3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
8 using C<GMP> or C<imath>.
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
171 =head3 Changes since isl-0.10
175 =item * The functions C<isl_set_dim_has_lower_bound> and
176 C<isl_set_dim_has_upper_bound> have been renamed to
177 C<isl_set_dim_has_any_lower_bound> and
178 C<isl_set_dim_has_any_upper_bound>.
179 The new C<isl_set_dim_has_lower_bound> and
180 C<isl_set_dim_has_upper_bound> have slightly different meanings.
184 =head3 Changes since isl-0.12
188 =item * C<isl_int> has been replaced by C<isl_val>.
189 Some of the old functions are still available in C<isl/deprecated/*.h>
190 but they will be removed in the future.
192 =item * The functions C<isl_pw_qpolynomial_eval>,
193 C<isl_union_pw_qpolynomial_eval>, C<isl_pw_qpolynomial_fold_eval>
194 and C<isl_union_pw_qpolynomial_fold_eval> have been changed to return
195 an C<isl_val> instead of an C<isl_qpolynomial>.
197 =item * The function C<isl_band_member_is_zero_distance>
198 has been removed. Essentially the same functionality is available
199 through C<isl_band_member_is_coincident>, except that it requires
200 setting up coincidence constraints.
201 The option C<schedule_outer_zero_distance> has accordingly been
202 replaced by the option C<schedule_outer_coincidence>.
204 =item * The function C<isl_vertex_get_expr> has been changed
205 to return an C<isl_multi_aff> instead of a rational C<isl_basic_set>.
206 The function C<isl_vertex_get_domain> has been changed to return
207 a regular basic set, rather than a rational basic set.
211 =head3 Changes since isl-0.14
215 =item * 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 __isl_give isl_val *isl_val_get_den_val(
645 __isl_keep isl_val *v);
646 double isl_val_get_d(__isl_keep isl_val *v);
647 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
649 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
650 size_t size, void *chunks);
652 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
653 of C<size> bytes needed to store the absolute value of the
655 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
656 which is assumed to have been preallocated by the caller.
657 The least significant digit is stored first.
658 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
659 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
660 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
662 An C<isl_val> can be modified using the following function.
665 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
668 The following unary properties are defined on C<isl_val>s.
671 int isl_val_sgn(__isl_keep isl_val *v);
672 isl_bool isl_val_is_zero(__isl_keep isl_val *v);
673 isl_bool isl_val_is_one(__isl_keep isl_val *v);
674 isl_bool isl_val_is_negone(__isl_keep isl_val *v);
675 isl_bool isl_val_is_nonneg(__isl_keep isl_val *v);
676 isl_bool isl_val_is_nonpos(__isl_keep isl_val *v);
677 isl_bool isl_val_is_pos(__isl_keep isl_val *v);
678 isl_bool isl_val_is_neg(__isl_keep isl_val *v);
679 isl_bool isl_val_is_int(__isl_keep isl_val *v);
680 isl_bool isl_val_is_rat(__isl_keep isl_val *v);
681 isl_bool isl_val_is_nan(__isl_keep isl_val *v);
682 isl_bool isl_val_is_infty(__isl_keep isl_val *v);
683 isl_bool isl_val_is_neginfty(__isl_keep isl_val *v);
685 Note that the sign of NaN is undefined.
687 The following binary properties are defined on pairs of C<isl_val>s.
690 isl_bool isl_val_lt(__isl_keep isl_val *v1,
691 __isl_keep isl_val *v2);
692 isl_bool isl_val_le(__isl_keep isl_val *v1,
693 __isl_keep isl_val *v2);
694 isl_bool isl_val_gt(__isl_keep isl_val *v1,
695 __isl_keep isl_val *v2);
696 isl_bool isl_val_ge(__isl_keep isl_val *v1,
697 __isl_keep isl_val *v2);
698 isl_bool isl_val_eq(__isl_keep isl_val *v1,
699 __isl_keep isl_val *v2);
700 isl_bool isl_val_ne(__isl_keep isl_val *v1,
701 __isl_keep isl_val *v2);
702 isl_bool isl_val_abs_eq(__isl_keep isl_val *v1,
703 __isl_keep isl_val *v2);
705 The function C<isl_val_abs_eq> checks whether its two arguments
706 are equal in absolute value.
708 For integer C<isl_val>s we additionally have the following binary property.
711 isl_bool isl_val_is_divisible_by(__isl_keep isl_val *v1,
712 __isl_keep isl_val *v2);
714 An C<isl_val> can also be compared to an integer using the following
715 function. The result is undefined for NaN.
718 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
720 The following unary operations are available on C<isl_val>s.
723 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
724 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
725 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
726 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
727 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
728 __isl_give isl_val *isl_val_inv(__isl_take isl_val *v);
729 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
731 The following binary operations are available on C<isl_val>s.
734 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
735 __isl_take isl_val *v2);
736 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
737 __isl_take isl_val *v2);
738 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
739 __isl_take isl_val *v2);
740 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
742 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
743 __isl_take isl_val *v2);
744 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
746 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
747 __isl_take isl_val *v2);
748 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
750 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
751 __isl_take isl_val *v2);
753 On integer values, we additionally have the following operations.
756 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
757 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
758 __isl_take isl_val *v2);
759 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
760 __isl_take isl_val *v2);
761 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
762 __isl_take isl_val *v2, __isl_give isl_val **x,
763 __isl_give isl_val **y);
765 The function C<isl_val_gcdext> returns the greatest common divisor g
766 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
767 that C<*x> * C<v1> + C<*y> * C<v2> = g.
769 =head3 GMP specific functions
771 These functions are only available if C<isl> has been compiled with C<GMP>
774 Specific integer and rational values can be created from C<GMP> values using
775 the following functions.
777 #include <isl/val_gmp.h>
778 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
780 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
781 const mpz_t n, const mpz_t d);
783 The numerator and denominator of a rational value can be extracted as
784 C<GMP> values using the following functions.
786 #include <isl/val_gmp.h>
787 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
788 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
790 =head2 Sets and Relations
792 C<isl> uses six types of objects for representing sets and relations,
793 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
794 C<isl_union_set> and C<isl_union_map>.
795 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
796 can be described as a conjunction of affine constraints, while
797 C<isl_set> and C<isl_map> represent unions of
798 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
799 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
800 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
801 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
802 where spaces are considered different if they have a different number
803 of dimensions and/or different names (see L<"Spaces">).
804 The difference between sets and relations (maps) is that sets have
805 one set of variables, while relations have two sets of variables,
806 input variables and output variables.
808 =head2 Error Handling
810 C<isl> supports different ways to react in case a runtime error is triggered.
811 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
812 with two maps that have incompatible spaces. There are three possible ways
813 to react on error: to warn, to continue or to abort.
815 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
816 the last error in the corresponding C<isl_ctx> and the function in which the
817 error was triggered returns a value indicating that some error has
818 occurred. In case of functions returning a pointer, this value is
819 C<NULL>. In case of functions returning an C<isl_bool> or an
820 C<isl_stat>, this valus is C<isl_bool_error> or C<isl_stat_error>.
821 An error does not corrupt internal state,
822 such that isl can continue to be used. C<isl> also provides functions to
823 read the last error and to reset the memory that stores the last error. The
824 last error is only stored for information purposes. Its presence does not
825 change the behavior of C<isl>. Hence, resetting an error is not required to
826 continue to use isl, but only to observe new errors.
829 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
830 void isl_ctx_reset_error(isl_ctx *ctx);
832 Another option is to continue on error. This is similar to warn on error mode,
833 except that C<isl> does not print any warning. This allows a program to
834 implement its own error reporting.
836 The last option is to directly abort the execution of the program from within
837 the isl library. This makes it obviously impossible to recover from an error,
838 but it allows to directly spot the error location. By aborting on error,
839 debuggers break at the location the error occurred and can provide a stack
840 trace. Other tools that automatically provide stack traces on abort or that do
841 not want to continue execution after an error was triggered may also prefer to
844 The on error behavior of isl can be specified by calling
845 C<isl_options_set_on_error> or by setting the command line option
846 C<--isl-on-error>. Valid arguments for the function call are
847 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
848 choices for the command line option are C<warn>, C<continue> and C<abort>.
849 It is also possible to query the current error mode.
851 #include <isl/options.h>
852 isl_stat isl_options_set_on_error(isl_ctx *ctx, int val);
853 int isl_options_get_on_error(isl_ctx *ctx);
857 Identifiers are used to identify both individual dimensions
858 and tuples of dimensions. They consist of an optional name and an optional
859 user pointer. The name and the user pointer cannot both be C<NULL>, however.
860 Identifiers with the same name but different pointer values
861 are considered to be distinct.
862 Similarly, identifiers with different names but the same pointer value
863 are also considered to be distinct.
864 Equal identifiers are represented using the same object.
865 Pairs of identifiers can therefore be tested for equality using the
867 Identifiers can be constructed, copied, freed, inspected and printed
868 using the following functions.
871 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
872 __isl_keep const char *name, void *user);
873 __isl_give isl_id *isl_id_set_free_user(
874 __isl_take isl_id *id,
875 __isl_give void (*free_user)(void *user));
876 __isl_give isl_id *isl_id_copy(isl_id *id);
877 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
879 void *isl_id_get_user(__isl_keep isl_id *id);
880 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
882 __isl_give isl_printer *isl_printer_print_id(
883 __isl_take isl_printer *p, __isl_keep isl_id *id);
885 The callback set by C<isl_id_set_free_user> is called on the user
886 pointer when the last reference to the C<isl_id> is freed.
887 Note that C<isl_id_get_name> returns a pointer to some internal
888 data structure, so the result can only be used while the
889 corresponding C<isl_id> is alive.
893 Whenever a new set, relation or similar object is created from scratch,
894 the space in which it lives needs to be specified using an C<isl_space>.
895 Each space involves zero or more parameters and zero, one or two
896 tuples of set or input/output dimensions. The parameters and dimensions
897 are identified by an C<isl_dim_type> and a position.
898 The type C<isl_dim_param> refers to parameters,
899 the type C<isl_dim_set> refers to set dimensions (for spaces
900 with a single tuple of dimensions) and the types C<isl_dim_in>
901 and C<isl_dim_out> refer to input and output dimensions
902 (for spaces with two tuples of dimensions).
903 Local spaces (see L</"Local Spaces">) also contain dimensions
904 of type C<isl_dim_div>.
905 Note that parameters are only identified by their position within
906 a given object. Across different objects, parameters are (usually)
907 identified by their names or identifiers. Only unnamed parameters
908 are identified by their positions across objects. The use of unnamed
909 parameters is discouraged.
911 #include <isl/space.h>
912 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
913 unsigned nparam, unsigned n_in, unsigned n_out);
914 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
916 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
917 unsigned nparam, unsigned dim);
918 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
919 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
921 The space used for creating a parameter domain
922 needs to be created using C<isl_space_params_alloc>.
923 For other sets, the space
924 needs to be created using C<isl_space_set_alloc>, while
925 for a relation, the space
926 needs to be created using C<isl_space_alloc>.
928 To check whether a given space is that of a set or a map
929 or whether it is a parameter space, use these functions:
931 #include <isl/space.h>
932 isl_bool isl_space_is_params(__isl_keep isl_space *space);
933 isl_bool isl_space_is_set(__isl_keep isl_space *space);
934 isl_bool isl_space_is_map(__isl_keep isl_space *space);
936 Spaces can be compared using the following functions:
938 #include <isl/space.h>
939 isl_bool isl_space_is_equal(__isl_keep isl_space *space1,
940 __isl_keep isl_space *space2);
941 isl_bool isl_space_is_domain(__isl_keep isl_space *space1,
942 __isl_keep isl_space *space2);
943 isl_bool isl_space_is_range(__isl_keep isl_space *space1,
944 __isl_keep isl_space *space2);
945 isl_bool isl_space_tuple_is_equal(
946 __isl_keep isl_space *space1,
947 enum isl_dim_type type1,
948 __isl_keep isl_space *space2,
949 enum isl_dim_type type2);
951 C<isl_space_is_domain> checks whether the first argument is equal
952 to the domain of the second argument. This requires in particular that
953 the first argument is a set space and that the second argument
954 is a map space. C<isl_space_tuple_is_equal> checks whether the given
955 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
956 spaces are the same. That is, it checks if they have the same
957 identifier (if any), the same dimension and the same internal structure
960 It is often useful to create objects that live in the
961 same space as some other object. This can be accomplished
962 by creating the new objects
963 (see L</"Creating New Sets and Relations"> or
964 L</"Functions">) based on the space
965 of the original object.
968 __isl_give isl_space *isl_basic_set_get_space(
969 __isl_keep isl_basic_set *bset);
970 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
972 #include <isl/union_set.h>
973 __isl_give isl_space *isl_union_set_get_space(
974 __isl_keep isl_union_set *uset);
977 __isl_give isl_space *isl_basic_map_get_space(
978 __isl_keep isl_basic_map *bmap);
979 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
981 #include <isl/union_map.h>
982 __isl_give isl_space *isl_union_map_get_space(
983 __isl_keep isl_union_map *umap);
985 #include <isl/constraint.h>
986 __isl_give isl_space *isl_constraint_get_space(
987 __isl_keep isl_constraint *constraint);
989 #include <isl/polynomial.h>
990 __isl_give isl_space *isl_qpolynomial_get_domain_space(
991 __isl_keep isl_qpolynomial *qp);
992 __isl_give isl_space *isl_qpolynomial_get_space(
993 __isl_keep isl_qpolynomial *qp);
994 __isl_give isl_space *isl_qpolynomial_fold_get_space(
995 __isl_keep isl_qpolynomial_fold *fold);
996 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
997 __isl_keep isl_pw_qpolynomial *pwqp);
998 __isl_give isl_space *isl_pw_qpolynomial_get_space(
999 __isl_keep isl_pw_qpolynomial *pwqp);
1000 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
1001 __isl_keep isl_pw_qpolynomial_fold *pwf);
1002 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
1003 __isl_keep isl_pw_qpolynomial_fold *pwf);
1004 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
1005 __isl_keep isl_union_pw_qpolynomial *upwqp);
1006 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
1007 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1009 #include <isl/val.h>
1010 __isl_give isl_space *isl_multi_val_get_space(
1011 __isl_keep isl_multi_val *mv);
1013 #include <isl/aff.h>
1014 __isl_give isl_space *isl_aff_get_domain_space(
1015 __isl_keep isl_aff *aff);
1016 __isl_give isl_space *isl_aff_get_space(
1017 __isl_keep isl_aff *aff);
1018 __isl_give isl_space *isl_pw_aff_get_domain_space(
1019 __isl_keep isl_pw_aff *pwaff);
1020 __isl_give isl_space *isl_pw_aff_get_space(
1021 __isl_keep isl_pw_aff *pwaff);
1022 __isl_give isl_space *isl_multi_aff_get_domain_space(
1023 __isl_keep isl_multi_aff *maff);
1024 __isl_give isl_space *isl_multi_aff_get_space(
1025 __isl_keep isl_multi_aff *maff);
1026 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
1027 __isl_keep isl_pw_multi_aff *pma);
1028 __isl_give isl_space *isl_pw_multi_aff_get_space(
1029 __isl_keep isl_pw_multi_aff *pma);
1030 __isl_give isl_space *isl_union_pw_aff_get_space(
1031 __isl_keep isl_union_pw_aff *upa);
1032 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
1033 __isl_keep isl_union_pw_multi_aff *upma);
1034 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
1035 __isl_keep isl_multi_pw_aff *mpa);
1036 __isl_give isl_space *isl_multi_pw_aff_get_space(
1037 __isl_keep isl_multi_pw_aff *mpa);
1038 __isl_give isl_space *
1039 isl_multi_union_pw_aff_get_domain_space(
1040 __isl_keep isl_multi_union_pw_aff *mupa);
1041 __isl_give isl_space *
1042 isl_multi_union_pw_aff_get_space(
1043 __isl_keep isl_multi_union_pw_aff *mupa);
1045 #include <isl/point.h>
1046 __isl_give isl_space *isl_point_get_space(
1047 __isl_keep isl_point *pnt);
1049 The number of dimensions of a given type of space
1050 may be read off from a space or an object that lives
1051 in a space using the following functions.
1052 In case of C<isl_space_dim>, type may be
1053 C<isl_dim_param>, C<isl_dim_in> (only for relations),
1054 C<isl_dim_out> (only for relations), C<isl_dim_set>
1055 (only for sets) or C<isl_dim_all>.
1057 #include <isl/space.h>
1058 unsigned isl_space_dim(__isl_keep isl_space *space,
1059 enum isl_dim_type type);
1061 #include <isl/local_space.h>
1062 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1063 enum isl_dim_type type);
1065 #include <isl/set.h>
1066 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1067 enum isl_dim_type type);
1068 unsigned isl_set_dim(__isl_keep isl_set *set,
1069 enum isl_dim_type type);
1071 #include <isl/union_set.h>
1072 unsigned isl_union_set_dim(__isl_keep isl_union_set *uset,
1073 enum isl_dim_type type);
1075 #include <isl/map.h>
1076 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1077 enum isl_dim_type type);
1078 unsigned isl_map_dim(__isl_keep isl_map *map,
1079 enum isl_dim_type type);
1081 #include <isl/union_map.h>
1082 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1083 enum isl_dim_type type);
1085 #include <isl/val.h>
1086 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
1087 enum isl_dim_type type);
1089 #include <isl/aff.h>
1090 int isl_aff_dim(__isl_keep isl_aff *aff,
1091 enum isl_dim_type type);
1092 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1093 enum isl_dim_type type);
1094 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1095 enum isl_dim_type type);
1096 unsigned isl_pw_multi_aff_dim(
1097 __isl_keep isl_pw_multi_aff *pma,
1098 enum isl_dim_type type);
1099 unsigned isl_multi_pw_aff_dim(
1100 __isl_keep isl_multi_pw_aff *mpa,
1101 enum isl_dim_type type);
1102 unsigned isl_union_pw_aff_dim(
1103 __isl_keep isl_union_pw_aff *upa,
1104 enum isl_dim_type type);
1105 unsigned isl_union_pw_multi_aff_dim(
1106 __isl_keep isl_union_pw_multi_aff *upma,
1107 enum isl_dim_type type);
1108 unsigned isl_multi_union_pw_aff_dim(
1109 __isl_keep isl_multi_union_pw_aff *mupa,
1110 enum isl_dim_type type);
1112 #include <isl/polynomial.h>
1113 unsigned isl_union_pw_qpolynomial_dim(
1114 __isl_keep isl_union_pw_qpolynomial *upwqp,
1115 enum isl_dim_type type);
1116 unsigned isl_union_pw_qpolynomial_fold_dim(
1117 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1118 enum isl_dim_type type);
1120 Note that an C<isl_union_set>, an C<isl_union_map>,
1121 an C<isl_union_pw_multi_aff>,
1122 an C<isl_union_pw_qpolynomial> and
1123 an C<isl_union_pw_qpolynomial_fold>
1124 only have parameters.
1126 The identifiers or names of the individual dimensions of spaces
1127 may be set or read off using the following functions on spaces
1128 or objects that live in spaces.
1129 These functions are mostly useful to obtain the identifiers, positions
1130 or names of the parameters. Identifiers of individual dimensions are
1131 essentially only useful for printing. They are ignored by all other
1132 operations and may not be preserved across those operations.
1134 #include <isl/space.h>
1135 __isl_give isl_space *isl_space_set_dim_id(
1136 __isl_take isl_space *space,
1137 enum isl_dim_type type, unsigned pos,
1138 __isl_take isl_id *id);
1139 isl_bool isl_space_has_dim_id(__isl_keep isl_space *space,
1140 enum isl_dim_type type, unsigned pos);
1141 __isl_give isl_id *isl_space_get_dim_id(
1142 __isl_keep isl_space *space,
1143 enum isl_dim_type type, unsigned pos);
1144 __isl_give isl_space *isl_space_set_dim_name(
1145 __isl_take isl_space *space,
1146 enum isl_dim_type type, unsigned pos,
1147 __isl_keep const char *name);
1148 isl_bool isl_space_has_dim_name(__isl_keep isl_space *space,
1149 enum isl_dim_type type, unsigned pos);
1150 __isl_keep const char *isl_space_get_dim_name(
1151 __isl_keep isl_space *space,
1152 enum isl_dim_type type, unsigned pos);
1154 #include <isl/local_space.h>
1155 __isl_give isl_local_space *isl_local_space_set_dim_id(
1156 __isl_take isl_local_space *ls,
1157 enum isl_dim_type type, unsigned pos,
1158 __isl_take isl_id *id);
1159 isl_bool isl_local_space_has_dim_id(
1160 __isl_keep isl_local_space *ls,
1161 enum isl_dim_type type, unsigned pos);
1162 __isl_give isl_id *isl_local_space_get_dim_id(
1163 __isl_keep isl_local_space *ls,
1164 enum isl_dim_type type, unsigned pos);
1165 __isl_give isl_local_space *isl_local_space_set_dim_name(
1166 __isl_take isl_local_space *ls,
1167 enum isl_dim_type type, unsigned pos, const char *s);
1168 isl_bool isl_local_space_has_dim_name(
1169 __isl_keep isl_local_space *ls,
1170 enum isl_dim_type type, unsigned pos)
1171 const char *isl_local_space_get_dim_name(
1172 __isl_keep isl_local_space *ls,
1173 enum isl_dim_type type, unsigned pos);
1175 #include <isl/constraint.h>
1176 const char *isl_constraint_get_dim_name(
1177 __isl_keep isl_constraint *constraint,
1178 enum isl_dim_type type, unsigned pos);
1180 #include <isl/set.h>
1181 __isl_give isl_id *isl_basic_set_get_dim_id(
1182 __isl_keep isl_basic_set *bset,
1183 enum isl_dim_type type, unsigned pos);
1184 __isl_give isl_set *isl_set_set_dim_id(
1185 __isl_take isl_set *set, enum isl_dim_type type,
1186 unsigned pos, __isl_take isl_id *id);
1187 isl_bool isl_set_has_dim_id(__isl_keep isl_set *set,
1188 enum isl_dim_type type, unsigned pos);
1189 __isl_give isl_id *isl_set_get_dim_id(
1190 __isl_keep isl_set *set, enum isl_dim_type type,
1192 const char *isl_basic_set_get_dim_name(
1193 __isl_keep isl_basic_set *bset,
1194 enum isl_dim_type type, unsigned pos);
1195 isl_bool isl_set_has_dim_name(__isl_keep isl_set *set,
1196 enum isl_dim_type type, unsigned pos);
1197 const char *isl_set_get_dim_name(
1198 __isl_keep isl_set *set,
1199 enum isl_dim_type type, unsigned pos);
1201 #include <isl/map.h>
1202 __isl_give isl_map *isl_map_set_dim_id(
1203 __isl_take isl_map *map, enum isl_dim_type type,
1204 unsigned pos, __isl_take isl_id *id);
1205 isl_bool isl_basic_map_has_dim_id(
1206 __isl_keep isl_basic_map *bmap,
1207 enum isl_dim_type type, unsigned pos);
1208 isl_bool isl_map_has_dim_id(__isl_keep isl_map *map,
1209 enum isl_dim_type type, unsigned pos);
1210 __isl_give isl_id *isl_map_get_dim_id(
1211 __isl_keep isl_map *map, enum isl_dim_type type,
1213 __isl_give isl_id *isl_union_map_get_dim_id(
1214 __isl_keep isl_union_map *umap,
1215 enum isl_dim_type type, unsigned pos);
1216 const char *isl_basic_map_get_dim_name(
1217 __isl_keep isl_basic_map *bmap,
1218 enum isl_dim_type type, unsigned pos);
1219 isl_bool isl_map_has_dim_name(__isl_keep isl_map *map,
1220 enum isl_dim_type type, unsigned pos);
1221 const char *isl_map_get_dim_name(
1222 __isl_keep isl_map *map,
1223 enum isl_dim_type type, unsigned pos);
1225 #include <isl/val.h>
1226 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1227 __isl_take isl_multi_val *mv,
1228 enum isl_dim_type type, unsigned pos,
1229 __isl_take isl_id *id);
1230 __isl_give isl_id *isl_multi_val_get_dim_id(
1231 __isl_keep isl_multi_val *mv,
1232 enum isl_dim_type type, unsigned pos);
1233 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1234 __isl_take isl_multi_val *mv,
1235 enum isl_dim_type type, unsigned pos, const char *s);
1237 #include <isl/aff.h>
1238 __isl_give isl_aff *isl_aff_set_dim_id(
1239 __isl_take isl_aff *aff, enum isl_dim_type type,
1240 unsigned pos, __isl_take isl_id *id);
1241 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1242 __isl_take isl_multi_aff *maff,
1243 enum isl_dim_type type, unsigned pos,
1244 __isl_take isl_id *id);
1245 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1246 __isl_take isl_pw_aff *pma,
1247 enum isl_dim_type type, unsigned pos,
1248 __isl_take isl_id *id);
1249 __isl_give isl_multi_pw_aff *
1250 isl_multi_pw_aff_set_dim_id(
1251 __isl_take isl_multi_pw_aff *mpa,
1252 enum isl_dim_type type, unsigned pos,
1253 __isl_take isl_id *id);
1254 __isl_give isl_multi_union_pw_aff *
1255 isl_multi_union_pw_aff_set_dim_id(
1256 __isl_take isl_multi_union_pw_aff *mupa,
1257 enum isl_dim_type type, unsigned pos,
1258 __isl_take isl_id *id);
1259 __isl_give isl_id *isl_multi_aff_get_dim_id(
1260 __isl_keep isl_multi_aff *ma,
1261 enum isl_dim_type type, unsigned pos);
1262 isl_bool isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1263 enum isl_dim_type type, unsigned pos);
1264 __isl_give isl_id *isl_pw_aff_get_dim_id(
1265 __isl_keep isl_pw_aff *pa,
1266 enum isl_dim_type type, unsigned pos);
1267 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1268 __isl_keep isl_pw_multi_aff *pma,
1269 enum isl_dim_type type, unsigned pos);
1270 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1271 __isl_keep isl_multi_pw_aff *mpa,
1272 enum isl_dim_type type, unsigned pos);
1273 __isl_give isl_id *isl_multi_union_pw_aff_get_dim_id(
1274 __isl_keep isl_multi_union_pw_aff *mupa,
1275 enum isl_dim_type type, unsigned pos);
1276 __isl_give isl_aff *isl_aff_set_dim_name(
1277 __isl_take isl_aff *aff, enum isl_dim_type type,
1278 unsigned pos, const char *s);
1279 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1280 __isl_take isl_multi_aff *maff,
1281 enum isl_dim_type type, unsigned pos, const char *s);
1282 __isl_give isl_multi_pw_aff *
1283 isl_multi_pw_aff_set_dim_name(
1284 __isl_take isl_multi_pw_aff *mpa,
1285 enum isl_dim_type type, unsigned pos, const char *s);
1286 __isl_give isl_union_pw_aff *
1287 isl_union_pw_aff_set_dim_name(
1288 __isl_take isl_union_pw_aff *upa,
1289 enum isl_dim_type type, unsigned pos,
1291 __isl_give isl_union_pw_multi_aff *
1292 isl_union_pw_multi_aff_set_dim_name(
1293 __isl_take isl_union_pw_multi_aff *upma,
1294 enum isl_dim_type type, unsigned pos,
1296 __isl_give isl_multi_union_pw_aff *
1297 isl_multi_union_pw_aff_set_dim_name(
1298 __isl_take isl_multi_union_pw_aff *mupa,
1299 enum isl_dim_type type, unsigned pos,
1300 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1301 enum isl_dim_type type, unsigned pos);
1302 const char *isl_pw_aff_get_dim_name(
1303 __isl_keep isl_pw_aff *pa,
1304 enum isl_dim_type type, unsigned pos);
1305 const char *isl_pw_multi_aff_get_dim_name(
1306 __isl_keep isl_pw_multi_aff *pma,
1307 enum isl_dim_type type, unsigned pos);
1309 #include <isl/polynomial.h>
1310 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1311 __isl_take isl_qpolynomial *qp,
1312 enum isl_dim_type type, unsigned pos,
1314 __isl_give isl_pw_qpolynomial *
1315 isl_pw_qpolynomial_set_dim_name(
1316 __isl_take isl_pw_qpolynomial *pwqp,
1317 enum isl_dim_type type, unsigned pos,
1319 __isl_give isl_pw_qpolynomial_fold *
1320 isl_pw_qpolynomial_fold_set_dim_name(
1321 __isl_take isl_pw_qpolynomial_fold *pwf,
1322 enum isl_dim_type type, unsigned pos,
1324 __isl_give isl_union_pw_qpolynomial *
1325 isl_union_pw_qpolynomial_set_dim_name(
1326 __isl_take isl_union_pw_qpolynomial *upwqp,
1327 enum isl_dim_type type, unsigned pos,
1329 __isl_give isl_union_pw_qpolynomial_fold *
1330 isl_union_pw_qpolynomial_fold_set_dim_name(
1331 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1332 enum isl_dim_type type, unsigned pos,
1335 Note that C<isl_space_get_name> returns a pointer to some internal
1336 data structure, so the result can only be used while the
1337 corresponding C<isl_space> is alive.
1338 Also note that every function that operates on two sets or relations
1339 requires that both arguments have the same parameters. This also
1340 means that if one of the arguments has named parameters, then the
1341 other needs to have named parameters too and the names need to match.
1342 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1343 arguments may have different parameters (as long as they are named),
1344 in which case the result will have as parameters the union of the parameters of
1347 Given the identifier or name of a dimension (typically a parameter),
1348 its position can be obtained from the following functions.
1350 #include <isl/space.h>
1351 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1352 enum isl_dim_type type, __isl_keep isl_id *id);
1353 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1354 enum isl_dim_type type, const char *name);
1356 #include <isl/local_space.h>
1357 int isl_local_space_find_dim_by_name(
1358 __isl_keep isl_local_space *ls,
1359 enum isl_dim_type type, const char *name);
1361 #include <isl/val.h>
1362 int isl_multi_val_find_dim_by_id(
1363 __isl_keep isl_multi_val *mv,
1364 enum isl_dim_type type, __isl_keep isl_id *id);
1365 int isl_multi_val_find_dim_by_name(
1366 __isl_keep isl_multi_val *mv,
1367 enum isl_dim_type type, const char *name);
1369 #include <isl/set.h>
1370 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1371 enum isl_dim_type type, __isl_keep isl_id *id);
1372 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1373 enum isl_dim_type type, const char *name);
1375 #include <isl/map.h>
1376 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1377 enum isl_dim_type type, __isl_keep isl_id *id);
1378 int isl_basic_map_find_dim_by_name(
1379 __isl_keep isl_basic_map *bmap,
1380 enum isl_dim_type type, const char *name);
1381 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1382 enum isl_dim_type type, const char *name);
1383 int isl_union_map_find_dim_by_name(
1384 __isl_keep isl_union_map *umap,
1385 enum isl_dim_type type, const char *name);
1387 #include <isl/aff.h>
1388 int isl_multi_aff_find_dim_by_id(
1389 __isl_keep isl_multi_aff *ma,
1390 enum isl_dim_type type, __isl_keep isl_id *id);
1391 int isl_multi_pw_aff_find_dim_by_id(
1392 __isl_keep isl_multi_pw_aff *mpa,
1393 enum isl_dim_type type, __isl_keep isl_id *id);
1394 int isl_multi_union_pw_aff_find_dim_by_id(
1395 __isl_keep isl_union_multi_pw_aff *mupa,
1396 enum isl_dim_type type, __isl_keep isl_id *id);
1397 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff,
1398 enum isl_dim_type type, const char *name);
1399 int isl_multi_aff_find_dim_by_name(
1400 __isl_keep isl_multi_aff *ma,
1401 enum isl_dim_type type, const char *name);
1402 int isl_pw_aff_find_dim_by_name(__isl_keep isl_pw_aff *pa,
1403 enum isl_dim_type type, const char *name);
1404 int isl_multi_pw_aff_find_dim_by_name(
1405 __isl_keep isl_multi_pw_aff *mpa,
1406 enum isl_dim_type type, const char *name);
1407 int isl_pw_multi_aff_find_dim_by_name(
1408 __isl_keep isl_pw_multi_aff *pma,
1409 enum isl_dim_type type, const char *name);
1410 int isl_union_pw_aff_find_dim_by_name(
1411 __isl_keep isl_union_pw_aff *upa,
1412 enum isl_dim_type type, const char *name);
1413 int isl_union_pw_multi_aff_find_dim_by_name(
1414 __isl_keep isl_union_pw_multi_aff *upma,
1415 enum isl_dim_type type, const char *name);
1416 int isl_multi_union_pw_aff_find_dim_by_name(
1417 __isl_keep isl_multi_union_pw_aff *mupa,
1418 enum isl_dim_type type, const char *name);
1420 #include <isl/polynomial.h>
1421 int isl_pw_qpolynomial_find_dim_by_name(
1422 __isl_keep isl_pw_qpolynomial *pwqp,
1423 enum isl_dim_type type, const char *name);
1424 int isl_pw_qpolynomial_fold_find_dim_by_name(
1425 __isl_keep isl_pw_qpolynomial_fold *pwf,
1426 enum isl_dim_type type, const char *name);
1427 int isl_union_pw_qpolynomial_find_dim_by_name(
1428 __isl_keep isl_union_pw_qpolynomial *upwqp,
1429 enum isl_dim_type type, const char *name);
1430 int isl_union_pw_qpolynomial_fold_find_dim_by_name(
1431 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1432 enum isl_dim_type type, const char *name);
1434 The identifiers or names of entire spaces may be set or read off
1435 using the following functions.
1437 #include <isl/space.h>
1438 __isl_give isl_space *isl_space_set_tuple_id(
1439 __isl_take isl_space *space,
1440 enum isl_dim_type type, __isl_take isl_id *id);
1441 __isl_give isl_space *isl_space_reset_tuple_id(
1442 __isl_take isl_space *space, enum isl_dim_type type);
1443 isl_bool isl_space_has_tuple_id(
1444 __isl_keep isl_space *space,
1445 enum isl_dim_type type);
1446 __isl_give isl_id *isl_space_get_tuple_id(
1447 __isl_keep isl_space *space, enum isl_dim_type type);
1448 __isl_give isl_space *isl_space_set_tuple_name(
1449 __isl_take isl_space *space,
1450 enum isl_dim_type type, const char *s);
1451 isl_bool isl_space_has_tuple_name(
1452 __isl_keep isl_space *space,
1453 enum isl_dim_type type);
1454 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
1455 enum isl_dim_type type);
1457 #include <isl/local_space.h>
1458 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1459 __isl_take isl_local_space *ls,
1460 enum isl_dim_type type, __isl_take isl_id *id);
1462 #include <isl/set.h>
1463 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1464 __isl_take isl_basic_set *bset,
1465 __isl_take isl_id *id);
1466 __isl_give isl_set *isl_set_set_tuple_id(
1467 __isl_take isl_set *set, __isl_take isl_id *id);
1468 __isl_give isl_set *isl_set_reset_tuple_id(
1469 __isl_take isl_set *set);
1470 isl_bool isl_set_has_tuple_id(__isl_keep isl_set *set);
1471 __isl_give isl_id *isl_set_get_tuple_id(
1472 __isl_keep isl_set *set);
1473 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1474 __isl_take isl_basic_set *set, const char *s);
1475 __isl_give isl_set *isl_set_set_tuple_name(
1476 __isl_take isl_set *set, const char *s);
1477 const char *isl_basic_set_get_tuple_name(
1478 __isl_keep isl_basic_set *bset);
1479 isl_bool isl_set_has_tuple_name(__isl_keep isl_set *set);
1480 const char *isl_set_get_tuple_name(
1481 __isl_keep isl_set *set);
1483 #include <isl/map.h>
1484 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1485 __isl_take isl_basic_map *bmap,
1486 enum isl_dim_type type, __isl_take isl_id *id);
1487 __isl_give isl_map *isl_map_set_tuple_id(
1488 __isl_take isl_map *map, enum isl_dim_type type,
1489 __isl_take isl_id *id);
1490 __isl_give isl_map *isl_map_reset_tuple_id(
1491 __isl_take isl_map *map, enum isl_dim_type type);
1492 isl_bool isl_map_has_tuple_id(__isl_keep isl_map *map,
1493 enum isl_dim_type type);
1494 __isl_give isl_id *isl_map_get_tuple_id(
1495 __isl_keep isl_map *map, enum isl_dim_type type);
1496 __isl_give isl_map *isl_map_set_tuple_name(
1497 __isl_take isl_map *map,
1498 enum isl_dim_type type, const char *s);
1499 const char *isl_basic_map_get_tuple_name(
1500 __isl_keep isl_basic_map *bmap,
1501 enum isl_dim_type type);
1502 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1503 __isl_take isl_basic_map *bmap,
1504 enum isl_dim_type type, const char *s);
1505 isl_bool isl_map_has_tuple_name(__isl_keep isl_map *map,
1506 enum isl_dim_type type);
1507 const char *isl_map_get_tuple_name(
1508 __isl_keep isl_map *map,
1509 enum isl_dim_type type);
1511 #include <isl/val.h>
1512 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1513 __isl_take isl_multi_val *mv,
1514 enum isl_dim_type type, __isl_take isl_id *id);
1515 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1516 __isl_take isl_multi_val *mv,
1517 enum isl_dim_type type);
1518 isl_bool isl_multi_val_has_tuple_id(
1519 __isl_keep isl_multi_val *mv,
1520 enum isl_dim_type type);
1521 __isl_give isl_id *isl_multi_val_get_tuple_id(
1522 __isl_keep isl_multi_val *mv,
1523 enum isl_dim_type type);
1524 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1525 __isl_take isl_multi_val *mv,
1526 enum isl_dim_type type, const char *s);
1527 const char *isl_multi_val_get_tuple_name(
1528 __isl_keep isl_multi_val *mv,
1529 enum isl_dim_type type);
1531 #include <isl/aff.h>
1532 __isl_give isl_aff *isl_aff_set_tuple_id(
1533 __isl_take isl_aff *aff,
1534 enum isl_dim_type type, __isl_take isl_id *id);
1535 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1536 __isl_take isl_multi_aff *maff,
1537 enum isl_dim_type type, __isl_take isl_id *id);
1538 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1539 __isl_take isl_pw_aff *pwaff,
1540 enum isl_dim_type type, __isl_take isl_id *id);
1541 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1542 __isl_take isl_pw_multi_aff *pma,
1543 enum isl_dim_type type, __isl_take isl_id *id);
1544 __isl_give isl_multi_union_pw_aff *
1545 isl_multi_union_pw_aff_set_tuple_id(
1546 __isl_take isl_multi_union_pw_aff *mupa,
1547 enum isl_dim_type type, __isl_take isl_id *id);
1548 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1549 __isl_take isl_multi_aff *ma,
1550 enum isl_dim_type type);
1551 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1552 __isl_take isl_pw_aff *pa,
1553 enum isl_dim_type type);
1554 __isl_give isl_multi_pw_aff *
1555 isl_multi_pw_aff_reset_tuple_id(
1556 __isl_take isl_multi_pw_aff *mpa,
1557 enum isl_dim_type type);
1558 __isl_give isl_pw_multi_aff *
1559 isl_pw_multi_aff_reset_tuple_id(
1560 __isl_take isl_pw_multi_aff *pma,
1561 enum isl_dim_type type);
1562 __isl_give isl_multi_union_pw_aff *
1563 isl_multi_union_pw_aff_reset_tuple_id(
1564 __isl_take isl_multi_union_pw_aff *mupa,
1565 enum isl_dim_type type);
1566 isl_bool isl_multi_aff_has_tuple_id(
1567 __isl_keep isl_multi_aff *ma,
1568 enum isl_dim_type type);
1569 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1570 __isl_keep isl_multi_aff *ma,
1571 enum isl_dim_type type);
1572 isl_bool isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1573 enum isl_dim_type type);
1574 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1575 __isl_keep isl_pw_aff *pa,
1576 enum isl_dim_type type);
1577 isl_bool isl_pw_multi_aff_has_tuple_id(
1578 __isl_keep isl_pw_multi_aff *pma,
1579 enum isl_dim_type type);
1580 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1581 __isl_keep isl_pw_multi_aff *pma,
1582 enum isl_dim_type type);
1583 isl_bool isl_multi_pw_aff_has_tuple_id(
1584 __isl_keep isl_multi_pw_aff *mpa,
1585 enum isl_dim_type type);
1586 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1587 __isl_keep isl_multi_pw_aff *mpa,
1588 enum isl_dim_type type);
1589 isl_bool isl_multi_union_pw_aff_has_tuple_id(
1590 __isl_keep isl_multi_union_pw_aff *mupa,
1591 enum isl_dim_type type);
1592 __isl_give isl_id *isl_multi_union_pw_aff_get_tuple_id(
1593 __isl_keep isl_multi_union_pw_aff *mupa,
1594 enum isl_dim_type type);
1595 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1596 __isl_take isl_multi_aff *maff,
1597 enum isl_dim_type type, const char *s);
1598 __isl_give isl_multi_pw_aff *
1599 isl_multi_pw_aff_set_tuple_name(
1600 __isl_take isl_multi_pw_aff *mpa,
1601 enum isl_dim_type type, const char *s);
1602 __isl_give isl_multi_union_pw_aff *
1603 isl_multi_union_pw_aff_set_tuple_name(
1604 __isl_take isl_multi_union_pw_aff *mupa,
1605 enum isl_dim_type type, const char *s);
1606 const char *isl_multi_aff_get_tuple_name(
1607 __isl_keep isl_multi_aff *multi,
1608 enum isl_dim_type type);
1609 isl_bool isl_pw_multi_aff_has_tuple_name(
1610 __isl_keep isl_pw_multi_aff *pma,
1611 enum isl_dim_type type);
1612 const char *isl_pw_multi_aff_get_tuple_name(
1613 __isl_keep isl_pw_multi_aff *pma,
1614 enum isl_dim_type type);
1615 const char *isl_multi_union_pw_aff_get_tuple_name(
1616 __isl_keep isl_multi_union_pw_aff *mupa,
1617 enum isl_dim_type type);
1619 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1620 or C<isl_dim_set>. As with C<isl_space_get_name>,
1621 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1623 Binary operations require the corresponding spaces of their arguments
1624 to have the same name.
1626 To keep the names of all parameters and tuples, but reset the user pointers
1627 of all the corresponding identifiers, use the following function.
1629 #include <isl/space.h>
1630 __isl_give isl_space *isl_space_reset_user(
1631 __isl_take isl_space *space);
1633 #include <isl/set.h>
1634 __isl_give isl_set *isl_set_reset_user(
1635 __isl_take isl_set *set);
1637 #include <isl/map.h>
1638 __isl_give isl_map *isl_map_reset_user(
1639 __isl_take isl_map *map);
1641 #include <isl/union_set.h>
1642 __isl_give isl_union_set *isl_union_set_reset_user(
1643 __isl_take isl_union_set *uset);
1645 #include <isl/union_map.h>
1646 __isl_give isl_union_map *isl_union_map_reset_user(
1647 __isl_take isl_union_map *umap);
1649 #include <isl/val.h>
1650 __isl_give isl_multi_val *isl_multi_val_reset_user(
1651 __isl_take isl_multi_val *mv);
1653 #include <isl/aff.h>
1654 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1655 __isl_take isl_multi_aff *ma);
1656 __isl_give isl_pw_aff *isl_pw_aff_reset_user(
1657 __isl_take isl_pw_aff *pa);
1658 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1659 __isl_take isl_multi_pw_aff *mpa);
1660 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_reset_user(
1661 __isl_take isl_pw_multi_aff *pma);
1662 __isl_give isl_union_pw_aff *isl_union_pw_aff_reset_user(
1663 __isl_take isl_union_pw_aff *upa);
1664 __isl_give isl_multi_union_pw_aff *
1665 isl_multi_union_pw_aff_reset_user(
1666 __isl_take isl_multi_union_pw_aff *mupa);
1667 __isl_give isl_union_pw_multi_aff *
1668 isl_union_pw_multi_aff_reset_user(
1669 __isl_take isl_union_pw_multi_aff *upma);
1671 #include <isl/polynomial.h>
1672 __isl_give isl_pw_qpolynomial *
1673 isl_pw_qpolynomial_reset_user(
1674 __isl_take isl_pw_qpolynomial *pwqp);
1675 __isl_give isl_union_pw_qpolynomial *
1676 isl_union_pw_qpolynomial_reset_user(
1677 __isl_take isl_union_pw_qpolynomial *upwqp);
1678 __isl_give isl_pw_qpolynomial_fold *
1679 isl_pw_qpolynomial_fold_reset_user(
1680 __isl_take isl_pw_qpolynomial_fold *pwf);
1681 __isl_give isl_union_pw_qpolynomial_fold *
1682 isl_union_pw_qpolynomial_fold_reset_user(
1683 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1685 Spaces can be nested. In particular, the domain of a set or
1686 the domain or range of a relation can be a nested relation.
1687 This process is also called I<wrapping>.
1688 The functions for detecting, constructing and deconstructing
1689 such nested spaces can be found in the wrapping properties
1690 of L</"Unary Properties">, the wrapping operations
1691 of L</"Unary Operations"> and the Cartesian product operations
1692 of L</"Basic Operations">.
1694 Spaces can be created from other spaces
1695 using the functions described in L</"Unary Operations">
1696 and L</"Binary Operations">.
1700 A local space is essentially a space with
1701 zero or more existentially quantified variables.
1702 The local space of various objects can be obtained
1703 using the following functions.
1705 #include <isl/constraint.h>
1706 __isl_give isl_local_space *isl_constraint_get_local_space(
1707 __isl_keep isl_constraint *constraint);
1709 #include <isl/set.h>
1710 __isl_give isl_local_space *isl_basic_set_get_local_space(
1711 __isl_keep isl_basic_set *bset);
1713 #include <isl/map.h>
1714 __isl_give isl_local_space *isl_basic_map_get_local_space(
1715 __isl_keep isl_basic_map *bmap);
1717 #include <isl/aff.h>
1718 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1719 __isl_keep isl_aff *aff);
1720 __isl_give isl_local_space *isl_aff_get_local_space(
1721 __isl_keep isl_aff *aff);
1723 A new local space can be created from a space using
1725 #include <isl/local_space.h>
1726 __isl_give isl_local_space *isl_local_space_from_space(
1727 __isl_take isl_space *space);
1729 They can be inspected, modified, copied and freed using the following functions.
1731 #include <isl/local_space.h>
1732 isl_bool isl_local_space_is_params(
1733 __isl_keep isl_local_space *ls);
1734 isl_bool isl_local_space_is_set(
1735 __isl_keep isl_local_space *ls);
1736 __isl_give isl_space *isl_local_space_get_space(
1737 __isl_keep isl_local_space *ls);
1738 __isl_give isl_aff *isl_local_space_get_div(
1739 __isl_keep isl_local_space *ls, int pos);
1740 __isl_give isl_local_space *isl_local_space_copy(
1741 __isl_keep isl_local_space *ls);
1742 __isl_null isl_local_space *isl_local_space_free(
1743 __isl_take isl_local_space *ls);
1745 Note that C<isl_local_space_get_div> can only be used on local spaces
1748 Two local spaces can be compared using
1750 isl_bool isl_local_space_is_equal(
1751 __isl_keep isl_local_space *ls1,
1752 __isl_keep isl_local_space *ls2);
1754 Local spaces can be created from other local spaces
1755 using the functions described in L</"Unary Operations">
1756 and L</"Binary Operations">.
1758 =head2 Creating New Sets and Relations
1760 C<isl> has functions for creating some standard sets and relations.
1764 =item * Empty sets and relations
1766 __isl_give isl_basic_set *isl_basic_set_empty(
1767 __isl_take isl_space *space);
1768 __isl_give isl_basic_map *isl_basic_map_empty(
1769 __isl_take isl_space *space);
1770 __isl_give isl_set *isl_set_empty(
1771 __isl_take isl_space *space);
1772 __isl_give isl_map *isl_map_empty(
1773 __isl_take isl_space *space);
1774 __isl_give isl_union_set *isl_union_set_empty(
1775 __isl_take isl_space *space);
1776 __isl_give isl_union_map *isl_union_map_empty(
1777 __isl_take isl_space *space);
1779 For C<isl_union_set>s and C<isl_union_map>s, the space
1780 is only used to specify the parameters.
1782 =item * Universe sets and relations
1784 __isl_give isl_basic_set *isl_basic_set_universe(
1785 __isl_take isl_space *space);
1786 __isl_give isl_basic_map *isl_basic_map_universe(
1787 __isl_take isl_space *space);
1788 __isl_give isl_set *isl_set_universe(
1789 __isl_take isl_space *space);
1790 __isl_give isl_map *isl_map_universe(
1791 __isl_take isl_space *space);
1792 __isl_give isl_union_set *isl_union_set_universe(
1793 __isl_take isl_union_set *uset);
1794 __isl_give isl_union_map *isl_union_map_universe(
1795 __isl_take isl_union_map *umap);
1797 The sets and relations constructed by the functions above
1798 contain all integer values, while those constructed by the
1799 functions below only contain non-negative values.
1801 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1802 __isl_take isl_space *space);
1803 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1804 __isl_take isl_space *space);
1805 __isl_give isl_set *isl_set_nat_universe(
1806 __isl_take isl_space *space);
1807 __isl_give isl_map *isl_map_nat_universe(
1808 __isl_take isl_space *space);
1810 =item * Identity relations
1812 __isl_give isl_basic_map *isl_basic_map_identity(
1813 __isl_take isl_space *space);
1814 __isl_give isl_map *isl_map_identity(
1815 __isl_take isl_space *space);
1817 The number of input and output dimensions in C<space> needs
1820 =item * Lexicographic order
1822 __isl_give isl_map *isl_map_lex_lt(
1823 __isl_take isl_space *set_space);
1824 __isl_give isl_map *isl_map_lex_le(
1825 __isl_take isl_space *set_space);
1826 __isl_give isl_map *isl_map_lex_gt(
1827 __isl_take isl_space *set_space);
1828 __isl_give isl_map *isl_map_lex_ge(
1829 __isl_take isl_space *set_space);
1830 __isl_give isl_map *isl_map_lex_lt_first(
1831 __isl_take isl_space *space, unsigned n);
1832 __isl_give isl_map *isl_map_lex_le_first(
1833 __isl_take isl_space *space, unsigned n);
1834 __isl_give isl_map *isl_map_lex_gt_first(
1835 __isl_take isl_space *space, unsigned n);
1836 __isl_give isl_map *isl_map_lex_ge_first(
1837 __isl_take isl_space *space, unsigned n);
1839 The first four functions take a space for a B<set>
1840 and return relations that express that the elements in the domain
1841 are lexicographically less
1842 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1843 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1844 than the elements in the range.
1845 The last four functions take a space for a map
1846 and return relations that express that the first C<n> dimensions
1847 in the domain are lexicographically less
1848 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1849 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1850 than the first C<n> dimensions in the range.
1854 A basic set or relation can be converted to a set or relation
1855 using the following functions.
1857 __isl_give isl_set *isl_set_from_basic_set(
1858 __isl_take isl_basic_set *bset);
1859 __isl_give isl_map *isl_map_from_basic_map(
1860 __isl_take isl_basic_map *bmap);
1862 Sets and relations can be converted to union sets and relations
1863 using the following functions.
1865 __isl_give isl_union_set *isl_union_set_from_basic_set(
1866 __isl_take isl_basic_set *bset);
1867 __isl_give isl_union_map *isl_union_map_from_basic_map(
1868 __isl_take isl_basic_map *bmap);
1869 __isl_give isl_union_set *isl_union_set_from_set(
1870 __isl_take isl_set *set);
1871 __isl_give isl_union_map *isl_union_map_from_map(
1872 __isl_take isl_map *map);
1874 The inverse conversions below can only be used if the input
1875 union set or relation is known to contain elements in exactly one
1878 __isl_give isl_set *isl_set_from_union_set(
1879 __isl_take isl_union_set *uset);
1880 __isl_give isl_map *isl_map_from_union_map(
1881 __isl_take isl_union_map *umap);
1883 Sets and relations can be copied and freed again using the following
1886 __isl_give isl_basic_set *isl_basic_set_copy(
1887 __isl_keep isl_basic_set *bset);
1888 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1889 __isl_give isl_union_set *isl_union_set_copy(
1890 __isl_keep isl_union_set *uset);
1891 __isl_give isl_basic_map *isl_basic_map_copy(
1892 __isl_keep isl_basic_map *bmap);
1893 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1894 __isl_give isl_union_map *isl_union_map_copy(
1895 __isl_keep isl_union_map *umap);
1896 __isl_null isl_basic_set *isl_basic_set_free(
1897 __isl_take isl_basic_set *bset);
1898 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1899 __isl_null isl_union_set *isl_union_set_free(
1900 __isl_take isl_union_set *uset);
1901 __isl_null isl_basic_map *isl_basic_map_free(
1902 __isl_take isl_basic_map *bmap);
1903 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1904 __isl_null isl_union_map *isl_union_map_free(
1905 __isl_take isl_union_map *umap);
1907 Other sets and relations can be constructed by starting
1908 from a universe set or relation, adding equality and/or
1909 inequality constraints and then projecting out the
1910 existentially quantified variables, if any.
1911 Constraints can be constructed, manipulated and
1912 added to (or removed from) (basic) sets and relations
1913 using the following functions.
1915 #include <isl/constraint.h>
1916 __isl_give isl_constraint *isl_constraint_alloc_equality(
1917 __isl_take isl_local_space *ls);
1918 __isl_give isl_constraint *isl_constraint_alloc_inequality(
1919 __isl_take isl_local_space *ls);
1920 __isl_give isl_constraint *isl_constraint_set_constant_si(
1921 __isl_take isl_constraint *constraint, int v);
1922 __isl_give isl_constraint *isl_constraint_set_constant_val(
1923 __isl_take isl_constraint *constraint,
1924 __isl_take isl_val *v);
1925 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1926 __isl_take isl_constraint *constraint,
1927 enum isl_dim_type type, int pos, int v);
1928 __isl_give isl_constraint *
1929 isl_constraint_set_coefficient_val(
1930 __isl_take isl_constraint *constraint,
1931 enum isl_dim_type type, int pos,
1932 __isl_take isl_val *v);
1933 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1934 __isl_take isl_basic_map *bmap,
1935 __isl_take isl_constraint *constraint);
1936 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1937 __isl_take isl_basic_set *bset,
1938 __isl_take isl_constraint *constraint);
1939 __isl_give isl_map *isl_map_add_constraint(
1940 __isl_take isl_map *map,
1941 __isl_take isl_constraint *constraint);
1942 __isl_give isl_set *isl_set_add_constraint(
1943 __isl_take isl_set *set,
1944 __isl_take isl_constraint *constraint);
1946 For example, to create a set containing the even integers
1947 between 10 and 42, you would use the following code.
1950 isl_local_space *ls;
1952 isl_basic_set *bset;
1954 space = isl_space_set_alloc(ctx, 0, 2);
1955 bset = isl_basic_set_universe(isl_space_copy(space));
1956 ls = isl_local_space_from_space(space);
1958 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
1959 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1960 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1961 bset = isl_basic_set_add_constraint(bset, c);
1963 c = isl_constraint_alloc_inequality(isl_local_space_copy(ls));
1964 c = isl_constraint_set_constant_si(c, -10);
1965 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1966 bset = isl_basic_set_add_constraint(bset, c);
1968 c = isl_constraint_alloc_inequality(ls);
1969 c = isl_constraint_set_constant_si(c, 42);
1970 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1971 bset = isl_basic_set_add_constraint(bset, c);
1973 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1977 isl_basic_set *bset;
1978 bset = isl_basic_set_read_from_str(ctx,
1979 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1981 A basic set or relation can also be constructed from two matrices
1982 describing the equalities and the inequalities.
1984 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1985 __isl_take isl_space *space,
1986 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1987 enum isl_dim_type c1,
1988 enum isl_dim_type c2, enum isl_dim_type c3,
1989 enum isl_dim_type c4);
1990 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1991 __isl_take isl_space *space,
1992 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1993 enum isl_dim_type c1,
1994 enum isl_dim_type c2, enum isl_dim_type c3,
1995 enum isl_dim_type c4, enum isl_dim_type c5);
1997 The C<isl_dim_type> arguments indicate the order in which
1998 different kinds of variables appear in the input matrices
1999 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
2000 C<isl_dim_set> and C<isl_dim_div> for sets and
2001 of C<isl_dim_cst>, C<isl_dim_param>,
2002 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
2004 A (basic or union) set or relation can also be constructed from a
2005 (union) (piecewise) (multiple) affine expression
2006 or a list of affine expressions
2007 (See L</"Functions">).
2009 __isl_give isl_basic_map *isl_basic_map_from_aff(
2010 __isl_take isl_aff *aff);
2011 __isl_give isl_map *isl_map_from_aff(
2012 __isl_take isl_aff *aff);
2013 __isl_give isl_set *isl_set_from_pw_aff(
2014 __isl_take isl_pw_aff *pwaff);
2015 __isl_give isl_map *isl_map_from_pw_aff(
2016 __isl_take isl_pw_aff *pwaff);
2017 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
2018 __isl_take isl_space *domain_space,
2019 __isl_take isl_aff_list *list);
2020 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
2021 __isl_take isl_multi_aff *maff)
2022 __isl_give isl_map *isl_map_from_multi_aff(
2023 __isl_take isl_multi_aff *maff)
2024 __isl_give isl_set *isl_set_from_pw_multi_aff(
2025 __isl_take isl_pw_multi_aff *pma);
2026 __isl_give isl_map *isl_map_from_pw_multi_aff(
2027 __isl_take isl_pw_multi_aff *pma);
2028 __isl_give isl_set *isl_set_from_multi_pw_aff(
2029 __isl_take isl_multi_pw_aff *mpa);
2030 __isl_give isl_map *isl_map_from_multi_pw_aff(
2031 __isl_take isl_multi_pw_aff *mpa);
2032 __isl_give isl_union_map *isl_union_map_from_union_pw_aff(
2033 __isl_take isl_union_pw_aff *upa);
2034 __isl_give isl_union_map *
2035 isl_union_map_from_union_pw_multi_aff(
2036 __isl_take isl_union_pw_multi_aff *upma);
2037 __isl_give isl_union_map *
2038 isl_union_map_from_multi_union_pw_aff(
2039 __isl_take isl_multi_union_pw_aff *mupa);
2041 The C<domain_space> argument describes the domain of the resulting
2042 basic relation. It is required because the C<list> may consist
2043 of zero affine expressions.
2044 The C<mupa> passed to C<isl_union_map_from_multi_union_pw_aff>
2045 is not allowed to be zero-dimensional. The domain of the result
2046 is the shared domain of the union piecewise affine elements.
2048 =head2 Inspecting Sets and Relations
2050 Usually, the user should not have to care about the actual constraints
2051 of the sets and maps, but should instead apply the abstract operations
2052 explained in the following sections.
2053 Occasionally, however, it may be required to inspect the individual
2054 coefficients of the constraints. This section explains how to do so.
2055 In these cases, it may also be useful to have C<isl> compute
2056 an explicit representation of the existentially quantified variables.
2058 __isl_give isl_set *isl_set_compute_divs(
2059 __isl_take isl_set *set);
2060 __isl_give isl_map *isl_map_compute_divs(
2061 __isl_take isl_map *map);
2062 __isl_give isl_union_set *isl_union_set_compute_divs(
2063 __isl_take isl_union_set *uset);
2064 __isl_give isl_union_map *isl_union_map_compute_divs(
2065 __isl_take isl_union_map *umap);
2067 This explicit representation defines the existentially quantified
2068 variables as integer divisions of the other variables, possibly
2069 including earlier existentially quantified variables.
2070 An explicitly represented existentially quantified variable therefore
2071 has a unique value when the values of the other variables are known.
2072 If, furthermore, the same existentials, i.e., existentials
2073 with the same explicit representations, should appear in the
2074 same order in each of the disjuncts of a set or map, then the user should call
2075 either of the following functions.
2077 __isl_give isl_set *isl_set_align_divs(
2078 __isl_take isl_set *set);
2079 __isl_give isl_map *isl_map_align_divs(
2080 __isl_take isl_map *map);
2082 Alternatively, the existentially quantified variables can be removed
2083 using the following functions, which compute an overapproximation.
2085 __isl_give isl_basic_set *isl_basic_set_remove_divs(
2086 __isl_take isl_basic_set *bset);
2087 __isl_give isl_basic_map *isl_basic_map_remove_divs(
2088 __isl_take isl_basic_map *bmap);
2089 __isl_give isl_set *isl_set_remove_divs(
2090 __isl_take isl_set *set);
2091 __isl_give isl_map *isl_map_remove_divs(
2092 __isl_take isl_map *map);
2094 It is also possible to only remove those divs that are defined
2095 in terms of a given range of dimensions or only those for which
2096 no explicit representation is known.
2098 __isl_give isl_basic_set *
2099 isl_basic_set_remove_divs_involving_dims(
2100 __isl_take isl_basic_set *bset,
2101 enum isl_dim_type type,
2102 unsigned first, unsigned n);
2103 __isl_give isl_basic_map *
2104 isl_basic_map_remove_divs_involving_dims(
2105 __isl_take isl_basic_map *bmap,
2106 enum isl_dim_type type,
2107 unsigned first, unsigned n);
2108 __isl_give isl_set *isl_set_remove_divs_involving_dims(
2109 __isl_take isl_set *set, enum isl_dim_type type,
2110 unsigned first, unsigned n);
2111 __isl_give isl_map *isl_map_remove_divs_involving_dims(
2112 __isl_take isl_map *map, enum isl_dim_type type,
2113 unsigned first, unsigned n);
2115 __isl_give isl_basic_set *
2116 isl_basic_set_remove_unknown_divs(
2117 __isl_take isl_basic_set *bset);
2118 __isl_give isl_set *isl_set_remove_unknown_divs(
2119 __isl_take isl_set *set);
2120 __isl_give isl_map *isl_map_remove_unknown_divs(
2121 __isl_take isl_map *map);
2123 To iterate over all the sets or maps in a union set or map, use
2125 isl_stat isl_union_set_foreach_set(
2126 __isl_keep isl_union_set *uset,
2127 isl_stat (*fn)(__isl_take isl_set *set, void *user),
2129 isl_stat isl_union_map_foreach_map(
2130 __isl_keep isl_union_map *umap,
2131 isl_stat (*fn)(__isl_take isl_map *map, void *user),
2134 The number of sets or maps in a union set or map can be obtained
2137 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
2138 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
2140 To extract the set or map in a given space from a union, use
2142 __isl_give isl_set *isl_union_set_extract_set(
2143 __isl_keep isl_union_set *uset,
2144 __isl_take isl_space *space);
2145 __isl_give isl_map *isl_union_map_extract_map(
2146 __isl_keep isl_union_map *umap,
2147 __isl_take isl_space *space);
2149 To iterate over all the basic sets or maps in a set or map, use
2151 isl_stat isl_set_foreach_basic_set(__isl_keep isl_set *set,
2152 isl_stat (*fn)(__isl_take isl_basic_set *bset,
2155 isl_stat isl_map_foreach_basic_map(__isl_keep isl_map *map,
2156 isl_stat (*fn)(__isl_take isl_basic_map *bmap,
2160 The callback function C<fn> should return 0 if successful and
2161 -1 if an error occurs. In the latter case, or if any other error
2162 occurs, the above functions will return -1.
2164 It should be noted that C<isl> does not guarantee that
2165 the basic sets or maps passed to C<fn> are disjoint.
2166 If this is required, then the user should call one of
2167 the following functions first.
2169 __isl_give isl_set *isl_set_make_disjoint(
2170 __isl_take isl_set *set);
2171 __isl_give isl_map *isl_map_make_disjoint(
2172 __isl_take isl_map *map);
2174 The number of basic sets in a set can be obtained
2175 or the number of basic maps in a map can be obtained
2178 #include <isl/set.h>
2179 int isl_set_n_basic_set(__isl_keep isl_set *set);
2181 #include <isl/map.h>
2182 int isl_map_n_basic_map(__isl_keep isl_map *map);
2184 It is also possible to obtain a list of basic sets from a set
2186 #include <isl/set.h>
2187 __isl_give isl_basic_set_list *isl_set_get_basic_set_list(
2188 __isl_keep isl_set *set);
2190 The returned list can be manipulated using the functions in L<"Lists">.
2192 To iterate over the constraints of a basic set or map, use
2194 #include <isl/constraint.h>
2196 int isl_basic_set_n_constraint(
2197 __isl_keep isl_basic_set *bset);
2198 isl_stat isl_basic_set_foreach_constraint(
2199 __isl_keep isl_basic_set *bset,
2200 isl_stat (*fn)(__isl_take isl_constraint *c,
2203 int isl_basic_map_n_constraint(
2204 __isl_keep isl_basic_map *bmap);
2205 isl_stat isl_basic_map_foreach_constraint(
2206 __isl_keep isl_basic_map *bmap,
2207 isl_stat (*fn)(__isl_take isl_constraint *c,
2210 __isl_null isl_constraint *isl_constraint_free(
2211 __isl_take isl_constraint *c);
2213 Again, the callback function C<fn> should return 0 if successful and
2214 -1 if an error occurs. In the latter case, or if any other error
2215 occurs, the above functions will return -1.
2216 The constraint C<c> represents either an equality or an inequality.
2217 Use the following function to find out whether a constraint
2218 represents an equality. If not, it represents an inequality.
2220 isl_bool isl_constraint_is_equality(
2221 __isl_keep isl_constraint *constraint);
2223 It is also possible to obtain a list of constraints from a basic
2226 #include <isl/constraint.h>
2227 __isl_give isl_constraint_list *
2228 isl_basic_map_get_constraint_list(
2229 __isl_keep isl_basic_map *bmap);
2230 __isl_give isl_constraint_list *
2231 isl_basic_set_get_constraint_list(
2232 __isl_keep isl_basic_set *bset);
2234 These functions require that all existentially quantified variables
2235 have an explicit representation.
2236 The returned list can be manipulated using the functions in L<"Lists">.
2238 The coefficients of the constraints can be inspected using
2239 the following functions.
2241 isl_bool isl_constraint_is_lower_bound(
2242 __isl_keep isl_constraint *constraint,
2243 enum isl_dim_type type, unsigned pos);
2244 isl_bool isl_constraint_is_upper_bound(
2245 __isl_keep isl_constraint *constraint,
2246 enum isl_dim_type type, unsigned pos);
2247 __isl_give isl_val *isl_constraint_get_constant_val(
2248 __isl_keep isl_constraint *constraint);
2249 __isl_give isl_val *isl_constraint_get_coefficient_val(
2250 __isl_keep isl_constraint *constraint,
2251 enum isl_dim_type type, int pos);
2253 The explicit representations of the existentially quantified
2254 variables can be inspected using the following function.
2255 Note that the user is only allowed to use this function
2256 if the inspected set or map is the result of a call
2257 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2258 The existentially quantified variable is equal to the floor
2259 of the returned affine expression. The affine expression
2260 itself can be inspected using the functions in
2263 __isl_give isl_aff *isl_constraint_get_div(
2264 __isl_keep isl_constraint *constraint, int pos);
2266 To obtain the constraints of a basic set or map in matrix
2267 form, use the following functions.
2269 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2270 __isl_keep isl_basic_set *bset,
2271 enum isl_dim_type c1, enum isl_dim_type c2,
2272 enum isl_dim_type c3, enum isl_dim_type c4);
2273 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2274 __isl_keep isl_basic_set *bset,
2275 enum isl_dim_type c1, enum isl_dim_type c2,
2276 enum isl_dim_type c3, enum isl_dim_type c4);
2277 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2278 __isl_keep isl_basic_map *bmap,
2279 enum isl_dim_type c1,
2280 enum isl_dim_type c2, enum isl_dim_type c3,
2281 enum isl_dim_type c4, enum isl_dim_type c5);
2282 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2283 __isl_keep isl_basic_map *bmap,
2284 enum isl_dim_type c1,
2285 enum isl_dim_type c2, enum isl_dim_type c3,
2286 enum isl_dim_type c4, enum isl_dim_type c5);
2288 The C<isl_dim_type> arguments dictate the order in which
2289 different kinds of variables appear in the resulting matrix.
2290 For set inputs, they should be a permutation of
2291 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
2292 For map inputs, they should be a permutation of
2293 C<isl_dim_cst>, C<isl_dim_param>,
2294 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2298 Points are elements of a set. They can be used to construct
2299 simple sets (boxes) or they can be used to represent the
2300 individual elements of a set.
2301 The zero point (the origin) can be created using
2303 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2305 The coordinates of a point can be inspected, set and changed
2308 __isl_give isl_val *isl_point_get_coordinate_val(
2309 __isl_keep isl_point *pnt,
2310 enum isl_dim_type type, int pos);
2311 __isl_give isl_point *isl_point_set_coordinate_val(
2312 __isl_take isl_point *pnt,
2313 enum isl_dim_type type, int pos,
2314 __isl_take isl_val *v);
2316 __isl_give isl_point *isl_point_add_ui(
2317 __isl_take isl_point *pnt,
2318 enum isl_dim_type type, int pos, unsigned val);
2319 __isl_give isl_point *isl_point_sub_ui(
2320 __isl_take isl_point *pnt,
2321 enum isl_dim_type type, int pos, unsigned val);
2323 Points can be copied or freed using
2325 __isl_give isl_point *isl_point_copy(
2326 __isl_keep isl_point *pnt);
2327 void isl_point_free(__isl_take isl_point *pnt);
2329 A singleton set can be created from a point using
2331 __isl_give isl_basic_set *isl_basic_set_from_point(
2332 __isl_take isl_point *pnt);
2333 __isl_give isl_set *isl_set_from_point(
2334 __isl_take isl_point *pnt);
2336 and a box can be created from two opposite extremal points using
2338 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2339 __isl_take isl_point *pnt1,
2340 __isl_take isl_point *pnt2);
2341 __isl_give isl_set *isl_set_box_from_points(
2342 __isl_take isl_point *pnt1,
2343 __isl_take isl_point *pnt2);
2345 All elements of a B<bounded> (union) set can be enumerated using
2346 the following functions.
2348 isl_stat isl_set_foreach_point(__isl_keep isl_set *set,
2349 isl_stat (*fn)(__isl_take isl_point *pnt,
2352 isl_stat isl_union_set_foreach_point(
2353 __isl_keep isl_union_set *uset,
2354 isl_stat (*fn)(__isl_take isl_point *pnt,
2358 The function C<fn> is called for each integer point in
2359 C<set> with as second argument the last argument of
2360 the C<isl_set_foreach_point> call. The function C<fn>
2361 should return C<0> on success and C<-1> on failure.
2362 In the latter case, C<isl_set_foreach_point> will stop
2363 enumerating and return C<-1> as well.
2364 If the enumeration is performed successfully and to completion,
2365 then C<isl_set_foreach_point> returns C<0>.
2367 To obtain a single point of a (basic) set, use
2369 __isl_give isl_point *isl_basic_set_sample_point(
2370 __isl_take isl_basic_set *bset);
2371 __isl_give isl_point *isl_set_sample_point(
2372 __isl_take isl_set *set);
2374 If C<set> does not contain any (integer) points, then the
2375 resulting point will be ``void'', a property that can be
2378 isl_bool isl_point_is_void(__isl_keep isl_point *pnt);
2382 Besides sets and relation, C<isl> also supports various types of functions.
2383 Each of these types is derived from the value type (see L</"Values">)
2384 or from one of two primitive function types
2385 through the application of zero or more type constructors.
2386 We first describe the primitive type and then we describe
2387 the types derived from these primitive types.
2389 =head3 Primitive Functions
2391 C<isl> support two primitive function types, quasi-affine
2392 expressions and quasipolynomials.
2393 A quasi-affine expression is defined either over a parameter
2394 space or over a set and is composed of integer constants,
2395 parameters and set variables, addition, subtraction and
2396 integer division by an integer constant.
2397 For example, the quasi-affine expression
2399 [n] -> { [x] -> [2*floor((4 n + x)/9] }
2401 maps C<x> to C<2*floor((4 n + x)/9>.
2402 A quasipolynomial is a polynomial expression in quasi-affine
2403 expression. That is, it additionally allows for multiplication.
2404 Note, though, that it is not allowed to construct an integer
2405 division of an expression involving multiplications.
2406 Here is an example of a quasipolynomial that is not
2407 quasi-affine expression
2409 [n] -> { [x] -> (n*floor((4 n + x)/9) }
2411 Note that the external representations of quasi-affine expressions
2412 and quasipolynomials are different. Quasi-affine expressions
2413 use a notation with square brackets just like binary relations,
2414 while quasipolynomials do not. This might change at some point.
2416 If a primitive function is defined over a parameter space,
2417 then the space of the function itself is that of a set.
2418 If it is defined over a set, then the space of the function
2419 is that of a relation. In both cases, the set space (or
2420 the output space) is single-dimensional, anonymous and unstructured.
2421 To create functions with multiple dimensions or with other kinds
2422 of set or output spaces, use multiple expressions
2423 (see L</"Multiple Expressions">).
2427 =item * Quasi-affine Expressions
2429 Besides the expressions described above, a quasi-affine
2430 expression can also be set to NaN. Such expressions
2431 typically represent a failure to represent a result
2432 as a quasi-affine expression.
2434 The zero quasi affine expression or the quasi affine expression
2435 that is equal to a given value or
2436 a specified dimension on a given domain can be created using
2438 #include <isl/aff.h>
2439 __isl_give isl_aff *isl_aff_zero_on_domain(
2440 __isl_take isl_local_space *ls);
2441 __isl_give isl_aff *isl_aff_val_on_domain(
2442 __isl_take isl_local_space *ls,
2443 __isl_take isl_val *val);
2444 __isl_give isl_aff *isl_aff_var_on_domain(
2445 __isl_take isl_local_space *ls,
2446 enum isl_dim_type type, unsigned pos);
2447 __isl_give isl_aff *isl_aff_nan_on_domain(
2448 __isl_take isl_local_space *ls);
2450 Quasi affine expressions can be copied and freed using
2452 #include <isl/aff.h>
2453 __isl_give isl_aff *isl_aff_copy(
2454 __isl_keep isl_aff *aff);
2455 __isl_null isl_aff *isl_aff_free(
2456 __isl_take isl_aff *aff);
2458 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2459 using the following function. The constraint is required to have
2460 a non-zero coefficient for the specified dimension.
2462 #include <isl/constraint.h>
2463 __isl_give isl_aff *isl_constraint_get_bound(
2464 __isl_keep isl_constraint *constraint,
2465 enum isl_dim_type type, int pos);
2467 The entire affine expression of the constraint can also be extracted
2468 using the following function.
2470 #include <isl/constraint.h>
2471 __isl_give isl_aff *isl_constraint_get_aff(
2472 __isl_keep isl_constraint *constraint);
2474 Conversely, an equality constraint equating
2475 the affine expression to zero or an inequality constraint enforcing
2476 the affine expression to be non-negative, can be constructed using
2478 __isl_give isl_constraint *isl_equality_from_aff(
2479 __isl_take isl_aff *aff);
2480 __isl_give isl_constraint *isl_inequality_from_aff(
2481 __isl_take isl_aff *aff);
2483 The coefficients and the integer divisions of an affine expression
2484 can be inspected using the following functions.
2486 #include <isl/aff.h>
2487 __isl_give isl_val *isl_aff_get_constant_val(
2488 __isl_keep isl_aff *aff);
2489 __isl_give isl_val *isl_aff_get_coefficient_val(
2490 __isl_keep isl_aff *aff,
2491 enum isl_dim_type type, int pos);
2492 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2493 enum isl_dim_type type, int pos);
2494 __isl_give isl_val *isl_aff_get_denominator_val(
2495 __isl_keep isl_aff *aff);
2496 __isl_give isl_aff *isl_aff_get_div(
2497 __isl_keep isl_aff *aff, int pos);
2499 They can be modified using the following functions.
2501 #include <isl/aff.h>
2502 __isl_give isl_aff *isl_aff_set_constant_si(
2503 __isl_take isl_aff *aff, int v);
2504 __isl_give isl_aff *isl_aff_set_constant_val(
2505 __isl_take isl_aff *aff, __isl_take isl_val *v);
2506 __isl_give isl_aff *isl_aff_set_coefficient_si(
2507 __isl_take isl_aff *aff,
2508 enum isl_dim_type type, int pos, int v);
2509 __isl_give isl_aff *isl_aff_set_coefficient_val(
2510 __isl_take isl_aff *aff,
2511 enum isl_dim_type type, int pos,
2512 __isl_take isl_val *v);
2514 __isl_give isl_aff *isl_aff_add_constant_si(
2515 __isl_take isl_aff *aff, int v);
2516 __isl_give isl_aff *isl_aff_add_constant_val(
2517 __isl_take isl_aff *aff, __isl_take isl_val *v);
2518 __isl_give isl_aff *isl_aff_add_constant_num_si(
2519 __isl_take isl_aff *aff, int v);
2520 __isl_give isl_aff *isl_aff_add_coefficient_si(
2521 __isl_take isl_aff *aff,
2522 enum isl_dim_type type, int pos, int v);
2523 __isl_give isl_aff *isl_aff_add_coefficient_val(
2524 __isl_take isl_aff *aff,
2525 enum isl_dim_type type, int pos,
2526 __isl_take isl_val *v);
2528 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
2529 set the I<numerator> of the constant or coefficient, while
2530 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
2531 the constant or coefficient as a whole.
2532 The C<add_constant> and C<add_coefficient> functions add an integer
2533 or rational value to
2534 the possibly rational constant or coefficient.
2535 The C<add_constant_num> functions add an integer value to
2538 =item * Quasipolynomials
2540 Some simple quasipolynomials can be created using the following functions.
2542 #include <isl/polynomial.h>
2543 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2544 __isl_take isl_space *domain);
2545 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2546 __isl_take isl_space *domain);
2547 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2548 __isl_take isl_space *domain);
2549 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2550 __isl_take isl_space *domain);
2551 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2552 __isl_take isl_space *domain);
2553 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2554 __isl_take isl_space *domain,
2555 __isl_take isl_val *val);
2556 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2557 __isl_take isl_space *domain,
2558 enum isl_dim_type type, unsigned pos);
2559 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2560 __isl_take isl_aff *aff);
2562 Recall that the space in which a quasipolynomial lives is a map space
2563 with a one-dimensional range. The C<domain> argument in some of
2564 the functions above corresponds to the domain of this map space.
2566 Quasipolynomials can be copied and freed again using the following
2569 #include <isl/polynomial.h>
2570 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2571 __isl_keep isl_qpolynomial *qp);
2572 __isl_null isl_qpolynomial *isl_qpolynomial_free(
2573 __isl_take isl_qpolynomial *qp);
2575 The constant term of a quasipolynomial can be extracted using
2577 __isl_give isl_val *isl_qpolynomial_get_constant_val(
2578 __isl_keep isl_qpolynomial *qp);
2580 To iterate over all terms in a quasipolynomial,
2583 isl_stat isl_qpolynomial_foreach_term(
2584 __isl_keep isl_qpolynomial *qp,
2585 isl_stat (*fn)(__isl_take isl_term *term,
2586 void *user), void *user);
2588 The terms themselves can be inspected and freed using
2591 unsigned isl_term_dim(__isl_keep isl_term *term,
2592 enum isl_dim_type type);
2593 __isl_give isl_val *isl_term_get_coefficient_val(
2594 __isl_keep isl_term *term);
2595 int isl_term_get_exp(__isl_keep isl_term *term,
2596 enum isl_dim_type type, unsigned pos);
2597 __isl_give isl_aff *isl_term_get_div(
2598 __isl_keep isl_term *term, unsigned pos);
2599 void isl_term_free(__isl_take isl_term *term);
2601 Each term is a product of parameters, set variables and
2602 integer divisions. The function C<isl_term_get_exp>
2603 returns the exponent of a given dimensions in the given term.
2609 A reduction represents a maximum or a minimum of its
2611 The only reduction type defined by C<isl> is
2612 C<isl_qpolynomial_fold>.
2614 There are currently no functions to directly create such
2615 objects, but they do appear in the piecewise quasipolynomial
2616 reductions returned by the C<isl_pw_qpolynomial_bound> function.
2618 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
2620 Reductions can be copied and freed using
2621 the following functions.
2623 #include <isl/polynomial.h>
2624 __isl_give isl_qpolynomial_fold *
2625 isl_qpolynomial_fold_copy(
2626 __isl_keep isl_qpolynomial_fold *fold);
2627 void isl_qpolynomial_fold_free(
2628 __isl_take isl_qpolynomial_fold *fold);
2630 To iterate over all quasipolynomials in a reduction, use
2632 isl_stat isl_qpolynomial_fold_foreach_qpolynomial(
2633 __isl_keep isl_qpolynomial_fold *fold,
2634 isl_stat (*fn)(__isl_take isl_qpolynomial *qp,
2635 void *user), void *user);
2637 =head3 Multiple Expressions
2639 A multiple expression represents a sequence of zero or
2640 more base expressions, all defined on the same domain space.
2641 The domain space of the multiple expression is the same
2642 as that of the base expressions, but the range space
2643 can be any space. In case the base expressions have
2644 a set space, the corresponding multiple expression
2645 also has a set space.
2646 Objects of the value type do not have an associated space.
2647 The space of a multiple value is therefore always a set space.
2648 Similarly, the space of a multiple union piecewise
2649 affine expression is always a set space.
2651 The multiple expression types defined by C<isl>
2652 are C<isl_multi_val>, C<isl_multi_aff>, C<isl_multi_pw_aff>,
2653 C<isl_multi_union_pw_aff>.
2655 A multiple expression with the value zero for
2656 each output (or set) dimension can be created
2657 using the following functions.
2659 #include <isl/val.h>
2660 __isl_give isl_multi_val *isl_multi_val_zero(
2661 __isl_take isl_space *space);
2663 #include <isl/aff.h>
2664 __isl_give isl_multi_aff *isl_multi_aff_zero(
2665 __isl_take isl_space *space);
2666 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
2667 __isl_take isl_space *space);
2668 __isl_give isl_multi_union_pw_aff *
2669 isl_multi_union_pw_aff_zero(
2670 __isl_take isl_space *space);
2672 Since there is no canonical way of representing a zero
2673 value of type C<isl_union_pw_aff>, the space passed
2674 to C<isl_multi_union_pw_aff_zero> needs to be zero-dimensional.
2676 An identity function can be created using the following
2677 functions. The space needs to be that of a relation
2678 with the same number of input and output dimensions.
2680 #include <isl/aff.h>
2681 __isl_give isl_multi_aff *isl_multi_aff_identity(
2682 __isl_take isl_space *space);
2683 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
2684 __isl_take isl_space *space);
2686 A function that performs a projection on a universe
2687 relation or set can be created using the following functions.
2688 See also the corresponding
2689 projection operations in L</"Unary Operations">.
2691 #include <isl/aff.h>
2692 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
2693 __isl_take isl_space *space);
2694 __isl_give isl_multi_aff *isl_multi_aff_range_map(
2695 __isl_take isl_space *space);
2696 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
2697 __isl_take isl_space *space,
2698 enum isl_dim_type type,
2699 unsigned first, unsigned n);
2701 A multiple expression can be created from a single
2702 base expression using the following functions.
2703 The space of the created multiple expression is the same
2704 as that of the base expression, except for
2705 C<isl_multi_union_pw_aff_from_union_pw_aff> where the input
2706 lives in a parameter space and the output lives
2707 in a single-dimensional set space.
2709 #include <isl/aff.h>
2710 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
2711 __isl_take isl_aff *aff);
2712 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
2713 __isl_take isl_pw_aff *pa);
2714 __isl_give isl_multi_union_pw_aff *
2715 isl_multi_union_pw_aff_from_union_pw_aff(
2716 __isl_take isl_union_pw_aff *upa);
2718 A multiple expression can be created from a list
2719 of base expression in a specified space.
2720 The domain of this space needs to be the same
2721 as the domains of the base expressions in the list.
2722 If the base expressions have a set space (or no associated space),
2723 then this space also needs to be a set space.
2725 #include <isl/val.h>
2726 __isl_give isl_multi_val *isl_multi_val_from_val_list(
2727 __isl_take isl_space *space,
2728 __isl_take isl_val_list *list);
2730 #include <isl/aff.h>
2731 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2732 __isl_take isl_space *space,
2733 __isl_take isl_aff_list *list);
2734 __isl_give isl_multi_union_pw_aff *
2735 isl_multi_union_pw_aff_from_union_pw_aff_list(
2736 __isl_take isl_space *space,
2737 __isl_take isl_union_pw_aff_list *list);
2739 As a convenience, a multiple piecewise expression can
2740 also be created from a multiple expression.
2741 Each piecewise expression in the result has a single
2744 #include <isl/aff.h>
2745 __isl_give isl_multi_pw_aff *
2746 isl_multi_pw_aff_from_multi_aff(
2747 __isl_take isl_multi_aff *ma);
2749 Similarly, a multiple union expression can be
2750 created from a multiple expression.
2752 #include <isl/aff.h>
2753 __isl_give isl_multi_union_pw_aff *
2754 isl_multi_union_pw_aff_from_multi_aff(
2755 __isl_take isl_multi_aff *ma);
2756 __isl_give isl_multi_union_pw_aff *
2757 isl_multi_union_pw_aff_from_multi_pw_aff(
2758 __isl_take isl_multi_pw_aff *mpa);
2760 A multiple quasi-affine expression can be created from
2761 a multiple value with a given domain space using the following
2764 #include <isl/aff.h>
2765 __isl_give isl_multi_aff *
2766 isl_multi_aff_multi_val_on_space(
2767 __isl_take isl_space *space,
2768 __isl_take isl_multi_val *mv);
2771 a multiple union piecewise affine expression can be created from
2772 a multiple value with a given domain or
2773 a multiple affine expression with a given domain
2774 using the following functions.
2776 #include <isl/aff.h>
2777 __isl_give isl_multi_union_pw_aff *
2778 isl_multi_union_pw_aff_multi_val_on_domain(
2779 __isl_take isl_union_set *domain,
2780 __isl_take isl_multi_val *mv);
2781 __isl_give isl_multi_union_pw_aff *
2782 isl_multi_union_pw_aff_multi_aff_on_domain(
2783 __isl_take isl_union_set *domain,
2784 __isl_take isl_multi_aff *ma);
2786 Multiple expressions can be copied and freed using
2787 the following functions.
2789 #include <isl/val.h>
2790 __isl_give isl_multi_val *isl_multi_val_copy(
2791 __isl_keep isl_multi_val *mv);
2792 __isl_null isl_multi_val *isl_multi_val_free(
2793 __isl_take isl_multi_val *mv);
2795 #include <isl/aff.h>
2796 __isl_give isl_multi_aff *isl_multi_aff_copy(
2797 __isl_keep isl_multi_aff *maff);
2798 __isl_null isl_multi_aff *isl_multi_aff_free(
2799 __isl_take isl_multi_aff *maff);
2800 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
2801 __isl_keep isl_multi_pw_aff *mpa);
2802 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
2803 __isl_take isl_multi_pw_aff *mpa);
2804 __isl_give isl_multi_union_pw_aff *
2805 isl_multi_union_pw_aff_copy(
2806 __isl_keep isl_multi_union_pw_aff *mupa);
2807 __isl_null isl_multi_union_pw_aff *
2808 isl_multi_union_pw_aff_free(
2809 __isl_take isl_multi_union_pw_aff *mupa);
2811 The base expression at a given position of a multiple
2812 expression can be extracted using the following functions.
2814 #include <isl/val.h>
2815 __isl_give isl_val *isl_multi_val_get_val(
2816 __isl_keep isl_multi_val *mv, int pos);
2818 #include <isl/aff.h>
2819 __isl_give isl_aff *isl_multi_aff_get_aff(
2820 __isl_keep isl_multi_aff *multi, int pos);
2821 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
2822 __isl_keep isl_multi_pw_aff *mpa, int pos);
2823 __isl_give isl_union_pw_aff *
2824 isl_multi_union_pw_aff_get_union_pw_aff(
2825 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
2827 It can be replaced using the following functions.
2829 #include <isl/val.h>
2830 __isl_give isl_multi_val *isl_multi_val_set_val(
2831 __isl_take isl_multi_val *mv, int pos,
2832 __isl_take isl_val *val);
2834 #include <isl/aff.h>
2835 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
2836 __isl_take isl_multi_aff *multi, int pos,
2837 __isl_take isl_aff *aff);
2838 __isl_give isl_multi_union_pw_aff *
2839 isl_multi_union_pw_aff_set_union_pw_aff(
2840 __isl_take isl_multi_union_pw_aff *mupa, int pos,
2841 __isl_take isl_union_pw_aff *upa);
2843 As a convenience, a sequence of base expressions that have
2844 their domains in a given space can be extracted from a sequence
2845 of union expressions using the following function.
2847 #include <isl/aff.h>
2848 __isl_give isl_multi_pw_aff *
2849 isl_multi_union_pw_aff_extract_multi_pw_aff(
2850 __isl_keep isl_multi_union_pw_aff *mupa,
2851 __isl_take isl_space *space);
2853 Note that there is a difference between C<isl_multi_union_pw_aff>
2854 and C<isl_union_pw_multi_aff> objects. The first is a sequence
2855 of unions of piecewise expressions, while the second is a union
2856 of piecewise sequences. In particular, multiple affine expressions
2857 in an C<isl_union_pw_multi_aff> may live in different spaces,
2858 while there is only a single multiple expression in
2859 an C<isl_multi_union_pw_aff>, which can therefore only live
2860 in a single space. This means that not every
2861 C<isl_union_pw_multi_aff> can be converted to
2862 an C<isl_multi_union_pw_aff>. Conversely, a zero-dimensional
2863 C<isl_multi_union_pw_aff> carries no information
2864 about any possible domain and therefore cannot be converted
2865 to an C<isl_union_pw_multi_aff>. Moreover, the elements
2866 of an C<isl_multi_union_pw_aff> may be defined over different domains,
2867 while each multiple expression inside an C<isl_union_pw_multi_aff>
2868 has a single domain. The conversion of an C<isl_union_pw_multi_aff>
2869 of dimension greater than one may therefore not be exact.
2870 The following functions can
2871 be used to perform these conversions when they are possible.
2873 #include <isl/aff.h>
2874 __isl_give isl_multi_union_pw_aff *
2875 isl_multi_union_pw_aff_from_union_pw_multi_aff(
2876 __isl_take isl_union_pw_multi_aff *upma);
2877 __isl_give isl_union_pw_multi_aff *
2878 isl_union_pw_multi_aff_from_multi_union_pw_aff(
2879 __isl_take isl_multi_union_pw_aff *mupa);
2881 =head3 Piecewise Expressions
2883 A piecewise expression is an expression that is described
2884 using zero or more base expression defined over the same
2885 number of cells in the domain space of the base expressions.
2886 All base expressions are defined over the same
2887 domain space and the cells are disjoint.
2888 The space of a piecewise expression is the same as
2889 that of the base expressions.
2890 If the union of the cells is a strict subset of the domain
2891 space, then the value of the piecewise expression outside
2892 this union is different for types derived from quasi-affine
2893 expressions and those derived from quasipolynomials.
2894 Piecewise expressions derived from quasi-affine expressions
2895 are considered to be undefined outside the union of their cells.
2896 Piecewise expressions derived from quasipolynomials
2897 are considered to be zero outside the union of their cells.
2899 Piecewise quasipolynomials are mainly used by the C<barvinok>
2900 library for representing the number of elements in a parametric set or map.
2901 For example, the piecewise quasipolynomial
2903 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2905 represents the number of points in the map
2907 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2909 The piecewise expression types defined by C<isl>
2910 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
2911 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
2913 A piecewise expression with no cells can be created using
2914 the following functions.
2916 #include <isl/aff.h>
2917 __isl_give isl_pw_aff *isl_pw_aff_empty(
2918 __isl_take isl_space *space);
2919 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
2920 __isl_take isl_space *space);
2922 A piecewise expression with a single universe cell can be
2923 created using the following functions.
2925 #include <isl/aff.h>
2926 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2927 __isl_take isl_aff *aff);
2928 __isl_give isl_pw_multi_aff *
2929 isl_pw_multi_aff_from_multi_aff(
2930 __isl_take isl_multi_aff *ma);
2932 #include <isl/polynomial.h>
2933 __isl_give isl_pw_qpolynomial *
2934 isl_pw_qpolynomial_from_qpolynomial(
2935 __isl_take isl_qpolynomial *qp);
2937 A piecewise expression with a single specified cell can be
2938 created using the following functions.
2940 #include <isl/aff.h>
2941 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2942 __isl_take isl_set *set, __isl_take isl_aff *aff);
2943 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
2944 __isl_take isl_set *set,
2945 __isl_take isl_multi_aff *maff);
2947 #include <isl/polynomial.h>
2948 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2949 __isl_take isl_set *set,
2950 __isl_take isl_qpolynomial *qp);
2952 The following convenience functions first create a base expression and
2953 then create a piecewise expression over a universe domain.
2955 #include <isl/aff.h>
2956 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
2957 __isl_take isl_local_space *ls);
2958 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
2959 __isl_take isl_local_space *ls,
2960 enum isl_dim_type type, unsigned pos);
2961 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
2962 __isl_take isl_local_space *ls);
2963 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
2964 __isl_take isl_space *space);
2965 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
2966 __isl_take isl_space *space);
2967 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
2968 __isl_take isl_space *space);
2969 __isl_give isl_pw_multi_aff *
2970 isl_pw_multi_aff_project_out_map(
2971 __isl_take isl_space *space,
2972 enum isl_dim_type type,
2973 unsigned first, unsigned n);
2975 #include <isl/polynomial.h>
2976 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2977 __isl_take isl_space *space);
2979 The following convenience functions first create a base expression and
2980 then create a piecewise expression over a given domain.
2982 #include <isl/aff.h>
2983 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
2984 __isl_take isl_set *domain,
2985 __isl_take isl_val *v);
2986 __isl_give isl_pw_multi_aff *
2987 isl_pw_multi_aff_multi_val_on_domain(
2988 __isl_take isl_set *domain,
2989 __isl_take isl_multi_val *mv);
2991 As a convenience, a piecewise multiple expression can
2992 also be created from a piecewise expression.
2993 Each multiple expression in the result is derived
2994 from the corresponding base expression.
2996 #include <isl/aff.h>
2997 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
2998 __isl_take isl_pw_aff *pa);
3000 Similarly, a piecewise quasipolynomial can be
3001 created from a piecewise quasi-affine expression using
3002 the following function.
3004 #include <isl/polynomial.h>
3005 __isl_give isl_pw_qpolynomial *
3006 isl_pw_qpolynomial_from_pw_aff(
3007 __isl_take isl_pw_aff *pwaff);
3009 Piecewise expressions can be copied and freed using the following functions.
3011 #include <isl/aff.h>
3012 __isl_give isl_pw_aff *isl_pw_aff_copy(
3013 __isl_keep isl_pw_aff *pwaff);
3014 __isl_null isl_pw_aff *isl_pw_aff_free(
3015 __isl_take isl_pw_aff *pwaff);
3016 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3017 __isl_keep isl_pw_multi_aff *pma);
3018 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
3019 __isl_take isl_pw_multi_aff *pma);
3021 #include <isl/polynomial.h>
3022 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3023 __isl_keep isl_pw_qpolynomial *pwqp);
3024 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
3025 __isl_take isl_pw_qpolynomial *pwqp);
3026 __isl_give isl_pw_qpolynomial_fold *
3027 isl_pw_qpolynomial_fold_copy(
3028 __isl_keep isl_pw_qpolynomial_fold *pwf);
3029 __isl_null isl_pw_qpolynomial_fold *
3030 isl_pw_qpolynomial_fold_free(
3031 __isl_take isl_pw_qpolynomial_fold *pwf);
3033 To iterate over the different cells of a piecewise expression,
3034 use the following functions.
3036 #include <isl/aff.h>
3037 isl_bool isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3038 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3039 isl_stat isl_pw_aff_foreach_piece(
3040 __isl_keep isl_pw_aff *pwaff,
3041 isl_stat (*fn)(__isl_take isl_set *set,
3042 __isl_take isl_aff *aff,
3043 void *user), void *user);
3044 isl_stat isl_pw_multi_aff_foreach_piece(
3045 __isl_keep isl_pw_multi_aff *pma,
3046 isl_stat (*fn)(__isl_take isl_set *set,
3047 __isl_take isl_multi_aff *maff,
3048 void *user), void *user);
3050 #include <isl/polynomial.h>
3051 isl_stat isl_pw_qpolynomial_foreach_piece(
3052 __isl_keep isl_pw_qpolynomial *pwqp,
3053 isl_stat (*fn)(__isl_take isl_set *set,
3054 __isl_take isl_qpolynomial *qp,
3055 void *user), void *user);
3056 isl_stat isl_pw_qpolynomial_foreach_lifted_piece(
3057 __isl_keep isl_pw_qpolynomial *pwqp,
3058 isl_stat (*fn)(__isl_take isl_set *set,
3059 __isl_take isl_qpolynomial *qp,
3060 void *user), void *user);
3061 isl_stat isl_pw_qpolynomial_fold_foreach_piece(
3062 __isl_keep isl_pw_qpolynomial_fold *pwf,
3063 isl_stat (*fn)(__isl_take isl_set *set,
3064 __isl_take isl_qpolynomial_fold *fold,
3065 void *user), void *user);
3066 isl_stat isl_pw_qpolynomial_fold_foreach_lifted_piece(
3067 __isl_keep isl_pw_qpolynomial_fold *pwf,
3068 isl_stat (*fn)(__isl_take isl_set *set,
3069 __isl_take isl_qpolynomial_fold *fold,
3070 void *user), void *user);
3072 As usual, the function C<fn> should return C<0> on success
3073 and C<-1> on failure. The difference between
3074 C<isl_pw_qpolynomial_foreach_piece> and
3075 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3076 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3077 compute unique representations for all existentially quantified
3078 variables and then turn these existentially quantified variables
3079 into extra set variables, adapting the associated quasipolynomial
3080 accordingly. This means that the C<set> passed to C<fn>
3081 will not have any existentially quantified variables, but that
3082 the dimensions of the sets may be different for different
3083 invocations of C<fn>.
3084 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
3085 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
3087 A piecewise expression consisting of the expressions at a given
3088 position of a piecewise multiple expression can be extracted
3089 using the following function.
3091 #include <isl/aff.h>
3092 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3093 __isl_keep isl_pw_multi_aff *pma, int pos);
3095 These expressions can be replaced using the following function.
3097 #include <isl/aff.h>
3098 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3099 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3100 __isl_take isl_pw_aff *pa);
3102 Note that there is a difference between C<isl_multi_pw_aff> and
3103 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
3104 affine expressions, while the second is a piecewise sequence
3105 of affine expressions. In particular, each of the piecewise
3106 affine expressions in an C<isl_multi_pw_aff> may have a different
3107 domain, while all multiple expressions associated to a cell
3108 in an C<isl_pw_multi_aff> have the same domain.
3109 It is possible to convert between the two, but when converting
3110 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
3111 of the result is the intersection of the domains of the input.
3112 The reverse conversion is exact.
3114 #include <isl/aff.h>
3115 __isl_give isl_pw_multi_aff *
3116 isl_pw_multi_aff_from_multi_pw_aff(
3117 __isl_take isl_multi_pw_aff *mpa);
3118 __isl_give isl_multi_pw_aff *
3119 isl_multi_pw_aff_from_pw_multi_aff(
3120 __isl_take isl_pw_multi_aff *pma);
3122 =head3 Union Expressions
3124 A union expression collects base expressions defined
3125 over different domains. The space of a union expression
3126 is that of the shared parameter space.
3128 The union expression types defined by C<isl>
3129 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
3130 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
3132 An empty union expression can be created using the following functions.
3134 #include <isl/aff.h>
3135 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
3136 __isl_take isl_space *space);
3137 __isl_give isl_union_pw_multi_aff *
3138 isl_union_pw_multi_aff_empty(
3139 __isl_take isl_space *space);
3141 #include <isl/polynomial.h>
3142 __isl_give isl_union_pw_qpolynomial *
3143 isl_union_pw_qpolynomial_zero(
3144 __isl_take isl_space *space);
3146 A union expression containing a single base expression
3147 can be created using the following functions.
3149 #include <isl/aff.h>
3150 __isl_give isl_union_pw_aff *
3151 isl_union_pw_aff_from_pw_aff(
3152 __isl_take isl_pw_aff *pa);
3153 __isl_give isl_union_pw_multi_aff *
3154 isl_union_pw_multi_aff_from_aff(
3155 __isl_take isl_aff *aff);
3156 __isl_give isl_union_pw_multi_aff *
3157 isl_union_pw_multi_aff_from_pw_multi_aff(
3158 __isl_take isl_pw_multi_aff *pma);
3160 #include <isl/polynomial.h>
3161 __isl_give isl_union_pw_qpolynomial *
3162 isl_union_pw_qpolynomial_from_pw_qpolynomial(
3163 __isl_take isl_pw_qpolynomial *pwqp);
3165 The following functions create a base expression on each
3166 of the sets in the union set and collect the results.
3168 #include <isl/aff.h>
3169 __isl_give isl_union_pw_multi_aff *
3170 isl_union_pw_multi_aff_from_union_pw_aff(
3171 __isl_take isl_union_pw_aff *upa);
3172 __isl_give isl_union_pw_aff *
3173 isl_union_pw_multi_aff_get_union_pw_aff(
3174 __isl_keep isl_union_pw_multi_aff *upma, int pos);
3175 __isl_give isl_union_pw_aff *
3176 isl_union_pw_aff_val_on_domain(
3177 __isl_take isl_union_set *domain,
3178 __isl_take isl_val *v);
3179 __isl_give isl_union_pw_multi_aff *
3180 isl_union_pw_multi_aff_multi_val_on_domain(
3181 __isl_take isl_union_set *domain,
3182 __isl_take isl_multi_val *mv);
3184 An C<isl_union_pw_aff> that is equal to a (parametric) affine
3185 expression on a given domain can be created using the following
3188 #include <isl/aff.h>
3189 __isl_give isl_union_pw_aff *
3190 isl_union_pw_aff_aff_on_domain(
3191 __isl_take isl_union_set *domain,
3192 __isl_take isl_aff *aff);
3194 A base expression can be added to a union expression using
3195 the following functions.
3197 #include <isl/aff.h>
3198 __isl_give isl_union_pw_aff *
3199 isl_union_pw_aff_add_pw_aff(
3200 __isl_take isl_union_pw_aff *upa,
3201 __isl_take isl_pw_aff *pa);
3202 __isl_give isl_union_pw_multi_aff *
3203 isl_union_pw_multi_aff_add_pw_multi_aff(
3204 __isl_take isl_union_pw_multi_aff *upma,
3205 __isl_take isl_pw_multi_aff *pma);
3207 #include <isl/polynomial.h>
3208 __isl_give isl_union_pw_qpolynomial *
3209 isl_union_pw_qpolynomial_add_pw_qpolynomial(
3210 __isl_take isl_union_pw_qpolynomial *upwqp,
3211 __isl_take isl_pw_qpolynomial *pwqp);
3213 Union expressions can be copied and freed using
3214 the following functions.
3216 #include <isl/aff.h>
3217 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
3218 __isl_keep isl_union_pw_aff *upa);
3219 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
3220 __isl_take isl_union_pw_aff *upa);
3221 __isl_give isl_union_pw_multi_aff *
3222 isl_union_pw_multi_aff_copy(
3223 __isl_keep isl_union_pw_multi_aff *upma);
3224 __isl_null isl_union_pw_multi_aff *
3225 isl_union_pw_multi_aff_free(
3226 __isl_take isl_union_pw_multi_aff *upma);
3228 #include <isl/polynomial.h>
3229 __isl_give isl_union_pw_qpolynomial *
3230 isl_union_pw_qpolynomial_copy(
3231 __isl_keep isl_union_pw_qpolynomial *upwqp);
3232 __isl_null isl_union_pw_qpolynomial *
3233 isl_union_pw_qpolynomial_free(
3234 __isl_take isl_union_pw_qpolynomial *upwqp);
3235 __isl_give isl_union_pw_qpolynomial_fold *
3236 isl_union_pw_qpolynomial_fold_copy(
3237 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3238 __isl_null isl_union_pw_qpolynomial_fold *
3239 isl_union_pw_qpolynomial_fold_free(
3240 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3242 To iterate over the base expressions in a union expression,
3243 use the following functions.
3245 #include <isl/aff.h>
3246 int isl_union_pw_aff_n_pw_aff(
3247 __isl_keep isl_union_pw_aff *upa);
3248 isl_stat isl_union_pw_aff_foreach_pw_aff(
3249 __isl_keep isl_union_pw_aff *upa,
3250 isl_stat (*fn)(__isl_take isl_pw_aff *ma,
3251 void *user), void *user);
3252 int isl_union_pw_multi_aff_n_pw_multi_aff(
3253 __isl_keep isl_union_pw_multi_aff *upma);
3254 isl_stat isl_union_pw_multi_aff_foreach_pw_multi_aff(
3255 __isl_keep isl_union_pw_multi_aff *upma,
3256 isl_stat (*fn)(__isl_take isl_pw_multi_aff *pma,
3257 void *user), void *user);
3259 #include <isl/polynomial.h>
3260 int isl_union_pw_qpolynomial_n_pw_qpolynomial(
3261 __isl_keep isl_union_pw_qpolynomial *upwqp);
3262 isl_stat isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3263 __isl_keep isl_union_pw_qpolynomial *upwqp,
3264 isl_stat (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
3265 void *user), void *user);
3266 int isl_union_pw_qpolynomial_fold_n_pw_qpolynomial_fold(
3267 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3268 isl_stat isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3269 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3270 isl_stat (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3271 void *user), void *user);
3273 To extract the base expression in a given space from a union, use
3274 the following functions.
3276 #include <isl/aff.h>
3277 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
3278 __isl_keep isl_union_pw_aff *upa,
3279 __isl_take isl_space *space);
3280 __isl_give isl_pw_multi_aff *
3281 isl_union_pw_multi_aff_extract_pw_multi_aff(
3282 __isl_keep isl_union_pw_multi_aff *upma,
3283 __isl_take isl_space *space);
3285 #include <isl/polynomial.h>
3286 __isl_give isl_pw_qpolynomial *
3287 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3288 __isl_keep isl_union_pw_qpolynomial *upwqp,
3289 __isl_take isl_space *space);
3291 =head2 Input and Output
3293 For set and relation,
3294 C<isl> supports its own input/output format, which is similar
3295 to the C<Omega> format, but also supports the C<PolyLib> format
3297 For other object types, typically only an C<isl> format is supported.
3299 =head3 C<isl> format
3301 The C<isl> format is similar to that of C<Omega>, but has a different
3302 syntax for describing the parameters and allows for the definition
3303 of an existentially quantified variable as the integer division
3304 of an affine expression.
3305 For example, the set of integers C<i> between C<0> and C<n>
3306 such that C<i % 10 <= 6> can be described as
3308 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
3311 A set or relation can have several disjuncts, separated
3312 by the keyword C<or>. Each disjunct is either a conjunction
3313 of constraints or a projection (C<exists>) of a conjunction
3314 of constraints. The constraints are separated by the keyword
3317 =head3 C<PolyLib> format
3319 If the represented set is a union, then the first line
3320 contains a single number representing the number of disjuncts.
3321 Otherwise, a line containing the number C<1> is optional.
3323 Each disjunct is represented by a matrix of constraints.
3324 The first line contains two numbers representing
3325 the number of rows and columns,
3326 where the number of rows is equal to the number of constraints
3327 and the number of columns is equal to two plus the number of variables.
3328 The following lines contain the actual rows of the constraint matrix.
3329 In each row, the first column indicates whether the constraint
3330 is an equality (C<0>) or inequality (C<1>). The final column
3331 corresponds to the constant term.
3333 If the set is parametric, then the coefficients of the parameters
3334 appear in the last columns before the constant column.
3335 The coefficients of any existentially quantified variables appear
3336 between those of the set variables and those of the parameters.
3338 =head3 Extended C<PolyLib> format
3340 The extended C<PolyLib> format is nearly identical to the
3341 C<PolyLib> format. The only difference is that the line
3342 containing the number of rows and columns of a constraint matrix
3343 also contains four additional numbers:
3344 the number of output dimensions, the number of input dimensions,
3345 the number of local dimensions (i.e., the number of existentially
3346 quantified variables) and the number of parameters.
3347 For sets, the number of ``output'' dimensions is equal
3348 to the number of set dimensions, while the number of ``input''
3353 Objects can be read from input using the following functions.
3355 #include <isl/val.h>
3356 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
3358 __isl_give isl_multi_val *isl_multi_val_read_from_str(
3359 isl_ctx *ctx, const char *str);
3361 #include <isl/set.h>
3362 __isl_give isl_basic_set *isl_basic_set_read_from_file(
3363 isl_ctx *ctx, FILE *input);
3364 __isl_give isl_basic_set *isl_basic_set_read_from_str(
3365 isl_ctx *ctx, const char *str);
3366 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
3368 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
3371 #include <isl/map.h>
3372 __isl_give isl_basic_map *isl_basic_map_read_from_file(
3373 isl_ctx *ctx, FILE *input);
3374 __isl_give isl_basic_map *isl_basic_map_read_from_str(
3375 isl_ctx *ctx, const char *str);
3376 __isl_give isl_map *isl_map_read_from_file(
3377 isl_ctx *ctx, FILE *input);
3378 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
3381 #include <isl/union_set.h>
3382 __isl_give isl_union_set *isl_union_set_read_from_file(
3383 isl_ctx *ctx, FILE *input);
3384 __isl_give isl_union_set *isl_union_set_read_from_str(
3385 isl_ctx *ctx, const char *str);
3387 #include <isl/union_map.h>
3388 __isl_give isl_union_map *isl_union_map_read_from_file(
3389 isl_ctx *ctx, FILE *input);
3390 __isl_give isl_union_map *isl_union_map_read_from_str(
3391 isl_ctx *ctx, const char *str);
3393 #include <isl/aff.h>
3394 __isl_give isl_aff *isl_aff_read_from_str(
3395 isl_ctx *ctx, const char *str);
3396 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3397 isl_ctx *ctx, const char *str);
3398 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3399 isl_ctx *ctx, const char *str);
3400 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3401 isl_ctx *ctx, const char *str);
3402 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
3403 isl_ctx *ctx, const char *str);
3404 __isl_give isl_union_pw_multi_aff *
3405 isl_union_pw_multi_aff_read_from_str(
3406 isl_ctx *ctx, const char *str);
3407 __isl_give isl_multi_union_pw_aff *
3408 isl_multi_union_pw_aff_read_from_str(
3409 isl_ctx *ctx, const char *str);
3411 #include <isl/polynomial.h>
3412 __isl_give isl_union_pw_qpolynomial *
3413 isl_union_pw_qpolynomial_read_from_str(
3414 isl_ctx *ctx, const char *str);
3416 For sets and relations,
3417 the input format is autodetected and may be either the C<PolyLib> format
3418 or the C<isl> format.
3422 Before anything can be printed, an C<isl_printer> needs to
3425 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
3427 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
3428 __isl_null isl_printer *isl_printer_free(
3429 __isl_take isl_printer *printer);
3430 __isl_give char *isl_printer_get_str(
3431 __isl_keep isl_printer *printer);
3433 The printer can be inspected using the following functions.
3435 FILE *isl_printer_get_file(
3436 __isl_keep isl_printer *printer);
3437 int isl_printer_get_output_format(
3438 __isl_keep isl_printer *p);
3439 int isl_printer_get_yaml_style(__isl_keep isl_printer *p);
3441 The behavior of the printer can be modified in various ways
3443 __isl_give isl_printer *isl_printer_set_output_format(
3444 __isl_take isl_printer *p, int output_format);
3445 __isl_give isl_printer *isl_printer_set_indent(
3446 __isl_take isl_printer *p, int indent);
3447 __isl_give isl_printer *isl_printer_set_indent_prefix(
3448 __isl_take isl_printer *p, const char *prefix);
3449 __isl_give isl_printer *isl_printer_indent(
3450 __isl_take isl_printer *p, int indent);
3451 __isl_give isl_printer *isl_printer_set_prefix(
3452 __isl_take isl_printer *p, const char *prefix);
3453 __isl_give isl_printer *isl_printer_set_suffix(
3454 __isl_take isl_printer *p, const char *suffix);
3455 __isl_give isl_printer *isl_printer_set_yaml_style(
3456 __isl_take isl_printer *p, int yaml_style);
3458 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
3459 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
3460 and defaults to C<ISL_FORMAT_ISL>.
3461 Each line in the output is prefixed by C<indent_prefix>,
3462 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
3463 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
3464 In the C<PolyLib> format output,
3465 the coefficients of the existentially quantified variables
3466 appear between those of the set variables and those
3468 The function C<isl_printer_indent> increases the indentation
3469 by the specified amount (which may be negative).
3470 The YAML style may be either C<ISL_YAML_STYLE_BLOCK> or
3471 C<ISL_YAML_STYLE_FLOW> and when we are printing something
3474 To actually print something, use
3476 #include <isl/printer.h>
3477 __isl_give isl_printer *isl_printer_print_double(
3478 __isl_take isl_printer *p, double d);
3480 #include <isl/val.h>
3481 __isl_give isl_printer *isl_printer_print_val(
3482 __isl_take isl_printer *p, __isl_keep isl_val *v);
3484 #include <isl/set.h>
3485 __isl_give isl_printer *isl_printer_print_basic_set(
3486 __isl_take isl_printer *printer,
3487 __isl_keep isl_basic_set *bset);
3488 __isl_give isl_printer *isl_printer_print_set(
3489 __isl_take isl_printer *printer,
3490 __isl_keep isl_set *set);
3492 #include <isl/map.h>
3493 __isl_give isl_printer *isl_printer_print_basic_map(
3494 __isl_take isl_printer *printer,
3495 __isl_keep isl_basic_map *bmap);
3496 __isl_give isl_printer *isl_printer_print_map(
3497 __isl_take isl_printer *printer,
3498 __isl_keep isl_map *map);
3500 #include <isl/union_set.h>
3501 __isl_give isl_printer *isl_printer_print_union_set(
3502 __isl_take isl_printer *p,
3503 __isl_keep isl_union_set *uset);
3505 #include <isl/union_map.h>
3506 __isl_give isl_printer *isl_printer_print_union_map(
3507 __isl_take isl_printer *p,
3508 __isl_keep isl_union_map *umap);
3510 #include <isl/val.h>
3511 __isl_give isl_printer *isl_printer_print_multi_val(
3512 __isl_take isl_printer *p,
3513 __isl_keep isl_multi_val *mv);
3515 #include <isl/aff.h>
3516 __isl_give isl_printer *isl_printer_print_aff(
3517 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3518 __isl_give isl_printer *isl_printer_print_multi_aff(
3519 __isl_take isl_printer *p,
3520 __isl_keep isl_multi_aff *maff);
3521 __isl_give isl_printer *isl_printer_print_pw_aff(
3522 __isl_take isl_printer *p,
3523 __isl_keep isl_pw_aff *pwaff);
3524 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3525 __isl_take isl_printer *p,
3526 __isl_keep isl_pw_multi_aff *pma);
3527 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3528 __isl_take isl_printer *p,
3529 __isl_keep isl_multi_pw_aff *mpa);
3530 __isl_give isl_printer *isl_printer_print_union_pw_aff(
3531 __isl_take isl_printer *p,
3532 __isl_keep isl_union_pw_aff *upa);
3533 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3534 __isl_take isl_printer *p,
3535 __isl_keep isl_union_pw_multi_aff *upma);
3536 __isl_give isl_printer *
3537 isl_printer_print_multi_union_pw_aff(
3538 __isl_take isl_printer *p,
3539 __isl_keep isl_multi_union_pw_aff *mupa);
3541 #include <isl/polynomial.h>
3542 __isl_give isl_printer *isl_printer_print_qpolynomial(
3543 __isl_take isl_printer *p,
3544 __isl_keep isl_qpolynomial *qp);
3545 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3546 __isl_take isl_printer *p,
3547 __isl_keep isl_pw_qpolynomial *pwqp);
3548 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3549 __isl_take isl_printer *p,
3550 __isl_keep isl_union_pw_qpolynomial *upwqp);
3552 __isl_give isl_printer *
3553 isl_printer_print_pw_qpolynomial_fold(
3554 __isl_take isl_printer *p,
3555 __isl_keep isl_pw_qpolynomial_fold *pwf);
3556 __isl_give isl_printer *
3557 isl_printer_print_union_pw_qpolynomial_fold(
3558 __isl_take isl_printer *p,
3559 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3561 For C<isl_printer_print_qpolynomial>,
3562 C<isl_printer_print_pw_qpolynomial> and
3563 C<isl_printer_print_pw_qpolynomial_fold>,
3564 the output format of the printer
3565 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3566 For C<isl_printer_print_union_pw_qpolynomial> and
3567 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
3569 In case of printing in C<ISL_FORMAT_C>, the user may want
3570 to set the names of all dimensions first.
3572 C<isl> also provides limited support for printing YAML documents,
3573 just enough for the internal use for printing such documents.
3575 #include <isl/printer.h>
3576 __isl_give isl_printer *isl_printer_yaml_start_mapping(
3577 __isl_take isl_printer *p);
3578 __isl_give isl_printer *isl_printer_yaml_end_mapping(
3579 __isl_take isl_printer *p);
3580 __isl_give isl_printer *isl_printer_yaml_start_sequence(
3581 __isl_take isl_printer *p);
3582 __isl_give isl_printer *isl_printer_yaml_end_sequence(
3583 __isl_take isl_printer *p);
3584 __isl_give isl_printer *isl_printer_yaml_next(
3585 __isl_take isl_printer *p);
3587 A document is started by a call to either
3588 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3589 Anything printed to the printer after such a call belong to the
3590 first key of the mapping or the first element in the sequence.
3591 The function C<isl_printer_yaml_next> moves to the value if
3592 we are currently printing a mapping key, the next key if we
3593 are printing a value or the next element if we are printing
3594 an element in a sequence.
3595 Nested mappings and sequences are initiated by the same
3596 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3597 Each call to these functions needs to have a corresponding call to
3598 C<isl_printer_yaml_end_mapping> or C<isl_printer_yaml_end_sequence>.
3600 When called on a file printer, the following function flushes
3601 the file. When called on a string printer, the buffer is cleared.
3603 __isl_give isl_printer *isl_printer_flush(
3604 __isl_take isl_printer *p);
3606 Alternatively, a string representation can be obtained
3607 directly using the following functions, which always print
3610 #include <isl/space.h>
3611 __isl_give char *isl_space_to_str(
3612 __isl_keep isl_space *space);
3614 #include <isl/val.h>
3615 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
3616 __isl_give char *isl_multi_val_to_str(
3617 __isl_keep isl_multi_val *mv);
3619 #include <isl/set.h>
3620 __isl_give char *isl_set_to_str(
3621 __isl_keep isl_set *set);
3623 #include <isl/union_set.h>
3624 __isl_give char *isl_union_set_to_str(
3625 __isl_keep isl_union_set *uset);
3627 #include <isl/map.h>
3628 __isl_give char *isl_map_to_str(
3629 __isl_keep isl_map *map);
3631 #include <isl/union_map.h>
3632 __isl_give char *isl_union_map_to_str(
3633 __isl_keep isl_union_map *umap);
3635 #include <isl/aff.h>
3636 __isl_give char *isl_multi_aff_to_str(
3637 __isl_keep isl_multi_aff *aff);
3638 __isl_give char *isl_union_pw_aff_to_str(
3639 __isl_keep isl_union_pw_aff *upa);
3640 __isl_give char *isl_union_pw_multi_aff_to_str(
3641 __isl_keep isl_union_pw_multi_aff *upma);
3642 __isl_give char *isl_multi_union_pw_aff_to_str(
3643 __isl_keep isl_multi_union_pw_aff *mupa);
3647 =head3 Unary Properties
3653 The following functions test whether the given set or relation
3654 contains any integer points. The ``plain'' variants do not perform
3655 any computations, but simply check if the given set or relation
3656 is already known to be empty.
3658 isl_bool isl_basic_set_plain_is_empty(
3659 __isl_keep isl_basic_set *bset);
3660 isl_bool isl_basic_set_is_empty(
3661 __isl_keep isl_basic_set *bset);
3662 isl_bool isl_set_plain_is_empty(
3663 __isl_keep isl_set *set);
3664 isl_bool isl_set_is_empty(__isl_keep isl_set *set);
3665 isl_bool isl_union_set_is_empty(
3666 __isl_keep isl_union_set *uset);
3667 isl_bool isl_basic_map_plain_is_empty(
3668 __isl_keep isl_basic_map *bmap);
3669 isl_bool isl_basic_map_is_empty(
3670 __isl_keep isl_basic_map *bmap);
3671 isl_bool isl_map_plain_is_empty(
3672 __isl_keep isl_map *map);
3673 isl_bool isl_map_is_empty(__isl_keep isl_map *map);
3674 isl_bool isl_union_map_is_empty(
3675 __isl_keep isl_union_map *umap);
3677 =item * Universality
3679 isl_bool isl_basic_set_is_universe(
3680 __isl_keep isl_basic_set *bset);
3681 isl_bool isl_basic_map_is_universe(
3682 __isl_keep isl_basic_map *bmap);
3683 isl_bool isl_set_plain_is_universe(
3684 __isl_keep isl_set *set);
3685 isl_bool isl_map_plain_is_universe(
3686 __isl_keep isl_map *map);
3688 =item * Single-valuedness
3690 #include <isl/set.h>
3691 isl_bool isl_set_is_singleton(__isl_keep isl_set *set);
3693 #include <isl/map.h>
3694 isl_bool isl_basic_map_is_single_valued(
3695 __isl_keep isl_basic_map *bmap);
3696 isl_bool isl_map_plain_is_single_valued(
3697 __isl_keep isl_map *map);
3698 isl_bool isl_map_is_single_valued(__isl_keep isl_map *map);
3700 #include <isl/union_map.h>
3701 isl_bool isl_union_map_is_single_valued(
3702 __isl_keep isl_union_map *umap);
3706 isl_bool isl_map_plain_is_injective(
3707 __isl_keep isl_map *map);
3708 isl_bool isl_map_is_injective(
3709 __isl_keep isl_map *map);
3710 isl_bool isl_union_map_plain_is_injective(
3711 __isl_keep isl_union_map *umap);
3712 isl_bool isl_union_map_is_injective(
3713 __isl_keep isl_union_map *umap);
3717 isl_bool isl_map_is_bijective(
3718 __isl_keep isl_map *map);
3719 isl_bool isl_union_map_is_bijective(
3720 __isl_keep isl_union_map *umap);
3724 __isl_give isl_val *
3725 isl_basic_map_plain_get_val_if_fixed(
3726 __isl_keep isl_basic_map *bmap,
3727 enum isl_dim_type type, unsigned pos);
3728 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
3729 __isl_keep isl_set *set,
3730 enum isl_dim_type type, unsigned pos);
3731 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
3732 __isl_keep isl_map *map,
3733 enum isl_dim_type type, unsigned pos);
3735 If the set or relation obviously lies on a hyperplane where the given dimension
3736 has a fixed value, then return that value.
3737 Otherwise return NaN.
3741 isl_stat isl_set_dim_residue_class_val(
3742 __isl_keep isl_set *set,
3743 int pos, __isl_give isl_val **modulo,
3744 __isl_give isl_val **residue);
3746 Check if the values of the given set dimension are equal to a fixed
3747 value modulo some integer value. If so, assign the modulo to C<*modulo>
3748 and the fixed value to C<*residue>. If the given dimension attains only
3749 a single value, then assign C<0> to C<*modulo> and the fixed value to
3751 If the dimension does not attain only a single value and if no modulo
3752 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
3756 To check whether the description of a set, relation or function depends
3757 on one or more given dimensions,
3758 the following functions can be used.
3760 #include <isl/constraint.h>
3761 isl_bool isl_constraint_involves_dims(
3762 __isl_keep isl_constraint *constraint,
3763 enum isl_dim_type type, unsigned first, unsigned n);
3765 #include <isl/set.h>
3766 isl_bool isl_basic_set_involves_dims(
3767 __isl_keep isl_basic_set *bset,
3768 enum isl_dim_type type, unsigned first, unsigned n);
3769 isl_bool isl_set_involves_dims(__isl_keep isl_set *set,
3770 enum isl_dim_type type, unsigned first, unsigned n);
3772 #include <isl/map.h>
3773 isl_bool isl_basic_map_involves_dims(
3774 __isl_keep isl_basic_map *bmap,
3775 enum isl_dim_type type, unsigned first, unsigned n);
3776 isl_bool isl_map_involves_dims(__isl_keep isl_map *map,
3777 enum isl_dim_type type, unsigned first, unsigned n);
3779 #include <isl/union_map.h>
3780 isl_bool isl_union_map_involves_dims(
3781 __isl_keep isl_union_map *umap,
3782 enum isl_dim_type type, unsigned first, unsigned n);
3784 #include <isl/aff.h>
3785 isl_bool isl_aff_involves_dims(__isl_keep isl_aff *aff,
3786 enum isl_dim_type type, unsigned first, unsigned n);
3787 isl_bool isl_pw_aff_involves_dims(
3788 __isl_keep isl_pw_aff *pwaff,
3789 enum isl_dim_type type, unsigned first, unsigned n);
3790 isl_bool isl_multi_aff_involves_dims(
3791 __isl_keep isl_multi_aff *ma,
3792 enum isl_dim_type type, unsigned first, unsigned n);
3793 isl_bool isl_multi_pw_aff_involves_dims(
3794 __isl_keep isl_multi_pw_aff *mpa,
3795 enum isl_dim_type type, unsigned first, unsigned n);
3797 #include <isl/polynomial.h>
3798 isl_bool isl_qpolynomial_involves_dims(
3799 __isl_keep isl_qpolynomial *qp,
3800 enum isl_dim_type type, unsigned first, unsigned n);
3802 Similarly, the following functions can be used to check whether
3803 a given dimension is involved in any lower or upper bound.
3805 #include <isl/set.h>
3806 isl_bool isl_set_dim_has_any_lower_bound(
3807 __isl_keep isl_set *set,
3808 enum isl_dim_type type, unsigned pos);
3809 isl_bool isl_set_dim_has_any_upper_bound(
3810 __isl_keep isl_set *set,
3811 enum isl_dim_type type, unsigned pos);
3813 Note that these functions return true even if there is a bound on
3814 the dimension on only some of the basic sets of C<set>.
3815 To check if they have a bound for all of the basic sets in C<set>,
3816 use the following functions instead.
3818 #include <isl/set.h>
3819 isl_bool isl_set_dim_has_lower_bound(
3820 __isl_keep isl_set *set,
3821 enum isl_dim_type type, unsigned pos);
3822 isl_bool isl_set_dim_has_upper_bound(
3823 __isl_keep isl_set *set,
3824 enum isl_dim_type type, unsigned pos);
3828 To check whether a set is a parameter domain, use this function:
3830 isl_bool isl_set_is_params(__isl_keep isl_set *set);
3831 isl_bool isl_union_set_is_params(
3832 __isl_keep isl_union_set *uset);
3836 The following functions check whether the space of the given
3837 (basic) set or relation range is a wrapped relation.
3839 #include <isl/space.h>
3840 isl_bool isl_space_is_wrapping(
3841 __isl_keep isl_space *space);
3842 isl_bool isl_space_domain_is_wrapping(
3843 __isl_keep isl_space *space);
3844 isl_bool isl_space_range_is_wrapping(
3845 __isl_keep isl_space *space);
3847 #include <isl/set.h>
3848 isl_bool isl_basic_set_is_wrapping(
3849 __isl_keep isl_basic_set *bset);
3850 isl_bool isl_set_is_wrapping(__isl_keep isl_set *set);
3852 #include <isl/map.h>
3853 isl_bool isl_map_domain_is_wrapping(
3854 __isl_keep isl_map *map);
3855 isl_bool isl_map_range_is_wrapping(
3856 __isl_keep isl_map *map);
3858 #include <isl/val.h>
3859 isl_bool isl_multi_val_range_is_wrapping(
3860 __isl_keep isl_multi_val *mv);
3862 #include <isl/aff.h>
3863 isl_bool isl_multi_aff_range_is_wrapping(
3864 __isl_keep isl_multi_aff *ma);
3865 isl_bool isl_multi_pw_aff_range_is_wrapping(
3866 __isl_keep isl_multi_pw_aff *mpa);
3867 isl_bool isl_multi_union_pw_aff_range_is_wrapping(
3868 __isl_keep isl_multi_union_pw_aff *mupa);
3870 The input to C<isl_space_is_wrapping> should
3871 be the space of a set, while that of
3872 C<isl_space_domain_is_wrapping> and
3873 C<isl_space_range_is_wrapping> should be the space of a relation.
3875 =item * Internal Product
3877 isl_bool isl_basic_map_can_zip(
3878 __isl_keep isl_basic_map *bmap);
3879 isl_bool isl_map_can_zip(__isl_keep isl_map *map);
3881 Check whether the product of domain and range of the given relation
3883 i.e., whether both domain and range are nested relations.
3887 isl_bool isl_basic_map_can_curry(
3888 __isl_keep isl_basic_map *bmap);
3889 isl_bool isl_map_can_curry(__isl_keep isl_map *map);
3891 Check whether the domain of the (basic) relation is a wrapped relation.
3893 isl_bool isl_basic_map_can_uncurry(
3894 __isl_keep isl_basic_map *bmap);
3895 isl_bool isl_map_can_uncurry(__isl_keep isl_map *map);
3897 Check whether the range of the (basic) relation is a wrapped relation.
3899 =item * Special Values
3901 #include <isl/aff.h>
3902 isl_bool isl_aff_is_cst(__isl_keep isl_aff *aff);
3903 isl_bool isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3905 Check whether the given expression is a constant.
3907 #include <isl/aff.h>
3908 isl_bool isl_aff_is_nan(__isl_keep isl_aff *aff);
3909 isl_bool isl_pw_aff_involves_nan(
3910 __isl_keep isl_pw_aff *pa);
3912 #include <isl/polynomial.h>
3913 isl_bool isl_qpolynomial_fold_is_nan(
3914 __isl_keep isl_qpolynomial_fold *fold);
3916 Check whether the given expression is equal to or involves NaN.
3918 #include <isl/aff.h>
3919 isl_bool isl_aff_plain_is_zero(
3920 __isl_keep isl_aff *aff);
3922 Check whether the affine expression is obviously zero.
3926 =head3 Binary Properties
3932 The following functions check whether two objects
3933 represent the same set, relation or function.
3934 The C<plain> variants only return true if the objects
3935 are obviously the same. That is, they may return false
3936 even if the objects are the same, but they will never
3937 return true if the objects are not the same.
3939 #include <isl/set.h>
3940 isl_bool isl_basic_set_plain_is_equal(
3941 __isl_keep isl_basic_set *bset1,
3942 __isl_keep isl_basic_set *bset2);
3943 isl_bool isl_basic_set_is_equal(
3944 __isl_keep isl_basic_set *bset1,
3945 __isl_keep isl_basic_set *bset2);
3946 isl_bool isl_set_plain_is_equal(
3947 __isl_keep isl_set *set1,
3948 __isl_keep isl_set *set2);
3949 isl_bool isl_set_is_equal(__isl_keep isl_set *set1,
3950 __isl_keep isl_set *set2);
3952 #include <isl/map.h>
3953 isl_bool isl_basic_map_is_equal(
3954 __isl_keep isl_basic_map *bmap1,
3955 __isl_keep isl_basic_map *bmap2);
3956 isl_bool isl_map_is_equal(__isl_keep isl_map *map1,
3957 __isl_keep isl_map *map2);
3958 isl_bool isl_map_plain_is_equal(
3959 __isl_keep isl_map *map1,
3960 __isl_keep isl_map *map2);
3962 #include <isl/union_set.h>
3963 isl_bool isl_union_set_is_equal(
3964 __isl_keep isl_union_set *uset1,
3965 __isl_keep isl_union_set *uset2);
3967 #include <isl/union_map.h>
3968 isl_bool isl_union_map_is_equal(
3969 __isl_keep isl_union_map *umap1,
3970 __isl_keep isl_union_map *umap2);
3972 #include <isl/aff.h>
3973 isl_bool isl_aff_plain_is_equal(
3974 __isl_keep isl_aff *aff1,
3975 __isl_keep isl_aff *aff2);
3976 isl_bool isl_multi_aff_plain_is_equal(
3977 __isl_keep isl_multi_aff *maff1,
3978 __isl_keep isl_multi_aff *maff2);
3979 isl_bool isl_pw_aff_plain_is_equal(
3980 __isl_keep isl_pw_aff *pwaff1,
3981 __isl_keep isl_pw_aff *pwaff2);
3982 isl_bool isl_pw_multi_aff_plain_is_equal(
3983 __isl_keep isl_pw_multi_aff *pma1,
3984 __isl_keep isl_pw_multi_aff *pma2);
3985 isl_bool isl_multi_pw_aff_plain_is_equal(
3986 __isl_keep isl_multi_pw_aff *mpa1,
3987 __isl_keep isl_multi_pw_aff *mpa2);
3988 isl_bool isl_multi_pw_aff_is_equal(
3989 __isl_keep isl_multi_pw_aff *mpa1,
3990 __isl_keep isl_multi_pw_aff *mpa2);
3991 isl_bool isl_union_pw_aff_plain_is_equal(
3992 __isl_keep isl_union_pw_aff *upa1,
3993 __isl_keep isl_union_pw_aff *upa2);
3994 isl_bool isl_union_pw_multi_aff_plain_is_equal(
3995 __isl_keep isl_union_pw_multi_aff *upma1,
3996 __isl_keep isl_union_pw_multi_aff *upma2);
3997 isl_bool isl_multi_union_pw_aff_plain_is_equal(
3998 __isl_keep isl_multi_union_pw_aff *mupa1,
3999 __isl_keep isl_multi_union_pw_aff *mupa2);
4001 #include <isl/polynomial.h>
4002 isl_bool isl_union_pw_qpolynomial_plain_is_equal(
4003 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4004 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4005 isl_bool isl_union_pw_qpolynomial_fold_plain_is_equal(
4006 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4007 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4009 =item * Disjointness
4011 #include <isl/set.h>
4012 isl_bool isl_basic_set_is_disjoint(
4013 __isl_keep isl_basic_set *bset1,
4014 __isl_keep isl_basic_set *bset2);
4015 isl_bool isl_set_plain_is_disjoint(
4016 __isl_keep isl_set *set1,
4017 __isl_keep isl_set *set2);
4018 isl_bool isl_set_is_disjoint(__isl_keep isl_set *set1,
4019 __isl_keep isl_set *set2);
4021 #include <isl/map.h>
4022 isl_bool isl_basic_map_is_disjoint(
4023 __isl_keep isl_basic_map *bmap1,
4024 __isl_keep isl_basic_map *bmap2);
4025 isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1,
4026 __isl_keep isl_map *map2);
4028 #include <isl/union_set.h>
4029 isl_bool isl_union_set_is_disjoint(
4030 __isl_keep isl_union_set *uset1,
4031 __isl_keep isl_union_set *uset2);
4033 #include <isl/union_map.h>
4034 isl_bool isl_union_map_is_disjoint(
4035 __isl_keep isl_union_map *umap1,
4036 __isl_keep isl_union_map *umap2);
4040 isl_bool isl_basic_set_is_subset(
4041 __isl_keep isl_basic_set *bset1,
4042 __isl_keep isl_basic_set *bset2);
4043 isl_bool isl_set_is_subset(__isl_keep isl_set *set1,
4044 __isl_keep isl_set *set2);
4045 isl_bool isl_set_is_strict_subset(
4046 __isl_keep isl_set *set1,
4047 __isl_keep isl_set *set2);
4048 isl_bool isl_union_set_is_subset(
4049 __isl_keep isl_union_set *uset1,
4050 __isl_keep isl_union_set *uset2);
4051 isl_bool isl_union_set_is_strict_subset(
4052 __isl_keep isl_union_set *uset1,
4053 __isl_keep isl_union_set *uset2);
4054 isl_bool isl_basic_map_is_subset(
4055 __isl_keep isl_basic_map *bmap1,
4056 __isl_keep isl_basic_map *bmap2);
4057 isl_bool isl_basic_map_is_strict_subset(
4058 __isl_keep isl_basic_map *bmap1,
4059 __isl_keep isl_basic_map *bmap2);
4060 isl_bool isl_map_is_subset(
4061 __isl_keep isl_map *map1,
4062 __isl_keep isl_map *map2);
4063 isl_bool isl_map_is_strict_subset(
4064 __isl_keep isl_map *map1,
4065 __isl_keep isl_map *map2);
4066 isl_bool isl_union_map_is_subset(
4067 __isl_keep isl_union_map *umap1,
4068 __isl_keep isl_union_map *umap2);
4069 isl_bool isl_union_map_is_strict_subset(
4070 __isl_keep isl_union_map *umap1,
4071 __isl_keep isl_union_map *umap2);
4073 Check whether the first argument is a (strict) subset of the
4078 Every comparison function returns a negative value if the first
4079 argument is considered smaller than the second, a positive value
4080 if the first argument is considered greater and zero if the two
4081 constraints are considered the same by the comparison criterion.
4083 #include <isl/constraint.h>
4084 int isl_constraint_plain_cmp(
4085 __isl_keep isl_constraint *c1,
4086 __isl_keep isl_constraint *c2);
4088 This function is useful for sorting C<isl_constraint>s.
4089 The order depends on the internal representation of the inputs.
4090 The order is fixed over different calls to the function (assuming
4091 the internal representation of the inputs has not changed), but may
4092 change over different versions of C<isl>.
4094 #include <isl/constraint.h>
4095 int isl_constraint_cmp_last_non_zero(
4096 __isl_keep isl_constraint *c1,
4097 __isl_keep isl_constraint *c2);
4099 This function can be used to sort constraints that live in the same
4100 local space. Constraints that involve ``earlier'' dimensions or
4101 that have a smaller coefficient for the shared latest dimension
4102 are considered smaller than other constraints.
4103 This function only defines a B<partial> order.
4105 #include <isl/set.h>
4106 int isl_set_plain_cmp(__isl_keep isl_set *set1,
4107 __isl_keep isl_set *set2);
4109 This function is useful for sorting C<isl_set>s.
4110 The order depends on the internal representation of the inputs.
4111 The order is fixed over different calls to the function (assuming
4112 the internal representation of the inputs has not changed), but may
4113 change over different versions of C<isl>.
4115 #include <isl/aff.h>
4116 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4117 __isl_keep isl_pw_aff *pa2);
4119 The function C<isl_pw_aff_plain_cmp> can be used to sort
4120 C<isl_pw_aff>s. The order is not strictly defined.
4121 The current order sorts expressions that only involve
4122 earlier dimensions before those that involve later dimensions.
4126 =head2 Unary Operations
4132 __isl_give isl_set *isl_set_complement(
4133 __isl_take isl_set *set);
4134 __isl_give isl_map *isl_map_complement(
4135 __isl_take isl_map *map);
4139 #include <isl/space.h>
4140 __isl_give isl_space *isl_space_reverse(
4141 __isl_take isl_space *space);
4143 #include <isl/map.h>
4144 __isl_give isl_basic_map *isl_basic_map_reverse(
4145 __isl_take isl_basic_map *bmap);
4146 __isl_give isl_map *isl_map_reverse(
4147 __isl_take isl_map *map);
4149 #include <isl/union_map.h>
4150 __isl_give isl_union_map *isl_union_map_reverse(
4151 __isl_take isl_union_map *umap);
4155 #include <isl/space.h>
4156 __isl_give isl_space *isl_space_domain(
4157 __isl_take isl_space *space);
4158 __isl_give isl_space *isl_space_range(
4159 __isl_take isl_space *space);
4160 __isl_give isl_space *isl_space_params(
4161 __isl_take isl_space *space);
4163 #include <isl/local_space.h>
4164 __isl_give isl_local_space *isl_local_space_domain(
4165 __isl_take isl_local_space *ls);
4166 __isl_give isl_local_space *isl_local_space_range(
4167 __isl_take isl_local_space *ls);
4169 #include <isl/set.h>
4170 __isl_give isl_basic_set *isl_basic_set_project_out(
4171 __isl_take isl_basic_set *bset,
4172 enum isl_dim_type type, unsigned first, unsigned n);
4173 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
4174 enum isl_dim_type type, unsigned first, unsigned n);
4175 __isl_give isl_basic_set *isl_basic_set_params(
4176 __isl_take isl_basic_set *bset);
4177 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
4179 #include <isl/map.h>
4180 __isl_give isl_basic_map *isl_basic_map_project_out(
4181 __isl_take isl_basic_map *bmap,
4182 enum isl_dim_type type, unsigned first, unsigned n);
4183 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
4184 enum isl_dim_type type, unsigned first, unsigned n);
4185 __isl_give isl_basic_set *isl_basic_map_domain(
4186 __isl_take isl_basic_map *bmap);
4187 __isl_give isl_basic_set *isl_basic_map_range(
4188 __isl_take isl_basic_map *bmap);
4189 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
4190 __isl_give isl_set *isl_map_domain(
4191 __isl_take isl_map *bmap);
4192 __isl_give isl_set *isl_map_range(
4193 __isl_take isl_map *map);
4195 #include <isl/union_set.h>
4196 __isl_give isl_union_set *isl_union_set_project_out(
4197 __isl_take isl_union_set *uset,
4198 enum isl_dim_type type,
4199 unsigned first, unsigned n);
4200 __isl_give isl_set *isl_union_set_params(
4201 __isl_take isl_union_set *uset);
4203 The function C<isl_union_set_project_out> can only project out
4206 #include <isl/union_map.h>
4207 __isl_give isl_union_map *isl_union_map_project_out(
4208 __isl_take isl_union_map *umap,
4209 enum isl_dim_type type, unsigned first, unsigned n);
4210 __isl_give isl_set *isl_union_map_params(
4211 __isl_take isl_union_map *umap);
4212 __isl_give isl_union_set *isl_union_map_domain(
4213 __isl_take isl_union_map *umap);
4214 __isl_give isl_union_set *isl_union_map_range(
4215 __isl_take isl_union_map *umap);
4217 The function C<isl_union_map_project_out> can only project out
4220 #include <isl/aff.h>
4221 __isl_give isl_aff *isl_aff_project_domain_on_params(
4222 __isl_take isl_aff *aff);
4223 __isl_give isl_pw_multi_aff *
4224 isl_pw_multi_aff_project_domain_on_params(
4225 __isl_take isl_pw_multi_aff *pma);
4226 __isl_give isl_set *isl_pw_aff_domain(
4227 __isl_take isl_pw_aff *pwaff);
4228 __isl_give isl_set *isl_pw_multi_aff_domain(
4229 __isl_take isl_pw_multi_aff *pma);
4230 __isl_give isl_set *isl_multi_pw_aff_domain(
4231 __isl_take isl_multi_pw_aff *mpa);
4232 __isl_give isl_union_set *isl_union_pw_aff_domain(
4233 __isl_take isl_union_pw_aff *upa);
4234 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4235 __isl_take isl_union_pw_multi_aff *upma);
4236 __isl_give isl_union_set *
4237 isl_multi_union_pw_aff_domain(
4238 __isl_take isl_multi_union_pw_aff *mupa);
4239 __isl_give isl_set *isl_pw_aff_params(
4240 __isl_take isl_pw_aff *pwa);
4242 The function C<isl_multi_union_pw_aff_domain> requires its
4243 input to have at least one set dimension.
4245 #include <isl/polynomial.h>
4246 __isl_give isl_qpolynomial *
4247 isl_qpolynomial_project_domain_on_params(
4248 __isl_take isl_qpolynomial *qp);
4249 __isl_give isl_pw_qpolynomial *
4250 isl_pw_qpolynomial_project_domain_on_params(
4251 __isl_take isl_pw_qpolynomial *pwqp);
4252 __isl_give isl_pw_qpolynomial_fold *
4253 isl_pw_qpolynomial_fold_project_domain_on_params(
4254 __isl_take isl_pw_qpolynomial_fold *pwf);
4255 __isl_give isl_set *isl_pw_qpolynomial_domain(
4256 __isl_take isl_pw_qpolynomial *pwqp);
4257 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4258 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4259 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4260 __isl_take isl_union_pw_qpolynomial *upwqp);
4262 #include <isl/space.h>
4263 __isl_give isl_space *isl_space_domain_map(
4264 __isl_take isl_space *space);
4265 __isl_give isl_space *isl_space_range_map(
4266 __isl_take isl_space *space);
4268 #include <isl/map.h>
4269 __isl_give isl_map *isl_set_wrapped_domain_map(
4270 __isl_take isl_set *set);
4271 __isl_give isl_basic_map *isl_basic_map_domain_map(
4272 __isl_take isl_basic_map *bmap);
4273 __isl_give isl_basic_map *isl_basic_map_range_map(
4274 __isl_take isl_basic_map *bmap);
4275 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
4276 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
4278 #include <isl/union_map.h>
4279 __isl_give isl_union_map *isl_union_map_domain_map(
4280 __isl_take isl_union_map *umap);
4281 __isl_give isl_union_pw_multi_aff *
4282 isl_union_map_domain_map_union_pw_multi_aff(
4283 __isl_take isl_union_map *umap);
4284 __isl_give isl_union_map *isl_union_map_range_map(
4285 __isl_take isl_union_map *umap);
4286 __isl_give isl_union_map *
4287 isl_union_set_wrapped_domain_map(
4288 __isl_take isl_union_set *uset);
4290 The functions above construct a (basic, regular or union) relation
4291 that maps (a wrapped version of) the input relation to its domain or range.
4292 C<isl_set_wrapped_domain_map> maps the input set to the domain
4293 of its wrapped relation.
4297 __isl_give isl_basic_set *isl_basic_set_eliminate(
4298 __isl_take isl_basic_set *bset,
4299 enum isl_dim_type type,
4300 unsigned first, unsigned n);
4301 __isl_give isl_set *isl_set_eliminate(
4302 __isl_take isl_set *set, enum isl_dim_type type,
4303 unsigned first, unsigned n);
4304 __isl_give isl_basic_map *isl_basic_map_eliminate(
4305 __isl_take isl_basic_map *bmap,
4306 enum isl_dim_type type,
4307 unsigned first, unsigned n);
4308 __isl_give isl_map *isl_map_eliminate(
4309 __isl_take isl_map *map, enum isl_dim_type type,
4310 unsigned first, unsigned n);
4312 Eliminate the coefficients for the given dimensions from the constraints,
4313 without removing the dimensions.
4315 =item * Constructing a set from a parameter domain
4317 A zero-dimensional space or (basic) set can be constructed
4318 on a given parameter domain using the following functions.
4320 #include <isl/space.h>
4321 __isl_give isl_space *isl_space_set_from_params(
4322 __isl_take isl_space *space);
4324 #include <isl/set.h>
4325 __isl_give isl_basic_set *isl_basic_set_from_params(
4326 __isl_take isl_basic_set *bset);
4327 __isl_give isl_set *isl_set_from_params(
4328 __isl_take isl_set *set);
4330 =item * Constructing a relation from a set
4332 Create a relation with the given set as domain or range.
4333 The range or domain of the created relation is a zero-dimensional
4334 flat anonymous space.
4336 #include <isl/space.h>
4337 __isl_give isl_space *isl_space_from_domain(
4338 __isl_take isl_space *space);
4339 __isl_give isl_space *isl_space_from_range(
4340 __isl_take isl_space *space);
4341 __isl_give isl_space *isl_space_map_from_set(
4342 __isl_take isl_space *space);
4343 __isl_give isl_space *isl_space_map_from_domain_and_range(
4344 __isl_take isl_space *domain,
4345 __isl_take isl_space *range);
4347 #include <isl/local_space.h>
4348 __isl_give isl_local_space *isl_local_space_from_domain(
4349 __isl_take isl_local_space *ls);
4351 #include <isl/map.h>
4352 __isl_give isl_map *isl_map_from_domain(
4353 __isl_take isl_set *set);
4354 __isl_give isl_map *isl_map_from_range(
4355 __isl_take isl_set *set);
4357 #include <isl/val.h>
4358 __isl_give isl_multi_val *isl_multi_val_from_range(
4359 __isl_take isl_multi_val *mv);
4361 #include <isl/aff.h>
4362 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4363 __isl_take isl_multi_aff *ma);
4364 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4365 __isl_take isl_pw_aff *pwa);
4366 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4367 __isl_take isl_multi_pw_aff *mpa);
4368 __isl_give isl_multi_union_pw_aff *
4369 isl_multi_union_pw_aff_from_range(
4370 __isl_take isl_multi_union_pw_aff *mupa);
4371 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4372 __isl_take isl_set *set);
4373 __isl_give isl_union_pw_multi_aff *
4374 isl_union_pw_multi_aff_from_domain(
4375 __isl_take isl_union_set *uset);
4379 #include <isl/set.h>
4380 __isl_give isl_basic_set *isl_basic_set_fix_si(
4381 __isl_take isl_basic_set *bset,
4382 enum isl_dim_type type, unsigned pos, int value);
4383 __isl_give isl_basic_set *isl_basic_set_fix_val(
4384 __isl_take isl_basic_set *bset,
4385 enum isl_dim_type type, unsigned pos,
4386 __isl_take isl_val *v);
4387 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
4388 enum isl_dim_type type, unsigned pos, int value);
4389 __isl_give isl_set *isl_set_fix_val(
4390 __isl_take isl_set *set,
4391 enum isl_dim_type type, unsigned pos,
4392 __isl_take isl_val *v);
4394 #include <isl/map.h>
4395 __isl_give isl_basic_map *isl_basic_map_fix_si(
4396 __isl_take isl_basic_map *bmap,
4397 enum isl_dim_type type, unsigned pos, int value);
4398 __isl_give isl_basic_map *isl_basic_map_fix_val(
4399 __isl_take isl_basic_map *bmap,
4400 enum isl_dim_type type, unsigned pos,
4401 __isl_take isl_val *v);
4402 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
4403 enum isl_dim_type type, unsigned pos, int value);
4404 __isl_give isl_map *isl_map_fix_val(
4405 __isl_take isl_map *map,
4406 enum isl_dim_type type, unsigned pos,
4407 __isl_take isl_val *v);
4409 #include <isl/aff.h>
4410 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4411 __isl_take isl_pw_multi_aff *pma,
4412 enum isl_dim_type type, unsigned pos, int value);
4414 #include <isl/polynomial.h>
4415 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4416 __isl_take isl_pw_qpolynomial *pwqp,
4417 enum isl_dim_type type, unsigned n,
4418 __isl_take isl_val *v);
4420 Intersect the set, relation or function domain
4421 with the hyperplane where the given
4422 dimension has the fixed given value.
4424 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
4425 __isl_take isl_basic_map *bmap,
4426 enum isl_dim_type type, unsigned pos, int value);
4427 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
4428 __isl_take isl_basic_map *bmap,
4429 enum isl_dim_type type, unsigned pos, int value);
4430 __isl_give isl_set *isl_set_lower_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_lower_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_lower_bound_si(
4438 __isl_take isl_map *map,
4439 enum isl_dim_type type, unsigned pos, int value);
4440 __isl_give isl_set *isl_set_upper_bound_si(
4441 __isl_take isl_set *set,
4442 enum isl_dim_type type, unsigned pos, int value);
4443 __isl_give isl_set *isl_set_upper_bound_val(
4444 __isl_take isl_set *set,
4445 enum isl_dim_type type, unsigned pos,
4446 __isl_take isl_val *value);
4447 __isl_give isl_map *isl_map_upper_bound_si(
4448 __isl_take isl_map *map,
4449 enum isl_dim_type type, unsigned pos, int value);
4451 Intersect the set or relation with the half-space where the given
4452 dimension has a value bounded by the fixed given integer value.
4454 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
4455 enum isl_dim_type type1, int pos1,
4456 enum isl_dim_type type2, int pos2);
4457 __isl_give isl_basic_map *isl_basic_map_equate(
4458 __isl_take isl_basic_map *bmap,
4459 enum isl_dim_type type1, int pos1,
4460 enum isl_dim_type type2, int pos2);
4461 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
4462 enum isl_dim_type type1, int pos1,
4463 enum isl_dim_type type2, int pos2);
4465 Intersect the set or relation with the hyperplane where the given
4466 dimensions are equal to each other.
4468 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
4469 enum isl_dim_type type1, int pos1,
4470 enum isl_dim_type type2, int pos2);
4472 Intersect the relation with the hyperplane where the given
4473 dimensions have opposite values.
4475 __isl_give isl_map *isl_map_order_le(
4476 __isl_take isl_map *map,
4477 enum isl_dim_type type1, int pos1,
4478 enum isl_dim_type type2, int pos2);
4479 __isl_give isl_basic_map *isl_basic_map_order_ge(
4480 __isl_take isl_basic_map *bmap,
4481 enum isl_dim_type type1, int pos1,
4482 enum isl_dim_type type2, int pos2);
4483 __isl_give isl_map *isl_map_order_ge(
4484 __isl_take isl_map *map,
4485 enum isl_dim_type type1, int pos1,
4486 enum isl_dim_type type2, int pos2);
4487 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
4488 enum isl_dim_type type1, int pos1,
4489 enum isl_dim_type type2, int pos2);
4490 __isl_give isl_basic_map *isl_basic_map_order_gt(
4491 __isl_take isl_basic_map *bmap,
4492 enum isl_dim_type type1, int pos1,
4493 enum isl_dim_type type2, int pos2);
4494 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
4495 enum isl_dim_type type1, int pos1,
4496 enum isl_dim_type type2, int pos2);
4498 Intersect the relation with the half-space where the given
4499 dimensions satisfy the given ordering.
4503 #include <isl/aff.h>
4504 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4505 __isl_take isl_aff *aff);
4506 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4507 __isl_take isl_aff *aff);
4508 __isl_give isl_set *isl_pw_aff_pos_set(
4509 __isl_take isl_pw_aff *pa);
4510 __isl_give isl_set *isl_pw_aff_nonneg_set(
4511 __isl_take isl_pw_aff *pwaff);
4512 __isl_give isl_set *isl_pw_aff_zero_set(
4513 __isl_take isl_pw_aff *pwaff);
4514 __isl_give isl_set *isl_pw_aff_non_zero_set(
4515 __isl_take isl_pw_aff *pwaff);
4516 __isl_give isl_union_set *
4517 isl_union_pw_aff_zero_union_set(
4518 __isl_take isl_union_pw_aff *upa);
4519 __isl_give isl_union_set *
4520 isl_multi_union_pw_aff_zero_union_set(
4521 __isl_take isl_multi_union_pw_aff *mupa);
4523 The function C<isl_aff_neg_basic_set> returns a basic set
4524 containing those elements in the domain space
4525 of C<aff> where C<aff> is negative.
4526 The function C<isl_pw_aff_nonneg_set> returns a set
4527 containing those elements in the domain
4528 of C<pwaff> where C<pwaff> is non-negative.
4529 The function C<isl_multi_union_pw_aff_zero_union_set>
4530 returns a union set containing those elements
4531 in the domains of its elements where they are all zero.
4535 __isl_give isl_map *isl_set_identity(
4536 __isl_take isl_set *set);
4537 __isl_give isl_union_map *isl_union_set_identity(
4538 __isl_take isl_union_set *uset);
4539 __isl_give isl_union_pw_multi_aff *
4540 isl_union_set_identity_union_pw_multi_aff(
4541 __isl_take isl_union_set *uset);
4543 Construct an identity relation on the given (union) set.
4545 =item * Function Extraction
4547 A piecewise quasi affine expression that is equal to 1 on a set
4548 and 0 outside the set can be created using the following function.
4550 #include <isl/aff.h>
4551 __isl_give isl_pw_aff *isl_set_indicator_function(
4552 __isl_take isl_set *set);
4554 A piecewise multiple quasi affine expression can be extracted
4555 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4556 and the C<isl_map> is single-valued.
4557 In case of a conversion from an C<isl_union_map>
4558 to an C<isl_union_pw_multi_aff>, these properties need to hold
4559 in each domain space.
4560 A conversion to a C<isl_multi_union_pw_aff> additionally
4561 requires that the input is non-empty and involves only a single
4564 #include <isl/aff.h>
4565 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4566 __isl_take isl_set *set);
4567 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4568 __isl_take isl_map *map);
4570 __isl_give isl_union_pw_multi_aff *
4571 isl_union_pw_multi_aff_from_union_set(
4572 __isl_take isl_union_set *uset);
4573 __isl_give isl_union_pw_multi_aff *
4574 isl_union_pw_multi_aff_from_union_map(
4575 __isl_take isl_union_map *umap);
4577 __isl_give isl_multi_union_pw_aff *
4578 isl_multi_union_pw_aff_from_union_map(
4579 __isl_take isl_union_map *umap);
4583 __isl_give isl_basic_set *isl_basic_map_deltas(
4584 __isl_take isl_basic_map *bmap);
4585 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
4586 __isl_give isl_union_set *isl_union_map_deltas(
4587 __isl_take isl_union_map *umap);
4589 These functions return a (basic) set containing the differences
4590 between image elements and corresponding domain elements in the input.
4592 __isl_give isl_basic_map *isl_basic_map_deltas_map(
4593 __isl_take isl_basic_map *bmap);
4594 __isl_give isl_map *isl_map_deltas_map(
4595 __isl_take isl_map *map);
4596 __isl_give isl_union_map *isl_union_map_deltas_map(
4597 __isl_take isl_union_map *umap);
4599 The functions above construct a (basic, regular or union) relation
4600 that maps (a wrapped version of) the input relation to its delta set.
4604 Simplify the representation of a set, relation or functions by trying
4605 to combine pairs of basic sets or relations into a single
4606 basic set or relation.
4608 #include <isl/set.h>
4609 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
4611 #include <isl/map.h>
4612 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
4614 #include <isl/union_set.h>
4615 __isl_give isl_union_set *isl_union_set_coalesce(
4616 __isl_take isl_union_set *uset);
4618 #include <isl/union_map.h>
4619 __isl_give isl_union_map *isl_union_map_coalesce(
4620 __isl_take isl_union_map *umap);
4622 #include <isl/aff.h>
4623 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4624 __isl_take isl_pw_aff *pwqp);
4625 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4626 __isl_take isl_pw_multi_aff *pma);
4627 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4628 __isl_take isl_multi_pw_aff *mpa);
4629 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
4630 __isl_take isl_union_pw_aff *upa);
4631 __isl_give isl_union_pw_multi_aff *
4632 isl_union_pw_multi_aff_coalesce(
4633 __isl_take isl_union_pw_multi_aff *upma);
4635 #include <isl/polynomial.h>
4636 __isl_give isl_pw_qpolynomial_fold *
4637 isl_pw_qpolynomial_fold_coalesce(
4638 __isl_take isl_pw_qpolynomial_fold *pwf);
4639 __isl_give isl_union_pw_qpolynomial *
4640 isl_union_pw_qpolynomial_coalesce(
4641 __isl_take isl_union_pw_qpolynomial *upwqp);
4642 __isl_give isl_union_pw_qpolynomial_fold *
4643 isl_union_pw_qpolynomial_fold_coalesce(
4644 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4646 One of the methods for combining pairs of basic sets or relations
4647 can result in coefficients that are much larger than those that appear
4648 in the constraints of the input. By default, the coefficients are
4649 not allowed to grow larger, but this can be changed by unsetting
4650 the following option.
4652 isl_stat isl_options_set_coalesce_bounded_wrapping(
4653 isl_ctx *ctx, int val);
4654 int isl_options_get_coalesce_bounded_wrapping(
4657 =item * Detecting equalities
4659 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
4660 __isl_take isl_basic_set *bset);
4661 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
4662 __isl_take isl_basic_map *bmap);
4663 __isl_give isl_set *isl_set_detect_equalities(
4664 __isl_take isl_set *set);
4665 __isl_give isl_map *isl_map_detect_equalities(
4666 __isl_take isl_map *map);
4667 __isl_give isl_union_set *isl_union_set_detect_equalities(
4668 __isl_take isl_union_set *uset);
4669 __isl_give isl_union_map *isl_union_map_detect_equalities(
4670 __isl_take isl_union_map *umap);
4672 Simplify the representation of a set or relation by detecting implicit
4675 =item * Removing redundant constraints
4677 #include <isl/set.h>
4678 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
4679 __isl_take isl_basic_set *bset);
4680 __isl_give isl_set *isl_set_remove_redundancies(
4681 __isl_take isl_set *set);
4683 #include <isl/union_set.h>
4684 __isl_give isl_union_set *
4685 isl_union_set_remove_redundancies(
4686 __isl_take isl_union_set *uset);
4688 #include <isl/map.h>
4689 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
4690 __isl_take isl_basic_map *bmap);
4691 __isl_give isl_map *isl_map_remove_redundancies(
4692 __isl_take isl_map *map);
4694 #include <isl/union_map.h>
4695 __isl_give isl_union_map *
4696 isl_union_map_remove_redundancies(
4697 __isl_take isl_union_map *umap);
4701 __isl_give isl_basic_set *isl_set_convex_hull(
4702 __isl_take isl_set *set);
4703 __isl_give isl_basic_map *isl_map_convex_hull(
4704 __isl_take isl_map *map);
4706 If the input set or relation has any existentially quantified
4707 variables, then the result of these operations is currently undefined.
4711 #include <isl/set.h>
4712 __isl_give isl_basic_set *
4713 isl_set_unshifted_simple_hull(
4714 __isl_take isl_set *set);
4715 __isl_give isl_basic_set *isl_set_simple_hull(
4716 __isl_take isl_set *set);
4717 __isl_give isl_basic_set *
4718 isl_set_unshifted_simple_hull_from_set_list(
4719 __isl_take isl_set *set,
4720 __isl_take isl_set_list *list);
4722 #include <isl/map.h>
4723 __isl_give isl_basic_map *
4724 isl_map_unshifted_simple_hull(
4725 __isl_take isl_map *map);
4726 __isl_give isl_basic_map *isl_map_simple_hull(
4727 __isl_take isl_map *map);
4728 __isl_give isl_basic_map *
4729 isl_map_unshifted_simple_hull_from_map_list(
4730 __isl_take isl_map *map,
4731 __isl_take isl_map_list *list);
4733 #include <isl/union_map.h>
4734 __isl_give isl_union_map *isl_union_map_simple_hull(
4735 __isl_take isl_union_map *umap);
4737 These functions compute a single basic set or relation
4738 that contains the whole input set or relation.
4739 In particular, the output is described by translates
4740 of the constraints describing the basic sets or relations in the input.
4741 In case of C<isl_set_unshifted_simple_hull>, only the original
4742 constraints are used, without any translation.
4743 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
4744 C<isl_map_unshifted_simple_hull_from_map_list>, the
4745 constraints are taken from the elements of the second argument.
4749 (See \autoref{s:simple hull}.)
4755 __isl_give isl_basic_set *isl_basic_set_affine_hull(
4756 __isl_take isl_basic_set *bset);
4757 __isl_give isl_basic_set *isl_set_affine_hull(
4758 __isl_take isl_set *set);
4759 __isl_give isl_union_set *isl_union_set_affine_hull(
4760 __isl_take isl_union_set *uset);
4761 __isl_give isl_basic_map *isl_basic_map_affine_hull(
4762 __isl_take isl_basic_map *bmap);
4763 __isl_give isl_basic_map *isl_map_affine_hull(
4764 __isl_take isl_map *map);
4765 __isl_give isl_union_map *isl_union_map_affine_hull(
4766 __isl_take isl_union_map *umap);
4768 In case of union sets and relations, the affine hull is computed
4771 =item * Polyhedral hull
4773 __isl_give isl_basic_set *isl_set_polyhedral_hull(
4774 __isl_take isl_set *set);
4775 __isl_give isl_basic_map *isl_map_polyhedral_hull(
4776 __isl_take isl_map *map);
4777 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
4778 __isl_take isl_union_set *uset);
4779 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
4780 __isl_take isl_union_map *umap);
4782 These functions compute a single basic set or relation
4783 not involving any existentially quantified variables
4784 that contains the whole input set or relation.
4785 In case of union sets and relations, the polyhedral hull is computed
4788 =item * Other approximations
4790 #include <isl/set.h>
4791 __isl_give isl_basic_set *
4792 isl_basic_set_drop_constraints_involving_dims(
4793 __isl_take isl_basic_set *bset,
4794 enum isl_dim_type type,
4795 unsigned first, unsigned n);
4796 __isl_give isl_basic_set *
4797 isl_basic_set_drop_constraints_not_involving_dims(
4798 __isl_take isl_basic_set *bset,
4799 enum isl_dim_type type,
4800 unsigned first, unsigned n);
4801 __isl_give isl_set *
4802 isl_set_drop_constraints_involving_dims(
4803 __isl_take isl_set *set,
4804 enum isl_dim_type type,
4805 unsigned first, unsigned n);
4807 #include <isl/map.h>
4808 __isl_give isl_basic_map *
4809 isl_basic_map_drop_constraints_involving_dims(
4810 __isl_take isl_basic_map *bmap,
4811 enum isl_dim_type type,
4812 unsigned first, unsigned n);
4813 __isl_give isl_map *
4814 isl_map_drop_constraints_involving_dims(
4815 __isl_take isl_map *map,
4816 enum isl_dim_type type,
4817 unsigned first, unsigned n);
4819 These functions drop any constraints (not) involving the specified dimensions.
4820 Note that the result depends on the representation of the input.
4822 #include <isl/polynomial.h>
4823 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4824 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4825 __isl_give isl_union_pw_qpolynomial *
4826 isl_union_pw_qpolynomial_to_polynomial(
4827 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4829 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4830 the polynomial will be an overapproximation. If C<sign> is negative,
4831 it will be an underapproximation. If C<sign> is zero, the approximation
4832 will lie somewhere in between.
4836 __isl_give isl_basic_set *isl_basic_set_sample(
4837 __isl_take isl_basic_set *bset);
4838 __isl_give isl_basic_set *isl_set_sample(
4839 __isl_take isl_set *set);
4840 __isl_give isl_basic_map *isl_basic_map_sample(
4841 __isl_take isl_basic_map *bmap);
4842 __isl_give isl_basic_map *isl_map_sample(
4843 __isl_take isl_map *map);
4845 If the input (basic) set or relation is non-empty, then return
4846 a singleton subset of the input. Otherwise, return an empty set.
4848 =item * Optimization
4850 #include <isl/ilp.h>
4851 __isl_give isl_val *isl_basic_set_max_val(
4852 __isl_keep isl_basic_set *bset,
4853 __isl_keep isl_aff *obj);
4854 __isl_give isl_val *isl_set_min_val(
4855 __isl_keep isl_set *set,
4856 __isl_keep isl_aff *obj);
4857 __isl_give isl_val *isl_set_max_val(
4858 __isl_keep isl_set *set,
4859 __isl_keep isl_aff *obj);
4861 Compute the minimum or maximum of the integer affine expression C<obj>
4862 over the points in C<set>, returning the result in C<opt>.
4863 The result is C<NULL> in case of an error, the optimal value in case
4864 there is one, negative infinity or infinity if the problem is unbounded and
4865 NaN if the problem is empty.
4867 =item * Parametric optimization
4869 __isl_give isl_pw_aff *isl_set_dim_min(
4870 __isl_take isl_set *set, int pos);
4871 __isl_give isl_pw_aff *isl_set_dim_max(
4872 __isl_take isl_set *set, int pos);
4873 __isl_give isl_pw_aff *isl_map_dim_max(
4874 __isl_take isl_map *map, int pos);
4876 Compute the minimum or maximum of the given set or output dimension
4877 as a function of the parameters (and input dimensions), but independently
4878 of the other set or output dimensions.
4879 For lexicographic optimization, see L<"Lexicographic Optimization">.
4883 The following functions compute either the set of (rational) coefficient
4884 values of valid constraints for the given set or the set of (rational)
4885 values satisfying the constraints with coefficients from the given set.
4886 Internally, these two sets of functions perform essentially the
4887 same operations, except that the set of coefficients is assumed to
4888 be a cone, while the set of values may be any polyhedron.
4889 The current implementation is based on the Farkas lemma and
4890 Fourier-Motzkin elimination, but this may change or be made optional
4891 in future. In particular, future implementations may use different
4892 dualization algorithms or skip the elimination step.
4894 __isl_give isl_basic_set *isl_basic_set_coefficients(
4895 __isl_take isl_basic_set *bset);
4896 __isl_give isl_basic_set *isl_set_coefficients(
4897 __isl_take isl_set *set);
4898 __isl_give isl_union_set *isl_union_set_coefficients(
4899 __isl_take isl_union_set *bset);
4900 __isl_give isl_basic_set *isl_basic_set_solutions(
4901 __isl_take isl_basic_set *bset);
4902 __isl_give isl_basic_set *isl_set_solutions(
4903 __isl_take isl_set *set);
4904 __isl_give isl_union_set *isl_union_set_solutions(
4905 __isl_take isl_union_set *bset);
4909 __isl_give isl_map *isl_map_fixed_power_val(
4910 __isl_take isl_map *map,
4911 __isl_take isl_val *exp);
4912 __isl_give isl_union_map *
4913 isl_union_map_fixed_power_val(
4914 __isl_take isl_union_map *umap,
4915 __isl_take isl_val *exp);
4917 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
4918 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
4919 of C<map> is computed.
4921 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
4923 __isl_give isl_union_map *isl_union_map_power(
4924 __isl_take isl_union_map *umap, int *exact);
4926 Compute a parametric representation for all positive powers I<k> of C<map>.
4927 The result maps I<k> to a nested relation corresponding to the
4928 I<k>th power of C<map>.
4929 The result may be an overapproximation. If the result is known to be exact,
4930 then C<*exact> is set to C<1>.
4932 =item * Transitive closure
4934 __isl_give isl_map *isl_map_transitive_closure(
4935 __isl_take isl_map *map, int *exact);
4936 __isl_give isl_union_map *isl_union_map_transitive_closure(
4937 __isl_take isl_union_map *umap, int *exact);
4939 Compute the transitive closure of C<map>.
4940 The result may be an overapproximation. If the result is known to be exact,
4941 then C<*exact> is set to C<1>.
4943 =item * Reaching path lengths
4945 __isl_give isl_map *isl_map_reaching_path_lengths(
4946 __isl_take isl_map *map, int *exact);
4948 Compute a relation that maps each element in the range of C<map>
4949 to the lengths of all paths composed of edges in C<map> that
4950 end up in the given element.
4951 The result may be an overapproximation. If the result is known to be exact,
4952 then C<*exact> is set to C<1>.
4953 To compute the I<maximal> path length, the resulting relation
4954 should be postprocessed by C<isl_map_lexmax>.
4955 In particular, if the input relation is a dependence relation
4956 (mapping sources to sinks), then the maximal path length corresponds
4957 to the free schedule.
4958 Note, however, that C<isl_map_lexmax> expects the maximum to be
4959 finite, so if the path lengths are unbounded (possibly due to
4960 the overapproximation), then you will get an error message.
4964 #include <isl/space.h>
4965 __isl_give isl_space *isl_space_wrap(
4966 __isl_take isl_space *space);
4967 __isl_give isl_space *isl_space_unwrap(
4968 __isl_take isl_space *space);
4970 #include <isl/local_space.h>
4971 __isl_give isl_local_space *isl_local_space_wrap(
4972 __isl_take isl_local_space *ls);
4974 #include <isl/set.h>
4975 __isl_give isl_basic_map *isl_basic_set_unwrap(
4976 __isl_take isl_basic_set *bset);
4977 __isl_give isl_map *isl_set_unwrap(
4978 __isl_take isl_set *set);
4980 #include <isl/map.h>
4981 __isl_give isl_basic_set *isl_basic_map_wrap(
4982 __isl_take isl_basic_map *bmap);
4983 __isl_give isl_set *isl_map_wrap(
4984 __isl_take isl_map *map);
4986 #include <isl/union_set.h>
4987 __isl_give isl_union_map *isl_union_set_unwrap(
4988 __isl_take isl_union_set *uset);
4990 #include <isl/union_map.h>
4991 __isl_give isl_union_set *isl_union_map_wrap(
4992 __isl_take isl_union_map *umap);
4994 The input to C<isl_space_unwrap> should
4995 be the space of a set, while that of
4996 C<isl_space_wrap> should be the space of a relation.
4997 Conversely, the output of C<isl_space_unwrap> is the space
4998 of a relation, while that of C<isl_space_wrap> is the space of a set.
5002 Remove any internal structure of domain (and range) of the given
5003 set or relation. If there is any such internal structure in the input,
5004 then the name of the space is also removed.
5006 #include <isl/local_space.h>
5007 __isl_give isl_local_space *
5008 isl_local_space_flatten_domain(
5009 __isl_take isl_local_space *ls);
5010 __isl_give isl_local_space *
5011 isl_local_space_flatten_range(
5012 __isl_take isl_local_space *ls);
5014 #include <isl/set.h>
5015 __isl_give isl_basic_set *isl_basic_set_flatten(
5016 __isl_take isl_basic_set *bset);
5017 __isl_give isl_set *isl_set_flatten(
5018 __isl_take isl_set *set);
5020 #include <isl/map.h>
5021 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
5022 __isl_take isl_basic_map *bmap);
5023 __isl_give isl_basic_map *isl_basic_map_flatten_range(
5024 __isl_take isl_basic_map *bmap);
5025 __isl_give isl_map *isl_map_flatten_range(
5026 __isl_take isl_map *map);
5027 __isl_give isl_map *isl_map_flatten_domain(
5028 __isl_take isl_map *map);
5029 __isl_give isl_basic_map *isl_basic_map_flatten(
5030 __isl_take isl_basic_map *bmap);
5031 __isl_give isl_map *isl_map_flatten(
5032 __isl_take isl_map *map);
5034 #include <isl/val.h>
5035 __isl_give isl_multi_val *isl_multi_val_flatten_range(
5036 __isl_take isl_multi_val *mv);
5038 #include <isl/aff.h>
5039 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
5040 __isl_take isl_multi_aff *ma);
5041 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
5042 __isl_take isl_multi_aff *ma);
5043 __isl_give isl_multi_pw_aff *
5044 isl_multi_pw_aff_flatten_range(
5045 __isl_take isl_multi_pw_aff *mpa);
5046 __isl_give isl_multi_union_pw_aff *
5047 isl_multi_union_pw_aff_flatten_range(
5048 __isl_take isl_multi_union_pw_aff *mupa);
5050 #include <isl/map.h>
5051 __isl_give isl_map *isl_set_flatten_map(
5052 __isl_take isl_set *set);
5054 The function above constructs a relation
5055 that maps the input set to a flattened version of the set.
5059 Lift the input set to a space with extra dimensions corresponding
5060 to the existentially quantified variables in the input.
5061 In particular, the result lives in a wrapped map where the domain
5062 is the original space and the range corresponds to the original
5063 existentially quantified variables.
5065 #include <isl/set.h>
5066 __isl_give isl_basic_set *isl_basic_set_lift(
5067 __isl_take isl_basic_set *bset);
5068 __isl_give isl_set *isl_set_lift(
5069 __isl_take isl_set *set);
5070 __isl_give isl_union_set *isl_union_set_lift(
5071 __isl_take isl_union_set *uset);
5073 Given a local space that contains the existentially quantified
5074 variables of a set, a basic relation that, when applied to
5075 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
5076 can be constructed using the following function.
5078 #include <isl/local_space.h>
5079 __isl_give isl_basic_map *isl_local_space_lifting(
5080 __isl_take isl_local_space *ls);
5082 #include <isl/aff.h>
5083 __isl_give isl_multi_aff *isl_multi_aff_lift(
5084 __isl_take isl_multi_aff *maff,
5085 __isl_give isl_local_space **ls);
5087 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
5088 then it is assigned the local space that lies at the basis of
5089 the lifting applied.
5091 =item * Internal Product
5093 #include <isl/space.h>
5094 __isl_give isl_space *isl_space_zip(
5095 __isl_take isl_space *space);
5097 #include <isl/map.h>
5098 __isl_give isl_basic_map *isl_basic_map_zip(
5099 __isl_take isl_basic_map *bmap);
5100 __isl_give isl_map *isl_map_zip(
5101 __isl_take isl_map *map);
5103 #include <isl/union_map.h>
5104 __isl_give isl_union_map *isl_union_map_zip(
5105 __isl_take isl_union_map *umap);
5107 Given a relation with nested relations for domain and range,
5108 interchange the range of the domain with the domain of the range.
5112 #include <isl/space.h>
5113 __isl_give isl_space *isl_space_curry(
5114 __isl_take isl_space *space);
5115 __isl_give isl_space *isl_space_uncurry(
5116 __isl_take isl_space *space);
5118 #include <isl/map.h>
5119 __isl_give isl_basic_map *isl_basic_map_curry(
5120 __isl_take isl_basic_map *bmap);
5121 __isl_give isl_basic_map *isl_basic_map_uncurry(
5122 __isl_take isl_basic_map *bmap);
5123 __isl_give isl_map *isl_map_curry(
5124 __isl_take isl_map *map);
5125 __isl_give isl_map *isl_map_uncurry(
5126 __isl_take isl_map *map);
5128 #include <isl/union_map.h>
5129 __isl_give isl_union_map *isl_union_map_curry(
5130 __isl_take isl_union_map *umap);
5131 __isl_give isl_union_map *isl_union_map_uncurry(
5132 __isl_take isl_union_map *umap);
5134 Given a relation with a nested relation for domain,
5135 the C<curry> functions
5136 move the range of the nested relation out of the domain
5137 and use it as the domain of a nested relation in the range,
5138 with the original range as range of this nested relation.
5139 The C<uncurry> functions perform the inverse operation.
5141 =item * Aligning parameters
5143 Change the order of the parameters of the given set, relation
5145 such that the first parameters match those of C<model>.
5146 This may involve the introduction of extra parameters.
5147 All parameters need to be named.
5149 #include <isl/space.h>
5150 __isl_give isl_space *isl_space_align_params(
5151 __isl_take isl_space *space1,
5152 __isl_take isl_space *space2)
5154 #include <isl/set.h>
5155 __isl_give isl_basic_set *isl_basic_set_align_params(
5156 __isl_take isl_basic_set *bset,
5157 __isl_take isl_space *model);
5158 __isl_give isl_set *isl_set_align_params(
5159 __isl_take isl_set *set,
5160 __isl_take isl_space *model);
5162 #include <isl/map.h>
5163 __isl_give isl_basic_map *isl_basic_map_align_params(
5164 __isl_take isl_basic_map *bmap,
5165 __isl_take isl_space *model);
5166 __isl_give isl_map *isl_map_align_params(
5167 __isl_take isl_map *map,
5168 __isl_take isl_space *model);
5170 #include <isl/val.h>
5171 __isl_give isl_multi_val *isl_multi_val_align_params(
5172 __isl_take isl_multi_val *mv,
5173 __isl_take isl_space *model);
5175 #include <isl/aff.h>
5176 __isl_give isl_aff *isl_aff_align_params(
5177 __isl_take isl_aff *aff,
5178 __isl_take isl_space *model);
5179 __isl_give isl_multi_aff *isl_multi_aff_align_params(
5180 __isl_take isl_multi_aff *multi,
5181 __isl_take isl_space *model);
5182 __isl_give isl_pw_aff *isl_pw_aff_align_params(
5183 __isl_take isl_pw_aff *pwaff,
5184 __isl_take isl_space *model);
5185 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
5186 __isl_take isl_pw_multi_aff *pma,
5187 __isl_take isl_space *model);
5188 __isl_give isl_union_pw_aff *
5189 isl_union_pw_aff_align_params(
5190 __isl_take isl_union_pw_aff *upa,
5191 __isl_take isl_space *model);
5192 __isl_give isl_union_pw_multi_aff *
5193 isl_union_pw_multi_aff_align_params(
5194 __isl_take isl_union_pw_multi_aff *upma,
5195 __isl_take isl_space *model);
5196 __isl_give isl_multi_union_pw_aff *
5197 isl_multi_union_pw_aff_align_params(
5198 __isl_take isl_multi_union_pw_aff *mupa,
5199 __isl_take isl_space *model);
5201 #include <isl/polynomial.h>
5202 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5203 __isl_take isl_qpolynomial *qp,
5204 __isl_take isl_space *model);
5206 =item * Unary Arithmethic Operations
5208 #include <isl/val.h>
5209 __isl_give isl_multi_val *isl_multi_val_neg(
5210 __isl_take isl_multi_val *mv);
5212 #include <isl/aff.h>
5213 __isl_give isl_aff *isl_aff_neg(
5214 __isl_take isl_aff *aff);
5215 __isl_give isl_multi_aff *isl_multi_aff_neg(
5216 __isl_take isl_multi_aff *ma);
5217 __isl_give isl_pw_aff *isl_pw_aff_neg(
5218 __isl_take isl_pw_aff *pwaff);
5219 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
5220 __isl_take isl_pw_multi_aff *pma);
5221 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
5222 __isl_take isl_multi_pw_aff *mpa);
5223 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
5224 __isl_take isl_union_pw_aff *upa);
5225 __isl_give isl_union_pw_multi_aff *
5226 isl_union_pw_multi_aff_neg(
5227 __isl_take isl_union_pw_multi_aff *upma);
5228 __isl_give isl_multi_union_pw_aff *
5229 isl_multi_union_pw_aff_neg(
5230 __isl_take isl_multi_union_pw_aff *mupa);
5231 __isl_give isl_aff *isl_aff_ceil(
5232 __isl_take isl_aff *aff);
5233 __isl_give isl_pw_aff *isl_pw_aff_ceil(
5234 __isl_take isl_pw_aff *pwaff);
5235 __isl_give isl_aff *isl_aff_floor(
5236 __isl_take isl_aff *aff);
5237 __isl_give isl_multi_aff *isl_multi_aff_floor(
5238 __isl_take isl_multi_aff *ma);
5239 __isl_give isl_pw_aff *isl_pw_aff_floor(
5240 __isl_take isl_pw_aff *pwaff);
5241 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
5242 __isl_take isl_union_pw_aff *upa);
5243 __isl_give isl_multi_union_pw_aff *
5244 isl_multi_union_pw_aff_floor(
5245 __isl_take isl_multi_union_pw_aff *mupa);
5247 #include <isl/aff.h>
5248 __isl_give isl_pw_aff *isl_pw_aff_list_min(
5249 __isl_take isl_pw_aff_list *list);
5250 __isl_give isl_pw_aff *isl_pw_aff_list_max(
5251 __isl_take isl_pw_aff_list *list);
5253 #include <isl/polynomial.h>
5254 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5255 __isl_take isl_qpolynomial *qp);
5256 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5257 __isl_take isl_pw_qpolynomial *pwqp);
5258 __isl_give isl_union_pw_qpolynomial *
5259 isl_union_pw_qpolynomial_neg(
5260 __isl_take isl_union_pw_qpolynomial *upwqp);
5261 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5262 __isl_take isl_qpolynomial *qp,
5264 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5265 __isl_take isl_pw_qpolynomial *pwqp,
5270 The following functions evaluate a function in a point.
5272 #include <isl/polynomial.h>
5273 __isl_give isl_val *isl_pw_qpolynomial_eval(
5274 __isl_take isl_pw_qpolynomial *pwqp,
5275 __isl_take isl_point *pnt);
5276 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5277 __isl_take isl_pw_qpolynomial_fold *pwf,
5278 __isl_take isl_point *pnt);
5279 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5280 __isl_take isl_union_pw_qpolynomial *upwqp,
5281 __isl_take isl_point *pnt);
5282 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5283 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5284 __isl_take isl_point *pnt);
5286 =item * Dimension manipulation
5288 It is usually not advisable to directly change the (input or output)
5289 space of a set or a relation as this removes the name and the internal
5290 structure of the space. However, the functions below can be useful
5291 to add new parameters, assuming
5292 C<isl_set_align_params> and C<isl_map_align_params>
5295 #include <isl/space.h>
5296 __isl_give isl_space *isl_space_add_dims(
5297 __isl_take isl_space *space,
5298 enum isl_dim_type type, unsigned n);
5299 __isl_give isl_space *isl_space_insert_dims(
5300 __isl_take isl_space *space,
5301 enum isl_dim_type type, unsigned pos, unsigned n);
5302 __isl_give isl_space *isl_space_drop_dims(
5303 __isl_take isl_space *space,
5304 enum isl_dim_type type, unsigned first, unsigned n);
5305 __isl_give isl_space *isl_space_move_dims(
5306 __isl_take isl_space *space,
5307 enum isl_dim_type dst_type, unsigned dst_pos,
5308 enum isl_dim_type src_type, unsigned src_pos,
5311 #include <isl/local_space.h>
5312 __isl_give isl_local_space *isl_local_space_add_dims(
5313 __isl_take isl_local_space *ls,
5314 enum isl_dim_type type, unsigned n);
5315 __isl_give isl_local_space *isl_local_space_insert_dims(
5316 __isl_take isl_local_space *ls,
5317 enum isl_dim_type type, unsigned first, unsigned n);
5318 __isl_give isl_local_space *isl_local_space_drop_dims(
5319 __isl_take isl_local_space *ls,
5320 enum isl_dim_type type, unsigned first, unsigned n);
5322 #include <isl/set.h>
5323 __isl_give isl_basic_set *isl_basic_set_add_dims(
5324 __isl_take isl_basic_set *bset,
5325 enum isl_dim_type type, unsigned n);
5326 __isl_give isl_set *isl_set_add_dims(
5327 __isl_take isl_set *set,
5328 enum isl_dim_type type, unsigned n);
5329 __isl_give isl_basic_set *isl_basic_set_insert_dims(
5330 __isl_take isl_basic_set *bset,
5331 enum isl_dim_type type, unsigned pos,
5333 __isl_give isl_set *isl_set_insert_dims(
5334 __isl_take isl_set *set,
5335 enum isl_dim_type type, unsigned pos, unsigned n);
5336 __isl_give isl_basic_set *isl_basic_set_move_dims(
5337 __isl_take isl_basic_set *bset,
5338 enum isl_dim_type dst_type, unsigned dst_pos,
5339 enum isl_dim_type src_type, unsigned src_pos,
5341 __isl_give isl_set *isl_set_move_dims(
5342 __isl_take isl_set *set,
5343 enum isl_dim_type dst_type, unsigned dst_pos,
5344 enum isl_dim_type src_type, unsigned src_pos,
5347 #include <isl/map.h>
5348 __isl_give isl_basic_map *isl_basic_map_add_dims(
5349 __isl_take isl_basic_map *bmap,
5350 enum isl_dim_type type, unsigned n);
5351 __isl_give isl_map *isl_map_add_dims(
5352 __isl_take isl_map *map,
5353 enum isl_dim_type type, unsigned n);
5354 __isl_give isl_basic_map *isl_basic_map_insert_dims(
5355 __isl_take isl_basic_map *bmap,
5356 enum isl_dim_type type, unsigned pos,
5358 __isl_give isl_map *isl_map_insert_dims(
5359 __isl_take isl_map *map,
5360 enum isl_dim_type type, unsigned pos, unsigned n);
5361 __isl_give isl_basic_map *isl_basic_map_move_dims(
5362 __isl_take isl_basic_map *bmap,
5363 enum isl_dim_type dst_type, unsigned dst_pos,
5364 enum isl_dim_type src_type, unsigned src_pos,
5366 __isl_give isl_map *isl_map_move_dims(
5367 __isl_take isl_map *map,
5368 enum isl_dim_type dst_type, unsigned dst_pos,
5369 enum isl_dim_type src_type, unsigned src_pos,
5372 #include <isl/val.h>
5373 __isl_give isl_multi_val *isl_multi_val_insert_dims(
5374 __isl_take isl_multi_val *mv,
5375 enum isl_dim_type type, unsigned first, unsigned n);
5376 __isl_give isl_multi_val *isl_multi_val_add_dims(
5377 __isl_take isl_multi_val *mv,
5378 enum isl_dim_type type, unsigned n);
5379 __isl_give isl_multi_val *isl_multi_val_drop_dims(
5380 __isl_take isl_multi_val *mv,
5381 enum isl_dim_type type, unsigned first, unsigned n);
5383 #include <isl/aff.h>
5384 __isl_give isl_aff *isl_aff_insert_dims(
5385 __isl_take isl_aff *aff,
5386 enum isl_dim_type type, unsigned first, unsigned n);
5387 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
5388 __isl_take isl_multi_aff *ma,
5389 enum isl_dim_type type, unsigned first, unsigned n);
5390 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
5391 __isl_take isl_pw_aff *pwaff,
5392 enum isl_dim_type type, unsigned first, unsigned n);
5393 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
5394 __isl_take isl_multi_pw_aff *mpa,
5395 enum isl_dim_type type, unsigned first, unsigned n);
5396 __isl_give isl_aff *isl_aff_add_dims(
5397 __isl_take isl_aff *aff,
5398 enum isl_dim_type type, unsigned n);
5399 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
5400 __isl_take isl_multi_aff *ma,
5401 enum isl_dim_type type, unsigned n);
5402 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
5403 __isl_take isl_pw_aff *pwaff,
5404 enum isl_dim_type type, unsigned n);
5405 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
5406 __isl_take isl_multi_pw_aff *mpa,
5407 enum isl_dim_type type, unsigned n);
5408 __isl_give isl_aff *isl_aff_drop_dims(
5409 __isl_take isl_aff *aff,
5410 enum isl_dim_type type, unsigned first, unsigned n);
5411 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
5412 __isl_take isl_multi_aff *maff,
5413 enum isl_dim_type type, unsigned first, unsigned n);
5414 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
5415 __isl_take isl_pw_aff *pwaff,
5416 enum isl_dim_type type, unsigned first, unsigned n);
5417 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
5418 __isl_take isl_pw_multi_aff *pma,
5419 enum isl_dim_type type, unsigned first, unsigned n);
5420 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
5421 __isl_take isl_union_pw_aff *upa,
5422 enum isl_dim_type type, unsigned first, unsigned n);
5423 __isl_give isl_union_pw_multi_aff *
5424 isl_union_pw_multi_aff_drop_dims(
5425 __isl_take isl_union_pw_multi_aff *upma,
5426 enum isl_dim_type type,
5427 unsigned first, unsigned n);
5428 __isl_give isl_multi_union_pw_aff *
5429 isl_multi_union_pw_aff_drop_dims(
5430 __isl_take isl_multi_union_pw_aff *mupa,
5431 enum isl_dim_type type, unsigned first,
5433 __isl_give isl_aff *isl_aff_move_dims(
5434 __isl_take isl_aff *aff,
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_aff *isl_multi_aff_move_dims(
5439 __isl_take isl_multi_aff *ma,
5440 enum isl_dim_type dst_type, unsigned dst_pos,
5441 enum isl_dim_type src_type, unsigned src_pos,
5443 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
5444 __isl_take isl_pw_aff *pa,
5445 enum isl_dim_type dst_type, unsigned dst_pos,
5446 enum isl_dim_type src_type, unsigned src_pos,
5448 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
5449 __isl_take isl_multi_pw_aff *pma,
5450 enum isl_dim_type dst_type, unsigned dst_pos,
5451 enum isl_dim_type src_type, unsigned src_pos,
5454 #include <isl/polynomial.h>
5455 __isl_give isl_union_pw_qpolynomial *
5456 isl_union_pw_qpolynomial_drop_dims(
5457 __isl_take isl_union_pw_qpolynomial *upwqp,
5458 enum isl_dim_type type,
5459 unsigned first, unsigned n);
5460 __isl_give isl_union_pw_qpolynomial_fold *
5461 isl_union_pw_qpolynomial_fold_drop_dims(
5462 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5463 enum isl_dim_type type,
5464 unsigned first, unsigned n);
5466 The operations on union expressions can only manipulate parameters.
5470 =head2 Binary Operations
5472 The two arguments of a binary operation not only need to live
5473 in the same C<isl_ctx>, they currently also need to have
5474 the same (number of) parameters.
5476 =head3 Basic Operations
5480 =item * Intersection
5482 #include <isl/local_space.h>
5483 __isl_give isl_local_space *isl_local_space_intersect(
5484 __isl_take isl_local_space *ls1,
5485 __isl_take isl_local_space *ls2);
5487 #include <isl/set.h>
5488 __isl_give isl_basic_set *isl_basic_set_intersect_params(
5489 __isl_take isl_basic_set *bset1,
5490 __isl_take isl_basic_set *bset2);
5491 __isl_give isl_basic_set *isl_basic_set_intersect(
5492 __isl_take isl_basic_set *bset1,
5493 __isl_take isl_basic_set *bset2);
5494 __isl_give isl_basic_set *isl_basic_set_list_intersect(
5495 __isl_take struct isl_basic_set_list *list);
5496 __isl_give isl_set *isl_set_intersect_params(
5497 __isl_take isl_set *set,
5498 __isl_take isl_set *params);
5499 __isl_give isl_set *isl_set_intersect(
5500 __isl_take isl_set *set1,
5501 __isl_take isl_set *set2);
5503 #include <isl/map.h>
5504 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
5505 __isl_take isl_basic_map *bmap,
5506 __isl_take isl_basic_set *bset);
5507 __isl_give isl_basic_map *isl_basic_map_intersect_range(
5508 __isl_take isl_basic_map *bmap,
5509 __isl_take isl_basic_set *bset);
5510 __isl_give isl_basic_map *isl_basic_map_intersect(
5511 __isl_take isl_basic_map *bmap1,
5512 __isl_take isl_basic_map *bmap2);
5513 __isl_give isl_basic_map *isl_basic_map_list_intersect(
5514 __isl_take isl_basic_map_list *list);
5515 __isl_give isl_map *isl_map_intersect_params(
5516 __isl_take isl_map *map,
5517 __isl_take isl_set *params);
5518 __isl_give isl_map *isl_map_intersect_domain(
5519 __isl_take isl_map *map,
5520 __isl_take isl_set *set);
5521 __isl_give isl_map *isl_map_intersect_range(
5522 __isl_take isl_map *map,
5523 __isl_take isl_set *set);
5524 __isl_give isl_map *isl_map_intersect(
5525 __isl_take isl_map *map1,
5526 __isl_take isl_map *map2);
5528 #include <isl/union_set.h>
5529 __isl_give isl_union_set *isl_union_set_intersect_params(
5530 __isl_take isl_union_set *uset,
5531 __isl_take isl_set *set);
5532 __isl_give isl_union_set *isl_union_set_intersect(
5533 __isl_take isl_union_set *uset1,
5534 __isl_take isl_union_set *uset2);
5536 #include <isl/union_map.h>
5537 __isl_give isl_union_map *isl_union_map_intersect_params(
5538 __isl_take isl_union_map *umap,
5539 __isl_take isl_set *set);
5540 __isl_give isl_union_map *isl_union_map_intersect_domain(
5541 __isl_take isl_union_map *umap,
5542 __isl_take isl_union_set *uset);
5543 __isl_give isl_union_map *isl_union_map_intersect_range(
5544 __isl_take isl_union_map *umap,
5545 __isl_take isl_union_set *uset);
5546 __isl_give isl_union_map *isl_union_map_intersect(
5547 __isl_take isl_union_map *umap1,
5548 __isl_take isl_union_map *umap2);
5550 #include <isl/aff.h>
5551 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
5552 __isl_take isl_pw_aff *pa,
5553 __isl_take isl_set *set);
5554 __isl_give isl_multi_pw_aff *
5555 isl_multi_pw_aff_intersect_domain(
5556 __isl_take isl_multi_pw_aff *mpa,
5557 __isl_take isl_set *domain);
5558 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
5559 __isl_take isl_pw_multi_aff *pma,
5560 __isl_take isl_set *set);
5561 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
5562 __isl_take isl_union_pw_aff *upa,
5563 __isl_take isl_union_set *uset);
5564 __isl_give isl_union_pw_multi_aff *
5565 isl_union_pw_multi_aff_intersect_domain(
5566 __isl_take isl_union_pw_multi_aff *upma,
5567 __isl_take isl_union_set *uset);
5568 __isl_give isl_multi_union_pw_aff *
5569 isl_multi_union_pw_aff_intersect_domain(
5570 __isl_take isl_multi_union_pw_aff *mupa,
5571 __isl_take isl_union_set *uset);
5572 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
5573 __isl_take isl_pw_aff *pa,
5574 __isl_take isl_set *set);
5575 __isl_give isl_multi_pw_aff *
5576 isl_multi_pw_aff_intersect_params(
5577 __isl_take isl_multi_pw_aff *mpa,
5578 __isl_take isl_set *set);
5579 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
5580 __isl_take isl_pw_multi_aff *pma,
5581 __isl_take isl_set *set);
5582 __isl_give isl_union_pw_aff *
5583 isl_union_pw_aff_intersect_params(
5584 __isl_take isl_union_pw_aff *upa,
5585 __isl_give isl_union_pw_multi_aff *
5586 isl_union_pw_multi_aff_intersect_params(
5587 __isl_take isl_union_pw_multi_aff *upma,
5588 __isl_take isl_set *set);
5589 __isl_give isl_multi_union_pw_aff *
5590 isl_multi_union_pw_aff_intersect_params(
5591 __isl_take isl_multi_union_pw_aff *mupa,
5592 __isl_take isl_set *params);
5593 isl_multi_union_pw_aff_intersect_range(
5594 __isl_take isl_multi_union_pw_aff *mupa,
5595 __isl_take isl_set *set);
5597 #include <isl/polynomial.h>
5598 __isl_give isl_pw_qpolynomial *
5599 isl_pw_qpolynomial_intersect_domain(
5600 __isl_take isl_pw_qpolynomial *pwpq,
5601 __isl_take isl_set *set);
5602 __isl_give isl_union_pw_qpolynomial *
5603 isl_union_pw_qpolynomial_intersect_domain(
5604 __isl_take isl_union_pw_qpolynomial *upwpq,
5605 __isl_take isl_union_set *uset);
5606 __isl_give isl_union_pw_qpolynomial_fold *
5607 isl_union_pw_qpolynomial_fold_intersect_domain(
5608 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5609 __isl_take isl_union_set *uset);
5610 __isl_give isl_pw_qpolynomial *
5611 isl_pw_qpolynomial_intersect_params(
5612 __isl_take isl_pw_qpolynomial *pwpq,
5613 __isl_take isl_set *set);
5614 __isl_give isl_pw_qpolynomial_fold *
5615 isl_pw_qpolynomial_fold_intersect_params(
5616 __isl_take isl_pw_qpolynomial_fold *pwf,
5617 __isl_take isl_set *set);
5618 __isl_give isl_union_pw_qpolynomial *
5619 isl_union_pw_qpolynomial_intersect_params(
5620 __isl_take isl_union_pw_qpolynomial *upwpq,
5621 __isl_take isl_set *set);
5622 __isl_give isl_union_pw_qpolynomial_fold *
5623 isl_union_pw_qpolynomial_fold_intersect_params(
5624 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5625 __isl_take isl_set *set);
5627 The second argument to the C<_params> functions needs to be
5628 a parametric (basic) set. For the other functions, a parametric set
5629 for either argument is only allowed if the other argument is
5630 a parametric set as well.
5631 The list passed to C<isl_basic_set_list_intersect> needs to have
5632 at least one element and all elements need to live in the same space.
5633 The function C<isl_multi_union_pw_aff_intersect_range>
5634 restricts the input function to those shared domain elements
5635 that map to the specified range.
5639 #include <isl/set.h>
5640 __isl_give isl_set *isl_basic_set_union(
5641 __isl_take isl_basic_set *bset1,
5642 __isl_take isl_basic_set *bset2);
5643 __isl_give isl_set *isl_set_union(
5644 __isl_take isl_set *set1,
5645 __isl_take isl_set *set2);
5647 #include <isl/map.h>
5648 __isl_give isl_map *isl_basic_map_union(
5649 __isl_take isl_basic_map *bmap1,
5650 __isl_take isl_basic_map *bmap2);
5651 __isl_give isl_map *isl_map_union(
5652 __isl_take isl_map *map1,
5653 __isl_take isl_map *map2);
5655 #include <isl/union_set.h>
5656 __isl_give isl_union_set *isl_union_set_union(
5657 __isl_take isl_union_set *uset1,
5658 __isl_take isl_union_set *uset2);
5659 __isl_give isl_union_set *isl_union_set_list_union(
5660 __isl_take isl_union_set_list *list);
5662 #include <isl/union_map.h>
5663 __isl_give isl_union_map *isl_union_map_union(
5664 __isl_take isl_union_map *umap1,
5665 __isl_take isl_union_map *umap2);
5667 =item * Set difference
5669 #include <isl/set.h>
5670 __isl_give isl_set *isl_set_subtract(
5671 __isl_take isl_set *set1,
5672 __isl_take isl_set *set2);
5674 #include <isl/map.h>
5675 __isl_give isl_map *isl_map_subtract(
5676 __isl_take isl_map *map1,
5677 __isl_take isl_map *map2);
5678 __isl_give isl_map *isl_map_subtract_domain(
5679 __isl_take isl_map *map,
5680 __isl_take isl_set *dom);
5681 __isl_give isl_map *isl_map_subtract_range(
5682 __isl_take isl_map *map,
5683 __isl_take isl_set *dom);
5685 #include <isl/union_set.h>
5686 __isl_give isl_union_set *isl_union_set_subtract(
5687 __isl_take isl_union_set *uset1,
5688 __isl_take isl_union_set *uset2);
5690 #include <isl/union_map.h>
5691 __isl_give isl_union_map *isl_union_map_subtract(
5692 __isl_take isl_union_map *umap1,
5693 __isl_take isl_union_map *umap2);
5694 __isl_give isl_union_map *isl_union_map_subtract_domain(
5695 __isl_take isl_union_map *umap,
5696 __isl_take isl_union_set *dom);
5697 __isl_give isl_union_map *isl_union_map_subtract_range(
5698 __isl_take isl_union_map *umap,
5699 __isl_take isl_union_set *dom);
5701 #include <isl/aff.h>
5702 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
5703 __isl_take isl_pw_aff *pa,
5704 __isl_take isl_set *set);
5705 __isl_give isl_pw_multi_aff *
5706 isl_pw_multi_aff_subtract_domain(
5707 __isl_take isl_pw_multi_aff *pma,
5708 __isl_take isl_set *set);
5709 __isl_give isl_union_pw_aff *
5710 isl_union_pw_aff_subtract_domain(
5711 __isl_take isl_union_pw_aff *upa,
5712 __isl_take isl_union_set *uset);
5713 __isl_give isl_union_pw_multi_aff *
5714 isl_union_pw_multi_aff_subtract_domain(
5715 __isl_take isl_union_pw_multi_aff *upma,
5716 __isl_take isl_set *set);
5718 #include <isl/polynomial.h>
5719 __isl_give isl_pw_qpolynomial *
5720 isl_pw_qpolynomial_subtract_domain(
5721 __isl_take isl_pw_qpolynomial *pwpq,
5722 __isl_take isl_set *set);
5723 __isl_give isl_pw_qpolynomial_fold *
5724 isl_pw_qpolynomial_fold_subtract_domain(
5725 __isl_take isl_pw_qpolynomial_fold *pwf,
5726 __isl_take isl_set *set);
5727 __isl_give isl_union_pw_qpolynomial *
5728 isl_union_pw_qpolynomial_subtract_domain(
5729 __isl_take isl_union_pw_qpolynomial *upwpq,
5730 __isl_take isl_union_set *uset);
5731 __isl_give isl_union_pw_qpolynomial_fold *
5732 isl_union_pw_qpolynomial_fold_subtract_domain(
5733 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5734 __isl_take isl_union_set *uset);
5738 #include <isl/space.h>
5739 __isl_give isl_space *isl_space_join(
5740 __isl_take isl_space *left,
5741 __isl_take isl_space *right);
5743 #include <isl/map.h>
5744 __isl_give isl_basic_set *isl_basic_set_apply(
5745 __isl_take isl_basic_set *bset,
5746 __isl_take isl_basic_map *bmap);
5747 __isl_give isl_set *isl_set_apply(
5748 __isl_take isl_set *set,
5749 __isl_take isl_map *map);
5750 __isl_give isl_union_set *isl_union_set_apply(
5751 __isl_take isl_union_set *uset,
5752 __isl_take isl_union_map *umap);
5753 __isl_give isl_basic_map *isl_basic_map_apply_domain(
5754 __isl_take isl_basic_map *bmap1,
5755 __isl_take isl_basic_map *bmap2);
5756 __isl_give isl_basic_map *isl_basic_map_apply_range(
5757 __isl_take isl_basic_map *bmap1,
5758 __isl_take isl_basic_map *bmap2);
5759 __isl_give isl_map *isl_map_apply_domain(
5760 __isl_take isl_map *map1,
5761 __isl_take isl_map *map2);
5762 __isl_give isl_map *isl_map_apply_range(
5763 __isl_take isl_map *map1,
5764 __isl_take isl_map *map2);
5766 #include <isl/union_map.h>
5767 __isl_give isl_union_map *isl_union_map_apply_domain(
5768 __isl_take isl_union_map *umap1,
5769 __isl_take isl_union_map *umap2);
5770 __isl_give isl_union_map *isl_union_map_apply_range(
5771 __isl_take isl_union_map *umap1,
5772 __isl_take isl_union_map *umap2);
5774 #include <isl/aff.h>
5775 __isl_give isl_union_pw_aff *
5776 isl_multi_union_pw_aff_apply_aff(
5777 __isl_take isl_multi_union_pw_aff *mupa,
5778 __isl_take isl_aff *aff);
5779 __isl_give isl_union_pw_aff *
5780 isl_multi_union_pw_aff_apply_pw_aff(
5781 __isl_take isl_multi_union_pw_aff *mupa,
5782 __isl_take isl_pw_aff *pa);
5783 __isl_give isl_multi_union_pw_aff *
5784 isl_multi_union_pw_aff_apply_multi_aff(
5785 __isl_take isl_multi_union_pw_aff *mupa,
5786 __isl_take isl_multi_aff *ma);
5787 __isl_give isl_multi_union_pw_aff *
5788 isl_multi_union_pw_aff_apply_pw_multi_aff(
5789 __isl_take isl_multi_union_pw_aff *mupa,
5790 __isl_take isl_pw_multi_aff *pma);
5792 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
5793 over the shared domain of the elements of the input. The dimension is
5794 required to be greater than zero.
5795 The C<isl_multi_union_pw_aff> argument of
5796 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
5797 but only if the range of the C<isl_multi_aff> argument
5798 is also zero-dimensional.
5799 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
5801 #include <isl/polynomial.h>
5802 __isl_give isl_pw_qpolynomial_fold *
5803 isl_set_apply_pw_qpolynomial_fold(
5804 __isl_take isl_set *set,
5805 __isl_take isl_pw_qpolynomial_fold *pwf,
5807 __isl_give isl_pw_qpolynomial_fold *
5808 isl_map_apply_pw_qpolynomial_fold(
5809 __isl_take isl_map *map,
5810 __isl_take isl_pw_qpolynomial_fold *pwf,
5812 __isl_give isl_union_pw_qpolynomial_fold *
5813 isl_union_set_apply_union_pw_qpolynomial_fold(
5814 __isl_take isl_union_set *uset,
5815 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5817 __isl_give isl_union_pw_qpolynomial_fold *
5818 isl_union_map_apply_union_pw_qpolynomial_fold(
5819 __isl_take isl_union_map *umap,
5820 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5823 The functions taking a map
5824 compose the given map with the given piecewise quasipolynomial reduction.
5825 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5826 over all elements in the intersection of the range of the map
5827 and the domain of the piecewise quasipolynomial reduction
5828 as a function of an element in the domain of the map.
5829 The functions taking a set compute a bound over all elements in the
5830 intersection of the set and the domain of the
5831 piecewise quasipolynomial reduction.
5835 #include <isl/set.h>
5836 __isl_give isl_basic_set *
5837 isl_basic_set_preimage_multi_aff(
5838 __isl_take isl_basic_set *bset,
5839 __isl_take isl_multi_aff *ma);
5840 __isl_give isl_set *isl_set_preimage_multi_aff(
5841 __isl_take isl_set *set,
5842 __isl_take isl_multi_aff *ma);
5843 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
5844 __isl_take isl_set *set,
5845 __isl_take isl_pw_multi_aff *pma);
5846 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
5847 __isl_take isl_set *set,
5848 __isl_take isl_multi_pw_aff *mpa);
5850 #include <isl/union_set.h>
5851 __isl_give isl_union_set *
5852 isl_union_set_preimage_multi_aff(
5853 __isl_take isl_union_set *uset,
5854 __isl_take isl_multi_aff *ma);
5855 __isl_give isl_union_set *
5856 isl_union_set_preimage_pw_multi_aff(
5857 __isl_take isl_union_set *uset,
5858 __isl_take isl_pw_multi_aff *pma);
5859 __isl_give isl_union_set *
5860 isl_union_set_preimage_union_pw_multi_aff(
5861 __isl_take isl_union_set *uset,
5862 __isl_take isl_union_pw_multi_aff *upma);
5864 #include <isl/map.h>
5865 __isl_give isl_basic_map *
5866 isl_basic_map_preimage_domain_multi_aff(
5867 __isl_take isl_basic_map *bmap,
5868 __isl_take isl_multi_aff *ma);
5869 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
5870 __isl_take isl_map *map,
5871 __isl_take isl_multi_aff *ma);
5872 __isl_give isl_map *isl_map_preimage_range_multi_aff(
5873 __isl_take isl_map *map,
5874 __isl_take isl_multi_aff *ma);
5875 __isl_give isl_map *
5876 isl_map_preimage_domain_pw_multi_aff(
5877 __isl_take isl_map *map,
5878 __isl_take isl_pw_multi_aff *pma);
5879 __isl_give isl_map *
5880 isl_map_preimage_range_pw_multi_aff(
5881 __isl_take isl_map *map,
5882 __isl_take isl_pw_multi_aff *pma);
5883 __isl_give isl_map *
5884 isl_map_preimage_domain_multi_pw_aff(
5885 __isl_take isl_map *map,
5886 __isl_take isl_multi_pw_aff *mpa);
5887 __isl_give isl_basic_map *
5888 isl_basic_map_preimage_range_multi_aff(
5889 __isl_take isl_basic_map *bmap,
5890 __isl_take isl_multi_aff *ma);
5892 #include <isl/union_map.h>
5893 __isl_give isl_union_map *
5894 isl_union_map_preimage_domain_multi_aff(
5895 __isl_take isl_union_map *umap,
5896 __isl_take isl_multi_aff *ma);
5897 __isl_give isl_union_map *
5898 isl_union_map_preimage_range_multi_aff(
5899 __isl_take isl_union_map *umap,
5900 __isl_take isl_multi_aff *ma);
5901 __isl_give isl_union_map *
5902 isl_union_map_preimage_domain_pw_multi_aff(
5903 __isl_take isl_union_map *umap,
5904 __isl_take isl_pw_multi_aff *pma);
5905 __isl_give isl_union_map *
5906 isl_union_map_preimage_range_pw_multi_aff(
5907 __isl_take isl_union_map *umap,
5908 __isl_take isl_pw_multi_aff *pma);
5909 __isl_give isl_union_map *
5910 isl_union_map_preimage_domain_union_pw_multi_aff(
5911 __isl_take isl_union_map *umap,
5912 __isl_take isl_union_pw_multi_aff *upma);
5913 __isl_give isl_union_map *
5914 isl_union_map_preimage_range_union_pw_multi_aff(
5915 __isl_take isl_union_map *umap,
5916 __isl_take isl_union_pw_multi_aff *upma);
5918 These functions compute the preimage of the given set or map domain/range under
5919 the given function. In other words, the expression is plugged
5920 into the set description or into the domain/range of the map.
5924 #include <isl/aff.h>
5925 __isl_give isl_aff *isl_aff_pullback_aff(
5926 __isl_take isl_aff *aff1,
5927 __isl_take isl_aff *aff2);
5928 __isl_give isl_aff *isl_aff_pullback_multi_aff(
5929 __isl_take isl_aff *aff,
5930 __isl_take isl_multi_aff *ma);
5931 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
5932 __isl_take isl_pw_aff *pa,
5933 __isl_take isl_multi_aff *ma);
5934 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
5935 __isl_take isl_pw_aff *pa,
5936 __isl_take isl_pw_multi_aff *pma);
5937 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
5938 __isl_take isl_pw_aff *pa,
5939 __isl_take isl_multi_pw_aff *mpa);
5940 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
5941 __isl_take isl_multi_aff *ma1,
5942 __isl_take isl_multi_aff *ma2);
5943 __isl_give isl_pw_multi_aff *
5944 isl_pw_multi_aff_pullback_multi_aff(
5945 __isl_take isl_pw_multi_aff *pma,
5946 __isl_take isl_multi_aff *ma);
5947 __isl_give isl_multi_pw_aff *
5948 isl_multi_pw_aff_pullback_multi_aff(
5949 __isl_take isl_multi_pw_aff *mpa,
5950 __isl_take isl_multi_aff *ma);
5951 __isl_give isl_pw_multi_aff *
5952 isl_pw_multi_aff_pullback_pw_multi_aff(
5953 __isl_take isl_pw_multi_aff *pma1,
5954 __isl_take isl_pw_multi_aff *pma2);
5955 __isl_give isl_multi_pw_aff *
5956 isl_multi_pw_aff_pullback_pw_multi_aff(
5957 __isl_take isl_multi_pw_aff *mpa,
5958 __isl_take isl_pw_multi_aff *pma);
5959 __isl_give isl_multi_pw_aff *
5960 isl_multi_pw_aff_pullback_multi_pw_aff(
5961 __isl_take isl_multi_pw_aff *mpa1,
5962 __isl_take isl_multi_pw_aff *mpa2);
5963 __isl_give isl_union_pw_aff *
5964 isl_union_pw_aff_pullback_union_pw_multi_aff(
5965 __isl_take isl_union_pw_aff *upa,
5966 __isl_take isl_union_pw_multi_aff *upma);
5967 __isl_give isl_union_pw_multi_aff *
5968 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
5969 __isl_take isl_union_pw_multi_aff *upma1,
5970 __isl_take isl_union_pw_multi_aff *upma2);
5971 __isl_give isl_multi_union_pw_aff *
5972 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
5973 __isl_take isl_multi_union_pw_aff *mupa,
5974 __isl_take isl_union_pw_multi_aff *upma);
5976 These functions precompose the first expression by the second function.
5977 In other words, the second function is plugged
5978 into the first expression.
5982 #include <isl/aff.h>
5983 __isl_give isl_basic_set *isl_aff_le_basic_set(
5984 __isl_take isl_aff *aff1,
5985 __isl_take isl_aff *aff2);
5986 __isl_give isl_basic_set *isl_aff_ge_basic_set(
5987 __isl_take isl_aff *aff1,
5988 __isl_take isl_aff *aff2);
5989 __isl_give isl_set *isl_pw_aff_eq_set(
5990 __isl_take isl_pw_aff *pwaff1,
5991 __isl_take isl_pw_aff *pwaff2);
5992 __isl_give isl_set *isl_pw_aff_ne_set(
5993 __isl_take isl_pw_aff *pwaff1,
5994 __isl_take isl_pw_aff *pwaff2);
5995 __isl_give isl_set *isl_pw_aff_le_set(
5996 __isl_take isl_pw_aff *pwaff1,
5997 __isl_take isl_pw_aff *pwaff2);
5998 __isl_give isl_set *isl_pw_aff_lt_set(
5999 __isl_take isl_pw_aff *pwaff1,
6000 __isl_take isl_pw_aff *pwaff2);
6001 __isl_give isl_set *isl_pw_aff_ge_set(
6002 __isl_take isl_pw_aff *pwaff1,
6003 __isl_take isl_pw_aff *pwaff2);
6004 __isl_give isl_set *isl_pw_aff_gt_set(
6005 __isl_take isl_pw_aff *pwaff1,
6006 __isl_take isl_pw_aff *pwaff2);
6008 __isl_give isl_set *isl_multi_aff_lex_le_set(
6009 __isl_take isl_multi_aff *ma1,
6010 __isl_take isl_multi_aff *ma2);
6011 __isl_give isl_set *isl_multi_aff_lex_ge_set(
6012 __isl_take isl_multi_aff *ma1,
6013 __isl_take isl_multi_aff *ma2);
6015 __isl_give isl_set *isl_pw_aff_list_eq_set(
6016 __isl_take isl_pw_aff_list *list1,
6017 __isl_take isl_pw_aff_list *list2);
6018 __isl_give isl_set *isl_pw_aff_list_ne_set(
6019 __isl_take isl_pw_aff_list *list1,
6020 __isl_take isl_pw_aff_list *list2);
6021 __isl_give isl_set *isl_pw_aff_list_le_set(
6022 __isl_take isl_pw_aff_list *list1,
6023 __isl_take isl_pw_aff_list *list2);
6024 __isl_give isl_set *isl_pw_aff_list_lt_set(
6025 __isl_take isl_pw_aff_list *list1,
6026 __isl_take isl_pw_aff_list *list2);
6027 __isl_give isl_set *isl_pw_aff_list_ge_set(
6028 __isl_take isl_pw_aff_list *list1,
6029 __isl_take isl_pw_aff_list *list2);
6030 __isl_give isl_set *isl_pw_aff_list_gt_set(
6031 __isl_take isl_pw_aff_list *list1,
6032 __isl_take isl_pw_aff_list *list2);
6034 The function C<isl_aff_ge_basic_set> returns a basic set
6035 containing those elements in the shared space
6036 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
6037 The function C<isl_pw_aff_ge_set> returns a set
6038 containing those elements in the shared domain
6039 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
6040 greater than or equal to C<pwaff2>.
6041 The function C<isl_multi_aff_lex_le_set> returns a set
6042 containing those elements in the shared domain space
6043 where C<ma1> is lexicographically smaller than or
6045 The functions operating on C<isl_pw_aff_list> apply the corresponding
6046 C<isl_pw_aff> function to each pair of elements in the two lists.
6048 #include <isl/aff.h>
6049 __isl_give isl_map *isl_pw_aff_eq_map(
6050 __isl_take isl_pw_aff *pa1,
6051 __isl_take isl_pw_aff *pa2);
6052 __isl_give isl_map *isl_pw_aff_lt_map(
6053 __isl_take isl_pw_aff *pa1,
6054 __isl_take isl_pw_aff *pa2);
6055 __isl_give isl_map *isl_pw_aff_gt_map(
6056 __isl_take isl_pw_aff *pa1,
6057 __isl_take isl_pw_aff *pa2);
6059 __isl_give isl_map *isl_multi_pw_aff_eq_map(
6060 __isl_take isl_multi_pw_aff *mpa1,
6061 __isl_take isl_multi_pw_aff *mpa2);
6062 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
6063 __isl_take isl_multi_pw_aff *mpa1,
6064 __isl_take isl_multi_pw_aff *mpa2);
6065 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
6066 __isl_take isl_multi_pw_aff *mpa1,
6067 __isl_take isl_multi_pw_aff *mpa2);
6069 These functions return a map between domain elements of the arguments
6070 where the function values satisfy the given relation.
6072 #include <isl/union_map.h>
6073 __isl_give isl_union_map *
6074 isl_union_map_eq_at_multi_union_pw_aff(
6075 __isl_take isl_union_map *umap,
6076 __isl_take isl_multi_union_pw_aff *mupa);
6077 __isl_give isl_union_map *
6078 isl_union_map_lex_lt_at_multi_union_pw_aff(
6079 __isl_take isl_union_map *umap,
6080 __isl_take isl_multi_union_pw_aff *mupa);
6081 __isl_give isl_union_map *
6082 isl_union_map_lex_gt_at_multi_union_pw_aff(
6083 __isl_take isl_union_map *umap,
6084 __isl_take isl_multi_union_pw_aff *mupa);
6086 These functions select the subset of elements in the union map
6087 that have an equal or lexicographically smaller function value.
6089 =item * Cartesian Product
6091 #include <isl/space.h>
6092 __isl_give isl_space *isl_space_product(
6093 __isl_take isl_space *space1,
6094 __isl_take isl_space *space2);
6095 __isl_give isl_space *isl_space_domain_product(
6096 __isl_take isl_space *space1,
6097 __isl_take isl_space *space2);
6098 __isl_give isl_space *isl_space_range_product(
6099 __isl_take isl_space *space1,
6100 __isl_take isl_space *space2);
6103 C<isl_space_product>, C<isl_space_domain_product>
6104 and C<isl_space_range_product> take pairs or relation spaces and
6105 produce a single relations space, where either the domain, the range
6106 or both domain and range are wrapped spaces of relations between
6107 the domains and/or ranges of the input spaces.
6108 If the product is only constructed over the domain or the range
6109 then the ranges or the domains of the inputs should be the same.
6110 The function C<isl_space_product> also accepts a pair of set spaces,
6111 in which case it returns a wrapped space of a relation between the
6114 #include <isl/set.h>
6115 __isl_give isl_set *isl_set_product(
6116 __isl_take isl_set *set1,
6117 __isl_take isl_set *set2);
6119 #include <isl/map.h>
6120 __isl_give isl_basic_map *isl_basic_map_domain_product(
6121 __isl_take isl_basic_map *bmap1,
6122 __isl_take isl_basic_map *bmap2);
6123 __isl_give isl_basic_map *isl_basic_map_range_product(
6124 __isl_take isl_basic_map *bmap1,
6125 __isl_take isl_basic_map *bmap2);
6126 __isl_give isl_basic_map *isl_basic_map_product(
6127 __isl_take isl_basic_map *bmap1,
6128 __isl_take isl_basic_map *bmap2);
6129 __isl_give isl_map *isl_map_domain_product(
6130 __isl_take isl_map *map1,
6131 __isl_take isl_map *map2);
6132 __isl_give isl_map *isl_map_range_product(
6133 __isl_take isl_map *map1,
6134 __isl_take isl_map *map2);
6135 __isl_give isl_map *isl_map_product(
6136 __isl_take isl_map *map1,
6137 __isl_take isl_map *map2);
6139 #include <isl/union_set.h>
6140 __isl_give isl_union_set *isl_union_set_product(
6141 __isl_take isl_union_set *uset1,
6142 __isl_take isl_union_set *uset2);
6144 #include <isl/union_map.h>
6145 __isl_give isl_union_map *isl_union_map_domain_product(
6146 __isl_take isl_union_map *umap1,
6147 __isl_take isl_union_map *umap2);
6148 __isl_give isl_union_map *isl_union_map_range_product(
6149 __isl_take isl_union_map *umap1,
6150 __isl_take isl_union_map *umap2);
6151 __isl_give isl_union_map *isl_union_map_product(
6152 __isl_take isl_union_map *umap1,
6153 __isl_take isl_union_map *umap2);
6155 #include <isl/val.h>
6156 __isl_give isl_multi_val *isl_multi_val_range_product(
6157 __isl_take isl_multi_val *mv1,
6158 __isl_take isl_multi_val *mv2);
6159 __isl_give isl_multi_val *isl_multi_val_product(
6160 __isl_take isl_multi_val *mv1,
6161 __isl_take isl_multi_val *mv2);
6163 #include <isl/aff.h>
6164 __isl_give isl_multi_aff *isl_multi_aff_range_product(
6165 __isl_take isl_multi_aff *ma1,
6166 __isl_take isl_multi_aff *ma2);
6167 __isl_give isl_multi_aff *isl_multi_aff_product(
6168 __isl_take isl_multi_aff *ma1,
6169 __isl_take isl_multi_aff *ma2);
6170 __isl_give isl_multi_pw_aff *
6171 isl_multi_pw_aff_range_product(
6172 __isl_take isl_multi_pw_aff *mpa1,
6173 __isl_take isl_multi_pw_aff *mpa2);
6174 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
6175 __isl_take isl_multi_pw_aff *mpa1,
6176 __isl_take isl_multi_pw_aff *mpa2);
6177 __isl_give isl_pw_multi_aff *
6178 isl_pw_multi_aff_range_product(
6179 __isl_take isl_pw_multi_aff *pma1,
6180 __isl_take isl_pw_multi_aff *pma2);
6181 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
6182 __isl_take isl_pw_multi_aff *pma1,
6183 __isl_take isl_pw_multi_aff *pma2);
6184 __isl_give isl_multi_union_pw_aff *
6185 isl_multi_union_pw_aff_range_product(
6186 __isl_take isl_multi_union_pw_aff *mupa1,
6187 __isl_take isl_multi_union_pw_aff *mupa2);
6189 The above functions compute the cross product of the given
6190 sets, relations or functions. The domains and ranges of the results
6191 are wrapped maps between domains and ranges of the inputs.
6192 To obtain a ``flat'' product, use the following functions
6195 #include <isl/set.h>
6196 __isl_give isl_basic_set *isl_basic_set_flat_product(
6197 __isl_take isl_basic_set *bset1,
6198 __isl_take isl_basic_set *bset2);
6199 __isl_give isl_set *isl_set_flat_product(
6200 __isl_take isl_set *set1,
6201 __isl_take isl_set *set2);
6203 #include <isl/map.h>
6204 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
6205 __isl_take isl_basic_map *bmap1,
6206 __isl_take isl_basic_map *bmap2);
6207 __isl_give isl_map *isl_map_flat_domain_product(
6208 __isl_take isl_map *map1,
6209 __isl_take isl_map *map2);
6210 __isl_give isl_map *isl_map_flat_range_product(
6211 __isl_take isl_map *map1,
6212 __isl_take isl_map *map2);
6213 __isl_give isl_basic_map *isl_basic_map_flat_product(
6214 __isl_take isl_basic_map *bmap1,
6215 __isl_take isl_basic_map *bmap2);
6216 __isl_give isl_map *isl_map_flat_product(
6217 __isl_take isl_map *map1,
6218 __isl_take isl_map *map2);
6220 #include <isl/union_map.h>
6221 __isl_give isl_union_map *
6222 isl_union_map_flat_domain_product(
6223 __isl_take isl_union_map *umap1,
6224 __isl_take isl_union_map *umap2);
6225 __isl_give isl_union_map *
6226 isl_union_map_flat_range_product(
6227 __isl_take isl_union_map *umap1,
6228 __isl_take isl_union_map *umap2);
6230 #include <isl/val.h>
6231 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
6232 __isl_take isl_multi_val *mv1,
6233 __isl_take isl_multi_aff *mv2);
6235 #include <isl/aff.h>
6236 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
6237 __isl_take isl_multi_aff *ma1,
6238 __isl_take isl_multi_aff *ma2);
6239 __isl_give isl_pw_multi_aff *
6240 isl_pw_multi_aff_flat_range_product(
6241 __isl_take isl_pw_multi_aff *pma1,
6242 __isl_take isl_pw_multi_aff *pma2);
6243 __isl_give isl_multi_pw_aff *
6244 isl_multi_pw_aff_flat_range_product(
6245 __isl_take isl_multi_pw_aff *mpa1,
6246 __isl_take isl_multi_pw_aff *mpa2);
6247 __isl_give isl_union_pw_multi_aff *
6248 isl_union_pw_multi_aff_flat_range_product(
6249 __isl_take isl_union_pw_multi_aff *upma1,
6250 __isl_take isl_union_pw_multi_aff *upma2);
6251 __isl_give isl_multi_union_pw_aff *
6252 isl_multi_union_pw_aff_flat_range_product(
6253 __isl_take isl_multi_union_pw_aff *mupa1,
6254 __isl_take isl_multi_union_pw_aff *mupa2);
6256 #include <isl/space.h>
6257 __isl_give isl_space *isl_space_factor_domain(
6258 __isl_take isl_space *space);
6259 __isl_give isl_space *isl_space_factor_range(
6260 __isl_take isl_space *space);
6261 __isl_give isl_space *isl_space_domain_factor_domain(
6262 __isl_take isl_space *space);
6263 __isl_give isl_space *isl_space_domain_factor_range(
6264 __isl_take isl_space *space);
6265 __isl_give isl_space *isl_space_range_factor_domain(
6266 __isl_take isl_space *space);
6267 __isl_give isl_space *isl_space_range_factor_range(
6268 __isl_take isl_space *space);
6270 The functions C<isl_space_range_factor_domain> and
6271 C<isl_space_range_factor_range> extract the two arguments from
6272 the result of a call to C<isl_space_range_product>.
6274 The arguments of a call to a product can be extracted
6275 from the result using the following functions.
6277 #include <isl/map.h>
6278 __isl_give isl_map *isl_map_factor_domain(
6279 __isl_take isl_map *map);
6280 __isl_give isl_map *isl_map_factor_range(
6281 __isl_take isl_map *map);
6282 __isl_give isl_map *isl_map_domain_factor_domain(
6283 __isl_take isl_map *map);
6284 __isl_give isl_map *isl_map_domain_factor_range(
6285 __isl_take isl_map *map);
6286 __isl_give isl_map *isl_map_range_factor_domain(
6287 __isl_take isl_map *map);
6288 __isl_give isl_map *isl_map_range_factor_range(
6289 __isl_take isl_map *map);
6291 #include <isl/union_map.h>
6292 __isl_give isl_union_map *isl_union_map_factor_domain(
6293 __isl_take isl_union_map *umap);
6294 __isl_give isl_union_map *isl_union_map_factor_range(
6295 __isl_take isl_union_map *umap);
6296 __isl_give isl_union_map *
6297 isl_union_map_domain_factor_domain(
6298 __isl_take isl_union_map *umap);
6299 __isl_give isl_union_map *
6300 isl_union_map_domain_factor_range(
6301 __isl_take isl_union_map *umap);
6302 __isl_give isl_union_map *
6303 isl_union_map_range_factor_range(
6304 __isl_take isl_union_map *umap);
6306 #include <isl/val.h>
6307 __isl_give isl_multi_val *isl_multi_val_factor_range(
6308 __isl_take isl_multi_val *mv);
6309 __isl_give isl_multi_val *
6310 isl_multi_val_range_factor_domain(
6311 __isl_take isl_multi_val *mv);
6312 __isl_give isl_multi_val *
6313 isl_multi_val_range_factor_range(
6314 __isl_take isl_multi_val *mv);
6316 #include <isl/aff.h>
6317 __isl_give isl_multi_aff *isl_multi_aff_factor_range(
6318 __isl_take isl_multi_aff *ma);
6319 __isl_give isl_multi_aff *
6320 isl_multi_aff_range_factor_domain(
6321 __isl_take isl_multi_aff *ma);
6322 __isl_give isl_multi_aff *
6323 isl_multi_aff_range_factor_range(
6324 __isl_take isl_multi_aff *ma);
6325 __isl_give isl_multi_pw_aff *
6326 isl_multi_pw_aff_factor_range(
6327 __isl_take isl_multi_pw_aff *mpa);
6328 __isl_give isl_multi_pw_aff *
6329 isl_multi_pw_aff_range_factor_domain(
6330 __isl_take isl_multi_pw_aff *mpa);
6331 __isl_give isl_multi_pw_aff *
6332 isl_multi_pw_aff_range_factor_range(
6333 __isl_take isl_multi_pw_aff *mpa);
6334 __isl_give isl_multi_union_pw_aff *
6335 isl_multi_union_pw_aff_factor_range(
6336 __isl_take isl_multi_union_pw_aff *mupa);
6337 __isl_give isl_multi_union_pw_aff *
6338 isl_multi_union_pw_aff_range_factor_domain(
6339 __isl_take isl_multi_union_pw_aff *mupa);
6340 __isl_give isl_multi_union_pw_aff *
6341 isl_multi_union_pw_aff_range_factor_range(
6342 __isl_take isl_multi_union_pw_aff *mupa);
6344 The splice functions are a generalization of the flat product functions,
6345 where the second argument may be inserted at any position inside
6346 the first argument rather than being placed at the end.
6347 The functions C<isl_multi_val_factor_range>,
6348 C<isl_multi_aff_factor_range>,
6349 C<isl_multi_pw_aff_factor_range> and
6350 C<isl_multi_union_pw_aff_factor_range>
6351 take functions that live in a set space.
6353 #include <isl/val.h>
6354 __isl_give isl_multi_val *isl_multi_val_range_splice(
6355 __isl_take isl_multi_val *mv1, unsigned pos,
6356 __isl_take isl_multi_val *mv2);
6358 #include <isl/aff.h>
6359 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
6360 __isl_take isl_multi_aff *ma1, unsigned pos,
6361 __isl_take isl_multi_aff *ma2);
6362 __isl_give isl_multi_aff *isl_multi_aff_splice(
6363 __isl_take isl_multi_aff *ma1,
6364 unsigned in_pos, unsigned out_pos,
6365 __isl_take isl_multi_aff *ma2);
6366 __isl_give isl_multi_pw_aff *
6367 isl_multi_pw_aff_range_splice(
6368 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
6369 __isl_take isl_multi_pw_aff *mpa2);
6370 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
6371 __isl_take isl_multi_pw_aff *mpa1,
6372 unsigned in_pos, unsigned out_pos,
6373 __isl_take isl_multi_pw_aff *mpa2);
6374 __isl_give isl_multi_union_pw_aff *
6375 isl_multi_union_pw_aff_range_splice(
6376 __isl_take isl_multi_union_pw_aff *mupa1,
6378 __isl_take isl_multi_union_pw_aff *mupa2);
6380 =item * Simplification
6382 When applied to a set or relation,
6383 the gist operation returns a set or relation that has the
6384 same intersection with the context as the input set or relation.
6385 Any implicit equality in the intersection is made explicit in the result,
6386 while all inequalities that are redundant with respect to the intersection
6388 In case of union sets and relations, the gist operation is performed
6391 When applied to a function,
6392 the gist operation applies the set gist operation to each of
6393 the cells in the domain of the input piecewise expression.
6394 The context is also exploited
6395 to simplify the expression associated to each cell.
6397 #include <isl/set.h>
6398 __isl_give isl_basic_set *isl_basic_set_gist(
6399 __isl_take isl_basic_set *bset,
6400 __isl_take isl_basic_set *context);
6401 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
6402 __isl_take isl_set *context);
6403 __isl_give isl_set *isl_set_gist_params(
6404 __isl_take isl_set *set,
6405 __isl_take isl_set *context);
6407 #include <isl/map.h>
6408 __isl_give isl_basic_map *isl_basic_map_gist(
6409 __isl_take isl_basic_map *bmap,
6410 __isl_take isl_basic_map *context);
6411 __isl_give isl_basic_map *isl_basic_map_gist_domain(
6412 __isl_take isl_basic_map *bmap,
6413 __isl_take isl_basic_set *context);
6414 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
6415 __isl_take isl_map *context);
6416 __isl_give isl_map *isl_map_gist_params(
6417 __isl_take isl_map *map,
6418 __isl_take isl_set *context);
6419 __isl_give isl_map *isl_map_gist_domain(
6420 __isl_take isl_map *map,
6421 __isl_take isl_set *context);
6422 __isl_give isl_map *isl_map_gist_range(
6423 __isl_take isl_map *map,
6424 __isl_take isl_set *context);
6426 #include <isl/union_set.h>
6427 __isl_give isl_union_set *isl_union_set_gist(
6428 __isl_take isl_union_set *uset,
6429 __isl_take isl_union_set *context);
6430 __isl_give isl_union_set *isl_union_set_gist_params(
6431 __isl_take isl_union_set *uset,
6432 __isl_take isl_set *set);
6434 #include <isl/union_map.h>
6435 __isl_give isl_union_map *isl_union_map_gist(
6436 __isl_take isl_union_map *umap,
6437 __isl_take isl_union_map *context);
6438 __isl_give isl_union_map *isl_union_map_gist_params(
6439 __isl_take isl_union_map *umap,
6440 __isl_take isl_set *set);
6441 __isl_give isl_union_map *isl_union_map_gist_domain(
6442 __isl_take isl_union_map *umap,
6443 __isl_take isl_union_set *uset);
6444 __isl_give isl_union_map *isl_union_map_gist_range(
6445 __isl_take isl_union_map *umap,
6446 __isl_take isl_union_set *uset);
6448 #include <isl/aff.h>
6449 __isl_give isl_aff *isl_aff_gist_params(
6450 __isl_take isl_aff *aff,
6451 __isl_take isl_set *context);
6452 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
6453 __isl_take isl_set *context);
6454 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
6455 __isl_take isl_multi_aff *maff,
6456 __isl_take isl_set *context);
6457 __isl_give isl_multi_aff *isl_multi_aff_gist(
6458 __isl_take isl_multi_aff *maff,
6459 __isl_take isl_set *context);
6460 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
6461 __isl_take isl_pw_aff *pwaff,
6462 __isl_take isl_set *context);
6463 __isl_give isl_pw_aff *isl_pw_aff_gist(
6464 __isl_take isl_pw_aff *pwaff,
6465 __isl_take isl_set *context);
6466 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
6467 __isl_take isl_pw_multi_aff *pma,
6468 __isl_take isl_set *set);
6469 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
6470 __isl_take isl_pw_multi_aff *pma,
6471 __isl_take isl_set *set);
6472 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
6473 __isl_take isl_multi_pw_aff *mpa,
6474 __isl_take isl_set *set);
6475 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
6476 __isl_take isl_multi_pw_aff *mpa,
6477 __isl_take isl_set *set);
6478 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
6479 __isl_take isl_union_pw_aff *upa,
6480 __isl_take isl_union_set *context);
6481 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
6482 __isl_take isl_union_pw_aff *upa,
6483 __isl_take isl_set *context);
6484 __isl_give isl_union_pw_multi_aff *
6485 isl_union_pw_multi_aff_gist_params(
6486 __isl_take isl_union_pw_multi_aff *upma,
6487 __isl_take isl_set *context);
6488 __isl_give isl_union_pw_multi_aff *
6489 isl_union_pw_multi_aff_gist(
6490 __isl_take isl_union_pw_multi_aff *upma,
6491 __isl_take isl_union_set *context);
6492 __isl_give isl_multi_union_pw_aff *
6493 isl_multi_union_pw_aff_gist_params(
6494 __isl_take isl_multi_union_pw_aff *aff,
6495 __isl_take isl_set *context);
6496 __isl_give isl_multi_union_pw_aff *
6497 isl_multi_union_pw_aff_gist(
6498 __isl_take isl_multi_union_pw_aff *aff,
6499 __isl_take isl_union_set *context);
6501 #include <isl/polynomial.h>
6502 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
6503 __isl_take isl_qpolynomial *qp,
6504 __isl_take isl_set *context);
6505 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
6506 __isl_take isl_qpolynomial *qp,
6507 __isl_take isl_set *context);
6508 __isl_give isl_qpolynomial_fold *
6509 isl_qpolynomial_fold_gist_params(
6510 __isl_take isl_qpolynomial_fold *fold,
6511 __isl_take isl_set *context);
6512 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
6513 __isl_take isl_qpolynomial_fold *fold,
6514 __isl_take isl_set *context);
6515 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
6516 __isl_take isl_pw_qpolynomial *pwqp,
6517 __isl_take isl_set *context);
6518 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
6519 __isl_take isl_pw_qpolynomial *pwqp,
6520 __isl_take isl_set *context);
6521 __isl_give isl_pw_qpolynomial_fold *
6522 isl_pw_qpolynomial_fold_gist(
6523 __isl_take isl_pw_qpolynomial_fold *pwf,
6524 __isl_take isl_set *context);
6525 __isl_give isl_pw_qpolynomial_fold *
6526 isl_pw_qpolynomial_fold_gist_params(
6527 __isl_take isl_pw_qpolynomial_fold *pwf,
6528 __isl_take isl_set *context);
6529 __isl_give isl_union_pw_qpolynomial *
6530 isl_union_pw_qpolynomial_gist_params(
6531 __isl_take isl_union_pw_qpolynomial *upwqp,
6532 __isl_take isl_set *context);
6533 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
6534 __isl_take isl_union_pw_qpolynomial *upwqp,
6535 __isl_take isl_union_set *context);
6536 __isl_give isl_union_pw_qpolynomial_fold *
6537 isl_union_pw_qpolynomial_fold_gist(
6538 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6539 __isl_take isl_union_set *context);
6540 __isl_give isl_union_pw_qpolynomial_fold *
6541 isl_union_pw_qpolynomial_fold_gist_params(
6542 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6543 __isl_take isl_set *context);
6545 =item * Binary Arithmethic Operations
6547 #include <isl/val.h>
6548 __isl_give isl_multi_val *isl_multi_val_add(
6549 __isl_take isl_multi_val *mv1,
6550 __isl_take isl_multi_val *mv2);
6551 __isl_give isl_multi_val *isl_multi_val_sub(
6552 __isl_take isl_multi_val *mv1,
6553 __isl_take isl_multi_val *mv2);
6555 #include <isl/aff.h>
6556 __isl_give isl_aff *isl_aff_add(
6557 __isl_take isl_aff *aff1,
6558 __isl_take isl_aff *aff2);
6559 __isl_give isl_multi_aff *isl_multi_aff_add(
6560 __isl_take isl_multi_aff *maff1,
6561 __isl_take isl_multi_aff *maff2);
6562 __isl_give isl_pw_aff *isl_pw_aff_add(
6563 __isl_take isl_pw_aff *pwaff1,
6564 __isl_take isl_pw_aff *pwaff2);
6565 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add(
6566 __isl_take isl_multi_pw_aff *mpa1,
6567 __isl_take isl_multi_pw_aff *mpa2);
6568 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
6569 __isl_take isl_pw_multi_aff *pma1,
6570 __isl_take isl_pw_multi_aff *pma2);
6571 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
6572 __isl_take isl_union_pw_aff *upa1,
6573 __isl_take isl_union_pw_aff *upa2);
6574 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
6575 __isl_take isl_union_pw_multi_aff *upma1,
6576 __isl_take isl_union_pw_multi_aff *upma2);
6577 __isl_give isl_multi_union_pw_aff *
6578 isl_multi_union_pw_aff_add(
6579 __isl_take isl_multi_union_pw_aff *mupa1,
6580 __isl_take isl_multi_union_pw_aff *mupa2);
6581 __isl_give isl_pw_aff *isl_pw_aff_min(
6582 __isl_take isl_pw_aff *pwaff1,
6583 __isl_take isl_pw_aff *pwaff2);
6584 __isl_give isl_pw_aff *isl_pw_aff_max(
6585 __isl_take isl_pw_aff *pwaff1,
6586 __isl_take isl_pw_aff *pwaff2);
6587 __isl_give isl_aff *isl_aff_sub(
6588 __isl_take isl_aff *aff1,
6589 __isl_take isl_aff *aff2);
6590 __isl_give isl_multi_aff *isl_multi_aff_sub(
6591 __isl_take isl_multi_aff *ma1,
6592 __isl_take isl_multi_aff *ma2);
6593 __isl_give isl_pw_aff *isl_pw_aff_sub(
6594 __isl_take isl_pw_aff *pwaff1,
6595 __isl_take isl_pw_aff *pwaff2);
6596 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
6597 __isl_take isl_multi_pw_aff *mpa1,
6598 __isl_take isl_multi_pw_aff *mpa2);
6599 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
6600 __isl_take isl_pw_multi_aff *pma1,
6601 __isl_take isl_pw_multi_aff *pma2);
6602 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
6603 __isl_take isl_union_pw_aff *upa1,
6604 __isl_take isl_union_pw_aff *upa2);
6605 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
6606 __isl_take isl_union_pw_multi_aff *upma1,
6607 __isl_take isl_union_pw_multi_aff *upma2);
6608 __isl_give isl_multi_union_pw_aff *
6609 isl_multi_union_pw_aff_sub(
6610 __isl_take isl_multi_union_pw_aff *mupa1,
6611 __isl_take isl_multi_union_pw_aff *mupa2);
6613 C<isl_aff_sub> subtracts the second argument from the first.
6615 #include <isl/polynomial.h>
6616 __isl_give isl_qpolynomial *isl_qpolynomial_add(
6617 __isl_take isl_qpolynomial *qp1,
6618 __isl_take isl_qpolynomial *qp2);
6619 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
6620 __isl_take isl_pw_qpolynomial *pwqp1,
6621 __isl_take isl_pw_qpolynomial *pwqp2);
6622 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
6623 __isl_take isl_pw_qpolynomial *pwqp1,
6624 __isl_take isl_pw_qpolynomial *pwqp2);
6625 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
6626 __isl_take isl_pw_qpolynomial_fold *pwf1,
6627 __isl_take isl_pw_qpolynomial_fold *pwf2);
6628 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
6629 __isl_take isl_union_pw_qpolynomial *upwqp1,
6630 __isl_take isl_union_pw_qpolynomial *upwqp2);
6631 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
6632 __isl_take isl_qpolynomial *qp1,
6633 __isl_take isl_qpolynomial *qp2);
6634 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
6635 __isl_take isl_pw_qpolynomial *pwqp1,
6636 __isl_take isl_pw_qpolynomial *pwqp2);
6637 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
6638 __isl_take isl_union_pw_qpolynomial *upwqp1,
6639 __isl_take isl_union_pw_qpolynomial *upwqp2);
6640 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
6641 __isl_take isl_pw_qpolynomial_fold *pwf1,
6642 __isl_take isl_pw_qpolynomial_fold *pwf2);
6643 __isl_give isl_union_pw_qpolynomial_fold *
6644 isl_union_pw_qpolynomial_fold_fold(
6645 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
6646 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
6648 #include <isl/aff.h>
6649 __isl_give isl_pw_aff *isl_pw_aff_union_add(
6650 __isl_take isl_pw_aff *pwaff1,
6651 __isl_take isl_pw_aff *pwaff2);
6652 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
6653 __isl_take isl_pw_multi_aff *pma1,
6654 __isl_take isl_pw_multi_aff *pma2);
6655 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
6656 __isl_take isl_union_pw_aff *upa1,
6657 __isl_take isl_union_pw_aff *upa2);
6658 __isl_give isl_union_pw_multi_aff *
6659 isl_union_pw_multi_aff_union_add(
6660 __isl_take isl_union_pw_multi_aff *upma1,
6661 __isl_take isl_union_pw_multi_aff *upma2);
6662 __isl_give isl_multi_union_pw_aff *
6663 isl_multi_union_pw_aff_union_add(
6664 __isl_take isl_multi_union_pw_aff *mupa1,
6665 __isl_take isl_multi_union_pw_aff *mupa2);
6666 __isl_give isl_pw_aff *isl_pw_aff_union_min(
6667 __isl_take isl_pw_aff *pwaff1,
6668 __isl_take isl_pw_aff *pwaff2);
6669 __isl_give isl_pw_aff *isl_pw_aff_union_max(
6670 __isl_take isl_pw_aff *pwaff1,
6671 __isl_take isl_pw_aff *pwaff2);
6673 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
6674 expression with a domain that is the union of those of C<pwaff1> and
6675 C<pwaff2> and such that on each cell, the quasi-affine expression is
6676 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
6677 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
6678 associated expression is the defined one.
6679 This in contrast to the C<isl_pw_aff_max> function, which is
6680 only defined on the shared definition domain of the arguments.
6682 #include <isl/val.h>
6683 __isl_give isl_multi_val *isl_multi_val_add_val(
6684 __isl_take isl_multi_val *mv,
6685 __isl_take isl_val *v);
6686 __isl_give isl_multi_val *isl_multi_val_mod_val(
6687 __isl_take isl_multi_val *mv,
6688 __isl_take isl_val *v);
6689 __isl_give isl_multi_val *isl_multi_val_scale_val(
6690 __isl_take isl_multi_val *mv,
6691 __isl_take isl_val *v);
6692 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
6693 __isl_take isl_multi_val *mv,
6694 __isl_take isl_val *v);
6696 #include <isl/aff.h>
6697 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
6698 __isl_take isl_val *mod);
6699 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
6700 __isl_take isl_pw_aff *pa,
6701 __isl_take isl_val *mod);
6702 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
6703 __isl_take isl_union_pw_aff *upa,
6704 __isl_take isl_val *f);
6705 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
6706 __isl_take isl_val *v);
6707 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
6708 __isl_take isl_multi_aff *ma,
6709 __isl_take isl_val *v);
6710 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
6711 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
6712 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
6713 __isl_take isl_multi_pw_aff *mpa,
6714 __isl_take isl_val *v);
6715 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
6716 __isl_take isl_pw_multi_aff *pma,
6717 __isl_take isl_val *v);
6718 __isl_give isl_union_pw_multi_aff *
6719 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
6720 __isl_take isl_union_pw_aff *upa,
6721 __isl_take isl_val *f);
6722 isl_union_pw_multi_aff_scale_val(
6723 __isl_take isl_union_pw_multi_aff *upma,
6724 __isl_take isl_val *val);
6725 __isl_give isl_multi_union_pw_aff *
6726 isl_multi_union_pw_aff_scale_val(
6727 __isl_take isl_multi_union_pw_aff *mupa,
6728 __isl_take isl_val *v);
6729 __isl_give isl_aff *isl_aff_scale_down_ui(
6730 __isl_take isl_aff *aff, unsigned f);
6731 __isl_give isl_aff *isl_aff_scale_down_val(
6732 __isl_take isl_aff *aff, __isl_take isl_val *v);
6733 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
6734 __isl_take isl_multi_aff *ma,
6735 __isl_take isl_val *v);
6736 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
6737 __isl_take isl_pw_aff *pa,
6738 __isl_take isl_val *f);
6739 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
6740 __isl_take isl_multi_pw_aff *mpa,
6741 __isl_take isl_val *v);
6742 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
6743 __isl_take isl_pw_multi_aff *pma,
6744 __isl_take isl_val *v);
6745 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
6746 __isl_take isl_union_pw_aff *upa,
6747 __isl_take isl_val *v);
6748 __isl_give isl_union_pw_multi_aff *
6749 isl_union_pw_multi_aff_scale_down_val(
6750 __isl_take isl_union_pw_multi_aff *upma,
6751 __isl_take isl_val *val);
6752 __isl_give isl_multi_union_pw_aff *
6753 isl_multi_union_pw_aff_scale_down_val(
6754 __isl_take isl_multi_union_pw_aff *mupa,
6755 __isl_take isl_val *v);
6757 #include <isl/polynomial.h>
6758 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
6759 __isl_take isl_qpolynomial *qp,
6760 __isl_take isl_val *v);
6761 __isl_give isl_qpolynomial_fold *
6762 isl_qpolynomial_fold_scale_val(
6763 __isl_take isl_qpolynomial_fold *fold,
6764 __isl_take isl_val *v);
6765 __isl_give isl_pw_qpolynomial *
6766 isl_pw_qpolynomial_scale_val(
6767 __isl_take isl_pw_qpolynomial *pwqp,
6768 __isl_take isl_val *v);
6769 __isl_give isl_pw_qpolynomial_fold *
6770 isl_pw_qpolynomial_fold_scale_val(
6771 __isl_take isl_pw_qpolynomial_fold *pwf,
6772 __isl_take isl_val *v);
6773 __isl_give isl_union_pw_qpolynomial *
6774 isl_union_pw_qpolynomial_scale_val(
6775 __isl_take isl_union_pw_qpolynomial *upwqp,
6776 __isl_take isl_val *v);
6777 __isl_give isl_union_pw_qpolynomial_fold *
6778 isl_union_pw_qpolynomial_fold_scale_val(
6779 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6780 __isl_take isl_val *v);
6781 __isl_give isl_qpolynomial *
6782 isl_qpolynomial_scale_down_val(
6783 __isl_take isl_qpolynomial *qp,
6784 __isl_take isl_val *v);
6785 __isl_give isl_qpolynomial_fold *
6786 isl_qpolynomial_fold_scale_down_val(
6787 __isl_take isl_qpolynomial_fold *fold,
6788 __isl_take isl_val *v);
6789 __isl_give isl_pw_qpolynomial *
6790 isl_pw_qpolynomial_scale_down_val(
6791 __isl_take isl_pw_qpolynomial *pwqp,
6792 __isl_take isl_val *v);
6793 __isl_give isl_pw_qpolynomial_fold *
6794 isl_pw_qpolynomial_fold_scale_down_val(
6795 __isl_take isl_pw_qpolynomial_fold *pwf,
6796 __isl_take isl_val *v);
6797 __isl_give isl_union_pw_qpolynomial *
6798 isl_union_pw_qpolynomial_scale_down_val(
6799 __isl_take isl_union_pw_qpolynomial *upwqp,
6800 __isl_take isl_val *v);
6801 __isl_give isl_union_pw_qpolynomial_fold *
6802 isl_union_pw_qpolynomial_fold_scale_down_val(
6803 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6804 __isl_take isl_val *v);
6806 #include <isl/val.h>
6807 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
6808 __isl_take isl_multi_val *mv1,
6809 __isl_take isl_multi_val *mv2);
6810 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
6811 __isl_take isl_multi_val *mv1,
6812 __isl_take isl_multi_val *mv2);
6813 __isl_give isl_multi_val *
6814 isl_multi_val_scale_down_multi_val(
6815 __isl_take isl_multi_val *mv1,
6816 __isl_take isl_multi_val *mv2);
6818 #include <isl/aff.h>
6819 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
6820 __isl_take isl_multi_aff *ma,
6821 __isl_take isl_multi_val *mv);
6822 __isl_give isl_multi_union_pw_aff *
6823 isl_multi_union_pw_aff_mod_multi_val(
6824 __isl_take isl_multi_union_pw_aff *upma,
6825 __isl_take isl_multi_val *mv);
6826 __isl_give isl_multi_pw_aff *
6827 isl_multi_pw_aff_mod_multi_val(
6828 __isl_take isl_multi_pw_aff *mpa,
6829 __isl_take isl_multi_val *mv);
6830 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
6831 __isl_take isl_multi_aff *ma,
6832 __isl_take isl_multi_val *mv);
6833 __isl_give isl_pw_multi_aff *
6834 isl_pw_multi_aff_scale_multi_val(
6835 __isl_take isl_pw_multi_aff *pma,
6836 __isl_take isl_multi_val *mv);
6837 __isl_give isl_multi_pw_aff *
6838 isl_multi_pw_aff_scale_multi_val(
6839 __isl_take isl_multi_pw_aff *mpa,
6840 __isl_take isl_multi_val *mv);
6841 __isl_give isl_multi_union_pw_aff *
6842 isl_multi_union_pw_aff_scale_multi_val(
6843 __isl_take isl_multi_union_pw_aff *mupa,
6844 __isl_take isl_multi_val *mv);
6845 __isl_give isl_union_pw_multi_aff *
6846 isl_union_pw_multi_aff_scale_multi_val(
6847 __isl_take isl_union_pw_multi_aff *upma,
6848 __isl_take isl_multi_val *mv);
6849 __isl_give isl_multi_aff *
6850 isl_multi_aff_scale_down_multi_val(
6851 __isl_take isl_multi_aff *ma,
6852 __isl_take isl_multi_val *mv);
6853 __isl_give isl_multi_pw_aff *
6854 isl_multi_pw_aff_scale_down_multi_val(
6855 __isl_take isl_multi_pw_aff *mpa,
6856 __isl_take isl_multi_val *mv);
6857 __isl_give isl_multi_union_pw_aff *
6858 isl_multi_union_pw_aff_scale_down_multi_val(
6859 __isl_take isl_multi_union_pw_aff *mupa,
6860 __isl_take isl_multi_val *mv);
6862 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
6863 by the corresponding elements of C<mv>.
6865 #include <isl/aff.h>
6866 __isl_give isl_aff *isl_aff_mul(
6867 __isl_take isl_aff *aff1,
6868 __isl_take isl_aff *aff2);
6869 __isl_give isl_aff *isl_aff_div(
6870 __isl_take isl_aff *aff1,
6871 __isl_take isl_aff *aff2);
6872 __isl_give isl_pw_aff *isl_pw_aff_mul(
6873 __isl_take isl_pw_aff *pwaff1,
6874 __isl_take isl_pw_aff *pwaff2);
6875 __isl_give isl_pw_aff *isl_pw_aff_div(
6876 __isl_take isl_pw_aff *pa1,
6877 __isl_take isl_pw_aff *pa2);
6878 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
6879 __isl_take isl_pw_aff *pa1,
6880 __isl_take isl_pw_aff *pa2);
6881 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
6882 __isl_take isl_pw_aff *pa1,
6883 __isl_take isl_pw_aff *pa2);
6885 When multiplying two affine expressions, at least one of the two needs
6886 to be a constant. Similarly, when dividing an affine expression by another,
6887 the second expression needs to be a constant.
6888 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
6889 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
6892 #include <isl/polynomial.h>
6893 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
6894 __isl_take isl_qpolynomial *qp1,
6895 __isl_take isl_qpolynomial *qp2);
6896 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
6897 __isl_take isl_pw_qpolynomial *pwqp1,
6898 __isl_take isl_pw_qpolynomial *pwqp2);
6899 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
6900 __isl_take isl_union_pw_qpolynomial *upwqp1,
6901 __isl_take isl_union_pw_qpolynomial *upwqp2);
6905 =head3 Lexicographic Optimization
6907 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
6908 the following functions
6909 compute a set that contains the lexicographic minimum or maximum
6910 of the elements in C<set> (or C<bset>) for those values of the parameters
6911 that satisfy C<dom>.
6912 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
6913 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
6915 In other words, the union of the parameter values
6916 for which the result is non-empty and of C<*empty>
6919 #include <isl/set.h>
6920 __isl_give isl_set *isl_basic_set_partial_lexmin(
6921 __isl_take isl_basic_set *bset,
6922 __isl_take isl_basic_set *dom,
6923 __isl_give isl_set **empty);
6924 __isl_give isl_set *isl_basic_set_partial_lexmax(
6925 __isl_take isl_basic_set *bset,
6926 __isl_take isl_basic_set *dom,
6927 __isl_give isl_set **empty);
6928 __isl_give isl_set *isl_set_partial_lexmin(
6929 __isl_take isl_set *set, __isl_take isl_set *dom,
6930 __isl_give isl_set **empty);
6931 __isl_give isl_set *isl_set_partial_lexmax(
6932 __isl_take isl_set *set, __isl_take isl_set *dom,
6933 __isl_give isl_set **empty);
6935 Given a (basic) set C<set> (or C<bset>), the following functions simply
6936 return a set containing the lexicographic minimum or maximum
6937 of the elements in C<set> (or C<bset>).
6938 In case of union sets, the optimum is computed per space.
6940 #include <isl/set.h>
6941 __isl_give isl_set *isl_basic_set_lexmin(
6942 __isl_take isl_basic_set *bset);
6943 __isl_give isl_set *isl_basic_set_lexmax(
6944 __isl_take isl_basic_set *bset);
6945 __isl_give isl_set *isl_set_lexmin(
6946 __isl_take isl_set *set);
6947 __isl_give isl_set *isl_set_lexmax(
6948 __isl_take isl_set *set);
6949 __isl_give isl_union_set *isl_union_set_lexmin(
6950 __isl_take isl_union_set *uset);
6951 __isl_give isl_union_set *isl_union_set_lexmax(
6952 __isl_take isl_union_set *uset);
6954 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
6955 the following functions
6956 compute a relation that maps each element of C<dom>
6957 to the single lexicographic minimum or maximum
6958 of the elements that are associated to that same
6959 element in C<map> (or C<bmap>).
6960 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
6961 that contains the elements in C<dom> that do not map
6962 to any elements in C<map> (or C<bmap>).
6963 In other words, the union of the domain of the result and of C<*empty>
6966 #include <isl/map.h>
6967 __isl_give isl_map *isl_basic_map_partial_lexmax(
6968 __isl_take isl_basic_map *bmap,
6969 __isl_take isl_basic_set *dom,
6970 __isl_give isl_set **empty);
6971 __isl_give isl_map *isl_basic_map_partial_lexmin(
6972 __isl_take isl_basic_map *bmap,
6973 __isl_take isl_basic_set *dom,
6974 __isl_give isl_set **empty);
6975 __isl_give isl_map *isl_map_partial_lexmax(
6976 __isl_take isl_map *map, __isl_take isl_set *dom,
6977 __isl_give isl_set **empty);
6978 __isl_give isl_map *isl_map_partial_lexmin(
6979 __isl_take isl_map *map, __isl_take isl_set *dom,
6980 __isl_give isl_set **empty);
6982 Given a (basic) map C<map> (or C<bmap>), the following functions simply
6983 return a map mapping each element in the domain of
6984 C<map> (or C<bmap>) to the lexicographic minimum or maximum
6985 of all elements associated to that element.
6986 In case of union relations, the optimum is computed per space.
6988 #include <isl/map.h>
6989 __isl_give isl_map *isl_basic_map_lexmin(
6990 __isl_take isl_basic_map *bmap);
6991 __isl_give isl_map *isl_basic_map_lexmax(
6992 __isl_take isl_basic_map *bmap);
6993 __isl_give isl_map *isl_map_lexmin(
6994 __isl_take isl_map *map);
6995 __isl_give isl_map *isl_map_lexmax(
6996 __isl_take isl_map *map);
6997 __isl_give isl_union_map *isl_union_map_lexmin(
6998 __isl_take isl_union_map *umap);
6999 __isl_give isl_union_map *isl_union_map_lexmax(
7000 __isl_take isl_union_map *umap);
7002 The following functions return their result in the form of
7003 a piecewise multi-affine expression,
7004 but are otherwise equivalent to the corresponding functions
7005 returning a basic set or relation.
7007 #include <isl/set.h>
7008 __isl_give isl_pw_multi_aff *
7009 isl_basic_set_partial_lexmin_pw_multi_aff(
7010 __isl_take isl_basic_set *bset,
7011 __isl_take isl_basic_set *dom,
7012 __isl_give isl_set **empty);
7013 __isl_give isl_pw_multi_aff *
7014 isl_basic_set_partial_lexmax_pw_multi_aff(
7015 __isl_take isl_basic_set *bset,
7016 __isl_take isl_basic_set *dom,
7017 __isl_give isl_set **empty);
7018 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
7019 __isl_take isl_set *set);
7020 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
7021 __isl_take isl_set *set);
7023 #include <isl/map.h>
7024 __isl_give isl_pw_multi_aff *
7025 isl_basic_map_lexmin_pw_multi_aff(
7026 __isl_take isl_basic_map *bmap);
7027 __isl_give isl_pw_multi_aff *
7028 isl_basic_map_partial_lexmin_pw_multi_aff(
7029 __isl_take isl_basic_map *bmap,
7030 __isl_take isl_basic_set *dom,
7031 __isl_give isl_set **empty);
7032 __isl_give isl_pw_multi_aff *
7033 isl_basic_map_partial_lexmax_pw_multi_aff(
7034 __isl_take isl_basic_map *bmap,
7035 __isl_take isl_basic_set *dom,
7036 __isl_give isl_set **empty);
7037 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
7038 __isl_take isl_map *map);
7039 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
7040 __isl_take isl_map *map);
7042 The following functions return the lexicographic minimum or maximum
7043 on the shared domain of the inputs and the single defined function
7044 on those parts of the domain where only a single function is defined.
7046 #include <isl/aff.h>
7047 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
7048 __isl_take isl_pw_multi_aff *pma1,
7049 __isl_take isl_pw_multi_aff *pma2);
7050 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
7051 __isl_take isl_pw_multi_aff *pma1,
7052 __isl_take isl_pw_multi_aff *pma2);
7054 =head2 Ternary Operations
7056 #include <isl/aff.h>
7057 __isl_give isl_pw_aff *isl_pw_aff_cond(
7058 __isl_take isl_pw_aff *cond,
7059 __isl_take isl_pw_aff *pwaff_true,
7060 __isl_take isl_pw_aff *pwaff_false);
7062 The function C<isl_pw_aff_cond> performs a conditional operator
7063 and returns an expression that is equal to C<pwaff_true>
7064 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
7065 where C<cond> is zero.
7069 Lists are defined over several element types, including
7070 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_union_pw_aff>,
7071 C<isl_union_pw_multi_aff>, C<isl_constraint>,
7072 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
7073 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
7074 Here we take lists of C<isl_set>s as an example.
7075 Lists can be created, copied, modified and freed using the following functions.
7077 #include <isl/set.h>
7078 __isl_give isl_set_list *isl_set_list_from_set(
7079 __isl_take isl_set *el);
7080 __isl_give isl_set_list *isl_set_list_alloc(
7081 isl_ctx *ctx, int n);
7082 __isl_give isl_set_list *isl_set_list_copy(
7083 __isl_keep isl_set_list *list);
7084 __isl_give isl_set_list *isl_set_list_insert(
7085 __isl_take isl_set_list *list, unsigned pos,
7086 __isl_take isl_set *el);
7087 __isl_give isl_set_list *isl_set_list_add(
7088 __isl_take isl_set_list *list,
7089 __isl_take isl_set *el);
7090 __isl_give isl_set_list *isl_set_list_drop(
7091 __isl_take isl_set_list *list,
7092 unsigned first, unsigned n);
7093 __isl_give isl_set_list *isl_set_list_set_set(
7094 __isl_take isl_set_list *list, int index,
7095 __isl_take isl_set *set);
7096 __isl_give isl_set_list *isl_set_list_concat(
7097 __isl_take isl_set_list *list1,
7098 __isl_take isl_set_list *list2);
7099 __isl_give isl_set_list *isl_set_list_sort(
7100 __isl_take isl_set_list *list,
7101 int (*cmp)(__isl_keep isl_set *a,
7102 __isl_keep isl_set *b, void *user),
7104 __isl_null isl_set_list *isl_set_list_free(
7105 __isl_take isl_set_list *list);
7107 C<isl_set_list_alloc> creates an empty list with an initial capacity
7108 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
7109 add elements to a list, increasing its capacity as needed.
7110 C<isl_set_list_from_set> creates a list with a single element.
7112 Lists can be inspected using the following functions.
7114 #include <isl/set.h>
7115 int isl_set_list_n_set(__isl_keep isl_set_list *list);
7116 __isl_give isl_set *isl_set_list_get_set(
7117 __isl_keep isl_set_list *list, int index);
7118 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list,
7119 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7121 isl_stat isl_set_list_foreach_scc(
7122 __isl_keep isl_set_list *list,
7123 isl_bool (*follows)(__isl_keep isl_set *a,
7124 __isl_keep isl_set *b, void *user),
7126 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7129 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
7130 strongly connected components of the graph with as vertices the elements
7131 of C<list> and a directed edge from vertex C<b> to vertex C<a>
7132 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
7133 should return C<-1> on error.
7135 Lists can be printed using
7137 #include <isl/set.h>
7138 __isl_give isl_printer *isl_printer_print_set_list(
7139 __isl_take isl_printer *p,
7140 __isl_keep isl_set_list *list);
7142 =head2 Associative arrays
7144 Associative arrays map isl objects of a specific type to isl objects
7145 of some (other) specific type. They are defined for several pairs
7146 of types, including (C<isl_map>, C<isl_basic_set>),
7147 (C<isl_id>, C<isl_ast_expr>) and.
7148 (C<isl_id>, C<isl_pw_aff>).
7149 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
7152 Associative arrays can be created, copied and freed using
7153 the following functions.
7155 #include <isl/id_to_ast_expr.h>
7156 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
7157 isl_ctx *ctx, int min_size);
7158 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
7159 __isl_keep isl_id_to_ast_expr *id2expr);
7160 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
7161 __isl_take isl_id_to_ast_expr *id2expr);
7163 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
7164 to specify the expected size of the associative array.
7165 The associative array will be grown automatically as needed.
7167 Associative arrays can be inspected using the following functions.
7169 #include <isl/id_to_ast_expr.h>
7170 isl_bool isl_id_to_ast_expr_has(
7171 __isl_keep isl_id_to_ast_expr *id2expr,
7172 __isl_keep isl_id *key);
7173 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
7174 __isl_keep isl_id_to_ast_expr *id2expr,
7175 __isl_take isl_id *key);
7176 isl_stat isl_id_to_ast_expr_foreach(
7177 __isl_keep isl_id_to_ast_expr *id2expr,
7178 isl_stat (*fn)(__isl_take isl_id *key,
7179 __isl_take isl_ast_expr *val, void *user),
7182 They can be modified using the following function.
7184 #include <isl/id_to_ast_expr.h>
7185 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
7186 __isl_take isl_id_to_ast_expr *id2expr,
7187 __isl_take isl_id *key,
7188 __isl_take isl_ast_expr *val);
7189 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
7190 __isl_take isl_id_to_ast_expr *id2expr,
7191 __isl_take isl_id *key);
7193 Associative arrays can be printed using the following function.
7195 #include <isl/id_to_ast_expr.h>
7196 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
7197 __isl_take isl_printer *p,
7198 __isl_keep isl_id_to_ast_expr *id2expr);
7202 Vectors can be created, copied and freed using the following functions.
7204 #include <isl/vec.h>
7205 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
7207 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
7208 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
7210 Note that the elements of a newly created vector may have arbitrary values.
7211 The elements can be changed and inspected using the following functions.
7213 int isl_vec_size(__isl_keep isl_vec *vec);
7214 __isl_give isl_val *isl_vec_get_element_val(
7215 __isl_keep isl_vec *vec, int pos);
7216 __isl_give isl_vec *isl_vec_set_element_si(
7217 __isl_take isl_vec *vec, int pos, int v);
7218 __isl_give isl_vec *isl_vec_set_element_val(
7219 __isl_take isl_vec *vec, int pos,
7220 __isl_take isl_val *v);
7221 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
7223 __isl_give isl_vec *isl_vec_set_val(
7224 __isl_take isl_vec *vec, __isl_take isl_val *v);
7225 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
7226 __isl_keep isl_vec *vec2, int pos);
7228 C<isl_vec_get_element> will return a negative value if anything went wrong.
7229 In that case, the value of C<*v> is undefined.
7231 The following function can be used to concatenate two vectors.
7233 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
7234 __isl_take isl_vec *vec2);
7238 Matrices can be created, copied and freed using the following functions.
7240 #include <isl/mat.h>
7241 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
7242 unsigned n_row, unsigned n_col);
7243 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
7244 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
7246 Note that the elements of a newly created matrix may have arbitrary values.
7247 The elements can be changed and inspected using the following functions.
7249 int isl_mat_rows(__isl_keep isl_mat *mat);
7250 int isl_mat_cols(__isl_keep isl_mat *mat);
7251 __isl_give isl_val *isl_mat_get_element_val(
7252 __isl_keep isl_mat *mat, int row, int col);
7253 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
7254 int row, int col, int v);
7255 __isl_give isl_mat *isl_mat_set_element_val(
7256 __isl_take isl_mat *mat, int row, int col,
7257 __isl_take isl_val *v);
7259 C<isl_mat_get_element> will return a negative value if anything went wrong.
7260 In that case, the value of C<*v> is undefined.
7262 The following function can be used to compute the (right) inverse
7263 of a matrix, i.e., a matrix such that the product of the original
7264 and the inverse (in that order) is a multiple of the identity matrix.
7265 The input matrix is assumed to be of full row-rank.
7267 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
7269 The following function can be used to compute the (right) kernel
7270 (or null space) of a matrix, i.e., a matrix such that the product of
7271 the original and the kernel (in that order) is the zero matrix.
7273 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
7275 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
7277 The following functions determine
7278 an upper or lower bound on a quasipolynomial over its domain.
7280 __isl_give isl_pw_qpolynomial_fold *
7281 isl_pw_qpolynomial_bound(
7282 __isl_take isl_pw_qpolynomial *pwqp,
7283 enum isl_fold type, int *tight);
7285 __isl_give isl_union_pw_qpolynomial_fold *
7286 isl_union_pw_qpolynomial_bound(
7287 __isl_take isl_union_pw_qpolynomial *upwqp,
7288 enum isl_fold type, int *tight);
7290 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
7291 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
7292 is the returned bound is known be tight, i.e., for each value
7293 of the parameters there is at least
7294 one element in the domain that reaches the bound.
7295 If the domain of C<pwqp> is not wrapping, then the bound is computed
7296 over all elements in that domain and the result has a purely parametric
7297 domain. If the domain of C<pwqp> is wrapping, then the bound is
7298 computed over the range of the wrapped relation. The domain of the
7299 wrapped relation becomes the domain of the result.
7301 =head2 Parametric Vertex Enumeration
7303 The parametric vertex enumeration described in this section
7304 is mainly intended to be used internally and by the C<barvinok>
7307 #include <isl/vertices.h>
7308 __isl_give isl_vertices *isl_basic_set_compute_vertices(
7309 __isl_keep isl_basic_set *bset);
7311 The function C<isl_basic_set_compute_vertices> performs the
7312 actual computation of the parametric vertices and the chamber
7313 decomposition and store the result in an C<isl_vertices> object.
7314 This information can be queried by either iterating over all
7315 the vertices or iterating over all the chambers or cells
7316 and then iterating over all vertices that are active on the chamber.
7318 isl_stat isl_vertices_foreach_vertex(
7319 __isl_keep isl_vertices *vertices,
7320 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7321 void *user), void *user);
7323 isl_stat isl_vertices_foreach_cell(
7324 __isl_keep isl_vertices *vertices,
7325 isl_stat (*fn)(__isl_take isl_cell *cell,
7326 void *user), void *user);
7327 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
7328 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7329 void *user), void *user);
7331 Other operations that can be performed on an C<isl_vertices> object are
7334 int isl_vertices_get_n_vertices(
7335 __isl_keep isl_vertices *vertices);
7336 void isl_vertices_free(__isl_take isl_vertices *vertices);
7338 Vertices can be inspected and destroyed using the following functions.
7340 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
7341 __isl_give isl_basic_set *isl_vertex_get_domain(
7342 __isl_keep isl_vertex *vertex);
7343 __isl_give isl_multi_aff *isl_vertex_get_expr(
7344 __isl_keep isl_vertex *vertex);
7345 void isl_vertex_free(__isl_take isl_vertex *vertex);
7347 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
7348 describing the vertex in terms of the parameters,
7349 while C<isl_vertex_get_domain> returns the activity domain
7352 Chambers can be inspected and destroyed using the following functions.
7354 __isl_give isl_basic_set *isl_cell_get_domain(
7355 __isl_keep isl_cell *cell);
7356 void isl_cell_free(__isl_take isl_cell *cell);
7358 =head1 Polyhedral Compilation Library
7360 This section collects functionality in C<isl> that has been specifically
7361 designed for use during polyhedral compilation.
7363 =head2 Schedule Trees
7365 A schedule tree is a structured representation of a schedule,
7366 assigning a relative order to a set of domain elements.
7367 The relative order expressed by the schedule tree is
7368 defined recursively. In particular, the order between
7369 two domain elements is determined by the node that is closest
7370 to the root that refers to both elements and that orders them apart.
7371 Each node in the tree is of one of several types.
7372 The root node is always of type C<isl_schedule_node_domain>
7373 (or C<isl_schedule_node_extension>)
7374 and it describes the (extra) domain elements to which the schedule applies.
7375 The other types of nodes are as follows.
7379 =item C<isl_schedule_node_band>
7381 A band of schedule dimensions. Each schedule dimension is represented
7382 by a union piecewise quasi-affine expression. If this expression
7383 assigns a different value to two domain elements, while all previous
7384 schedule dimensions in the same band assign them the same value,
7385 then the two domain elements are ordered according to these two
7388 =item C<isl_schedule_node_expansion>
7390 An expansion node maps each of the domain elements that reach the node
7391 to one or more domain elements. The image of this mapping forms
7392 the set of domain elements that reach the child of the expansion node.
7393 The function that maps each of the expanded domain elements
7394 to the original domain element from which it was expanded
7395 is called the contraction.
7397 =item C<isl_schedule_node_filter>
7399 A filter node does not impose any ordering, but rather intersects
7400 the set of domain elements that the current subtree refers to
7401 with a given union set. The subtree of the filter node only
7402 refers to domain elements in the intersection.
7403 A filter node is typically only used a child of a sequence or
7406 =item C<isl_schedule_node_leaf>
7408 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
7410 =item C<isl_schedule_node_mark>
7412 A mark node can be used to attach any kind of information to a subtree
7413 of the schedule tree.
7415 =item C<isl_schedule_node_sequence>
7417 A sequence node has one or more children, each of which is a filter node.
7418 The filters on these filter nodes form a partition of
7419 the domain elements that the current subtree refers to.
7420 If two domain elements appear in distinct filters then the sequence
7421 node orders them according to the child positions of the corresponding
7424 =item C<isl_schedule_node_set>
7426 A set node is similar to a sequence node, except that
7427 it expresses that domain elements appearing in distinct filters
7428 may have any order. The order of the children of a set node
7429 is therefore also immaterial.
7433 The following node types are only supported by the AST generator.
7437 =item C<isl_schedule_node_context>
7439 The context describes constraints on the parameters and
7440 the schedule dimensions of outer
7441 bands that the AST generator may assume to hold. It is also the only
7442 kind of node that may introduce additional parameters.
7443 The space of the context is that of the flat product of the outer
7444 band nodes. In particular, if there are no outer band nodes, then
7445 this space is the unnamed zero-dimensional space.
7446 Since a context node references the outer band nodes, any tree
7447 containing a context node is considered to be anchored.
7449 =item C<isl_schedule_node_extension>
7451 An extension node instructs the AST generator to add additional
7452 domain elements that need to be scheduled.
7453 The additional domain elements are described by the range of
7454 the extension map in terms of the outer schedule dimensions,
7455 i.e., the flat product of the outer band nodes.
7456 Note that domain elements are added whenever the AST generator
7457 reaches the extension node, meaning that there are still some
7458 active domain elements for which an AST needs to be generated.
7459 The conditions under which some domain elements are still active
7460 may however not be completely described by the outer AST nodes
7461 generated at that point.
7463 An extension node may also appear as the root of a schedule tree,
7464 when it is intended to be inserted into another tree
7465 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
7466 In this case, the domain of the extension node should
7467 correspond to the flat product of the outer band nodes
7468 in this other schedule tree at the point where the extension tree
7471 =item C<isl_schedule_node_guard>
7473 The guard describes constraints on the parameters and
7474 the schedule dimensions of outer
7475 bands that need to be enforced by the outer nodes
7476 in the generated AST.
7477 The space of the guard is that of the flat product of the outer
7478 band nodes. In particular, if there are no outer band nodes, then
7479 this space is the unnamed zero-dimensional space.
7480 Since a guard node references the outer band nodes, any tree
7481 containing a guard node is considered to be anchored.
7485 Except for the C<isl_schedule_node_context> nodes,
7486 none of the nodes may introduce any parameters that were not
7487 already present in the root domain node.
7489 A schedule tree is encapsulated in an C<isl_schedule> object.
7490 The simplest such objects, those with a tree consisting of single domain node,
7491 can be created using the following functions with either an empty
7492 domain or a given domain.
7494 #include <isl/schedule.h>
7495 __isl_give isl_schedule *isl_schedule_empty(
7496 __isl_take isl_space *space);
7497 __isl_give isl_schedule *isl_schedule_from_domain(
7498 __isl_take isl_union_set *domain);
7500 The function C<isl_schedule_constraints_compute_schedule> described
7501 in L</"Scheduling"> can also be used to construct schedules.
7503 C<isl_schedule> objects may be copied and freed using the following functions.
7505 #include <isl/schedule.h>
7506 __isl_give isl_schedule *isl_schedule_copy(
7507 __isl_keep isl_schedule *sched);
7508 __isl_null isl_schedule *isl_schedule_free(
7509 __isl_take isl_schedule *sched);
7511 The following functions checks whether two C<isl_schedule> objects
7512 are obviously the same.
7514 #include <isl/schedule.h>
7515 isl_bool isl_schedule_plain_is_equal(
7516 __isl_keep isl_schedule *schedule1,
7517 __isl_keep isl_schedule *schedule2);
7519 The domain of the schedule, i.e., the domain described by the root node,
7520 can be obtained using the following function.
7522 #include <isl/schedule.h>
7523 __isl_give isl_union_set *isl_schedule_get_domain(
7524 __isl_keep isl_schedule *schedule);
7526 An extra top-level band node (right underneath the domain node) can
7527 be introduced into the schedule using the following function.
7528 The schedule tree is assumed not to have any anchored nodes.
7530 #include <isl/schedule.h>
7531 __isl_give isl_schedule *
7532 isl_schedule_insert_partial_schedule(
7533 __isl_take isl_schedule *schedule,
7534 __isl_take isl_multi_union_pw_aff *partial);
7536 A top-level context node (right underneath the domain node) can
7537 be introduced into the schedule using the following function.
7539 #include <isl/schedule.h>
7540 __isl_give isl_schedule *isl_schedule_insert_context(
7541 __isl_take isl_schedule *schedule,
7542 __isl_take isl_set *context)
7544 A top-level guard node (right underneath the domain node) can
7545 be introduced into the schedule using the following function.
7547 #include <isl/schedule.h>
7548 __isl_give isl_schedule *isl_schedule_insert_guard(
7549 __isl_take isl_schedule *schedule,
7550 __isl_take isl_set *guard)
7552 A schedule that combines two schedules either in the given
7553 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
7554 or an C<isl_schedule_node_set> node,
7555 can be created using the following functions.
7557 #include <isl/schedule.h>
7558 __isl_give isl_schedule *isl_schedule_sequence(
7559 __isl_take isl_schedule *schedule1,
7560 __isl_take isl_schedule *schedule2);
7561 __isl_give isl_schedule *isl_schedule_set(
7562 __isl_take isl_schedule *schedule1,
7563 __isl_take isl_schedule *schedule2);
7565 The domains of the two input schedules need to be disjoint.
7567 The following function can be used to restrict the domain
7568 of a schedule with a domain node as root to be a subset of the given union set.
7569 This operation may remove nodes in the tree that have become
7572 #include <isl/schedule.h>
7573 __isl_give isl_schedule *isl_schedule_intersect_domain(
7574 __isl_take isl_schedule *schedule,
7575 __isl_take isl_union_set *domain);
7577 The following function resets the user pointers on all parameter
7578 and tuple identifiers referenced by the nodes of the given schedule.
7580 #include <isl/schedule.h>
7581 __isl_give isl_schedule *isl_schedule_reset_user(
7582 __isl_take isl_schedule *schedule);
7584 The following function aligns the parameters of all nodes
7585 in the given schedule to the given space.
7587 #include <isl/schedule.h>
7588 __isl_give isl_schedule *isl_schedule_align_params(
7589 __isl_take isl_schedule *schedule,
7590 __isl_take isl_space *space);
7592 The following function allows the user to plug in a given function
7593 in the iteration domains. The input schedule is not allowed to contain
7594 any expansion nodes.
7596 #include <isl/schedule.h>
7597 __isl_give isl_schedule *
7598 isl_schedule_pullback_union_pw_multi_aff(
7599 __isl_take isl_schedule *schedule,
7600 __isl_take isl_union_pw_multi_aff *upma);
7602 An C<isl_union_map> representation of the schedule can be obtained
7603 from an C<isl_schedule> using the following function.
7605 #include <isl/schedule.h>
7606 __isl_give isl_union_map *isl_schedule_get_map(
7607 __isl_keep isl_schedule *sched);
7609 The resulting relation encodes the same relative ordering as
7610 the schedule by mapping the domain elements to a common schedule space.
7611 If the schedule_separate_components option is set, then the order
7612 of the children of a set node is explicitly encoded in the result.
7613 If the tree contains any expansion nodes, then the relation
7614 is formulated in terms of the expanded domain elements.
7616 Schedules can be read from input using the following functions.
7618 #include <isl/schedule.h>
7619 __isl_give isl_schedule *isl_schedule_read_from_file(
7620 isl_ctx *ctx, FILE *input);
7621 __isl_give isl_schedule *isl_schedule_read_from_str(
7622 isl_ctx *ctx, const char *str);
7624 A representation of the schedule can be printed using
7626 #include <isl/schedule.h>
7627 __isl_give isl_printer *isl_printer_print_schedule(
7628 __isl_take isl_printer *p,
7629 __isl_keep isl_schedule *schedule);
7631 The schedule tree can be traversed through the use of
7632 C<isl_schedule_node> objects that point to a particular
7633 position in the schedule tree. Whenever a C<isl_schedule_node>
7634 is use to modify a node in the schedule tree, the original schedule
7635 tree is left untouched and the modifications are performed to a copy
7636 of the tree. The returned C<isl_schedule_node> then points to
7637 this modified copy of the tree.
7639 The root of the schedule tree can be obtained using the following function.
7641 #include <isl/schedule.h>
7642 __isl_give isl_schedule_node *isl_schedule_get_root(
7643 __isl_keep isl_schedule *schedule);
7645 A pointer to a newly created schedule tree with a single domain
7646 node can be created using the following functions.
7648 #include <isl/schedule_node.h>
7649 __isl_give isl_schedule_node *
7650 isl_schedule_node_from_domain(
7651 __isl_take isl_union_set *domain);
7652 __isl_give isl_schedule_node *
7653 isl_schedule_node_from_extension(
7654 __isl_take isl_union_map *extension);
7656 C<isl_schedule_node_from_extension> creates a tree with an extension
7659 Schedule nodes can be copied and freed using the following functions.
7661 #include <isl/schedule_node.h>
7662 __isl_give isl_schedule_node *isl_schedule_node_copy(
7663 __isl_keep isl_schedule_node *node);
7664 __isl_null isl_schedule_node *isl_schedule_node_free(
7665 __isl_take isl_schedule_node *node);
7667 The following functions can be used to check if two schedule
7668 nodes point to the same position in the same schedule.
7670 #include <isl/schedule_node.h>
7671 isl_bool isl_schedule_node_is_equal(
7672 __isl_keep isl_schedule_node *node1,
7673 __isl_keep isl_schedule_node *node2);
7675 The following properties can be obtained from a schedule node.
7677 #include <isl/schedule_node.h>
7678 enum isl_schedule_node_type isl_schedule_node_get_type(
7679 __isl_keep isl_schedule_node *node);
7680 enum isl_schedule_node_type
7681 isl_schedule_node_get_parent_type(
7682 __isl_keep isl_schedule_node *node);
7683 __isl_give isl_schedule *isl_schedule_node_get_schedule(
7684 __isl_keep isl_schedule_node *node);
7686 The function C<isl_schedule_node_get_type> returns the type of
7687 the node, while C<isl_schedule_node_get_parent_type> returns
7688 type of the parent of the node, which is required to exist.
7689 The function C<isl_schedule_node_get_schedule> returns a copy
7690 to the schedule to which the node belongs.
7692 The following functions can be used to move the schedule node
7693 to a different position in the tree or to check if such a position
7696 #include <isl/schedule_node.h>
7697 isl_bool isl_schedule_node_has_parent(
7698 __isl_keep isl_schedule_node *node);
7699 __isl_give isl_schedule_node *isl_schedule_node_parent(
7700 __isl_take isl_schedule_node *node);
7701 __isl_give isl_schedule_node *isl_schedule_node_root(
7702 __isl_take isl_schedule_node *node);
7703 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
7704 __isl_take isl_schedule_node *node,
7706 int isl_schedule_node_n_children(
7707 __isl_keep isl_schedule_node *node);
7708 __isl_give isl_schedule_node *isl_schedule_node_child(
7709 __isl_take isl_schedule_node *node, int pos);
7710 isl_bool isl_schedule_node_has_children(
7711 __isl_keep isl_schedule_node *node);
7712 __isl_give isl_schedule_node *isl_schedule_node_first_child(
7713 __isl_take isl_schedule_node *node);
7714 isl_bool isl_schedule_node_has_previous_sibling(
7715 __isl_keep isl_schedule_node *node);
7716 __isl_give isl_schedule_node *
7717 isl_schedule_node_previous_sibling(
7718 __isl_take isl_schedule_node *node);
7719 isl_bool isl_schedule_node_has_next_sibling(
7720 __isl_keep isl_schedule_node *node);
7721 __isl_give isl_schedule_node *
7722 isl_schedule_node_next_sibling(
7723 __isl_take isl_schedule_node *node);
7725 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
7726 is the node itself, the ancestor of generation 1 is its parent and so on.
7728 It is also possible to query the number of ancestors of a node,
7729 the position of the current node
7730 within the children of its parent, the position of the subtree
7731 containing a node within the children of an ancestor
7732 or to obtain a copy of a given
7733 child without destroying the current node.
7734 Given two nodes that point to the same schedule, their closest
7735 shared ancestor can be obtained using
7736 C<isl_schedule_node_get_shared_ancestor>.
7738 #include <isl/schedule_node.h>
7739 int isl_schedule_node_get_tree_depth(
7740 __isl_keep isl_schedule_node *node);
7741 int isl_schedule_node_get_child_position(
7742 __isl_keep isl_schedule_node *node);
7743 int isl_schedule_node_get_ancestor_child_position(
7744 __isl_keep isl_schedule_node *node,
7745 __isl_keep isl_schedule_node *ancestor);
7746 __isl_give isl_schedule_node *isl_schedule_node_get_child(
7747 __isl_keep isl_schedule_node *node, int pos);
7748 __isl_give isl_schedule_node *
7749 isl_schedule_node_get_shared_ancestor(
7750 __isl_keep isl_schedule_node *node1,
7751 __isl_keep isl_schedule_node *node2);
7753 All nodes in a schedule tree or
7754 all descendants of a specific node (including the node) can be visited
7755 in depth-first pre-order using the following functions.
7757 #include <isl/schedule.h>
7758 isl_stat isl_schedule_foreach_schedule_node_top_down(
7759 __isl_keep isl_schedule *sched,
7760 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
7761 void *user), void *user);
7763 #include <isl/schedule_node.h>
7764 isl_stat isl_schedule_node_foreach_descendant_top_down(
7765 __isl_keep isl_schedule_node *node,
7766 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
7767 void *user), void *user);
7769 The callback function is slightly different from the usual
7770 callbacks in that it not only indicates success (non-negative result)
7771 or failure (negative result), but also indicates whether the children
7772 of the given node should be visited. In particular, if the callback
7773 returns a positive value, then the children are visited, but if
7774 the callback returns zero, then the children are not visited.
7776 The ancestors of a node in a schedule tree can be visited from
7777 the root down to and including the parent of the node using
7778 the following function.
7780 #include <isl/schedule_node.h>
7781 isl_stat isl_schedule_node_foreach_ancestor_top_down(
7782 __isl_keep isl_schedule_node *node,
7783 isl_stat (*fn)(__isl_keep isl_schedule_node *node,
7784 void *user), void *user);
7786 The following functions allows for a depth-first post-order
7787 traversal of the nodes in a schedule tree or
7788 of the descendants of a specific node (including the node
7789 itself), where the user callback is allowed to modify the
7792 #include <isl/schedule.h>
7793 __isl_give isl_schedule *
7794 isl_schedule_map_schedule_node_bottom_up(
7795 __isl_take isl_schedule *schedule,
7796 __isl_give isl_schedule_node *(*fn)(
7797 __isl_take isl_schedule_node *node,
7798 void *user), void *user);
7800 #include <isl/schedule_node.h>
7801 __isl_give isl_schedule_node *
7802 isl_schedule_node_map_descendant_bottom_up(
7803 __isl_take isl_schedule_node *node,
7804 __isl_give isl_schedule_node *(*fn)(
7805 __isl_take isl_schedule_node *node,
7806 void *user), void *user);
7808 The traversal continues from the node returned by the callback function.
7809 It is the responsibility of the user to ensure that this does not
7810 lead to an infinite loop. It is safest to always return a pointer
7811 to the same position (same ancestors and child positions) as the input node.
7813 The following function removes a node (along with its descendants)
7814 from a schedule tree and returns a pointer to the leaf at the
7815 same position in the updated tree.
7816 It is not allowed to remove the root of a schedule tree or
7817 a child of a set or sequence node.
7819 #include <isl/schedule_node.h>
7820 __isl_give isl_schedule_node *isl_schedule_node_cut(
7821 __isl_take isl_schedule_node *node);
7823 The following function removes a single node
7824 from a schedule tree and returns a pointer to the child
7825 of the node, now located at the position of the original node
7826 or to a leaf node at that position if there was no child.
7827 It is not allowed to remove the root of a schedule tree,
7828 a set or sequence node, a child of a set or sequence node or
7829 a band node with an anchored subtree.
7831 #include <isl/schedule_node.h>
7832 __isl_give isl_schedule_node *isl_schedule_node_delete(
7833 __isl_take isl_schedule_node *node);
7835 Most nodes in a schedule tree only contain local information.
7836 In some cases, however, a node may also refer to outer band nodes.
7837 This means that the position of the node within the tree should
7838 not be changed, or at least that no changes are performed to the
7839 outer band nodes. The following function can be used to test
7840 whether the subtree rooted at a given node contains any such nodes.
7842 #include <isl/schedule_node.h>
7843 isl_bool isl_schedule_node_is_subtree_anchored(
7844 __isl_keep isl_schedule_node *node);
7846 The following function resets the user pointers on all parameter
7847 and tuple identifiers referenced by the given schedule node.
7849 #include <isl/schedule_node.h>
7850 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
7851 __isl_take isl_schedule_node *node);
7853 The following function aligns the parameters of the given schedule
7854 node to the given space.
7856 #include <isl/schedule_node.h>
7857 __isl_give isl_schedule_node *
7858 isl_schedule_node_align_params(
7859 __isl_take isl_schedule_node *node,
7860 __isl_take isl_space *space);
7862 Several node types have their own functions for querying
7863 (and in some cases setting) some node type specific properties.
7865 #include <isl/schedule_node.h>
7866 __isl_give isl_space *isl_schedule_node_band_get_space(
7867 __isl_keep isl_schedule_node *node);
7868 __isl_give isl_multi_union_pw_aff *
7869 isl_schedule_node_band_get_partial_schedule(
7870 __isl_keep isl_schedule_node *node);
7871 __isl_give isl_union_map *
7872 isl_schedule_node_band_get_partial_schedule_union_map(
7873 __isl_keep isl_schedule_node *node);
7874 unsigned isl_schedule_node_band_n_member(
7875 __isl_keep isl_schedule_node *node);
7876 isl_bool isl_schedule_node_band_member_get_coincident(
7877 __isl_keep isl_schedule_node *node, int pos);
7878 __isl_give isl_schedule_node *
7879 isl_schedule_node_band_member_set_coincident(
7880 __isl_take isl_schedule_node *node, int pos,
7882 isl_bool isl_schedule_node_band_get_permutable(
7883 __isl_keep isl_schedule_node *node);
7884 __isl_give isl_schedule_node *
7885 isl_schedule_node_band_set_permutable(
7886 __isl_take isl_schedule_node *node, int permutable);
7887 enum isl_ast_loop_type
7888 isl_schedule_node_band_member_get_ast_loop_type(
7889 __isl_keep isl_schedule_node *node, int pos);
7890 __isl_give isl_schedule_node *
7891 isl_schedule_node_band_member_set_ast_loop_type(
7892 __isl_take isl_schedule_node *node, int pos,
7893 enum isl_ast_loop_type type);
7894 __isl_give isl_union_set *
7895 enum isl_ast_loop_type
7896 isl_schedule_node_band_member_get_isolate_ast_loop_type(
7897 __isl_keep isl_schedule_node *node, int pos);
7898 __isl_give isl_schedule_node *
7899 isl_schedule_node_band_member_set_isolate_ast_loop_type(
7900 __isl_take isl_schedule_node *node, int pos,
7901 enum isl_ast_loop_type type);
7902 isl_schedule_node_band_get_ast_build_options(
7903 __isl_keep isl_schedule_node *node);
7904 __isl_give isl_schedule_node *
7905 isl_schedule_node_band_set_ast_build_options(
7906 __isl_take isl_schedule_node *node,
7907 __isl_take isl_union_set *options);
7909 The function C<isl_schedule_node_band_get_space> returns the space
7910 of the partial schedule of the band.
7911 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
7912 returns a representation of the partial schedule of the band node
7913 in the form of an C<isl_union_map>.
7914 The coincident and permutable properties are set by
7915 C<isl_schedule_constraints_compute_schedule> on the schedule tree
7917 A scheduling dimension is considered to be ``coincident''
7918 if it satisfies the coincidence constraints within its band.
7919 That is, if the dependence distances of the coincidence
7920 constraints are all zero in that direction (for fixed
7921 iterations of outer bands).
7922 A band is marked permutable if it was produced using the Pluto-like scheduler.
7923 Note that the scheduler may have to resort to a Feautrier style scheduling
7924 step even if the default scheduler is used.
7925 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
7926 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
7927 For the meaning of these loop AST generation types and the difference
7928 between the regular loop AST generation type and the isolate
7929 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
7930 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
7931 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
7932 may return C<isl_ast_loop_error> if an error occurs.
7933 The AST build options govern how an AST is generated for
7934 the individual schedule dimensions during AST generation.
7935 See L</"AST Generation Options (Schedule Tree)">.
7937 #include <isl/schedule_node.h>
7938 __isl_give isl_set *
7939 isl_schedule_node_context_get_context(
7940 __isl_keep isl_schedule_node *node);
7942 #include <isl/schedule_node.h>
7943 __isl_give isl_union_set *
7944 isl_schedule_node_domain_get_domain(
7945 __isl_keep isl_schedule_node *node);
7947 #include <isl/schedule_node.h>
7948 __isl_give isl_union_map *
7949 isl_schedule_node_expansion_get_expansion(
7950 __isl_keep isl_schedule_node *node);
7951 __isl_give isl_union_pw_multi_aff *
7952 isl_schedule_node_expansion_get_contraction(
7953 __isl_keep isl_schedule_node *node);
7955 #include <isl/schedule_node.h>
7956 __isl_give isl_union_map *
7957 isl_schedule_node_extension_get_extension(
7958 __isl_keep isl_schedule_node *node);
7960 #include <isl/schedule_node.h>
7961 __isl_give isl_union_set *
7962 isl_schedule_node_filter_get_filter(
7963 __isl_keep isl_schedule_node *node);
7965 #include <isl/schedule_node.h>
7966 __isl_give isl_set *isl_schedule_node_guard_get_guard(
7967 __isl_keep isl_schedule_node *node);
7969 #include <isl/schedule_node.h>
7970 __isl_give isl_id *isl_schedule_node_mark_get_id(
7971 __isl_keep isl_schedule_node *node);
7973 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
7974 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
7975 partial schedules related to the node.
7977 #include <isl/schedule_node.h>
7978 __isl_give isl_multi_union_pw_aff *
7979 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
7980 __isl_keep isl_schedule_node *node);
7981 __isl_give isl_union_pw_multi_aff *
7982 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
7983 __isl_keep isl_schedule_node *node);
7984 __isl_give isl_union_map *
7985 isl_schedule_node_get_prefix_schedule_union_map(
7986 __isl_keep isl_schedule_node *node);
7987 __isl_give isl_union_map *
7988 isl_schedule_node_get_prefix_schedule_relation(
7989 __isl_keep isl_schedule_node *node);
7990 __isl_give isl_union_map *
7991 isl_schedule_node_get_subtree_schedule_union_map(
7992 __isl_keep isl_schedule_node *node);
7994 In particular, the functions
7995 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
7996 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
7997 and C<isl_schedule_node_get_prefix_schedule_union_map>
7998 return a relative ordering on the domain elements that reach the given
7999 node determined by its ancestors.
8000 The function C<isl_schedule_node_get_prefix_schedule_relation>
8001 additionally includes the domain constraints in the result.
8002 The function C<isl_schedule_node_get_subtree_schedule_union_map>
8003 returns a representation of the partial schedule defined by the
8004 subtree rooted at the given node.
8005 If the tree contains any expansion nodes, then the subtree schedule
8006 is formulated in terms of the expanded domain elements.
8007 The tree passed to functions returning a prefix schedule
8008 may only contain extension nodes if these would not affect
8009 the result of these functions. That is, if one of the ancestors
8010 is an extension node, then all of the domain elements that were
8011 added by the extension node need to have been filtered out
8012 by filter nodes between the extension node and the input node.
8013 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
8014 may not contain in extension nodes in the selected subtree.
8016 The expansion/contraction defined by an entire subtree, combining
8017 the expansions/contractions
8018 on the expansion nodes in the subtree, can be obtained using
8019 the following functions.
8021 #include <isl/schedule_node.h>
8022 __isl_give isl_union_map *
8023 isl_schedule_node_get_subtree_expansion(
8024 __isl_keep isl_schedule_node *node);
8025 __isl_give isl_union_pw_multi_aff *
8026 isl_schedule_node_get_subtree_contraction(
8027 __isl_keep isl_schedule_node *node);
8029 The total number of outer band members of given node, i.e.,
8030 the shared output dimension of the maps in the result
8031 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
8032 using the following function.
8034 #include <isl/schedule_node.h>
8035 int isl_schedule_node_get_schedule_depth(
8036 __isl_keep isl_schedule_node *node);
8038 The following functions return the elements that reach the given node
8039 or the union of universes in the spaces that contain these elements.
8041 #include <isl/schedule_node.h>
8042 __isl_give isl_union_set *
8043 isl_schedule_node_get_domain(
8044 __isl_keep isl_schedule_node *node);
8045 __isl_give isl_union_set *
8046 isl_schedule_node_get_universe_domain(
8047 __isl_keep isl_schedule_node *node);
8049 The input tree of C<isl_schedule_node_get_domain>
8050 may only contain extension nodes if these would not affect
8051 the result of this function. That is, if one of the ancestors
8052 is an extension node, then all of the domain elements that were
8053 added by the extension node need to have been filtered out
8054 by filter nodes between the extension node and the input node.
8056 The following functions can be used to introduce additional nodes
8057 in the schedule tree. The new node is introduced at the point
8058 in the tree where the C<isl_schedule_node> points to and
8059 the results points to the new node.
8061 #include <isl/schedule_node.h>
8062 __isl_give isl_schedule_node *
8063 isl_schedule_node_insert_partial_schedule(
8064 __isl_take isl_schedule_node *node,
8065 __isl_take isl_multi_union_pw_aff *schedule);
8067 This function inserts a new band node with (the greatest integer
8068 part of) the given partial schedule.
8069 The subtree rooted at the given node is assumed not to have
8072 #include <isl/schedule_node.h>
8073 __isl_give isl_schedule_node *
8074 isl_schedule_node_insert_context(
8075 __isl_take isl_schedule_node *node,
8076 __isl_take isl_set *context);
8078 This function inserts a new context node with the given context constraints.
8080 #include <isl/schedule_node.h>
8081 __isl_give isl_schedule_node *
8082 isl_schedule_node_insert_filter(
8083 __isl_take isl_schedule_node *node,
8084 __isl_take isl_union_set *filter);
8086 This function inserts a new filter node with the given filter.
8087 If the original node already pointed to a filter node, then the
8088 two filter nodes are merged into one.
8090 #include <isl/schedule_node.h>
8091 __isl_give isl_schedule_node *
8092 isl_schedule_node_insert_guard(
8093 __isl_take isl_schedule_node *node,
8094 __isl_take isl_set *guard);
8096 This function inserts a new guard node with the given guard constraints.
8098 #include <isl/schedule_node.h>
8099 __isl_give isl_schedule_node *
8100 isl_schedule_node_insert_mark(
8101 __isl_take isl_schedule_node *node,
8102 __isl_take isl_id *mark);
8104 This function inserts a new mark node with the give mark identifier.
8106 #include <isl/schedule_node.h>
8107 __isl_give isl_schedule_node *
8108 isl_schedule_node_insert_sequence(
8109 __isl_take isl_schedule_node *node,
8110 __isl_take isl_union_set_list *filters);
8111 __isl_give isl_schedule_node *
8112 isl_schedule_node_insert_set(
8113 __isl_take isl_schedule_node *node,
8114 __isl_take isl_union_set_list *filters);
8116 These functions insert a new sequence or set node with the given
8117 filters as children.
8119 #include <isl/schedule_node.h>
8120 __isl_give isl_schedule_node *isl_schedule_node_group(
8121 __isl_take isl_schedule_node *node,
8122 __isl_take isl_id *group_id);
8124 This function introduces an expansion node in between the current
8125 node and its parent that expands instances of a space with tuple
8126 identifier C<group_id> to the original domain elements that reach
8127 the node. The group instances are identified by the prefix schedule
8128 of those domain elements. The ancestors of the node are adjusted
8129 to refer to the group instances instead of the original domain
8130 elements. The return value points to the same node in the updated
8131 schedule tree as the input node, i.e., to the child of the newly
8132 introduced expansion node. Grouping instances of different statements
8133 ensures that they will be treated as a single statement by the
8134 AST generator up to the point of the expansion node.
8136 The partial schedule of a band node can be scaled (down) or reduced using
8137 the following functions.
8139 #include <isl/schedule_node.h>
8140 __isl_give isl_schedule_node *
8141 isl_schedule_node_band_scale(
8142 __isl_take isl_schedule_node *node,
8143 __isl_take isl_multi_val *mv);
8144 __isl_give isl_schedule_node *
8145 isl_schedule_node_band_scale_down(
8146 __isl_take isl_schedule_node *node,
8147 __isl_take isl_multi_val *mv);
8148 __isl_give isl_schedule_node *
8149 isl_schedule_node_band_mod(
8150 __isl_take isl_schedule_node *node,
8151 __isl_take isl_multi_val *mv);
8153 The spaces of the two arguments need to match.
8154 After scaling, the partial schedule is replaced by its greatest
8155 integer part to ensure that the schedule remains integral.
8157 The partial schedule of a band node can be shifted by an
8158 C<isl_multi_union_pw_aff> with a domain that is a superset
8159 of the domain of the partial schedule using
8160 the following function.
8162 #include <isl/schedule_node.h>
8163 __isl_give isl_schedule_node *
8164 isl_schedule_node_band_shift(
8165 __isl_take isl_schedule_node *node,
8166 __isl_take isl_multi_union_pw_aff *shift);
8168 A band node can be tiled using the following function.
8170 #include <isl/schedule_node.h>
8171 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
8172 __isl_take isl_schedule_node *node,
8173 __isl_take isl_multi_val *sizes);
8175 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
8177 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
8178 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
8180 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
8182 The C<isl_schedule_node_band_tile> function tiles
8183 the band using the given tile sizes inside its schedule.
8184 A new child band node is created to represent the point loops and it is
8185 inserted between the modified band and its children.
8186 The subtree rooted at the given node is assumed not to have
8188 The C<tile_scale_tile_loops> option specifies whether the tile
8189 loops iterators should be scaled by the tile sizes.
8190 If the C<tile_shift_point_loops> option is set, then the point loops
8191 are shifted to start at zero.
8193 A band node can be split into two nested band nodes
8194 using the following function.
8196 #include <isl/schedule_node.h>
8197 __isl_give isl_schedule_node *isl_schedule_node_band_split(
8198 __isl_take isl_schedule_node *node, int pos);
8200 The resulting outer band node contains the first C<pos> dimensions of
8201 the schedule of C<node> while the inner band contains the remaining dimensions.
8202 The schedules of the two band nodes live in anonymous spaces.
8204 A band node can be moved down to the leaves of the subtree rooted
8205 at the band node using the following function.
8207 #include <isl/schedule_node.h>
8208 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
8209 __isl_take isl_schedule_node *node);
8211 The subtree rooted at the given node is assumed not to have
8213 The result points to the node in the resulting tree that is in the same
8214 position as the node pointed to by C<node> in the original tree.
8216 #include <isl/schedule_node.h>
8217 __isl_give isl_schedule_node *
8218 isl_schedule_node_order_after(
8219 __isl_take isl_schedule_node *node,
8220 __isl_take isl_union_set *filter);
8222 This function splits the domain elements that reach C<node>
8223 into those that satisfy C<filter> and those that do not and
8224 arranges for the elements that do satisfy the filter to be
8225 executed after those that do not. The order is imposed by
8226 a sequence node, possibly reusing the grandparent of C<node>
8227 on two copies of the subtree attached to the original C<node>.
8228 Both copies are simplified with respect to their filter.
8230 Return a pointer to the copy of the subtree that does not
8231 satisfy C<filter>. If there is no such copy (because all
8232 reaching domain elements satisfy the filter), then return
8233 the original pointer.
8235 #include <isl/schedule_node.h>
8236 __isl_give isl_schedule_node *
8237 isl_schedule_node_graft_before(
8238 __isl_take isl_schedule_node *node,
8239 __isl_take isl_schedule_node *graft);
8240 __isl_give isl_schedule_node *
8241 isl_schedule_node_graft_after(
8242 __isl_take isl_schedule_node *node,
8243 __isl_take isl_schedule_node *graft);
8245 This function inserts the C<graft> tree into the tree containing C<node>
8246 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
8247 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
8248 The root node of C<graft>
8249 should be an extension node where the domain of the extension
8250 is the flat product of all outer band nodes of C<node>.
8251 The root node may also be a domain node.
8252 The elements of the domain or the range of the extension may not
8253 intersect with the domain elements that reach "node".
8254 The schedule tree of C<graft> may not be anchored.
8256 The schedule tree of C<node> is modified to include an extension node
8257 corresponding to the root node of C<graft> as a child of the original
8258 parent of C<node>. The original node that C<node> points to and the
8259 child of the root node of C<graft> are attached to this extension node
8260 through a sequence, with appropriate filters and with the child
8261 of C<graft> appearing before or after the original C<node>.
8263 If C<node> already appears inside a sequence that is the child of
8264 an extension node and if the spaces of the new domain elements
8265 do not overlap with those of the original domain elements,
8266 then that extension node is extended with the new extension
8267 rather than introducing a new segment of extension and sequence nodes.
8269 Return a pointer to the same node in the modified tree that
8270 C<node> pointed to in the original tree.
8272 A representation of the schedule node can be printed using
8274 #include <isl/schedule_node.h>
8275 __isl_give isl_printer *isl_printer_print_schedule_node(
8276 __isl_take isl_printer *p,
8277 __isl_keep isl_schedule_node *node);
8279 =head2 Dependence Analysis
8281 C<isl> contains specialized functionality for performing
8282 array dataflow analysis. That is, given a I<sink> access relation
8283 and a collection of possible I<source> access relations,
8284 C<isl> can compute relations that describe
8285 for each iteration of the sink access, which iteration
8286 of which of the source access relations was the last
8287 to access the same data element before the given iteration
8289 The resulting dependence relations map source iterations
8290 to the corresponding sink iterations.
8291 To compute standard flow dependences, the sink should be
8292 a read, while the sources should be writes.
8293 If any of the source accesses are marked as being I<may>
8294 accesses, then there will be a dependence from the last
8295 I<must> access B<and> from any I<may> access that follows
8296 this last I<must> access.
8297 In particular, if I<all> sources are I<may> accesses,
8298 then memory based dependence analysis is performed.
8299 If, on the other hand, all sources are I<must> accesses,
8300 then value based dependence analysis is performed.
8302 =head3 High-level Interface
8304 A high-level interface to dependence analysis is provided
8305 by the following function.
8307 #include <isl/flow.h>
8308 __isl_give isl_union_flow *
8309 isl_union_access_info_compute_flow(
8310 __isl_take isl_union_access_info *access);
8312 The input C<isl_union_access_info> object describes the sink
8313 access relations, the source access relations and a schedule,
8314 while the output C<isl_union_flow> object describes
8315 the resulting dependence relations and the subsets of the
8316 sink relations for which no source was found.
8318 An C<isl_union_access_info> is created, modified, copied and freed using
8319 the following functions.
8321 #include <isl/flow.h>
8322 __isl_give isl_union_access_info *
8323 isl_union_access_info_from_sink(
8324 __isl_take isl_union_map *sink);
8325 __isl_give isl_union_access_info *
8326 isl_union_access_info_set_must_source(
8327 __isl_take isl_union_access_info *access,
8328 __isl_take isl_union_map *must_source);
8329 __isl_give isl_union_access_info *
8330 isl_union_access_info_set_may_source(
8331 __isl_take isl_union_access_info *access,
8332 __isl_take isl_union_map *may_source);
8333 __isl_give isl_union_access_info *
8334 isl_union_access_info_set_schedule(
8335 __isl_take isl_union_access_info *access,
8336 __isl_take isl_schedule *schedule);
8337 __isl_give isl_union_access_info *
8338 isl_union_access_info_set_schedule_map(
8339 __isl_take isl_union_access_info *access,
8340 __isl_take isl_union_map *schedule_map);
8341 __isl_give isl_union_access_info *
8342 isl_union_access_info_copy(
8343 __isl_keep isl_union_access_info *access);
8344 __isl_null isl_union_access_info *
8345 isl_union_access_info_free(
8346 __isl_take isl_union_access_info *access);
8348 The may sources set by C<isl_union_access_info_set_may_source>
8349 do not need to include the must sources set by
8350 C<isl_union_access_info_set_must_source> as a subset.
8351 The user is free not to call one (or both) of these functions,
8352 in which case the corresponding set is kept to its empty default.
8353 Similarly, the default schedule initialized by
8354 C<isl_union_access_info_from_sink> is empty.
8355 The current schedule is determined by the last call to either
8356 C<isl_union_access_info_set_schedule> or
8357 C<isl_union_access_info_set_schedule_map>.
8358 The domain of the schedule corresponds to the domains of
8359 the access relations. In particular, the domains of the access
8360 relations are effectively intersected with the domain of the schedule
8361 and only the resulting accesses are considered by the dependence analysis.
8363 The output of C<isl_union_access_info_compute_flow> can be examined
8364 and freed using the following functions.
8366 #include <isl/flow.h>
8367 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
8368 __isl_keep isl_union_flow *flow);
8369 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
8370 __isl_keep isl_union_flow *flow);
8371 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
8372 __isl_keep isl_union_flow *flow);
8373 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
8374 __isl_keep isl_union_flow *flow);
8375 __isl_null isl_union_flow *isl_union_flow_free(
8376 __isl_take isl_union_flow *flow);
8378 The relation returned by C<isl_union_flow_get_must_dependence>
8379 relates domain elements of must sources to domain elements of the sink.
8380 The relation returned by C<isl_union_flow_get_may_dependence>
8381 relates domain elements of must or may sources to domain elements of the sink
8382 and includes the previous relation as a subset.
8383 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
8384 of the sink relation for which no dependences have been found.
8385 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
8386 of the sink relation for which no definite dependences have been found.
8387 That is, it contains those sink access that do not contribute to any
8388 of the elements in the relation returned
8389 by C<isl_union_flow_get_must_dependence>.
8391 =head3 Low-level Interface
8393 A lower-level interface is provided by the following functions.
8395 #include <isl/flow.h>
8397 typedef int (*isl_access_level_before)(void *first, void *second);
8399 __isl_give isl_access_info *isl_access_info_alloc(
8400 __isl_take isl_map *sink,
8401 void *sink_user, isl_access_level_before fn,
8403 __isl_give isl_access_info *isl_access_info_add_source(
8404 __isl_take isl_access_info *acc,
8405 __isl_take isl_map *source, int must,
8407 __isl_null isl_access_info *isl_access_info_free(
8408 __isl_take isl_access_info *acc);
8410 __isl_give isl_flow *isl_access_info_compute_flow(
8411 __isl_take isl_access_info *acc);
8413 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,
8414 isl_stat (*fn)(__isl_take isl_map *dep, int must,
8415 void *dep_user, void *user),
8417 __isl_give isl_map *isl_flow_get_no_source(
8418 __isl_keep isl_flow *deps, int must);
8419 void isl_flow_free(__isl_take isl_flow *deps);
8421 The function C<isl_access_info_compute_flow> performs the actual
8422 dependence analysis. The other functions are used to construct
8423 the input for this function or to read off the output.
8425 The input is collected in an C<isl_access_info>, which can
8426 be created through a call to C<isl_access_info_alloc>.
8427 The arguments to this functions are the sink access relation
8428 C<sink>, a token C<sink_user> used to identify the sink
8429 access to the user, a callback function for specifying the
8430 relative order of source and sink accesses, and the number
8431 of source access relations that will be added.
8432 The callback function has type C<int (*)(void *first, void *second)>.
8433 The function is called with two user supplied tokens identifying
8434 either a source or the sink and it should return the shared nesting
8435 level and the relative order of the two accesses.
8436 In particular, let I<n> be the number of loops shared by
8437 the two accesses. If C<first> precedes C<second> textually,
8438 then the function should return I<2 * n + 1>; otherwise,
8439 it should return I<2 * n>.
8440 The sources can be added to the C<isl_access_info> by performing
8441 (at most) C<max_source> calls to C<isl_access_info_add_source>.
8442 C<must> indicates whether the source is a I<must> access
8443 or a I<may> access. Note that a multi-valued access relation
8444 should only be marked I<must> if every iteration in the domain
8445 of the relation accesses I<all> elements in its image.
8446 The C<source_user> token is again used to identify
8447 the source access. The range of the source access relation
8448 C<source> should have the same dimension as the range
8449 of the sink access relation.
8450 The C<isl_access_info_free> function should usually not be
8451 called explicitly, because it is called implicitly by
8452 C<isl_access_info_compute_flow>.
8454 The result of the dependence analysis is collected in an
8455 C<isl_flow>. There may be elements of
8456 the sink access for which no preceding source access could be
8457 found or for which all preceding sources are I<may> accesses.
8458 The relations containing these elements can be obtained through
8459 calls to C<isl_flow_get_no_source>, the first with C<must> set
8460 and the second with C<must> unset.
8461 In the case of standard flow dependence analysis,
8462 with the sink a read and the sources I<must> writes,
8463 the first relation corresponds to the reads from uninitialized
8464 array elements and the second relation is empty.
8465 The actual flow dependences can be extracted using
8466 C<isl_flow_foreach>. This function will call the user-specified
8467 callback function C<fn> for each B<non-empty> dependence between
8468 a source and the sink. The callback function is called
8469 with four arguments, the actual flow dependence relation
8470 mapping source iterations to sink iterations, a boolean that
8471 indicates whether it is a I<must> or I<may> dependence, a token
8472 identifying the source and an additional C<void *> with value
8473 equal to the third argument of the C<isl_flow_foreach> call.
8474 A dependence is marked I<must> if it originates from a I<must>
8475 source and if it is not followed by any I<may> sources.
8477 After finishing with an C<isl_flow>, the user should call
8478 C<isl_flow_free> to free all associated memory.
8480 =head3 Interaction with the Low-level Interface
8482 During the dependence analysis, we frequently need to perform
8483 the following operation. Given a relation between sink iterations
8484 and potential source iterations from a particular source domain,
8485 what is the last potential source iteration corresponding to each
8486 sink iteration. It can sometimes be convenient to adjust
8487 the set of potential source iterations before or after each such operation.
8488 The prototypical example is fuzzy array dataflow analysis,
8489 where we need to analyze if, based on data-dependent constraints,
8490 the sink iteration can ever be executed without one or more of
8491 the corresponding potential source iterations being executed.
8492 If so, we can introduce extra parameters and select an unknown
8493 but fixed source iteration from the potential source iterations.
8494 To be able to perform such manipulations, C<isl> provides the following
8497 #include <isl/flow.h>
8499 typedef __isl_give isl_restriction *(*isl_access_restrict)(
8500 __isl_keep isl_map *source_map,
8501 __isl_keep isl_set *sink, void *source_user,
8503 __isl_give isl_access_info *isl_access_info_set_restrict(
8504 __isl_take isl_access_info *acc,
8505 isl_access_restrict fn, void *user);
8507 The function C<isl_access_info_set_restrict> should be called
8508 before calling C<isl_access_info_compute_flow> and registers a callback function
8509 that will be called any time C<isl> is about to compute the last
8510 potential source. The first argument is the (reverse) proto-dependence,
8511 mapping sink iterations to potential source iterations.
8512 The second argument represents the sink iterations for which
8513 we want to compute the last source iteration.
8514 The third argument is the token corresponding to the source
8515 and the final argument is the token passed to C<isl_access_info_set_restrict>.
8516 The callback is expected to return a restriction on either the input or
8517 the output of the operation computing the last potential source.
8518 If the input needs to be restricted then restrictions are needed
8519 for both the source and the sink iterations. The sink iterations
8520 and the potential source iterations will be intersected with these sets.
8521 If the output needs to be restricted then only a restriction on the source
8522 iterations is required.
8523 If any error occurs, the callback should return C<NULL>.
8524 An C<isl_restriction> object can be created, freed and inspected
8525 using the following functions.
8527 #include <isl/flow.h>
8529 __isl_give isl_restriction *isl_restriction_input(
8530 __isl_take isl_set *source_restr,
8531 __isl_take isl_set *sink_restr);
8532 __isl_give isl_restriction *isl_restriction_output(
8533 __isl_take isl_set *source_restr);
8534 __isl_give isl_restriction *isl_restriction_none(
8535 __isl_take isl_map *source_map);
8536 __isl_give isl_restriction *isl_restriction_empty(
8537 __isl_take isl_map *source_map);
8538 __isl_null isl_restriction *isl_restriction_free(
8539 __isl_take isl_restriction *restr);
8541 C<isl_restriction_none> and C<isl_restriction_empty> are special
8542 cases of C<isl_restriction_input>. C<isl_restriction_none>
8543 is essentially equivalent to
8545 isl_restriction_input(isl_set_universe(
8546 isl_space_range(isl_map_get_space(source_map))),
8548 isl_space_domain(isl_map_get_space(source_map))));
8550 whereas C<isl_restriction_empty> is essentially equivalent to
8552 isl_restriction_input(isl_set_empty(
8553 isl_space_range(isl_map_get_space(source_map))),
8555 isl_space_domain(isl_map_get_space(source_map))));
8559 B<The functionality described in this section is fairly new
8560 and may be subject to change.>
8562 #include <isl/schedule.h>
8563 __isl_give isl_schedule *
8564 isl_schedule_constraints_compute_schedule(
8565 __isl_take isl_schedule_constraints *sc);
8567 The function C<isl_schedule_constraints_compute_schedule> can be
8568 used to compute a schedule that satisfies the given schedule constraints.
8569 These schedule constraints include the iteration domain for which
8570 a schedule should be computed and dependences between pairs of
8571 iterations. In particular, these dependences include
8572 I<validity> dependences and I<proximity> dependences.
8573 By default, the algorithm used to construct the schedule is similar
8574 to that of C<Pluto>.
8575 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
8577 The generated schedule respects all validity dependences.
8578 That is, all dependence distances over these dependences in the
8579 scheduled space are lexicographically positive.
8581 The default algorithm tries to ensure that the dependence distances
8582 over coincidence constraints are zero and to minimize the
8583 dependence distances over proximity dependences.
8584 Moreover, it tries to obtain sequences (bands) of schedule dimensions
8585 for groups of domains where the dependence distances over validity
8586 dependences have only non-negative values.
8587 Note that when minimizing the maximal dependence distance
8588 over proximity dependences, a single affine expression in the parameters
8589 is constructed that bounds all dependence distances. If no such expression
8590 exists, then the algorithm will fail and resort to an alternative
8591 scheduling algorithm. In particular, this means that adding proximity
8592 dependences may eliminate valid solutions. A typical example where this
8593 phenomenon may occur is when some subset of the proximity dependences
8594 has no restriction on some parameter, forcing the coefficient of that
8595 parameter to be zero, while some other subset forces the dependence
8596 distance to depend on that parameter, requiring the same coefficient
8598 When using Feautrier's algorithm, the coincidence and proximity constraints
8599 are only taken into account during the extension to a
8600 full-dimensional schedule.
8602 An C<isl_schedule_constraints> object can be constructed
8603 and manipulated using the following functions.
8605 #include <isl/schedule.h>
8606 __isl_give isl_schedule_constraints *
8607 isl_schedule_constraints_copy(
8608 __isl_keep isl_schedule_constraints *sc);
8609 __isl_give isl_schedule_constraints *
8610 isl_schedule_constraints_on_domain(
8611 __isl_take isl_union_set *domain);
8612 __isl_give isl_schedule_constraints *
8613 isl_schedule_constraints_set_context(
8614 __isl_take isl_schedule_constraints *sc,
8615 __isl_take isl_set *context);
8616 __isl_give isl_schedule_constraints *
8617 isl_schedule_constraints_set_validity(
8618 __isl_take isl_schedule_constraints *sc,
8619 __isl_take isl_union_map *validity);
8620 __isl_give isl_schedule_constraints *
8621 isl_schedule_constraints_set_coincidence(
8622 __isl_take isl_schedule_constraints *sc,
8623 __isl_take isl_union_map *coincidence);
8624 __isl_give isl_schedule_constraints *
8625 isl_schedule_constraints_set_proximity(
8626 __isl_take isl_schedule_constraints *sc,
8627 __isl_take isl_union_map *proximity);
8628 __isl_give isl_schedule_constraints *
8629 isl_schedule_constraints_set_conditional_validity(
8630 __isl_take isl_schedule_constraints *sc,
8631 __isl_take isl_union_map *condition,
8632 __isl_take isl_union_map *validity);
8633 __isl_null isl_schedule_constraints *
8634 isl_schedule_constraints_free(
8635 __isl_take isl_schedule_constraints *sc);
8637 The initial C<isl_schedule_constraints> object created by
8638 C<isl_schedule_constraints_on_domain> does not impose any constraints.
8639 That is, it has an empty set of dependences.
8640 The function C<isl_schedule_constraints_set_context> allows the user
8641 to specify additional constraints on the parameters that may
8642 be assumed to hold during the construction of the schedule.
8643 The function C<isl_schedule_constraints_set_validity> replaces the
8644 validity dependences, mapping domain elements I<i> to domain
8645 elements that should be scheduled after I<i>.
8646 The function C<isl_schedule_constraints_set_coincidence> replaces the
8647 coincidence dependences, mapping domain elements I<i> to domain
8648 elements that should be scheduled together with I<I>, if possible.
8649 The function C<isl_schedule_constraints_set_proximity> replaces the
8650 proximity dependences, mapping domain elements I<i> to domain
8651 elements that should be scheduled either before I<I>
8652 or as early as possible after I<i>.
8654 The function C<isl_schedule_constraints_set_conditional_validity>
8655 replaces the conditional validity constraints.
8656 A conditional validity constraint is only imposed when any of the corresponding
8657 conditions is satisfied, i.e., when any of them is non-zero.
8658 That is, the scheduler ensures that within each band if the dependence
8659 distances over the condition constraints are not all zero
8660 then all corresponding conditional validity constraints are respected.
8661 A conditional validity constraint corresponds to a condition
8662 if the two are adjacent, i.e., if the domain of one relation intersect
8663 the range of the other relation.
8664 The typical use case of conditional validity constraints is
8665 to allow order constraints between live ranges to be violated
8666 as long as the live ranges themselves are local to the band.
8667 To allow more fine-grained control over which conditions correspond
8668 to which conditional validity constraints, the domains and ranges
8669 of these relations may include I<tags>. That is, the domains and
8670 ranges of those relation may themselves be wrapped relations
8671 where the iteration domain appears in the domain of those wrapped relations
8672 and the range of the wrapped relations can be arbitrarily chosen
8673 by the user. Conditions and conditional validity constraints are only
8674 considered adjacent to each other if the entire wrapped relation matches.
8675 In particular, a relation with a tag will never be considered adjacent
8676 to a relation without a tag.
8678 An C<isl_schedule_constraints> object can be inspected
8679 using the following functions.
8681 #include <isl/schedule.h>
8682 __isl_give isl_union_map *
8683 isl_schedule_constraints_get_validity(
8684 __isl_keep isl_schedule_constraints *sc);
8685 __isl_give isl_union_map *
8686 isl_schedule_constraints_get_coincidence(
8687 __isl_keep isl_schedule_constraints *sc);
8688 __isl_give isl_union_map *
8689 isl_schedule_constraints_get_conditional_validity(
8690 __isl_keep isl_schedule_constraints *sc);
8691 __isl_give isl_union_map *
8692 isl_schedule_constraints_get_conditional_validity_condition(
8693 __isl_keep isl_schedule_constraints *sc);
8695 The following function computes a schedule directly from
8696 an iteration domain and validity and proximity dependences
8697 and is implemented in terms of the functions described above.
8698 The use of C<isl_union_set_compute_schedule> is discouraged.
8700 #include <isl/schedule.h>
8701 __isl_give isl_schedule *isl_union_set_compute_schedule(
8702 __isl_take isl_union_set *domain,
8703 __isl_take isl_union_map *validity,
8704 __isl_take isl_union_map *proximity);
8706 The generated schedule represents a schedule tree.
8707 For more information on schedule trees, see
8708 L</"Schedule Trees">.
8712 #include <isl/schedule.h>
8713 isl_stat isl_options_set_schedule_max_coefficient(
8714 isl_ctx *ctx, int val);
8715 int isl_options_get_schedule_max_coefficient(
8717 isl_stat isl_options_set_schedule_max_constant_term(
8718 isl_ctx *ctx, int val);
8719 int isl_options_get_schedule_max_constant_term(
8721 isl_stat isl_options_set_schedule_serialize_sccs(
8722 isl_ctx *ctx, int val);
8723 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx);
8724 isl_stat isl_options_set_schedule_maximize_band_depth(
8725 isl_ctx *ctx, int val);
8726 int isl_options_get_schedule_maximize_band_depth(
8728 isl_stat isl_options_set_schedule_outer_coincidence(
8729 isl_ctx *ctx, int val);
8730 int isl_options_get_schedule_outer_coincidence(
8732 isl_stat isl_options_set_schedule_split_scaled(
8733 isl_ctx *ctx, int val);
8734 int isl_options_get_schedule_split_scaled(
8736 isl_stat isl_options_set_schedule_algorithm(
8737 isl_ctx *ctx, int val);
8738 int isl_options_get_schedule_algorithm(
8740 isl_stat isl_options_set_schedule_separate_components(
8741 isl_ctx *ctx, int val);
8742 int isl_options_get_schedule_separate_components(
8747 =item * schedule_max_coefficient
8749 This option enforces that the coefficients for variable and parameter
8750 dimensions in the calculated schedule are not larger than the specified value.
8751 This option can significantly increase the speed of the scheduling calculation
8752 and may also prevent fusing of unrelated dimensions. A value of -1 means that
8753 this option does not introduce bounds on the variable or parameter
8756 =item * schedule_max_constant_term
8758 This option enforces that the constant coefficients in the calculated schedule
8759 are not larger than the maximal constant term. This option can significantly
8760 increase the speed of the scheduling calculation and may also prevent fusing of
8761 unrelated dimensions. A value of -1 means that this option does not introduce
8762 bounds on the constant coefficients.
8764 =item * schedule_serialize_sccs
8766 If this option is set, then all strongly connected components
8767 in the dependence graph are serialized as soon as they are detected.
8768 This means in particular that instances of statements will only
8769 appear in the same band node if these statements belong
8770 to the same strongly connected component at the point where
8771 the band node is constructed.
8773 =item * schedule_maximize_band_depth
8775 If this option is set, we do not split bands at the point
8776 where we detect splitting is necessary. Instead, we
8777 backtrack and split bands as early as possible. This
8778 reduces the number of splits and maximizes the width of
8779 the bands. Wider bands give more possibilities for tiling.
8780 Note that if the C<schedule_serialize_sccs> options is set,
8781 then bands will be split as early as possible, even if there is no need.
8782 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
8784 =item * schedule_outer_coincidence
8786 If this option is set, then we try to construct schedules
8787 where the outermost scheduling dimension in each band
8788 satisfies the coincidence constraints.
8790 =item * schedule_split_scaled
8792 If this option is set, then we try to construct schedules in which the
8793 constant term is split off from the linear part if the linear parts of
8794 the scheduling rows for all nodes in the graphs have a common non-trivial
8796 The constant term is then placed in a separate band and the linear
8799 =item * schedule_algorithm
8801 Selects the scheduling algorithm to be used.
8802 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
8803 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
8805 =item * schedule_separate_components
8807 If this option is set then the function C<isl_schedule_get_map>
8808 will treat set nodes in the same way as sequence nodes.
8812 =head2 AST Generation
8814 This section describes the C<isl> functionality for generating
8815 ASTs that visit all the elements
8816 in a domain in an order specified by a schedule tree or
8818 In case the schedule given as a C<isl_union_map>, an AST is generated
8819 that visits all the elements in the domain of the C<isl_union_map>
8820 according to the lexicographic order of the corresponding image
8821 element(s). If the range of the C<isl_union_map> consists of
8822 elements in more than one space, then each of these spaces is handled
8823 separately in an arbitrary order.
8824 It should be noted that the schedule tree or the image elements
8825 in a schedule map only specify the I<order>
8826 in which the corresponding domain elements should be visited.
8827 No direct relation between the partial schedule values
8828 or the image elements on the one hand and the loop iterators
8829 in the generated AST on the other hand should be assumed.
8831 Each AST is generated within a build. The initial build
8832 simply specifies the constraints on the parameters (if any)
8833 and can be created, inspected, copied and freed using the following functions.
8835 #include <isl/ast_build.h>
8836 __isl_give isl_ast_build *isl_ast_build_alloc(
8838 __isl_give isl_ast_build *isl_ast_build_from_context(
8839 __isl_take isl_set *set);
8840 __isl_give isl_ast_build *isl_ast_build_copy(
8841 __isl_keep isl_ast_build *build);
8842 __isl_null isl_ast_build *isl_ast_build_free(
8843 __isl_take isl_ast_build *build);
8845 The C<set> argument is usually a parameter set with zero or more parameters.
8846 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
8847 this set is required to be a parameter set.
8848 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
8849 specify any parameter constraints.
8850 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
8851 and L</"Fine-grained Control over AST Generation">.
8852 Finally, the AST itself can be constructed using one of the following
8855 #include <isl/ast_build.h>
8856 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
8857 __isl_keep isl_ast_build *build,
8858 __isl_take isl_schedule *schedule);
8859 __isl_give isl_ast_node *
8860 isl_ast_build_node_from_schedule_map(
8861 __isl_keep isl_ast_build *build,
8862 __isl_take isl_union_map *schedule);
8864 =head3 Inspecting the AST
8866 The basic properties of an AST node can be obtained as follows.
8868 #include <isl/ast.h>
8869 enum isl_ast_node_type isl_ast_node_get_type(
8870 __isl_keep isl_ast_node *node);
8872 The type of an AST node is one of
8873 C<isl_ast_node_for>,
8875 C<isl_ast_node_block>,
8876 C<isl_ast_node_mark> or
8877 C<isl_ast_node_user>.
8878 An C<isl_ast_node_for> represents a for node.
8879 An C<isl_ast_node_if> represents an if node.
8880 An C<isl_ast_node_block> represents a compound node.
8881 An C<isl_ast_node_mark> introduces a mark in the AST.
8882 An C<isl_ast_node_user> represents an expression statement.
8883 An expression statement typically corresponds to a domain element, i.e.,
8884 one of the elements that is visited by the AST.
8886 Each type of node has its own additional properties.
8888 #include <isl/ast.h>
8889 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
8890 __isl_keep isl_ast_node *node);
8891 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
8892 __isl_keep isl_ast_node *node);
8893 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
8894 __isl_keep isl_ast_node *node);
8895 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
8896 __isl_keep isl_ast_node *node);
8897 __isl_give isl_ast_node *isl_ast_node_for_get_body(
8898 __isl_keep isl_ast_node *node);
8899 isl_bool isl_ast_node_for_is_degenerate(
8900 __isl_keep isl_ast_node *node);
8902 An C<isl_ast_for> is considered degenerate if it is known to execute
8905 #include <isl/ast.h>
8906 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
8907 __isl_keep isl_ast_node *node);
8908 __isl_give isl_ast_node *isl_ast_node_if_get_then(
8909 __isl_keep isl_ast_node *node);
8910 isl_bool isl_ast_node_if_has_else(
8911 __isl_keep isl_ast_node *node);
8912 __isl_give isl_ast_node *isl_ast_node_if_get_else(
8913 __isl_keep isl_ast_node *node);
8915 __isl_give isl_ast_node_list *
8916 isl_ast_node_block_get_children(
8917 __isl_keep isl_ast_node *node);
8919 __isl_give isl_id *isl_ast_node_mark_get_id(
8920 __isl_keep isl_ast_node *node);
8921 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
8922 __isl_keep isl_ast_node *node);
8924 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
8925 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
8927 #include <isl/ast.h>
8928 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
8929 __isl_keep isl_ast_node *node);
8931 Each of the returned C<isl_ast_expr>s can in turn be inspected using
8932 the following functions.
8934 #include <isl/ast.h>
8935 enum isl_ast_expr_type isl_ast_expr_get_type(
8936 __isl_keep isl_ast_expr *expr);
8938 The type of an AST expression is one of
8940 C<isl_ast_expr_id> or
8941 C<isl_ast_expr_int>.
8942 An C<isl_ast_expr_op> represents the result of an operation.
8943 An C<isl_ast_expr_id> represents an identifier.
8944 An C<isl_ast_expr_int> represents an integer value.
8946 Each type of expression has its own additional properties.
8948 #include <isl/ast.h>
8949 enum isl_ast_op_type isl_ast_expr_get_op_type(
8950 __isl_keep isl_ast_expr *expr);
8951 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
8952 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
8953 __isl_keep isl_ast_expr *expr, int pos);
8954 isl_stat isl_ast_node_foreach_ast_op_type(
8955 __isl_keep isl_ast_node *node,
8956 isl_stat (*fn)(enum isl_ast_op_type type,
8957 void *user), void *user);
8959 C<isl_ast_expr_get_op_type> returns the type of the operation
8960 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
8961 arguments. C<isl_ast_expr_get_op_arg> returns the specified
8963 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
8964 C<isl_ast_op_type> that appears in C<node>.
8965 The operation type is one of the following.
8969 =item C<isl_ast_op_and>
8971 Logical I<and> of two arguments.
8972 Both arguments can be evaluated.
8974 =item C<isl_ast_op_and_then>
8976 Logical I<and> of two arguments.
8977 The second argument can only be evaluated if the first evaluates to true.
8979 =item C<isl_ast_op_or>
8981 Logical I<or> of two arguments.
8982 Both arguments can be evaluated.
8984 =item C<isl_ast_op_or_else>
8986 Logical I<or> of two arguments.
8987 The second argument can only be evaluated if the first evaluates to false.
8989 =item C<isl_ast_op_max>
8991 Maximum of two or more arguments.
8993 =item C<isl_ast_op_min>
8995 Minimum of two or more arguments.
8997 =item C<isl_ast_op_minus>
9001 =item C<isl_ast_op_add>
9003 Sum of two arguments.
9005 =item C<isl_ast_op_sub>
9007 Difference of two arguments.
9009 =item C<isl_ast_op_mul>
9011 Product of two arguments.
9013 =item C<isl_ast_op_div>
9015 Exact division. That is, the result is known to be an integer.
9017 =item C<isl_ast_op_fdiv_q>
9019 Result of integer division, rounded towards negative
9022 =item C<isl_ast_op_pdiv_q>
9024 Result of integer division, where dividend is known to be non-negative.
9026 =item C<isl_ast_op_pdiv_r>
9028 Remainder of integer division, where dividend is known to be non-negative.
9030 =item C<isl_ast_op_zdiv_r>
9032 Equal to zero iff the remainder on integer division is zero.
9034 =item C<isl_ast_op_cond>
9036 Conditional operator defined on three arguments.
9037 If the first argument evaluates to true, then the result
9038 is equal to the second argument. Otherwise, the result
9039 is equal to the third argument.
9040 The second and third argument may only be evaluated if
9041 the first argument evaluates to true and false, respectively.
9042 Corresponds to C<a ? b : c> in C.
9044 =item C<isl_ast_op_select>
9046 Conditional operator defined on three arguments.
9047 If the first argument evaluates to true, then the result
9048 is equal to the second argument. Otherwise, the result
9049 is equal to the third argument.
9050 The second and third argument may be evaluated independently
9051 of the value of the first argument.
9052 Corresponds to C<a * b + (1 - a) * c> in C.
9054 =item C<isl_ast_op_eq>
9058 =item C<isl_ast_op_le>
9060 Less than or equal relation.
9062 =item C<isl_ast_op_lt>
9066 =item C<isl_ast_op_ge>
9068 Greater than or equal relation.
9070 =item C<isl_ast_op_gt>
9072 Greater than relation.
9074 =item C<isl_ast_op_call>
9077 The number of arguments of the C<isl_ast_expr> is one more than
9078 the number of arguments in the function call, the first argument
9079 representing the function being called.
9081 =item C<isl_ast_op_access>
9084 The number of arguments of the C<isl_ast_expr> is one more than
9085 the number of index expressions in the array access, the first argument
9086 representing the array being accessed.
9088 =item C<isl_ast_op_member>
9091 This operation has two arguments, a structure and the name of
9092 the member of the structure being accessed.
9096 #include <isl/ast.h>
9097 __isl_give isl_id *isl_ast_expr_get_id(
9098 __isl_keep isl_ast_expr *expr);
9100 Return the identifier represented by the AST expression.
9102 #include <isl/ast.h>
9103 __isl_give isl_val *isl_ast_expr_get_val(
9104 __isl_keep isl_ast_expr *expr);
9106 Return the integer represented by the AST expression.
9108 =head3 Properties of ASTs
9110 #include <isl/ast.h>
9111 isl_bool isl_ast_expr_is_equal(
9112 __isl_keep isl_ast_expr *expr1,
9113 __isl_keep isl_ast_expr *expr2);
9115 Check if two C<isl_ast_expr>s are equal to each other.
9117 =head3 Manipulating and printing the AST
9119 AST nodes can be copied and freed using the following functions.
9121 #include <isl/ast.h>
9122 __isl_give isl_ast_node *isl_ast_node_copy(
9123 __isl_keep isl_ast_node *node);
9124 __isl_null isl_ast_node *isl_ast_node_free(
9125 __isl_take isl_ast_node *node);
9127 AST expressions can be copied and freed using the following functions.
9129 #include <isl/ast.h>
9130 __isl_give isl_ast_expr *isl_ast_expr_copy(
9131 __isl_keep isl_ast_expr *expr);
9132 __isl_null isl_ast_expr *isl_ast_expr_free(
9133 __isl_take isl_ast_expr *expr);
9135 New AST expressions can be created either directly or within
9136 the context of an C<isl_ast_build>.
9138 #include <isl/ast.h>
9139 __isl_give isl_ast_expr *isl_ast_expr_from_val(
9140 __isl_take isl_val *v);
9141 __isl_give isl_ast_expr *isl_ast_expr_from_id(
9142 __isl_take isl_id *id);
9143 __isl_give isl_ast_expr *isl_ast_expr_neg(
9144 __isl_take isl_ast_expr *expr);
9145 __isl_give isl_ast_expr *isl_ast_expr_address_of(
9146 __isl_take isl_ast_expr *expr);
9147 __isl_give isl_ast_expr *isl_ast_expr_add(
9148 __isl_take isl_ast_expr *expr1,
9149 __isl_take isl_ast_expr *expr2);
9150 __isl_give isl_ast_expr *isl_ast_expr_sub(
9151 __isl_take isl_ast_expr *expr1,
9152 __isl_take isl_ast_expr *expr2);
9153 __isl_give isl_ast_expr *isl_ast_expr_mul(
9154 __isl_take isl_ast_expr *expr1,
9155 __isl_take isl_ast_expr *expr2);
9156 __isl_give isl_ast_expr *isl_ast_expr_div(
9157 __isl_take isl_ast_expr *expr1,
9158 __isl_take isl_ast_expr *expr2);
9159 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
9160 __isl_take isl_ast_expr *expr1,
9161 __isl_take isl_ast_expr *expr2);
9162 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
9163 __isl_take isl_ast_expr *expr1,
9164 __isl_take isl_ast_expr *expr2);
9165 __isl_give isl_ast_expr *isl_ast_expr_and(
9166 __isl_take isl_ast_expr *expr1,
9167 __isl_take isl_ast_expr *expr2)
9168 __isl_give isl_ast_expr *isl_ast_expr_and_then(
9169 __isl_take isl_ast_expr *expr1,
9170 __isl_take isl_ast_expr *expr2)
9171 __isl_give isl_ast_expr *isl_ast_expr_or(
9172 __isl_take isl_ast_expr *expr1,
9173 __isl_take isl_ast_expr *expr2)
9174 __isl_give isl_ast_expr *isl_ast_expr_or_else(
9175 __isl_take isl_ast_expr *expr1,
9176 __isl_take isl_ast_expr *expr2)
9177 __isl_give isl_ast_expr *isl_ast_expr_eq(
9178 __isl_take isl_ast_expr *expr1,
9179 __isl_take isl_ast_expr *expr2);
9180 __isl_give isl_ast_expr *isl_ast_expr_le(
9181 __isl_take isl_ast_expr *expr1,
9182 __isl_take isl_ast_expr *expr2);
9183 __isl_give isl_ast_expr *isl_ast_expr_lt(
9184 __isl_take isl_ast_expr *expr1,
9185 __isl_take isl_ast_expr *expr2);
9186 __isl_give isl_ast_expr *isl_ast_expr_ge(
9187 __isl_take isl_ast_expr *expr1,
9188 __isl_take isl_ast_expr *expr2);
9189 __isl_give isl_ast_expr *isl_ast_expr_gt(
9190 __isl_take isl_ast_expr *expr1,
9191 __isl_take isl_ast_expr *expr2);
9192 __isl_give isl_ast_expr *isl_ast_expr_access(
9193 __isl_take isl_ast_expr *array,
9194 __isl_take isl_ast_expr_list *indices);
9195 __isl_give isl_ast_expr *isl_ast_expr_call(
9196 __isl_take isl_ast_expr *function,
9197 __isl_take isl_ast_expr_list *arguments);
9199 The function C<isl_ast_expr_address_of> can be applied to an
9200 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
9201 to represent the address of the C<isl_ast_expr_access>. The function
9202 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
9203 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
9205 #include <isl/ast_build.h>
9206 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
9207 __isl_keep isl_ast_build *build,
9208 __isl_take isl_set *set);
9209 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
9210 __isl_keep isl_ast_build *build,
9211 __isl_take isl_pw_aff *pa);
9212 __isl_give isl_ast_expr *
9213 isl_ast_build_access_from_pw_multi_aff(
9214 __isl_keep isl_ast_build *build,
9215 __isl_take isl_pw_multi_aff *pma);
9216 __isl_give isl_ast_expr *
9217 isl_ast_build_access_from_multi_pw_aff(
9218 __isl_keep isl_ast_build *build,
9219 __isl_take isl_multi_pw_aff *mpa);
9220 __isl_give isl_ast_expr *
9221 isl_ast_build_call_from_pw_multi_aff(
9222 __isl_keep isl_ast_build *build,
9223 __isl_take isl_pw_multi_aff *pma);
9224 __isl_give isl_ast_expr *
9225 isl_ast_build_call_from_multi_pw_aff(
9226 __isl_keep isl_ast_build *build,
9227 __isl_take isl_multi_pw_aff *mpa);
9230 the domains of C<pa>, C<mpa> and C<pma> should correspond
9231 to the schedule space of C<build>.
9232 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
9233 the function being called.
9234 If the accessed space is a nested relation, then it is taken
9235 to represent an access of the member specified by the range
9236 of this nested relation of the structure specified by the domain
9237 of the nested relation.
9239 The following functions can be used to modify an C<isl_ast_expr>.
9241 #include <isl/ast.h>
9242 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
9243 __isl_take isl_ast_expr *expr, int pos,
9244 __isl_take isl_ast_expr *arg);
9246 Replace the argument of C<expr> at position C<pos> by C<arg>.
9248 #include <isl/ast.h>
9249 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
9250 __isl_take isl_ast_expr *expr,
9251 __isl_take isl_id_to_ast_expr *id2expr);
9253 The function C<isl_ast_expr_substitute_ids> replaces the
9254 subexpressions of C<expr> of type C<isl_ast_expr_id>
9255 by the corresponding expression in C<id2expr>, if there is any.
9258 User specified data can be attached to an C<isl_ast_node> and obtained
9259 from the same C<isl_ast_node> using the following functions.
9261 #include <isl/ast.h>
9262 __isl_give isl_ast_node *isl_ast_node_set_annotation(
9263 __isl_take isl_ast_node *node,
9264 __isl_take isl_id *annotation);
9265 __isl_give isl_id *isl_ast_node_get_annotation(
9266 __isl_keep isl_ast_node *node);
9268 Basic printing can be performed using the following functions.
9270 #include <isl/ast.h>
9271 __isl_give isl_printer *isl_printer_print_ast_expr(
9272 __isl_take isl_printer *p,
9273 __isl_keep isl_ast_expr *expr);
9274 __isl_give isl_printer *isl_printer_print_ast_node(
9275 __isl_take isl_printer *p,
9276 __isl_keep isl_ast_node *node);
9277 __isl_give char *isl_ast_expr_to_str(
9278 __isl_keep isl_ast_expr *expr);
9280 More advanced printing can be performed using the following functions.
9282 #include <isl/ast.h>
9283 __isl_give isl_printer *isl_ast_op_type_print_macro(
9284 enum isl_ast_op_type type,
9285 __isl_take isl_printer *p);
9286 __isl_give isl_printer *isl_ast_node_print_macros(
9287 __isl_keep isl_ast_node *node,
9288 __isl_take isl_printer *p);
9289 __isl_give isl_printer *isl_ast_node_print(
9290 __isl_keep isl_ast_node *node,
9291 __isl_take isl_printer *p,
9292 __isl_take isl_ast_print_options *options);
9293 __isl_give isl_printer *isl_ast_node_for_print(
9294 __isl_keep isl_ast_node *node,
9295 __isl_take isl_printer *p,
9296 __isl_take isl_ast_print_options *options);
9297 __isl_give isl_printer *isl_ast_node_if_print(
9298 __isl_keep isl_ast_node *node,
9299 __isl_take isl_printer *p,
9300 __isl_take isl_ast_print_options *options);
9302 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
9303 C<isl> may print out an AST that makes use of macros such
9304 as C<floord>, C<min> and C<max>.
9305 C<isl_ast_op_type_print_macro> prints out the macro
9306 corresponding to a specific C<isl_ast_op_type>.
9307 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
9308 for expressions where these macros would be used and prints
9309 out the required macro definitions.
9310 Essentially, C<isl_ast_node_print_macros> calls
9311 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
9312 as function argument.
9313 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
9314 C<isl_ast_node_if_print> print an C<isl_ast_node>
9315 in C<ISL_FORMAT_C>, but allow for some extra control
9316 through an C<isl_ast_print_options> object.
9317 This object can be created using the following functions.
9319 #include <isl/ast.h>
9320 __isl_give isl_ast_print_options *
9321 isl_ast_print_options_alloc(isl_ctx *ctx);
9322 __isl_give isl_ast_print_options *
9323 isl_ast_print_options_copy(
9324 __isl_keep isl_ast_print_options *options);
9325 __isl_null isl_ast_print_options *
9326 isl_ast_print_options_free(
9327 __isl_take isl_ast_print_options *options);
9329 __isl_give isl_ast_print_options *
9330 isl_ast_print_options_set_print_user(
9331 __isl_take isl_ast_print_options *options,
9332 __isl_give isl_printer *(*print_user)(
9333 __isl_take isl_printer *p,
9334 __isl_take isl_ast_print_options *options,
9335 __isl_keep isl_ast_node *node, void *user),
9337 __isl_give isl_ast_print_options *
9338 isl_ast_print_options_set_print_for(
9339 __isl_take isl_ast_print_options *options,
9340 __isl_give isl_printer *(*print_for)(
9341 __isl_take isl_printer *p,
9342 __isl_take isl_ast_print_options *options,
9343 __isl_keep isl_ast_node *node, void *user),
9346 The callback set by C<isl_ast_print_options_set_print_user>
9347 is called whenever a node of type C<isl_ast_node_user> needs to
9349 The callback set by C<isl_ast_print_options_set_print_for>
9350 is called whenever a node of type C<isl_ast_node_for> needs to
9352 Note that C<isl_ast_node_for_print> will I<not> call the
9353 callback set by C<isl_ast_print_options_set_print_for> on the node
9354 on which C<isl_ast_node_for_print> is called, but only on nested
9355 nodes of type C<isl_ast_node_for>. It is therefore safe to
9356 call C<isl_ast_node_for_print> from within the callback set by
9357 C<isl_ast_print_options_set_print_for>.
9359 The following option determines the type to be used for iterators
9360 while printing the AST.
9362 isl_stat isl_options_set_ast_iterator_type(
9363 isl_ctx *ctx, const char *val);
9364 const char *isl_options_get_ast_iterator_type(
9367 The AST printer only prints body nodes as blocks if these
9368 blocks cannot be safely omitted.
9369 For example, a C<for> node with one body node will not be
9370 surrounded with braces in C<ISL_FORMAT_C>.
9371 A block will always be printed by setting the following option.
9373 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx,
9375 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
9379 #include <isl/ast_build.h>
9380 isl_stat isl_options_set_ast_build_atomic_upper_bound(
9381 isl_ctx *ctx, int val);
9382 int isl_options_get_ast_build_atomic_upper_bound(
9384 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
9386 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
9387 isl_stat isl_options_set_ast_build_exploit_nested_bounds(
9388 isl_ctx *ctx, int val);
9389 int isl_options_get_ast_build_exploit_nested_bounds(
9391 isl_stat isl_options_set_ast_build_group_coscheduled(
9392 isl_ctx *ctx, int val);
9393 int isl_options_get_ast_build_group_coscheduled(
9395 isl_stat isl_options_set_ast_build_scale_strides(
9396 isl_ctx *ctx, int val);
9397 int isl_options_get_ast_build_scale_strides(
9399 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx,
9401 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
9402 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx,
9404 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
9408 =item * ast_build_atomic_upper_bound
9410 Generate loop upper bounds that consist of the current loop iterator,
9411 an operator and an expression not involving the iterator.
9412 If this option is not set, then the current loop iterator may appear
9413 several times in the upper bound.
9414 For example, when this option is turned off, AST generation
9417 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
9421 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
9424 When the option is turned on, the following AST is generated
9426 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
9429 =item * ast_build_prefer_pdiv
9431 If this option is turned off, then the AST generation will
9432 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
9433 operators, but no C<isl_ast_op_pdiv_q> or
9434 C<isl_ast_op_pdiv_r> operators.
9435 If this options is turned on, then C<isl> will try to convert
9436 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
9437 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
9439 =item * ast_build_exploit_nested_bounds
9441 Simplify conditions based on bounds of nested for loops.
9442 In particular, remove conditions that are implied by the fact
9443 that one or more nested loops have at least one iteration,
9444 meaning that the upper bound is at least as large as the lower bound.
9445 For example, when this option is turned off, AST generation
9448 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
9454 for (int c0 = 0; c0 <= N; c0 += 1)
9455 for (int c1 = 0; c1 <= M; c1 += 1)
9458 When the option is turned on, the following AST is generated
9460 for (int c0 = 0; c0 <= N; c0 += 1)
9461 for (int c1 = 0; c1 <= M; c1 += 1)
9464 =item * ast_build_group_coscheduled
9466 If two domain elements are assigned the same schedule point, then
9467 they may be executed in any order and they may even appear in different
9468 loops. If this options is set, then the AST generator will make
9469 sure that coscheduled domain elements do not appear in separate parts
9470 of the AST. This is useful in case of nested AST generation
9471 if the outer AST generation is given only part of a schedule
9472 and the inner AST generation should handle the domains that are
9473 coscheduled by this initial part of the schedule together.
9474 For example if an AST is generated for a schedule
9476 { A[i] -> [0]; B[i] -> [0] }
9478 then the C<isl_ast_build_set_create_leaf> callback described
9479 below may get called twice, once for each domain.
9480 Setting this option ensures that the callback is only called once
9481 on both domains together.
9483 =item * ast_build_separation_bounds
9485 This option specifies which bounds to use during separation.
9486 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
9487 then all (possibly implicit) bounds on the current dimension will
9488 be used during separation.
9489 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
9490 then only those bounds that are explicitly available will
9491 be used during separation.
9493 =item * ast_build_scale_strides
9495 This option specifies whether the AST generator is allowed
9496 to scale down iterators of strided loops.
9498 =item * ast_build_allow_else
9500 This option specifies whether the AST generator is allowed
9501 to construct if statements with else branches.
9503 =item * ast_build_allow_or
9505 This option specifies whether the AST generator is allowed
9506 to construct if conditions with disjunctions.
9510 =head3 AST Generation Options (Schedule Tree)
9512 In case of AST construction from a schedule tree, the options
9513 that control how an AST is created from the individual schedule
9514 dimensions are stored in the band nodes of the tree
9515 (see L</"Schedule Trees">).
9517 In particular, a schedule dimension can be handled in four
9518 different ways, atomic, separate, unroll or the default.
9519 This loop AST generation type can be set using
9520 C<isl_schedule_node_band_member_set_ast_loop_type>.
9522 the first three can be selected by including a one-dimensional
9523 element with as value the position of the schedule dimension
9524 within the band and as name one of C<atomic>, C<separate>
9525 or C<unroll> in the options
9526 set by C<isl_schedule_node_band_set_ast_build_options>.
9527 Only one of these three may be specified for
9528 any given schedule dimension within a band node.
9529 If none of these is specified, then the default
9530 is used. The meaning of the options is as follows.
9536 When this option is specified, the AST generator will make
9537 sure that a given domains space only appears in a single
9538 loop at the specified level.
9540 For example, for the schedule tree
9542 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
9544 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
9545 options: "{ atomic[x] }"
9547 the following AST will be generated
9549 for (int c0 = 0; c0 <= 10; c0 += 1) {
9556 On the other hand, for the schedule tree
9558 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
9560 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
9561 options: "{ separate[x] }"
9563 the following AST will be generated
9567 for (int c0 = 1; c0 <= 9; c0 += 1) {
9574 If neither C<atomic> nor C<separate> is specified, then the AST generator
9575 may produce either of these two results or some intermediate form.
9579 When this option is specified, the AST generator will
9580 split the domain of the specified schedule dimension
9581 into pieces with a fixed set of statements for which
9582 instances need to be executed by the iterations in
9583 the schedule domain part. This option tends to avoid
9584 the generation of guards inside the corresponding loops.
9585 See also the C<atomic> option.
9589 When this option is specified, the AST generator will
9590 I<completely> unroll the corresponding schedule dimension.
9591 It is the responsibility of the user to ensure that such
9592 unrolling is possible.
9593 To obtain a partial unrolling, the user should apply an additional
9594 strip-mining to the schedule and fully unroll the inner schedule
9599 The C<isolate> option is a bit more involved. It allows the user
9600 to isolate a range of schedule dimension values from smaller and
9601 greater values. Additionally, the user may specify a different
9602 atomic/separate/unroll choice for the isolated part and the remaining
9603 parts. The typical use case of the C<isolate> option is to isolate
9604 full tiles from partial tiles.
9605 The part that needs to be isolated may depend on outer schedule dimensions.
9606 The option therefore needs to be able to reference those outer schedule
9607 dimensions. In particular, the space of the C<isolate> option is that
9608 of a wrapped map with as domain the flat product of all outer band nodes
9609 and as range the space of the current band node.
9610 The atomic/separate/unroll choice for the isolated part is determined
9611 by an option that lives in an unnamed wrapped space with as domain
9612 a zero-dimensional C<isolate> space and as range the regular
9613 C<atomic>, C<separate> or C<unroll> space.
9614 This option may also be set directly using
9615 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
9616 The atomic/separate/unroll choice for the remaining part is determined
9617 by the regular C<atomic>, C<separate> or C<unroll> option.
9618 The use of the C<isolate> option causes any tree containing the node
9619 to be considered anchored.
9621 As an example, consider the isolation of full tiles from partial tiles
9622 in a tiling of a triangular domain. The original schedule is as follows.
9624 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
9626 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
9627 { A[i,j] -> [floor(j/10)] }, \
9628 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
9632 for (int c0 = 0; c0 <= 10; c0 += 1)
9633 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
9634 for (int c2 = 10 * c0;
9635 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
9636 for (int c3 = 10 * c1;
9637 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
9640 Isolating the full tiles, we have the following input
9642 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
9644 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
9645 { A[i,j] -> [floor(j/10)] }, \
9646 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
9647 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
9648 10a+9+10b+9 <= 100 }"
9653 for (int c0 = 0; c0 <= 8; c0 += 1) {
9654 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
9655 for (int c2 = 10 * c0;
9656 c2 <= 10 * c0 + 9; c2 += 1)
9657 for (int c3 = 10 * c1;
9658 c3 <= 10 * c1 + 9; c3 += 1)
9660 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
9661 for (int c2 = 10 * c0;
9662 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
9663 for (int c3 = 10 * c1;
9664 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
9667 for (int c0 = 9; c0 <= 10; c0 += 1)
9668 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
9669 for (int c2 = 10 * c0;
9670 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
9671 for (int c3 = 10 * c1;
9672 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
9676 We may then additionally unroll the innermost loop of the isolated part
9678 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
9680 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
9681 { A[i,j] -> [floor(j/10)] }, \
9682 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
9683 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
9684 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
9689 for (int c0 = 0; c0 <= 8; c0 += 1) {
9690 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
9691 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
9703 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
9704 for (int c2 = 10 * c0;
9705 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
9706 for (int c3 = 10 * c1;
9707 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
9710 for (int c0 = 9; c0 <= 10; c0 += 1)
9711 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
9712 for (int c2 = 10 * c0;
9713 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
9714 for (int c3 = 10 * c1;
9715 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
9720 =head3 AST Generation Options (Schedule Map)
9722 In case of AST construction using
9723 C<isl_ast_build_node_from_schedule_map>, the options
9724 that control how an AST is created from the individual schedule
9725 dimensions are stored in the C<isl_ast_build>.
9726 They can be set using the following function.
9728 #include <isl/ast_build.h>
9729 __isl_give isl_ast_build *
9730 isl_ast_build_set_options(
9731 __isl_take isl_ast_build *control,
9732 __isl_take isl_union_map *options);
9734 The options are encoded in an C<isl_union_map>.
9735 The domain of this union relation refers to the schedule domain,
9736 i.e., the range of the schedule passed
9737 to C<isl_ast_build_node_from_schedule_map>.
9738 In the case of nested AST generation (see L</"Nested AST Generation">),
9739 the domain of C<options> should refer to the extra piece of the schedule.
9740 That is, it should be equal to the range of the wrapped relation in the
9741 range of the schedule.
9742 The range of the options can consist of elements in one or more spaces,
9743 the names of which determine the effect of the option.
9744 The values of the range typically also refer to the schedule dimension
9745 to which the option applies. In case of nested AST generation
9746 (see L</"Nested AST Generation">), these values refer to the position
9747 of the schedule dimension within the innermost AST generation.
9748 The constraints on the domain elements of
9749 the option should only refer to this dimension and earlier dimensions.
9750 We consider the following spaces.
9754 =item C<separation_class>
9756 B<This option has been deprecated. Use the isolate option on
9757 schedule trees instead.>
9759 This space is a wrapped relation between two one dimensional spaces.
9760 The input space represents the schedule dimension to which the option
9761 applies and the output space represents the separation class.
9762 While constructing a loop corresponding to the specified schedule
9763 dimension(s), the AST generator will try to generate separate loops
9764 for domain elements that are assigned different classes.
9765 If only some of the elements are assigned a class, then those elements
9766 that are not assigned any class will be treated as belonging to a class
9767 that is separate from the explicitly assigned classes.
9768 The typical use case for this option is to separate full tiles from
9770 The other options, described below, are applied after the separation
9773 As an example, consider the separation into full and partial tiles
9774 of a tiling of a triangular domain.
9775 Take, for example, the domain
9777 { A[i,j] : 0 <= i,j and i + j <= 100 }
9779 and a tiling into tiles of 10 by 10. The input to the AST generator
9780 is then the schedule
9782 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
9785 Without any options, the following AST is generated
9787 for (int c0 = 0; c0 <= 10; c0 += 1)
9788 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
9789 for (int c2 = 10 * c0;
9790 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
9792 for (int c3 = 10 * c1;
9793 c3 <= min(10 * c1 + 9, -c2 + 100);
9797 Separation into full and partial tiles can be obtained by assigning
9798 a class, say C<0>, to the full tiles. The full tiles are represented by those
9799 values of the first and second schedule dimensions for which there are
9800 values of the third and fourth dimensions to cover an entire tile.
9801 That is, we need to specify the following option
9803 { [a,b,c,d] -> separation_class[[0]->[0]] :
9804 exists b': 0 <= 10a,10b' and
9805 10a+9+10b'+9 <= 100;
9806 [a,b,c,d] -> separation_class[[1]->[0]] :
9807 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
9811 { [a, b, c, d] -> separation_class[[1] -> [0]] :
9812 a >= 0 and b >= 0 and b <= 8 - a;
9813 [a, b, c, d] -> separation_class[[0] -> [0]] :
9816 With this option, the generated AST is as follows
9819 for (int c0 = 0; c0 <= 8; c0 += 1) {
9820 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
9821 for (int c2 = 10 * c0;
9822 c2 <= 10 * c0 + 9; c2 += 1)
9823 for (int c3 = 10 * c1;
9824 c3 <= 10 * c1 + 9; c3 += 1)
9826 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
9827 for (int c2 = 10 * c0;
9828 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
9830 for (int c3 = 10 * c1;
9831 c3 <= min(-c2 + 100, 10 * c1 + 9);
9835 for (int c0 = 9; c0 <= 10; c0 += 1)
9836 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
9837 for (int c2 = 10 * c0;
9838 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
9840 for (int c3 = 10 * c1;
9841 c3 <= min(10 * c1 + 9, -c2 + 100);
9848 This is a single-dimensional space representing the schedule dimension(s)
9849 to which ``separation'' should be applied. Separation tries to split
9850 a loop into several pieces if this can avoid the generation of guards
9852 See also the C<atomic> option.
9856 This is a single-dimensional space representing the schedule dimension(s)
9857 for which the domains should be considered ``atomic''. That is, the
9858 AST generator will make sure that any given domain space will only appear
9859 in a single loop at the specified level.
9861 Consider the following schedule
9863 { a[i] -> [i] : 0 <= i < 10;
9864 b[i] -> [i+1] : 0 <= i < 10 }
9866 If the following option is specified
9868 { [i] -> separate[x] }
9870 then the following AST will be generated
9874 for (int c0 = 1; c0 <= 9; c0 += 1) {
9881 If, on the other hand, the following option is specified
9883 { [i] -> atomic[x] }
9885 then the following AST will be generated
9887 for (int c0 = 0; c0 <= 10; c0 += 1) {
9894 If neither C<atomic> nor C<separate> is specified, then the AST generator
9895 may produce either of these two results or some intermediate form.
9899 This is a single-dimensional space representing the schedule dimension(s)
9900 that should be I<completely> unrolled.
9901 To obtain a partial unrolling, the user should apply an additional
9902 strip-mining to the schedule and fully unroll the inner loop.
9906 =head3 Fine-grained Control over AST Generation
9908 Besides specifying the constraints on the parameters,
9909 an C<isl_ast_build> object can be used to control
9910 various aspects of the AST generation process.
9911 In case of AST construction using
9912 C<isl_ast_build_node_from_schedule_map>,
9913 the most prominent way of control is through ``options'',
9916 Additional control is available through the following functions.
9918 #include <isl/ast_build.h>
9919 __isl_give isl_ast_build *
9920 isl_ast_build_set_iterators(
9921 __isl_take isl_ast_build *control,
9922 __isl_take isl_id_list *iterators);
9924 The function C<isl_ast_build_set_iterators> allows the user to
9925 specify a list of iterator C<isl_id>s to be used as iterators.
9926 If the input schedule is injective, then
9927 the number of elements in this list should be as large as the dimension
9928 of the schedule space, but no direct correspondence should be assumed
9929 between dimensions and elements.
9930 If the input schedule is not injective, then an additional number
9931 of C<isl_id>s equal to the largest dimension of the input domains
9933 If the number of provided C<isl_id>s is insufficient, then additional
9934 names are automatically generated.
9936 #include <isl/ast_build.h>
9937 __isl_give isl_ast_build *
9938 isl_ast_build_set_create_leaf(
9939 __isl_take isl_ast_build *control,
9940 __isl_give isl_ast_node *(*fn)(
9941 __isl_take isl_ast_build *build,
9942 void *user), void *user);
9945 C<isl_ast_build_set_create_leaf> function allows for the
9946 specification of a callback that should be called whenever the AST
9947 generator arrives at an element of the schedule domain.
9948 The callback should return an AST node that should be inserted
9949 at the corresponding position of the AST. The default action (when
9950 the callback is not set) is to continue generating parts of the AST to scan
9951 all the domain elements associated to the schedule domain element
9952 and to insert user nodes, ``calling'' the domain element, for each of them.
9953 The C<build> argument contains the current state of the C<isl_ast_build>.
9954 To ease nested AST generation (see L</"Nested AST Generation">),
9955 all control information that is
9956 specific to the current AST generation such as the options and
9957 the callbacks has been removed from this C<isl_ast_build>.
9958 The callback would typically return the result of a nested
9960 user defined node created using the following function.
9962 #include <isl/ast.h>
9963 __isl_give isl_ast_node *isl_ast_node_alloc_user(
9964 __isl_take isl_ast_expr *expr);
9966 #include <isl/ast_build.h>
9967 __isl_give isl_ast_build *
9968 isl_ast_build_set_at_each_domain(
9969 __isl_take isl_ast_build *build,
9970 __isl_give isl_ast_node *(*fn)(
9971 __isl_take isl_ast_node *node,
9972 __isl_keep isl_ast_build *build,
9973 void *user), void *user);
9974 __isl_give isl_ast_build *
9975 isl_ast_build_set_before_each_for(
9976 __isl_take isl_ast_build *build,
9977 __isl_give isl_id *(*fn)(
9978 __isl_keep isl_ast_build *build,
9979 void *user), void *user);
9980 __isl_give isl_ast_build *
9981 isl_ast_build_set_after_each_for(
9982 __isl_take isl_ast_build *build,
9983 __isl_give isl_ast_node *(*fn)(
9984 __isl_take isl_ast_node *node,
9985 __isl_keep isl_ast_build *build,
9986 void *user), void *user);
9987 __isl_give isl_ast_build *
9988 isl_ast_build_set_before_each_mark(
9989 __isl_take isl_ast_build *build,
9990 isl_stat (*fn)(__isl_keep isl_id *mark,
9991 __isl_keep isl_ast_build *build,
9992 void *user), void *user);
9993 __isl_give isl_ast_build *
9994 isl_ast_build_set_after_each_mark(
9995 __isl_take isl_ast_build *build,
9996 __isl_give isl_ast_node *(*fn)(
9997 __isl_take isl_ast_node *node,
9998 __isl_keep isl_ast_build *build,
9999 void *user), void *user);
10001 The callback set by C<isl_ast_build_set_at_each_domain> will
10002 be called for each domain AST node.
10003 The callbacks set by C<isl_ast_build_set_before_each_for>
10004 and C<isl_ast_build_set_after_each_for> will be called
10005 for each for AST node. The first will be called in depth-first
10006 pre-order, while the second will be called in depth-first post-order.
10007 Since C<isl_ast_build_set_before_each_for> is called before the for
10008 node is actually constructed, it is only passed an C<isl_ast_build>.
10009 The returned C<isl_id> will be added as an annotation (using
10010 C<isl_ast_node_set_annotation>) to the constructed for node.
10011 In particular, if the user has also specified an C<after_each_for>
10012 callback, then the annotation can be retrieved from the node passed to
10013 that callback using C<isl_ast_node_get_annotation>.
10014 The callbacks set by C<isl_ast_build_set_before_each_mark>
10015 and C<isl_ast_build_set_after_each_mark> will be called for each
10016 mark AST node that is created, i.e., for each mark schedule node
10017 in the input schedule tree. The first will be called in depth-first
10018 pre-order, while the second will be called in depth-first post-order.
10019 Since the callback set by C<isl_ast_build_set_before_each_mark>
10020 is called before the mark AST node is actually constructed, it is passed
10021 the identifier of the mark node.
10022 All callbacks should C<NULL> (or -1) on failure.
10023 The given C<isl_ast_build> can be used to create new
10024 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
10025 or C<isl_ast_build_call_from_pw_multi_aff>.
10027 =head3 Nested AST Generation
10029 C<isl> allows the user to create an AST within the context
10030 of another AST. These nested ASTs are created using the
10031 same C<isl_ast_build_node_from_schedule_map> function that is used to create
10032 the outer AST. The C<build> argument should be an C<isl_ast_build>
10033 passed to a callback set by
10034 C<isl_ast_build_set_create_leaf>.
10035 The space of the range of the C<schedule> argument should refer
10036 to this build. In particular, the space should be a wrapped
10037 relation and the domain of this wrapped relation should be the
10038 same as that of the range of the schedule returned by
10039 C<isl_ast_build_get_schedule> below.
10040 In practice, the new schedule is typically
10041 created by calling C<isl_union_map_range_product> on the old schedule
10042 and some extra piece of the schedule.
10043 The space of the schedule domain is also available from
10044 the C<isl_ast_build>.
10046 #include <isl/ast_build.h>
10047 __isl_give isl_union_map *isl_ast_build_get_schedule(
10048 __isl_keep isl_ast_build *build);
10049 __isl_give isl_space *isl_ast_build_get_schedule_space(
10050 __isl_keep isl_ast_build *build);
10051 __isl_give isl_ast_build *isl_ast_build_restrict(
10052 __isl_take isl_ast_build *build,
10053 __isl_take isl_set *set);
10055 The C<isl_ast_build_get_schedule> function returns a (partial)
10056 schedule for the domains elements for which part of the AST still needs to
10057 be generated in the current build.
10058 In particular, the domain elements are mapped to those iterations of the loops
10059 enclosing the current point of the AST generation inside which
10060 the domain elements are executed.
10061 No direct correspondence between
10062 the input schedule and this schedule should be assumed.
10063 The space obtained from C<isl_ast_build_get_schedule_space> can be used
10064 to create a set for C<isl_ast_build_restrict> to intersect
10065 with the current build. In particular, the set passed to
10066 C<isl_ast_build_restrict> can have additional parameters.
10067 The ids of the set dimensions in the space returned by
10068 C<isl_ast_build_get_schedule_space> correspond to the
10069 iterators of the already generated loops.
10070 The user should not rely on the ids of the output dimensions
10071 of the relations in the union relation returned by
10072 C<isl_ast_build_get_schedule> having any particular value.
10074 =head1 Applications
10076 Although C<isl> is mainly meant to be used as a library,
10077 it also contains some basic applications that use some
10078 of the functionality of C<isl>.
10079 The input may be specified in either the L<isl format>
10080 or the L<PolyLib format>.
10082 =head2 C<isl_polyhedron_sample>
10084 C<isl_polyhedron_sample> takes a polyhedron as input and prints
10085 an integer element of the polyhedron, if there is any.
10086 The first column in the output is the denominator and is always
10087 equal to 1. If the polyhedron contains no integer points,
10088 then a vector of length zero is printed.
10092 C<isl_pip> takes the same input as the C<example> program
10093 from the C<piplib> distribution, i.e., a set of constraints
10094 on the parameters, a line containing only -1 and finally a set
10095 of constraints on a parametric polyhedron.
10096 The coefficients of the parameters appear in the last columns
10097 (but before the final constant column).
10098 The output is the lexicographic minimum of the parametric polyhedron.
10099 As C<isl> currently does not have its own output format, the output
10100 is just a dump of the internal state.
10102 =head2 C<isl_polyhedron_minimize>
10104 C<isl_polyhedron_minimize> computes the minimum of some linear
10105 or affine objective function over the integer points in a polyhedron.
10106 If an affine objective function
10107 is given, then the constant should appear in the last column.
10109 =head2 C<isl_polytope_scan>
10111 Given a polytope, C<isl_polytope_scan> prints
10112 all integer points in the polytope.
10114 =head2 C<isl_codegen>
10116 Given a schedule, a context set and an options relation,
10117 C<isl_codegen> prints out an AST that scans the domain elements
10118 of the schedule in the order of their image(s) taking into account
10119 the constraints in the context set.