_keep isl_pw_aff *pa,
1446 enum isl_dim_type type, const char *name);
1447 int isl_multi_pw_aff_find_dim_by_name(
1448 __isl_keep isl_multi_pw_aff *mpa,
1449 enum isl_dim_type type, const char *name);
1450 int isl_pw_multi_aff_find_dim_by_name(
1451 __isl_keep isl_pw_multi_aff *pma,
1452 enum isl_dim_type type, const char *name);
1453 int isl_union_pw_aff_find_dim_by_name(
1454 __isl_keep isl_union_pw_aff *upa,
1455 enum isl_dim_type type, const char *name);
1456 int isl_union_pw_multi_aff_find_dim_by_name(
1457 __isl_keep isl_union_pw_multi_aff *upma,
1458 enum isl_dim_type type, const char *name);
1459 int isl_multi_union_pw_aff_find_dim_by_name(
1460 __isl_keep isl_multi_union_pw_aff *mupa,
1461 enum isl_dim_type type, const char *name);
1463 #include <isl/polynomial.h>
1464 int isl_pw_qpolynomial_find_dim_by_name(
1465 __isl_keep isl_pw_qpolynomial *pwqp,
1466 enum isl_dim_type type, const char *name);
1467 int isl_pw_qpolynomial_fold_find_dim_by_name(
1468 __isl_keep isl_pw_qpolynomial_fold *pwf,
1469 enum isl_dim_type type, const char *name);
1470 int isl_union_pw_qpolynomial_find_dim_by_name(
1471 __isl_keep isl_union_pw_qpolynomial *upwqp,
1472 enum isl_dim_type type, const char *name);
1473 int isl_union_pw_qpolynomial_fold_find_dim_by_name(
1474 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1475 enum isl_dim_type type, const char *name);
1477 The identifiers or names of entire spaces may be set or read off
1478 using the following functions.
1480 #include <isl/space.h>
1481 __isl_give isl_space *isl_space_set_tuple_id(
1482 __isl_take isl_space *space,
1483 enum isl_dim_type type, __isl_take isl_id *id);
1484 __isl_give isl_space *isl_space_reset_tuple_id(
1485 __isl_take isl_space *space, enum isl_dim_type type);
1486 isl_bool isl_space_has_tuple_id(
1487 __isl_keep isl_space *space,
1488 enum isl_dim_type type);
1489 __isl_give isl_id *isl_space_get_tuple_id(
1490 __isl_keep isl_space *space, enum isl_dim_type type);
1491 __isl_give isl_space *isl_space_set_tuple_name(
1492 __isl_take isl_space *space,
1493 enum isl_dim_type type, const char *s);
1494 isl_bool isl_space_has_tuple_name(
1495 __isl_keep isl_space *space,
1496 enum isl_dim_type type);
1497 __isl_keep const char *isl_space_get_tuple_name(
1498 __isl_keep isl_space *space,
1499 enum isl_dim_type type);
1501 #include <isl/local_space.h>
1502 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1503 __isl_take isl_local_space *ls,
1504 enum isl_dim_type type, __isl_take isl_id *id);
1506 #include <isl/set.h>
1507 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1508 __isl_take isl_basic_set *bset,
1509 __isl_take isl_id *id);
1510 __isl_give isl_set *isl_set_set_tuple_id(
1511 __isl_take isl_set *set, __isl_take isl_id *id);
1512 __isl_give isl_set *isl_set_reset_tuple_id(
1513 __isl_take isl_set *set);
1514 isl_bool isl_set_has_tuple_id(__isl_keep isl_set *set);
1515 __isl_give isl_id *isl_set_get_tuple_id(
1516 __isl_keep isl_set *set);
1517 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1518 __isl_take isl_basic_set *set, const char *s);
1519 __isl_give isl_set *isl_set_set_tuple_name(
1520 __isl_take isl_set *set, const char *s);
1521 const char *isl_basic_set_get_tuple_name(
1522 __isl_keep isl_basic_set *bset);
1523 isl_bool isl_set_has_tuple_name(__isl_keep isl_set *set);
1524 const char *isl_set_get_tuple_name(
1525 __isl_keep isl_set *set);
1527 #include <isl/map.h>
1528 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1529 __isl_take isl_basic_map *bmap,
1530 enum isl_dim_type type, __isl_take isl_id *id);
1531 __isl_give isl_map *isl_map_set_tuple_id(
1532 __isl_take isl_map *map, enum isl_dim_type type,
1533 __isl_take isl_id *id);
1534 __isl_give isl_map *isl_map_reset_tuple_id(
1535 __isl_take isl_map *map, enum isl_dim_type type);
1536 isl_bool isl_map_has_tuple_id(__isl_keep isl_map *map,
1537 enum isl_dim_type type);
1538 __isl_give isl_id *isl_map_get_tuple_id(
1539 __isl_keep isl_map *map, enum isl_dim_type type);
1540 __isl_give isl_map *isl_map_set_tuple_name(
1541 __isl_take isl_map *map,
1542 enum isl_dim_type type, const char *s);
1543 const char *isl_basic_map_get_tuple_name(
1544 __isl_keep isl_basic_map *bmap,
1545 enum isl_dim_type type);
1546 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1547 __isl_take isl_basic_map *bmap,
1548 enum isl_dim_type type, const char *s);
1549 isl_bool isl_map_has_tuple_name(__isl_keep isl_map *map,
1550 enum isl_dim_type type);
1551 const char *isl_map_get_tuple_name(
1552 __isl_keep isl_map *map,
1553 enum isl_dim_type type);
1555 #include <isl/val.h>
1556 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1557 __isl_take isl_multi_val *mv,
1558 enum isl_dim_type type, __isl_take isl_id *id);
1559 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1560 __isl_take isl_multi_val *mv,
1561 enum isl_dim_type type);
1562 isl_bool isl_multi_val_has_tuple_id(
1563 __isl_keep isl_multi_val *mv,
1564 enum isl_dim_type type);
1565 __isl_give isl_id *isl_multi_val_get_tuple_id(
1566 __isl_keep isl_multi_val *mv,
1567 enum isl_dim_type type);
1568 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1569 __isl_take isl_multi_val *mv,
1570 enum isl_dim_type type, const char *s);
1571 const char *isl_multi_val_get_tuple_name(
1572 __isl_keep isl_multi_val *mv,
1573 enum isl_dim_type type);
1575 #include <isl/aff.h>
1576 __isl_give isl_aff *isl_aff_set_tuple_id(
1577 __isl_take isl_aff *aff,
1578 enum isl_dim_type type, __isl_take isl_id *id);
1579 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1580 __isl_take isl_multi_aff *maff,
1581 enum isl_dim_type type, __isl_take isl_id *id);
1582 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1583 __isl_take isl_pw_aff *pwaff,
1584 enum isl_dim_type type, __isl_take isl_id *id);
1585 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1586 __isl_take isl_pw_multi_aff *pma,
1587 enum isl_dim_type type, __isl_take isl_id *id);
1588 __isl_give isl_multi_union_pw_aff *
1589 isl_multi_union_pw_aff_set_tuple_id(
1590 __isl_take isl_multi_union_pw_aff *mupa,
1591 enum isl_dim_type type, __isl_take isl_id *id);
1592 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1593 __isl_take isl_multi_aff *ma,
1594 enum isl_dim_type type);
1595 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1596 __isl_take isl_pw_aff *pa,
1597 enum isl_dim_type type);
1598 __isl_give isl_multi_pw_aff *
1599 isl_multi_pw_aff_reset_tuple_id(
1600 __isl_take isl_multi_pw_aff *mpa,
1601 enum isl_dim_type type);
1602 __isl_give isl_pw_multi_aff *
1603 isl_pw_multi_aff_reset_tuple_id(
1604 __isl_take isl_pw_multi_aff *pma,
1605 enum isl_dim_type type);
1606 __isl_give isl_multi_union_pw_aff *
1607 isl_multi_union_pw_aff_reset_tuple_id(
1608 __isl_take isl_multi_union_pw_aff *mupa,
1609 enum isl_dim_type type);
1610 isl_bool isl_multi_aff_has_tuple_id(
1611 __isl_keep isl_multi_aff *ma,
1612 enum isl_dim_type type);
1613 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1614 __isl_keep isl_multi_aff *ma,
1615 enum isl_dim_type type);
1616 isl_bool isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1617 enum isl_dim_type type);
1618 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1619 __isl_keep isl_pw_aff *pa,
1620 enum isl_dim_type type);
1621 isl_bool isl_pw_multi_aff_has_tuple_id(
1622 __isl_keep isl_pw_multi_aff *pma,
1623 enum isl_dim_type type);
1624 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1625 __isl_keep isl_pw_multi_aff *pma,
1626 enum isl_dim_type type);
1627 isl_bool isl_multi_pw_aff_has_tuple_id(
1628 __isl_keep isl_multi_pw_aff *mpa,
1629 enum isl_dim_type type);
1630 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1631 __isl_keep isl_multi_pw_aff *mpa,
1632 enum isl_dim_type type);
1633 isl_bool isl_multi_union_pw_aff_has_tuple_id(
1634 __isl_keep isl_multi_union_pw_aff *mupa,
1635 enum isl_dim_type type);
1636 __isl_give isl_id *isl_multi_union_pw_aff_get_tuple_id(
1637 __isl_keep isl_multi_union_pw_aff *mupa,
1638 enum isl_dim_type type);
1639 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1640 __isl_take isl_multi_aff *maff,
1641 enum isl_dim_type type, const char *s);
1642 __isl_give isl_multi_pw_aff *
1643 isl_multi_pw_aff_set_tuple_name(
1644 __isl_take isl_multi_pw_aff *mpa,
1645 enum isl_dim_type type, const char *s);
1646 __isl_give isl_multi_union_pw_aff *
1647 isl_multi_union_pw_aff_set_tuple_name(
1648 __isl_take isl_multi_union_pw_aff *mupa,
1649 enum isl_dim_type type, const char *s);
1650 const char *isl_multi_aff_get_tuple_name(
1651 __isl_keep isl_multi_aff *multi,
1652 enum isl_dim_type type);
1653 isl_bool isl_pw_multi_aff_has_tuple_name(
1654 __isl_keep isl_pw_multi_aff *pma,
1655 enum isl_dim_type type);
1656 const char *isl_pw_multi_aff_get_tuple_name(
1657 __isl_keep isl_pw_multi_aff *pma,
1658 enum isl_dim_type type);
1659 const char *isl_multi_union_pw_aff_get_tuple_name(
1660 __isl_keep isl_multi_union_pw_aff *mupa,
1661 enum isl_dim_type type);
1663 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1664 or C<isl_dim_set>. As with C<isl_space_get_name>,
1665 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1667 Binary operations require the corresponding spaces of their arguments
1668 to have the same name.
1670 To keep the names of all parameters and tuples, but reset the user pointers
1671 of all the corresponding identifiers, use the following function.
1673 #include <isl/space.h>
1674 __isl_give isl_space *isl_space_reset_user(
1675 __isl_take isl_space *space);
1677 #include <isl/set.h>
1678 __isl_give isl_set *isl_set_reset_user(
1679 __isl_take isl_set *set);
1681 #include <isl/map.h>
1682 __isl_give isl_map *isl_map_reset_user(
1683 __isl_take isl_map *map);
1685 #include <isl/union_set.h>
1686 __isl_give isl_union_set *isl_union_set_reset_user(
1687 __isl_take isl_union_set *uset);
1689 #include <isl/union_map.h>
1690 __isl_give isl_union_map *isl_union_map_reset_user(
1691 __isl_take isl_union_map *umap);
1693 #include <isl/val.h>
1694 __isl_give isl_multi_val *isl_multi_val_reset_user(
1695 __isl_take isl_multi_val *mv);
1697 #include <isl/aff.h>
1698 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1699 __isl_take isl_multi_aff *ma);
1700 __isl_give isl_pw_aff *isl_pw_aff_reset_user(
1701 __isl_take isl_pw_aff *pa);
1702 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1703 __isl_take isl_multi_pw_aff *mpa);
1704 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_reset_user(
1705 __isl_take isl_pw_multi_aff *pma);
1706 __isl_give isl_union_pw_aff *isl_union_pw_aff_reset_user(
1707 __isl_take isl_union_pw_aff *upa);
1708 __isl_give isl_multi_union_pw_aff *
1709 isl_multi_union_pw_aff_reset_user(
1710 __isl_take isl_multi_union_pw_aff *mupa);
1711 __isl_give isl_union_pw_multi_aff *
1712 isl_union_pw_multi_aff_reset_user(
1713 __isl_take isl_union_pw_multi_aff *upma);
1715 #include <isl/polynomial.h>
1716 __isl_give isl_pw_qpolynomial *
1717 isl_pw_qpolynomial_reset_user(
1718 __isl_take isl_pw_qpolynomial *pwqp);
1719 __isl_give isl_union_pw_qpolynomial *
1720 isl_union_pw_qpolynomial_reset_user(
1721 __isl_take isl_union_pw_qpolynomial *upwqp);
1722 __isl_give isl_pw_qpolynomial_fold *
1723 isl_pw_qpolynomial_fold_reset_user(
1724 __isl_take isl_pw_qpolynomial_fold *pwf);
1725 __isl_give isl_union_pw_qpolynomial_fold *
1726 isl_union_pw_qpolynomial_fold_reset_user(
1727 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1729 Spaces can be nested. In particular, the domain of a set or
1730 the domain or range of a relation can be a nested relation.
1731 This process is also called I<wrapping>.
1732 The functions for detecting, constructing and deconstructing
1733 such nested spaces can be found in the wrapping properties
1734 of L</"Unary Properties">, the wrapping operations
1735 of L</"Unary Operations"> and the Cartesian product operations
1736 of L</"Basic Operations">.
1738 Spaces can be created from other spaces
1739 using the functions described in L</"Unary Operations">
1740 and L</"Binary Operations">.
1744 A local space is essentially a space with
1745 zero or more existentially quantified variables.
1746 The local space of various objects can be obtained
1747 using the following functions.
1749 #include <isl/constraint.h>
1750 __isl_give isl_local_space *isl_constraint_get_local_space(
1751 __isl_keep isl_constraint *constraint);
1753 #include <isl/set.h>
1754 __isl_give isl_local_space *isl_basic_set_get_local_space(
1755 __isl_keep isl_basic_set *bset);
1757 #include <isl/map.h>
1758 __isl_give isl_local_space *isl_basic_map_get_local_space(
1759 __isl_keep isl_basic_map *bmap);
1761 #include <isl/aff.h>
1762 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1763 __isl_keep isl_aff *aff);
1764 __isl_give isl_local_space *isl_aff_get_local_space(
1765 __isl_keep isl_aff *aff);
1767 A new local space can be created from a space using
1769 #include <isl/local_space.h>
1770 __isl_give isl_local_space *isl_local_space_from_space(
1771 __isl_take isl_space *space);
1773 They can be inspected, modified, copied and freed using the following functions.
1775 #include <isl/local_space.h>
1776 isl_bool isl_local_space_is_params(
1777 __isl_keep isl_local_space *ls);
1778 isl_bool isl_local_space_is_set(
1779 __isl_keep isl_local_space *ls);
1780 __isl_give isl_space *isl_local_space_get_space(
1781 __isl_keep isl_local_space *ls);
1782 __isl_give isl_aff *isl_local_space_get_div(
1783 __isl_keep isl_local_space *ls, int pos);
1784 __isl_give isl_local_space *isl_local_space_copy(
1785 __isl_keep isl_local_space *ls);
1786 __isl_null isl_local_space *isl_local_space_free(
1787 __isl_take isl_local_space *ls);
1789 Note that C<isl_local_space_get_div> can only be used on local spaces
1792 Two local spaces can be compared using
1794 isl_bool isl_local_space_is_equal(
1795 __isl_keep isl_local_space *ls1,
1796 __isl_keep isl_local_space *ls2);
1798 Local spaces can be created from other local spaces
1799 using the functions described in L</"Unary Operations">
1800 and L</"Binary Operations">.
1802 =head2 Creating New Sets and Relations
1804 C<isl> has functions for creating some standard sets and relations.
1808 =item * Empty sets and relations
1810 __isl_give isl_basic_set *isl_basic_set_empty(
1811 __isl_take isl_space *space);
1812 __isl_give isl_basic_map *isl_basic_map_empty(
1813 __isl_take isl_space *space);
1814 __isl_give isl_set *isl_set_empty(
1815 __isl_take isl_space *space);
1816 __isl_give isl_map *isl_map_empty(
1817 __isl_take isl_space *space);
1818 __isl_give isl_union_set *isl_union_set_empty(
1819 __isl_take isl_space *space);
1820 __isl_give isl_union_map *isl_union_map_empty(
1821 __isl_take isl_space *space);
1823 For C<isl_union_set>s and C<isl_union_map>s, the space
1824 is only used to specify the parameters.
1826 =item * Universe sets and relations
1828 __isl_give isl_basic_set *isl_basic_set_universe(
1829 __isl_take isl_space *space);
1830 __isl_give isl_basic_map *isl_basic_map_universe(
1831 __isl_take isl_space *space);
1832 __isl_give isl_set *isl_set_universe(
1833 __isl_take isl_space *space);
1834 __isl_give isl_map *isl_map_universe(
1835 __isl_take isl_space *space);
1836 __isl_give isl_union_set *isl_union_set_universe(
1837 __isl_take isl_union_set *uset);
1838 __isl_give isl_union_map *isl_union_map_universe(
1839 __isl_take isl_union_map *umap);
1841 The sets and relations constructed by the functions above
1842 contain all integer values, while those constructed by the
1843 functions below only contain non-negative values.
1845 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1846 __isl_take isl_space *space);
1847 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1848 __isl_take isl_space *space);
1849 __isl_give isl_set *isl_set_nat_universe(
1850 __isl_take isl_space *space);
1851 __isl_give isl_map *isl_map_nat_universe(
1852 __isl_take isl_space *space);
1854 =item * Identity relations
1856 __isl_give isl_basic_map *isl_basic_map_identity(
1857 __isl_take isl_space *space);
1858 __isl_give isl_map *isl_map_identity(
1859 __isl_take isl_space *space);
1861 The number of input and output dimensions in C<space> needs
1864 =item * Lexicographic order
1866 __isl_give isl_map *isl_map_lex_lt(
1867 __isl_take isl_space *set_space);
1868 __isl_give isl_map *isl_map_lex_le(
1869 __isl_take isl_space *set_space);
1870 __isl_give isl_map *isl_map_lex_gt(
1871 __isl_take isl_space *set_space);
1872 __isl_give isl_map *isl_map_lex_ge(
1873 __isl_take isl_space *set_space);
1874 __isl_give isl_map *isl_map_lex_lt_first(
1875 __isl_take isl_space *space, unsigned n);
1876 __isl_give isl_map *isl_map_lex_le_first(
1877 __isl_take isl_space *space, unsigned n);
1878 __isl_give isl_map *isl_map_lex_gt_first(
1879 __isl_take isl_space *space, unsigned n);
1880 __isl_give isl_map *isl_map_lex_ge_first(
1881 __isl_take isl_space *space, unsigned n);
1883 The first four functions take a space for a B<set>
1884 and return relations that express that the elements in the domain
1885 are lexicographically less
1886 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1887 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1888 than the elements in the range.
1889 The last four functions take a space for a map
1890 and return relations that express that the first C<n> dimensions
1891 in the domain are lexicographically less
1892 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1893 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1894 than the first C<n> dimensions in the range.
1898 A basic set or relation can be converted to a set or relation
1899 using the following functions.
1901 __isl_give isl_set *isl_set_from_basic_set(
1902 __isl_take isl_basic_set *bset);
1903 __isl_give isl_map *isl_map_from_basic_map(
1904 __isl_take isl_basic_map *bmap);
1906 Sets and relations can be converted to union sets and relations
1907 using the following functions.
1909 __isl_give isl_union_set *isl_union_set_from_basic_set(
1910 __isl_take isl_basic_set *bset);
1911 __isl_give isl_union_map *isl_union_map_from_basic_map(
1912 __isl_take isl_basic_map *bmap);
1913 __isl_give isl_union_set *isl_union_set_from_set(
1914 __isl_take isl_set *set);
1915 __isl_give isl_union_map *isl_union_map_from_map(
1916 __isl_take isl_map *map);
1918 The inverse conversions below can only be used if the input
1919 union set or relation is known to contain elements in exactly one
1922 __isl_give isl_set *isl_set_from_union_set(
1923 __isl_take isl_union_set *uset);
1924 __isl_give isl_map *isl_map_from_union_map(
1925 __isl_take isl_union_map *umap);
1927 Sets and relations can be copied and freed again using the following
1930 __isl_give isl_basic_set *isl_basic_set_copy(
1931 __isl_keep isl_basic_set *bset);
1932 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1933 __isl_give isl_union_set *isl_union_set_copy(
1934 __isl_keep isl_union_set *uset);
1935 __isl_give isl_basic_map *isl_basic_map_copy(
1936 __isl_keep isl_basic_map *bmap);
1937 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1938 __isl_give isl_union_map *isl_union_map_copy(
1939 __isl_keep isl_union_map *umap);
1940 __isl_null isl_basic_set *isl_basic_set_free(
1941 __isl_take isl_basic_set *bset);
1942 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1943 __isl_null isl_union_set *isl_union_set_free(
1944 __isl_take isl_union_set *uset);
1945 __isl_null isl_basic_map *isl_basic_map_free(
1946 __isl_take isl_basic_map *bmap);
1947 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1948 __isl_null isl_union_map *isl_union_map_free(
1949 __isl_take isl_union_map *umap);
1951 Other sets and relations can be constructed by starting
1952 from a universe set or relation, adding equality and/or
1953 inequality constraints and then projecting out the
1954 existentially quantified variables, if any.
1955 Constraints can be constructed, manipulated and
1956 added to (or removed from) (basic) sets and relations
1957 using the following functions.
1959 #include <isl/constraint.h>
1960 __isl_give isl_constraint *isl_constraint_alloc_equality(
1961 __isl_take isl_local_space *ls);
1962 __isl_give isl_constraint *isl_constraint_alloc_inequality(
1963 __isl_take isl_local_space *ls);
1964 __isl_give isl_constraint *isl_constraint_set_constant_si(
1965 __isl_take isl_constraint *constraint, int v);
1966 __isl_give isl_constraint *isl_constraint_set_constant_val(
1967 __isl_take isl_constraint *constraint,
1968 __isl_take isl_val *v);
1969 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1970 __isl_take isl_constraint *constraint,
1971 enum isl_dim_type type, int pos, int v);
1972 __isl_give isl_constraint *
1973 isl_constraint_set_coefficient_val(
1974 __isl_take isl_constraint *constraint,
1975 enum isl_dim_type type, int pos,
1976 __isl_take isl_val *v);
1977 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1978 __isl_take isl_basic_map *bmap,
1979 __isl_take isl_constraint *constraint);
1980 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1981 __isl_take isl_basic_set *bset,
1982 __isl_take isl_constraint *constraint);
1983 __isl_give isl_map *isl_map_add_constraint(
1984 __isl_take isl_map *map,
1985 __isl_take isl_constraint *constraint);
1986 __isl_give isl_set *isl_set_add_constraint(
1987 __isl_take isl_set *set,
1988 __isl_take isl_constraint *constraint);
1990 For example, to create a set containing the even integers
1991 between 10 and 42, you would use the following code.
1994 isl_local_space *ls;
1996 isl_basic_set *bset;
1998 space = isl_space_set_alloc(ctx, 0, 2);
1999 bset = isl_basic_set_universe(isl_space_copy(space));
2000 ls = isl_local_space_from_space(space);
2002 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
2003 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2004 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
2005 bset = isl_basic_set_add_constraint(bset, c);
2007 c = isl_constraint_alloc_inequality(isl_local_space_copy(ls));
2008 c = isl_constraint_set_constant_si(c, -10);
2009 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
2010 bset = isl_basic_set_add_constraint(bset, c);
2012 c = isl_constraint_alloc_inequality(ls);
2013 c = isl_constraint_set_constant_si(c, 42);
2014 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2015 bset = isl_basic_set_add_constraint(bset, c);
2017 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
2021 isl_basic_set *bset;
2022 bset = isl_basic_set_read_from_str(ctx,
2023 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
2025 A basic set or relation can also be constructed from two matrices
2026 describing the equalities and the inequalities.
2028 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
2029 __isl_take isl_space *space,
2030 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2031 enum isl_dim_type c1,
2032 enum isl_dim_type c2, enum isl_dim_type c3,
2033 enum isl_dim_type c4);
2034 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
2035 __isl_take isl_space *space,
2036 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2037 enum isl_dim_type c1,
2038 enum isl_dim_type c2, enum isl_dim_type c3,
2039 enum isl_dim_type c4, enum isl_dim_type c5);
2041 The C<isl_dim_type> arguments indicate the order in which
2042 different kinds of variables appear in the input matrices
2043 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
2044 C<isl_dim_set> and C<isl_dim_div> for sets and
2045 of C<isl_dim_cst>, C<isl_dim_param>,
2046 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
2048 A (basic or union) set or relation can also be constructed from a
2049 (union) (piecewise) (multiple) affine expression
2050 or a list of affine expressions
2051 (See L</"Functions">), provided these affine expressions do not
2054 __isl_give isl_basic_map *isl_basic_map_from_aff(
2055 __isl_take isl_aff *aff);
2056 __isl_give isl_map *isl_map_from_aff(
2057 __isl_take isl_aff *aff);
2058 __isl_give isl_set *isl_set_from_pw_aff(
2059 __isl_take isl_pw_aff *pwaff);
2060 __isl_give isl_map *isl_map_from_pw_aff(
2061 __isl_take isl_pw_aff *pwaff);
2062 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
2063 __isl_take isl_space *domain_space,
2064 __isl_take isl_aff_list *list);
2065 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
2066 __isl_take isl_multi_aff *maff)
2067 __isl_give isl_map *isl_map_from_multi_aff(
2068 __isl_take isl_multi_aff *maff)
2069 __isl_give isl_set *isl_set_from_pw_multi_aff(
2070 __isl_take isl_pw_multi_aff *pma);
2071 __isl_give isl_map *isl_map_from_pw_multi_aff(
2072 __isl_take isl_pw_multi_aff *pma);
2073 __isl_give isl_set *isl_set_from_multi_pw_aff(
2074 __isl_take isl_multi_pw_aff *mpa);
2075 __isl_give isl_map *isl_map_from_multi_pw_aff(
2076 __isl_take isl_multi_pw_aff *mpa);
2077 __isl_give isl_union_map *isl_union_map_from_union_pw_aff(
2078 __isl_take isl_union_pw_aff *upa);
2079 __isl_give isl_union_map *
2080 isl_union_map_from_union_pw_multi_aff(
2081 __isl_take isl_union_pw_multi_aff *upma);
2082 __isl_give isl_union_map *
2083 isl_union_map_from_multi_union_pw_aff(
2084 __isl_take isl_multi_union_pw_aff *mupa);
2086 The C<domain_space> argument describes the domain of the resulting
2087 basic relation. It is required because the C<list> may consist
2088 of zero affine expressions.
2089 The C<mupa> passed to C<isl_union_map_from_multi_union_pw_aff>
2090 is not allowed to be zero-dimensional. The domain of the result
2091 is the shared domain of the union piecewise affine elements.
2093 =head2 Inspecting Sets and Relations
2095 Usually, the user should not have to care about the actual constraints
2096 of the sets and maps, but should instead apply the abstract operations
2097 explained in the following sections.
2098 Occasionally, however, it may be required to inspect the individual
2099 coefficients of the constraints. This section explains how to do so.
2100 In these cases, it may also be useful to have C<isl> compute
2101 an explicit representation of the existentially quantified variables.
2103 __isl_give isl_set *isl_set_compute_divs(
2104 __isl_take isl_set *set);
2105 __isl_give isl_map *isl_map_compute_divs(
2106 __isl_take isl_map *map);
2107 __isl_give isl_union_set *isl_union_set_compute_divs(
2108 __isl_take isl_union_set *uset);
2109 __isl_give isl_union_map *isl_union_map_compute_divs(
2110 __isl_take isl_union_map *umap);
2112 This explicit representation defines the existentially quantified
2113 variables as integer divisions of the other variables, possibly
2114 including earlier existentially quantified variables.
2115 An explicitly represented existentially quantified variable therefore
2116 has a unique value when the values of the other variables are known.
2118 Alternatively, the existentially quantified variables can be removed
2119 using the following functions, which compute an overapproximation.
2121 #include <isl/set.h>
2122 __isl_give isl_basic_set *isl_basic_set_remove_divs(
2123 __isl_take isl_basic_set *bset);
2124 __isl_give isl_set *isl_set_remove_divs(
2125 __isl_take isl_set *set);
2127 #include <isl/map.h>
2128 __isl_give isl_basic_map *isl_basic_map_remove_divs(
2129 __isl_take isl_basic_map *bmap);
2130 __isl_give isl_map *isl_map_remove_divs(
2131 __isl_take isl_map *map);
2133 #include <isl/union_set.h>
2134 __isl_give isl_union_set *isl_union_set_remove_divs(
2135 __isl_take isl_union_set *bset);
2137 #include <isl/union_map.h>
2138 __isl_give isl_union_map *isl_union_map_remove_divs(
2139 __isl_take isl_union_map *bmap);
2141 It is also possible to only remove those divs that are defined
2142 in terms of a given range of dimensions or only those for which
2143 no explicit representation is known.
2145 __isl_give isl_basic_set *
2146 isl_basic_set_remove_divs_involving_dims(
2147 __isl_take isl_basic_set *bset,
2148 enum isl_dim_type type,
2149 unsigned first, unsigned n);
2150 __isl_give isl_basic_map *
2151 isl_basic_map_remove_divs_involving_dims(
2152 __isl_take isl_basic_map *bmap,
2153 enum isl_dim_type type,
2154 unsigned first, unsigned n);
2155 __isl_give isl_set *isl_set_remove_divs_involving_dims(
2156 __isl_take isl_set *set, enum isl_dim_type type,
2157 unsigned first, unsigned n);
2158 __isl_give isl_map *isl_map_remove_divs_involving_dims(
2159 __isl_take isl_map *map, enum isl_dim_type type,
2160 unsigned first, unsigned n);
2162 __isl_give isl_basic_set *
2163 isl_basic_set_remove_unknown_divs(
2164 __isl_take isl_basic_set *bset);
2165 __isl_give isl_set *isl_set_remove_unknown_divs(
2166 __isl_take isl_set *set);
2167 __isl_give isl_map *isl_map_remove_unknown_divs(
2168 __isl_take isl_map *map);
2170 To iterate over all the sets or maps in a union set or map, use
2172 isl_stat isl_union_set_foreach_set(
2173 __isl_keep isl_union_set *uset,
2174 isl_stat (*fn)(__isl_take isl_set *set, void *user),
2176 isl_stat isl_union_map_foreach_map(
2177 __isl_keep isl_union_map *umap,
2178 isl_stat (*fn)(__isl_take isl_map *map, void *user),
2181 These functions call the callback function once for each
2182 (pair of) space(s) for which there are elements in the input.
2183 The argument to the callback contains all elements in the input
2184 with that (pair of) space(s).
2186 The number of sets or maps in a union set or map can be obtained
2189 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
2190 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
2192 To extract the set or map in a given space from a union, use
2194 __isl_give isl_set *isl_union_set_extract_set(
2195 __isl_keep isl_union_set *uset,
2196 __isl_take isl_space *space);
2197 __isl_give isl_map *isl_union_map_extract_map(
2198 __isl_keep isl_union_map *umap,
2199 __isl_take isl_space *space);
2201 To iterate over all the basic sets or maps in a set or map, use
2203 isl_stat isl_set_foreach_basic_set(__isl_keep isl_set *set,
2204 isl_stat (*fn)(__isl_take isl_basic_set *bset,
2207 isl_stat isl_map_foreach_basic_map(__isl_keep isl_map *map,
2208 isl_stat (*fn)(__isl_take isl_basic_map *bmap,
2212 The callback function C<fn> should return 0 if successful and
2213 -1 if an error occurs. In the latter case, or if any other error
2214 occurs, the above functions will return -1.
2216 It should be noted that C<isl> does not guarantee that
2217 the basic sets or maps passed to C<fn> are disjoint.
2218 If this is required, then the user should call one of
2219 the following functions first.
2221 __isl_give isl_set *isl_set_make_disjoint(
2222 __isl_take isl_set *set);
2223 __isl_give isl_map *isl_map_make_disjoint(
2224 __isl_take isl_map *map);
2226 The number of basic sets in a set can be obtained
2227 or the number of basic maps in a map can be obtained
2230 #include <isl/set.h>
2231 int isl_set_n_basic_set(__isl_keep isl_set *set);
2233 #include <isl/map.h>
2234 int isl_map_n_basic_map(__isl_keep isl_map *map);
2236 It is also possible to obtain a list of basic sets from a set
2239 #include <isl/set.h>
2240 __isl_give isl_basic_set_list *isl_set_get_basic_set_list(
2241 __isl_keep isl_set *set);
2243 #include <isl/union_set.h>
2244 __isl_give isl_basic_set_list *
2245 isl_union_set_get_basic_set_list(
2246 __isl_keep isl_union_set *uset);
2248 The returned list can be manipulated using the functions in L<"Lists">.
2250 To iterate over the constraints of a basic set or map, use
2252 #include <isl/constraint.h>
2254 int isl_basic_set_n_constraint(
2255 __isl_keep isl_basic_set *bset);
2256 isl_stat isl_basic_set_foreach_constraint(
2257 __isl_keep isl_basic_set *bset,
2258 isl_stat (*fn)(__isl_take isl_constraint *c,
2261 int isl_basic_map_n_constraint(
2262 __isl_keep isl_basic_map *bmap);
2263 isl_stat isl_basic_map_foreach_constraint(
2264 __isl_keep isl_basic_map *bmap,
2265 isl_stat (*fn)(__isl_take isl_constraint *c,
2268 __isl_null isl_constraint *isl_constraint_free(
2269 __isl_take isl_constraint *c);
2271 Again, the callback function C<fn> should return 0 if successful and
2272 -1 if an error occurs. In the latter case, or if any other error
2273 occurs, the above functions will return -1.
2274 The constraint C<c> represents either an equality or an inequality.
2275 Use the following function to find out whether a constraint
2276 represents an equality. If not, it represents an inequality.
2278 isl_bool isl_constraint_is_equality(
2279 __isl_keep isl_constraint *constraint);
2281 It is also possible to obtain a list of constraints from a basic
2284 #include <isl/constraint.h>
2285 __isl_give isl_constraint_list *
2286 isl_basic_map_get_constraint_list(
2287 __isl_keep isl_basic_map *bmap);
2288 __isl_give isl_constraint_list *
2289 isl_basic_set_get_constraint_list(
2290 __isl_keep isl_basic_set *bset);
2292 These functions require that all existentially quantified variables
2293 have an explicit representation.
2294 The returned list can be manipulated using the functions in L<"Lists">.
2296 The coefficients of the constraints can be inspected using
2297 the following functions.
2299 isl_bool isl_constraint_is_lower_bound(
2300 __isl_keep isl_constraint *constraint,
2301 enum isl_dim_type type, unsigned pos);
2302 isl_bool isl_constraint_is_upper_bound(
2303 __isl_keep isl_constraint *constraint,
2304 enum isl_dim_type type, unsigned pos);
2305 __isl_give isl_val *isl_constraint_get_constant_val(
2306 __isl_keep isl_constraint *constraint);
2307 __isl_give isl_val *isl_constraint_get_coefficient_val(
2308 __isl_keep isl_constraint *constraint,
2309 enum isl_dim_type type, int pos);
2311 The explicit representations of the existentially quantified
2312 variables can be inspected using the following function.
2313 Note that the user is only allowed to use this function
2314 if the inspected set or map is the result of a call
2315 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2316 The existentially quantified variable is equal to the floor
2317 of the returned affine expression. The affine expression
2318 itself can be inspected using the functions in
2321 __isl_give isl_aff *isl_constraint_get_div(
2322 __isl_keep isl_constraint *constraint, int pos);
2324 To obtain the constraints of a basic set or map in matrix
2325 form, use the following functions.
2327 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2328 __isl_keep isl_basic_set *bset,
2329 enum isl_dim_type c1, enum isl_dim_type c2,
2330 enum isl_dim_type c3, enum isl_dim_type c4);
2331 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2332 __isl_keep isl_basic_set *bset,
2333 enum isl_dim_type c1, enum isl_dim_type c2,
2334 enum isl_dim_type c3, enum isl_dim_type c4);
2335 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2336 __isl_keep isl_basic_map *bmap,
2337 enum isl_dim_type c1,
2338 enum isl_dim_type c2, enum isl_dim_type c3,
2339 enum isl_dim_type c4, enum isl_dim_type c5);
2340 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2341 __isl_keep isl_basic_map *bmap,
2342 enum isl_dim_type c1,
2343 enum isl_dim_type c2, enum isl_dim_type c3,
2344 enum isl_dim_type c4, enum isl_dim_type c5);
2346 The C<isl_dim_type> arguments dictate the order in which
2347 different kinds of variables appear in the resulting matrix.
2348 For set inputs, they should be a permutation of
2349 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
2350 For map inputs, they should be a permutation of
2351 C<isl_dim_cst>, C<isl_dim_param>,
2352 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2356 Points are elements of a set. They can be used to construct
2357 simple sets (boxes) or they can be used to represent the
2358 individual elements of a set.
2359 The zero point (the origin) can be created using
2361 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2363 The coordinates of a point can be inspected, set and changed
2366 __isl_give isl_val *isl_point_get_coordinate_val(
2367 __isl_keep isl_point *pnt,
2368 enum isl_dim_type type, int pos);
2369 __isl_give isl_point *isl_point_set_coordinate_val(
2370 __isl_take isl_point *pnt,
2371 enum isl_dim_type type, int pos,
2372 __isl_take isl_val *v);
2374 __isl_give isl_point *isl_point_add_ui(
2375 __isl_take isl_point *pnt,
2376 enum isl_dim_type type, int pos, unsigned val);
2377 __isl_give isl_point *isl_point_sub_ui(
2378 __isl_take isl_point *pnt,
2379 enum isl_dim_type type, int pos, unsigned val);
2381 Points can be copied or freed using
2383 __isl_give isl_point *isl_point_copy(
2384 __isl_keep isl_point *pnt);
2385 __isl_null isl_point *isl_point_free(
2386 __isl_take isl_point *pnt);
2388 A singleton set can be created from a point using
2390 __isl_give isl_basic_set *isl_basic_set_from_point(
2391 __isl_take isl_point *pnt);
2392 __isl_give isl_set *isl_set_from_point(
2393 __isl_take isl_point *pnt);
2394 __isl_give isl_union_set *isl_union_set_from_point(
2395 __isl_take isl_point *pnt);
2397 and a box can be created from two opposite extremal points using
2399 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2400 __isl_take isl_point *pnt1,
2401 __isl_take isl_point *pnt2);
2402 __isl_give isl_set *isl_set_box_from_points(
2403 __isl_take isl_point *pnt1,
2404 __isl_take isl_point *pnt2);
2406 All elements of a B<bounded> (union) set can be enumerated using
2407 the following functions.
2409 isl_stat isl_set_foreach_point(__isl_keep isl_set *set,
2410 isl_stat (*fn)(__isl_take isl_point *pnt,
2413 isl_stat isl_union_set_foreach_point(
2414 __isl_keep isl_union_set *uset,
2415 isl_stat (*fn)(__isl_take isl_point *pnt,
2419 The function C<fn> is called for each integer point in
2420 C<set> with as second argument the last argument of
2421 the C<isl_set_foreach_point> call. The function C<fn>
2422 should return C<0> on success and C<-1> on failure.
2423 In the latter case, C<isl_set_foreach_point> will stop
2424 enumerating and return C<-1> as well.
2425 If the enumeration is performed successfully and to completion,
2426 then C<isl_set_foreach_point> returns C<0>.
2428 To obtain a single point of a (basic or union) set, use
2430 __isl_give isl_point *isl_basic_set_sample_point(
2431 __isl_take isl_basic_set *bset);
2432 __isl_give isl_point *isl_set_sample_point(
2433 __isl_take isl_set *set);
2434 __isl_give isl_point *isl_union_set_sample_point(
2435 __isl_take isl_union_set *uset);
2437 If C<set> does not contain any (integer) points, then the
2438 resulting point will be ``void'', a property that can be
2441 isl_bool isl_point_is_void(__isl_keep isl_point *pnt);
2445 Besides sets and relation, C<isl> also supports various types of functions.
2446 Each of these types is derived from the value type (see L</"Values">)
2447 or from one of two primitive function types
2448 through the application of zero or more type constructors.
2449 We first describe the primitive type and then we describe
2450 the types derived from these primitive types.
2452 =head3 Primitive Functions
2454 C<isl> support two primitive function types, quasi-affine
2455 expressions and quasipolynomials.
2456 A quasi-affine expression is defined either over a parameter
2457 space or over a set and is composed of integer constants,
2458 parameters and set variables, addition, subtraction and
2459 integer division by an integer constant.
2460 For example, the quasi-affine expression
2462 [n] -> { [x] -> [2*floor((4 n + x)/9] }
2464 maps C<x> to C<2*floor((4 n + x)/9>.
2465 A quasipolynomial is a polynomial expression in quasi-affine
2466 expression. That is, it additionally allows for multiplication.
2467 Note, though, that it is not allowed to construct an integer
2468 division of an expression involving multiplications.
2469 Here is an example of a quasipolynomial that is not
2470 quasi-affine expression
2472 [n] -> { [x] -> (n*floor((4 n + x)/9) }
2474 Note that the external representations of quasi-affine expressions
2475 and quasipolynomials are different. Quasi-affine expressions
2476 use a notation with square brackets just like binary relations,
2477 while quasipolynomials do not. This might change at some point.
2479 If a primitive function is defined over a parameter space,
2480 then the space of the function itself is that of a set.
2481 If it is defined over a set, then the space of the function
2482 is that of a relation. In both cases, the set space (or
2483 the output space) is single-dimensional, anonymous and unstructured.
2484 To create functions with multiple dimensions or with other kinds
2485 of set or output spaces, use multiple expressions
2486 (see L</"Multiple Expressions">).
2490 =item * Quasi-affine Expressions
2492 Besides the expressions described above, a quasi-affine
2493 expression can also be set to NaN. Such expressions
2494 typically represent a failure to represent a result
2495 as a quasi-affine expression.
2497 The zero quasi affine expression or the quasi affine expression
2498 that is equal to a given value or
2499 a specified dimension on a given domain can be created using
2501 #include <isl/aff.h>
2502 __isl_give isl_aff *isl_aff_zero_on_domain(
2503 __isl_take isl_local_space *ls);
2504 __isl_give isl_aff *isl_aff_val_on_domain(
2505 __isl_take isl_local_space *ls,
2506 __isl_take isl_val *val);
2507 __isl_give isl_aff *isl_aff_var_on_domain(
2508 __isl_take isl_local_space *ls,
2509 enum isl_dim_type type, unsigned pos);
2510 __isl_give isl_aff *isl_aff_nan_on_domain(
2511 __isl_take isl_local_space *ls);
2513 Quasi affine expressions can be copied and freed using
2515 #include <isl/aff.h>
2516 __isl_give isl_aff *isl_aff_copy(
2517 __isl_keep isl_aff *aff);
2518 __isl_null isl_aff *isl_aff_free(
2519 __isl_take isl_aff *aff);
2521 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2522 using the following function. The constraint is required to have
2523 a non-zero coefficient for the specified dimension.
2525 #include <isl/constraint.h>
2526 __isl_give isl_aff *isl_constraint_get_bound(
2527 __isl_keep isl_constraint *constraint,
2528 enum isl_dim_type type, int pos);
2530 The entire affine expression of the constraint can also be extracted
2531 using the following function.
2533 #include <isl/constraint.h>
2534 __isl_give isl_aff *isl_constraint_get_aff(
2535 __isl_keep isl_constraint *constraint);
2537 Conversely, an equality constraint equating
2538 the affine expression to zero or an inequality constraint enforcing
2539 the affine expression to be non-negative, can be constructed using
2541 __isl_give isl_constraint *isl_equality_from_aff(
2542 __isl_take isl_aff *aff);
2543 __isl_give isl_constraint *isl_inequality_from_aff(
2544 __isl_take isl_aff *aff);
2546 The coefficients and the integer divisions of an affine expression
2547 can be inspected using the following functions.
2549 #include <isl/aff.h>
2550 __isl_give isl_val *isl_aff_get_constant_val(
2551 __isl_keep isl_aff *aff);
2552 __isl_give isl_val *isl_aff_get_coefficient_val(
2553 __isl_keep isl_aff *aff,
2554 enum isl_dim_type type, int pos);
2555 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2556 enum isl_dim_type type, int pos);
2557 __isl_give isl_val *isl_aff_get_denominator_val(
2558 __isl_keep isl_aff *aff);
2559 __isl_give isl_aff *isl_aff_get_div(
2560 __isl_keep isl_aff *aff, int pos);
2562 They can be modified using the following functions.
2564 #include <isl/aff.h>
2565 __isl_give isl_aff *isl_aff_set_constant_si(
2566 __isl_take isl_aff *aff, int v);
2567 __isl_give isl_aff *isl_aff_set_constant_val(
2568 __isl_take isl_aff *aff, __isl_take isl_val *v);
2569 __isl_give isl_aff *isl_aff_set_coefficient_si(
2570 __isl_take isl_aff *aff,
2571 enum isl_dim_type type, int pos, int v);
2572 __isl_give isl_aff *isl_aff_set_coefficient_val(
2573 __isl_take isl_aff *aff,
2574 enum isl_dim_type type, int pos,
2575 __isl_take isl_val *v);
2577 __isl_give isl_aff *isl_aff_add_constant_si(
2578 __isl_take isl_aff *aff, int v);
2579 __isl_give isl_aff *isl_aff_add_constant_val(
2580 __isl_take isl_aff *aff, __isl_take isl_val *v);
2581 __isl_give isl_aff *isl_aff_add_constant_num_si(
2582 __isl_take isl_aff *aff, int v);
2583 __isl_give isl_aff *isl_aff_add_coefficient_si(
2584 __isl_take isl_aff *aff,
2585 enum isl_dim_type type, int pos, int v);
2586 __isl_give isl_aff *isl_aff_add_coefficient_val(
2587 __isl_take isl_aff *aff,
2588 enum isl_dim_type type, int pos,
2589 __isl_take isl_val *v);
2591 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
2592 set the I<numerator> of the constant or coefficient, while
2593 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
2594 the constant or coefficient as a whole.
2595 The C<add_constant> and C<add_coefficient> functions add an integer
2596 or rational value to
2597 the possibly rational constant or coefficient.
2598 The C<add_constant_num> functions add an integer value to
2601 =item * Quasipolynomials
2603 Some simple quasipolynomials can be created using the following functions.
2605 #include <isl/polynomial.h>
2606 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2607 __isl_take isl_space *domain);
2608 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2609 __isl_take isl_space *domain);
2610 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2611 __isl_take isl_space *domain);
2612 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2613 __isl_take isl_space *domain);
2614 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2615 __isl_take isl_space *domain);
2616 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2617 __isl_take isl_space *domain,
2618 __isl_take isl_val *val);
2619 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2620 __isl_take isl_space *domain,
2621 enum isl_dim_type type, unsigned pos);
2622 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2623 __isl_take isl_aff *aff);
2625 Recall that the space in which a quasipolynomial lives is a map space
2626 with a one-dimensional range. The C<domain> argument in some of
2627 the functions above corresponds to the domain of this map space.
2629 Quasipolynomials can be copied and freed again using the following
2632 #include <isl/polynomial.h>
2633 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2634 __isl_keep isl_qpolynomial *qp);
2635 __isl_null isl_qpolynomial *isl_qpolynomial_free(
2636 __isl_take isl_qpolynomial *qp);
2638 The constant term of a quasipolynomial can be extracted using
2640 __isl_give isl_val *isl_qpolynomial_get_constant_val(
2641 __isl_keep isl_qpolynomial *qp);
2643 To iterate over all terms in a quasipolynomial,
2646 isl_stat isl_qpolynomial_foreach_term(
2647 __isl_keep isl_qpolynomial *qp,
2648 isl_stat (*fn)(__isl_take isl_term *term,
2649 void *user), void *user);
2651 The terms themselves can be inspected and freed using
2654 unsigned isl_term_dim(__isl_keep isl_term *term,
2655 enum isl_dim_type type);
2656 __isl_give isl_val *isl_term_get_coefficient_val(
2657 __isl_keep isl_term *term);
2658 int isl_term_get_exp(__isl_keep isl_term *term,
2659 enum isl_dim_type type, unsigned pos);
2660 __isl_give isl_aff *isl_term_get_div(
2661 __isl_keep isl_term *term, unsigned pos);
2662 void isl_term_free(__isl_take isl_term *term);
2664 Each term is a product of parameters, set variables and
2665 integer divisions. The function C<isl_term_get_exp>
2666 returns the exponent of a given dimensions in the given term.
2672 A reduction represents a maximum or a minimum of its
2674 The only reduction type defined by C<isl> is
2675 C<isl_qpolynomial_fold>.
2677 There are currently no functions to directly create such
2678 objects, but they do appear in the piecewise quasipolynomial
2679 reductions returned by the C<isl_pw_qpolynomial_bound> function.
2681 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
2683 Reductions can be copied and freed using
2684 the following functions.
2686 #include <isl/polynomial.h>
2687 __isl_give isl_qpolynomial_fold *
2688 isl_qpolynomial_fold_copy(
2689 __isl_keep isl_qpolynomial_fold *fold);
2690 void isl_qpolynomial_fold_free(
2691 __isl_take isl_qpolynomial_fold *fold);
2693 To iterate over all quasipolynomials in a reduction, use
2695 isl_stat isl_qpolynomial_fold_foreach_qpolynomial(
2696 __isl_keep isl_qpolynomial_fold *fold,
2697 isl_stat (*fn)(__isl_take isl_qpolynomial *qp,
2698 void *user), void *user);
2700 =head3 Multiple Expressions
2702 A multiple expression represents a sequence of zero or
2703 more base expressions, all defined on the same domain space.
2704 The domain space of the multiple expression is the same
2705 as that of the base expressions, but the range space
2706 can be any space. In case the base expressions have
2707 a set space, the corresponding multiple expression
2708 also has a set space.
2709 Objects of the value type do not have an associated space.
2710 The space of a multiple value is therefore always a set space.
2711 Similarly, the space of a multiple union piecewise
2712 affine expression is always a set space.
2714 The multiple expression types defined by C<isl>
2715 are C<isl_multi_val>, C<isl_multi_aff>, C<isl_multi_pw_aff>,
2716 C<isl_multi_union_pw_aff>.
2718 A multiple expression with the value zero for
2719 each output (or set) dimension can be created
2720 using the following functions.
2722 #include <isl/val.h>
2723 __isl_give isl_multi_val *isl_multi_val_zero(
2724 __isl_take isl_space *space);
2726 #include <isl/aff.h>
2727 __isl_give isl_multi_aff *isl_multi_aff_zero(
2728 __isl_take isl_space *space);
2729 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
2730 __isl_take isl_space *space);
2731 __isl_give isl_multi_union_pw_aff *
2732 isl_multi_union_pw_aff_zero(
2733 __isl_take isl_space *space);
2735 Since there is no canonical way of representing a zero
2736 value of type C<isl_union_pw_aff>, the space passed
2737 to C<isl_multi_union_pw_aff_zero> needs to be zero-dimensional.
2739 An identity function can be created using the following
2740 functions. The space needs to be that of a relation
2741 with the same number of input and output dimensions.
2743 #include <isl/aff.h>
2744 __isl_give isl_multi_aff *isl_multi_aff_identity(
2745 __isl_take isl_space *space);
2746 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
2747 __isl_take isl_space *space);
2749 A function that performs a projection on a universe
2750 relation or set can be created using the following functions.
2751 See also the corresponding
2752 projection operations in L</"Unary Operations">.
2754 #include <isl/aff.h>
2755 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
2756 __isl_take isl_space *space);
2757 __isl_give isl_multi_aff *isl_multi_aff_range_map(
2758 __isl_take isl_space *space);
2759 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
2760 __isl_take isl_space *space,
2761 enum isl_dim_type type,
2762 unsigned first, unsigned n);
2764 A multiple expression can be created from a single
2765 base expression using the following functions.
2766 The space of the created multiple expression is the same
2767 as that of the base expression, except for
2768 C<isl_multi_union_pw_aff_from_union_pw_aff> where the input
2769 lives in a parameter space and the output lives
2770 in a single-dimensional set space.
2772 #include <isl/aff.h>
2773 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
2774 __isl_take isl_aff *aff);
2775 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
2776 __isl_take isl_pw_aff *pa);
2777 __isl_give isl_multi_union_pw_aff *
2778 isl_multi_union_pw_aff_from_union_pw_aff(
2779 __isl_take isl_union_pw_aff *upa);
2781 A multiple expression can be created from a list
2782 of base expression in a specified space.
2783 The domain of this space needs to be the same
2784 as the domains of the base expressions in the list.
2785 If the base expressions have a set space (or no associated space),
2786 then this space also needs to be a set space.
2788 #include <isl/val.h>
2789 __isl_give isl_multi_val *isl_multi_val_from_val_list(
2790 __isl_take isl_space *space,
2791 __isl_take isl_val_list *list);
2793 #include <isl/aff.h>
2794 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2795 __isl_take isl_space *space,
2796 __isl_take isl_aff_list *list);
2797 __isl_give isl_multi_pw_aff *
2798 isl_multi_pw_aff_from_pw_aff_list(
2799 __isl_take isl_space *space,
2800 __isl_take isl_pw_aff_list *list);
2801 __isl_give isl_multi_union_pw_aff *
2802 isl_multi_union_pw_aff_from_union_pw_aff_list(
2803 __isl_take isl_space *space,
2804 __isl_take isl_union_pw_aff_list *list);
2806 As a convenience, a multiple piecewise expression can
2807 also be created from a multiple expression.
2808 Each piecewise expression in the result has a single
2811 #include <isl/aff.h>
2812 __isl_give isl_multi_pw_aff *
2813 isl_multi_pw_aff_from_multi_aff(
2814 __isl_take isl_multi_aff *ma);
2816 Similarly, a multiple union expression can be
2817 created from a multiple expression.
2819 #include <isl/aff.h>
2820 __isl_give isl_multi_union_pw_aff *
2821 isl_multi_union_pw_aff_from_multi_aff(
2822 __isl_take isl_multi_aff *ma);
2823 __isl_give isl_multi_union_pw_aff *
2824 isl_multi_union_pw_aff_from_multi_pw_aff(
2825 __isl_take isl_multi_pw_aff *mpa);
2827 A multiple quasi-affine expression can be created from
2828 a multiple value with a given domain space using the following
2831 #include <isl/aff.h>
2832 __isl_give isl_multi_aff *
2833 isl_multi_aff_multi_val_on_space(
2834 __isl_take isl_space *space,
2835 __isl_take isl_multi_val *mv);
2838 a multiple union piecewise affine expression can be created from
2839 a multiple value with a given domain or
2840 a multiple affine expression with a given domain
2841 using the following functions.
2843 #include <isl/aff.h>
2844 __isl_give isl_multi_union_pw_aff *
2845 isl_multi_union_pw_aff_multi_val_on_domain(
2846 __isl_take isl_union_set *domain,
2847 __isl_take isl_multi_val *mv);
2848 __isl_give isl_multi_union_pw_aff *
2849 isl_multi_union_pw_aff_multi_aff_on_domain(
2850 __isl_take isl_union_set *domain,
2851 __isl_take isl_multi_aff *ma);
2853 Multiple expressions can be copied and freed using
2854 the following functions.
2856 #include <isl/val.h>
2857 __isl_give isl_multi_val *isl_multi_val_copy(
2858 __isl_keep isl_multi_val *mv);
2859 __isl_null isl_multi_val *isl_multi_val_free(
2860 __isl_take isl_multi_val *mv);
2862 #include <isl/aff.h>
2863 __isl_give isl_multi_aff *isl_multi_aff_copy(
2864 __isl_keep isl_multi_aff *maff);
2865 __isl_null isl_multi_aff *isl_multi_aff_free(
2866 __isl_take isl_multi_aff *maff);
2867 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
2868 __isl_keep isl_multi_pw_aff *mpa);
2869 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
2870 __isl_take isl_multi_pw_aff *mpa);
2871 __isl_give isl_multi_union_pw_aff *
2872 isl_multi_union_pw_aff_copy(
2873 __isl_keep isl_multi_union_pw_aff *mupa);
2874 __isl_null isl_multi_union_pw_aff *
2875 isl_multi_union_pw_aff_free(
2876 __isl_take isl_multi_union_pw_aff *mupa);
2878 The base expression at a given position of a multiple
2879 expression can be extracted using the following functions.
2881 #include <isl/val.h>
2882 __isl_give isl_val *isl_multi_val_get_val(
2883 __isl_keep isl_multi_val *mv, int pos);
2885 #include <isl/aff.h>
2886 __isl_give isl_aff *isl_multi_aff_get_aff(
2887 __isl_keep isl_multi_aff *multi, int pos);
2888 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
2889 __isl_keep isl_multi_pw_aff *mpa, int pos);
2890 __isl_give isl_union_pw_aff *
2891 isl_multi_union_pw_aff_get_union_pw_aff(
2892 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
2894 It can be replaced using the following functions.
2896 #include <isl/val.h>
2897 __isl_give isl_multi_val *isl_multi_val_set_val(
2898 __isl_take isl_multi_val *mv, int pos,
2899 __isl_take isl_val *val);
2901 #include <isl/aff.h>
2902 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
2903 __isl_take isl_multi_aff *multi, int pos,
2904 __isl_take isl_aff *aff);
2905 __isl_give isl_multi_union_pw_aff *
2906 isl_multi_union_pw_aff_set_union_pw_aff(
2907 __isl_take isl_multi_union_pw_aff *mupa, int pos,
2908 __isl_take isl_union_pw_aff *upa);
2910 As a convenience, a sequence of base expressions that have
2911 their domains in a given space can be extracted from a sequence
2912 of union expressions using the following function.
2914 #include <isl/aff.h>
2915 __isl_give isl_multi_pw_aff *
2916 isl_multi_union_pw_aff_extract_multi_pw_aff(
2917 __isl_keep isl_multi_union_pw_aff *mupa,
2918 __isl_take isl_space *space);
2920 Note that there is a difference between C<isl_multi_union_pw_aff>
2921 and C<isl_union_pw_multi_aff> objects. The first is a sequence
2922 of unions of piecewise expressions, while the second is a union
2923 of piecewise sequences. In particular, multiple affine expressions
2924 in an C<isl_union_pw_multi_aff> may live in different spaces,
2925 while there is only a single multiple expression in
2926 an C<isl_multi_union_pw_aff>, which can therefore only live
2927 in a single space. This means that not every
2928 C<isl_union_pw_multi_aff> can be converted to
2929 an C<isl_multi_union_pw_aff>. Conversely, a zero-dimensional
2930 C<isl_multi_union_pw_aff> carries no information
2931 about any possible domain and therefore cannot be converted
2932 to an C<isl_union_pw_multi_aff>. Moreover, the elements
2933 of an C<isl_multi_union_pw_aff> may be defined over different domains,
2934 while each multiple expression inside an C<isl_union_pw_multi_aff>
2935 has a single domain. The conversion of an C<isl_union_pw_multi_aff>
2936 of dimension greater than one may therefore not be exact.
2937 The following functions can
2938 be used to perform these conversions when they are possible.
2940 #include <isl/aff.h>
2941 __isl_give isl_multi_union_pw_aff *
2942 isl_multi_union_pw_aff_from_union_pw_multi_aff(
2943 __isl_take isl_union_pw_multi_aff *upma);
2944 __isl_give isl_union_pw_multi_aff *
2945 isl_union_pw_multi_aff_from_multi_union_pw_aff(
2946 __isl_take isl_multi_union_pw_aff *mupa);
2948 =head3 Piecewise Expressions
2950 A piecewise expression is an expression that is described
2951 using zero or more base expression defined over the same
2952 number of cells in the domain space of the base expressions.
2953 All base expressions are defined over the same
2954 domain space and the cells are disjoint.
2955 The space of a piecewise expression is the same as
2956 that of the base expressions.
2957 If the union of the cells is a strict subset of the domain
2958 space, then the value of the piecewise expression outside
2959 this union is different for types derived from quasi-affine
2960 expressions and those derived from quasipolynomials.
2961 Piecewise expressions derived from quasi-affine expressions
2962 are considered to be undefined outside the union of their cells.
2963 Piecewise expressions derived from quasipolynomials
2964 are considered to be zero outside the union of their cells.
2966 Piecewise quasipolynomials are mainly used by the C<barvinok>
2967 library for representing the number of elements in a parametric set or map.
2968 For example, the piecewise quasipolynomial
2970 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2972 represents the number of points in the map
2974 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2976 The piecewise expression types defined by C<isl>
2977 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
2978 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
2980 A piecewise expression with no cells can be created using
2981 the following functions.
2983 #include <isl/aff.h>
2984 __isl_give isl_pw_aff *isl_pw_aff_empty(
2985 __isl_take isl_space *space);
2986 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
2987 __isl_take isl_space *space);
2989 A piecewise expression with a single universe cell can be
2990 created using the following functions.
2992 #include <isl/aff.h>
2993 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2994 __isl_take isl_aff *aff);
2995 __isl_give isl_pw_multi_aff *
2996 isl_pw_multi_aff_from_multi_aff(
2997 __isl_take isl_multi_aff *ma);
2999 #include <isl/polynomial.h>
3000 __isl_give isl_pw_qpolynomial *
3001 isl_pw_qpolynomial_from_qpolynomial(
3002 __isl_take isl_qpolynomial *qp);
3004 A piecewise expression with a single specified cell can be
3005 created using the following functions.
3007 #include <isl/aff.h>
3008 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3009 __isl_take isl_set *set, __isl_take isl_aff *aff);
3010 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3011 __isl_take isl_set *set,
3012 __isl_take isl_multi_aff *maff);
3014 #include <isl/polynomial.h>
3015 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3016 __isl_take isl_set *set,
3017 __isl_take isl_qpolynomial *qp);
3019 The following convenience functions first create a base expression and
3020 then create a piecewise expression over a universe domain.
3022 #include <isl/aff.h>
3023 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3024 __isl_take isl_local_space *ls);
3025 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3026 __isl_take isl_local_space *ls,
3027 enum isl_dim_type type, unsigned pos);
3028 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3029 __isl_take isl_local_space *ls);
3030 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
3031 __isl_take isl_space *space);
3032 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3033 __isl_take isl_space *space);
3034 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
3035 __isl_take isl_space *space);
3036 __isl_give isl_pw_multi_aff *
3037 isl_pw_multi_aff_project_out_map(
3038 __isl_take isl_space *space,
3039 enum isl_dim_type type,
3040 unsigned first, unsigned n);
3042 #include <isl/polynomial.h>
3043 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3044 __isl_take isl_space *space);
3046 The following convenience functions first create a base expression and
3047 then create a piecewise expression over a given domain.
3049 #include <isl/aff.h>
3050 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
3051 __isl_take isl_set *domain,
3052 __isl_take isl_val *v);
3053 __isl_give isl_pw_multi_aff *
3054 isl_pw_multi_aff_multi_val_on_domain(
3055 __isl_take isl_set *domain,
3056 __isl_take isl_multi_val *mv);
3058 As a convenience, a piecewise multiple expression can
3059 also be created from a piecewise expression.
3060 Each multiple expression in the result is derived
3061 from the corresponding base expression.
3063 #include <isl/aff.h>
3064 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
3065 __isl_take isl_pw_aff *pa);
3067 Similarly, a piecewise quasipolynomial can be
3068 created from a piecewise quasi-affine expression using
3069 the following function.
3071 #include <isl/polynomial.h>
3072 __isl_give isl_pw_qpolynomial *
3073 isl_pw_qpolynomial_from_pw_aff(
3074 __isl_take isl_pw_aff *pwaff);
3076 Piecewise expressions can be copied and freed using the following functions.
3078 #include <isl/aff.h>
3079 __isl_give isl_pw_aff *isl_pw_aff_copy(
3080 __isl_keep isl_pw_aff *pwaff);
3081 __isl_null isl_pw_aff *isl_pw_aff_free(
3082 __isl_take isl_pw_aff *pwaff);
3083 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3084 __isl_keep isl_pw_multi_aff *pma);
3085 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
3086 __isl_take isl_pw_multi_aff *pma);
3088 #include <isl/polynomial.h>
3089 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3090 __isl_keep isl_pw_qpolynomial *pwqp);
3091 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
3092 __isl_take isl_pw_qpolynomial *pwqp);
3093 __isl_give isl_pw_qpolynomial_fold *
3094 isl_pw_qpolynomial_fold_copy(
3095 __isl_keep isl_pw_qpolynomial_fold *pwf);
3096 __isl_null isl_pw_qpolynomial_fold *
3097 isl_pw_qpolynomial_fold_free(
3098 __isl_take isl_pw_qpolynomial_fold *pwf);
3100 To iterate over the different cells of a piecewise expression,
3101 use the following functions.
3103 #include <isl/aff.h>
3104 isl_bool isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3105 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3106 isl_stat isl_pw_aff_foreach_piece(
3107 __isl_keep isl_pw_aff *pwaff,
3108 isl_stat (*fn)(__isl_take isl_set *set,
3109 __isl_take isl_aff *aff,
3110 void *user), void *user);
3111 int isl_pw_multi_aff_n_piece(
3112 __isl_keep isl_pw_multi_aff *pma);
3113 isl_stat isl_pw_multi_aff_foreach_piece(
3114 __isl_keep isl_pw_multi_aff *pma,
3115 isl_stat (*fn)(__isl_take isl_set *set,
3116 __isl_take isl_multi_aff *maff,
3117 void *user), void *user);
3119 #include <isl/polynomial.h>
3120 int isl_pw_qpolynomial_n_piece(
3121 __isl_keep isl_pw_qpolynomial *pwqp);
3122 isl_stat isl_pw_qpolynomial_foreach_piece(
3123 __isl_keep isl_pw_qpolynomial *pwqp,
3124 isl_stat (*fn)(__isl_take isl_set *set,
3125 __isl_take isl_qpolynomial *qp,
3126 void *user), void *user);
3127 isl_stat isl_pw_qpolynomial_foreach_lifted_piece(
3128 __isl_keep isl_pw_qpolynomial *pwqp,
3129 isl_stat (*fn)(__isl_take isl_set *set,
3130 __isl_take isl_qpolynomial *qp,
3131 void *user), void *user);
3132 int isl_pw_qpolynomial_fold_n_piece(
3133 __isl_keep isl_pw_qpolynomial_fold *pwf);
3134 isl_stat isl_pw_qpolynomial_fold_foreach_piece(
3135 __isl_keep isl_pw_qpolynomial_fold *pwf,
3136 isl_stat (*fn)(__isl_take isl_set *set,
3137 __isl_take isl_qpolynomial_fold *fold,
3138 void *user), void *user);
3139 isl_stat isl_pw_qpolynomial_fold_foreach_lifted_piece(
3140 __isl_keep isl_pw_qpolynomial_fold *pwf,
3141 isl_stat (*fn)(__isl_take isl_set *set,
3142 __isl_take isl_qpolynomial_fold *fold,
3143 void *user), void *user);
3145 As usual, the function C<fn> should return C<0> on success
3146 and C<-1> on failure. The difference between
3147 C<isl_pw_qpolynomial_foreach_piece> and
3148 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3149 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3150 compute unique representations for all existentially quantified
3151 variables and then turn these existentially quantified variables
3152 into extra set variables, adapting the associated quasipolynomial
3153 accordingly. This means that the C<set> passed to C<fn>
3154 will not have any existentially quantified variables, but that
3155 the dimensions of the sets may be different for different
3156 invocations of C<fn>.
3157 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
3158 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
3160 A piecewise expression consisting of the expressions at a given
3161 position of a piecewise multiple expression can be extracted
3162 using the following function.
3164 #include <isl/aff.h>
3165 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3166 __isl_keep isl_pw_multi_aff *pma, int pos);
3168 These expressions can be replaced using the following function.
3170 #include <isl/aff.h>
3171 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3172 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3173 __isl_take isl_pw_aff *pa);
3175 Note that there is a difference between C<isl_multi_pw_aff> and
3176 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
3177 affine expressions, while the second is a piecewise sequence
3178 of affine expressions. In particular, each of the piecewise
3179 affine expressions in an C<isl_multi_pw_aff> may have a different
3180 domain, while all multiple expressions associated to a cell
3181 in an C<isl_pw_multi_aff> have the same domain.
3182 It is possible to convert between the two, but when converting
3183 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
3184 of the result is the intersection of the domains of the input.
3185 The reverse conversion is exact.
3187 #include <isl/aff.h>
3188 __isl_give isl_pw_multi_aff *
3189 isl_pw_multi_aff_from_multi_pw_aff(
3190 __isl_take isl_multi_pw_aff *mpa);
3191 __isl_give isl_multi_pw_aff *
3192 isl_multi_pw_aff_from_pw_multi_aff(
3193 __isl_take isl_pw_multi_aff *pma);
3195 =head3 Union Expressions
3197 A union expression collects base expressions defined
3198 over different domains. The space of a union expression
3199 is that of the shared parameter space.
3201 The union expression types defined by C<isl>
3202 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
3203 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
3205 C<isl_union_pw_aff>,
3206 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>,
3207 there can be at most one base expression for a given domain space.
3209 C<isl_union_pw_multi_aff>,
3210 there can be multiple such expressions for a given domain space,
3211 but the domains of these expressions need to be disjoint.
3213 An empty union expression can be created using the following functions.
3215 #include <isl/aff.h>
3216 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
3217 __isl_take isl_space *space);
3218 __isl_give isl_union_pw_multi_aff *
3219 isl_union_pw_multi_aff_empty(
3220 __isl_take isl_space *space);
3222 #include <isl/polynomial.h>
3223 __isl_give isl_union_pw_qpolynomial *
3224 isl_union_pw_qpolynomial_zero(
3225 __isl_take isl_space *space);
3227 A union expression containing a single base expression
3228 can be created using the following functions.
3230 #include <isl/aff.h>
3231 __isl_give isl_union_pw_aff *
3232 isl_union_pw_aff_from_pw_aff(
3233 __isl_take isl_pw_aff *pa);
3234 __isl_give isl_union_pw_multi_aff *
3235 isl_union_pw_multi_aff_from_aff(
3236 __isl_take isl_aff *aff);
3237 __isl_give isl_union_pw_multi_aff *
3238 isl_union_pw_multi_aff_from_pw_multi_aff(
3239 __isl_take isl_pw_multi_aff *pma);
3241 #include <isl/polynomial.h>
3242 __isl_give isl_union_pw_qpolynomial *
3243 isl_union_pw_qpolynomial_from_pw_qpolynomial(
3244 __isl_take isl_pw_qpolynomial *pwqp);
3246 The following functions create a base expression on each
3247 of the sets in the union set and collect the results.
3249 #include <isl/aff.h>
3250 __isl_give isl_union_pw_multi_aff *
3251 isl_union_pw_multi_aff_from_union_pw_aff(
3252 __isl_take isl_union_pw_aff *upa);
3253 __isl_give isl_union_pw_aff *
3254 isl_union_pw_multi_aff_get_union_pw_aff(
3255 __isl_keep isl_union_pw_multi_aff *upma, int pos);
3256 __isl_give isl_union_pw_aff *
3257 isl_union_pw_aff_val_on_domain(
3258 __isl_take isl_union_set *domain,
3259 __isl_take isl_val *v);
3260 __isl_give isl_union_pw_multi_aff *
3261 isl_union_pw_multi_aff_multi_val_on_domain(
3262 __isl_take isl_union_set *domain,
3263 __isl_take isl_multi_val *mv);
3265 An C<isl_union_pw_aff> that is equal to a (parametric) affine
3266 expression on a given domain can be created using the following
3269 #include <isl/aff.h>
3270 __isl_give isl_union_pw_aff *
3271 isl_union_pw_aff_aff_on_domain(
3272 __isl_take isl_union_set *domain,
3273 __isl_take isl_aff *aff);
3275 A base expression can be added to a union expression using
3276 the following functions.
3278 #include <isl/aff.h>
3279 __isl_give isl_union_pw_aff *
3280 isl_union_pw_aff_add_pw_aff(
3281 __isl_take isl_union_pw_aff *upa,
3282 __isl_take isl_pw_aff *pa);
3283 __isl_give isl_union_pw_multi_aff *
3284 isl_union_pw_multi_aff_add_pw_multi_aff(
3285 __isl_take isl_union_pw_multi_aff *upma,
3286 __isl_take isl_pw_multi_aff *pma);
3288 #include <isl/polynomial.h>
3289 __isl_give isl_union_pw_qpolynomial *
3290 isl_union_pw_qpolynomial_add_pw_qpolynomial(
3291 __isl_take isl_union_pw_qpolynomial *upwqp,
3292 __isl_take isl_pw_qpolynomial *pwqp);
3294 Union expressions can be copied and freed using
3295 the following functions.
3297 #include <isl/aff.h>
3298 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
3299 __isl_keep isl_union_pw_aff *upa);
3300 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
3301 __isl_take isl_union_pw_aff *upa);
3302 __isl_give isl_union_pw_multi_aff *
3303 isl_union_pw_multi_aff_copy(
3304 __isl_keep isl_union_pw_multi_aff *upma);
3305 __isl_null isl_union_pw_multi_aff *
3306 isl_union_pw_multi_aff_free(
3307 __isl_take isl_union_pw_multi_aff *upma);
3309 #include <isl/polynomial.h>
3310 __isl_give isl_union_pw_qpolynomial *
3311 isl_union_pw_qpolynomial_copy(
3312 __isl_keep isl_union_pw_qpolynomial *upwqp);
3313 __isl_null isl_union_pw_qpolynomial *
3314 isl_union_pw_qpolynomial_free(
3315 __isl_take isl_union_pw_qpolynomial *upwqp);
3316 __isl_give isl_union_pw_qpolynomial_fold *
3317 isl_union_pw_qpolynomial_fold_copy(
3318 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3319 __isl_null isl_union_pw_qpolynomial_fold *
3320 isl_union_pw_qpolynomial_fold_free(
3321 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3323 To iterate over the base expressions in a union expression,
3324 use the following functions.
3326 #include <isl/aff.h>
3327 int isl_union_pw_aff_n_pw_aff(
3328 __isl_keep isl_union_pw_aff *upa);
3329 isl_stat isl_union_pw_aff_foreach_pw_aff(
3330 __isl_keep isl_union_pw_aff *upa,
3331 isl_stat (*fn)(__isl_take isl_pw_aff *pa,
3332 void *user), void *user);
3333 int isl_union_pw_multi_aff_n_pw_multi_aff(
3334 __isl_keep isl_union_pw_multi_aff *upma);
3335 isl_stat isl_union_pw_multi_aff_foreach_pw_multi_aff(
3336 __isl_keep isl_union_pw_multi_aff *upma,
3337 isl_stat (*fn)(__isl_take isl_pw_multi_aff *pma,
3338 void *user), void *user);
3340 #include <isl/polynomial.h>
3341 int isl_union_pw_qpolynomial_n_pw_qpolynomial(
3342 __isl_keep isl_union_pw_qpolynomial *upwqp);
3343 isl_stat isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3344 __isl_keep isl_union_pw_qpolynomial *upwqp,
3345 isl_stat (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
3346 void *user), void *user);
3347 int isl_union_pw_qpolynomial_fold_n_pw_qpolynomial_fold(
3348 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3349 isl_stat isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3350 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3351 isl_stat (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3352 void *user), void *user);
3354 To extract the base expression in a given space from a union, use
3355 the following functions.
3357 #include <isl/aff.h>
3358 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
3359 __isl_keep isl_union_pw_aff *upa,
3360 __isl_take isl_space *space);
3361 __isl_give isl_pw_multi_aff *
3362 isl_union_pw_multi_aff_extract_pw_multi_aff(
3363 __isl_keep isl_union_pw_multi_aff *upma,
3364 __isl_take isl_space *space);
3366 #include <isl/polynomial.h>
3367 __isl_give isl_pw_qpolynomial *
3368 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3369 __isl_keep isl_union_pw_qpolynomial *upwqp,
3370 __isl_take isl_space *space);
3372 =head2 Input and Output
3374 For set and relation,
3375 C<isl> supports its own input/output format, which is similar
3376 to the C<Omega> format, but also supports the C<PolyLib> format
3378 For other object types, typically only an C<isl> format is supported.
3380 =head3 C<isl> format
3382 The C<isl> format is similar to that of C<Omega>, but has a different
3383 syntax for describing the parameters and allows for the definition
3384 of an existentially quantified variable as the integer division
3385 of an affine expression.
3386 For example, the set of integers C<i> between C<0> and C<n>
3387 such that C<i % 10 <= 6> can be described as
3389 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
3392 A set or relation can have several disjuncts, separated
3393 by the keyword C<or>. Each disjunct is either a conjunction
3394 of constraints or a projection (C<exists>) of a conjunction
3395 of constraints. The constraints are separated by the keyword
3398 =head3 C<PolyLib> format
3400 If the represented set is a union, then the first line
3401 contains a single number representing the number of disjuncts.
3402 Otherwise, a line containing the number C<1> is optional.
3404 Each disjunct is represented by a matrix of constraints.
3405 The first line contains two numbers representing
3406 the number of rows and columns,
3407 where the number of rows is equal to the number of constraints
3408 and the number of columns is equal to two plus the number of variables.
3409 The following lines contain the actual rows of the constraint matrix.
3410 In each row, the first column indicates whether the constraint
3411 is an equality (C<0>) or inequality (C<1>). The final column
3412 corresponds to the constant term.
3414 If the set is parametric, then the coefficients of the parameters
3415 appear in the last columns before the constant column.
3416 The coefficients of any existentially quantified variables appear
3417 between those of the set variables and those of the parameters.
3419 =head3 Extended C<PolyLib> format
3421 The extended C<PolyLib> format is nearly identical to the
3422 C<PolyLib> format. The only difference is that the line
3423 containing the number of rows and columns of a constraint matrix
3424 also contains four additional numbers:
3425 the number of output dimensions, the number of input dimensions,
3426 the number of local dimensions (i.e., the number of existentially
3427 quantified variables) and the number of parameters.
3428 For sets, the number of ``output'' dimensions is equal
3429 to the number of set dimensions, while the number of ``input''
3434 Objects can be read from input using the following functions.
3436 #include <isl/val.h>
3437 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
3439 __isl_give isl_multi_val *isl_multi_val_read_from_str(
3440 isl_ctx *ctx, const char *str);
3442 #include <isl/set.h>
3443 __isl_give isl_basic_set *isl_basic_set_read_from_file(
3444 isl_ctx *ctx, FILE *input);
3445 __isl_give isl_basic_set *isl_basic_set_read_from_str(
3446 isl_ctx *ctx, const char *str);
3447 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
3449 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
3452 #include <isl/map.h>
3453 __isl_give isl_basic_map *isl_basic_map_read_from_file(
3454 isl_ctx *ctx, FILE *input);
3455 __isl_give isl_basic_map *isl_basic_map_read_from_str(
3456 isl_ctx *ctx, const char *str);
3457 __isl_give isl_map *isl_map_read_from_file(
3458 isl_ctx *ctx, FILE *input);
3459 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
3462 #include <isl/union_set.h>
3463 __isl_give isl_union_set *isl_union_set_read_from_file(
3464 isl_ctx *ctx, FILE *input);
3465 __isl_give isl_union_set *isl_union_set_read_from_str(
3466 isl_ctx *ctx, const char *str);
3468 #include <isl/union_map.h>
3469 __isl_give isl_union_map *isl_union_map_read_from_file(
3470 isl_ctx *ctx, FILE *input);
3471 __isl_give isl_union_map *isl_union_map_read_from_str(
3472 isl_ctx *ctx, const char *str);
3474 #include <isl/aff.h>
3475 __isl_give isl_aff *isl_aff_read_from_str(
3476 isl_ctx *ctx, const char *str);
3477 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3478 isl_ctx *ctx, const char *str);
3479 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3480 isl_ctx *ctx, const char *str);
3481 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3482 isl_ctx *ctx, const char *str);
3483 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
3484 isl_ctx *ctx, const char *str);
3485 __isl_give isl_union_pw_aff *
3486 isl_union_pw_aff_read_from_str(
3487 isl_ctx *ctx, const char *str);
3488 __isl_give isl_union_pw_multi_aff *
3489 isl_union_pw_multi_aff_read_from_str(
3490 isl_ctx *ctx, const char *str);
3491 __isl_give isl_multi_union_pw_aff *
3492 isl_multi_union_pw_aff_read_from_str(
3493 isl_ctx *ctx, const char *str);
3495 #include <isl/polynomial.h>
3496 __isl_give isl_union_pw_qpolynomial *
3497 isl_union_pw_qpolynomial_read_from_str(
3498 isl_ctx *ctx, const char *str);
3500 For sets and relations,
3501 the input format is autodetected and may be either the C<PolyLib> format
3502 or the C<isl> format.
3506 Before anything can be printed, an C<isl_printer> needs to
3509 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
3511 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
3512 __isl_null isl_printer *isl_printer_free(
3513 __isl_take isl_printer *printer);
3515 C<isl_printer_to_file> prints to the given file, while
3516 C<isl_printer_to_str> prints to a string that can be extracted
3517 using the following function.
3519 #include <isl/printer.h>
3520 __isl_give char *isl_printer_get_str(
3521 __isl_keep isl_printer *printer);
3523 The printer can be inspected using the following functions.
3525 FILE *isl_printer_get_file(
3526 __isl_keep isl_printer *printer);
3527 int isl_printer_get_output_format(
3528 __isl_keep isl_printer *p);
3529 int isl_printer_get_yaml_style(__isl_keep isl_printer *p);
3531 The behavior of the printer can be modified in various ways
3533 __isl_give isl_printer *isl_printer_set_output_format(
3534 __isl_take isl_printer *p, int output_format);
3535 __isl_give isl_printer *isl_printer_set_indent(
3536 __isl_take isl_printer *p, int indent);
3537 __isl_give isl_printer *isl_printer_set_indent_prefix(
3538 __isl_take isl_printer *p, const char *prefix);
3539 __isl_give isl_printer *isl_printer_indent(
3540 __isl_take isl_printer *p, int indent);
3541 __isl_give isl_printer *isl_printer_set_prefix(
3542 __isl_take isl_printer *p, const char *prefix);
3543 __isl_give isl_printer *isl_printer_set_suffix(
3544 __isl_take isl_printer *p, const char *suffix);
3545 __isl_give isl_printer *isl_printer_set_yaml_style(
3546 __isl_take isl_printer *p, int yaml_style);
3548 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
3549 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
3550 and defaults to C<ISL_FORMAT_ISL>.
3551 Each line in the output is prefixed by C<indent_prefix>,
3552 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
3553 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
3554 In the C<PolyLib> format output,
3555 the coefficients of the existentially quantified variables
3556 appear between those of the set variables and those
3558 The function C<isl_printer_indent> increases the indentation
3559 by the specified amount (which may be negative).
3560 The YAML style may be either C<ISL_YAML_STYLE_BLOCK> or
3561 C<ISL_YAML_STYLE_FLOW> and when we are printing something
3564 To actually print something, use
3566 #include <isl/printer.h>
3567 __isl_give isl_printer *isl_printer_print_double(
3568 __isl_take isl_printer *p, double d);
3570 #include <isl/val.h>
3571 __isl_give isl_printer *isl_printer_print_val(
3572 __isl_take isl_printer *p, __isl_keep isl_val *v);
3574 #include <isl/set.h>
3575 __isl_give isl_printer *isl_printer_print_basic_set(
3576 __isl_take isl_printer *printer,
3577 __isl_keep isl_basic_set *bset);
3578 __isl_give isl_printer *isl_printer_print_set(
3579 __isl_take isl_printer *printer,
3580 __isl_keep isl_set *set);
3582 #include <isl/map.h>
3583 __isl_give isl_printer *isl_printer_print_basic_map(
3584 __isl_take isl_printer *printer,
3585 __isl_keep isl_basic_map *bmap);
3586 __isl_give isl_printer *isl_printer_print_map(
3587 __isl_take isl_printer *printer,
3588 __isl_keep isl_map *map);
3590 #include <isl/union_set.h>
3591 __isl_give isl_printer *isl_printer_print_union_set(
3592 __isl_take isl_printer *p,
3593 __isl_keep isl_union_set *uset);
3595 #include <isl/union_map.h>
3596 __isl_give isl_printer *isl_printer_print_union_map(
3597 __isl_take isl_printer *p,
3598 __isl_keep isl_union_map *umap);
3600 #include <isl/val.h>
3601 __isl_give isl_printer *isl_printer_print_multi_val(
3602 __isl_take isl_printer *p,
3603 __isl_keep isl_multi_val *mv);
3605 #include <isl/aff.h>
3606 __isl_give isl_printer *isl_printer_print_aff(
3607 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3608 __isl_give isl_printer *isl_printer_print_multi_aff(
3609 __isl_take isl_printer *p,
3610 __isl_keep isl_multi_aff *maff);
3611 __isl_give isl_printer *isl_printer_print_pw_aff(
3612 __isl_take isl_printer *p,
3613 __isl_keep isl_pw_aff *pwaff);
3614 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3615 __isl_take isl_printer *p,
3616 __isl_keep isl_pw_multi_aff *pma);
3617 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3618 __isl_take isl_printer *p,
3619 __isl_keep isl_multi_pw_aff *mpa);
3620 __isl_give isl_printer *isl_printer_print_union_pw_aff(
3621 __isl_take isl_printer *p,
3622 __isl_keep isl_union_pw_aff *upa);
3623 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3624 __isl_take isl_printer *p,
3625 __isl_keep isl_union_pw_multi_aff *upma);
3626 __isl_give isl_printer *
3627 isl_printer_print_multi_union_pw_aff(
3628 __isl_take isl_printer *p,
3629 __isl_keep isl_multi_union_pw_aff *mupa);
3631 #include <isl/polynomial.h>
3632 __isl_give isl_printer *isl_printer_print_qpolynomial(
3633 __isl_take isl_printer *p,
3634 __isl_keep isl_qpolynomial *qp);
3635 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3636 __isl_take isl_printer *p,
3637 __isl_keep isl_pw_qpolynomial *pwqp);
3638 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3639 __isl_take isl_printer *p,
3640 __isl_keep isl_union_pw_qpolynomial *upwqp);
3642 __isl_give isl_printer *
3643 isl_printer_print_pw_qpolynomial_fold(
3644 __isl_take isl_printer *p,
3645 __isl_keep isl_pw_qpolynomial_fold *pwf);
3646 __isl_give isl_printer *
3647 isl_printer_print_union_pw_qpolynomial_fold(
3648 __isl_take isl_printer *p,
3649 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3651 For C<isl_printer_print_qpolynomial>,
3652 C<isl_printer_print_pw_qpolynomial> and
3653 C<isl_printer_print_pw_qpolynomial_fold>,
3654 the output format of the printer
3655 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3656 For C<isl_printer_print_union_pw_qpolynomial> and
3657 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
3659 In case of printing in C<ISL_FORMAT_C>, the user may want
3660 to set the names of all dimensions first.
3662 C<isl> also provides limited support for printing YAML documents,
3663 just enough for the internal use for printing such documents.
3665 #include <isl/printer.h>
3666 __isl_give isl_printer *isl_printer_yaml_start_mapping(
3667 __isl_take isl_printer *p);
3668 __isl_give isl_printer *isl_printer_yaml_end_mapping(
3669 __isl_take isl_printer *p);
3670 __isl_give isl_printer *isl_printer_yaml_start_sequence(
3671 __isl_take isl_printer *p);
3672 __isl_give isl_printer *isl_printer_yaml_end_sequence(
3673 __isl_take isl_printer *p);
3674 __isl_give isl_printer *isl_printer_yaml_next(
3675 __isl_take isl_printer *p);
3677 A document is started by a call to either
3678 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3679 Anything printed to the printer after such a call belong to the
3680 first key of the mapping or the first element in the sequence.
3681 The function C<isl_printer_yaml_next> moves to the value if
3682 we are currently printing a mapping key, the next key if we
3683 are printing a value or the next element if we are printing
3684 an element in a sequence.
3685 Nested mappings and sequences are initiated by the same
3686 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3687 Each call to these functions needs to have a corresponding call to
3688 C<isl_printer_yaml_end_mapping> or C<isl_printer_yaml_end_sequence>.
3690 When called on a file printer, the following function flushes
3691 the file. When called on a string printer, the buffer is cleared.
3693 __isl_give isl_printer *isl_printer_flush(
3694 __isl_take isl_printer *p);
3696 The following functions allow the user to attach
3697 notes to a printer in order to keep track of additional state.
3699 #include <isl/printer.h>
3700 isl_bool isl_printer_has_note(__isl_keep isl_printer *p,
3701 __isl_keep isl_id *id);
3702 __isl_give isl_id *isl_printer_get_note(
3703 __isl_keep isl_printer *p, __isl_take isl_id *id);
3704 __isl_give isl_printer *isl_printer_set_note(
3705 __isl_take isl_printer *p,
3706 __isl_take isl_id *id, __isl_take isl_id *note);
3708 C<isl_printer_set_note> associates the given note to the given
3709 identifier in the printer.
3710 C<isl_printer_get_note> retrieves a note associated to an
3712 C<isl_printer_has_note> checks if there is such a note.
3713 C<isl_printer_get_note> fails if the requested note does not exist.
3715 Alternatively, a string representation can be obtained
3716 directly using the following functions, which always print
3720 __isl_give char *isl_id_to_str(
3721 __isl_keep isl_id *id);
3723 #include <isl/space.h>
3724 __isl_give char *isl_space_to_str(
3725 __isl_keep isl_space *space);
3727 #include <isl/val.h>
3728 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
3729 __isl_give char *isl_multi_val_to_str(
3730 __isl_keep isl_multi_val *mv);
3732 #include <isl/set.h>
3733 __isl_give char *isl_basic_set_to_str(
3734 __isl_keep isl_basic_set *bset);
3735 __isl_give char *isl_set_to_str(
3736 __isl_keep isl_set *set);
3738 #include <isl/union_set.h>
3739 __isl_give char *isl_union_set_to_str(
3740 __isl_keep isl_union_set *uset);
3742 #include <isl/map.h>
3743 __isl_give char *isl_basic_map_to_str(
3744 __isl_keep isl_basic_map *bmap);
3745 __isl_give char *isl_map_to_str(
3746 __isl_keep isl_map *map);
3748 #include <isl/union_map.h>
3749 __isl_give char *isl_union_map_to_str(
3750 __isl_keep isl_union_map *umap);
3752 #include <isl/aff.h>
3753 __isl_give char *isl_aff_to_str(__isl_keep isl_aff *aff);
3754 __isl_give char *isl_pw_aff_to_str(
3755 __isl_keep isl_pw_aff *pa);
3756 __isl_give char *isl_multi_aff_to_str(
3757 __isl_keep isl_multi_aff *ma);
3758 __isl_give char *isl_pw_multi_aff_to_str(
3759 __isl_keep isl_pw_multi_aff *pma);
3760 __isl_give char *isl_multi_pw_aff_to_str(
3761 __isl_keep isl_multi_pw_aff *mpa);
3762 __isl_give char *isl_union_pw_aff_to_str(
3763 __isl_keep isl_union_pw_aff *upa);
3764 __isl_give char *isl_union_pw_multi_aff_to_str(
3765 __isl_keep isl_union_pw_multi_aff *upma);
3766 __isl_give char *isl_multi_union_pw_aff_to_str(
3767 __isl_keep isl_multi_union_pw_aff *mupa);
3769 #include <isl/point.h>
3770 __isl_give char *isl_point_to_str(
3771 __isl_keep isl_point *pnt);
3773 #include <isl/polynomial.h>
3774 __isl_give char *isl_pw_qpolynomial_to_str(
3775 __isl_keep isl_pw_qpolynomial *pwqp);
3776 __isl_give char *isl_union_pw_qpolynomial_to_str(
3777 __isl_keep isl_union_pw_qpolynomial *upwqp);
3781 =head3 Unary Properties
3787 The following functions test whether the given set or relation
3788 contains any integer points. The ``plain'' variants do not perform
3789 any computations, but simply check if the given set or relation
3790 is already known to be empty.
3792 isl_bool isl_basic_set_plain_is_empty(
3793 __isl_keep isl_basic_set *bset);
3794 isl_bool isl_basic_set_is_empty(
3795 __isl_keep isl_basic_set *bset);
3796 isl_bool isl_set_plain_is_empty(
3797 __isl_keep isl_set *set);
3798 isl_bool isl_set_is_empty(__isl_keep isl_set *set);
3799 isl_bool isl_union_set_is_empty(
3800 __isl_keep isl_union_set *uset);
3801 isl_bool isl_basic_map_plain_is_empty(
3802 __isl_keep isl_basic_map *bmap);
3803 isl_bool isl_basic_map_is_empty(
3804 __isl_keep isl_basic_map *bmap);
3805 isl_bool isl_map_plain_is_empty(
3806 __isl_keep isl_map *map);
3807 isl_bool isl_map_is_empty(__isl_keep isl_map *map);
3808 isl_bool isl_union_map_is_empty(
3809 __isl_keep isl_union_map *umap);
3811 =item * Universality
3813 isl_bool isl_basic_set_plain_is_universe(
3814 __isl_keep isl_basic_set *bset);
3815 isl_bool isl_basic_set_is_universe(
3816 __isl_keep isl_basic_set *bset);
3817 isl_bool isl_basic_map_plain_is_universe(
3818 __isl_keep isl_basic_map *bmap);
3819 isl_bool isl_basic_map_is_universe(
3820 __isl_keep isl_basic_map *bmap);
3821 isl_bool isl_set_plain_is_universe(
3822 __isl_keep isl_set *set);
3823 isl_bool isl_map_plain_is_universe(
3824 __isl_keep isl_map *map);
3826 =item * Single-valuedness
3828 #include <isl/set.h>
3829 isl_bool isl_set_is_singleton(__isl_keep isl_set *set);
3831 #include <isl/map.h>
3832 isl_bool isl_basic_map_is_single_valued(
3833 __isl_keep isl_basic_map *bmap);
3834 isl_bool isl_map_plain_is_single_valued(
3835 __isl_keep isl_map *map);
3836 isl_bool isl_map_is_single_valued(__isl_keep isl_map *map);
3838 #include <isl/union_map.h>
3839 isl_bool isl_union_map_is_single_valued(
3840 __isl_keep isl_union_map *umap);
3844 isl_bool isl_map_plain_is_injective(
3845 __isl_keep isl_map *map);
3846 isl_bool isl_map_is_injective(
3847 __isl_keep isl_map *map);
3848 isl_bool isl_union_map_plain_is_injective(
3849 __isl_keep isl_union_map *umap);
3850 isl_bool isl_union_map_is_injective(
3851 __isl_keep isl_union_map *umap);
3855 isl_bool isl_map_is_bijective(
3856 __isl_keep isl_map *map);
3857 isl_bool isl_union_map_is_bijective(
3858 __isl_keep isl_union_map *umap);
3862 The following functions test whether the given relation
3863 only maps elements to themselves.
3865 #include <isl/map.h>
3866 isl_bool isl_map_is_identity(
3867 __isl_keep isl_map *map);
3869 #include <isl/union_map.h>
3870 isl_bool isl_union_map_is_identity(
3871 __isl_keep isl_union_map *umap);
3875 __isl_give isl_val *
3876 isl_basic_map_plain_get_val_if_fixed(
3877 __isl_keep isl_basic_map *bmap,
3878 enum isl_dim_type type, unsigned pos);
3879 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
3880 __isl_keep isl_set *set,
3881 enum isl_dim_type type, unsigned pos);
3882 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
3883 __isl_keep isl_map *map,
3884 enum isl_dim_type type, unsigned pos);
3886 If the set or relation obviously lies on a hyperplane where the given dimension
3887 has a fixed value, then return that value.
3888 Otherwise return NaN.
3892 isl_stat isl_set_dim_residue_class_val(
3893 __isl_keep isl_set *set,
3894 int pos, __isl_give isl_val **modulo,
3895 __isl_give isl_val **residue);
3897 Check if the values of the given set dimension are equal to a fixed
3898 value modulo some integer value. If so, assign the modulo to C<*modulo>
3899 and the fixed value to C<*residue>. If the given dimension attains only
3900 a single value, then assign C<0> to C<*modulo> and the fixed value to
3902 If the dimension does not attain only a single value and if no modulo
3903 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
3907 To check whether the description of a set, relation or function depends
3908 on one or more given dimensions,
3909 the following functions can be used.
3911 #include <isl/constraint.h>
3912 isl_bool isl_constraint_involves_dims(
3913 __isl_keep isl_constraint *constraint,
3914 enum isl_dim_type type, unsigned first, unsigned n);
3916 #include <isl/set.h>
3917 isl_bool isl_basic_set_involves_dims(
3918 __isl_keep isl_basic_set *bset,
3919 enum isl_dim_type type, unsigned first, unsigned n);
3920 isl_bool isl_set_involves_dims(__isl_keep isl_set *set,
3921 enum isl_dim_type type, unsigned first, unsigned n);
3923 #include <isl/map.h>
3924 isl_bool isl_basic_map_involves_dims(
3925 __isl_keep isl_basic_map *bmap,
3926 enum isl_dim_type type, unsigned first, unsigned n);
3927 isl_bool isl_map_involves_dims(__isl_keep isl_map *map,
3928 enum isl_dim_type type, unsigned first, unsigned n);
3930 #include <isl/union_map.h>
3931 isl_bool isl_union_map_involves_dims(
3932 __isl_keep isl_union_map *umap,
3933 enum isl_dim_type type, unsigned first, unsigned n);
3935 #include <isl/aff.h>
3936 isl_bool isl_aff_involves_dims(__isl_keep isl_aff *aff,
3937 enum isl_dim_type type, unsigned first, unsigned n);
3938 isl_bool isl_pw_aff_involves_dims(
3939 __isl_keep isl_pw_aff *pwaff,
3940 enum isl_dim_type type, unsigned first, unsigned n);
3941 isl_bool isl_multi_aff_involves_dims(
3942 __isl_keep isl_multi_aff *ma,
3943 enum isl_dim_type type, unsigned first, unsigned n);
3944 isl_bool isl_multi_pw_aff_involves_dims(
3945 __isl_keep isl_multi_pw_aff *mpa,
3946 enum isl_dim_type type, unsigned first, unsigned n);
3948 #include <isl/polynomial.h>
3949 isl_bool isl_qpolynomial_involves_dims(
3950 __isl_keep isl_qpolynomial *qp,
3951 enum isl_dim_type type, unsigned first, unsigned n);
3953 Similarly, the following functions can be used to check whether
3954 a given dimension is involved in any lower or upper bound.
3956 #include <isl/set.h>
3957 isl_bool isl_set_dim_has_any_lower_bound(
3958 __isl_keep isl_set *set,
3959 enum isl_dim_type type, unsigned pos);
3960 isl_bool isl_set_dim_has_any_upper_bound(
3961 __isl_keep isl_set *set,
3962 enum isl_dim_type type, unsigned pos);
3964 Note that these functions return true even if there is a bound on
3965 the dimension on only some of the basic sets of C<set>.
3966 To check if they have a bound for all of the basic sets in C<set>,
3967 use the following functions instead.
3969 #include <isl/set.h>
3970 isl_bool isl_set_dim_has_lower_bound(
3971 __isl_keep isl_set *set,
3972 enum isl_dim_type type, unsigned pos);
3973 isl_bool isl_set_dim_has_upper_bound(
3974 __isl_keep isl_set *set,
3975 enum isl_dim_type type, unsigned pos);
3979 To check whether a set is a parameter domain, use this function:
3981 isl_bool isl_set_is_params(__isl_keep isl_set *set);
3982 isl_bool isl_union_set_is_params(
3983 __isl_keep isl_union_set *uset);
3987 The following functions check whether the space of the given
3988 (basic) set or relation domain and/or range is a wrapped relation.
3990 #include <isl/space.h>
3991 isl_bool isl_space_is_wrapping(
3992 __isl_keep isl_space *space);
3993 isl_bool isl_space_domain_is_wrapping(
3994 __isl_keep isl_space *space);
3995 isl_bool isl_space_range_is_wrapping(
3996 __isl_keep isl_space *space);
3997 isl_bool isl_space_is_product(
3998 __isl_keep isl_space *space);
4000 #include <isl/set.h>
4001 isl_bool isl_basic_set_is_wrapping(
4002 __isl_keep isl_basic_set *bset);
4003 isl_bool isl_set_is_wrapping(__isl_keep isl_set *set);
4005 #include <isl/map.h>
4006 isl_bool isl_map_domain_is_wrapping(
4007 __isl_keep isl_map *map);
4008 isl_bool isl_map_range_is_wrapping(
4009 __isl_keep isl_map *map);
4010 isl_bool isl_map_is_product(__isl_keep isl_map *map);
4012 #include <isl/val.h>
4013 isl_bool isl_multi_val_range_is_wrapping(
4014 __isl_keep isl_multi_val *mv);
4016 #include <isl/aff.h>
4017 isl_bool isl_multi_aff_range_is_wrapping(
4018 __isl_keep isl_multi_aff *ma);
4019 isl_bool isl_multi_pw_aff_range_is_wrapping(
4020 __isl_keep isl_multi_pw_aff *mpa);
4021 isl_bool isl_multi_union_pw_aff_range_is_wrapping(
4022 __isl_keep isl_multi_union_pw_aff *mupa);
4024 The input to C<isl_space_is_wrapping> should
4025 be the space of a set, while that of
4026 C<isl_space_domain_is_wrapping> and
4027 C<isl_space_range_is_wrapping> should be the space of a relation.
4028 The input to C<isl_space_is_product> can be either the space
4029 of a set or that of a binary relation.
4030 In case the input is the space of a binary relation, it checks
4031 whether both domain and range are wrapping.
4033 =item * Internal Product
4035 isl_bool isl_basic_map_can_zip(
4036 __isl_keep isl_basic_map *bmap);
4037 isl_bool isl_map_can_zip(__isl_keep isl_map *map);
4039 Check whether the product of domain and range of the given relation
4041 i.e., whether both domain and range are nested relations.
4045 #include <isl/space.h>
4046 isl_bool isl_space_can_curry(
4047 __isl_keep isl_space *space);
4049 #include <isl/map.h>
4050 isl_bool isl_basic_map_can_curry(
4051 __isl_keep isl_basic_map *bmap);
4052 isl_bool isl_map_can_curry(__isl_keep isl_map *map);
4054 Check whether the domain of the (basic) relation is a wrapped relation.
4056 #include <isl/space.h>
4057 __isl_give isl_space *isl_space_uncurry(
4058 __isl_take isl_space *space);
4060 #include <isl/map.h>
4061 isl_bool isl_basic_map_can_uncurry(
4062 __isl_keep isl_basic_map *bmap);
4063 isl_bool isl_map_can_uncurry(__isl_keep isl_map *map);
4065 Check whether the range of the (basic) relation is a wrapped relation.
4067 #include <isl/space.h>
4068 isl_bool isl_space_can_range_curry(
4069 __isl_keep isl_space *space);
4071 #include <isl/map.h>
4072 isl_bool isl_map_can_range_curry(
4073 __isl_keep isl_map *map);
4075 Check whether the domain of the relation wrapped in the range of
4076 the input is itself a wrapped relation.
4078 =item * Special Values
4080 #include <isl/aff.h>
4081 isl_bool isl_aff_is_cst(__isl_keep isl_aff *aff);
4082 isl_bool isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
4083 isl_bool isl_multi_pw_aff_is_cst(
4084 __isl_keep isl_multi_pw_aff *mpa);
4086 Check whether the given expression is a constant.
4088 #include <isl/val.h>
4089 isl_bool isl_multi_val_involves_nan(
4090 __isl_keep isl_multi_val *mv);
4092 #include <isl/aff.h>
4093 isl_bool isl_aff_is_nan(__isl_keep isl_aff *aff);
4094 isl_bool isl_multi_aff_involves_nan(
4095 __isl_keep isl_multi_aff *ma);
4096 isl_bool isl_pw_aff_involves_nan(
4097 __isl_keep isl_pw_aff *pa);
4098 isl_bool isl_pw_multi_aff_involves_nan(
4099 __isl_keep isl_pw_multi_aff *pma);
4100 isl_bool isl_multi_pw_aff_involves_nan(
4101 __isl_keep isl_multi_pw_aff *mpa);
4102 isl_bool isl_union_pw_aff_involves_nan(
4103 __isl_keep isl_union_pw_aff *upa);
4104 isl_bool isl_union_pw_multi_aff_involves_nan(
4105 __isl_keep isl_union_pw_multi_aff *upma);
4106 isl_bool isl_multi_union_pw_aff_involves_nan(
4107 __isl_keep isl_multi_union_pw_aff *mupa);
4109 #include <isl/polynomial.h>
4110 isl_bool isl_qpolynomial_is_nan(
4111 __isl_keep isl_qpolynomial *qp);
4112 isl_bool isl_qpolynomial_fold_is_nan(
4113 __isl_keep isl_qpolynomial_fold *fold);
4114 isl_bool isl_pw_qpolynomial_involves_nan(
4115 __isl_keep isl_pw_qpolynomial *pwqp);
4116 isl_bool isl_pw_qpolynomial_fold_involves_nan(
4117 __isl_keep isl_pw_qpolynomial_fold *pwf);
4118 isl_bool isl_union_pw_qpolynomial_involves_nan(
4119 __isl_keep isl_union_pw_qpolynomial *upwqp);
4120 isl_bool isl_union_pw_qpolynomial_fold_involves_nan(
4121 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4123 Check whether the given expression is equal to or involves NaN.
4125 #include <isl/aff.h>
4126 isl_bool isl_aff_plain_is_zero(
4127 __isl_keep isl_aff *aff);
4129 Check whether the affine expression is obviously zero.
4133 =head3 Binary Properties
4139 The following functions check whether two objects
4140 represent the same set, relation or function.
4141 The C<plain> variants only return true if the objects
4142 are obviously the same. That is, they may return false
4143 even if the objects are the same, but they will never
4144 return true if the objects are not the same.
4146 #include <isl/set.h>
4147 isl_bool isl_basic_set_plain_is_equal(
4148 __isl_keep isl_basic_set *bset1,
4149 __isl_keep isl_basic_set *bset2);
4150 isl_bool isl_basic_set_is_equal(
4151 __isl_keep isl_basic_set *bset1,
4152 __isl_keep isl_basic_set *bset2);
4153 isl_bool isl_set_plain_is_equal(
4154 __isl_keep isl_set *set1,
4155 __isl_keep isl_set *set2);
4156 isl_bool isl_set_is_equal(__isl_keep isl_set *set1,
4157 __isl_keep isl_set *set2);
4159 #include <isl/map.h>
4160 isl_bool isl_basic_map_is_equal(
4161 __isl_keep isl_basic_map *bmap1,
4162 __isl_keep isl_basic_map *bmap2);
4163 isl_bool isl_map_is_equal(__isl_keep isl_map *map1,
4164 __isl_keep isl_map *map2);
4165 isl_bool isl_map_plain_is_equal(
4166 __isl_keep isl_map *map1,
4167 __isl_keep isl_map *map2);
4169 #include <isl/union_set.h>
4170 isl_bool isl_union_set_is_equal(
4171 __isl_keep isl_union_set *uset1,
4172 __isl_keep isl_union_set *uset2);
4174 #include <isl/union_map.h>
4175 isl_bool isl_union_map_is_equal(
4176 __isl_keep isl_union_map *umap1,
4177 __isl_keep isl_union_map *umap2);
4179 #include <isl/aff.h>
4180 isl_bool isl_aff_plain_is_equal(
4181 __isl_keep isl_aff *aff1,
4182 __isl_keep isl_aff *aff2);
4183 isl_bool isl_multi_aff_plain_is_equal(
4184 __isl_keep isl_multi_aff *maff1,
4185 __isl_keep isl_multi_aff *maff2);
4186 isl_bool isl_pw_aff_plain_is_equal(
4187 __isl_keep isl_pw_aff *pwaff1,
4188 __isl_keep isl_pw_aff *pwaff2);
4189 isl_bool isl_pw_aff_is_equal(
4190 __isl_keep isl_pw_aff *pa1,
4191 __isl_keep isl_pw_aff *pa2);
4192 isl_bool isl_pw_multi_aff_plain_is_equal(
4193 __isl_keep isl_pw_multi_aff *pma1,
4194 __isl_keep isl_pw_multi_aff *pma2);
4195 isl_bool isl_pw_multi_aff_is_equal(
4196 __isl_keep isl_pw_multi_aff *pma1,
4197 __isl_keep isl_pw_multi_aff *pma2);
4198 isl_bool isl_multi_pw_aff_plain_is_equal(
4199 __isl_keep isl_multi_pw_aff *mpa1,
4200 __isl_keep isl_multi_pw_aff *mpa2);
4201 isl_bool isl_multi_pw_aff_is_equal(
4202 __isl_keep isl_multi_pw_aff *mpa1,
4203 __isl_keep isl_multi_pw_aff *mpa2);
4204 isl_bool isl_union_pw_aff_plain_is_equal(
4205 __isl_keep isl_union_pw_aff *upa1,
4206 __isl_keep isl_union_pw_aff *upa2);
4207 isl_bool isl_union_pw_multi_aff_plain_is_equal(
4208 __isl_keep isl_union_pw_multi_aff *upma1,
4209 __isl_keep isl_union_pw_multi_aff *upma2);
4210 isl_bool isl_multi_union_pw_aff_plain_is_equal(
4211 __isl_keep isl_multi_union_pw_aff *mupa1,
4212 __isl_keep isl_multi_union_pw_aff *mupa2);
4214 #include <isl/polynomial.h>
4215 isl_bool isl_union_pw_qpolynomial_plain_is_equal(
4216 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4217 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4218 isl_bool isl_union_pw_qpolynomial_fold_plain_is_equal(
4219 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4220 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4222 =item * Disjointness
4224 #include <isl/set.h>
4225 isl_bool isl_basic_set_is_disjoint(
4226 __isl_keep isl_basic_set *bset1,
4227 __isl_keep isl_basic_set *bset2);
4228 isl_bool isl_set_plain_is_disjoint(
4229 __isl_keep isl_set *set1,
4230 __isl_keep isl_set *set2);
4231 isl_bool isl_set_is_disjoint(__isl_keep isl_set *set1,
4232 __isl_keep isl_set *set2);
4234 #include <isl/map.h>
4235 isl_bool isl_basic_map_is_disjoint(
4236 __isl_keep isl_basic_map *bmap1,
4237 __isl_keep isl_basic_map *bmap2);
4238 isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1,
4239 __isl_keep isl_map *map2);
4241 #include <isl/union_set.h>
4242 isl_bool isl_union_set_is_disjoint(
4243 __isl_keep isl_union_set *uset1,
4244 __isl_keep isl_union_set *uset2);
4246 #include <isl/union_map.h>
4247 isl_bool isl_union_map_is_disjoint(
4248 __isl_keep isl_union_map *umap1,
4249 __isl_keep isl_union_map *umap2);
4253 isl_bool isl_basic_set_is_subset(
4254 __isl_keep isl_basic_set *bset1,
4255 __isl_keep isl_basic_set *bset2);
4256 isl_bool isl_set_is_subset(__isl_keep isl_set *set1,
4257 __isl_keep isl_set *set2);
4258 isl_bool isl_set_is_strict_subset(
4259 __isl_keep isl_set *set1,
4260 __isl_keep isl_set *set2);
4261 isl_bool isl_union_set_is_subset(
4262 __isl_keep isl_union_set *uset1,
4263 __isl_keep isl_union_set *uset2);
4264 isl_bool isl_union_set_is_strict_subset(
4265 __isl_keep isl_union_set *uset1,
4266 __isl_keep isl_union_set *uset2);
4267 isl_bool isl_basic_map_is_subset(
4268 __isl_keep isl_basic_map *bmap1,
4269 __isl_keep isl_basic_map *bmap2);
4270 isl_bool isl_basic_map_is_strict_subset(
4271 __isl_keep isl_basic_map *bmap1,
4272 __isl_keep isl_basic_map *bmap2);
4273 isl_bool isl_map_is_subset(
4274 __isl_keep isl_map *map1,
4275 __isl_keep isl_map *map2);
4276 isl_bool isl_map_is_strict_subset(
4277 __isl_keep isl_map *map1,
4278 __isl_keep isl_map *map2);
4279 isl_bool isl_union_map_is_subset(
4280 __isl_keep isl_union_map *umap1,
4281 __isl_keep isl_union_map *umap2);
4282 isl_bool isl_union_map_is_strict_subset(
4283 __isl_keep isl_union_map *umap1,
4284 __isl_keep isl_union_map *umap2);
4286 Check whether the first argument is a (strict) subset of the
4291 Every comparison function returns a negative value if the first
4292 argument is considered smaller than the second, a positive value
4293 if the first argument is considered greater and zero if the two
4294 constraints are considered the same by the comparison criterion.
4296 #include <isl/constraint.h>
4297 int isl_constraint_plain_cmp(
4298 __isl_keep isl_constraint *c1,
4299 __isl_keep isl_constraint *c2);
4301 This function is useful for sorting C<isl_constraint>s.
4302 The order depends on the internal representation of the inputs.
4303 The order is fixed over different calls to the function (assuming
4304 the internal representation of the inputs has not changed), but may
4305 change over different versions of C<isl>.
4307 #include <isl/constraint.h>
4308 int isl_constraint_cmp_last_non_zero(
4309 __isl_keep isl_constraint *c1,
4310 __isl_keep isl_constraint *c2);
4312 This function can be used to sort constraints that live in the same
4313 local space. Constraints that involve ``earlier'' dimensions or
4314 that have a smaller coefficient for the shared latest dimension
4315 are considered smaller than other constraints.
4316 This function only defines a B<partial> order.
4318 #include <isl/set.h>
4319 int isl_set_plain_cmp(__isl_keep isl_set *set1,
4320 __isl_keep isl_set *set2);
4322 This function is useful for sorting C<isl_set>s.
4323 The order depends on the internal representation of the inputs.
4324 The order is fixed over different calls to the function (assuming
4325 the internal representation of the inputs has not changed), but may
4326 change over different versions of C<isl>.
4328 #include <isl/aff.h>
4329 int isl_multi_aff_plain_cmp(
4330 __isl_keep isl_multi_aff *ma1,
4331 __isl_keep isl_multi_aff *ma2);
4332 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4333 __isl_keep isl_pw_aff *pa2);
4335 The functions C<isl_multi_aff_plain_cmp> and
4336 C<isl_pw_aff_plain_cmp> can be used to sort C<isl_multi_aff>s and
4337 C<isl_pw_aff>s. The order is not strictly defined.
4338 The current order sorts expressions that only involve
4339 earlier dimensions before those that involve later dimensions.
4343 =head2 Unary Operations
4349 __isl_give isl_set *isl_set_complement(
4350 __isl_take isl_set *set);
4351 __isl_give isl_map *isl_map_complement(
4352 __isl_take isl_map *map);
4356 #include <isl/space.h>
4357 __isl_give isl_space *isl_space_reverse(
4358 __isl_take isl_space *space);
4360 #include <isl/map.h>
4361 __isl_give isl_basic_map *isl_basic_map_reverse(
4362 __isl_take isl_basic_map *bmap);
4363 __isl_give isl_map *isl_map_reverse(
4364 __isl_take isl_map *map);
4366 #include <isl/union_map.h>
4367 __isl_give isl_union_map *isl_union_map_reverse(
4368 __isl_take isl_union_map *umap);
4372 #include <isl/space.h>
4373 __isl_give isl_space *isl_space_domain(
4374 __isl_take isl_space *space);
4375 __isl_give isl_space *isl_space_range(
4376 __isl_take isl_space *space);
4377 __isl_give isl_space *isl_space_params(
4378 __isl_take isl_space *space);
4380 #include <isl/local_space.h>
4381 __isl_give isl_local_space *isl_local_space_domain(
4382 __isl_take isl_local_space *ls);
4383 __isl_give isl_local_space *isl_local_space_range(
4384 __isl_take isl_local_space *ls);
4386 #include <isl/set.h>
4387 __isl_give isl_basic_set *isl_basic_set_project_out(
4388 __isl_take isl_basic_set *bset,
4389 enum isl_dim_type type, unsigned first, unsigned n);
4390 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
4391 enum isl_dim_type type, unsigned first, unsigned n);
4392 __isl_give isl_map *isl_set_project_onto_map(
4393 __isl_take isl_set *set,
4394 enum isl_dim_type type, unsigned first,
4396 __isl_give isl_basic_set *isl_basic_set_params(
4397 __isl_take isl_basic_set *bset);
4398 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
4400 The function C<isl_set_project_onto_map> returns a relation
4401 that projects the input set onto the given set dimensions.
4403 #include <isl/map.h>
4404 __isl_give isl_basic_map *isl_basic_map_project_out(
4405 __isl_take isl_basic_map *bmap,
4406 enum isl_dim_type type, unsigned first, unsigned n);
4407 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
4408 enum isl_dim_type type, unsigned first, unsigned n);
4409 __isl_give isl_basic_set *isl_basic_map_domain(
4410 __isl_take isl_basic_map *bmap);
4411 __isl_give isl_basic_set *isl_basic_map_range(
4412 __isl_take isl_basic_map *bmap);
4413 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
4414 __isl_give isl_set *isl_map_domain(
4415 __isl_take isl_map *bmap);
4416 __isl_give isl_set *isl_map_range(
4417 __isl_take isl_map *map);
4419 #include <isl/union_set.h>
4420 __isl_give isl_union_set *isl_union_set_project_out(
4421 __isl_take isl_union_set *uset,
4422 enum isl_dim_type type,
4423 unsigned first, unsigned n);
4424 __isl_give isl_set *isl_union_set_params(
4425 __isl_take isl_union_set *uset);
4427 The function C<isl_union_set_project_out> can only project out
4430 #include <isl/union_map.h>
4431 __isl_give isl_union_map *isl_union_map_project_out(
4432 __isl_take isl_union_map *umap,
4433 enum isl_dim_type type, unsigned first, unsigned n);
4434 __isl_give isl_set *isl_union_map_params(
4435 __isl_take isl_union_map *umap);
4436 __isl_give isl_union_set *isl_union_map_domain(
4437 __isl_take isl_union_map *umap);
4438 __isl_give isl_union_set *isl_union_map_range(
4439 __isl_take isl_union_map *umap);
4441 The function C<isl_union_map_project_out> can only project out
4444 #include <isl/aff.h>
4445 __isl_give isl_aff *isl_aff_project_domain_on_params(
4446 __isl_take isl_aff *aff);
4447 __isl_give isl_pw_aff *
4448 isl_pw_aff_project_domain_on_params(
4449 __isl_take isl_pw_aff *pa);
4450 __isl_give isl_pw_multi_aff *
4451 isl_pw_multi_aff_project_domain_on_params(
4452 __isl_take isl_pw_multi_aff *pma);
4453 __isl_give isl_set *isl_pw_aff_domain(
4454 __isl_take isl_pw_aff *pwaff);
4455 __isl_give isl_set *isl_pw_multi_aff_domain(
4456 __isl_take isl_pw_multi_aff *pma);
4457 __isl_give isl_set *isl_multi_pw_aff_domain(
4458 __isl_take isl_multi_pw_aff *mpa);
4459 __isl_give isl_union_set *isl_union_pw_aff_domain(
4460 __isl_take isl_union_pw_aff *upa);
4461 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4462 __isl_take isl_union_pw_multi_aff *upma);
4463 __isl_give isl_union_set *
4464 isl_multi_union_pw_aff_domain(
4465 __isl_take isl_multi_union_pw_aff *mupa);
4466 __isl_give isl_set *isl_pw_aff_params(
4467 __isl_take isl_pw_aff *pwa);
4469 The function C<isl_multi_union_pw_aff_domain> requires its
4470 input to have at least one set dimension.
4472 #include <isl/polynomial.h>
4473 __isl_give isl_qpolynomial *
4474 isl_qpolynomial_project_domain_on_params(
4475 __isl_take isl_qpolynomial *qp);
4476 __isl_give isl_pw_qpolynomial *
4477 isl_pw_qpolynomial_project_domain_on_params(
4478 __isl_take isl_pw_qpolynomial *pwqp);
4479 __isl_give isl_pw_qpolynomial_fold *
4480 isl_pw_qpolynomial_fold_project_domain_on_params(
4481 __isl_take isl_pw_qpolynomial_fold *pwf);
4482 __isl_give isl_set *isl_pw_qpolynomial_domain(
4483 __isl_take isl_pw_qpolynomial *pwqp);
4484 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4485 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4486 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4487 __isl_take isl_union_pw_qpolynomial *upwqp);
4489 #include <isl/space.h>
4490 __isl_give isl_space *isl_space_domain_map(
4491 __isl_take isl_space *space);
4492 __isl_give isl_space *isl_space_range_map(
4493 __isl_take isl_space *space);
4495 #include <isl/map.h>
4496 __isl_give isl_map *isl_set_wrapped_domain_map(
4497 __isl_take isl_set *set);
4498 __isl_give isl_basic_map *isl_basic_map_domain_map(
4499 __isl_take isl_basic_map *bmap);
4500 __isl_give isl_basic_map *isl_basic_map_range_map(
4501 __isl_take isl_basic_map *bmap);
4502 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
4503 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
4505 #include <isl/union_map.h>
4506 __isl_give isl_union_map *isl_union_map_domain_map(
4507 __isl_take isl_union_map *umap);
4508 __isl_give isl_union_pw_multi_aff *
4509 isl_union_map_domain_map_union_pw_multi_aff(
4510 __isl_take isl_union_map *umap);
4511 __isl_give isl_union_map *isl_union_map_range_map(
4512 __isl_take isl_union_map *umap);
4513 __isl_give isl_union_map *
4514 isl_union_set_wrapped_domain_map(
4515 __isl_take isl_union_set *uset);
4517 The functions above construct a (basic, regular or union) relation
4518 that maps (a wrapped version of) the input relation to its domain or range.
4519 C<isl_set_wrapped_domain_map> maps the input set to the domain
4520 of its wrapped relation.
4524 __isl_give isl_basic_set *isl_basic_set_eliminate(
4525 __isl_take isl_basic_set *bset,
4526 enum isl_dim_type type,
4527 unsigned first, unsigned n);
4528 __isl_give isl_set *isl_set_eliminate(
4529 __isl_take isl_set *set, enum isl_dim_type type,
4530 unsigned first, unsigned n);
4531 __isl_give isl_basic_map *isl_basic_map_eliminate(
4532 __isl_take isl_basic_map *bmap,
4533 enum isl_dim_type type,
4534 unsigned first, unsigned n);
4535 __isl_give isl_map *isl_map_eliminate(
4536 __isl_take isl_map *map, enum isl_dim_type type,
4537 unsigned first, unsigned n);
4539 Eliminate the coefficients for the given dimensions from the constraints,
4540 without removing the dimensions.
4542 =item * Constructing a set from a parameter domain
4544 A zero-dimensional space or (basic) set can be constructed
4545 on a given parameter domain using the following functions.
4547 #include <isl/space.h>
4548 __isl_give isl_space *isl_space_set_from_params(
4549 __isl_take isl_space *space);
4551 #include <isl/set.h>
4552 __isl_give isl_basic_set *isl_basic_set_from_params(
4553 __isl_take isl_basic_set *bset);
4554 __isl_give isl_set *isl_set_from_params(
4555 __isl_take isl_set *set);
4557 =item * Constructing a relation from one or two sets
4559 Create a relation with the given set(s) as domain and/or range.
4560 If only the domain or the range is specified, then
4561 the range or domain of the created relation is a zero-dimensional
4562 flat anonymous space.
4564 #include <isl/space.h>
4565 __isl_give isl_space *isl_space_from_domain(
4566 __isl_take isl_space *space);
4567 __isl_give isl_space *isl_space_from_range(
4568 __isl_take isl_space *space);
4569 __isl_give isl_space *isl_space_map_from_set(
4570 __isl_take isl_space *space);
4571 __isl_give isl_space *isl_space_map_from_domain_and_range(
4572 __isl_take isl_space *domain,
4573 __isl_take isl_space *range);
4575 #include <isl/local_space.h>
4576 __isl_give isl_local_space *isl_local_space_from_domain(
4577 __isl_take isl_local_space *ls);
4579 #include <isl/map.h>
4580 __isl_give isl_map *isl_map_from_domain(
4581 __isl_take isl_set *set);
4582 __isl_give isl_map *isl_map_from_range(
4583 __isl_take isl_set *set);
4585 #include <isl/union_map.h>
4586 __isl_give isl_union_map *
4587 isl_union_map_from_domain_and_range(
4588 __isl_take isl_union_set *domain,
4589 __isl_take isl_union_set *range);
4591 #include <isl/val.h>
4592 __isl_give isl_multi_val *isl_multi_val_from_range(
4593 __isl_take isl_multi_val *mv);
4595 #include <isl/aff.h>
4596 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4597 __isl_take isl_multi_aff *ma);
4598 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4599 __isl_take isl_pw_aff *pwa);
4600 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4601 __isl_take isl_multi_pw_aff *mpa);
4602 __isl_give isl_multi_union_pw_aff *
4603 isl_multi_union_pw_aff_from_range(
4604 __isl_take isl_multi_union_pw_aff *mupa);
4605 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4606 __isl_take isl_set *set);
4607 __isl_give isl_union_pw_multi_aff *
4608 isl_union_pw_multi_aff_from_domain(
4609 __isl_take isl_union_set *uset);
4611 #include <isl/polynomial.h>
4612 __isl_give isl_pw_qpolynomial *
4613 isl_pw_qpolynomial_from_range(
4614 __isl_take isl_pw_qpolynomial *pwqp);
4615 __isl_give isl_pw_qpolynomial_fold *
4616 isl_pw_qpolynomial_fold_from_range(
4617 __isl_take isl_pw_qpolynomial_fold *pwf);
4621 #include <isl/set.h>
4622 __isl_give isl_basic_set *isl_basic_set_fix_si(
4623 __isl_take isl_basic_set *bset,
4624 enum isl_dim_type type, unsigned pos, int value);
4625 __isl_give isl_basic_set *isl_basic_set_fix_val(
4626 __isl_take isl_basic_set *bset,
4627 enum isl_dim_type type, unsigned pos,
4628 __isl_take isl_val *v);
4629 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
4630 enum isl_dim_type type, unsigned pos, int value);
4631 __isl_give isl_set *isl_set_fix_val(
4632 __isl_take isl_set *set,
4633 enum isl_dim_type type, unsigned pos,
4634 __isl_take isl_val *v);
4636 #include <isl/map.h>
4637 __isl_give isl_basic_map *isl_basic_map_fix_si(
4638 __isl_take isl_basic_map *bmap,
4639 enum isl_dim_type type, unsigned pos, int value);
4640 __isl_give isl_basic_map *isl_basic_map_fix_val(
4641 __isl_take isl_basic_map *bmap,
4642 enum isl_dim_type type, unsigned pos,
4643 __isl_take isl_val *v);
4644 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
4645 enum isl_dim_type type, unsigned pos, int value);
4646 __isl_give isl_map *isl_map_fix_val(
4647 __isl_take isl_map *map,
4648 enum isl_dim_type type, unsigned pos,
4649 __isl_take isl_val *v);
4651 #include <isl/aff.h>
4652 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4653 __isl_take isl_pw_multi_aff *pma,
4654 enum isl_dim_type type, unsigned pos, int value);
4656 #include <isl/polynomial.h>
4657 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4658 __isl_take isl_pw_qpolynomial *pwqp,
4659 enum isl_dim_type type, unsigned n,
4660 __isl_take isl_val *v);
4662 Intersect the set, relation or function domain
4663 with the hyperplane where the given
4664 dimension has the fixed given value.
4666 #include <isl/set.h>
4667 __isl_give isl_basic_set *
4668 isl_basic_set_lower_bound_val(
4669 __isl_take isl_basic_set *bset,
4670 enum isl_dim_type type, unsigned pos,
4671 __isl_take isl_val *value);
4672 __isl_give isl_basic_set *
4673 isl_basic_set_upper_bound_val(
4674 __isl_take isl_basic_set *bset,
4675 enum isl_dim_type type, unsigned pos,
4676 __isl_take isl_val *value);
4677 __isl_give isl_set *isl_set_lower_bound_si(
4678 __isl_take isl_set *set,
4679 enum isl_dim_type type, unsigned pos, int value);
4680 __isl_give isl_set *isl_set_lower_bound_val(
4681 __isl_take isl_set *set,
4682 enum isl_dim_type type, unsigned pos,
4683 __isl_take isl_val *value);
4684 __isl_give isl_set *isl_set_upper_bound_si(
4685 __isl_take isl_set *set,
4686 enum isl_dim_type type, unsigned pos, int value);
4687 __isl_give isl_set *isl_set_upper_bound_val(
4688 __isl_take isl_set *set,
4689 enum isl_dim_type type, unsigned pos,
4690 __isl_take isl_val *value);
4692 #include <isl/map.h>
4693 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
4694 __isl_take isl_basic_map *bmap,
4695 enum isl_dim_type type, unsigned pos, int value);
4696 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
4697 __isl_take isl_basic_map *bmap,
4698 enum isl_dim_type type, unsigned pos, int value);
4699 __isl_give isl_map *isl_map_lower_bound_si(
4700 __isl_take isl_map *map,
4701 enum isl_dim_type type, unsigned pos, int value);
4702 __isl_give isl_map *isl_map_upper_bound_si(
4703 __isl_take isl_map *map,
4704 enum isl_dim_type type, unsigned pos, int value);
4706 Intersect the set or relation with the half-space where the given
4707 dimension has a value bounded by the fixed given integer value.
4709 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
4710 enum isl_dim_type type1, int pos1,
4711 enum isl_dim_type type2, int pos2);
4712 __isl_give isl_basic_map *isl_basic_map_equate(
4713 __isl_take isl_basic_map *bmap,
4714 enum isl_dim_type type1, int pos1,
4715 enum isl_dim_type type2, int pos2);
4716 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
4717 enum isl_dim_type type1, int pos1,
4718 enum isl_dim_type type2, int pos2);
4720 Intersect the set or relation with the hyperplane where the given
4721 dimensions are equal to each other.
4723 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
4724 enum isl_dim_type type1, int pos1,
4725 enum isl_dim_type type2, int pos2);
4727 Intersect the relation with the hyperplane where the given
4728 dimensions have opposite values.
4730 __isl_give isl_map *isl_map_order_le(
4731 __isl_take isl_map *map,
4732 enum isl_dim_type type1, int pos1,
4733 enum isl_dim_type type2, int pos2);
4734 __isl_give isl_basic_map *isl_basic_map_order_ge(
4735 __isl_take isl_basic_map *bmap,
4736 enum isl_dim_type type1, int pos1,
4737 enum isl_dim_type type2, int pos2);
4738 __isl_give isl_map *isl_map_order_ge(
4739 __isl_take isl_map *map,
4740 enum isl_dim_type type1, int pos1,
4741 enum isl_dim_type type2, int pos2);
4742 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
4743 enum isl_dim_type type1, int pos1,
4744 enum isl_dim_type type2, int pos2);
4745 __isl_give isl_basic_map *isl_basic_map_order_gt(
4746 __isl_take isl_basic_map *bmap,
4747 enum isl_dim_type type1, int pos1,
4748 enum isl_dim_type type2, int pos2);
4749 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
4750 enum isl_dim_type type1, int pos1,
4751 enum isl_dim_type type2, int pos2);
4753 Intersect the relation with the half-space where the given
4754 dimensions satisfy the given ordering.
4758 #include <isl/aff.h>
4759 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4760 __isl_take isl_aff *aff);
4761 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4762 __isl_take isl_aff *aff);
4763 __isl_give isl_set *isl_pw_aff_pos_set(
4764 __isl_take isl_pw_aff *pa);
4765 __isl_give isl_set *isl_pw_aff_nonneg_set(
4766 __isl_take isl_pw_aff *pwaff);
4767 __isl_give isl_set *isl_pw_aff_zero_set(
4768 __isl_take isl_pw_aff *pwaff);
4769 __isl_give isl_set *isl_pw_aff_non_zero_set(
4770 __isl_take isl_pw_aff *pwaff);
4771 __isl_give isl_union_set *
4772 isl_union_pw_aff_zero_union_set(
4773 __isl_take isl_union_pw_aff *upa);
4774 __isl_give isl_union_set *
4775 isl_multi_union_pw_aff_zero_union_set(
4776 __isl_take isl_multi_union_pw_aff *mupa);
4778 The function C<isl_aff_neg_basic_set> returns a basic set
4779 containing those elements in the domain space
4780 of C<aff> where C<aff> is negative.
4781 The function C<isl_pw_aff_nonneg_set> returns a set
4782 containing those elements in the domain
4783 of C<pwaff> where C<pwaff> is non-negative.
4784 The function C<isl_multi_union_pw_aff_zero_union_set>
4785 returns a union set containing those elements
4786 in the domains of its elements where they are all zero.
4790 __isl_give isl_map *isl_set_identity(
4791 __isl_take isl_set *set);
4792 __isl_give isl_union_map *isl_union_set_identity(
4793 __isl_take isl_union_set *uset);
4794 __isl_give isl_union_pw_multi_aff *
4795 isl_union_set_identity_union_pw_multi_aff(
4796 __isl_take isl_union_set *uset);
4798 Construct an identity relation on the given (union) set.
4800 =item * Function Extraction
4802 A piecewise quasi affine expression that is equal to 1 on a set
4803 and 0 outside the set can be created using the following function.
4805 #include <isl/aff.h>
4806 __isl_give isl_pw_aff *isl_set_indicator_function(
4807 __isl_take isl_set *set);
4809 A piecewise multiple quasi affine expression can be extracted
4810 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4811 and the C<isl_map> is single-valued.
4812 In case of a conversion from an C<isl_union_map>
4813 to an C<isl_union_pw_multi_aff>, these properties need to hold
4814 in each domain space.
4815 A conversion to a C<isl_multi_union_pw_aff> additionally
4816 requires that the input is non-empty and involves only a single
4819 #include <isl/aff.h>
4820 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4821 __isl_take isl_set *set);
4822 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4823 __isl_take isl_map *map);
4825 __isl_give isl_union_pw_multi_aff *
4826 isl_union_pw_multi_aff_from_union_set(
4827 __isl_take isl_union_set *uset);
4828 __isl_give isl_union_pw_multi_aff *
4829 isl_union_pw_multi_aff_from_union_map(
4830 __isl_take isl_union_map *umap);
4832 __isl_give isl_multi_union_pw_aff *
4833 isl_multi_union_pw_aff_from_union_map(
4834 __isl_take isl_union_map *umap);
4838 __isl_give isl_basic_set *isl_basic_map_deltas(
4839 __isl_take isl_basic_map *bmap);
4840 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
4841 __isl_give isl_union_set *isl_union_map_deltas(
4842 __isl_take isl_union_map *umap);
4844 These functions return a (basic) set containing the differences
4845 between image elements and corresponding domain elements in the input.
4847 __isl_give isl_basic_map *isl_basic_map_deltas_map(
4848 __isl_take isl_basic_map *bmap);
4849 __isl_give isl_map *isl_map_deltas_map(
4850 __isl_take isl_map *map);
4851 __isl_give isl_union_map *isl_union_map_deltas_map(
4852 __isl_take isl_union_map *umap);
4854 The functions above construct a (basic, regular or union) relation
4855 that maps (a wrapped version of) the input relation to its delta set.
4859 Simplify the representation of a set, relation or functions by trying
4860 to combine pairs of basic sets or relations into a single
4861 basic set or relation.
4863 #include <isl/set.h>
4864 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
4866 #include <isl/map.h>
4867 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
4869 #include <isl/union_set.h>
4870 __isl_give isl_union_set *isl_union_set_coalesce(
4871 __isl_take isl_union_set *uset);
4873 #include <isl/union_map.h>
4874 __isl_give isl_union_map *isl_union_map_coalesce(
4875 __isl_take isl_union_map *umap);
4877 #include <isl/aff.h>
4878 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4879 __isl_take isl_pw_aff *pwqp);
4880 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4881 __isl_take isl_pw_multi_aff *pma);
4882 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4883 __isl_take isl_multi_pw_aff *mpa);
4884 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
4885 __isl_take isl_union_pw_aff *upa);
4886 __isl_give isl_union_pw_multi_aff *
4887 isl_union_pw_multi_aff_coalesce(
4888 __isl_take isl_union_pw_multi_aff *upma);
4889 __isl_give isl_multi_union_pw_aff *
4890 isl_multi_union_pw_aff_coalesce(
4891 __isl_take isl_multi_union_pw_aff *aff);
4893 #include <isl/polynomial.h>
4894 __isl_give isl_pw_qpolynomial_fold *
4895 isl_pw_qpolynomial_fold_coalesce(
4896 __isl_take isl_pw_qpolynomial_fold *pwf);
4897 __isl_give isl_union_pw_qpolynomial *
4898 isl_union_pw_qpolynomial_coalesce(
4899 __isl_take isl_union_pw_qpolynomial *upwqp);
4900 __isl_give isl_union_pw_qpolynomial_fold *
4901 isl_union_pw_qpolynomial_fold_coalesce(
4902 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4904 One of the methods for combining pairs of basic sets or relations
4905 can result in coefficients that are much larger than those that appear
4906 in the constraints of the input. By default, the coefficients are
4907 not allowed to grow larger, but this can be changed by unsetting
4908 the following option.
4910 isl_stat isl_options_set_coalesce_bounded_wrapping(
4911 isl_ctx *ctx, int val);
4912 int isl_options_get_coalesce_bounded_wrapping(
4915 =item * Detecting equalities
4917 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
4918 __isl_take isl_basic_set *bset);
4919 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
4920 __isl_take isl_basic_map *bmap);
4921 __isl_give isl_set *isl_set_detect_equalities(
4922 __isl_take isl_set *set);
4923 __isl_give isl_map *isl_map_detect_equalities(
4924 __isl_take isl_map *map);
4925 __isl_give isl_union_set *isl_union_set_detect_equalities(
4926 __isl_take isl_union_set *uset);
4927 __isl_give isl_union_map *isl_union_map_detect_equalities(
4928 __isl_take isl_union_map *umap);
4930 Simplify the representation of a set or relation by detecting implicit
4933 =item * Removing redundant constraints
4935 #include <isl/set.h>
4936 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
4937 __isl_take isl_basic_set *bset);
4938 __isl_give isl_set *isl_set_remove_redundancies(
4939 __isl_take isl_set *set);
4941 #include <isl/union_set.h>
4942 __isl_give isl_union_set *
4943 isl_union_set_remove_redundancies(
4944 __isl_take isl_union_set *uset);
4946 #include <isl/map.h>
4947 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
4948 __isl_take isl_basic_map *bmap);
4949 __isl_give isl_map *isl_map_remove_redundancies(
4950 __isl_take isl_map *map);
4952 #include <isl/union_map.h>
4953 __isl_give isl_union_map *
4954 isl_union_map_remove_redundancies(
4955 __isl_take isl_union_map *umap);
4959 __isl_give isl_basic_set *isl_set_convex_hull(
4960 __isl_take isl_set *set);
4961 __isl_give isl_basic_map *isl_map_convex_hull(
4962 __isl_take isl_map *map);
4964 If the input set or relation has any existentially quantified
4965 variables, then the result of these operations is currently undefined.
4969 #include <isl/set.h>
4970 __isl_give isl_basic_set *
4971 isl_set_unshifted_simple_hull(
4972 __isl_take isl_set *set);
4973 __isl_give isl_basic_set *isl_set_simple_hull(
4974 __isl_take isl_set *set);
4975 __isl_give isl_basic_set *
4976 isl_set_plain_unshifted_simple_hull(
4977 __isl_take isl_set *set);
4978 __isl_give isl_basic_set *
4979 isl_set_unshifted_simple_hull_from_set_list(
4980 __isl_take isl_set *set,
4981 __isl_take isl_set_list *list);
4983 #include <isl/map.h>
4984 __isl_give isl_basic_map *
4985 isl_map_unshifted_simple_hull(
4986 __isl_take isl_map *map);
4987 __isl_give isl_basic_map *isl_map_simple_hull(
4988 __isl_take isl_map *map);
4989 __isl_give isl_basic_map *
4990 isl_map_plain_unshifted_simple_hull(
4991 __isl_take isl_map *map);
4992 __isl_give isl_basic_map *
4993 isl_map_unshifted_simple_hull_from_map_list(
4994 __isl_take isl_map *map,
4995 __isl_take isl_map_list *list);
4997 #include <isl/union_map.h>
4998 __isl_give isl_union_map *isl_union_map_simple_hull(
4999 __isl_take isl_union_map *umap);
5001 These functions compute a single basic set or relation
5002 that contains the whole input set or relation.
5003 In particular, the output is described by translates
5004 of the constraints describing the basic sets or relations in the input.
5005 In case of C<isl_set_unshifted_simple_hull>, only the original
5006 constraints are used, without any translation.
5007 In case of C<isl_set_plain_unshifted_simple_hull> and
5008 C<isl_map_plain_unshifted_simple_hull>, the result is described
5009 by original constraints that are obviously satisfied
5010 by the entire input set or relation.
5011 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
5012 C<isl_map_unshifted_simple_hull_from_map_list>, the
5013 constraints are taken from the elements of the second argument.
5017 (See \autoref{s:simple hull}.)
5023 __isl_give isl_basic_set *isl_basic_set_affine_hull(
5024 __isl_take isl_basic_set *bset);
5025 __isl_give isl_basic_set *isl_set_affine_hull(
5026 __isl_take isl_set *set);
5027 __isl_give isl_union_set *isl_union_set_affine_hull(
5028 __isl_take isl_union_set *uset);
5029 __isl_give isl_basic_map *isl_basic_map_affine_hull(
5030 __isl_take isl_basic_map *bmap);
5031 __isl_give isl_basic_map *isl_map_affine_hull(
5032 __isl_take isl_map *map);
5033 __isl_give isl_union_map *isl_union_map_affine_hull(
5034 __isl_take isl_union_map *umap);
5036 In case of union sets and relations, the affine hull is computed
5039 =item * Polyhedral hull
5041 __isl_give isl_basic_set *isl_set_polyhedral_hull(
5042 __isl_take isl_set *set);
5043 __isl_give isl_basic_map *isl_map_polyhedral_hull(
5044 __isl_take isl_map *map);
5045 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
5046 __isl_take isl_union_set *uset);
5047 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
5048 __isl_take isl_union_map *umap);
5050 These functions compute a single basic set or relation
5051 not involving any existentially quantified variables
5052 that contains the whole input set or relation.
5053 In case of union sets and relations, the polyhedral hull is computed
5056 =item * Other approximations
5058 #include <isl/set.h>
5059 __isl_give isl_basic_set *
5060 isl_basic_set_drop_constraints_involving_dims(
5061 __isl_take isl_basic_set *bset,
5062 enum isl_dim_type type,
5063 unsigned first, unsigned n);
5064 __isl_give isl_basic_set *
5065 isl_basic_set_drop_constraints_not_involving_dims(
5066 __isl_take isl_basic_set *bset,
5067 enum isl_dim_type type,
5068 unsigned first, unsigned n);
5069 __isl_give isl_set *
5070 isl_set_drop_constraints_involving_dims(
5071 __isl_take isl_set *set,
5072 enum isl_dim_type type,
5073 unsigned first, unsigned n);
5074 __isl_give isl_set *
5075 isl_set_drop_constraints_not_involving_dims(
5076 __isl_take isl_set *set,
5077 enum isl_dim_type type,
5078 unsigned first, unsigned n);
5080 #include <isl/map.h>
5081 __isl_give isl_basic_map *
5082 isl_basic_map_drop_constraints_involving_dims(
5083 __isl_take isl_basic_map *bmap,
5084 enum isl_dim_type type,
5085 unsigned first, unsigned n);
5086 __isl_give isl_basic_map *
5087 isl_basic_map_drop_constraints_not_involving_dims(
5088 __isl_take isl_basic_map *bmap,
5089 enum isl_dim_type type,
5090 unsigned first, unsigned n);
5091 __isl_give isl_map *
5092 isl_map_drop_constraints_involving_dims(
5093 __isl_take isl_map *map,
5094 enum isl_dim_type type,
5095 unsigned first, unsigned n);
5096 __isl_give isl_map *
5097 isl_map_drop_constraints_not_involving_dims(
5098 __isl_take isl_map *map,
5099 enum isl_dim_type type,
5100 unsigned first, unsigned n);
5102 These functions drop any constraints (not) involving the specified dimensions.
5103 Note that the result depends on the representation of the input.
5105 #include <isl/polynomial.h>
5106 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5107 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5108 __isl_give isl_union_pw_qpolynomial *
5109 isl_union_pw_qpolynomial_to_polynomial(
5110 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5112 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5113 the polynomial will be an overapproximation. If C<sign> is negative,
5114 it will be an underapproximation. If C<sign> is zero, the approximation
5115 will lie somewhere in between.
5119 __isl_give isl_basic_set *isl_basic_set_sample(
5120 __isl_take isl_basic_set *bset);
5121 __isl_give isl_basic_set *isl_set_sample(
5122 __isl_take isl_set *set);
5123 __isl_give isl_basic_map *isl_basic_map_sample(
5124 __isl_take isl_basic_map *bmap);
5125 __isl_give isl_basic_map *isl_map_sample(
5126 __isl_take isl_map *map);
5128 If the input (basic) set or relation is non-empty, then return
5129 a singleton subset of the input. Otherwise, return an empty set.
5131 =item * Optimization
5133 #include <isl/ilp.h>
5134 __isl_give isl_val *isl_basic_set_max_val(
5135 __isl_keep isl_basic_set *bset,
5136 __isl_keep isl_aff *obj);
5137 __isl_give isl_val *isl_set_min_val(
5138 __isl_keep isl_set *set,
5139 __isl_keep isl_aff *obj);
5140 __isl_give isl_val *isl_set_max_val(
5141 __isl_keep isl_set *set,
5142 __isl_keep isl_aff *obj);
5143 __isl_give isl_multi_val *
5144 isl_union_set_min_multi_union_pw_aff(
5145 __isl_keep isl_union_set *set,
5146 __isl_keep isl_multi_union_pw_aff *obj);
5148 Compute the minimum or maximum of the integer affine expression C<obj>
5149 over the points in C<set>, returning the result in C<opt>.
5150 The result is C<NULL> in case of an error, the optimal value in case
5151 there is one, negative infinity or infinity if the problem is unbounded and
5152 NaN if the problem is empty.
5154 =item * Parametric optimization
5156 __isl_give isl_pw_aff *isl_set_dim_min(
5157 __isl_take isl_set *set, int pos);
5158 __isl_give isl_pw_aff *isl_set_dim_max(
5159 __isl_take isl_set *set, int pos);
5160 __isl_give isl_pw_aff *isl_map_dim_min(
5161 __isl_take isl_map *map, int pos);
5162 __isl_give isl_pw_aff *isl_map_dim_max(
5163 __isl_take isl_map *map, int pos);
5165 Compute the minimum or maximum of the given set or output dimension
5166 as a function of the parameters (and input dimensions), but independently
5167 of the other set or output dimensions.
5168 For lexicographic optimization, see L<"Lexicographic Optimization">.
5172 The following functions compute either the set of (rational) coefficient
5173 values of valid constraints for the given set or the set of (rational)
5174 values satisfying the constraints with coefficients from the given set.
5175 Internally, these two sets of functions perform essentially the
5176 same operations, except that the set of coefficients is assumed to
5177 be a cone, while the set of values may be any polyhedron.
5178 The current implementation is based on the Farkas lemma and
5179 Fourier-Motzkin elimination, but this may change or be made optional
5180 in future. In particular, future implementations may use different
5181 dualization algorithms or skip the elimination step.
5183 #include <isl/set.h>
5184 __isl_give isl_basic_set *isl_basic_set_coefficients(
5185 __isl_take isl_basic_set *bset);
5186 __isl_give isl_basic_set_list *
5187 isl_basic_set_list_coefficients(
5188 __isl_take isl_basic_set_list *list);
5189 __isl_give isl_basic_set *isl_set_coefficients(
5190 __isl_take isl_set *set);
5191 __isl_give isl_union_set *isl_union_set_coefficients(
5192 __isl_take isl_union_set *bset);
5193 __isl_give isl_basic_set *isl_basic_set_solutions(
5194 __isl_take isl_basic_set *bset);
5195 __isl_give isl_basic_set *isl_set_solutions(
5196 __isl_take isl_set *set);
5197 __isl_give isl_union_set *isl_union_set_solutions(
5198 __isl_take isl_union_set *bset);
5202 __isl_give isl_map *isl_map_fixed_power_val(
5203 __isl_take isl_map *map,
5204 __isl_take isl_val *exp);
5205 __isl_give isl_union_map *
5206 isl_union_map_fixed_power_val(
5207 __isl_take isl_union_map *umap,
5208 __isl_take isl_val *exp);
5210 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
5211 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
5212 of C<map> is computed.
5214 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
5216 __isl_give isl_union_map *isl_union_map_power(
5217 __isl_take isl_union_map *umap, int *exact);
5219 Compute a parametric representation for all positive powers I<k> of C<map>.
5220 The result maps I<k> to a nested relation corresponding to the
5221 I<k>th power of C<map>.
5222 The result may be an overapproximation. If the result is known to be exact,
5223 then C<*exact> is set to C<1>.
5225 =item * Transitive closure
5227 __isl_give isl_map *isl_map_transitive_closure(
5228 __isl_take isl_map *map, int *exact);
5229 __isl_give isl_union_map *isl_union_map_transitive_closure(
5230 __isl_take isl_union_map *umap, int *exact);
5232 Compute the transitive closure of C<map>.
5233 The result may be an overapproximation. If the result is known to be exact,
5234 then C<*exact> is set to C<1>.
5236 =item * Reaching path lengths
5238 __isl_give isl_map *isl_map_reaching_path_lengths(
5239 __isl_take isl_map *map, int *exact);
5241 Compute a relation that maps each element in the range of C<map>
5242 to the lengths of all paths composed of edges in C<map> that
5243 end up in the given element.
5244 The result may be an overapproximation. If the result is known to be exact,
5245 then C<*exact> is set to C<1>.
5246 To compute the I<maximal> path length, the resulting relation
5247 should be postprocessed by C<isl_map_lexmax>.
5248 In particular, if the input relation is a dependence relation
5249 (mapping sources to sinks), then the maximal path length corresponds
5250 to the free schedule.
5251 Note, however, that C<isl_map_lexmax> expects the maximum to be
5252 finite, so if the path lengths are unbounded (possibly due to
5253 the overapproximation), then you will get an error message.
5257 #include <isl/space.h>
5258 __isl_give isl_space *isl_space_wrap(
5259 __isl_take isl_space *space);
5260 __isl_give isl_space *isl_space_unwrap(
5261 __isl_take isl_space *space);
5263 #include <isl/local_space.h>
5264 __isl_give isl_local_space *isl_local_space_wrap(
5265 __isl_take isl_local_space *ls);
5267 #include <isl/set.h>
5268 __isl_give isl_basic_map *isl_basic_set_unwrap(
5269 __isl_take isl_basic_set *bset);
5270 __isl_give isl_map *isl_set_unwrap(
5271 __isl_take isl_set *set);
5273 #include <isl/map.h>
5274 __isl_give isl_basic_set *isl_basic_map_wrap(
5275 __isl_take isl_basic_map *bmap);
5276 __isl_give isl_set *isl_map_wrap(
5277 __isl_take isl_map *map);
5279 #include <isl/union_set.h>
5280 __isl_give isl_union_map *isl_union_set_unwrap(
5281 __isl_take isl_union_set *uset);
5283 #include <isl/union_map.h>
5284 __isl_give isl_union_set *isl_union_map_wrap(
5285 __isl_take isl_union_map *umap);
5287 The input to C<isl_space_unwrap> should
5288 be the space of a set, while that of
5289 C<isl_space_wrap> should be the space of a relation.
5290 Conversely, the output of C<isl_space_unwrap> is the space
5291 of a relation, while that of C<isl_space_wrap> is the space of a set.
5295 Remove any internal structure of domain (and range) of the given
5296 set or relation. If there is any such internal structure in the input,
5297 then the name of the space is also removed.
5299 #include <isl/local_space.h>
5300 __isl_give isl_local_space *
5301 isl_local_space_flatten_domain(
5302 __isl_take isl_local_space *ls);
5303 __isl_give isl_local_space *
5304 isl_local_space_flatten_range(
5305 __isl_take isl_local_space *ls);
5307 #include <isl/set.h>
5308 __isl_give isl_basic_set *isl_basic_set_flatten(
5309 __isl_take isl_basic_set *bset);
5310 __isl_give isl_set *isl_set_flatten(
5311 __isl_take isl_set *set);
5313 #include <isl/map.h>
5314 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
5315 __isl_take isl_basic_map *bmap);
5316 __isl_give isl_basic_map *isl_basic_map_flatten_range(
5317 __isl_take isl_basic_map *bmap);
5318 __isl_give isl_map *isl_map_flatten_range(
5319 __isl_take isl_map *map);
5320 __isl_give isl_map *isl_map_flatten_domain(
5321 __isl_take isl_map *map);
5322 __isl_give isl_basic_map *isl_basic_map_flatten(
5323 __isl_take isl_basic_map *bmap);
5324 __isl_give isl_map *isl_map_flatten(
5325 __isl_take isl_map *map);
5327 #include <isl/val.h>
5328 __isl_give isl_multi_val *isl_multi_val_flatten_range(
5329 __isl_take isl_multi_val *mv);
5331 #include <isl/aff.h>
5332 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
5333 __isl_take isl_multi_aff *ma);
5334 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
5335 __isl_take isl_multi_aff *ma);
5336 __isl_give isl_multi_pw_aff *
5337 isl_multi_pw_aff_flatten_range(
5338 __isl_take isl_multi_pw_aff *mpa);
5339 __isl_give isl_multi_union_pw_aff *
5340 isl_multi_union_pw_aff_flatten_range(
5341 __isl_take isl_multi_union_pw_aff *mupa);
5343 #include <isl/map.h>
5344 __isl_give isl_map *isl_set_flatten_map(
5345 __isl_take isl_set *set);
5347 The function above constructs a relation
5348 that maps the input set to a flattened version of the set.
5352 Lift the input set to a space with extra dimensions corresponding
5353 to the existentially quantified variables in the input.
5354 In particular, the result lives in a wrapped map where the domain
5355 is the original space and the range corresponds to the original
5356 existentially quantified variables.
5358 #include <isl/set.h>
5359 __isl_give isl_basic_set *isl_basic_set_lift(
5360 __isl_take isl_basic_set *bset);
5361 __isl_give isl_set *isl_set_lift(
5362 __isl_take isl_set *set);
5363 __isl_give isl_union_set *isl_union_set_lift(
5364 __isl_take isl_union_set *uset);
5366 Given a local space that contains the existentially quantified
5367 variables of a set, a basic relation that, when applied to
5368 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
5369 can be constructed using the following function.
5371 #include <isl/local_space.h>
5372 __isl_give isl_basic_map *isl_local_space_lifting(
5373 __isl_take isl_local_space *ls);
5375 #include <isl/aff.h>
5376 __isl_give isl_multi_aff *isl_multi_aff_lift(
5377 __isl_take isl_multi_aff *maff,
5378 __isl_give isl_local_space **ls);
5380 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
5381 then it is assigned the local space that lies at the basis of
5382 the lifting applied.
5384 =item * Internal Product
5386 #include <isl/space.h>
5387 __isl_give isl_space *isl_space_zip(
5388 __isl_take isl_space *space);
5390 #include <isl/map.h>
5391 __isl_give isl_basic_map *isl_basic_map_zip(
5392 __isl_take isl_basic_map *bmap);
5393 __isl_give isl_map *isl_map_zip(
5394 __isl_take isl_map *map);
5396 #include <isl/union_map.h>
5397 __isl_give isl_union_map *isl_union_map_zip(
5398 __isl_take isl_union_map *umap);
5400 Given a relation with nested relations for domain and range,
5401 interchange the range of the domain with the domain of the range.
5405 #include <isl/space.h>
5406 __isl_give isl_space *isl_space_curry(
5407 __isl_take isl_space *space);
5408 __isl_give isl_space *isl_space_uncurry(
5409 __isl_take isl_space *space);
5411 #include <isl/map.h>
5412 __isl_give isl_basic_map *isl_basic_map_curry(
5413 __isl_take isl_basic_map *bmap);
5414 __isl_give isl_basic_map *isl_basic_map_uncurry(
5415 __isl_take isl_basic_map *bmap);
5416 __isl_give isl_map *isl_map_curry(
5417 __isl_take isl_map *map);
5418 __isl_give isl_map *isl_map_uncurry(
5419 __isl_take isl_map *map);
5421 #include <isl/union_map.h>
5422 __isl_give isl_union_map *isl_union_map_curry(
5423 __isl_take isl_union_map *umap);
5424 __isl_give isl_union_map *isl_union_map_uncurry(
5425 __isl_take isl_union_map *umap);
5427 Given a relation with a nested relation for domain,
5428 the C<curry> functions
5429 move the range of the nested relation out of the domain
5430 and use it as the domain of a nested relation in the range,
5431 with the original range as range of this nested relation.
5432 The C<uncurry> functions perform the inverse operation.
5434 #include <isl/space.h>
5435 __isl_give isl_space *isl_space_range_curry(
5436 __isl_take isl_space *space);
5438 #include <isl/map.h>
5439 __isl_give isl_map *isl_map_range_curry(
5440 __isl_take isl_map *map);
5442 #include <isl/union_map.h>
5443 __isl_give isl_union_map *isl_union_map_range_curry(
5444 __isl_take isl_union_map *umap);
5446 These functions apply the currying to the relation that
5447 is nested inside the range of the input.
5449 =item * Aligning parameters
5451 Change the order of the parameters of the given set, relation
5453 such that the first parameters match those of C<model>.
5454 This may involve the introduction of extra parameters.
5455 All parameters need to be named.
5457 #include <isl/space.h>
5458 __isl_give isl_space *isl_space_align_params(
5459 __isl_take isl_space *space1,
5460 __isl_take isl_space *space2)
5462 #include <isl/set.h>
5463 __isl_give isl_basic_set *isl_basic_set_align_params(
5464 __isl_take isl_basic_set *bset,
5465 __isl_take isl_space *model);
5466 __isl_give isl_set *isl_set_align_params(
5467 __isl_take isl_set *set,
5468 __isl_take isl_space *model);
5470 #include <isl/map.h>
5471 __isl_give isl_basic_map *isl_basic_map_align_params(
5472 __isl_take isl_basic_map *bmap,
5473 __isl_take isl_space *model);
5474 __isl_give isl_map *isl_map_align_params(
5475 __isl_take isl_map *map,
5476 __isl_take isl_space *model);
5478 #include <isl/val.h>
5479 __isl_give isl_multi_val *isl_multi_val_align_params(
5480 __isl_take isl_multi_val *mv,
5481 __isl_take isl_space *model);
5483 #include <isl/aff.h>
5484 __isl_give isl_aff *isl_aff_align_params(
5485 __isl_take isl_aff *aff,
5486 __isl_take isl_space *model);
5487 __isl_give isl_multi_aff *isl_multi_aff_align_params(
5488 __isl_take isl_multi_aff *multi,
5489 __isl_take isl_space *model);
5490 __isl_give isl_pw_aff *isl_pw_aff_align_params(
5491 __isl_take isl_pw_aff *pwaff,
5492 __isl_take isl_space *model);
5493 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
5494 __isl_take isl_pw_multi_aff *pma,
5495 __isl_take isl_space *model);
5496 __isl_give isl_union_pw_aff *
5497 isl_union_pw_aff_align_params(
5498 __isl_take isl_union_pw_aff *upa,
5499 __isl_take isl_space *model);
5500 __isl_give isl_union_pw_multi_aff *
5501 isl_union_pw_multi_aff_align_params(
5502 __isl_take isl_union_pw_multi_aff *upma,
5503 __isl_take isl_space *model);
5504 __isl_give isl_multi_union_pw_aff *
5505 isl_multi_union_pw_aff_align_params(
5506 __isl_take isl_multi_union_pw_aff *mupa,
5507 __isl_take isl_space *model);
5509 #include <isl/polynomial.h>
5510 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5511 __isl_take isl_qpolynomial *qp,
5512 __isl_take isl_space *model);
5514 =item * Unary Arithmetic Operations
5516 #include <isl/set.h>
5517 __isl_give isl_set *isl_set_neg(
5518 __isl_take isl_set *set);
5519 #include <isl/map.h>
5520 __isl_give isl_map *isl_map_neg(
5521 __isl_take isl_map *map);
5523 C<isl_set_neg> constructs a set containing the opposites of
5524 the elements in its argument.
5525 The domain of the result of C<isl_map_neg> is the same
5526 as the domain of its argument. The corresponding range
5527 elements are the opposites of the corresponding range
5528 elements in the argument.
5530 #include <isl/val.h>
5531 __isl_give isl_multi_val *isl_multi_val_neg(
5532 __isl_take isl_multi_val *mv);
5534 #include <isl/aff.h>
5535 __isl_give isl_aff *isl_aff_neg(
5536 __isl_take isl_aff *aff);
5537 __isl_give isl_multi_aff *isl_multi_aff_neg(
5538 __isl_take isl_multi_aff *ma);
5539 __isl_give isl_pw_aff *isl_pw_aff_neg(
5540 __isl_take isl_pw_aff *pwaff);
5541 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
5542 __isl_take isl_pw_multi_aff *pma);
5543 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
5544 __isl_take isl_multi_pw_aff *mpa);
5545 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
5546 __isl_take isl_union_pw_aff *upa);
5547 __isl_give isl_union_pw_multi_aff *
5548 isl_union_pw_multi_aff_neg(
5549 __isl_take isl_union_pw_multi_aff *upma);
5550 __isl_give isl_multi_union_pw_aff *
5551 isl_multi_union_pw_aff_neg(
5552 __isl_take isl_multi_union_pw_aff *mupa);
5553 __isl_give isl_aff *isl_aff_ceil(
5554 __isl_take isl_aff *aff);
5555 __isl_give isl_pw_aff *isl_pw_aff_ceil(
5556 __isl_take isl_pw_aff *pwaff);
5557 __isl_give isl_aff *isl_aff_floor(
5558 __isl_take isl_aff *aff);
5559 __isl_give isl_multi_aff *isl_multi_aff_floor(
5560 __isl_take isl_multi_aff *ma);
5561 __isl_give isl_pw_aff *isl_pw_aff_floor(
5562 __isl_take isl_pw_aff *pwaff);
5563 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
5564 __isl_take isl_union_pw_aff *upa);
5565 __isl_give isl_multi_union_pw_aff *
5566 isl_multi_union_pw_aff_floor(
5567 __isl_take isl_multi_union_pw_aff *mupa);
5569 #include <isl/aff.h>
5570 __isl_give isl_pw_aff *isl_pw_aff_list_min(
5571 __isl_take isl_pw_aff_list *list);
5572 __isl_give isl_pw_aff *isl_pw_aff_list_max(
5573 __isl_take isl_pw_aff_list *list);
5575 #include <isl/polynomial.h>
5576 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5577 __isl_take isl_qpolynomial *qp);
5578 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5579 __isl_take isl_pw_qpolynomial *pwqp);
5580 __isl_give isl_union_pw_qpolynomial *
5581 isl_union_pw_qpolynomial_neg(
5582 __isl_take isl_union_pw_qpolynomial *upwqp);
5583 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5584 __isl_take isl_qpolynomial *qp,
5586 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5587 __isl_take isl_pw_qpolynomial *pwqp,
5592 The following functions evaluate a function in a point.
5594 #include <isl/polynomial.h>
5595 __isl_give isl_val *isl_pw_qpolynomial_eval(
5596 __isl_take isl_pw_qpolynomial *pwqp,
5597 __isl_take isl_point *pnt);
5598 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5599 __isl_take isl_pw_qpolynomial_fold *pwf,
5600 __isl_take isl_point *pnt);
5601 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5602 __isl_take isl_union_pw_qpolynomial *upwqp,
5603 __isl_take isl_point *pnt);
5604 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5605 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5606 __isl_take isl_point *pnt);
5608 =item * Dimension manipulation
5610 It is usually not advisable to directly change the (input or output)
5611 space of a set or a relation as this removes the name and the internal
5612 structure of the space. However, the functions below can be useful
5613 to add new parameters, assuming
5614 C<isl_set_align_params> and C<isl_map_align_params>
5617 #include <isl/space.h>
5618 __isl_give isl_space *isl_space_add_dims(
5619 __isl_take isl_space *space,
5620 enum isl_dim_type type, unsigned n);
5621 __isl_give isl_space *isl_space_insert_dims(
5622 __isl_take isl_space *space,
5623 enum isl_dim_type type, unsigned pos, unsigned n);
5624 __isl_give isl_space *isl_space_drop_dims(
5625 __isl_take isl_space *space,
5626 enum isl_dim_type type, unsigned first, unsigned n);
5627 __isl_give isl_space *isl_space_move_dims(
5628 __isl_take isl_space *space,
5629 enum isl_dim_type dst_type, unsigned dst_pos,
5630 enum isl_dim_type src_type, unsigned src_pos,
5633 #include <isl/local_space.h>
5634 __isl_give isl_local_space *isl_local_space_add_dims(
5635 __isl_take isl_local_space *ls,
5636 enum isl_dim_type type, unsigned n);
5637 __isl_give isl_local_space *isl_local_space_insert_dims(
5638 __isl_take isl_local_space *ls,
5639 enum isl_dim_type type, unsigned first, unsigned n);
5640 __isl_give isl_local_space *isl_local_space_drop_dims(
5641 __isl_take isl_local_space *ls,
5642 enum isl_dim_type type, unsigned first, unsigned n);
5644 #include <isl/set.h>
5645 __isl_give isl_basic_set *isl_basic_set_add_dims(
5646 __isl_take isl_basic_set *bset,
5647 enum isl_dim_type type, unsigned n);
5648 __isl_give isl_set *isl_set_add_dims(
5649 __isl_take isl_set *set,
5650 enum isl_dim_type type, unsigned n);
5651 __isl_give isl_basic_set *isl_basic_set_insert_dims(
5652 __isl_take isl_basic_set *bset,
5653 enum isl_dim_type type, unsigned pos,
5655 __isl_give isl_set *isl_set_insert_dims(
5656 __isl_take isl_set *set,
5657 enum isl_dim_type type, unsigned pos, unsigned n);
5658 __isl_give isl_basic_set *isl_basic_set_move_dims(
5659 __isl_take isl_basic_set *bset,
5660 enum isl_dim_type dst_type, unsigned dst_pos,
5661 enum isl_dim_type src_type, unsigned src_pos,
5663 __isl_give isl_set *isl_set_move_dims(
5664 __isl_take isl_set *set,
5665 enum isl_dim_type dst_type, unsigned dst_pos,
5666 enum isl_dim_type src_type, unsigned src_pos,
5669 #include <isl/map.h>
5670 __isl_give isl_basic_map *isl_basic_map_add_dims(
5671 __isl_take isl_basic_map *bmap,
5672 enum isl_dim_type type, unsigned n);
5673 __isl_give isl_map *isl_map_add_dims(
5674 __isl_take isl_map *map,
5675 enum isl_dim_type type, unsigned n);
5676 __isl_give isl_basic_map *isl_basic_map_insert_dims(
5677 __isl_take isl_basic_map *bmap,
5678 enum isl_dim_type type, unsigned pos,
5680 __isl_give isl_map *isl_map_insert_dims(
5681 __isl_take isl_map *map,
5682 enum isl_dim_type type, unsigned pos, unsigned n);
5683 __isl_give isl_basic_map *isl_basic_map_move_dims(
5684 __isl_take isl_basic_map *bmap,
5685 enum isl_dim_type dst_type, unsigned dst_pos,
5686 enum isl_dim_type src_type, unsigned src_pos,
5688 __isl_give isl_map *isl_map_move_dims(
5689 __isl_take isl_map *map,
5690 enum isl_dim_type dst_type, unsigned dst_pos,
5691 enum isl_dim_type src_type, unsigned src_pos,
5694 #include <isl/val.h>
5695 __isl_give isl_multi_val *isl_multi_val_insert_dims(
5696 __isl_take isl_multi_val *mv,
5697 enum isl_dim_type type, unsigned first, unsigned n);
5698 __isl_give isl_multi_val *isl_multi_val_add_dims(
5699 __isl_take isl_multi_val *mv,
5700 enum isl_dim_type type, unsigned n);
5701 __isl_give isl_multi_val *isl_multi_val_drop_dims(
5702 __isl_take isl_multi_val *mv,
5703 enum isl_dim_type type, unsigned first, unsigned n);
5705 #include <isl/aff.h>
5706 __isl_give isl_aff *isl_aff_insert_dims(
5707 __isl_take isl_aff *aff,
5708 enum isl_dim_type type, unsigned first, unsigned n);
5709 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
5710 __isl_take isl_multi_aff *ma,
5711 enum isl_dim_type type, unsigned first, unsigned n);
5712 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
5713 __isl_take isl_pw_aff *pwaff,
5714 enum isl_dim_type type, unsigned first, unsigned n);
5715 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
5716 __isl_take isl_multi_pw_aff *mpa,
5717 enum isl_dim_type type, unsigned first, unsigned n);
5718 __isl_give isl_aff *isl_aff_add_dims(
5719 __isl_take isl_aff *aff,
5720 enum isl_dim_type type, unsigned n);
5721 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
5722 __isl_take isl_multi_aff *ma,
5723 enum isl_dim_type type, unsigned n);
5724 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
5725 __isl_take isl_pw_aff *pwaff,
5726 enum isl_dim_type type, unsigned n);
5727 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
5728 __isl_take isl_multi_pw_aff *mpa,
5729 enum isl_dim_type type, unsigned n);
5730 __isl_give isl_aff *isl_aff_drop_dims(
5731 __isl_take isl_aff *aff,
5732 enum isl_dim_type type, unsigned first, unsigned n);
5733 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
5734 __isl_take isl_multi_aff *maff,
5735 enum isl_dim_type type, unsigned first, unsigned n);
5736 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
5737 __isl_take isl_pw_aff *pwaff,
5738 enum isl_dim_type type, unsigned first, unsigned n);
5739 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
5740 __isl_take isl_pw_multi_aff *pma,
5741 enum isl_dim_type type, unsigned first, unsigned n);
5742 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
5743 __isl_take isl_union_pw_aff *upa,
5744 enum isl_dim_type type, unsigned first, unsigned n);
5745 __isl_give isl_union_pw_multi_aff *
5746 isl_union_pw_multi_aff_drop_dims(
5747 __isl_take isl_union_pw_multi_aff *upma,
5748 enum isl_dim_type type,
5749 unsigned first, unsigned n);
5750 __isl_give isl_multi_union_pw_aff *
5751 isl_multi_union_pw_aff_drop_dims(
5752 __isl_take isl_multi_union_pw_aff *mupa,
5753 enum isl_dim_type type, unsigned first,
5755 __isl_give isl_aff *isl_aff_move_dims(
5756 __isl_take isl_aff *aff,
5757 enum isl_dim_type dst_type, unsigned dst_pos,
5758 enum isl_dim_type src_type, unsigned src_pos,
5760 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
5761 __isl_take isl_multi_aff *ma,
5762 enum isl_dim_type dst_type, unsigned dst_pos,
5763 enum isl_dim_type src_type, unsigned src_pos,
5765 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
5766 __isl_take isl_pw_aff *pa,
5767 enum isl_dim_type dst_type, unsigned dst_pos,
5768 enum isl_dim_type src_type, unsigned src_pos,
5770 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
5771 __isl_take isl_multi_pw_aff *pma,
5772 enum isl_dim_type dst_type, unsigned dst_pos,
5773 enum isl_dim_type src_type, unsigned src_pos,
5776 #include <isl/polynomial.h>
5777 __isl_give isl_union_pw_qpolynomial *
5778 isl_union_pw_qpolynomial_drop_dims(
5779 __isl_take isl_union_pw_qpolynomial *upwqp,
5780 enum isl_dim_type type,
5781 unsigned first, unsigned n);
5782 __isl_give isl_union_pw_qpolynomial_fold *
5783 isl_union_pw_qpolynomial_fold_drop_dims(
5784 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5785 enum isl_dim_type type,
5786 unsigned first, unsigned n);
5788 The operations on union expressions can only manipulate parameters.
5792 =head2 Binary Operations
5794 The two arguments of a binary operation not only need to live
5795 in the same C<isl_ctx>, they currently also need to have
5796 the same (number of) parameters.
5798 =head3 Basic Operations
5802 =item * Intersection
5804 #include <isl/local_space.h>
5805 __isl_give isl_local_space *isl_local_space_intersect(
5806 __isl_take isl_local_space *ls1,
5807 __isl_take isl_local_space *ls2);
5809 #include <isl/set.h>
5810 __isl_give isl_basic_set *isl_basic_set_intersect_params(
5811 __isl_take isl_basic_set *bset1,
5812 __isl_take isl_basic_set *bset2);
5813 __isl_give isl_basic_set *isl_basic_set_intersect(
5814 __isl_take isl_basic_set *bset1,
5815 __isl_take isl_basic_set *bset2);
5816 __isl_give isl_basic_set *isl_basic_set_list_intersect(
5817 __isl_take struct isl_basic_set_list *list);
5818 __isl_give isl_set *isl_set_intersect_params(
5819 __isl_take isl_set *set,
5820 __isl_take isl_set *params);
5821 __isl_give isl_set *isl_set_intersect(
5822 __isl_take isl_set *set1,
5823 __isl_take isl_set *set2);
5825 #include <isl/map.h>
5826 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
5827 __isl_take isl_basic_map *bmap,
5828 __isl_take isl_basic_set *bset);
5829 __isl_give isl_basic_map *isl_basic_map_intersect_range(
5830 __isl_take isl_basic_map *bmap,
5831 __isl_take isl_basic_set *bset);
5832 __isl_give isl_basic_map *isl_basic_map_intersect(
5833 __isl_take isl_basic_map *bmap1,
5834 __isl_take isl_basic_map *bmap2);
5835 __isl_give isl_basic_map *isl_basic_map_list_intersect(
5836 __isl_take isl_basic_map_list *list);
5837 __isl_give isl_map *isl_map_intersect_params(
5838 __isl_take isl_map *map,
5839 __isl_take isl_set *params);
5840 __isl_give isl_map *isl_map_intersect_domain(
5841 __isl_take isl_map *map,
5842 __isl_take isl_set *set);
5843 __isl_give isl_map *isl_map_intersect_range(
5844 __isl_take isl_map *map,
5845 __isl_take isl_set *set);
5846 __isl_give isl_map *isl_map_intersect(
5847 __isl_take isl_map *map1,
5848 __isl_take isl_map *map2);
5850 #include <isl/union_set.h>
5851 __isl_give isl_union_set *isl_union_set_intersect_params(
5852 __isl_take isl_union_set *uset,
5853 __isl_take isl_set *set);
5854 __isl_give isl_union_set *isl_union_set_intersect(
5855 __isl_take isl_union_set *uset1,
5856 __isl_take isl_union_set *uset2);
5858 #include <isl/union_map.h>
5859 __isl_give isl_union_map *isl_union_map_intersect_params(
5860 __isl_take isl_union_map *umap,
5861 __isl_take isl_set *set);
5862 __isl_give isl_union_map *isl_union_map_intersect_domain(
5863 __isl_take isl_union_map *umap,
5864 __isl_take isl_union_set *uset);
5865 __isl_give isl_union_map *isl_union_map_intersect_range(
5866 __isl_take isl_union_map *umap,
5867 __isl_take isl_union_set *uset);
5868 __isl_give isl_union_map *isl_union_map_intersect(
5869 __isl_take isl_union_map *umap1,
5870 __isl_take isl_union_map *umap2);
5872 #include <isl/aff.h>
5873 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
5874 __isl_take isl_pw_aff *pa,
5875 __isl_take isl_set *set);
5876 __isl_give isl_multi_pw_aff *
5877 isl_multi_pw_aff_intersect_domain(
5878 __isl_take isl_multi_pw_aff *mpa,
5879 __isl_take isl_set *domain);
5880 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
5881 __isl_take isl_pw_multi_aff *pma,
5882 __isl_take isl_set *set);
5883 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
5884 __isl_take isl_union_pw_aff *upa,
5885 __isl_take isl_union_set *uset);
5886 __isl_give isl_union_pw_multi_aff *
5887 isl_union_pw_multi_aff_intersect_domain(
5888 __isl_take isl_union_pw_multi_aff *upma,
5889 __isl_take isl_union_set *uset);
5890 __isl_give isl_multi_union_pw_aff *
5891 isl_multi_union_pw_aff_intersect_domain(
5892 __isl_take isl_multi_union_pw_aff *mupa,
5893 __isl_take isl_union_set *uset);
5894 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
5895 __isl_take isl_pw_aff *pa,
5896 __isl_take isl_set *set);
5897 __isl_give isl_multi_pw_aff *
5898 isl_multi_pw_aff_intersect_params(
5899 __isl_take isl_multi_pw_aff *mpa,
5900 __isl_take isl_set *set);
5901 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
5902 __isl_take isl_pw_multi_aff *pma,
5903 __isl_take isl_set *set);
5904 __isl_give isl_union_pw_aff *
5905 isl_union_pw_aff_intersect_params(
5906 __isl_take isl_union_pw_aff *upa,
5907 __isl_give isl_union_pw_multi_aff *
5908 isl_union_pw_multi_aff_intersect_params(
5909 __isl_take isl_union_pw_multi_aff *upma,
5910 __isl_take isl_set *set);
5911 __isl_give isl_multi_union_pw_aff *
5912 isl_multi_union_pw_aff_intersect_params(
5913 __isl_take isl_multi_union_pw_aff *mupa,
5914 __isl_take isl_set *params);
5915 isl_multi_union_pw_aff_intersect_range(
5916 __isl_take isl_multi_union_pw_aff *mupa,
5917 __isl_take isl_set *set);
5919 #include <isl/polynomial.h>
5920 __isl_give isl_pw_qpolynomial *
5921 isl_pw_qpolynomial_intersect_domain(
5922 __isl_take isl_pw_qpolynomial *pwpq,
5923 __isl_take isl_set *set);
5924 __isl_give isl_union_pw_qpolynomial *
5925 isl_union_pw_qpolynomial_intersect_domain(
5926 __isl_take isl_union_pw_qpolynomial *upwpq,
5927 __isl_take isl_union_set *uset);
5928 __isl_give isl_union_pw_qpolynomial_fold *
5929 isl_union_pw_qpolynomial_fold_intersect_domain(
5930 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5931 __isl_take isl_union_set *uset);
5932 __isl_give isl_pw_qpolynomial *
5933 isl_pw_qpolynomial_intersect_params(
5934 __isl_take isl_pw_qpolynomial *pwpq,
5935 __isl_take isl_set *set);
5936 __isl_give isl_pw_qpolynomial_fold *
5937 isl_pw_qpolynomial_fold_intersect_params(
5938 __isl_take isl_pw_qpolynomial_fold *pwf,
5939 __isl_take isl_set *set);
5940 __isl_give isl_union_pw_qpolynomial *
5941 isl_union_pw_qpolynomial_intersect_params(
5942 __isl_take isl_union_pw_qpolynomial *upwpq,
5943 __isl_take isl_set *set);
5944 __isl_give isl_union_pw_qpolynomial_fold *
5945 isl_union_pw_qpolynomial_fold_intersect_params(
5946 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5947 __isl_take isl_set *set);
5949 The second argument to the C<_params> functions needs to be
5950 a parametric (basic) set. For the other functions, a parametric set
5951 for either argument is only allowed if the other argument is
5952 a parametric set as well.
5953 The list passed to C<isl_basic_set_list_intersect> needs to have
5954 at least one element and all elements need to live in the same space.
5955 The function C<isl_multi_union_pw_aff_intersect_range>
5956 restricts the input function to those shared domain elements
5957 that map to the specified range.
5961 #include <isl/set.h>
5962 __isl_give isl_set *isl_basic_set_union(
5963 __isl_take isl_basic_set *bset1,
5964 __isl_take isl_basic_set *bset2);
5965 __isl_give isl_set *isl_set_union(
5966 __isl_take isl_set *set1,
5967 __isl_take isl_set *set2);
5968 __isl_give isl_set *isl_set_list_union(
5969 __isl_take isl_set_list *list);
5971 #include <isl/map.h>
5972 __isl_give isl_map *isl_basic_map_union(
5973 __isl_take isl_basic_map *bmap1,
5974 __isl_take isl_basic_map *bmap2);
5975 __isl_give isl_map *isl_map_union(
5976 __isl_take isl_map *map1,
5977 __isl_take isl_map *map2);
5979 #include <isl/union_set.h>
5980 __isl_give isl_union_set *isl_union_set_union(
5981 __isl_take isl_union_set *uset1,
5982 __isl_take isl_union_set *uset2);
5983 __isl_give isl_union_set *isl_union_set_list_union(
5984 __isl_take isl_union_set_list *list);
5986 #include <isl/union_map.h>
5987 __isl_give isl_union_map *isl_union_map_union(
5988 __isl_take isl_union_map *umap1,
5989 __isl_take isl_union_map *umap2);
5991 The list passed to C<isl_set_list_union> needs to have
5992 at least one element and all elements need to live in the same space.
5994 =item * Set difference
5996 #include <isl/set.h>
5997 __isl_give isl_set *isl_set_subtract(
5998 __isl_take isl_set *set1,
5999 __isl_take isl_set *set2);
6001 #include <isl/map.h>
6002 __isl_give isl_map *isl_map_subtract(
6003 __isl_take isl_map *map1,
6004 __isl_take isl_map *map2);
6005 __isl_give isl_map *isl_map_subtract_domain(
6006 __isl_take isl_map *map,
6007 __isl_take isl_set *dom);
6008 __isl_give isl_map *isl_map_subtract_range(
6009 __isl_take isl_map *map,
6010 __isl_take isl_set *dom);
6012 #include <isl/union_set.h>
6013 __isl_give isl_union_set *isl_union_set_subtract(
6014 __isl_take isl_union_set *uset1,
6015 __isl_take isl_union_set *uset2);
6017 #include <isl/union_map.h>
6018 __isl_give isl_union_map *isl_union_map_subtract(
6019 __isl_take isl_union_map *umap1,
6020 __isl_take isl_union_map *umap2);
6021 __isl_give isl_union_map *isl_union_map_subtract_domain(
6022 __isl_take isl_union_map *umap,
6023 __isl_take isl_union_set *dom);
6024 __isl_give isl_union_map *isl_union_map_subtract_range(
6025 __isl_take isl_union_map *umap,
6026 __isl_take isl_union_set *dom);
6028 #include <isl/aff.h>
6029 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
6030 __isl_take isl_pw_aff *pa,
6031 __isl_take isl_set *set);
6032 __isl_give isl_pw_multi_aff *
6033 isl_pw_multi_aff_subtract_domain(
6034 __isl_take isl_pw_multi_aff *pma,
6035 __isl_take isl_set *set);
6036 __isl_give isl_union_pw_aff *
6037 isl_union_pw_aff_subtract_domain(
6038 __isl_take isl_union_pw_aff *upa,
6039 __isl_take isl_union_set *uset);
6040 __isl_give isl_union_pw_multi_aff *
6041 isl_union_pw_multi_aff_subtract_domain(
6042 __isl_take isl_union_pw_multi_aff *upma,
6043 __isl_take isl_set *set);
6045 #include <isl/polynomial.h>
6046 __isl_give isl_pw_qpolynomial *
6047 isl_pw_qpolynomial_subtract_domain(
6048 __isl_take isl_pw_qpolynomial *pwpq,
6049 __isl_take isl_set *set);
6050 __isl_give isl_pw_qpolynomial_fold *
6051 isl_pw_qpolynomial_fold_subtract_domain(
6052 __isl_take isl_pw_qpolynomial_fold *pwf,
6053 __isl_take isl_set *set);
6054 __isl_give isl_union_pw_qpolynomial *
6055 isl_union_pw_qpolynomial_subtract_domain(
6056 __isl_take isl_union_pw_qpolynomial *upwpq,
6057 __isl_take isl_union_set *uset);
6058 __isl_give isl_union_pw_qpolynomial_fold *
6059 isl_union_pw_qpolynomial_fold_subtract_domain(
6060 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6061 __isl_take isl_union_set *uset);
6065 #include <isl/space.h>
6066 __isl_give isl_space *isl_space_join(
6067 __isl_take isl_space *left,
6068 __isl_take isl_space *right);
6070 #include <isl/map.h>
6071 __isl_give isl_basic_set *isl_basic_set_apply(
6072 __isl_take isl_basic_set *bset,
6073 __isl_take isl_basic_map *bmap);
6074 __isl_give isl_set *isl_set_apply(
6075 __isl_take isl_set *set,
6076 __isl_take isl_map *map);
6077 __isl_give isl_union_set *isl_union_set_apply(
6078 __isl_take isl_union_set *uset,
6079 __isl_take isl_union_map *umap);
6080 __isl_give isl_basic_map *isl_basic_map_apply_domain(
6081 __isl_take isl_basic_map *bmap1,
6082 __isl_take isl_basic_map *bmap2);
6083 __isl_give isl_basic_map *isl_basic_map_apply_range(
6084 __isl_take isl_basic_map *bmap1,
6085 __isl_take isl_basic_map *bmap2);
6086 __isl_give isl_map *isl_map_apply_domain(
6087 __isl_take isl_map *map1,
6088 __isl_take isl_map *map2);
6089 __isl_give isl_map *isl_map_apply_range(
6090 __isl_take isl_map *map1,
6091 __isl_take isl_map *map2);
6093 #include <isl/union_map.h>
6094 __isl_give isl_union_map *isl_union_map_apply_domain(
6095 __isl_take isl_union_map *umap1,
6096 __isl_take isl_union_map *umap2);
6097 __isl_give isl_union_map *isl_union_map_apply_range(
6098 __isl_take isl_union_map *umap1,
6099 __isl_take isl_union_map *umap2);
6101 #include <isl/aff.h>
6102 __isl_give isl_union_pw_aff *
6103 isl_multi_union_pw_aff_apply_aff(
6104 __isl_take isl_multi_union_pw_aff *mupa,
6105 __isl_take isl_aff *aff);
6106 __isl_give isl_union_pw_aff *
6107 isl_multi_union_pw_aff_apply_pw_aff(
6108 __isl_take isl_multi_union_pw_aff *mupa,
6109 __isl_take isl_pw_aff *pa);
6110 __isl_give isl_multi_union_pw_aff *
6111 isl_multi_union_pw_aff_apply_multi_aff(
6112 __isl_take isl_multi_union_pw_aff *mupa,
6113 __isl_take isl_multi_aff *ma);
6114 __isl_give isl_multi_union_pw_aff *
6115 isl_multi_union_pw_aff_apply_pw_multi_aff(
6116 __isl_take isl_multi_union_pw_aff *mupa,
6117 __isl_take isl_pw_multi_aff *pma);
6119 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
6120 over the shared domain of the elements of the input. The dimension is
6121 required to be greater than zero.
6122 The C<isl_multi_union_pw_aff> argument of
6123 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
6124 but only if the range of the C<isl_multi_aff> argument
6125 is also zero-dimensional.
6126 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
6128 #include <isl/polynomial.h>
6129 __isl_give isl_pw_qpolynomial_fold *
6130 isl_set_apply_pw_qpolynomial_fold(
6131 __isl_take isl_set *set,
6132 __isl_take isl_pw_qpolynomial_fold *pwf,
6134 __isl_give isl_pw_qpolynomial_fold *
6135 isl_map_apply_pw_qpolynomial_fold(
6136 __isl_take isl_map *map,
6137 __isl_take isl_pw_qpolynomial_fold *pwf,
6139 __isl_give isl_union_pw_qpolynomial_fold *
6140 isl_union_set_apply_union_pw_qpolynomial_fold(
6141 __isl_take isl_union_set *uset,
6142 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6144 __isl_give isl_union_pw_qpolynomial_fold *
6145 isl_union_map_apply_union_pw_qpolynomial_fold(
6146 __isl_take isl_union_map *umap,
6147 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6150 The functions taking a map
6151 compose the given map with the given piecewise quasipolynomial reduction.
6152 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
6153 over all elements in the intersection of the range of the map
6154 and the domain of the piecewise quasipolynomial reduction
6155 as a function of an element in the domain of the map.
6156 The functions taking a set compute a bound over all elements in the
6157 intersection of the set and the domain of the
6158 piecewise quasipolynomial reduction.
6162 #include <isl/set.h>
6163 __isl_give isl_basic_set *
6164 isl_basic_set_preimage_multi_aff(
6165 __isl_take isl_basic_set *bset,
6166 __isl_take isl_multi_aff *ma);
6167 __isl_give isl_set *isl_set_preimage_multi_aff(
6168 __isl_take isl_set *set,
6169 __isl_take isl_multi_aff *ma);
6170 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
6171 __isl_take isl_set *set,
6172 __isl_take isl_pw_multi_aff *pma);
6173 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
6174 __isl_take isl_set *set,
6175 __isl_take isl_multi_pw_aff *mpa);
6177 #include <isl/union_set.h>
6178 __isl_give isl_union_set *
6179 isl_union_set_preimage_multi_aff(
6180 __isl_take isl_union_set *uset,
6181 __isl_take isl_multi_aff *ma);
6182 __isl_give isl_union_set *
6183 isl_union_set_preimage_pw_multi_aff(
6184 __isl_take isl_union_set *uset,
6185 __isl_take isl_pw_multi_aff *pma);
6186 __isl_give isl_union_set *
6187 isl_union_set_preimage_union_pw_multi_aff(
6188 __isl_take isl_union_set *uset,
6189 __isl_take isl_union_pw_multi_aff *upma);
6191 #include <isl/map.h>
6192 __isl_give isl_basic_map *
6193 isl_basic_map_preimage_domain_multi_aff(
6194 __isl_take isl_basic_map *bmap,
6195 __isl_take isl_multi_aff *ma);
6196 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
6197 __isl_take isl_map *map,
6198 __isl_take isl_multi_aff *ma);
6199 __isl_give isl_map *isl_map_preimage_range_multi_aff(
6200 __isl_take isl_map *map,
6201 __isl_take isl_multi_aff *ma);
6202 __isl_give isl_map *
6203 isl_map_preimage_domain_pw_multi_aff(
6204 __isl_take isl_map *map,
6205 __isl_take isl_pw_multi_aff *pma);
6206 __isl_give isl_map *
6207 isl_map_preimage_range_pw_multi_aff(
6208 __isl_take isl_map *map,
6209 __isl_take isl_pw_multi_aff *pma);
6210 __isl_give isl_map *
6211 isl_map_preimage_domain_multi_pw_aff(
6212 __isl_take isl_map *map,
6213 __isl_take isl_multi_pw_aff *mpa);
6214 __isl_give isl_basic_map *
6215 isl_basic_map_preimage_range_multi_aff(
6216 __isl_take isl_basic_map *bmap,
6217 __isl_take isl_multi_aff *ma);
6219 #include <isl/union_map.h>
6220 __isl_give isl_union_map *
6221 isl_union_map_preimage_domain_multi_aff(
6222 __isl_take isl_union_map *umap,
6223 __isl_take isl_multi_aff *ma);
6224 __isl_give isl_union_map *
6225 isl_union_map_preimage_range_multi_aff(
6226 __isl_take isl_union_map *umap,
6227 __isl_take isl_multi_aff *ma);
6228 __isl_give isl_union_map *
6229 isl_union_map_preimage_domain_pw_multi_aff(
6230 __isl_take isl_union_map *umap,
6231 __isl_take isl_pw_multi_aff *pma);
6232 __isl_give isl_union_map *
6233 isl_union_map_preimage_range_pw_multi_aff(
6234 __isl_take isl_union_map *umap,
6235 __isl_take isl_pw_multi_aff *pma);
6236 __isl_give isl_union_map *
6237 isl_union_map_preimage_domain_union_pw_multi_aff(
6238 __isl_take isl_union_map *umap,
6239 __isl_take isl_union_pw_multi_aff *upma);
6240 __isl_give isl_union_map *
6241 isl_union_map_preimage_range_union_pw_multi_aff(
6242 __isl_take isl_union_map *umap,
6243 __isl_take isl_union_pw_multi_aff *upma);
6245 These functions compute the preimage of the given set or map domain/range under
6246 the given function. In other words, the expression is plugged
6247 into the set description or into the domain/range of the map.
6251 #include <isl/aff.h>
6252 __isl_give isl_aff *isl_aff_pullback_aff(
6253 __isl_take isl_aff *aff1,
6254 __isl_take isl_aff *aff2);
6255 __isl_give isl_aff *isl_aff_pullback_multi_aff(
6256 __isl_take isl_aff *aff,
6257 __isl_take isl_multi_aff *ma);
6258 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
6259 __isl_take isl_pw_aff *pa,
6260 __isl_take isl_multi_aff *ma);
6261 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
6262 __isl_take isl_pw_aff *pa,
6263 __isl_take isl_pw_multi_aff *pma);
6264 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
6265 __isl_take isl_pw_aff *pa,
6266 __isl_take isl_multi_pw_aff *mpa);
6267 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
6268 __isl_take isl_multi_aff *ma1,
6269 __isl_take isl_multi_aff *ma2);
6270 __isl_give isl_pw_multi_aff *
6271 isl_pw_multi_aff_pullback_multi_aff(
6272 __isl_take isl_pw_multi_aff *pma,
6273 __isl_take isl_multi_aff *ma);
6274 __isl_give isl_multi_pw_aff *
6275 isl_multi_pw_aff_pullback_multi_aff(
6276 __isl_take isl_multi_pw_aff *mpa,
6277 __isl_take isl_multi_aff *ma);
6278 __isl_give isl_pw_multi_aff *
6279 isl_pw_multi_aff_pullback_pw_multi_aff(
6280 __isl_take isl_pw_multi_aff *pma1,
6281 __isl_take isl_pw_multi_aff *pma2);
6282 __isl_give isl_multi_pw_aff *
6283 isl_multi_pw_aff_pullback_pw_multi_aff(
6284 __isl_take isl_multi_pw_aff *mpa,
6285 __isl_take isl_pw_multi_aff *pma);
6286 __isl_give isl_multi_pw_aff *
6287 isl_multi_pw_aff_pullback_multi_pw_aff(
6288 __isl_take isl_multi_pw_aff *mpa1,
6289 __isl_take isl_multi_pw_aff *mpa2);
6290 __isl_give isl_union_pw_aff *
6291 isl_union_pw_aff_pullback_union_pw_multi_aff(
6292 __isl_take isl_union_pw_aff *upa,
6293 __isl_take isl_union_pw_multi_aff *upma);
6294 __isl_give isl_union_pw_multi_aff *
6295 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
6296 __isl_take isl_union_pw_multi_aff *upma1,
6297 __isl_take isl_union_pw_multi_aff *upma2);
6298 __isl_give isl_multi_union_pw_aff *
6299 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
6300 __isl_take isl_multi_union_pw_aff *mupa,
6301 __isl_take isl_union_pw_multi_aff *upma);
6303 These functions precompose the first expression by the second function.
6304 In other words, the second function is plugged
6305 into the first expression.
6309 #include <isl/aff.h>
6310 __isl_give isl_basic_set *isl_aff_eq_basic_set(
6311 __isl_take isl_aff *aff1,
6312 __isl_take isl_aff *aff2);
6313 __isl_give isl_set *isl_aff_eq_set(
6314 __isl_take isl_aff *aff1,
6315 __isl_take isl_aff *aff2);
6316 __isl_give isl_basic_set *isl_aff_le_basic_set(
6317 __isl_take isl_aff *aff1,
6318 __isl_take isl_aff *aff2);
6319 __isl_give isl_set *isl_aff_le_set(
6320 __isl_take isl_aff *aff1,
6321 __isl_take isl_aff *aff2);
6322 __isl_give isl_basic_set *isl_aff_lt_basic_set(
6323 __isl_take isl_aff *aff1,
6324 __isl_take isl_aff *aff2);
6325 __isl_give isl_set *isl_aff_lt_set(
6326 __isl_take isl_aff *aff1,
6327 __isl_take isl_aff *aff2);
6328 __isl_give isl_basic_set *isl_aff_ge_basic_set(
6329 __isl_take isl_aff *aff1,
6330 __isl_take isl_aff *aff2);
6331 __isl_give isl_set *isl_aff_ge_set(
6332 __isl_take isl_aff *aff1,
6333 __isl_take isl_aff *aff2);
6334 __isl_give isl_basic_set *isl_aff_gt_basic_set(
6335 __isl_take isl_aff *aff1,
6336 __isl_take isl_aff *aff2);
6337 __isl_give isl_set *isl_pw_aff_eq_set(
6338 __isl_take isl_pw_aff *pwaff1,
6339 __isl_take isl_pw_aff *pwaff2);
6340 __isl_give isl_set *isl_pw_aff_ne_set(
6341 __isl_take isl_pw_aff *pwaff1,
6342 __isl_take isl_pw_aff *pwaff2);
6343 __isl_give isl_set *isl_pw_aff_le_set(
6344 __isl_take isl_pw_aff *pwaff1,
6345 __isl_take isl_pw_aff *pwaff2);
6346 __isl_give isl_set *isl_pw_aff_lt_set(
6347 __isl_take isl_pw_aff *pwaff1,
6348 __isl_take isl_pw_aff *pwaff2);
6349 __isl_give isl_set *isl_pw_aff_ge_set(
6350 __isl_take isl_pw_aff *pwaff1,
6351 __isl_take isl_pw_aff *pwaff2);
6352 __isl_give isl_set *isl_pw_aff_gt_set(
6353 __isl_take isl_pw_aff *pwaff1,
6354 __isl_take isl_pw_aff *pwaff2);
6356 __isl_give isl_set *isl_multi_aff_lex_le_set(
6357 __isl_take isl_multi_aff *ma1,
6358 __isl_take isl_multi_aff *ma2);
6359 __isl_give isl_set *isl_multi_aff_lex_lt_set(
6360 __isl_take isl_multi_aff *ma1,
6361 __isl_take isl_multi_aff *ma2);
6362 __isl_give isl_set *isl_multi_aff_lex_ge_set(
6363 __isl_take isl_multi_aff *ma1,
6364 __isl_take isl_multi_aff *ma2);
6365 __isl_give isl_set *isl_multi_aff_lex_gt_set(
6366 __isl_take isl_multi_aff *ma1,
6367 __isl_take isl_multi_aff *ma2);
6369 __isl_give isl_set *isl_pw_aff_list_eq_set(
6370 __isl_take isl_pw_aff_list *list1,
6371 __isl_take isl_pw_aff_list *list2);
6372 __isl_give isl_set *isl_pw_aff_list_ne_set(
6373 __isl_take isl_pw_aff_list *list1,
6374 __isl_take isl_pw_aff_list *list2);
6375 __isl_give isl_set *isl_pw_aff_list_le_set(
6376 __isl_take isl_pw_aff_list *list1,
6377 __isl_take isl_pw_aff_list *list2);
6378 __isl_give isl_set *isl_pw_aff_list_lt_set(
6379 __isl_take isl_pw_aff_list *list1,
6380 __isl_take isl_pw_aff_list *list2);
6381 __isl_give isl_set *isl_pw_aff_list_ge_set(
6382 __isl_take isl_pw_aff_list *list1,
6383 __isl_take isl_pw_aff_list *list2);
6384 __isl_give isl_set *isl_pw_aff_list_gt_set(
6385 __isl_take isl_pw_aff_list *list1,
6386 __isl_take isl_pw_aff_list *list2);
6388 The function C<isl_aff_ge_basic_set> returns a basic set
6389 containing those elements in the shared space
6390 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
6391 The function C<isl_pw_aff_ge_set> returns a set
6392 containing those elements in the shared domain
6393 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
6394 greater than or equal to C<pwaff2>.
6395 The function C<isl_multi_aff_lex_le_set> returns a set
6396 containing those elements in the shared domain space
6397 where C<ma1> is lexicographically smaller than or
6399 The functions operating on C<isl_pw_aff_list> apply the corresponding
6400 C<isl_pw_aff> function to each pair of elements in the two lists.
6402 #include <isl/aff.h>
6403 __isl_give isl_map *isl_pw_aff_eq_map(
6404 __isl_take isl_pw_aff *pa1,
6405 __isl_take isl_pw_aff *pa2);
6406 __isl_give isl_map *isl_pw_aff_lt_map(
6407 __isl_take isl_pw_aff *pa1,
6408 __isl_take isl_pw_aff *pa2);
6409 __isl_give isl_map *isl_pw_aff_gt_map(
6410 __isl_take isl_pw_aff *pa1,
6411 __isl_take isl_pw_aff *pa2);
6413 __isl_give isl_map *isl_multi_pw_aff_eq_map(
6414 __isl_take isl_multi_pw_aff *mpa1,
6415 __isl_take isl_multi_pw_aff *mpa2);
6416 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
6417 __isl_take isl_multi_pw_aff *mpa1,
6418 __isl_take isl_multi_pw_aff *mpa2);
6419 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
6420 __isl_take isl_multi_pw_aff *mpa1,
6421 __isl_take isl_multi_pw_aff *mpa2);
6423 These functions return a map between domain elements of the arguments
6424 where the function values satisfy the given relation.
6426 #include <isl/union_map.h>
6427 __isl_give isl_union_map *
6428 isl_union_map_eq_at_multi_union_pw_aff(
6429 __isl_take isl_union_map *umap,
6430 __isl_take isl_multi_union_pw_aff *mupa);
6431 __isl_give isl_union_map *
6432 isl_union_map_lex_lt_at_multi_union_pw_aff(
6433 __isl_take isl_union_map *umap,
6434 __isl_take isl_multi_union_pw_aff *mupa);
6435 __isl_give isl_union_map *
6436 isl_union_map_lex_gt_at_multi_union_pw_aff(
6437 __isl_take isl_union_map *umap,
6438 __isl_take isl_multi_union_pw_aff *mupa);
6440 These functions select the subset of elements in the union map
6441 that have an equal or lexicographically smaller function value.
6443 =item * Cartesian Product
6445 #include <isl/space.h>
6446 __isl_give isl_space *isl_space_product(
6447 __isl_take isl_space *space1,
6448 __isl_take isl_space *space2);
6449 __isl_give isl_space *isl_space_domain_product(
6450 __isl_take isl_space *space1,
6451 __isl_take isl_space *space2);
6452 __isl_give isl_space *isl_space_range_product(
6453 __isl_take isl_space *space1,
6454 __isl_take isl_space *space2);
6457 C<isl_space_product>, C<isl_space_domain_product>
6458 and C<isl_space_range_product> take pairs or relation spaces and
6459 produce a single relations space, where either the domain, the range
6460 or both domain and range are wrapped spaces of relations between
6461 the domains and/or ranges of the input spaces.
6462 If the product is only constructed over the domain or the range
6463 then the ranges or the domains of the inputs should be the same.
6464 The function C<isl_space_product> also accepts a pair of set spaces,
6465 in which case it returns a wrapped space of a relation between the
6468 #include <isl/set.h>
6469 __isl_give isl_set *isl_set_product(
6470 __isl_take isl_set *set1,
6471 __isl_take isl_set *set2);
6473 #include <isl/map.h>
6474 __isl_give isl_basic_map *isl_basic_map_domain_product(
6475 __isl_take isl_basic_map *bmap1,
6476 __isl_take isl_basic_map *bmap2);
6477 __isl_give isl_basic_map *isl_basic_map_range_product(
6478 __isl_take isl_basic_map *bmap1,
6479 __isl_take isl_basic_map *bmap2);
6480 __isl_give isl_basic_map *isl_basic_map_product(
6481 __isl_take isl_basic_map *bmap1,
6482 __isl_take isl_basic_map *bmap2);
6483 __isl_give isl_map *isl_map_domain_product(
6484 __isl_take isl_map *map1,
6485 __isl_take isl_map *map2);
6486 __isl_give isl_map *isl_map_range_product(
6487 __isl_take isl_map *map1,
6488 __isl_take isl_map *map2);
6489 __isl_give isl_map *isl_map_product(
6490 __isl_take isl_map *map1,
6491 __isl_take isl_map *map2);
6493 #include <isl/union_set.h>
6494 __isl_give isl_union_set *isl_union_set_product(
6495 __isl_take isl_union_set *uset1,
6496 __isl_take isl_union_set *uset2);
6498 #include <isl/union_map.h>
6499 __isl_give isl_union_map *isl_union_map_domain_product(
6500 __isl_take isl_union_map *umap1,
6501 __isl_take isl_union_map *umap2);
6502 __isl_give isl_union_map *isl_union_map_range_product(
6503 __isl_take isl_union_map *umap1,
6504 __isl_take isl_union_map *umap2);
6505 __isl_give isl_union_map *isl_union_map_product(
6506 __isl_take isl_union_map *umap1,
6507 __isl_take isl_union_map *umap2);
6509 #include <isl/val.h>
6510 __isl_give isl_multi_val *isl_multi_val_range_product(
6511 __isl_take isl_multi_val *mv1,
6512 __isl_take isl_multi_val *mv2);
6513 __isl_give isl_multi_val *isl_multi_val_product(
6514 __isl_take isl_multi_val *mv1,
6515 __isl_take isl_multi_val *mv2);
6517 #include <isl/aff.h>
6518 __isl_give isl_multi_aff *isl_multi_aff_range_product(
6519 __isl_take isl_multi_aff *ma1,
6520 __isl_take isl_multi_aff *ma2);
6521 __isl_give isl_multi_aff *isl_multi_aff_product(
6522 __isl_take isl_multi_aff *ma1,
6523 __isl_take isl_multi_aff *ma2);
6524 __isl_give isl_multi_pw_aff *
6525 isl_multi_pw_aff_range_product(
6526 __isl_take isl_multi_pw_aff *mpa1,
6527 __isl_take isl_multi_pw_aff *mpa2);
6528 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
6529 __isl_take isl_multi_pw_aff *mpa1,
6530 __isl_take isl_multi_pw_aff *mpa2);
6531 __isl_give isl_pw_multi_aff *
6532 isl_pw_multi_aff_range_product(
6533 __isl_take isl_pw_multi_aff *pma1,
6534 __isl_take isl_pw_multi_aff *pma2);
6535 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
6536 __isl_take isl_pw_multi_aff *pma1,
6537 __isl_take isl_pw_multi_aff *pma2);
6538 __isl_give isl_multi_union_pw_aff *
6539 isl_multi_union_pw_aff_range_product(
6540 __isl_take isl_multi_union_pw_aff *mupa1,
6541 __isl_take isl_multi_union_pw_aff *mupa2);
6543 The above functions compute the cross product of the given
6544 sets, relations or functions. The domains and ranges of the results
6545 are wrapped maps between domains and ranges of the inputs.
6546 To obtain a ``flat'' product, use the following functions
6549 #include <isl/set.h>
6550 __isl_give isl_basic_set *isl_basic_set_flat_product(
6551 __isl_take isl_basic_set *bset1,
6552 __isl_take isl_basic_set *bset2);
6553 __isl_give isl_set *isl_set_flat_product(
6554 __isl_take isl_set *set1,
6555 __isl_take isl_set *set2);
6557 #include <isl/map.h>
6558 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
6559 __isl_take isl_basic_map *bmap1,
6560 __isl_take isl_basic_map *bmap2);
6561 __isl_give isl_map *isl_map_flat_domain_product(
6562 __isl_take isl_map *map1,
6563 __isl_take isl_map *map2);
6564 __isl_give isl_map *isl_map_flat_range_product(
6565 __isl_take isl_map *map1,
6566 __isl_take isl_map *map2);
6567 __isl_give isl_basic_map *isl_basic_map_flat_product(
6568 __isl_take isl_basic_map *bmap1,
6569 __isl_take isl_basic_map *bmap2);
6570 __isl_give isl_map *isl_map_flat_product(
6571 __isl_take isl_map *map1,
6572 __isl_take isl_map *map2);
6574 #include <isl/union_map.h>
6575 __isl_give isl_union_map *
6576 isl_union_map_flat_domain_product(
6577 __isl_take isl_union_map *umap1,
6578 __isl_take isl_union_map *umap2);
6579 __isl_give isl_union_map *
6580 isl_union_map_flat_range_product(
6581 __isl_take isl_union_map *umap1,
6582 __isl_take isl_union_map *umap2);
6584 #include <isl/val.h>
6585 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
6586 __isl_take isl_multi_val *mv1,
6587 __isl_take isl_multi_aff *mv2);
6589 #include <isl/aff.h>
6590 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
6591 __isl_take isl_multi_aff *ma1,
6592 __isl_take isl_multi_aff *ma2);
6593 __isl_give isl_pw_multi_aff *
6594 isl_pw_multi_aff_flat_range_product(
6595 __isl_take isl_pw_multi_aff *pma1,
6596 __isl_take isl_pw_multi_aff *pma2);
6597 __isl_give isl_multi_pw_aff *
6598 isl_multi_pw_aff_flat_range_product(
6599 __isl_take isl_multi_pw_aff *mpa1,
6600 __isl_take isl_multi_pw_aff *mpa2);
6601 __isl_give isl_union_pw_multi_aff *
6602 isl_union_pw_multi_aff_flat_range_product(
6603 __isl_take isl_union_pw_multi_aff *upma1,
6604 __isl_take isl_union_pw_multi_aff *upma2);
6605 __isl_give isl_multi_union_pw_aff *
6606 isl_multi_union_pw_aff_flat_range_product(
6607 __isl_take isl_multi_union_pw_aff *mupa1,
6608 __isl_take isl_multi_union_pw_aff *mupa2);
6610 #include <isl/space.h>
6611 __isl_give isl_space *isl_space_factor_domain(
6612 __isl_take isl_space *space);
6613 __isl_give isl_space *isl_space_factor_range(
6614 __isl_take isl_space *space);
6615 __isl_give isl_space *isl_space_domain_factor_domain(
6616 __isl_take isl_space *space);
6617 __isl_give isl_space *isl_space_domain_factor_range(
6618 __isl_take isl_space *space);
6619 __isl_give isl_space *isl_space_range_factor_domain(
6620 __isl_take isl_space *space);
6621 __isl_give isl_space *isl_space_range_factor_range(
6622 __isl_take isl_space *space);
6624 The functions C<isl_space_range_factor_domain> and
6625 C<isl_space_range_factor_range> extract the two arguments from
6626 the result of a call to C<isl_space_range_product>.
6628 The arguments of a call to a product can be extracted
6629 from the result using the following functions.
6631 #include <isl/map.h>
6632 __isl_give isl_map *isl_map_factor_domain(
6633 __isl_take isl_map *map);
6634 __isl_give isl_map *isl_map_factor_range(
6635 __isl_take isl_map *map);
6636 __isl_give isl_map *isl_map_domain_factor_domain(
6637 __isl_take isl_map *map);
6638 __isl_give isl_map *isl_map_domain_factor_range(
6639 __isl_take isl_map *map);
6640 __isl_give isl_map *isl_map_range_factor_domain(
6641 __isl_take isl_map *map);
6642 __isl_give isl_map *isl_map_range_factor_range(
6643 __isl_take isl_map *map);
6645 #include <isl/union_map.h>
6646 __isl_give isl_union_map *isl_union_map_factor_domain(
6647 __isl_take isl_union_map *umap);
6648 __isl_give isl_union_map *isl_union_map_factor_range(
6649 __isl_take isl_union_map *umap);
6650 __isl_give isl_union_map *
6651 isl_union_map_domain_factor_domain(
6652 __isl_take isl_union_map *umap);
6653 __isl_give isl_union_map *
6654 isl_union_map_domain_factor_range(
6655 __isl_take isl_union_map *umap);
6656 __isl_give isl_union_map *
6657 isl_union_map_range_factor_domain(
6658 __isl_take isl_union_map *umap);
6659 __isl_give isl_union_map *
6660 isl_union_map_range_factor_range(
6661 __isl_take isl_union_map *umap);
6663 #include <isl/val.h>
6664 __isl_give isl_multi_val *isl_multi_val_factor_range(
6665 __isl_take isl_multi_val *mv);
6666 __isl_give isl_multi_val *
6667 isl_multi_val_range_factor_domain(
6668 __isl_take isl_multi_val *mv);
6669 __isl_give isl_multi_val *
6670 isl_multi_val_range_factor_range(
6671 __isl_take isl_multi_val *mv);
6673 #include <isl/aff.h>
6674 __isl_give isl_multi_aff *isl_multi_aff_factor_range(
6675 __isl_take isl_multi_aff *ma);
6676 __isl_give isl_multi_aff *
6677 isl_multi_aff_range_factor_domain(
6678 __isl_take isl_multi_aff *ma);
6679 __isl_give isl_multi_aff *
6680 isl_multi_aff_range_factor_range(
6681 __isl_take isl_multi_aff *ma);
6682 __isl_give isl_multi_pw_aff *
6683 isl_multi_pw_aff_factor_range(
6684 __isl_take isl_multi_pw_aff *mpa);
6685 __isl_give isl_multi_pw_aff *
6686 isl_multi_pw_aff_range_factor_domain(
6687 __isl_take isl_multi_pw_aff *mpa);
6688 __isl_give isl_multi_pw_aff *
6689 isl_multi_pw_aff_range_factor_range(
6690 __isl_take isl_multi_pw_aff *mpa);
6691 __isl_give isl_multi_union_pw_aff *
6692 isl_multi_union_pw_aff_factor_range(
6693 __isl_take isl_multi_union_pw_aff *mupa);
6694 __isl_give isl_multi_union_pw_aff *
6695 isl_multi_union_pw_aff_range_factor_domain(
6696 __isl_take isl_multi_union_pw_aff *mupa);
6697 __isl_give isl_multi_union_pw_aff *
6698 isl_multi_union_pw_aff_range_factor_range(
6699 __isl_take isl_multi_union_pw_aff *mupa);
6701 The splice functions are a generalization of the flat product functions,
6702 where the second argument may be inserted at any position inside
6703 the first argument rather than being placed at the end.
6704 The functions C<isl_multi_val_factor_range>,
6705 C<isl_multi_aff_factor_range>,
6706 C<isl_multi_pw_aff_factor_range> and
6707 C<isl_multi_union_pw_aff_factor_range>
6708 take functions that live in a set space.
6710 #include <isl/val.h>
6711 __isl_give isl_multi_val *isl_multi_val_range_splice(
6712 __isl_take isl_multi_val *mv1, unsigned pos,
6713 __isl_take isl_multi_val *mv2);
6715 #include <isl/aff.h>
6716 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
6717 __isl_take isl_multi_aff *ma1, unsigned pos,
6718 __isl_take isl_multi_aff *ma2);
6719 __isl_give isl_multi_aff *isl_multi_aff_splice(
6720 __isl_take isl_multi_aff *ma1,
6721 unsigned in_pos, unsigned out_pos,
6722 __isl_take isl_multi_aff *ma2);
6723 __isl_give isl_multi_pw_aff *
6724 isl_multi_pw_aff_range_splice(
6725 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
6726 __isl_take isl_multi_pw_aff *mpa2);
6727 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
6728 __isl_take isl_multi_pw_aff *mpa1,
6729 unsigned in_pos, unsigned out_pos,
6730 __isl_take isl_multi_pw_aff *mpa2);
6731 __isl_give isl_multi_union_pw_aff *
6732 isl_multi_union_pw_aff_range_splice(
6733 __isl_take isl_multi_union_pw_aff *mupa1,
6735 __isl_take isl_multi_union_pw_aff *mupa2);
6737 =item * Simplification
6739 When applied to a set or relation,
6740 the gist operation returns a set or relation that has the
6741 same intersection with the context as the input set or relation.
6742 Any implicit equality in the intersection is made explicit in the result,
6743 while all inequalities that are redundant with respect to the intersection
6745 In case of union sets and relations, the gist operation is performed
6748 When applied to a function,
6749 the gist operation applies the set gist operation to each of
6750 the cells in the domain of the input piecewise expression.
6751 The context is also exploited
6752 to simplify the expression associated to each cell.
6754 #include <isl/set.h>
6755 __isl_give isl_basic_set *isl_basic_set_gist(
6756 __isl_take isl_basic_set *bset,
6757 __isl_take isl_basic_set *context);
6758 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
6759 __isl_take isl_set *context);
6760 __isl_give isl_set *isl_set_gist_params(
6761 __isl_take isl_set *set,
6762 __isl_take isl_set *context);
6764 #include <isl/map.h>
6765 __isl_give isl_basic_map *isl_basic_map_gist(
6766 __isl_take isl_basic_map *bmap,
6767 __isl_take isl_basic_map *context);
6768 __isl_give isl_basic_map *isl_basic_map_gist_domain(
6769 __isl_take isl_basic_map *bmap,
6770 __isl_take isl_basic_set *context);
6771 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
6772 __isl_take isl_map *context);
6773 __isl_give isl_map *isl_map_gist_params(
6774 __isl_take isl_map *map,
6775 __isl_take isl_set *context);
6776 __isl_give isl_map *isl_map_gist_domain(
6777 __isl_take isl_map *map,
6778 __isl_take isl_set *context);
6779 __isl_give isl_map *isl_map_gist_range(
6780 __isl_take isl_map *map,
6781 __isl_take isl_set *context);
6783 #include <isl/union_set.h>
6784 __isl_give isl_union_set *isl_union_set_gist(
6785 __isl_take isl_union_set *uset,
6786 __isl_take isl_union_set *context);
6787 __isl_give isl_union_set *isl_union_set_gist_params(
6788 __isl_take isl_union_set *uset,
6789 __isl_take isl_set *set);
6791 #include <isl/union_map.h>
6792 __isl_give isl_union_map *isl_union_map_gist(
6793 __isl_take isl_union_map *umap,
6794 __isl_take isl_union_map *context);
6795 __isl_give isl_union_map *isl_union_map_gist_params(
6796 __isl_take isl_union_map *umap,
6797 __isl_take isl_set *set);
6798 __isl_give isl_union_map *isl_union_map_gist_domain(
6799 __isl_take isl_union_map *umap,
6800 __isl_take isl_union_set *uset);
6801 __isl_give isl_union_map *isl_union_map_gist_range(
6802 __isl_take isl_union_map *umap,
6803 __isl_take isl_union_set *uset);
6805 #include <isl/aff.h>
6806 __isl_give isl_aff *isl_aff_gist_params(
6807 __isl_take isl_aff *aff,
6808 __isl_take isl_set *context);
6809 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
6810 __isl_take isl_set *context);
6811 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
6812 __isl_take isl_multi_aff *maff,
6813 __isl_take isl_set *context);
6814 __isl_give isl_multi_aff *isl_multi_aff_gist(
6815 __isl_take isl_multi_aff *maff,
6816 __isl_take isl_set *context);
6817 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
6818 __isl_take isl_pw_aff *pwaff,
6819 __isl_take isl_set *context);
6820 __isl_give isl_pw_aff *isl_pw_aff_gist(
6821 __isl_take isl_pw_aff *pwaff,
6822 __isl_take isl_set *context);
6823 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
6824 __isl_take isl_pw_multi_aff *pma,
6825 __isl_take isl_set *set);
6826 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
6827 __isl_take isl_pw_multi_aff *pma,
6828 __isl_take isl_set *set);
6829 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
6830 __isl_take isl_multi_pw_aff *mpa,
6831 __isl_take isl_set *set);
6832 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
6833 __isl_take isl_multi_pw_aff *mpa,
6834 __isl_take isl_set *set);
6835 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
6836 __isl_take isl_union_pw_aff *upa,
6837 __isl_take isl_union_set *context);
6838 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
6839 __isl_take isl_union_pw_aff *upa,
6840 __isl_take isl_set *context);
6841 __isl_give isl_union_pw_multi_aff *
6842 isl_union_pw_multi_aff_gist_params(
6843 __isl_take isl_union_pw_multi_aff *upma,
6844 __isl_take isl_set *context);
6845 __isl_give isl_union_pw_multi_aff *
6846 isl_union_pw_multi_aff_gist(
6847 __isl_take isl_union_pw_multi_aff *upma,
6848 __isl_take isl_union_set *context);
6849 __isl_give isl_multi_union_pw_aff *
6850 isl_multi_union_pw_aff_gist_params(
6851 __isl_take isl_multi_union_pw_aff *aff,
6852 __isl_take isl_set *context);
6853 __isl_give isl_multi_union_pw_aff *
6854 isl_multi_union_pw_aff_gist(
6855 __isl_take isl_multi_union_pw_aff *aff,
6856 __isl_take isl_union_set *context);
6858 #include <isl/polynomial.h>
6859 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
6860 __isl_take isl_qpolynomial *qp,
6861 __isl_take isl_set *context);
6862 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
6863 __isl_take isl_qpolynomial *qp,
6864 __isl_take isl_set *context);
6865 __isl_give isl_qpolynomial_fold *
6866 isl_qpolynomial_fold_gist_params(
6867 __isl_take isl_qpolynomial_fold *fold,
6868 __isl_take isl_set *context);
6869 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
6870 __isl_take isl_qpolynomial_fold *fold,
6871 __isl_take isl_set *context);
6872 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
6873 __isl_take isl_pw_qpolynomial *pwqp,
6874 __isl_take isl_set *context);
6875 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
6876 __isl_take isl_pw_qpolynomial *pwqp,
6877 __isl_take isl_set *context);
6878 __isl_give isl_pw_qpolynomial_fold *
6879 isl_pw_qpolynomial_fold_gist(
6880 __isl_take isl_pw_qpolynomial_fold *pwf,
6881 __isl_take isl_set *context);
6882 __isl_give isl_pw_qpolynomial_fold *
6883 isl_pw_qpolynomial_fold_gist_params(
6884 __isl_take isl_pw_qpolynomial_fold *pwf,
6885 __isl_take isl_set *context);
6886 __isl_give isl_union_pw_qpolynomial *
6887 isl_union_pw_qpolynomial_gist_params(
6888 __isl_take isl_union_pw_qpolynomial *upwqp,
6889 __isl_take isl_set *context);
6890 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
6891 __isl_take isl_union_pw_qpolynomial *upwqp,
6892 __isl_take isl_union_set *context);
6893 __isl_give isl_union_pw_qpolynomial_fold *
6894 isl_union_pw_qpolynomial_fold_gist(
6895 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6896 __isl_take isl_union_set *context);
6897 __isl_give isl_union_pw_qpolynomial_fold *
6898 isl_union_pw_qpolynomial_fold_gist_params(
6899 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6900 __isl_take isl_set *context);
6902 =item * Binary Arithmetic Operations
6904 #include <isl/set.h>
6905 __isl_give isl_set *isl_set_sum(
6906 __isl_take isl_set *set1,
6907 __isl_take isl_set *set2);
6908 #include <isl/map.h>
6909 __isl_give isl_map *isl_map_sum(
6910 __isl_take isl_map *map1,
6911 __isl_take isl_map *map2);
6913 C<isl_set_sum> computes the Minkowski sum of its two arguments,
6914 i.e., the set containing the sums of pairs of elements from
6915 C<set1> and C<set2>.
6916 The domain of the result of C<isl_map_sum> is the intersection
6917 of the domains of its two arguments. The corresponding range
6918 elements are the sums of the corresponding range elements
6919 in the two arguments.
6921 #include <isl/val.h>
6922 __isl_give isl_multi_val *isl_multi_val_add(
6923 __isl_take isl_multi_val *mv1,
6924 __isl_take isl_multi_val *mv2);
6925 __isl_give isl_multi_val *isl_multi_val_sub(
6926 __isl_take isl_multi_val *mv1,
6927 __isl_take isl_multi_val *mv2);
6929 #include <isl/aff.h>
6930 __isl_give isl_aff *isl_aff_add(
6931 __isl_take isl_aff *aff1,
6932 __isl_take isl_aff *aff2);
6933 __isl_give isl_multi_aff *isl_multi_aff_add(
6934 __isl_take isl_multi_aff *maff1,
6935 __isl_take isl_multi_aff *maff2);
6936 __isl_give isl_pw_aff *isl_pw_aff_add(
6937 __isl_take isl_pw_aff *pwaff1,
6938 __isl_take isl_pw_aff *pwaff2);
6939 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add(
6940 __isl_take isl_multi_pw_aff *mpa1,
6941 __isl_take isl_multi_pw_aff *mpa2);
6942 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
6943 __isl_take isl_pw_multi_aff *pma1,
6944 __isl_take isl_pw_multi_aff *pma2);
6945 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
6946 __isl_take isl_union_pw_aff *upa1,
6947 __isl_take isl_union_pw_aff *upa2);
6948 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
6949 __isl_take isl_union_pw_multi_aff *upma1,
6950 __isl_take isl_union_pw_multi_aff *upma2);
6951 __isl_give isl_multi_union_pw_aff *
6952 isl_multi_union_pw_aff_add(
6953 __isl_take isl_multi_union_pw_aff *mupa1,
6954 __isl_take isl_multi_union_pw_aff *mupa2);
6955 __isl_give isl_pw_aff *isl_pw_aff_min(
6956 __isl_take isl_pw_aff *pwaff1,
6957 __isl_take isl_pw_aff *pwaff2);
6958 __isl_give isl_pw_aff *isl_pw_aff_max(
6959 __isl_take isl_pw_aff *pwaff1,
6960 __isl_take isl_pw_aff *pwaff2);
6961 __isl_give isl_aff *isl_aff_sub(
6962 __isl_take isl_aff *aff1,
6963 __isl_take isl_aff *aff2);
6964 __isl_give isl_multi_aff *isl_multi_aff_sub(
6965 __isl_take isl_multi_aff *ma1,
6966 __isl_take isl_multi_aff *ma2);
6967 __isl_give isl_pw_aff *isl_pw_aff_sub(
6968 __isl_take isl_pw_aff *pwaff1,
6969 __isl_take isl_pw_aff *pwaff2);
6970 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
6971 __isl_take isl_multi_pw_aff *mpa1,
6972 __isl_take isl_multi_pw_aff *mpa2);
6973 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
6974 __isl_take isl_pw_multi_aff *pma1,
6975 __isl_take isl_pw_multi_aff *pma2);
6976 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
6977 __isl_take isl_union_pw_aff *upa1,
6978 __isl_take isl_union_pw_aff *upa2);
6979 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
6980 __isl_take isl_union_pw_multi_aff *upma1,
6981 __isl_take isl_union_pw_multi_aff *upma2);
6982 __isl_give isl_multi_union_pw_aff *
6983 isl_multi_union_pw_aff_sub(
6984 __isl_take isl_multi_union_pw_aff *mupa1,
6985 __isl_take isl_multi_union_pw_aff *mupa2);
6987 C<isl_aff_sub> subtracts the second argument from the first.
6989 #include <isl/polynomial.h>
6990 __isl_give isl_qpolynomial *isl_qpolynomial_add(
6991 __isl_take isl_qpolynomial *qp1,
6992 __isl_take isl_qpolynomial *qp2);
6993 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
6994 __isl_take isl_pw_qpolynomial *pwqp1,
6995 __isl_take isl_pw_qpolynomial *pwqp2);
6996 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
6997 __isl_take isl_pw_qpolynomial *pwqp1,
6998 __isl_take isl_pw_qpolynomial *pwqp2);
6999 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
7000 __isl_take isl_pw_qpolynomial_fold *pwf1,
7001 __isl_take isl_pw_qpolynomial_fold *pwf2);
7002 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
7003 __isl_take isl_union_pw_qpolynomial *upwqp1,
7004 __isl_take isl_union_pw_qpolynomial *upwqp2);
7005 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
7006 __isl_take isl_qpolynomial *qp1,
7007 __isl_take isl_qpolynomial *qp2);
7008 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
7009 __isl_take isl_pw_qpolynomial *pwqp1,
7010 __isl_take isl_pw_qpolynomial *pwqp2);
7011 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
7012 __isl_take isl_union_pw_qpolynomial *upwqp1,
7013 __isl_take isl_union_pw_qpolynomial *upwqp2);
7014 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
7015 __isl_take isl_pw_qpolynomial_fold *pwf1,
7016 __isl_take isl_pw_qpolynomial_fold *pwf2);
7017 __isl_give isl_union_pw_qpolynomial_fold *
7018 isl_union_pw_qpolynomial_fold_fold(
7019 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
7020 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
7022 #include <isl/aff.h>
7023 __isl_give isl_pw_aff *isl_pw_aff_union_add(
7024 __isl_take isl_pw_aff *pwaff1,
7025 __isl_take isl_pw_aff *pwaff2);
7026 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
7027 __isl_take isl_pw_multi_aff *pma1,
7028 __isl_take isl_pw_multi_aff *pma2);
7029 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
7030 __isl_take isl_union_pw_aff *upa1,
7031 __isl_take isl_union_pw_aff *upa2);
7032 __isl_give isl_union_pw_multi_aff *
7033 isl_union_pw_multi_aff_union_add(
7034 __isl_take isl_union_pw_multi_aff *upma1,
7035 __isl_take isl_union_pw_multi_aff *upma2);
7036 __isl_give isl_multi_union_pw_aff *
7037 isl_multi_union_pw_aff_union_add(
7038 __isl_take isl_multi_union_pw_aff *mupa1,
7039 __isl_take isl_multi_union_pw_aff *mupa2);
7040 __isl_give isl_pw_aff *isl_pw_aff_union_min(
7041 __isl_take isl_pw_aff *pwaff1,
7042 __isl_take isl_pw_aff *pwaff2);
7043 __isl_give isl_pw_aff *isl_pw_aff_union_max(
7044 __isl_take isl_pw_aff *pwaff1,
7045 __isl_take isl_pw_aff *pwaff2);
7047 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
7048 expression with a domain that is the union of those of C<pwaff1> and
7049 C<pwaff2> and such that on each cell, the quasi-affine expression is
7050 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
7051 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
7052 associated expression is the defined one.
7053 This in contrast to the C<isl_pw_aff_max> function, which is
7054 only defined on the shared definition domain of the arguments.
7056 #include <isl/val.h>
7057 __isl_give isl_multi_val *isl_multi_val_add_val(
7058 __isl_take isl_multi_val *mv,
7059 __isl_take isl_val *v);
7060 __isl_give isl_multi_val *isl_multi_val_mod_val(
7061 __isl_take isl_multi_val *mv,
7062 __isl_take isl_val *v);
7063 __isl_give isl_multi_val *isl_multi_val_scale_val(
7064 __isl_take isl_multi_val *mv,
7065 __isl_take isl_val *v);
7066 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
7067 __isl_take isl_multi_val *mv,
7068 __isl_take isl_val *v);
7070 #include <isl/aff.h>
7071 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
7072 __isl_take isl_val *mod);
7073 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
7074 __isl_take isl_pw_aff *pa,
7075 __isl_take isl_val *mod);
7076 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
7077 __isl_take isl_union_pw_aff *upa,
7078 __isl_take isl_val *f);
7079 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
7080 __isl_take isl_val *v);
7081 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
7082 __isl_take isl_multi_aff *ma,
7083 __isl_take isl_val *v);
7084 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
7085 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
7086 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
7087 __isl_take isl_multi_pw_aff *mpa,
7088 __isl_take isl_val *v);
7089 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
7090 __isl_take isl_pw_multi_aff *pma,
7091 __isl_take isl_val *v);
7092 __isl_give isl_union_pw_multi_aff *
7093 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
7094 __isl_take isl_union_pw_aff *upa,
7095 __isl_take isl_val *f);
7096 isl_union_pw_multi_aff_scale_val(
7097 __isl_take isl_union_pw_multi_aff *upma,
7098 __isl_take isl_val *val);
7099 __isl_give isl_multi_union_pw_aff *
7100 isl_multi_union_pw_aff_scale_val(
7101 __isl_take isl_multi_union_pw_aff *mupa,
7102 __isl_take isl_val *v);
7103 __isl_give isl_aff *isl_aff_scale_down_ui(
7104 __isl_take isl_aff *aff, unsigned f);
7105 __isl_give isl_aff *isl_aff_scale_down_val(
7106 __isl_take isl_aff *aff, __isl_take isl_val *v);
7107 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
7108 __isl_take isl_multi_aff *ma,
7109 __isl_take isl_val *v);
7110 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
7111 __isl_take isl_pw_aff *pa,
7112 __isl_take isl_val *f);
7113 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
7114 __isl_take isl_multi_pw_aff *mpa,
7115 __isl_take isl_val *v);
7116 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
7117 __isl_take isl_pw_multi_aff *pma,
7118 __isl_take isl_val *v);
7119 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
7120 __isl_take isl_union_pw_aff *upa,
7121 __isl_take isl_val *v);
7122 __isl_give isl_union_pw_multi_aff *
7123 isl_union_pw_multi_aff_scale_down_val(
7124 __isl_take isl_union_pw_multi_aff *upma,
7125 __isl_take isl_val *val);
7126 __isl_give isl_multi_union_pw_aff *
7127 isl_multi_union_pw_aff_scale_down_val(
7128 __isl_take isl_multi_union_pw_aff *mupa,
7129 __isl_take isl_val *v);
7131 #include <isl/polynomial.h>
7132 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
7133 __isl_take isl_qpolynomial *qp,
7134 __isl_take isl_val *v);
7135 __isl_give isl_qpolynomial_fold *
7136 isl_qpolynomial_fold_scale_val(
7137 __isl_take isl_qpolynomial_fold *fold,
7138 __isl_take isl_val *v);
7139 __isl_give isl_pw_qpolynomial *
7140 isl_pw_qpolynomial_scale_val(
7141 __isl_take isl_pw_qpolynomial *pwqp,
7142 __isl_take isl_val *v);
7143 __isl_give isl_pw_qpolynomial_fold *
7144 isl_pw_qpolynomial_fold_scale_val(
7145 __isl_take isl_pw_qpolynomial_fold *pwf,
7146 __isl_take isl_val *v);
7147 __isl_give isl_union_pw_qpolynomial *
7148 isl_union_pw_qpolynomial_scale_val(
7149 __isl_take isl_union_pw_qpolynomial *upwqp,
7150 __isl_take isl_val *v);
7151 __isl_give isl_union_pw_qpolynomial_fold *
7152 isl_union_pw_qpolynomial_fold_scale_val(
7153 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7154 __isl_take isl_val *v);
7155 __isl_give isl_qpolynomial *
7156 isl_qpolynomial_scale_down_val(
7157 __isl_take isl_qpolynomial *qp,
7158 __isl_take isl_val *v);
7159 __isl_give isl_qpolynomial_fold *
7160 isl_qpolynomial_fold_scale_down_val(
7161 __isl_take isl_qpolynomial_fold *fold,
7162 __isl_take isl_val *v);
7163 __isl_give isl_pw_qpolynomial *
7164 isl_pw_qpolynomial_scale_down_val(
7165 __isl_take isl_pw_qpolynomial *pwqp,
7166 __isl_take isl_val *v);
7167 __isl_give isl_pw_qpolynomial_fold *
7168 isl_pw_qpolynomial_fold_scale_down_val(
7169 __isl_take isl_pw_qpolynomial_fold *pwf,
7170 __isl_take isl_val *v);
7171 __isl_give isl_union_pw_qpolynomial *
7172 isl_union_pw_qpolynomial_scale_down_val(
7173 __isl_take isl_union_pw_qpolynomial *upwqp,
7174 __isl_take isl_val *v);
7175 __isl_give isl_union_pw_qpolynomial_fold *
7176 isl_union_pw_qpolynomial_fold_scale_down_val(
7177 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7178 __isl_take isl_val *v);
7180 #include <isl/val.h>
7181 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
7182 __isl_take isl_multi_val *mv1,
7183 __isl_take isl_multi_val *mv2);
7184 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
7185 __isl_take isl_multi_val *mv1,
7186 __isl_take isl_multi_val *mv2);
7187 __isl_give isl_multi_val *
7188 isl_multi_val_scale_down_multi_val(
7189 __isl_take isl_multi_val *mv1,
7190 __isl_take isl_multi_val *mv2);
7192 #include <isl/aff.h>
7193 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
7194 __isl_take isl_multi_aff *ma,
7195 __isl_take isl_multi_val *mv);
7196 __isl_give isl_multi_union_pw_aff *
7197 isl_multi_union_pw_aff_mod_multi_val(
7198 __isl_take isl_multi_union_pw_aff *upma,
7199 __isl_take isl_multi_val *mv);
7200 __isl_give isl_multi_pw_aff *
7201 isl_multi_pw_aff_mod_multi_val(
7202 __isl_take isl_multi_pw_aff *mpa,
7203 __isl_take isl_multi_val *mv);
7204 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
7205 __isl_take isl_multi_aff *ma,
7206 __isl_take isl_multi_val *mv);
7207 __isl_give isl_pw_multi_aff *
7208 isl_pw_multi_aff_scale_multi_val(
7209 __isl_take isl_pw_multi_aff *pma,
7210 __isl_take isl_multi_val *mv);
7211 __isl_give isl_multi_pw_aff *
7212 isl_multi_pw_aff_scale_multi_val(
7213 __isl_take isl_multi_pw_aff *mpa,
7214 __isl_take isl_multi_val *mv);
7215 __isl_give isl_multi_union_pw_aff *
7216 isl_multi_union_pw_aff_scale_multi_val(
7217 __isl_take isl_multi_union_pw_aff *mupa,
7218 __isl_take isl_multi_val *mv);
7219 __isl_give isl_union_pw_multi_aff *
7220 isl_union_pw_multi_aff_scale_multi_val(
7221 __isl_take isl_union_pw_multi_aff *upma,
7222 __isl_take isl_multi_val *mv);
7223 __isl_give isl_multi_aff *
7224 isl_multi_aff_scale_down_multi_val(
7225 __isl_take isl_multi_aff *ma,
7226 __isl_take isl_multi_val *mv);
7227 __isl_give isl_multi_pw_aff *
7228 isl_multi_pw_aff_scale_down_multi_val(
7229 __isl_take isl_multi_pw_aff *mpa,
7230 __isl_take isl_multi_val *mv);
7231 __isl_give isl_multi_union_pw_aff *
7232 isl_multi_union_pw_aff_scale_down_multi_val(
7233 __isl_take isl_multi_union_pw_aff *mupa,
7234 __isl_take isl_multi_val *mv);
7236 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
7237 by the corresponding elements of C<mv>.
7239 #include <isl/aff.h>
7240 __isl_give isl_aff *isl_aff_mul(
7241 __isl_take isl_aff *aff1,
7242 __isl_take isl_aff *aff2);
7243 __isl_give isl_aff *isl_aff_div(
7244 __isl_take isl_aff *aff1,
7245 __isl_take isl_aff *aff2);
7246 __isl_give isl_pw_aff *isl_pw_aff_mul(
7247 __isl_take isl_pw_aff *pwaff1,
7248 __isl_take isl_pw_aff *pwaff2);
7249 __isl_give isl_pw_aff *isl_pw_aff_div(
7250 __isl_take isl_pw_aff *pa1,
7251 __isl_take isl_pw_aff *pa2);
7252 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
7253 __isl_take isl_pw_aff *pa1,
7254 __isl_take isl_pw_aff *pa2);
7255 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
7256 __isl_take isl_pw_aff *pa1,
7257 __isl_take isl_pw_aff *pa2);
7259 When multiplying two affine expressions, at least one of the two needs
7260 to be a constant. Similarly, when dividing an affine expression by another,
7261 the second expression needs to be a constant.
7262 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
7263 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
7266 #include <isl/polynomial.h>
7267 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
7268 __isl_take isl_qpolynomial *qp1,
7269 __isl_take isl_qpolynomial *qp2);
7270 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
7271 __isl_take isl_pw_qpolynomial *pwqp1,
7272 __isl_take isl_pw_qpolynomial *pwqp2);
7273 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
7274 __isl_take isl_union_pw_qpolynomial *upwqp1,
7275 __isl_take isl_union_pw_qpolynomial *upwqp2);
7279 =head3 Lexicographic Optimization
7281 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
7282 the following functions
7283 compute a set that contains the lexicographic minimum or maximum
7284 of the elements in C<set> (or C<bset>) for those values of the parameters
7285 that satisfy C<dom>.
7286 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7287 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
7289 In other words, the union of the parameter values
7290 for which the result is non-empty and of C<*empty>
7293 #include <isl/set.h>
7294 __isl_give isl_set *isl_basic_set_partial_lexmin(
7295 __isl_take isl_basic_set *bset,
7296 __isl_take isl_basic_set *dom,
7297 __isl_give isl_set **empty);
7298 __isl_give isl_set *isl_basic_set_partial_lexmax(
7299 __isl_take isl_basic_set *bset,
7300 __isl_take isl_basic_set *dom,
7301 __isl_give isl_set **empty);
7302 __isl_give isl_set *isl_set_partial_lexmin(
7303 __isl_take isl_set *set, __isl_take isl_set *dom,
7304 __isl_give isl_set **empty);
7305 __isl_give isl_set *isl_set_partial_lexmax(
7306 __isl_take isl_set *set, __isl_take isl_set *dom,
7307 __isl_give isl_set **empty);
7309 Given a (basic) set C<set> (or C<bset>), the following functions simply
7310 return a set containing the lexicographic minimum or maximum
7311 of the elements in C<set> (or C<bset>).
7312 In case of union sets, the optimum is computed per space.
7314 #include <isl/set.h>
7315 __isl_give isl_set *isl_basic_set_lexmin(
7316 __isl_take isl_basic_set *bset);
7317 __isl_give isl_set *isl_basic_set_lexmax(
7318 __isl_take isl_basic_set *bset);
7319 __isl_give isl_set *isl_set_lexmin(
7320 __isl_take isl_set *set);
7321 __isl_give isl_set *isl_set_lexmax(
7322 __isl_take isl_set *set);
7323 __isl_give isl_union_set *isl_union_set_lexmin(
7324 __isl_take isl_union_set *uset);
7325 __isl_give isl_union_set *isl_union_set_lexmax(
7326 __isl_take isl_union_set *uset);
7328 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
7329 the following functions
7330 compute a relation that maps each element of C<dom>
7331 to the single lexicographic minimum or maximum
7332 of the elements that are associated to that same
7333 element in C<map> (or C<bmap>).
7334 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7335 that contains the elements in C<dom> that do not map
7336 to any elements in C<map> (or C<bmap>).
7337 In other words, the union of the domain of the result and of C<*empty>
7340 #include <isl/map.h>
7341 __isl_give isl_map *isl_basic_map_partial_lexmax(
7342 __isl_take isl_basic_map *bmap,
7343 __isl_take isl_basic_set *dom,
7344 __isl_give isl_set **empty);
7345 __isl_give isl_map *isl_basic_map_partial_lexmin(
7346 __isl_take isl_basic_map *bmap,
7347 __isl_take isl_basic_set *dom,
7348 __isl_give isl_set **empty);
7349 __isl_give isl_map *isl_map_partial_lexmax(
7350 __isl_take isl_map *map, __isl_take isl_set *dom,
7351 __isl_give isl_set **empty);
7352 __isl_give isl_map *isl_map_partial_lexmin(
7353 __isl_take isl_map *map, __isl_take isl_set *dom,
7354 __isl_give isl_set **empty);
7356 Given a (basic) map C<map> (or C<bmap>), the following functions simply
7357 return a map mapping each element in the domain of
7358 C<map> (or C<bmap>) to the lexicographic minimum or maximum
7359 of all elements associated to that element.
7360 In case of union relations, the optimum is computed per space.
7362 #include <isl/map.h>
7363 __isl_give isl_map *isl_basic_map_lexmin(
7364 __isl_take isl_basic_map *bmap);
7365 __isl_give isl_map *isl_basic_map_lexmax(
7366 __isl_take isl_basic_map *bmap);
7367 __isl_give isl_map *isl_map_lexmin(
7368 __isl_take isl_map *map);
7369 __isl_give isl_map *isl_map_lexmax(
7370 __isl_take isl_map *map);
7371 __isl_give isl_union_map *isl_union_map_lexmin(
7372 __isl_take isl_union_map *umap);
7373 __isl_give isl_union_map *isl_union_map_lexmax(
7374 __isl_take isl_union_map *umap);
7376 The following functions return their result in the form of
7377 a piecewise multi-affine expression,
7378 but are otherwise equivalent to the corresponding functions
7379 returning a basic set or relation.
7381 #include <isl/set.h>
7382 __isl_give isl_pw_multi_aff *
7383 isl_basic_set_partial_lexmin_pw_multi_aff(
7384 __isl_take isl_basic_set *bset,
7385 __isl_take isl_basic_set *dom,
7386 __isl_give isl_set **empty);
7387 __isl_give isl_pw_multi_aff *
7388 isl_basic_set_partial_lexmax_pw_multi_aff(
7389 __isl_take isl_basic_set *bset,
7390 __isl_take isl_basic_set *dom,
7391 __isl_give isl_set **empty);
7392 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
7393 __isl_take isl_set *set);
7394 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
7395 __isl_take isl_set *set);
7397 #include <isl/map.h>
7398 __isl_give isl_pw_multi_aff *
7399 isl_basic_map_lexmin_pw_multi_aff(
7400 __isl_take isl_basic_map *bmap);
7401 __isl_give isl_pw_multi_aff *
7402 isl_basic_map_partial_lexmin_pw_multi_aff(
7403 __isl_take isl_basic_map *bmap,
7404 __isl_take isl_basic_set *dom,
7405 __isl_give isl_set **empty);
7406 __isl_give isl_pw_multi_aff *
7407 isl_basic_map_partial_lexmax_pw_multi_aff(
7408 __isl_take isl_basic_map *bmap,
7409 __isl_take isl_basic_set *dom,
7410 __isl_give isl_set **empty);
7411 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
7412 __isl_take isl_map *map);
7413 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
7414 __isl_take isl_map *map);
7416 The following functions return the lexicographic minimum or maximum
7417 on the shared domain of the inputs and the single defined function
7418 on those parts of the domain where only a single function is defined.
7420 #include <isl/aff.h>
7421 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
7422 __isl_take isl_pw_multi_aff *pma1,
7423 __isl_take isl_pw_multi_aff *pma2);
7424 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
7425 __isl_take isl_pw_multi_aff *pma1,
7426 __isl_take isl_pw_multi_aff *pma2);
7428 If the input to a lexicographic optimization problem has
7429 multiple constraints with the same coefficients for the optimized
7430 variables, then, by default, this symmetry is exploited by
7431 replacing those constraints by a single constraint with
7432 an abstract bound, which is in turn bounded by the corresponding terms
7433 in the original constraints.
7434 Without this optimization, the solver would typically consider
7435 all possible orderings of those original bounds, resulting in a needless
7436 decomposition of the domain.
7437 However, the optimization can also result in slowdowns since
7438 an extra parameter is introduced that may get used in additional
7440 The following option determines whether symmetry detection is applied
7441 during lexicographic optimization.
7443 #include <isl/options.h>
7444 isl_stat isl_options_set_pip_symmetry(isl_ctx *ctx,
7446 int isl_options_get_pip_symmetry(isl_ctx *ctx);
7450 See also \autoref{s:offline}.
7454 =head2 Ternary Operations
7456 #include <isl/aff.h>
7457 __isl_give isl_pw_aff *isl_pw_aff_cond(
7458 __isl_take isl_pw_aff *cond,
7459 __isl_take isl_pw_aff *pwaff_true,
7460 __isl_take isl_pw_aff *pwaff_false);
7462 The function C<isl_pw_aff_cond> performs a conditional operator
7463 and returns an expression that is equal to C<pwaff_true>
7464 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
7465 where C<cond> is zero.
7469 Lists are defined over several element types, including
7470 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_union_pw_aff>,
7471 C<isl_union_pw_multi_aff>, C<isl_constraint>,
7472 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
7473 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
7474 Here we take lists of C<isl_set>s as an example.
7475 Lists can be created, copied, modified and freed using the following functions.
7477 #include <isl/set.h>
7478 __isl_give isl_set_list *isl_set_list_from_set(
7479 __isl_take isl_set *el);
7480 __isl_give isl_set_list *isl_set_list_alloc(
7481 isl_ctx *ctx, int n);
7482 __isl_give isl_set_list *isl_set_list_copy(
7483 __isl_keep isl_set_list *list);
7484 __isl_give isl_set_list *isl_set_list_insert(
7485 __isl_take isl_set_list *list, unsigned pos,
7486 __isl_take isl_set *el);
7487 __isl_give isl_set_list *isl_set_list_add(
7488 __isl_take isl_set_list *list,
7489 __isl_take isl_set *el);
7490 __isl_give isl_set_list *isl_set_list_drop(
7491 __isl_take isl_set_list *list,
7492 unsigned first, unsigned n);
7493 __isl_give isl_set_list *isl_set_list_set_set(
7494 __isl_take isl_set_list *list, int index,
7495 __isl_take isl_set *set);
7496 __isl_give isl_set_list *isl_set_list_concat(
7497 __isl_take isl_set_list *list1,
7498 __isl_take isl_set_list *list2);
7499 __isl_give isl_set_list *isl_set_list_map(
7500 __isl_take isl_set_list *list,
7501 __isl_give isl_set *(*fn)(__isl_take isl_set *el,
7504 __isl_give isl_set_list *isl_set_list_sort(
7505 __isl_take isl_set_list *list,
7506 int (*cmp)(__isl_keep isl_set *a,
7507 __isl_keep isl_set *b, void *user),
7509 __isl_null isl_set_list *isl_set_list_free(
7510 __isl_take isl_set_list *list);
7512 C<isl_set_list_alloc> creates an empty list with an initial capacity
7513 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
7514 add elements to a list, increasing its capacity as needed.
7515 C<isl_set_list_from_set> creates a list with a single element.
7517 Lists can be inspected using the following functions.
7519 #include <isl/set.h>
7520 int isl_set_list_n_set(__isl_keep isl_set_list *list);
7521 __isl_give isl_set *isl_set_list_get_set(
7522 __isl_keep isl_set_list *list, int index);
7523 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list,
7524 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7526 isl_stat isl_set_list_foreach_scc(
7527 __isl_keep isl_set_list *list,
7528 isl_bool (*follows)(__isl_keep isl_set *a,
7529 __isl_keep isl_set *b, void *user),
7531 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7534 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
7535 strongly connected components of the graph with as vertices the elements
7536 of C<list> and a directed edge from vertex C<b> to vertex C<a>
7537 iff C<follows(a, b)> returns C<isl_bool_true>. The callbacks C<follows> and
7538 C<fn> should return C<isl_bool_error> or C<isl_stat_error> on error.
7540 Lists can be printed using
7542 #include <isl/set.h>
7543 __isl_give isl_printer *isl_printer_print_set_list(
7544 __isl_take isl_printer *p,
7545 __isl_keep isl_set_list *list);
7547 =head2 Associative arrays
7549 Associative arrays map isl objects of a specific type to isl objects
7550 of some (other) specific type. They are defined for several pairs
7551 of types, including (C<isl_map>, C<isl_basic_set>),
7552 (C<isl_id>, C<isl_ast_expr>),
7553 (C<isl_id>, C<isl_id>) and
7554 (C<isl_id>, C<isl_pw_aff>).
7555 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
7558 Associative arrays can be created, copied and freed using
7559 the following functions.
7561 #include <isl/id_to_ast_expr.h>
7562 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
7563 isl_ctx *ctx, int min_size);
7564 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
7565 __isl_keep isl_id_to_ast_expr *id2expr);
7566 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
7567 __isl_take isl_id_to_ast_expr *id2expr);
7569 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
7570 to specify the expected size of the associative array.
7571 The associative array will be grown automatically as needed.
7573 Associative arrays can be inspected using the following functions.
7575 #include <isl/id_to_ast_expr.h>
7576 __isl_give isl_maybe_isl_ast_expr
7577 isl_id_to_ast_expr_try_get(
7578 __isl_keep isl_id_to_ast_expr *id2expr,
7579 __isl_keep isl_id *key);
7580 isl_bool isl_id_to_ast_expr_has(
7581 __isl_keep isl_id_to_ast_expr *id2expr,
7582 __isl_keep isl_id *key);
7583 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
7584 __isl_keep isl_id_to_ast_expr *id2expr,
7585 __isl_take isl_id *key);
7586 isl_stat isl_id_to_ast_expr_foreach(
7587 __isl_keep isl_id_to_ast_expr *id2expr,
7588 isl_stat (*fn)(__isl_take isl_id *key,
7589 __isl_take isl_ast_expr *val, void *user),
7592 The function C<isl_id_to_ast_expr_try_get> returns a structure
7593 containing two elements, C<valid> and C<value>.
7594 If there is a value associated to the key, then C<valid>
7595 is set to C<isl_bool_true> and C<value> contains a copy of
7596 the associated value. Otherwise C<value> is C<NULL> and
7597 C<valid> may be C<isl_bool_error> or C<isl_bool_false> depending
7598 on whether some error has occurred or there simply is no associated value.
7599 The function C<isl_id_to_ast_expr_has> returns the C<valid> field
7600 in the structure and
7601 the function C<isl_id_to_ast_expr_get> returns the C<value> field.
7603 Associative arrays can be modified using the following functions.
7605 #include <isl/id_to_ast_expr.h>
7606 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
7607 __isl_take isl_id_to_ast_expr *id2expr,
7608 __isl_take isl_id *key,
7609 __isl_take isl_ast_expr *val);
7610 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
7611 __isl_take isl_id_to_ast_expr *id2expr,
7612 __isl_take isl_id *key);
7614 Associative arrays can be printed using the following function.
7616 #include <isl/id_to_ast_expr.h>
7617 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
7618 __isl_take isl_printer *p,
7619 __isl_keep isl_id_to_ast_expr *id2expr);
7623 Vectors can be created, copied and freed using the following functions.
7625 #include <isl/vec.h>
7626 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
7628 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
7629 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
7631 Note that the elements of a newly created vector may have arbitrary values.
7632 The elements can be changed and inspected using the following functions.
7634 int isl_vec_size(__isl_keep isl_vec *vec);
7635 __isl_give isl_val *isl_vec_get_element_val(
7636 __isl_keep isl_vec *vec, int pos);
7637 __isl_give isl_vec *isl_vec_set_element_si(
7638 __isl_take isl_vec *vec, int pos, int v);
7639 __isl_give isl_vec *isl_vec_set_element_val(
7640 __isl_take isl_vec *vec, int pos,
7641 __isl_take isl_val *v);
7642 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
7644 __isl_give isl_vec *isl_vec_set_val(
7645 __isl_take isl_vec *vec, __isl_take isl_val *v);
7646 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
7647 __isl_keep isl_vec *vec2, int pos);
7649 C<isl_vec_get_element> will return a negative value if anything went wrong.
7650 In that case, the value of C<*v> is undefined.
7652 The following function can be used to concatenate two vectors.
7654 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
7655 __isl_take isl_vec *vec2);
7659 Matrices can be created, copied and freed using the following functions.
7661 #include <isl/mat.h>
7662 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
7663 unsigned n_row, unsigned n_col);
7664 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
7665 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
7667 Note that the elements of a newly created matrix may have arbitrary values.
7668 The elements can be changed and inspected using the following functions.
7670 int isl_mat_rows(__isl_keep isl_mat *mat);
7671 int isl_mat_cols(__isl_keep isl_mat *mat);
7672 __isl_give isl_val *isl_mat_get_element_val(
7673 __isl_keep isl_mat *mat, int row, int col);
7674 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
7675 int row, int col, int v);
7676 __isl_give isl_mat *isl_mat_set_element_val(
7677 __isl_take isl_mat *mat, int row, int col,
7678 __isl_take isl_val *v);
7680 C<isl_mat_get_element> will return a negative value if anything went wrong.
7681 In that case, the value of C<*v> is undefined.
7683 The following function can be used to compute the (right) inverse
7684 of a matrix, i.e., a matrix such that the product of the original
7685 and the inverse (in that order) is a multiple of the identity matrix.
7686 The input matrix is assumed to be of full row-rank.
7688 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
7690 The following function can be used to compute the (right) kernel
7691 (or null space) of a matrix, i.e., a matrix such that the product of
7692 the original and the kernel (in that order) is the zero matrix.
7694 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
7696 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
7698 The following functions determine
7699 an upper or lower bound on a quasipolynomial over its domain.
7701 __isl_give isl_pw_qpolynomial_fold *
7702 isl_pw_qpolynomial_bound(
7703 __isl_take isl_pw_qpolynomial *pwqp,
7704 enum isl_fold type, int *tight);
7706 __isl_give isl_union_pw_qpolynomial_fold *
7707 isl_union_pw_qpolynomial_bound(
7708 __isl_take isl_union_pw_qpolynomial *upwqp,
7709 enum isl_fold type, int *tight);
7711 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
7712 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
7713 is the returned bound is known be tight, i.e., for each value
7714 of the parameters there is at least
7715 one element in the domain that reaches the bound.
7716 If the domain of C<pwqp> is not wrapping, then the bound is computed
7717 over all elements in that domain and the result has a purely parametric
7718 domain. If the domain of C<pwqp> is wrapping, then the bound is
7719 computed over the range of the wrapped relation. The domain of the
7720 wrapped relation becomes the domain of the result.
7722 =head2 Parametric Vertex Enumeration
7724 The parametric vertex enumeration described in this section
7725 is mainly intended to be used internally and by the C<barvinok>
7728 #include <isl/vertices.h>
7729 __isl_give isl_vertices *isl_basic_set_compute_vertices(
7730 __isl_keep isl_basic_set *bset);
7732 The function C<isl_basic_set_compute_vertices> performs the
7733 actual computation of the parametric vertices and the chamber
7734 decomposition and stores the result in an C<isl_vertices> object.
7735 This information can be queried by either iterating over all
7736 the vertices or iterating over all the chambers or cells
7737 and then iterating over all vertices that are active on the chamber.
7739 isl_stat isl_vertices_foreach_vertex(
7740 __isl_keep isl_vertices *vertices,
7741 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7742 void *user), void *user);
7744 isl_stat isl_vertices_foreach_cell(
7745 __isl_keep isl_vertices *vertices,
7746 isl_stat (*fn)(__isl_take isl_cell *cell,
7747 void *user), void *user);
7748 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
7749 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7750 void *user), void *user);
7752 Other operations that can be performed on an C<isl_vertices> object are
7755 int isl_vertices_get_n_vertices(
7756 __isl_keep isl_vertices *vertices);
7757 __isl_null isl_vertices *isl_vertices_free(
7758 __isl_take isl_vertices *vertices);
7760 Vertices can be inspected and destroyed using the following functions.
7762 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
7763 __isl_give isl_basic_set *isl_vertex_get_domain(
7764 __isl_keep isl_vertex *vertex);
7765 __isl_give isl_multi_aff *isl_vertex_get_expr(
7766 __isl_keep isl_vertex *vertex);
7767 void isl_vertex_free(__isl_take isl_vertex *vertex);
7769 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
7770 describing the vertex in terms of the parameters,
7771 while C<isl_vertex_get_domain> returns the activity domain
7774 Chambers can be inspected and destroyed using the following functions.
7776 __isl_give isl_basic_set *isl_cell_get_domain(
7777 __isl_keep isl_cell *cell);
7778 void isl_cell_free(__isl_take isl_cell *cell);
7780 =head1 Polyhedral Compilation Library
7782 This section collects functionality in C<isl> that has been specifically
7783 designed for use during polyhedral compilation.
7785 =head2 Schedule Trees
7787 A schedule tree is a structured representation of a schedule,
7788 assigning a relative order to a set of domain elements.
7789 The relative order expressed by the schedule tree is
7790 defined recursively. In particular, the order between
7791 two domain elements is determined by the node that is closest
7792 to the root that refers to both elements and that orders them apart.
7793 Each node in the tree is of one of several types.
7794 The root node is always of type C<isl_schedule_node_domain>
7795 (or C<isl_schedule_node_extension>)
7796 and it describes the (extra) domain elements to which the schedule applies.
7797 The other types of nodes are as follows.
7801 =item C<isl_schedule_node_band>
7803 A band of schedule dimensions. Each schedule dimension is represented
7804 by a union piecewise quasi-affine expression. If this expression
7805 assigns a different value to two domain elements, while all previous
7806 schedule dimensions in the same band assign them the same value,
7807 then the two domain elements are ordered according to these two
7809 Each expression is required to be total in the domain elements
7810 that reach the band node.
7812 =item C<isl_schedule_node_expansion>
7814 An expansion node maps each of the domain elements that reach the node
7815 to one or more domain elements. The image of this mapping forms
7816 the set of domain elements that reach the child of the expansion node.
7817 The function that maps each of the expanded domain elements
7818 to the original domain element from which it was expanded
7819 is called the contraction.
7821 =item C<isl_schedule_node_filter>
7823 A filter node does not impose any ordering, but rather intersects
7824 the set of domain elements that the current subtree refers to
7825 with a given union set. The subtree of the filter node only
7826 refers to domain elements in the intersection.
7827 A filter node is typically only used as a child of a sequence or
7830 =item C<isl_schedule_node_leaf>
7832 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
7834 =item C<isl_schedule_node_mark>
7836 A mark node can be used to attach any kind of information to a subtree
7837 of the schedule tree.
7839 =item C<isl_schedule_node_sequence>
7841 A sequence node has one or more children, each of which is a filter node.
7842 The filters on these filter nodes form a partition of
7843 the domain elements that the current subtree refers to.
7844 If two domain elements appear in distinct filters then the sequence
7845 node orders them according to the child positions of the corresponding
7848 =item C<isl_schedule_node_set>
7850 A set node is similar to a sequence node, except that
7851 it expresses that domain elements appearing in distinct filters
7852 may have any order. The order of the children of a set node
7853 is therefore also immaterial.
7857 The following node types are only supported by the AST generator.
7861 =item C<isl_schedule_node_context>
7863 The context describes constraints on the parameters and
7864 the schedule dimensions of outer
7865 bands that the AST generator may assume to hold. It is also the only
7866 kind of node that may introduce additional parameters.
7867 The space of the context is that of the flat product of the outer
7868 band nodes. In particular, if there are no outer band nodes, then
7869 this space is the unnamed zero-dimensional space.
7870 Since a context node references the outer band nodes, any tree
7871 containing a context node is considered to be anchored.
7873 =item C<isl_schedule_node_extension>
7875 An extension node instructs the AST generator to add additional
7876 domain elements that need to be scheduled.
7877 The additional domain elements are described by the range of
7878 the extension map in terms of the outer schedule dimensions,
7879 i.e., the flat product of the outer band nodes.
7880 Note that domain elements are added whenever the AST generator
7881 reaches the extension node, meaning that there are still some
7882 active domain elements for which an AST needs to be generated.
7883 The conditions under which some domain elements are still active
7884 may however not be completely described by the outer AST nodes
7885 generated at that point.
7887 An extension node may also appear as the root of a schedule tree,
7888 when it is intended to be inserted into another tree
7889 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
7890 In this case, the domain of the extension node should
7891 correspond to the flat product of the outer band nodes
7892 in this other schedule tree at the point where the extension tree
7895 =item C<isl_schedule_node_guard>
7897 The guard describes constraints on the parameters and
7898 the schedule dimensions of outer
7899 bands that need to be enforced by the outer nodes
7900 in the generated AST.
7901 The space of the guard is that of the flat product of the outer
7902 band nodes. In particular, if there are no outer band nodes, then
7903 this space is the unnamed zero-dimensional space.
7904 Since a guard node references the outer band nodes, any tree
7905 containing a guard node is considered to be anchored.
7909 Except for the C<isl_schedule_node_context> nodes,
7910 none of the nodes may introduce any parameters that were not
7911 already present in the root domain node.
7913 A schedule tree is encapsulated in an C<isl_schedule> object.
7914 The simplest such objects, those with a tree consisting of single domain node,
7915 can be created using the following functions with either an empty
7916 domain or a given domain.
7918 #include <isl/schedule.h>
7919 __isl_give isl_schedule *isl_schedule_empty(
7920 __isl_take isl_space *space);
7921 __isl_give isl_schedule *isl_schedule_from_domain(
7922 __isl_take isl_union_set *domain);
7924 The function C<isl_schedule_constraints_compute_schedule> described
7925 in L</"Scheduling"> can also be used to construct schedules.
7927 C<isl_schedule> objects may be copied and freed using the following functions.
7929 #include <isl/schedule.h>
7930 __isl_give isl_schedule *isl_schedule_copy(
7931 __isl_keep isl_schedule *sched);
7932 __isl_null isl_schedule *isl_schedule_free(
7933 __isl_take isl_schedule *sched);
7935 The following functions checks whether two C<isl_schedule> objects
7936 are obviously the same.
7938 #include <isl/schedule.h>
7939 isl_bool isl_schedule_plain_is_equal(
7940 __isl_keep isl_schedule *schedule1,
7941 __isl_keep isl_schedule *schedule2);
7943 The domain of the schedule, i.e., the domain described by the root node,
7944 can be obtained using the following function.
7946 #include <isl/schedule.h>
7947 __isl_give isl_union_set *isl_schedule_get_domain(
7948 __isl_keep isl_schedule *schedule);
7950 An extra top-level band node (right underneath the domain node) can
7951 be introduced into the schedule using the following function.
7952 The schedule tree is assumed not to have any anchored nodes.
7954 #include <isl/schedule.h>
7955 __isl_give isl_schedule *
7956 isl_schedule_insert_partial_schedule(
7957 __isl_take isl_schedule *schedule,
7958 __isl_take isl_multi_union_pw_aff *partial);
7960 A top-level context node (right underneath the domain node) can
7961 be introduced into the schedule using the following function.
7963 #include <isl/schedule.h>
7964 __isl_give isl_schedule *isl_schedule_insert_context(
7965 __isl_take isl_schedule *schedule,
7966 __isl_take isl_set *context)
7968 A top-level guard node (right underneath the domain node) can
7969 be introduced into the schedule using the following function.
7971 #include <isl/schedule.h>
7972 __isl_give isl_schedule *isl_schedule_insert_guard(
7973 __isl_take isl_schedule *schedule,
7974 __isl_take isl_set *guard)
7976 A schedule that combines two schedules either in the given
7977 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
7978 or an C<isl_schedule_node_set> node,
7979 can be created using the following functions.
7981 #include <isl/schedule.h>
7982 __isl_give isl_schedule *isl_schedule_sequence(
7983 __isl_take isl_schedule *schedule1,
7984 __isl_take isl_schedule *schedule2);
7985 __isl_give isl_schedule *isl_schedule_set(
7986 __isl_take isl_schedule *schedule1,
7987 __isl_take isl_schedule *schedule2);
7989 The domains of the two input schedules need to be disjoint.
7991 The following function can be used to restrict the domain
7992 of a schedule with a domain node as root to be a subset of the given union set.
7993 This operation may remove nodes in the tree that have become
7996 #include <isl/schedule.h>
7997 __isl_give isl_schedule *isl_schedule_intersect_domain(
7998 __isl_take isl_schedule *schedule,
7999 __isl_take isl_union_set *domain);
8001 The following function can be used to simplify the domain
8002 of a schedule with a domain node as root with respect to the given
8005 #include <isl/schedule.h>
8006 __isl_give isl_schedule *isl_schedule_gist_domain_params(
8007 __isl_take isl_schedule *schedule,
8008 __isl_take isl_set *context);
8010 The following function resets the user pointers on all parameter
8011 and tuple identifiers referenced by the nodes of the given schedule.
8013 #include <isl/schedule.h>
8014 __isl_give isl_schedule *isl_schedule_reset_user(
8015 __isl_take isl_schedule *schedule);
8017 The following function aligns the parameters of all nodes
8018 in the given schedule to the given space.
8020 #include <isl/schedule.h>
8021 __isl_give isl_schedule *isl_schedule_align_params(
8022 __isl_take isl_schedule *schedule,
8023 __isl_take isl_space *space);
8025 The following function allows the user to plug in a given function
8026 in the iteration domains. The input schedule is not allowed to contain
8027 any expansion nodes.
8029 #include <isl/schedule.h>
8030 __isl_give isl_schedule *
8031 isl_schedule_pullback_union_pw_multi_aff(
8032 __isl_take isl_schedule *schedule,
8033 __isl_take isl_union_pw_multi_aff *upma);
8035 The following function can be used to plug in the schedule C<expansion>
8036 in the leaves of C<schedule>, where C<contraction> describes how
8037 the domain elements of C<expansion> map to the domain elements
8038 at the original leaves of C<schedule>.
8039 The resulting schedule will contain expansion nodes, unless
8040 C<contraction> is an identity function.
8042 #include <isl/schedule.h>
8043 __isl_give isl_schedule *isl_schedule_expand(
8044 __isl_take isl_schedule *schedule,
8045 __isl_take isl_union_pw_multi_aff *contraction,
8046 __isl_take isl_schedule *expansion);
8048 An C<isl_union_map> representation of the schedule can be obtained
8049 from an C<isl_schedule> using the following function.
8051 #include <isl/schedule.h>
8052 __isl_give isl_union_map *isl_schedule_get_map(
8053 __isl_keep isl_schedule *sched);
8055 The resulting relation encodes the same relative ordering as
8056 the schedule by mapping the domain elements to a common schedule space.
8057 If the schedule_separate_components option is set, then the order
8058 of the children of a set node is explicitly encoded in the result.
8059 If the tree contains any expansion nodes, then the relation
8060 is formulated in terms of the expanded domain elements.
8062 Schedules can be read from input using the following functions.
8064 #include <isl/schedule.h>
8065 __isl_give isl_schedule *isl_schedule_read_from_file(
8066 isl_ctx *ctx, FILE *input);
8067 __isl_give isl_schedule *isl_schedule_read_from_str(
8068 isl_ctx *ctx, const char *str);
8070 A representation of the schedule can be printed using
8072 #include <isl/schedule.h>
8073 __isl_give isl_printer *isl_printer_print_schedule(
8074 __isl_take isl_printer *p,
8075 __isl_keep isl_schedule *schedule);
8076 __isl_give char *isl_schedule_to_str(
8077 __isl_keep isl_schedule *schedule);
8079 C<isl_schedule_to_str> prints the schedule in flow format.
8081 The schedule tree can be traversed through the use of
8082 C<isl_schedule_node> objects that point to a particular
8083 position in the schedule tree. Whenever a C<isl_schedule_node>
8084 is use to modify a node in the schedule tree, the original schedule
8085 tree is left untouched and the modifications are performed to a copy
8086 of the tree. The returned C<isl_schedule_node> then points to
8087 this modified copy of the tree.
8089 The root of the schedule tree can be obtained using the following function.
8091 #include <isl/schedule.h>
8092 __isl_give isl_schedule_node *isl_schedule_get_root(
8093 __isl_keep isl_schedule *schedule);
8095 A pointer to a newly created schedule tree with a single domain
8096 node can be created using the following functions.
8098 #include <isl/schedule_node.h>
8099 __isl_give isl_schedule_node *
8100 isl_schedule_node_from_domain(
8101 __isl_take isl_union_set *domain);
8102 __isl_give isl_schedule_node *
8103 isl_schedule_node_from_extension(
8104 __isl_take isl_union_map *extension);
8106 C<isl_schedule_node_from_extension> creates a tree with an extension
8109 Schedule nodes can be copied and freed using the following functions.
8111 #include <isl/schedule_node.h>
8112 __isl_give isl_schedule_node *isl_schedule_node_copy(
8113 __isl_keep isl_schedule_node *node);
8114 __isl_null isl_schedule_node *isl_schedule_node_free(
8115 __isl_take isl_schedule_node *node);
8117 The following functions can be used to check if two schedule
8118 nodes point to the same position in the same schedule.
8120 #include <isl/schedule_node.h>
8121 isl_bool isl_schedule_node_is_equal(
8122 __isl_keep isl_schedule_node *node1,
8123 __isl_keep isl_schedule_node *node2);
8125 The following properties can be obtained from a schedule node.
8127 #include <isl/schedule_node.h>
8128 enum isl_schedule_node_type isl_schedule_node_get_type(
8129 __isl_keep isl_schedule_node *node);
8130 enum isl_schedule_node_type
8131 isl_schedule_node_get_parent_type(
8132 __isl_keep isl_schedule_node *node);
8133 __isl_give isl_schedule *isl_schedule_node_get_schedule(
8134 __isl_keep isl_schedule_node *node);
8136 The function C<isl_schedule_node_get_type> returns the type of
8137 the node, while C<isl_schedule_node_get_parent_type> returns
8138 type of the parent of the node, which is required to exist.
8139 The function C<isl_schedule_node_get_schedule> returns a copy
8140 to the schedule to which the node belongs.
8142 The following functions can be used to move the schedule node
8143 to a different position in the tree or to check if such a position
8146 #include <isl/schedule_node.h>
8147 isl_bool isl_schedule_node_has_parent(
8148 __isl_keep isl_schedule_node *node);
8149 __isl_give isl_schedule_node *isl_schedule_node_parent(
8150 __isl_take isl_schedule_node *node);
8151 __isl_give isl_schedule_node *isl_schedule_node_root(
8152 __isl_take isl_schedule_node *node);
8153 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
8154 __isl_take isl_schedule_node *node,
8156 int isl_schedule_node_n_children(
8157 __isl_keep isl_schedule_node *node);
8158 __isl_give isl_schedule_node *isl_schedule_node_child(
8159 __isl_take isl_schedule_node *node, int pos);
8160 isl_bool isl_schedule_node_has_children(
8161 __isl_keep isl_schedule_node *node);
8162 __isl_give isl_schedule_node *isl_schedule_node_first_child(
8163 __isl_take isl_schedule_node *node);
8164 isl_bool isl_schedule_node_has_previous_sibling(
8165 __isl_keep isl_schedule_node *node);
8166 __isl_give isl_schedule_node *
8167 isl_schedule_node_previous_sibling(
8168 __isl_take isl_schedule_node *node);
8169 isl_bool isl_schedule_node_has_next_sibling(
8170 __isl_keep isl_schedule_node *node);
8171 __isl_give isl_schedule_node *
8172 isl_schedule_node_next_sibling(
8173 __isl_take isl_schedule_node *node);
8175 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
8176 is the node itself, the ancestor of generation 1 is its parent and so on.
8178 It is also possible to query the number of ancestors of a node,
8179 the position of the current node
8180 within the children of its parent, the position of the subtree
8181 containing a node within the children of an ancestor
8182 or to obtain a copy of a given
8183 child without destroying the current node.
8184 Given two nodes that point to the same schedule, their closest
8185 shared ancestor can be obtained using
8186 C<isl_schedule_node_get_shared_ancestor>.
8188 #include <isl/schedule_node.h>
8189 int isl_schedule_node_get_tree_depth(
8190 __isl_keep isl_schedule_node *node);
8191 int isl_schedule_node_get_child_position(
8192 __isl_keep isl_schedule_node *node);
8193 int isl_schedule_node_get_ancestor_child_position(
8194 __isl_keep isl_schedule_node *node,
8195 __isl_keep isl_schedule_node *ancestor);
8196 __isl_give isl_schedule_node *isl_schedule_node_get_child(
8197 __isl_keep isl_schedule_node *node, int pos);
8198 __isl_give isl_schedule_node *
8199 isl_schedule_node_get_shared_ancestor(
8200 __isl_keep isl_schedule_node *node1,
8201 __isl_keep isl_schedule_node *node2);
8203 All nodes in a schedule tree or
8204 all descendants of a specific node (including the node) can be visited
8205 in depth-first pre-order using the following functions.
8207 #include <isl/schedule.h>
8208 isl_stat isl_schedule_foreach_schedule_node_top_down(
8209 __isl_keep isl_schedule *sched,
8210 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8211 void *user), void *user);
8213 #include <isl/schedule_node.h>
8214 isl_stat isl_schedule_node_foreach_descendant_top_down(
8215 __isl_keep isl_schedule_node *node,
8216 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8217 void *user), void *user);
8219 The callback function is slightly different from the usual
8220 callbacks in that it not only indicates success (non-negative result)
8221 or failure (negative result), but also indicates whether the children
8222 of the given node should be visited. In particular, if the callback
8223 returns a positive value, then the children are visited, but if
8224 the callback returns zero, then the children are not visited.
8226 The ancestors of a node in a schedule tree can be visited from
8227 the root down to and including the parent of the node using
8228 the following function.
8230 #include <isl/schedule_node.h>
8231 isl_stat isl_schedule_node_foreach_ancestor_top_down(
8232 __isl_keep isl_schedule_node *node,
8233 isl_stat (*fn)(__isl_keep isl_schedule_node *node,
8234 void *user), void *user);
8236 The following functions allows for a depth-first post-order
8237 traversal of the nodes in a schedule tree or
8238 of the descendants of a specific node (including the node
8239 itself), where the user callback is allowed to modify the
8242 #include <isl/schedule.h>
8243 __isl_give isl_schedule *
8244 isl_schedule_map_schedule_node_bottom_up(
8245 __isl_take isl_schedule *schedule,
8246 __isl_give isl_schedule_node *(*fn)(
8247 __isl_take isl_schedule_node *node,
8248 void *user), void *user);
8250 #include <isl/schedule_node.h>
8251 __isl_give isl_schedule_node *
8252 isl_schedule_node_map_descendant_bottom_up(
8253 __isl_take isl_schedule_node *node,
8254 __isl_give isl_schedule_node *(*fn)(
8255 __isl_take isl_schedule_node *node,
8256 void *user), void *user);
8258 The traversal continues from the node returned by the callback function.
8259 It is the responsibility of the user to ensure that this does not
8260 lead to an infinite loop. It is safest to always return a pointer
8261 to the same position (same ancestors and child positions) as the input node.
8263 The following function removes a node (along with its descendants)
8264 from a schedule tree and returns a pointer to the leaf at the
8265 same position in the updated tree.
8266 It is not allowed to remove the root of a schedule tree or
8267 a child of a set or sequence node.
8269 #include <isl/schedule_node.h>
8270 __isl_give isl_schedule_node *isl_schedule_node_cut(
8271 __isl_take isl_schedule_node *node);
8273 The following function removes a single node
8274 from a schedule tree and returns a pointer to the child
8275 of the node, now located at the position of the original node
8276 or to a leaf node at that position if there was no child.
8277 It is not allowed to remove the root of a schedule tree,
8278 a set or sequence node, a child of a set or sequence node or
8279 a band node with an anchored subtree.
8281 #include <isl/schedule_node.h>
8282 __isl_give isl_schedule_node *isl_schedule_node_delete(
8283 __isl_take isl_schedule_node *node);
8285 Most nodes in a schedule tree only contain local information.
8286 In some cases, however, a node may also refer to the schedule dimensions
8287 of its outer band nodes.
8288 This means that the position of the node within the tree should
8289 not be changed, or at least that no changes are performed to the
8290 outer band nodes. The following function can be used to test
8291 whether the subtree rooted at a given node contains any such nodes.
8293 #include <isl/schedule_node.h>
8294 isl_bool isl_schedule_node_is_subtree_anchored(
8295 __isl_keep isl_schedule_node *node);
8297 The following function resets the user pointers on all parameter
8298 and tuple identifiers referenced by the given schedule node.
8300 #include <isl/schedule_node.h>
8301 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
8302 __isl_take isl_schedule_node *node);
8304 The following function aligns the parameters of the given schedule
8305 node to the given space.
8307 #include <isl/schedule_node.h>
8308 __isl_give isl_schedule_node *
8309 isl_schedule_node_align_params(
8310 __isl_take isl_schedule_node *node,
8311 __isl_take isl_space *space);
8313 Several node types have their own functions for querying
8314 (and in some cases setting) some node type specific properties.
8316 #include <isl/schedule_node.h>
8317 __isl_give isl_space *isl_schedule_node_band_get_space(
8318 __isl_keep isl_schedule_node *node);
8319 __isl_give isl_multi_union_pw_aff *
8320 isl_schedule_node_band_get_partial_schedule(
8321 __isl_keep isl_schedule_node *node);
8322 __isl_give isl_union_map *
8323 isl_schedule_node_band_get_partial_schedule_union_map(
8324 __isl_keep isl_schedule_node *node);
8325 unsigned isl_schedule_node_band_n_member(
8326 __isl_keep isl_schedule_node *node);
8327 isl_bool isl_schedule_node_band_member_get_coincident(
8328 __isl_keep isl_schedule_node *node, int pos);
8329 __isl_give isl_schedule_node *
8330 isl_schedule_node_band_member_set_coincident(
8331 __isl_take isl_schedule_node *node, int pos,
8333 isl_bool isl_schedule_node_band_get_permutable(
8334 __isl_keep isl_schedule_node *node);
8335 __isl_give isl_schedule_node *
8336 isl_schedule_node_band_set_permutable(
8337 __isl_take isl_schedule_node *node, int permutable);
8338 enum isl_ast_loop_type
8339 isl_schedule_node_band_member_get_ast_loop_type(
8340 __isl_keep isl_schedule_node *node, int pos);
8341 __isl_give isl_schedule_node *
8342 isl_schedule_node_band_member_set_ast_loop_type(
8343 __isl_take isl_schedule_node *node, int pos,
8344 enum isl_ast_loop_type type);
8345 __isl_give isl_union_set *
8346 enum isl_ast_loop_type
8347 isl_schedule_node_band_member_get_isolate_ast_loop_type(
8348 __isl_keep isl_schedule_node *node, int pos);
8349 __isl_give isl_schedule_node *
8350 isl_schedule_node_band_member_set_isolate_ast_loop_type(
8351 __isl_take isl_schedule_node *node, int pos,
8352 enum isl_ast_loop_type type);
8353 isl_schedule_node_band_get_ast_build_options(
8354 __isl_keep isl_schedule_node *node);
8355 __isl_give isl_schedule_node *
8356 isl_schedule_node_band_set_ast_build_options(
8357 __isl_take isl_schedule_node *node,
8358 __isl_take isl_union_set *options);
8359 __isl_give isl_set *
8360 isl_schedule_node_band_get_ast_isolate_option(
8361 __isl_keep isl_schedule_node *node);
8363 The function C<isl_schedule_node_band_get_space> returns the space
8364 of the partial schedule of the band.
8365 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
8366 returns a representation of the partial schedule of the band node
8367 in the form of an C<isl_union_map>.
8368 The coincident and permutable properties are set by
8369 C<isl_schedule_constraints_compute_schedule> on the schedule tree
8371 A scheduling dimension is considered to be ``coincident''
8372 if it satisfies the coincidence constraints within its band.
8373 That is, if the dependence distances of the coincidence
8374 constraints are all zero in that direction (for fixed
8375 iterations of outer bands).
8376 A band is marked permutable if it was produced using the Pluto-like scheduler.
8377 Note that the scheduler may have to resort to a Feautrier style scheduling
8378 step even if the default scheduler is used.
8379 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
8380 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
8381 For the meaning of these loop AST generation types and the difference
8382 between the regular loop AST generation type and the isolate
8383 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
8384 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
8385 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
8386 may return C<isl_ast_loop_error> if an error occurs.
8387 The AST build options govern how an AST is generated for
8388 the individual schedule dimensions during AST generation.
8389 See L</"AST Generation Options (Schedule Tree)">.
8390 The isolate option for the given node can be extracted from these
8391 AST build options using the function
8392 C<isl_schedule_node_band_get_ast_isolate_option>.
8394 #include <isl/schedule_node.h>
8395 __isl_give isl_set *
8396 isl_schedule_node_context_get_context(
8397 __isl_keep isl_schedule_node *node);
8399 #include <isl/schedule_node.h>
8400 __isl_give isl_union_set *
8401 isl_schedule_node_domain_get_domain(
8402 __isl_keep isl_schedule_node *node);
8404 #include <isl/schedule_node.h>
8405 __isl_give isl_union_map *
8406 isl_schedule_node_expansion_get_expansion(
8407 __isl_keep isl_schedule_node *node);
8408 __isl_give isl_union_pw_multi_aff *
8409 isl_schedule_node_expansion_get_contraction(
8410 __isl_keep isl_schedule_node *node);
8412 #include <isl/schedule_node.h>
8413 __isl_give isl_union_map *
8414 isl_schedule_node_extension_get_extension(
8415 __isl_keep isl_schedule_node *node);
8417 #include <isl/schedule_node.h>
8418 __isl_give isl_union_set *
8419 isl_schedule_node_filter_get_filter(
8420 __isl_keep isl_schedule_node *node);
8422 #include <isl/schedule_node.h>
8423 __isl_give isl_set *isl_schedule_node_guard_get_guard(
8424 __isl_keep isl_schedule_node *node);
8426 #include <isl/schedule_node.h>
8427 __isl_give isl_id *isl_schedule_node_mark_get_id(
8428 __isl_keep isl_schedule_node *node);
8430 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
8431 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
8432 partial schedules related to the node.
8434 #include <isl/schedule_node.h>
8435 __isl_give isl_multi_union_pw_aff *
8436 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
8437 __isl_keep isl_schedule_node *node);
8438 __isl_give isl_union_pw_multi_aff *
8439 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
8440 __isl_keep isl_schedule_node *node);
8441 __isl_give isl_union_map *
8442 isl_schedule_node_get_prefix_schedule_union_map(
8443 __isl_keep isl_schedule_node *node);
8444 __isl_give isl_union_map *
8445 isl_schedule_node_get_prefix_schedule_relation(
8446 __isl_keep isl_schedule_node *node);
8447 __isl_give isl_union_map *
8448 isl_schedule_node_get_subtree_schedule_union_map(
8449 __isl_keep isl_schedule_node *node);
8451 In particular, the functions
8452 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
8453 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
8454 and C<isl_schedule_node_get_prefix_schedule_union_map>
8455 return a relative ordering on the domain elements that reach the given
8456 node determined by its ancestors.
8457 The function C<isl_schedule_node_get_prefix_schedule_relation>
8458 additionally includes the domain constraints in the result.
8459 The function C<isl_schedule_node_get_subtree_schedule_union_map>
8460 returns a representation of the partial schedule defined by the
8461 subtree rooted at the given node.
8462 If the tree contains any expansion nodes, then the subtree schedule
8463 is formulated in terms of the expanded domain elements.
8464 The tree passed to functions returning a prefix schedule
8465 may only contain extension nodes if these would not affect
8466 the result of these functions. That is, if one of the ancestors
8467 is an extension node, then all of the domain elements that were
8468 added by the extension node need to have been filtered out
8469 by filter nodes between the extension node and the input node.
8470 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
8471 may not contain in extension nodes in the selected subtree.
8473 The expansion/contraction defined by an entire subtree, combining
8474 the expansions/contractions
8475 on the expansion nodes in the subtree, can be obtained using
8476 the following functions.
8478 #include <isl/schedule_node.h>
8479 __isl_give isl_union_map *
8480 isl_schedule_node_get_subtree_expansion(
8481 __isl_keep isl_schedule_node *node);
8482 __isl_give isl_union_pw_multi_aff *
8483 isl_schedule_node_get_subtree_contraction(
8484 __isl_keep isl_schedule_node *node);
8486 The total number of outer band members of given node, i.e.,
8487 the shared output dimension of the maps in the result
8488 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
8489 using the following function.
8491 #include <isl/schedule_node.h>
8492 int isl_schedule_node_get_schedule_depth(
8493 __isl_keep isl_schedule_node *node);
8495 The following functions return the elements that reach the given node
8496 or the union of universes in the spaces that contain these elements.
8498 #include <isl/schedule_node.h>
8499 __isl_give isl_union_set *
8500 isl_schedule_node_get_domain(
8501 __isl_keep isl_schedule_node *node);
8502 __isl_give isl_union_set *
8503 isl_schedule_node_get_universe_domain(
8504 __isl_keep isl_schedule_node *node);
8506 The input tree of C<isl_schedule_node_get_domain>
8507 may only contain extension nodes if these would not affect
8508 the result of this function. That is, if one of the ancestors
8509 is an extension node, then all of the domain elements that were
8510 added by the extension node need to have been filtered out
8511 by filter nodes between the extension node and the input node.
8513 The following functions can be used to introduce additional nodes
8514 in the schedule tree. The new node is introduced at the point
8515 in the tree where the C<isl_schedule_node> points to and
8516 the results points to the new node.
8518 #include <isl/schedule_node.h>
8519 __isl_give isl_schedule_node *
8520 isl_schedule_node_insert_partial_schedule(
8521 __isl_take isl_schedule_node *node,
8522 __isl_take isl_multi_union_pw_aff *schedule);
8524 This function inserts a new band node with (the greatest integer
8525 part of) the given partial schedule.
8526 The subtree rooted at the given node is assumed not to have
8529 #include <isl/schedule_node.h>
8530 __isl_give isl_schedule_node *
8531 isl_schedule_node_insert_context(
8532 __isl_take isl_schedule_node *node,
8533 __isl_take isl_set *context);
8535 This function inserts a new context node with the given context constraints.
8537 #include <isl/schedule_node.h>
8538 __isl_give isl_schedule_node *
8539 isl_schedule_node_insert_filter(
8540 __isl_take isl_schedule_node *node,
8541 __isl_take isl_union_set *filter);
8543 This function inserts a new filter node with the given filter.
8544 If the original node already pointed to a filter node, then the
8545 two filter nodes are merged into one.
8547 #include <isl/schedule_node.h>
8548 __isl_give isl_schedule_node *
8549 isl_schedule_node_insert_guard(
8550 __isl_take isl_schedule_node *node,
8551 __isl_take isl_set *guard);
8553 This function inserts a new guard node with the given guard constraints.
8555 #include <isl/schedule_node.h>
8556 __isl_give isl_schedule_node *
8557 isl_schedule_node_insert_mark(
8558 __isl_take isl_schedule_node *node,
8559 __isl_take isl_id *mark);
8561 This function inserts a new mark node with the give mark identifier.
8563 #include <isl/schedule_node.h>
8564 __isl_give isl_schedule_node *
8565 isl_schedule_node_insert_sequence(
8566 __isl_take isl_schedule_node *node,
8567 __isl_take isl_union_set_list *filters);
8568 __isl_give isl_schedule_node *
8569 isl_schedule_node_insert_set(
8570 __isl_take isl_schedule_node *node,
8571 __isl_take isl_union_set_list *filters);
8573 These functions insert a new sequence or set node with the given
8574 filters as children.
8576 #include <isl/schedule_node.h>
8577 __isl_give isl_schedule_node *isl_schedule_node_group(
8578 __isl_take isl_schedule_node *node,
8579 __isl_take isl_id *group_id);
8581 This function introduces an expansion node in between the current
8582 node and its parent that expands instances of a space with tuple
8583 identifier C<group_id> to the original domain elements that reach
8584 the node. The group instances are identified by the prefix schedule
8585 of those domain elements. The ancestors of the node are adjusted
8586 to refer to the group instances instead of the original domain
8587 elements. The return value points to the same node in the updated
8588 schedule tree as the input node, i.e., to the child of the newly
8589 introduced expansion node. Grouping instances of different statements
8590 ensures that they will be treated as a single statement by the
8591 AST generator up to the point of the expansion node.
8593 The following function can be used to flatten a nested
8596 #include <isl/schedule_node.h>
8597 __isl_give isl_schedule_node *
8598 isl_schedule_node_sequence_splice_child(
8599 __isl_take isl_schedule_node *node, int pos);
8601 That is, given a sequence node C<node> that has another sequence node
8602 in its child at position C<pos> (in particular, the child of that filter
8603 node is a sequence node), attach the children of that other sequence
8604 node as children of C<node>, replacing the original child at position
8607 The partial schedule of a band node can be scaled (down) or reduced using
8608 the following functions.
8610 #include <isl/schedule_node.h>
8611 __isl_give isl_schedule_node *
8612 isl_schedule_node_band_scale(
8613 __isl_take isl_schedule_node *node,
8614 __isl_take isl_multi_val *mv);
8615 __isl_give isl_schedule_node *
8616 isl_schedule_node_band_scale_down(
8617 __isl_take isl_schedule_node *node,
8618 __isl_take isl_multi_val *mv);
8619 __isl_give isl_schedule_node *
8620 isl_schedule_node_band_mod(
8621 __isl_take isl_schedule_node *node,
8622 __isl_take isl_multi_val *mv);
8624 The spaces of the two arguments need to match.
8625 After scaling, the partial schedule is replaced by its greatest
8626 integer part to ensure that the schedule remains integral.
8628 The partial schedule of a band node can be shifted by an
8629 C<isl_multi_union_pw_aff> with a domain that is a superset
8630 of the domain of the partial schedule using
8631 the following function.
8633 #include <isl/schedule_node.h>
8634 __isl_give isl_schedule_node *
8635 isl_schedule_node_band_shift(
8636 __isl_take isl_schedule_node *node,
8637 __isl_take isl_multi_union_pw_aff *shift);
8639 A band node can be tiled using the following function.
8641 #include <isl/schedule_node.h>
8642 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
8643 __isl_take isl_schedule_node *node,
8644 __isl_take isl_multi_val *sizes);
8646 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
8648 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
8649 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
8651 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
8653 The C<isl_schedule_node_band_tile> function tiles
8654 the band using the given tile sizes inside its schedule.
8655 A new child band node is created to represent the point loops and it is
8656 inserted between the modified band and its children.
8657 The subtree rooted at the given node is assumed not to have
8659 The C<tile_scale_tile_loops> option specifies whether the tile
8660 loops iterators should be scaled by the tile sizes.
8661 If the C<tile_shift_point_loops> option is set, then the point loops
8662 are shifted to start at zero.
8664 A band node can be split into two nested band nodes
8665 using the following function.
8667 #include <isl/schedule_node.h>
8668 __isl_give isl_schedule_node *isl_schedule_node_band_split(
8669 __isl_take isl_schedule_node *node, int pos);
8671 The resulting outer band node contains the first C<pos> dimensions of
8672 the schedule of C<node> while the inner band contains the remaining dimensions.
8673 The schedules of the two band nodes live in anonymous spaces.
8674 The loop AST generation type options and the isolate option
8675 are split over the the two band nodes.
8677 A band node can be moved down to the leaves of the subtree rooted
8678 at the band node using the following function.
8680 #include <isl/schedule_node.h>
8681 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
8682 __isl_take isl_schedule_node *node);
8684 The subtree rooted at the given node is assumed not to have
8686 The result points to the node in the resulting tree that is in the same
8687 position as the node pointed to by C<node> in the original tree.
8689 #include <isl/schedule_node.h>
8690 __isl_give isl_schedule_node *
8691 isl_schedule_node_order_before(
8692 __isl_take isl_schedule_node *node,
8693 __isl_take isl_union_set *filter);
8694 __isl_give isl_schedule_node *
8695 isl_schedule_node_order_after(
8696 __isl_take isl_schedule_node *node,
8697 __isl_take isl_union_set *filter);
8699 These functions split the domain elements that reach C<node>
8700 into those that satisfy C<filter> and those that do not and
8701 arranges for the elements that do satisfy the filter to be
8702 executed before (in case of C<isl_schedule_node_order_before>)
8703 or after (in case of C<isl_schedule_node_order_after>)
8704 those that do not. The order is imposed by
8705 a sequence node, possibly reusing the grandparent of C<node>
8706 on two copies of the subtree attached to the original C<node>.
8707 Both copies are simplified with respect to their filter.
8709 Return a pointer to the copy of the subtree that does not
8710 satisfy C<filter>. If there is no such copy (because all
8711 reaching domain elements satisfy the filter), then return
8712 the original pointer.
8714 #include <isl/schedule_node.h>
8715 __isl_give isl_schedule_node *
8716 isl_schedule_node_graft_before(
8717 __isl_take isl_schedule_node *node,
8718 __isl_take isl_schedule_node *graft);
8719 __isl_give isl_schedule_node *
8720 isl_schedule_node_graft_after(
8721 __isl_take isl_schedule_node *node,
8722 __isl_take isl_schedule_node *graft);
8724 This function inserts the C<graft> tree into the tree containing C<node>
8725 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
8726 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
8727 The root node of C<graft>
8728 should be an extension node where the domain of the extension
8729 is the flat product of all outer band nodes of C<node>.
8730 The root node may also be a domain node.
8731 The elements of the domain or the range of the extension may not
8732 intersect with the domain elements that reach "node".
8733 The schedule tree of C<graft> may not be anchored.
8735 The schedule tree of C<node> is modified to include an extension node
8736 corresponding to the root node of C<graft> as a child of the original
8737 parent of C<node>. The original node that C<node> points to and the
8738 child of the root node of C<graft> are attached to this extension node
8739 through a sequence, with appropriate filters and with the child
8740 of C<graft> appearing before or after the original C<node>.
8742 If C<node> already appears inside a sequence that is the child of
8743 an extension node and if the spaces of the new domain elements
8744 do not overlap with those of the original domain elements,
8745 then that extension node is extended with the new extension
8746 rather than introducing a new segment of extension and sequence nodes.
8748 Return a pointer to the same node in the modified tree that
8749 C<node> pointed to in the original tree.
8751 A representation of the schedule node can be printed using
8753 #include <isl/schedule_node.h>
8754 __isl_give isl_printer *isl_printer_print_schedule_node(
8755 __isl_take isl_printer *p,
8756 __isl_keep isl_schedule_node *node);
8757 __isl_give char *isl_schedule_node_to_str(
8758 __isl_keep isl_schedule_node *node);
8760 C<isl_schedule_node_to_str> prints the schedule node in block format.
8762 =head2 Dependence Analysis
8764 C<isl> contains specialized functionality for performing
8765 array dataflow analysis. That is, given a I<sink> access relation
8766 and a collection of possible I<source> access relations,
8767 C<isl> can compute relations that describe
8768 for each iteration of the sink access, which iteration
8769 of which of the source access relations was the last
8770 to access the same data element before the given iteration
8772 The resulting dependence relations map source iterations
8773 to either the corresponding sink iterations or
8774 pairs of corresponding sink iterations and accessed data elements.
8775 To compute standard flow dependences, the sink should be
8776 a read, while the sources should be writes.
8777 If any of the source accesses are marked as being I<may>
8778 accesses, then there will be a (may) dependence from the last
8779 I<must> access B<and> from any I<may> access that follows
8780 this last I<must> access, but still precedes the sink access.
8781 Only dependences originating in a must access and without
8782 any may accesses between the must access and the sink access
8783 are considered to be must dependences.
8784 In particular, if I<all> sources are I<may> accesses,
8785 then memory based dependence analysis is performed.
8786 If, on the other hand, all sources are I<must> accesses,
8787 then value based dependence analysis is performed.
8789 =head3 High-level Interface
8791 A high-level interface to dependence analysis is provided
8792 by the following function.
8794 #include <isl/flow.h>
8795 __isl_give isl_union_flow *
8796 isl_union_access_info_compute_flow(
8797 __isl_take isl_union_access_info *access);
8799 The input C<isl_union_access_info> object describes the sink
8800 access relations, the source access relations and a schedule,
8801 while the output C<isl_union_flow> object describes
8802 the resulting dependence relations and the subsets of the
8803 sink relations for which no source was found.
8805 An C<isl_union_access_info> is created, modified, copied and freed using
8806 the following functions.
8808 #include <isl/flow.h>
8809 __isl_give isl_union_access_info *
8810 isl_union_access_info_from_sink(
8811 __isl_take isl_union_map *sink);
8812 __isl_give isl_union_access_info *
8813 isl_union_access_info_set_must_source(
8814 __isl_take isl_union_access_info *access,
8815 __isl_take isl_union_map *must_source);
8816 __isl_give isl_union_access_info *
8817 isl_union_access_info_set_may_source(
8818 __isl_take isl_union_access_info *access,
8819 __isl_take isl_union_map *may_source);
8820 __isl_give isl_union_access_info *
8821 isl_union_access_info_set_schedule(
8822 __isl_take isl_union_access_info *access,
8823 __isl_take isl_schedule *schedule);
8824 __isl_give isl_union_access_info *
8825 isl_union_access_info_set_schedule_map(
8826 __isl_take isl_union_access_info *access,
8827 __isl_take isl_union_map *schedule_map);
8828 __isl_give isl_union_access_info *
8829 isl_union_access_info_copy(
8830 __isl_keep isl_union_access_info *access);
8831 __isl_null isl_union_access_info *
8832 isl_union_access_info_free(
8833 __isl_take isl_union_access_info *access);
8835 The may sources set by C<isl_union_access_info_set_may_source>
8836 do not need to include the must sources set by
8837 C<isl_union_access_info_set_must_source> as a subset.
8838 The user is free not to call one (or both) of these functions,
8839 in which case the corresponding set is kept to its empty default.
8840 Similarly, the default schedule initialized by
8841 C<isl_union_access_info_from_sink> is empty.
8842 The current schedule is determined by the last call to either
8843 C<isl_union_access_info_set_schedule> or
8844 C<isl_union_access_info_set_schedule_map>.
8845 The domain of the schedule corresponds to the domains of
8846 the access relations. In particular, the domains of the access
8847 relations are effectively intersected with the domain of the schedule
8848 and only the resulting accesses are considered by the dependence analysis.
8850 A representation of the information contained in an object
8851 of type C<isl_union_access_info> can be obtained using
8853 #include <isl/flow.h>
8854 __isl_give isl_printer *
8855 isl_printer_print_union_access_info(
8856 __isl_take isl_printer *p,
8857 __isl_keep isl_union_access_info *access);
8858 __isl_give char *isl_union_access_info_to_str(
8859 __isl_keep isl_union_access_info *access);
8861 C<isl_union_access_info_to_str> prints the information in flow format.
8863 The output of C<isl_union_access_info_compute_flow> can be examined,
8864 copied, and freed using the following functions.
8866 #include <isl/flow.h>
8867 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
8868 __isl_keep isl_union_flow *flow);
8869 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
8870 __isl_keep isl_union_flow *flow);
8871 __isl_give isl_union_map *
8872 isl_union_flow_get_full_must_dependence(
8873 __isl_keep isl_union_flow *flow);
8874 __isl_give isl_union_map *
8875 isl_union_flow_get_full_may_dependence(
8876 __isl_keep isl_union_flow *flow);
8877 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
8878 __isl_keep isl_union_flow *flow);
8879 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
8880 __isl_keep isl_union_flow *flow);
8881 __isl_give isl_union_flow *isl_union_flow_copy(
8882 __isl_keep isl_union_flow *flow);
8883 __isl_null isl_union_flow *isl_union_flow_free(
8884 __isl_take isl_union_flow *flow);
8886 The relation returned by C<isl_union_flow_get_must_dependence>
8887 relates domain elements of must sources to domain elements of the sink.
8888 The relation returned by C<isl_union_flow_get_may_dependence>
8889 relates domain elements of must or may sources to domain elements of the sink
8890 and includes the previous relation as a subset.
8891 The relation returned by C<isl_union_flow_get_full_must_dependence>
8892 relates domain elements of must sources to pairs of domain elements of the sink
8893 and accessed data elements.
8894 The relation returned by C<isl_union_flow_get_full_may_dependence>
8895 relates domain elements of must or may sources to pairs of
8896 domain elements of the sink and accessed data elements.
8897 This relation includes the previous relation as a subset.
8898 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
8899 of the sink relation for which no dependences have been found.
8900 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
8901 of the sink relation for which no definite dependences have been found.
8902 That is, it contains those sink access that do not contribute to any
8903 of the elements in the relation returned
8904 by C<isl_union_flow_get_must_dependence>.
8906 A representation of the information contained in an object
8907 of type C<isl_union_flow> can be obtained using
8909 #include <isl/flow.h>
8910 __isl_give isl_printer *isl_printer_print_union_flow(
8911 __isl_take isl_printer *p,
8912 __isl_keep isl_union_flow *flow);
8913 __isl_give char *isl_union_flow_to_str(
8914 __isl_keep isl_union_flow *flow);
8916 C<isl_union_flow_to_str> prints the information in flow format.
8918 =head3 Low-level Interface
8920 A lower-level interface is provided by the following functions.
8922 #include <isl/flow.h>
8924 typedef int (*isl_access_level_before)(void *first, void *second);
8926 __isl_give isl_access_info *isl_access_info_alloc(
8927 __isl_take isl_map *sink,
8928 void *sink_user, isl_access_level_before fn,
8930 __isl_give isl_access_info *isl_access_info_add_source(
8931 __isl_take isl_access_info *acc,
8932 __isl_take isl_map *source, int must,
8934 __isl_null isl_access_info *isl_access_info_free(
8935 __isl_take isl_access_info *acc);
8937 __isl_give isl_flow *isl_access_info_compute_flow(
8938 __isl_take isl_access_info *acc);
8940 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,
8941 isl_stat (*fn)(__isl_take isl_map *dep, int must,
8942 void *dep_user, void *user),
8944 __isl_give isl_map *isl_flow_get_no_source(
8945 __isl_keep isl_flow *deps, int must);
8946 void isl_flow_free(__isl_take isl_flow *deps);
8948 The function C<isl_access_info_compute_flow> performs the actual
8949 dependence analysis. The other functions are used to construct
8950 the input for this function or to read off the output.
8952 The input is collected in an C<isl_access_info>, which can
8953 be created through a call to C<isl_access_info_alloc>.
8954 The arguments to this functions are the sink access relation
8955 C<sink>, a token C<sink_user> used to identify the sink
8956 access to the user, a callback function for specifying the
8957 relative order of source and sink accesses, and the number
8958 of source access relations that will be added.
8959 The callback function has type C<int (*)(void *first, void *second)>.
8960 The function is called with two user supplied tokens identifying
8961 either a source or the sink and it should return the shared nesting
8962 level and the relative order of the two accesses.
8963 In particular, let I<n> be the number of loops shared by
8964 the two accesses. If C<first> precedes C<second> textually,
8965 then the function should return I<2 * n + 1>; otherwise,
8966 it should return I<2 * n>.
8967 The sources can be added to the C<isl_access_info> by performing
8968 (at most) C<max_source> calls to C<isl_access_info_add_source>.
8969 C<must> indicates whether the source is a I<must> access
8970 or a I<may> access. Note that a multi-valued access relation
8971 should only be marked I<must> if every iteration in the domain
8972 of the relation accesses I<all> elements in its image.
8973 The C<source_user> token is again used to identify
8974 the source access. The range of the source access relation
8975 C<source> should have the same dimension as the range
8976 of the sink access relation.
8977 The C<isl_access_info_free> function should usually not be
8978 called explicitly, because it is called implicitly by
8979 C<isl_access_info_compute_flow>.
8981 The result of the dependence analysis is collected in an
8982 C<isl_flow>. There may be elements of
8983 the sink access for which no preceding source access could be
8984 found or for which all preceding sources are I<may> accesses.
8985 The relations containing these elements can be obtained through
8986 calls to C<isl_flow_get_no_source>, the first with C<must> set
8987 and the second with C<must> unset.
8988 In the case of standard flow dependence analysis,
8989 with the sink a read and the sources I<must> writes,
8990 the first relation corresponds to the reads from uninitialized
8991 array elements and the second relation is empty.
8992 The actual flow dependences can be extracted using
8993 C<isl_flow_foreach>. This function will call the user-specified
8994 callback function C<fn> for each B<non-empty> dependence between
8995 a source and the sink. The callback function is called
8996 with four arguments, the actual flow dependence relation
8997 mapping source iterations to sink iterations, a boolean that
8998 indicates whether it is a I<must> or I<may> dependence, a token
8999 identifying the source and an additional C<void *> with value
9000 equal to the third argument of the C<isl_flow_foreach> call.
9001 A dependence is marked I<must> if it originates from a I<must>
9002 source and if it is not followed by any I<may> sources.
9004 After finishing with an C<isl_flow>, the user should call
9005 C<isl_flow_free> to free all associated memory.
9007 =head3 Interaction with the Low-level Interface
9009 During the dependence analysis, we frequently need to perform
9010 the following operation. Given a relation between sink iterations
9011 and potential source iterations from a particular source domain,
9012 what is the last potential source iteration corresponding to each
9013 sink iteration. It can sometimes be convenient to adjust
9014 the set of potential source iterations before or after each such operation.
9015 The prototypical example is fuzzy array dataflow analysis,
9016 where we need to analyze if, based on data-dependent constraints,
9017 the sink iteration can ever be executed without one or more of
9018 the corresponding potential source iterations being executed.
9019 If so, we can introduce extra parameters and select an unknown
9020 but fixed source iteration from the potential source iterations.
9021 To be able to perform such manipulations, C<isl> provides the following
9024 #include <isl/flow.h>
9026 typedef __isl_give isl_restriction *(*isl_access_restrict)(
9027 __isl_keep isl_map *source_map,
9028 __isl_keep isl_set *sink, void *source_user,
9030 __isl_give isl_access_info *isl_access_info_set_restrict(
9031 __isl_take isl_access_info *acc,
9032 isl_access_restrict fn, void *user);
9034 The function C<isl_access_info_set_restrict> should be called
9035 before calling C<isl_access_info_compute_flow> and registers a callback function
9036 that will be called any time C<isl> is about to compute the last
9037 potential source. The first argument is the (reverse) proto-dependence,
9038 mapping sink iterations to potential source iterations.
9039 The second argument represents the sink iterations for which
9040 we want to compute the last source iteration.
9041 The third argument is the token corresponding to the source
9042 and the final argument is the token passed to C<isl_access_info_set_restrict>.
9043 The callback is expected to return a restriction on either the input or
9044 the output of the operation computing the last potential source.
9045 If the input needs to be restricted then restrictions are needed
9046 for both the source and the sink iterations. The sink iterations
9047 and the potential source iterations will be intersected with these sets.
9048 If the output needs to be restricted then only a restriction on the source
9049 iterations is required.
9050 If any error occurs, the callback should return C<NULL>.
9051 An C<isl_restriction> object can be created, freed and inspected
9052 using the following functions.
9054 #include <isl/flow.h>
9056 __isl_give isl_restriction *isl_restriction_input(
9057 __isl_take isl_set *source_restr,
9058 __isl_take isl_set *sink_restr);
9059 __isl_give isl_restriction *isl_restriction_output(
9060 __isl_take isl_set *source_restr);
9061 __isl_give isl_restriction *isl_restriction_none(
9062 __isl_take isl_map *source_map);
9063 __isl_give isl_restriction *isl_restriction_empty(
9064 __isl_take isl_map *source_map);
9065 __isl_null isl_restriction *isl_restriction_free(
9066 __isl_take isl_restriction *restr);
9068 C<isl_restriction_none> and C<isl_restriction_empty> are special
9069 cases of C<isl_restriction_input>. C<isl_restriction_none>
9070 is essentially equivalent to
9072 isl_restriction_input(isl_set_universe(
9073 isl_space_range(isl_map_get_space(source_map))),
9075 isl_space_domain(isl_map_get_space(source_map))));
9077 whereas C<isl_restriction_empty> is essentially equivalent to
9079 isl_restriction_input(isl_set_empty(
9080 isl_space_range(isl_map_get_space(source_map))),
9082 isl_space_domain(isl_map_get_space(source_map))));
9086 #include <isl/schedule.h>
9087 __isl_give isl_schedule *
9088 isl_schedule_constraints_compute_schedule(
9089 __isl_take isl_schedule_constraints *sc);
9091 The function C<isl_schedule_constraints_compute_schedule> can be
9092 used to compute a schedule that satisfies the given schedule constraints.
9093 These schedule constraints include the iteration domain for which
9094 a schedule should be computed and dependences between pairs of
9095 iterations. In particular, these dependences include
9096 I<validity> dependences and I<proximity> dependences.
9097 By default, the algorithm used to construct the schedule is similar
9098 to that of C<Pluto>.
9099 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
9101 The generated schedule respects all validity dependences.
9102 That is, all dependence distances over these dependences in the
9103 scheduled space are lexicographically positive.
9105 The default algorithm tries to ensure that the dependence distances
9106 over coincidence constraints are zero and to minimize the
9107 dependence distances over proximity dependences.
9108 Moreover, it tries to obtain sequences (bands) of schedule dimensions
9109 for groups of domains where the dependence distances over validity
9110 dependences have only non-negative values.
9111 Note that when minimizing the maximal dependence distance
9112 over proximity dependences, a single affine expression in the parameters
9113 is constructed that bounds all dependence distances. If no such expression
9114 exists, then the algorithm will fail and resort to an alternative
9115 scheduling algorithm. In particular, this means that adding proximity
9116 dependences may eliminate valid solutions. A typical example where this
9117 phenomenon may occur is when some subset of the proximity dependences
9118 has no restriction on some parameter, forcing the coefficient of that
9119 parameter to be zero, while some other subset forces the dependence
9120 distance to depend on that parameter, requiring the same coefficient
9122 When using Feautrier's algorithm, the coincidence and proximity constraints
9123 are only taken into account during the extension to a
9124 full-dimensional schedule.
9126 An C<isl_schedule_constraints> object can be constructed
9127 and manipulated using the following functions.
9129 #include <isl/schedule.h>
9130 __isl_give isl_schedule_constraints *
9131 isl_schedule_constraints_copy(
9132 __isl_keep isl_schedule_constraints *sc);
9133 __isl_give isl_schedule_constraints *
9134 isl_schedule_constraints_on_domain(
9135 __isl_take isl_union_set *domain);
9136 __isl_give isl_schedule_constraints *
9137 isl_schedule_constraints_set_context(
9138 __isl_take isl_schedule_constraints *sc,
9139 __isl_take isl_set *context);
9140 __isl_give isl_schedule_constraints *
9141 isl_schedule_constraints_set_validity(
9142 __isl_take isl_schedule_constraints *sc,
9143 __isl_take isl_union_map *validity);
9144 __isl_give isl_schedule_constraints *
9145 isl_schedule_constraints_set_coincidence(
9146 __isl_take isl_schedule_constraints *sc,
9147 __isl_take isl_union_map *coincidence);
9148 __isl_give isl_schedule_constraints *
9149 isl_schedule_constraints_set_proximity(
9150 __isl_take isl_schedule_constraints *sc,
9151 __isl_take isl_union_map *proximity);
9152 __isl_give isl_schedule_constraints *
9153 isl_schedule_constraints_set_conditional_validity(
9154 __isl_take isl_schedule_constraints *sc,
9155 __isl_take isl_union_map *condition,
9156 __isl_take isl_union_map *validity);
9157 __isl_give isl_schedule_constraints *
9158 isl_schedule_constraints_apply(
9159 __isl_take isl_schedule_constraints *sc,
9160 __isl_take isl_union_map *umap);
9161 __isl_null isl_schedule_constraints *
9162 isl_schedule_constraints_free(
9163 __isl_take isl_schedule_constraints *sc);
9165 The initial C<isl_schedule_constraints> object created by
9166 C<isl_schedule_constraints_on_domain> does not impose any constraints.
9167 That is, it has an empty set of dependences.
9168 The function C<isl_schedule_constraints_set_context> allows the user
9169 to specify additional constraints on the parameters that may
9170 be assumed to hold during the construction of the schedule.
9171 The function C<isl_schedule_constraints_set_validity> replaces the
9172 validity dependences, mapping domain elements I<i> to domain
9173 elements that should be scheduled after I<i>.
9174 The function C<isl_schedule_constraints_set_coincidence> replaces the
9175 coincidence dependences, mapping domain elements I<i> to domain
9176 elements that should be scheduled together with I<I>, if possible.
9177 The function C<isl_schedule_constraints_set_proximity> replaces the
9178 proximity dependences, mapping domain elements I<i> to domain
9179 elements that should be scheduled either before I<I>
9180 or as early as possible after I<i>.
9182 The function C<isl_schedule_constraints_set_conditional_validity>
9183 replaces the conditional validity constraints.
9184 A conditional validity constraint is only imposed when any of the corresponding
9185 conditions is satisfied, i.e., when any of them is non-zero.
9186 That is, the scheduler ensures that within each band if the dependence
9187 distances over the condition constraints are not all zero
9188 then all corresponding conditional validity constraints are respected.
9189 A conditional validity constraint corresponds to a condition
9190 if the two are adjacent, i.e., if the domain of one relation intersect
9191 the range of the other relation.
9192 The typical use case of conditional validity constraints is
9193 to allow order constraints between live ranges to be violated
9194 as long as the live ranges themselves are local to the band.
9195 To allow more fine-grained control over which conditions correspond
9196 to which conditional validity constraints, the domains and ranges
9197 of these relations may include I<tags>. That is, the domains and
9198 ranges of those relation may themselves be wrapped relations
9199 where the iteration domain appears in the domain of those wrapped relations
9200 and the range of the wrapped relations can be arbitrarily chosen
9201 by the user. Conditions and conditional validity constraints are only
9202 considered adjacent to each other if the entire wrapped relation matches.
9203 In particular, a relation with a tag will never be considered adjacent
9204 to a relation without a tag.
9206 The function C<isl_schedule_constraints_compute_schedule> takes
9207 schedule constraints that are defined on some set of domain elements
9208 and transforms them to schedule constraints on the elements
9209 to which these domain elements are mapped by the given transformation.
9211 An C<isl_schedule_constraints> object can be inspected
9212 using the following functions.
9214 #include <isl/schedule.h>
9215 __isl_give isl_union_set *
9216 isl_schedule_constraints_get_domain(
9217 __isl_keep isl_schedule_constraints *sc);
9218 __isl_give isl_set *isl_schedule_constraints_get_context(
9219 __isl_keep isl_schedule_constraints *sc);
9220 __isl_give isl_union_map *
9221 isl_schedule_constraints_get_validity(
9222 __isl_keep isl_schedule_constraints *sc);
9223 __isl_give isl_union_map *
9224 isl_schedule_constraints_get_coincidence(
9225 __isl_keep isl_schedule_constraints *sc);
9226 __isl_give isl_union_map *
9227 isl_schedule_constraints_get_proximity(
9228 __isl_keep isl_schedule_constraints *sc);
9229 __isl_give isl_union_map *
9230 isl_schedule_constraints_get_conditional_validity(
9231 __isl_keep isl_schedule_constraints *sc);
9232 __isl_give isl_union_map *
9233 isl_schedule_constraints_get_conditional_validity_condition(
9234 __isl_keep isl_schedule_constraints *sc);
9236 An C<isl_schedule_constraints> object can be read from input
9237 using the following functions.
9239 #include <isl/schedule.h>
9240 __isl_give isl_schedule_constraints *
9241 isl_schedule_constraints_read_from_str(isl_ctx *ctx,
9243 __isl_give isl_schedule_constraints *
9244 isl_schedule_constraints_read_from_file(isl_ctx *ctx,
9247 The contents of an C<isl_schedule_constraints> object can be printed
9248 using the following functions.
9250 #include <isl/schedule.h>
9251 __isl_give isl_printer *
9252 isl_printer_print_schedule_constraints(
9253 __isl_take isl_printer *p,
9254 __isl_keep isl_schedule_constraints *sc);
9255 __isl_give char *isl_schedule_constraints_to_str(
9256 __isl_keep isl_schedule_constraints *sc);
9258 The following function computes a schedule directly from
9259 an iteration domain and validity and proximity dependences
9260 and is implemented in terms of the functions described above.
9261 The use of C<isl_union_set_compute_schedule> is discouraged.
9263 #include <isl/schedule.h>
9264 __isl_give isl_schedule *isl_union_set_compute_schedule(
9265 __isl_take isl_union_set *domain,
9266 __isl_take isl_union_map *validity,
9267 __isl_take isl_union_map *proximity);
9269 The generated schedule represents a schedule tree.
9270 For more information on schedule trees, see
9271 L</"Schedule Trees">.
9275 #include <isl/schedule.h>
9276 isl_stat isl_options_set_schedule_max_coefficient(
9277 isl_ctx *ctx, int val);
9278 int isl_options_get_schedule_max_coefficient(
9280 isl_stat isl_options_set_schedule_max_constant_term(
9281 isl_ctx *ctx, int val);
9282 int isl_options_get_schedule_max_constant_term(
9284 isl_stat isl_options_set_schedule_serialize_sccs(
9285 isl_ctx *ctx, int val);
9286 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx);
9287 isl_stat isl_options_set_schedule_whole_component(
9288 isl_ctx *ctx, int val);
9289 int isl_options_get_schedule_whole_component(
9291 isl_stat isl_options_set_schedule_maximize_band_depth(
9292 isl_ctx *ctx, int val);
9293 int isl_options_get_schedule_maximize_band_depth(
9295 isl_stat isl_options_set_schedule_maximize_coincidence(
9296 isl_ctx *ctx, int val);
9297 int isl_options_get_schedule_maximize_coincidence(
9299 isl_stat isl_options_set_schedule_outer_coincidence(
9300 isl_ctx *ctx, int val);
9301 int isl_options_get_schedule_outer_coincidence(
9303 isl_stat isl_options_set_schedule_split_scaled(
9304 isl_ctx *ctx, int val);
9305 int isl_options_get_schedule_split_scaled(
9307 isl_stat isl_options_set_schedule_treat_coalescing(
9308 isl_ctx *ctx, int val);
9309 int isl_options_get_schedule_treat_coalescing(
9311 isl_stat isl_options_set_schedule_algorithm(
9312 isl_ctx *ctx, int val);
9313 int isl_options_get_schedule_algorithm(
9315 isl_stat isl_options_set_schedule_carry_self_first(
9316 isl_ctx *ctx, int val);
9317 int isl_options_get_schedule_carry_self_first(
9319 isl_stat isl_options_set_schedule_separate_components(
9320 isl_ctx *ctx, int val);
9321 int isl_options_get_schedule_separate_components(
9326 =item * schedule_max_coefficient
9328 This option enforces that the coefficients for variable and parameter
9329 dimensions in the calculated schedule are not larger than the specified value.
9330 This option can significantly increase the speed of the scheduling calculation
9331 and may also prevent fusing of unrelated dimensions. A value of -1 means that
9332 this option does not introduce bounds on the variable or parameter
9335 =item * schedule_max_constant_term
9337 This option enforces that the constant coefficients in the calculated schedule
9338 are not larger than the maximal constant term. This option can significantly
9339 increase the speed of the scheduling calculation and may also prevent fusing of
9340 unrelated dimensions. A value of -1 means that this option does not introduce
9341 bounds on the constant coefficients.
9343 =item * schedule_serialize_sccs
9345 If this option is set, then all strongly connected components
9346 in the dependence graph are serialized as soon as they are detected.
9347 This means in particular that instances of statements will only
9348 appear in the same band node if these statements belong
9349 to the same strongly connected component at the point where
9350 the band node is constructed.
9352 =item * schedule_whole_component
9354 If this option is set, then entire (weakly) connected
9355 components in the dependence graph are scheduled together
9357 Otherwise, each strongly connected component within
9358 such a weakly connected component is first scheduled separately
9359 and then combined with other strongly connected components.
9360 This option has no effect if C<schedule_serialize_sccs> is set.
9362 =item * schedule_maximize_band_depth
9364 If this option is set, then the scheduler tries to maximize
9365 the width of the bands. Wider bands give more possibilities for tiling.
9366 In particular, if the C<schedule_whole_component> option is set,
9367 then bands are split if this might result in wider bands.
9368 Otherwise, the effect of this option is to only allow
9369 strongly connected components to be combined if this does
9370 not reduce the width of the bands.
9371 Note that if the C<schedule_serialize_sccs> options is set, then
9372 the C<schedule_maximize_band_depth> option therefore has no effect.
9374 =item * schedule_maximize_coincidence
9376 This option is only effective if the C<schedule_whole_component>
9377 option is turned off.
9378 If the C<schedule_maximize_coincidence> option is set, then (clusters of)
9379 strongly connected components are only combined with each other
9380 if this does not reduce the number of coincident band members.
9382 =item * schedule_outer_coincidence
9384 If this option is set, then we try to construct schedules
9385 where the outermost scheduling dimension in each band
9386 satisfies the coincidence constraints.
9388 =item * schedule_algorithm
9390 Selects the scheduling algorithm to be used.
9391 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
9392 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
9394 =item * schedule_split_scaled
9396 If this option is set, then we try to construct schedules in which the
9397 constant term is split off from the linear part if the linear parts of
9398 the scheduling rows for all nodes in the graph have a common non-trivial
9400 The constant term is then dropped and the linear
9402 This option is only effective when the Feautrier style scheduler is
9403 being used, either as the main scheduler or as a fallback for the
9404 Pluto-like scheduler.
9406 =item * schedule_treat_coalescing
9408 If this option is set, then the scheduler will try and avoid
9409 producing schedules that perform loop coalescing.
9410 In particular, for the Pluto-like scheduler, this option places
9411 bounds on the schedule coefficients based on the sizes of the instance sets.
9412 For the Feautrier style scheduler, this option detects potentially
9413 coalescing schedules and then tries to adjust the schedule to avoid
9416 =item * schedule_carry_self_first
9418 If this option is set, then the Feautrier style scheduler
9419 (when used as a fallback for the Pluto-like scheduler) will
9420 first try to only carry self-dependences.
9422 =item * schedule_separate_components
9424 If this option is set then the function C<isl_schedule_get_map>
9425 will treat set nodes in the same way as sequence nodes.
9429 =head2 AST Generation
9431 This section describes the C<isl> functionality for generating
9432 ASTs that visit all the elements
9433 in a domain in an order specified by a schedule tree or
9435 In case the schedule given as a C<isl_union_map>, an AST is generated
9436 that visits all the elements in the domain of the C<isl_union_map>
9437 according to the lexicographic order of the corresponding image
9438 element(s). If the range of the C<isl_union_map> consists of
9439 elements in more than one space, then each of these spaces is handled
9440 separately in an arbitrary order.
9441 It should be noted that the schedule tree or the image elements
9442 in a schedule map only specify the I<order>
9443 in which the corresponding domain elements should be visited.
9444 No direct relation between the partial schedule values
9445 or the image elements on the one hand and the loop iterators
9446 in the generated AST on the other hand should be assumed.
9448 Each AST is generated within a build. The initial build
9449 simply specifies the constraints on the parameters (if any)
9450 and can be created, inspected, copied and freed using the following functions.
9452 #include <isl/ast_build.h>
9453 __isl_give isl_ast_build *isl_ast_build_alloc(
9455 __isl_give isl_ast_build *isl_ast_build_from_context(
9456 __isl_take isl_set *set);
9457 __isl_give isl_ast_build *isl_ast_build_copy(
9458 __isl_keep isl_ast_build *build);
9459 __isl_null isl_ast_build *isl_ast_build_free(
9460 __isl_take isl_ast_build *build);
9462 The C<set> argument is usually a parameter set with zero or more parameters.
9463 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
9464 this set is required to be a parameter set.
9465 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
9466 specify any parameter constraints.
9467 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
9468 and L</"Fine-grained Control over AST Generation">.
9469 Finally, the AST itself can be constructed using one of the following
9472 #include <isl/ast_build.h>
9473 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
9474 __isl_keep isl_ast_build *build,
9475 __isl_take isl_schedule *schedule);
9476 __isl_give isl_ast_node *
9477 isl_ast_build_node_from_schedule_map(
9478 __isl_keep isl_ast_build *build,
9479 __isl_take isl_union_map *schedule);
9481 =head3 Inspecting the AST
9483 The basic properties of an AST node can be obtained as follows.
9485 #include <isl/ast.h>
9486 enum isl_ast_node_type isl_ast_node_get_type(
9487 __isl_keep isl_ast_node *node);
9489 The type of an AST node is one of
9490 C<isl_ast_node_for>,
9492 C<isl_ast_node_block>,
9493 C<isl_ast_node_mark> or
9494 C<isl_ast_node_user>.
9495 An C<isl_ast_node_for> represents a for node.
9496 An C<isl_ast_node_if> represents an if node.
9497 An C<isl_ast_node_block> represents a compound node.
9498 An C<isl_ast_node_mark> introduces a mark in the AST.
9499 An C<isl_ast_node_user> represents an expression statement.
9500 An expression statement typically corresponds to a domain element, i.e.,
9501 one of the elements that is visited by the AST.
9503 Each type of node has its own additional properties.
9505 #include <isl/ast.h>
9506 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
9507 __isl_keep isl_ast_node *node);
9508 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
9509 __isl_keep isl_ast_node *node);
9510 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
9511 __isl_keep isl_ast_node *node);
9512 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
9513 __isl_keep isl_ast_node *node);
9514 __isl_give isl_ast_node *isl_ast_node_for_get_body(
9515 __isl_keep isl_ast_node *node);
9516 isl_bool isl_ast_node_for_is_degenerate(
9517 __isl_keep isl_ast_node *node);
9519 An C<isl_ast_for> is considered degenerate if it is known to execute
9522 #include <isl/ast.h>
9523 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
9524 __isl_keep isl_ast_node *node);
9525 __isl_give isl_ast_node *isl_ast_node_if_get_then(
9526 __isl_keep isl_ast_node *node);
9527 isl_bool isl_ast_node_if_has_else(
9528 __isl_keep isl_ast_node *node);
9529 __isl_give isl_ast_node *isl_ast_node_if_get_else(
9530 __isl_keep isl_ast_node *node);
9532 __isl_give isl_ast_node_list *
9533 isl_ast_node_block_get_children(
9534 __isl_keep isl_ast_node *node);
9536 __isl_give isl_id *isl_ast_node_mark_get_id(
9537 __isl_keep isl_ast_node *node);
9538 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
9539 __isl_keep isl_ast_node *node);
9541 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
9542 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
9544 #include <isl/ast.h>
9545 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
9546 __isl_keep isl_ast_node *node);
9548 All descendants of a specific node in the AST (including the node itself)
9550 in depth-first pre-order using the following function.
9552 #include <isl/ast.h>
9553 isl_stat isl_ast_node_foreach_descendant_top_down(
9554 __isl_keep isl_ast_node *node,
9555 isl_bool (*fn)(__isl_keep isl_ast_node *node,
9556 void *user), void *user);
9558 The callback function should return C<isl_bool_true> if the children
9559 of the given node should be visited and C<isl_bool_false> if they should not.
9560 It should return C<isl_bool_error> in case of failure, in which case
9561 the entire traversal is aborted.
9563 Each of the returned C<isl_ast_expr>s can in turn be inspected using
9564 the following functions.
9566 #include <isl/ast.h>
9567 enum isl_ast_expr_type isl_ast_expr_get_type(
9568 __isl_keep isl_ast_expr *expr);
9570 The type of an AST expression is one of
9572 C<isl_ast_expr_id> or
9573 C<isl_ast_expr_int>.
9574 An C<isl_ast_expr_op> represents the result of an operation.
9575 An C<isl_ast_expr_id> represents an identifier.
9576 An C<isl_ast_expr_int> represents an integer value.
9578 Each type of expression has its own additional properties.
9580 #include <isl/ast.h>
9581 enum isl_ast_op_type isl_ast_expr_get_op_type(
9582 __isl_keep isl_ast_expr *expr);
9583 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
9584 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
9585 __isl_keep isl_ast_expr *expr, int pos);
9586 isl_stat isl_ast_expr_foreach_ast_op_type(
9587 __isl_keep isl_ast_expr *expr,
9588 isl_stat (*fn)(enum isl_ast_op_type type,
9589 void *user), void *user);
9590 isl_stat isl_ast_node_foreach_ast_op_type(
9591 __isl_keep isl_ast_node *node,
9592 isl_stat (*fn)(enum isl_ast_op_type type,
9593 void *user), void *user);
9595 C<isl_ast_expr_get_op_type> returns the type of the operation
9596 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
9597 arguments. C<isl_ast_expr_get_op_arg> returns the specified
9599 C<isl_ast_expr_foreach_ast_op_type> calls C<fn> for each distinct
9600 C<isl_ast_op_type> that appears in C<expr>.
9601 C<isl_ast_node_foreach_ast_op_type> does the same for each distinct
9602 C<isl_ast_op_type> that appears in C<node>.
9603 The operation type is one of the following.
9607 =item C<isl_ast_op_and>
9609 Logical I<and> of two arguments.
9610 Both arguments can be evaluated.
9612 =item C<isl_ast_op_and_then>
9614 Logical I<and> of two arguments.
9615 The second argument can only be evaluated if the first evaluates to true.
9617 =item C<isl_ast_op_or>
9619 Logical I<or> of two arguments.
9620 Both arguments can be evaluated.
9622 =item C<isl_ast_op_or_else>
9624 Logical I<or> of two arguments.
9625 The second argument can only be evaluated if the first evaluates to false.
9627 =item C<isl_ast_op_max>
9629 Maximum of two or more arguments.
9631 =item C<isl_ast_op_min>
9633 Minimum of two or more arguments.
9635 =item C<isl_ast_op_minus>
9639 =item C<isl_ast_op_add>
9641 Sum of two arguments.
9643 =item C<isl_ast_op_sub>
9645 Difference of two arguments.
9647 =item C<isl_ast_op_mul>
9649 Product of two arguments.
9651 =item C<isl_ast_op_div>
9653 Exact division. That is, the result is known to be an integer.
9655 =item C<isl_ast_op_fdiv_q>
9657 Result of integer division, rounded towards negative
9660 =item C<isl_ast_op_pdiv_q>
9662 Result of integer division, where dividend is known to be non-negative.
9664 =item C<isl_ast_op_pdiv_r>
9666 Remainder of integer division, where dividend is known to be non-negative.
9668 =item C<isl_ast_op_zdiv_r>
9670 Equal to zero iff the remainder on integer division is zero.
9672 =item C<isl_ast_op_cond>
9674 Conditional operator defined on three arguments.
9675 If the first argument evaluates to true, then the result
9676 is equal to the second argument. Otherwise, the result
9677 is equal to the third argument.
9678 The second and third argument may only be evaluated if
9679 the first argument evaluates to true and false, respectively.
9680 Corresponds to C<a ? b : c> in C.
9682 =item C<isl_ast_op_select>
9684 Conditional operator defined on three arguments.
9685 If the first argument evaluates to true, then the result
9686 is equal to the second argument. Otherwise, the result
9687 is equal to the third argument.
9688 The second and third argument may be evaluated independently
9689 of the value of the first argument.
9690 Corresponds to C<a * b + (1 - a) * c> in C.
9692 =item C<isl_ast_op_eq>
9696 =item C<isl_ast_op_le>
9698 Less than or equal relation.
9700 =item C<isl_ast_op_lt>
9704 =item C<isl_ast_op_ge>
9706 Greater than or equal relation.
9708 =item C<isl_ast_op_gt>
9710 Greater than relation.
9712 =item C<isl_ast_op_call>
9715 The number of arguments of the C<isl_ast_expr> is one more than
9716 the number of arguments in the function call, the first argument
9717 representing the function being called.
9719 =item C<isl_ast_op_access>
9722 The number of arguments of the C<isl_ast_expr> is one more than
9723 the number of index expressions in the array access, the first argument
9724 representing the array being accessed.
9726 =item C<isl_ast_op_member>
9729 This operation has two arguments, a structure and the name of
9730 the member of the structure being accessed.
9734 #include <isl/ast.h>
9735 __isl_give isl_id *isl_ast_expr_get_id(
9736 __isl_keep isl_ast_expr *expr);
9738 Return the identifier represented by the AST expression.
9740 #include <isl/ast.h>
9741 __isl_give isl_val *isl_ast_expr_get_val(
9742 __isl_keep isl_ast_expr *expr);
9744 Return the integer represented by the AST expression.
9746 =head3 Properties of ASTs
9748 #include <isl/ast.h>
9749 isl_bool isl_ast_expr_is_equal(
9750 __isl_keep isl_ast_expr *expr1,
9751 __isl_keep isl_ast_expr *expr2);
9753 Check if two C<isl_ast_expr>s are equal to each other.
9755 =head3 Manipulating and printing the AST
9757 AST nodes can be copied and freed using the following functions.
9759 #include <isl/ast.h>
9760 __isl_give isl_ast_node *isl_ast_node_copy(
9761 __isl_keep isl_ast_node *node);
9762 __isl_null isl_ast_node *isl_ast_node_free(
9763 __isl_take isl_ast_node *node);
9765 AST expressions can be copied and freed using the following functions.
9767 #include <isl/ast.h>
9768 __isl_give isl_ast_expr *isl_ast_expr_copy(
9769 __isl_keep isl_ast_expr *expr);
9770 __isl_null isl_ast_expr *isl_ast_expr_free(
9771 __isl_take isl_ast_expr *expr);
9773 New AST expressions can be created either directly or within
9774 the context of an C<isl_ast_build>.
9776 #include <isl/ast.h>
9777 __isl_give isl_ast_expr *isl_ast_expr_from_val(
9778 __isl_take isl_val *v);
9779 __isl_give isl_ast_expr *isl_ast_expr_from_id(
9780 __isl_take isl_id *id);
9781 __isl_give isl_ast_expr *isl_ast_expr_neg(
9782 __isl_take isl_ast_expr *expr);
9783 __isl_give isl_ast_expr *isl_ast_expr_address_of(
9784 __isl_take isl_ast_expr *expr);
9785 __isl_give isl_ast_expr *isl_ast_expr_add(
9786 __isl_take isl_ast_expr *expr1,
9787 __isl_take isl_ast_expr *expr2);
9788 __isl_give isl_ast_expr *isl_ast_expr_sub(
9789 __isl_take isl_ast_expr *expr1,
9790 __isl_take isl_ast_expr *expr2);
9791 __isl_give isl_ast_expr *isl_ast_expr_mul(
9792 __isl_take isl_ast_expr *expr1,
9793 __isl_take isl_ast_expr *expr2);
9794 __isl_give isl_ast_expr *isl_ast_expr_div(
9795 __isl_take isl_ast_expr *expr1,
9796 __isl_take isl_ast_expr *expr2);
9797 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
9798 __isl_take isl_ast_expr *expr1,
9799 __isl_take isl_ast_expr *expr2);
9800 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
9801 __isl_take isl_ast_expr *expr1,
9802 __isl_take isl_ast_expr *expr2);
9803 __isl_give isl_ast_expr *isl_ast_expr_and(
9804 __isl_take isl_ast_expr *expr1,
9805 __isl_take isl_ast_expr *expr2)
9806 __isl_give isl_ast_expr *isl_ast_expr_and_then(
9807 __isl_take isl_ast_expr *expr1,
9808 __isl_take isl_ast_expr *expr2)
9809 __isl_give isl_ast_expr *isl_ast_expr_or(
9810 __isl_take isl_ast_expr *expr1,
9811 __isl_take isl_ast_expr *expr2)
9812 __isl_give isl_ast_expr *isl_ast_expr_or_else(
9813 __isl_take isl_ast_expr *expr1,
9814 __isl_take isl_ast_expr *expr2)
9815 __isl_give isl_ast_expr *isl_ast_expr_eq(
9816 __isl_take isl_ast_expr *expr1,
9817 __isl_take isl_ast_expr *expr2);
9818 __isl_give isl_ast_expr *isl_ast_expr_le(
9819 __isl_take isl_ast_expr *expr1,
9820 __isl_take isl_ast_expr *expr2);
9821 __isl_give isl_ast_expr *isl_ast_expr_lt(
9822 __isl_take isl_ast_expr *expr1,
9823 __isl_take isl_ast_expr *expr2);
9824 __isl_give isl_ast_expr *isl_ast_expr_ge(
9825 __isl_take isl_ast_expr *expr1,
9826 __isl_take isl_ast_expr *expr2);
9827 __isl_give isl_ast_expr *isl_ast_expr_gt(
9828 __isl_take isl_ast_expr *expr1,
9829 __isl_take isl_ast_expr *expr2);
9830 __isl_give isl_ast_expr *isl_ast_expr_access(
9831 __isl_take isl_ast_expr *array,
9832 __isl_take isl_ast_expr_list *indices);
9833 __isl_give isl_ast_expr *isl_ast_expr_call(
9834 __isl_take isl_ast_expr *function,
9835 __isl_take isl_ast_expr_list *arguments);
9837 The function C<isl_ast_expr_address_of> can be applied to an
9838 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
9839 to represent the address of the C<isl_ast_expr_access>. The function
9840 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
9841 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
9843 #include <isl/ast_build.h>
9844 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
9845 __isl_keep isl_ast_build *build,
9846 __isl_take isl_set *set);
9847 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
9848 __isl_keep isl_ast_build *build,
9849 __isl_take isl_pw_aff *pa);
9850 __isl_give isl_ast_expr *
9851 isl_ast_build_access_from_pw_multi_aff(
9852 __isl_keep isl_ast_build *build,
9853 __isl_take isl_pw_multi_aff *pma);
9854 __isl_give isl_ast_expr *
9855 isl_ast_build_access_from_multi_pw_aff(
9856 __isl_keep isl_ast_build *build,
9857 __isl_take isl_multi_pw_aff *mpa);
9858 __isl_give isl_ast_expr *
9859 isl_ast_build_call_from_pw_multi_aff(
9860 __isl_keep isl_ast_build *build,
9861 __isl_take isl_pw_multi_aff *pma);
9862 __isl_give isl_ast_expr *
9863 isl_ast_build_call_from_multi_pw_aff(
9864 __isl_keep isl_ast_build *build,
9865 __isl_take isl_multi_pw_aff *mpa);
9868 the domains of C<pa>, C<mpa> and C<pma> should correspond
9869 to the schedule space of C<build>.
9870 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
9871 the function being called.
9872 If the accessed space is a nested relation, then it is taken
9873 to represent an access of the member specified by the range
9874 of this nested relation of the structure specified by the domain
9875 of the nested relation.
9877 The following functions can be used to modify an C<isl_ast_expr>.
9879 #include <isl/ast.h>
9880 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
9881 __isl_take isl_ast_expr *expr, int pos,
9882 __isl_take isl_ast_expr *arg);
9884 Replace the argument of C<expr> at position C<pos> by C<arg>.
9886 #include <isl/ast.h>
9887 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
9888 __isl_take isl_ast_expr *expr,
9889 __isl_take isl_id_to_ast_expr *id2expr);
9891 The function C<isl_ast_expr_substitute_ids> replaces the
9892 subexpressions of C<expr> of type C<isl_ast_expr_id>
9893 by the corresponding expression in C<id2expr>, if there is any.
9896 User specified data can be attached to an C<isl_ast_node> and obtained
9897 from the same C<isl_ast_node> using the following functions.
9899 #include <isl/ast.h>
9900 __isl_give isl_ast_node *isl_ast_node_set_annotation(
9901 __isl_take isl_ast_node *node,
9902 __isl_take isl_id *annotation);
9903 __isl_give isl_id *isl_ast_node_get_annotation(
9904 __isl_keep isl_ast_node *node);
9906 Basic printing can be performed using the following functions.
9908 #include <isl/ast.h>
9909 __isl_give isl_printer *isl_printer_print_ast_expr(
9910 __isl_take isl_printer *p,
9911 __isl_keep isl_ast_expr *expr);
9912 __isl_give isl_printer *isl_printer_print_ast_node(
9913 __isl_take isl_printer *p,
9914 __isl_keep isl_ast_node *node);
9915 __isl_give char *isl_ast_expr_to_str(
9916 __isl_keep isl_ast_expr *expr);
9917 __isl_give char *isl_ast_node_to_str(
9918 __isl_keep isl_ast_node *node);
9919 __isl_give char *isl_ast_expr_to_C_str(
9920 __isl_keep isl_ast_expr *expr);
9921 __isl_give char *isl_ast_node_to_C_str(
9922 __isl_keep isl_ast_node *node);
9924 The functions C<isl_ast_expr_to_C_str> and
9925 C<isl_ast_node_to_C_str> are convenience functions
9926 that return a string representation of the input in C format.
9928 More advanced printing can be performed using the following functions.
9930 #include <isl/ast.h>
9931 __isl_give isl_printer *isl_ast_op_type_set_print_name(
9932 __isl_take isl_printer *p,
9933 enum isl_ast_op_type type,
9934 __isl_keep const char *name);
9935 isl_stat isl_options_set_ast_print_macro_once(
9936 isl_ctx *ctx, int val);
9937 int isl_options_get_ast_print_macro_once(isl_ctx *ctx);
9938 __isl_give isl_printer *isl_ast_op_type_print_macro(
9939 enum isl_ast_op_type type,
9940 __isl_take isl_printer *p);
9941 __isl_give isl_printer *isl_ast_expr_print_macros(
9942 __isl_keep isl_ast_expr *expr,
9943 __isl_take isl_printer *p);
9944 __isl_give isl_printer *isl_ast_node_print_macros(
9945 __isl_keep isl_ast_node *node,
9946 __isl_take isl_printer *p);
9947 __isl_give isl_printer *isl_ast_node_print(
9948 __isl_keep isl_ast_node *node,
9949 __isl_take isl_printer *p,
9950 __isl_take isl_ast_print_options *options);
9951 __isl_give isl_printer *isl_ast_node_for_print(
9952 __isl_keep isl_ast_node *node,
9953 __isl_take isl_printer *p,
9954 __isl_take isl_ast_print_options *options);
9955 __isl_give isl_printer *isl_ast_node_if_print(
9956 __isl_keep isl_ast_node *node,
9957 __isl_take isl_printer *p,
9958 __isl_take isl_ast_print_options *options);
9960 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
9961 C<isl> may print out an AST that makes use of macros such
9962 as C<floord>, C<min> and C<max>.
9963 The names of these macros may be modified by a call
9964 to C<isl_ast_op_type_set_print_name>. The user-specified
9965 names are associated to the printer object.
9966 C<isl_ast_op_type_print_macro> prints out the macro
9967 corresponding to a specific C<isl_ast_op_type>.
9968 If the print-macro-once option is set, then a given macro definition
9969 is only printed once to any given printer object.
9970 C<isl_ast_expr_print_macros> scans the C<isl_ast_expr>
9971 for subexpressions where these macros would be used and prints
9972 out the required macro definitions.
9973 Essentially, C<isl_ast_expr_print_macros> calls
9974 C<isl_ast_expr_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
9975 as function argument.
9976 C<isl_ast_node_print_macros> does the same
9977 for expressions in its C<isl_ast_node> argument.
9978 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
9979 C<isl_ast_node_if_print> print an C<isl_ast_node>
9980 in C<ISL_FORMAT_C>, but allow for some extra control
9981 through an C<isl_ast_print_options> object.
9982 This object can be created using the following functions.
9984 #include <isl/ast.h>
9985 __isl_give isl_ast_print_options *
9986 isl_ast_print_options_alloc(isl_ctx *ctx);
9987 __isl_give isl_ast_print_options *
9988 isl_ast_print_options_copy(
9989 __isl_keep isl_ast_print_options *options);
9990 __isl_null isl_ast_print_options *
9991 isl_ast_print_options_free(
9992 __isl_take isl_ast_print_options *options);
9994 __isl_give isl_ast_print_options *
9995 isl_ast_print_options_set_print_user(
9996 __isl_take isl_ast_print_options *options,
9997 __isl_give isl_printer *(*print_user)(
9998 __isl_take isl_printer *p,
9999 __isl_take isl_ast_print_options *options,
10000 __isl_keep isl_ast_node *node, void *user),
10002 __isl_give isl_ast_print_options *
10003 isl_ast_print_options_set_print_for(
10004 __isl_take isl_ast_print_options *options,
10005 __isl_give isl_printer *(*print_for)(
10006 __isl_take isl_printer *p,
10007 __isl_take isl_ast_print_options *options,
10008 __isl_keep isl_ast_node *node, void *user),
10011 The callback set by C<isl_ast_print_options_set_print_user>
10012 is called whenever a node of type C<isl_ast_node_user> needs to
10014 The callback set by C<isl_ast_print_options_set_print_for>
10015 is called whenever a node of type C<isl_ast_node_for> needs to
10017 Note that C<isl_ast_node_for_print> will I<not> call the
10018 callback set by C<isl_ast_print_options_set_print_for> on the node
10019 on which C<isl_ast_node_for_print> is called, but only on nested
10020 nodes of type C<isl_ast_node_for>. It is therefore safe to
10021 call C<isl_ast_node_for_print> from within the callback set by
10022 C<isl_ast_print_options_set_print_for>.
10024 The following option determines the type to be used for iterators
10025 while printing the AST.
10027 isl_stat isl_options_set_ast_iterator_type(
10028 isl_ctx *ctx, const char *val);
10029 const char *isl_options_get_ast_iterator_type(
10032 The AST printer only prints body nodes as blocks if these
10033 blocks cannot be safely omitted.
10034 For example, a C<for> node with one body node will not be
10035 surrounded with braces in C<ISL_FORMAT_C>.
10036 A block will always be printed by setting the following option.
10038 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx,
10040 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
10044 #include <isl/ast_build.h>
10045 isl_stat isl_options_set_ast_build_atomic_upper_bound(
10046 isl_ctx *ctx, int val);
10047 int isl_options_get_ast_build_atomic_upper_bound(
10049 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
10051 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
10052 isl_stat isl_options_set_ast_build_detect_min_max(
10053 isl_ctx *ctx, int val);
10054 int isl_options_get_ast_build_detect_min_max(
10056 isl_stat isl_options_set_ast_build_exploit_nested_bounds(
10057 isl_ctx *ctx, int val);
10058 int isl_options_get_ast_build_exploit_nested_bounds(
10060 isl_stat isl_options_set_ast_build_group_coscheduled(
10061 isl_ctx *ctx, int val);
10062 int isl_options_get_ast_build_group_coscheduled(
10064 isl_stat isl_options_set_ast_build_scale_strides(
10065 isl_ctx *ctx, int val);
10066 int isl_options_get_ast_build_scale_strides(
10068 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx,
10070 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
10071 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx,
10073 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
10077 =item * ast_build_atomic_upper_bound
10079 Generate loop upper bounds that consist of the current loop iterator,
10080 an operator and an expression not involving the iterator.
10081 If this option is not set, then the current loop iterator may appear
10082 several times in the upper bound.
10083 For example, when this option is turned off, AST generation
10086 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
10090 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
10093 When the option is turned on, the following AST is generated
10095 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
10098 =item * ast_build_prefer_pdiv
10100 If this option is turned off, then the AST generation will
10101 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
10102 operators, but no C<isl_ast_op_pdiv_q> or
10103 C<isl_ast_op_pdiv_r> operators.
10104 If this option is turned on, then C<isl> will try to convert
10105 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
10106 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
10108 =item * ast_build_detect_min_max
10110 If this option is turned on, then C<isl> will try and detect
10111 min or max-expressions when building AST expressions from
10112 piecewise affine expressions.
10114 =item * ast_build_exploit_nested_bounds
10116 Simplify conditions based on bounds of nested for loops.
10117 In particular, remove conditions that are implied by the fact
10118 that one or more nested loops have at least one iteration,
10119 meaning that the upper bound is at least as large as the lower bound.
10120 For example, when this option is turned off, AST generation
10123 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
10129 for (int c0 = 0; c0 <= N; c0 += 1)
10130 for (int c1 = 0; c1 <= M; c1 += 1)
10133 When the option is turned on, the following AST is generated
10135 for (int c0 = 0; c0 <= N; c0 += 1)
10136 for (int c1 = 0; c1 <= M; c1 += 1)
10139 =item * ast_build_group_coscheduled
10141 If two domain elements are assigned the same schedule point, then
10142 they may be executed in any order and they may even appear in different
10143 loops. If this options is set, then the AST generator will make
10144 sure that coscheduled domain elements do not appear in separate parts
10145 of the AST. This is useful in case of nested AST generation
10146 if the outer AST generation is given only part of a schedule
10147 and the inner AST generation should handle the domains that are
10148 coscheduled by this initial part of the schedule together.
10149 For example if an AST is generated for a schedule
10151 { A[i] -> [0]; B[i] -> [0] }
10153 then the C<isl_ast_build_set_create_leaf> callback described
10154 below may get called twice, once for each domain.
10155 Setting this option ensures that the callback is only called once
10156 on both domains together.
10158 =item * ast_build_separation_bounds
10160 This option specifies which bounds to use during separation.
10161 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
10162 then all (possibly implicit) bounds on the current dimension will
10163 be used during separation.
10164 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
10165 then only those bounds that are explicitly available will
10166 be used during separation.
10168 =item * ast_build_scale_strides
10170 This option specifies whether the AST generator is allowed
10171 to scale down iterators of strided loops.
10173 =item * ast_build_allow_else
10175 This option specifies whether the AST generator is allowed
10176 to construct if statements with else branches.
10178 =item * ast_build_allow_or
10180 This option specifies whether the AST generator is allowed
10181 to construct if conditions with disjunctions.
10185 =head3 AST Generation Options (Schedule Tree)
10187 In case of AST construction from a schedule tree, the options
10188 that control how an AST is created from the individual schedule
10189 dimensions are stored in the band nodes of the tree
10190 (see L</"Schedule Trees">).
10192 In particular, a schedule dimension can be handled in four
10193 different ways, atomic, separate, unroll or the default.
10194 This loop AST generation type can be set using
10195 C<isl_schedule_node_band_member_set_ast_loop_type>.
10197 the first three can be selected by including a one-dimensional
10198 element with as value the position of the schedule dimension
10199 within the band and as name one of C<atomic>, C<separate>
10200 or C<unroll> in the options
10201 set by C<isl_schedule_node_band_set_ast_build_options>.
10202 Only one of these three may be specified for
10203 any given schedule dimension within a band node.
10204 If none of these is specified, then the default
10205 is used. The meaning of the options is as follows.
10211 When this option is specified, the AST generator will make
10212 sure that a given domains space only appears in a single
10213 loop at the specified level.
10215 For example, for the schedule tree
10217 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10219 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10220 options: "{ atomic[x] }"
10222 the following AST will be generated
10224 for (int c0 = 0; c0 <= 10; c0 += 1) {
10231 On the other hand, for the schedule tree
10233 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10235 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10236 options: "{ separate[x] }"
10238 the following AST will be generated
10242 for (int c0 = 1; c0 <= 9; c0 += 1) {
10249 If neither C<atomic> nor C<separate> is specified, then the AST generator
10250 may produce either of these two results or some intermediate form.
10254 When this option is specified, the AST generator will
10255 split the domain of the specified schedule dimension
10256 into pieces with a fixed set of statements for which
10257 instances need to be executed by the iterations in
10258 the schedule domain part. This option tends to avoid
10259 the generation of guards inside the corresponding loops.
10260 See also the C<atomic> option.
10264 When this option is specified, the AST generator will
10265 I<completely> unroll the corresponding schedule dimension.
10266 It is the responsibility of the user to ensure that such
10267 unrolling is possible.
10268 To obtain a partial unrolling, the user should apply an additional
10269 strip-mining to the schedule and fully unroll the inner schedule
10274 The C<isolate> option is a bit more involved. It allows the user
10275 to isolate a range of schedule dimension values from smaller and
10276 greater values. Additionally, the user may specify a different
10277 atomic/separate/unroll choice for the isolated part and the remaining
10278 parts. The typical use case of the C<isolate> option is to isolate
10279 full tiles from partial tiles.
10280 The part that needs to be isolated may depend on outer schedule dimensions.
10281 The option therefore needs to be able to reference those outer schedule
10282 dimensions. In particular, the space of the C<isolate> option is that
10283 of a wrapped map with as domain the flat product of all outer band nodes
10284 and as range the space of the current band node.
10285 The atomic/separate/unroll choice for the isolated part is determined
10286 by an option that lives in an unnamed wrapped space with as domain
10287 a zero-dimensional C<isolate> space and as range the regular
10288 C<atomic>, C<separate> or C<unroll> space.
10289 This option may also be set directly using
10290 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
10291 The atomic/separate/unroll choice for the remaining part is determined
10292 by the regular C<atomic>, C<separate> or C<unroll> option.
10293 Since the C<isolate> option references outer schedule dimensions,
10294 its use in a band node causes any tree containing the node
10295 to be considered anchored.
10297 As an example, consider the isolation of full tiles from partial tiles
10298 in a tiling of a triangular domain. The original schedule is as follows.
10300 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10302 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10303 { A[i,j] -> [floor(j/10)] }, \
10304 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10308 for (int c0 = 0; c0 <= 10; c0 += 1)
10309 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10310 for (int c2 = 10 * c0;
10311 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10312 for (int c3 = 10 * c1;
10313 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10316 Isolating the full tiles, we have the following input
10318 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10320 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10321 { A[i,j] -> [floor(j/10)] }, \
10322 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10323 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10324 10a+9+10b+9 <= 100 }"
10329 for (int c0 = 0; c0 <= 8; c0 += 1) {
10330 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10331 for (int c2 = 10 * c0;
10332 c2 <= 10 * c0 + 9; c2 += 1)
10333 for (int c3 = 10 * c1;
10334 c3 <= 10 * c1 + 9; c3 += 1)
10336 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10337 for (int c2 = 10 * c0;
10338 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10339 for (int c3 = 10 * c1;
10340 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10343 for (int c0 = 9; c0 <= 10; c0 += 1)
10344 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10345 for (int c2 = 10 * c0;
10346 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10347 for (int c3 = 10 * c1;
10348 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10352 We may then additionally unroll the innermost loop of the isolated part
10354 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10356 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10357 { A[i,j] -> [floor(j/10)] }, \
10358 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10359 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10360 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
10365 for (int c0 = 0; c0 <= 8; c0 += 1) {
10366 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10367 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
10369 A(c2, 10 * c1 + 1);
10370 A(c2, 10 * c1 + 2);
10371 A(c2, 10 * c1 + 3);
10372 A(c2, 10 * c1 + 4);
10373 A(c2, 10 * c1 + 5);
10374 A(c2, 10 * c1 + 6);
10375 A(c2, 10 * c1 + 7);
10376 A(c2, 10 * c1 + 8);
10377 A(c2, 10 * c1 + 9);
10379 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10380 for (int c2 = 10 * c0;
10381 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10382 for (int c3 = 10 * c1;
10383 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10386 for (int c0 = 9; c0 <= 10; c0 += 1)
10387 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10388 for (int c2 = 10 * c0;
10389 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10390 for (int c3 = 10 * c1;
10391 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10396 =head3 AST Generation Options (Schedule Map)
10398 In case of AST construction using
10399 C<isl_ast_build_node_from_schedule_map>, the options
10400 that control how an AST is created from the individual schedule
10401 dimensions are stored in the C<isl_ast_build>.
10402 They can be set using the following function.
10404 #include <isl/ast_build.h>
10405 __isl_give isl_ast_build *
10406 isl_ast_build_set_options(
10407 __isl_take isl_ast_build *control,
10408 __isl_take isl_union_map *options);
10410 The options are encoded in an C<isl_union_map>.
10411 The domain of this union relation refers to the schedule domain,
10412 i.e., the range of the schedule passed
10413 to C<isl_ast_build_node_from_schedule_map>.
10414 In the case of nested AST generation (see L</"Nested AST Generation">),
10415 the domain of C<options> should refer to the extra piece of the schedule.
10416 That is, it should be equal to the range of the wrapped relation in the
10417 range of the schedule.
10418 The range of the options can consist of elements in one or more spaces,
10419 the names of which determine the effect of the option.
10420 The values of the range typically also refer to the schedule dimension
10421 to which the option applies. In case of nested AST generation
10422 (see L</"Nested AST Generation">), these values refer to the position
10423 of the schedule dimension within the innermost AST generation.
10424 The constraints on the domain elements of
10425 the option should only refer to this dimension and earlier dimensions.
10426 We consider the following spaces.
10430 =item C<separation_class>
10432 B<This option has been deprecated. Use the isolate option on
10433 schedule trees instead.>
10435 This space is a wrapped relation between two one dimensional spaces.
10436 The input space represents the schedule dimension to which the option
10437 applies and the output space represents the separation class.
10438 While constructing a loop corresponding to the specified schedule
10439 dimension(s), the AST generator will try to generate separate loops
10440 for domain elements that are assigned different classes.
10441 If only some of the elements are assigned a class, then those elements
10442 that are not assigned any class will be treated as belonging to a class
10443 that is separate from the explicitly assigned classes.
10444 The typical use case for this option is to separate full tiles from
10446 The other options, described below, are applied after the separation
10449 As an example, consider the separation into full and partial tiles
10450 of a tiling of a triangular domain.
10451 Take, for example, the domain
10453 { A[i,j] : 0 <= i,j and i + j <= 100 }
10455 and a tiling into tiles of 10 by 10. The input to the AST generator
10456 is then the schedule
10458 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
10461 Without any options, the following AST is generated
10463 for (int c0 = 0; c0 <= 10; c0 += 1)
10464 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10465 for (int c2 = 10 * c0;
10466 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10468 for (int c3 = 10 * c1;
10469 c3 <= min(10 * c1 + 9, -c2 + 100);
10473 Separation into full and partial tiles can be obtained by assigning
10474 a class, say C<0>, to the full tiles. The full tiles are represented by those
10475 values of the first and second schedule dimensions for which there are
10476 values of the third and fourth dimensions to cover an entire tile.
10477 That is, we need to specify the following option
10479 { [a,b,c,d] -> separation_class[[0]->[0]] :
10480 exists b': 0 <= 10a,10b' and
10481 10a+9+10b'+9 <= 100;
10482 [a,b,c,d] -> separation_class[[1]->[0]] :
10483 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
10485 which simplifies to
10487 { [a, b, c, d] -> separation_class[[1] -> [0]] :
10488 a >= 0 and b >= 0 and b <= 8 - a;
10489 [a, b, c, d] -> separation_class[[0] -> [0]] :
10490 a >= 0 and a <= 8 }
10492 With this option, the generated AST is as follows
10495 for (int c0 = 0; c0 <= 8; c0 += 1) {
10496 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10497 for (int c2 = 10 * c0;
10498 c2 <= 10 * c0 + 9; c2 += 1)
10499 for (int c3 = 10 * c1;
10500 c3 <= 10 * c1 + 9; c3 += 1)
10502 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10503 for (int c2 = 10 * c0;
10504 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10506 for (int c3 = 10 * c1;
10507 c3 <= min(-c2 + 100, 10 * c1 + 9);
10511 for (int c0 = 9; c0 <= 10; c0 += 1)
10512 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10513 for (int c2 = 10 * c0;
10514 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10516 for (int c3 = 10 * c1;
10517 c3 <= min(10 * c1 + 9, -c2 + 100);
10524 This is a single-dimensional space representing the schedule dimension(s)
10525 to which ``separation'' should be applied. Separation tries to split
10526 a loop into several pieces if this can avoid the generation of guards
10528 See also the C<atomic> option.
10532 This is a single-dimensional space representing the schedule dimension(s)
10533 for which the domains should be considered ``atomic''. That is, the
10534 AST generator will make sure that any given domain space will only appear
10535 in a single loop at the specified level.
10537 Consider the following schedule
10539 { a[i] -> [i] : 0 <= i < 10;
10540 b[i] -> [i+1] : 0 <= i < 10 }
10542 If the following option is specified
10544 { [i] -> separate[x] }
10546 then the following AST will be generated
10550 for (int c0 = 1; c0 <= 9; c0 += 1) {
10557 If, on the other hand, the following option is specified
10559 { [i] -> atomic[x] }
10561 then the following AST will be generated
10563 for (int c0 = 0; c0 <= 10; c0 += 1) {
10570 If neither C<atomic> nor C<separate> is specified, then the AST generator
10571 may produce either of these two results or some intermediate form.
10575 This is a single-dimensional space representing the schedule dimension(s)
10576 that should be I<completely> unrolled.
10577 To obtain a partial unrolling, the user should apply an additional
10578 strip-mining to the schedule and fully unroll the inner loop.
10582 =head3 Fine-grained Control over AST Generation
10584 Besides specifying the constraints on the parameters,
10585 an C<isl_ast_build> object can be used to control
10586 various aspects of the AST generation process.
10587 In case of AST construction using
10588 C<isl_ast_build_node_from_schedule_map>,
10589 the most prominent way of control is through ``options'',
10590 as explained above.
10592 Additional control is available through the following functions.
10594 #include <isl/ast_build.h>
10595 __isl_give isl_ast_build *
10596 isl_ast_build_set_iterators(
10597 __isl_take isl_ast_build *control,
10598 __isl_take isl_id_list *iterators);
10600 The function C<isl_ast_build_set_iterators> allows the user to
10601 specify a list of iterator C<isl_id>s to be used as iterators.
10602 If the input schedule is injective, then
10603 the number of elements in this list should be as large as the dimension
10604 of the schedule space, but no direct correspondence should be assumed
10605 between dimensions and elements.
10606 If the input schedule is not injective, then an additional number
10607 of C<isl_id>s equal to the largest dimension of the input domains
10609 If the number of provided C<isl_id>s is insufficient, then additional
10610 names are automatically generated.
10612 #include <isl/ast_build.h>
10613 __isl_give isl_ast_build *
10614 isl_ast_build_set_create_leaf(
10615 __isl_take isl_ast_build *control,
10616 __isl_give isl_ast_node *(*fn)(
10617 __isl_take isl_ast_build *build,
10618 void *user), void *user);
10621 C<isl_ast_build_set_create_leaf> function allows for the
10622 specification of a callback that should be called whenever the AST
10623 generator arrives at an element of the schedule domain.
10624 The callback should return an AST node that should be inserted
10625 at the corresponding position of the AST. The default action (when
10626 the callback is not set) is to continue generating parts of the AST to scan
10627 all the domain elements associated to the schedule domain element
10628 and to insert user nodes, ``calling'' the domain element, for each of them.
10629 The C<build> argument contains the current state of the C<isl_ast_build>.
10630 To ease nested AST generation (see L</"Nested AST Generation">),
10631 all control information that is
10632 specific to the current AST generation such as the options and
10633 the callbacks has been removed from this C<isl_ast_build>.
10634 The callback would typically return the result of a nested
10635 AST generation or a
10636 user defined node created using the following function.
10638 #include <isl/ast.h>
10639 __isl_give isl_ast_node *isl_ast_node_alloc_user(
10640 __isl_take isl_ast_expr *expr);
10642 #include <isl/ast_build.h>
10643 __isl_give isl_ast_build *
10644 isl_ast_build_set_at_each_domain(
10645 __isl_take isl_ast_build *build,
10646 __isl_give isl_ast_node *(*fn)(
10647 __isl_take isl_ast_node *node,
10648 __isl_keep isl_ast_build *build,
10649 void *user), void *user);
10650 __isl_give isl_ast_build *
10651 isl_ast_build_set_before_each_for(
10652 __isl_take isl_ast_build *build,
10653 __isl_give isl_id *(*fn)(
10654 __isl_keep isl_ast_build *build,
10655 void *user), void *user);
10656 __isl_give isl_ast_build *
10657 isl_ast_build_set_after_each_for(
10658 __isl_take isl_ast_build *build,
10659 __isl_give isl_ast_node *(*fn)(
10660 __isl_take isl_ast_node *node,
10661 __isl_keep isl_ast_build *build,
10662 void *user), void *user);
10663 __isl_give isl_ast_build *
10664 isl_ast_build_set_before_each_mark(
10665 __isl_take isl_ast_build *build,
10666 isl_stat (*fn)(__isl_keep isl_id *mark,
10667 __isl_keep isl_ast_build *build,
10668 void *user), void *user);
10669 __isl_give isl_ast_build *
10670 isl_ast_build_set_after_each_mark(
10671 __isl_take isl_ast_build *build,
10672 __isl_give isl_ast_node *(*fn)(
10673 __isl_take isl_ast_node *node,
10674 __isl_keep isl_ast_build *build,
10675 void *user), void *user);
10677 The callback set by C<isl_ast_build_set_at_each_domain> will
10678 be called for each domain AST node.
10679 The callbacks set by C<isl_ast_build_set_before_each_for>
10680 and C<isl_ast_build_set_after_each_for> will be called
10681 for each for AST node. The first will be called in depth-first
10682 pre-order, while the second will be called in depth-first post-order.
10683 Since C<isl_ast_build_set_before_each_for> is called before the for
10684 node is actually constructed, it is only passed an C<isl_ast_build>.
10685 The returned C<isl_id> will be added as an annotation (using
10686 C<isl_ast_node_set_annotation>) to the constructed for node.
10687 In particular, if the user has also specified an C<after_each_for>
10688 callback, then the annotation can be retrieved from the node passed to
10689 that callback using C<isl_ast_node_get_annotation>.
10690 The callbacks set by C<isl_ast_build_set_before_each_mark>
10691 and C<isl_ast_build_set_after_each_mark> will be called for each
10692 mark AST node that is created, i.e., for each mark schedule node
10693 in the input schedule tree. The first will be called in depth-first
10694 pre-order, while the second will be called in depth-first post-order.
10695 Since the callback set by C<isl_ast_build_set_before_each_mark>
10696 is called before the mark AST node is actually constructed, it is passed
10697 the identifier of the mark node.
10698 All callbacks should C<NULL> (or -1) on failure.
10699 The given C<isl_ast_build> can be used to create new
10700 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
10701 or C<isl_ast_build_call_from_pw_multi_aff>.
10703 =head3 Nested AST Generation
10705 C<isl> allows the user to create an AST within the context
10706 of another AST. These nested ASTs are created using the
10707 same C<isl_ast_build_node_from_schedule_map> function that is used to create
10708 the outer AST. The C<build> argument should be an C<isl_ast_build>
10709 passed to a callback set by
10710 C<isl_ast_build_set_create_leaf>.
10711 The space of the range of the C<schedule> argument should refer
10712 to this build. In particular, the space should be a wrapped
10713 relation and the domain of this wrapped relation should be the
10714 same as that of the range of the schedule returned by
10715 C<isl_ast_build_get_schedule> below.
10716 In practice, the new schedule is typically
10717 created by calling C<isl_union_map_range_product> on the old schedule
10718 and some extra piece of the schedule.
10719 The space of the schedule domain is also available from
10720 the C<isl_ast_build>.
10722 #include <isl/ast_build.h>
10723 __isl_give isl_union_map *isl_ast_build_get_schedule(
10724 __isl_keep isl_ast_build *build);
10725 __isl_give isl_space *isl_ast_build_get_schedule_space(
10726 __isl_keep isl_ast_build *build);
10727 __isl_give isl_ast_build *isl_ast_build_restrict(
10728 __isl_take isl_ast_build *build,
10729 __isl_take isl_set *set);
10731 The C<isl_ast_build_get_schedule> function returns a (partial)
10732 schedule for the domains elements for which part of the AST still needs to
10733 be generated in the current build.
10734 In particular, the domain elements are mapped to those iterations of the loops
10735 enclosing the current point of the AST generation inside which
10736 the domain elements are executed.
10737 No direct correspondence between
10738 the input schedule and this schedule should be assumed.
10739 The space obtained from C<isl_ast_build_get_schedule_space> can be used
10740 to create a set for C<isl_ast_build_restrict> to intersect
10741 with the current build. In particular, the set passed to
10742 C<isl_ast_build_restrict> can have additional parameters.
10743 The ids of the set dimensions in the space returned by
10744 C<isl_ast_build_get_schedule_space> correspond to the
10745 iterators of the already generated loops.
10746 The user should not rely on the ids of the output dimensions
10747 of the relations in the union relation returned by
10748 C<isl_ast_build_get_schedule> having any particular value.
10750 =head1 Applications
10752 Although C<isl> is mainly meant to be used as a library,
10753 it also contains some basic applications that use some
10754 of the functionality of C<isl>.
10755 For applications that take one or more polytopes or polyhedra
10756 as input, this input may be specified in either the L<isl format>
10757 or the L<PolyLib format>.
10759 =head2 C<isl_polyhedron_sample>
10761 C<isl_polyhedron_sample> takes a polyhedron as input and prints
10762 an integer element of the polyhedron, if there is any.
10763 The first column in the output is the denominator and is always
10764 equal to 1. If the polyhedron contains no integer points,
10765 then a vector of length zero is printed.
10769 C<isl_pip> takes the same input as the C<example> program
10770 from the C<piplib> distribution, i.e., a set of constraints
10771 on the parameters, a line containing only -1 and finally a set
10772 of constraints on a parametric polyhedron.
10773 The coefficients of the parameters appear in the last columns
10774 (but before the final constant column).
10775 The output is the lexicographic minimum of the parametric polyhedron.
10776 As C<isl> currently does not have its own output format, the output
10777 is just a dump of the internal state.
10779 =head2 C<isl_polyhedron_minimize>
10781 C<isl_polyhedron_minimize> computes the minimum of some linear
10782 or affine objective function over the integer points in a polyhedron.
10783 If an affine objective function
10784 is given, then the constant should appear in the last column.
10786 =head2 C<isl_polytope_scan>
10788 Given a polytope, C<isl_polytope_scan> prints
10789 all integer points in the polytope.
10791 =head2 C<isl_codegen>
10793 Given either a schedule tree or a sequence consisting of
10794 a schedule map, a context set and an options relation,
10795 C<isl_codegen> prints out an AST that scans the domain elements
10796 of the schedule in the order of their image(s) taking into account
10797 the constraints in the context set.
10799 =head2 C<isl_schedule>
10801 Given an C<isl_schedule_constraints> object as input,
10802 C<isl_schedule> prints out a schedule that satisfies the given