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 is 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 * Objects of type C<isl_union_pw_multi_aff> can no longer contain
216 two or more C<isl_pw_multi_aff> objects with the same domain space.
218 =item * The function C<isl_union_pw_multi_aff_add> now consistently
219 computes the sum on the shared definition domain.
220 The function C<isl_union_pw_multi_aff_union_add> has been added
221 to compute the sum on the union of definition domains.
222 The original behavior of C<isl_union_pw_multi_aff_add> was
223 confused and is no longer available.
225 =item * Band forests have been replaced by schedule trees.
227 =item * The function C<isl_union_map_compute_flow> has been
228 replaced by the function C<isl_union_access_info_compute_flow>.
229 Note that the may dependence relation returned by
230 C<isl_union_flow_get_may_dependence> is the union of
231 the two dependence relations returned by
232 C<isl_union_map_compute_flow>. Similarly for the no source relations.
233 The function C<isl_union_map_compute_flow> is still available
234 for backward compatibility, but it will be removed in the future.
236 =item * The function C<isl_basic_set_drop_constraint> has been
239 =item * The function C<isl_ast_build_ast_from_schedule> has been
240 renamed to C<isl_ast_build_node_from_schedule_map>.
241 The original name is still available
242 for backward compatibility, but it will be removed in the future.
244 =item * The C<separation_class> AST generation option has been
247 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
248 have been renamed to C<isl_constraint_alloc_equality> and
249 C<isl_constraint_alloc_inequality>. The original names have been
250 kept for backward compatibility, but they will be removed in the future.
252 =item * The C<schedule_fuse> option has been replaced
253 by the C<schedule_serialize_sccs> option. The effect
254 of setting the C<schedule_fuse> option to C<ISL_SCHEDULE_FUSE_MIN>
255 is now obtained by turning on the C<schedule_serialize_sccs> option.
261 C<isl> is released under the MIT license.
265 Permission is hereby granted, free of charge, to any person obtaining a copy of
266 this software and associated documentation files (the "Software"), to deal in
267 the Software without restriction, including without limitation the rights to
268 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
269 of the Software, and to permit persons to whom the Software is furnished to do
270 so, subject to the following conditions:
272 The above copyright notice and this permission notice shall be included in all
273 copies or substantial portions of the Software.
275 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
276 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
277 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
278 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
279 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
280 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
285 Note that by default C<isl> requires C<GMP>, which is released
286 under the GNU Lesser General Public License (LGPL). This means
287 that code linked against C<isl> is also linked against LGPL code.
289 When configuring with C<--with-int=imath> or C<--with-int=imath-32>, C<isl>
290 will link against C<imath>, a library for exact integer arithmetic released
291 under the MIT license.
295 The source of C<isl> can be obtained either as a tarball
296 or from the git repository. Both are available from
297 L<http://freshmeat.net/projects/isl/>.
298 The installation process depends on how you obtained
301 =head2 Installation from the git repository
305 =item 1 Clone or update the repository
307 The first time the source is obtained, you need to clone
310 git clone git://repo.or.cz/isl.git
312 To obtain updates, you need to pull in the latest changes
316 =item 2 Optionally get C<imath> submodule
318 To build C<isl> with C<imath>, you need to obtain the C<imath>
319 submodule by running in the git source tree of C<isl>
324 This will fetch the required version of C<imath> in a subdirectory of C<isl>.
326 =item 2 Generate C<configure>
332 After performing the above steps, continue
333 with the L<Common installation instructions>.
335 =head2 Common installation instructions
339 =item 1 Obtain C<GMP>
341 By default, building C<isl> requires C<GMP>, including its headers files.
342 Your distribution may not provide these header files by default
343 and you may need to install a package called C<gmp-devel> or something
344 similar. Alternatively, C<GMP> can be built from
345 source, available from L<http://gmplib.org/>.
346 C<GMP> is not needed if you build C<isl> with C<imath>.
350 C<isl> uses the standard C<autoconf> C<configure> script.
355 optionally followed by some configure options.
356 A complete list of options can be obtained by running
360 Below we discuss some of the more common options.
366 Installation prefix for C<isl>
368 =item C<--with-int=[gmp|imath|imath-32]>
370 Select the integer library to be used by C<isl>, the default is C<gmp>.
371 With C<imath-32>, C<isl> will use 32 bit integers, but fall back to C<imath>
372 for values out of the 32 bit range. In most applications, C<isl> will run
373 fastest with the C<imath-32> option, followed by C<gmp> and C<imath>, the
376 =item C<--with-gmp-prefix>
378 Installation prefix for C<GMP> (architecture-independent files).
380 =item C<--with-gmp-exec-prefix>
382 Installation prefix for C<GMP> (architecture-dependent files).
390 =item 4 Install (optional)
396 =head1 Integer Set Library
398 =head2 Memory Management
400 Since a high-level operation on isl objects usually involves
401 several substeps and since the user is usually not interested in
402 the intermediate results, most functions that return a new object
403 will also release all the objects passed as arguments.
404 If the user still wants to use one or more of these arguments
405 after the function call, she should pass along a copy of the
406 object rather than the object itself.
407 The user is then responsible for making sure that the original
408 object gets used somewhere else or is explicitly freed.
410 The arguments and return values of all documented functions are
411 annotated to make clear which arguments are released and which
412 arguments are preserved. In particular, the following annotations
419 C<__isl_give> means that a new object is returned.
420 The user should make sure that the returned pointer is
421 used exactly once as a value for an C<__isl_take> argument.
422 In between, it can be used as a value for as many
423 C<__isl_keep> arguments as the user likes.
424 There is one exception, and that is the case where the
425 pointer returned is C<NULL>. Is this case, the user
426 is free to use it as an C<__isl_take> argument or not.
427 When applied to a C<char *>, the returned pointer needs to be
432 C<__isl_null> means that a C<NULL> value is returned.
436 C<__isl_take> means that the object the argument points to
437 is taken over by the function and may no longer be used
438 by the user as an argument to any other function.
439 The pointer value must be one returned by a function
440 returning an C<__isl_give> pointer.
441 If the user passes in a C<NULL> value, then this will
442 be treated as an error in the sense that the function will
443 not perform its usual operation. However, it will still
444 make sure that all the other C<__isl_take> arguments
449 C<__isl_keep> means that the function will only use the object
450 temporarily. After the function has finished, the user
451 can still use it as an argument to other functions.
452 A C<NULL> value will be treated in the same way as
453 a C<NULL> value for an C<__isl_take> argument.
454 This annotation may also be used on return values of
455 type C<const char *>, in which case the returned pointer should
456 not be freed by the user and is only valid until the object
457 from which it was derived is updated or freed.
461 =head2 Initialization
463 All manipulations of integer sets and relations occur within
464 the context of an C<isl_ctx>.
465 A given C<isl_ctx> can only be used within a single thread.
466 All arguments of a function are required to have been allocated
467 within the same context.
468 There are currently no functions available for moving an object
469 from one C<isl_ctx> to another C<isl_ctx>. This means that
470 there is currently no way of safely moving an object from one
471 thread to another, unless the whole C<isl_ctx> is moved.
473 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
474 freed using C<isl_ctx_free>.
475 All objects allocated within an C<isl_ctx> should be freed
476 before the C<isl_ctx> itself is freed.
478 isl_ctx *isl_ctx_alloc();
479 void isl_ctx_free(isl_ctx *ctx);
481 The user can impose a bound on the number of low-level I<operations>
482 that can be performed by an C<isl_ctx>. This bound can be set and
483 retrieved using the following functions. A bound of zero means that
484 no bound is imposed. The number of operations performed can be
485 reset using C<isl_ctx_reset_operations>. Note that the number
486 of low-level operations needed to perform a high-level computation
487 may differ significantly across different versions
488 of C<isl>, but it should be the same across different platforms
489 for the same version of C<isl>.
491 Warning: This feature is experimental. C<isl> has good support to abort and
492 bail out during the computation, but this feature may exercise error code paths
493 that are normally not used that much. Consequently, it is not unlikely that
494 hidden bugs will be exposed.
496 void isl_ctx_set_max_operations(isl_ctx *ctx,
497 unsigned long max_operations);
498 unsigned long isl_ctx_get_max_operations(isl_ctx *ctx);
499 void isl_ctx_reset_operations(isl_ctx *ctx);
501 In order to be able to create an object in the same context
502 as another object, most object types (described later in
503 this document) provide a function to obtain the context
504 in which the object was created.
507 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
508 isl_ctx *isl_multi_val_get_ctx(
509 __isl_keep isl_multi_val *mv);
512 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
514 #include <isl/local_space.h>
515 isl_ctx *isl_local_space_get_ctx(
516 __isl_keep isl_local_space *ls);
519 isl_ctx *isl_set_list_get_ctx(
520 __isl_keep isl_set_list *list);
523 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
524 isl_ctx *isl_multi_aff_get_ctx(
525 __isl_keep isl_multi_aff *maff);
526 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pa);
527 isl_ctx *isl_pw_multi_aff_get_ctx(
528 __isl_keep isl_pw_multi_aff *pma);
529 isl_ctx *isl_multi_pw_aff_get_ctx(
530 __isl_keep isl_multi_pw_aff *mpa);
531 isl_ctx *isl_union_pw_aff_get_ctx(
532 __isl_keep isl_union_pw_aff *upa);
533 isl_ctx *isl_union_pw_multi_aff_get_ctx(
534 __isl_keep isl_union_pw_multi_aff *upma);
535 isl_ctx *isl_multi_union_pw_aff_get_ctx(
536 __isl_keep isl_multi_union_pw_aff *mupa);
538 #include <isl/id_to_ast_expr.h>
539 isl_ctx *isl_id_to_ast_expr_get_ctx(
540 __isl_keep isl_id_to_ast_expr *id2expr);
542 #include <isl/point.h>
543 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
546 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
549 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
551 #include <isl/vertices.h>
552 isl_ctx *isl_vertices_get_ctx(
553 __isl_keep isl_vertices *vertices);
554 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
555 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
557 #include <isl/flow.h>
558 isl_ctx *isl_restriction_get_ctx(
559 __isl_keep isl_restriction *restr);
560 isl_ctx *isl_union_access_info_get_ctx(
561 __isl_keep isl_union_access_info *access);
562 isl_ctx *isl_union_flow_get_ctx(
563 __isl_keep isl_union_flow *flow);
565 #include <isl/schedule.h>
566 isl_ctx *isl_schedule_get_ctx(
567 __isl_keep isl_schedule *sched);
568 isl_ctx *isl_schedule_constraints_get_ctx(
569 __isl_keep isl_schedule_constraints *sc);
571 #include <isl/schedule_node.h>
572 isl_ctx *isl_schedule_node_get_ctx(
573 __isl_keep isl_schedule_node *node);
575 #include <isl/band.h>
576 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
578 #include <isl/ast_build.h>
579 isl_ctx *isl_ast_build_get_ctx(
580 __isl_keep isl_ast_build *build);
583 isl_ctx *isl_ast_expr_get_ctx(
584 __isl_keep isl_ast_expr *expr);
585 isl_ctx *isl_ast_node_get_ctx(
586 __isl_keep isl_ast_node *node);
590 C<isl> uses two special return types for functions that either return
591 a boolean or that in principle do not return anything.
592 In particular, the C<isl_bool> type has three possible values:
593 C<isl_bool_true> (a positive integer value), indicating I<true> or I<yes>;
594 C<isl_bool_false> (the integer value zero), indicating I<false> or I<no>; and
595 C<isl_bool_error> (a negative integer value), indicating that something
597 The C<isl_stat> type has two possible values:
598 C<isl_stat_ok> (the integer value zero), indicating a successful
600 C<isl_stat_error> (a negative integer value), indicating that something
602 See L</"Error Handling"> for more information on
603 C<isl_bool_error> and C<isl_stat_error>.
607 An C<isl_val> represents an integer value, a rational value
608 or one of three special values, infinity, negative infinity and NaN.
609 Some predefined values can be created using the following functions.
612 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
613 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
614 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
615 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
616 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
617 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
619 Specific integer values can be created using the following functions.
622 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
624 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
626 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
627 size_t n, size_t size, const void *chunks);
629 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
630 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
631 The least significant digit is assumed to be stored first.
633 Value objects can be copied and freed using the following functions.
636 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
637 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
639 They can be inspected using the following functions.
642 long isl_val_get_num_si(__isl_keep isl_val *v);
643 long isl_val_get_den_si(__isl_keep isl_val *v);
644 double isl_val_get_d(__isl_keep isl_val *v);
645 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
647 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
648 size_t size, void *chunks);
650 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
651 of C<size> bytes needed to store the absolute value of the
653 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
654 which is assumed to have been preallocated by the caller.
655 The least significant digit is stored first.
656 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
657 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
658 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
660 An C<isl_val> can be modified using the following function.
663 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
666 The following unary properties are defined on C<isl_val>s.
669 int isl_val_sgn(__isl_keep isl_val *v);
670 isl_bool isl_val_is_zero(__isl_keep isl_val *v);
671 isl_bool isl_val_is_one(__isl_keep isl_val *v);
672 isl_bool isl_val_is_negone(__isl_keep isl_val *v);
673 isl_bool isl_val_is_nonneg(__isl_keep isl_val *v);
674 isl_bool isl_val_is_nonpos(__isl_keep isl_val *v);
675 isl_bool isl_val_is_pos(__isl_keep isl_val *v);
676 isl_bool isl_val_is_neg(__isl_keep isl_val *v);
677 isl_bool isl_val_is_int(__isl_keep isl_val *v);
678 isl_bool isl_val_is_rat(__isl_keep isl_val *v);
679 isl_bool isl_val_is_nan(__isl_keep isl_val *v);
680 isl_bool isl_val_is_infty(__isl_keep isl_val *v);
681 isl_bool isl_val_is_neginfty(__isl_keep isl_val *v);
683 Note that the sign of NaN is undefined.
685 The following binary properties are defined on pairs of C<isl_val>s.
688 isl_bool isl_val_lt(__isl_keep isl_val *v1,
689 __isl_keep isl_val *v2);
690 isl_bool isl_val_le(__isl_keep isl_val *v1,
691 __isl_keep isl_val *v2);
692 isl_bool isl_val_gt(__isl_keep isl_val *v1,
693 __isl_keep isl_val *v2);
694 isl_bool isl_val_ge(__isl_keep isl_val *v1,
695 __isl_keep isl_val *v2);
696 isl_bool isl_val_eq(__isl_keep isl_val *v1,
697 __isl_keep isl_val *v2);
698 isl_bool isl_val_ne(__isl_keep isl_val *v1,
699 __isl_keep isl_val *v2);
700 isl_bool isl_val_abs_eq(__isl_keep isl_val *v1,
701 __isl_keep isl_val *v2);
703 The function C<isl_val_abs_eq> checks whether its two arguments
704 are equal in absolute value.
706 For integer C<isl_val>s we additionally have the following binary property.
709 isl_bool isl_val_is_divisible_by(__isl_keep isl_val *v1,
710 __isl_keep isl_val *v2);
712 An C<isl_val> can also be compared to an integer using the following
713 function. The result is undefined for NaN.
716 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
718 The following unary operations are available on C<isl_val>s.
721 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
722 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
723 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
724 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
725 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
726 __isl_give isl_val *isl_val_inv(__isl_take isl_val *v);
727 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
729 The following binary operations are available on C<isl_val>s.
732 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
733 __isl_take isl_val *v2);
734 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
735 __isl_take isl_val *v2);
736 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
737 __isl_take isl_val *v2);
738 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
740 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
741 __isl_take isl_val *v2);
742 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
744 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
745 __isl_take isl_val *v2);
746 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
748 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
749 __isl_take isl_val *v2);
751 On integer values, we additionally have the following operations.
754 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
755 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
756 __isl_take isl_val *v2);
757 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
758 __isl_take isl_val *v2);
759 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
760 __isl_take isl_val *v2, __isl_give isl_val **x,
761 __isl_give isl_val **y);
763 The function C<isl_val_gcdext> returns the greatest common divisor g
764 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
765 that C<*x> * C<v1> + C<*y> * C<v2> = g.
767 =head3 GMP specific functions
769 These functions are only available if C<isl> has been compiled with C<GMP>
772 Specific integer and rational values can be created from C<GMP> values using
773 the following functions.
775 #include <isl/val_gmp.h>
776 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
778 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
779 const mpz_t n, const mpz_t d);
781 The numerator and denominator of a rational value can be extracted as
782 C<GMP> values using the following functions.
784 #include <isl/val_gmp.h>
785 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
786 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
788 =head2 Sets and Relations
790 C<isl> uses six types of objects for representing sets and relations,
791 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
792 C<isl_union_set> and C<isl_union_map>.
793 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
794 can be described as a conjunction of affine constraints, while
795 C<isl_set> and C<isl_map> represent unions of
796 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
797 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
798 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
799 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
800 where spaces are considered different if they have a different number
801 of dimensions and/or different names (see L<"Spaces">).
802 The difference between sets and relations (maps) is that sets have
803 one set of variables, while relations have two sets of variables,
804 input variables and output variables.
806 =head2 Error Handling
808 C<isl> supports different ways to react in case a runtime error is triggered.
809 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
810 with two maps that have incompatible spaces. There are three possible ways
811 to react on error: to warn, to continue or to abort.
813 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
814 the last error in the corresponding C<isl_ctx> and the function in which the
815 error was triggered returns a value indicating that some error has
816 occurred. In case of functions returning a pointer, this value is
817 C<NULL>. In case of functions returning an C<isl_bool> or an
818 C<isl_stat>, this valus is C<isl_bool_error> or C<isl_stat_error>.
819 An error does not corrupt internal state,
820 such that isl can continue to be used. C<isl> also provides functions to
821 read the last error and to reset the memory that stores the last error. The
822 last error is only stored for information purposes. Its presence does not
823 change the behavior of C<isl>. Hence, resetting an error is not required to
824 continue to use isl, but only to observe new errors.
827 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
828 void isl_ctx_reset_error(isl_ctx *ctx);
830 Another option is to continue on error. This is similar to warn on error mode,
831 except that C<isl> does not print any warning. This allows a program to
832 implement its own error reporting.
834 The last option is to directly abort the execution of the program from within
835 the isl library. This makes it obviously impossible to recover from an error,
836 but it allows to directly spot the error location. By aborting on error,
837 debuggers break at the location the error occurred and can provide a stack
838 trace. Other tools that automatically provide stack traces on abort or that do
839 not want to continue execution after an error was triggered may also prefer to
842 The on error behavior of isl can be specified by calling
843 C<isl_options_set_on_error> or by setting the command line option
844 C<--isl-on-error>. Valid arguments for the function call are
845 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
846 choices for the command line option are C<warn>, C<continue> and C<abort>.
847 It is also possible to query the current error mode.
849 #include <isl/options.h>
850 isl_stat isl_options_set_on_error(isl_ctx *ctx, int val);
851 int isl_options_get_on_error(isl_ctx *ctx);
855 Identifiers are used to identify both individual dimensions
856 and tuples of dimensions. They consist of an optional name and an optional
857 user pointer. The name and the user pointer cannot both be C<NULL>, however.
858 Identifiers with the same name but different pointer values
859 are considered to be distinct.
860 Similarly, identifiers with different names but the same pointer value
861 are also considered to be distinct.
862 Equal identifiers are represented using the same object.
863 Pairs of identifiers can therefore be tested for equality using the
865 Identifiers can be constructed, copied, freed, inspected and printed
866 using the following functions.
869 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
870 __isl_keep const char *name, void *user);
871 __isl_give isl_id *isl_id_set_free_user(
872 __isl_take isl_id *id,
873 __isl_give void (*free_user)(void *user));
874 __isl_give isl_id *isl_id_copy(isl_id *id);
875 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
877 void *isl_id_get_user(__isl_keep isl_id *id);
878 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
880 __isl_give isl_printer *isl_printer_print_id(
881 __isl_take isl_printer *p, __isl_keep isl_id *id);
883 The callback set by C<isl_id_set_free_user> is called on the user
884 pointer when the last reference to the C<isl_id> is freed.
885 Note that C<isl_id_get_name> returns a pointer to some internal
886 data structure, so the result can only be used while the
887 corresponding C<isl_id> is alive.
891 Whenever a new set, relation or similar object is created from scratch,
892 the space in which it lives needs to be specified using an C<isl_space>.
893 Each space involves zero or more parameters and zero, one or two
894 tuples of set or input/output dimensions. The parameters and dimensions
895 are identified by an C<isl_dim_type> and a position.
896 The type C<isl_dim_param> refers to parameters,
897 the type C<isl_dim_set> refers to set dimensions (for spaces
898 with a single tuple of dimensions) and the types C<isl_dim_in>
899 and C<isl_dim_out> refer to input and output dimensions
900 (for spaces with two tuples of dimensions).
901 Local spaces (see L</"Local Spaces">) also contain dimensions
902 of type C<isl_dim_div>.
903 Note that parameters are only identified by their position within
904 a given object. Across different objects, parameters are (usually)
905 identified by their names or identifiers. Only unnamed parameters
906 are identified by their positions across objects. The use of unnamed
907 parameters is discouraged.
909 #include <isl/space.h>
910 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
911 unsigned nparam, unsigned n_in, unsigned n_out);
912 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
914 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
915 unsigned nparam, unsigned dim);
916 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
917 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
919 The space used for creating a parameter domain
920 needs to be created using C<isl_space_params_alloc>.
921 For other sets, the space
922 needs to be created using C<isl_space_set_alloc>, while
923 for a relation, the space
924 needs to be created using C<isl_space_alloc>.
926 To check whether a given space is that of a set or a map
927 or whether it is a parameter space, use these functions:
929 #include <isl/space.h>
930 isl_bool isl_space_is_params(__isl_keep isl_space *space);
931 isl_bool isl_space_is_set(__isl_keep isl_space *space);
932 isl_bool isl_space_is_map(__isl_keep isl_space *space);
934 Spaces can be compared using the following functions:
936 #include <isl/space.h>
937 isl_bool isl_space_is_equal(__isl_keep isl_space *space1,
938 __isl_keep isl_space *space2);
939 isl_bool isl_space_is_domain(__isl_keep isl_space *space1,
940 __isl_keep isl_space *space2);
941 isl_bool isl_space_is_range(__isl_keep isl_space *space1,
942 __isl_keep isl_space *space2);
943 isl_bool isl_space_tuple_is_equal(
944 __isl_keep isl_space *space1,
945 enum isl_dim_type type1,
946 __isl_keep isl_space *space2,
947 enum isl_dim_type type2);
949 C<isl_space_is_domain> checks whether the first argument is equal
950 to the domain of the second argument. This requires in particular that
951 the first argument is a set space and that the second argument
952 is a map space. C<isl_space_tuple_is_equal> checks whether the given
953 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
954 spaces are the same. That is, it checks if they have the same
955 identifier (if any), the same dimension and the same internal structure
958 It is often useful to create objects that live in the
959 same space as some other object. This can be accomplished
960 by creating the new objects
961 (see L</"Creating New Sets and Relations"> or
962 L</"Functions">) based on the space
963 of the original object.
966 __isl_give isl_space *isl_basic_set_get_space(
967 __isl_keep isl_basic_set *bset);
968 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
970 #include <isl/union_set.h>
971 __isl_give isl_space *isl_union_set_get_space(
972 __isl_keep isl_union_set *uset);
975 __isl_give isl_space *isl_basic_map_get_space(
976 __isl_keep isl_basic_map *bmap);
977 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
979 #include <isl/union_map.h>
980 __isl_give isl_space *isl_union_map_get_space(
981 __isl_keep isl_union_map *umap);
983 #include <isl/constraint.h>
984 __isl_give isl_space *isl_constraint_get_space(
985 __isl_keep isl_constraint *constraint);
987 #include <isl/polynomial.h>
988 __isl_give isl_space *isl_qpolynomial_get_domain_space(
989 __isl_keep isl_qpolynomial *qp);
990 __isl_give isl_space *isl_qpolynomial_get_space(
991 __isl_keep isl_qpolynomial *qp);
992 __isl_give isl_space *isl_qpolynomial_fold_get_space(
993 __isl_keep isl_qpolynomial_fold *fold);
994 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
995 __isl_keep isl_pw_qpolynomial *pwqp);
996 __isl_give isl_space *isl_pw_qpolynomial_get_space(
997 __isl_keep isl_pw_qpolynomial *pwqp);
998 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
999 __isl_keep isl_pw_qpolynomial_fold *pwf);
1000 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
1001 __isl_keep isl_pw_qpolynomial_fold *pwf);
1002 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
1003 __isl_keep isl_union_pw_qpolynomial *upwqp);
1004 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
1005 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1007 #include <isl/val.h>
1008 __isl_give isl_space *isl_multi_val_get_space(
1009 __isl_keep isl_multi_val *mv);
1011 #include <isl/aff.h>
1012 __isl_give isl_space *isl_aff_get_domain_space(
1013 __isl_keep isl_aff *aff);
1014 __isl_give isl_space *isl_aff_get_space(
1015 __isl_keep isl_aff *aff);
1016 __isl_give isl_space *isl_pw_aff_get_domain_space(
1017 __isl_keep isl_pw_aff *pwaff);
1018 __isl_give isl_space *isl_pw_aff_get_space(
1019 __isl_keep isl_pw_aff *pwaff);
1020 __isl_give isl_space *isl_multi_aff_get_domain_space(
1021 __isl_keep isl_multi_aff *maff);
1022 __isl_give isl_space *isl_multi_aff_get_space(
1023 __isl_keep isl_multi_aff *maff);
1024 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
1025 __isl_keep isl_pw_multi_aff *pma);
1026 __isl_give isl_space *isl_pw_multi_aff_get_space(
1027 __isl_keep isl_pw_multi_aff *pma);
1028 __isl_give isl_space *isl_union_pw_aff_get_space(
1029 __isl_keep isl_union_pw_aff *upa);
1030 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
1031 __isl_keep isl_union_pw_multi_aff *upma);
1032 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
1033 __isl_keep isl_multi_pw_aff *mpa);
1034 __isl_give isl_space *isl_multi_pw_aff_get_space(
1035 __isl_keep isl_multi_pw_aff *mpa);
1036 __isl_give isl_space *
1037 isl_multi_union_pw_aff_get_domain_space(
1038 __isl_keep isl_multi_union_pw_aff *mupa);
1039 __isl_give isl_space *
1040 isl_multi_union_pw_aff_get_space(
1041 __isl_keep isl_multi_union_pw_aff *mupa);
1043 #include <isl/point.h>
1044 __isl_give isl_space *isl_point_get_space(
1045 __isl_keep isl_point *pnt);
1047 The number of dimensions of a given type of space
1048 may be read off from a space or an object that lives
1049 in a space using the following functions.
1050 In case of C<isl_space_dim>, type may be
1051 C<isl_dim_param>, C<isl_dim_in> (only for relations),
1052 C<isl_dim_out> (only for relations), C<isl_dim_set>
1053 (only for sets) or C<isl_dim_all>.
1055 #include <isl/space.h>
1056 unsigned isl_space_dim(__isl_keep isl_space *space,
1057 enum isl_dim_type type);
1059 #include <isl/local_space.h>
1060 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1061 enum isl_dim_type type);
1063 #include <isl/set.h>
1064 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1065 enum isl_dim_type type);
1066 unsigned isl_set_dim(__isl_keep isl_set *set,
1067 enum isl_dim_type type);
1069 #include <isl/union_set.h>
1070 unsigned isl_union_set_dim(__isl_keep isl_union_set *uset,
1071 enum isl_dim_type type);
1073 #include <isl/map.h>
1074 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1075 enum isl_dim_type type);
1076 unsigned isl_map_dim(__isl_keep isl_map *map,
1077 enum isl_dim_type type);
1079 #include <isl/union_map.h>
1080 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1081 enum isl_dim_type type);
1083 #include <isl/val.h>
1084 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
1085 enum isl_dim_type type);
1087 #include <isl/aff.h>
1088 int isl_aff_dim(__isl_keep isl_aff *aff,
1089 enum isl_dim_type type);
1090 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1091 enum isl_dim_type type);
1092 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1093 enum isl_dim_type type);
1094 unsigned isl_pw_multi_aff_dim(
1095 __isl_keep isl_pw_multi_aff *pma,
1096 enum isl_dim_type type);
1097 unsigned isl_multi_pw_aff_dim(
1098 __isl_keep isl_multi_pw_aff *mpa,
1099 enum isl_dim_type type);
1100 unsigned isl_union_pw_aff_dim(
1101 __isl_keep isl_union_pw_aff *upa,
1102 enum isl_dim_type type);
1103 unsigned isl_union_pw_multi_aff_dim(
1104 __isl_keep isl_union_pw_multi_aff *upma,
1105 enum isl_dim_type type);
1106 unsigned isl_multi_union_pw_aff_dim(
1107 __isl_keep isl_multi_union_pw_aff *mupa,
1108 enum isl_dim_type type);
1110 #include <isl/polynomial.h>
1111 unsigned isl_union_pw_qpolynomial_dim(
1112 __isl_keep isl_union_pw_qpolynomial *upwqp,
1113 enum isl_dim_type type);
1114 unsigned isl_union_pw_qpolynomial_fold_dim(
1115 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1116 enum isl_dim_type type);
1118 Note that an C<isl_union_set>, an C<isl_union_map>,
1119 an C<isl_union_pw_multi_aff>,
1120 an C<isl_union_pw_qpolynomial> and
1121 an C<isl_union_pw_qpolynomial_fold>
1122 only have parameters.
1124 The identifiers or names of the individual dimensions of spaces
1125 may be set or read off using the following functions on spaces
1126 or objects that live in spaces.
1127 These functions are mostly useful to obtain the identifiers, positions
1128 or names of the parameters. Identifiers of individual dimensions are
1129 essentially only useful for printing. They are ignored by all other
1130 operations and may not be preserved across those operations.
1132 #include <isl/space.h>
1133 __isl_give isl_space *isl_space_set_dim_id(
1134 __isl_take isl_space *space,
1135 enum isl_dim_type type, unsigned pos,
1136 __isl_take isl_id *id);
1137 isl_bool isl_space_has_dim_id(__isl_keep isl_space *space,
1138 enum isl_dim_type type, unsigned pos);
1139 __isl_give isl_id *isl_space_get_dim_id(
1140 __isl_keep isl_space *space,
1141 enum isl_dim_type type, unsigned pos);
1142 __isl_give isl_space *isl_space_set_dim_name(
1143 __isl_take isl_space *space,
1144 enum isl_dim_type type, unsigned pos,
1145 __isl_keep const char *name);
1146 isl_bool isl_space_has_dim_name(__isl_keep isl_space *space,
1147 enum isl_dim_type type, unsigned pos);
1148 __isl_keep const char *isl_space_get_dim_name(
1149 __isl_keep isl_space *space,
1150 enum isl_dim_type type, unsigned pos);
1152 #include <isl/local_space.h>
1153 __isl_give isl_local_space *isl_local_space_set_dim_id(
1154 __isl_take isl_local_space *ls,
1155 enum isl_dim_type type, unsigned pos,
1156 __isl_take isl_id *id);
1157 isl_bool isl_local_space_has_dim_id(
1158 __isl_keep isl_local_space *ls,
1159 enum isl_dim_type type, unsigned pos);
1160 __isl_give isl_id *isl_local_space_get_dim_id(
1161 __isl_keep isl_local_space *ls,
1162 enum isl_dim_type type, unsigned pos);
1163 __isl_give isl_local_space *isl_local_space_set_dim_name(
1164 __isl_take isl_local_space *ls,
1165 enum isl_dim_type type, unsigned pos, const char *s);
1166 isl_bool isl_local_space_has_dim_name(
1167 __isl_keep isl_local_space *ls,
1168 enum isl_dim_type type, unsigned pos)
1169 const char *isl_local_space_get_dim_name(
1170 __isl_keep isl_local_space *ls,
1171 enum isl_dim_type type, unsigned pos);
1173 #include <isl/constraint.h>
1174 const char *isl_constraint_get_dim_name(
1175 __isl_keep isl_constraint *constraint,
1176 enum isl_dim_type type, unsigned pos);
1178 #include <isl/set.h>
1179 __isl_give isl_id *isl_basic_set_get_dim_id(
1180 __isl_keep isl_basic_set *bset,
1181 enum isl_dim_type type, unsigned pos);
1182 __isl_give isl_set *isl_set_set_dim_id(
1183 __isl_take isl_set *set, enum isl_dim_type type,
1184 unsigned pos, __isl_take isl_id *id);
1185 isl_bool isl_set_has_dim_id(__isl_keep isl_set *set,
1186 enum isl_dim_type type, unsigned pos);
1187 __isl_give isl_id *isl_set_get_dim_id(
1188 __isl_keep isl_set *set, enum isl_dim_type type,
1190 const char *isl_basic_set_get_dim_name(
1191 __isl_keep isl_basic_set *bset,
1192 enum isl_dim_type type, unsigned pos);
1193 isl_bool isl_set_has_dim_name(__isl_keep isl_set *set,
1194 enum isl_dim_type type, unsigned pos);
1195 const char *isl_set_get_dim_name(
1196 __isl_keep isl_set *set,
1197 enum isl_dim_type type, unsigned pos);
1199 #include <isl/map.h>
1200 __isl_give isl_map *isl_map_set_dim_id(
1201 __isl_take isl_map *map, enum isl_dim_type type,
1202 unsigned pos, __isl_take isl_id *id);
1203 isl_bool isl_basic_map_has_dim_id(
1204 __isl_keep isl_basic_map *bmap,
1205 enum isl_dim_type type, unsigned pos);
1206 isl_bool isl_map_has_dim_id(__isl_keep isl_map *map,
1207 enum isl_dim_type type, unsigned pos);
1208 __isl_give isl_id *isl_map_get_dim_id(
1209 __isl_keep isl_map *map, enum isl_dim_type type,
1211 __isl_give isl_id *isl_union_map_get_dim_id(
1212 __isl_keep isl_union_map *umap,
1213 enum isl_dim_type type, unsigned pos);
1214 const char *isl_basic_map_get_dim_name(
1215 __isl_keep isl_basic_map *bmap,
1216 enum isl_dim_type type, unsigned pos);
1217 isl_bool isl_map_has_dim_name(__isl_keep isl_map *map,
1218 enum isl_dim_type type, unsigned pos);
1219 const char *isl_map_get_dim_name(
1220 __isl_keep isl_map *map,
1221 enum isl_dim_type type, unsigned pos);
1223 #include <isl/val.h>
1224 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1225 __isl_take isl_multi_val *mv,
1226 enum isl_dim_type type, unsigned pos,
1227 __isl_take isl_id *id);
1228 __isl_give isl_id *isl_multi_val_get_dim_id(
1229 __isl_keep isl_multi_val *mv,
1230 enum isl_dim_type type, unsigned pos);
1231 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1232 __isl_take isl_multi_val *mv,
1233 enum isl_dim_type type, unsigned pos, const char *s);
1235 #include <isl/aff.h>
1236 __isl_give isl_aff *isl_aff_set_dim_id(
1237 __isl_take isl_aff *aff, enum isl_dim_type type,
1238 unsigned pos, __isl_take isl_id *id);
1239 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1240 __isl_take isl_multi_aff *maff,
1241 enum isl_dim_type type, unsigned pos,
1242 __isl_take isl_id *id);
1243 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1244 __isl_take isl_pw_aff *pma,
1245 enum isl_dim_type type, unsigned pos,
1246 __isl_take isl_id *id);
1247 __isl_give isl_multi_pw_aff *
1248 isl_multi_pw_aff_set_dim_id(
1249 __isl_take isl_multi_pw_aff *mpa,
1250 enum isl_dim_type type, unsigned pos,
1251 __isl_take isl_id *id);
1252 __isl_give isl_multi_union_pw_aff *
1253 isl_multi_union_pw_aff_set_dim_id(
1254 __isl_take isl_multi_union_pw_aff *mupa,
1255 enum isl_dim_type type, unsigned pos,
1256 __isl_take isl_id *id);
1257 __isl_give isl_id *isl_multi_aff_get_dim_id(
1258 __isl_keep isl_multi_aff *ma,
1259 enum isl_dim_type type, unsigned pos);
1260 isl_bool isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1261 enum isl_dim_type type, unsigned pos);
1262 __isl_give isl_id *isl_pw_aff_get_dim_id(
1263 __isl_keep isl_pw_aff *pa,
1264 enum isl_dim_type type, unsigned pos);
1265 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1266 __isl_keep isl_pw_multi_aff *pma,
1267 enum isl_dim_type type, unsigned pos);
1268 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1269 __isl_keep isl_multi_pw_aff *mpa,
1270 enum isl_dim_type type, unsigned pos);
1271 __isl_give isl_id *isl_multi_union_pw_aff_get_dim_id(
1272 __isl_keep isl_multi_union_pw_aff *mupa,
1273 enum isl_dim_type type, unsigned pos);
1274 __isl_give isl_aff *isl_aff_set_dim_name(
1275 __isl_take isl_aff *aff, enum isl_dim_type type,
1276 unsigned pos, const char *s);
1277 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1278 __isl_take isl_multi_aff *maff,
1279 enum isl_dim_type type, unsigned pos, const char *s);
1280 __isl_give isl_multi_pw_aff *
1281 isl_multi_pw_aff_set_dim_name(
1282 __isl_take isl_multi_pw_aff *mpa,
1283 enum isl_dim_type type, unsigned pos, const char *s);
1284 __isl_give isl_union_pw_aff *
1285 isl_union_pw_aff_set_dim_name(
1286 __isl_take isl_union_pw_aff *upa,
1287 enum isl_dim_type type, unsigned pos,
1289 __isl_give isl_union_pw_multi_aff *
1290 isl_union_pw_multi_aff_set_dim_name(
1291 __isl_take isl_union_pw_multi_aff *upma,
1292 enum isl_dim_type type, unsigned pos,
1294 __isl_give isl_multi_union_pw_aff *
1295 isl_multi_union_pw_aff_set_dim_name(
1296 __isl_take isl_multi_union_pw_aff *mupa,
1297 enum isl_dim_type type, unsigned pos,
1298 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1299 enum isl_dim_type type, unsigned pos);
1300 const char *isl_pw_aff_get_dim_name(
1301 __isl_keep isl_pw_aff *pa,
1302 enum isl_dim_type type, unsigned pos);
1303 const char *isl_pw_multi_aff_get_dim_name(
1304 __isl_keep isl_pw_multi_aff *pma,
1305 enum isl_dim_type type, unsigned pos);
1307 #include <isl/polynomial.h>
1308 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1309 __isl_take isl_qpolynomial *qp,
1310 enum isl_dim_type type, unsigned pos,
1312 __isl_give isl_pw_qpolynomial *
1313 isl_pw_qpolynomial_set_dim_name(
1314 __isl_take isl_pw_qpolynomial *pwqp,
1315 enum isl_dim_type type, unsigned pos,
1317 __isl_give isl_pw_qpolynomial_fold *
1318 isl_pw_qpolynomial_fold_set_dim_name(
1319 __isl_take isl_pw_qpolynomial_fold *pwf,
1320 enum isl_dim_type type, unsigned pos,
1322 __isl_give isl_union_pw_qpolynomial *
1323 isl_union_pw_qpolynomial_set_dim_name(
1324 __isl_take isl_union_pw_qpolynomial *upwqp,
1325 enum isl_dim_type type, unsigned pos,
1327 __isl_give isl_union_pw_qpolynomial_fold *
1328 isl_union_pw_qpolynomial_fold_set_dim_name(
1329 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1330 enum isl_dim_type type, unsigned pos,
1333 Note that C<isl_space_get_name> returns a pointer to some internal
1334 data structure, so the result can only be used while the
1335 corresponding C<isl_space> is alive.
1336 Also note that every function that operates on two sets or relations
1337 requires that both arguments have the same parameters. This also
1338 means that if one of the arguments has named parameters, then the
1339 other needs to have named parameters too and the names need to match.
1340 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1341 arguments may have different parameters (as long as they are named),
1342 in which case the result will have as parameters the union of the parameters of
1345 Given the identifier or name of a dimension (typically a parameter),
1346 its position can be obtained from the following functions.
1348 #include <isl/space.h>
1349 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1350 enum isl_dim_type type, __isl_keep isl_id *id);
1351 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1352 enum isl_dim_type type, const char *name);
1354 #include <isl/local_space.h>
1355 int isl_local_space_find_dim_by_name(
1356 __isl_keep isl_local_space *ls,
1357 enum isl_dim_type type, const char *name);
1359 #include <isl/val.h>
1360 int isl_multi_val_find_dim_by_id(
1361 __isl_keep isl_multi_val *mv,
1362 enum isl_dim_type type, __isl_keep isl_id *id);
1363 int isl_multi_val_find_dim_by_name(
1364 __isl_keep isl_multi_val *mv,
1365 enum isl_dim_type type, const char *name);
1367 #include <isl/set.h>
1368 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1369 enum isl_dim_type type, __isl_keep isl_id *id);
1370 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1371 enum isl_dim_type type, const char *name);
1373 #include <isl/map.h>
1374 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1375 enum isl_dim_type type, __isl_keep isl_id *id);
1376 int isl_basic_map_find_dim_by_name(
1377 __isl_keep isl_basic_map *bmap,
1378 enum isl_dim_type type, const char *name);
1379 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1380 enum isl_dim_type type, const char *name);
1381 int isl_union_map_find_dim_by_name(
1382 __isl_keep isl_union_map *umap,
1383 enum isl_dim_type type, const char *name);
1385 #include <isl/aff.h>
1386 int isl_multi_aff_find_dim_by_id(
1387 __isl_keep isl_multi_aff *ma,
1388 enum isl_dim_type type, __isl_keep isl_id *id);
1389 int isl_multi_pw_aff_find_dim_by_id(
1390 __isl_keep isl_multi_pw_aff *mpa,
1391 enum isl_dim_type type, __isl_keep isl_id *id);
1392 int isl_multi_union_pw_aff_find_dim_by_id(
1393 __isl_keep isl_union_multi_pw_aff *mupa,
1394 enum isl_dim_type type, __isl_keep isl_id *id);
1395 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff,
1396 enum isl_dim_type type, const char *name);
1397 int isl_multi_aff_find_dim_by_name(
1398 __isl_keep isl_multi_aff *ma,
1399 enum isl_dim_type type, const char *name);
1400 int isl_pw_aff_find_dim_by_name(__isl_keep isl_pw_aff *pa,
1401 enum isl_dim_type type, const char *name);
1402 int isl_multi_pw_aff_find_dim_by_name(
1403 __isl_keep isl_multi_pw_aff *mpa,
1404 enum isl_dim_type type, const char *name);
1405 int isl_pw_multi_aff_find_dim_by_name(
1406 __isl_keep isl_pw_multi_aff *pma,
1407 enum isl_dim_type type, const char *name);
1408 int isl_union_pw_aff_find_dim_by_name(
1409 __isl_keep isl_union_pw_aff *upa,
1410 enum isl_dim_type type, const char *name);
1411 int isl_union_pw_multi_aff_find_dim_by_name(
1412 __isl_keep isl_union_pw_multi_aff *upma,
1413 enum isl_dim_type type, const char *name);
1414 int isl_multi_union_pw_aff_find_dim_by_name(
1415 __isl_keep isl_multi_union_pw_aff *mupa,
1416 enum isl_dim_type type, const char *name);
1418 #include <isl/polynomial.h>
1419 int isl_pw_qpolynomial_find_dim_by_name(
1420 __isl_keep isl_pw_qpolynomial *pwqp,
1421 enum isl_dim_type type, const char *name);
1422 int isl_pw_qpolynomial_fold_find_dim_by_name(
1423 __isl_keep isl_pw_qpolynomial_fold *pwf,
1424 enum isl_dim_type type, const char *name);
1425 int isl_union_pw_qpolynomial_find_dim_by_name(
1426 __isl_keep isl_union_pw_qpolynomial *upwqp,
1427 enum isl_dim_type type, const char *name);
1428 int isl_union_pw_qpolynomial_fold_find_dim_by_name(
1429 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1430 enum isl_dim_type type, const char *name);
1432 The identifiers or names of entire spaces may be set or read off
1433 using the following functions.
1435 #include <isl/space.h>
1436 __isl_give isl_space *isl_space_set_tuple_id(
1437 __isl_take isl_space *space,
1438 enum isl_dim_type type, __isl_take isl_id *id);
1439 __isl_give isl_space *isl_space_reset_tuple_id(
1440 __isl_take isl_space *space, enum isl_dim_type type);
1441 isl_bool isl_space_has_tuple_id(
1442 __isl_keep isl_space *space,
1443 enum isl_dim_type type);
1444 __isl_give isl_id *isl_space_get_tuple_id(
1445 __isl_keep isl_space *space, enum isl_dim_type type);
1446 __isl_give isl_space *isl_space_set_tuple_name(
1447 __isl_take isl_space *space,
1448 enum isl_dim_type type, const char *s);
1449 isl_bool isl_space_has_tuple_name(
1450 __isl_keep isl_space *space,
1451 enum isl_dim_type type);
1452 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
1453 enum isl_dim_type type);
1455 #include <isl/local_space.h>
1456 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1457 __isl_take isl_local_space *ls,
1458 enum isl_dim_type type, __isl_take isl_id *id);
1460 #include <isl/set.h>
1461 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1462 __isl_take isl_basic_set *bset,
1463 __isl_take isl_id *id);
1464 __isl_give isl_set *isl_set_set_tuple_id(
1465 __isl_take isl_set *set, __isl_take isl_id *id);
1466 __isl_give isl_set *isl_set_reset_tuple_id(
1467 __isl_take isl_set *set);
1468 isl_bool isl_set_has_tuple_id(__isl_keep isl_set *set);
1469 __isl_give isl_id *isl_set_get_tuple_id(
1470 __isl_keep isl_set *set);
1471 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1472 __isl_take isl_basic_set *set, const char *s);
1473 __isl_give isl_set *isl_set_set_tuple_name(
1474 __isl_take isl_set *set, const char *s);
1475 const char *isl_basic_set_get_tuple_name(
1476 __isl_keep isl_basic_set *bset);
1477 isl_bool isl_set_has_tuple_name(__isl_keep isl_set *set);
1478 const char *isl_set_get_tuple_name(
1479 __isl_keep isl_set *set);
1481 #include <isl/map.h>
1482 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1483 __isl_take isl_basic_map *bmap,
1484 enum isl_dim_type type, __isl_take isl_id *id);
1485 __isl_give isl_map *isl_map_set_tuple_id(
1486 __isl_take isl_map *map, enum isl_dim_type type,
1487 __isl_take isl_id *id);
1488 __isl_give isl_map *isl_map_reset_tuple_id(
1489 __isl_take isl_map *map, enum isl_dim_type type);
1490 isl_bool isl_map_has_tuple_id(__isl_keep isl_map *map,
1491 enum isl_dim_type type);
1492 __isl_give isl_id *isl_map_get_tuple_id(
1493 __isl_keep isl_map *map, enum isl_dim_type type);
1494 __isl_give isl_map *isl_map_set_tuple_name(
1495 __isl_take isl_map *map,
1496 enum isl_dim_type type, const char *s);
1497 const char *isl_basic_map_get_tuple_name(
1498 __isl_keep isl_basic_map *bmap,
1499 enum isl_dim_type type);
1500 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1501 __isl_take isl_basic_map *bmap,
1502 enum isl_dim_type type, const char *s);
1503 isl_bool isl_map_has_tuple_name(__isl_keep isl_map *map,
1504 enum isl_dim_type type);
1505 const char *isl_map_get_tuple_name(
1506 __isl_keep isl_map *map,
1507 enum isl_dim_type type);
1509 #include <isl/val.h>
1510 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1511 __isl_take isl_multi_val *mv,
1512 enum isl_dim_type type, __isl_take isl_id *id);
1513 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1514 __isl_take isl_multi_val *mv,
1515 enum isl_dim_type type);
1516 isl_bool isl_multi_val_has_tuple_id(
1517 __isl_keep isl_multi_val *mv,
1518 enum isl_dim_type type);
1519 __isl_give isl_id *isl_multi_val_get_tuple_id(
1520 __isl_keep isl_multi_val *mv,
1521 enum isl_dim_type type);
1522 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1523 __isl_take isl_multi_val *mv,
1524 enum isl_dim_type type, const char *s);
1525 const char *isl_multi_val_get_tuple_name(
1526 __isl_keep isl_multi_val *mv,
1527 enum isl_dim_type type);
1529 #include <isl/aff.h>
1530 __isl_give isl_aff *isl_aff_set_tuple_id(
1531 __isl_take isl_aff *aff,
1532 enum isl_dim_type type, __isl_take isl_id *id);
1533 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1534 __isl_take isl_multi_aff *maff,
1535 enum isl_dim_type type, __isl_take isl_id *id);
1536 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1537 __isl_take isl_pw_aff *pwaff,
1538 enum isl_dim_type type, __isl_take isl_id *id);
1539 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1540 __isl_take isl_pw_multi_aff *pma,
1541 enum isl_dim_type type, __isl_take isl_id *id);
1542 __isl_give isl_multi_union_pw_aff *
1543 isl_multi_union_pw_aff_set_tuple_id(
1544 __isl_take isl_multi_union_pw_aff *mupa,
1545 enum isl_dim_type type, __isl_take isl_id *id);
1546 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1547 __isl_take isl_multi_aff *ma,
1548 enum isl_dim_type type);
1549 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1550 __isl_take isl_pw_aff *pa,
1551 enum isl_dim_type type);
1552 __isl_give isl_multi_pw_aff *
1553 isl_multi_pw_aff_reset_tuple_id(
1554 __isl_take isl_multi_pw_aff *mpa,
1555 enum isl_dim_type type);
1556 __isl_give isl_pw_multi_aff *
1557 isl_pw_multi_aff_reset_tuple_id(
1558 __isl_take isl_pw_multi_aff *pma,
1559 enum isl_dim_type type);
1560 __isl_give isl_multi_union_pw_aff *
1561 isl_multi_union_pw_aff_reset_tuple_id(
1562 __isl_take isl_multi_union_pw_aff *mupa,
1563 enum isl_dim_type type);
1564 isl_bool isl_multi_aff_has_tuple_id(
1565 __isl_keep isl_multi_aff *ma,
1566 enum isl_dim_type type);
1567 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1568 __isl_keep isl_multi_aff *ma,
1569 enum isl_dim_type type);
1570 isl_bool isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1571 enum isl_dim_type type);
1572 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1573 __isl_keep isl_pw_aff *pa,
1574 enum isl_dim_type type);
1575 isl_bool isl_pw_multi_aff_has_tuple_id(
1576 __isl_keep isl_pw_multi_aff *pma,
1577 enum isl_dim_type type);
1578 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1579 __isl_keep isl_pw_multi_aff *pma,
1580 enum isl_dim_type type);
1581 isl_bool isl_multi_pw_aff_has_tuple_id(
1582 __isl_keep isl_multi_pw_aff *mpa,
1583 enum isl_dim_type type);
1584 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1585 __isl_keep isl_multi_pw_aff *mpa,
1586 enum isl_dim_type type);
1587 isl_bool isl_multi_union_pw_aff_has_tuple_id(
1588 __isl_keep isl_multi_union_pw_aff *mupa,
1589 enum isl_dim_type type);
1590 __isl_give isl_id *isl_multi_union_pw_aff_get_tuple_id(
1591 __isl_keep isl_multi_union_pw_aff *mupa,
1592 enum isl_dim_type type);
1593 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1594 __isl_take isl_multi_aff *maff,
1595 enum isl_dim_type type, const char *s);
1596 __isl_give isl_multi_pw_aff *
1597 isl_multi_pw_aff_set_tuple_name(
1598 __isl_take isl_multi_pw_aff *mpa,
1599 enum isl_dim_type type, const char *s);
1600 __isl_give isl_multi_union_pw_aff *
1601 isl_multi_union_pw_aff_set_tuple_name(
1602 __isl_take isl_multi_union_pw_aff *mupa,
1603 enum isl_dim_type type, const char *s);
1604 const char *isl_multi_aff_get_tuple_name(
1605 __isl_keep isl_multi_aff *multi,
1606 enum isl_dim_type type);
1607 isl_bool isl_pw_multi_aff_has_tuple_name(
1608 __isl_keep isl_pw_multi_aff *pma,
1609 enum isl_dim_type type);
1610 const char *isl_pw_multi_aff_get_tuple_name(
1611 __isl_keep isl_pw_multi_aff *pma,
1612 enum isl_dim_type type);
1613 const char *isl_multi_union_pw_aff_get_tuple_name(
1614 __isl_keep isl_multi_union_pw_aff *mupa,
1615 enum isl_dim_type type);
1617 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1618 or C<isl_dim_set>. As with C<isl_space_get_name>,
1619 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1621 Binary operations require the corresponding spaces of their arguments
1622 to have the same name.
1624 To keep the names of all parameters and tuples, but reset the user pointers
1625 of all the corresponding identifiers, use the following function.
1627 #include <isl/space.h>
1628 __isl_give isl_space *isl_space_reset_user(
1629 __isl_take isl_space *space);
1631 #include <isl/set.h>
1632 __isl_give isl_set *isl_set_reset_user(
1633 __isl_take isl_set *set);
1635 #include <isl/map.h>
1636 __isl_give isl_map *isl_map_reset_user(
1637 __isl_take isl_map *map);
1639 #include <isl/union_set.h>
1640 __isl_give isl_union_set *isl_union_set_reset_user(
1641 __isl_take isl_union_set *uset);
1643 #include <isl/union_map.h>
1644 __isl_give isl_union_map *isl_union_map_reset_user(
1645 __isl_take isl_union_map *umap);
1647 #include <isl/val.h>
1648 __isl_give isl_multi_val *isl_multi_val_reset_user(
1649 __isl_take isl_multi_val *mv);
1651 #include <isl/aff.h>
1652 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1653 __isl_take isl_multi_aff *ma);
1654 __isl_give isl_pw_aff *isl_pw_aff_reset_user(
1655 __isl_take isl_pw_aff *pa);
1656 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1657 __isl_take isl_multi_pw_aff *mpa);
1658 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_reset_user(
1659 __isl_take isl_pw_multi_aff *pma);
1660 __isl_give isl_union_pw_aff *isl_union_pw_aff_reset_user(
1661 __isl_take isl_union_pw_aff *upa);
1662 __isl_give isl_multi_union_pw_aff *
1663 isl_multi_union_pw_aff_reset_user(
1664 __isl_take isl_multi_union_pw_aff *mupa);
1665 __isl_give isl_union_pw_multi_aff *
1666 isl_union_pw_multi_aff_reset_user(
1667 __isl_take isl_union_pw_multi_aff *upma);
1669 #include <isl/polynomial.h>
1670 __isl_give isl_pw_qpolynomial *
1671 isl_pw_qpolynomial_reset_user(
1672 __isl_take isl_pw_qpolynomial *pwqp);
1673 __isl_give isl_union_pw_qpolynomial *
1674 isl_union_pw_qpolynomial_reset_user(
1675 __isl_take isl_union_pw_qpolynomial *upwqp);
1676 __isl_give isl_pw_qpolynomial_fold *
1677 isl_pw_qpolynomial_fold_reset_user(
1678 __isl_take isl_pw_qpolynomial_fold *pwf);
1679 __isl_give isl_union_pw_qpolynomial_fold *
1680 isl_union_pw_qpolynomial_fold_reset_user(
1681 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1683 Spaces can be nested. In particular, the domain of a set or
1684 the domain or range of a relation can be a nested relation.
1685 This process is also called I<wrapping>.
1686 The functions for detecting, constructing and deconstructing
1687 such nested spaces can be found in the wrapping properties
1688 of L</"Unary Properties">, the wrapping operations
1689 of L</"Unary Operations"> and the Cartesian product operations
1690 of L</"Basic Operations">.
1692 Spaces can be created from other spaces
1693 using the functions described in L</"Unary Operations">
1694 and L</"Binary Operations">.
1698 A local space is essentially a space with
1699 zero or more existentially quantified variables.
1700 The local space of various objects can be obtained
1701 using the following functions.
1703 #include <isl/constraint.h>
1704 __isl_give isl_local_space *isl_constraint_get_local_space(
1705 __isl_keep isl_constraint *constraint);
1707 #include <isl/set.h>
1708 __isl_give isl_local_space *isl_basic_set_get_local_space(
1709 __isl_keep isl_basic_set *bset);
1711 #include <isl/map.h>
1712 __isl_give isl_local_space *isl_basic_map_get_local_space(
1713 __isl_keep isl_basic_map *bmap);
1715 #include <isl/aff.h>
1716 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1717 __isl_keep isl_aff *aff);
1718 __isl_give isl_local_space *isl_aff_get_local_space(
1719 __isl_keep isl_aff *aff);
1721 A new local space can be created from a space using
1723 #include <isl/local_space.h>
1724 __isl_give isl_local_space *isl_local_space_from_space(
1725 __isl_take isl_space *space);
1727 They can be inspected, modified, copied and freed using the following functions.
1729 #include <isl/local_space.h>
1730 isl_bool isl_local_space_is_params(
1731 __isl_keep isl_local_space *ls);
1732 isl_bool isl_local_space_is_set(
1733 __isl_keep isl_local_space *ls);
1734 __isl_give isl_space *isl_local_space_get_space(
1735 __isl_keep isl_local_space *ls);
1736 __isl_give isl_aff *isl_local_space_get_div(
1737 __isl_keep isl_local_space *ls, int pos);
1738 __isl_give isl_local_space *isl_local_space_copy(
1739 __isl_keep isl_local_space *ls);
1740 __isl_null isl_local_space *isl_local_space_free(
1741 __isl_take isl_local_space *ls);
1743 Note that C<isl_local_space_get_div> can only be used on local spaces
1746 Two local spaces can be compared using
1748 isl_bool isl_local_space_is_equal(
1749 __isl_keep isl_local_space *ls1,
1750 __isl_keep isl_local_space *ls2);
1752 Local spaces can be created from other local spaces
1753 using the functions described in L</"Unary Operations">
1754 and L</"Binary Operations">.
1756 =head2 Creating New Sets and Relations
1758 C<isl> has functions for creating some standard sets and relations.
1762 =item * Empty sets and relations
1764 __isl_give isl_basic_set *isl_basic_set_empty(
1765 __isl_take isl_space *space);
1766 __isl_give isl_basic_map *isl_basic_map_empty(
1767 __isl_take isl_space *space);
1768 __isl_give isl_set *isl_set_empty(
1769 __isl_take isl_space *space);
1770 __isl_give isl_map *isl_map_empty(
1771 __isl_take isl_space *space);
1772 __isl_give isl_union_set *isl_union_set_empty(
1773 __isl_take isl_space *space);
1774 __isl_give isl_union_map *isl_union_map_empty(
1775 __isl_take isl_space *space);
1777 For C<isl_union_set>s and C<isl_union_map>s, the space
1778 is only used to specify the parameters.
1780 =item * Universe sets and relations
1782 __isl_give isl_basic_set *isl_basic_set_universe(
1783 __isl_take isl_space *space);
1784 __isl_give isl_basic_map *isl_basic_map_universe(
1785 __isl_take isl_space *space);
1786 __isl_give isl_set *isl_set_universe(
1787 __isl_take isl_space *space);
1788 __isl_give isl_map *isl_map_universe(
1789 __isl_take isl_space *space);
1790 __isl_give isl_union_set *isl_union_set_universe(
1791 __isl_take isl_union_set *uset);
1792 __isl_give isl_union_map *isl_union_map_universe(
1793 __isl_take isl_union_map *umap);
1795 The sets and relations constructed by the functions above
1796 contain all integer values, while those constructed by the
1797 functions below only contain non-negative values.
1799 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1800 __isl_take isl_space *space);
1801 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1802 __isl_take isl_space *space);
1803 __isl_give isl_set *isl_set_nat_universe(
1804 __isl_take isl_space *space);
1805 __isl_give isl_map *isl_map_nat_universe(
1806 __isl_take isl_space *space);
1808 =item * Identity relations
1810 __isl_give isl_basic_map *isl_basic_map_identity(
1811 __isl_take isl_space *space);
1812 __isl_give isl_map *isl_map_identity(
1813 __isl_take isl_space *space);
1815 The number of input and output dimensions in C<space> needs
1818 =item * Lexicographic order
1820 __isl_give isl_map *isl_map_lex_lt(
1821 __isl_take isl_space *set_space);
1822 __isl_give isl_map *isl_map_lex_le(
1823 __isl_take isl_space *set_space);
1824 __isl_give isl_map *isl_map_lex_gt(
1825 __isl_take isl_space *set_space);
1826 __isl_give isl_map *isl_map_lex_ge(
1827 __isl_take isl_space *set_space);
1828 __isl_give isl_map *isl_map_lex_lt_first(
1829 __isl_take isl_space *space, unsigned n);
1830 __isl_give isl_map *isl_map_lex_le_first(
1831 __isl_take isl_space *space, unsigned n);
1832 __isl_give isl_map *isl_map_lex_gt_first(
1833 __isl_take isl_space *space, unsigned n);
1834 __isl_give isl_map *isl_map_lex_ge_first(
1835 __isl_take isl_space *space, unsigned n);
1837 The first four functions take a space for a B<set>
1838 and return relations that express that the elements in the domain
1839 are lexicographically less
1840 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1841 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1842 than the elements in the range.
1843 The last four functions take a space for a map
1844 and return relations that express that the first C<n> dimensions
1845 in the domain are lexicographically less
1846 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1847 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1848 than the first C<n> dimensions in the range.
1852 A basic set or relation can be converted to a set or relation
1853 using the following functions.
1855 __isl_give isl_set *isl_set_from_basic_set(
1856 __isl_take isl_basic_set *bset);
1857 __isl_give isl_map *isl_map_from_basic_map(
1858 __isl_take isl_basic_map *bmap);
1860 Sets and relations can be converted to union sets and relations
1861 using the following functions.
1863 __isl_give isl_union_set *isl_union_set_from_basic_set(
1864 __isl_take isl_basic_set *bset);
1865 __isl_give isl_union_map *isl_union_map_from_basic_map(
1866 __isl_take isl_basic_map *bmap);
1867 __isl_give isl_union_set *isl_union_set_from_set(
1868 __isl_take isl_set *set);
1869 __isl_give isl_union_map *isl_union_map_from_map(
1870 __isl_take isl_map *map);
1872 The inverse conversions below can only be used if the input
1873 union set or relation is known to contain elements in exactly one
1876 __isl_give isl_set *isl_set_from_union_set(
1877 __isl_take isl_union_set *uset);
1878 __isl_give isl_map *isl_map_from_union_map(
1879 __isl_take isl_union_map *umap);
1881 Sets and relations can be copied and freed again using the following
1884 __isl_give isl_basic_set *isl_basic_set_copy(
1885 __isl_keep isl_basic_set *bset);
1886 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1887 __isl_give isl_union_set *isl_union_set_copy(
1888 __isl_keep isl_union_set *uset);
1889 __isl_give isl_basic_map *isl_basic_map_copy(
1890 __isl_keep isl_basic_map *bmap);
1891 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1892 __isl_give isl_union_map *isl_union_map_copy(
1893 __isl_keep isl_union_map *umap);
1894 __isl_null isl_basic_set *isl_basic_set_free(
1895 __isl_take isl_basic_set *bset);
1896 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1897 __isl_null isl_union_set *isl_union_set_free(
1898 __isl_take isl_union_set *uset);
1899 __isl_null isl_basic_map *isl_basic_map_free(
1900 __isl_take isl_basic_map *bmap);
1901 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1902 __isl_null isl_union_map *isl_union_map_free(
1903 __isl_take isl_union_map *umap);
1905 Other sets and relations can be constructed by starting
1906 from a universe set or relation, adding equality and/or
1907 inequality constraints and then projecting out the
1908 existentially quantified variables, if any.
1909 Constraints can be constructed, manipulated and
1910 added to (or removed from) (basic) sets and relations
1911 using the following functions.
1913 #include <isl/constraint.h>
1914 __isl_give isl_constraint *isl_constraint_alloc_equality(
1915 __isl_take isl_local_space *ls);
1916 __isl_give isl_constraint *isl_constraint_alloc_inequality(
1917 __isl_take isl_local_space *ls);
1918 __isl_give isl_constraint *isl_constraint_set_constant_si(
1919 __isl_take isl_constraint *constraint, int v);
1920 __isl_give isl_constraint *isl_constraint_set_constant_val(
1921 __isl_take isl_constraint *constraint,
1922 __isl_take isl_val *v);
1923 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1924 __isl_take isl_constraint *constraint,
1925 enum isl_dim_type type, int pos, int v);
1926 __isl_give isl_constraint *
1927 isl_constraint_set_coefficient_val(
1928 __isl_take isl_constraint *constraint,
1929 enum isl_dim_type type, int pos,
1930 __isl_take isl_val *v);
1931 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1932 __isl_take isl_basic_map *bmap,
1933 __isl_take isl_constraint *constraint);
1934 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1935 __isl_take isl_basic_set *bset,
1936 __isl_take isl_constraint *constraint);
1937 __isl_give isl_map *isl_map_add_constraint(
1938 __isl_take isl_map *map,
1939 __isl_take isl_constraint *constraint);
1940 __isl_give isl_set *isl_set_add_constraint(
1941 __isl_take isl_set *set,
1942 __isl_take isl_constraint *constraint);
1944 For example, to create a set containing the even integers
1945 between 10 and 42, you would use the following code.
1948 isl_local_space *ls;
1950 isl_basic_set *bset;
1952 space = isl_space_set_alloc(ctx, 0, 2);
1953 bset = isl_basic_set_universe(isl_space_copy(space));
1954 ls = isl_local_space_from_space(space);
1956 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
1957 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1958 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1959 bset = isl_basic_set_add_constraint(bset, c);
1961 c = isl_constraint_alloc_inequality(isl_local_space_copy(ls));
1962 c = isl_constraint_set_constant_si(c, -10);
1963 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1964 bset = isl_basic_set_add_constraint(bset, c);
1966 c = isl_constraint_alloc_inequality(ls);
1967 c = isl_constraint_set_constant_si(c, 42);
1968 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1969 bset = isl_basic_set_add_constraint(bset, c);
1971 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1975 isl_basic_set *bset;
1976 bset = isl_basic_set_read_from_str(ctx,
1977 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1979 A basic set or relation can also be constructed from two matrices
1980 describing the equalities and the inequalities.
1982 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1983 __isl_take isl_space *space,
1984 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1985 enum isl_dim_type c1,
1986 enum isl_dim_type c2, enum isl_dim_type c3,
1987 enum isl_dim_type c4);
1988 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1989 __isl_take isl_space *space,
1990 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1991 enum isl_dim_type c1,
1992 enum isl_dim_type c2, enum isl_dim_type c3,
1993 enum isl_dim_type c4, enum isl_dim_type c5);
1995 The C<isl_dim_type> arguments indicate the order in which
1996 different kinds of variables appear in the input matrices
1997 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1998 C<isl_dim_set> and C<isl_dim_div> for sets and
1999 of C<isl_dim_cst>, C<isl_dim_param>,
2000 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
2002 A (basic or union) set or relation can also be constructed from a
2003 (union) (piecewise) (multiple) affine expression
2004 or a list of affine expressions
2005 (See L</"Functions">).
2007 __isl_give isl_basic_map *isl_basic_map_from_aff(
2008 __isl_take isl_aff *aff);
2009 __isl_give isl_map *isl_map_from_aff(
2010 __isl_take isl_aff *aff);
2011 __isl_give isl_set *isl_set_from_pw_aff(
2012 __isl_take isl_pw_aff *pwaff);
2013 __isl_give isl_map *isl_map_from_pw_aff(
2014 __isl_take isl_pw_aff *pwaff);
2015 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
2016 __isl_take isl_space *domain_space,
2017 __isl_take isl_aff_list *list);
2018 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
2019 __isl_take isl_multi_aff *maff)
2020 __isl_give isl_map *isl_map_from_multi_aff(
2021 __isl_take isl_multi_aff *maff)
2022 __isl_give isl_set *isl_set_from_pw_multi_aff(
2023 __isl_take isl_pw_multi_aff *pma);
2024 __isl_give isl_map *isl_map_from_pw_multi_aff(
2025 __isl_take isl_pw_multi_aff *pma);
2026 __isl_give isl_set *isl_set_from_multi_pw_aff(
2027 __isl_take isl_multi_pw_aff *mpa);
2028 __isl_give isl_map *isl_map_from_multi_pw_aff(
2029 __isl_take isl_multi_pw_aff *mpa);
2030 __isl_give isl_union_map *isl_union_map_from_union_pw_aff(
2031 __isl_take isl_union_pw_aff *upa);
2032 __isl_give isl_union_map *
2033 isl_union_map_from_union_pw_multi_aff(
2034 __isl_take isl_union_pw_multi_aff *upma);
2035 __isl_give isl_union_map *
2036 isl_union_map_from_multi_union_pw_aff(
2037 __isl_take isl_multi_union_pw_aff *mupa);
2039 The C<domain_space> argument describes the domain of the resulting
2040 basic relation. It is required because the C<list> may consist
2041 of zero affine expressions.
2042 The C<mupa> passed to C<isl_union_map_from_multi_union_pw_aff>
2043 is not allowed to be zero-dimensional. The domain of the result
2044 is the shared domain of the union piecewise affine elements.
2046 =head2 Inspecting Sets and Relations
2048 Usually, the user should not have to care about the actual constraints
2049 of the sets and maps, but should instead apply the abstract operations
2050 explained in the following sections.
2051 Occasionally, however, it may be required to inspect the individual
2052 coefficients of the constraints. This section explains how to do so.
2053 In these cases, it may also be useful to have C<isl> compute
2054 an explicit representation of the existentially quantified variables.
2056 __isl_give isl_set *isl_set_compute_divs(
2057 __isl_take isl_set *set);
2058 __isl_give isl_map *isl_map_compute_divs(
2059 __isl_take isl_map *map);
2060 __isl_give isl_union_set *isl_union_set_compute_divs(
2061 __isl_take isl_union_set *uset);
2062 __isl_give isl_union_map *isl_union_map_compute_divs(
2063 __isl_take isl_union_map *umap);
2065 This explicit representation defines the existentially quantified
2066 variables as integer divisions of the other variables, possibly
2067 including earlier existentially quantified variables.
2068 An explicitly represented existentially quantified variable therefore
2069 has a unique value when the values of the other variables are known.
2070 If, furthermore, the same existentials, i.e., existentials
2071 with the same explicit representations, should appear in the
2072 same order in each of the disjuncts of a set or map, then the user should call
2073 either of the following functions.
2075 __isl_give isl_set *isl_set_align_divs(
2076 __isl_take isl_set *set);
2077 __isl_give isl_map *isl_map_align_divs(
2078 __isl_take isl_map *map);
2080 Alternatively, the existentially quantified variables can be removed
2081 using the following functions, which compute an overapproximation.
2083 __isl_give isl_basic_set *isl_basic_set_remove_divs(
2084 __isl_take isl_basic_set *bset);
2085 __isl_give isl_basic_map *isl_basic_map_remove_divs(
2086 __isl_take isl_basic_map *bmap);
2087 __isl_give isl_set *isl_set_remove_divs(
2088 __isl_take isl_set *set);
2089 __isl_give isl_map *isl_map_remove_divs(
2090 __isl_take isl_map *map);
2092 It is also possible to only remove those divs that are defined
2093 in terms of a given range of dimensions or only those for which
2094 no explicit representation is known.
2096 __isl_give isl_basic_set *
2097 isl_basic_set_remove_divs_involving_dims(
2098 __isl_take isl_basic_set *bset,
2099 enum isl_dim_type type,
2100 unsigned first, unsigned n);
2101 __isl_give isl_basic_map *
2102 isl_basic_map_remove_divs_involving_dims(
2103 __isl_take isl_basic_map *bmap,
2104 enum isl_dim_type type,
2105 unsigned first, unsigned n);
2106 __isl_give isl_set *isl_set_remove_divs_involving_dims(
2107 __isl_take isl_set *set, enum isl_dim_type type,
2108 unsigned first, unsigned n);
2109 __isl_give isl_map *isl_map_remove_divs_involving_dims(
2110 __isl_take isl_map *map, enum isl_dim_type type,
2111 unsigned first, unsigned n);
2113 __isl_give isl_basic_set *
2114 isl_basic_set_remove_unknown_divs(
2115 __isl_take isl_basic_set *bset);
2116 __isl_give isl_set *isl_set_remove_unknown_divs(
2117 __isl_take isl_set *set);
2118 __isl_give isl_map *isl_map_remove_unknown_divs(
2119 __isl_take isl_map *map);
2121 To iterate over all the sets or maps in a union set or map, use
2123 isl_stat isl_union_set_foreach_set(
2124 __isl_keep isl_union_set *uset,
2125 isl_stat (*fn)(__isl_take isl_set *set, void *user),
2127 isl_stat isl_union_map_foreach_map(
2128 __isl_keep isl_union_map *umap,
2129 isl_stat (*fn)(__isl_take isl_map *map, void *user),
2132 The number of sets or maps in a union set or map can be obtained
2135 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
2136 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
2138 To extract the set or map in a given space from a union, use
2140 __isl_give isl_set *isl_union_set_extract_set(
2141 __isl_keep isl_union_set *uset,
2142 __isl_take isl_space *space);
2143 __isl_give isl_map *isl_union_map_extract_map(
2144 __isl_keep isl_union_map *umap,
2145 __isl_take isl_space *space);
2147 To iterate over all the basic sets or maps in a set or map, use
2149 isl_stat isl_set_foreach_basic_set(__isl_keep isl_set *set,
2150 isl_stat (*fn)(__isl_take isl_basic_set *bset,
2153 isl_stat isl_map_foreach_basic_map(__isl_keep isl_map *map,
2154 isl_stat (*fn)(__isl_take isl_basic_map *bmap,
2158 The callback function C<fn> should return 0 if successful and
2159 -1 if an error occurs. In the latter case, or if any other error
2160 occurs, the above functions will return -1.
2162 It should be noted that C<isl> does not guarantee that
2163 the basic sets or maps passed to C<fn> are disjoint.
2164 If this is required, then the user should call one of
2165 the following functions first.
2167 __isl_give isl_set *isl_set_make_disjoint(
2168 __isl_take isl_set *set);
2169 __isl_give isl_map *isl_map_make_disjoint(
2170 __isl_take isl_map *map);
2172 The number of basic sets in a set can be obtained
2173 or the number of basic maps in a map can be obtained
2176 #include <isl/set.h>
2177 int isl_set_n_basic_set(__isl_keep isl_set *set);
2179 #include <isl/map.h>
2180 int isl_map_n_basic_map(__isl_keep isl_map *map);
2182 To iterate over the constraints of a basic set or map, use
2184 #include <isl/constraint.h>
2186 int isl_basic_set_n_constraint(
2187 __isl_keep isl_basic_set *bset);
2188 isl_stat isl_basic_set_foreach_constraint(
2189 __isl_keep isl_basic_set *bset,
2190 isl_stat (*fn)(__isl_take isl_constraint *c,
2193 int isl_basic_map_n_constraint(
2194 __isl_keep isl_basic_map *bmap);
2195 isl_stat isl_basic_map_foreach_constraint(
2196 __isl_keep isl_basic_map *bmap,
2197 isl_stat (*fn)(__isl_take isl_constraint *c,
2200 __isl_null isl_constraint *isl_constraint_free(
2201 __isl_take isl_constraint *c);
2203 Again, the callback function C<fn> should return 0 if successful and
2204 -1 if an error occurs. In the latter case, or if any other error
2205 occurs, the above functions will return -1.
2206 The constraint C<c> represents either an equality or an inequality.
2207 Use the following function to find out whether a constraint
2208 represents an equality. If not, it represents an inequality.
2210 isl_bool isl_constraint_is_equality(
2211 __isl_keep isl_constraint *constraint);
2213 It is also possible to obtain a list of constraints from a basic
2216 #include <isl/constraint.h>
2217 __isl_give isl_constraint_list *
2218 isl_basic_map_get_constraint_list(
2219 __isl_keep isl_basic_map *bmap);
2220 __isl_give isl_constraint_list *
2221 isl_basic_set_get_constraint_list(
2222 __isl_keep isl_basic_set *bset);
2224 These functions require that all existentially quantified variables
2225 have an explicit representation.
2226 The returned list can be manipulated using the functions in L<"Lists">.
2228 The coefficients of the constraints can be inspected using
2229 the following functions.
2231 isl_bool isl_constraint_is_lower_bound(
2232 __isl_keep isl_constraint *constraint,
2233 enum isl_dim_type type, unsigned pos);
2234 isl_bool isl_constraint_is_upper_bound(
2235 __isl_keep isl_constraint *constraint,
2236 enum isl_dim_type type, unsigned pos);
2237 __isl_give isl_val *isl_constraint_get_constant_val(
2238 __isl_keep isl_constraint *constraint);
2239 __isl_give isl_val *isl_constraint_get_coefficient_val(
2240 __isl_keep isl_constraint *constraint,
2241 enum isl_dim_type type, int pos);
2243 The explicit representations of the existentially quantified
2244 variables can be inspected using the following function.
2245 Note that the user is only allowed to use this function
2246 if the inspected set or map is the result of a call
2247 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2248 The existentially quantified variable is equal to the floor
2249 of the returned affine expression. The affine expression
2250 itself can be inspected using the functions in
2253 __isl_give isl_aff *isl_constraint_get_div(
2254 __isl_keep isl_constraint *constraint, int pos);
2256 To obtain the constraints of a basic set or map in matrix
2257 form, use the following functions.
2259 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2260 __isl_keep isl_basic_set *bset,
2261 enum isl_dim_type c1, enum isl_dim_type c2,
2262 enum isl_dim_type c3, enum isl_dim_type c4);
2263 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2264 __isl_keep isl_basic_set *bset,
2265 enum isl_dim_type c1, enum isl_dim_type c2,
2266 enum isl_dim_type c3, enum isl_dim_type c4);
2267 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2268 __isl_keep isl_basic_map *bmap,
2269 enum isl_dim_type c1,
2270 enum isl_dim_type c2, enum isl_dim_type c3,
2271 enum isl_dim_type c4, enum isl_dim_type c5);
2272 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2273 __isl_keep isl_basic_map *bmap,
2274 enum isl_dim_type c1,
2275 enum isl_dim_type c2, enum isl_dim_type c3,
2276 enum isl_dim_type c4, enum isl_dim_type c5);
2278 The C<isl_dim_type> arguments dictate the order in which
2279 different kinds of variables appear in the resulting matrix.
2280 For set inputs, they should be a permutation of
2281 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
2282 For map inputs, they should be a permutation of
2283 C<isl_dim_cst>, C<isl_dim_param>,
2284 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2288 Points are elements of a set. They can be used to construct
2289 simple sets (boxes) or they can be used to represent the
2290 individual elements of a set.
2291 The zero point (the origin) can be created using
2293 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2295 The coordinates of a point can be inspected, set and changed
2298 __isl_give isl_val *isl_point_get_coordinate_val(
2299 __isl_keep isl_point *pnt,
2300 enum isl_dim_type type, int pos);
2301 __isl_give isl_point *isl_point_set_coordinate_val(
2302 __isl_take isl_point *pnt,
2303 enum isl_dim_type type, int pos,
2304 __isl_take isl_val *v);
2306 __isl_give isl_point *isl_point_add_ui(
2307 __isl_take isl_point *pnt,
2308 enum isl_dim_type type, int pos, unsigned val);
2309 __isl_give isl_point *isl_point_sub_ui(
2310 __isl_take isl_point *pnt,
2311 enum isl_dim_type type, int pos, unsigned val);
2313 Points can be copied or freed using
2315 __isl_give isl_point *isl_point_copy(
2316 __isl_keep isl_point *pnt);
2317 void isl_point_free(__isl_take isl_point *pnt);
2319 A singleton set can be created from a point using
2321 __isl_give isl_basic_set *isl_basic_set_from_point(
2322 __isl_take isl_point *pnt);
2323 __isl_give isl_set *isl_set_from_point(
2324 __isl_take isl_point *pnt);
2326 and a box can be created from two opposite extremal points using
2328 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2329 __isl_take isl_point *pnt1,
2330 __isl_take isl_point *pnt2);
2331 __isl_give isl_set *isl_set_box_from_points(
2332 __isl_take isl_point *pnt1,
2333 __isl_take isl_point *pnt2);
2335 All elements of a B<bounded> (union) set can be enumerated using
2336 the following functions.
2338 isl_stat isl_set_foreach_point(__isl_keep isl_set *set,
2339 isl_stat (*fn)(__isl_take isl_point *pnt,
2342 isl_stat isl_union_set_foreach_point(
2343 __isl_keep isl_union_set *uset,
2344 isl_stat (*fn)(__isl_take isl_point *pnt,
2348 The function C<fn> is called for each integer point in
2349 C<set> with as second argument the last argument of
2350 the C<isl_set_foreach_point> call. The function C<fn>
2351 should return C<0> on success and C<-1> on failure.
2352 In the latter case, C<isl_set_foreach_point> will stop
2353 enumerating and return C<-1> as well.
2354 If the enumeration is performed successfully and to completion,
2355 then C<isl_set_foreach_point> returns C<0>.
2357 To obtain a single point of a (basic) set, use
2359 __isl_give isl_point *isl_basic_set_sample_point(
2360 __isl_take isl_basic_set *bset);
2361 __isl_give isl_point *isl_set_sample_point(
2362 __isl_take isl_set *set);
2364 If C<set> does not contain any (integer) points, then the
2365 resulting point will be ``void'', a property that can be
2368 isl_bool isl_point_is_void(__isl_keep isl_point *pnt);
2372 Besides sets and relation, C<isl> also supports various types of functions.
2373 Each of these types is derived from the value type (see L</"Values">)
2374 or from one of two primitive function types
2375 through the application of zero or more type constructors.
2376 We first describe the primitive type and then we describe
2377 the types derived from these primitive types.
2379 =head3 Primitive Functions
2381 C<isl> support two primitive function types, quasi-affine
2382 expressions and quasipolynomials.
2383 A quasi-affine expression is defined either over a parameter
2384 space or over a set and is composed of integer constants,
2385 parameters and set variables, addition, subtraction and
2386 integer division by an integer constant.
2387 For example, the quasi-affine expression
2389 [n] -> { [x] -> [2*floor((4 n + x)/9] }
2391 maps C<x> to C<2*floor((4 n + x)/9>.
2392 A quasipolynomial is a polynomial expression in quasi-affine
2393 expression. That is, it additionally allows for multiplication.
2394 Note, though, that it is not allowed to construct an integer
2395 division of an expression involving multiplications.
2396 Here is an example of a quasipolynomial that is not
2397 quasi-affine expression
2399 [n] -> { [x] -> (n*floor((4 n + x)/9) }
2401 Note that the external representations of quasi-affine expressions
2402 and quasipolynomials are different. Quasi-affine expressions
2403 use a notation with square brackets just like binary relations,
2404 while quasipolynomials do not. This might change at some point.
2406 If a primitive function is defined over a parameter space,
2407 then the space of the function itself is that of a set.
2408 If it is defined over a set, then the space of the function
2409 is that of a relation. In both cases, the set space (or
2410 the output space) is single-dimensional, anonymous and unstructured.
2411 To create functions with multiple dimensions or with other kinds
2412 of set or output spaces, use multiple expressions
2413 (see L</"Multiple Expressions">).
2417 =item * Quasi-affine Expressions
2419 Besides the expressions described above, a quasi-affine
2420 expression can also be set to NaN. Such expressions
2421 typically represent a failure to represent a result
2422 as a quasi-affine expression.
2424 The zero quasi affine expression or the quasi affine expression
2425 that is equal to a given value or
2426 a specified dimension on a given domain can be created using
2428 #include <isl/aff.h>
2429 __isl_give isl_aff *isl_aff_zero_on_domain(
2430 __isl_take isl_local_space *ls);
2431 __isl_give isl_aff *isl_aff_val_on_domain(
2432 __isl_take isl_local_space *ls,
2433 __isl_take isl_val *val);
2434 __isl_give isl_aff *isl_aff_var_on_domain(
2435 __isl_take isl_local_space *ls,
2436 enum isl_dim_type type, unsigned pos);
2437 __isl_give isl_aff *isl_aff_nan_on_domain(
2438 __isl_take isl_local_space *ls);
2440 Quasi affine expressions can be copied and freed using
2442 #include <isl/aff.h>
2443 __isl_give isl_aff *isl_aff_copy(
2444 __isl_keep isl_aff *aff);
2445 __isl_null isl_aff *isl_aff_free(
2446 __isl_take isl_aff *aff);
2448 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2449 using the following function. The constraint is required to have
2450 a non-zero coefficient for the specified dimension.
2452 #include <isl/constraint.h>
2453 __isl_give isl_aff *isl_constraint_get_bound(
2454 __isl_keep isl_constraint *constraint,
2455 enum isl_dim_type type, int pos);
2457 The entire affine expression of the constraint can also be extracted
2458 using the following function.
2460 #include <isl/constraint.h>
2461 __isl_give isl_aff *isl_constraint_get_aff(
2462 __isl_keep isl_constraint *constraint);
2464 Conversely, an equality constraint equating
2465 the affine expression to zero or an inequality constraint enforcing
2466 the affine expression to be non-negative, can be constructed using
2468 __isl_give isl_constraint *isl_equality_from_aff(
2469 __isl_take isl_aff *aff);
2470 __isl_give isl_constraint *isl_inequality_from_aff(
2471 __isl_take isl_aff *aff);
2473 The coefficients and the integer divisions of an affine expression
2474 can be inspected using the following functions.
2476 #include <isl/aff.h>
2477 __isl_give isl_val *isl_aff_get_constant_val(
2478 __isl_keep isl_aff *aff);
2479 __isl_give isl_val *isl_aff_get_coefficient_val(
2480 __isl_keep isl_aff *aff,
2481 enum isl_dim_type type, int pos);
2482 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2483 enum isl_dim_type type, int pos);
2484 __isl_give isl_val *isl_aff_get_denominator_val(
2485 __isl_keep isl_aff *aff);
2486 __isl_give isl_aff *isl_aff_get_div(
2487 __isl_keep isl_aff *aff, int pos);
2489 They can be modified using the following functions.
2491 #include <isl/aff.h>
2492 __isl_give isl_aff *isl_aff_set_constant_si(
2493 __isl_take isl_aff *aff, int v);
2494 __isl_give isl_aff *isl_aff_set_constant_val(
2495 __isl_take isl_aff *aff, __isl_take isl_val *v);
2496 __isl_give isl_aff *isl_aff_set_coefficient_si(
2497 __isl_take isl_aff *aff,
2498 enum isl_dim_type type, int pos, int v);
2499 __isl_give isl_aff *isl_aff_set_coefficient_val(
2500 __isl_take isl_aff *aff,
2501 enum isl_dim_type type, int pos,
2502 __isl_take isl_val *v);
2504 __isl_give isl_aff *isl_aff_add_constant_si(
2505 __isl_take isl_aff *aff, int v);
2506 __isl_give isl_aff *isl_aff_add_constant_val(
2507 __isl_take isl_aff *aff, __isl_take isl_val *v);
2508 __isl_give isl_aff *isl_aff_add_constant_num_si(
2509 __isl_take isl_aff *aff, int v);
2510 __isl_give isl_aff *isl_aff_add_coefficient_si(
2511 __isl_take isl_aff *aff,
2512 enum isl_dim_type type, int pos, int v);
2513 __isl_give isl_aff *isl_aff_add_coefficient_val(
2514 __isl_take isl_aff *aff,
2515 enum isl_dim_type type, int pos,
2516 __isl_take isl_val *v);
2518 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
2519 set the I<numerator> of the constant or coefficient, while
2520 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
2521 the constant or coefficient as a whole.
2522 The C<add_constant> and C<add_coefficient> functions add an integer
2523 or rational value to
2524 the possibly rational constant or coefficient.
2525 The C<add_constant_num> functions add an integer value to
2528 =item * Quasipolynomials
2530 Some simple quasipolynomials can be created using the following functions.
2532 #include <isl/polynomial.h>
2533 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2534 __isl_take isl_space *domain);
2535 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2536 __isl_take isl_space *domain);
2537 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2538 __isl_take isl_space *domain);
2539 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2540 __isl_take isl_space *domain);
2541 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2542 __isl_take isl_space *domain);
2543 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2544 __isl_take isl_space *domain,
2545 __isl_take isl_val *val);
2546 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2547 __isl_take isl_space *domain,
2548 enum isl_dim_type type, unsigned pos);
2549 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2550 __isl_take isl_aff *aff);
2552 Recall that the space in which a quasipolynomial lives is a map space
2553 with a one-dimensional range. The C<domain> argument in some of
2554 the functions above corresponds to the domain of this map space.
2556 Quasipolynomials can be copied and freed again using the following
2559 #include <isl/polynomial.h>
2560 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2561 __isl_keep isl_qpolynomial *qp);
2562 __isl_null isl_qpolynomial *isl_qpolynomial_free(
2563 __isl_take isl_qpolynomial *qp);
2565 The constant term of a quasipolynomial can be extracted using
2567 __isl_give isl_val *isl_qpolynomial_get_constant_val(
2568 __isl_keep isl_qpolynomial *qp);
2570 To iterate over all terms in a quasipolynomial,
2573 isl_stat isl_qpolynomial_foreach_term(
2574 __isl_keep isl_qpolynomial *qp,
2575 isl_stat (*fn)(__isl_take isl_term *term,
2576 void *user), void *user);
2578 The terms themselves can be inspected and freed using
2581 unsigned isl_term_dim(__isl_keep isl_term *term,
2582 enum isl_dim_type type);
2583 __isl_give isl_val *isl_term_get_coefficient_val(
2584 __isl_keep isl_term *term);
2585 int isl_term_get_exp(__isl_keep isl_term *term,
2586 enum isl_dim_type type, unsigned pos);
2587 __isl_give isl_aff *isl_term_get_div(
2588 __isl_keep isl_term *term, unsigned pos);
2589 void isl_term_free(__isl_take isl_term *term);
2591 Each term is a product of parameters, set variables and
2592 integer divisions. The function C<isl_term_get_exp>
2593 returns the exponent of a given dimensions in the given term.
2599 A reduction represents a maximum or a minimum of its
2601 The only reduction type defined by C<isl> is
2602 C<isl_qpolynomial_fold>.
2604 There are currently no functions to directly create such
2605 objects, but they do appear in the piecewise quasipolynomial
2606 reductions returned by the C<isl_pw_qpolynomial_bound> function.
2608 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
2610 Reductions can be copied and freed using
2611 the following functions.
2613 #include <isl/polynomial.h>
2614 __isl_give isl_qpolynomial_fold *
2615 isl_qpolynomial_fold_copy(
2616 __isl_keep isl_qpolynomial_fold *fold);
2617 void isl_qpolynomial_fold_free(
2618 __isl_take isl_qpolynomial_fold *fold);
2620 To iterate over all quasipolynomials in a reduction, use
2622 isl_stat isl_qpolynomial_fold_foreach_qpolynomial(
2623 __isl_keep isl_qpolynomial_fold *fold,
2624 isl_stat (*fn)(__isl_take isl_qpolynomial *qp,
2625 void *user), void *user);
2627 =head3 Multiple Expressions
2629 A multiple expression represents a sequence of zero or
2630 more base expressions, all defined on the same domain space.
2631 The domain space of the multiple expression is the same
2632 as that of the base expressions, but the range space
2633 can be any space. In case the base expressions have
2634 a set space, the corresponding multiple expression
2635 also has a set space.
2636 Objects of the value type do not have an associated space.
2637 The space of a multiple value is therefore always a set space.
2638 Similarly, the space of a multiple union piecewise
2639 affine expression is always a set space.
2641 The multiple expression types defined by C<isl>
2642 are C<isl_multi_val>, C<isl_multi_aff>, C<isl_multi_pw_aff>,
2643 C<isl_multi_union_pw_aff>.
2645 A multiple expression with the value zero for
2646 each output (or set) dimension can be created
2647 using the following functions.
2649 #include <isl/val.h>
2650 __isl_give isl_multi_val *isl_multi_val_zero(
2651 __isl_take isl_space *space);
2653 #include <isl/aff.h>
2654 __isl_give isl_multi_aff *isl_multi_aff_zero(
2655 __isl_take isl_space *space);
2656 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
2657 __isl_take isl_space *space);
2658 __isl_give isl_multi_union_pw_aff *
2659 isl_multi_union_pw_aff_zero(
2660 __isl_take isl_space *space);
2662 Since there is no canonical way of representing a zero
2663 value of type C<isl_union_pw_aff>, the space passed
2664 to C<isl_multi_union_pw_aff_zero> needs to be zero-dimensional.
2666 An identity function can be created using the following
2667 functions. The space needs to be that of a relation
2668 with the same number of input and output dimensions.
2670 #include <isl/aff.h>
2671 __isl_give isl_multi_aff *isl_multi_aff_identity(
2672 __isl_take isl_space *space);
2673 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
2674 __isl_take isl_space *space);
2676 A function that performs a projection on a universe
2677 relation or set can be created using the following functions.
2678 See also the corresponding
2679 projection operations in L</"Unary Operations">.
2681 #include <isl/aff.h>
2682 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
2683 __isl_take isl_space *space);
2684 __isl_give isl_multi_aff *isl_multi_aff_range_map(
2685 __isl_take isl_space *space);
2686 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
2687 __isl_take isl_space *space,
2688 enum isl_dim_type type,
2689 unsigned first, unsigned n);
2691 A multiple expression can be created from a single
2692 base expression using the following functions.
2693 The space of the created multiple expression is the same
2694 as that of the base expression, except for
2695 C<isl_multi_union_pw_aff_from_union_pw_aff> where the input
2696 lives in a parameter space and the output lives
2697 in a single-dimensional set space.
2699 #include <isl/aff.h>
2700 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
2701 __isl_take isl_aff *aff);
2702 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
2703 __isl_take isl_pw_aff *pa);
2704 __isl_give isl_multi_union_pw_aff *
2705 isl_multi_union_pw_aff_from_union_pw_aff(
2706 __isl_take isl_union_pw_aff *upa);
2708 A multiple expression can be created from a list
2709 of base expression in a specified space.
2710 The domain of this space needs to be the same
2711 as the domains of the base expressions in the list.
2712 If the base expressions have a set space (or no associated space),
2713 then this space also needs to be a set space.
2715 #include <isl/val.h>
2716 __isl_give isl_multi_val *isl_multi_val_from_val_list(
2717 __isl_take isl_space *space,
2718 __isl_take isl_val_list *list);
2720 #include <isl/aff.h>
2721 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2722 __isl_take isl_space *space,
2723 __isl_take isl_aff_list *list);
2724 __isl_give isl_multi_union_pw_aff *
2725 isl_multi_union_pw_aff_from_union_pw_aff_list(
2726 __isl_take isl_space *space,
2727 __isl_take isl_union_pw_aff_list *list);
2729 As a convenience, a multiple piecewise expression can
2730 also be created from a multiple expression.
2731 Each piecewise expression in the result has a single
2734 #include <isl/aff.h>
2735 __isl_give isl_multi_pw_aff *
2736 isl_multi_pw_aff_from_multi_aff(
2737 __isl_take isl_multi_aff *ma);
2739 Similarly, a multiple union expression can be
2740 created from a multiple expression.
2742 #include <isl/aff.h>
2743 __isl_give isl_multi_union_pw_aff *
2744 isl_multi_union_pw_aff_from_multi_aff(
2745 __isl_take isl_multi_aff *ma);
2746 __isl_give isl_multi_union_pw_aff *
2747 isl_multi_union_pw_aff_from_multi_pw_aff(
2748 __isl_take isl_multi_pw_aff *mpa);
2750 A multiple quasi-affine expression can be created from
2751 a multiple value with a given domain space using the following
2754 #include <isl/aff.h>
2755 __isl_give isl_multi_aff *
2756 isl_multi_aff_multi_val_on_space(
2757 __isl_take isl_space *space,
2758 __isl_take isl_multi_val *mv);
2761 a multiple union piecewise affine expression can be created from
2762 a multiple value with a given domain or
2763 a multiple affine expression with a given domain
2764 using the following functions.
2766 #include <isl/aff.h>
2767 __isl_give isl_multi_union_pw_aff *
2768 isl_multi_union_pw_aff_multi_val_on_domain(
2769 __isl_take isl_union_set *domain,
2770 __isl_take isl_multi_val *mv);
2771 __isl_give isl_multi_union_pw_aff *
2772 isl_multi_union_pw_aff_multi_aff_on_domain(
2773 __isl_take isl_union_set *domain,
2774 __isl_take isl_multi_aff *ma);
2776 Multiple expressions can be copied and freed using
2777 the following functions.
2779 #include <isl/val.h>
2780 __isl_give isl_multi_val *isl_multi_val_copy(
2781 __isl_keep isl_multi_val *mv);
2782 __isl_null isl_multi_val *isl_multi_val_free(
2783 __isl_take isl_multi_val *mv);
2785 #include <isl/aff.h>
2786 __isl_give isl_multi_aff *isl_multi_aff_copy(
2787 __isl_keep isl_multi_aff *maff);
2788 __isl_null isl_multi_aff *isl_multi_aff_free(
2789 __isl_take isl_multi_aff *maff);
2790 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
2791 __isl_keep isl_multi_pw_aff *mpa);
2792 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
2793 __isl_take isl_multi_pw_aff *mpa);
2794 __isl_give isl_multi_union_pw_aff *
2795 isl_multi_union_pw_aff_copy(
2796 __isl_keep isl_multi_union_pw_aff *mupa);
2797 __isl_null isl_multi_union_pw_aff *
2798 isl_multi_union_pw_aff_free(
2799 __isl_take isl_multi_union_pw_aff *mupa);
2801 The base expression at a given position of a multiple
2802 expression can be extracted using the following functions.
2804 #include <isl/val.h>
2805 __isl_give isl_val *isl_multi_val_get_val(
2806 __isl_keep isl_multi_val *mv, int pos);
2808 #include <isl/aff.h>
2809 __isl_give isl_aff *isl_multi_aff_get_aff(
2810 __isl_keep isl_multi_aff *multi, int pos);
2811 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
2812 __isl_keep isl_multi_pw_aff *mpa, int pos);
2813 __isl_give isl_union_pw_aff *
2814 isl_multi_union_pw_aff_get_union_pw_aff(
2815 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
2817 It can be replaced using the following functions.
2819 #include <isl/val.h>
2820 __isl_give isl_multi_val *isl_multi_val_set_val(
2821 __isl_take isl_multi_val *mv, int pos,
2822 __isl_take isl_val *val);
2824 #include <isl/aff.h>
2825 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
2826 __isl_take isl_multi_aff *multi, int pos,
2827 __isl_take isl_aff *aff);
2828 __isl_give isl_multi_union_pw_aff *
2829 isl_multi_union_pw_aff_set_union_pw_aff(
2830 __isl_take isl_multi_union_pw_aff *mupa, int pos,
2831 __isl_take isl_union_pw_aff *upa);
2833 As a convenience, a sequence of base expressions that have
2834 their domains in a given space can be extracted from a sequence
2835 of union expressions using the following function.
2837 #include <isl/aff.h>
2838 __isl_give isl_multi_pw_aff *
2839 isl_multi_union_pw_aff_extract_multi_pw_aff(
2840 __isl_keep isl_multi_union_pw_aff *mupa,
2841 __isl_take isl_space *space);
2843 Note that there is a difference between C<isl_multi_union_pw_aff>
2844 and C<isl_union_pw_multi_aff> objects. The first is a sequence
2845 of unions of piecewise expressions, while the second is a union
2846 of piecewise sequences. In particular, multiple affine expressions
2847 in an C<isl_union_pw_multi_aff> may live in different spaces,
2848 while there is only a single multiple expression in
2849 an C<isl_multi_union_pw_aff>, which can therefore only live
2850 in a single space. This means that not every
2851 C<isl_union_pw_multi_aff> can be converted to
2852 an C<isl_multi_union_pw_aff>. Conversely, a zero-dimensional
2853 C<isl_multi_union_pw_aff> carries no information
2854 about any possible domain and therefore cannot be converted
2855 to an C<isl_union_pw_multi_aff>. Moreover, the elements
2856 of an C<isl_multi_union_pw_aff> may be defined over different domains,
2857 while each multiple expression inside an C<isl_union_pw_multi_aff>
2858 has a single domain. The conversion of an C<isl_union_pw_multi_aff>
2859 of dimension greater than one may therefore not be exact.
2860 The following functions can
2861 be used to perform these conversions when they are possible.
2863 #include <isl/aff.h>
2864 __isl_give isl_multi_union_pw_aff *
2865 isl_multi_union_pw_aff_from_union_pw_multi_aff(
2866 __isl_take isl_union_pw_multi_aff *upma);
2867 __isl_give isl_union_pw_multi_aff *
2868 isl_union_pw_multi_aff_from_multi_union_pw_aff(
2869 __isl_take isl_multi_union_pw_aff *mupa);
2871 =head3 Piecewise Expressions
2873 A piecewise expression is an expression that is described
2874 using zero or more base expression defined over the same
2875 number of cells in the domain space of the base expressions.
2876 All base expressions are defined over the same
2877 domain space and the cells are disjoint.
2878 The space of a piecewise expression is the same as
2879 that of the base expressions.
2880 If the union of the cells is a strict subset of the domain
2881 space, then the value of the piecewise expression outside
2882 this union is different for types derived from quasi-affine
2883 expressions and those derived from quasipolynomials.
2884 Piecewise expressions derived from quasi-affine expressions
2885 are considered to be undefined outside the union of their cells.
2886 Piecewise expressions derived from quasipolynomials
2887 are considered to be zero outside the union of their cells.
2889 Piecewise quasipolynomials are mainly used by the C<barvinok>
2890 library for representing the number of elements in a parametric set or map.
2891 For example, the piecewise quasipolynomial
2893 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2895 represents the number of points in the map
2897 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2899 The piecewise expression types defined by C<isl>
2900 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
2901 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
2903 A piecewise expression with no cells can be created using
2904 the following functions.
2906 #include <isl/aff.h>
2907 __isl_give isl_pw_aff *isl_pw_aff_empty(
2908 __isl_take isl_space *space);
2909 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
2910 __isl_take isl_space *space);
2912 A piecewise expression with a single universe cell can be
2913 created using the following functions.
2915 #include <isl/aff.h>
2916 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2917 __isl_take isl_aff *aff);
2918 __isl_give isl_pw_multi_aff *
2919 isl_pw_multi_aff_from_multi_aff(
2920 __isl_take isl_multi_aff *ma);
2922 #include <isl/polynomial.h>
2923 __isl_give isl_pw_qpolynomial *
2924 isl_pw_qpolynomial_from_qpolynomial(
2925 __isl_take isl_qpolynomial *qp);
2927 A piecewise expression with a single specified cell can be
2928 created using the following functions.
2930 #include <isl/aff.h>
2931 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2932 __isl_take isl_set *set, __isl_take isl_aff *aff);
2933 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
2934 __isl_take isl_set *set,
2935 __isl_take isl_multi_aff *maff);
2937 #include <isl/polynomial.h>
2938 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2939 __isl_take isl_set *set,
2940 __isl_take isl_qpolynomial *qp);
2942 The following convenience functions first create a base expression and
2943 then create a piecewise expression over a universe domain.
2945 #include <isl/aff.h>
2946 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
2947 __isl_take isl_local_space *ls);
2948 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
2949 __isl_take isl_local_space *ls,
2950 enum isl_dim_type type, unsigned pos);
2951 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
2952 __isl_take isl_local_space *ls);
2953 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
2954 __isl_take isl_space *space);
2955 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
2956 __isl_take isl_space *space);
2957 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
2958 __isl_take isl_space *space);
2959 __isl_give isl_pw_multi_aff *
2960 isl_pw_multi_aff_project_out_map(
2961 __isl_take isl_space *space,
2962 enum isl_dim_type type,
2963 unsigned first, unsigned n);
2965 #include <isl/polynomial.h>
2966 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2967 __isl_take isl_space *space);
2969 The following convenience functions first create a base expression and
2970 then create a piecewise expression over a given domain.
2972 #include <isl/aff.h>
2973 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
2974 __isl_take isl_set *domain,
2975 __isl_take isl_val *v);
2976 __isl_give isl_pw_multi_aff *
2977 isl_pw_multi_aff_multi_val_on_domain(
2978 __isl_take isl_set *domain,
2979 __isl_take isl_multi_val *mv);
2981 As a convenience, a piecewise multiple expression can
2982 also be created from a piecewise expression.
2983 Each multiple expression in the result is derived
2984 from the corresponding base expression.
2986 #include <isl/aff.h>
2987 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
2988 __isl_take isl_pw_aff *pa);
2990 Similarly, a piecewise quasipolynomial can be
2991 created from a piecewise quasi-affine expression using
2992 the following function.
2994 #include <isl/polynomial.h>
2995 __isl_give isl_pw_qpolynomial *
2996 isl_pw_qpolynomial_from_pw_aff(
2997 __isl_take isl_pw_aff *pwaff);
2999 Piecewise expressions can be copied and freed using the following functions.
3001 #include <isl/aff.h>
3002 __isl_give isl_pw_aff *isl_pw_aff_copy(
3003 __isl_keep isl_pw_aff *pwaff);
3004 __isl_null isl_pw_aff *isl_pw_aff_free(
3005 __isl_take isl_pw_aff *pwaff);
3006 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3007 __isl_keep isl_pw_multi_aff *pma);
3008 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
3009 __isl_take isl_pw_multi_aff *pma);
3011 #include <isl/polynomial.h>
3012 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3013 __isl_keep isl_pw_qpolynomial *pwqp);
3014 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
3015 __isl_take isl_pw_qpolynomial *pwqp);
3016 __isl_give isl_pw_qpolynomial_fold *
3017 isl_pw_qpolynomial_fold_copy(
3018 __isl_keep isl_pw_qpolynomial_fold *pwf);
3019 __isl_null isl_pw_qpolynomial_fold *
3020 isl_pw_qpolynomial_fold_free(
3021 __isl_take isl_pw_qpolynomial_fold *pwf);
3023 To iterate over the different cells of a piecewise expression,
3024 use the following functions.
3026 #include <isl/aff.h>
3027 isl_bool isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3028 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3029 isl_stat isl_pw_aff_foreach_piece(
3030 __isl_keep isl_pw_aff *pwaff,
3031 isl_stat (*fn)(__isl_take isl_set *set,
3032 __isl_take isl_aff *aff,
3033 void *user), void *user);
3034 isl_stat isl_pw_multi_aff_foreach_piece(
3035 __isl_keep isl_pw_multi_aff *pma,
3036 isl_stat (*fn)(__isl_take isl_set *set,
3037 __isl_take isl_multi_aff *maff,
3038 void *user), void *user);
3040 #include <isl/polynomial.h>
3041 isl_stat isl_pw_qpolynomial_foreach_piece(
3042 __isl_keep isl_pw_qpolynomial *pwqp,
3043 isl_stat (*fn)(__isl_take isl_set *set,
3044 __isl_take isl_qpolynomial *qp,
3045 void *user), void *user);
3046 isl_stat isl_pw_qpolynomial_foreach_lifted_piece(
3047 __isl_keep isl_pw_qpolynomial *pwqp,
3048 isl_stat (*fn)(__isl_take isl_set *set,
3049 __isl_take isl_qpolynomial *qp,
3050 void *user), void *user);
3051 isl_stat isl_pw_qpolynomial_fold_foreach_piece(
3052 __isl_keep isl_pw_qpolynomial_fold *pwf,
3053 isl_stat (*fn)(__isl_take isl_set *set,
3054 __isl_take isl_qpolynomial_fold *fold,
3055 void *user), void *user);
3056 isl_stat isl_pw_qpolynomial_fold_foreach_lifted_piece(
3057 __isl_keep isl_pw_qpolynomial_fold *pwf,
3058 isl_stat (*fn)(__isl_take isl_set *set,
3059 __isl_take isl_qpolynomial_fold *fold,
3060 void *user), void *user);
3062 As usual, the function C<fn> should return C<0> on success
3063 and C<-1> on failure. The difference between
3064 C<isl_pw_qpolynomial_foreach_piece> and
3065 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3066 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3067 compute unique representations for all existentially quantified
3068 variables and then turn these existentially quantified variables
3069 into extra set variables, adapting the associated quasipolynomial
3070 accordingly. This means that the C<set> passed to C<fn>
3071 will not have any existentially quantified variables, but that
3072 the dimensions of the sets may be different for different
3073 invocations of C<fn>.
3074 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
3075 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
3077 A piecewise expression consisting of the expressions at a given
3078 position of a piecewise multiple expression can be extracted
3079 using the following function.
3081 #include <isl/aff.h>
3082 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3083 __isl_keep isl_pw_multi_aff *pma, int pos);
3085 These expressions can be replaced using the following function.
3087 #include <isl/aff.h>
3088 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3089 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3090 __isl_take isl_pw_aff *pa);
3092 Note that there is a difference between C<isl_multi_pw_aff> and
3093 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
3094 affine expressions, while the second is a piecewise sequence
3095 of affine expressions. In particular, each of the piecewise
3096 affine expressions in an C<isl_multi_pw_aff> may have a different
3097 domain, while all multiple expressions associated to a cell
3098 in an C<isl_pw_multi_aff> have the same domain.
3099 It is possible to convert between the two, but when converting
3100 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
3101 of the result is the intersection of the domains of the input.
3102 The reverse conversion is exact.
3104 #include <isl/aff.h>
3105 __isl_give isl_pw_multi_aff *
3106 isl_pw_multi_aff_from_multi_pw_aff(
3107 __isl_take isl_multi_pw_aff *mpa);
3108 __isl_give isl_multi_pw_aff *
3109 isl_multi_pw_aff_from_pw_multi_aff(
3110 __isl_take isl_pw_multi_aff *pma);
3112 =head3 Union Expressions
3114 A union expression collects base expressions defined
3115 over different domains. The space of a union expression
3116 is that of the shared parameter space.
3118 The union expression types defined by C<isl>
3119 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
3120 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
3122 An empty union expression can be created using the following functions.
3124 #include <isl/aff.h>
3125 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
3126 __isl_take isl_space *space);
3127 __isl_give isl_union_pw_multi_aff *
3128 isl_union_pw_multi_aff_empty(
3129 __isl_take isl_space *space);
3131 #include <isl/polynomial.h>
3132 __isl_give isl_union_pw_qpolynomial *
3133 isl_union_pw_qpolynomial_zero(
3134 __isl_take isl_space *space);
3136 A union expression containing a single base expression
3137 can be created using the following functions.
3139 #include <isl/aff.h>
3140 __isl_give isl_union_pw_aff *
3141 isl_union_pw_aff_from_pw_aff(
3142 __isl_take isl_pw_aff *pa);
3143 __isl_give isl_union_pw_multi_aff *
3144 isl_union_pw_multi_aff_from_aff(
3145 __isl_take isl_aff *aff);
3146 __isl_give isl_union_pw_multi_aff *
3147 isl_union_pw_multi_aff_from_pw_multi_aff(
3148 __isl_take isl_pw_multi_aff *pma);
3150 #include <isl/polynomial.h>
3151 __isl_give isl_union_pw_qpolynomial *
3152 isl_union_pw_qpolynomial_from_pw_qpolynomial(
3153 __isl_take isl_pw_qpolynomial *pwqp);
3155 The following functions create a base expression on each
3156 of the sets in the union set and collect the results.
3158 #include <isl/aff.h>
3159 __isl_give isl_union_pw_multi_aff *
3160 isl_union_pw_multi_aff_from_union_pw_aff(
3161 __isl_take isl_union_pw_aff *upa);
3162 __isl_give isl_union_pw_aff *
3163 isl_union_pw_multi_aff_get_union_pw_aff(
3164 __isl_keep isl_union_pw_multi_aff *upma, int pos);
3165 __isl_give isl_union_pw_aff *
3166 isl_union_pw_aff_val_on_domain(
3167 __isl_take isl_union_set *domain,
3168 __isl_take isl_val *v);
3169 __isl_give isl_union_pw_multi_aff *
3170 isl_union_pw_multi_aff_multi_val_on_domain(
3171 __isl_take isl_union_set *domain,
3172 __isl_take isl_multi_val *mv);
3174 An C<isl_union_pw_aff> that is equal to a (parametric) affine
3175 expression on a given domain can be created using the following
3178 #include <isl/aff.h>
3179 __isl_give isl_union_pw_aff *
3180 isl_union_pw_aff_aff_on_domain(
3181 __isl_take isl_union_set *domain,
3182 __isl_take isl_aff *aff);
3184 A base expression can be added to a union expression using
3185 the following functions.
3187 #include <isl/aff.h>
3188 __isl_give isl_union_pw_aff *
3189 isl_union_pw_aff_add_pw_aff(
3190 __isl_take isl_union_pw_aff *upa,
3191 __isl_take isl_pw_aff *pa);
3192 __isl_give isl_union_pw_multi_aff *
3193 isl_union_pw_multi_aff_add_pw_multi_aff(
3194 __isl_take isl_union_pw_multi_aff *upma,
3195 __isl_take isl_pw_multi_aff *pma);
3197 #include <isl/polynomial.h>
3198 __isl_give isl_union_pw_qpolynomial *
3199 isl_union_pw_qpolynomial_add_pw_qpolynomial(
3200 __isl_take isl_union_pw_qpolynomial *upwqp,
3201 __isl_take isl_pw_qpolynomial *pwqp);
3203 Union expressions can be copied and freed using
3204 the following functions.
3206 #include <isl/aff.h>
3207 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
3208 __isl_keep isl_union_pw_aff *upa);
3209 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
3210 __isl_take isl_union_pw_aff *upa);
3211 __isl_give isl_union_pw_multi_aff *
3212 isl_union_pw_multi_aff_copy(
3213 __isl_keep isl_union_pw_multi_aff *upma);
3214 __isl_null isl_union_pw_multi_aff *
3215 isl_union_pw_multi_aff_free(
3216 __isl_take isl_union_pw_multi_aff *upma);
3218 #include <isl/polynomial.h>
3219 __isl_give isl_union_pw_qpolynomial *
3220 isl_union_pw_qpolynomial_copy(
3221 __isl_keep isl_union_pw_qpolynomial *upwqp);
3222 __isl_null isl_union_pw_qpolynomial *
3223 isl_union_pw_qpolynomial_free(
3224 __isl_take isl_union_pw_qpolynomial *upwqp);
3225 __isl_give isl_union_pw_qpolynomial_fold *
3226 isl_union_pw_qpolynomial_fold_copy(
3227 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3228 __isl_null isl_union_pw_qpolynomial_fold *
3229 isl_union_pw_qpolynomial_fold_free(
3230 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3232 To iterate over the base expressions in a union expression,
3233 use the following functions.
3235 #include <isl/aff.h>
3236 int isl_union_pw_aff_n_pw_aff(
3237 __isl_keep isl_union_pw_aff *upa);
3238 isl_stat isl_union_pw_aff_foreach_pw_aff(
3239 __isl_keep isl_union_pw_aff *upa,
3240 isl_stat (*fn)(__isl_take isl_pw_aff *ma,
3241 void *user), void *user);
3242 int isl_union_pw_multi_aff_n_pw_multi_aff(
3243 __isl_keep isl_union_pw_multi_aff *upma);
3244 isl_stat isl_union_pw_multi_aff_foreach_pw_multi_aff(
3245 __isl_keep isl_union_pw_multi_aff *upma,
3246 isl_stat (*fn)(__isl_take isl_pw_multi_aff *pma,
3247 void *user), void *user);
3249 #include <isl/polynomial.h>
3250 int isl_union_pw_qpolynomial_n_pw_qpolynomial(
3251 __isl_keep isl_union_pw_qpolynomial *upwqp);
3252 isl_stat isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3253 __isl_keep isl_union_pw_qpolynomial *upwqp,
3254 isl_stat (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
3255 void *user), void *user);
3256 int isl_union_pw_qpolynomial_fold_n_pw_qpolynomial_fold(
3257 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3258 isl_stat isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3259 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3260 isl_stat (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3261 void *user), void *user);
3263 To extract the base expression in a given space from a union, use
3264 the following functions.
3266 #include <isl/aff.h>
3267 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
3268 __isl_keep isl_union_pw_aff *upa,
3269 __isl_take isl_space *space);
3270 __isl_give isl_pw_multi_aff *
3271 isl_union_pw_multi_aff_extract_pw_multi_aff(
3272 __isl_keep isl_union_pw_multi_aff *upma,
3273 __isl_take isl_space *space);
3275 #include <isl/polynomial.h>
3276 __isl_give isl_pw_qpolynomial *
3277 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3278 __isl_keep isl_union_pw_qpolynomial *upwqp,
3279 __isl_take isl_space *space);
3281 =head2 Input and Output
3283 For set and relation,
3284 C<isl> supports its own input/output format, which is similar
3285 to the C<Omega> format, but also supports the C<PolyLib> format
3287 For other object types, typically only an C<isl> format is supported.
3289 =head3 C<isl> format
3291 The C<isl> format is similar to that of C<Omega>, but has a different
3292 syntax for describing the parameters and allows for the definition
3293 of an existentially quantified variable as the integer division
3294 of an affine expression.
3295 For example, the set of integers C<i> between C<0> and C<n>
3296 such that C<i % 10 <= 6> can be described as
3298 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
3301 A set or relation can have several disjuncts, separated
3302 by the keyword C<or>. Each disjunct is either a conjunction
3303 of constraints or a projection (C<exists>) of a conjunction
3304 of constraints. The constraints are separated by the keyword
3307 =head3 C<PolyLib> format
3309 If the represented set is a union, then the first line
3310 contains a single number representing the number of disjuncts.
3311 Otherwise, a line containing the number C<1> is optional.
3313 Each disjunct is represented by a matrix of constraints.
3314 The first line contains two numbers representing
3315 the number of rows and columns,
3316 where the number of rows is equal to the number of constraints
3317 and the number of columns is equal to two plus the number of variables.
3318 The following lines contain the actual rows of the constraint matrix.
3319 In each row, the first column indicates whether the constraint
3320 is an equality (C<0>) or inequality (C<1>). The final column
3321 corresponds to the constant term.
3323 If the set is parametric, then the coefficients of the parameters
3324 appear in the last columns before the constant column.
3325 The coefficients of any existentially quantified variables appear
3326 between those of the set variables and those of the parameters.
3328 =head3 Extended C<PolyLib> format
3330 The extended C<PolyLib> format is nearly identical to the
3331 C<PolyLib> format. The only difference is that the line
3332 containing the number of rows and columns of a constraint matrix
3333 also contains four additional numbers:
3334 the number of output dimensions, the number of input dimensions,
3335 the number of local dimensions (i.e., the number of existentially
3336 quantified variables) and the number of parameters.
3337 For sets, the number of ``output'' dimensions is equal
3338 to the number of set dimensions, while the number of ``input''
3343 Objects can be read from input using the following functions.
3345 #include <isl/val.h>
3346 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
3348 __isl_give isl_multi_val *isl_multi_val_read_from_str(
3349 isl_ctx *ctx, const char *str);
3351 #include <isl/set.h>
3352 __isl_give isl_basic_set *isl_basic_set_read_from_file(
3353 isl_ctx *ctx, FILE *input);
3354 __isl_give isl_basic_set *isl_basic_set_read_from_str(
3355 isl_ctx *ctx, const char *str);
3356 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
3358 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
3361 #include <isl/map.h>
3362 __isl_give isl_basic_map *isl_basic_map_read_from_file(
3363 isl_ctx *ctx, FILE *input);
3364 __isl_give isl_basic_map *isl_basic_map_read_from_str(
3365 isl_ctx *ctx, const char *str);
3366 __isl_give isl_map *isl_map_read_from_file(
3367 isl_ctx *ctx, FILE *input);
3368 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
3371 #include <isl/union_set.h>
3372 __isl_give isl_union_set *isl_union_set_read_from_file(
3373 isl_ctx *ctx, FILE *input);
3374 __isl_give isl_union_set *isl_union_set_read_from_str(
3375 isl_ctx *ctx, const char *str);
3377 #include <isl/union_map.h>
3378 __isl_give isl_union_map *isl_union_map_read_from_file(
3379 isl_ctx *ctx, FILE *input);
3380 __isl_give isl_union_map *isl_union_map_read_from_str(
3381 isl_ctx *ctx, const char *str);
3383 #include <isl/aff.h>
3384 __isl_give isl_aff *isl_aff_read_from_str(
3385 isl_ctx *ctx, const char *str);
3386 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3387 isl_ctx *ctx, const char *str);
3388 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3389 isl_ctx *ctx, const char *str);
3390 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3391 isl_ctx *ctx, const char *str);
3392 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
3393 isl_ctx *ctx, const char *str);
3394 __isl_give isl_union_pw_multi_aff *
3395 isl_union_pw_multi_aff_read_from_str(
3396 isl_ctx *ctx, const char *str);
3397 __isl_give isl_multi_union_pw_aff *
3398 isl_multi_union_pw_aff_read_from_str(
3399 isl_ctx *ctx, const char *str);
3401 #include <isl/polynomial.h>
3402 __isl_give isl_union_pw_qpolynomial *
3403 isl_union_pw_qpolynomial_read_from_str(
3404 isl_ctx *ctx, const char *str);
3406 For sets and relations,
3407 the input format is autodetected and may be either the C<PolyLib> format
3408 or the C<isl> format.
3412 Before anything can be printed, an C<isl_printer> needs to
3415 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
3417 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
3418 __isl_null isl_printer *isl_printer_free(
3419 __isl_take isl_printer *printer);
3420 __isl_give char *isl_printer_get_str(
3421 __isl_keep isl_printer *printer);
3423 The printer can be inspected using the following functions.
3425 FILE *isl_printer_get_file(
3426 __isl_keep isl_printer *printer);
3427 int isl_printer_get_output_format(
3428 __isl_keep isl_printer *p);
3429 int isl_printer_get_yaml_style(__isl_keep isl_printer *p);
3431 The behavior of the printer can be modified in various ways
3433 __isl_give isl_printer *isl_printer_set_output_format(
3434 __isl_take isl_printer *p, int output_format);
3435 __isl_give isl_printer *isl_printer_set_indent(
3436 __isl_take isl_printer *p, int indent);
3437 __isl_give isl_printer *isl_printer_set_indent_prefix(
3438 __isl_take isl_printer *p, const char *prefix);
3439 __isl_give isl_printer *isl_printer_indent(
3440 __isl_take isl_printer *p, int indent);
3441 __isl_give isl_printer *isl_printer_set_prefix(
3442 __isl_take isl_printer *p, const char *prefix);
3443 __isl_give isl_printer *isl_printer_set_suffix(
3444 __isl_take isl_printer *p, const char *suffix);
3445 __isl_give isl_printer *isl_printer_set_yaml_style(
3446 __isl_take isl_printer *p, int yaml_style);
3448 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
3449 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
3450 and defaults to C<ISL_FORMAT_ISL>.
3451 Each line in the output is prefixed by C<indent_prefix>,
3452 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
3453 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
3454 In the C<PolyLib> format output,
3455 the coefficients of the existentially quantified variables
3456 appear between those of the set variables and those
3458 The function C<isl_printer_indent> increases the indentation
3459 by the specified amount (which may be negative).
3460 The YAML style may be either C<ISL_YAML_STYLE_BLOCK> or
3461 C<ISL_YAML_STYLE_FLOW> and when we are printing something
3464 To actually print something, use
3466 #include <isl/printer.h>
3467 __isl_give isl_printer *isl_printer_print_double(
3468 __isl_take isl_printer *p, double d);
3470 #include <isl/val.h>
3471 __isl_give isl_printer *isl_printer_print_val(
3472 __isl_take isl_printer *p, __isl_keep isl_val *v);
3474 #include <isl/set.h>
3475 __isl_give isl_printer *isl_printer_print_basic_set(
3476 __isl_take isl_printer *printer,
3477 __isl_keep isl_basic_set *bset);
3478 __isl_give isl_printer *isl_printer_print_set(
3479 __isl_take isl_printer *printer,
3480 __isl_keep isl_set *set);
3482 #include <isl/map.h>
3483 __isl_give isl_printer *isl_printer_print_basic_map(
3484 __isl_take isl_printer *printer,
3485 __isl_keep isl_basic_map *bmap);
3486 __isl_give isl_printer *isl_printer_print_map(
3487 __isl_take isl_printer *printer,
3488 __isl_keep isl_map *map);
3490 #include <isl/union_set.h>
3491 __isl_give isl_printer *isl_printer_print_union_set(
3492 __isl_take isl_printer *p,
3493 __isl_keep isl_union_set *uset);
3495 #include <isl/union_map.h>
3496 __isl_give isl_printer *isl_printer_print_union_map(
3497 __isl_take isl_printer *p,
3498 __isl_keep isl_union_map *umap);
3500 #include <isl/val.h>
3501 __isl_give isl_printer *isl_printer_print_multi_val(
3502 __isl_take isl_printer *p,
3503 __isl_keep isl_multi_val *mv);
3505 #include <isl/aff.h>
3506 __isl_give isl_printer *isl_printer_print_aff(
3507 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3508 __isl_give isl_printer *isl_printer_print_multi_aff(
3509 __isl_take isl_printer *p,
3510 __isl_keep isl_multi_aff *maff);
3511 __isl_give isl_printer *isl_printer_print_pw_aff(
3512 __isl_take isl_printer *p,
3513 __isl_keep isl_pw_aff *pwaff);
3514 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3515 __isl_take isl_printer *p,
3516 __isl_keep isl_pw_multi_aff *pma);
3517 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3518 __isl_take isl_printer *p,
3519 __isl_keep isl_multi_pw_aff *mpa);
3520 __isl_give isl_printer *isl_printer_print_union_pw_aff(
3521 __isl_take isl_printer *p,
3522 __isl_keep isl_union_pw_aff *upa);
3523 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3524 __isl_take isl_printer *p,
3525 __isl_keep isl_union_pw_multi_aff *upma);
3526 __isl_give isl_printer *
3527 isl_printer_print_multi_union_pw_aff(
3528 __isl_take isl_printer *p,
3529 __isl_keep isl_multi_union_pw_aff *mupa);
3531 #include <isl/polynomial.h>
3532 __isl_give isl_printer *isl_printer_print_qpolynomial(
3533 __isl_take isl_printer *p,
3534 __isl_keep isl_qpolynomial *qp);
3535 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3536 __isl_take isl_printer *p,
3537 __isl_keep isl_pw_qpolynomial *pwqp);
3538 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3539 __isl_take isl_printer *p,
3540 __isl_keep isl_union_pw_qpolynomial *upwqp);
3542 __isl_give isl_printer *
3543 isl_printer_print_pw_qpolynomial_fold(
3544 __isl_take isl_printer *p,
3545 __isl_keep isl_pw_qpolynomial_fold *pwf);
3546 __isl_give isl_printer *
3547 isl_printer_print_union_pw_qpolynomial_fold(
3548 __isl_take isl_printer *p,
3549 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3551 For C<isl_printer_print_qpolynomial>,
3552 C<isl_printer_print_pw_qpolynomial> and
3553 C<isl_printer_print_pw_qpolynomial_fold>,
3554 the output format of the printer
3555 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3556 For C<isl_printer_print_union_pw_qpolynomial> and
3557 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
3559 In case of printing in C<ISL_FORMAT_C>, the user may want
3560 to set the names of all dimensions first.
3562 C<isl> also provides limited support for printing YAML documents,
3563 just enough for the internal use for printing such documents.
3565 #include <isl/printer.h>
3566 __isl_give isl_printer *isl_printer_yaml_start_mapping(
3567 __isl_take isl_printer *p);
3568 __isl_give isl_printer *isl_printer_yaml_end_mapping(
3569 __isl_take isl_printer *p);
3570 __isl_give isl_printer *isl_printer_yaml_start_sequence(
3571 __isl_take isl_printer *p);
3572 __isl_give isl_printer *isl_printer_yaml_end_sequence(
3573 __isl_take isl_printer *p);
3574 __isl_give isl_printer *isl_printer_yaml_next(
3575 __isl_take isl_printer *p);
3577 A document is started by a call to either
3578 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3579 Anything printed to the printer after such a call belong to the
3580 first key of the mapping or the first element in the sequence.
3581 The function C<isl_printer_yaml_next> moves to the value if
3582 we are currently printing a mapping key, the next key if we
3583 are printing a value or the next element if we are printing
3584 an element in a sequence.
3585 Nested mappings and sequences are initiated by the same
3586 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3587 Each call to these functions needs to have a corresponding call to
3588 C<isl_printer_yaml_end_mapping> or C<isl_printer_yaml_end_sequence>.
3590 When called on a file printer, the following function flushes
3591 the file. When called on a string printer, the buffer is cleared.
3593 __isl_give isl_printer *isl_printer_flush(
3594 __isl_take isl_printer *p);
3596 Alternatively, a string representation can be obtained
3597 directly using the following functions, which always print
3600 #include <isl/space.h>
3601 __isl_give char *isl_space_to_str(
3602 __isl_keep isl_space *space);
3604 #include <isl/val.h>
3605 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
3606 __isl_give char *isl_multi_val_to_str(
3607 __isl_keep isl_multi_val *mv);
3609 #include <isl/set.h>
3610 __isl_give char *isl_set_to_str(
3611 __isl_keep isl_set *set);
3613 #include <isl/union_set.h>
3614 __isl_give char *isl_union_set_to_str(
3615 __isl_keep isl_union_set *uset);
3617 #include <isl/map.h>
3618 __isl_give char *isl_map_to_str(
3619 __isl_keep isl_map *map);
3621 #include <isl/union_map.h>
3622 __isl_give char *isl_union_map_to_str(
3623 __isl_keep isl_union_map *umap);
3625 #include <isl/aff.h>
3626 __isl_give char *isl_multi_aff_to_str(
3627 __isl_keep isl_multi_aff *aff);
3628 __isl_give char *isl_union_pw_aff_to_str(
3629 __isl_keep isl_union_pw_aff *upa);
3630 __isl_give char *isl_union_pw_multi_aff_to_str(
3631 __isl_keep isl_union_pw_multi_aff *upma);
3632 __isl_give char *isl_multi_union_pw_aff_to_str(
3633 __isl_keep isl_multi_union_pw_aff *mupa);
3637 =head3 Unary Properties
3643 The following functions test whether the given set or relation
3644 contains any integer points. The ``plain'' variants do not perform
3645 any computations, but simply check if the given set or relation
3646 is already known to be empty.
3648 isl_bool isl_basic_set_plain_is_empty(
3649 __isl_keep isl_basic_set *bset);
3650 isl_bool isl_basic_set_is_empty(
3651 __isl_keep isl_basic_set *bset);
3652 isl_bool isl_set_plain_is_empty(
3653 __isl_keep isl_set *set);
3654 isl_bool isl_set_is_empty(__isl_keep isl_set *set);
3655 isl_bool isl_union_set_is_empty(
3656 __isl_keep isl_union_set *uset);
3657 isl_bool isl_basic_map_plain_is_empty(
3658 __isl_keep isl_basic_map *bmap);
3659 isl_bool isl_basic_map_is_empty(
3660 __isl_keep isl_basic_map *bmap);
3661 isl_bool isl_map_plain_is_empty(
3662 __isl_keep isl_map *map);
3663 isl_bool isl_map_is_empty(__isl_keep isl_map *map);
3664 isl_bool isl_union_map_is_empty(
3665 __isl_keep isl_union_map *umap);
3667 =item * Universality
3669 isl_bool isl_basic_set_is_universe(
3670 __isl_keep isl_basic_set *bset);
3671 isl_bool isl_basic_map_is_universe(
3672 __isl_keep isl_basic_map *bmap);
3673 isl_bool isl_set_plain_is_universe(
3674 __isl_keep isl_set *set);
3675 isl_bool isl_map_plain_is_universe(
3676 __isl_keep isl_map *map);
3678 =item * Single-valuedness
3680 #include <isl/set.h>
3681 isl_bool isl_set_is_singleton(__isl_keep isl_set *set);
3683 #include <isl/map.h>
3684 isl_bool isl_basic_map_is_single_valued(
3685 __isl_keep isl_basic_map *bmap);
3686 isl_bool isl_map_plain_is_single_valued(
3687 __isl_keep isl_map *map);
3688 isl_bool isl_map_is_single_valued(__isl_keep isl_map *map);
3690 #include <isl/union_map.h>
3691 isl_bool isl_union_map_is_single_valued(
3692 __isl_keep isl_union_map *umap);
3696 isl_bool isl_map_plain_is_injective(
3697 __isl_keep isl_map *map);
3698 isl_bool isl_map_is_injective(
3699 __isl_keep isl_map *map);
3700 isl_bool isl_union_map_plain_is_injective(
3701 __isl_keep isl_union_map *umap);
3702 isl_bool isl_union_map_is_injective(
3703 __isl_keep isl_union_map *umap);
3707 isl_bool isl_map_is_bijective(
3708 __isl_keep isl_map *map);
3709 isl_bool isl_union_map_is_bijective(
3710 __isl_keep isl_union_map *umap);
3714 __isl_give isl_val *
3715 isl_basic_map_plain_get_val_if_fixed(
3716 __isl_keep isl_basic_map *bmap,
3717 enum isl_dim_type type, unsigned pos);
3718 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
3719 __isl_keep isl_set *set,
3720 enum isl_dim_type type, unsigned pos);
3721 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
3722 __isl_keep isl_map *map,
3723 enum isl_dim_type type, unsigned pos);
3725 If the set or relation obviously lies on a hyperplane where the given dimension
3726 has a fixed value, then return that value.
3727 Otherwise return NaN.
3731 isl_stat isl_set_dim_residue_class_val(
3732 __isl_keep isl_set *set,
3733 int pos, __isl_give isl_val **modulo,
3734 __isl_give isl_val **residue);
3736 Check if the values of the given set dimension are equal to a fixed
3737 value modulo some integer value. If so, assign the modulo to C<*modulo>
3738 and the fixed value to C<*residue>. If the given dimension attains only
3739 a single value, then assign C<0> to C<*modulo> and the fixed value to
3741 If the dimension does not attain only a single value and if no modulo
3742 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
3746 To check whether the description of a set, relation or function depends
3747 on one or more given dimensions,
3748 the following functions can be used.
3750 #include <isl/constraint.h>
3751 isl_bool isl_constraint_involves_dims(
3752 __isl_keep isl_constraint *constraint,
3753 enum isl_dim_type type, unsigned first, unsigned n);
3755 #include <isl/set.h>
3756 isl_bool isl_basic_set_involves_dims(
3757 __isl_keep isl_basic_set *bset,
3758 enum isl_dim_type type, unsigned first, unsigned n);
3759 isl_bool isl_set_involves_dims(__isl_keep isl_set *set,
3760 enum isl_dim_type type, unsigned first, unsigned n);
3762 #include <isl/map.h>
3763 isl_bool isl_basic_map_involves_dims(
3764 __isl_keep isl_basic_map *bmap,
3765 enum isl_dim_type type, unsigned first, unsigned n);
3766 isl_bool isl_map_involves_dims(__isl_keep isl_map *map,
3767 enum isl_dim_type type, unsigned first, unsigned n);
3769 #include <isl/union_map.h>
3770 isl_bool isl_union_map_involves_dims(
3771 __isl_keep isl_union_map *umap,
3772 enum isl_dim_type type, unsigned first, unsigned n);
3774 #include <isl/aff.h>
3775 isl_bool isl_aff_involves_dims(__isl_keep isl_aff *aff,
3776 enum isl_dim_type type, unsigned first, unsigned n);
3777 isl_bool isl_pw_aff_involves_dims(
3778 __isl_keep isl_pw_aff *pwaff,
3779 enum isl_dim_type type, unsigned first, unsigned n);
3780 isl_bool isl_multi_aff_involves_dims(
3781 __isl_keep isl_multi_aff *ma,
3782 enum isl_dim_type type, unsigned first, unsigned n);
3783 isl_bool isl_multi_pw_aff_involves_dims(
3784 __isl_keep isl_multi_pw_aff *mpa,
3785 enum isl_dim_type type, unsigned first, unsigned n);
3787 #include <isl/polynomial.h>
3788 isl_bool isl_qpolynomial_involves_dims(
3789 __isl_keep isl_qpolynomial *qp,
3790 enum isl_dim_type type, unsigned first, unsigned n);
3792 Similarly, the following functions can be used to check whether
3793 a given dimension is involved in any lower or upper bound.
3795 #include <isl/set.h>
3796 isl_bool isl_set_dim_has_any_lower_bound(
3797 __isl_keep isl_set *set,
3798 enum isl_dim_type type, unsigned pos);
3799 isl_bool isl_set_dim_has_any_upper_bound(
3800 __isl_keep isl_set *set,
3801 enum isl_dim_type type, unsigned pos);
3803 Note that these functions return true even if there is a bound on
3804 the dimension on only some of the basic sets of C<set>.
3805 To check if they have a bound for all of the basic sets in C<set>,
3806 use the following functions instead.
3808 #include <isl/set.h>
3809 isl_bool isl_set_dim_has_lower_bound(
3810 __isl_keep isl_set *set,
3811 enum isl_dim_type type, unsigned pos);
3812 isl_bool isl_set_dim_has_upper_bound(
3813 __isl_keep isl_set *set,
3814 enum isl_dim_type type, unsigned pos);
3818 To check whether a set is a parameter domain, use this function:
3820 isl_bool isl_set_is_params(__isl_keep isl_set *set);
3821 isl_bool isl_union_set_is_params(
3822 __isl_keep isl_union_set *uset);
3826 The following functions check whether the space of the given
3827 (basic) set or relation range is a wrapped relation.
3829 #include <isl/space.h>
3830 isl_bool isl_space_is_wrapping(
3831 __isl_keep isl_space *space);
3832 isl_bool isl_space_domain_is_wrapping(
3833 __isl_keep isl_space *space);
3834 isl_bool isl_space_range_is_wrapping(
3835 __isl_keep isl_space *space);
3837 #include <isl/set.h>
3838 isl_bool isl_basic_set_is_wrapping(
3839 __isl_keep isl_basic_set *bset);
3840 isl_bool isl_set_is_wrapping(__isl_keep isl_set *set);
3842 #include <isl/map.h>
3843 isl_bool isl_map_domain_is_wrapping(
3844 __isl_keep isl_map *map);
3845 isl_bool isl_map_range_is_wrapping(
3846 __isl_keep isl_map *map);
3848 #include <isl/val.h>
3849 isl_bool isl_multi_val_range_is_wrapping(
3850 __isl_keep isl_multi_val *mv);
3852 #include <isl/aff.h>
3853 isl_bool isl_multi_aff_range_is_wrapping(
3854 __isl_keep isl_multi_aff *ma);
3855 isl_bool isl_multi_pw_aff_range_is_wrapping(
3856 __isl_keep isl_multi_pw_aff *mpa);
3857 isl_bool isl_multi_union_pw_aff_range_is_wrapping(
3858 __isl_keep isl_multi_union_pw_aff *mupa);
3860 The input to C<isl_space_is_wrapping> should
3861 be the space of a set, while that of
3862 C<isl_space_domain_is_wrapping> and
3863 C<isl_space_range_is_wrapping> should be the space of a relation.
3865 =item * Internal Product
3867 isl_bool isl_basic_map_can_zip(
3868 __isl_keep isl_basic_map *bmap);
3869 isl_bool isl_map_can_zip(__isl_keep isl_map *map);
3871 Check whether the product of domain and range of the given relation
3873 i.e., whether both domain and range are nested relations.
3877 isl_bool isl_basic_map_can_curry(
3878 __isl_keep isl_basic_map *bmap);
3879 isl_bool isl_map_can_curry(__isl_keep isl_map *map);
3881 Check whether the domain of the (basic) relation is a wrapped relation.
3883 isl_bool isl_basic_map_can_uncurry(
3884 __isl_keep isl_basic_map *bmap);
3885 isl_bool isl_map_can_uncurry(__isl_keep isl_map *map);
3887 Check whether the range of the (basic) relation is a wrapped relation.
3889 =item * Special Values
3891 #include <isl/aff.h>
3892 isl_bool isl_aff_is_cst(__isl_keep isl_aff *aff);
3893 isl_bool isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3895 Check whether the given expression is a constant.
3897 #include <isl/aff.h>
3898 isl_bool isl_aff_is_nan(__isl_keep isl_aff *aff);
3899 isl_bool isl_pw_aff_involves_nan(
3900 __isl_keep isl_pw_aff *pa);
3902 #include <isl/polynomial.h>
3903 isl_bool isl_qpolynomial_fold_is_nan(
3904 __isl_keep isl_qpolynomial_fold *fold);
3906 Check whether the given expression is equal to or involves NaN.
3908 #include <isl/aff.h>
3909 isl_bool isl_aff_plain_is_zero(
3910 __isl_keep isl_aff *aff);
3912 Check whether the affine expression is obviously zero.
3916 =head3 Binary Properties
3922 The following functions check whether two objects
3923 represent the same set, relation or function.
3924 The C<plain> variants only return true if the objects
3925 are obviously the same. That is, they may return false
3926 even if the objects are the same, but they will never
3927 return true if the objects are not the same.
3929 #include <isl/set.h>
3930 isl_bool isl_basic_set_plain_is_equal(
3931 __isl_keep isl_basic_set *bset1,
3932 __isl_keep isl_basic_set *bset2);
3933 isl_bool isl_basic_set_is_equal(
3934 __isl_keep isl_basic_set *bset1,
3935 __isl_keep isl_basic_set *bset2);
3936 isl_bool isl_set_plain_is_equal(
3937 __isl_keep isl_set *set1,
3938 __isl_keep isl_set *set2);
3939 isl_bool isl_set_is_equal(__isl_keep isl_set *set1,
3940 __isl_keep isl_set *set2);
3942 #include <isl/map.h>
3943 isl_bool isl_basic_map_is_equal(
3944 __isl_keep isl_basic_map *bmap1,
3945 __isl_keep isl_basic_map *bmap2);
3946 isl_bool isl_map_is_equal(__isl_keep isl_map *map1,
3947 __isl_keep isl_map *map2);
3948 isl_bool isl_map_plain_is_equal(
3949 __isl_keep isl_map *map1,
3950 __isl_keep isl_map *map2);
3952 #include <isl/union_set.h>
3953 isl_bool isl_union_set_is_equal(
3954 __isl_keep isl_union_set *uset1,
3955 __isl_keep isl_union_set *uset2);
3957 #include <isl/union_map.h>
3958 isl_bool isl_union_map_is_equal(
3959 __isl_keep isl_union_map *umap1,
3960 __isl_keep isl_union_map *umap2);
3962 #include <isl/aff.h>
3963 isl_bool isl_aff_plain_is_equal(
3964 __isl_keep isl_aff *aff1,
3965 __isl_keep isl_aff *aff2);
3966 isl_bool isl_multi_aff_plain_is_equal(
3967 __isl_keep isl_multi_aff *maff1,
3968 __isl_keep isl_multi_aff *maff2);
3969 isl_bool isl_pw_aff_plain_is_equal(
3970 __isl_keep isl_pw_aff *pwaff1,
3971 __isl_keep isl_pw_aff *pwaff2);
3972 isl_bool isl_pw_multi_aff_plain_is_equal(
3973 __isl_keep isl_pw_multi_aff *pma1,
3974 __isl_keep isl_pw_multi_aff *pma2);
3975 isl_bool isl_multi_pw_aff_plain_is_equal(
3976 __isl_keep isl_multi_pw_aff *mpa1,
3977 __isl_keep isl_multi_pw_aff *mpa2);
3978 isl_bool isl_multi_pw_aff_is_equal(
3979 __isl_keep isl_multi_pw_aff *mpa1,
3980 __isl_keep isl_multi_pw_aff *mpa2);
3981 isl_bool isl_union_pw_aff_plain_is_equal(
3982 __isl_keep isl_union_pw_aff *upa1,
3983 __isl_keep isl_union_pw_aff *upa2);
3984 isl_bool isl_union_pw_multi_aff_plain_is_equal(
3985 __isl_keep isl_union_pw_multi_aff *upma1,
3986 __isl_keep isl_union_pw_multi_aff *upma2);
3987 isl_bool isl_multi_union_pw_aff_plain_is_equal(
3988 __isl_keep isl_multi_union_pw_aff *mupa1,
3989 __isl_keep isl_multi_union_pw_aff *mupa2);
3991 #include <isl/polynomial.h>
3992 isl_bool isl_union_pw_qpolynomial_plain_is_equal(
3993 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3994 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3995 isl_bool isl_union_pw_qpolynomial_fold_plain_is_equal(
3996 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3997 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3999 =item * Disjointness
4001 #include <isl/set.h>
4002 isl_bool isl_basic_set_is_disjoint(
4003 __isl_keep isl_basic_set *bset1,
4004 __isl_keep isl_basic_set *bset2);
4005 isl_bool isl_set_plain_is_disjoint(
4006 __isl_keep isl_set *set1,
4007 __isl_keep isl_set *set2);
4008 isl_bool isl_set_is_disjoint(__isl_keep isl_set *set1,
4009 __isl_keep isl_set *set2);
4011 #include <isl/map.h>
4012 isl_bool isl_basic_map_is_disjoint(
4013 __isl_keep isl_basic_map *bmap1,
4014 __isl_keep isl_basic_map *bmap2);
4015 isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1,
4016 __isl_keep isl_map *map2);
4018 #include <isl/union_set.h>
4019 isl_bool isl_union_set_is_disjoint(
4020 __isl_keep isl_union_set *uset1,
4021 __isl_keep isl_union_set *uset2);
4023 #include <isl/union_map.h>
4024 isl_bool isl_union_map_is_disjoint(
4025 __isl_keep isl_union_map *umap1,
4026 __isl_keep isl_union_map *umap2);
4030 isl_bool isl_basic_set_is_subset(
4031 __isl_keep isl_basic_set *bset1,
4032 __isl_keep isl_basic_set *bset2);
4033 isl_bool isl_set_is_subset(__isl_keep isl_set *set1,
4034 __isl_keep isl_set *set2);
4035 isl_bool isl_set_is_strict_subset(
4036 __isl_keep isl_set *set1,
4037 __isl_keep isl_set *set2);
4038 isl_bool isl_union_set_is_subset(
4039 __isl_keep isl_union_set *uset1,
4040 __isl_keep isl_union_set *uset2);
4041 isl_bool isl_union_set_is_strict_subset(
4042 __isl_keep isl_union_set *uset1,
4043 __isl_keep isl_union_set *uset2);
4044 isl_bool isl_basic_map_is_subset(
4045 __isl_keep isl_basic_map *bmap1,
4046 __isl_keep isl_basic_map *bmap2);
4047 isl_bool isl_basic_map_is_strict_subset(
4048 __isl_keep isl_basic_map *bmap1,
4049 __isl_keep isl_basic_map *bmap2);
4050 isl_bool isl_map_is_subset(
4051 __isl_keep isl_map *map1,
4052 __isl_keep isl_map *map2);
4053 isl_bool isl_map_is_strict_subset(
4054 __isl_keep isl_map *map1,
4055 __isl_keep isl_map *map2);
4056 isl_bool isl_union_map_is_subset(
4057 __isl_keep isl_union_map *umap1,
4058 __isl_keep isl_union_map *umap2);
4059 isl_bool isl_union_map_is_strict_subset(
4060 __isl_keep isl_union_map *umap1,
4061 __isl_keep isl_union_map *umap2);
4063 Check whether the first argument is a (strict) subset of the
4068 Every comparison function returns a negative value if the first
4069 argument is considered smaller than the second, a positive value
4070 if the first argument is considered greater and zero if the two
4071 constraints are considered the same by the comparison criterion.
4073 #include <isl/constraint.h>
4074 int isl_constraint_plain_cmp(
4075 __isl_keep isl_constraint *c1,
4076 __isl_keep isl_constraint *c2);
4078 This function is useful for sorting C<isl_constraint>s.
4079 The order depends on the internal representation of the inputs.
4080 The order is fixed over different calls to the function (assuming
4081 the internal representation of the inputs has not changed), but may
4082 change over different versions of C<isl>.
4084 #include <isl/constraint.h>
4085 int isl_constraint_cmp_last_non_zero(
4086 __isl_keep isl_constraint *c1,
4087 __isl_keep isl_constraint *c2);
4089 This function can be used to sort constraints that live in the same
4090 local space. Constraints that involve ``earlier'' dimensions or
4091 that have a smaller coefficient for the shared latest dimension
4092 are considered smaller than other constraints.
4093 This function only defines a B<partial> order.
4095 #include <isl/set.h>
4096 int isl_set_plain_cmp(__isl_keep isl_set *set1,
4097 __isl_keep isl_set *set2);
4099 This function is useful for sorting C<isl_set>s.
4100 The order depends on the internal representation of the inputs.
4101 The order is fixed over different calls to the function (assuming
4102 the internal representation of the inputs has not changed), but may
4103 change over different versions of C<isl>.
4105 #include <isl/aff.h>
4106 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4107 __isl_keep isl_pw_aff *pa2);
4109 The function C<isl_pw_aff_plain_cmp> can be used to sort
4110 C<isl_pw_aff>s. The order is not strictly defined.
4111 The current order sorts expressions that only involve
4112 earlier dimensions before those that involve later dimensions.
4116 =head2 Unary Operations
4122 __isl_give isl_set *isl_set_complement(
4123 __isl_take isl_set *set);
4124 __isl_give isl_map *isl_map_complement(
4125 __isl_take isl_map *map);
4129 #include <isl/space.h>
4130 __isl_give isl_space *isl_space_reverse(
4131 __isl_take isl_space *space);
4133 #include <isl/map.h>
4134 __isl_give isl_basic_map *isl_basic_map_reverse(
4135 __isl_take isl_basic_map *bmap);
4136 __isl_give isl_map *isl_map_reverse(
4137 __isl_take isl_map *map);
4139 #include <isl/union_map.h>
4140 __isl_give isl_union_map *isl_union_map_reverse(
4141 __isl_take isl_union_map *umap);
4145 #include <isl/space.h>
4146 __isl_give isl_space *isl_space_domain(
4147 __isl_take isl_space *space);
4148 __isl_give isl_space *isl_space_range(
4149 __isl_take isl_space *space);
4150 __isl_give isl_space *isl_space_params(
4151 __isl_take isl_space *space);
4153 #include <isl/local_space.h>
4154 __isl_give isl_local_space *isl_local_space_domain(
4155 __isl_take isl_local_space *ls);
4156 __isl_give isl_local_space *isl_local_space_range(
4157 __isl_take isl_local_space *ls);
4159 #include <isl/set.h>
4160 __isl_give isl_basic_set *isl_basic_set_project_out(
4161 __isl_take isl_basic_set *bset,
4162 enum isl_dim_type type, unsigned first, unsigned n);
4163 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
4164 enum isl_dim_type type, unsigned first, unsigned n);
4165 __isl_give isl_basic_set *isl_basic_set_params(
4166 __isl_take isl_basic_set *bset);
4167 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
4169 #include <isl/map.h>
4170 __isl_give isl_basic_map *isl_basic_map_project_out(
4171 __isl_take isl_basic_map *bmap,
4172 enum isl_dim_type type, unsigned first, unsigned n);
4173 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
4174 enum isl_dim_type type, unsigned first, unsigned n);
4175 __isl_give isl_basic_set *isl_basic_map_domain(
4176 __isl_take isl_basic_map *bmap);
4177 __isl_give isl_basic_set *isl_basic_map_range(
4178 __isl_take isl_basic_map *bmap);
4179 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
4180 __isl_give isl_set *isl_map_domain(
4181 __isl_take isl_map *bmap);
4182 __isl_give isl_set *isl_map_range(
4183 __isl_take isl_map *map);
4185 #include <isl/union_set.h>
4186 __isl_give isl_union_set *isl_union_set_project_out(
4187 __isl_take isl_union_set *uset,
4188 enum isl_dim_type type,
4189 unsigned first, unsigned n);
4190 __isl_give isl_set *isl_union_set_params(
4191 __isl_take isl_union_set *uset);
4193 The function C<isl_union_set_project_out> can only project out
4196 #include <isl/union_map.h>
4197 __isl_give isl_union_map *isl_union_map_project_out(
4198 __isl_take isl_union_map *umap,
4199 enum isl_dim_type type, unsigned first, unsigned n);
4200 __isl_give isl_set *isl_union_map_params(
4201 __isl_take isl_union_map *umap);
4202 __isl_give isl_union_set *isl_union_map_domain(
4203 __isl_take isl_union_map *umap);
4204 __isl_give isl_union_set *isl_union_map_range(
4205 __isl_take isl_union_map *umap);
4207 The function C<isl_union_map_project_out> can only project out
4210 #include <isl/aff.h>
4211 __isl_give isl_aff *isl_aff_project_domain_on_params(
4212 __isl_take isl_aff *aff);
4213 __isl_give isl_pw_multi_aff *
4214 isl_pw_multi_aff_project_domain_on_params(
4215 __isl_take isl_pw_multi_aff *pma);
4216 __isl_give isl_set *isl_pw_aff_domain(
4217 __isl_take isl_pw_aff *pwaff);
4218 __isl_give isl_set *isl_pw_multi_aff_domain(
4219 __isl_take isl_pw_multi_aff *pma);
4220 __isl_give isl_set *isl_multi_pw_aff_domain(
4221 __isl_take isl_multi_pw_aff *mpa);
4222 __isl_give isl_union_set *isl_union_pw_aff_domain(
4223 __isl_take isl_union_pw_aff *upa);
4224 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4225 __isl_take isl_union_pw_multi_aff *upma);
4226 __isl_give isl_union_set *
4227 isl_multi_union_pw_aff_domain(
4228 __isl_take isl_multi_union_pw_aff *mupa);
4229 __isl_give isl_set *isl_pw_aff_params(
4230 __isl_take isl_pw_aff *pwa);
4232 The function C<isl_multi_union_pw_aff_domain> requires its
4233 input to have at least one set dimension.
4235 #include <isl/polynomial.h>
4236 __isl_give isl_qpolynomial *
4237 isl_qpolynomial_project_domain_on_params(
4238 __isl_take isl_qpolynomial *qp);
4239 __isl_give isl_pw_qpolynomial *
4240 isl_pw_qpolynomial_project_domain_on_params(
4241 __isl_take isl_pw_qpolynomial *pwqp);
4242 __isl_give isl_pw_qpolynomial_fold *
4243 isl_pw_qpolynomial_fold_project_domain_on_params(
4244 __isl_take isl_pw_qpolynomial_fold *pwf);
4245 __isl_give isl_set *isl_pw_qpolynomial_domain(
4246 __isl_take isl_pw_qpolynomial *pwqp);
4247 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4248 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4249 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4250 __isl_take isl_union_pw_qpolynomial *upwqp);
4252 #include <isl/space.h>
4253 __isl_give isl_space *isl_space_domain_map(
4254 __isl_take isl_space *space);
4255 __isl_give isl_space *isl_space_range_map(
4256 __isl_take isl_space *space);
4258 #include <isl/map.h>
4259 __isl_give isl_map *isl_set_wrapped_domain_map(
4260 __isl_take isl_set *set);
4261 __isl_give isl_basic_map *isl_basic_map_domain_map(
4262 __isl_take isl_basic_map *bmap);
4263 __isl_give isl_basic_map *isl_basic_map_range_map(
4264 __isl_take isl_basic_map *bmap);
4265 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
4266 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
4268 #include <isl/union_map.h>
4269 __isl_give isl_union_map *isl_union_map_domain_map(
4270 __isl_take isl_union_map *umap);
4271 __isl_give isl_union_pw_multi_aff *
4272 isl_union_map_domain_map_union_pw_multi_aff(
4273 __isl_take isl_union_map *umap);
4274 __isl_give isl_union_map *isl_union_map_range_map(
4275 __isl_take isl_union_map *umap);
4276 __isl_give isl_union_map *
4277 isl_union_set_wrapped_domain_map(
4278 __isl_take isl_union_set *uset);
4280 The functions above construct a (basic, regular or union) relation
4281 that maps (a wrapped version of) the input relation to its domain or range.
4282 C<isl_set_wrapped_domain_map> maps the input set to the domain
4283 of its wrapped relation.
4287 __isl_give isl_basic_set *isl_basic_set_eliminate(
4288 __isl_take isl_basic_set *bset,
4289 enum isl_dim_type type,
4290 unsigned first, unsigned n);
4291 __isl_give isl_set *isl_set_eliminate(
4292 __isl_take isl_set *set, enum isl_dim_type type,
4293 unsigned first, unsigned n);
4294 __isl_give isl_basic_map *isl_basic_map_eliminate(
4295 __isl_take isl_basic_map *bmap,
4296 enum isl_dim_type type,
4297 unsigned first, unsigned n);
4298 __isl_give isl_map *isl_map_eliminate(
4299 __isl_take isl_map *map, enum isl_dim_type type,
4300 unsigned first, unsigned n);
4302 Eliminate the coefficients for the given dimensions from the constraints,
4303 without removing the dimensions.
4305 =item * Constructing a set from a parameter domain
4307 A zero-dimensional space or (basic) set can be constructed
4308 on a given parameter domain using the following functions.
4310 #include <isl/space.h>
4311 __isl_give isl_space *isl_space_set_from_params(
4312 __isl_take isl_space *space);
4314 #include <isl/set.h>
4315 __isl_give isl_basic_set *isl_basic_set_from_params(
4316 __isl_take isl_basic_set *bset);
4317 __isl_give isl_set *isl_set_from_params(
4318 __isl_take isl_set *set);
4320 =item * Constructing a relation from a set
4322 Create a relation with the given set as domain or range.
4323 The range or domain of the created relation is a zero-dimensional
4324 flat anonymous space.
4326 #include <isl/space.h>
4327 __isl_give isl_space *isl_space_from_domain(
4328 __isl_take isl_space *space);
4329 __isl_give isl_space *isl_space_from_range(
4330 __isl_take isl_space *space);
4331 __isl_give isl_space *isl_space_map_from_set(
4332 __isl_take isl_space *space);
4333 __isl_give isl_space *isl_space_map_from_domain_and_range(
4334 __isl_take isl_space *domain,
4335 __isl_take isl_space *range);
4337 #include <isl/local_space.h>
4338 __isl_give isl_local_space *isl_local_space_from_domain(
4339 __isl_take isl_local_space *ls);
4341 #include <isl/map.h>
4342 __isl_give isl_map *isl_map_from_domain(
4343 __isl_take isl_set *set);
4344 __isl_give isl_map *isl_map_from_range(
4345 __isl_take isl_set *set);
4347 #include <isl/val.h>
4348 __isl_give isl_multi_val *isl_multi_val_from_range(
4349 __isl_take isl_multi_val *mv);
4351 #include <isl/aff.h>
4352 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4353 __isl_take isl_multi_aff *ma);
4354 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4355 __isl_take isl_pw_aff *pwa);
4356 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4357 __isl_take isl_multi_pw_aff *mpa);
4358 __isl_give isl_multi_union_pw_aff *
4359 isl_multi_union_pw_aff_from_range(
4360 __isl_take isl_multi_union_pw_aff *mupa);
4361 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4362 __isl_take isl_set *set);
4363 __isl_give isl_union_pw_multi_aff *
4364 isl_union_pw_multi_aff_from_domain(
4365 __isl_take isl_union_set *uset);
4369 #include <isl/set.h>
4370 __isl_give isl_basic_set *isl_basic_set_fix_si(
4371 __isl_take isl_basic_set *bset,
4372 enum isl_dim_type type, unsigned pos, int value);
4373 __isl_give isl_basic_set *isl_basic_set_fix_val(
4374 __isl_take isl_basic_set *bset,
4375 enum isl_dim_type type, unsigned pos,
4376 __isl_take isl_val *v);
4377 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
4378 enum isl_dim_type type, unsigned pos, int value);
4379 __isl_give isl_set *isl_set_fix_val(
4380 __isl_take isl_set *set,
4381 enum isl_dim_type type, unsigned pos,
4382 __isl_take isl_val *v);
4384 #include <isl/map.h>
4385 __isl_give isl_basic_map *isl_basic_map_fix_si(
4386 __isl_take isl_basic_map *bmap,
4387 enum isl_dim_type type, unsigned pos, int value);
4388 __isl_give isl_basic_map *isl_basic_map_fix_val(
4389 __isl_take isl_basic_map *bmap,
4390 enum isl_dim_type type, unsigned pos,
4391 __isl_take isl_val *v);
4392 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
4393 enum isl_dim_type type, unsigned pos, int value);
4394 __isl_give isl_map *isl_map_fix_val(
4395 __isl_take isl_map *map,
4396 enum isl_dim_type type, unsigned pos,
4397 __isl_take isl_val *v);
4399 #include <isl/aff.h>
4400 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4401 __isl_take isl_pw_multi_aff *pma,
4402 enum isl_dim_type type, unsigned pos, int value);
4404 #include <isl/polynomial.h>
4405 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4406 __isl_take isl_pw_qpolynomial *pwqp,
4407 enum isl_dim_type type, unsigned n,
4408 __isl_take isl_val *v);
4410 Intersect the set, relation or function domain
4411 with the hyperplane where the given
4412 dimension has the fixed given value.
4414 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
4415 __isl_take isl_basic_map *bmap,
4416 enum isl_dim_type type, unsigned pos, int value);
4417 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
4418 __isl_take isl_basic_map *bmap,
4419 enum isl_dim_type type, unsigned pos, int value);
4420 __isl_give isl_set *isl_set_lower_bound_si(
4421 __isl_take isl_set *set,
4422 enum isl_dim_type type, unsigned pos, int value);
4423 __isl_give isl_set *isl_set_lower_bound_val(
4424 __isl_take isl_set *set,
4425 enum isl_dim_type type, unsigned pos,
4426 __isl_take isl_val *value);
4427 __isl_give isl_map *isl_map_lower_bound_si(
4428 __isl_take isl_map *map,
4429 enum isl_dim_type type, unsigned pos, int value);
4430 __isl_give isl_set *isl_set_upper_bound_si(
4431 __isl_take isl_set *set,
4432 enum isl_dim_type type, unsigned pos, int value);
4433 __isl_give isl_set *isl_set_upper_bound_val(
4434 __isl_take isl_set *set,
4435 enum isl_dim_type type, unsigned pos,
4436 __isl_take isl_val *value);
4437 __isl_give isl_map *isl_map_upper_bound_si(
4438 __isl_take isl_map *map,
4439 enum isl_dim_type type, unsigned pos, int value);
4441 Intersect the set or relation with the half-space where the given
4442 dimension has a value bounded by the fixed given integer value.
4444 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
4445 enum isl_dim_type type1, int pos1,
4446 enum isl_dim_type type2, int pos2);
4447 __isl_give isl_basic_map *isl_basic_map_equate(
4448 __isl_take isl_basic_map *bmap,
4449 enum isl_dim_type type1, int pos1,
4450 enum isl_dim_type type2, int pos2);
4451 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
4452 enum isl_dim_type type1, int pos1,
4453 enum isl_dim_type type2, int pos2);
4455 Intersect the set or relation with the hyperplane where the given
4456 dimensions are equal to each other.
4458 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
4459 enum isl_dim_type type1, int pos1,
4460 enum isl_dim_type type2, int pos2);
4462 Intersect the relation with the hyperplane where the given
4463 dimensions have opposite values.
4465 __isl_give isl_map *isl_map_order_le(
4466 __isl_take isl_map *map,
4467 enum isl_dim_type type1, int pos1,
4468 enum isl_dim_type type2, int pos2);
4469 __isl_give isl_basic_map *isl_basic_map_order_ge(
4470 __isl_take isl_basic_map *bmap,
4471 enum isl_dim_type type1, int pos1,
4472 enum isl_dim_type type2, int pos2);
4473 __isl_give isl_map *isl_map_order_ge(
4474 __isl_take isl_map *map,
4475 enum isl_dim_type type1, int pos1,
4476 enum isl_dim_type type2, int pos2);
4477 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
4478 enum isl_dim_type type1, int pos1,
4479 enum isl_dim_type type2, int pos2);
4480 __isl_give isl_basic_map *isl_basic_map_order_gt(
4481 __isl_take isl_basic_map *bmap,
4482 enum isl_dim_type type1, int pos1,
4483 enum isl_dim_type type2, int pos2);
4484 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
4485 enum isl_dim_type type1, int pos1,
4486 enum isl_dim_type type2, int pos2);
4488 Intersect the relation with the half-space where the given
4489 dimensions satisfy the given ordering.
4493 #include <isl/aff.h>
4494 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4495 __isl_take isl_aff *aff);
4496 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4497 __isl_take isl_aff *aff);
4498 __isl_give isl_set *isl_pw_aff_pos_set(
4499 __isl_take isl_pw_aff *pa);
4500 __isl_give isl_set *isl_pw_aff_nonneg_set(
4501 __isl_take isl_pw_aff *pwaff);
4502 __isl_give isl_set *isl_pw_aff_zero_set(
4503 __isl_take isl_pw_aff *pwaff);
4504 __isl_give isl_set *isl_pw_aff_non_zero_set(
4505 __isl_take isl_pw_aff *pwaff);
4506 __isl_give isl_union_set *
4507 isl_union_pw_aff_zero_union_set(
4508 __isl_take isl_union_pw_aff *upa);
4509 __isl_give isl_union_set *
4510 isl_multi_union_pw_aff_zero_union_set(
4511 __isl_take isl_multi_union_pw_aff *mupa);
4513 The function C<isl_aff_neg_basic_set> returns a basic set
4514 containing those elements in the domain space
4515 of C<aff> where C<aff> is negative.
4516 The function C<isl_pw_aff_nonneg_set> returns a set
4517 containing those elements in the domain
4518 of C<pwaff> where C<pwaff> is non-negative.
4519 The function C<isl_multi_union_pw_aff_zero_union_set>
4520 returns a union set containing those elements
4521 in the domains of its elements where they are all zero.
4525 __isl_give isl_map *isl_set_identity(
4526 __isl_take isl_set *set);
4527 __isl_give isl_union_map *isl_union_set_identity(
4528 __isl_take isl_union_set *uset);
4529 __isl_give isl_union_pw_multi_aff *
4530 isl_union_set_identity_union_pw_multi_aff(
4531 __isl_take isl_union_set *uset);
4533 Construct an identity relation on the given (union) set.
4535 =item * Function Extraction
4537 A piecewise quasi affine expression that is equal to 1 on a set
4538 and 0 outside the set can be created using the following function.
4540 #include <isl/aff.h>
4541 __isl_give isl_pw_aff *isl_set_indicator_function(
4542 __isl_take isl_set *set);
4544 A piecewise multiple quasi affine expression can be extracted
4545 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4546 and the C<isl_map> is single-valued.
4547 In case of a conversion from an C<isl_union_map>
4548 to an C<isl_union_pw_multi_aff>, these properties need to hold
4549 in each domain space.
4550 A conversion to a C<isl_multi_union_pw_aff> additionally
4551 requires that the input is non-empty and involves only a single
4554 #include <isl/aff.h>
4555 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4556 __isl_take isl_set *set);
4557 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4558 __isl_take isl_map *map);
4560 __isl_give isl_union_pw_multi_aff *
4561 isl_union_pw_multi_aff_from_union_set(
4562 __isl_take isl_union_set *uset);
4563 __isl_give isl_union_pw_multi_aff *
4564 isl_union_pw_multi_aff_from_union_map(
4565 __isl_take isl_union_map *umap);
4567 __isl_give isl_multi_union_pw_aff *
4568 isl_multi_union_pw_aff_from_union_map(
4569 __isl_take isl_union_map *umap);
4573 __isl_give isl_basic_set *isl_basic_map_deltas(
4574 __isl_take isl_basic_map *bmap);
4575 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
4576 __isl_give isl_union_set *isl_union_map_deltas(
4577 __isl_take isl_union_map *umap);
4579 These functions return a (basic) set containing the differences
4580 between image elements and corresponding domain elements in the input.
4582 __isl_give isl_basic_map *isl_basic_map_deltas_map(
4583 __isl_take isl_basic_map *bmap);
4584 __isl_give isl_map *isl_map_deltas_map(
4585 __isl_take isl_map *map);
4586 __isl_give isl_union_map *isl_union_map_deltas_map(
4587 __isl_take isl_union_map *umap);
4589 The functions above construct a (basic, regular or union) relation
4590 that maps (a wrapped version of) the input relation to its delta set.
4594 Simplify the representation of a set, relation or functions by trying
4595 to combine pairs of basic sets or relations into a single
4596 basic set or relation.
4598 #include <isl/set.h>
4599 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
4601 #include <isl/map.h>
4602 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
4604 #include <isl/union_set.h>
4605 __isl_give isl_union_set *isl_union_set_coalesce(
4606 __isl_take isl_union_set *uset);
4608 #include <isl/union_map.h>
4609 __isl_give isl_union_map *isl_union_map_coalesce(
4610 __isl_take isl_union_map *umap);
4612 #include <isl/aff.h>
4613 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4614 __isl_take isl_pw_aff *pwqp);
4615 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4616 __isl_take isl_pw_multi_aff *pma);
4617 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4618 __isl_take isl_multi_pw_aff *mpa);
4619 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
4620 __isl_take isl_union_pw_aff *upa);
4621 __isl_give isl_union_pw_multi_aff *
4622 isl_union_pw_multi_aff_coalesce(
4623 __isl_take isl_union_pw_multi_aff *upma);
4625 #include <isl/polynomial.h>
4626 __isl_give isl_pw_qpolynomial_fold *
4627 isl_pw_qpolynomial_fold_coalesce(
4628 __isl_take isl_pw_qpolynomial_fold *pwf);
4629 __isl_give isl_union_pw_qpolynomial *
4630 isl_union_pw_qpolynomial_coalesce(
4631 __isl_take isl_union_pw_qpolynomial *upwqp);
4632 __isl_give isl_union_pw_qpolynomial_fold *
4633 isl_union_pw_qpolynomial_fold_coalesce(
4634 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4636 One of the methods for combining pairs of basic sets or relations
4637 can result in coefficients that are much larger than those that appear
4638 in the constraints of the input. By default, the coefficients are
4639 not allowed to grow larger, but this can be changed by unsetting
4640 the following option.
4642 isl_stat isl_options_set_coalesce_bounded_wrapping(
4643 isl_ctx *ctx, int val);
4644 int isl_options_get_coalesce_bounded_wrapping(
4647 =item * Detecting equalities
4649 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
4650 __isl_take isl_basic_set *bset);
4651 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
4652 __isl_take isl_basic_map *bmap);
4653 __isl_give isl_set *isl_set_detect_equalities(
4654 __isl_take isl_set *set);
4655 __isl_give isl_map *isl_map_detect_equalities(
4656 __isl_take isl_map *map);
4657 __isl_give isl_union_set *isl_union_set_detect_equalities(
4658 __isl_take isl_union_set *uset);
4659 __isl_give isl_union_map *isl_union_map_detect_equalities(
4660 __isl_take isl_union_map *umap);
4662 Simplify the representation of a set or relation by detecting implicit
4665 =item * Removing redundant constraints
4667 #include <isl/set.h>
4668 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
4669 __isl_take isl_basic_set *bset);
4670 __isl_give isl_set *isl_set_remove_redundancies(
4671 __isl_take isl_set *set);
4673 #include <isl/union_set.h>
4674 __isl_give isl_union_set *
4675 isl_union_set_remove_redundancies(
4676 __isl_take isl_union_set *uset);
4678 #include <isl/map.h>
4679 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
4680 __isl_take isl_basic_map *bmap);
4681 __isl_give isl_map *isl_map_remove_redundancies(
4682 __isl_take isl_map *map);
4684 #include <isl/union_map.h>
4685 __isl_give isl_union_map *
4686 isl_union_map_remove_redundancies(
4687 __isl_take isl_union_map *umap);
4691 __isl_give isl_basic_set *isl_set_convex_hull(
4692 __isl_take isl_set *set);
4693 __isl_give isl_basic_map *isl_map_convex_hull(
4694 __isl_take isl_map *map);
4696 If the input set or relation has any existentially quantified
4697 variables, then the result of these operations is currently undefined.
4701 #include <isl/set.h>
4702 __isl_give isl_basic_set *
4703 isl_set_unshifted_simple_hull(
4704 __isl_take isl_set *set);
4705 __isl_give isl_basic_set *isl_set_simple_hull(
4706 __isl_take isl_set *set);
4707 __isl_give isl_basic_set *
4708 isl_set_unshifted_simple_hull_from_set_list(
4709 __isl_take isl_set *set,
4710 __isl_take isl_set_list *list);
4712 #include <isl/map.h>
4713 __isl_give isl_basic_map *
4714 isl_map_unshifted_simple_hull(
4715 __isl_take isl_map *map);
4716 __isl_give isl_basic_map *isl_map_simple_hull(
4717 __isl_take isl_map *map);
4718 __isl_give isl_basic_map *
4719 isl_map_unshifted_simple_hull_from_map_list(
4720 __isl_take isl_map *map,
4721 __isl_take isl_map_list *list);
4723 #include <isl/union_map.h>
4724 __isl_give isl_union_map *isl_union_map_simple_hull(
4725 __isl_take isl_union_map *umap);
4727 These functions compute a single basic set or relation
4728 that contains the whole input set or relation.
4729 In particular, the output is described by translates
4730 of the constraints describing the basic sets or relations in the input.
4731 In case of C<isl_set_unshifted_simple_hull>, only the original
4732 constraints are used, without any translation.
4733 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
4734 C<isl_map_unshifted_simple_hull_from_map_list>, the
4735 constraints are taken from the elements of the second argument.
4739 (See \autoref{s:simple hull}.)
4745 __isl_give isl_basic_set *isl_basic_set_affine_hull(
4746 __isl_take isl_basic_set *bset);
4747 __isl_give isl_basic_set *isl_set_affine_hull(
4748 __isl_take isl_set *set);
4749 __isl_give isl_union_set *isl_union_set_affine_hull(
4750 __isl_take isl_union_set *uset);
4751 __isl_give isl_basic_map *isl_basic_map_affine_hull(
4752 __isl_take isl_basic_map *bmap);
4753 __isl_give isl_basic_map *isl_map_affine_hull(
4754 __isl_take isl_map *map);
4755 __isl_give isl_union_map *isl_union_map_affine_hull(
4756 __isl_take isl_union_map *umap);
4758 In case of union sets and relations, the affine hull is computed
4761 =item * Polyhedral hull
4763 __isl_give isl_basic_set *isl_set_polyhedral_hull(
4764 __isl_take isl_set *set);
4765 __isl_give isl_basic_map *isl_map_polyhedral_hull(
4766 __isl_take isl_map *map);
4767 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
4768 __isl_take isl_union_set *uset);
4769 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
4770 __isl_take isl_union_map *umap);
4772 These functions compute a single basic set or relation
4773 not involving any existentially quantified variables
4774 that contains the whole input set or relation.
4775 In case of union sets and relations, the polyhedral hull is computed
4778 =item * Other approximations
4780 #include <isl/set.h>
4781 __isl_give isl_basic_set *
4782 isl_basic_set_drop_constraints_involving_dims(
4783 __isl_take isl_basic_set *bset,
4784 enum isl_dim_type type,
4785 unsigned first, unsigned n);
4786 __isl_give isl_basic_set *
4787 isl_basic_set_drop_constraints_not_involving_dims(
4788 __isl_take isl_basic_set *bset,
4789 enum isl_dim_type type,
4790 unsigned first, unsigned n);
4791 __isl_give isl_set *
4792 isl_set_drop_constraints_involving_dims(
4793 __isl_take isl_set *set,
4794 enum isl_dim_type type,
4795 unsigned first, unsigned n);
4797 #include <isl/map.h>
4798 __isl_give isl_basic_map *
4799 isl_basic_map_drop_constraints_involving_dims(
4800 __isl_take isl_basic_map *bmap,
4801 enum isl_dim_type type,
4802 unsigned first, unsigned n);
4803 __isl_give isl_map *
4804 isl_map_drop_constraints_involving_dims(
4805 __isl_take isl_map *map,
4806 enum isl_dim_type type,
4807 unsigned first, unsigned n);
4809 These functions drop any constraints (not) involving the specified dimensions.
4810 Note that the result depends on the representation of the input.
4812 #include <isl/polynomial.h>
4813 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4814 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4815 __isl_give isl_union_pw_qpolynomial *
4816 isl_union_pw_qpolynomial_to_polynomial(
4817 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4819 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4820 the polynomial will be an overapproximation. If C<sign> is negative,
4821 it will be an underapproximation. If C<sign> is zero, the approximation
4822 will lie somewhere in between.
4826 __isl_give isl_basic_set *isl_basic_set_sample(
4827 __isl_take isl_basic_set *bset);
4828 __isl_give isl_basic_set *isl_set_sample(
4829 __isl_take isl_set *set);
4830 __isl_give isl_basic_map *isl_basic_map_sample(
4831 __isl_take isl_basic_map *bmap);
4832 __isl_give isl_basic_map *isl_map_sample(
4833 __isl_take isl_map *map);
4835 If the input (basic) set or relation is non-empty, then return
4836 a singleton subset of the input. Otherwise, return an empty set.
4838 =item * Optimization
4840 #include <isl/ilp.h>
4841 __isl_give isl_val *isl_basic_set_max_val(
4842 __isl_keep isl_basic_set *bset,
4843 __isl_keep isl_aff *obj);
4844 __isl_give isl_val *isl_set_min_val(
4845 __isl_keep isl_set *set,
4846 __isl_keep isl_aff *obj);
4847 __isl_give isl_val *isl_set_max_val(
4848 __isl_keep isl_set *set,
4849 __isl_keep isl_aff *obj);
4851 Compute the minimum or maximum of the integer affine expression C<obj>
4852 over the points in C<set>, returning the result in C<opt>.
4853 The result is C<NULL> in case of an error, the optimal value in case
4854 there is one, negative infinity or infinity if the problem is unbounded and
4855 NaN if the problem is empty.
4857 =item * Parametric optimization
4859 __isl_give isl_pw_aff *isl_set_dim_min(
4860 __isl_take isl_set *set, int pos);
4861 __isl_give isl_pw_aff *isl_set_dim_max(
4862 __isl_take isl_set *set, int pos);
4863 __isl_give isl_pw_aff *isl_map_dim_max(
4864 __isl_take isl_map *map, int pos);
4866 Compute the minimum or maximum of the given set or output dimension
4867 as a function of the parameters (and input dimensions), but independently
4868 of the other set or output dimensions.
4869 For lexicographic optimization, see L<"Lexicographic Optimization">.
4873 The following functions compute either the set of (rational) coefficient
4874 values of valid constraints for the given set or the set of (rational)
4875 values satisfying the constraints with coefficients from the given set.
4876 Internally, these two sets of functions perform essentially the
4877 same operations, except that the set of coefficients is assumed to
4878 be a cone, while the set of values may be any polyhedron.
4879 The current implementation is based on the Farkas lemma and
4880 Fourier-Motzkin elimination, but this may change or be made optional
4881 in future. In particular, future implementations may use different
4882 dualization algorithms or skip the elimination step.
4884 __isl_give isl_basic_set *isl_basic_set_coefficients(
4885 __isl_take isl_basic_set *bset);
4886 __isl_give isl_basic_set *isl_set_coefficients(
4887 __isl_take isl_set *set);
4888 __isl_give isl_union_set *isl_union_set_coefficients(
4889 __isl_take isl_union_set *bset);
4890 __isl_give isl_basic_set *isl_basic_set_solutions(
4891 __isl_take isl_basic_set *bset);
4892 __isl_give isl_basic_set *isl_set_solutions(
4893 __isl_take isl_set *set);
4894 __isl_give isl_union_set *isl_union_set_solutions(
4895 __isl_take isl_union_set *bset);
4899 __isl_give isl_map *isl_map_fixed_power_val(
4900 __isl_take isl_map *map,
4901 __isl_take isl_val *exp);
4902 __isl_give isl_union_map *
4903 isl_union_map_fixed_power_val(
4904 __isl_take isl_union_map *umap,
4905 __isl_take isl_val *exp);
4907 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
4908 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
4909 of C<map> is computed.
4911 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
4913 __isl_give isl_union_map *isl_union_map_power(
4914 __isl_take isl_union_map *umap, int *exact);
4916 Compute a parametric representation for all positive powers I<k> of C<map>.
4917 The result maps I<k> to a nested relation corresponding to the
4918 I<k>th power of C<map>.
4919 The result may be an overapproximation. If the result is known to be exact,
4920 then C<*exact> is set to C<1>.
4922 =item * Transitive closure
4924 __isl_give isl_map *isl_map_transitive_closure(
4925 __isl_take isl_map *map, int *exact);
4926 __isl_give isl_union_map *isl_union_map_transitive_closure(
4927 __isl_take isl_union_map *umap, int *exact);
4929 Compute the transitive closure of C<map>.
4930 The result may be an overapproximation. If the result is known to be exact,
4931 then C<*exact> is set to C<1>.
4933 =item * Reaching path lengths
4935 __isl_give isl_map *isl_map_reaching_path_lengths(
4936 __isl_take isl_map *map, int *exact);
4938 Compute a relation that maps each element in the range of C<map>
4939 to the lengths of all paths composed of edges in C<map> that
4940 end up in the given element.
4941 The result may be an overapproximation. If the result is known to be exact,
4942 then C<*exact> is set to C<1>.
4943 To compute the I<maximal> path length, the resulting relation
4944 should be postprocessed by C<isl_map_lexmax>.
4945 In particular, if the input relation is a dependence relation
4946 (mapping sources to sinks), then the maximal path length corresponds
4947 to the free schedule.
4948 Note, however, that C<isl_map_lexmax> expects the maximum to be
4949 finite, so if the path lengths are unbounded (possibly due to
4950 the overapproximation), then you will get an error message.
4954 #include <isl/space.h>
4955 __isl_give isl_space *isl_space_wrap(
4956 __isl_take isl_space *space);
4957 __isl_give isl_space *isl_space_unwrap(
4958 __isl_take isl_space *space);
4960 #include <isl/local_space.h>
4961 __isl_give isl_local_space *isl_local_space_wrap(
4962 __isl_take isl_local_space *ls);
4964 #include <isl/set.h>
4965 __isl_give isl_basic_map *isl_basic_set_unwrap(
4966 __isl_take isl_basic_set *bset);
4967 __isl_give isl_map *isl_set_unwrap(
4968 __isl_take isl_set *set);
4970 #include <isl/map.h>
4971 __isl_give isl_basic_set *isl_basic_map_wrap(
4972 __isl_take isl_basic_map *bmap);
4973 __isl_give isl_set *isl_map_wrap(
4974 __isl_take isl_map *map);
4976 #include <isl/union_set.h>
4977 __isl_give isl_union_map *isl_union_set_unwrap(
4978 __isl_take isl_union_set *uset);
4980 #include <isl/union_map.h>
4981 __isl_give isl_union_set *isl_union_map_wrap(
4982 __isl_take isl_union_map *umap);
4984 The input to C<isl_space_unwrap> should
4985 be the space of a set, while that of
4986 C<isl_space_wrap> should be the space of a relation.
4987 Conversely, the output of C<isl_space_unwrap> is the space
4988 of a relation, while that of C<isl_space_wrap> is the space of a set.
4992 Remove any internal structure of domain (and range) of the given
4993 set or relation. If there is any such internal structure in the input,
4994 then the name of the space is also removed.
4996 #include <isl/local_space.h>
4997 __isl_give isl_local_space *
4998 isl_local_space_flatten_domain(
4999 __isl_take isl_local_space *ls);
5000 __isl_give isl_local_space *
5001 isl_local_space_flatten_range(
5002 __isl_take isl_local_space *ls);
5004 #include <isl/set.h>
5005 __isl_give isl_basic_set *isl_basic_set_flatten(
5006 __isl_take isl_basic_set *bset);
5007 __isl_give isl_set *isl_set_flatten(
5008 __isl_take isl_set *set);
5010 #include <isl/map.h>
5011 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
5012 __isl_take isl_basic_map *bmap);
5013 __isl_give isl_basic_map *isl_basic_map_flatten_range(
5014 __isl_take isl_basic_map *bmap);
5015 __isl_give isl_map *isl_map_flatten_range(
5016 __isl_take isl_map *map);
5017 __isl_give isl_map *isl_map_flatten_domain(
5018 __isl_take isl_map *map);
5019 __isl_give isl_basic_map *isl_basic_map_flatten(
5020 __isl_take isl_basic_map *bmap);
5021 __isl_give isl_map *isl_map_flatten(
5022 __isl_take isl_map *map);
5024 #include <isl/val.h>
5025 __isl_give isl_multi_val *isl_multi_val_flatten_range(
5026 __isl_take isl_multi_val *mv);
5028 #include <isl/aff.h>
5029 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
5030 __isl_take isl_multi_aff *ma);
5031 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
5032 __isl_take isl_multi_aff *ma);
5033 __isl_give isl_multi_pw_aff *
5034 isl_multi_pw_aff_flatten_range(
5035 __isl_take isl_multi_pw_aff *mpa);
5036 __isl_give isl_multi_union_pw_aff *
5037 isl_multi_union_pw_aff_flatten_range(
5038 __isl_take isl_multi_union_pw_aff *mupa);
5040 #include <isl/map.h>
5041 __isl_give isl_map *isl_set_flatten_map(
5042 __isl_take isl_set *set);
5044 The function above constructs a relation
5045 that maps the input set to a flattened version of the set.
5049 Lift the input set to a space with extra dimensions corresponding
5050 to the existentially quantified variables in the input.
5051 In particular, the result lives in a wrapped map where the domain
5052 is the original space and the range corresponds to the original
5053 existentially quantified variables.
5055 #include <isl/set.h>
5056 __isl_give isl_basic_set *isl_basic_set_lift(
5057 __isl_take isl_basic_set *bset);
5058 __isl_give isl_set *isl_set_lift(
5059 __isl_take isl_set *set);
5060 __isl_give isl_union_set *isl_union_set_lift(
5061 __isl_take isl_union_set *uset);
5063 Given a local space that contains the existentially quantified
5064 variables of a set, a basic relation that, when applied to
5065 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
5066 can be constructed using the following function.
5068 #include <isl/local_space.h>
5069 __isl_give isl_basic_map *isl_local_space_lifting(
5070 __isl_take isl_local_space *ls);
5072 #include <isl/aff.h>
5073 __isl_give isl_multi_aff *isl_multi_aff_lift(
5074 __isl_take isl_multi_aff *maff,
5075 __isl_give isl_local_space **ls);
5077 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
5078 then it is assigned the local space that lies at the basis of
5079 the lifting applied.
5081 =item * Internal Product
5083 #include <isl/space.h>
5084 __isl_give isl_space *isl_space_zip(
5085 __isl_take isl_space *space);
5087 #include <isl/map.h>
5088 __isl_give isl_basic_map *isl_basic_map_zip(
5089 __isl_take isl_basic_map *bmap);
5090 __isl_give isl_map *isl_map_zip(
5091 __isl_take isl_map *map);
5093 #include <isl/union_map.h>
5094 __isl_give isl_union_map *isl_union_map_zip(
5095 __isl_take isl_union_map *umap);
5097 Given a relation with nested relations for domain and range,
5098 interchange the range of the domain with the domain of the range.
5102 #include <isl/space.h>
5103 __isl_give isl_space *isl_space_curry(
5104 __isl_take isl_space *space);
5105 __isl_give isl_space *isl_space_uncurry(
5106 __isl_take isl_space *space);
5108 #include <isl/map.h>
5109 __isl_give isl_basic_map *isl_basic_map_curry(
5110 __isl_take isl_basic_map *bmap);
5111 __isl_give isl_basic_map *isl_basic_map_uncurry(
5112 __isl_take isl_basic_map *bmap);
5113 __isl_give isl_map *isl_map_curry(
5114 __isl_take isl_map *map);
5115 __isl_give isl_map *isl_map_uncurry(
5116 __isl_take isl_map *map);
5118 #include <isl/union_map.h>
5119 __isl_give isl_union_map *isl_union_map_curry(
5120 __isl_take isl_union_map *umap);
5121 __isl_give isl_union_map *isl_union_map_uncurry(
5122 __isl_take isl_union_map *umap);
5124 Given a relation with a nested relation for domain,
5125 the C<curry> functions
5126 move the range of the nested relation out of the domain
5127 and use it as the domain of a nested relation in the range,
5128 with the original range as range of this nested relation.
5129 The C<uncurry> functions perform the inverse operation.
5131 =item * Aligning parameters
5133 Change the order of the parameters of the given set, relation
5135 such that the first parameters match those of C<model>.
5136 This may involve the introduction of extra parameters.
5137 All parameters need to be named.
5139 #include <isl/space.h>
5140 __isl_give isl_space *isl_space_align_params(
5141 __isl_take isl_space *space1,
5142 __isl_take isl_space *space2)
5144 #include <isl/set.h>
5145 __isl_give isl_basic_set *isl_basic_set_align_params(
5146 __isl_take isl_basic_set *bset,
5147 __isl_take isl_space *model);
5148 __isl_give isl_set *isl_set_align_params(
5149 __isl_take isl_set *set,
5150 __isl_take isl_space *model);
5152 #include <isl/map.h>
5153 __isl_give isl_basic_map *isl_basic_map_align_params(
5154 __isl_take isl_basic_map *bmap,
5155 __isl_take isl_space *model);
5156 __isl_give isl_map *isl_map_align_params(
5157 __isl_take isl_map *map,
5158 __isl_take isl_space *model);
5160 #include <isl/val.h>
5161 __isl_give isl_multi_val *isl_multi_val_align_params(
5162 __isl_take isl_multi_val *mv,
5163 __isl_take isl_space *model);
5165 #include <isl/aff.h>
5166 __isl_give isl_aff *isl_aff_align_params(
5167 __isl_take isl_aff *aff,
5168 __isl_take isl_space *model);
5169 __isl_give isl_multi_aff *isl_multi_aff_align_params(
5170 __isl_take isl_multi_aff *multi,
5171 __isl_take isl_space *model);
5172 __isl_give isl_pw_aff *isl_pw_aff_align_params(
5173 __isl_take isl_pw_aff *pwaff,
5174 __isl_take isl_space *model);
5175 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
5176 __isl_take isl_pw_multi_aff *pma,
5177 __isl_take isl_space *model);
5178 __isl_give isl_union_pw_aff *
5179 isl_union_pw_aff_align_params(
5180 __isl_take isl_union_pw_aff *upa,
5181 __isl_take isl_space *model);
5182 __isl_give isl_union_pw_multi_aff *
5183 isl_union_pw_multi_aff_align_params(
5184 __isl_take isl_union_pw_multi_aff *upma,
5185 __isl_take isl_space *model);
5186 __isl_give isl_multi_union_pw_aff *
5187 isl_multi_union_pw_aff_align_params(
5188 __isl_take isl_multi_union_pw_aff *mupa,
5189 __isl_take isl_space *model);
5191 #include <isl/polynomial.h>
5192 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5193 __isl_take isl_qpolynomial *qp,
5194 __isl_take isl_space *model);
5196 =item * Unary Arithmethic Operations
5198 #include <isl/val.h>
5199 __isl_give isl_multi_val *isl_multi_val_neg(
5200 __isl_take isl_multi_val *mv);
5202 #include <isl/aff.h>
5203 __isl_give isl_aff *isl_aff_neg(
5204 __isl_take isl_aff *aff);
5205 __isl_give isl_multi_aff *isl_multi_aff_neg(
5206 __isl_take isl_multi_aff *ma);
5207 __isl_give isl_pw_aff *isl_pw_aff_neg(
5208 __isl_take isl_pw_aff *pwaff);
5209 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
5210 __isl_take isl_pw_multi_aff *pma);
5211 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
5212 __isl_take isl_multi_pw_aff *mpa);
5213 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
5214 __isl_take isl_union_pw_aff *upa);
5215 __isl_give isl_union_pw_multi_aff *
5216 isl_union_pw_multi_aff_neg(
5217 __isl_take isl_union_pw_multi_aff *upma);
5218 __isl_give isl_multi_union_pw_aff *
5219 isl_multi_union_pw_aff_neg(
5220 __isl_take isl_multi_union_pw_aff *mupa);
5221 __isl_give isl_aff *isl_aff_ceil(
5222 __isl_take isl_aff *aff);
5223 __isl_give isl_pw_aff *isl_pw_aff_ceil(
5224 __isl_take isl_pw_aff *pwaff);
5225 __isl_give isl_aff *isl_aff_floor(
5226 __isl_take isl_aff *aff);
5227 __isl_give isl_multi_aff *isl_multi_aff_floor(
5228 __isl_take isl_multi_aff *ma);
5229 __isl_give isl_pw_aff *isl_pw_aff_floor(
5230 __isl_take isl_pw_aff *pwaff);
5231 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
5232 __isl_take isl_union_pw_aff *upa);
5233 __isl_give isl_multi_union_pw_aff *
5234 isl_multi_union_pw_aff_floor(
5235 __isl_take isl_multi_union_pw_aff *mupa);
5237 #include <isl/aff.h>
5238 __isl_give isl_pw_aff *isl_pw_aff_list_min(
5239 __isl_take isl_pw_aff_list *list);
5240 __isl_give isl_pw_aff *isl_pw_aff_list_max(
5241 __isl_take isl_pw_aff_list *list);
5243 #include <isl/polynomial.h>
5244 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5245 __isl_take isl_qpolynomial *qp);
5246 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5247 __isl_take isl_pw_qpolynomial *pwqp);
5248 __isl_give isl_union_pw_qpolynomial *
5249 isl_union_pw_qpolynomial_neg(
5250 __isl_take isl_union_pw_qpolynomial *upwqp);
5251 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5252 __isl_take isl_qpolynomial *qp,
5254 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5255 __isl_take isl_pw_qpolynomial *pwqp,
5260 The following functions evaluate a function in a point.
5262 #include <isl/polynomial.h>
5263 __isl_give isl_val *isl_pw_qpolynomial_eval(
5264 __isl_take isl_pw_qpolynomial *pwqp,
5265 __isl_take isl_point *pnt);
5266 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5267 __isl_take isl_pw_qpolynomial_fold *pwf,
5268 __isl_take isl_point *pnt);
5269 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5270 __isl_take isl_union_pw_qpolynomial *upwqp,
5271 __isl_take isl_point *pnt);
5272 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5273 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5274 __isl_take isl_point *pnt);
5276 =item * Dimension manipulation
5278 It is usually not advisable to directly change the (input or output)
5279 space of a set or a relation as this removes the name and the internal
5280 structure of the space. However, the functions below can be useful
5281 to add new parameters, assuming
5282 C<isl_set_align_params> and C<isl_map_align_params>
5285 #include <isl/space.h>
5286 __isl_give isl_space *isl_space_add_dims(
5287 __isl_take isl_space *space,
5288 enum isl_dim_type type, unsigned n);
5289 __isl_give isl_space *isl_space_insert_dims(
5290 __isl_take isl_space *space,
5291 enum isl_dim_type type, unsigned pos, unsigned n);
5292 __isl_give isl_space *isl_space_drop_dims(
5293 __isl_take isl_space *space,
5294 enum isl_dim_type type, unsigned first, unsigned n);
5295 __isl_give isl_space *isl_space_move_dims(
5296 __isl_take isl_space *space,
5297 enum isl_dim_type dst_type, unsigned dst_pos,
5298 enum isl_dim_type src_type, unsigned src_pos,
5301 #include <isl/local_space.h>
5302 __isl_give isl_local_space *isl_local_space_add_dims(
5303 __isl_take isl_local_space *ls,
5304 enum isl_dim_type type, unsigned n);
5305 __isl_give isl_local_space *isl_local_space_insert_dims(
5306 __isl_take isl_local_space *ls,
5307 enum isl_dim_type type, unsigned first, unsigned n);
5308 __isl_give isl_local_space *isl_local_space_drop_dims(
5309 __isl_take isl_local_space *ls,
5310 enum isl_dim_type type, unsigned first, unsigned n);
5312 #include <isl/set.h>
5313 __isl_give isl_basic_set *isl_basic_set_add_dims(
5314 __isl_take isl_basic_set *bset,
5315 enum isl_dim_type type, unsigned n);
5316 __isl_give isl_set *isl_set_add_dims(
5317 __isl_take isl_set *set,
5318 enum isl_dim_type type, unsigned n);
5319 __isl_give isl_basic_set *isl_basic_set_insert_dims(
5320 __isl_take isl_basic_set *bset,
5321 enum isl_dim_type type, unsigned pos,
5323 __isl_give isl_set *isl_set_insert_dims(
5324 __isl_take isl_set *set,
5325 enum isl_dim_type type, unsigned pos, unsigned n);
5326 __isl_give isl_basic_set *isl_basic_set_move_dims(
5327 __isl_take isl_basic_set *bset,
5328 enum isl_dim_type dst_type, unsigned dst_pos,
5329 enum isl_dim_type src_type, unsigned src_pos,
5331 __isl_give isl_set *isl_set_move_dims(
5332 __isl_take isl_set *set,
5333 enum isl_dim_type dst_type, unsigned dst_pos,
5334 enum isl_dim_type src_type, unsigned src_pos,
5337 #include <isl/map.h>
5338 __isl_give isl_basic_map *isl_basic_map_add_dims(
5339 __isl_take isl_basic_map *bmap,
5340 enum isl_dim_type type, unsigned n);
5341 __isl_give isl_map *isl_map_add_dims(
5342 __isl_take isl_map *map,
5343 enum isl_dim_type type, unsigned n);
5344 __isl_give isl_basic_map *isl_basic_map_insert_dims(
5345 __isl_take isl_basic_map *bmap,
5346 enum isl_dim_type type, unsigned pos,
5348 __isl_give isl_map *isl_map_insert_dims(
5349 __isl_take isl_map *map,
5350 enum isl_dim_type type, unsigned pos, unsigned n);
5351 __isl_give isl_basic_map *isl_basic_map_move_dims(
5352 __isl_take isl_basic_map *bmap,
5353 enum isl_dim_type dst_type, unsigned dst_pos,
5354 enum isl_dim_type src_type, unsigned src_pos,
5356 __isl_give isl_map *isl_map_move_dims(
5357 __isl_take isl_map *map,
5358 enum isl_dim_type dst_type, unsigned dst_pos,
5359 enum isl_dim_type src_type, unsigned src_pos,
5362 #include <isl/val.h>
5363 __isl_give isl_multi_val *isl_multi_val_insert_dims(
5364 __isl_take isl_multi_val *mv,
5365 enum isl_dim_type type, unsigned first, unsigned n);
5366 __isl_give isl_multi_val *isl_multi_val_add_dims(
5367 __isl_take isl_multi_val *mv,
5368 enum isl_dim_type type, unsigned n);
5369 __isl_give isl_multi_val *isl_multi_val_drop_dims(
5370 __isl_take isl_multi_val *mv,
5371 enum isl_dim_type type, unsigned first, unsigned n);
5373 #include <isl/aff.h>
5374 __isl_give isl_aff *isl_aff_insert_dims(
5375 __isl_take isl_aff *aff,
5376 enum isl_dim_type type, unsigned first, unsigned n);
5377 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
5378 __isl_take isl_multi_aff *ma,
5379 enum isl_dim_type type, unsigned first, unsigned n);
5380 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
5381 __isl_take isl_pw_aff *pwaff,
5382 enum isl_dim_type type, unsigned first, unsigned n);
5383 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
5384 __isl_take isl_multi_pw_aff *mpa,
5385 enum isl_dim_type type, unsigned first, unsigned n);
5386 __isl_give isl_aff *isl_aff_add_dims(
5387 __isl_take isl_aff *aff,
5388 enum isl_dim_type type, unsigned n);
5389 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
5390 __isl_take isl_multi_aff *ma,
5391 enum isl_dim_type type, unsigned n);
5392 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
5393 __isl_take isl_pw_aff *pwaff,
5394 enum isl_dim_type type, unsigned n);
5395 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
5396 __isl_take isl_multi_pw_aff *mpa,
5397 enum isl_dim_type type, unsigned n);
5398 __isl_give isl_aff *isl_aff_drop_dims(
5399 __isl_take isl_aff *aff,
5400 enum isl_dim_type type, unsigned first, unsigned n);
5401 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
5402 __isl_take isl_multi_aff *maff,
5403 enum isl_dim_type type, unsigned first, unsigned n);
5404 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
5405 __isl_take isl_pw_aff *pwaff,
5406 enum isl_dim_type type, unsigned first, unsigned n);
5407 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
5408 __isl_take isl_pw_multi_aff *pma,
5409 enum isl_dim_type type, unsigned first, unsigned n);
5410 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
5411 __isl_take isl_union_pw_aff *upa,
5412 enum isl_dim_type type, unsigned first, unsigned n);
5413 __isl_give isl_union_pw_multi_aff *
5414 isl_union_pw_multi_aff_drop_dims(
5415 __isl_take isl_union_pw_multi_aff *upma,
5416 enum isl_dim_type type,
5417 unsigned first, unsigned n);
5418 __isl_give isl_multi_union_pw_aff *
5419 isl_multi_union_pw_aff_drop_dims(
5420 __isl_take isl_multi_union_pw_aff *mupa,
5421 enum isl_dim_type type, unsigned first,
5423 __isl_give isl_aff *isl_aff_move_dims(
5424 __isl_take isl_aff *aff,
5425 enum isl_dim_type dst_type, unsigned dst_pos,
5426 enum isl_dim_type src_type, unsigned src_pos,
5428 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
5429 __isl_take isl_multi_aff *ma,
5430 enum isl_dim_type dst_type, unsigned dst_pos,
5431 enum isl_dim_type src_type, unsigned src_pos,
5433 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
5434 __isl_take isl_pw_aff *pa,
5435 enum isl_dim_type dst_type, unsigned dst_pos,
5436 enum isl_dim_type src_type, unsigned src_pos,
5438 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
5439 __isl_take isl_multi_pw_aff *pma,
5440 enum isl_dim_type dst_type, unsigned dst_pos,
5441 enum isl_dim_type src_type, unsigned src_pos,
5444 #include <isl/polynomial.h>
5445 __isl_give isl_union_pw_qpolynomial *
5446 isl_union_pw_qpolynomial_drop_dims(
5447 __isl_take isl_union_pw_qpolynomial *upwqp,
5448 enum isl_dim_type type,
5449 unsigned first, unsigned n);
5450 __isl_give isl_union_pw_qpolynomial_fold *
5451 isl_union_pw_qpolynomial_fold_drop_dims(
5452 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5453 enum isl_dim_type type,
5454 unsigned first, unsigned n);
5456 The operations on union expressions can only manipulate parameters.
5460 =head2 Binary Operations
5462 The two arguments of a binary operation not only need to live
5463 in the same C<isl_ctx>, they currently also need to have
5464 the same (number of) parameters.
5466 =head3 Basic Operations
5470 =item * Intersection
5472 #include <isl/local_space.h>
5473 __isl_give isl_local_space *isl_local_space_intersect(
5474 __isl_take isl_local_space *ls1,
5475 __isl_take isl_local_space *ls2);
5477 #include <isl/set.h>
5478 __isl_give isl_basic_set *isl_basic_set_intersect_params(
5479 __isl_take isl_basic_set *bset1,
5480 __isl_take isl_basic_set *bset2);
5481 __isl_give isl_basic_set *isl_basic_set_intersect(
5482 __isl_take isl_basic_set *bset1,
5483 __isl_take isl_basic_set *bset2);
5484 __isl_give isl_basic_set *isl_basic_set_list_intersect(
5485 __isl_take struct isl_basic_set_list *list);
5486 __isl_give isl_set *isl_set_intersect_params(
5487 __isl_take isl_set *set,
5488 __isl_take isl_set *params);
5489 __isl_give isl_set *isl_set_intersect(
5490 __isl_take isl_set *set1,
5491 __isl_take isl_set *set2);
5493 #include <isl/map.h>
5494 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
5495 __isl_take isl_basic_map *bmap,
5496 __isl_take isl_basic_set *bset);
5497 __isl_give isl_basic_map *isl_basic_map_intersect_range(
5498 __isl_take isl_basic_map *bmap,
5499 __isl_take isl_basic_set *bset);
5500 __isl_give isl_basic_map *isl_basic_map_intersect(
5501 __isl_take isl_basic_map *bmap1,
5502 __isl_take isl_basic_map *bmap2);
5503 __isl_give isl_basic_map *isl_basic_map_list_intersect(
5504 __isl_take isl_basic_map_list *list);
5505 __isl_give isl_map *isl_map_intersect_params(
5506 __isl_take isl_map *map,
5507 __isl_take isl_set *params);
5508 __isl_give isl_map *isl_map_intersect_domain(
5509 __isl_take isl_map *map,
5510 __isl_take isl_set *set);
5511 __isl_give isl_map *isl_map_intersect_range(
5512 __isl_take isl_map *map,
5513 __isl_take isl_set *set);
5514 __isl_give isl_map *isl_map_intersect(
5515 __isl_take isl_map *map1,
5516 __isl_take isl_map *map2);
5518 #include <isl/union_set.h>
5519 __isl_give isl_union_set *isl_union_set_intersect_params(
5520 __isl_take isl_union_set *uset,
5521 __isl_take isl_set *set);
5522 __isl_give isl_union_set *isl_union_set_intersect(
5523 __isl_take isl_union_set *uset1,
5524 __isl_take isl_union_set *uset2);
5526 #include <isl/union_map.h>
5527 __isl_give isl_union_map *isl_union_map_intersect_params(
5528 __isl_take isl_union_map *umap,
5529 __isl_take isl_set *set);
5530 __isl_give isl_union_map *isl_union_map_intersect_domain(
5531 __isl_take isl_union_map *umap,
5532 __isl_take isl_union_set *uset);
5533 __isl_give isl_union_map *isl_union_map_intersect_range(
5534 __isl_take isl_union_map *umap,
5535 __isl_take isl_union_set *uset);
5536 __isl_give isl_union_map *isl_union_map_intersect(
5537 __isl_take isl_union_map *umap1,
5538 __isl_take isl_union_map *umap2);
5540 #include <isl/aff.h>
5541 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
5542 __isl_take isl_pw_aff *pa,
5543 __isl_take isl_set *set);
5544 __isl_give isl_multi_pw_aff *
5545 isl_multi_pw_aff_intersect_domain(
5546 __isl_take isl_multi_pw_aff *mpa,
5547 __isl_take isl_set *domain);
5548 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
5549 __isl_take isl_pw_multi_aff *pma,
5550 __isl_take isl_set *set);
5551 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
5552 __isl_take isl_union_pw_aff *upa,
5553 __isl_take isl_union_set *uset);
5554 __isl_give isl_union_pw_multi_aff *
5555 isl_union_pw_multi_aff_intersect_domain(
5556 __isl_take isl_union_pw_multi_aff *upma,
5557 __isl_take isl_union_set *uset);
5558 __isl_give isl_multi_union_pw_aff *
5559 isl_multi_union_pw_aff_intersect_domain(
5560 __isl_take isl_multi_union_pw_aff *mupa,
5561 __isl_take isl_union_set *uset);
5562 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
5563 __isl_take isl_pw_aff *pa,
5564 __isl_take isl_set *set);
5565 __isl_give isl_multi_pw_aff *
5566 isl_multi_pw_aff_intersect_params(
5567 __isl_take isl_multi_pw_aff *mpa,
5568 __isl_take isl_set *set);
5569 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
5570 __isl_take isl_pw_multi_aff *pma,
5571 __isl_take isl_set *set);
5572 __isl_give isl_union_pw_aff *
5573 isl_union_pw_aff_intersect_params(
5574 __isl_take isl_union_pw_aff *upa,
5575 __isl_give isl_union_pw_multi_aff *
5576 isl_union_pw_multi_aff_intersect_params(
5577 __isl_take isl_union_pw_multi_aff *upma,
5578 __isl_take isl_set *set);
5579 __isl_give isl_multi_union_pw_aff *
5580 isl_multi_union_pw_aff_intersect_params(
5581 __isl_take isl_multi_union_pw_aff *mupa,
5582 __isl_take isl_set *params);
5583 isl_multi_union_pw_aff_intersect_range(
5584 __isl_take isl_multi_union_pw_aff *mupa,
5585 __isl_take isl_set *set);
5587 #include <isl/polynomial.h>
5588 __isl_give isl_pw_qpolynomial *
5589 isl_pw_qpolynomial_intersect_domain(
5590 __isl_take isl_pw_qpolynomial *pwpq,
5591 __isl_take isl_set *set);
5592 __isl_give isl_union_pw_qpolynomial *
5593 isl_union_pw_qpolynomial_intersect_domain(
5594 __isl_take isl_union_pw_qpolynomial *upwpq,
5595 __isl_take isl_union_set *uset);
5596 __isl_give isl_union_pw_qpolynomial_fold *
5597 isl_union_pw_qpolynomial_fold_intersect_domain(
5598 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5599 __isl_take isl_union_set *uset);
5600 __isl_give isl_pw_qpolynomial *
5601 isl_pw_qpolynomial_intersect_params(
5602 __isl_take isl_pw_qpolynomial *pwpq,
5603 __isl_take isl_set *set);
5604 __isl_give isl_pw_qpolynomial_fold *
5605 isl_pw_qpolynomial_fold_intersect_params(
5606 __isl_take isl_pw_qpolynomial_fold *pwf,
5607 __isl_take isl_set *set);
5608 __isl_give isl_union_pw_qpolynomial *
5609 isl_union_pw_qpolynomial_intersect_params(
5610 __isl_take isl_union_pw_qpolynomial *upwpq,
5611 __isl_take isl_set *set);
5612 __isl_give isl_union_pw_qpolynomial_fold *
5613 isl_union_pw_qpolynomial_fold_intersect_params(
5614 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5615 __isl_take isl_set *set);
5617 The second argument to the C<_params> functions needs to be
5618 a parametric (basic) set. For the other functions, a parametric set
5619 for either argument is only allowed if the other argument is
5620 a parametric set as well.
5621 The list passed to C<isl_basic_set_list_intersect> needs to have
5622 at least one element and all elements need to live in the same space.
5623 The function C<isl_multi_union_pw_aff_intersect_range>
5624 restricts the input function to those shared domain elements
5625 that map to the specified range.
5629 #include <isl/set.h>
5630 __isl_give isl_set *isl_basic_set_union(
5631 __isl_take isl_basic_set *bset1,
5632 __isl_take isl_basic_set *bset2);
5633 __isl_give isl_set *isl_set_union(
5634 __isl_take isl_set *set1,
5635 __isl_take isl_set *set2);
5637 #include <isl/map.h>
5638 __isl_give isl_map *isl_basic_map_union(
5639 __isl_take isl_basic_map *bmap1,
5640 __isl_take isl_basic_map *bmap2);
5641 __isl_give isl_map *isl_map_union(
5642 __isl_take isl_map *map1,
5643 __isl_take isl_map *map2);
5645 #include <isl/union_set.h>
5646 __isl_give isl_union_set *isl_union_set_union(
5647 __isl_take isl_union_set *uset1,
5648 __isl_take isl_union_set *uset2);
5649 __isl_give isl_union_set *isl_union_set_list_union(
5650 __isl_take isl_union_set_list *list);
5652 #include <isl/union_map.h>
5653 __isl_give isl_union_map *isl_union_map_union(
5654 __isl_take isl_union_map *umap1,
5655 __isl_take isl_union_map *umap2);
5657 =item * Set difference
5659 #include <isl/set.h>
5660 __isl_give isl_set *isl_set_subtract(
5661 __isl_take isl_set *set1,
5662 __isl_take isl_set *set2);
5664 #include <isl/map.h>
5665 __isl_give isl_map *isl_map_subtract(
5666 __isl_take isl_map *map1,
5667 __isl_take isl_map *map2);
5668 __isl_give isl_map *isl_map_subtract_domain(
5669 __isl_take isl_map *map,
5670 __isl_take isl_set *dom);
5671 __isl_give isl_map *isl_map_subtract_range(
5672 __isl_take isl_map *map,
5673 __isl_take isl_set *dom);
5675 #include <isl/union_set.h>
5676 __isl_give isl_union_set *isl_union_set_subtract(
5677 __isl_take isl_union_set *uset1,
5678 __isl_take isl_union_set *uset2);
5680 #include <isl/union_map.h>
5681 __isl_give isl_union_map *isl_union_map_subtract(
5682 __isl_take isl_union_map *umap1,
5683 __isl_take isl_union_map *umap2);
5684 __isl_give isl_union_map *isl_union_map_subtract_domain(
5685 __isl_take isl_union_map *umap,
5686 __isl_take isl_union_set *dom);
5687 __isl_give isl_union_map *isl_union_map_subtract_range(
5688 __isl_take isl_union_map *umap,
5689 __isl_take isl_union_set *dom);
5691 #include <isl/aff.h>
5692 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
5693 __isl_take isl_pw_aff *pa,
5694 __isl_take isl_set *set);
5695 __isl_give isl_pw_multi_aff *
5696 isl_pw_multi_aff_subtract_domain(
5697 __isl_take isl_pw_multi_aff *pma,
5698 __isl_take isl_set *set);
5699 __isl_give isl_union_pw_aff *
5700 isl_union_pw_aff_subtract_domain(
5701 __isl_take isl_union_pw_aff *upa,
5702 __isl_take isl_union_set *uset);
5703 __isl_give isl_union_pw_multi_aff *
5704 isl_union_pw_multi_aff_subtract_domain(
5705 __isl_take isl_union_pw_multi_aff *upma,
5706 __isl_take isl_set *set);
5708 #include <isl/polynomial.h>
5709 __isl_give isl_pw_qpolynomial *
5710 isl_pw_qpolynomial_subtract_domain(
5711 __isl_take isl_pw_qpolynomial *pwpq,
5712 __isl_take isl_set *set);
5713 __isl_give isl_pw_qpolynomial_fold *
5714 isl_pw_qpolynomial_fold_subtract_domain(
5715 __isl_take isl_pw_qpolynomial_fold *pwf,
5716 __isl_take isl_set *set);
5717 __isl_give isl_union_pw_qpolynomial *
5718 isl_union_pw_qpolynomial_subtract_domain(
5719 __isl_take isl_union_pw_qpolynomial *upwpq,
5720 __isl_take isl_union_set *uset);
5721 __isl_give isl_union_pw_qpolynomial_fold *
5722 isl_union_pw_qpolynomial_fold_subtract_domain(
5723 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5724 __isl_take isl_union_set *uset);
5728 #include <isl/space.h>
5729 __isl_give isl_space *isl_space_join(
5730 __isl_take isl_space *left,
5731 __isl_take isl_space *right);
5733 #include <isl/map.h>
5734 __isl_give isl_basic_set *isl_basic_set_apply(
5735 __isl_take isl_basic_set *bset,
5736 __isl_take isl_basic_map *bmap);
5737 __isl_give isl_set *isl_set_apply(
5738 __isl_take isl_set *set,
5739 __isl_take isl_map *map);
5740 __isl_give isl_union_set *isl_union_set_apply(
5741 __isl_take isl_union_set *uset,
5742 __isl_take isl_union_map *umap);
5743 __isl_give isl_basic_map *isl_basic_map_apply_domain(
5744 __isl_take isl_basic_map *bmap1,
5745 __isl_take isl_basic_map *bmap2);
5746 __isl_give isl_basic_map *isl_basic_map_apply_range(
5747 __isl_take isl_basic_map *bmap1,
5748 __isl_take isl_basic_map *bmap2);
5749 __isl_give isl_map *isl_map_apply_domain(
5750 __isl_take isl_map *map1,
5751 __isl_take isl_map *map2);
5752 __isl_give isl_map *isl_map_apply_range(
5753 __isl_take isl_map *map1,
5754 __isl_take isl_map *map2);
5756 #include <isl/union_map.h>
5757 __isl_give isl_union_map *isl_union_map_apply_domain(
5758 __isl_take isl_union_map *umap1,
5759 __isl_take isl_union_map *umap2);
5760 __isl_give isl_union_map *isl_union_map_apply_range(
5761 __isl_take isl_union_map *umap1,
5762 __isl_take isl_union_map *umap2);
5764 #include <isl/aff.h>
5765 __isl_give isl_union_pw_aff *
5766 isl_multi_union_pw_aff_apply_aff(
5767 __isl_take isl_multi_union_pw_aff *mupa,
5768 __isl_take isl_aff *aff);
5769 __isl_give isl_union_pw_aff *
5770 isl_multi_union_pw_aff_apply_pw_aff(
5771 __isl_take isl_multi_union_pw_aff *mupa,
5772 __isl_take isl_pw_aff *pa);
5773 __isl_give isl_multi_union_pw_aff *
5774 isl_multi_union_pw_aff_apply_multi_aff(
5775 __isl_take isl_multi_union_pw_aff *mupa,
5776 __isl_take isl_multi_aff *ma);
5777 __isl_give isl_multi_union_pw_aff *
5778 isl_multi_union_pw_aff_apply_pw_multi_aff(
5779 __isl_take isl_multi_union_pw_aff *mupa,
5780 __isl_take isl_pw_multi_aff *pma);
5782 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
5783 over the shared domain of the elements of the input. The dimension is
5784 required to be greater than zero.
5785 The C<isl_multi_union_pw_aff> argument of
5786 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
5787 but only if the range of the C<isl_multi_aff> argument
5788 is also zero-dimensional.
5789 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
5791 #include <isl/polynomial.h>
5792 __isl_give isl_pw_qpolynomial_fold *
5793 isl_set_apply_pw_qpolynomial_fold(
5794 __isl_take isl_set *set,
5795 __isl_take isl_pw_qpolynomial_fold *pwf,
5797 __isl_give isl_pw_qpolynomial_fold *
5798 isl_map_apply_pw_qpolynomial_fold(
5799 __isl_take isl_map *map,
5800 __isl_take isl_pw_qpolynomial_fold *pwf,
5802 __isl_give isl_union_pw_qpolynomial_fold *
5803 isl_union_set_apply_union_pw_qpolynomial_fold(
5804 __isl_take isl_union_set *uset,
5805 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5807 __isl_give isl_union_pw_qpolynomial_fold *
5808 isl_union_map_apply_union_pw_qpolynomial_fold(
5809 __isl_take isl_union_map *umap,
5810 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5813 The functions taking a map
5814 compose the given map with the given piecewise quasipolynomial reduction.
5815 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5816 over all elements in the intersection of the range of the map
5817 and the domain of the piecewise quasipolynomial reduction
5818 as a function of an element in the domain of the map.
5819 The functions taking a set compute a bound over all elements in the
5820 intersection of the set and the domain of the
5821 piecewise quasipolynomial reduction.
5825 #include <isl/set.h>
5826 __isl_give isl_basic_set *
5827 isl_basic_set_preimage_multi_aff(
5828 __isl_take isl_basic_set *bset,
5829 __isl_take isl_multi_aff *ma);
5830 __isl_give isl_set *isl_set_preimage_multi_aff(
5831 __isl_take isl_set *set,
5832 __isl_take isl_multi_aff *ma);
5833 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
5834 __isl_take isl_set *set,
5835 __isl_take isl_pw_multi_aff *pma);
5836 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
5837 __isl_take isl_set *set,
5838 __isl_take isl_multi_pw_aff *mpa);
5840 #include <isl/union_set.h>
5841 __isl_give isl_union_set *
5842 isl_union_set_preimage_multi_aff(
5843 __isl_take isl_union_set *uset,
5844 __isl_take isl_multi_aff *ma);
5845 __isl_give isl_union_set *
5846 isl_union_set_preimage_pw_multi_aff(
5847 __isl_take isl_union_set *uset,
5848 __isl_take isl_pw_multi_aff *pma);
5849 __isl_give isl_union_set *
5850 isl_union_set_preimage_union_pw_multi_aff(
5851 __isl_take isl_union_set *uset,
5852 __isl_take isl_union_pw_multi_aff *upma);
5854 #include <isl/map.h>
5855 __isl_give isl_basic_map *
5856 isl_basic_map_preimage_domain_multi_aff(
5857 __isl_take isl_basic_map *bmap,
5858 __isl_take isl_multi_aff *ma);
5859 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
5860 __isl_take isl_map *map,
5861 __isl_take isl_multi_aff *ma);
5862 __isl_give isl_map *isl_map_preimage_range_multi_aff(
5863 __isl_take isl_map *map,
5864 __isl_take isl_multi_aff *ma);
5865 __isl_give isl_map *
5866 isl_map_preimage_domain_pw_multi_aff(
5867 __isl_take isl_map *map,
5868 __isl_take isl_pw_multi_aff *pma);
5869 __isl_give isl_map *
5870 isl_map_preimage_range_pw_multi_aff(
5871 __isl_take isl_map *map,
5872 __isl_take isl_pw_multi_aff *pma);
5873 __isl_give isl_map *
5874 isl_map_preimage_domain_multi_pw_aff(
5875 __isl_take isl_map *map,
5876 __isl_take isl_multi_pw_aff *mpa);
5877 __isl_give isl_basic_map *
5878 isl_basic_map_preimage_range_multi_aff(
5879 __isl_take isl_basic_map *bmap,
5880 __isl_take isl_multi_aff *ma);
5882 #include <isl/union_map.h>
5883 __isl_give isl_union_map *
5884 isl_union_map_preimage_domain_multi_aff(
5885 __isl_take isl_union_map *umap,
5886 __isl_take isl_multi_aff *ma);
5887 __isl_give isl_union_map *
5888 isl_union_map_preimage_range_multi_aff(
5889 __isl_take isl_union_map *umap,
5890 __isl_take isl_multi_aff *ma);
5891 __isl_give isl_union_map *
5892 isl_union_map_preimage_domain_pw_multi_aff(
5893 __isl_take isl_union_map *umap,
5894 __isl_take isl_pw_multi_aff *pma);
5895 __isl_give isl_union_map *
5896 isl_union_map_preimage_range_pw_multi_aff(
5897 __isl_take isl_union_map *umap,
5898 __isl_take isl_pw_multi_aff *pma);
5899 __isl_give isl_union_map *
5900 isl_union_map_preimage_domain_union_pw_multi_aff(
5901 __isl_take isl_union_map *umap,
5902 __isl_take isl_union_pw_multi_aff *upma);
5903 __isl_give isl_union_map *
5904 isl_union_map_preimage_range_union_pw_multi_aff(
5905 __isl_take isl_union_map *umap,
5906 __isl_take isl_union_pw_multi_aff *upma);
5908 These functions compute the preimage of the given set or map domain/range under
5909 the given function. In other words, the expression is plugged
5910 into the set description or into the domain/range of the map.
5914 #include <isl/aff.h>
5915 __isl_give isl_aff *isl_aff_pullback_aff(
5916 __isl_take isl_aff *aff1,
5917 __isl_take isl_aff *aff2);
5918 __isl_give isl_aff *isl_aff_pullback_multi_aff(
5919 __isl_take isl_aff *aff,
5920 __isl_take isl_multi_aff *ma);
5921 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
5922 __isl_take isl_pw_aff *pa,
5923 __isl_take isl_multi_aff *ma);
5924 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
5925 __isl_take isl_pw_aff *pa,
5926 __isl_take isl_pw_multi_aff *pma);
5927 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
5928 __isl_take isl_pw_aff *pa,
5929 __isl_take isl_multi_pw_aff *mpa);
5930 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
5931 __isl_take isl_multi_aff *ma1,
5932 __isl_take isl_multi_aff *ma2);
5933 __isl_give isl_pw_multi_aff *
5934 isl_pw_multi_aff_pullback_multi_aff(
5935 __isl_take isl_pw_multi_aff *pma,
5936 __isl_take isl_multi_aff *ma);
5937 __isl_give isl_multi_pw_aff *
5938 isl_multi_pw_aff_pullback_multi_aff(
5939 __isl_take isl_multi_pw_aff *mpa,
5940 __isl_take isl_multi_aff *ma);
5941 __isl_give isl_pw_multi_aff *
5942 isl_pw_multi_aff_pullback_pw_multi_aff(
5943 __isl_take isl_pw_multi_aff *pma1,
5944 __isl_take isl_pw_multi_aff *pma2);
5945 __isl_give isl_multi_pw_aff *
5946 isl_multi_pw_aff_pullback_pw_multi_aff(
5947 __isl_take isl_multi_pw_aff *mpa,
5948 __isl_take isl_pw_multi_aff *pma);
5949 __isl_give isl_multi_pw_aff *
5950 isl_multi_pw_aff_pullback_multi_pw_aff(
5951 __isl_take isl_multi_pw_aff *mpa1,
5952 __isl_take isl_multi_pw_aff *mpa2);
5953 __isl_give isl_union_pw_aff *
5954 isl_union_pw_aff_pullback_union_pw_multi_aff(
5955 __isl_take isl_union_pw_aff *upa,
5956 __isl_take isl_union_pw_multi_aff *upma);
5957 __isl_give isl_union_pw_multi_aff *
5958 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
5959 __isl_take isl_union_pw_multi_aff *upma1,
5960 __isl_take isl_union_pw_multi_aff *upma2);
5961 __isl_give isl_multi_union_pw_aff *
5962 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
5963 __isl_take isl_multi_union_pw_aff *mupa,
5964 __isl_take isl_union_pw_multi_aff *upma);
5966 These functions precompose the first expression by the second function.
5967 In other words, the second function is plugged
5968 into the first expression.
5972 #include <isl/aff.h>
5973 __isl_give isl_basic_set *isl_aff_le_basic_set(
5974 __isl_take isl_aff *aff1,
5975 __isl_take isl_aff *aff2);
5976 __isl_give isl_basic_set *isl_aff_ge_basic_set(
5977 __isl_take isl_aff *aff1,
5978 __isl_take isl_aff *aff2);
5979 __isl_give isl_set *isl_pw_aff_eq_set(
5980 __isl_take isl_pw_aff *pwaff1,
5981 __isl_take isl_pw_aff *pwaff2);
5982 __isl_give isl_set *isl_pw_aff_ne_set(
5983 __isl_take isl_pw_aff *pwaff1,
5984 __isl_take isl_pw_aff *pwaff2);
5985 __isl_give isl_set *isl_pw_aff_le_set(
5986 __isl_take isl_pw_aff *pwaff1,
5987 __isl_take isl_pw_aff *pwaff2);
5988 __isl_give isl_set *isl_pw_aff_lt_set(
5989 __isl_take isl_pw_aff *pwaff1,
5990 __isl_take isl_pw_aff *pwaff2);
5991 __isl_give isl_set *isl_pw_aff_ge_set(
5992 __isl_take isl_pw_aff *pwaff1,
5993 __isl_take isl_pw_aff *pwaff2);
5994 __isl_give isl_set *isl_pw_aff_gt_set(
5995 __isl_take isl_pw_aff *pwaff1,
5996 __isl_take isl_pw_aff *pwaff2);
5998 __isl_give isl_set *isl_multi_aff_lex_le_set(
5999 __isl_take isl_multi_aff *ma1,
6000 __isl_take isl_multi_aff *ma2);
6001 __isl_give isl_set *isl_multi_aff_lex_ge_set(
6002 __isl_take isl_multi_aff *ma1,
6003 __isl_take isl_multi_aff *ma2);
6005 __isl_give isl_set *isl_pw_aff_list_eq_set(
6006 __isl_take isl_pw_aff_list *list1,
6007 __isl_take isl_pw_aff_list *list2);
6008 __isl_give isl_set *isl_pw_aff_list_ne_set(
6009 __isl_take isl_pw_aff_list *list1,
6010 __isl_take isl_pw_aff_list *list2);
6011 __isl_give isl_set *isl_pw_aff_list_le_set(
6012 __isl_take isl_pw_aff_list *list1,
6013 __isl_take isl_pw_aff_list *list2);
6014 __isl_give isl_set *isl_pw_aff_list_lt_set(
6015 __isl_take isl_pw_aff_list *list1,
6016 __isl_take isl_pw_aff_list *list2);
6017 __isl_give isl_set *isl_pw_aff_list_ge_set(
6018 __isl_take isl_pw_aff_list *list1,
6019 __isl_take isl_pw_aff_list *list2);
6020 __isl_give isl_set *isl_pw_aff_list_gt_set(
6021 __isl_take isl_pw_aff_list *list1,
6022 __isl_take isl_pw_aff_list *list2);
6024 The function C<isl_aff_ge_basic_set> returns a basic set
6025 containing those elements in the shared space
6026 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
6027 The function C<isl_pw_aff_ge_set> returns a set
6028 containing those elements in the shared domain
6029 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
6030 greater than or equal to C<pwaff2>.
6031 The function C<isl_multi_aff_lex_le_set> returns a set
6032 containing those elements in the shared domain space
6033 where C<ma1> is lexicographically smaller than or
6035 The functions operating on C<isl_pw_aff_list> apply the corresponding
6036 C<isl_pw_aff> function to each pair of elements in the two lists.
6038 #include <isl/aff.h>
6039 __isl_give isl_map *isl_pw_aff_eq_map(
6040 __isl_take isl_pw_aff *pa1,
6041 __isl_take isl_pw_aff *pa2);
6042 __isl_give isl_map *isl_pw_aff_lt_map(
6043 __isl_take isl_pw_aff *pa1,
6044 __isl_take isl_pw_aff *pa2);
6045 __isl_give isl_map *isl_pw_aff_gt_map(
6046 __isl_take isl_pw_aff *pa1,
6047 __isl_take isl_pw_aff *pa2);
6049 __isl_give isl_map *isl_multi_pw_aff_eq_map(
6050 __isl_take isl_multi_pw_aff *mpa1,
6051 __isl_take isl_multi_pw_aff *mpa2);
6052 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
6053 __isl_take isl_multi_pw_aff *mpa1,
6054 __isl_take isl_multi_pw_aff *mpa2);
6055 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
6056 __isl_take isl_multi_pw_aff *mpa1,
6057 __isl_take isl_multi_pw_aff *mpa2);
6059 These functions return a map between domain elements of the arguments
6060 where the function values satisfy the given relation.
6062 #include <isl/union_map.h>
6063 __isl_give isl_union_map *
6064 isl_union_map_eq_at_multi_union_pw_aff(
6065 __isl_take isl_union_map *umap,
6066 __isl_take isl_multi_union_pw_aff *mupa);
6067 __isl_give isl_union_map *
6068 isl_union_map_lex_lt_at_multi_union_pw_aff(
6069 __isl_take isl_union_map *umap,
6070 __isl_take isl_multi_union_pw_aff *mupa);
6071 __isl_give isl_union_map *
6072 isl_union_map_lex_gt_at_multi_union_pw_aff(
6073 __isl_take isl_union_map *umap,
6074 __isl_take isl_multi_union_pw_aff *mupa);
6076 These functions select the subset of elements in the union map
6077 that have an equal or lexicographically smaller function value.
6079 =item * Cartesian Product
6081 #include <isl/space.h>
6082 __isl_give isl_space *isl_space_product(
6083 __isl_take isl_space *space1,
6084 __isl_take isl_space *space2);
6085 __isl_give isl_space *isl_space_domain_product(
6086 __isl_take isl_space *space1,
6087 __isl_take isl_space *space2);
6088 __isl_give isl_space *isl_space_range_product(
6089 __isl_take isl_space *space1,
6090 __isl_take isl_space *space2);
6093 C<isl_space_product>, C<isl_space_domain_product>
6094 and C<isl_space_range_product> take pairs or relation spaces and
6095 produce a single relations space, where either the domain, the range
6096 or both domain and range are wrapped spaces of relations between
6097 the domains and/or ranges of the input spaces.
6098 If the product is only constructed over the domain or the range
6099 then the ranges or the domains of the inputs should be the same.
6100 The function C<isl_space_product> also accepts a pair of set spaces,
6101 in which case it returns a wrapped space of a relation between the
6104 #include <isl/set.h>
6105 __isl_give isl_set *isl_set_product(
6106 __isl_take isl_set *set1,
6107 __isl_take isl_set *set2);
6109 #include <isl/map.h>
6110 __isl_give isl_basic_map *isl_basic_map_domain_product(
6111 __isl_take isl_basic_map *bmap1,
6112 __isl_take isl_basic_map *bmap2);
6113 __isl_give isl_basic_map *isl_basic_map_range_product(
6114 __isl_take isl_basic_map *bmap1,
6115 __isl_take isl_basic_map *bmap2);
6116 __isl_give isl_basic_map *isl_basic_map_product(
6117 __isl_take isl_basic_map *bmap1,
6118 __isl_take isl_basic_map *bmap2);
6119 __isl_give isl_map *isl_map_domain_product(
6120 __isl_take isl_map *map1,
6121 __isl_take isl_map *map2);
6122 __isl_give isl_map *isl_map_range_product(
6123 __isl_take isl_map *map1,
6124 __isl_take isl_map *map2);
6125 __isl_give isl_map *isl_map_product(
6126 __isl_take isl_map *map1,
6127 __isl_take isl_map *map2);
6129 #include <isl/union_set.h>
6130 __isl_give isl_union_set *isl_union_set_product(
6131 __isl_take isl_union_set *uset1,
6132 __isl_take isl_union_set *uset2);
6134 #include <isl/union_map.h>
6135 __isl_give isl_union_map *isl_union_map_domain_product(
6136 __isl_take isl_union_map *umap1,
6137 __isl_take isl_union_map *umap2);
6138 __isl_give isl_union_map *isl_union_map_range_product(
6139 __isl_take isl_union_map *umap1,
6140 __isl_take isl_union_map *umap2);
6141 __isl_give isl_union_map *isl_union_map_product(
6142 __isl_take isl_union_map *umap1,
6143 __isl_take isl_union_map *umap2);
6145 #include <isl/val.h>
6146 __isl_give isl_multi_val *isl_multi_val_range_product(
6147 __isl_take isl_multi_val *mv1,
6148 __isl_take isl_multi_val *mv2);
6149 __isl_give isl_multi_val *isl_multi_val_product(
6150 __isl_take isl_multi_val *mv1,
6151 __isl_take isl_multi_val *mv2);
6153 #include <isl/aff.h>
6154 __isl_give isl_multi_aff *isl_multi_aff_range_product(
6155 __isl_take isl_multi_aff *ma1,
6156 __isl_take isl_multi_aff *ma2);
6157 __isl_give isl_multi_aff *isl_multi_aff_product(
6158 __isl_take isl_multi_aff *ma1,
6159 __isl_take isl_multi_aff *ma2);
6160 __isl_give isl_multi_pw_aff *
6161 isl_multi_pw_aff_range_product(
6162 __isl_take isl_multi_pw_aff *mpa1,
6163 __isl_take isl_multi_pw_aff *mpa2);
6164 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
6165 __isl_take isl_multi_pw_aff *mpa1,
6166 __isl_take isl_multi_pw_aff *mpa2);
6167 __isl_give isl_pw_multi_aff *
6168 isl_pw_multi_aff_range_product(
6169 __isl_take isl_pw_multi_aff *pma1,
6170 __isl_take isl_pw_multi_aff *pma2);
6171 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
6172 __isl_take isl_pw_multi_aff *pma1,
6173 __isl_take isl_pw_multi_aff *pma2);
6174 __isl_give isl_multi_union_pw_aff *
6175 isl_multi_union_pw_aff_range_product(
6176 __isl_take isl_multi_union_pw_aff *mupa1,
6177 __isl_take isl_multi_union_pw_aff *mupa2);
6179 The above functions compute the cross product of the given
6180 sets, relations or functions. The domains and ranges of the results
6181 are wrapped maps between domains and ranges of the inputs.
6182 To obtain a ``flat'' product, use the following functions
6185 #include <isl/set.h>
6186 __isl_give isl_basic_set *isl_basic_set_flat_product(
6187 __isl_take isl_basic_set *bset1,
6188 __isl_take isl_basic_set *bset2);
6189 __isl_give isl_set *isl_set_flat_product(
6190 __isl_take isl_set *set1,
6191 __isl_take isl_set *set2);
6193 #include <isl/map.h>
6194 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
6195 __isl_take isl_basic_map *bmap1,
6196 __isl_take isl_basic_map *bmap2);
6197 __isl_give isl_map *isl_map_flat_domain_product(
6198 __isl_take isl_map *map1,
6199 __isl_take isl_map *map2);
6200 __isl_give isl_map *isl_map_flat_range_product(
6201 __isl_take isl_map *map1,
6202 __isl_take isl_map *map2);
6203 __isl_give isl_basic_map *isl_basic_map_flat_product(
6204 __isl_take isl_basic_map *bmap1,
6205 __isl_take isl_basic_map *bmap2);
6206 __isl_give isl_map *isl_map_flat_product(
6207 __isl_take isl_map *map1,
6208 __isl_take isl_map *map2);
6210 #include <isl/union_map.h>
6211 __isl_give isl_union_map *
6212 isl_union_map_flat_domain_product(
6213 __isl_take isl_union_map *umap1,
6214 __isl_take isl_union_map *umap2);
6215 __isl_give isl_union_map *
6216 isl_union_map_flat_range_product(
6217 __isl_take isl_union_map *umap1,
6218 __isl_take isl_union_map *umap2);
6220 #include <isl/val.h>
6221 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
6222 __isl_take isl_multi_val *mv1,
6223 __isl_take isl_multi_aff *mv2);
6225 #include <isl/aff.h>
6226 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
6227 __isl_take isl_multi_aff *ma1,
6228 __isl_take isl_multi_aff *ma2);
6229 __isl_give isl_pw_multi_aff *
6230 isl_pw_multi_aff_flat_range_product(
6231 __isl_take isl_pw_multi_aff *pma1,
6232 __isl_take isl_pw_multi_aff *pma2);
6233 __isl_give isl_multi_pw_aff *
6234 isl_multi_pw_aff_flat_range_product(
6235 __isl_take isl_multi_pw_aff *mpa1,
6236 __isl_take isl_multi_pw_aff *mpa2);
6237 __isl_give isl_union_pw_multi_aff *
6238 isl_union_pw_multi_aff_flat_range_product(
6239 __isl_take isl_union_pw_multi_aff *upma1,
6240 __isl_take isl_union_pw_multi_aff *upma2);
6241 __isl_give isl_multi_union_pw_aff *
6242 isl_multi_union_pw_aff_flat_range_product(
6243 __isl_take isl_multi_union_pw_aff *mupa1,
6244 __isl_take isl_multi_union_pw_aff *mupa2);
6246 #include <isl/space.h>
6247 __isl_give isl_space *isl_space_factor_domain(
6248 __isl_take isl_space *space);
6249 __isl_give isl_space *isl_space_factor_range(
6250 __isl_take isl_space *space);
6251 __isl_give isl_space *isl_space_domain_factor_domain(
6252 __isl_take isl_space *space);
6253 __isl_give isl_space *isl_space_domain_factor_range(
6254 __isl_take isl_space *space);
6255 __isl_give isl_space *isl_space_range_factor_domain(
6256 __isl_take isl_space *space);
6257 __isl_give isl_space *isl_space_range_factor_range(
6258 __isl_take isl_space *space);
6260 The functions C<isl_space_range_factor_domain> and
6261 C<isl_space_range_factor_range> extract the two arguments from
6262 the result of a call to C<isl_space_range_product>.
6264 The arguments of a call to C<isl_map_range_product> can be extracted
6265 from the result using the following functions.
6267 #include <isl/map.h>
6268 __isl_give isl_map *isl_map_factor_domain(
6269 __isl_take isl_map *map);
6270 __isl_give isl_map *isl_map_factor_range(
6271 __isl_take isl_map *map);
6272 __isl_give isl_map *isl_map_domain_factor_domain(
6273 __isl_take isl_map *map);
6274 __isl_give isl_map *isl_map_domain_factor_range(
6275 __isl_take isl_map *map);
6276 __isl_give isl_map *isl_map_range_factor_domain(
6277 __isl_take isl_map *map);
6278 __isl_give isl_map *isl_map_range_factor_range(
6279 __isl_take isl_map *map);
6281 #include <isl/union_map.h>
6282 __isl_give isl_union_map *isl_union_map_factor_domain(
6283 __isl_take isl_union_map *umap);
6284 __isl_give isl_union_map *isl_union_map_factor_range(
6285 __isl_take isl_union_map *umap);
6286 __isl_give isl_union_map *
6287 isl_union_map_domain_factor_domain(
6288 __isl_take isl_union_map *umap);
6289 __isl_give isl_union_map *
6290 isl_union_map_domain_factor_range(
6291 __isl_take isl_union_map *umap);
6292 __isl_give isl_union_map *
6293 isl_union_map_range_factor_range(
6294 __isl_take isl_union_map *umap);
6296 #include <isl/val.h>
6297 __isl_give isl_multi_val *
6298 isl_multi_val_range_factor_domain(
6299 __isl_take isl_multi_val *mv);
6300 __isl_give isl_multi_val *
6301 isl_multi_val_range_factor_range(
6302 __isl_take isl_multi_val *mv);
6304 #include <isl/aff.h>
6305 __isl_give isl_multi_aff *
6306 isl_multi_aff_range_factor_domain(
6307 __isl_take isl_multi_aff *ma);
6308 __isl_give isl_multi_aff *
6309 isl_multi_aff_range_factor_range(
6310 __isl_take isl_multi_aff *ma);
6311 __isl_give isl_multi_pw_aff *
6312 isl_multi_pw_aff_range_factor_domain(
6313 __isl_take isl_multi_pw_aff *mpa);
6314 __isl_give isl_multi_pw_aff *
6315 isl_multi_pw_aff_range_factor_range(
6316 __isl_take isl_multi_pw_aff *mpa);
6317 __isl_give isl_multi_union_pw_aff *
6318 isl_multi_union_pw_aff_range_factor_domain(
6319 __isl_take isl_multi_union_pw_aff *mupa);
6320 __isl_give isl_multi_union_pw_aff *
6321 isl_multi_union_pw_aff_range_factor_range(
6322 __isl_take isl_multi_union_pw_aff *mupa);
6324 The splice functions are a generalization of the flat product functions,
6325 where the second argument may be inserted at any position inside
6326 the first argument rather than being placed at the end.
6328 #include <isl/val.h>
6329 __isl_give isl_multi_val *isl_multi_val_range_splice(
6330 __isl_take isl_multi_val *mv1, unsigned pos,
6331 __isl_take isl_multi_val *mv2);
6333 #include <isl/aff.h>
6334 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
6335 __isl_take isl_multi_aff *ma1, unsigned pos,
6336 __isl_take isl_multi_aff *ma2);
6337 __isl_give isl_multi_aff *isl_multi_aff_splice(
6338 __isl_take isl_multi_aff *ma1,
6339 unsigned in_pos, unsigned out_pos,
6340 __isl_take isl_multi_aff *ma2);
6341 __isl_give isl_multi_pw_aff *
6342 isl_multi_pw_aff_range_splice(
6343 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
6344 __isl_take isl_multi_pw_aff *mpa2);
6345 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
6346 __isl_take isl_multi_pw_aff *mpa1,
6347 unsigned in_pos, unsigned out_pos,
6348 __isl_take isl_multi_pw_aff *mpa2);
6349 __isl_give isl_multi_union_pw_aff *
6350 isl_multi_union_pw_aff_range_splice(
6351 __isl_take isl_multi_union_pw_aff *mupa1,
6353 __isl_take isl_multi_union_pw_aff *mupa2);
6355 =item * Simplification
6357 When applied to a set or relation,
6358 the gist operation returns a set or relation that has the
6359 same intersection with the context as the input set or relation.
6360 Any implicit equality in the intersection is made explicit in the result,
6361 while all inequalities that are redundant with respect to the intersection
6363 In case of union sets and relations, the gist operation is performed
6366 When applied to a function,
6367 the gist operation applies the set gist operation to each of
6368 the cells in the domain of the input piecewise expression.
6369 The context is also exploited
6370 to simplify the expression associated to each cell.
6372 #include <isl/set.h>
6373 __isl_give isl_basic_set *isl_basic_set_gist(
6374 __isl_take isl_basic_set *bset,
6375 __isl_take isl_basic_set *context);
6376 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
6377 __isl_take isl_set *context);
6378 __isl_give isl_set *isl_set_gist_params(
6379 __isl_take isl_set *set,
6380 __isl_take isl_set *context);
6382 #include <isl/map.h>
6383 __isl_give isl_basic_map *isl_basic_map_gist(
6384 __isl_take isl_basic_map *bmap,
6385 __isl_take isl_basic_map *context);
6386 __isl_give isl_basic_map *isl_basic_map_gist_domain(
6387 __isl_take isl_basic_map *bmap,
6388 __isl_take isl_basic_set *context);
6389 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
6390 __isl_take isl_map *context);
6391 __isl_give isl_map *isl_map_gist_params(
6392 __isl_take isl_map *map,
6393 __isl_take isl_set *context);
6394 __isl_give isl_map *isl_map_gist_domain(
6395 __isl_take isl_map *map,
6396 __isl_take isl_set *context);
6397 __isl_give isl_map *isl_map_gist_range(
6398 __isl_take isl_map *map,
6399 __isl_take isl_set *context);
6401 #include <isl/union_set.h>
6402 __isl_give isl_union_set *isl_union_set_gist(
6403 __isl_take isl_union_set *uset,
6404 __isl_take isl_union_set *context);
6405 __isl_give isl_union_set *isl_union_set_gist_params(
6406 __isl_take isl_union_set *uset,
6407 __isl_take isl_set *set);
6409 #include <isl/union_map.h>
6410 __isl_give isl_union_map *isl_union_map_gist(
6411 __isl_take isl_union_map *umap,
6412 __isl_take isl_union_map *context);
6413 __isl_give isl_union_map *isl_union_map_gist_params(
6414 __isl_take isl_union_map *umap,
6415 __isl_take isl_set *set);
6416 __isl_give isl_union_map *isl_union_map_gist_domain(
6417 __isl_take isl_union_map *umap,
6418 __isl_take isl_union_set *uset);
6419 __isl_give isl_union_map *isl_union_map_gist_range(
6420 __isl_take isl_union_map *umap,
6421 __isl_take isl_union_set *uset);
6423 #include <isl/aff.h>
6424 __isl_give isl_aff *isl_aff_gist_params(
6425 __isl_take isl_aff *aff,
6426 __isl_take isl_set *context);
6427 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
6428 __isl_take isl_set *context);
6429 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
6430 __isl_take isl_multi_aff *maff,
6431 __isl_take isl_set *context);
6432 __isl_give isl_multi_aff *isl_multi_aff_gist(
6433 __isl_take isl_multi_aff *maff,
6434 __isl_take isl_set *context);
6435 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
6436 __isl_take isl_pw_aff *pwaff,
6437 __isl_take isl_set *context);
6438 __isl_give isl_pw_aff *isl_pw_aff_gist(
6439 __isl_take isl_pw_aff *pwaff,
6440 __isl_take isl_set *context);
6441 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
6442 __isl_take isl_pw_multi_aff *pma,
6443 __isl_take isl_set *set);
6444 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
6445 __isl_take isl_pw_multi_aff *pma,
6446 __isl_take isl_set *set);
6447 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
6448 __isl_take isl_multi_pw_aff *mpa,
6449 __isl_take isl_set *set);
6450 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
6451 __isl_take isl_multi_pw_aff *mpa,
6452 __isl_take isl_set *set);
6453 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
6454 __isl_take isl_union_pw_aff *upa,
6455 __isl_take isl_union_set *context);
6456 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
6457 __isl_take isl_union_pw_aff *upa,
6458 __isl_take isl_set *context);
6459 __isl_give isl_union_pw_multi_aff *
6460 isl_union_pw_multi_aff_gist_params(
6461 __isl_take isl_union_pw_multi_aff *upma,
6462 __isl_take isl_set *context);
6463 __isl_give isl_union_pw_multi_aff *
6464 isl_union_pw_multi_aff_gist(
6465 __isl_take isl_union_pw_multi_aff *upma,
6466 __isl_take isl_union_set *context);
6467 __isl_give isl_multi_union_pw_aff *
6468 isl_multi_union_pw_aff_gist_params(
6469 __isl_take isl_multi_union_pw_aff *aff,
6470 __isl_take isl_set *context);
6471 __isl_give isl_multi_union_pw_aff *
6472 isl_multi_union_pw_aff_gist(
6473 __isl_take isl_multi_union_pw_aff *aff,
6474 __isl_take isl_union_set *context);
6476 #include <isl/polynomial.h>
6477 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
6478 __isl_take isl_qpolynomial *qp,
6479 __isl_take isl_set *context);
6480 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
6481 __isl_take isl_qpolynomial *qp,
6482 __isl_take isl_set *context);
6483 __isl_give isl_qpolynomial_fold *
6484 isl_qpolynomial_fold_gist_params(
6485 __isl_take isl_qpolynomial_fold *fold,
6486 __isl_take isl_set *context);
6487 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
6488 __isl_take isl_qpolynomial_fold *fold,
6489 __isl_take isl_set *context);
6490 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
6491 __isl_take isl_pw_qpolynomial *pwqp,
6492 __isl_take isl_set *context);
6493 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
6494 __isl_take isl_pw_qpolynomial *pwqp,
6495 __isl_take isl_set *context);
6496 __isl_give isl_pw_qpolynomial_fold *
6497 isl_pw_qpolynomial_fold_gist(
6498 __isl_take isl_pw_qpolynomial_fold *pwf,
6499 __isl_take isl_set *context);
6500 __isl_give isl_pw_qpolynomial_fold *
6501 isl_pw_qpolynomial_fold_gist_params(
6502 __isl_take isl_pw_qpolynomial_fold *pwf,
6503 __isl_take isl_set *context);
6504 __isl_give isl_union_pw_qpolynomial *
6505 isl_union_pw_qpolynomial_gist_params(
6506 __isl_take isl_union_pw_qpolynomial *upwqp,
6507 __isl_take isl_set *context);
6508 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
6509 __isl_take isl_union_pw_qpolynomial *upwqp,
6510 __isl_take isl_union_set *context);
6511 __isl_give isl_union_pw_qpolynomial_fold *
6512 isl_union_pw_qpolynomial_fold_gist(
6513 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6514 __isl_take isl_union_set *context);
6515 __isl_give isl_union_pw_qpolynomial_fold *
6516 isl_union_pw_qpolynomial_fold_gist_params(
6517 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6518 __isl_take isl_set *context);
6520 =item * Binary Arithmethic Operations
6522 #include <isl/val.h>
6523 __isl_give isl_multi_val *isl_multi_val_sub(
6524 __isl_take isl_multi_val *mv1,
6525 __isl_take isl_multi_val *mv2);
6527 #include <isl/aff.h>
6528 __isl_give isl_aff *isl_aff_add(
6529 __isl_take isl_aff *aff1,
6530 __isl_take isl_aff *aff2);
6531 __isl_give isl_multi_aff *isl_multi_aff_add(
6532 __isl_take isl_multi_aff *maff1,
6533 __isl_take isl_multi_aff *maff2);
6534 __isl_give isl_pw_aff *isl_pw_aff_add(
6535 __isl_take isl_pw_aff *pwaff1,
6536 __isl_take isl_pw_aff *pwaff2);
6537 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
6538 __isl_take isl_pw_multi_aff *pma1,
6539 __isl_take isl_pw_multi_aff *pma2);
6540 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
6541 __isl_take isl_union_pw_aff *upa1,
6542 __isl_take isl_union_pw_aff *upa2);
6543 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
6544 __isl_take isl_union_pw_multi_aff *upma1,
6545 __isl_take isl_union_pw_multi_aff *upma2);
6546 __isl_give isl_pw_aff *isl_pw_aff_min(
6547 __isl_take isl_pw_aff *pwaff1,
6548 __isl_take isl_pw_aff *pwaff2);
6549 __isl_give isl_pw_aff *isl_pw_aff_max(
6550 __isl_take isl_pw_aff *pwaff1,
6551 __isl_take isl_pw_aff *pwaff2);
6552 __isl_give isl_aff *isl_aff_sub(
6553 __isl_take isl_aff *aff1,
6554 __isl_take isl_aff *aff2);
6555 __isl_give isl_multi_aff *isl_multi_aff_sub(
6556 __isl_take isl_multi_aff *ma1,
6557 __isl_take isl_multi_aff *ma2);
6558 __isl_give isl_pw_aff *isl_pw_aff_sub(
6559 __isl_take isl_pw_aff *pwaff1,
6560 __isl_take isl_pw_aff *pwaff2);
6561 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
6562 __isl_take isl_multi_pw_aff *mpa1,
6563 __isl_take isl_multi_pw_aff *mpa2);
6564 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
6565 __isl_take isl_pw_multi_aff *pma1,
6566 __isl_take isl_pw_multi_aff *pma2);
6567 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
6568 __isl_take isl_union_pw_aff *upa1,
6569 __isl_take isl_union_pw_aff *upa2);
6570 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
6571 __isl_take isl_union_pw_multi_aff *upma1,
6572 __isl_take isl_union_pw_multi_aff *upma2);
6573 __isl_give isl_multi_union_pw_aff *
6574 isl_multi_union_pw_aff_sub(
6575 __isl_take isl_multi_union_pw_aff *mupa1,
6576 __isl_take isl_multi_union_pw_aff *mupa2);
6578 C<isl_aff_sub> subtracts the second argument from the first.
6580 #include <isl/polynomial.h>
6581 __isl_give isl_qpolynomial *isl_qpolynomial_add(
6582 __isl_take isl_qpolynomial *qp1,
6583 __isl_take isl_qpolynomial *qp2);
6584 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
6585 __isl_take isl_pw_qpolynomial *pwqp1,
6586 __isl_take isl_pw_qpolynomial *pwqp2);
6587 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
6588 __isl_take isl_pw_qpolynomial *pwqp1,
6589 __isl_take isl_pw_qpolynomial *pwqp2);
6590 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
6591 __isl_take isl_pw_qpolynomial_fold *pwf1,
6592 __isl_take isl_pw_qpolynomial_fold *pwf2);
6593 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
6594 __isl_take isl_union_pw_qpolynomial *upwqp1,
6595 __isl_take isl_union_pw_qpolynomial *upwqp2);
6596 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
6597 __isl_take isl_qpolynomial *qp1,
6598 __isl_take isl_qpolynomial *qp2);
6599 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
6600 __isl_take isl_pw_qpolynomial *pwqp1,
6601 __isl_take isl_pw_qpolynomial *pwqp2);
6602 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
6603 __isl_take isl_union_pw_qpolynomial *upwqp1,
6604 __isl_take isl_union_pw_qpolynomial *upwqp2);
6605 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
6606 __isl_take isl_pw_qpolynomial_fold *pwf1,
6607 __isl_take isl_pw_qpolynomial_fold *pwf2);
6608 __isl_give isl_union_pw_qpolynomial_fold *
6609 isl_union_pw_qpolynomial_fold_fold(
6610 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
6611 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
6613 #include <isl/aff.h>
6614 __isl_give isl_pw_aff *isl_pw_aff_union_add(
6615 __isl_take isl_pw_aff *pwaff1,
6616 __isl_take isl_pw_aff *pwaff2);
6617 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
6618 __isl_take isl_pw_multi_aff *pma1,
6619 __isl_take isl_pw_multi_aff *pma2);
6620 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
6621 __isl_take isl_union_pw_aff *upa1,
6622 __isl_take isl_union_pw_aff *upa2);
6623 __isl_give isl_union_pw_multi_aff *
6624 isl_union_pw_multi_aff_union_add(
6625 __isl_take isl_union_pw_multi_aff *upma1,
6626 __isl_take isl_union_pw_multi_aff *upma2);
6627 __isl_give isl_multi_union_pw_aff *
6628 isl_multi_union_pw_aff_union_add(
6629 __isl_take isl_multi_union_pw_aff *mupa1,
6630 __isl_take isl_multi_union_pw_aff *mupa2);
6631 __isl_give isl_pw_aff *isl_pw_aff_union_min(
6632 __isl_take isl_pw_aff *pwaff1,
6633 __isl_take isl_pw_aff *pwaff2);
6634 __isl_give isl_pw_aff *isl_pw_aff_union_max(
6635 __isl_take isl_pw_aff *pwaff1,
6636 __isl_take isl_pw_aff *pwaff2);
6638 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
6639 expression with a domain that is the union of those of C<pwaff1> and
6640 C<pwaff2> and such that on each cell, the quasi-affine expression is
6641 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
6642 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
6643 associated expression is the defined one.
6644 This in contrast to the C<isl_pw_aff_max> function, which is
6645 only defined on the shared definition domain of the arguments.
6647 #include <isl/val.h>
6648 __isl_give isl_multi_val *isl_multi_val_add_val(
6649 __isl_take isl_multi_val *mv,
6650 __isl_take isl_val *v);
6651 __isl_give isl_multi_val *isl_multi_val_mod_val(
6652 __isl_take isl_multi_val *mv,
6653 __isl_take isl_val *v);
6654 __isl_give isl_multi_val *isl_multi_val_scale_val(
6655 __isl_take isl_multi_val *mv,
6656 __isl_take isl_val *v);
6657 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
6658 __isl_take isl_multi_val *mv,
6659 __isl_take isl_val *v);
6661 #include <isl/aff.h>
6662 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
6663 __isl_take isl_val *mod);
6664 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
6665 __isl_take isl_pw_aff *pa,
6666 __isl_take isl_val *mod);
6667 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
6668 __isl_take isl_union_pw_aff *upa,
6669 __isl_take isl_val *f);
6670 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
6671 __isl_take isl_val *v);
6672 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
6673 __isl_take isl_multi_aff *ma,
6674 __isl_take isl_val *v);
6675 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
6676 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
6677 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
6678 __isl_take isl_multi_pw_aff *mpa,
6679 __isl_take isl_val *v);
6680 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
6681 __isl_take isl_pw_multi_aff *pma,
6682 __isl_take isl_val *v);
6683 __isl_give isl_union_pw_multi_aff *
6684 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
6685 __isl_take isl_union_pw_aff *upa,
6686 __isl_take isl_val *f);
6687 isl_union_pw_multi_aff_scale_val(
6688 __isl_take isl_union_pw_multi_aff *upma,
6689 __isl_take isl_val *val);
6690 __isl_give isl_multi_union_pw_aff *
6691 isl_multi_union_pw_aff_scale_val(
6692 __isl_take isl_multi_union_pw_aff *mupa,
6693 __isl_take isl_val *v);
6694 __isl_give isl_aff *isl_aff_scale_down_ui(
6695 __isl_take isl_aff *aff, unsigned f);
6696 __isl_give isl_aff *isl_aff_scale_down_val(
6697 __isl_take isl_aff *aff, __isl_take isl_val *v);
6698 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
6699 __isl_take isl_multi_aff *ma,
6700 __isl_take isl_val *v);
6701 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
6702 __isl_take isl_pw_aff *pa,
6703 __isl_take isl_val *f);
6704 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
6705 __isl_take isl_multi_pw_aff *mpa,
6706 __isl_take isl_val *v);
6707 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
6708 __isl_take isl_pw_multi_aff *pma,
6709 __isl_take isl_val *v);
6710 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
6711 __isl_take isl_union_pw_aff *upa,
6712 __isl_take isl_val *v);
6713 __isl_give isl_union_pw_multi_aff *
6714 isl_union_pw_multi_aff_scale_down_val(
6715 __isl_take isl_union_pw_multi_aff *upma,
6716 __isl_take isl_val *val);
6717 __isl_give isl_multi_union_pw_aff *
6718 isl_multi_union_pw_aff_scale_down_val(
6719 __isl_take isl_multi_union_pw_aff *mupa,
6720 __isl_take isl_val *v);
6722 #include <isl/polynomial.h>
6723 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
6724 __isl_take isl_qpolynomial *qp,
6725 __isl_take isl_val *v);
6726 __isl_give isl_qpolynomial_fold *
6727 isl_qpolynomial_fold_scale_val(
6728 __isl_take isl_qpolynomial_fold *fold,
6729 __isl_take isl_val *v);
6730 __isl_give isl_pw_qpolynomial *
6731 isl_pw_qpolynomial_scale_val(
6732 __isl_take isl_pw_qpolynomial *pwqp,
6733 __isl_take isl_val *v);
6734 __isl_give isl_pw_qpolynomial_fold *
6735 isl_pw_qpolynomial_fold_scale_val(
6736 __isl_take isl_pw_qpolynomial_fold *pwf,
6737 __isl_take isl_val *v);
6738 __isl_give isl_union_pw_qpolynomial *
6739 isl_union_pw_qpolynomial_scale_val(
6740 __isl_take isl_union_pw_qpolynomial *upwqp,
6741 __isl_take isl_val *v);
6742 __isl_give isl_union_pw_qpolynomial_fold *
6743 isl_union_pw_qpolynomial_fold_scale_val(
6744 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6745 __isl_take isl_val *v);
6746 __isl_give isl_qpolynomial *
6747 isl_qpolynomial_scale_down_val(
6748 __isl_take isl_qpolynomial *qp,
6749 __isl_take isl_val *v);
6750 __isl_give isl_qpolynomial_fold *
6751 isl_qpolynomial_fold_scale_down_val(
6752 __isl_take isl_qpolynomial_fold *fold,
6753 __isl_take isl_val *v);
6754 __isl_give isl_pw_qpolynomial *
6755 isl_pw_qpolynomial_scale_down_val(
6756 __isl_take isl_pw_qpolynomial *pwqp,
6757 __isl_take isl_val *v);
6758 __isl_give isl_pw_qpolynomial_fold *
6759 isl_pw_qpolynomial_fold_scale_down_val(
6760 __isl_take isl_pw_qpolynomial_fold *pwf,
6761 __isl_take isl_val *v);
6762 __isl_give isl_union_pw_qpolynomial *
6763 isl_union_pw_qpolynomial_scale_down_val(
6764 __isl_take isl_union_pw_qpolynomial *upwqp,
6765 __isl_take isl_val *v);
6766 __isl_give isl_union_pw_qpolynomial_fold *
6767 isl_union_pw_qpolynomial_fold_scale_down_val(
6768 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6769 __isl_take isl_val *v);
6771 #include <isl/val.h>
6772 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
6773 __isl_take isl_multi_val *mv1,
6774 __isl_take isl_multi_val *mv2);
6775 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
6776 __isl_take isl_multi_val *mv1,
6777 __isl_take isl_multi_val *mv2);
6778 __isl_give isl_multi_val *
6779 isl_multi_val_scale_down_multi_val(
6780 __isl_take isl_multi_val *mv1,
6781 __isl_take isl_multi_val *mv2);
6783 #include <isl/aff.h>
6784 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
6785 __isl_take isl_multi_aff *ma,
6786 __isl_take isl_multi_val *mv);
6787 __isl_give isl_multi_union_pw_aff *
6788 isl_multi_union_pw_aff_mod_multi_val(
6789 __isl_take isl_multi_union_pw_aff *upma,
6790 __isl_take isl_multi_val *mv);
6791 __isl_give isl_multi_pw_aff *
6792 isl_multi_pw_aff_mod_multi_val(
6793 __isl_take isl_multi_pw_aff *mpa,
6794 __isl_take isl_multi_val *mv);
6795 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
6796 __isl_take isl_multi_aff *ma,
6797 __isl_take isl_multi_val *mv);
6798 __isl_give isl_pw_multi_aff *
6799 isl_pw_multi_aff_scale_multi_val(
6800 __isl_take isl_pw_multi_aff *pma,
6801 __isl_take isl_multi_val *mv);
6802 __isl_give isl_multi_pw_aff *
6803 isl_multi_pw_aff_scale_multi_val(
6804 __isl_take isl_multi_pw_aff *mpa,
6805 __isl_take isl_multi_val *mv);
6806 __isl_give isl_multi_union_pw_aff *
6807 isl_multi_union_pw_aff_scale_multi_val(
6808 __isl_take isl_multi_union_pw_aff *mupa,
6809 __isl_take isl_multi_val *mv);
6810 __isl_give isl_union_pw_multi_aff *
6811 isl_union_pw_multi_aff_scale_multi_val(
6812 __isl_take isl_union_pw_multi_aff *upma,
6813 __isl_take isl_multi_val *mv);
6814 __isl_give isl_multi_aff *
6815 isl_multi_aff_scale_down_multi_val(
6816 __isl_take isl_multi_aff *ma,
6817 __isl_take isl_multi_val *mv);
6818 __isl_give isl_multi_pw_aff *
6819 isl_multi_pw_aff_scale_down_multi_val(
6820 __isl_take isl_multi_pw_aff *mpa,
6821 __isl_take isl_multi_val *mv);
6822 __isl_give isl_multi_union_pw_aff *
6823 isl_multi_union_pw_aff_scale_down_multi_val(
6824 __isl_take isl_multi_union_pw_aff *mupa,
6825 __isl_take isl_multi_val *mv);
6827 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
6828 by the corresponding elements of C<mv>.
6830 #include <isl/aff.h>
6831 __isl_give isl_aff *isl_aff_mul(
6832 __isl_take isl_aff *aff1,
6833 __isl_take isl_aff *aff2);
6834 __isl_give isl_aff *isl_aff_div(
6835 __isl_take isl_aff *aff1,
6836 __isl_take isl_aff *aff2);
6837 __isl_give isl_pw_aff *isl_pw_aff_mul(
6838 __isl_take isl_pw_aff *pwaff1,
6839 __isl_take isl_pw_aff *pwaff2);
6840 __isl_give isl_pw_aff *isl_pw_aff_div(
6841 __isl_take isl_pw_aff *pa1,
6842 __isl_take isl_pw_aff *pa2);
6843 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
6844 __isl_take isl_pw_aff *pa1,
6845 __isl_take isl_pw_aff *pa2);
6846 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
6847 __isl_take isl_pw_aff *pa1,
6848 __isl_take isl_pw_aff *pa2);
6850 When multiplying two affine expressions, at least one of the two needs
6851 to be a constant. Similarly, when dividing an affine expression by another,
6852 the second expression needs to be a constant.
6853 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
6854 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
6857 #include <isl/polynomial.h>
6858 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
6859 __isl_take isl_qpolynomial *qp1,
6860 __isl_take isl_qpolynomial *qp2);
6861 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
6862 __isl_take isl_pw_qpolynomial *pwqp1,
6863 __isl_take isl_pw_qpolynomial *pwqp2);
6864 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
6865 __isl_take isl_union_pw_qpolynomial *upwqp1,
6866 __isl_take isl_union_pw_qpolynomial *upwqp2);
6870 =head3 Lexicographic Optimization
6872 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
6873 the following functions
6874 compute a set that contains the lexicographic minimum or maximum
6875 of the elements in C<set> (or C<bset>) for those values of the parameters
6876 that satisfy C<dom>.
6877 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
6878 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
6880 In other words, the union of the parameter values
6881 for which the result is non-empty and of C<*empty>
6884 #include <isl/set.h>
6885 __isl_give isl_set *isl_basic_set_partial_lexmin(
6886 __isl_take isl_basic_set *bset,
6887 __isl_take isl_basic_set *dom,
6888 __isl_give isl_set **empty);
6889 __isl_give isl_set *isl_basic_set_partial_lexmax(
6890 __isl_take isl_basic_set *bset,
6891 __isl_take isl_basic_set *dom,
6892 __isl_give isl_set **empty);
6893 __isl_give isl_set *isl_set_partial_lexmin(
6894 __isl_take isl_set *set, __isl_take isl_set *dom,
6895 __isl_give isl_set **empty);
6896 __isl_give isl_set *isl_set_partial_lexmax(
6897 __isl_take isl_set *set, __isl_take isl_set *dom,
6898 __isl_give isl_set **empty);
6900 Given a (basic) set C<set> (or C<bset>), the following functions simply
6901 return a set containing the lexicographic minimum or maximum
6902 of the elements in C<set> (or C<bset>).
6903 In case of union sets, the optimum is computed per space.
6905 #include <isl/set.h>
6906 __isl_give isl_set *isl_basic_set_lexmin(
6907 __isl_take isl_basic_set *bset);
6908 __isl_give isl_set *isl_basic_set_lexmax(
6909 __isl_take isl_basic_set *bset);
6910 __isl_give isl_set *isl_set_lexmin(
6911 __isl_take isl_set *set);
6912 __isl_give isl_set *isl_set_lexmax(
6913 __isl_take isl_set *set);
6914 __isl_give isl_union_set *isl_union_set_lexmin(
6915 __isl_take isl_union_set *uset);
6916 __isl_give isl_union_set *isl_union_set_lexmax(
6917 __isl_take isl_union_set *uset);
6919 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
6920 the following functions
6921 compute a relation that maps each element of C<dom>
6922 to the single lexicographic minimum or maximum
6923 of the elements that are associated to that same
6924 element in C<map> (or C<bmap>).
6925 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
6926 that contains the elements in C<dom> that do not map
6927 to any elements in C<map> (or C<bmap>).
6928 In other words, the union of the domain of the result and of C<*empty>
6931 #include <isl/map.h>
6932 __isl_give isl_map *isl_basic_map_partial_lexmax(
6933 __isl_take isl_basic_map *bmap,
6934 __isl_take isl_basic_set *dom,
6935 __isl_give isl_set **empty);
6936 __isl_give isl_map *isl_basic_map_partial_lexmin(
6937 __isl_take isl_basic_map *bmap,
6938 __isl_take isl_basic_set *dom,
6939 __isl_give isl_set **empty);
6940 __isl_give isl_map *isl_map_partial_lexmax(
6941 __isl_take isl_map *map, __isl_take isl_set *dom,
6942 __isl_give isl_set **empty);
6943 __isl_give isl_map *isl_map_partial_lexmin(
6944 __isl_take isl_map *map, __isl_take isl_set *dom,
6945 __isl_give isl_set **empty);
6947 Given a (basic) map C<map> (or C<bmap>), the following functions simply
6948 return a map mapping each element in the domain of
6949 C<map> (or C<bmap>) to the lexicographic minimum or maximum
6950 of all elements associated to that element.
6951 In case of union relations, the optimum is computed per space.
6953 #include <isl/map.h>
6954 __isl_give isl_map *isl_basic_map_lexmin(
6955 __isl_take isl_basic_map *bmap);
6956 __isl_give isl_map *isl_basic_map_lexmax(
6957 __isl_take isl_basic_map *bmap);
6958 __isl_give isl_map *isl_map_lexmin(
6959 __isl_take isl_map *map);
6960 __isl_give isl_map *isl_map_lexmax(
6961 __isl_take isl_map *map);
6962 __isl_give isl_union_map *isl_union_map_lexmin(
6963 __isl_take isl_union_map *umap);
6964 __isl_give isl_union_map *isl_union_map_lexmax(
6965 __isl_take isl_union_map *umap);
6967 The following functions return their result in the form of
6968 a piecewise multi-affine expression,
6969 but are otherwise equivalent to the corresponding functions
6970 returning a basic set or relation.
6972 #include <isl/set.h>
6973 __isl_give isl_pw_multi_aff *
6974 isl_basic_set_partial_lexmin_pw_multi_aff(
6975 __isl_take isl_basic_set *bset,
6976 __isl_take isl_basic_set *dom,
6977 __isl_give isl_set **empty);
6978 __isl_give isl_pw_multi_aff *
6979 isl_basic_set_partial_lexmax_pw_multi_aff(
6980 __isl_take isl_basic_set *bset,
6981 __isl_take isl_basic_set *dom,
6982 __isl_give isl_set **empty);
6983 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
6984 __isl_take isl_set *set);
6985 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
6986 __isl_take isl_set *set);
6988 #include <isl/map.h>
6989 __isl_give isl_pw_multi_aff *
6990 isl_basic_map_lexmin_pw_multi_aff(
6991 __isl_take isl_basic_map *bmap);
6992 __isl_give isl_pw_multi_aff *
6993 isl_basic_map_partial_lexmin_pw_multi_aff(
6994 __isl_take isl_basic_map *bmap,
6995 __isl_take isl_basic_set *dom,
6996 __isl_give isl_set **empty);
6997 __isl_give isl_pw_multi_aff *
6998 isl_basic_map_partial_lexmax_pw_multi_aff(
6999 __isl_take isl_basic_map *bmap,
7000 __isl_take isl_basic_set *dom,
7001 __isl_give isl_set **empty);
7002 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
7003 __isl_take isl_map *map);
7004 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
7005 __isl_take isl_map *map);
7007 The following functions return the lexicographic minimum or maximum
7008 on the shared domain of the inputs and the single defined function
7009 on those parts of the domain where only a single function is defined.
7011 #include <isl/aff.h>
7012 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
7013 __isl_take isl_pw_multi_aff *pma1,
7014 __isl_take isl_pw_multi_aff *pma2);
7015 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
7016 __isl_take isl_pw_multi_aff *pma1,
7017 __isl_take isl_pw_multi_aff *pma2);
7019 =head2 Ternary Operations
7021 #include <isl/aff.h>
7022 __isl_give isl_pw_aff *isl_pw_aff_cond(
7023 __isl_take isl_pw_aff *cond,
7024 __isl_take isl_pw_aff *pwaff_true,
7025 __isl_take isl_pw_aff *pwaff_false);
7027 The function C<isl_pw_aff_cond> performs a conditional operator
7028 and returns an expression that is equal to C<pwaff_true>
7029 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
7030 where C<cond> is zero.
7034 Lists are defined over several element types, including
7035 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_union_pw_aff>,
7036 C<isl_union_pw_multi_aff>, C<isl_constraint>,
7037 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
7038 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
7039 Here we take lists of C<isl_set>s as an example.
7040 Lists can be created, copied, modified and freed using the following functions.
7042 #include <isl/set.h>
7043 __isl_give isl_set_list *isl_set_list_from_set(
7044 __isl_take isl_set *el);
7045 __isl_give isl_set_list *isl_set_list_alloc(
7046 isl_ctx *ctx, int n);
7047 __isl_give isl_set_list *isl_set_list_copy(
7048 __isl_keep isl_set_list *list);
7049 __isl_give isl_set_list *isl_set_list_insert(
7050 __isl_take isl_set_list *list, unsigned pos,
7051 __isl_take isl_set *el);
7052 __isl_give isl_set_list *isl_set_list_add(
7053 __isl_take isl_set_list *list,
7054 __isl_take isl_set *el);
7055 __isl_give isl_set_list *isl_set_list_drop(
7056 __isl_take isl_set_list *list,
7057 unsigned first, unsigned n);
7058 __isl_give isl_set_list *isl_set_list_set_set(
7059 __isl_take isl_set_list *list, int index,
7060 __isl_take isl_set *set);
7061 __isl_give isl_set_list *isl_set_list_concat(
7062 __isl_take isl_set_list *list1,
7063 __isl_take isl_set_list *list2);
7064 __isl_give isl_set_list *isl_set_list_sort(
7065 __isl_take isl_set_list *list,
7066 int (*cmp)(__isl_keep isl_set *a,
7067 __isl_keep isl_set *b, void *user),
7069 __isl_null isl_set_list *isl_set_list_free(
7070 __isl_take isl_set_list *list);
7072 C<isl_set_list_alloc> creates an empty list with an initial capacity
7073 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
7074 add elements to a list, increasing its capacity as needed.
7075 C<isl_set_list_from_set> creates a list with a single element.
7077 Lists can be inspected using the following functions.
7079 #include <isl/set.h>
7080 int isl_set_list_n_set(__isl_keep isl_set_list *list);
7081 __isl_give isl_set *isl_set_list_get_set(
7082 __isl_keep isl_set_list *list, int index);
7083 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list,
7084 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7086 isl_stat isl_set_list_foreach_scc(
7087 __isl_keep isl_set_list *list,
7088 isl_bool (*follows)(__isl_keep isl_set *a,
7089 __isl_keep isl_set *b, void *user),
7091 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7094 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
7095 strongly connected components of the graph with as vertices the elements
7096 of C<list> and a directed edge from vertex C<b> to vertex C<a>
7097 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
7098 should return C<-1> on error.
7100 Lists can be printed using
7102 #include <isl/set.h>
7103 __isl_give isl_printer *isl_printer_print_set_list(
7104 __isl_take isl_printer *p,
7105 __isl_keep isl_set_list *list);
7107 =head2 Associative arrays
7109 Associative arrays map isl objects of a specific type to isl objects
7110 of some (other) specific type. They are defined for several pairs
7111 of types, including (C<isl_map>, C<isl_basic_set>),
7112 (C<isl_id>, C<isl_ast_expr>) and.
7113 (C<isl_id>, C<isl_pw_aff>).
7114 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
7117 Associative arrays can be created, copied and freed using
7118 the following functions.
7120 #include <isl/id_to_ast_expr.h>
7121 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
7122 isl_ctx *ctx, int min_size);
7123 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
7124 __isl_keep isl_id_to_ast_expr *id2expr);
7125 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
7126 __isl_take isl_id_to_ast_expr *id2expr);
7128 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
7129 to specify the expected size of the associative array.
7130 The associative array will be grown automatically as needed.
7132 Associative arrays can be inspected using the following functions.
7134 #include <isl/id_to_ast_expr.h>
7135 isl_bool isl_id_to_ast_expr_has(
7136 __isl_keep isl_id_to_ast_expr *id2expr,
7137 __isl_keep isl_id *key);
7138 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
7139 __isl_keep isl_id_to_ast_expr *id2expr,
7140 __isl_take isl_id *key);
7141 isl_stat isl_id_to_ast_expr_foreach(
7142 __isl_keep isl_id_to_ast_expr *id2expr,
7143 isl_stat (*fn)(__isl_take isl_id *key,
7144 __isl_take isl_ast_expr *val, void *user),
7147 They can be modified using the following function.
7149 #include <isl/id_to_ast_expr.h>
7150 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
7151 __isl_take isl_id_to_ast_expr *id2expr,
7152 __isl_take isl_id *key,
7153 __isl_take isl_ast_expr *val);
7154 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
7155 __isl_take isl_id_to_ast_expr *id2expr,
7156 __isl_take isl_id *key);
7158 Associative arrays can be printed using the following function.
7160 #include <isl/id_to_ast_expr.h>
7161 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
7162 __isl_take isl_printer *p,
7163 __isl_keep isl_id_to_ast_expr *id2expr);
7167 Vectors can be created, copied and freed using the following functions.
7169 #include <isl/vec.h>
7170 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
7172 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
7173 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
7175 Note that the elements of a newly created vector may have arbitrary values.
7176 The elements can be changed and inspected using the following functions.
7178 int isl_vec_size(__isl_keep isl_vec *vec);
7179 __isl_give isl_val *isl_vec_get_element_val(
7180 __isl_keep isl_vec *vec, int pos);
7181 __isl_give isl_vec *isl_vec_set_element_si(
7182 __isl_take isl_vec *vec, int pos, int v);
7183 __isl_give isl_vec *isl_vec_set_element_val(
7184 __isl_take isl_vec *vec, int pos,
7185 __isl_take isl_val *v);
7186 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
7188 __isl_give isl_vec *isl_vec_set_val(
7189 __isl_take isl_vec *vec, __isl_take isl_val *v);
7190 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
7191 __isl_keep isl_vec *vec2, int pos);
7193 C<isl_vec_get_element> will return a negative value if anything went wrong.
7194 In that case, the value of C<*v> is undefined.
7196 The following function can be used to concatenate two vectors.
7198 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
7199 __isl_take isl_vec *vec2);
7203 Matrices can be created, copied and freed using the following functions.
7205 #include <isl/mat.h>
7206 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
7207 unsigned n_row, unsigned n_col);
7208 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
7209 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
7211 Note that the elements of a newly created matrix may have arbitrary values.
7212 The elements can be changed and inspected using the following functions.
7214 int isl_mat_rows(__isl_keep isl_mat *mat);
7215 int isl_mat_cols(__isl_keep isl_mat *mat);
7216 __isl_give isl_val *isl_mat_get_element_val(
7217 __isl_keep isl_mat *mat, int row, int col);
7218 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
7219 int row, int col, int v);
7220 __isl_give isl_mat *isl_mat_set_element_val(
7221 __isl_take isl_mat *mat, int row, int col,
7222 __isl_take isl_val *v);
7224 C<isl_mat_get_element> will return a negative value if anything went wrong.
7225 In that case, the value of C<*v> is undefined.
7227 The following function can be used to compute the (right) inverse
7228 of a matrix, i.e., a matrix such that the product of the original
7229 and the inverse (in that order) is a multiple of the identity matrix.
7230 The input matrix is assumed to be of full row-rank.
7232 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
7234 The following function can be used to compute the (right) kernel
7235 (or null space) of a matrix, i.e., a matrix such that the product of
7236 the original and the kernel (in that order) is the zero matrix.
7238 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
7240 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
7242 The following functions determine
7243 an upper or lower bound on a quasipolynomial over its domain.
7245 __isl_give isl_pw_qpolynomial_fold *
7246 isl_pw_qpolynomial_bound(
7247 __isl_take isl_pw_qpolynomial *pwqp,
7248 enum isl_fold type, int *tight);
7250 __isl_give isl_union_pw_qpolynomial_fold *
7251 isl_union_pw_qpolynomial_bound(
7252 __isl_take isl_union_pw_qpolynomial *upwqp,
7253 enum isl_fold type, int *tight);
7255 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
7256 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
7257 is the returned bound is known be tight, i.e., for each value
7258 of the parameters there is at least
7259 one element in the domain that reaches the bound.
7260 If the domain of C<pwqp> is not wrapping, then the bound is computed
7261 over all elements in that domain and the result has a purely parametric
7262 domain. If the domain of C<pwqp> is wrapping, then the bound is
7263 computed over the range of the wrapped relation. The domain of the
7264 wrapped relation becomes the domain of the result.
7266 =head2 Parametric Vertex Enumeration
7268 The parametric vertex enumeration described in this section
7269 is mainly intended to be used internally and by the C<barvinok>
7272 #include <isl/vertices.h>
7273 __isl_give isl_vertices *isl_basic_set_compute_vertices(
7274 __isl_keep isl_basic_set *bset);
7276 The function C<isl_basic_set_compute_vertices> performs the
7277 actual computation of the parametric vertices and the chamber
7278 decomposition and store the result in an C<isl_vertices> object.
7279 This information can be queried by either iterating over all
7280 the vertices or iterating over all the chambers or cells
7281 and then iterating over all vertices that are active on the chamber.
7283 isl_stat isl_vertices_foreach_vertex(
7284 __isl_keep isl_vertices *vertices,
7285 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7286 void *user), void *user);
7288 isl_stat isl_vertices_foreach_cell(
7289 __isl_keep isl_vertices *vertices,
7290 isl_stat (*fn)(__isl_take isl_cell *cell,
7291 void *user), void *user);
7292 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
7293 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7294 void *user), void *user);
7296 Other operations that can be performed on an C<isl_vertices> object are
7299 int isl_vertices_get_n_vertices(
7300 __isl_keep isl_vertices *vertices);
7301 void isl_vertices_free(__isl_take isl_vertices *vertices);
7303 Vertices can be inspected and destroyed using the following functions.
7305 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
7306 __isl_give isl_basic_set *isl_vertex_get_domain(
7307 __isl_keep isl_vertex *vertex);
7308 __isl_give isl_multi_aff *isl_vertex_get_expr(
7309 __isl_keep isl_vertex *vertex);
7310 void isl_vertex_free(__isl_take isl_vertex *vertex);
7312 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
7313 describing the vertex in terms of the parameters,
7314 while C<isl_vertex_get_domain> returns the activity domain
7317 Chambers can be inspected and destroyed using the following functions.
7319 __isl_give isl_basic_set *isl_cell_get_domain(
7320 __isl_keep isl_cell *cell);
7321 void isl_cell_free(__isl_take isl_cell *cell);
7323 =head1 Polyhedral Compilation Library
7325 This section collects functionality in C<isl> that has been specifically
7326 designed for use during polyhedral compilation.
7328 =head2 Schedule Trees
7330 A schedule tree is a structured representation of a schedule,
7331 assigning a relative order to a set of domain elements.
7332 The relative order expressed by the schedule tree is
7333 defined recursively. In particular, the order between
7334 two domain elements is determined by the node that is closest
7335 to the root that refers to both elements and that orders them apart.
7336 Each node in the tree is of one of several types.
7337 The root node is always of type C<isl_schedule_node_domain>
7338 (or C<isl_schedule_node_extension>)
7339 and it describes the (extra) domain elements to which the schedule applies.
7340 The other types of nodes are as follows.
7344 =item C<isl_schedule_node_band>
7346 A band of schedule dimensions. Each schedule dimension is represented
7347 by a union piecewise quasi-affine expression. If this expression
7348 assigns a different value to two domain elements, while all previous
7349 schedule dimensions in the same band assign them the same value,
7350 then the two domain elements are ordered according to these two
7353 =item C<isl_schedule_node_expansion>
7355 An expansion node maps each of the domain elements that reach the node
7356 to one or more domain elements. The image of this mapping forms
7357 the set of domain elements that reach the child of the expansion node.
7358 The function that maps each of the expanded domain elements
7359 to the original domain element from which it was expanded
7360 is called the contraction.
7362 =item C<isl_schedule_node_filter>
7364 A filter node does not impose any ordering, but rather intersects
7365 the set of domain elements that the current subtree refers to
7366 with a given union set. The subtree of the filter node only
7367 refers to domain elements in the intersection.
7368 A filter node is typically only used a child of a sequence or
7371 =item C<isl_schedule_node_leaf>
7373 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
7375 =item C<isl_schedule_node_mark>
7377 A mark node can be used to attach any kind of information to a subtree
7378 of the schedule tree.
7380 =item C<isl_schedule_node_sequence>
7382 A sequence node has one or more children, each of which is a filter node.
7383 The filters on these filter nodes form a partition of
7384 the domain elements that the current subtree refers to.
7385 If two domain elements appear in distinct filters then the sequence
7386 node orders them according to the child positions of the corresponding
7389 =item C<isl_schedule_node_set>
7391 A set node is similar to a sequence node, except that
7392 it expresses that domain elements appearing in distinct filters
7393 may have any order. The order of the children of a set node
7394 is therefore also immaterial.
7398 The following node types are only supported by the AST generator.
7402 =item C<isl_schedule_node_context>
7404 The context describes constraints on the parameters and
7405 the schedule dimensions of outer
7406 bands that the AST generator may assume to hold. It is also the only
7407 kind of node that may introduce additional parameters.
7408 The space of the context is that of the flat product of the outer
7409 band nodes. In particular, if there are no outer band nodes, then
7410 this space is the unnamed zero-dimensional space.
7411 Since a context node references the outer band nodes, any tree
7412 containing a context node is considered to be anchored.
7414 =item C<isl_schedule_node_extension>
7416 An extension node instructs the AST generator to add additional
7417 domain elements that need to be scheduled.
7418 The additional domain elements are described by the range of
7419 the extension map in terms of the outer schedule dimensions,
7420 i.e., the flat product of the outer band nodes.
7421 Note that domain elements are added whenever the AST generator
7422 reaches the extension node, meaning that there are still some
7423 active domain elements for which an AST needs to be generated.
7424 The conditions under which some domain elements are still active
7425 may however not be completely described by the outer AST nodes
7426 generated at that point.
7428 An extension node may also appear as the root of a schedule tree,
7429 when it is intended to be inserted into another tree
7430 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
7431 In this case, the domain of the extension node should
7432 correspond to the flat product of the outer band nodes
7433 in this other schedule tree at the point where the extension tree
7436 =item C<isl_schedule_node_guard>
7438 The guard describes constraints on the parameters and
7439 the schedule dimensions of outer
7440 bands that need to be enforced by the outer nodes
7441 in the generated AST.
7442 The space of the guard is that of the flat product of the outer
7443 band nodes. In particular, if there are no outer band nodes, then
7444 this space is the unnamed zero-dimensional space.
7445 Since a guard node references the outer band nodes, any tree
7446 containing a guard node is considered to be anchored.
7450 Except for the C<isl_schedule_node_context> nodes,
7451 none of the nodes may introduce any parameters that were not
7452 already present in the root domain node.
7454 A schedule tree is encapsulated in an C<isl_schedule> object.
7455 The simplest such objects, those with a tree consisting of single domain node,
7456 can be created using the following functions with either an empty
7457 domain or a given domain.
7459 #include <isl/schedule.h>
7460 __isl_give isl_schedule *isl_schedule_empty(
7461 __isl_take isl_space *space);
7462 __isl_give isl_schedule *isl_schedule_from_domain(
7463 __isl_take isl_union_set *domain);
7465 The function C<isl_schedule_constraints_compute_schedule> described
7466 in L</"Scheduling"> can also be used to construct schedules.
7468 C<isl_schedule> objects may be copied and freed using the following functions.
7470 #include <isl/schedule.h>
7471 __isl_give isl_schedule *isl_schedule_copy(
7472 __isl_keep isl_schedule *sched);
7473 __isl_null isl_schedule *isl_schedule_free(
7474 __isl_take isl_schedule *sched);
7476 The following functions checks whether two C<isl_schedule> objects
7477 are obviously the same.
7479 #include <isl/schedule.h>
7480 isl_bool isl_schedule_plain_is_equal(
7481 __isl_keep isl_schedule *schedule1,
7482 __isl_keep isl_schedule *schedule2);
7484 The domain of the schedule, i.e., the domain described by the root node,
7485 can be obtained using the following function.
7487 #include <isl/schedule.h>
7488 __isl_give isl_union_set *isl_schedule_get_domain(
7489 __isl_keep isl_schedule *schedule);
7491 An extra top-level band node (right underneath the domain node) can
7492 be introduced into the schedule using the following function.
7493 The schedule tree is assumed not to have any anchored nodes.
7495 #include <isl/schedule.h>
7496 __isl_give isl_schedule *
7497 isl_schedule_insert_partial_schedule(
7498 __isl_take isl_schedule *schedule,
7499 __isl_take isl_multi_union_pw_aff *partial);
7501 A top-level context node (right underneath the domain node) can
7502 be introduced into the schedule using the following function.
7504 #include <isl/schedule.h>
7505 __isl_give isl_schedule *isl_schedule_insert_context(
7506 __isl_take isl_schedule *schedule,
7507 __isl_take isl_set *context)
7509 A top-level guard node (right underneath the domain node) can
7510 be introduced into the schedule using the following function.
7512 #include <isl/schedule.h>
7513 __isl_give isl_schedule *isl_schedule_insert_guard(
7514 __isl_take isl_schedule *schedule,
7515 __isl_take isl_set *guard)
7517 A schedule that combines two schedules either in the given
7518 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
7519 or an C<isl_schedule_node_set> node,
7520 can be created using the following functions.
7522 #include <isl/schedule.h>
7523 __isl_give isl_schedule *isl_schedule_sequence(
7524 __isl_take isl_schedule *schedule1,
7525 __isl_take isl_schedule *schedule2);
7526 __isl_give isl_schedule *isl_schedule_set(
7527 __isl_take isl_schedule *schedule1,
7528 __isl_take isl_schedule *schedule2);
7530 The domains of the two input schedules need to be disjoint.
7532 The following function can be used to restrict the domain
7533 of a schedule with a domain node as root to be a subset of the given union set.
7534 This operation may remove nodes in the tree that have become
7537 #include <isl/schedule.h>
7538 __isl_give isl_schedule *isl_schedule_intersect_domain(
7539 __isl_take isl_schedule *schedule,
7540 __isl_take isl_union_set *domain);
7542 The following function resets the user pointers on all parameter
7543 and tuple identifiers referenced by the nodes of the given schedule.
7545 #include <isl/schedule.h>
7546 __isl_give isl_schedule *isl_schedule_reset_user(
7547 __isl_take isl_schedule *schedule);
7549 The following function aligns the parameters of all nodes
7550 in the given schedule to the given space.
7552 #include <isl/schedule.h>
7553 __isl_give isl_schedule *isl_schedule_align_params(
7554 __isl_take isl_schedule *schedule,
7555 __isl_take isl_space *space);
7557 The following function allows the user to plug in a given function
7558 in the iteration domains. The input schedule is not allowed to contain
7559 any expansion nodes.
7561 #include <isl/schedule.h>
7562 __isl_give isl_schedule *
7563 isl_schedule_pullback_union_pw_multi_aff(
7564 __isl_take isl_schedule *schedule,
7565 __isl_take isl_union_pw_multi_aff *upma);
7567 An C<isl_union_map> representation of the schedule can be obtained
7568 from an C<isl_schedule> using the following function.
7570 #include <isl/schedule.h>
7571 __isl_give isl_union_map *isl_schedule_get_map(
7572 __isl_keep isl_schedule *sched);
7574 The resulting relation encodes the same relative ordering as
7575 the schedule by mapping the domain elements to a common schedule space.
7576 If the schedule_separate_components option is set, then the order
7577 of the children of a set node is explicitly encoded in the result.
7578 If the tree contains any expansion nodes, then the relation
7579 is formulated in terms of the expanded domain elements.
7581 Schedules can be read from input using the following functions.
7583 #include <isl/schedule.h>
7584 __isl_give isl_schedule *isl_schedule_read_from_file(
7585 isl_ctx *ctx, FILE *input);
7586 __isl_give isl_schedule *isl_schedule_read_from_str(
7587 isl_ctx *ctx, const char *str);
7589 A representation of the schedule can be printed using
7591 #include <isl/schedule.h>
7592 __isl_give isl_printer *isl_printer_print_schedule(
7593 __isl_take isl_printer *p,
7594 __isl_keep isl_schedule *schedule);
7596 The schedule tree can be traversed through the use of
7597 C<isl_schedule_node> objects that point to a particular
7598 position in the schedule tree. Whenever a C<isl_schedule_node>
7599 is use to modify a node in the schedule tree, the original schedule
7600 tree is left untouched and the modifications are performed to a copy
7601 of the tree. The returned C<isl_schedule_node> then points to
7602 this modified copy of the tree.
7604 The root of the schedule tree can be obtained using the following function.
7606 #include <isl/schedule.h>
7607 __isl_give isl_schedule_node *isl_schedule_get_root(
7608 __isl_keep isl_schedule *schedule);
7610 A pointer to a newly created schedule tree with a single domain
7611 node can be created using the following functions.
7613 #include <isl/schedule_node.h>
7614 __isl_give isl_schedule_node *
7615 isl_schedule_node_from_domain(
7616 __isl_take isl_union_set *domain);
7617 __isl_give isl_schedule_node *
7618 isl_schedule_node_from_extension(
7619 __isl_take isl_union_map *extension);
7621 C<isl_schedule_node_from_extension> creates a tree with an extension
7624 Schedule nodes can be copied and freed using the following functions.
7626 #include <isl/schedule_node.h>
7627 __isl_give isl_schedule_node *isl_schedule_node_copy(
7628 __isl_keep isl_schedule_node *node);
7629 __isl_null isl_schedule_node *isl_schedule_node_free(
7630 __isl_take isl_schedule_node *node);
7632 The following functions can be used to check if two schedule
7633 nodes point to the same position in the same schedule.
7635 #include <isl/schedule_node.h>
7636 isl_bool isl_schedule_node_is_equal(
7637 __isl_keep isl_schedule_node *node1,
7638 __isl_keep isl_schedule_node *node2);
7640 The following properties can be obtained from a schedule node.
7642 #include <isl/schedule_node.h>
7643 enum isl_schedule_node_type isl_schedule_node_get_type(
7644 __isl_keep isl_schedule_node *node);
7645 enum isl_schedule_node_type
7646 isl_schedule_node_get_parent_type(
7647 __isl_keep isl_schedule_node *node);
7648 __isl_give isl_schedule *isl_schedule_node_get_schedule(
7649 __isl_keep isl_schedule_node *node);
7651 The function C<isl_schedule_node_get_type> returns the type of
7652 the node, while C<isl_schedule_node_get_parent_type> returns
7653 type of the parent of the node, which is required to exist.
7654 The function C<isl_schedule_node_get_schedule> returns a copy
7655 to the schedule to which the node belongs.
7657 The following functions can be used to move the schedule node
7658 to a different position in the tree or to check if such a position
7661 #include <isl/schedule_node.h>
7662 isl_bool isl_schedule_node_has_parent(
7663 __isl_keep isl_schedule_node *node);
7664 __isl_give isl_schedule_node *isl_schedule_node_parent(
7665 __isl_take isl_schedule_node *node);
7666 __isl_give isl_schedule_node *isl_schedule_node_root(
7667 __isl_take isl_schedule_node *node);
7668 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
7669 __isl_take isl_schedule_node *node,
7671 int isl_schedule_node_n_children(
7672 __isl_keep isl_schedule_node *node);
7673 __isl_give isl_schedule_node *isl_schedule_node_child(
7674 __isl_take isl_schedule_node *node, int pos);
7675 isl_bool isl_schedule_node_has_children(
7676 __isl_keep isl_schedule_node *node);
7677 __isl_give isl_schedule_node *isl_schedule_node_first_child(
7678 __isl_take isl_schedule_node *node);
7679 isl_bool isl_schedule_node_has_previous_sibling(
7680 __isl_keep isl_schedule_node *node);
7681 __isl_give isl_schedule_node *
7682 isl_schedule_node_previous_sibling(
7683 __isl_take isl_schedule_node *node);
7684 isl_bool isl_schedule_node_has_next_sibling(
7685 __isl_keep isl_schedule_node *node);
7686 __isl_give isl_schedule_node *
7687 isl_schedule_node_next_sibling(
7688 __isl_take isl_schedule_node *node);
7690 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
7691 is the node itself, the ancestor of generation 1 is its parent and so on.
7693 It is also possible to query the number of ancestors of a node,
7694 the position of the current node
7695 within the children of its parent, the position of the subtree
7696 containing a node within the children of an ancestor
7697 or to obtain a copy of a given
7698 child without destroying the current node.
7699 Given two nodes that point to the same schedule, their closest
7700 shared ancestor can be obtained using
7701 C<isl_schedule_node_get_shared_ancestor>.
7703 #include <isl/schedule_node.h>
7704 int isl_schedule_node_get_tree_depth(
7705 __isl_keep isl_schedule_node *node);
7706 int isl_schedule_node_get_child_position(
7707 __isl_keep isl_schedule_node *node);
7708 int isl_schedule_node_get_ancestor_child_position(
7709 __isl_keep isl_schedule_node *node,
7710 __isl_keep isl_schedule_node *ancestor);
7711 __isl_give isl_schedule_node *isl_schedule_node_get_child(
7712 __isl_keep isl_schedule_node *node, int pos);
7713 __isl_give isl_schedule_node *
7714 isl_schedule_node_get_shared_ancestor(
7715 __isl_keep isl_schedule_node *node1,
7716 __isl_keep isl_schedule_node *node2);
7718 All nodes in a schedule tree or
7719 all descendants of a specific node (including the node) can be visited
7720 in depth-first pre-order using the following functions.
7722 #include <isl/schedule.h>
7723 isl_stat isl_schedule_foreach_schedule_node_top_down(
7724 __isl_keep isl_schedule *sched,
7725 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
7726 void *user), void *user);
7728 #include <isl/schedule_node.h>
7729 isl_stat isl_schedule_node_foreach_descendant_top_down(
7730 __isl_keep isl_schedule_node *node,
7731 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
7732 void *user), void *user);
7734 The callback function is slightly different from the usual
7735 callbacks in that it not only indicates success (non-negative result)
7736 or failure (negative result), but also indicates whether the children
7737 of the given node should be visited. In particular, if the callback
7738 returns a positive value, then the children are visited, but if
7739 the callback returns zero, then the children are not visited.
7741 The ancestors of a node in a schedule tree can be visited from
7742 the root down to and including the parent of the node using
7743 the following function.
7745 #include <isl/schedule_node.h>
7746 isl_stat isl_schedule_node_foreach_ancestor_top_down(
7747 __isl_keep isl_schedule_node *node,
7748 isl_stat (*fn)(__isl_keep isl_schedule_node *node,
7749 void *user), void *user);
7751 The following functions allows for a depth-first post-order
7752 traversal of the nodes in a schedule tree or
7753 of the descendants of a specific node (including the node
7754 itself), where the user callback is allowed to modify the
7757 #include <isl/schedule.h>
7758 __isl_give isl_schedule *
7759 isl_schedule_map_schedule_node_bottom_up(
7760 __isl_take isl_schedule *schedule,
7761 __isl_give isl_schedule_node *(*fn)(
7762 __isl_take isl_schedule_node *node,
7763 void *user), void *user);
7765 #include <isl/schedule_node.h>
7766 __isl_give isl_schedule_node *
7767 isl_schedule_node_map_descendant_bottom_up(
7768 __isl_take isl_schedule_node *node,
7769 __isl_give isl_schedule_node *(*fn)(
7770 __isl_take isl_schedule_node *node,
7771 void *user), void *user);
7773 The traversal continues from the node returned by the callback function.
7774 It is the responsibility of the user to ensure that this does not
7775 lead to an infinite loop. It is safest to always return a pointer
7776 to the same position (same ancestors and child positions) as the input node.
7778 The following function removes a node (along with its descendants)
7779 from a schedule tree and returns a pointer to the leaf at the
7780 same position in the updated tree.
7781 It is not allowed to remove the root of a schedule tree or
7782 a child of a set or sequence node.
7784 #include <isl/schedule_node.h>
7785 __isl_give isl_schedule_node *isl_schedule_node_cut(
7786 __isl_take isl_schedule_node *node);
7788 The following function removes a single node
7789 from a schedule tree and returns a pointer to the child
7790 of the node, now located at the position of the original node
7791 or to a leaf node at that position if there was no child.
7792 It is not allowed to remove the root of a schedule tree,
7793 a set or sequence node, a child of a set or sequence node or
7794 a band node with an anchored subtree.
7796 #include <isl/schedule_node.h>
7797 __isl_give isl_schedule_node *isl_schedule_node_delete(
7798 __isl_take isl_schedule_node *node);
7800 Most nodes in a schedule tree only contain local information.
7801 In some cases, however, a node may also refer to outer band nodes.
7802 This means that the position of the node within the tree should
7803 not be changed, or at least that no changes are performed to the
7804 outer band nodes. The following function can be used to test
7805 whether the subtree rooted at a given node contains any such nodes.
7807 #include <isl/schedule_node.h>
7808 isl_bool isl_schedule_node_is_subtree_anchored(
7809 __isl_keep isl_schedule_node *node);
7811 The following function resets the user pointers on all parameter
7812 and tuple identifiers referenced by the given schedule node.
7814 #include <isl/schedule_node.h>
7815 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
7816 __isl_take isl_schedule_node *node);
7818 The following function aligns the parameters of the given schedule
7819 node to the given space.
7821 #include <isl/schedule_node.h>
7822 __isl_give isl_schedule_node *
7823 isl_schedule_node_align_params(
7824 __isl_take isl_schedule_node *node,
7825 __isl_take isl_space *space);
7827 Several node types have their own functions for querying
7828 (and in some cases setting) some node type specific properties.
7830 #include <isl/schedule_node.h>
7831 __isl_give isl_space *isl_schedule_node_band_get_space(
7832 __isl_keep isl_schedule_node *node);
7833 __isl_give isl_multi_union_pw_aff *
7834 isl_schedule_node_band_get_partial_schedule(
7835 __isl_keep isl_schedule_node *node);
7836 __isl_give isl_union_map *
7837 isl_schedule_node_band_get_partial_schedule_union_map(
7838 __isl_keep isl_schedule_node *node);
7839 unsigned isl_schedule_node_band_n_member(
7840 __isl_keep isl_schedule_node *node);
7841 isl_bool isl_schedule_node_band_member_get_coincident(
7842 __isl_keep isl_schedule_node *node, int pos);
7843 __isl_give isl_schedule_node *
7844 isl_schedule_node_band_member_set_coincident(
7845 __isl_take isl_schedule_node *node, int pos,
7847 isl_bool isl_schedule_node_band_get_permutable(
7848 __isl_keep isl_schedule_node *node);
7849 __isl_give isl_schedule_node *
7850 isl_schedule_node_band_set_permutable(
7851 __isl_take isl_schedule_node *node, int permutable);
7852 enum isl_ast_loop_type
7853 isl_schedule_node_band_member_get_ast_loop_type(
7854 __isl_keep isl_schedule_node *node, int pos);
7855 __isl_give isl_schedule_node *
7856 isl_schedule_node_band_member_set_ast_loop_type(
7857 __isl_take isl_schedule_node *node, int pos,
7858 enum isl_ast_loop_type type);
7859 __isl_give isl_union_set *
7860 enum isl_ast_loop_type
7861 isl_schedule_node_band_member_get_isolate_ast_loop_type(
7862 __isl_keep isl_schedule_node *node, int pos);
7863 __isl_give isl_schedule_node *
7864 isl_schedule_node_band_member_set_isolate_ast_loop_type(
7865 __isl_take isl_schedule_node *node, int pos,
7866 enum isl_ast_loop_type type);
7867 isl_schedule_node_band_get_ast_build_options(
7868 __isl_keep isl_schedule_node *node);
7869 __isl_give isl_schedule_node *
7870 isl_schedule_node_band_set_ast_build_options(
7871 __isl_take isl_schedule_node *node,
7872 __isl_take isl_union_set *options);
7874 The function C<isl_schedule_node_band_get_space> returns the space
7875 of the partial schedule of the band.
7876 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
7877 returns a representation of the partial schedule of the band node
7878 in the form of an C<isl_union_map>.
7879 The coincident and permutable properties are set by
7880 C<isl_schedule_constraints_compute_schedule> on the schedule tree
7882 A scheduling dimension is considered to be ``coincident''
7883 if it satisfies the coincidence constraints within its band.
7884 That is, if the dependence distances of the coincidence
7885 constraints are all zero in that direction (for fixed
7886 iterations of outer bands).
7887 A band is marked permutable if it was produced using the Pluto-like scheduler.
7888 Note that the scheduler may have to resort to a Feautrier style scheduling
7889 step even if the default scheduler is used.
7890 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
7891 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
7892 For the meaning of these loop AST generation types and the difference
7893 between the regular loop AST generation type and the isolate
7894 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
7895 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
7896 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
7897 may return C<isl_ast_loop_error> if an error occurs.
7898 The AST build options govern how an AST is generated for
7899 the individual schedule dimensions during AST generation.
7900 See L</"AST Generation Options (Schedule Tree)">.
7902 #include <isl/schedule_node.h>
7903 __isl_give isl_set *
7904 isl_schedule_node_context_get_context(
7905 __isl_keep isl_schedule_node *node);
7907 #include <isl/schedule_node.h>
7908 __isl_give isl_union_set *
7909 isl_schedule_node_domain_get_domain(
7910 __isl_keep isl_schedule_node *node);
7912 #include <isl/schedule_node.h>
7913 __isl_give isl_union_map *
7914 isl_schedule_node_expansion_get_expansion(
7915 __isl_keep isl_schedule_node *node);
7916 __isl_give isl_union_pw_multi_aff *
7917 isl_schedule_node_expansion_get_contraction(
7918 __isl_keep isl_schedule_node *node);
7920 #include <isl/schedule_node.h>
7921 __isl_give isl_union_map *
7922 isl_schedule_node_extension_get_extension(
7923 __isl_keep isl_schedule_node *node);
7925 #include <isl/schedule_node.h>
7926 __isl_give isl_union_set *
7927 isl_schedule_node_filter_get_filter(
7928 __isl_keep isl_schedule_node *node);
7930 #include <isl/schedule_node.h>
7931 __isl_give isl_set *isl_schedule_node_guard_get_guard(
7932 __isl_keep isl_schedule_node *node);
7934 #include <isl/schedule_node.h>
7935 __isl_give isl_id *isl_schedule_node_mark_get_id(
7936 __isl_keep isl_schedule_node *node);
7938 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
7939 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
7940 partial schedules related to the node.
7942 #include <isl/schedule_node.h>
7943 __isl_give isl_multi_union_pw_aff *
7944 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
7945 __isl_keep isl_schedule_node *node);
7946 __isl_give isl_union_pw_multi_aff *
7947 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
7948 __isl_keep isl_schedule_node *node);
7949 __isl_give isl_union_map *
7950 isl_schedule_node_get_prefix_schedule_union_map(
7951 __isl_keep isl_schedule_node *node);
7952 __isl_give isl_union_map *
7953 isl_schedule_node_get_prefix_schedule_relation(
7954 __isl_keep isl_schedule_node *node);
7955 __isl_give isl_union_map *
7956 isl_schedule_node_get_subtree_schedule_union_map(
7957 __isl_keep isl_schedule_node *node);
7959 In particular, the functions
7960 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
7961 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
7962 and C<isl_schedule_node_get_prefix_schedule_union_map>
7963 return a relative ordering on the domain elements that reach the given
7964 node determined by its ancestors.
7965 The function C<isl_schedule_node_get_prefix_schedule_relation>
7966 additionally includes the domain constraints in the result.
7967 The function C<isl_schedule_node_get_subtree_schedule_union_map>
7968 returns a representation of the partial schedule defined by the
7969 subtree rooted at the given node.
7970 If the tree contains any expansion nodes, then the subtree schedule
7971 is formulated in terms of the expanded domain elements.
7972 The tree passed to functions returning a prefix schedule
7973 may only contain extension nodes if these would not affect
7974 the result of these functions. That is, if one of the ancestors
7975 is an extension node, then all of the domain elements that were
7976 added by the extension node need to have been filtered out
7977 by filter nodes between the extension node and the input node.
7978 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
7979 may not contain in extension nodes in the selected subtree.
7981 The expansion/contraction defined by an entire subtree, combining
7982 the expansions/contractions
7983 on the expansion nodes in the subtree, can be obtained using
7984 the following functions.
7986 #include <isl/schedule_node.h>
7987 __isl_give isl_union_map *
7988 isl_schedule_node_get_subtree_expansion(
7989 __isl_keep isl_schedule_node *node);
7990 __isl_give isl_union_pw_multi_aff *
7991 isl_schedule_node_get_subtree_contraction(
7992 __isl_keep isl_schedule_node *node);
7994 The total number of outer band members of given node, i.e.,
7995 the shared output dimension of the maps in the result
7996 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
7997 using the following function.
7999 #include <isl/schedule_node.h>
8000 int isl_schedule_node_get_schedule_depth(
8001 __isl_keep isl_schedule_node *node);
8003 The following functions return the elements that reach the given node
8004 or the union of universes in the spaces that contain these elements.
8006 #include <isl/schedule_node.h>
8007 __isl_give isl_union_set *
8008 isl_schedule_node_get_domain(
8009 __isl_keep isl_schedule_node *node);
8010 __isl_give isl_union_set *
8011 isl_schedule_node_get_universe_domain(
8012 __isl_keep isl_schedule_node *node);
8014 The input tree of C<isl_schedule_node_get_domain>
8015 may only contain extension nodes if these would not affect
8016 the result of this function. That is, if one of the ancestors
8017 is an extension node, then all of the domain elements that were
8018 added by the extension node need to have been filtered out
8019 by filter nodes between the extension node and the input node.
8021 The following functions can be used to introduce additional nodes
8022 in the schedule tree. The new node is introduced at the point
8023 in the tree where the C<isl_schedule_node> points to and
8024 the results points to the new node.
8026 #include <isl/schedule_node.h>
8027 __isl_give isl_schedule_node *
8028 isl_schedule_node_insert_partial_schedule(
8029 __isl_take isl_schedule_node *node,
8030 __isl_take isl_multi_union_pw_aff *schedule);
8032 This function inserts a new band node with (the greatest integer
8033 part of) the given partial schedule.
8034 The subtree rooted at the given node is assumed not to have
8037 #include <isl/schedule_node.h>
8038 __isl_give isl_schedule_node *
8039 isl_schedule_node_insert_context(
8040 __isl_take isl_schedule_node *node,
8041 __isl_take isl_set *context);
8043 This function inserts a new context node with the given context constraints.
8045 #include <isl/schedule_node.h>
8046 __isl_give isl_schedule_node *
8047 isl_schedule_node_insert_filter(
8048 __isl_take isl_schedule_node *node,
8049 __isl_take isl_union_set *filter);
8051 This function inserts a new filter node with the given filter.
8052 If the original node already pointed to a filter node, then the
8053 two filter nodes are merged into one.
8055 #include <isl/schedule_node.h>
8056 __isl_give isl_schedule_node *
8057 isl_schedule_node_insert_guard(
8058 __isl_take isl_schedule_node *node,
8059 __isl_take isl_set *guard);
8061 This function inserts a new guard node with the given guard constraints.
8063 #include <isl/schedule_node.h>
8064 __isl_give isl_schedule_node *
8065 isl_schedule_node_insert_mark(
8066 __isl_take isl_schedule_node *node,
8067 __isl_take isl_id *mark);
8069 This function inserts a new mark node with the give mark identifier.
8071 #include <isl/schedule_node.h>
8072 __isl_give isl_schedule_node *
8073 isl_schedule_node_insert_sequence(
8074 __isl_take isl_schedule_node *node,
8075 __isl_take isl_union_set_list *filters);
8076 __isl_give isl_schedule_node *
8077 isl_schedule_node_insert_set(
8078 __isl_take isl_schedule_node *node,
8079 __isl_take isl_union_set_list *filters);
8081 These functions insert a new sequence or set node with the given
8082 filters as children.
8084 #include <isl/schedule_node.h>
8085 __isl_give isl_schedule_node *isl_schedule_node_group(
8086 __isl_take isl_schedule_node *node,
8087 __isl_take isl_id *group_id);
8089 This function introduces an expansion node in between the current
8090 node and its parent that expands instances of a space with tuple
8091 identifier C<group_id> to the original domain elements that reach
8092 the node. The group instances are identified by the prefix schedule
8093 of those domain elements. The ancestors of the node are adjusted
8094 to refer to the group instances instead of the original domain
8095 elements. The return value points to the same node in the updated
8096 schedule tree as the input node, i.e., to the child of the newly
8097 introduced expansion node. Grouping instances of different statements
8098 ensures that they will be treated as a single statement by the
8099 AST generator up to the point of the expansion node.
8101 The partial schedule of a band node can be scaled (down) using
8102 the following functions.
8104 #include <isl/schedule_node.h>
8105 __isl_give isl_schedule_node *
8106 isl_schedule_node_band_scale(
8107 __isl_take isl_schedule_node *node,
8108 __isl_take isl_multi_val *mv);
8109 __isl_give isl_schedule_node *
8110 isl_schedule_node_band_scale_down(
8111 __isl_take isl_schedule_node *node,
8112 __isl_take isl_multi_val *mv);
8114 The spaces of the two arguments need to match.
8115 After scaling, the partial schedule is replaced by its greatest
8116 integer part to ensure that the schedule remains integral.
8118 A band node can be tiled using the following function.
8120 #include <isl/schedule_node.h>
8121 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
8122 __isl_take isl_schedule_node *node,
8123 __isl_take isl_multi_val *sizes);
8125 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
8127 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
8128 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
8130 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
8132 The C<isl_schedule_node_band_tile> function tiles
8133 the band using the given tile sizes inside its schedule.
8134 A new child band node is created to represent the point loops and it is
8135 inserted between the modified band and its children.
8136 The subtree rooted at the given node is assumed not to have
8138 The C<tile_scale_tile_loops> option specifies whether the tile
8139 loops iterators should be scaled by the tile sizes.
8140 If the C<tile_shift_point_loops> option is set, then the point loops
8141 are shifted to start at zero.
8143 A band node can be split into two nested band nodes
8144 using the following function.
8146 #include <isl/schedule_node.h>
8147 __isl_give isl_schedule_node *isl_schedule_node_band_split(
8148 __isl_take isl_schedule_node *node, int pos);
8150 The resulting outer band node contains the first C<pos> dimensions of
8151 the schedule of C<node> while the inner band contains the remaining dimensions.
8152 The schedules of the two band nodes live in anonymous spaces.
8154 A band node can be moved down to the leaves of the subtree rooted
8155 at the band node using the following function.
8157 #include <isl/schedule_node.h>
8158 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
8159 __isl_take isl_schedule_node *node);
8161 The subtree rooted at the given node is assumed not to have
8163 The result points to the node in the resulting tree that is in the same
8164 position as the node pointed to by C<node> in the original tree.
8166 #include <isl/schedule_node.h>
8167 __isl_give isl_schedule_node *
8168 isl_schedule_node_order_after(
8169 __isl_take isl_schedule_node *node,
8170 __isl_take isl_union_set *filter);
8172 This function splits the domain elements that reach C<node>
8173 into those that satisfy C<filter> and those that do not and
8174 arranges for the elements that do satisfy the filter to be
8175 executed after those that do not. The order is imposed by
8176 a sequence node, possibly reusing the grandparent of C<node>
8177 on two copies of the subtree attached to the original C<node>.
8178 Both copies are simplified with respect to their filter.
8180 Return a pointer to the copy of the subtree that does not
8181 satisfy C<filter>. If there is no such copy (because all
8182 reaching domain elements satisfy the filter), then return
8183 the original pointer.
8185 #include <isl/schedule_node.h>
8186 __isl_give isl_schedule_node *
8187 isl_schedule_node_graft_before(
8188 __isl_take isl_schedule_node *node,
8189 __isl_take isl_schedule_node *graft);
8190 __isl_give isl_schedule_node *
8191 isl_schedule_node_graft_after(
8192 __isl_take isl_schedule_node *node,
8193 __isl_take isl_schedule_node *graft);
8195 This function inserts the C<graft> tree into the tree containing C<node>
8196 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
8197 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
8198 The root node of C<graft>
8199 should be an extension node where the domain of the extension
8200 is the flat product of all outer band nodes of C<node>.
8201 The root node may also be a domain node.
8202 The elements of the domain or the range of the extension may not
8203 intersect with the domain elements that reach "node".
8204 The schedule tree of C<graft> may not be anchored.
8206 The schedule tree of C<node> is modified to include an extension node
8207 corresponding to the root node of C<graft> as a child of the original
8208 parent of C<node>. The original node that C<node> points to and the
8209 child of the root node of C<graft> are attached to this extension node
8210 through a sequence, with appropriate filters and with the child
8211 of C<graft> appearing before or after the original C<node>.
8213 If C<node> already appears inside a sequence that is the child of
8214 an extension node and if the spaces of the new domain elements
8215 do not overlap with those of the original domain elements,
8216 then that extension node is extended with the new extension
8217 rather than introducing a new segment of extension and sequence nodes.
8219 Return a pointer to the same node in the modified tree that
8220 C<node> pointed to in the original tree.
8222 A representation of the schedule node can be printed using
8224 #include <isl/schedule_node.h>
8225 __isl_give isl_printer *isl_printer_print_schedule_node(
8226 __isl_take isl_printer *p,
8227 __isl_keep isl_schedule_node *node);
8229 =head2 Dependence Analysis
8231 C<isl> contains specialized functionality for performing
8232 array dataflow analysis. That is, given a I<sink> access relation
8233 and a collection of possible I<source> access relations,
8234 C<isl> can compute relations that describe
8235 for each iteration of the sink access, which iteration
8236 of which of the source access relations was the last
8237 to access the same data element before the given iteration
8239 The resulting dependence relations map source iterations
8240 to the corresponding sink iterations.
8241 To compute standard flow dependences, the sink should be
8242 a read, while the sources should be writes.
8243 If any of the source accesses are marked as being I<may>
8244 accesses, then there will be a dependence from the last
8245 I<must> access B<and> from any I<may> access that follows
8246 this last I<must> access.
8247 In particular, if I<all> sources are I<may> accesses,
8248 then memory based dependence analysis is performed.
8249 If, on the other hand, all sources are I<must> accesses,
8250 then value based dependence analysis is performed.
8252 =head3 High-level Interface
8254 A high-level interface to dependence analysis is provided
8255 by the following function.
8257 #include <isl/flow.h>
8258 __isl_give isl_union_flow *
8259 isl_union_access_info_compute_flow(
8260 __isl_take isl_union_access_info *access);
8262 The input C<isl_union_access_info> object describes the sink
8263 access relations, the source access relations and a schedule,
8264 while the output C<isl_union_flow> object describes
8265 the resulting dependence relations and the subsets of the
8266 sink relations for which no source was found.
8268 An C<isl_union_access_info> is created, modified, copied and freed using
8269 the following functions.
8271 #include <isl/flow.h>
8272 __isl_give isl_union_access_info *
8273 isl_union_access_info_from_sink(
8274 __isl_take isl_union_map *sink);
8275 __isl_give isl_union_access_info *
8276 isl_union_access_info_set_must_source(
8277 __isl_take isl_union_access_info *access,
8278 __isl_take isl_union_map *must_source);
8279 __isl_give isl_union_access_info *
8280 isl_union_access_info_set_may_source(
8281 __isl_take isl_union_access_info *access,
8282 __isl_take isl_union_map *may_source);
8283 __isl_give isl_union_access_info *
8284 isl_union_access_info_set_schedule(
8285 __isl_take isl_union_access_info *access,
8286 __isl_take isl_schedule *schedule);
8287 __isl_give isl_union_access_info *
8288 isl_union_access_info_set_schedule_map(
8289 __isl_take isl_union_access_info *access,
8290 __isl_take isl_union_map *schedule_map);
8291 __isl_give isl_union_access_info *
8292 isl_union_access_info_copy(
8293 __isl_keep isl_union_access_info *access);
8294 __isl_null isl_union_access_info *
8295 isl_union_access_info_free(
8296 __isl_take isl_union_access_info *access);
8298 The may sources set by C<isl_union_access_info_set_may_source>
8299 do not need to include the must sources set by
8300 C<isl_union_access_info_set_must_source> as a subset.
8301 The user is free not to call one (or both) of these functions,
8302 in which case the corresponding set is kept to its empty default.
8303 Similarly, the default schedule initialized by
8304 C<isl_union_access_info_from_sink> is empty.
8305 The current schedule is determined by the last call to either
8306 C<isl_union_access_info_set_schedule> or
8307 C<isl_union_access_info_set_schedule_map>.
8308 The domain of the schedule corresponds to the domains of
8309 the access relations. In particular, the domains of the access
8310 relations are effectively intersected with the domain of the schedule
8311 and only the resulting accesses are considered by the dependence analysis.
8313 The output of C<isl_union_access_info_compute_flow> can be examined
8314 and freed using the following functions.
8316 #include <isl/flow.h>
8317 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
8318 __isl_keep isl_union_flow *flow);
8319 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
8320 __isl_keep isl_union_flow *flow);
8321 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
8322 __isl_keep isl_union_flow *flow);
8323 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
8324 __isl_keep isl_union_flow *flow);
8325 __isl_null isl_union_flow *isl_union_flow_free(
8326 __isl_take isl_union_flow *flow);
8328 The relation returned by C<isl_union_flow_get_must_dependence>
8329 relates domain elements of must sources to domain elements of the sink.
8330 The relation returned by C<isl_union_flow_get_may_dependence>
8331 relates domain elements of must or may sources to domain elements of the sink
8332 and includes the previous relation as a subset.
8333 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
8334 of the sink relation for which no dependences have been found.
8335 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
8336 of the sink relation for which no definite dependences have been found.
8337 That is, it contains those sink access that do not contribute to any
8338 of the elements in the relation returned
8339 by C<isl_union_flow_get_must_dependence>.
8341 =head3 Low-level Interface
8343 A lower-level interface is provided by the following functions.
8345 #include <isl/flow.h>
8347 typedef int (*isl_access_level_before)(void *first, void *second);
8349 __isl_give isl_access_info *isl_access_info_alloc(
8350 __isl_take isl_map *sink,
8351 void *sink_user, isl_access_level_before fn,
8353 __isl_give isl_access_info *isl_access_info_add_source(
8354 __isl_take isl_access_info *acc,
8355 __isl_take isl_map *source, int must,
8357 __isl_null isl_access_info *isl_access_info_free(
8358 __isl_take isl_access_info *acc);
8360 __isl_give isl_flow *isl_access_info_compute_flow(
8361 __isl_take isl_access_info *acc);
8363 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,
8364 isl_stat (*fn)(__isl_take isl_map *dep, int must,
8365 void *dep_user, void *user),
8367 __isl_give isl_map *isl_flow_get_no_source(
8368 __isl_keep isl_flow *deps, int must);
8369 void isl_flow_free(__isl_take isl_flow *deps);
8371 The function C<isl_access_info_compute_flow> performs the actual
8372 dependence analysis. The other functions are used to construct
8373 the input for this function or to read off the output.
8375 The input is collected in an C<isl_access_info>, which can
8376 be created through a call to C<isl_access_info_alloc>.
8377 The arguments to this functions are the sink access relation
8378 C<sink>, a token C<sink_user> used to identify the sink
8379 access to the user, a callback function for specifying the
8380 relative order of source and sink accesses, and the number
8381 of source access relations that will be added.
8382 The callback function has type C<int (*)(void *first, void *second)>.
8383 The function is called with two user supplied tokens identifying
8384 either a source or the sink and it should return the shared nesting
8385 level and the relative order of the two accesses.
8386 In particular, let I<n> be the number of loops shared by
8387 the two accesses. If C<first> precedes C<second> textually,
8388 then the function should return I<2 * n + 1>; otherwise,
8389 it should return I<2 * n>.
8390 The sources can be added to the C<isl_access_info> by performing
8391 (at most) C<max_source> calls to C<isl_access_info_add_source>.
8392 C<must> indicates whether the source is a I<must> access
8393 or a I<may> access. Note that a multi-valued access relation
8394 should only be marked I<must> if every iteration in the domain
8395 of the relation accesses I<all> elements in its image.
8396 The C<source_user> token is again used to identify
8397 the source access. The range of the source access relation
8398 C<source> should have the same dimension as the range
8399 of the sink access relation.
8400 The C<isl_access_info_free> function should usually not be
8401 called explicitly, because it is called implicitly by
8402 C<isl_access_info_compute_flow>.
8404 The result of the dependence analysis is collected in an
8405 C<isl_flow>. There may be elements of
8406 the sink access for which no preceding source access could be
8407 found or for which all preceding sources are I<may> accesses.
8408 The relations containing these elements can be obtained through
8409 calls to C<isl_flow_get_no_source>, the first with C<must> set
8410 and the second with C<must> unset.
8411 In the case of standard flow dependence analysis,
8412 with the sink a read and the sources I<must> writes,
8413 the first relation corresponds to the reads from uninitialized
8414 array elements and the second relation is empty.
8415 The actual flow dependences can be extracted using
8416 C<isl_flow_foreach>. This function will call the user-specified
8417 callback function C<fn> for each B<non-empty> dependence between
8418 a source and the sink. The callback function is called
8419 with four arguments, the actual flow dependence relation
8420 mapping source iterations to sink iterations, a boolean that
8421 indicates whether it is a I<must> or I<may> dependence, a token
8422 identifying the source and an additional C<void *> with value
8423 equal to the third argument of the C<isl_flow_foreach> call.
8424 A dependence is marked I<must> if it originates from a I<must>
8425 source and if it is not followed by any I<may> sources.
8427 After finishing with an C<isl_flow>, the user should call
8428 C<isl_flow_free> to free all associated memory.
8430 =head3 Interaction with the Low-level Interface
8432 During the dependence analysis, we frequently need to perform
8433 the following operation. Given a relation between sink iterations
8434 and potential source iterations from a particular source domain,
8435 what is the last potential source iteration corresponding to each
8436 sink iteration. It can sometimes be convenient to adjust
8437 the set of potential source iterations before or after each such operation.
8438 The prototypical example is fuzzy array dataflow analysis,
8439 where we need to analyze if, based on data-dependent constraints,
8440 the sink iteration can ever be executed without one or more of
8441 the corresponding potential source iterations being executed.
8442 If so, we can introduce extra parameters and select an unknown
8443 but fixed source iteration from the potential source iterations.
8444 To be able to perform such manipulations, C<isl> provides the following
8447 #include <isl/flow.h>
8449 typedef __isl_give isl_restriction *(*isl_access_restrict)(
8450 __isl_keep isl_map *source_map,
8451 __isl_keep isl_set *sink, void *source_user,
8453 __isl_give isl_access_info *isl_access_info_set_restrict(
8454 __isl_take isl_access_info *acc,
8455 isl_access_restrict fn, void *user);
8457 The function C<isl_access_info_set_restrict> should be called
8458 before calling C<isl_access_info_compute_flow> and registers a callback function
8459 that will be called any time C<isl> is about to compute the last
8460 potential source. The first argument is the (reverse) proto-dependence,
8461 mapping sink iterations to potential source iterations.
8462 The second argument represents the sink iterations for which
8463 we want to compute the last source iteration.
8464 The third argument is the token corresponding to the source
8465 and the final argument is the token passed to C<isl_access_info_set_restrict>.
8466 The callback is expected to return a restriction on either the input or
8467 the output of the operation computing the last potential source.
8468 If the input needs to be restricted then restrictions are needed
8469 for both the source and the sink iterations. The sink iterations
8470 and the potential source iterations will be intersected with these sets.
8471 If the output needs to be restricted then only a restriction on the source
8472 iterations is required.
8473 If any error occurs, the callback should return C<NULL>.
8474 An C<isl_restriction> object can be created, freed and inspected
8475 using the following functions.
8477 #include <isl/flow.h>
8479 __isl_give isl_restriction *isl_restriction_input(
8480 __isl_take isl_set *source_restr,
8481 __isl_take isl_set *sink_restr);
8482 __isl_give isl_restriction *isl_restriction_output(
8483 __isl_take isl_set *source_restr);
8484 __isl_give isl_restriction *isl_restriction_none(
8485 __isl_take isl_map *source_map);
8486 __isl_give isl_restriction *isl_restriction_empty(
8487 __isl_take isl_map *source_map);
8488 __isl_null isl_restriction *isl_restriction_free(
8489 __isl_take isl_restriction *restr);
8491 C<isl_restriction_none> and C<isl_restriction_empty> are special
8492 cases of C<isl_restriction_input>. C<isl_restriction_none>
8493 is essentially equivalent to
8495 isl_restriction_input(isl_set_universe(
8496 isl_space_range(isl_map_get_space(source_map))),
8498 isl_space_domain(isl_map_get_space(source_map))));
8500 whereas C<isl_restriction_empty> is essentially equivalent to
8502 isl_restriction_input(isl_set_empty(
8503 isl_space_range(isl_map_get_space(source_map))),
8505 isl_space_domain(isl_map_get_space(source_map))));
8509 B<The functionality described in this section is fairly new
8510 and may be subject to change.>
8512 #include <isl/schedule.h>
8513 __isl_give isl_schedule *
8514 isl_schedule_constraints_compute_schedule(
8515 __isl_take isl_schedule_constraints *sc);
8517 The function C<isl_schedule_constraints_compute_schedule> can be
8518 used to compute a schedule that satisfies the given schedule constraints.
8519 These schedule constraints include the iteration domain for which
8520 a schedule should be computed and dependences between pairs of
8521 iterations. In particular, these dependences include
8522 I<validity> dependences and I<proximity> dependences.
8523 By default, the algorithm used to construct the schedule is similar
8524 to that of C<Pluto>.
8525 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
8527 The generated schedule respects all validity dependences.
8528 That is, all dependence distances over these dependences in the
8529 scheduled space are lexicographically positive.
8531 The default algorithm tries to ensure that the dependence distances
8532 over coincidence constraints are zero and to minimize the
8533 dependence distances over proximity dependences.
8534 Moreover, it tries to obtain sequences (bands) of schedule dimensions
8535 for groups of domains where the dependence distances over validity
8536 dependences have only non-negative values.
8537 Note that when minimizing the maximal dependence distance
8538 over proximity dependences, a single affine expression in the parameters
8539 is constructed that bounds all dependence distances. If no such expression
8540 exists, then the algorithm will fail and resort to an alternative
8541 scheduling algorithm. In particular, this means that adding proximity
8542 dependences may eliminate valid solutions. A typical example where this
8543 phenomenon may occur is when some subset of the proximity dependences
8544 has no restriction on some parameter, forcing the coefficient of that
8545 parameter to be zero, while some other subset forces the dependence
8546 distance to depend on that parameter, requiring the same coefficient
8548 When using Feautrier's algorithm, the coincidence and proximity constraints
8549 are only taken into account during the extension to a
8550 full-dimensional schedule.
8552 An C<isl_schedule_constraints> object can be constructed
8553 and manipulated using the following functions.
8555 #include <isl/schedule.h>
8556 __isl_give isl_schedule_constraints *
8557 isl_schedule_constraints_copy(
8558 __isl_keep isl_schedule_constraints *sc);
8559 __isl_give isl_schedule_constraints *
8560 isl_schedule_constraints_on_domain(
8561 __isl_take isl_union_set *domain);
8562 __isl_give isl_schedule_constraints *
8563 isl_schedule_constraints_set_context(
8564 __isl_take isl_schedule_constraints *sc,
8565 __isl_take isl_set *context);
8566 __isl_give isl_schedule_constraints *
8567 isl_schedule_constraints_set_validity(
8568 __isl_take isl_schedule_constraints *sc,
8569 __isl_take isl_union_map *validity);
8570 __isl_give isl_schedule_constraints *
8571 isl_schedule_constraints_set_coincidence(
8572 __isl_take isl_schedule_constraints *sc,
8573 __isl_take isl_union_map *coincidence);
8574 __isl_give isl_schedule_constraints *
8575 isl_schedule_constraints_set_proximity(
8576 __isl_take isl_schedule_constraints *sc,
8577 __isl_take isl_union_map *proximity);
8578 __isl_give isl_schedule_constraints *
8579 isl_schedule_constraints_set_conditional_validity(
8580 __isl_take isl_schedule_constraints *sc,
8581 __isl_take isl_union_map *condition,
8582 __isl_take isl_union_map *validity);
8583 __isl_null isl_schedule_constraints *
8584 isl_schedule_constraints_free(
8585 __isl_take isl_schedule_constraints *sc);
8587 The initial C<isl_schedule_constraints> object created by
8588 C<isl_schedule_constraints_on_domain> does not impose any constraints.
8589 That is, it has an empty set of dependences.
8590 The function C<isl_schedule_constraints_set_context> allows the user
8591 to specify additional constraints on the parameters that may
8592 be assumed to hold during the construction of the schedule.
8593 The function C<isl_schedule_constraints_set_validity> replaces the
8594 validity dependences, mapping domain elements I<i> to domain
8595 elements that should be scheduled after I<i>.
8596 The function C<isl_schedule_constraints_set_coincidence> replaces the
8597 coincidence dependences, mapping domain elements I<i> to domain
8598 elements that should be scheduled together with I<I>, if possible.
8599 The function C<isl_schedule_constraints_set_proximity> replaces the
8600 proximity dependences, mapping domain elements I<i> to domain
8601 elements that should be scheduled either before I<I>
8602 or as early as possible after I<i>.
8604 The function C<isl_schedule_constraints_set_conditional_validity>
8605 replaces the conditional validity constraints.
8606 A conditional validity constraint is only imposed when any of the corresponding
8607 conditions is satisfied, i.e., when any of them is non-zero.
8608 That is, the scheduler ensures that within each band if the dependence
8609 distances over the condition constraints are not all zero
8610 then all corresponding conditional validity constraints are respected.
8611 A conditional validity constraint corresponds to a condition
8612 if the two are adjacent, i.e., if the domain of one relation intersect
8613 the range of the other relation.
8614 The typical use case of conditional validity constraints is
8615 to allow order constraints between live ranges to be violated
8616 as long as the live ranges themselves are local to the band.
8617 To allow more fine-grained control over which conditions correspond
8618 to which conditional validity constraints, the domains and ranges
8619 of these relations may include I<tags>. That is, the domains and
8620 ranges of those relation may themselves be wrapped relations
8621 where the iteration domain appears in the domain of those wrapped relations
8622 and the range of the wrapped relations can be arbitrarily chosen
8623 by the user. Conditions and conditional validity constraints are only
8624 considered adjacent to each other if the entire wrapped relation matches.
8625 In particular, a relation with a tag will never be considered adjacent
8626 to a relation without a tag.
8628 An C<isl_schedule_constraints> object can be inspected
8629 using the following functions.
8631 #include <isl/schedule.h>
8632 __isl_give isl_union_map *
8633 isl_schedule_constraints_get_validity(
8634 __isl_keep isl_schedule_constraints *sc);
8635 __isl_give isl_union_map *
8636 isl_schedule_constraints_get_coincidence(
8637 __isl_keep isl_schedule_constraints *sc);
8638 __isl_give isl_union_map *
8639 isl_schedule_constraints_get_conditional_validity(
8640 __isl_keep isl_schedule_constraints *sc);
8641 __isl_give isl_union_map *
8642 isl_schedule_constraints_get_conditional_validity_condition(
8643 __isl_keep isl_schedule_constraints *sc);
8645 The following function computes a schedule directly from
8646 an iteration domain and validity and proximity dependences
8647 and is implemented in terms of the functions described above.
8648 The use of C<isl_union_set_compute_schedule> is discouraged.
8650 #include <isl/schedule.h>
8651 __isl_give isl_schedule *isl_union_set_compute_schedule(
8652 __isl_take isl_union_set *domain,
8653 __isl_take isl_union_map *validity,
8654 __isl_take isl_union_map *proximity);
8656 The generated schedule represents a schedule tree.
8657 For more information on schedule trees, see
8658 L</"Schedule Trees">.
8662 #include <isl/schedule.h>
8663 isl_stat isl_options_set_schedule_max_coefficient(
8664 isl_ctx *ctx, int val);
8665 int isl_options_get_schedule_max_coefficient(
8667 isl_stat isl_options_set_schedule_max_constant_term(
8668 isl_ctx *ctx, int val);
8669 int isl_options_get_schedule_max_constant_term(
8671 isl_stat isl_options_set_schedule_serialize_sccs(
8672 isl_ctx *ctx, int val);
8673 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx);
8674 isl_stat isl_options_set_schedule_maximize_band_depth(
8675 isl_ctx *ctx, int val);
8676 int isl_options_get_schedule_maximize_band_depth(
8678 isl_stat isl_options_set_schedule_outer_coincidence(
8679 isl_ctx *ctx, int val);
8680 int isl_options_get_schedule_outer_coincidence(
8682 isl_stat isl_options_set_schedule_split_scaled(
8683 isl_ctx *ctx, int val);
8684 int isl_options_get_schedule_split_scaled(
8686 isl_stat isl_options_set_schedule_algorithm(
8687 isl_ctx *ctx, int val);
8688 int isl_options_get_schedule_algorithm(
8690 isl_stat isl_options_set_schedule_separate_components(
8691 isl_ctx *ctx, int val);
8692 int isl_options_get_schedule_separate_components(
8697 =item * schedule_max_coefficient
8699 This option enforces that the coefficients for variable and parameter
8700 dimensions in the calculated schedule are not larger than the specified value.
8701 This option can significantly increase the speed of the scheduling calculation
8702 and may also prevent fusing of unrelated dimensions. A value of -1 means that
8703 this option does not introduce bounds on the variable or parameter
8706 =item * schedule_max_constant_term
8708 This option enforces that the constant coefficients in the calculated schedule
8709 are not larger than the maximal constant term. This option can significantly
8710 increase the speed of the scheduling calculation and may also prevent fusing of
8711 unrelated dimensions. A value of -1 means that this option does not introduce
8712 bounds on the constant coefficients.
8714 =item * schedule_serialize_sccs
8716 If this option is set, then all strongly connected components
8717 in the dependence graph are serialized as soon as they are detected.
8718 This means in particular that instances of statements will only
8719 appear in the same band node if these statements belong
8720 to the same strongly connected component at the point where
8721 the band node is constructed.
8723 =item * schedule_maximize_band_depth
8725 If this option is set, we do not split bands at the point
8726 where we detect splitting is necessary. Instead, we
8727 backtrack and split bands as early as possible. This
8728 reduces the number of splits and maximizes the width of
8729 the bands. Wider bands give more possibilities for tiling.
8730 Note that if the C<schedule_serialize_sccs> options is set,
8731 then bands will be split as early as possible, even if there is no need.
8732 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
8734 =item * schedule_outer_coincidence
8736 If this option is set, then we try to construct schedules
8737 where the outermost scheduling dimension in each band
8738 satisfies the coincidence constraints.
8740 =item * schedule_split_scaled
8742 If this option is set, then we try to construct schedules in which the
8743 constant term is split off from the linear part if the linear parts of
8744 the scheduling rows for all nodes in the graphs have a common non-trivial
8746 The constant term is then placed in a separate band and the linear
8749 =item * schedule_algorithm
8751 Selects the scheduling algorithm to be used.
8752 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
8753 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
8755 =item * schedule_separate_components
8757 If this option is set then the function C<isl_schedule_get_map>
8758 will treat set nodes in the same way as sequence nodes.
8762 =head2 AST Generation
8764 This section describes the C<isl> functionality for generating
8765 ASTs that visit all the elements
8766 in a domain in an order specified by a schedule tree or
8768 In case the schedule given as a C<isl_union_map>, an AST is generated
8769 that visits all the elements in the domain of the C<isl_union_map>
8770 according to the lexicographic order of the corresponding image
8771 element(s). If the range of the C<isl_union_map> consists of
8772 elements in more than one space, then each of these spaces is handled
8773 separately in an arbitrary order.
8774 It should be noted that the schedule tree or the image elements
8775 in a schedule map only specify the I<order>
8776 in which the corresponding domain elements should be visited.
8777 No direct relation between the partial schedule values
8778 or the image elements on the one hand and the loop iterators
8779 in the generated AST on the other hand should be assumed.
8781 Each AST is generated within a build. The initial build
8782 simply specifies the constraints on the parameters (if any)
8783 and can be created, inspected, copied and freed using the following functions.
8785 #include <isl/ast_build.h>
8786 __isl_give isl_ast_build *isl_ast_build_alloc(
8788 __isl_give isl_ast_build *isl_ast_build_from_context(
8789 __isl_take isl_set *set);
8790 __isl_give isl_ast_build *isl_ast_build_copy(
8791 __isl_keep isl_ast_build *build);
8792 __isl_null isl_ast_build *isl_ast_build_free(
8793 __isl_take isl_ast_build *build);
8795 The C<set> argument is usually a parameter set with zero or more parameters.
8796 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
8797 this set is required to be a parameter set.
8798 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
8799 specify any parameter constraints.
8800 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
8801 and L</"Fine-grained Control over AST Generation">.
8802 Finally, the AST itself can be constructed using one of the following
8805 #include <isl/ast_build.h>
8806 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
8807 __isl_keep isl_ast_build *build,
8808 __isl_take isl_schedule *schedule);
8809 __isl_give isl_ast_node *
8810 isl_ast_build_node_from_schedule_map(
8811 __isl_keep isl_ast_build *build,
8812 __isl_take isl_union_map *schedule);
8814 =head3 Inspecting the AST
8816 The basic properties of an AST node can be obtained as follows.
8818 #include <isl/ast.h>
8819 enum isl_ast_node_type isl_ast_node_get_type(
8820 __isl_keep isl_ast_node *node);
8822 The type of an AST node is one of
8823 C<isl_ast_node_for>,
8825 C<isl_ast_node_block>,
8826 C<isl_ast_node_mark> or
8827 C<isl_ast_node_user>.
8828 An C<isl_ast_node_for> represents a for node.
8829 An C<isl_ast_node_if> represents an if node.
8830 An C<isl_ast_node_block> represents a compound node.
8831 An C<isl_ast_node_mark> introduces a mark in the AST.
8832 An C<isl_ast_node_user> represents an expression statement.
8833 An expression statement typically corresponds to a domain element, i.e.,
8834 one of the elements that is visited by the AST.
8836 Each type of node has its own additional properties.
8838 #include <isl/ast.h>
8839 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
8840 __isl_keep isl_ast_node *node);
8841 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
8842 __isl_keep isl_ast_node *node);
8843 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
8844 __isl_keep isl_ast_node *node);
8845 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
8846 __isl_keep isl_ast_node *node);
8847 __isl_give isl_ast_node *isl_ast_node_for_get_body(
8848 __isl_keep isl_ast_node *node);
8849 isl_bool isl_ast_node_for_is_degenerate(
8850 __isl_keep isl_ast_node *node);
8852 An C<isl_ast_for> is considered degenerate if it is known to execute
8855 #include <isl/ast.h>
8856 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
8857 __isl_keep isl_ast_node *node);
8858 __isl_give isl_ast_node *isl_ast_node_if_get_then(
8859 __isl_keep isl_ast_node *node);
8860 isl_bool isl_ast_node_if_has_else(
8861 __isl_keep isl_ast_node *node);
8862 __isl_give isl_ast_node *isl_ast_node_if_get_else(
8863 __isl_keep isl_ast_node *node);
8865 __isl_give isl_ast_node_list *
8866 isl_ast_node_block_get_children(
8867 __isl_keep isl_ast_node *node);
8869 __isl_give isl_id *isl_ast_node_mark_get_id(
8870 __isl_keep isl_ast_node *node);
8871 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
8872 __isl_keep isl_ast_node *node);
8874 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
8875 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
8877 #include <isl/ast.h>
8878 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
8879 __isl_keep isl_ast_node *node);
8881 Each of the returned C<isl_ast_expr>s can in turn be inspected using
8882 the following functions.
8884 #include <isl/ast.h>
8885 enum isl_ast_expr_type isl_ast_expr_get_type(
8886 __isl_keep isl_ast_expr *expr);
8888 The type of an AST expression is one of
8890 C<isl_ast_expr_id> or
8891 C<isl_ast_expr_int>.
8892 An C<isl_ast_expr_op> represents the result of an operation.
8893 An C<isl_ast_expr_id> represents an identifier.
8894 An C<isl_ast_expr_int> represents an integer value.
8896 Each type of expression has its own additional properties.
8898 #include <isl/ast.h>
8899 enum isl_ast_op_type isl_ast_expr_get_op_type(
8900 __isl_keep isl_ast_expr *expr);
8901 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
8902 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
8903 __isl_keep isl_ast_expr *expr, int pos);
8904 isl_stat isl_ast_node_foreach_ast_op_type(
8905 __isl_keep isl_ast_node *node,
8906 isl_stat (*fn)(enum isl_ast_op_type type,
8907 void *user), void *user);
8909 C<isl_ast_expr_get_op_type> returns the type of the operation
8910 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
8911 arguments. C<isl_ast_expr_get_op_arg> returns the specified
8913 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
8914 C<isl_ast_op_type> that appears in C<node>.
8915 The operation type is one of the following.
8919 =item C<isl_ast_op_and>
8921 Logical I<and> of two arguments.
8922 Both arguments can be evaluated.
8924 =item C<isl_ast_op_and_then>
8926 Logical I<and> of two arguments.
8927 The second argument can only be evaluated if the first evaluates to true.
8929 =item C<isl_ast_op_or>
8931 Logical I<or> of two arguments.
8932 Both arguments can be evaluated.
8934 =item C<isl_ast_op_or_else>
8936 Logical I<or> of two arguments.
8937 The second argument can only be evaluated if the first evaluates to false.
8939 =item C<isl_ast_op_max>
8941 Maximum of two or more arguments.
8943 =item C<isl_ast_op_min>
8945 Minimum of two or more arguments.
8947 =item C<isl_ast_op_minus>
8951 =item C<isl_ast_op_add>
8953 Sum of two arguments.
8955 =item C<isl_ast_op_sub>
8957 Difference of two arguments.
8959 =item C<isl_ast_op_mul>
8961 Product of two arguments.
8963 =item C<isl_ast_op_div>
8965 Exact division. That is, the result is known to be an integer.
8967 =item C<isl_ast_op_fdiv_q>
8969 Result of integer division, rounded towards negative
8972 =item C<isl_ast_op_pdiv_q>
8974 Result of integer division, where dividend is known to be non-negative.
8976 =item C<isl_ast_op_pdiv_r>
8978 Remainder of integer division, where dividend is known to be non-negative.
8980 =item C<isl_ast_op_zdiv_r>
8982 Equal to zero iff the remainder on integer division is zero.
8984 =item C<isl_ast_op_cond>
8986 Conditional operator defined on three arguments.
8987 If the first argument evaluates to true, then the result
8988 is equal to the second argument. Otherwise, the result
8989 is equal to the third argument.
8990 The second and third argument may only be evaluated if
8991 the first argument evaluates to true and false, respectively.
8992 Corresponds to C<a ? b : c> in C.
8994 =item C<isl_ast_op_select>
8996 Conditional operator defined on three arguments.
8997 If the first argument evaluates to true, then the result
8998 is equal to the second argument. Otherwise, the result
8999 is equal to the third argument.
9000 The second and third argument may be evaluated independently
9001 of the value of the first argument.
9002 Corresponds to C<a * b + (1 - a) * c> in C.
9004 =item C<isl_ast_op_eq>
9008 =item C<isl_ast_op_le>
9010 Less than or equal relation.
9012 =item C<isl_ast_op_lt>
9016 =item C<isl_ast_op_ge>
9018 Greater than or equal relation.
9020 =item C<isl_ast_op_gt>
9022 Greater than relation.
9024 =item C<isl_ast_op_call>
9027 The number of arguments of the C<isl_ast_expr> is one more than
9028 the number of arguments in the function call, the first argument
9029 representing the function being called.
9031 =item C<isl_ast_op_access>
9034 The number of arguments of the C<isl_ast_expr> is one more than
9035 the number of index expressions in the array access, the first argument
9036 representing the array being accessed.
9038 =item C<isl_ast_op_member>
9041 This operation has two arguments, a structure and the name of
9042 the member of the structure being accessed.
9046 #include <isl/ast.h>
9047 __isl_give isl_id *isl_ast_expr_get_id(
9048 __isl_keep isl_ast_expr *expr);
9050 Return the identifier represented by the AST expression.
9052 #include <isl/ast.h>
9053 __isl_give isl_val *isl_ast_expr_get_val(
9054 __isl_keep isl_ast_expr *expr);
9056 Return the integer represented by the AST expression.
9058 =head3 Properties of ASTs
9060 #include <isl/ast.h>
9061 isl_bool isl_ast_expr_is_equal(
9062 __isl_keep isl_ast_expr *expr1,
9063 __isl_keep isl_ast_expr *expr2);
9065 Check if two C<isl_ast_expr>s are equal to each other.
9067 =head3 Manipulating and printing the AST
9069 AST nodes can be copied and freed using the following functions.
9071 #include <isl/ast.h>
9072 __isl_give isl_ast_node *isl_ast_node_copy(
9073 __isl_keep isl_ast_node *node);
9074 __isl_null isl_ast_node *isl_ast_node_free(
9075 __isl_take isl_ast_node *node);
9077 AST expressions can be copied and freed using the following functions.
9079 #include <isl/ast.h>
9080 __isl_give isl_ast_expr *isl_ast_expr_copy(
9081 __isl_keep isl_ast_expr *expr);
9082 __isl_null isl_ast_expr *isl_ast_expr_free(
9083 __isl_take isl_ast_expr *expr);
9085 New AST expressions can be created either directly or within
9086 the context of an C<isl_ast_build>.
9088 #include <isl/ast.h>
9089 __isl_give isl_ast_expr *isl_ast_expr_from_val(
9090 __isl_take isl_val *v);
9091 __isl_give isl_ast_expr *isl_ast_expr_from_id(
9092 __isl_take isl_id *id);
9093 __isl_give isl_ast_expr *isl_ast_expr_neg(
9094 __isl_take isl_ast_expr *expr);
9095 __isl_give isl_ast_expr *isl_ast_expr_address_of(
9096 __isl_take isl_ast_expr *expr);
9097 __isl_give isl_ast_expr *isl_ast_expr_add(
9098 __isl_take isl_ast_expr *expr1,
9099 __isl_take isl_ast_expr *expr2);
9100 __isl_give isl_ast_expr *isl_ast_expr_sub(
9101 __isl_take isl_ast_expr *expr1,
9102 __isl_take isl_ast_expr *expr2);
9103 __isl_give isl_ast_expr *isl_ast_expr_mul(
9104 __isl_take isl_ast_expr *expr1,
9105 __isl_take isl_ast_expr *expr2);
9106 __isl_give isl_ast_expr *isl_ast_expr_div(
9107 __isl_take isl_ast_expr *expr1,
9108 __isl_take isl_ast_expr *expr2);
9109 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
9110 __isl_take isl_ast_expr *expr1,
9111 __isl_take isl_ast_expr *expr2);
9112 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
9113 __isl_take isl_ast_expr *expr1,
9114 __isl_take isl_ast_expr *expr2);
9115 __isl_give isl_ast_expr *isl_ast_expr_and(
9116 __isl_take isl_ast_expr *expr1,
9117 __isl_take isl_ast_expr *expr2)
9118 __isl_give isl_ast_expr *isl_ast_expr_and_then(
9119 __isl_take isl_ast_expr *expr1,
9120 __isl_take isl_ast_expr *expr2)
9121 __isl_give isl_ast_expr *isl_ast_expr_or(
9122 __isl_take isl_ast_expr *expr1,
9123 __isl_take isl_ast_expr *expr2)
9124 __isl_give isl_ast_expr *isl_ast_expr_or_else(
9125 __isl_take isl_ast_expr *expr1,
9126 __isl_take isl_ast_expr *expr2)
9127 __isl_give isl_ast_expr *isl_ast_expr_eq(
9128 __isl_take isl_ast_expr *expr1,
9129 __isl_take isl_ast_expr *expr2);
9130 __isl_give isl_ast_expr *isl_ast_expr_le(
9131 __isl_take isl_ast_expr *expr1,
9132 __isl_take isl_ast_expr *expr2);
9133 __isl_give isl_ast_expr *isl_ast_expr_lt(
9134 __isl_take isl_ast_expr *expr1,
9135 __isl_take isl_ast_expr *expr2);
9136 __isl_give isl_ast_expr *isl_ast_expr_ge(
9137 __isl_take isl_ast_expr *expr1,
9138 __isl_take isl_ast_expr *expr2);
9139 __isl_give isl_ast_expr *isl_ast_expr_gt(
9140 __isl_take isl_ast_expr *expr1,
9141 __isl_take isl_ast_expr *expr2);
9142 __isl_give isl_ast_expr *isl_ast_expr_access(
9143 __isl_take isl_ast_expr *array,
9144 __isl_take isl_ast_expr_list *indices);
9145 __isl_give isl_ast_expr *isl_ast_expr_call(
9146 __isl_take isl_ast_expr *function,
9147 __isl_take isl_ast_expr_list *arguments);
9149 The function C<isl_ast_expr_address_of> can be applied to an
9150 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
9151 to represent the address of the C<isl_ast_expr_access>. The function
9152 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
9153 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
9155 #include <isl/ast_build.h>
9156 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
9157 __isl_keep isl_ast_build *build,
9158 __isl_take isl_set *set);
9159 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
9160 __isl_keep isl_ast_build *build,
9161 __isl_take isl_pw_aff *pa);
9162 __isl_give isl_ast_expr *
9163 isl_ast_build_access_from_pw_multi_aff(
9164 __isl_keep isl_ast_build *build,
9165 __isl_take isl_pw_multi_aff *pma);
9166 __isl_give isl_ast_expr *
9167 isl_ast_build_access_from_multi_pw_aff(
9168 __isl_keep isl_ast_build *build,
9169 __isl_take isl_multi_pw_aff *mpa);
9170 __isl_give isl_ast_expr *
9171 isl_ast_build_call_from_pw_multi_aff(
9172 __isl_keep isl_ast_build *build,
9173 __isl_take isl_pw_multi_aff *pma);
9174 __isl_give isl_ast_expr *
9175 isl_ast_build_call_from_multi_pw_aff(
9176 __isl_keep isl_ast_build *build,
9177 __isl_take isl_multi_pw_aff *mpa);
9180 the domains of C<pa>, C<mpa> and C<pma> should correspond
9181 to the schedule space of C<build>.
9182 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
9183 the function being called.
9184 If the accessed space is a nested relation, then it is taken
9185 to represent an access of the member specified by the range
9186 of this nested relation of the structure specified by the domain
9187 of the nested relation.
9189 The following functions can be used to modify an C<isl_ast_expr>.
9191 #include <isl/ast.h>
9192 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
9193 __isl_take isl_ast_expr *expr, int pos,
9194 __isl_take isl_ast_expr *arg);
9196 Replace the argument of C<expr> at position C<pos> by C<arg>.
9198 #include <isl/ast.h>
9199 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
9200 __isl_take isl_ast_expr *expr,
9201 __isl_take isl_id_to_ast_expr *id2expr);
9203 The function C<isl_ast_expr_substitute_ids> replaces the
9204 subexpressions of C<expr> of type C<isl_ast_expr_id>
9205 by the corresponding expression in C<id2expr>, if there is any.
9208 User specified data can be attached to an C<isl_ast_node> and obtained
9209 from the same C<isl_ast_node> using the following functions.
9211 #include <isl/ast.h>
9212 __isl_give isl_ast_node *isl_ast_node_set_annotation(
9213 __isl_take isl_ast_node *node,
9214 __isl_take isl_id *annotation);
9215 __isl_give isl_id *isl_ast_node_get_annotation(
9216 __isl_keep isl_ast_node *node);
9218 Basic printing can be performed using the following functions.
9220 #include <isl/ast.h>
9221 __isl_give isl_printer *isl_printer_print_ast_expr(
9222 __isl_take isl_printer *p,
9223 __isl_keep isl_ast_expr *expr);
9224 __isl_give isl_printer *isl_printer_print_ast_node(
9225 __isl_take isl_printer *p,
9226 __isl_keep isl_ast_node *node);
9227 __isl_give char *isl_ast_expr_to_str(
9228 __isl_keep isl_ast_expr *expr);
9230 More advanced printing can be performed using the following functions.
9232 #include <isl/ast.h>
9233 __isl_give isl_printer *isl_ast_op_type_print_macro(
9234 enum isl_ast_op_type type,
9235 __isl_take isl_printer *p);
9236 __isl_give isl_printer *isl_ast_node_print_macros(
9237 __isl_keep isl_ast_node *node,
9238 __isl_take isl_printer *p);
9239 __isl_give isl_printer *isl_ast_node_print(
9240 __isl_keep isl_ast_node *node,
9241 __isl_take isl_printer *p,
9242 __isl_take isl_ast_print_options *options);
9243 __isl_give isl_printer *isl_ast_node_for_print(
9244 __isl_keep isl_ast_node *node,
9245 __isl_take isl_printer *p,
9246 __isl_take isl_ast_print_options *options);
9247 __isl_give isl_printer *isl_ast_node_if_print(
9248 __isl_keep isl_ast_node *node,
9249 __isl_take isl_printer *p,
9250 __isl_take isl_ast_print_options *options);
9252 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
9253 C<isl> may print out an AST that makes use of macros such
9254 as C<floord>, C<min> and C<max>.
9255 C<isl_ast_op_type_print_macro> prints out the macro
9256 corresponding to a specific C<isl_ast_op_type>.
9257 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
9258 for expressions where these macros would be used and prints
9259 out the required macro definitions.
9260 Essentially, C<isl_ast_node_print_macros> calls
9261 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
9262 as function argument.
9263 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
9264 C<isl_ast_node_if_print> print an C<isl_ast_node>
9265 in C<ISL_FORMAT_C>, but allow for some extra control
9266 through an C<isl_ast_print_options> object.
9267 This object can be created using the following functions.
9269 #include <isl/ast.h>
9270 __isl_give isl_ast_print_options *
9271 isl_ast_print_options_alloc(isl_ctx *ctx);
9272 __isl_give isl_ast_print_options *
9273 isl_ast_print_options_copy(
9274 __isl_keep isl_ast_print_options *options);
9275 __isl_null isl_ast_print_options *
9276 isl_ast_print_options_free(
9277 __isl_take isl_ast_print_options *options);
9279 __isl_give isl_ast_print_options *
9280 isl_ast_print_options_set_print_user(
9281 __isl_take isl_ast_print_options *options,
9282 __isl_give isl_printer *(*print_user)(
9283 __isl_take isl_printer *p,
9284 __isl_take isl_ast_print_options *options,
9285 __isl_keep isl_ast_node *node, void *user),
9287 __isl_give isl_ast_print_options *
9288 isl_ast_print_options_set_print_for(
9289 __isl_take isl_ast_print_options *options,
9290 __isl_give isl_printer *(*print_for)(
9291 __isl_take isl_printer *p,
9292 __isl_take isl_ast_print_options *options,
9293 __isl_keep isl_ast_node *node, void *user),
9296 The callback set by C<isl_ast_print_options_set_print_user>
9297 is called whenever a node of type C<isl_ast_node_user> needs to
9299 The callback set by C<isl_ast_print_options_set_print_for>
9300 is called whenever a node of type C<isl_ast_node_for> needs to
9302 Note that C<isl_ast_node_for_print> will I<not> call the
9303 callback set by C<isl_ast_print_options_set_print_for> on the node
9304 on which C<isl_ast_node_for_print> is called, but only on nested
9305 nodes of type C<isl_ast_node_for>. It is therefore safe to
9306 call C<isl_ast_node_for_print> from within the callback set by
9307 C<isl_ast_print_options_set_print_for>.
9309 The following option determines the type to be used for iterators
9310 while printing the AST.
9312 isl_stat isl_options_set_ast_iterator_type(
9313 isl_ctx *ctx, const char *val);
9314 const char *isl_options_get_ast_iterator_type(
9317 The AST printer only prints body nodes as blocks if these
9318 blocks cannot be safely omitted.
9319 For example, a C<for> node with one body node will not be
9320 surrounded with braces in C<ISL_FORMAT_C>.
9321 A block will always be printed by setting the following option.
9323 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx,
9325 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
9329 #include <isl/ast_build.h>
9330 isl_stat isl_options_set_ast_build_atomic_upper_bound(
9331 isl_ctx *ctx, int val);
9332 int isl_options_get_ast_build_atomic_upper_bound(
9334 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
9336 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
9337 isl_stat isl_options_set_ast_build_exploit_nested_bounds(
9338 isl_ctx *ctx, int val);
9339 int isl_options_get_ast_build_exploit_nested_bounds(
9341 isl_stat isl_options_set_ast_build_group_coscheduled(
9342 isl_ctx *ctx, int val);
9343 int isl_options_get_ast_build_group_coscheduled(
9345 isl_stat isl_options_set_ast_build_scale_strides(
9346 isl_ctx *ctx, int val);
9347 int isl_options_get_ast_build_scale_strides(
9349 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx,
9351 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
9352 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx,
9354 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
9358 =item * ast_build_atomic_upper_bound
9360 Generate loop upper bounds that consist of the current loop iterator,
9361 an operator and an expression not involving the iterator.
9362 If this option is not set, then the current loop iterator may appear
9363 several times in the upper bound.
9364 For example, when this option is turned off, AST generation
9367 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
9371 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
9374 When the option is turned on, the following AST is generated
9376 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
9379 =item * ast_build_prefer_pdiv
9381 If this option is turned off, then the AST generation will
9382 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
9383 operators, but no C<isl_ast_op_pdiv_q> or
9384 C<isl_ast_op_pdiv_r> operators.
9385 If this options is turned on, then C<isl> will try to convert
9386 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
9387 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
9389 =item * ast_build_exploit_nested_bounds
9391 Simplify conditions based on bounds of nested for loops.
9392 In particular, remove conditions that are implied by the fact
9393 that one or more nested loops have at least one iteration,
9394 meaning that the upper bound is at least as large as the lower bound.
9395 For example, when this option is turned off, AST generation
9398 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
9404 for (int c0 = 0; c0 <= N; c0 += 1)
9405 for (int c1 = 0; c1 <= M; c1 += 1)
9408 When the option is turned on, the following AST is generated
9410 for (int c0 = 0; c0 <= N; c0 += 1)
9411 for (int c1 = 0; c1 <= M; c1 += 1)
9414 =item * ast_build_group_coscheduled
9416 If two domain elements are assigned the same schedule point, then
9417 they may be executed in any order and they may even appear in different
9418 loops. If this options is set, then the AST generator will make
9419 sure that coscheduled domain elements do not appear in separate parts
9420 of the AST. This is useful in case of nested AST generation
9421 if the outer AST generation is given only part of a schedule
9422 and the inner AST generation should handle the domains that are
9423 coscheduled by this initial part of the schedule together.
9424 For example if an AST is generated for a schedule
9426 { A[i] -> [0]; B[i] -> [0] }
9428 then the C<isl_ast_build_set_create_leaf> callback described
9429 below may get called twice, once for each domain.
9430 Setting this option ensures that the callback is only called once
9431 on both domains together.
9433 =item * ast_build_separation_bounds
9435 This option specifies which bounds to use during separation.
9436 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
9437 then all (possibly implicit) bounds on the current dimension will
9438 be used during separation.
9439 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
9440 then only those bounds that are explicitly available will
9441 be used during separation.
9443 =item * ast_build_scale_strides
9445 This option specifies whether the AST generator is allowed
9446 to scale down iterators of strided loops.
9448 =item * ast_build_allow_else
9450 This option specifies whether the AST generator is allowed
9451 to construct if statements with else branches.
9453 =item * ast_build_allow_or
9455 This option specifies whether the AST generator is allowed
9456 to construct if conditions with disjunctions.
9460 =head3 AST Generation Options (Schedule Tree)
9462 In case of AST construction from a schedule tree, the options
9463 that control how an AST is created from the individual schedule
9464 dimensions are stored in the band nodes of the tree
9465 (see L</"Schedule Trees">).
9467 In particular, a schedule dimension can be handled in four
9468 different ways, atomic, separate, unroll or the default.
9469 This loop AST generation type can be set using
9470 C<isl_schedule_node_band_member_set_ast_loop_type>.
9472 the first three can be selected by including a one-dimensional
9473 element with as value the position of the schedule dimension
9474 within the band and as name one of C<atomic>, C<separate>
9475 or C<unroll> in the options
9476 set by C<isl_schedule_node_band_set_ast_build_options>.
9477 Only one of these three may be specified for
9478 any given schedule dimension within a band node.
9479 If none of these is specified, then the default
9480 is used. The meaning of the options is as follows.
9486 When this option is specified, the AST generator will make
9487 sure that a given domains space only appears in a single
9488 loop at the specified level.
9490 For example, for the schedule tree
9492 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
9494 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
9495 options: "{ atomic[x] }"
9497 the following AST will be generated
9499 for (int c0 = 0; c0 <= 10; c0 += 1) {
9506 On the other hand, for the schedule tree
9508 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
9510 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
9511 options: "{ separate[x] }"
9513 the following AST will be generated
9517 for (int c0 = 1; c0 <= 9; c0 += 1) {
9524 If neither C<atomic> nor C<separate> is specified, then the AST generator
9525 may produce either of these two results or some intermediate form.
9529 When this option is specified, the AST generator will
9530 split the domain of the specified schedule dimension
9531 into pieces with a fixed set of statements for which
9532 instances need to be executed by the iterations in
9533 the schedule domain part. This option tends to avoid
9534 the generation of guards inside the corresponding loops.
9535 See also the C<atomic> option.
9539 When this option is specified, the AST generator will
9540 I<completely> unroll the corresponding schedule dimension.
9541 It is the responsibility of the user to ensure that such
9542 unrolling is possible.
9543 To obtain a partial unrolling, the user should apply an additional
9544 strip-mining to the schedule and fully unroll the inner schedule
9549 The C<isolate> option is a bit more involved. It allows the user
9550 to isolate a range of schedule dimension values from smaller and
9551 greater values. Additionally, the user may specify a different
9552 atomic/separate/unroll choice for the isolated part and the remaining
9553 parts. The typical use case of the C<isolate> option is to isolate
9554 full tiles from partial tiles.
9555 The part that needs to be isolated may depend on outer schedule dimensions.
9556 The option therefore needs to be able to reference those outer schedule
9557 dimensions. In particular, the space of the C<isolate> option is that
9558 of a wrapped map with as domain the flat product of all outer band nodes
9559 and as range the space of the current band node.
9560 The atomic/separate/unroll choice for the isolated part is determined
9561 by an option that lives in an unnamed wrapped space with as domain
9562 a zero-dimensional C<isolate> space and as range the regular
9563 C<atomic>, C<separate> or C<unroll> space.
9564 This option may also be set directly using
9565 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
9566 The atomic/separate/unroll choice for the remaining part is determined
9567 by the regular C<atomic>, C<separate> or C<unroll> option.
9568 The use of the C<isolate> option causes any tree containing the node
9569 to be considered anchored.
9571 As an example, consider the isolation of full tiles from partial tiles
9572 in a tiling of a triangular domain. The original schedule is as follows.
9574 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
9576 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
9577 { A[i,j] -> [floor(j/10)] }, \
9578 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
9582 for (int c0 = 0; c0 <= 10; c0 += 1)
9583 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
9584 for (int c2 = 10 * c0;
9585 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
9586 for (int c3 = 10 * c1;
9587 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
9590 Isolating the full tiles, we have the following input
9592 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
9594 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
9595 { A[i,j] -> [floor(j/10)] }, \
9596 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
9597 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
9598 10a+9+10b+9 <= 100 }"
9603 for (int c0 = 0; c0 <= 8; c0 += 1) {
9604 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
9605 for (int c2 = 10 * c0;
9606 c2 <= 10 * c0 + 9; c2 += 1)
9607 for (int c3 = 10 * c1;
9608 c3 <= 10 * c1 + 9; c3 += 1)
9610 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
9611 for (int c2 = 10 * c0;
9612 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
9613 for (int c3 = 10 * c1;
9614 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
9617 for (int c0 = 9; c0 <= 10; c0 += 1)
9618 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
9619 for (int c2 = 10 * c0;
9620 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
9621 for (int c3 = 10 * c1;
9622 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
9626 We may then additionally unroll the innermost loop of the isolated part
9628 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
9630 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
9631 { A[i,j] -> [floor(j/10)] }, \
9632 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
9633 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
9634 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
9639 for (int c0 = 0; c0 <= 8; c0 += 1) {
9640 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
9641 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
9653 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
9654 for (int c2 = 10 * c0;
9655 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
9656 for (int c3 = 10 * c1;
9657 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
9660 for (int c0 = 9; c0 <= 10; c0 += 1)
9661 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
9662 for (int c2 = 10 * c0;
9663 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
9664 for (int c3 = 10 * c1;
9665 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
9670 =head3 AST Generation Options (Schedule Map)
9672 In case of AST construction using
9673 C<isl_ast_build_node_from_schedule_map>, the options
9674 that control how an AST is created from the individual schedule
9675 dimensions are stored in the C<isl_ast_build>.
9676 They can be set using the following function.
9678 #include <isl/ast_build.h>
9679 __isl_give isl_ast_build *
9680 isl_ast_build_set_options(
9681 __isl_take isl_ast_build *control,
9682 __isl_take isl_union_map *options);
9684 The options are encoded in an C<isl_union_map>.
9685 The domain of this union relation refers to the schedule domain,
9686 i.e., the range of the schedule passed
9687 to C<isl_ast_build_node_from_schedule_map>.
9688 In the case of nested AST generation (see L</"Nested AST Generation">),
9689 the domain of C<options> should refer to the extra piece of the schedule.
9690 That is, it should be equal to the range of the wrapped relation in the
9691 range of the schedule.
9692 The range of the options can consist of elements in one or more spaces,
9693 the names of which determine the effect of the option.
9694 The values of the range typically also refer to the schedule dimension
9695 to which the option applies. In case of nested AST generation
9696 (see L</"Nested AST Generation">), these values refer to the position
9697 of the schedule dimension within the innermost AST generation.
9698 The constraints on the domain elements of
9699 the option should only refer to this dimension and earlier dimensions.
9700 We consider the following spaces.
9704 =item C<separation_class>
9706 B<This option has been deprecated. Use the isolate option on
9707 schedule trees instead.>
9709 This space is a wrapped relation between two one dimensional spaces.
9710 The input space represents the schedule dimension to which the option
9711 applies and the output space represents the separation class.
9712 While constructing a loop corresponding to the specified schedule
9713 dimension(s), the AST generator will try to generate separate loops
9714 for domain elements that are assigned different classes.
9715 If only some of the elements are assigned a class, then those elements
9716 that are not assigned any class will be treated as belonging to a class
9717 that is separate from the explicitly assigned classes.
9718 The typical use case for this option is to separate full tiles from
9720 The other options, described below, are applied after the separation
9723 As an example, consider the separation into full and partial tiles
9724 of a tiling of a triangular domain.
9725 Take, for example, the domain
9727 { A[i,j] : 0 <= i,j and i + j <= 100 }
9729 and a tiling into tiles of 10 by 10. The input to the AST generator
9730 is then the schedule
9732 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
9735 Without any options, the following AST is generated
9737 for (int c0 = 0; c0 <= 10; c0 += 1)
9738 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
9739 for (int c2 = 10 * c0;
9740 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
9742 for (int c3 = 10 * c1;
9743 c3 <= min(10 * c1 + 9, -c2 + 100);
9747 Separation into full and partial tiles can be obtained by assigning
9748 a class, say C<0>, to the full tiles. The full tiles are represented by those
9749 values of the first and second schedule dimensions for which there are
9750 values of the third and fourth dimensions to cover an entire tile.
9751 That is, we need to specify the following option
9753 { [a,b,c,d] -> separation_class[[0]->[0]] :
9754 exists b': 0 <= 10a,10b' and
9755 10a+9+10b'+9 <= 100;
9756 [a,b,c,d] -> separation_class[[1]->[0]] :
9757 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
9761 { [a, b, c, d] -> separation_class[[1] -> [0]] :
9762 a >= 0 and b >= 0 and b <= 8 - a;
9763 [a, b, c, d] -> separation_class[[0] -> [0]] :
9766 With this option, the generated AST is as follows
9769 for (int c0 = 0; c0 <= 8; c0 += 1) {
9770 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
9771 for (int c2 = 10 * c0;
9772 c2 <= 10 * c0 + 9; c2 += 1)
9773 for (int c3 = 10 * c1;
9774 c3 <= 10 * c1 + 9; c3 += 1)
9776 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
9777 for (int c2 = 10 * c0;
9778 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
9780 for (int c3 = 10 * c1;
9781 c3 <= min(-c2 + 100, 10 * c1 + 9);
9785 for (int c0 = 9; c0 <= 10; c0 += 1)
9786 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
9787 for (int c2 = 10 * c0;
9788 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
9790 for (int c3 = 10 * c1;
9791 c3 <= min(10 * c1 + 9, -c2 + 100);
9798 This is a single-dimensional space representing the schedule dimension(s)
9799 to which ``separation'' should be applied. Separation tries to split
9800 a loop into several pieces if this can avoid the generation of guards
9802 See also the C<atomic> option.
9806 This is a single-dimensional space representing the schedule dimension(s)
9807 for which the domains should be considered ``atomic''. That is, the
9808 AST generator will make sure that any given domain space will only appear
9809 in a single loop at the specified level.
9811 Consider the following schedule
9813 { a[i] -> [i] : 0 <= i < 10;
9814 b[i] -> [i+1] : 0 <= i < 10 }
9816 If the following option is specified
9818 { [i] -> separate[x] }
9820 then the following AST will be generated
9824 for (int c0 = 1; c0 <= 9; c0 += 1) {
9831 If, on the other hand, the following option is specified
9833 { [i] -> atomic[x] }
9835 then the following AST will be generated
9837 for (int c0 = 0; c0 <= 10; c0 += 1) {
9844 If neither C<atomic> nor C<separate> is specified, then the AST generator
9845 may produce either of these two results or some intermediate form.
9849 This is a single-dimensional space representing the schedule dimension(s)
9850 that should be I<completely> unrolled.
9851 To obtain a partial unrolling, the user should apply an additional
9852 strip-mining to the schedule and fully unroll the inner loop.
9856 =head3 Fine-grained Control over AST Generation
9858 Besides specifying the constraints on the parameters,
9859 an C<isl_ast_build> object can be used to control
9860 various aspects of the AST generation process.
9861 In case of AST construction using
9862 C<isl_ast_build_node_from_schedule_map>,
9863 the most prominent way of control is through ``options'',
9866 Additional control is available through the following functions.
9868 #include <isl/ast_build.h>
9869 __isl_give isl_ast_build *
9870 isl_ast_build_set_iterators(
9871 __isl_take isl_ast_build *control,
9872 __isl_take isl_id_list *iterators);
9874 The function C<isl_ast_build_set_iterators> allows the user to
9875 specify a list of iterator C<isl_id>s to be used as iterators.
9876 If the input schedule is injective, then
9877 the number of elements in this list should be as large as the dimension
9878 of the schedule space, but no direct correspondence should be assumed
9879 between dimensions and elements.
9880 If the input schedule is not injective, then an additional number
9881 of C<isl_id>s equal to the largest dimension of the input domains
9883 If the number of provided C<isl_id>s is insufficient, then additional
9884 names are automatically generated.
9886 #include <isl/ast_build.h>
9887 __isl_give isl_ast_build *
9888 isl_ast_build_set_create_leaf(
9889 __isl_take isl_ast_build *control,
9890 __isl_give isl_ast_node *(*fn)(
9891 __isl_take isl_ast_build *build,
9892 void *user), void *user);
9895 C<isl_ast_build_set_create_leaf> function allows for the
9896 specification of a callback that should be called whenever the AST
9897 generator arrives at an element of the schedule domain.
9898 The callback should return an AST node that should be inserted
9899 at the corresponding position of the AST. The default action (when
9900 the callback is not set) is to continue generating parts of the AST to scan
9901 all the domain elements associated to the schedule domain element
9902 and to insert user nodes, ``calling'' the domain element, for each of them.
9903 The C<build> argument contains the current state of the C<isl_ast_build>.
9904 To ease nested AST generation (see L</"Nested AST Generation">),
9905 all control information that is
9906 specific to the current AST generation such as the options and
9907 the callbacks has been removed from this C<isl_ast_build>.
9908 The callback would typically return the result of a nested
9910 user defined node created using the following function.
9912 #include <isl/ast.h>
9913 __isl_give isl_ast_node *isl_ast_node_alloc_user(
9914 __isl_take isl_ast_expr *expr);
9916 #include <isl/ast_build.h>
9917 __isl_give isl_ast_build *
9918 isl_ast_build_set_at_each_domain(
9919 __isl_take isl_ast_build *build,
9920 __isl_give isl_ast_node *(*fn)(
9921 __isl_take isl_ast_node *node,
9922 __isl_keep isl_ast_build *build,
9923 void *user), void *user);
9924 __isl_give isl_ast_build *
9925 isl_ast_build_set_before_each_for(
9926 __isl_take isl_ast_build *build,
9927 __isl_give isl_id *(*fn)(
9928 __isl_keep isl_ast_build *build,
9929 void *user), void *user);
9930 __isl_give isl_ast_build *
9931 isl_ast_build_set_after_each_for(
9932 __isl_take isl_ast_build *build,
9933 __isl_give isl_ast_node *(*fn)(
9934 __isl_take isl_ast_node *node,
9935 __isl_keep isl_ast_build *build,
9936 void *user), void *user);
9937 __isl_give isl_ast_build *
9938 isl_ast_build_set_before_each_mark(
9939 __isl_take isl_ast_build *build,
9940 isl_stat (*fn)(__isl_keep isl_id *mark,
9941 __isl_keep isl_ast_build *build,
9942 void *user), void *user);
9943 __isl_give isl_ast_build *
9944 isl_ast_build_set_after_each_mark(
9945 __isl_take isl_ast_build *build,
9946 __isl_give isl_ast_node *(*fn)(
9947 __isl_take isl_ast_node *node,
9948 __isl_keep isl_ast_build *build,
9949 void *user), void *user);
9951 The callback set by C<isl_ast_build_set_at_each_domain> will
9952 be called for each domain AST node.
9953 The callbacks set by C<isl_ast_build_set_before_each_for>
9954 and C<isl_ast_build_set_after_each_for> will be called
9955 for each for AST node. The first will be called in depth-first
9956 pre-order, while the second will be called in depth-first post-order.
9957 Since C<isl_ast_build_set_before_each_for> is called before the for
9958 node is actually constructed, it is only passed an C<isl_ast_build>.
9959 The returned C<isl_id> will be added as an annotation (using
9960 C<isl_ast_node_set_annotation>) to the constructed for node.
9961 In particular, if the user has also specified an C<after_each_for>
9962 callback, then the annotation can be retrieved from the node passed to
9963 that callback using C<isl_ast_node_get_annotation>.
9964 The callbacks set by C<isl_ast_build_set_before_each_mark>
9965 and C<isl_ast_build_set_after_each_mark> will be called for each
9966 mark AST node that is created, i.e., for each mark schedule node
9967 in the input schedule tree. The first will be called in depth-first
9968 pre-order, while the second will be called in depth-first post-order.
9969 Since the callback set by C<isl_ast_build_set_before_each_mark>
9970 is called before the mark AST node is actually constructed, it is passed
9971 the identifier of the mark node.
9972 All callbacks should C<NULL> (or -1) on failure.
9973 The given C<isl_ast_build> can be used to create new
9974 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
9975 or C<isl_ast_build_call_from_pw_multi_aff>.
9977 =head3 Nested AST Generation
9979 C<isl> allows the user to create an AST within the context
9980 of another AST. These nested ASTs are created using the
9981 same C<isl_ast_build_node_from_schedule_map> function that is used to create
9982 the outer AST. The C<build> argument should be an C<isl_ast_build>
9983 passed to a callback set by
9984 C<isl_ast_build_set_create_leaf>.
9985 The space of the range of the C<schedule> argument should refer
9986 to this build. In particular, the space should be a wrapped
9987 relation and the domain of this wrapped relation should be the
9988 same as that of the range of the schedule returned by
9989 C<isl_ast_build_get_schedule> below.
9990 In practice, the new schedule is typically
9991 created by calling C<isl_union_map_range_product> on the old schedule
9992 and some extra piece of the schedule.
9993 The space of the schedule domain is also available from
9994 the C<isl_ast_build>.
9996 #include <isl/ast_build.h>
9997 __isl_give isl_union_map *isl_ast_build_get_schedule(
9998 __isl_keep isl_ast_build *build);
9999 __isl_give isl_space *isl_ast_build_get_schedule_space(
10000 __isl_keep isl_ast_build *build);
10001 __isl_give isl_ast_build *isl_ast_build_restrict(
10002 __isl_take isl_ast_build *build,
10003 __isl_take isl_set *set);
10005 The C<isl_ast_build_get_schedule> function returns a (partial)
10006 schedule for the domains elements for which part of the AST still needs to
10007 be generated in the current build.
10008 In particular, the domain elements are mapped to those iterations of the loops
10009 enclosing the current point of the AST generation inside which
10010 the domain elements are executed.
10011 No direct correspondence between
10012 the input schedule and this schedule should be assumed.
10013 The space obtained from C<isl_ast_build_get_schedule_space> can be used
10014 to create a set for C<isl_ast_build_restrict> to intersect
10015 with the current build. In particular, the set passed to
10016 C<isl_ast_build_restrict> can have additional parameters.
10017 The ids of the set dimensions in the space returned by
10018 C<isl_ast_build_get_schedule_space> correspond to the
10019 iterators of the already generated loops.
10020 The user should not rely on the ids of the output dimensions
10021 of the relations in the union relation returned by
10022 C<isl_ast_build_get_schedule> having any particular value.
10024 =head1 Applications
10026 Although C<isl> is mainly meant to be used as a library,
10027 it also contains some basic applications that use some
10028 of the functionality of C<isl>.
10029 The input may be specified in either the L<isl format>
10030 or the L<PolyLib format>.
10032 =head2 C<isl_polyhedron_sample>
10034 C<isl_polyhedron_sample> takes a polyhedron as input and prints
10035 an integer element of the polyhedron, if there is any.
10036 The first column in the output is the denominator and is always
10037 equal to 1. If the polyhedron contains no integer points,
10038 then a vector of length zero is printed.
10042 C<isl_pip> takes the same input as the C<example> program
10043 from the C<piplib> distribution, i.e., a set of constraints
10044 on the parameters, a line containing only -1 and finally a set
10045 of constraints on a parametric polyhedron.
10046 The coefficients of the parameters appear in the last columns
10047 (but before the final constant column).
10048 The output is the lexicographic minimum of the parametric polyhedron.
10049 As C<isl> currently does not have its own output format, the output
10050 is just a dump of the internal state.
10052 =head2 C<isl_polyhedron_minimize>
10054 C<isl_polyhedron_minimize> computes the minimum of some linear
10055 or affine objective function over the integer points in a polyhedron.
10056 If an affine objective function
10057 is given, then the constant should appear in the last column.
10059 =head2 C<isl_polytope_scan>
10061 Given a polytope, C<isl_polytope_scan> prints
10062 all integer points in the polytope.
10064 =head2 C<isl_codegen>
10066 Given a schedule, a context set and an options relation,
10067 C<isl_codegen> prints out an AST that scans the domain elements
10068 of the schedule in the order of their image(s) taking into account
10069 the constraints in the context set.