3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
8 using C<GMP> or C<imath>.
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
171 =head3 Changes since isl-0.10
175 =item * The functions C<isl_set_dim_has_lower_bound> and
176 C<isl_set_dim_has_upper_bound> have been renamed to
177 C<isl_set_dim_has_any_lower_bound> and
178 C<isl_set_dim_has_any_upper_bound>.
179 The new C<isl_set_dim_has_lower_bound> and
180 C<isl_set_dim_has_upper_bound> have slightly different meanings.
184 =head3 Changes since isl-0.12
188 =item * C<isl_int> has been replaced by C<isl_val>.
189 Some of the old functions are still available in C<isl/deprecated/*.h>
190 but they will be removed in the future.
192 =item * The functions C<isl_pw_qpolynomial_eval>,
193 C<isl_union_pw_qpolynomial_eval>, C<isl_pw_qpolynomial_fold_eval>
194 and C<isl_union_pw_qpolynomial_fold_eval> have been changed to return
195 an C<isl_val> instead of an C<isl_qpolynomial>.
197 =item * The function C<isl_band_member_is_zero_distance>
198 has been removed. Essentially the same functionality is available
199 through C<isl_band_member_is_coincident>, except that it requires
200 setting up coincidence constraints.
201 The option C<schedule_outer_zero_distance> has accordingly been
202 replaced by the option C<schedule_outer_coincidence>.
204 =item * The function C<isl_vertex_get_expr> has been changed
205 to return an C<isl_multi_aff> instead of a rational C<isl_basic_set>.
206 The function C<isl_vertex_get_domain> has been changed to return
207 a regular basic set, rather than a rational basic set.
211 =head3 Changes since isl-0.14
215 =item * The function C<isl_union_pw_multi_aff_add> now consistently
216 computes the sum on the shared definition domain.
217 The function C<isl_union_pw_multi_aff_union_add> has been added
218 to compute the sum on the union of definition domains.
219 The original behavior of C<isl_union_pw_multi_aff_add> was
220 confused and is no longer available.
222 =item * Band forests have been replaced by schedule trees.
224 =item * The function C<isl_union_map_compute_flow> has been
225 replaced by the function C<isl_union_access_info_compute_flow>.
226 Note that the may dependence relation returned by
227 C<isl_union_flow_get_may_dependence> is the union of
228 the two dependence relations returned by
229 C<isl_union_map_compute_flow>. Similarly for the no source relations.
230 The function C<isl_union_map_compute_flow> is still available
231 for backward compatibility, but it will be removed in the future.
233 =item * The function C<isl_basic_set_drop_constraint> has been
236 =item * The function C<isl_ast_build_ast_from_schedule> has been
237 renamed to C<isl_ast_build_node_from_schedule_map>.
238 The original name is still available
239 for backward compatibility, but it will be removed in the future.
241 =item * The C<separation_class> AST generation option has been
244 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
245 have been renamed to C<isl_constraint_alloc_equality> and
246 C<isl_constraint_alloc_inequality>. The original names have been
247 kept for backward compatibility, but they will be removed in the future.
249 =item * The C<schedule_fuse> option has been replaced
250 by the C<schedule_serialize_sccs> option. The effect
251 of setting the C<schedule_fuse> option to C<ISL_SCHEDULE_FUSE_MIN>
252 is now obtained by turning on the C<schedule_serialize_sccs> option.
258 C<isl> is released under the MIT license.
262 Permission is hereby granted, free of charge, to any person obtaining a copy of
263 this software and associated documentation files (the "Software"), to deal in
264 the Software without restriction, including without limitation the rights to
265 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
266 of the Software, and to permit persons to whom the Software is furnished to do
267 so, subject to the following conditions:
269 The above copyright notice and this permission notice shall be included in all
270 copies or substantial portions of the Software.
272 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
273 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
274 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
275 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
276 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
277 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
282 Note that by default C<isl> requires C<GMP>, which is released
283 under the GNU Lesser General Public License (LGPL). This means
284 that code linked against C<isl> is also linked against LGPL code.
286 When configuring with C<--with-int=imath> or C<--with-int=imath-32>, C<isl>
287 will link against C<imath>, a library for exact integer arithmetic released
288 under the MIT license.
292 The source of C<isl> can be obtained either as a tarball
293 or from the git repository. Both are available from
294 L<http://freshmeat.net/projects/isl/>.
295 The installation process depends on how you obtained
298 =head2 Installation from the git repository
302 =item 1 Clone or update the repository
304 The first time the source is obtained, you need to clone
307 git clone git://repo.or.cz/isl.git
309 To obtain updates, you need to pull in the latest changes
313 =item 2 Optionally get C<imath> submodule
315 To build C<isl> with C<imath>, you need to obtain the C<imath>
316 submodule by running in the git source tree of C<isl>
321 This will fetch the required version of C<imath> in a subdirectory of C<isl>.
323 =item 2 Generate C<configure>
329 After performing the above steps, continue
330 with the L<Common installation instructions>.
332 =head2 Common installation instructions
336 =item 1 Obtain C<GMP>
338 By default, building C<isl> requires C<GMP>, including its headers files.
339 Your distribution may not provide these header files by default
340 and you may need to install a package called C<gmp-devel> or something
341 similar. Alternatively, C<GMP> can be built from
342 source, available from L<http://gmplib.org/>.
343 C<GMP> is not needed if you build C<isl> with C<imath>.
347 C<isl> uses the standard C<autoconf> C<configure> script.
352 optionally followed by some configure options.
353 A complete list of options can be obtained by running
357 Below we discuss some of the more common options.
363 Installation prefix for C<isl>
365 =item C<--with-int=[gmp|imath|imath-32]>
367 Select the integer library to be used by C<isl>, the default is C<gmp>.
368 With C<imath-32>, C<isl> will use 32 bit integers, but fall back to C<imath>
369 for values out of the 32 bit range. In most applications, C<isl> will run
370 fastest with the C<imath-32> option, followed by C<gmp> and C<imath>, the
373 =item C<--with-gmp-prefix>
375 Installation prefix for C<GMP> (architecture-independent files).
377 =item C<--with-gmp-exec-prefix>
379 Installation prefix for C<GMP> (architecture-dependent files).
387 =item 4 Install (optional)
393 =head1 Integer Set Library
395 =head2 Memory Management
397 Since a high-level operation on isl objects usually involves
398 several substeps and since the user is usually not interested in
399 the intermediate results, most functions that return a new object
400 will also release all the objects passed as arguments.
401 If the user still wants to use one or more of these arguments
402 after the function call, she should pass along a copy of the
403 object rather than the object itself.
404 The user is then responsible for making sure that the original
405 object gets used somewhere else or is explicitly freed.
407 The arguments and return values of all documented functions are
408 annotated to make clear which arguments are released and which
409 arguments are preserved. In particular, the following annotations
416 C<__isl_give> means that a new object is returned.
417 The user should make sure that the returned pointer is
418 used exactly once as a value for an C<__isl_take> argument.
419 In between, it can be used as a value for as many
420 C<__isl_keep> arguments as the user likes.
421 There is one exception, and that is the case where the
422 pointer returned is C<NULL>. Is this case, the user
423 is free to use it as an C<__isl_take> argument or not.
424 When applied to a C<char *>, the returned pointer needs to be
429 C<__isl_null> means that a C<NULL> value is returned.
433 C<__isl_take> means that the object the argument points to
434 is taken over by the function and may no longer be used
435 by the user as an argument to any other function.
436 The pointer value must be one returned by a function
437 returning an C<__isl_give> pointer.
438 If the user passes in a C<NULL> value, then this will
439 be treated as an error in the sense that the function will
440 not perform its usual operation. However, it will still
441 make sure that all the other C<__isl_take> arguments
446 C<__isl_keep> means that the function will only use the object
447 temporarily. After the function has finished, the user
448 can still use it as an argument to other functions.
449 A C<NULL> value will be treated in the same way as
450 a C<NULL> value for an C<__isl_take> argument.
451 This annotation may also be used on return values of
452 type C<const char *>, in which case the returned pointer should
453 not be freed by the user and is only valid until the object
454 from which it was derived is updated or freed.
458 =head2 Initialization
460 All manipulations of integer sets and relations occur within
461 the context of an C<isl_ctx>.
462 A given C<isl_ctx> can only be used within a single thread.
463 All arguments of a function are required to have been allocated
464 within the same context.
465 There are currently no functions available for moving an object
466 from one C<isl_ctx> to another C<isl_ctx>. This means that
467 there is currently no way of safely moving an object from one
468 thread to another, unless the whole C<isl_ctx> is moved.
470 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
471 freed using C<isl_ctx_free>.
472 All objects allocated within an C<isl_ctx> should be freed
473 before the C<isl_ctx> itself is freed.
475 isl_ctx *isl_ctx_alloc();
476 void isl_ctx_free(isl_ctx *ctx);
478 The user can impose a bound on the number of low-level I<operations>
479 that can be performed by an C<isl_ctx>. This bound can be set and
480 retrieved using the following functions. A bound of zero means that
481 no bound is imposed. The number of operations performed can be
482 reset using C<isl_ctx_reset_operations>. Note that the number
483 of low-level operations needed to perform a high-level computation
484 may differ significantly across different versions
485 of C<isl>, but it should be the same across different platforms
486 for the same version of C<isl>.
488 Warning: This feature is experimental. C<isl> has good support to abort and
489 bail out during the computation, but this feature may exercise error code paths
490 that are normally not used that much. Consequently, it is not unlikely that
491 hidden bugs will be exposed.
493 void isl_ctx_set_max_operations(isl_ctx *ctx,
494 unsigned long max_operations);
495 unsigned long isl_ctx_get_max_operations(isl_ctx *ctx);
496 void isl_ctx_reset_operations(isl_ctx *ctx);
498 In order to be able to create an object in the same context
499 as another object, most object types (described later in
500 this document) provide a function to obtain the context
501 in which the object was created.
504 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
505 isl_ctx *isl_multi_val_get_ctx(
506 __isl_keep isl_multi_val *mv);
509 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
511 #include <isl/local_space.h>
512 isl_ctx *isl_local_space_get_ctx(
513 __isl_keep isl_local_space *ls);
516 isl_ctx *isl_set_list_get_ctx(
517 __isl_keep isl_set_list *list);
520 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
521 isl_ctx *isl_multi_aff_get_ctx(
522 __isl_keep isl_multi_aff *maff);
523 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pa);
524 isl_ctx *isl_pw_multi_aff_get_ctx(
525 __isl_keep isl_pw_multi_aff *pma);
526 isl_ctx *isl_multi_pw_aff_get_ctx(
527 __isl_keep isl_multi_pw_aff *mpa);
528 isl_ctx *isl_union_pw_aff_get_ctx(
529 __isl_keep isl_union_pw_aff *upa);
530 isl_ctx *isl_union_pw_multi_aff_get_ctx(
531 __isl_keep isl_union_pw_multi_aff *upma);
532 isl_ctx *isl_multi_union_pw_aff_get_ctx(
533 __isl_keep isl_multi_union_pw_aff *mupa);
535 #include <isl/id_to_ast_expr.h>
536 isl_ctx *isl_id_to_ast_expr_get_ctx(
537 __isl_keep isl_id_to_ast_expr *id2expr);
539 #include <isl/point.h>
540 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
543 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
546 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
548 #include <isl/vertices.h>
549 isl_ctx *isl_vertices_get_ctx(
550 __isl_keep isl_vertices *vertices);
551 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
552 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
554 #include <isl/flow.h>
555 isl_ctx *isl_restriction_get_ctx(
556 __isl_keep isl_restriction *restr);
557 isl_ctx *isl_union_access_info_get_ctx(
558 __isl_keep isl_union_access_info *access);
559 isl_ctx *isl_union_flow_get_ctx(
560 __isl_keep isl_union_flow *flow);
562 #include <isl/schedule.h>
563 isl_ctx *isl_schedule_get_ctx(
564 __isl_keep isl_schedule *sched);
565 isl_ctx *isl_schedule_constraints_get_ctx(
566 __isl_keep isl_schedule_constraints *sc);
568 #include <isl/schedule_node.h>
569 isl_ctx *isl_schedule_node_get_ctx(
570 __isl_keep isl_schedule_node *node);
572 #include <isl/band.h>
573 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
575 #include <isl/ast_build.h>
576 isl_ctx *isl_ast_build_get_ctx(
577 __isl_keep isl_ast_build *build);
580 isl_ctx *isl_ast_expr_get_ctx(
581 __isl_keep isl_ast_expr *expr);
582 isl_ctx *isl_ast_node_get_ctx(
583 __isl_keep isl_ast_node *node);
587 C<isl> uses two special return types for functions that either return
588 a boolean or that in principle do not return anything.
589 In particular, the C<isl_bool> type has three possible values:
590 C<isl_bool_true> (a positive integer value), indicating I<true> or I<yes>;
591 C<isl_bool_false> (the integer value zero), indicating I<false> or I<no>; and
592 C<isl_bool_error> (a negative integer value), indicating that something
594 The C<isl_stat> type has two possible values:
595 C<isl_stat_ok> (the integer value zero), indicating a successful
597 C<isl_stat_error> (a negative integer value), indicating that something
599 See L</"Error Handling"> for more information on
600 C<isl_bool_error> and C<isl_stat_error>.
604 An C<isl_val> represents an integer value, a rational value
605 or one of three special values, infinity, negative infinity and NaN.
606 Some predefined values can be created using the following functions.
609 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
610 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
611 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
612 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
613 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
614 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
616 Specific integer values can be created using the following functions.
619 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
621 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
623 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
624 size_t n, size_t size, const void *chunks);
626 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
627 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
628 The least significant digit is assumed to be stored first.
630 Value objects can be copied and freed using the following functions.
633 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
634 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
636 They can be inspected using the following functions.
639 long isl_val_get_num_si(__isl_keep isl_val *v);
640 long isl_val_get_den_si(__isl_keep isl_val *v);
641 __isl_give isl_val *isl_val_get_den_val(
642 __isl_keep isl_val *v);
643 double isl_val_get_d(__isl_keep isl_val *v);
644 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
646 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
647 size_t size, void *chunks);
649 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
650 of C<size> bytes needed to store the absolute value of the
652 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
653 which is assumed to have been preallocated by the caller.
654 The least significant digit is stored first.
655 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
656 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
657 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
659 An C<isl_val> can be modified using the following function.
662 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
665 The following unary properties are defined on C<isl_val>s.
668 int isl_val_sgn(__isl_keep isl_val *v);
669 isl_bool isl_val_is_zero(__isl_keep isl_val *v);
670 isl_bool isl_val_is_one(__isl_keep isl_val *v);
671 isl_bool isl_val_is_negone(__isl_keep isl_val *v);
672 isl_bool isl_val_is_nonneg(__isl_keep isl_val *v);
673 isl_bool isl_val_is_nonpos(__isl_keep isl_val *v);
674 isl_bool isl_val_is_pos(__isl_keep isl_val *v);
675 isl_bool isl_val_is_neg(__isl_keep isl_val *v);
676 isl_bool isl_val_is_int(__isl_keep isl_val *v);
677 isl_bool isl_val_is_rat(__isl_keep isl_val *v);
678 isl_bool isl_val_is_nan(__isl_keep isl_val *v);
679 isl_bool isl_val_is_infty(__isl_keep isl_val *v);
680 isl_bool isl_val_is_neginfty(__isl_keep isl_val *v);
682 Note that the sign of NaN is undefined.
684 The following binary properties are defined on pairs of C<isl_val>s.
687 isl_bool isl_val_lt(__isl_keep isl_val *v1,
688 __isl_keep isl_val *v2);
689 isl_bool isl_val_le(__isl_keep isl_val *v1,
690 __isl_keep isl_val *v2);
691 isl_bool isl_val_gt(__isl_keep isl_val *v1,
692 __isl_keep isl_val *v2);
693 isl_bool isl_val_ge(__isl_keep isl_val *v1,
694 __isl_keep isl_val *v2);
695 isl_bool isl_val_eq(__isl_keep isl_val *v1,
696 __isl_keep isl_val *v2);
697 isl_bool isl_val_ne(__isl_keep isl_val *v1,
698 __isl_keep isl_val *v2);
699 isl_bool isl_val_abs_eq(__isl_keep isl_val *v1,
700 __isl_keep isl_val *v2);
702 The function C<isl_val_abs_eq> checks whether its two arguments
703 are equal in absolute value.
705 For integer C<isl_val>s we additionally have the following binary property.
708 isl_bool isl_val_is_divisible_by(__isl_keep isl_val *v1,
709 __isl_keep isl_val *v2);
711 An C<isl_val> can also be compared to an integer using the following
712 function. The result is undefined for NaN.
715 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
717 The following unary operations are available on C<isl_val>s.
720 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
721 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
722 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
723 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
724 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
725 __isl_give isl_val *isl_val_inv(__isl_take isl_val *v);
726 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
728 The following binary operations are available on C<isl_val>s.
731 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
732 __isl_take isl_val *v2);
733 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
734 __isl_take isl_val *v2);
735 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
736 __isl_take isl_val *v2);
737 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
739 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
740 __isl_take isl_val *v2);
741 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
743 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
744 __isl_take isl_val *v2);
745 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
747 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
748 __isl_take isl_val *v2);
750 On integer values, we additionally have the following operations.
753 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
754 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
755 __isl_take isl_val *v2);
756 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
757 __isl_take isl_val *v2);
758 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
759 __isl_take isl_val *v2, __isl_give isl_val **x,
760 __isl_give isl_val **y);
762 The function C<isl_val_gcdext> returns the greatest common divisor g
763 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
764 that C<*x> * C<v1> + C<*y> * C<v2> = g.
766 =head3 GMP specific functions
768 These functions are only available if C<isl> has been compiled with C<GMP>
771 Specific integer and rational values can be created from C<GMP> values using
772 the following functions.
774 #include <isl/val_gmp.h>
775 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
777 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
778 const mpz_t n, const mpz_t d);
780 The numerator and denominator of a rational value can be extracted as
781 C<GMP> values using the following functions.
783 #include <isl/val_gmp.h>
784 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
785 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
787 =head2 Sets and Relations
789 C<isl> uses six types of objects for representing sets and relations,
790 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
791 C<isl_union_set> and C<isl_union_map>.
792 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
793 can be described as a conjunction of affine constraints, while
794 C<isl_set> and C<isl_map> represent unions of
795 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
796 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
797 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
798 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
799 where spaces are considered different if they have a different number
800 of dimensions and/or different names (see L<"Spaces">).
801 The difference between sets and relations (maps) is that sets have
802 one set of variables, while relations have two sets of variables,
803 input variables and output variables.
805 =head2 Error Handling
807 C<isl> supports different ways to react in case a runtime error is triggered.
808 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
809 with two maps that have incompatible spaces. There are three possible ways
810 to react on error: to warn, to continue or to abort.
812 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
813 the last error in the corresponding C<isl_ctx> and the function in which the
814 error was triggered returns a value indicating that some error has
815 occurred. In case of functions returning a pointer, this value is
816 C<NULL>. In case of functions returning an C<isl_bool> or an
817 C<isl_stat>, this valus is C<isl_bool_error> or C<isl_stat_error>.
818 An error does not corrupt internal state,
819 such that isl can continue to be used. C<isl> also provides functions to
820 read the last error and to reset the memory that stores the last error. The
821 last error is only stored for information purposes. Its presence does not
822 change the behavior of C<isl>. Hence, resetting an error is not required to
823 continue to use isl, but only to observe new errors.
826 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
827 void isl_ctx_reset_error(isl_ctx *ctx);
829 Another option is to continue on error. This is similar to warn on error mode,
830 except that C<isl> does not print any warning. This allows a program to
831 implement its own error reporting.
833 The last option is to directly abort the execution of the program from within
834 the isl library. This makes it obviously impossible to recover from an error,
835 but it allows to directly spot the error location. By aborting on error,
836 debuggers break at the location the error occurred and can provide a stack
837 trace. Other tools that automatically provide stack traces on abort or that do
838 not want to continue execution after an error was triggered may also prefer to
841 The on error behavior of isl can be specified by calling
842 C<isl_options_set_on_error> or by setting the command line option
843 C<--isl-on-error>. Valid arguments for the function call are
844 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
845 choices for the command line option are C<warn>, C<continue> and C<abort>.
846 It is also possible to query the current error mode.
848 #include <isl/options.h>
849 isl_stat isl_options_set_on_error(isl_ctx *ctx, int val);
850 int isl_options_get_on_error(isl_ctx *ctx);
854 Identifiers are used to identify both individual dimensions
855 and tuples of dimensions. They consist of an optional name and an optional
856 user pointer. The name and the user pointer cannot both be C<NULL>, however.
857 Identifiers with the same name but different pointer values
858 are considered to be distinct.
859 Similarly, identifiers with different names but the same pointer value
860 are also considered to be distinct.
861 Equal identifiers are represented using the same object.
862 Pairs of identifiers can therefore be tested for equality using the
864 Identifiers can be constructed, copied, freed, inspected and printed
865 using the following functions.
868 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
869 __isl_keep const char *name, void *user);
870 __isl_give isl_id *isl_id_set_free_user(
871 __isl_take isl_id *id,
872 __isl_give void (*free_user)(void *user));
873 __isl_give isl_id *isl_id_copy(isl_id *id);
874 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
876 void *isl_id_get_user(__isl_keep isl_id *id);
877 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
879 __isl_give isl_printer *isl_printer_print_id(
880 __isl_take isl_printer *p, __isl_keep isl_id *id);
882 The callback set by C<isl_id_set_free_user> is called on the user
883 pointer when the last reference to the C<isl_id> is freed.
884 Note that C<isl_id_get_name> returns a pointer to some internal
885 data structure, so the result can only be used while the
886 corresponding C<isl_id> is alive.
890 Whenever a new set, relation or similar object is created from scratch,
891 the space in which it lives needs to be specified using an C<isl_space>.
892 Each space involves zero or more parameters and zero, one or two
893 tuples of set or input/output dimensions. The parameters and dimensions
894 are identified by an C<isl_dim_type> and a position.
895 The type C<isl_dim_param> refers to parameters,
896 the type C<isl_dim_set> refers to set dimensions (for spaces
897 with a single tuple of dimensions) and the types C<isl_dim_in>
898 and C<isl_dim_out> refer to input and output dimensions
899 (for spaces with two tuples of dimensions).
900 Local spaces (see L</"Local Spaces">) also contain dimensions
901 of type C<isl_dim_div>.
902 Note that parameters are only identified by their position within
903 a given object. Across different objects, parameters are (usually)
904 identified by their names or identifiers. Only unnamed parameters
905 are identified by their positions across objects. The use of unnamed
906 parameters is discouraged.
908 #include <isl/space.h>
909 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
910 unsigned nparam, unsigned n_in, unsigned n_out);
911 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
913 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
914 unsigned nparam, unsigned dim);
915 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
916 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
918 The space used for creating a parameter domain
919 needs to be created using C<isl_space_params_alloc>.
920 For other sets, the space
921 needs to be created using C<isl_space_set_alloc>, while
922 for a relation, the space
923 needs to be created using C<isl_space_alloc>.
925 To check whether a given space is that of a set or a map
926 or whether it is a parameter space, use these functions:
928 #include <isl/space.h>
929 isl_bool isl_space_is_params(__isl_keep isl_space *space);
930 isl_bool isl_space_is_set(__isl_keep isl_space *space);
931 isl_bool isl_space_is_map(__isl_keep isl_space *space);
933 Spaces can be compared using the following functions:
935 #include <isl/space.h>
936 isl_bool isl_space_is_equal(__isl_keep isl_space *space1,
937 __isl_keep isl_space *space2);
938 isl_bool isl_space_is_domain(__isl_keep isl_space *space1,
939 __isl_keep isl_space *space2);
940 isl_bool isl_space_is_range(__isl_keep isl_space *space1,
941 __isl_keep isl_space *space2);
942 isl_bool isl_space_tuple_is_equal(
943 __isl_keep isl_space *space1,
944 enum isl_dim_type type1,
945 __isl_keep isl_space *space2,
946 enum isl_dim_type type2);
948 C<isl_space_is_domain> checks whether the first argument is equal
949 to the domain of the second argument. This requires in particular that
950 the first argument is a set space and that the second argument
951 is a map space. C<isl_space_tuple_is_equal> checks whether the given
952 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
953 spaces are the same. That is, it checks if they have the same
954 identifier (if any), the same dimension and the same internal structure
957 It is often useful to create objects that live in the
958 same space as some other object. This can be accomplished
959 by creating the new objects
960 (see L</"Creating New Sets and Relations"> or
961 L</"Functions">) based on the space
962 of the original object.
965 __isl_give isl_space *isl_basic_set_get_space(
966 __isl_keep isl_basic_set *bset);
967 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
969 #include <isl/union_set.h>
970 __isl_give isl_space *isl_union_set_get_space(
971 __isl_keep isl_union_set *uset);
974 __isl_give isl_space *isl_basic_map_get_space(
975 __isl_keep isl_basic_map *bmap);
976 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
978 #include <isl/union_map.h>
979 __isl_give isl_space *isl_union_map_get_space(
980 __isl_keep isl_union_map *umap);
982 #include <isl/constraint.h>
983 __isl_give isl_space *isl_constraint_get_space(
984 __isl_keep isl_constraint *constraint);
986 #include <isl/polynomial.h>
987 __isl_give isl_space *isl_qpolynomial_get_domain_space(
988 __isl_keep isl_qpolynomial *qp);
989 __isl_give isl_space *isl_qpolynomial_get_space(
990 __isl_keep isl_qpolynomial *qp);
991 __isl_give isl_space *isl_qpolynomial_fold_get_space(
992 __isl_keep isl_qpolynomial_fold *fold);
993 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
994 __isl_keep isl_pw_qpolynomial *pwqp);
995 __isl_give isl_space *isl_pw_qpolynomial_get_space(
996 __isl_keep isl_pw_qpolynomial *pwqp);
997 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
998 __isl_keep isl_pw_qpolynomial_fold *pwf);
999 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
1000 __isl_keep isl_pw_qpolynomial_fold *pwf);
1001 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
1002 __isl_keep isl_union_pw_qpolynomial *upwqp);
1003 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
1004 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1006 #include <isl/val.h>
1007 __isl_give isl_space *isl_multi_val_get_space(
1008 __isl_keep isl_multi_val *mv);
1010 #include <isl/aff.h>
1011 __isl_give isl_space *isl_aff_get_domain_space(
1012 __isl_keep isl_aff *aff);
1013 __isl_give isl_space *isl_aff_get_space(
1014 __isl_keep isl_aff *aff);
1015 __isl_give isl_space *isl_pw_aff_get_domain_space(
1016 __isl_keep isl_pw_aff *pwaff);
1017 __isl_give isl_space *isl_pw_aff_get_space(
1018 __isl_keep isl_pw_aff *pwaff);
1019 __isl_give isl_space *isl_multi_aff_get_domain_space(
1020 __isl_keep isl_multi_aff *maff);
1021 __isl_give isl_space *isl_multi_aff_get_space(
1022 __isl_keep isl_multi_aff *maff);
1023 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
1024 __isl_keep isl_pw_multi_aff *pma);
1025 __isl_give isl_space *isl_pw_multi_aff_get_space(
1026 __isl_keep isl_pw_multi_aff *pma);
1027 __isl_give isl_space *isl_union_pw_aff_get_space(
1028 __isl_keep isl_union_pw_aff *upa);
1029 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
1030 __isl_keep isl_union_pw_multi_aff *upma);
1031 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
1032 __isl_keep isl_multi_pw_aff *mpa);
1033 __isl_give isl_space *isl_multi_pw_aff_get_space(
1034 __isl_keep isl_multi_pw_aff *mpa);
1035 __isl_give isl_space *
1036 isl_multi_union_pw_aff_get_domain_space(
1037 __isl_keep isl_multi_union_pw_aff *mupa);
1038 __isl_give isl_space *
1039 isl_multi_union_pw_aff_get_space(
1040 __isl_keep isl_multi_union_pw_aff *mupa);
1042 #include <isl/point.h>
1043 __isl_give isl_space *isl_point_get_space(
1044 __isl_keep isl_point *pnt);
1046 The number of dimensions of a given type of space
1047 may be read off from a space or an object that lives
1048 in a space using the following functions.
1049 In case of C<isl_space_dim>, type may be
1050 C<isl_dim_param>, C<isl_dim_in> (only for relations),
1051 C<isl_dim_out> (only for relations), C<isl_dim_set>
1052 (only for sets) or C<isl_dim_all>.
1054 #include <isl/space.h>
1055 unsigned isl_space_dim(__isl_keep isl_space *space,
1056 enum isl_dim_type type);
1058 #include <isl/local_space.h>
1059 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1060 enum isl_dim_type type);
1062 #include <isl/set.h>
1063 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1064 enum isl_dim_type type);
1065 unsigned isl_set_dim(__isl_keep isl_set *set,
1066 enum isl_dim_type type);
1068 #include <isl/union_set.h>
1069 unsigned isl_union_set_dim(__isl_keep isl_union_set *uset,
1070 enum isl_dim_type type);
1072 #include <isl/map.h>
1073 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1074 enum isl_dim_type type);
1075 unsigned isl_map_dim(__isl_keep isl_map *map,
1076 enum isl_dim_type type);
1078 #include <isl/union_map.h>
1079 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1080 enum isl_dim_type type);
1082 #include <isl/val.h>
1083 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
1084 enum isl_dim_type type);
1086 #include <isl/aff.h>
1087 int isl_aff_dim(__isl_keep isl_aff *aff,
1088 enum isl_dim_type type);
1089 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1090 enum isl_dim_type type);
1091 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1092 enum isl_dim_type type);
1093 unsigned isl_pw_multi_aff_dim(
1094 __isl_keep isl_pw_multi_aff *pma,
1095 enum isl_dim_type type);
1096 unsigned isl_multi_pw_aff_dim(
1097 __isl_keep isl_multi_pw_aff *mpa,
1098 enum isl_dim_type type);
1099 unsigned isl_union_pw_aff_dim(
1100 __isl_keep isl_union_pw_aff *upa,
1101 enum isl_dim_type type);
1102 unsigned isl_union_pw_multi_aff_dim(
1103 __isl_keep isl_union_pw_multi_aff *upma,
1104 enum isl_dim_type type);
1105 unsigned isl_multi_union_pw_aff_dim(
1106 __isl_keep isl_multi_union_pw_aff *mupa,
1107 enum isl_dim_type type);
1109 #include <isl/polynomial.h>
1110 unsigned isl_union_pw_qpolynomial_dim(
1111 __isl_keep isl_union_pw_qpolynomial *upwqp,
1112 enum isl_dim_type type);
1113 unsigned isl_union_pw_qpolynomial_fold_dim(
1114 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1115 enum isl_dim_type type);
1117 Note that an C<isl_union_set>, an C<isl_union_map>,
1118 an C<isl_union_pw_multi_aff>,
1119 an C<isl_union_pw_qpolynomial> and
1120 an C<isl_union_pw_qpolynomial_fold>
1121 only have parameters.
1123 The identifiers or names of the individual dimensions of spaces
1124 may be set or read off using the following functions on spaces
1125 or objects that live in spaces.
1126 These functions are mostly useful to obtain the identifiers, positions
1127 or names of the parameters. Identifiers of individual dimensions are
1128 essentially only useful for printing. They are ignored by all other
1129 operations and may not be preserved across those operations.
1131 #include <isl/space.h>
1132 __isl_give isl_space *isl_space_set_dim_id(
1133 __isl_take isl_space *space,
1134 enum isl_dim_type type, unsigned pos,
1135 __isl_take isl_id *id);
1136 isl_bool isl_space_has_dim_id(__isl_keep isl_space *space,
1137 enum isl_dim_type type, unsigned pos);
1138 __isl_give isl_id *isl_space_get_dim_id(
1139 __isl_keep isl_space *space,
1140 enum isl_dim_type type, unsigned pos);
1141 __isl_give isl_space *isl_space_set_dim_name(
1142 __isl_take isl_space *space,
1143 enum isl_dim_type type, unsigned pos,
1144 __isl_keep const char *name);
1145 isl_bool isl_space_has_dim_name(__isl_keep isl_space *space,
1146 enum isl_dim_type type, unsigned pos);
1147 __isl_keep const char *isl_space_get_dim_name(
1148 __isl_keep isl_space *space,
1149 enum isl_dim_type type, unsigned pos);
1151 #include <isl/local_space.h>
1152 __isl_give isl_local_space *isl_local_space_set_dim_id(
1153 __isl_take isl_local_space *ls,
1154 enum isl_dim_type type, unsigned pos,
1155 __isl_take isl_id *id);
1156 isl_bool isl_local_space_has_dim_id(
1157 __isl_keep isl_local_space *ls,
1158 enum isl_dim_type type, unsigned pos);
1159 __isl_give isl_id *isl_local_space_get_dim_id(
1160 __isl_keep isl_local_space *ls,
1161 enum isl_dim_type type, unsigned pos);
1162 __isl_give isl_local_space *isl_local_space_set_dim_name(
1163 __isl_take isl_local_space *ls,
1164 enum isl_dim_type type, unsigned pos, const char *s);
1165 isl_bool isl_local_space_has_dim_name(
1166 __isl_keep isl_local_space *ls,
1167 enum isl_dim_type type, unsigned pos)
1168 const char *isl_local_space_get_dim_name(
1169 __isl_keep isl_local_space *ls,
1170 enum isl_dim_type type, unsigned pos);
1172 #include <isl/constraint.h>
1173 const char *isl_constraint_get_dim_name(
1174 __isl_keep isl_constraint *constraint,
1175 enum isl_dim_type type, unsigned pos);
1177 #include <isl/set.h>
1178 __isl_give isl_id *isl_basic_set_get_dim_id(
1179 __isl_keep isl_basic_set *bset,
1180 enum isl_dim_type type, unsigned pos);
1181 __isl_give isl_set *isl_set_set_dim_id(
1182 __isl_take isl_set *set, enum isl_dim_type type,
1183 unsigned pos, __isl_take isl_id *id);
1184 isl_bool isl_set_has_dim_id(__isl_keep isl_set *set,
1185 enum isl_dim_type type, unsigned pos);
1186 __isl_give isl_id *isl_set_get_dim_id(
1187 __isl_keep isl_set *set, enum isl_dim_type type,
1189 const char *isl_basic_set_get_dim_name(
1190 __isl_keep isl_basic_set *bset,
1191 enum isl_dim_type type, unsigned pos);
1192 isl_bool isl_set_has_dim_name(__isl_keep isl_set *set,
1193 enum isl_dim_type type, unsigned pos);
1194 const char *isl_set_get_dim_name(
1195 __isl_keep isl_set *set,
1196 enum isl_dim_type type, unsigned pos);
1198 #include <isl/map.h>
1199 __isl_give isl_map *isl_map_set_dim_id(
1200 __isl_take isl_map *map, enum isl_dim_type type,
1201 unsigned pos, __isl_take isl_id *id);
1202 isl_bool isl_basic_map_has_dim_id(
1203 __isl_keep isl_basic_map *bmap,
1204 enum isl_dim_type type, unsigned pos);
1205 isl_bool isl_map_has_dim_id(__isl_keep isl_map *map,
1206 enum isl_dim_type type, unsigned pos);
1207 __isl_give isl_id *isl_map_get_dim_id(
1208 __isl_keep isl_map *map, enum isl_dim_type type,
1210 __isl_give isl_id *isl_union_map_get_dim_id(
1211 __isl_keep isl_union_map *umap,
1212 enum isl_dim_type type, unsigned pos);
1213 const char *isl_basic_map_get_dim_name(
1214 __isl_keep isl_basic_map *bmap,
1215 enum isl_dim_type type, unsigned pos);
1216 isl_bool isl_map_has_dim_name(__isl_keep isl_map *map,
1217 enum isl_dim_type type, unsigned pos);
1218 const char *isl_map_get_dim_name(
1219 __isl_keep isl_map *map,
1220 enum isl_dim_type type, unsigned pos);
1222 #include <isl/val.h>
1223 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1224 __isl_take isl_multi_val *mv,
1225 enum isl_dim_type type, unsigned pos,
1226 __isl_take isl_id *id);
1227 __isl_give isl_id *isl_multi_val_get_dim_id(
1228 __isl_keep isl_multi_val *mv,
1229 enum isl_dim_type type, unsigned pos);
1230 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1231 __isl_take isl_multi_val *mv,
1232 enum isl_dim_type type, unsigned pos, const char *s);
1234 #include <isl/aff.h>
1235 __isl_give isl_aff *isl_aff_set_dim_id(
1236 __isl_take isl_aff *aff, enum isl_dim_type type,
1237 unsigned pos, __isl_take isl_id *id);
1238 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1239 __isl_take isl_multi_aff *maff,
1240 enum isl_dim_type type, unsigned pos,
1241 __isl_take isl_id *id);
1242 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1243 __isl_take isl_pw_aff *pma,
1244 enum isl_dim_type type, unsigned pos,
1245 __isl_take isl_id *id);
1246 __isl_give isl_multi_pw_aff *
1247 isl_multi_pw_aff_set_dim_id(
1248 __isl_take isl_multi_pw_aff *mpa,
1249 enum isl_dim_type type, unsigned pos,
1250 __isl_take isl_id *id);
1251 __isl_give isl_multi_union_pw_aff *
1252 isl_multi_union_pw_aff_set_dim_id(
1253 __isl_take isl_multi_union_pw_aff *mupa,
1254 enum isl_dim_type type, unsigned pos,
1255 __isl_take isl_id *id);
1256 __isl_give isl_id *isl_multi_aff_get_dim_id(
1257 __isl_keep isl_multi_aff *ma,
1258 enum isl_dim_type type, unsigned pos);
1259 isl_bool isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1260 enum isl_dim_type type, unsigned pos);
1261 __isl_give isl_id *isl_pw_aff_get_dim_id(
1262 __isl_keep isl_pw_aff *pa,
1263 enum isl_dim_type type, unsigned pos);
1264 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1265 __isl_keep isl_pw_multi_aff *pma,
1266 enum isl_dim_type type, unsigned pos);
1267 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1268 __isl_keep isl_multi_pw_aff *mpa,
1269 enum isl_dim_type type, unsigned pos);
1270 __isl_give isl_id *isl_multi_union_pw_aff_get_dim_id(
1271 __isl_keep isl_multi_union_pw_aff *mupa,
1272 enum isl_dim_type type, unsigned pos);
1273 __isl_give isl_aff *isl_aff_set_dim_name(
1274 __isl_take isl_aff *aff, enum isl_dim_type type,
1275 unsigned pos, const char *s);
1276 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1277 __isl_take isl_multi_aff *maff,
1278 enum isl_dim_type type, unsigned pos, const char *s);
1279 __isl_give isl_multi_pw_aff *
1280 isl_multi_pw_aff_set_dim_name(
1281 __isl_take isl_multi_pw_aff *mpa,
1282 enum isl_dim_type type, unsigned pos, const char *s);
1283 __isl_give isl_union_pw_aff *
1284 isl_union_pw_aff_set_dim_name(
1285 __isl_take isl_union_pw_aff *upa,
1286 enum isl_dim_type type, unsigned pos,
1288 __isl_give isl_union_pw_multi_aff *
1289 isl_union_pw_multi_aff_set_dim_name(
1290 __isl_take isl_union_pw_multi_aff *upma,
1291 enum isl_dim_type type, unsigned pos,
1293 __isl_give isl_multi_union_pw_aff *
1294 isl_multi_union_pw_aff_set_dim_name(
1295 __isl_take isl_multi_union_pw_aff *mupa,
1296 enum isl_dim_type type, unsigned pos,
1297 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1298 enum isl_dim_type type, unsigned pos);
1299 const char *isl_pw_aff_get_dim_name(
1300 __isl_keep isl_pw_aff *pa,
1301 enum isl_dim_type type, unsigned pos);
1302 const char *isl_pw_multi_aff_get_dim_name(
1303 __isl_keep isl_pw_multi_aff *pma,
1304 enum isl_dim_type type, unsigned pos);
1306 #include <isl/polynomial.h>
1307 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1308 __isl_take isl_qpolynomial *qp,
1309 enum isl_dim_type type, unsigned pos,
1311 __isl_give isl_pw_qpolynomial *
1312 isl_pw_qpolynomial_set_dim_name(
1313 __isl_take isl_pw_qpolynomial *pwqp,
1314 enum isl_dim_type type, unsigned pos,
1316 __isl_give isl_pw_qpolynomial_fold *
1317 isl_pw_qpolynomial_fold_set_dim_name(
1318 __isl_take isl_pw_qpolynomial_fold *pwf,
1319 enum isl_dim_type type, unsigned pos,
1321 __isl_give isl_union_pw_qpolynomial *
1322 isl_union_pw_qpolynomial_set_dim_name(
1323 __isl_take isl_union_pw_qpolynomial *upwqp,
1324 enum isl_dim_type type, unsigned pos,
1326 __isl_give isl_union_pw_qpolynomial_fold *
1327 isl_union_pw_qpolynomial_fold_set_dim_name(
1328 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1329 enum isl_dim_type type, unsigned pos,
1332 Note that C<isl_space_get_name> returns a pointer to some internal
1333 data structure, so the result can only be used while the
1334 corresponding C<isl_space> is alive.
1335 Also note that every function that operates on two sets or relations
1336 requires that both arguments have the same parameters. This also
1337 means that if one of the arguments has named parameters, then the
1338 other needs to have named parameters too and the names need to match.
1339 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1340 arguments may have different parameters (as long as they are named),
1341 in which case the result will have as parameters the union of the parameters of
1344 Given the identifier or name of a dimension (typically a parameter),
1345 its position can be obtained from the following functions.
1347 #include <isl/space.h>
1348 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1349 enum isl_dim_type type, __isl_keep isl_id *id);
1350 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1351 enum isl_dim_type type, const char *name);
1353 #include <isl/local_space.h>
1354 int isl_local_space_find_dim_by_name(
1355 __isl_keep isl_local_space *ls,
1356 enum isl_dim_type type, const char *name);
1358 #include <isl/val.h>
1359 int isl_multi_val_find_dim_by_id(
1360 __isl_keep isl_multi_val *mv,
1361 enum isl_dim_type type, __isl_keep isl_id *id);
1362 int isl_multi_val_find_dim_by_name(
1363 __isl_keep isl_multi_val *mv,
1364 enum isl_dim_type type, const char *name);
1366 #include <isl/set.h>
1367 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1368 enum isl_dim_type type, __isl_keep isl_id *id);
1369 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1370 enum isl_dim_type type, const char *name);
1372 #include <isl/map.h>
1373 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1374 enum isl_dim_type type, __isl_keep isl_id *id);
1375 int isl_basic_map_find_dim_by_name(
1376 __isl_keep isl_basic_map *bmap,
1377 enum isl_dim_type type, const char *name);
1378 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1379 enum isl_dim_type type, const char *name);
1380 int isl_union_map_find_dim_by_name(
1381 __isl_keep isl_union_map *umap,
1382 enum isl_dim_type type, const char *name);
1384 #include <isl/aff.h>
1385 int isl_multi_aff_find_dim_by_id(
1386 __isl_keep isl_multi_aff *ma,
1387 enum isl_dim_type type, __isl_keep isl_id *id);
1388 int isl_multi_pw_aff_find_dim_by_id(
1389 __isl_keep isl_multi_pw_aff *mpa,
1390 enum isl_dim_type type, __isl_keep isl_id *id);
1391 int isl_multi_union_pw_aff_find_dim_by_id(
1392 __isl_keep isl_union_multi_pw_aff *mupa,
1393 enum isl_dim_type type, __isl_keep isl_id *id);
1394 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff,
1395 enum isl_dim_type type, const char *name);
1396 int isl_multi_aff_find_dim_by_name(
1397 __isl_keep isl_multi_aff *ma,
1398 enum isl_dim_type type, const char *name);
1399 int isl_pw_aff_find_dim_by_name(__isl_keep isl_pw_aff *pa,
1400 enum isl_dim_type type, const char *name);
1401 int isl_multi_pw_aff_find_dim_by_name(
1402 __isl_keep isl_multi_pw_aff *mpa,
1403 enum isl_dim_type type, const char *name);
1404 int isl_pw_multi_aff_find_dim_by_name(
1405 __isl_keep isl_pw_multi_aff *pma,
1406 enum isl_dim_type type, const char *name);
1407 int isl_union_pw_aff_find_dim_by_name(
1408 __isl_keep isl_union_pw_aff *upa,
1409 enum isl_dim_type type, const char *name);
1410 int isl_union_pw_multi_aff_find_dim_by_name(
1411 __isl_keep isl_union_pw_multi_aff *upma,
1412 enum isl_dim_type type, const char *name);
1413 int isl_multi_union_pw_aff_find_dim_by_name(
1414 __isl_keep isl_multi_union_pw_aff *mupa,
1415 enum isl_dim_type type, const char *name);
1417 #include <isl/polynomial.h>
1418 int isl_pw_qpolynomial_find_dim_by_name(
1419 __isl_keep isl_pw_qpolynomial *pwqp,
1420 enum isl_dim_type type, const char *name);
1421 int isl_pw_qpolynomial_fold_find_dim_by_name(
1422 __isl_keep isl_pw_qpolynomial_fold *pwf,
1423 enum isl_dim_type type, const char *name);
1424 int isl_union_pw_qpolynomial_find_dim_by_name(
1425 __isl_keep isl_union_pw_qpolynomial *upwqp,
1426 enum isl_dim_type type, const char *name);
1427 int isl_union_pw_qpolynomial_fold_find_dim_by_name(
1428 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1429 enum isl_dim_type type, const char *name);
1431 The identifiers or names of entire spaces may be set or read off
1432 using the following functions.
1434 #include <isl/space.h>
1435 __isl_give isl_space *isl_space_set_tuple_id(
1436 __isl_take isl_space *space,
1437 enum isl_dim_type type, __isl_take isl_id *id);
1438 __isl_give isl_space *isl_space_reset_tuple_id(
1439 __isl_take isl_space *space, enum isl_dim_type type);
1440 isl_bool isl_space_has_tuple_id(
1441 __isl_keep isl_space *space,
1442 enum isl_dim_type type);
1443 __isl_give isl_id *isl_space_get_tuple_id(
1444 __isl_keep isl_space *space, enum isl_dim_type type);
1445 __isl_give isl_space *isl_space_set_tuple_name(
1446 __isl_take isl_space *space,
1447 enum isl_dim_type type, const char *s);
1448 isl_bool isl_space_has_tuple_name(
1449 __isl_keep isl_space *space,
1450 enum isl_dim_type type);
1451 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
1452 enum isl_dim_type type);
1454 #include <isl/local_space.h>
1455 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1456 __isl_take isl_local_space *ls,
1457 enum isl_dim_type type, __isl_take isl_id *id);
1459 #include <isl/set.h>
1460 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1461 __isl_take isl_basic_set *bset,
1462 __isl_take isl_id *id);
1463 __isl_give isl_set *isl_set_set_tuple_id(
1464 __isl_take isl_set *set, __isl_take isl_id *id);
1465 __isl_give isl_set *isl_set_reset_tuple_id(
1466 __isl_take isl_set *set);
1467 isl_bool isl_set_has_tuple_id(__isl_keep isl_set *set);
1468 __isl_give isl_id *isl_set_get_tuple_id(
1469 __isl_keep isl_set *set);
1470 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1471 __isl_take isl_basic_set *set, const char *s);
1472 __isl_give isl_set *isl_set_set_tuple_name(
1473 __isl_take isl_set *set, const char *s);
1474 const char *isl_basic_set_get_tuple_name(
1475 __isl_keep isl_basic_set *bset);
1476 isl_bool isl_set_has_tuple_name(__isl_keep isl_set *set);
1477 const char *isl_set_get_tuple_name(
1478 __isl_keep isl_set *set);
1480 #include <isl/map.h>
1481 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1482 __isl_take isl_basic_map *bmap,
1483 enum isl_dim_type type, __isl_take isl_id *id);
1484 __isl_give isl_map *isl_map_set_tuple_id(
1485 __isl_take isl_map *map, enum isl_dim_type type,
1486 __isl_take isl_id *id);
1487 __isl_give isl_map *isl_map_reset_tuple_id(
1488 __isl_take isl_map *map, enum isl_dim_type type);
1489 isl_bool isl_map_has_tuple_id(__isl_keep isl_map *map,
1490 enum isl_dim_type type);
1491 __isl_give isl_id *isl_map_get_tuple_id(
1492 __isl_keep isl_map *map, enum isl_dim_type type);
1493 __isl_give isl_map *isl_map_set_tuple_name(
1494 __isl_take isl_map *map,
1495 enum isl_dim_type type, const char *s);
1496 const char *isl_basic_map_get_tuple_name(
1497 __isl_keep isl_basic_map *bmap,
1498 enum isl_dim_type type);
1499 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1500 __isl_take isl_basic_map *bmap,
1501 enum isl_dim_type type, const char *s);
1502 isl_bool isl_map_has_tuple_name(__isl_keep isl_map *map,
1503 enum isl_dim_type type);
1504 const char *isl_map_get_tuple_name(
1505 __isl_keep isl_map *map,
1506 enum isl_dim_type type);
1508 #include <isl/val.h>
1509 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1510 __isl_take isl_multi_val *mv,
1511 enum isl_dim_type type, __isl_take isl_id *id);
1512 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1513 __isl_take isl_multi_val *mv,
1514 enum isl_dim_type type);
1515 isl_bool isl_multi_val_has_tuple_id(
1516 __isl_keep isl_multi_val *mv,
1517 enum isl_dim_type type);
1518 __isl_give isl_id *isl_multi_val_get_tuple_id(
1519 __isl_keep isl_multi_val *mv,
1520 enum isl_dim_type type);
1521 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1522 __isl_take isl_multi_val *mv,
1523 enum isl_dim_type type, const char *s);
1524 const char *isl_multi_val_get_tuple_name(
1525 __isl_keep isl_multi_val *mv,
1526 enum isl_dim_type type);
1528 #include <isl/aff.h>
1529 __isl_give isl_aff *isl_aff_set_tuple_id(
1530 __isl_take isl_aff *aff,
1531 enum isl_dim_type type, __isl_take isl_id *id);
1532 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1533 __isl_take isl_multi_aff *maff,
1534 enum isl_dim_type type, __isl_take isl_id *id);
1535 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1536 __isl_take isl_pw_aff *pwaff,
1537 enum isl_dim_type type, __isl_take isl_id *id);
1538 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1539 __isl_take isl_pw_multi_aff *pma,
1540 enum isl_dim_type type, __isl_take isl_id *id);
1541 __isl_give isl_multi_union_pw_aff *
1542 isl_multi_union_pw_aff_set_tuple_id(
1543 __isl_take isl_multi_union_pw_aff *mupa,
1544 enum isl_dim_type type, __isl_take isl_id *id);
1545 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1546 __isl_take isl_multi_aff *ma,
1547 enum isl_dim_type type);
1548 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1549 __isl_take isl_pw_aff *pa,
1550 enum isl_dim_type type);
1551 __isl_give isl_multi_pw_aff *
1552 isl_multi_pw_aff_reset_tuple_id(
1553 __isl_take isl_multi_pw_aff *mpa,
1554 enum isl_dim_type type);
1555 __isl_give isl_pw_multi_aff *
1556 isl_pw_multi_aff_reset_tuple_id(
1557 __isl_take isl_pw_multi_aff *pma,
1558 enum isl_dim_type type);
1559 __isl_give isl_multi_union_pw_aff *
1560 isl_multi_union_pw_aff_reset_tuple_id(
1561 __isl_take isl_multi_union_pw_aff *mupa,
1562 enum isl_dim_type type);
1563 isl_bool isl_multi_aff_has_tuple_id(
1564 __isl_keep isl_multi_aff *ma,
1565 enum isl_dim_type type);
1566 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1567 __isl_keep isl_multi_aff *ma,
1568 enum isl_dim_type type);
1569 isl_bool isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1570 enum isl_dim_type type);
1571 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1572 __isl_keep isl_pw_aff *pa,
1573 enum isl_dim_type type);
1574 isl_bool isl_pw_multi_aff_has_tuple_id(
1575 __isl_keep isl_pw_multi_aff *pma,
1576 enum isl_dim_type type);
1577 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1578 __isl_keep isl_pw_multi_aff *pma,
1579 enum isl_dim_type type);
1580 isl_bool isl_multi_pw_aff_has_tuple_id(
1581 __isl_keep isl_multi_pw_aff *mpa,
1582 enum isl_dim_type type);
1583 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1584 __isl_keep isl_multi_pw_aff *mpa,
1585 enum isl_dim_type type);
1586 isl_bool isl_multi_union_pw_aff_has_tuple_id(
1587 __isl_keep isl_multi_union_pw_aff *mupa,
1588 enum isl_dim_type type);
1589 __isl_give isl_id *isl_multi_union_pw_aff_get_tuple_id(
1590 __isl_keep isl_multi_union_pw_aff *mupa,
1591 enum isl_dim_type type);
1592 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1593 __isl_take isl_multi_aff *maff,
1594 enum isl_dim_type type, const char *s);
1595 __isl_give isl_multi_pw_aff *
1596 isl_multi_pw_aff_set_tuple_name(
1597 __isl_take isl_multi_pw_aff *mpa,
1598 enum isl_dim_type type, const char *s);
1599 __isl_give isl_multi_union_pw_aff *
1600 isl_multi_union_pw_aff_set_tuple_name(
1601 __isl_take isl_multi_union_pw_aff *mupa,
1602 enum isl_dim_type type, const char *s);
1603 const char *isl_multi_aff_get_tuple_name(
1604 __isl_keep isl_multi_aff *multi,
1605 enum isl_dim_type type);
1606 isl_bool isl_pw_multi_aff_has_tuple_name(
1607 __isl_keep isl_pw_multi_aff *pma,
1608 enum isl_dim_type type);
1609 const char *isl_pw_multi_aff_get_tuple_name(
1610 __isl_keep isl_pw_multi_aff *pma,
1611 enum isl_dim_type type);
1612 const char *isl_multi_union_pw_aff_get_tuple_name(
1613 __isl_keep isl_multi_union_pw_aff *mupa,
1614 enum isl_dim_type type);
1616 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1617 or C<isl_dim_set>. As with C<isl_space_get_name>,
1618 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1620 Binary operations require the corresponding spaces of their arguments
1621 to have the same name.
1623 To keep the names of all parameters and tuples, but reset the user pointers
1624 of all the corresponding identifiers, use the following function.
1626 #include <isl/space.h>
1627 __isl_give isl_space *isl_space_reset_user(
1628 __isl_take isl_space *space);
1630 #include <isl/set.h>
1631 __isl_give isl_set *isl_set_reset_user(
1632 __isl_take isl_set *set);
1634 #include <isl/map.h>
1635 __isl_give isl_map *isl_map_reset_user(
1636 __isl_take isl_map *map);
1638 #include <isl/union_set.h>
1639 __isl_give isl_union_set *isl_union_set_reset_user(
1640 __isl_take isl_union_set *uset);
1642 #include <isl/union_map.h>
1643 __isl_give isl_union_map *isl_union_map_reset_user(
1644 __isl_take isl_union_map *umap);
1646 #include <isl/val.h>
1647 __isl_give isl_multi_val *isl_multi_val_reset_user(
1648 __isl_take isl_multi_val *mv);
1650 #include <isl/aff.h>
1651 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1652 __isl_take isl_multi_aff *ma);
1653 __isl_give isl_pw_aff *isl_pw_aff_reset_user(
1654 __isl_take isl_pw_aff *pa);
1655 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1656 __isl_take isl_multi_pw_aff *mpa);
1657 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_reset_user(
1658 __isl_take isl_pw_multi_aff *pma);
1659 __isl_give isl_union_pw_aff *isl_union_pw_aff_reset_user(
1660 __isl_take isl_union_pw_aff *upa);
1661 __isl_give isl_multi_union_pw_aff *
1662 isl_multi_union_pw_aff_reset_user(
1663 __isl_take isl_multi_union_pw_aff *mupa);
1664 __isl_give isl_union_pw_multi_aff *
1665 isl_union_pw_multi_aff_reset_user(
1666 __isl_take isl_union_pw_multi_aff *upma);
1668 #include <isl/polynomial.h>
1669 __isl_give isl_pw_qpolynomial *
1670 isl_pw_qpolynomial_reset_user(
1671 __isl_take isl_pw_qpolynomial *pwqp);
1672 __isl_give isl_union_pw_qpolynomial *
1673 isl_union_pw_qpolynomial_reset_user(
1674 __isl_take isl_union_pw_qpolynomial *upwqp);
1675 __isl_give isl_pw_qpolynomial_fold *
1676 isl_pw_qpolynomial_fold_reset_user(
1677 __isl_take isl_pw_qpolynomial_fold *pwf);
1678 __isl_give isl_union_pw_qpolynomial_fold *
1679 isl_union_pw_qpolynomial_fold_reset_user(
1680 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1682 Spaces can be nested. In particular, the domain of a set or
1683 the domain or range of a relation can be a nested relation.
1684 This process is also called I<wrapping>.
1685 The functions for detecting, constructing and deconstructing
1686 such nested spaces can be found in the wrapping properties
1687 of L</"Unary Properties">, the wrapping operations
1688 of L</"Unary Operations"> and the Cartesian product operations
1689 of L</"Basic Operations">.
1691 Spaces can be created from other spaces
1692 using the functions described in L</"Unary Operations">
1693 and L</"Binary Operations">.
1697 A local space is essentially a space with
1698 zero or more existentially quantified variables.
1699 The local space of various objects can be obtained
1700 using the following functions.
1702 #include <isl/constraint.h>
1703 __isl_give isl_local_space *isl_constraint_get_local_space(
1704 __isl_keep isl_constraint *constraint);
1706 #include <isl/set.h>
1707 __isl_give isl_local_space *isl_basic_set_get_local_space(
1708 __isl_keep isl_basic_set *bset);
1710 #include <isl/map.h>
1711 __isl_give isl_local_space *isl_basic_map_get_local_space(
1712 __isl_keep isl_basic_map *bmap);
1714 #include <isl/aff.h>
1715 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1716 __isl_keep isl_aff *aff);
1717 __isl_give isl_local_space *isl_aff_get_local_space(
1718 __isl_keep isl_aff *aff);
1720 A new local space can be created from a space using
1722 #include <isl/local_space.h>
1723 __isl_give isl_local_space *isl_local_space_from_space(
1724 __isl_take isl_space *space);
1726 They can be inspected, modified, copied and freed using the following functions.
1728 #include <isl/local_space.h>
1729 isl_bool isl_local_space_is_params(
1730 __isl_keep isl_local_space *ls);
1731 isl_bool isl_local_space_is_set(
1732 __isl_keep isl_local_space *ls);
1733 __isl_give isl_space *isl_local_space_get_space(
1734 __isl_keep isl_local_space *ls);
1735 __isl_give isl_aff *isl_local_space_get_div(
1736 __isl_keep isl_local_space *ls, int pos);
1737 __isl_give isl_local_space *isl_local_space_copy(
1738 __isl_keep isl_local_space *ls);
1739 __isl_null isl_local_space *isl_local_space_free(
1740 __isl_take isl_local_space *ls);
1742 Note that C<isl_local_space_get_div> can only be used on local spaces
1745 Two local spaces can be compared using
1747 isl_bool isl_local_space_is_equal(
1748 __isl_keep isl_local_space *ls1,
1749 __isl_keep isl_local_space *ls2);
1751 Local spaces can be created from other local spaces
1752 using the functions described in L</"Unary Operations">
1753 and L</"Binary Operations">.
1755 =head2 Creating New Sets and Relations
1757 C<isl> has functions for creating some standard sets and relations.
1761 =item * Empty sets and relations
1763 __isl_give isl_basic_set *isl_basic_set_empty(
1764 __isl_take isl_space *space);
1765 __isl_give isl_basic_map *isl_basic_map_empty(
1766 __isl_take isl_space *space);
1767 __isl_give isl_set *isl_set_empty(
1768 __isl_take isl_space *space);
1769 __isl_give isl_map *isl_map_empty(
1770 __isl_take isl_space *space);
1771 __isl_give isl_union_set *isl_union_set_empty(
1772 __isl_take isl_space *space);
1773 __isl_give isl_union_map *isl_union_map_empty(
1774 __isl_take isl_space *space);
1776 For C<isl_union_set>s and C<isl_union_map>s, the space
1777 is only used to specify the parameters.
1779 =item * Universe sets and relations
1781 __isl_give isl_basic_set *isl_basic_set_universe(
1782 __isl_take isl_space *space);
1783 __isl_give isl_basic_map *isl_basic_map_universe(
1784 __isl_take isl_space *space);
1785 __isl_give isl_set *isl_set_universe(
1786 __isl_take isl_space *space);
1787 __isl_give isl_map *isl_map_universe(
1788 __isl_take isl_space *space);
1789 __isl_give isl_union_set *isl_union_set_universe(
1790 __isl_take isl_union_set *uset);
1791 __isl_give isl_union_map *isl_union_map_universe(
1792 __isl_take isl_union_map *umap);
1794 The sets and relations constructed by the functions above
1795 contain all integer values, while those constructed by the
1796 functions below only contain non-negative values.
1798 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1799 __isl_take isl_space *space);
1800 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1801 __isl_take isl_space *space);
1802 __isl_give isl_set *isl_set_nat_universe(
1803 __isl_take isl_space *space);
1804 __isl_give isl_map *isl_map_nat_universe(
1805 __isl_take isl_space *space);
1807 =item * Identity relations
1809 __isl_give isl_basic_map *isl_basic_map_identity(
1810 __isl_take isl_space *space);
1811 __isl_give isl_map *isl_map_identity(
1812 __isl_take isl_space *space);
1814 The number of input and output dimensions in C<space> needs
1817 =item * Lexicographic order
1819 __isl_give isl_map *isl_map_lex_lt(
1820 __isl_take isl_space *set_space);
1821 __isl_give isl_map *isl_map_lex_le(
1822 __isl_take isl_space *set_space);
1823 __isl_give isl_map *isl_map_lex_gt(
1824 __isl_take isl_space *set_space);
1825 __isl_give isl_map *isl_map_lex_ge(
1826 __isl_take isl_space *set_space);
1827 __isl_give isl_map *isl_map_lex_lt_first(
1828 __isl_take isl_space *space, unsigned n);
1829 __isl_give isl_map *isl_map_lex_le_first(
1830 __isl_take isl_space *space, unsigned n);
1831 __isl_give isl_map *isl_map_lex_gt_first(
1832 __isl_take isl_space *space, unsigned n);
1833 __isl_give isl_map *isl_map_lex_ge_first(
1834 __isl_take isl_space *space, unsigned n);
1836 The first four functions take a space for a B<set>
1837 and return relations that express that the elements in the domain
1838 are lexicographically less
1839 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1840 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1841 than the elements in the range.
1842 The last four functions take a space for a map
1843 and return relations that express that the first C<n> dimensions
1844 in the domain are lexicographically less
1845 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1846 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1847 than the first C<n> dimensions in the range.
1851 A basic set or relation can be converted to a set or relation
1852 using the following functions.
1854 __isl_give isl_set *isl_set_from_basic_set(
1855 __isl_take isl_basic_set *bset);
1856 __isl_give isl_map *isl_map_from_basic_map(
1857 __isl_take isl_basic_map *bmap);
1859 Sets and relations can be converted to union sets and relations
1860 using the following functions.
1862 __isl_give isl_union_set *isl_union_set_from_basic_set(
1863 __isl_take isl_basic_set *bset);
1864 __isl_give isl_union_map *isl_union_map_from_basic_map(
1865 __isl_take isl_basic_map *bmap);
1866 __isl_give isl_union_set *isl_union_set_from_set(
1867 __isl_take isl_set *set);
1868 __isl_give isl_union_map *isl_union_map_from_map(
1869 __isl_take isl_map *map);
1871 The inverse conversions below can only be used if the input
1872 union set or relation is known to contain elements in exactly one
1875 __isl_give isl_set *isl_set_from_union_set(
1876 __isl_take isl_union_set *uset);
1877 __isl_give isl_map *isl_map_from_union_map(
1878 __isl_take isl_union_map *umap);
1880 Sets and relations can be copied and freed again using the following
1883 __isl_give isl_basic_set *isl_basic_set_copy(
1884 __isl_keep isl_basic_set *bset);
1885 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1886 __isl_give isl_union_set *isl_union_set_copy(
1887 __isl_keep isl_union_set *uset);
1888 __isl_give isl_basic_map *isl_basic_map_copy(
1889 __isl_keep isl_basic_map *bmap);
1890 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1891 __isl_give isl_union_map *isl_union_map_copy(
1892 __isl_keep isl_union_map *umap);
1893 __isl_null isl_basic_set *isl_basic_set_free(
1894 __isl_take isl_basic_set *bset);
1895 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1896 __isl_null isl_union_set *isl_union_set_free(
1897 __isl_take isl_union_set *uset);
1898 __isl_null isl_basic_map *isl_basic_map_free(
1899 __isl_take isl_basic_map *bmap);
1900 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1901 __isl_null isl_union_map *isl_union_map_free(
1902 __isl_take isl_union_map *umap);
1904 Other sets and relations can be constructed by starting
1905 from a universe set or relation, adding equality and/or
1906 inequality constraints and then projecting out the
1907 existentially quantified variables, if any.
1908 Constraints can be constructed, manipulated and
1909 added to (or removed from) (basic) sets and relations
1910 using the following functions.
1912 #include <isl/constraint.h>
1913 __isl_give isl_constraint *isl_constraint_alloc_equality(
1914 __isl_take isl_local_space *ls);
1915 __isl_give isl_constraint *isl_constraint_alloc_inequality(
1916 __isl_take isl_local_space *ls);
1917 __isl_give isl_constraint *isl_constraint_set_constant_si(
1918 __isl_take isl_constraint *constraint, int v);
1919 __isl_give isl_constraint *isl_constraint_set_constant_val(
1920 __isl_take isl_constraint *constraint,
1921 __isl_take isl_val *v);
1922 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1923 __isl_take isl_constraint *constraint,
1924 enum isl_dim_type type, int pos, int v);
1925 __isl_give isl_constraint *
1926 isl_constraint_set_coefficient_val(
1927 __isl_take isl_constraint *constraint,
1928 enum isl_dim_type type, int pos,
1929 __isl_take isl_val *v);
1930 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1931 __isl_take isl_basic_map *bmap,
1932 __isl_take isl_constraint *constraint);
1933 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1934 __isl_take isl_basic_set *bset,
1935 __isl_take isl_constraint *constraint);
1936 __isl_give isl_map *isl_map_add_constraint(
1937 __isl_take isl_map *map,
1938 __isl_take isl_constraint *constraint);
1939 __isl_give isl_set *isl_set_add_constraint(
1940 __isl_take isl_set *set,
1941 __isl_take isl_constraint *constraint);
1943 For example, to create a set containing the even integers
1944 between 10 and 42, you would use the following code.
1947 isl_local_space *ls;
1949 isl_basic_set *bset;
1951 space = isl_space_set_alloc(ctx, 0, 2);
1952 bset = isl_basic_set_universe(isl_space_copy(space));
1953 ls = isl_local_space_from_space(space);
1955 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
1956 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1957 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1958 bset = isl_basic_set_add_constraint(bset, c);
1960 c = isl_constraint_alloc_inequality(isl_local_space_copy(ls));
1961 c = isl_constraint_set_constant_si(c, -10);
1962 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1963 bset = isl_basic_set_add_constraint(bset, c);
1965 c = isl_constraint_alloc_inequality(ls);
1966 c = isl_constraint_set_constant_si(c, 42);
1967 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1968 bset = isl_basic_set_add_constraint(bset, c);
1970 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1974 isl_basic_set *bset;
1975 bset = isl_basic_set_read_from_str(ctx,
1976 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1978 A basic set or relation can also be constructed from two matrices
1979 describing the equalities and the inequalities.
1981 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1982 __isl_take isl_space *space,
1983 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1984 enum isl_dim_type c1,
1985 enum isl_dim_type c2, enum isl_dim_type c3,
1986 enum isl_dim_type c4);
1987 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1988 __isl_take isl_space *space,
1989 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1990 enum isl_dim_type c1,
1991 enum isl_dim_type c2, enum isl_dim_type c3,
1992 enum isl_dim_type c4, enum isl_dim_type c5);
1994 The C<isl_dim_type> arguments indicate the order in which
1995 different kinds of variables appear in the input matrices
1996 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1997 C<isl_dim_set> and C<isl_dim_div> for sets and
1998 of C<isl_dim_cst>, C<isl_dim_param>,
1999 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
2001 A (basic or union) set or relation can also be constructed from a
2002 (union) (piecewise) (multiple) affine expression
2003 or a list of affine expressions
2004 (See L</"Functions">).
2006 __isl_give isl_basic_map *isl_basic_map_from_aff(
2007 __isl_take isl_aff *aff);
2008 __isl_give isl_map *isl_map_from_aff(
2009 __isl_take isl_aff *aff);
2010 __isl_give isl_set *isl_set_from_pw_aff(
2011 __isl_take isl_pw_aff *pwaff);
2012 __isl_give isl_map *isl_map_from_pw_aff(
2013 __isl_take isl_pw_aff *pwaff);
2014 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
2015 __isl_take isl_space *domain_space,
2016 __isl_take isl_aff_list *list);
2017 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
2018 __isl_take isl_multi_aff *maff)
2019 __isl_give isl_map *isl_map_from_multi_aff(
2020 __isl_take isl_multi_aff *maff)
2021 __isl_give isl_set *isl_set_from_pw_multi_aff(
2022 __isl_take isl_pw_multi_aff *pma);
2023 __isl_give isl_map *isl_map_from_pw_multi_aff(
2024 __isl_take isl_pw_multi_aff *pma);
2025 __isl_give isl_set *isl_set_from_multi_pw_aff(
2026 __isl_take isl_multi_pw_aff *mpa);
2027 __isl_give isl_map *isl_map_from_multi_pw_aff(
2028 __isl_take isl_multi_pw_aff *mpa);
2029 __isl_give isl_union_map *isl_union_map_from_union_pw_aff(
2030 __isl_take isl_union_pw_aff *upa);
2031 __isl_give isl_union_map *
2032 isl_union_map_from_union_pw_multi_aff(
2033 __isl_take isl_union_pw_multi_aff *upma);
2034 __isl_give isl_union_map *
2035 isl_union_map_from_multi_union_pw_aff(
2036 __isl_take isl_multi_union_pw_aff *mupa);
2038 The C<domain_space> argument describes the domain of the resulting
2039 basic relation. It is required because the C<list> may consist
2040 of zero affine expressions.
2041 The C<mupa> passed to C<isl_union_map_from_multi_union_pw_aff>
2042 is not allowed to be zero-dimensional. The domain of the result
2043 is the shared domain of the union piecewise affine elements.
2045 =head2 Inspecting Sets and Relations
2047 Usually, the user should not have to care about the actual constraints
2048 of the sets and maps, but should instead apply the abstract operations
2049 explained in the following sections.
2050 Occasionally, however, it may be required to inspect the individual
2051 coefficients of the constraints. This section explains how to do so.
2052 In these cases, it may also be useful to have C<isl> compute
2053 an explicit representation of the existentially quantified variables.
2055 __isl_give isl_set *isl_set_compute_divs(
2056 __isl_take isl_set *set);
2057 __isl_give isl_map *isl_map_compute_divs(
2058 __isl_take isl_map *map);
2059 __isl_give isl_union_set *isl_union_set_compute_divs(
2060 __isl_take isl_union_set *uset);
2061 __isl_give isl_union_map *isl_union_map_compute_divs(
2062 __isl_take isl_union_map *umap);
2064 This explicit representation defines the existentially quantified
2065 variables as integer divisions of the other variables, possibly
2066 including earlier existentially quantified variables.
2067 An explicitly represented existentially quantified variable therefore
2068 has a unique value when the values of the other variables are known.
2069 If, furthermore, the same existentials, i.e., existentials
2070 with the same explicit representations, should appear in the
2071 same order in each of the disjuncts of a set or map, then the user should call
2072 either of the following functions.
2074 __isl_give isl_set *isl_set_align_divs(
2075 __isl_take isl_set *set);
2076 __isl_give isl_map *isl_map_align_divs(
2077 __isl_take isl_map *map);
2079 Alternatively, the existentially quantified variables can be removed
2080 using the following functions, which compute an overapproximation.
2082 __isl_give isl_basic_set *isl_basic_set_remove_divs(
2083 __isl_take isl_basic_set *bset);
2084 __isl_give isl_basic_map *isl_basic_map_remove_divs(
2085 __isl_take isl_basic_map *bmap);
2086 __isl_give isl_set *isl_set_remove_divs(
2087 __isl_take isl_set *set);
2088 __isl_give isl_map *isl_map_remove_divs(
2089 __isl_take isl_map *map);
2091 It is also possible to only remove those divs that are defined
2092 in terms of a given range of dimensions or only those for which
2093 no explicit representation is known.
2095 __isl_give isl_basic_set *
2096 isl_basic_set_remove_divs_involving_dims(
2097 __isl_take isl_basic_set *bset,
2098 enum isl_dim_type type,
2099 unsigned first, unsigned n);
2100 __isl_give isl_basic_map *
2101 isl_basic_map_remove_divs_involving_dims(
2102 __isl_take isl_basic_map *bmap,
2103 enum isl_dim_type type,
2104 unsigned first, unsigned n);
2105 __isl_give isl_set *isl_set_remove_divs_involving_dims(
2106 __isl_take isl_set *set, enum isl_dim_type type,
2107 unsigned first, unsigned n);
2108 __isl_give isl_map *isl_map_remove_divs_involving_dims(
2109 __isl_take isl_map *map, enum isl_dim_type type,
2110 unsigned first, unsigned n);
2112 __isl_give isl_basic_set *
2113 isl_basic_set_remove_unknown_divs(
2114 __isl_take isl_basic_set *bset);
2115 __isl_give isl_set *isl_set_remove_unknown_divs(
2116 __isl_take isl_set *set);
2117 __isl_give isl_map *isl_map_remove_unknown_divs(
2118 __isl_take isl_map *map);
2120 To iterate over all the sets or maps in a union set or map, use
2122 isl_stat isl_union_set_foreach_set(
2123 __isl_keep isl_union_set *uset,
2124 isl_stat (*fn)(__isl_take isl_set *set, void *user),
2126 isl_stat isl_union_map_foreach_map(
2127 __isl_keep isl_union_map *umap,
2128 isl_stat (*fn)(__isl_take isl_map *map, void *user),
2131 The number of sets or maps in a union set or map can be obtained
2134 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
2135 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
2137 To extract the set or map in a given space from a union, use
2139 __isl_give isl_set *isl_union_set_extract_set(
2140 __isl_keep isl_union_set *uset,
2141 __isl_take isl_space *space);
2142 __isl_give isl_map *isl_union_map_extract_map(
2143 __isl_keep isl_union_map *umap,
2144 __isl_take isl_space *space);
2146 To iterate over all the basic sets or maps in a set or map, use
2148 isl_stat isl_set_foreach_basic_set(__isl_keep isl_set *set,
2149 isl_stat (*fn)(__isl_take isl_basic_set *bset,
2152 isl_stat isl_map_foreach_basic_map(__isl_keep isl_map *map,
2153 isl_stat (*fn)(__isl_take isl_basic_map *bmap,
2157 The callback function C<fn> should return 0 if successful and
2158 -1 if an error occurs. In the latter case, or if any other error
2159 occurs, the above functions will return -1.
2161 It should be noted that C<isl> does not guarantee that
2162 the basic sets or maps passed to C<fn> are disjoint.
2163 If this is required, then the user should call one of
2164 the following functions first.
2166 __isl_give isl_set *isl_set_make_disjoint(
2167 __isl_take isl_set *set);
2168 __isl_give isl_map *isl_map_make_disjoint(
2169 __isl_take isl_map *map);
2171 The number of basic sets in a set can be obtained
2172 or the number of basic maps in a map can be obtained
2175 #include <isl/set.h>
2176 int isl_set_n_basic_set(__isl_keep isl_set *set);
2178 #include <isl/map.h>
2179 int isl_map_n_basic_map(__isl_keep isl_map *map);
2181 It is also possible to obtain a list of basic sets from a set
2183 #include <isl/set.h>
2184 __isl_give isl_basic_set_list *isl_set_get_basic_set_list(
2185 __isl_keep isl_set *set);
2187 The returned list can be manipulated using the functions in L<"Lists">.
2189 To iterate over the constraints of a basic set or map, use
2191 #include <isl/constraint.h>
2193 int isl_basic_set_n_constraint(
2194 __isl_keep isl_basic_set *bset);
2195 isl_stat isl_basic_set_foreach_constraint(
2196 __isl_keep isl_basic_set *bset,
2197 isl_stat (*fn)(__isl_take isl_constraint *c,
2200 int isl_basic_map_n_constraint(
2201 __isl_keep isl_basic_map *bmap);
2202 isl_stat isl_basic_map_foreach_constraint(
2203 __isl_keep isl_basic_map *bmap,
2204 isl_stat (*fn)(__isl_take isl_constraint *c,
2207 __isl_null isl_constraint *isl_constraint_free(
2208 __isl_take isl_constraint *c);
2210 Again, the callback function C<fn> should return 0 if successful and
2211 -1 if an error occurs. In the latter case, or if any other error
2212 occurs, the above functions will return -1.
2213 The constraint C<c> represents either an equality or an inequality.
2214 Use the following function to find out whether a constraint
2215 represents an equality. If not, it represents an inequality.
2217 isl_bool isl_constraint_is_equality(
2218 __isl_keep isl_constraint *constraint);
2220 It is also possible to obtain a list of constraints from a basic
2223 #include <isl/constraint.h>
2224 __isl_give isl_constraint_list *
2225 isl_basic_map_get_constraint_list(
2226 __isl_keep isl_basic_map *bmap);
2227 __isl_give isl_constraint_list *
2228 isl_basic_set_get_constraint_list(
2229 __isl_keep isl_basic_set *bset);
2231 These functions require that all existentially quantified variables
2232 have an explicit representation.
2233 The returned list can be manipulated using the functions in L<"Lists">.
2235 The coefficients of the constraints can be inspected using
2236 the following functions.
2238 isl_bool isl_constraint_is_lower_bound(
2239 __isl_keep isl_constraint *constraint,
2240 enum isl_dim_type type, unsigned pos);
2241 isl_bool isl_constraint_is_upper_bound(
2242 __isl_keep isl_constraint *constraint,
2243 enum isl_dim_type type, unsigned pos);
2244 __isl_give isl_val *isl_constraint_get_constant_val(
2245 __isl_keep isl_constraint *constraint);
2246 __isl_give isl_val *isl_constraint_get_coefficient_val(
2247 __isl_keep isl_constraint *constraint,
2248 enum isl_dim_type type, int pos);
2250 The explicit representations of the existentially quantified
2251 variables can be inspected using the following function.
2252 Note that the user is only allowed to use this function
2253 if the inspected set or map is the result of a call
2254 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2255 The existentially quantified variable is equal to the floor
2256 of the returned affine expression. The affine expression
2257 itself can be inspected using the functions in
2260 __isl_give isl_aff *isl_constraint_get_div(
2261 __isl_keep isl_constraint *constraint, int pos);
2263 To obtain the constraints of a basic set or map in matrix
2264 form, use the following functions.
2266 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2267 __isl_keep isl_basic_set *bset,
2268 enum isl_dim_type c1, enum isl_dim_type c2,
2269 enum isl_dim_type c3, enum isl_dim_type c4);
2270 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2271 __isl_keep isl_basic_set *bset,
2272 enum isl_dim_type c1, enum isl_dim_type c2,
2273 enum isl_dim_type c3, enum isl_dim_type c4);
2274 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2275 __isl_keep isl_basic_map *bmap,
2276 enum isl_dim_type c1,
2277 enum isl_dim_type c2, enum isl_dim_type c3,
2278 enum isl_dim_type c4, enum isl_dim_type c5);
2279 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2280 __isl_keep isl_basic_map *bmap,
2281 enum isl_dim_type c1,
2282 enum isl_dim_type c2, enum isl_dim_type c3,
2283 enum isl_dim_type c4, enum isl_dim_type c5);
2285 The C<isl_dim_type> arguments dictate the order in which
2286 different kinds of variables appear in the resulting matrix.
2287 For set inputs, they should be a permutation of
2288 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
2289 For map inputs, they should be a permutation of
2290 C<isl_dim_cst>, C<isl_dim_param>,
2291 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2295 Points are elements of a set. They can be used to construct
2296 simple sets (boxes) or they can be used to represent the
2297 individual elements of a set.
2298 The zero point (the origin) can be created using
2300 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2302 The coordinates of a point can be inspected, set and changed
2305 __isl_give isl_val *isl_point_get_coordinate_val(
2306 __isl_keep isl_point *pnt,
2307 enum isl_dim_type type, int pos);
2308 __isl_give isl_point *isl_point_set_coordinate_val(
2309 __isl_take isl_point *pnt,
2310 enum isl_dim_type type, int pos,
2311 __isl_take isl_val *v);
2313 __isl_give isl_point *isl_point_add_ui(
2314 __isl_take isl_point *pnt,
2315 enum isl_dim_type type, int pos, unsigned val);
2316 __isl_give isl_point *isl_point_sub_ui(
2317 __isl_take isl_point *pnt,
2318 enum isl_dim_type type, int pos, unsigned val);
2320 Points can be copied or freed using
2322 __isl_give isl_point *isl_point_copy(
2323 __isl_keep isl_point *pnt);
2324 void isl_point_free(__isl_take isl_point *pnt);
2326 A singleton set can be created from a point using
2328 __isl_give isl_basic_set *isl_basic_set_from_point(
2329 __isl_take isl_point *pnt);
2330 __isl_give isl_set *isl_set_from_point(
2331 __isl_take isl_point *pnt);
2333 and a box can be created from two opposite extremal points using
2335 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2336 __isl_take isl_point *pnt1,
2337 __isl_take isl_point *pnt2);
2338 __isl_give isl_set *isl_set_box_from_points(
2339 __isl_take isl_point *pnt1,
2340 __isl_take isl_point *pnt2);
2342 All elements of a B<bounded> (union) set can be enumerated using
2343 the following functions.
2345 isl_stat isl_set_foreach_point(__isl_keep isl_set *set,
2346 isl_stat (*fn)(__isl_take isl_point *pnt,
2349 isl_stat isl_union_set_foreach_point(
2350 __isl_keep isl_union_set *uset,
2351 isl_stat (*fn)(__isl_take isl_point *pnt,
2355 The function C<fn> is called for each integer point in
2356 C<set> with as second argument the last argument of
2357 the C<isl_set_foreach_point> call. The function C<fn>
2358 should return C<0> on success and C<-1> on failure.
2359 In the latter case, C<isl_set_foreach_point> will stop
2360 enumerating and return C<-1> as well.
2361 If the enumeration is performed successfully and to completion,
2362 then C<isl_set_foreach_point> returns C<0>.
2364 To obtain a single point of a (basic) set, use
2366 __isl_give isl_point *isl_basic_set_sample_point(
2367 __isl_take isl_basic_set *bset);
2368 __isl_give isl_point *isl_set_sample_point(
2369 __isl_take isl_set *set);
2371 If C<set> does not contain any (integer) points, then the
2372 resulting point will be ``void'', a property that can be
2375 isl_bool isl_point_is_void(__isl_keep isl_point *pnt);
2379 Besides sets and relation, C<isl> also supports various types of functions.
2380 Each of these types is derived from the value type (see L</"Values">)
2381 or from one of two primitive function types
2382 through the application of zero or more type constructors.
2383 We first describe the primitive type and then we describe
2384 the types derived from these primitive types.
2386 =head3 Primitive Functions
2388 C<isl> support two primitive function types, quasi-affine
2389 expressions and quasipolynomials.
2390 A quasi-affine expression is defined either over a parameter
2391 space or over a set and is composed of integer constants,
2392 parameters and set variables, addition, subtraction and
2393 integer division by an integer constant.
2394 For example, the quasi-affine expression
2396 [n] -> { [x] -> [2*floor((4 n + x)/9] }
2398 maps C<x> to C<2*floor((4 n + x)/9>.
2399 A quasipolynomial is a polynomial expression in quasi-affine
2400 expression. That is, it additionally allows for multiplication.
2401 Note, though, that it is not allowed to construct an integer
2402 division of an expression involving multiplications.
2403 Here is an example of a quasipolynomial that is not
2404 quasi-affine expression
2406 [n] -> { [x] -> (n*floor((4 n + x)/9) }
2408 Note that the external representations of quasi-affine expressions
2409 and quasipolynomials are different. Quasi-affine expressions
2410 use a notation with square brackets just like binary relations,
2411 while quasipolynomials do not. This might change at some point.
2413 If a primitive function is defined over a parameter space,
2414 then the space of the function itself is that of a set.
2415 If it is defined over a set, then the space of the function
2416 is that of a relation. In both cases, the set space (or
2417 the output space) is single-dimensional, anonymous and unstructured.
2418 To create functions with multiple dimensions or with other kinds
2419 of set or output spaces, use multiple expressions
2420 (see L</"Multiple Expressions">).
2424 =item * Quasi-affine Expressions
2426 Besides the expressions described above, a quasi-affine
2427 expression can also be set to NaN. Such expressions
2428 typically represent a failure to represent a result
2429 as a quasi-affine expression.
2431 The zero quasi affine expression or the quasi affine expression
2432 that is equal to a given value or
2433 a specified dimension on a given domain can be created using
2435 #include <isl/aff.h>
2436 __isl_give isl_aff *isl_aff_zero_on_domain(
2437 __isl_take isl_local_space *ls);
2438 __isl_give isl_aff *isl_aff_val_on_domain(
2439 __isl_take isl_local_space *ls,
2440 __isl_take isl_val *val);
2441 __isl_give isl_aff *isl_aff_var_on_domain(
2442 __isl_take isl_local_space *ls,
2443 enum isl_dim_type type, unsigned pos);
2444 __isl_give isl_aff *isl_aff_nan_on_domain(
2445 __isl_take isl_local_space *ls);
2447 Quasi affine expressions can be copied and freed using
2449 #include <isl/aff.h>
2450 __isl_give isl_aff *isl_aff_copy(
2451 __isl_keep isl_aff *aff);
2452 __isl_null isl_aff *isl_aff_free(
2453 __isl_take isl_aff *aff);
2455 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2456 using the following function. The constraint is required to have
2457 a non-zero coefficient for the specified dimension.
2459 #include <isl/constraint.h>
2460 __isl_give isl_aff *isl_constraint_get_bound(
2461 __isl_keep isl_constraint *constraint,
2462 enum isl_dim_type type, int pos);
2464 The entire affine expression of the constraint can also be extracted
2465 using the following function.
2467 #include <isl/constraint.h>
2468 __isl_give isl_aff *isl_constraint_get_aff(
2469 __isl_keep isl_constraint *constraint);
2471 Conversely, an equality constraint equating
2472 the affine expression to zero or an inequality constraint enforcing
2473 the affine expression to be non-negative, can be constructed using
2475 __isl_give isl_constraint *isl_equality_from_aff(
2476 __isl_take isl_aff *aff);
2477 __isl_give isl_constraint *isl_inequality_from_aff(
2478 __isl_take isl_aff *aff);
2480 The coefficients and the integer divisions of an affine expression
2481 can be inspected using the following functions.
2483 #include <isl/aff.h>
2484 __isl_give isl_val *isl_aff_get_constant_val(
2485 __isl_keep isl_aff *aff);
2486 __isl_give isl_val *isl_aff_get_coefficient_val(
2487 __isl_keep isl_aff *aff,
2488 enum isl_dim_type type, int pos);
2489 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2490 enum isl_dim_type type, int pos);
2491 __isl_give isl_val *isl_aff_get_denominator_val(
2492 __isl_keep isl_aff *aff);
2493 __isl_give isl_aff *isl_aff_get_div(
2494 __isl_keep isl_aff *aff, int pos);
2496 They can be modified using the following functions.
2498 #include <isl/aff.h>
2499 __isl_give isl_aff *isl_aff_set_constant_si(
2500 __isl_take isl_aff *aff, int v);
2501 __isl_give isl_aff *isl_aff_set_constant_val(
2502 __isl_take isl_aff *aff, __isl_take isl_val *v);
2503 __isl_give isl_aff *isl_aff_set_coefficient_si(
2504 __isl_take isl_aff *aff,
2505 enum isl_dim_type type, int pos, int v);
2506 __isl_give isl_aff *isl_aff_set_coefficient_val(
2507 __isl_take isl_aff *aff,
2508 enum isl_dim_type type, int pos,
2509 __isl_take isl_val *v);
2511 __isl_give isl_aff *isl_aff_add_constant_si(
2512 __isl_take isl_aff *aff, int v);
2513 __isl_give isl_aff *isl_aff_add_constant_val(
2514 __isl_take isl_aff *aff, __isl_take isl_val *v);
2515 __isl_give isl_aff *isl_aff_add_constant_num_si(
2516 __isl_take isl_aff *aff, int v);
2517 __isl_give isl_aff *isl_aff_add_coefficient_si(
2518 __isl_take isl_aff *aff,
2519 enum isl_dim_type type, int pos, int v);
2520 __isl_give isl_aff *isl_aff_add_coefficient_val(
2521 __isl_take isl_aff *aff,
2522 enum isl_dim_type type, int pos,
2523 __isl_take isl_val *v);
2525 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
2526 set the I<numerator> of the constant or coefficient, while
2527 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
2528 the constant or coefficient as a whole.
2529 The C<add_constant> and C<add_coefficient> functions add an integer
2530 or rational value to
2531 the possibly rational constant or coefficient.
2532 The C<add_constant_num> functions add an integer value to
2535 =item * Quasipolynomials
2537 Some simple quasipolynomials can be created using the following functions.
2539 #include <isl/polynomial.h>
2540 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2541 __isl_take isl_space *domain);
2542 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2543 __isl_take isl_space *domain);
2544 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2545 __isl_take isl_space *domain);
2546 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2547 __isl_take isl_space *domain);
2548 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2549 __isl_take isl_space *domain);
2550 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2551 __isl_take isl_space *domain,
2552 __isl_take isl_val *val);
2553 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2554 __isl_take isl_space *domain,
2555 enum isl_dim_type type, unsigned pos);
2556 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2557 __isl_take isl_aff *aff);
2559 Recall that the space in which a quasipolynomial lives is a map space
2560 with a one-dimensional range. The C<domain> argument in some of
2561 the functions above corresponds to the domain of this map space.
2563 Quasipolynomials can be copied and freed again using the following
2566 #include <isl/polynomial.h>
2567 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2568 __isl_keep isl_qpolynomial *qp);
2569 __isl_null isl_qpolynomial *isl_qpolynomial_free(
2570 __isl_take isl_qpolynomial *qp);
2572 The constant term of a quasipolynomial can be extracted using
2574 __isl_give isl_val *isl_qpolynomial_get_constant_val(
2575 __isl_keep isl_qpolynomial *qp);
2577 To iterate over all terms in a quasipolynomial,
2580 isl_stat isl_qpolynomial_foreach_term(
2581 __isl_keep isl_qpolynomial *qp,
2582 isl_stat (*fn)(__isl_take isl_term *term,
2583 void *user), void *user);
2585 The terms themselves can be inspected and freed using
2588 unsigned isl_term_dim(__isl_keep isl_term *term,
2589 enum isl_dim_type type);
2590 __isl_give isl_val *isl_term_get_coefficient_val(
2591 __isl_keep isl_term *term);
2592 int isl_term_get_exp(__isl_keep isl_term *term,
2593 enum isl_dim_type type, unsigned pos);
2594 __isl_give isl_aff *isl_term_get_div(
2595 __isl_keep isl_term *term, unsigned pos);
2596 void isl_term_free(__isl_take isl_term *term);
2598 Each term is a product of parameters, set variables and
2599 integer divisions. The function C<isl_term_get_exp>
2600 returns the exponent of a given dimensions in the given term.
2606 A reduction represents a maximum or a minimum of its
2608 The only reduction type defined by C<isl> is
2609 C<isl_qpolynomial_fold>.
2611 There are currently no functions to directly create such
2612 objects, but they do appear in the piecewise quasipolynomial
2613 reductions returned by the C<isl_pw_qpolynomial_bound> function.
2615 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
2617 Reductions can be copied and freed using
2618 the following functions.
2620 #include <isl/polynomial.h>
2621 __isl_give isl_qpolynomial_fold *
2622 isl_qpolynomial_fold_copy(
2623 __isl_keep isl_qpolynomial_fold *fold);
2624 void isl_qpolynomial_fold_free(
2625 __isl_take isl_qpolynomial_fold *fold);
2627 To iterate over all quasipolynomials in a reduction, use
2629 isl_stat isl_qpolynomial_fold_foreach_qpolynomial(
2630 __isl_keep isl_qpolynomial_fold *fold,
2631 isl_stat (*fn)(__isl_take isl_qpolynomial *qp,
2632 void *user), void *user);
2634 =head3 Multiple Expressions
2636 A multiple expression represents a sequence of zero or
2637 more base expressions, all defined on the same domain space.
2638 The domain space of the multiple expression is the same
2639 as that of the base expressions, but the range space
2640 can be any space. In case the base expressions have
2641 a set space, the corresponding multiple expression
2642 also has a set space.
2643 Objects of the value type do not have an associated space.
2644 The space of a multiple value is therefore always a set space.
2645 Similarly, the space of a multiple union piecewise
2646 affine expression is always a set space.
2648 The multiple expression types defined by C<isl>
2649 are C<isl_multi_val>, C<isl_multi_aff>, C<isl_multi_pw_aff>,
2650 C<isl_multi_union_pw_aff>.
2652 A multiple expression with the value zero for
2653 each output (or set) dimension can be created
2654 using the following functions.
2656 #include <isl/val.h>
2657 __isl_give isl_multi_val *isl_multi_val_zero(
2658 __isl_take isl_space *space);
2660 #include <isl/aff.h>
2661 __isl_give isl_multi_aff *isl_multi_aff_zero(
2662 __isl_take isl_space *space);
2663 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
2664 __isl_take isl_space *space);
2665 __isl_give isl_multi_union_pw_aff *
2666 isl_multi_union_pw_aff_zero(
2667 __isl_take isl_space *space);
2669 Since there is no canonical way of representing a zero
2670 value of type C<isl_union_pw_aff>, the space passed
2671 to C<isl_multi_union_pw_aff_zero> needs to be zero-dimensional.
2673 An identity function can be created using the following
2674 functions. The space needs to be that of a relation
2675 with the same number of input and output dimensions.
2677 #include <isl/aff.h>
2678 __isl_give isl_multi_aff *isl_multi_aff_identity(
2679 __isl_take isl_space *space);
2680 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
2681 __isl_take isl_space *space);
2683 A function that performs a projection on a universe
2684 relation or set can be created using the following functions.
2685 See also the corresponding
2686 projection operations in L</"Unary Operations">.
2688 #include <isl/aff.h>
2689 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
2690 __isl_take isl_space *space);
2691 __isl_give isl_multi_aff *isl_multi_aff_range_map(
2692 __isl_take isl_space *space);
2693 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
2694 __isl_take isl_space *space,
2695 enum isl_dim_type type,
2696 unsigned first, unsigned n);
2698 A multiple expression can be created from a single
2699 base expression using the following functions.
2700 The space of the created multiple expression is the same
2701 as that of the base expression, except for
2702 C<isl_multi_union_pw_aff_from_union_pw_aff> where the input
2703 lives in a parameter space and the output lives
2704 in a single-dimensional set space.
2706 #include <isl/aff.h>
2707 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
2708 __isl_take isl_aff *aff);
2709 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
2710 __isl_take isl_pw_aff *pa);
2711 __isl_give isl_multi_union_pw_aff *
2712 isl_multi_union_pw_aff_from_union_pw_aff(
2713 __isl_take isl_union_pw_aff *upa);
2715 A multiple expression can be created from a list
2716 of base expression in a specified space.
2717 The domain of this space needs to be the same
2718 as the domains of the base expressions in the list.
2719 If the base expressions have a set space (or no associated space),
2720 then this space also needs to be a set space.
2722 #include <isl/val.h>
2723 __isl_give isl_multi_val *isl_multi_val_from_val_list(
2724 __isl_take isl_space *space,
2725 __isl_take isl_val_list *list);
2727 #include <isl/aff.h>
2728 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2729 __isl_take isl_space *space,
2730 __isl_take isl_aff_list *list);
2731 __isl_give isl_multi_union_pw_aff *
2732 isl_multi_union_pw_aff_from_union_pw_aff_list(
2733 __isl_take isl_space *space,
2734 __isl_take isl_union_pw_aff_list *list);
2736 As a convenience, a multiple piecewise expression can
2737 also be created from a multiple expression.
2738 Each piecewise expression in the result has a single
2741 #include <isl/aff.h>
2742 __isl_give isl_multi_pw_aff *
2743 isl_multi_pw_aff_from_multi_aff(
2744 __isl_take isl_multi_aff *ma);
2746 Similarly, a multiple union expression can be
2747 created from a multiple expression.
2749 #include <isl/aff.h>
2750 __isl_give isl_multi_union_pw_aff *
2751 isl_multi_union_pw_aff_from_multi_aff(
2752 __isl_take isl_multi_aff *ma);
2753 __isl_give isl_multi_union_pw_aff *
2754 isl_multi_union_pw_aff_from_multi_pw_aff(
2755 __isl_take isl_multi_pw_aff *mpa);
2757 A multiple quasi-affine expression can be created from
2758 a multiple value with a given domain space using the following
2761 #include <isl/aff.h>
2762 __isl_give isl_multi_aff *
2763 isl_multi_aff_multi_val_on_space(
2764 __isl_take isl_space *space,
2765 __isl_take isl_multi_val *mv);
2768 a multiple union piecewise affine expression can be created from
2769 a multiple value with a given domain or
2770 a multiple affine expression with a given domain
2771 using the following functions.
2773 #include <isl/aff.h>
2774 __isl_give isl_multi_union_pw_aff *
2775 isl_multi_union_pw_aff_multi_val_on_domain(
2776 __isl_take isl_union_set *domain,
2777 __isl_take isl_multi_val *mv);
2778 __isl_give isl_multi_union_pw_aff *
2779 isl_multi_union_pw_aff_multi_aff_on_domain(
2780 __isl_take isl_union_set *domain,
2781 __isl_take isl_multi_aff *ma);
2783 Multiple expressions can be copied and freed using
2784 the following functions.
2786 #include <isl/val.h>
2787 __isl_give isl_multi_val *isl_multi_val_copy(
2788 __isl_keep isl_multi_val *mv);
2789 __isl_null isl_multi_val *isl_multi_val_free(
2790 __isl_take isl_multi_val *mv);
2792 #include <isl/aff.h>
2793 __isl_give isl_multi_aff *isl_multi_aff_copy(
2794 __isl_keep isl_multi_aff *maff);
2795 __isl_null isl_multi_aff *isl_multi_aff_free(
2796 __isl_take isl_multi_aff *maff);
2797 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
2798 __isl_keep isl_multi_pw_aff *mpa);
2799 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
2800 __isl_take isl_multi_pw_aff *mpa);
2801 __isl_give isl_multi_union_pw_aff *
2802 isl_multi_union_pw_aff_copy(
2803 __isl_keep isl_multi_union_pw_aff *mupa);
2804 __isl_null isl_multi_union_pw_aff *
2805 isl_multi_union_pw_aff_free(
2806 __isl_take isl_multi_union_pw_aff *mupa);
2808 The base expression at a given position of a multiple
2809 expression can be extracted using the following functions.
2811 #include <isl/val.h>
2812 __isl_give isl_val *isl_multi_val_get_val(
2813 __isl_keep isl_multi_val *mv, int pos);
2815 #include <isl/aff.h>
2816 __isl_give isl_aff *isl_multi_aff_get_aff(
2817 __isl_keep isl_multi_aff *multi, int pos);
2818 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
2819 __isl_keep isl_multi_pw_aff *mpa, int pos);
2820 __isl_give isl_union_pw_aff *
2821 isl_multi_union_pw_aff_get_union_pw_aff(
2822 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
2824 It can be replaced using the following functions.
2826 #include <isl/val.h>
2827 __isl_give isl_multi_val *isl_multi_val_set_val(
2828 __isl_take isl_multi_val *mv, int pos,
2829 __isl_take isl_val *val);
2831 #include <isl/aff.h>
2832 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
2833 __isl_take isl_multi_aff *multi, int pos,
2834 __isl_take isl_aff *aff);
2835 __isl_give isl_multi_union_pw_aff *
2836 isl_multi_union_pw_aff_set_union_pw_aff(
2837 __isl_take isl_multi_union_pw_aff *mupa, int pos,
2838 __isl_take isl_union_pw_aff *upa);
2840 As a convenience, a sequence of base expressions that have
2841 their domains in a given space can be extracted from a sequence
2842 of union expressions using the following function.
2844 #include <isl/aff.h>
2845 __isl_give isl_multi_pw_aff *
2846 isl_multi_union_pw_aff_extract_multi_pw_aff(
2847 __isl_keep isl_multi_union_pw_aff *mupa,
2848 __isl_take isl_space *space);
2850 Note that there is a difference between C<isl_multi_union_pw_aff>
2851 and C<isl_union_pw_multi_aff> objects. The first is a sequence
2852 of unions of piecewise expressions, while the second is a union
2853 of piecewise sequences. In particular, multiple affine expressions
2854 in an C<isl_union_pw_multi_aff> may live in different spaces,
2855 while there is only a single multiple expression in
2856 an C<isl_multi_union_pw_aff>, which can therefore only live
2857 in a single space. This means that not every
2858 C<isl_union_pw_multi_aff> can be converted to
2859 an C<isl_multi_union_pw_aff>. Conversely, a zero-dimensional
2860 C<isl_multi_union_pw_aff> carries no information
2861 about any possible domain and therefore cannot be converted
2862 to an C<isl_union_pw_multi_aff>. Moreover, the elements
2863 of an C<isl_multi_union_pw_aff> may be defined over different domains,
2864 while each multiple expression inside an C<isl_union_pw_multi_aff>
2865 has a single domain. The conversion of an C<isl_union_pw_multi_aff>
2866 of dimension greater than one may therefore not be exact.
2867 The following functions can
2868 be used to perform these conversions when they are possible.
2870 #include <isl/aff.h>
2871 __isl_give isl_multi_union_pw_aff *
2872 isl_multi_union_pw_aff_from_union_pw_multi_aff(
2873 __isl_take isl_union_pw_multi_aff *upma);
2874 __isl_give isl_union_pw_multi_aff *
2875 isl_union_pw_multi_aff_from_multi_union_pw_aff(
2876 __isl_take isl_multi_union_pw_aff *mupa);
2878 =head3 Piecewise Expressions
2880 A piecewise expression is an expression that is described
2881 using zero or more base expression defined over the same
2882 number of cells in the domain space of the base expressions.
2883 All base expressions are defined over the same
2884 domain space and the cells are disjoint.
2885 The space of a piecewise expression is the same as
2886 that of the base expressions.
2887 If the union of the cells is a strict subset of the domain
2888 space, then the value of the piecewise expression outside
2889 this union is different for types derived from quasi-affine
2890 expressions and those derived from quasipolynomials.
2891 Piecewise expressions derived from quasi-affine expressions
2892 are considered to be undefined outside the union of their cells.
2893 Piecewise expressions derived from quasipolynomials
2894 are considered to be zero outside the union of their cells.
2896 Piecewise quasipolynomials are mainly used by the C<barvinok>
2897 library for representing the number of elements in a parametric set or map.
2898 For example, the piecewise quasipolynomial
2900 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2902 represents the number of points in the map
2904 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2906 The piecewise expression types defined by C<isl>
2907 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
2908 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
2910 A piecewise expression with no cells can be created using
2911 the following functions.
2913 #include <isl/aff.h>
2914 __isl_give isl_pw_aff *isl_pw_aff_empty(
2915 __isl_take isl_space *space);
2916 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
2917 __isl_take isl_space *space);
2919 A piecewise expression with a single universe cell can be
2920 created using the following functions.
2922 #include <isl/aff.h>
2923 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2924 __isl_take isl_aff *aff);
2925 __isl_give isl_pw_multi_aff *
2926 isl_pw_multi_aff_from_multi_aff(
2927 __isl_take isl_multi_aff *ma);
2929 #include <isl/polynomial.h>
2930 __isl_give isl_pw_qpolynomial *
2931 isl_pw_qpolynomial_from_qpolynomial(
2932 __isl_take isl_qpolynomial *qp);
2934 A piecewise expression with a single specified cell can be
2935 created using the following functions.
2937 #include <isl/aff.h>
2938 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2939 __isl_take isl_set *set, __isl_take isl_aff *aff);
2940 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
2941 __isl_take isl_set *set,
2942 __isl_take isl_multi_aff *maff);
2944 #include <isl/polynomial.h>
2945 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2946 __isl_take isl_set *set,
2947 __isl_take isl_qpolynomial *qp);
2949 The following convenience functions first create a base expression and
2950 then create a piecewise expression over a universe domain.
2952 #include <isl/aff.h>
2953 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
2954 __isl_take isl_local_space *ls);
2955 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
2956 __isl_take isl_local_space *ls,
2957 enum isl_dim_type type, unsigned pos);
2958 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
2959 __isl_take isl_local_space *ls);
2960 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
2961 __isl_take isl_space *space);
2962 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
2963 __isl_take isl_space *space);
2964 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
2965 __isl_take isl_space *space);
2966 __isl_give isl_pw_multi_aff *
2967 isl_pw_multi_aff_project_out_map(
2968 __isl_take isl_space *space,
2969 enum isl_dim_type type,
2970 unsigned first, unsigned n);
2972 #include <isl/polynomial.h>
2973 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2974 __isl_take isl_space *space);
2976 The following convenience functions first create a base expression and
2977 then create a piecewise expression over a given domain.
2979 #include <isl/aff.h>
2980 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
2981 __isl_take isl_set *domain,
2982 __isl_take isl_val *v);
2983 __isl_give isl_pw_multi_aff *
2984 isl_pw_multi_aff_multi_val_on_domain(
2985 __isl_take isl_set *domain,
2986 __isl_take isl_multi_val *mv);
2988 As a convenience, a piecewise multiple expression can
2989 also be created from a piecewise expression.
2990 Each multiple expression in the result is derived
2991 from the corresponding base expression.
2993 #include <isl/aff.h>
2994 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
2995 __isl_take isl_pw_aff *pa);
2997 Similarly, a piecewise quasipolynomial can be
2998 created from a piecewise quasi-affine expression using
2999 the following function.
3001 #include <isl/polynomial.h>
3002 __isl_give isl_pw_qpolynomial *
3003 isl_pw_qpolynomial_from_pw_aff(
3004 __isl_take isl_pw_aff *pwaff);
3006 Piecewise expressions can be copied and freed using the following functions.
3008 #include <isl/aff.h>
3009 __isl_give isl_pw_aff *isl_pw_aff_copy(
3010 __isl_keep isl_pw_aff *pwaff);
3011 __isl_null isl_pw_aff *isl_pw_aff_free(
3012 __isl_take isl_pw_aff *pwaff);
3013 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3014 __isl_keep isl_pw_multi_aff *pma);
3015 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
3016 __isl_take isl_pw_multi_aff *pma);
3018 #include <isl/polynomial.h>
3019 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3020 __isl_keep isl_pw_qpolynomial *pwqp);
3021 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
3022 __isl_take isl_pw_qpolynomial *pwqp);
3023 __isl_give isl_pw_qpolynomial_fold *
3024 isl_pw_qpolynomial_fold_copy(
3025 __isl_keep isl_pw_qpolynomial_fold *pwf);
3026 __isl_null isl_pw_qpolynomial_fold *
3027 isl_pw_qpolynomial_fold_free(
3028 __isl_take isl_pw_qpolynomial_fold *pwf);
3030 To iterate over the different cells of a piecewise expression,
3031 use the following functions.
3033 #include <isl/aff.h>
3034 isl_bool isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3035 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3036 isl_stat isl_pw_aff_foreach_piece(
3037 __isl_keep isl_pw_aff *pwaff,
3038 isl_stat (*fn)(__isl_take isl_set *set,
3039 __isl_take isl_aff *aff,
3040 void *user), void *user);
3041 isl_stat isl_pw_multi_aff_foreach_piece(
3042 __isl_keep isl_pw_multi_aff *pma,
3043 isl_stat (*fn)(__isl_take isl_set *set,
3044 __isl_take isl_multi_aff *maff,
3045 void *user), void *user);
3047 #include <isl/polynomial.h>
3048 isl_stat isl_pw_qpolynomial_foreach_piece(
3049 __isl_keep isl_pw_qpolynomial *pwqp,
3050 isl_stat (*fn)(__isl_take isl_set *set,
3051 __isl_take isl_qpolynomial *qp,
3052 void *user), void *user);
3053 isl_stat isl_pw_qpolynomial_foreach_lifted_piece(
3054 __isl_keep isl_pw_qpolynomial *pwqp,
3055 isl_stat (*fn)(__isl_take isl_set *set,
3056 __isl_take isl_qpolynomial *qp,
3057 void *user), void *user);
3058 isl_stat isl_pw_qpolynomial_fold_foreach_piece(
3059 __isl_keep isl_pw_qpolynomial_fold *pwf,
3060 isl_stat (*fn)(__isl_take isl_set *set,
3061 __isl_take isl_qpolynomial_fold *fold,
3062 void *user), void *user);
3063 isl_stat isl_pw_qpolynomial_fold_foreach_lifted_piece(
3064 __isl_keep isl_pw_qpolynomial_fold *pwf,
3065 isl_stat (*fn)(__isl_take isl_set *set,
3066 __isl_take isl_qpolynomial_fold *fold,
3067 void *user), void *user);
3069 As usual, the function C<fn> should return C<0> on success
3070 and C<-1> on failure. The difference between
3071 C<isl_pw_qpolynomial_foreach_piece> and
3072 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3073 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3074 compute unique representations for all existentially quantified
3075 variables and then turn these existentially quantified variables
3076 into extra set variables, adapting the associated quasipolynomial
3077 accordingly. This means that the C<set> passed to C<fn>
3078 will not have any existentially quantified variables, but that
3079 the dimensions of the sets may be different for different
3080 invocations of C<fn>.
3081 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
3082 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
3084 A piecewise expression consisting of the expressions at a given
3085 position of a piecewise multiple expression can be extracted
3086 using the following function.
3088 #include <isl/aff.h>
3089 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3090 __isl_keep isl_pw_multi_aff *pma, int pos);
3092 These expressions can be replaced using the following function.
3094 #include <isl/aff.h>
3095 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3096 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3097 __isl_take isl_pw_aff *pa);
3099 Note that there is a difference between C<isl_multi_pw_aff> and
3100 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
3101 affine expressions, while the second is a piecewise sequence
3102 of affine expressions. In particular, each of the piecewise
3103 affine expressions in an C<isl_multi_pw_aff> may have a different
3104 domain, while all multiple expressions associated to a cell
3105 in an C<isl_pw_multi_aff> have the same domain.
3106 It is possible to convert between the two, but when converting
3107 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
3108 of the result is the intersection of the domains of the input.
3109 The reverse conversion is exact.
3111 #include <isl/aff.h>
3112 __isl_give isl_pw_multi_aff *
3113 isl_pw_multi_aff_from_multi_pw_aff(
3114 __isl_take isl_multi_pw_aff *mpa);
3115 __isl_give isl_multi_pw_aff *
3116 isl_multi_pw_aff_from_pw_multi_aff(
3117 __isl_take isl_pw_multi_aff *pma);
3119 =head3 Union Expressions
3121 A union expression collects base expressions defined
3122 over different domains. The space of a union expression
3123 is that of the shared parameter space.
3125 The union expression types defined by C<isl>
3126 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
3127 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
3129 C<isl_union_pw_aff>,
3130 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>,
3131 there can be at most one base expression for a given domain space.
3133 C<isl_union_pw_multi_aff>,
3134 there can be multiple such expressions for a given domain space,
3135 but the domains of these expressions need to be disjoint.
3137 An empty union expression can be created using the following functions.
3139 #include <isl/aff.h>
3140 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
3141 __isl_take isl_space *space);
3142 __isl_give isl_union_pw_multi_aff *
3143 isl_union_pw_multi_aff_empty(
3144 __isl_take isl_space *space);
3146 #include <isl/polynomial.h>
3147 __isl_give isl_union_pw_qpolynomial *
3148 isl_union_pw_qpolynomial_zero(
3149 __isl_take isl_space *space);
3151 A union expression containing a single base expression
3152 can be created using the following functions.
3154 #include <isl/aff.h>
3155 __isl_give isl_union_pw_aff *
3156 isl_union_pw_aff_from_pw_aff(
3157 __isl_take isl_pw_aff *pa);
3158 __isl_give isl_union_pw_multi_aff *
3159 isl_union_pw_multi_aff_from_aff(
3160 __isl_take isl_aff *aff);
3161 __isl_give isl_union_pw_multi_aff *
3162 isl_union_pw_multi_aff_from_pw_multi_aff(
3163 __isl_take isl_pw_multi_aff *pma);
3165 #include <isl/polynomial.h>
3166 __isl_give isl_union_pw_qpolynomial *
3167 isl_union_pw_qpolynomial_from_pw_qpolynomial(
3168 __isl_take isl_pw_qpolynomial *pwqp);
3170 The following functions create a base expression on each
3171 of the sets in the union set and collect the results.
3173 #include <isl/aff.h>
3174 __isl_give isl_union_pw_multi_aff *
3175 isl_union_pw_multi_aff_from_union_pw_aff(
3176 __isl_take isl_union_pw_aff *upa);
3177 __isl_give isl_union_pw_aff *
3178 isl_union_pw_multi_aff_get_union_pw_aff(
3179 __isl_keep isl_union_pw_multi_aff *upma, int pos);
3180 __isl_give isl_union_pw_aff *
3181 isl_union_pw_aff_val_on_domain(
3182 __isl_take isl_union_set *domain,
3183 __isl_take isl_val *v);
3184 __isl_give isl_union_pw_multi_aff *
3185 isl_union_pw_multi_aff_multi_val_on_domain(
3186 __isl_take isl_union_set *domain,
3187 __isl_take isl_multi_val *mv);
3189 An C<isl_union_pw_aff> that is equal to a (parametric) affine
3190 expression on a given domain can be created using the following
3193 #include <isl/aff.h>
3194 __isl_give isl_union_pw_aff *
3195 isl_union_pw_aff_aff_on_domain(
3196 __isl_take isl_union_set *domain,
3197 __isl_take isl_aff *aff);
3199 A base expression can be added to a union expression using
3200 the following functions.
3202 #include <isl/aff.h>
3203 __isl_give isl_union_pw_aff *
3204 isl_union_pw_aff_add_pw_aff(
3205 __isl_take isl_union_pw_aff *upa,
3206 __isl_take isl_pw_aff *pa);
3207 __isl_give isl_union_pw_multi_aff *
3208 isl_union_pw_multi_aff_add_pw_multi_aff(
3209 __isl_take isl_union_pw_multi_aff *upma,
3210 __isl_take isl_pw_multi_aff *pma);
3212 #include <isl/polynomial.h>
3213 __isl_give isl_union_pw_qpolynomial *
3214 isl_union_pw_qpolynomial_add_pw_qpolynomial(
3215 __isl_take isl_union_pw_qpolynomial *upwqp,
3216 __isl_take isl_pw_qpolynomial *pwqp);
3218 Union expressions can be copied and freed using
3219 the following functions.
3221 #include <isl/aff.h>
3222 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
3223 __isl_keep isl_union_pw_aff *upa);
3224 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
3225 __isl_take isl_union_pw_aff *upa);
3226 __isl_give isl_union_pw_multi_aff *
3227 isl_union_pw_multi_aff_copy(
3228 __isl_keep isl_union_pw_multi_aff *upma);
3229 __isl_null isl_union_pw_multi_aff *
3230 isl_union_pw_multi_aff_free(
3231 __isl_take isl_union_pw_multi_aff *upma);
3233 #include <isl/polynomial.h>
3234 __isl_give isl_union_pw_qpolynomial *
3235 isl_union_pw_qpolynomial_copy(
3236 __isl_keep isl_union_pw_qpolynomial *upwqp);
3237 __isl_null isl_union_pw_qpolynomial *
3238 isl_union_pw_qpolynomial_free(
3239 __isl_take isl_union_pw_qpolynomial *upwqp);
3240 __isl_give isl_union_pw_qpolynomial_fold *
3241 isl_union_pw_qpolynomial_fold_copy(
3242 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3243 __isl_null isl_union_pw_qpolynomial_fold *
3244 isl_union_pw_qpolynomial_fold_free(
3245 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3247 To iterate over the base expressions in a union expression,
3248 use the following functions.
3250 #include <isl/aff.h>
3251 int isl_union_pw_aff_n_pw_aff(
3252 __isl_keep isl_union_pw_aff *upa);
3253 isl_stat isl_union_pw_aff_foreach_pw_aff(
3254 __isl_keep isl_union_pw_aff *upa,
3255 isl_stat (*fn)(__isl_take isl_pw_aff *ma,
3256 void *user), void *user);
3257 int isl_union_pw_multi_aff_n_pw_multi_aff(
3258 __isl_keep isl_union_pw_multi_aff *upma);
3259 isl_stat isl_union_pw_multi_aff_foreach_pw_multi_aff(
3260 __isl_keep isl_union_pw_multi_aff *upma,
3261 isl_stat (*fn)(__isl_take isl_pw_multi_aff *pma,
3262 void *user), void *user);
3264 #include <isl/polynomial.h>
3265 int isl_union_pw_qpolynomial_n_pw_qpolynomial(
3266 __isl_keep isl_union_pw_qpolynomial *upwqp);
3267 isl_stat isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3268 __isl_keep isl_union_pw_qpolynomial *upwqp,
3269 isl_stat (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
3270 void *user), void *user);
3271 int isl_union_pw_qpolynomial_fold_n_pw_qpolynomial_fold(
3272 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3273 isl_stat isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3274 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3275 isl_stat (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3276 void *user), void *user);
3278 To extract the base expression in a given space from a union, use
3279 the following functions.
3281 #include <isl/aff.h>
3282 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
3283 __isl_keep isl_union_pw_aff *upa,
3284 __isl_take isl_space *space);
3285 __isl_give isl_pw_multi_aff *
3286 isl_union_pw_multi_aff_extract_pw_multi_aff(
3287 __isl_keep isl_union_pw_multi_aff *upma,
3288 __isl_take isl_space *space);
3290 #include <isl/polynomial.h>
3291 __isl_give isl_pw_qpolynomial *
3292 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3293 __isl_keep isl_union_pw_qpolynomial *upwqp,
3294 __isl_take isl_space *space);
3296 =head2 Input and Output
3298 For set and relation,
3299 C<isl> supports its own input/output format, which is similar
3300 to the C<Omega> format, but also supports the C<PolyLib> format
3302 For other object types, typically only an C<isl> format is supported.
3304 =head3 C<isl> format
3306 The C<isl> format is similar to that of C<Omega>, but has a different
3307 syntax for describing the parameters and allows for the definition
3308 of an existentially quantified variable as the integer division
3309 of an affine expression.
3310 For example, the set of integers C<i> between C<0> and C<n>
3311 such that C<i % 10 <= 6> can be described as
3313 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
3316 A set or relation can have several disjuncts, separated
3317 by the keyword C<or>. Each disjunct is either a conjunction
3318 of constraints or a projection (C<exists>) of a conjunction
3319 of constraints. The constraints are separated by the keyword
3322 =head3 C<PolyLib> format
3324 If the represented set is a union, then the first line
3325 contains a single number representing the number of disjuncts.
3326 Otherwise, a line containing the number C<1> is optional.
3328 Each disjunct is represented by a matrix of constraints.
3329 The first line contains two numbers representing
3330 the number of rows and columns,
3331 where the number of rows is equal to the number of constraints
3332 and the number of columns is equal to two plus the number of variables.
3333 The following lines contain the actual rows of the constraint matrix.
3334 In each row, the first column indicates whether the constraint
3335 is an equality (C<0>) or inequality (C<1>). The final column
3336 corresponds to the constant term.
3338 If the set is parametric, then the coefficients of the parameters
3339 appear in the last columns before the constant column.
3340 The coefficients of any existentially quantified variables appear
3341 between those of the set variables and those of the parameters.
3343 =head3 Extended C<PolyLib> format
3345 The extended C<PolyLib> format is nearly identical to the
3346 C<PolyLib> format. The only difference is that the line
3347 containing the number of rows and columns of a constraint matrix
3348 also contains four additional numbers:
3349 the number of output dimensions, the number of input dimensions,
3350 the number of local dimensions (i.e., the number of existentially
3351 quantified variables) and the number of parameters.
3352 For sets, the number of ``output'' dimensions is equal
3353 to the number of set dimensions, while the number of ``input''
3358 Objects can be read from input using the following functions.
3360 #include <isl/val.h>
3361 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
3363 __isl_give isl_multi_val *isl_multi_val_read_from_str(
3364 isl_ctx *ctx, const char *str);
3366 #include <isl/set.h>
3367 __isl_give isl_basic_set *isl_basic_set_read_from_file(
3368 isl_ctx *ctx, FILE *input);
3369 __isl_give isl_basic_set *isl_basic_set_read_from_str(
3370 isl_ctx *ctx, const char *str);
3371 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
3373 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
3376 #include <isl/map.h>
3377 __isl_give isl_basic_map *isl_basic_map_read_from_file(
3378 isl_ctx *ctx, FILE *input);
3379 __isl_give isl_basic_map *isl_basic_map_read_from_str(
3380 isl_ctx *ctx, const char *str);
3381 __isl_give isl_map *isl_map_read_from_file(
3382 isl_ctx *ctx, FILE *input);
3383 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
3386 #include <isl/union_set.h>
3387 __isl_give isl_union_set *isl_union_set_read_from_file(
3388 isl_ctx *ctx, FILE *input);
3389 __isl_give isl_union_set *isl_union_set_read_from_str(
3390 isl_ctx *ctx, const char *str);
3392 #include <isl/union_map.h>
3393 __isl_give isl_union_map *isl_union_map_read_from_file(
3394 isl_ctx *ctx, FILE *input);
3395 __isl_give isl_union_map *isl_union_map_read_from_str(
3396 isl_ctx *ctx, const char *str);
3398 #include <isl/aff.h>
3399 __isl_give isl_aff *isl_aff_read_from_str(
3400 isl_ctx *ctx, const char *str);
3401 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3402 isl_ctx *ctx, const char *str);
3403 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3404 isl_ctx *ctx, const char *str);
3405 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3406 isl_ctx *ctx, const char *str);
3407 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
3408 isl_ctx *ctx, const char *str);
3409 __isl_give isl_union_pw_multi_aff *
3410 isl_union_pw_multi_aff_read_from_str(
3411 isl_ctx *ctx, const char *str);
3412 __isl_give isl_multi_union_pw_aff *
3413 isl_multi_union_pw_aff_read_from_str(
3414 isl_ctx *ctx, const char *str);
3416 #include <isl/polynomial.h>
3417 __isl_give isl_union_pw_qpolynomial *
3418 isl_union_pw_qpolynomial_read_from_str(
3419 isl_ctx *ctx, const char *str);
3421 For sets and relations,
3422 the input format is autodetected and may be either the C<PolyLib> format
3423 or the C<isl> format.
3427 Before anything can be printed, an C<isl_printer> needs to
3430 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
3432 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
3433 __isl_null isl_printer *isl_printer_free(
3434 __isl_take isl_printer *printer);
3435 __isl_give char *isl_printer_get_str(
3436 __isl_keep isl_printer *printer);
3438 The printer can be inspected using the following functions.
3440 FILE *isl_printer_get_file(
3441 __isl_keep isl_printer *printer);
3442 int isl_printer_get_output_format(
3443 __isl_keep isl_printer *p);
3444 int isl_printer_get_yaml_style(__isl_keep isl_printer *p);
3446 The behavior of the printer can be modified in various ways
3448 __isl_give isl_printer *isl_printer_set_output_format(
3449 __isl_take isl_printer *p, int output_format);
3450 __isl_give isl_printer *isl_printer_set_indent(
3451 __isl_take isl_printer *p, int indent);
3452 __isl_give isl_printer *isl_printer_set_indent_prefix(
3453 __isl_take isl_printer *p, const char *prefix);
3454 __isl_give isl_printer *isl_printer_indent(
3455 __isl_take isl_printer *p, int indent);
3456 __isl_give isl_printer *isl_printer_set_prefix(
3457 __isl_take isl_printer *p, const char *prefix);
3458 __isl_give isl_printer *isl_printer_set_suffix(
3459 __isl_take isl_printer *p, const char *suffix);
3460 __isl_give isl_printer *isl_printer_set_yaml_style(
3461 __isl_take isl_printer *p, int yaml_style);
3463 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
3464 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
3465 and defaults to C<ISL_FORMAT_ISL>.
3466 Each line in the output is prefixed by C<indent_prefix>,
3467 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
3468 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
3469 In the C<PolyLib> format output,
3470 the coefficients of the existentially quantified variables
3471 appear between those of the set variables and those
3473 The function C<isl_printer_indent> increases the indentation
3474 by the specified amount (which may be negative).
3475 The YAML style may be either C<ISL_YAML_STYLE_BLOCK> or
3476 C<ISL_YAML_STYLE_FLOW> and when we are printing something
3479 To actually print something, use
3481 #include <isl/printer.h>
3482 __isl_give isl_printer *isl_printer_print_double(
3483 __isl_take isl_printer *p, double d);
3485 #include <isl/val.h>
3486 __isl_give isl_printer *isl_printer_print_val(
3487 __isl_take isl_printer *p, __isl_keep isl_val *v);
3489 #include <isl/set.h>
3490 __isl_give isl_printer *isl_printer_print_basic_set(
3491 __isl_take isl_printer *printer,
3492 __isl_keep isl_basic_set *bset);
3493 __isl_give isl_printer *isl_printer_print_set(
3494 __isl_take isl_printer *printer,
3495 __isl_keep isl_set *set);
3497 #include <isl/map.h>
3498 __isl_give isl_printer *isl_printer_print_basic_map(
3499 __isl_take isl_printer *printer,
3500 __isl_keep isl_basic_map *bmap);
3501 __isl_give isl_printer *isl_printer_print_map(
3502 __isl_take isl_printer *printer,
3503 __isl_keep isl_map *map);
3505 #include <isl/union_set.h>
3506 __isl_give isl_printer *isl_printer_print_union_set(
3507 __isl_take isl_printer *p,
3508 __isl_keep isl_union_set *uset);
3510 #include <isl/union_map.h>
3511 __isl_give isl_printer *isl_printer_print_union_map(
3512 __isl_take isl_printer *p,
3513 __isl_keep isl_union_map *umap);
3515 #include <isl/val.h>
3516 __isl_give isl_printer *isl_printer_print_multi_val(
3517 __isl_take isl_printer *p,
3518 __isl_keep isl_multi_val *mv);
3520 #include <isl/aff.h>
3521 __isl_give isl_printer *isl_printer_print_aff(
3522 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3523 __isl_give isl_printer *isl_printer_print_multi_aff(
3524 __isl_take isl_printer *p,
3525 __isl_keep isl_multi_aff *maff);
3526 __isl_give isl_printer *isl_printer_print_pw_aff(
3527 __isl_take isl_printer *p,
3528 __isl_keep isl_pw_aff *pwaff);
3529 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3530 __isl_take isl_printer *p,
3531 __isl_keep isl_pw_multi_aff *pma);
3532 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3533 __isl_take isl_printer *p,
3534 __isl_keep isl_multi_pw_aff *mpa);
3535 __isl_give isl_printer *isl_printer_print_union_pw_aff(
3536 __isl_take isl_printer *p,
3537 __isl_keep isl_union_pw_aff *upa);
3538 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3539 __isl_take isl_printer *p,
3540 __isl_keep isl_union_pw_multi_aff *upma);
3541 __isl_give isl_printer *
3542 isl_printer_print_multi_union_pw_aff(
3543 __isl_take isl_printer *p,
3544 __isl_keep isl_multi_union_pw_aff *mupa);
3546 #include <isl/polynomial.h>
3547 __isl_give isl_printer *isl_printer_print_qpolynomial(
3548 __isl_take isl_printer *p,
3549 __isl_keep isl_qpolynomial *qp);
3550 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3551 __isl_take isl_printer *p,
3552 __isl_keep isl_pw_qpolynomial *pwqp);
3553 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3554 __isl_take isl_printer *p,
3555 __isl_keep isl_union_pw_qpolynomial *upwqp);
3557 __isl_give isl_printer *
3558 isl_printer_print_pw_qpolynomial_fold(
3559 __isl_take isl_printer *p,
3560 __isl_keep isl_pw_qpolynomial_fold *pwf);
3561 __isl_give isl_printer *
3562 isl_printer_print_union_pw_qpolynomial_fold(
3563 __isl_take isl_printer *p,
3564 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3566 For C<isl_printer_print_qpolynomial>,
3567 C<isl_printer_print_pw_qpolynomial> and
3568 C<isl_printer_print_pw_qpolynomial_fold>,
3569 the output format of the printer
3570 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3571 For C<isl_printer_print_union_pw_qpolynomial> and
3572 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
3574 In case of printing in C<ISL_FORMAT_C>, the user may want
3575 to set the names of all dimensions first.
3577 C<isl> also provides limited support for printing YAML documents,
3578 just enough for the internal use for printing such documents.
3580 #include <isl/printer.h>
3581 __isl_give isl_printer *isl_printer_yaml_start_mapping(
3582 __isl_take isl_printer *p);
3583 __isl_give isl_printer *isl_printer_yaml_end_mapping(
3584 __isl_take isl_printer *p);
3585 __isl_give isl_printer *isl_printer_yaml_start_sequence(
3586 __isl_take isl_printer *p);
3587 __isl_give isl_printer *isl_printer_yaml_end_sequence(
3588 __isl_take isl_printer *p);
3589 __isl_give isl_printer *isl_printer_yaml_next(
3590 __isl_take isl_printer *p);
3592 A document is started by a call to either
3593 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3594 Anything printed to the printer after such a call belong to the
3595 first key of the mapping or the first element in the sequence.
3596 The function C<isl_printer_yaml_next> moves to the value if
3597 we are currently printing a mapping key, the next key if we
3598 are printing a value or the next element if we are printing
3599 an element in a sequence.
3600 Nested mappings and sequences are initiated by the same
3601 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3602 Each call to these functions needs to have a corresponding call to
3603 C<isl_printer_yaml_end_mapping> or C<isl_printer_yaml_end_sequence>.
3605 When called on a file printer, the following function flushes
3606 the file. When called on a string printer, the buffer is cleared.
3608 __isl_give isl_printer *isl_printer_flush(
3609 __isl_take isl_printer *p);
3611 Alternatively, a string representation can be obtained
3612 directly using the following functions, which always print
3615 #include <isl/space.h>
3616 __isl_give char *isl_space_to_str(
3617 __isl_keep isl_space *space);
3619 #include <isl/val.h>
3620 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
3621 __isl_give char *isl_multi_val_to_str(
3622 __isl_keep isl_multi_val *mv);
3624 #include <isl/set.h>
3625 __isl_give char *isl_set_to_str(
3626 __isl_keep isl_set *set);
3628 #include <isl/union_set.h>
3629 __isl_give char *isl_union_set_to_str(
3630 __isl_keep isl_union_set *uset);
3632 #include <isl/map.h>
3633 __isl_give char *isl_map_to_str(
3634 __isl_keep isl_map *map);
3636 #include <isl/union_map.h>
3637 __isl_give char *isl_union_map_to_str(
3638 __isl_keep isl_union_map *umap);
3640 #include <isl/aff.h>
3641 __isl_give char *isl_multi_aff_to_str(
3642 __isl_keep isl_multi_aff *aff);
3643 __isl_give char *isl_union_pw_aff_to_str(
3644 __isl_keep isl_union_pw_aff *upa);
3645 __isl_give char *isl_union_pw_multi_aff_to_str(
3646 __isl_keep isl_union_pw_multi_aff *upma);
3647 __isl_give char *isl_multi_union_pw_aff_to_str(
3648 __isl_keep isl_multi_union_pw_aff *mupa);
3652 =head3 Unary Properties
3658 The following functions test whether the given set or relation
3659 contains any integer points. The ``plain'' variants do not perform
3660 any computations, but simply check if the given set or relation
3661 is already known to be empty.
3663 isl_bool isl_basic_set_plain_is_empty(
3664 __isl_keep isl_basic_set *bset);
3665 isl_bool isl_basic_set_is_empty(
3666 __isl_keep isl_basic_set *bset);
3667 isl_bool isl_set_plain_is_empty(
3668 __isl_keep isl_set *set);
3669 isl_bool isl_set_is_empty(__isl_keep isl_set *set);
3670 isl_bool isl_union_set_is_empty(
3671 __isl_keep isl_union_set *uset);
3672 isl_bool isl_basic_map_plain_is_empty(
3673 __isl_keep isl_basic_map *bmap);
3674 isl_bool isl_basic_map_is_empty(
3675 __isl_keep isl_basic_map *bmap);
3676 isl_bool isl_map_plain_is_empty(
3677 __isl_keep isl_map *map);
3678 isl_bool isl_map_is_empty(__isl_keep isl_map *map);
3679 isl_bool isl_union_map_is_empty(
3680 __isl_keep isl_union_map *umap);
3682 =item * Universality
3684 isl_bool isl_basic_set_is_universe(
3685 __isl_keep isl_basic_set *bset);
3686 isl_bool isl_basic_map_is_universe(
3687 __isl_keep isl_basic_map *bmap);
3688 isl_bool isl_set_plain_is_universe(
3689 __isl_keep isl_set *set);
3690 isl_bool isl_map_plain_is_universe(
3691 __isl_keep isl_map *map);
3693 =item * Single-valuedness
3695 #include <isl/set.h>
3696 isl_bool isl_set_is_singleton(__isl_keep isl_set *set);
3698 #include <isl/map.h>
3699 isl_bool isl_basic_map_is_single_valued(
3700 __isl_keep isl_basic_map *bmap);
3701 isl_bool isl_map_plain_is_single_valued(
3702 __isl_keep isl_map *map);
3703 isl_bool isl_map_is_single_valued(__isl_keep isl_map *map);
3705 #include <isl/union_map.h>
3706 isl_bool isl_union_map_is_single_valued(
3707 __isl_keep isl_union_map *umap);
3711 isl_bool isl_map_plain_is_injective(
3712 __isl_keep isl_map *map);
3713 isl_bool isl_map_is_injective(
3714 __isl_keep isl_map *map);
3715 isl_bool isl_union_map_plain_is_injective(
3716 __isl_keep isl_union_map *umap);
3717 isl_bool isl_union_map_is_injective(
3718 __isl_keep isl_union_map *umap);
3722 isl_bool isl_map_is_bijective(
3723 __isl_keep isl_map *map);
3724 isl_bool isl_union_map_is_bijective(
3725 __isl_keep isl_union_map *umap);
3729 __isl_give isl_val *
3730 isl_basic_map_plain_get_val_if_fixed(
3731 __isl_keep isl_basic_map *bmap,
3732 enum isl_dim_type type, unsigned pos);
3733 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
3734 __isl_keep isl_set *set,
3735 enum isl_dim_type type, unsigned pos);
3736 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
3737 __isl_keep isl_map *map,
3738 enum isl_dim_type type, unsigned pos);
3740 If the set or relation obviously lies on a hyperplane where the given dimension
3741 has a fixed value, then return that value.
3742 Otherwise return NaN.
3746 isl_stat isl_set_dim_residue_class_val(
3747 __isl_keep isl_set *set,
3748 int pos, __isl_give isl_val **modulo,
3749 __isl_give isl_val **residue);
3751 Check if the values of the given set dimension are equal to a fixed
3752 value modulo some integer value. If so, assign the modulo to C<*modulo>
3753 and the fixed value to C<*residue>. If the given dimension attains only
3754 a single value, then assign C<0> to C<*modulo> and the fixed value to
3756 If the dimension does not attain only a single value and if no modulo
3757 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
3761 To check whether the description of a set, relation or function depends
3762 on one or more given dimensions,
3763 the following functions can be used.
3765 #include <isl/constraint.h>
3766 isl_bool isl_constraint_involves_dims(
3767 __isl_keep isl_constraint *constraint,
3768 enum isl_dim_type type, unsigned first, unsigned n);
3770 #include <isl/set.h>
3771 isl_bool isl_basic_set_involves_dims(
3772 __isl_keep isl_basic_set *bset,
3773 enum isl_dim_type type, unsigned first, unsigned n);
3774 isl_bool isl_set_involves_dims(__isl_keep isl_set *set,
3775 enum isl_dim_type type, unsigned first, unsigned n);
3777 #include <isl/map.h>
3778 isl_bool isl_basic_map_involves_dims(
3779 __isl_keep isl_basic_map *bmap,
3780 enum isl_dim_type type, unsigned first, unsigned n);
3781 isl_bool isl_map_involves_dims(__isl_keep isl_map *map,
3782 enum isl_dim_type type, unsigned first, unsigned n);
3784 #include <isl/union_map.h>
3785 isl_bool isl_union_map_involves_dims(
3786 __isl_keep isl_union_map *umap,
3787 enum isl_dim_type type, unsigned first, unsigned n);
3789 #include <isl/aff.h>
3790 isl_bool isl_aff_involves_dims(__isl_keep isl_aff *aff,
3791 enum isl_dim_type type, unsigned first, unsigned n);
3792 isl_bool isl_pw_aff_involves_dims(
3793 __isl_keep isl_pw_aff *pwaff,
3794 enum isl_dim_type type, unsigned first, unsigned n);
3795 isl_bool isl_multi_aff_involves_dims(
3796 __isl_keep isl_multi_aff *ma,
3797 enum isl_dim_type type, unsigned first, unsigned n);
3798 isl_bool isl_multi_pw_aff_involves_dims(
3799 __isl_keep isl_multi_pw_aff *mpa,
3800 enum isl_dim_type type, unsigned first, unsigned n);
3802 #include <isl/polynomial.h>
3803 isl_bool isl_qpolynomial_involves_dims(
3804 __isl_keep isl_qpolynomial *qp,
3805 enum isl_dim_type type, unsigned first, unsigned n);
3807 Similarly, the following functions can be used to check whether
3808 a given dimension is involved in any lower or upper bound.
3810 #include <isl/set.h>
3811 isl_bool isl_set_dim_has_any_lower_bound(
3812 __isl_keep isl_set *set,
3813 enum isl_dim_type type, unsigned pos);
3814 isl_bool isl_set_dim_has_any_upper_bound(
3815 __isl_keep isl_set *set,
3816 enum isl_dim_type type, unsigned pos);
3818 Note that these functions return true even if there is a bound on
3819 the dimension on only some of the basic sets of C<set>.
3820 To check if they have a bound for all of the basic sets in C<set>,
3821 use the following functions instead.
3823 #include <isl/set.h>
3824 isl_bool isl_set_dim_has_lower_bound(
3825 __isl_keep isl_set *set,
3826 enum isl_dim_type type, unsigned pos);
3827 isl_bool isl_set_dim_has_upper_bound(
3828 __isl_keep isl_set *set,
3829 enum isl_dim_type type, unsigned pos);
3833 To check whether a set is a parameter domain, use this function:
3835 isl_bool isl_set_is_params(__isl_keep isl_set *set);
3836 isl_bool isl_union_set_is_params(
3837 __isl_keep isl_union_set *uset);
3841 The following functions check whether the space of the given
3842 (basic) set or relation range is a wrapped relation.
3844 #include <isl/space.h>
3845 isl_bool isl_space_is_wrapping(
3846 __isl_keep isl_space *space);
3847 isl_bool isl_space_domain_is_wrapping(
3848 __isl_keep isl_space *space);
3849 isl_bool isl_space_range_is_wrapping(
3850 __isl_keep isl_space *space);
3852 #include <isl/set.h>
3853 isl_bool isl_basic_set_is_wrapping(
3854 __isl_keep isl_basic_set *bset);
3855 isl_bool isl_set_is_wrapping(__isl_keep isl_set *set);
3857 #include <isl/map.h>
3858 isl_bool isl_map_domain_is_wrapping(
3859 __isl_keep isl_map *map);
3860 isl_bool isl_map_range_is_wrapping(
3861 __isl_keep isl_map *map);
3863 #include <isl/val.h>
3864 isl_bool isl_multi_val_range_is_wrapping(
3865 __isl_keep isl_multi_val *mv);
3867 #include <isl/aff.h>
3868 isl_bool isl_multi_aff_range_is_wrapping(
3869 __isl_keep isl_multi_aff *ma);
3870 isl_bool isl_multi_pw_aff_range_is_wrapping(
3871 __isl_keep isl_multi_pw_aff *mpa);
3872 isl_bool isl_multi_union_pw_aff_range_is_wrapping(
3873 __isl_keep isl_multi_union_pw_aff *mupa);
3875 The input to C<isl_space_is_wrapping> should
3876 be the space of a set, while that of
3877 C<isl_space_domain_is_wrapping> and
3878 C<isl_space_range_is_wrapping> should be the space of a relation.
3880 =item * Internal Product
3882 isl_bool isl_basic_map_can_zip(
3883 __isl_keep isl_basic_map *bmap);
3884 isl_bool isl_map_can_zip(__isl_keep isl_map *map);
3886 Check whether the product of domain and range of the given relation
3888 i.e., whether both domain and range are nested relations.
3892 isl_bool isl_basic_map_can_curry(
3893 __isl_keep isl_basic_map *bmap);
3894 isl_bool isl_map_can_curry(__isl_keep isl_map *map);
3896 Check whether the domain of the (basic) relation is a wrapped relation.
3898 isl_bool isl_basic_map_can_uncurry(
3899 __isl_keep isl_basic_map *bmap);
3900 isl_bool isl_map_can_uncurry(__isl_keep isl_map *map);
3902 Check whether the range of the (basic) relation is a wrapped relation.
3904 =item * Special Values
3906 #include <isl/aff.h>
3907 isl_bool isl_aff_is_cst(__isl_keep isl_aff *aff);
3908 isl_bool isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3910 Check whether the given expression is a constant.
3912 #include <isl/aff.h>
3913 isl_bool isl_aff_is_nan(__isl_keep isl_aff *aff);
3914 isl_bool isl_pw_aff_involves_nan(
3915 __isl_keep isl_pw_aff *pa);
3917 #include <isl/polynomial.h>
3918 isl_bool isl_qpolynomial_fold_is_nan(
3919 __isl_keep isl_qpolynomial_fold *fold);
3921 Check whether the given expression is equal to or involves NaN.
3923 #include <isl/aff.h>
3924 isl_bool isl_aff_plain_is_zero(
3925 __isl_keep isl_aff *aff);
3927 Check whether the affine expression is obviously zero.
3931 =head3 Binary Properties
3937 The following functions check whether two objects
3938 represent the same set, relation or function.
3939 The C<plain> variants only return true if the objects
3940 are obviously the same. That is, they may return false
3941 even if the objects are the same, but they will never
3942 return true if the objects are not the same.
3944 #include <isl/set.h>
3945 isl_bool isl_basic_set_plain_is_equal(
3946 __isl_keep isl_basic_set *bset1,
3947 __isl_keep isl_basic_set *bset2);
3948 isl_bool isl_basic_set_is_equal(
3949 __isl_keep isl_basic_set *bset1,
3950 __isl_keep isl_basic_set *bset2);
3951 isl_bool isl_set_plain_is_equal(
3952 __isl_keep isl_set *set1,
3953 __isl_keep isl_set *set2);
3954 isl_bool isl_set_is_equal(__isl_keep isl_set *set1,
3955 __isl_keep isl_set *set2);
3957 #include <isl/map.h>
3958 isl_bool isl_basic_map_is_equal(
3959 __isl_keep isl_basic_map *bmap1,
3960 __isl_keep isl_basic_map *bmap2);
3961 isl_bool isl_map_is_equal(__isl_keep isl_map *map1,
3962 __isl_keep isl_map *map2);
3963 isl_bool isl_map_plain_is_equal(
3964 __isl_keep isl_map *map1,
3965 __isl_keep isl_map *map2);
3967 #include <isl/union_set.h>
3968 isl_bool isl_union_set_is_equal(
3969 __isl_keep isl_union_set *uset1,
3970 __isl_keep isl_union_set *uset2);
3972 #include <isl/union_map.h>
3973 isl_bool isl_union_map_is_equal(
3974 __isl_keep isl_union_map *umap1,
3975 __isl_keep isl_union_map *umap2);
3977 #include <isl/aff.h>
3978 isl_bool isl_aff_plain_is_equal(
3979 __isl_keep isl_aff *aff1,
3980 __isl_keep isl_aff *aff2);
3981 isl_bool isl_multi_aff_plain_is_equal(
3982 __isl_keep isl_multi_aff *maff1,
3983 __isl_keep isl_multi_aff *maff2);
3984 isl_bool isl_pw_aff_plain_is_equal(
3985 __isl_keep isl_pw_aff *pwaff1,
3986 __isl_keep isl_pw_aff *pwaff2);
3987 isl_bool isl_pw_multi_aff_plain_is_equal(
3988 __isl_keep isl_pw_multi_aff *pma1,
3989 __isl_keep isl_pw_multi_aff *pma2);
3990 isl_bool isl_multi_pw_aff_plain_is_equal(
3991 __isl_keep isl_multi_pw_aff *mpa1,
3992 __isl_keep isl_multi_pw_aff *mpa2);
3993 isl_bool isl_multi_pw_aff_is_equal(
3994 __isl_keep isl_multi_pw_aff *mpa1,
3995 __isl_keep isl_multi_pw_aff *mpa2);
3996 isl_bool isl_union_pw_aff_plain_is_equal(
3997 __isl_keep isl_union_pw_aff *upa1,
3998 __isl_keep isl_union_pw_aff *upa2);
3999 isl_bool isl_union_pw_multi_aff_plain_is_equal(
4000 __isl_keep isl_union_pw_multi_aff *upma1,
4001 __isl_keep isl_union_pw_multi_aff *upma2);
4002 isl_bool isl_multi_union_pw_aff_plain_is_equal(
4003 __isl_keep isl_multi_union_pw_aff *mupa1,
4004 __isl_keep isl_multi_union_pw_aff *mupa2);
4006 #include <isl/polynomial.h>
4007 isl_bool isl_union_pw_qpolynomial_plain_is_equal(
4008 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4009 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4010 isl_bool isl_union_pw_qpolynomial_fold_plain_is_equal(
4011 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4012 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4014 =item * Disjointness
4016 #include <isl/set.h>
4017 isl_bool isl_basic_set_is_disjoint(
4018 __isl_keep isl_basic_set *bset1,
4019 __isl_keep isl_basic_set *bset2);
4020 isl_bool isl_set_plain_is_disjoint(
4021 __isl_keep isl_set *set1,
4022 __isl_keep isl_set *set2);
4023 isl_bool isl_set_is_disjoint(__isl_keep isl_set *set1,
4024 __isl_keep isl_set *set2);
4026 #include <isl/map.h>
4027 isl_bool isl_basic_map_is_disjoint(
4028 __isl_keep isl_basic_map *bmap1,
4029 __isl_keep isl_basic_map *bmap2);
4030 isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1,
4031 __isl_keep isl_map *map2);
4033 #include <isl/union_set.h>
4034 isl_bool isl_union_set_is_disjoint(
4035 __isl_keep isl_union_set *uset1,
4036 __isl_keep isl_union_set *uset2);
4038 #include <isl/union_map.h>
4039 isl_bool isl_union_map_is_disjoint(
4040 __isl_keep isl_union_map *umap1,
4041 __isl_keep isl_union_map *umap2);
4045 isl_bool isl_basic_set_is_subset(
4046 __isl_keep isl_basic_set *bset1,
4047 __isl_keep isl_basic_set *bset2);
4048 isl_bool isl_set_is_subset(__isl_keep isl_set *set1,
4049 __isl_keep isl_set *set2);
4050 isl_bool isl_set_is_strict_subset(
4051 __isl_keep isl_set *set1,
4052 __isl_keep isl_set *set2);
4053 isl_bool isl_union_set_is_subset(
4054 __isl_keep isl_union_set *uset1,
4055 __isl_keep isl_union_set *uset2);
4056 isl_bool isl_union_set_is_strict_subset(
4057 __isl_keep isl_union_set *uset1,
4058 __isl_keep isl_union_set *uset2);
4059 isl_bool isl_basic_map_is_subset(
4060 __isl_keep isl_basic_map *bmap1,
4061 __isl_keep isl_basic_map *bmap2);
4062 isl_bool isl_basic_map_is_strict_subset(
4063 __isl_keep isl_basic_map *bmap1,
4064 __isl_keep isl_basic_map *bmap2);
4065 isl_bool isl_map_is_subset(
4066 __isl_keep isl_map *map1,
4067 __isl_keep isl_map *map2);
4068 isl_bool isl_map_is_strict_subset(
4069 __isl_keep isl_map *map1,
4070 __isl_keep isl_map *map2);
4071 isl_bool isl_union_map_is_subset(
4072 __isl_keep isl_union_map *umap1,
4073 __isl_keep isl_union_map *umap2);
4074 isl_bool isl_union_map_is_strict_subset(
4075 __isl_keep isl_union_map *umap1,
4076 __isl_keep isl_union_map *umap2);
4078 Check whether the first argument is a (strict) subset of the
4083 Every comparison function returns a negative value if the first
4084 argument is considered smaller than the second, a positive value
4085 if the first argument is considered greater and zero if the two
4086 constraints are considered the same by the comparison criterion.
4088 #include <isl/constraint.h>
4089 int isl_constraint_plain_cmp(
4090 __isl_keep isl_constraint *c1,
4091 __isl_keep isl_constraint *c2);
4093 This function is useful for sorting C<isl_constraint>s.
4094 The order depends on the internal representation of the inputs.
4095 The order is fixed over different calls to the function (assuming
4096 the internal representation of the inputs has not changed), but may
4097 change over different versions of C<isl>.
4099 #include <isl/constraint.h>
4100 int isl_constraint_cmp_last_non_zero(
4101 __isl_keep isl_constraint *c1,
4102 __isl_keep isl_constraint *c2);
4104 This function can be used to sort constraints that live in the same
4105 local space. Constraints that involve ``earlier'' dimensions or
4106 that have a smaller coefficient for the shared latest dimension
4107 are considered smaller than other constraints.
4108 This function only defines a B<partial> order.
4110 #include <isl/set.h>
4111 int isl_set_plain_cmp(__isl_keep isl_set *set1,
4112 __isl_keep isl_set *set2);
4114 This function is useful for sorting C<isl_set>s.
4115 The order depends on the internal representation of the inputs.
4116 The order is fixed over different calls to the function (assuming
4117 the internal representation of the inputs has not changed), but may
4118 change over different versions of C<isl>.
4120 #include <isl/aff.h>
4121 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4122 __isl_keep isl_pw_aff *pa2);
4124 The function C<isl_pw_aff_plain_cmp> can be used to sort
4125 C<isl_pw_aff>s. The order is not strictly defined.
4126 The current order sorts expressions that only involve
4127 earlier dimensions before those that involve later dimensions.
4131 =head2 Unary Operations
4137 __isl_give isl_set *isl_set_complement(
4138 __isl_take isl_set *set);
4139 __isl_give isl_map *isl_map_complement(
4140 __isl_take isl_map *map);
4144 #include <isl/space.h>
4145 __isl_give isl_space *isl_space_reverse(
4146 __isl_take isl_space *space);
4148 #include <isl/map.h>
4149 __isl_give isl_basic_map *isl_basic_map_reverse(
4150 __isl_take isl_basic_map *bmap);
4151 __isl_give isl_map *isl_map_reverse(
4152 __isl_take isl_map *map);
4154 #include <isl/union_map.h>
4155 __isl_give isl_union_map *isl_union_map_reverse(
4156 __isl_take isl_union_map *umap);
4160 #include <isl/space.h>
4161 __isl_give isl_space *isl_space_domain(
4162 __isl_take isl_space *space);
4163 __isl_give isl_space *isl_space_range(
4164 __isl_take isl_space *space);
4165 __isl_give isl_space *isl_space_params(
4166 __isl_take isl_space *space);
4168 #include <isl/local_space.h>
4169 __isl_give isl_local_space *isl_local_space_domain(
4170 __isl_take isl_local_space *ls);
4171 __isl_give isl_local_space *isl_local_space_range(
4172 __isl_take isl_local_space *ls);
4174 #include <isl/set.h>
4175 __isl_give isl_basic_set *isl_basic_set_project_out(
4176 __isl_take isl_basic_set *bset,
4177 enum isl_dim_type type, unsigned first, unsigned n);
4178 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
4179 enum isl_dim_type type, unsigned first, unsigned n);
4180 __isl_give isl_basic_set *isl_basic_set_params(
4181 __isl_take isl_basic_set *bset);
4182 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
4184 #include <isl/map.h>
4185 __isl_give isl_basic_map *isl_basic_map_project_out(
4186 __isl_take isl_basic_map *bmap,
4187 enum isl_dim_type type, unsigned first, unsigned n);
4188 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
4189 enum isl_dim_type type, unsigned first, unsigned n);
4190 __isl_give isl_basic_set *isl_basic_map_domain(
4191 __isl_take isl_basic_map *bmap);
4192 __isl_give isl_basic_set *isl_basic_map_range(
4193 __isl_take isl_basic_map *bmap);
4194 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
4195 __isl_give isl_set *isl_map_domain(
4196 __isl_take isl_map *bmap);
4197 __isl_give isl_set *isl_map_range(
4198 __isl_take isl_map *map);
4200 #include <isl/union_set.h>
4201 __isl_give isl_union_set *isl_union_set_project_out(
4202 __isl_take isl_union_set *uset,
4203 enum isl_dim_type type,
4204 unsigned first, unsigned n);
4205 __isl_give isl_set *isl_union_set_params(
4206 __isl_take isl_union_set *uset);
4208 The function C<isl_union_set_project_out> can only project out
4211 #include <isl/union_map.h>
4212 __isl_give isl_union_map *isl_union_map_project_out(
4213 __isl_take isl_union_map *umap,
4214 enum isl_dim_type type, unsigned first, unsigned n);
4215 __isl_give isl_set *isl_union_map_params(
4216 __isl_take isl_union_map *umap);
4217 __isl_give isl_union_set *isl_union_map_domain(
4218 __isl_take isl_union_map *umap);
4219 __isl_give isl_union_set *isl_union_map_range(
4220 __isl_take isl_union_map *umap);
4222 The function C<isl_union_map_project_out> can only project out
4225 #include <isl/aff.h>
4226 __isl_give isl_aff *isl_aff_project_domain_on_params(
4227 __isl_take isl_aff *aff);
4228 __isl_give isl_pw_multi_aff *
4229 isl_pw_multi_aff_project_domain_on_params(
4230 __isl_take isl_pw_multi_aff *pma);
4231 __isl_give isl_set *isl_pw_aff_domain(
4232 __isl_take isl_pw_aff *pwaff);
4233 __isl_give isl_set *isl_pw_multi_aff_domain(
4234 __isl_take isl_pw_multi_aff *pma);
4235 __isl_give isl_set *isl_multi_pw_aff_domain(
4236 __isl_take isl_multi_pw_aff *mpa);
4237 __isl_give isl_union_set *isl_union_pw_aff_domain(
4238 __isl_take isl_union_pw_aff *upa);
4239 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4240 __isl_take isl_union_pw_multi_aff *upma);
4241 __isl_give isl_union_set *
4242 isl_multi_union_pw_aff_domain(
4243 __isl_take isl_multi_union_pw_aff *mupa);
4244 __isl_give isl_set *isl_pw_aff_params(
4245 __isl_take isl_pw_aff *pwa);
4247 The function C<isl_multi_union_pw_aff_domain> requires its
4248 input to have at least one set dimension.
4250 #include <isl/polynomial.h>
4251 __isl_give isl_qpolynomial *
4252 isl_qpolynomial_project_domain_on_params(
4253 __isl_take isl_qpolynomial *qp);
4254 __isl_give isl_pw_qpolynomial *
4255 isl_pw_qpolynomial_project_domain_on_params(
4256 __isl_take isl_pw_qpolynomial *pwqp);
4257 __isl_give isl_pw_qpolynomial_fold *
4258 isl_pw_qpolynomial_fold_project_domain_on_params(
4259 __isl_take isl_pw_qpolynomial_fold *pwf);
4260 __isl_give isl_set *isl_pw_qpolynomial_domain(
4261 __isl_take isl_pw_qpolynomial *pwqp);
4262 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4263 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4264 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4265 __isl_take isl_union_pw_qpolynomial *upwqp);
4267 #include <isl/space.h>
4268 __isl_give isl_space *isl_space_domain_map(
4269 __isl_take isl_space *space);
4270 __isl_give isl_space *isl_space_range_map(
4271 __isl_take isl_space *space);
4273 #include <isl/map.h>
4274 __isl_give isl_map *isl_set_wrapped_domain_map(
4275 __isl_take isl_set *set);
4276 __isl_give isl_basic_map *isl_basic_map_domain_map(
4277 __isl_take isl_basic_map *bmap);
4278 __isl_give isl_basic_map *isl_basic_map_range_map(
4279 __isl_take isl_basic_map *bmap);
4280 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
4281 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
4283 #include <isl/union_map.h>
4284 __isl_give isl_union_map *isl_union_map_domain_map(
4285 __isl_take isl_union_map *umap);
4286 __isl_give isl_union_pw_multi_aff *
4287 isl_union_map_domain_map_union_pw_multi_aff(
4288 __isl_take isl_union_map *umap);
4289 __isl_give isl_union_map *isl_union_map_range_map(
4290 __isl_take isl_union_map *umap);
4291 __isl_give isl_union_map *
4292 isl_union_set_wrapped_domain_map(
4293 __isl_take isl_union_set *uset);
4295 The functions above construct a (basic, regular or union) relation
4296 that maps (a wrapped version of) the input relation to its domain or range.
4297 C<isl_set_wrapped_domain_map> maps the input set to the domain
4298 of its wrapped relation.
4302 __isl_give isl_basic_set *isl_basic_set_eliminate(
4303 __isl_take isl_basic_set *bset,
4304 enum isl_dim_type type,
4305 unsigned first, unsigned n);
4306 __isl_give isl_set *isl_set_eliminate(
4307 __isl_take isl_set *set, enum isl_dim_type type,
4308 unsigned first, unsigned n);
4309 __isl_give isl_basic_map *isl_basic_map_eliminate(
4310 __isl_take isl_basic_map *bmap,
4311 enum isl_dim_type type,
4312 unsigned first, unsigned n);
4313 __isl_give isl_map *isl_map_eliminate(
4314 __isl_take isl_map *map, enum isl_dim_type type,
4315 unsigned first, unsigned n);
4317 Eliminate the coefficients for the given dimensions from the constraints,
4318 without removing the dimensions.
4320 =item * Constructing a set from a parameter domain
4322 A zero-dimensional space or (basic) set can be constructed
4323 on a given parameter domain using the following functions.
4325 #include <isl/space.h>
4326 __isl_give isl_space *isl_space_set_from_params(
4327 __isl_take isl_space *space);
4329 #include <isl/set.h>
4330 __isl_give isl_basic_set *isl_basic_set_from_params(
4331 __isl_take isl_basic_set *bset);
4332 __isl_give isl_set *isl_set_from_params(
4333 __isl_take isl_set *set);
4335 =item * Constructing a relation from a set
4337 Create a relation with the given set as domain or range.
4338 The range or domain of the created relation is a zero-dimensional
4339 flat anonymous space.
4341 #include <isl/space.h>
4342 __isl_give isl_space *isl_space_from_domain(
4343 __isl_take isl_space *space);
4344 __isl_give isl_space *isl_space_from_range(
4345 __isl_take isl_space *space);
4346 __isl_give isl_space *isl_space_map_from_set(
4347 __isl_take isl_space *space);
4348 __isl_give isl_space *isl_space_map_from_domain_and_range(
4349 __isl_take isl_space *domain,
4350 __isl_take isl_space *range);
4352 #include <isl/local_space.h>
4353 __isl_give isl_local_space *isl_local_space_from_domain(
4354 __isl_take isl_local_space *ls);
4356 #include <isl/map.h>
4357 __isl_give isl_map *isl_map_from_domain(
4358 __isl_take isl_set *set);
4359 __isl_give isl_map *isl_map_from_range(
4360 __isl_take isl_set *set);
4362 #include <isl/val.h>
4363 __isl_give isl_multi_val *isl_multi_val_from_range(
4364 __isl_take isl_multi_val *mv);
4366 #include <isl/aff.h>
4367 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4368 __isl_take isl_multi_aff *ma);
4369 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4370 __isl_take isl_pw_aff *pwa);
4371 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4372 __isl_take isl_multi_pw_aff *mpa);
4373 __isl_give isl_multi_union_pw_aff *
4374 isl_multi_union_pw_aff_from_range(
4375 __isl_take isl_multi_union_pw_aff *mupa);
4376 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4377 __isl_take isl_set *set);
4378 __isl_give isl_union_pw_multi_aff *
4379 isl_union_pw_multi_aff_from_domain(
4380 __isl_take isl_union_set *uset);
4384 #include <isl/set.h>
4385 __isl_give isl_basic_set *isl_basic_set_fix_si(
4386 __isl_take isl_basic_set *bset,
4387 enum isl_dim_type type, unsigned pos, int value);
4388 __isl_give isl_basic_set *isl_basic_set_fix_val(
4389 __isl_take isl_basic_set *bset,
4390 enum isl_dim_type type, unsigned pos,
4391 __isl_take isl_val *v);
4392 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
4393 enum isl_dim_type type, unsigned pos, int value);
4394 __isl_give isl_set *isl_set_fix_val(
4395 __isl_take isl_set *set,
4396 enum isl_dim_type type, unsigned pos,
4397 __isl_take isl_val *v);
4399 #include <isl/map.h>
4400 __isl_give isl_basic_map *isl_basic_map_fix_si(
4401 __isl_take isl_basic_map *bmap,
4402 enum isl_dim_type type, unsigned pos, int value);
4403 __isl_give isl_basic_map *isl_basic_map_fix_val(
4404 __isl_take isl_basic_map *bmap,
4405 enum isl_dim_type type, unsigned pos,
4406 __isl_take isl_val *v);
4407 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
4408 enum isl_dim_type type, unsigned pos, int value);
4409 __isl_give isl_map *isl_map_fix_val(
4410 __isl_take isl_map *map,
4411 enum isl_dim_type type, unsigned pos,
4412 __isl_take isl_val *v);
4414 #include <isl/aff.h>
4415 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4416 __isl_take isl_pw_multi_aff *pma,
4417 enum isl_dim_type type, unsigned pos, int value);
4419 #include <isl/polynomial.h>
4420 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4421 __isl_take isl_pw_qpolynomial *pwqp,
4422 enum isl_dim_type type, unsigned n,
4423 __isl_take isl_val *v);
4425 Intersect the set, relation or function domain
4426 with the hyperplane where the given
4427 dimension has the fixed given value.
4429 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
4430 __isl_take isl_basic_map *bmap,
4431 enum isl_dim_type type, unsigned pos, int value);
4432 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
4433 __isl_take isl_basic_map *bmap,
4434 enum isl_dim_type type, unsigned pos, int value);
4435 __isl_give isl_set *isl_set_lower_bound_si(
4436 __isl_take isl_set *set,
4437 enum isl_dim_type type, unsigned pos, int value);
4438 __isl_give isl_set *isl_set_lower_bound_val(
4439 __isl_take isl_set *set,
4440 enum isl_dim_type type, unsigned pos,
4441 __isl_take isl_val *value);
4442 __isl_give isl_map *isl_map_lower_bound_si(
4443 __isl_take isl_map *map,
4444 enum isl_dim_type type, unsigned pos, int value);
4445 __isl_give isl_set *isl_set_upper_bound_si(
4446 __isl_take isl_set *set,
4447 enum isl_dim_type type, unsigned pos, int value);
4448 __isl_give isl_set *isl_set_upper_bound_val(
4449 __isl_take isl_set *set,
4450 enum isl_dim_type type, unsigned pos,
4451 __isl_take isl_val *value);
4452 __isl_give isl_map *isl_map_upper_bound_si(
4453 __isl_take isl_map *map,
4454 enum isl_dim_type type, unsigned pos, int value);
4456 Intersect the set or relation with the half-space where the given
4457 dimension has a value bounded by the fixed given integer value.
4459 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
4460 enum isl_dim_type type1, int pos1,
4461 enum isl_dim_type type2, int pos2);
4462 __isl_give isl_basic_map *isl_basic_map_equate(
4463 __isl_take isl_basic_map *bmap,
4464 enum isl_dim_type type1, int pos1,
4465 enum isl_dim_type type2, int pos2);
4466 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
4467 enum isl_dim_type type1, int pos1,
4468 enum isl_dim_type type2, int pos2);
4470 Intersect the set or relation with the hyperplane where the given
4471 dimensions are equal to each other.
4473 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
4474 enum isl_dim_type type1, int pos1,
4475 enum isl_dim_type type2, int pos2);
4477 Intersect the relation with the hyperplane where the given
4478 dimensions have opposite values.
4480 __isl_give isl_map *isl_map_order_le(
4481 __isl_take isl_map *map,
4482 enum isl_dim_type type1, int pos1,
4483 enum isl_dim_type type2, int pos2);
4484 __isl_give isl_basic_map *isl_basic_map_order_ge(
4485 __isl_take isl_basic_map *bmap,
4486 enum isl_dim_type type1, int pos1,
4487 enum isl_dim_type type2, int pos2);
4488 __isl_give isl_map *isl_map_order_ge(
4489 __isl_take isl_map *map,
4490 enum isl_dim_type type1, int pos1,
4491 enum isl_dim_type type2, int pos2);
4492 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
4493 enum isl_dim_type type1, int pos1,
4494 enum isl_dim_type type2, int pos2);
4495 __isl_give isl_basic_map *isl_basic_map_order_gt(
4496 __isl_take isl_basic_map *bmap,
4497 enum isl_dim_type type1, int pos1,
4498 enum isl_dim_type type2, int pos2);
4499 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
4500 enum isl_dim_type type1, int pos1,
4501 enum isl_dim_type type2, int pos2);
4503 Intersect the relation with the half-space where the given
4504 dimensions satisfy the given ordering.
4508 #include <isl/aff.h>
4509 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4510 __isl_take isl_aff *aff);
4511 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4512 __isl_take isl_aff *aff);
4513 __isl_give isl_set *isl_pw_aff_pos_set(
4514 __isl_take isl_pw_aff *pa);
4515 __isl_give isl_set *isl_pw_aff_nonneg_set(
4516 __isl_take isl_pw_aff *pwaff);
4517 __isl_give isl_set *isl_pw_aff_zero_set(
4518 __isl_take isl_pw_aff *pwaff);
4519 __isl_give isl_set *isl_pw_aff_non_zero_set(
4520 __isl_take isl_pw_aff *pwaff);
4521 __isl_give isl_union_set *
4522 isl_union_pw_aff_zero_union_set(
4523 __isl_take isl_union_pw_aff *upa);
4524 __isl_give isl_union_set *
4525 isl_multi_union_pw_aff_zero_union_set(
4526 __isl_take isl_multi_union_pw_aff *mupa);
4528 The function C<isl_aff_neg_basic_set> returns a basic set
4529 containing those elements in the domain space
4530 of C<aff> where C<aff> is negative.
4531 The function C<isl_pw_aff_nonneg_set> returns a set
4532 containing those elements in the domain
4533 of C<pwaff> where C<pwaff> is non-negative.
4534 The function C<isl_multi_union_pw_aff_zero_union_set>
4535 returns a union set containing those elements
4536 in the domains of its elements where they are all zero.
4540 __isl_give isl_map *isl_set_identity(
4541 __isl_take isl_set *set);
4542 __isl_give isl_union_map *isl_union_set_identity(
4543 __isl_take isl_union_set *uset);
4544 __isl_give isl_union_pw_multi_aff *
4545 isl_union_set_identity_union_pw_multi_aff(
4546 __isl_take isl_union_set *uset);
4548 Construct an identity relation on the given (union) set.
4550 =item * Function Extraction
4552 A piecewise quasi affine expression that is equal to 1 on a set
4553 and 0 outside the set can be created using the following function.
4555 #include <isl/aff.h>
4556 __isl_give isl_pw_aff *isl_set_indicator_function(
4557 __isl_take isl_set *set);
4559 A piecewise multiple quasi affine expression can be extracted
4560 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4561 and the C<isl_map> is single-valued.
4562 In case of a conversion from an C<isl_union_map>
4563 to an C<isl_union_pw_multi_aff>, these properties need to hold
4564 in each domain space.
4565 A conversion to a C<isl_multi_union_pw_aff> additionally
4566 requires that the input is non-empty and involves only a single
4569 #include <isl/aff.h>
4570 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4571 __isl_take isl_set *set);
4572 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4573 __isl_take isl_map *map);
4575 __isl_give isl_union_pw_multi_aff *
4576 isl_union_pw_multi_aff_from_union_set(
4577 __isl_take isl_union_set *uset);
4578 __isl_give isl_union_pw_multi_aff *
4579 isl_union_pw_multi_aff_from_union_map(
4580 __isl_take isl_union_map *umap);
4582 __isl_give isl_multi_union_pw_aff *
4583 isl_multi_union_pw_aff_from_union_map(
4584 __isl_take isl_union_map *umap);
4588 __isl_give isl_basic_set *isl_basic_map_deltas(
4589 __isl_take isl_basic_map *bmap);
4590 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
4591 __isl_give isl_union_set *isl_union_map_deltas(
4592 __isl_take isl_union_map *umap);
4594 These functions return a (basic) set containing the differences
4595 between image elements and corresponding domain elements in the input.
4597 __isl_give isl_basic_map *isl_basic_map_deltas_map(
4598 __isl_take isl_basic_map *bmap);
4599 __isl_give isl_map *isl_map_deltas_map(
4600 __isl_take isl_map *map);
4601 __isl_give isl_union_map *isl_union_map_deltas_map(
4602 __isl_take isl_union_map *umap);
4604 The functions above construct a (basic, regular or union) relation
4605 that maps (a wrapped version of) the input relation to its delta set.
4609 Simplify the representation of a set, relation or functions by trying
4610 to combine pairs of basic sets or relations into a single
4611 basic set or relation.
4613 #include <isl/set.h>
4614 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
4616 #include <isl/map.h>
4617 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
4619 #include <isl/union_set.h>
4620 __isl_give isl_union_set *isl_union_set_coalesce(
4621 __isl_take isl_union_set *uset);
4623 #include <isl/union_map.h>
4624 __isl_give isl_union_map *isl_union_map_coalesce(
4625 __isl_take isl_union_map *umap);
4627 #include <isl/aff.h>
4628 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4629 __isl_take isl_pw_aff *pwqp);
4630 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4631 __isl_take isl_pw_multi_aff *pma);
4632 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4633 __isl_take isl_multi_pw_aff *mpa);
4634 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
4635 __isl_take isl_union_pw_aff *upa);
4636 __isl_give isl_union_pw_multi_aff *
4637 isl_union_pw_multi_aff_coalesce(
4638 __isl_take isl_union_pw_multi_aff *upma);
4640 #include <isl/polynomial.h>
4641 __isl_give isl_pw_qpolynomial_fold *
4642 isl_pw_qpolynomial_fold_coalesce(
4643 __isl_take isl_pw_qpolynomial_fold *pwf);
4644 __isl_give isl_union_pw_qpolynomial *
4645 isl_union_pw_qpolynomial_coalesce(
4646 __isl_take isl_union_pw_qpolynomial *upwqp);
4647 __isl_give isl_union_pw_qpolynomial_fold *
4648 isl_union_pw_qpolynomial_fold_coalesce(
4649 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4651 One of the methods for combining pairs of basic sets or relations
4652 can result in coefficients that are much larger than those that appear
4653 in the constraints of the input. By default, the coefficients are
4654 not allowed to grow larger, but this can be changed by unsetting
4655 the following option.
4657 isl_stat isl_options_set_coalesce_bounded_wrapping(
4658 isl_ctx *ctx, int val);
4659 int isl_options_get_coalesce_bounded_wrapping(
4662 =item * Detecting equalities
4664 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
4665 __isl_take isl_basic_set *bset);
4666 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
4667 __isl_take isl_basic_map *bmap);
4668 __isl_give isl_set *isl_set_detect_equalities(
4669 __isl_take isl_set *set);
4670 __isl_give isl_map *isl_map_detect_equalities(
4671 __isl_take isl_map *map);
4672 __isl_give isl_union_set *isl_union_set_detect_equalities(
4673 __isl_take isl_union_set *uset);
4674 __isl_give isl_union_map *isl_union_map_detect_equalities(
4675 __isl_take isl_union_map *umap);
4677 Simplify the representation of a set or relation by detecting implicit
4680 =item * Removing redundant constraints
4682 #include <isl/set.h>
4683 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
4684 __isl_take isl_basic_set *bset);
4685 __isl_give isl_set *isl_set_remove_redundancies(
4686 __isl_take isl_set *set);
4688 #include <isl/union_set.h>
4689 __isl_give isl_union_set *
4690 isl_union_set_remove_redundancies(
4691 __isl_take isl_union_set *uset);
4693 #include <isl/map.h>
4694 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
4695 __isl_take isl_basic_map *bmap);
4696 __isl_give isl_map *isl_map_remove_redundancies(
4697 __isl_take isl_map *map);
4699 #include <isl/union_map.h>
4700 __isl_give isl_union_map *
4701 isl_union_map_remove_redundancies(
4702 __isl_take isl_union_map *umap);
4706 __isl_give isl_basic_set *isl_set_convex_hull(
4707 __isl_take isl_set *set);
4708 __isl_give isl_basic_map *isl_map_convex_hull(
4709 __isl_take isl_map *map);
4711 If the input set or relation has any existentially quantified
4712 variables, then the result of these operations is currently undefined.
4716 #include <isl/set.h>
4717 __isl_give isl_basic_set *
4718 isl_set_unshifted_simple_hull(
4719 __isl_take isl_set *set);
4720 __isl_give isl_basic_set *isl_set_simple_hull(
4721 __isl_take isl_set *set);
4722 __isl_give isl_basic_set *
4723 isl_set_unshifted_simple_hull_from_set_list(
4724 __isl_take isl_set *set,
4725 __isl_take isl_set_list *list);
4727 #include <isl/map.h>
4728 __isl_give isl_basic_map *
4729 isl_map_unshifted_simple_hull(
4730 __isl_take isl_map *map);
4731 __isl_give isl_basic_map *isl_map_simple_hull(
4732 __isl_take isl_map *map);
4733 __isl_give isl_basic_map *
4734 isl_map_unshifted_simple_hull_from_map_list(
4735 __isl_take isl_map *map,
4736 __isl_take isl_map_list *list);
4738 #include <isl/union_map.h>
4739 __isl_give isl_union_map *isl_union_map_simple_hull(
4740 __isl_take isl_union_map *umap);
4742 These functions compute a single basic set or relation
4743 that contains the whole input set or relation.
4744 In particular, the output is described by translates
4745 of the constraints describing the basic sets or relations in the input.
4746 In case of C<isl_set_unshifted_simple_hull>, only the original
4747 constraints are used, without any translation.
4748 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
4749 C<isl_map_unshifted_simple_hull_from_map_list>, the
4750 constraints are taken from the elements of the second argument.
4754 (See \autoref{s:simple hull}.)
4760 __isl_give isl_basic_set *isl_basic_set_affine_hull(
4761 __isl_take isl_basic_set *bset);
4762 __isl_give isl_basic_set *isl_set_affine_hull(
4763 __isl_take isl_set *set);
4764 __isl_give isl_union_set *isl_union_set_affine_hull(
4765 __isl_take isl_union_set *uset);
4766 __isl_give isl_basic_map *isl_basic_map_affine_hull(
4767 __isl_take isl_basic_map *bmap);
4768 __isl_give isl_basic_map *isl_map_affine_hull(
4769 __isl_take isl_map *map);
4770 __isl_give isl_union_map *isl_union_map_affine_hull(
4771 __isl_take isl_union_map *umap);
4773 In case of union sets and relations, the affine hull is computed
4776 =item * Polyhedral hull
4778 __isl_give isl_basic_set *isl_set_polyhedral_hull(
4779 __isl_take isl_set *set);
4780 __isl_give isl_basic_map *isl_map_polyhedral_hull(
4781 __isl_take isl_map *map);
4782 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
4783 __isl_take isl_union_set *uset);
4784 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
4785 __isl_take isl_union_map *umap);
4787 These functions compute a single basic set or relation
4788 not involving any existentially quantified variables
4789 that contains the whole input set or relation.
4790 In case of union sets and relations, the polyhedral hull is computed
4793 =item * Other approximations
4795 #include <isl/set.h>
4796 __isl_give isl_basic_set *
4797 isl_basic_set_drop_constraints_involving_dims(
4798 __isl_take isl_basic_set *bset,
4799 enum isl_dim_type type,
4800 unsigned first, unsigned n);
4801 __isl_give isl_basic_set *
4802 isl_basic_set_drop_constraints_not_involving_dims(
4803 __isl_take isl_basic_set *bset,
4804 enum isl_dim_type type,
4805 unsigned first, unsigned n);
4806 __isl_give isl_set *
4807 isl_set_drop_constraints_involving_dims(
4808 __isl_take isl_set *set,
4809 enum isl_dim_type type,
4810 unsigned first, unsigned n);
4812 #include <isl/map.h>
4813 __isl_give isl_basic_map *
4814 isl_basic_map_drop_constraints_involving_dims(
4815 __isl_take isl_basic_map *bmap,
4816 enum isl_dim_type type,
4817 unsigned first, unsigned n);
4818 __isl_give isl_map *
4819 isl_map_drop_constraints_involving_dims(
4820 __isl_take isl_map *map,
4821 enum isl_dim_type type,
4822 unsigned first, unsigned n);
4824 These functions drop any constraints (not) involving the specified dimensions.
4825 Note that the result depends on the representation of the input.
4827 #include <isl/polynomial.h>
4828 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4829 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4830 __isl_give isl_union_pw_qpolynomial *
4831 isl_union_pw_qpolynomial_to_polynomial(
4832 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4834 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4835 the polynomial will be an overapproximation. If C<sign> is negative,
4836 it will be an underapproximation. If C<sign> is zero, the approximation
4837 will lie somewhere in between.
4841 __isl_give isl_basic_set *isl_basic_set_sample(
4842 __isl_take isl_basic_set *bset);
4843 __isl_give isl_basic_set *isl_set_sample(
4844 __isl_take isl_set *set);
4845 __isl_give isl_basic_map *isl_basic_map_sample(
4846 __isl_take isl_basic_map *bmap);
4847 __isl_give isl_basic_map *isl_map_sample(
4848 __isl_take isl_map *map);
4850 If the input (basic) set or relation is non-empty, then return
4851 a singleton subset of the input. Otherwise, return an empty set.
4853 =item * Optimization
4855 #include <isl/ilp.h>
4856 __isl_give isl_val *isl_basic_set_max_val(
4857 __isl_keep isl_basic_set *bset,
4858 __isl_keep isl_aff *obj);
4859 __isl_give isl_val *isl_set_min_val(
4860 __isl_keep isl_set *set,
4861 __isl_keep isl_aff *obj);
4862 __isl_give isl_val *isl_set_max_val(
4863 __isl_keep isl_set *set,
4864 __isl_keep isl_aff *obj);
4866 Compute the minimum or maximum of the integer affine expression C<obj>
4867 over the points in C<set>, returning the result in C<opt>.
4868 The result is C<NULL> in case of an error, the optimal value in case
4869 there is one, negative infinity or infinity if the problem is unbounded and
4870 NaN if the problem is empty.
4872 =item * Parametric optimization
4874 __isl_give isl_pw_aff *isl_set_dim_min(
4875 __isl_take isl_set *set, int pos);
4876 __isl_give isl_pw_aff *isl_set_dim_max(
4877 __isl_take isl_set *set, int pos);
4878 __isl_give isl_pw_aff *isl_map_dim_max(
4879 __isl_take isl_map *map, int pos);
4881 Compute the minimum or maximum of the given set or output dimension
4882 as a function of the parameters (and input dimensions), but independently
4883 of the other set or output dimensions.
4884 For lexicographic optimization, see L<"Lexicographic Optimization">.
4888 The following functions compute either the set of (rational) coefficient
4889 values of valid constraints for the given set or the set of (rational)
4890 values satisfying the constraints with coefficients from the given set.
4891 Internally, these two sets of functions perform essentially the
4892 same operations, except that the set of coefficients is assumed to
4893 be a cone, while the set of values may be any polyhedron.
4894 The current implementation is based on the Farkas lemma and
4895 Fourier-Motzkin elimination, but this may change or be made optional
4896 in future. In particular, future implementations may use different
4897 dualization algorithms or skip the elimination step.
4899 __isl_give isl_basic_set *isl_basic_set_coefficients(
4900 __isl_take isl_basic_set *bset);
4901 __isl_give isl_basic_set *isl_set_coefficients(
4902 __isl_take isl_set *set);
4903 __isl_give isl_union_set *isl_union_set_coefficients(
4904 __isl_take isl_union_set *bset);
4905 __isl_give isl_basic_set *isl_basic_set_solutions(
4906 __isl_take isl_basic_set *bset);
4907 __isl_give isl_basic_set *isl_set_solutions(
4908 __isl_take isl_set *set);
4909 __isl_give isl_union_set *isl_union_set_solutions(
4910 __isl_take isl_union_set *bset);
4914 __isl_give isl_map *isl_map_fixed_power_val(
4915 __isl_take isl_map *map,
4916 __isl_take isl_val *exp);
4917 __isl_give isl_union_map *
4918 isl_union_map_fixed_power_val(
4919 __isl_take isl_union_map *umap,
4920 __isl_take isl_val *exp);
4922 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
4923 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
4924 of C<map> is computed.
4926 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
4928 __isl_give isl_union_map *isl_union_map_power(
4929 __isl_take isl_union_map *umap, int *exact);
4931 Compute a parametric representation for all positive powers I<k> of C<map>.
4932 The result maps I<k> to a nested relation corresponding to the
4933 I<k>th power of C<map>.
4934 The result may be an overapproximation. If the result is known to be exact,
4935 then C<*exact> is set to C<1>.
4937 =item * Transitive closure
4939 __isl_give isl_map *isl_map_transitive_closure(
4940 __isl_take isl_map *map, int *exact);
4941 __isl_give isl_union_map *isl_union_map_transitive_closure(
4942 __isl_take isl_union_map *umap, int *exact);
4944 Compute the transitive closure of C<map>.
4945 The result may be an overapproximation. If the result is known to be exact,
4946 then C<*exact> is set to C<1>.
4948 =item * Reaching path lengths
4950 __isl_give isl_map *isl_map_reaching_path_lengths(
4951 __isl_take isl_map *map, int *exact);
4953 Compute a relation that maps each element in the range of C<map>
4954 to the lengths of all paths composed of edges in C<map> that
4955 end up in the given element.
4956 The result may be an overapproximation. If the result is known to be exact,
4957 then C<*exact> is set to C<1>.
4958 To compute the I<maximal> path length, the resulting relation
4959 should be postprocessed by C<isl_map_lexmax>.
4960 In particular, if the input relation is a dependence relation
4961 (mapping sources to sinks), then the maximal path length corresponds
4962 to the free schedule.
4963 Note, however, that C<isl_map_lexmax> expects the maximum to be
4964 finite, so if the path lengths are unbounded (possibly due to
4965 the overapproximation), then you will get an error message.
4969 #include <isl/space.h>
4970 __isl_give isl_space *isl_space_wrap(
4971 __isl_take isl_space *space);
4972 __isl_give isl_space *isl_space_unwrap(
4973 __isl_take isl_space *space);
4975 #include <isl/local_space.h>
4976 __isl_give isl_local_space *isl_local_space_wrap(
4977 __isl_take isl_local_space *ls);
4979 #include <isl/set.h>
4980 __isl_give isl_basic_map *isl_basic_set_unwrap(
4981 __isl_take isl_basic_set *bset);
4982 __isl_give isl_map *isl_set_unwrap(
4983 __isl_take isl_set *set);
4985 #include <isl/map.h>
4986 __isl_give isl_basic_set *isl_basic_map_wrap(
4987 __isl_take isl_basic_map *bmap);
4988 __isl_give isl_set *isl_map_wrap(
4989 __isl_take isl_map *map);
4991 #include <isl/union_set.h>
4992 __isl_give isl_union_map *isl_union_set_unwrap(
4993 __isl_take isl_union_set *uset);
4995 #include <isl/union_map.h>
4996 __isl_give isl_union_set *isl_union_map_wrap(
4997 __isl_take isl_union_map *umap);
4999 The input to C<isl_space_unwrap> should
5000 be the space of a set, while that of
5001 C<isl_space_wrap> should be the space of a relation.
5002 Conversely, the output of C<isl_space_unwrap> is the space
5003 of a relation, while that of C<isl_space_wrap> is the space of a set.
5007 Remove any internal structure of domain (and range) of the given
5008 set or relation. If there is any such internal structure in the input,
5009 then the name of the space is also removed.
5011 #include <isl/local_space.h>
5012 __isl_give isl_local_space *
5013 isl_local_space_flatten_domain(
5014 __isl_take isl_local_space *ls);
5015 __isl_give isl_local_space *
5016 isl_local_space_flatten_range(
5017 __isl_take isl_local_space *ls);
5019 #include <isl/set.h>
5020 __isl_give isl_basic_set *isl_basic_set_flatten(
5021 __isl_take isl_basic_set *bset);
5022 __isl_give isl_set *isl_set_flatten(
5023 __isl_take isl_set *set);
5025 #include <isl/map.h>
5026 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
5027 __isl_take isl_basic_map *bmap);
5028 __isl_give isl_basic_map *isl_basic_map_flatten_range(
5029 __isl_take isl_basic_map *bmap);
5030 __isl_give isl_map *isl_map_flatten_range(
5031 __isl_take isl_map *map);
5032 __isl_give isl_map *isl_map_flatten_domain(
5033 __isl_take isl_map *map);
5034 __isl_give isl_basic_map *isl_basic_map_flatten(
5035 __isl_take isl_basic_map *bmap);
5036 __isl_give isl_map *isl_map_flatten(
5037 __isl_take isl_map *map);
5039 #include <isl/val.h>
5040 __isl_give isl_multi_val *isl_multi_val_flatten_range(
5041 __isl_take isl_multi_val *mv);
5043 #include <isl/aff.h>
5044 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
5045 __isl_take isl_multi_aff *ma);
5046 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
5047 __isl_take isl_multi_aff *ma);
5048 __isl_give isl_multi_pw_aff *
5049 isl_multi_pw_aff_flatten_range(
5050 __isl_take isl_multi_pw_aff *mpa);
5051 __isl_give isl_multi_union_pw_aff *
5052 isl_multi_union_pw_aff_flatten_range(
5053 __isl_take isl_multi_union_pw_aff *mupa);
5055 #include <isl/map.h>
5056 __isl_give isl_map *isl_set_flatten_map(
5057 __isl_take isl_set *set);
5059 The function above constructs a relation
5060 that maps the input set to a flattened version of the set.
5064 Lift the input set to a space with extra dimensions corresponding
5065 to the existentially quantified variables in the input.
5066 In particular, the result lives in a wrapped map where the domain
5067 is the original space and the range corresponds to the original
5068 existentially quantified variables.
5070 #include <isl/set.h>
5071 __isl_give isl_basic_set *isl_basic_set_lift(
5072 __isl_take isl_basic_set *bset);
5073 __isl_give isl_set *isl_set_lift(
5074 __isl_take isl_set *set);
5075 __isl_give isl_union_set *isl_union_set_lift(
5076 __isl_take isl_union_set *uset);
5078 Given a local space that contains the existentially quantified
5079 variables of a set, a basic relation that, when applied to
5080 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
5081 can be constructed using the following function.
5083 #include <isl/local_space.h>
5084 __isl_give isl_basic_map *isl_local_space_lifting(
5085 __isl_take isl_local_space *ls);
5087 #include <isl/aff.h>
5088 __isl_give isl_multi_aff *isl_multi_aff_lift(
5089 __isl_take isl_multi_aff *maff,
5090 __isl_give isl_local_space **ls);
5092 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
5093 then it is assigned the local space that lies at the basis of
5094 the lifting applied.
5096 =item * Internal Product
5098 #include <isl/space.h>
5099 __isl_give isl_space *isl_space_zip(
5100 __isl_take isl_space *space);
5102 #include <isl/map.h>
5103 __isl_give isl_basic_map *isl_basic_map_zip(
5104 __isl_take isl_basic_map *bmap);
5105 __isl_give isl_map *isl_map_zip(
5106 __isl_take isl_map *map);
5108 #include <isl/union_map.h>
5109 __isl_give isl_union_map *isl_union_map_zip(
5110 __isl_take isl_union_map *umap);
5112 Given a relation with nested relations for domain and range,
5113 interchange the range of the domain with the domain of the range.
5117 #include <isl/space.h>
5118 __isl_give isl_space *isl_space_curry(
5119 __isl_take isl_space *space);
5120 __isl_give isl_space *isl_space_uncurry(
5121 __isl_take isl_space *space);
5123 #include <isl/map.h>
5124 __isl_give isl_basic_map *isl_basic_map_curry(
5125 __isl_take isl_basic_map *bmap);
5126 __isl_give isl_basic_map *isl_basic_map_uncurry(
5127 __isl_take isl_basic_map *bmap);
5128 __isl_give isl_map *isl_map_curry(
5129 __isl_take isl_map *map);
5130 __isl_give isl_map *isl_map_uncurry(
5131 __isl_take isl_map *map);
5133 #include <isl/union_map.h>
5134 __isl_give isl_union_map *isl_union_map_curry(
5135 __isl_take isl_union_map *umap);
5136 __isl_give isl_union_map *isl_union_map_uncurry(
5137 __isl_take isl_union_map *umap);
5139 Given a relation with a nested relation for domain,
5140 the C<curry> functions
5141 move the range of the nested relation out of the domain
5142 and use it as the domain of a nested relation in the range,
5143 with the original range as range of this nested relation.
5144 The C<uncurry> functions perform the inverse operation.
5146 =item * Aligning parameters
5148 Change the order of the parameters of the given set, relation
5150 such that the first parameters match those of C<model>.
5151 This may involve the introduction of extra parameters.
5152 All parameters need to be named.
5154 #include <isl/space.h>
5155 __isl_give isl_space *isl_space_align_params(
5156 __isl_take isl_space *space1,
5157 __isl_take isl_space *space2)
5159 #include <isl/set.h>
5160 __isl_give isl_basic_set *isl_basic_set_align_params(
5161 __isl_take isl_basic_set *bset,
5162 __isl_take isl_space *model);
5163 __isl_give isl_set *isl_set_align_params(
5164 __isl_take isl_set *set,
5165 __isl_take isl_space *model);
5167 #include <isl/map.h>
5168 __isl_give isl_basic_map *isl_basic_map_align_params(
5169 __isl_take isl_basic_map *bmap,
5170 __isl_take isl_space *model);
5171 __isl_give isl_map *isl_map_align_params(
5172 __isl_take isl_map *map,
5173 __isl_take isl_space *model);
5175 #include <isl/val.h>
5176 __isl_give isl_multi_val *isl_multi_val_align_params(
5177 __isl_take isl_multi_val *mv,
5178 __isl_take isl_space *model);
5180 #include <isl/aff.h>
5181 __isl_give isl_aff *isl_aff_align_params(
5182 __isl_take isl_aff *aff,
5183 __isl_take isl_space *model);
5184 __isl_give isl_multi_aff *isl_multi_aff_align_params(
5185 __isl_take isl_multi_aff *multi,
5186 __isl_take isl_space *model);
5187 __isl_give isl_pw_aff *isl_pw_aff_align_params(
5188 __isl_take isl_pw_aff *pwaff,
5189 __isl_take isl_space *model);
5190 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
5191 __isl_take isl_pw_multi_aff *pma,
5192 __isl_take isl_space *model);
5193 __isl_give isl_union_pw_aff *
5194 isl_union_pw_aff_align_params(
5195 __isl_take isl_union_pw_aff *upa,
5196 __isl_take isl_space *model);
5197 __isl_give isl_union_pw_multi_aff *
5198 isl_union_pw_multi_aff_align_params(
5199 __isl_take isl_union_pw_multi_aff *upma,
5200 __isl_take isl_space *model);
5201 __isl_give isl_multi_union_pw_aff *
5202 isl_multi_union_pw_aff_align_params(
5203 __isl_take isl_multi_union_pw_aff *mupa,
5204 __isl_take isl_space *model);
5206 #include <isl/polynomial.h>
5207 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5208 __isl_take isl_qpolynomial *qp,
5209 __isl_take isl_space *model);
5211 =item * Unary Arithmethic Operations
5213 #include <isl/val.h>
5214 __isl_give isl_multi_val *isl_multi_val_neg(
5215 __isl_take isl_multi_val *mv);
5217 #include <isl/aff.h>
5218 __isl_give isl_aff *isl_aff_neg(
5219 __isl_take isl_aff *aff);
5220 __isl_give isl_multi_aff *isl_multi_aff_neg(
5221 __isl_take isl_multi_aff *ma);
5222 __isl_give isl_pw_aff *isl_pw_aff_neg(
5223 __isl_take isl_pw_aff *pwaff);
5224 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
5225 __isl_take isl_pw_multi_aff *pma);
5226 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
5227 __isl_take isl_multi_pw_aff *mpa);
5228 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
5229 __isl_take isl_union_pw_aff *upa);
5230 __isl_give isl_union_pw_multi_aff *
5231 isl_union_pw_multi_aff_neg(
5232 __isl_take isl_union_pw_multi_aff *upma);
5233 __isl_give isl_multi_union_pw_aff *
5234 isl_multi_union_pw_aff_neg(
5235 __isl_take isl_multi_union_pw_aff *mupa);
5236 __isl_give isl_aff *isl_aff_ceil(
5237 __isl_take isl_aff *aff);
5238 __isl_give isl_pw_aff *isl_pw_aff_ceil(
5239 __isl_take isl_pw_aff *pwaff);
5240 __isl_give isl_aff *isl_aff_floor(
5241 __isl_take isl_aff *aff);
5242 __isl_give isl_multi_aff *isl_multi_aff_floor(
5243 __isl_take isl_multi_aff *ma);
5244 __isl_give isl_pw_aff *isl_pw_aff_floor(
5245 __isl_take isl_pw_aff *pwaff);
5246 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
5247 __isl_take isl_union_pw_aff *upa);
5248 __isl_give isl_multi_union_pw_aff *
5249 isl_multi_union_pw_aff_floor(
5250 __isl_take isl_multi_union_pw_aff *mupa);
5252 #include <isl/aff.h>
5253 __isl_give isl_pw_aff *isl_pw_aff_list_min(
5254 __isl_take isl_pw_aff_list *list);
5255 __isl_give isl_pw_aff *isl_pw_aff_list_max(
5256 __isl_take isl_pw_aff_list *list);
5258 #include <isl/polynomial.h>
5259 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5260 __isl_take isl_qpolynomial *qp);
5261 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5262 __isl_take isl_pw_qpolynomial *pwqp);
5263 __isl_give isl_union_pw_qpolynomial *
5264 isl_union_pw_qpolynomial_neg(
5265 __isl_take isl_union_pw_qpolynomial *upwqp);
5266 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5267 __isl_take isl_qpolynomial *qp,
5269 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5270 __isl_take isl_pw_qpolynomial *pwqp,
5275 The following functions evaluate a function in a point.
5277 #include <isl/polynomial.h>
5278 __isl_give isl_val *isl_pw_qpolynomial_eval(
5279 __isl_take isl_pw_qpolynomial *pwqp,
5280 __isl_take isl_point *pnt);
5281 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5282 __isl_take isl_pw_qpolynomial_fold *pwf,
5283 __isl_take isl_point *pnt);
5284 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5285 __isl_take isl_union_pw_qpolynomial *upwqp,
5286 __isl_take isl_point *pnt);
5287 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5288 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5289 __isl_take isl_point *pnt);
5291 =item * Dimension manipulation
5293 It is usually not advisable to directly change the (input or output)
5294 space of a set or a relation as this removes the name and the internal
5295 structure of the space. However, the functions below can be useful
5296 to add new parameters, assuming
5297 C<isl_set_align_params> and C<isl_map_align_params>
5300 #include <isl/space.h>
5301 __isl_give isl_space *isl_space_add_dims(
5302 __isl_take isl_space *space,
5303 enum isl_dim_type type, unsigned n);
5304 __isl_give isl_space *isl_space_insert_dims(
5305 __isl_take isl_space *space,
5306 enum isl_dim_type type, unsigned pos, unsigned n);
5307 __isl_give isl_space *isl_space_drop_dims(
5308 __isl_take isl_space *space,
5309 enum isl_dim_type type, unsigned first, unsigned n);
5310 __isl_give isl_space *isl_space_move_dims(
5311 __isl_take isl_space *space,
5312 enum isl_dim_type dst_type, unsigned dst_pos,
5313 enum isl_dim_type src_type, unsigned src_pos,
5316 #include <isl/local_space.h>
5317 __isl_give isl_local_space *isl_local_space_add_dims(
5318 __isl_take isl_local_space *ls,
5319 enum isl_dim_type type, unsigned n);
5320 __isl_give isl_local_space *isl_local_space_insert_dims(
5321 __isl_take isl_local_space *ls,
5322 enum isl_dim_type type, unsigned first, unsigned n);
5323 __isl_give isl_local_space *isl_local_space_drop_dims(
5324 __isl_take isl_local_space *ls,
5325 enum isl_dim_type type, unsigned first, unsigned n);
5327 #include <isl/set.h>
5328 __isl_give isl_basic_set *isl_basic_set_add_dims(
5329 __isl_take isl_basic_set *bset,
5330 enum isl_dim_type type, unsigned n);
5331 __isl_give isl_set *isl_set_add_dims(
5332 __isl_take isl_set *set,
5333 enum isl_dim_type type, unsigned n);
5334 __isl_give isl_basic_set *isl_basic_set_insert_dims(
5335 __isl_take isl_basic_set *bset,
5336 enum isl_dim_type type, unsigned pos,
5338 __isl_give isl_set *isl_set_insert_dims(
5339 __isl_take isl_set *set,
5340 enum isl_dim_type type, unsigned pos, unsigned n);
5341 __isl_give isl_basic_set *isl_basic_set_move_dims(
5342 __isl_take isl_basic_set *bset,
5343 enum isl_dim_type dst_type, unsigned dst_pos,
5344 enum isl_dim_type src_type, unsigned src_pos,
5346 __isl_give isl_set *isl_set_move_dims(
5347 __isl_take isl_set *set,
5348 enum isl_dim_type dst_type, unsigned dst_pos,
5349 enum isl_dim_type src_type, unsigned src_pos,
5352 #include <isl/map.h>
5353 __isl_give isl_basic_map *isl_basic_map_add_dims(
5354 __isl_take isl_basic_map *bmap,
5355 enum isl_dim_type type, unsigned n);
5356 __isl_give isl_map *isl_map_add_dims(
5357 __isl_take isl_map *map,
5358 enum isl_dim_type type, unsigned n);
5359 __isl_give isl_basic_map *isl_basic_map_insert_dims(
5360 __isl_take isl_basic_map *bmap,
5361 enum isl_dim_type type, unsigned pos,
5363 __isl_give isl_map *isl_map_insert_dims(
5364 __isl_take isl_map *map,
5365 enum isl_dim_type type, unsigned pos, unsigned n);
5366 __isl_give isl_basic_map *isl_basic_map_move_dims(
5367 __isl_take isl_basic_map *bmap,
5368 enum isl_dim_type dst_type, unsigned dst_pos,
5369 enum isl_dim_type src_type, unsigned src_pos,
5371 __isl_give isl_map *isl_map_move_dims(
5372 __isl_take isl_map *map,
5373 enum isl_dim_type dst_type, unsigned dst_pos,
5374 enum isl_dim_type src_type, unsigned src_pos,
5377 #include <isl/val.h>
5378 __isl_give isl_multi_val *isl_multi_val_insert_dims(
5379 __isl_take isl_multi_val *mv,
5380 enum isl_dim_type type, unsigned first, unsigned n);
5381 __isl_give isl_multi_val *isl_multi_val_add_dims(
5382 __isl_take isl_multi_val *mv,
5383 enum isl_dim_type type, unsigned n);
5384 __isl_give isl_multi_val *isl_multi_val_drop_dims(
5385 __isl_take isl_multi_val *mv,
5386 enum isl_dim_type type, unsigned first, unsigned n);
5388 #include <isl/aff.h>
5389 __isl_give isl_aff *isl_aff_insert_dims(
5390 __isl_take isl_aff *aff,
5391 enum isl_dim_type type, unsigned first, unsigned n);
5392 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
5393 __isl_take isl_multi_aff *ma,
5394 enum isl_dim_type type, unsigned first, unsigned n);
5395 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
5396 __isl_take isl_pw_aff *pwaff,
5397 enum isl_dim_type type, unsigned first, unsigned n);
5398 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
5399 __isl_take isl_multi_pw_aff *mpa,
5400 enum isl_dim_type type, unsigned first, unsigned n);
5401 __isl_give isl_aff *isl_aff_add_dims(
5402 __isl_take isl_aff *aff,
5403 enum isl_dim_type type, unsigned n);
5404 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
5405 __isl_take isl_multi_aff *ma,
5406 enum isl_dim_type type, unsigned n);
5407 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
5408 __isl_take isl_pw_aff *pwaff,
5409 enum isl_dim_type type, unsigned n);
5410 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
5411 __isl_take isl_multi_pw_aff *mpa,
5412 enum isl_dim_type type, unsigned n);
5413 __isl_give isl_aff *isl_aff_drop_dims(
5414 __isl_take isl_aff *aff,
5415 enum isl_dim_type type, unsigned first, unsigned n);
5416 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
5417 __isl_take isl_multi_aff *maff,
5418 enum isl_dim_type type, unsigned first, unsigned n);
5419 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
5420 __isl_take isl_pw_aff *pwaff,
5421 enum isl_dim_type type, unsigned first, unsigned n);
5422 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
5423 __isl_take isl_pw_multi_aff *pma,
5424 enum isl_dim_type type, unsigned first, unsigned n);
5425 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
5426 __isl_take isl_union_pw_aff *upa,
5427 enum isl_dim_type type, unsigned first, unsigned n);
5428 __isl_give isl_union_pw_multi_aff *
5429 isl_union_pw_multi_aff_drop_dims(
5430 __isl_take isl_union_pw_multi_aff *upma,
5431 enum isl_dim_type type,
5432 unsigned first, unsigned n);
5433 __isl_give isl_multi_union_pw_aff *
5434 isl_multi_union_pw_aff_drop_dims(
5435 __isl_take isl_multi_union_pw_aff *mupa,
5436 enum isl_dim_type type, unsigned first,
5438 __isl_give isl_aff *isl_aff_move_dims(
5439 __isl_take isl_aff *aff,
5440 enum isl_dim_type dst_type, unsigned dst_pos,
5441 enum isl_dim_type src_type, unsigned src_pos,
5443 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
5444 __isl_take isl_multi_aff *ma,
5445 enum isl_dim_type dst_type, unsigned dst_pos,
5446 enum isl_dim_type src_type, unsigned src_pos,
5448 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
5449 __isl_take isl_pw_aff *pa,
5450 enum isl_dim_type dst_type, unsigned dst_pos,
5451 enum isl_dim_type src_type, unsigned src_pos,
5453 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
5454 __isl_take isl_multi_pw_aff *pma,
5455 enum isl_dim_type dst_type, unsigned dst_pos,
5456 enum isl_dim_type src_type, unsigned src_pos,
5459 #include <isl/polynomial.h>
5460 __isl_give isl_union_pw_qpolynomial *
5461 isl_union_pw_qpolynomial_drop_dims(
5462 __isl_take isl_union_pw_qpolynomial *upwqp,
5463 enum isl_dim_type type,
5464 unsigned first, unsigned n);
5465 __isl_give isl_union_pw_qpolynomial_fold *
5466 isl_union_pw_qpolynomial_fold_drop_dims(
5467 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5468 enum isl_dim_type type,
5469 unsigned first, unsigned n);
5471 The operations on union expressions can only manipulate parameters.
5475 =head2 Binary Operations
5477 The two arguments of a binary operation not only need to live
5478 in the same C<isl_ctx>, they currently also need to have
5479 the same (number of) parameters.
5481 =head3 Basic Operations
5485 =item * Intersection
5487 #include <isl/local_space.h>
5488 __isl_give isl_local_space *isl_local_space_intersect(
5489 __isl_take isl_local_space *ls1,
5490 __isl_take isl_local_space *ls2);
5492 #include <isl/set.h>
5493 __isl_give isl_basic_set *isl_basic_set_intersect_params(
5494 __isl_take isl_basic_set *bset1,
5495 __isl_take isl_basic_set *bset2);
5496 __isl_give isl_basic_set *isl_basic_set_intersect(
5497 __isl_take isl_basic_set *bset1,
5498 __isl_take isl_basic_set *bset2);
5499 __isl_give isl_basic_set *isl_basic_set_list_intersect(
5500 __isl_take struct isl_basic_set_list *list);
5501 __isl_give isl_set *isl_set_intersect_params(
5502 __isl_take isl_set *set,
5503 __isl_take isl_set *params);
5504 __isl_give isl_set *isl_set_intersect(
5505 __isl_take isl_set *set1,
5506 __isl_take isl_set *set2);
5508 #include <isl/map.h>
5509 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
5510 __isl_take isl_basic_map *bmap,
5511 __isl_take isl_basic_set *bset);
5512 __isl_give isl_basic_map *isl_basic_map_intersect_range(
5513 __isl_take isl_basic_map *bmap,
5514 __isl_take isl_basic_set *bset);
5515 __isl_give isl_basic_map *isl_basic_map_intersect(
5516 __isl_take isl_basic_map *bmap1,
5517 __isl_take isl_basic_map *bmap2);
5518 __isl_give isl_basic_map *isl_basic_map_list_intersect(
5519 __isl_take isl_basic_map_list *list);
5520 __isl_give isl_map *isl_map_intersect_params(
5521 __isl_take isl_map *map,
5522 __isl_take isl_set *params);
5523 __isl_give isl_map *isl_map_intersect_domain(
5524 __isl_take isl_map *map,
5525 __isl_take isl_set *set);
5526 __isl_give isl_map *isl_map_intersect_range(
5527 __isl_take isl_map *map,
5528 __isl_take isl_set *set);
5529 __isl_give isl_map *isl_map_intersect(
5530 __isl_take isl_map *map1,
5531 __isl_take isl_map *map2);
5533 #include <isl/union_set.h>
5534 __isl_give isl_union_set *isl_union_set_intersect_params(
5535 __isl_take isl_union_set *uset,
5536 __isl_take isl_set *set);
5537 __isl_give isl_union_set *isl_union_set_intersect(
5538 __isl_take isl_union_set *uset1,
5539 __isl_take isl_union_set *uset2);
5541 #include <isl/union_map.h>
5542 __isl_give isl_union_map *isl_union_map_intersect_params(
5543 __isl_take isl_union_map *umap,
5544 __isl_take isl_set *set);
5545 __isl_give isl_union_map *isl_union_map_intersect_domain(
5546 __isl_take isl_union_map *umap,
5547 __isl_take isl_union_set *uset);
5548 __isl_give isl_union_map *isl_union_map_intersect_range(
5549 __isl_take isl_union_map *umap,
5550 __isl_take isl_union_set *uset);
5551 __isl_give isl_union_map *isl_union_map_intersect(
5552 __isl_take isl_union_map *umap1,
5553 __isl_take isl_union_map *umap2);
5555 #include <isl/aff.h>
5556 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
5557 __isl_take isl_pw_aff *pa,
5558 __isl_take isl_set *set);
5559 __isl_give isl_multi_pw_aff *
5560 isl_multi_pw_aff_intersect_domain(
5561 __isl_take isl_multi_pw_aff *mpa,
5562 __isl_take isl_set *domain);
5563 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
5564 __isl_take isl_pw_multi_aff *pma,
5565 __isl_take isl_set *set);
5566 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
5567 __isl_take isl_union_pw_aff *upa,
5568 __isl_take isl_union_set *uset);
5569 __isl_give isl_union_pw_multi_aff *
5570 isl_union_pw_multi_aff_intersect_domain(
5571 __isl_take isl_union_pw_multi_aff *upma,
5572 __isl_take isl_union_set *uset);
5573 __isl_give isl_multi_union_pw_aff *
5574 isl_multi_union_pw_aff_intersect_domain(
5575 __isl_take isl_multi_union_pw_aff *mupa,
5576 __isl_take isl_union_set *uset);
5577 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
5578 __isl_take isl_pw_aff *pa,
5579 __isl_take isl_set *set);
5580 __isl_give isl_multi_pw_aff *
5581 isl_multi_pw_aff_intersect_params(
5582 __isl_take isl_multi_pw_aff *mpa,
5583 __isl_take isl_set *set);
5584 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
5585 __isl_take isl_pw_multi_aff *pma,
5586 __isl_take isl_set *set);
5587 __isl_give isl_union_pw_aff *
5588 isl_union_pw_aff_intersect_params(
5589 __isl_take isl_union_pw_aff *upa,
5590 __isl_give isl_union_pw_multi_aff *
5591 isl_union_pw_multi_aff_intersect_params(
5592 __isl_take isl_union_pw_multi_aff *upma,
5593 __isl_take isl_set *set);
5594 __isl_give isl_multi_union_pw_aff *
5595 isl_multi_union_pw_aff_intersect_params(
5596 __isl_take isl_multi_union_pw_aff *mupa,
5597 __isl_take isl_set *params);
5598 isl_multi_union_pw_aff_intersect_range(
5599 __isl_take isl_multi_union_pw_aff *mupa,
5600 __isl_take isl_set *set);
5602 #include <isl/polynomial.h>
5603 __isl_give isl_pw_qpolynomial *
5604 isl_pw_qpolynomial_intersect_domain(
5605 __isl_take isl_pw_qpolynomial *pwpq,
5606 __isl_take isl_set *set);
5607 __isl_give isl_union_pw_qpolynomial *
5608 isl_union_pw_qpolynomial_intersect_domain(
5609 __isl_take isl_union_pw_qpolynomial *upwpq,
5610 __isl_take isl_union_set *uset);
5611 __isl_give isl_union_pw_qpolynomial_fold *
5612 isl_union_pw_qpolynomial_fold_intersect_domain(
5613 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5614 __isl_take isl_union_set *uset);
5615 __isl_give isl_pw_qpolynomial *
5616 isl_pw_qpolynomial_intersect_params(
5617 __isl_take isl_pw_qpolynomial *pwpq,
5618 __isl_take isl_set *set);
5619 __isl_give isl_pw_qpolynomial_fold *
5620 isl_pw_qpolynomial_fold_intersect_params(
5621 __isl_take isl_pw_qpolynomial_fold *pwf,
5622 __isl_take isl_set *set);
5623 __isl_give isl_union_pw_qpolynomial *
5624 isl_union_pw_qpolynomial_intersect_params(
5625 __isl_take isl_union_pw_qpolynomial *upwpq,
5626 __isl_take isl_set *set);
5627 __isl_give isl_union_pw_qpolynomial_fold *
5628 isl_union_pw_qpolynomial_fold_intersect_params(
5629 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5630 __isl_take isl_set *set);
5632 The second argument to the C<_params> functions needs to be
5633 a parametric (basic) set. For the other functions, a parametric set
5634 for either argument is only allowed if the other argument is
5635 a parametric set as well.
5636 The list passed to C<isl_basic_set_list_intersect> needs to have
5637 at least one element and all elements need to live in the same space.
5638 The function C<isl_multi_union_pw_aff_intersect_range>
5639 restricts the input function to those shared domain elements
5640 that map to the specified range.
5644 #include <isl/set.h>
5645 __isl_give isl_set *isl_basic_set_union(
5646 __isl_take isl_basic_set *bset1,
5647 __isl_take isl_basic_set *bset2);
5648 __isl_give isl_set *isl_set_union(
5649 __isl_take isl_set *set1,
5650 __isl_take isl_set *set2);
5652 #include <isl/map.h>
5653 __isl_give isl_map *isl_basic_map_union(
5654 __isl_take isl_basic_map *bmap1,
5655 __isl_take isl_basic_map *bmap2);
5656 __isl_give isl_map *isl_map_union(
5657 __isl_take isl_map *map1,
5658 __isl_take isl_map *map2);
5660 #include <isl/union_set.h>
5661 __isl_give isl_union_set *isl_union_set_union(
5662 __isl_take isl_union_set *uset1,
5663 __isl_take isl_union_set *uset2);
5664 __isl_give isl_union_set *isl_union_set_list_union(
5665 __isl_take isl_union_set_list *list);
5667 #include <isl/union_map.h>
5668 __isl_give isl_union_map *isl_union_map_union(
5669 __isl_take isl_union_map *umap1,
5670 __isl_take isl_union_map *umap2);
5672 =item * Set difference
5674 #include <isl/set.h>
5675 __isl_give isl_set *isl_set_subtract(
5676 __isl_take isl_set *set1,
5677 __isl_take isl_set *set2);
5679 #include <isl/map.h>
5680 __isl_give isl_map *isl_map_subtract(
5681 __isl_take isl_map *map1,
5682 __isl_take isl_map *map2);
5683 __isl_give isl_map *isl_map_subtract_domain(
5684 __isl_take isl_map *map,
5685 __isl_take isl_set *dom);
5686 __isl_give isl_map *isl_map_subtract_range(
5687 __isl_take isl_map *map,
5688 __isl_take isl_set *dom);
5690 #include <isl/union_set.h>
5691 __isl_give isl_union_set *isl_union_set_subtract(
5692 __isl_take isl_union_set *uset1,
5693 __isl_take isl_union_set *uset2);
5695 #include <isl/union_map.h>
5696 __isl_give isl_union_map *isl_union_map_subtract(
5697 __isl_take isl_union_map *umap1,
5698 __isl_take isl_union_map *umap2);
5699 __isl_give isl_union_map *isl_union_map_subtract_domain(
5700 __isl_take isl_union_map *umap,
5701 __isl_take isl_union_set *dom);
5702 __isl_give isl_union_map *isl_union_map_subtract_range(
5703 __isl_take isl_union_map *umap,
5704 __isl_take isl_union_set *dom);
5706 #include <isl/aff.h>
5707 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
5708 __isl_take isl_pw_aff *pa,
5709 __isl_take isl_set *set);
5710 __isl_give isl_pw_multi_aff *
5711 isl_pw_multi_aff_subtract_domain(
5712 __isl_take isl_pw_multi_aff *pma,
5713 __isl_take isl_set *set);
5714 __isl_give isl_union_pw_aff *
5715 isl_union_pw_aff_subtract_domain(
5716 __isl_take isl_union_pw_aff *upa,
5717 __isl_take isl_union_set *uset);
5718 __isl_give isl_union_pw_multi_aff *
5719 isl_union_pw_multi_aff_subtract_domain(
5720 __isl_take isl_union_pw_multi_aff *upma,
5721 __isl_take isl_set *set);
5723 #include <isl/polynomial.h>
5724 __isl_give isl_pw_qpolynomial *
5725 isl_pw_qpolynomial_subtract_domain(
5726 __isl_take isl_pw_qpolynomial *pwpq,
5727 __isl_take isl_set *set);
5728 __isl_give isl_pw_qpolynomial_fold *
5729 isl_pw_qpolynomial_fold_subtract_domain(
5730 __isl_take isl_pw_qpolynomial_fold *pwf,
5731 __isl_take isl_set *set);
5732 __isl_give isl_union_pw_qpolynomial *
5733 isl_union_pw_qpolynomial_subtract_domain(
5734 __isl_take isl_union_pw_qpolynomial *upwpq,
5735 __isl_take isl_union_set *uset);
5736 __isl_give isl_union_pw_qpolynomial_fold *
5737 isl_union_pw_qpolynomial_fold_subtract_domain(
5738 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5739 __isl_take isl_union_set *uset);
5743 #include <isl/space.h>
5744 __isl_give isl_space *isl_space_join(
5745 __isl_take isl_space *left,
5746 __isl_take isl_space *right);
5748 #include <isl/map.h>
5749 __isl_give isl_basic_set *isl_basic_set_apply(
5750 __isl_take isl_basic_set *bset,
5751 __isl_take isl_basic_map *bmap);
5752 __isl_give isl_set *isl_set_apply(
5753 __isl_take isl_set *set,
5754 __isl_take isl_map *map);
5755 __isl_give isl_union_set *isl_union_set_apply(
5756 __isl_take isl_union_set *uset,
5757 __isl_take isl_union_map *umap);
5758 __isl_give isl_basic_map *isl_basic_map_apply_domain(
5759 __isl_take isl_basic_map *bmap1,
5760 __isl_take isl_basic_map *bmap2);
5761 __isl_give isl_basic_map *isl_basic_map_apply_range(
5762 __isl_take isl_basic_map *bmap1,
5763 __isl_take isl_basic_map *bmap2);
5764 __isl_give isl_map *isl_map_apply_domain(
5765 __isl_take isl_map *map1,
5766 __isl_take isl_map *map2);
5767 __isl_give isl_map *isl_map_apply_range(
5768 __isl_take isl_map *map1,
5769 __isl_take isl_map *map2);
5771 #include <isl/union_map.h>
5772 __isl_give isl_union_map *isl_union_map_apply_domain(
5773 __isl_take isl_union_map *umap1,
5774 __isl_take isl_union_map *umap2);
5775 __isl_give isl_union_map *isl_union_map_apply_range(
5776 __isl_take isl_union_map *umap1,
5777 __isl_take isl_union_map *umap2);
5779 #include <isl/aff.h>
5780 __isl_give isl_union_pw_aff *
5781 isl_multi_union_pw_aff_apply_aff(
5782 __isl_take isl_multi_union_pw_aff *mupa,
5783 __isl_take isl_aff *aff);
5784 __isl_give isl_union_pw_aff *
5785 isl_multi_union_pw_aff_apply_pw_aff(
5786 __isl_take isl_multi_union_pw_aff *mupa,
5787 __isl_take isl_pw_aff *pa);
5788 __isl_give isl_multi_union_pw_aff *
5789 isl_multi_union_pw_aff_apply_multi_aff(
5790 __isl_take isl_multi_union_pw_aff *mupa,
5791 __isl_take isl_multi_aff *ma);
5792 __isl_give isl_multi_union_pw_aff *
5793 isl_multi_union_pw_aff_apply_pw_multi_aff(
5794 __isl_take isl_multi_union_pw_aff *mupa,
5795 __isl_take isl_pw_multi_aff *pma);
5797 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
5798 over the shared domain of the elements of the input. The dimension is
5799 required to be greater than zero.
5800 The C<isl_multi_union_pw_aff> argument of
5801 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
5802 but only if the range of the C<isl_multi_aff> argument
5803 is also zero-dimensional.
5804 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
5806 #include <isl/polynomial.h>
5807 __isl_give isl_pw_qpolynomial_fold *
5808 isl_set_apply_pw_qpolynomial_fold(
5809 __isl_take isl_set *set,
5810 __isl_take isl_pw_qpolynomial_fold *pwf,
5812 __isl_give isl_pw_qpolynomial_fold *
5813 isl_map_apply_pw_qpolynomial_fold(
5814 __isl_take isl_map *map,
5815 __isl_take isl_pw_qpolynomial_fold *pwf,
5817 __isl_give isl_union_pw_qpolynomial_fold *
5818 isl_union_set_apply_union_pw_qpolynomial_fold(
5819 __isl_take isl_union_set *uset,
5820 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5822 __isl_give isl_union_pw_qpolynomial_fold *
5823 isl_union_map_apply_union_pw_qpolynomial_fold(
5824 __isl_take isl_union_map *umap,
5825 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5828 The functions taking a map
5829 compose the given map with the given piecewise quasipolynomial reduction.
5830 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5831 over all elements in the intersection of the range of the map
5832 and the domain of the piecewise quasipolynomial reduction
5833 as a function of an element in the domain of the map.
5834 The functions taking a set compute a bound over all elements in the
5835 intersection of the set and the domain of the
5836 piecewise quasipolynomial reduction.
5840 #include <isl/set.h>
5841 __isl_give isl_basic_set *
5842 isl_basic_set_preimage_multi_aff(
5843 __isl_take isl_basic_set *bset,
5844 __isl_take isl_multi_aff *ma);
5845 __isl_give isl_set *isl_set_preimage_multi_aff(
5846 __isl_take isl_set *set,
5847 __isl_take isl_multi_aff *ma);
5848 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
5849 __isl_take isl_set *set,
5850 __isl_take isl_pw_multi_aff *pma);
5851 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
5852 __isl_take isl_set *set,
5853 __isl_take isl_multi_pw_aff *mpa);
5855 #include <isl/union_set.h>
5856 __isl_give isl_union_set *
5857 isl_union_set_preimage_multi_aff(
5858 __isl_take isl_union_set *uset,
5859 __isl_take isl_multi_aff *ma);
5860 __isl_give isl_union_set *
5861 isl_union_set_preimage_pw_multi_aff(
5862 __isl_take isl_union_set *uset,
5863 __isl_take isl_pw_multi_aff *pma);
5864 __isl_give isl_union_set *
5865 isl_union_set_preimage_union_pw_multi_aff(
5866 __isl_take isl_union_set *uset,
5867 __isl_take isl_union_pw_multi_aff *upma);
5869 #include <isl/map.h>
5870 __isl_give isl_basic_map *
5871 isl_basic_map_preimage_domain_multi_aff(
5872 __isl_take isl_basic_map *bmap,
5873 __isl_take isl_multi_aff *ma);
5874 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
5875 __isl_take isl_map *map,
5876 __isl_take isl_multi_aff *ma);
5877 __isl_give isl_map *isl_map_preimage_range_multi_aff(
5878 __isl_take isl_map *map,
5879 __isl_take isl_multi_aff *ma);
5880 __isl_give isl_map *
5881 isl_map_preimage_domain_pw_multi_aff(
5882 __isl_take isl_map *map,
5883 __isl_take isl_pw_multi_aff *pma);
5884 __isl_give isl_map *
5885 isl_map_preimage_range_pw_multi_aff(
5886 __isl_take isl_map *map,
5887 __isl_take isl_pw_multi_aff *pma);
5888 __isl_give isl_map *
5889 isl_map_preimage_domain_multi_pw_aff(
5890 __isl_take isl_map *map,
5891 __isl_take isl_multi_pw_aff *mpa);
5892 __isl_give isl_basic_map *
5893 isl_basic_map_preimage_range_multi_aff(
5894 __isl_take isl_basic_map *bmap,
5895 __isl_take isl_multi_aff *ma);
5897 #include <isl/union_map.h>
5898 __isl_give isl_union_map *
5899 isl_union_map_preimage_domain_multi_aff(
5900 __isl_take isl_union_map *umap,
5901 __isl_take isl_multi_aff *ma);
5902 __isl_give isl_union_map *
5903 isl_union_map_preimage_range_multi_aff(
5904 __isl_take isl_union_map *umap,
5905 __isl_take isl_multi_aff *ma);
5906 __isl_give isl_union_map *
5907 isl_union_map_preimage_domain_pw_multi_aff(
5908 __isl_take isl_union_map *umap,
5909 __isl_take isl_pw_multi_aff *pma);
5910 __isl_give isl_union_map *
5911 isl_union_map_preimage_range_pw_multi_aff(
5912 __isl_take isl_union_map *umap,
5913 __isl_take isl_pw_multi_aff *pma);
5914 __isl_give isl_union_map *
5915 isl_union_map_preimage_domain_union_pw_multi_aff(
5916 __isl_take isl_union_map *umap,
5917 __isl_take isl_union_pw_multi_aff *upma);
5918 __isl_give isl_union_map *
5919 isl_union_map_preimage_range_union_pw_multi_aff(
5920 __isl_take isl_union_map *umap,
5921 __isl_take isl_union_pw_multi_aff *upma);
5923 These functions compute the preimage of the given set or map domain/range under
5924 the given function. In other words, the expression is plugged
5925 into the set description or into the domain/range of the map.
5929 #include <isl/aff.h>
5930 __isl_give isl_aff *isl_aff_pullback_aff(
5931 __isl_take isl_aff *aff1,
5932 __isl_take isl_aff *aff2);
5933 __isl_give isl_aff *isl_aff_pullback_multi_aff(
5934 __isl_take isl_aff *aff,
5935 __isl_take isl_multi_aff *ma);
5936 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
5937 __isl_take isl_pw_aff *pa,
5938 __isl_take isl_multi_aff *ma);
5939 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
5940 __isl_take isl_pw_aff *pa,
5941 __isl_take isl_pw_multi_aff *pma);
5942 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
5943 __isl_take isl_pw_aff *pa,
5944 __isl_take isl_multi_pw_aff *mpa);
5945 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
5946 __isl_take isl_multi_aff *ma1,
5947 __isl_take isl_multi_aff *ma2);
5948 __isl_give isl_pw_multi_aff *
5949 isl_pw_multi_aff_pullback_multi_aff(
5950 __isl_take isl_pw_multi_aff *pma,
5951 __isl_take isl_multi_aff *ma);
5952 __isl_give isl_multi_pw_aff *
5953 isl_multi_pw_aff_pullback_multi_aff(
5954 __isl_take isl_multi_pw_aff *mpa,
5955 __isl_take isl_multi_aff *ma);
5956 __isl_give isl_pw_multi_aff *
5957 isl_pw_multi_aff_pullback_pw_multi_aff(
5958 __isl_take isl_pw_multi_aff *pma1,
5959 __isl_take isl_pw_multi_aff *pma2);
5960 __isl_give isl_multi_pw_aff *
5961 isl_multi_pw_aff_pullback_pw_multi_aff(
5962 __isl_take isl_multi_pw_aff *mpa,
5963 __isl_take isl_pw_multi_aff *pma);
5964 __isl_give isl_multi_pw_aff *
5965 isl_multi_pw_aff_pullback_multi_pw_aff(
5966 __isl_take isl_multi_pw_aff *mpa1,
5967 __isl_take isl_multi_pw_aff *mpa2);
5968 __isl_give isl_union_pw_aff *
5969 isl_union_pw_aff_pullback_union_pw_multi_aff(
5970 __isl_take isl_union_pw_aff *upa,
5971 __isl_take isl_union_pw_multi_aff *upma);
5972 __isl_give isl_union_pw_multi_aff *
5973 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
5974 __isl_take isl_union_pw_multi_aff *upma1,
5975 __isl_take isl_union_pw_multi_aff *upma2);
5976 __isl_give isl_multi_union_pw_aff *
5977 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
5978 __isl_take isl_multi_union_pw_aff *mupa,
5979 __isl_take isl_union_pw_multi_aff *upma);
5981 These functions precompose the first expression by the second function.
5982 In other words, the second function is plugged
5983 into the first expression.
5987 #include <isl/aff.h>
5988 __isl_give isl_basic_set *isl_aff_le_basic_set(
5989 __isl_take isl_aff *aff1,
5990 __isl_take isl_aff *aff2);
5991 __isl_give isl_basic_set *isl_aff_ge_basic_set(
5992 __isl_take isl_aff *aff1,
5993 __isl_take isl_aff *aff2);
5994 __isl_give isl_set *isl_pw_aff_eq_set(
5995 __isl_take isl_pw_aff *pwaff1,
5996 __isl_take isl_pw_aff *pwaff2);
5997 __isl_give isl_set *isl_pw_aff_ne_set(
5998 __isl_take isl_pw_aff *pwaff1,
5999 __isl_take isl_pw_aff *pwaff2);
6000 __isl_give isl_set *isl_pw_aff_le_set(
6001 __isl_take isl_pw_aff *pwaff1,
6002 __isl_take isl_pw_aff *pwaff2);
6003 __isl_give isl_set *isl_pw_aff_lt_set(
6004 __isl_take isl_pw_aff *pwaff1,
6005 __isl_take isl_pw_aff *pwaff2);
6006 __isl_give isl_set *isl_pw_aff_ge_set(
6007 __isl_take isl_pw_aff *pwaff1,
6008 __isl_take isl_pw_aff *pwaff2);
6009 __isl_give isl_set *isl_pw_aff_gt_set(
6010 __isl_take isl_pw_aff *pwaff1,
6011 __isl_take isl_pw_aff *pwaff2);
6013 __isl_give isl_set *isl_multi_aff_lex_le_set(
6014 __isl_take isl_multi_aff *ma1,
6015 __isl_take isl_multi_aff *ma2);
6016 __isl_give isl_set *isl_multi_aff_lex_ge_set(
6017 __isl_take isl_multi_aff *ma1,
6018 __isl_take isl_multi_aff *ma2);
6020 __isl_give isl_set *isl_pw_aff_list_eq_set(
6021 __isl_take isl_pw_aff_list *list1,
6022 __isl_take isl_pw_aff_list *list2);
6023 __isl_give isl_set *isl_pw_aff_list_ne_set(
6024 __isl_take isl_pw_aff_list *list1,
6025 __isl_take isl_pw_aff_list *list2);
6026 __isl_give isl_set *isl_pw_aff_list_le_set(
6027 __isl_take isl_pw_aff_list *list1,
6028 __isl_take isl_pw_aff_list *list2);
6029 __isl_give isl_set *isl_pw_aff_list_lt_set(
6030 __isl_take isl_pw_aff_list *list1,
6031 __isl_take isl_pw_aff_list *list2);
6032 __isl_give isl_set *isl_pw_aff_list_ge_set(
6033 __isl_take isl_pw_aff_list *list1,
6034 __isl_take isl_pw_aff_list *list2);
6035 __isl_give isl_set *isl_pw_aff_list_gt_set(
6036 __isl_take isl_pw_aff_list *list1,
6037 __isl_take isl_pw_aff_list *list2);
6039 The function C<isl_aff_ge_basic_set> returns a basic set
6040 containing those elements in the shared space
6041 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
6042 The function C<isl_pw_aff_ge_set> returns a set
6043 containing those elements in the shared domain
6044 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
6045 greater than or equal to C<pwaff2>.
6046 The function C<isl_multi_aff_lex_le_set> returns a set
6047 containing those elements in the shared domain space
6048 where C<ma1> is lexicographically smaller than or
6050 The functions operating on C<isl_pw_aff_list> apply the corresponding
6051 C<isl_pw_aff> function to each pair of elements in the two lists.
6053 #include <isl/aff.h>
6054 __isl_give isl_map *isl_pw_aff_eq_map(
6055 __isl_take isl_pw_aff *pa1,
6056 __isl_take isl_pw_aff *pa2);
6057 __isl_give isl_map *isl_pw_aff_lt_map(
6058 __isl_take isl_pw_aff *pa1,
6059 __isl_take isl_pw_aff *pa2);
6060 __isl_give isl_map *isl_pw_aff_gt_map(
6061 __isl_take isl_pw_aff *pa1,
6062 __isl_take isl_pw_aff *pa2);
6064 __isl_give isl_map *isl_multi_pw_aff_eq_map(
6065 __isl_take isl_multi_pw_aff *mpa1,
6066 __isl_take isl_multi_pw_aff *mpa2);
6067 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
6068 __isl_take isl_multi_pw_aff *mpa1,
6069 __isl_take isl_multi_pw_aff *mpa2);
6070 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
6071 __isl_take isl_multi_pw_aff *mpa1,
6072 __isl_take isl_multi_pw_aff *mpa2);
6074 These functions return a map between domain elements of the arguments
6075 where the function values satisfy the given relation.
6077 #include <isl/union_map.h>
6078 __isl_give isl_union_map *
6079 isl_union_map_eq_at_multi_union_pw_aff(
6080 __isl_take isl_union_map *umap,
6081 __isl_take isl_multi_union_pw_aff *mupa);
6082 __isl_give isl_union_map *
6083 isl_union_map_lex_lt_at_multi_union_pw_aff(
6084 __isl_take isl_union_map *umap,
6085 __isl_take isl_multi_union_pw_aff *mupa);
6086 __isl_give isl_union_map *
6087 isl_union_map_lex_gt_at_multi_union_pw_aff(
6088 __isl_take isl_union_map *umap,
6089 __isl_take isl_multi_union_pw_aff *mupa);
6091 These functions select the subset of elements in the union map
6092 that have an equal or lexicographically smaller function value.
6094 =item * Cartesian Product
6096 #include <isl/space.h>
6097 __isl_give isl_space *isl_space_product(
6098 __isl_take isl_space *space1,
6099 __isl_take isl_space *space2);
6100 __isl_give isl_space *isl_space_domain_product(
6101 __isl_take isl_space *space1,
6102 __isl_take isl_space *space2);
6103 __isl_give isl_space *isl_space_range_product(
6104 __isl_take isl_space *space1,
6105 __isl_take isl_space *space2);
6108 C<isl_space_product>, C<isl_space_domain_product>
6109 and C<isl_space_range_product> take pairs or relation spaces and
6110 produce a single relations space, where either the domain, the range
6111 or both domain and range are wrapped spaces of relations between
6112 the domains and/or ranges of the input spaces.
6113 If the product is only constructed over the domain or the range
6114 then the ranges or the domains of the inputs should be the same.
6115 The function C<isl_space_product> also accepts a pair of set spaces,
6116 in which case it returns a wrapped space of a relation between the
6119 #include <isl/set.h>
6120 __isl_give isl_set *isl_set_product(
6121 __isl_take isl_set *set1,
6122 __isl_take isl_set *set2);
6124 #include <isl/map.h>
6125 __isl_give isl_basic_map *isl_basic_map_domain_product(
6126 __isl_take isl_basic_map *bmap1,
6127 __isl_take isl_basic_map *bmap2);
6128 __isl_give isl_basic_map *isl_basic_map_range_product(
6129 __isl_take isl_basic_map *bmap1,
6130 __isl_take isl_basic_map *bmap2);
6131 __isl_give isl_basic_map *isl_basic_map_product(
6132 __isl_take isl_basic_map *bmap1,
6133 __isl_take isl_basic_map *bmap2);
6134 __isl_give isl_map *isl_map_domain_product(
6135 __isl_take isl_map *map1,
6136 __isl_take isl_map *map2);
6137 __isl_give isl_map *isl_map_range_product(
6138 __isl_take isl_map *map1,
6139 __isl_take isl_map *map2);
6140 __isl_give isl_map *isl_map_product(
6141 __isl_take isl_map *map1,
6142 __isl_take isl_map *map2);
6144 #include <isl/union_set.h>
6145 __isl_give isl_union_set *isl_union_set_product(
6146 __isl_take isl_union_set *uset1,
6147 __isl_take isl_union_set *uset2);
6149 #include <isl/union_map.h>
6150 __isl_give isl_union_map *isl_union_map_domain_product(
6151 __isl_take isl_union_map *umap1,
6152 __isl_take isl_union_map *umap2);
6153 __isl_give isl_union_map *isl_union_map_range_product(
6154 __isl_take isl_union_map *umap1,
6155 __isl_take isl_union_map *umap2);
6156 __isl_give isl_union_map *isl_union_map_product(
6157 __isl_take isl_union_map *umap1,
6158 __isl_take isl_union_map *umap2);
6160 #include <isl/val.h>
6161 __isl_give isl_multi_val *isl_multi_val_range_product(
6162 __isl_take isl_multi_val *mv1,
6163 __isl_take isl_multi_val *mv2);
6164 __isl_give isl_multi_val *isl_multi_val_product(
6165 __isl_take isl_multi_val *mv1,
6166 __isl_take isl_multi_val *mv2);
6168 #include <isl/aff.h>
6169 __isl_give isl_multi_aff *isl_multi_aff_range_product(
6170 __isl_take isl_multi_aff *ma1,
6171 __isl_take isl_multi_aff *ma2);
6172 __isl_give isl_multi_aff *isl_multi_aff_product(
6173 __isl_take isl_multi_aff *ma1,
6174 __isl_take isl_multi_aff *ma2);
6175 __isl_give isl_multi_pw_aff *
6176 isl_multi_pw_aff_range_product(
6177 __isl_take isl_multi_pw_aff *mpa1,
6178 __isl_take isl_multi_pw_aff *mpa2);
6179 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
6180 __isl_take isl_multi_pw_aff *mpa1,
6181 __isl_take isl_multi_pw_aff *mpa2);
6182 __isl_give isl_pw_multi_aff *
6183 isl_pw_multi_aff_range_product(
6184 __isl_take isl_pw_multi_aff *pma1,
6185 __isl_take isl_pw_multi_aff *pma2);
6186 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
6187 __isl_take isl_pw_multi_aff *pma1,
6188 __isl_take isl_pw_multi_aff *pma2);
6189 __isl_give isl_multi_union_pw_aff *
6190 isl_multi_union_pw_aff_range_product(
6191 __isl_take isl_multi_union_pw_aff *mupa1,
6192 __isl_take isl_multi_union_pw_aff *mupa2);
6194 The above functions compute the cross product of the given
6195 sets, relations or functions. The domains and ranges of the results
6196 are wrapped maps between domains and ranges of the inputs.
6197 To obtain a ``flat'' product, use the following functions
6200 #include <isl/set.h>
6201 __isl_give isl_basic_set *isl_basic_set_flat_product(
6202 __isl_take isl_basic_set *bset1,
6203 __isl_take isl_basic_set *bset2);
6204 __isl_give isl_set *isl_set_flat_product(
6205 __isl_take isl_set *set1,
6206 __isl_take isl_set *set2);
6208 #include <isl/map.h>
6209 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
6210 __isl_take isl_basic_map *bmap1,
6211 __isl_take isl_basic_map *bmap2);
6212 __isl_give isl_map *isl_map_flat_domain_product(
6213 __isl_take isl_map *map1,
6214 __isl_take isl_map *map2);
6215 __isl_give isl_map *isl_map_flat_range_product(
6216 __isl_take isl_map *map1,
6217 __isl_take isl_map *map2);
6218 __isl_give isl_basic_map *isl_basic_map_flat_product(
6219 __isl_take isl_basic_map *bmap1,
6220 __isl_take isl_basic_map *bmap2);
6221 __isl_give isl_map *isl_map_flat_product(
6222 __isl_take isl_map *map1,
6223 __isl_take isl_map *map2);
6225 #include <isl/union_map.h>
6226 __isl_give isl_union_map *
6227 isl_union_map_flat_domain_product(
6228 __isl_take isl_union_map *umap1,
6229 __isl_take isl_union_map *umap2);
6230 __isl_give isl_union_map *
6231 isl_union_map_flat_range_product(
6232 __isl_take isl_union_map *umap1,
6233 __isl_take isl_union_map *umap2);
6235 #include <isl/val.h>
6236 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
6237 __isl_take isl_multi_val *mv1,
6238 __isl_take isl_multi_aff *mv2);
6240 #include <isl/aff.h>
6241 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
6242 __isl_take isl_multi_aff *ma1,
6243 __isl_take isl_multi_aff *ma2);
6244 __isl_give isl_pw_multi_aff *
6245 isl_pw_multi_aff_flat_range_product(
6246 __isl_take isl_pw_multi_aff *pma1,
6247 __isl_take isl_pw_multi_aff *pma2);
6248 __isl_give isl_multi_pw_aff *
6249 isl_multi_pw_aff_flat_range_product(
6250 __isl_take isl_multi_pw_aff *mpa1,
6251 __isl_take isl_multi_pw_aff *mpa2);
6252 __isl_give isl_union_pw_multi_aff *
6253 isl_union_pw_multi_aff_flat_range_product(
6254 __isl_take isl_union_pw_multi_aff *upma1,
6255 __isl_take isl_union_pw_multi_aff *upma2);
6256 __isl_give isl_multi_union_pw_aff *
6257 isl_multi_union_pw_aff_flat_range_product(
6258 __isl_take isl_multi_union_pw_aff *mupa1,
6259 __isl_take isl_multi_union_pw_aff *mupa2);
6261 #include <isl/space.h>
6262 __isl_give isl_space *isl_space_factor_domain(
6263 __isl_take isl_space *space);
6264 __isl_give isl_space *isl_space_factor_range(
6265 __isl_take isl_space *space);
6266 __isl_give isl_space *isl_space_domain_factor_domain(
6267 __isl_take isl_space *space);
6268 __isl_give isl_space *isl_space_domain_factor_range(
6269 __isl_take isl_space *space);
6270 __isl_give isl_space *isl_space_range_factor_domain(
6271 __isl_take isl_space *space);
6272 __isl_give isl_space *isl_space_range_factor_range(
6273 __isl_take isl_space *space);
6275 The functions C<isl_space_range_factor_domain> and
6276 C<isl_space_range_factor_range> extract the two arguments from
6277 the result of a call to C<isl_space_range_product>.
6279 The arguments of a call to a product can be extracted
6280 from the result using the following functions.
6282 #include <isl/map.h>
6283 __isl_give isl_map *isl_map_factor_domain(
6284 __isl_take isl_map *map);
6285 __isl_give isl_map *isl_map_factor_range(
6286 __isl_take isl_map *map);
6287 __isl_give isl_map *isl_map_domain_factor_domain(
6288 __isl_take isl_map *map);
6289 __isl_give isl_map *isl_map_domain_factor_range(
6290 __isl_take isl_map *map);
6291 __isl_give isl_map *isl_map_range_factor_domain(
6292 __isl_take isl_map *map);
6293 __isl_give isl_map *isl_map_range_factor_range(
6294 __isl_take isl_map *map);
6296 #include <isl/union_map.h>
6297 __isl_give isl_union_map *isl_union_map_factor_domain(
6298 __isl_take isl_union_map *umap);
6299 __isl_give isl_union_map *isl_union_map_factor_range(
6300 __isl_take isl_union_map *umap);
6301 __isl_give isl_union_map *
6302 isl_union_map_domain_factor_domain(
6303 __isl_take isl_union_map *umap);
6304 __isl_give isl_union_map *
6305 isl_union_map_domain_factor_range(
6306 __isl_take isl_union_map *umap);
6307 __isl_give isl_union_map *
6308 isl_union_map_range_factor_range(
6309 __isl_take isl_union_map *umap);
6311 #include <isl/val.h>
6312 __isl_give isl_multi_val *isl_multi_val_factor_range(
6313 __isl_take isl_multi_val *mv);
6314 __isl_give isl_multi_val *
6315 isl_multi_val_range_factor_domain(
6316 __isl_take isl_multi_val *mv);
6317 __isl_give isl_multi_val *
6318 isl_multi_val_range_factor_range(
6319 __isl_take isl_multi_val *mv);
6321 #include <isl/aff.h>
6322 __isl_give isl_multi_aff *isl_multi_aff_factor_range(
6323 __isl_take isl_multi_aff *ma);
6324 __isl_give isl_multi_aff *
6325 isl_multi_aff_range_factor_domain(
6326 __isl_take isl_multi_aff *ma);
6327 __isl_give isl_multi_aff *
6328 isl_multi_aff_range_factor_range(
6329 __isl_take isl_multi_aff *ma);
6330 __isl_give isl_multi_pw_aff *
6331 isl_multi_pw_aff_factor_range(
6332 __isl_take isl_multi_pw_aff *mpa);
6333 __isl_give isl_multi_pw_aff *
6334 isl_multi_pw_aff_range_factor_domain(
6335 __isl_take isl_multi_pw_aff *mpa);
6336 __isl_give isl_multi_pw_aff *
6337 isl_multi_pw_aff_range_factor_range(
6338 __isl_take isl_multi_pw_aff *mpa);
6339 __isl_give isl_multi_union_pw_aff *
6340 isl_multi_union_pw_aff_factor_range(
6341 __isl_take isl_multi_union_pw_aff *mupa);
6342 __isl_give isl_multi_union_pw_aff *
6343 isl_multi_union_pw_aff_range_factor_domain(
6344 __isl_take isl_multi_union_pw_aff *mupa);
6345 __isl_give isl_multi_union_pw_aff *
6346 isl_multi_union_pw_aff_range_factor_range(
6347 __isl_take isl_multi_union_pw_aff *mupa);
6349 The splice functions are a generalization of the flat product functions,
6350 where the second argument may be inserted at any position inside
6351 the first argument rather than being placed at the end.
6352 The functions C<isl_multi_val_factor_range>,
6353 C<isl_multi_aff_factor_range>,
6354 C<isl_multi_pw_aff_factor_range> and
6355 C<isl_multi_union_pw_aff_factor_range>
6356 take functions that live in a set space.
6358 #include <isl/val.h>
6359 __isl_give isl_multi_val *isl_multi_val_range_splice(
6360 __isl_take isl_multi_val *mv1, unsigned pos,
6361 __isl_take isl_multi_val *mv2);
6363 #include <isl/aff.h>
6364 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
6365 __isl_take isl_multi_aff *ma1, unsigned pos,
6366 __isl_take isl_multi_aff *ma2);
6367 __isl_give isl_multi_aff *isl_multi_aff_splice(
6368 __isl_take isl_multi_aff *ma1,
6369 unsigned in_pos, unsigned out_pos,
6370 __isl_take isl_multi_aff *ma2);
6371 __isl_give isl_multi_pw_aff *
6372 isl_multi_pw_aff_range_splice(
6373 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
6374 __isl_take isl_multi_pw_aff *mpa2);
6375 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
6376 __isl_take isl_multi_pw_aff *mpa1,
6377 unsigned in_pos, unsigned out_pos,
6378 __isl_take isl_multi_pw_aff *mpa2);
6379 __isl_give isl_multi_union_pw_aff *
6380 isl_multi_union_pw_aff_range_splice(
6381 __isl_take isl_multi_union_pw_aff *mupa1,
6383 __isl_take isl_multi_union_pw_aff *mupa2);
6385 =item * Simplification
6387 When applied to a set or relation,
6388 the gist operation returns a set or relation that has the
6389 same intersection with the context as the input set or relation.
6390 Any implicit equality in the intersection is made explicit in the result,
6391 while all inequalities that are redundant with respect to the intersection
6393 In case of union sets and relations, the gist operation is performed
6396 When applied to a function,
6397 the gist operation applies the set gist operation to each of
6398 the cells in the domain of the input piecewise expression.
6399 The context is also exploited
6400 to simplify the expression associated to each cell.
6402 #include <isl/set.h>
6403 __isl_give isl_basic_set *isl_basic_set_gist(
6404 __isl_take isl_basic_set *bset,
6405 __isl_take isl_basic_set *context);
6406 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
6407 __isl_take isl_set *context);
6408 __isl_give isl_set *isl_set_gist_params(
6409 __isl_take isl_set *set,
6410 __isl_take isl_set *context);
6412 #include <isl/map.h>
6413 __isl_give isl_basic_map *isl_basic_map_gist(
6414 __isl_take isl_basic_map *bmap,
6415 __isl_take isl_basic_map *context);
6416 __isl_give isl_basic_map *isl_basic_map_gist_domain(
6417 __isl_take isl_basic_map *bmap,
6418 __isl_take isl_basic_set *context);
6419 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
6420 __isl_take isl_map *context);
6421 __isl_give isl_map *isl_map_gist_params(
6422 __isl_take isl_map *map,
6423 __isl_take isl_set *context);
6424 __isl_give isl_map *isl_map_gist_domain(
6425 __isl_take isl_map *map,
6426 __isl_take isl_set *context);
6427 __isl_give isl_map *isl_map_gist_range(
6428 __isl_take isl_map *map,
6429 __isl_take isl_set *context);
6431 #include <isl/union_set.h>
6432 __isl_give isl_union_set *isl_union_set_gist(
6433 __isl_take isl_union_set *uset,
6434 __isl_take isl_union_set *context);
6435 __isl_give isl_union_set *isl_union_set_gist_params(
6436 __isl_take isl_union_set *uset,
6437 __isl_take isl_set *set);
6439 #include <isl/union_map.h>
6440 __isl_give isl_union_map *isl_union_map_gist(
6441 __isl_take isl_union_map *umap,
6442 __isl_take isl_union_map *context);
6443 __isl_give isl_union_map *isl_union_map_gist_params(
6444 __isl_take isl_union_map *umap,
6445 __isl_take isl_set *set);
6446 __isl_give isl_union_map *isl_union_map_gist_domain(
6447 __isl_take isl_union_map *umap,
6448 __isl_take isl_union_set *uset);
6449 __isl_give isl_union_map *isl_union_map_gist_range(
6450 __isl_take isl_union_map *umap,
6451 __isl_take isl_union_set *uset);
6453 #include <isl/aff.h>
6454 __isl_give isl_aff *isl_aff_gist_params(
6455 __isl_take isl_aff *aff,
6456 __isl_take isl_set *context);
6457 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
6458 __isl_take isl_set *context);
6459 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
6460 __isl_take isl_multi_aff *maff,
6461 __isl_take isl_set *context);
6462 __isl_give isl_multi_aff *isl_multi_aff_gist(
6463 __isl_take isl_multi_aff *maff,
6464 __isl_take isl_set *context);
6465 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
6466 __isl_take isl_pw_aff *pwaff,
6467 __isl_take isl_set *context);
6468 __isl_give isl_pw_aff *isl_pw_aff_gist(
6469 __isl_take isl_pw_aff *pwaff,
6470 __isl_take isl_set *context);
6471 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
6472 __isl_take isl_pw_multi_aff *pma,
6473 __isl_take isl_set *set);
6474 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
6475 __isl_take isl_pw_multi_aff *pma,
6476 __isl_take isl_set *set);
6477 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
6478 __isl_take isl_multi_pw_aff *mpa,
6479 __isl_take isl_set *set);
6480 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
6481 __isl_take isl_multi_pw_aff *mpa,
6482 __isl_take isl_set *set);
6483 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
6484 __isl_take isl_union_pw_aff *upa,
6485 __isl_take isl_union_set *context);
6486 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
6487 __isl_take isl_union_pw_aff *upa,
6488 __isl_take isl_set *context);
6489 __isl_give isl_union_pw_multi_aff *
6490 isl_union_pw_multi_aff_gist_params(
6491 __isl_take isl_union_pw_multi_aff *upma,
6492 __isl_take isl_set *context);
6493 __isl_give isl_union_pw_multi_aff *
6494 isl_union_pw_multi_aff_gist(
6495 __isl_take isl_union_pw_multi_aff *upma,
6496 __isl_take isl_union_set *context);
6497 __isl_give isl_multi_union_pw_aff *
6498 isl_multi_union_pw_aff_gist_params(
6499 __isl_take isl_multi_union_pw_aff *aff,
6500 __isl_take isl_set *context);
6501 __isl_give isl_multi_union_pw_aff *
6502 isl_multi_union_pw_aff_gist(
6503 __isl_take isl_multi_union_pw_aff *aff,
6504 __isl_take isl_union_set *context);
6506 #include <isl/polynomial.h>
6507 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
6508 __isl_take isl_qpolynomial *qp,
6509 __isl_take isl_set *context);
6510 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
6511 __isl_take isl_qpolynomial *qp,
6512 __isl_take isl_set *context);
6513 __isl_give isl_qpolynomial_fold *
6514 isl_qpolynomial_fold_gist_params(
6515 __isl_take isl_qpolynomial_fold *fold,
6516 __isl_take isl_set *context);
6517 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
6518 __isl_take isl_qpolynomial_fold *fold,
6519 __isl_take isl_set *context);
6520 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
6521 __isl_take isl_pw_qpolynomial *pwqp,
6522 __isl_take isl_set *context);
6523 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
6524 __isl_take isl_pw_qpolynomial *pwqp,
6525 __isl_take isl_set *context);
6526 __isl_give isl_pw_qpolynomial_fold *
6527 isl_pw_qpolynomial_fold_gist(
6528 __isl_take isl_pw_qpolynomial_fold *pwf,
6529 __isl_take isl_set *context);
6530 __isl_give isl_pw_qpolynomial_fold *
6531 isl_pw_qpolynomial_fold_gist_params(
6532 __isl_take isl_pw_qpolynomial_fold *pwf,
6533 __isl_take isl_set *context);
6534 __isl_give isl_union_pw_qpolynomial *
6535 isl_union_pw_qpolynomial_gist_params(
6536 __isl_take isl_union_pw_qpolynomial *upwqp,
6537 __isl_take isl_set *context);
6538 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
6539 __isl_take isl_union_pw_qpolynomial *upwqp,
6540 __isl_take isl_union_set *context);
6541 __isl_give isl_union_pw_qpolynomial_fold *
6542 isl_union_pw_qpolynomial_fold_gist(
6543 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6544 __isl_take isl_union_set *context);
6545 __isl_give isl_union_pw_qpolynomial_fold *
6546 isl_union_pw_qpolynomial_fold_gist_params(
6547 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6548 __isl_take isl_set *context);
6550 =item * Binary Arithmethic Operations
6552 #include <isl/val.h>
6553 __isl_give isl_multi_val *isl_multi_val_add(
6554 __isl_take isl_multi_val *mv1,
6555 __isl_take isl_multi_val *mv2);
6556 __isl_give isl_multi_val *isl_multi_val_sub(
6557 __isl_take isl_multi_val *mv1,
6558 __isl_take isl_multi_val *mv2);
6560 #include <isl/aff.h>
6561 __isl_give isl_aff *isl_aff_add(
6562 __isl_take isl_aff *aff1,
6563 __isl_take isl_aff *aff2);
6564 __isl_give isl_multi_aff *isl_multi_aff_add(
6565 __isl_take isl_multi_aff *maff1,
6566 __isl_take isl_multi_aff *maff2);
6567 __isl_give isl_pw_aff *isl_pw_aff_add(
6568 __isl_take isl_pw_aff *pwaff1,
6569 __isl_take isl_pw_aff *pwaff2);
6570 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add(
6571 __isl_take isl_multi_pw_aff *mpa1,
6572 __isl_take isl_multi_pw_aff *mpa2);
6573 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
6574 __isl_take isl_pw_multi_aff *pma1,
6575 __isl_take isl_pw_multi_aff *pma2);
6576 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
6577 __isl_take isl_union_pw_aff *upa1,
6578 __isl_take isl_union_pw_aff *upa2);
6579 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
6580 __isl_take isl_union_pw_multi_aff *upma1,
6581 __isl_take isl_union_pw_multi_aff *upma2);
6582 __isl_give isl_multi_union_pw_aff *
6583 isl_multi_union_pw_aff_add(
6584 __isl_take isl_multi_union_pw_aff *mupa1,
6585 __isl_take isl_multi_union_pw_aff *mupa2);
6586 __isl_give isl_pw_aff *isl_pw_aff_min(
6587 __isl_take isl_pw_aff *pwaff1,
6588 __isl_take isl_pw_aff *pwaff2);
6589 __isl_give isl_pw_aff *isl_pw_aff_max(
6590 __isl_take isl_pw_aff *pwaff1,
6591 __isl_take isl_pw_aff *pwaff2);
6592 __isl_give isl_aff *isl_aff_sub(
6593 __isl_take isl_aff *aff1,
6594 __isl_take isl_aff *aff2);
6595 __isl_give isl_multi_aff *isl_multi_aff_sub(
6596 __isl_take isl_multi_aff *ma1,
6597 __isl_take isl_multi_aff *ma2);
6598 __isl_give isl_pw_aff *isl_pw_aff_sub(
6599 __isl_take isl_pw_aff *pwaff1,
6600 __isl_take isl_pw_aff *pwaff2);
6601 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
6602 __isl_take isl_multi_pw_aff *mpa1,
6603 __isl_take isl_multi_pw_aff *mpa2);
6604 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
6605 __isl_take isl_pw_multi_aff *pma1,
6606 __isl_take isl_pw_multi_aff *pma2);
6607 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
6608 __isl_take isl_union_pw_aff *upa1,
6609 __isl_take isl_union_pw_aff *upa2);
6610 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
6611 __isl_take isl_union_pw_multi_aff *upma1,
6612 __isl_take isl_union_pw_multi_aff *upma2);
6613 __isl_give isl_multi_union_pw_aff *
6614 isl_multi_union_pw_aff_sub(
6615 __isl_take isl_multi_union_pw_aff *mupa1,
6616 __isl_take isl_multi_union_pw_aff *mupa2);
6618 C<isl_aff_sub> subtracts the second argument from the first.
6620 #include <isl/polynomial.h>
6621 __isl_give isl_qpolynomial *isl_qpolynomial_add(
6622 __isl_take isl_qpolynomial *qp1,
6623 __isl_take isl_qpolynomial *qp2);
6624 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
6625 __isl_take isl_pw_qpolynomial *pwqp1,
6626 __isl_take isl_pw_qpolynomial *pwqp2);
6627 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
6628 __isl_take isl_pw_qpolynomial *pwqp1,
6629 __isl_take isl_pw_qpolynomial *pwqp2);
6630 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
6631 __isl_take isl_pw_qpolynomial_fold *pwf1,
6632 __isl_take isl_pw_qpolynomial_fold *pwf2);
6633 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
6634 __isl_take isl_union_pw_qpolynomial *upwqp1,
6635 __isl_take isl_union_pw_qpolynomial *upwqp2);
6636 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
6637 __isl_take isl_qpolynomial *qp1,
6638 __isl_take isl_qpolynomial *qp2);
6639 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
6640 __isl_take isl_pw_qpolynomial *pwqp1,
6641 __isl_take isl_pw_qpolynomial *pwqp2);
6642 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
6643 __isl_take isl_union_pw_qpolynomial *upwqp1,
6644 __isl_take isl_union_pw_qpolynomial *upwqp2);
6645 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
6646 __isl_take isl_pw_qpolynomial_fold *pwf1,
6647 __isl_take isl_pw_qpolynomial_fold *pwf2);
6648 __isl_give isl_union_pw_qpolynomial_fold *
6649 isl_union_pw_qpolynomial_fold_fold(
6650 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
6651 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
6653 #include <isl/aff.h>
6654 __isl_give isl_pw_aff *isl_pw_aff_union_add(
6655 __isl_take isl_pw_aff *pwaff1,
6656 __isl_take isl_pw_aff *pwaff2);
6657 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
6658 __isl_take isl_pw_multi_aff *pma1,
6659 __isl_take isl_pw_multi_aff *pma2);
6660 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
6661 __isl_take isl_union_pw_aff *upa1,
6662 __isl_take isl_union_pw_aff *upa2);
6663 __isl_give isl_union_pw_multi_aff *
6664 isl_union_pw_multi_aff_union_add(
6665 __isl_take isl_union_pw_multi_aff *upma1,
6666 __isl_take isl_union_pw_multi_aff *upma2);
6667 __isl_give isl_multi_union_pw_aff *
6668 isl_multi_union_pw_aff_union_add(
6669 __isl_take isl_multi_union_pw_aff *mupa1,
6670 __isl_take isl_multi_union_pw_aff *mupa2);
6671 __isl_give isl_pw_aff *isl_pw_aff_union_min(
6672 __isl_take isl_pw_aff *pwaff1,
6673 __isl_take isl_pw_aff *pwaff2);
6674 __isl_give isl_pw_aff *isl_pw_aff_union_max(
6675 __isl_take isl_pw_aff *pwaff1,
6676 __isl_take isl_pw_aff *pwaff2);
6678 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
6679 expression with a domain that is the union of those of C<pwaff1> and
6680 C<pwaff2> and such that on each cell, the quasi-affine expression is
6681 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
6682 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
6683 associated expression is the defined one.
6684 This in contrast to the C<isl_pw_aff_max> function, which is
6685 only defined on the shared definition domain of the arguments.
6687 #include <isl/val.h>
6688 __isl_give isl_multi_val *isl_multi_val_add_val(
6689 __isl_take isl_multi_val *mv,
6690 __isl_take isl_val *v);
6691 __isl_give isl_multi_val *isl_multi_val_mod_val(
6692 __isl_take isl_multi_val *mv,
6693 __isl_take isl_val *v);
6694 __isl_give isl_multi_val *isl_multi_val_scale_val(
6695 __isl_take isl_multi_val *mv,
6696 __isl_take isl_val *v);
6697 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
6698 __isl_take isl_multi_val *mv,
6699 __isl_take isl_val *v);
6701 #include <isl/aff.h>
6702 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
6703 __isl_take isl_val *mod);
6704 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
6705 __isl_take isl_pw_aff *pa,
6706 __isl_take isl_val *mod);
6707 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
6708 __isl_take isl_union_pw_aff *upa,
6709 __isl_take isl_val *f);
6710 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
6711 __isl_take isl_val *v);
6712 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
6713 __isl_take isl_multi_aff *ma,
6714 __isl_take isl_val *v);
6715 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
6716 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
6717 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
6718 __isl_take isl_multi_pw_aff *mpa,
6719 __isl_take isl_val *v);
6720 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
6721 __isl_take isl_pw_multi_aff *pma,
6722 __isl_take isl_val *v);
6723 __isl_give isl_union_pw_multi_aff *
6724 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
6725 __isl_take isl_union_pw_aff *upa,
6726 __isl_take isl_val *f);
6727 isl_union_pw_multi_aff_scale_val(
6728 __isl_take isl_union_pw_multi_aff *upma,
6729 __isl_take isl_val *val);
6730 __isl_give isl_multi_union_pw_aff *
6731 isl_multi_union_pw_aff_scale_val(
6732 __isl_take isl_multi_union_pw_aff *mupa,
6733 __isl_take isl_val *v);
6734 __isl_give isl_aff *isl_aff_scale_down_ui(
6735 __isl_take isl_aff *aff, unsigned f);
6736 __isl_give isl_aff *isl_aff_scale_down_val(
6737 __isl_take isl_aff *aff, __isl_take isl_val *v);
6738 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
6739 __isl_take isl_multi_aff *ma,
6740 __isl_take isl_val *v);
6741 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
6742 __isl_take isl_pw_aff *pa,
6743 __isl_take isl_val *f);
6744 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
6745 __isl_take isl_multi_pw_aff *mpa,
6746 __isl_take isl_val *v);
6747 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
6748 __isl_take isl_pw_multi_aff *pma,
6749 __isl_take isl_val *v);
6750 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
6751 __isl_take isl_union_pw_aff *upa,
6752 __isl_take isl_val *v);
6753 __isl_give isl_union_pw_multi_aff *
6754 isl_union_pw_multi_aff_scale_down_val(
6755 __isl_take isl_union_pw_multi_aff *upma,
6756 __isl_take isl_val *val);
6757 __isl_give isl_multi_union_pw_aff *
6758 isl_multi_union_pw_aff_scale_down_val(
6759 __isl_take isl_multi_union_pw_aff *mupa,
6760 __isl_take isl_val *v);
6762 #include <isl/polynomial.h>
6763 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
6764 __isl_take isl_qpolynomial *qp,
6765 __isl_take isl_val *v);
6766 __isl_give isl_qpolynomial_fold *
6767 isl_qpolynomial_fold_scale_val(
6768 __isl_take isl_qpolynomial_fold *fold,
6769 __isl_take isl_val *v);
6770 __isl_give isl_pw_qpolynomial *
6771 isl_pw_qpolynomial_scale_val(
6772 __isl_take isl_pw_qpolynomial *pwqp,
6773 __isl_take isl_val *v);
6774 __isl_give isl_pw_qpolynomial_fold *
6775 isl_pw_qpolynomial_fold_scale_val(
6776 __isl_take isl_pw_qpolynomial_fold *pwf,
6777 __isl_take isl_val *v);
6778 __isl_give isl_union_pw_qpolynomial *
6779 isl_union_pw_qpolynomial_scale_val(
6780 __isl_take isl_union_pw_qpolynomial *upwqp,
6781 __isl_take isl_val *v);
6782 __isl_give isl_union_pw_qpolynomial_fold *
6783 isl_union_pw_qpolynomial_fold_scale_val(
6784 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6785 __isl_take isl_val *v);
6786 __isl_give isl_qpolynomial *
6787 isl_qpolynomial_scale_down_val(
6788 __isl_take isl_qpolynomial *qp,
6789 __isl_take isl_val *v);
6790 __isl_give isl_qpolynomial_fold *
6791 isl_qpolynomial_fold_scale_down_val(
6792 __isl_take isl_qpolynomial_fold *fold,
6793 __isl_take isl_val *v);
6794 __isl_give isl_pw_qpolynomial *
6795 isl_pw_qpolynomial_scale_down_val(
6796 __isl_take isl_pw_qpolynomial *pwqp,
6797 __isl_take isl_val *v);
6798 __isl_give isl_pw_qpolynomial_fold *
6799 isl_pw_qpolynomial_fold_scale_down_val(
6800 __isl_take isl_pw_qpolynomial_fold *pwf,
6801 __isl_take isl_val *v);
6802 __isl_give isl_union_pw_qpolynomial *
6803 isl_union_pw_qpolynomial_scale_down_val(
6804 __isl_take isl_union_pw_qpolynomial *upwqp,
6805 __isl_take isl_val *v);
6806 __isl_give isl_union_pw_qpolynomial_fold *
6807 isl_union_pw_qpolynomial_fold_scale_down_val(
6808 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6809 __isl_take isl_val *v);
6811 #include <isl/val.h>
6812 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
6813 __isl_take isl_multi_val *mv1,
6814 __isl_take isl_multi_val *mv2);
6815 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
6816 __isl_take isl_multi_val *mv1,
6817 __isl_take isl_multi_val *mv2);
6818 __isl_give isl_multi_val *
6819 isl_multi_val_scale_down_multi_val(
6820 __isl_take isl_multi_val *mv1,
6821 __isl_take isl_multi_val *mv2);
6823 #include <isl/aff.h>
6824 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
6825 __isl_take isl_multi_aff *ma,
6826 __isl_take isl_multi_val *mv);
6827 __isl_give isl_multi_union_pw_aff *
6828 isl_multi_union_pw_aff_mod_multi_val(
6829 __isl_take isl_multi_union_pw_aff *upma,
6830 __isl_take isl_multi_val *mv);
6831 __isl_give isl_multi_pw_aff *
6832 isl_multi_pw_aff_mod_multi_val(
6833 __isl_take isl_multi_pw_aff *mpa,
6834 __isl_take isl_multi_val *mv);
6835 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
6836 __isl_take isl_multi_aff *ma,
6837 __isl_take isl_multi_val *mv);
6838 __isl_give isl_pw_multi_aff *
6839 isl_pw_multi_aff_scale_multi_val(
6840 __isl_take isl_pw_multi_aff *pma,
6841 __isl_take isl_multi_val *mv);
6842 __isl_give isl_multi_pw_aff *
6843 isl_multi_pw_aff_scale_multi_val(
6844 __isl_take isl_multi_pw_aff *mpa,
6845 __isl_take isl_multi_val *mv);
6846 __isl_give isl_multi_union_pw_aff *
6847 isl_multi_union_pw_aff_scale_multi_val(
6848 __isl_take isl_multi_union_pw_aff *mupa,
6849 __isl_take isl_multi_val *mv);
6850 __isl_give isl_union_pw_multi_aff *
6851 isl_union_pw_multi_aff_scale_multi_val(
6852 __isl_take isl_union_pw_multi_aff *upma,
6853 __isl_take isl_multi_val *mv);
6854 __isl_give isl_multi_aff *
6855 isl_multi_aff_scale_down_multi_val(
6856 __isl_take isl_multi_aff *ma,
6857 __isl_take isl_multi_val *mv);
6858 __isl_give isl_multi_pw_aff *
6859 isl_multi_pw_aff_scale_down_multi_val(
6860 __isl_take isl_multi_pw_aff *mpa,
6861 __isl_take isl_multi_val *mv);
6862 __isl_give isl_multi_union_pw_aff *
6863 isl_multi_union_pw_aff_scale_down_multi_val(
6864 __isl_take isl_multi_union_pw_aff *mupa,
6865 __isl_take isl_multi_val *mv);
6867 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
6868 by the corresponding elements of C<mv>.
6870 #include <isl/aff.h>
6871 __isl_give isl_aff *isl_aff_mul(
6872 __isl_take isl_aff *aff1,
6873 __isl_take isl_aff *aff2);
6874 __isl_give isl_aff *isl_aff_div(
6875 __isl_take isl_aff *aff1,
6876 __isl_take isl_aff *aff2);
6877 __isl_give isl_pw_aff *isl_pw_aff_mul(
6878 __isl_take isl_pw_aff *pwaff1,
6879 __isl_take isl_pw_aff *pwaff2);
6880 __isl_give isl_pw_aff *isl_pw_aff_div(
6881 __isl_take isl_pw_aff *pa1,
6882 __isl_take isl_pw_aff *pa2);
6883 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
6884 __isl_take isl_pw_aff *pa1,
6885 __isl_take isl_pw_aff *pa2);
6886 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
6887 __isl_take isl_pw_aff *pa1,
6888 __isl_take isl_pw_aff *pa2);
6890 When multiplying two affine expressions, at least one of the two needs
6891 to be a constant. Similarly, when dividing an affine expression by another,
6892 the second expression needs to be a constant.
6893 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
6894 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
6897 #include <isl/polynomial.h>
6898 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
6899 __isl_take isl_qpolynomial *qp1,
6900 __isl_take isl_qpolynomial *qp2);
6901 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
6902 __isl_take isl_pw_qpolynomial *pwqp1,
6903 __isl_take isl_pw_qpolynomial *pwqp2);
6904 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
6905 __isl_take isl_union_pw_qpolynomial *upwqp1,
6906 __isl_take isl_union_pw_qpolynomial *upwqp2);
6910 =head3 Lexicographic Optimization
6912 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
6913 the following functions
6914 compute a set that contains the lexicographic minimum or maximum
6915 of the elements in C<set> (or C<bset>) for those values of the parameters
6916 that satisfy C<dom>.
6917 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
6918 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
6920 In other words, the union of the parameter values
6921 for which the result is non-empty and of C<*empty>
6924 #include <isl/set.h>
6925 __isl_give isl_set *isl_basic_set_partial_lexmin(
6926 __isl_take isl_basic_set *bset,
6927 __isl_take isl_basic_set *dom,
6928 __isl_give isl_set **empty);
6929 __isl_give isl_set *isl_basic_set_partial_lexmax(
6930 __isl_take isl_basic_set *bset,
6931 __isl_take isl_basic_set *dom,
6932 __isl_give isl_set **empty);
6933 __isl_give isl_set *isl_set_partial_lexmin(
6934 __isl_take isl_set *set, __isl_take isl_set *dom,
6935 __isl_give isl_set **empty);
6936 __isl_give isl_set *isl_set_partial_lexmax(
6937 __isl_take isl_set *set, __isl_take isl_set *dom,
6938 __isl_give isl_set **empty);
6940 Given a (basic) set C<set> (or C<bset>), the following functions simply
6941 return a set containing the lexicographic minimum or maximum
6942 of the elements in C<set> (or C<bset>).
6943 In case of union sets, the optimum is computed per space.
6945 #include <isl/set.h>
6946 __isl_give isl_set *isl_basic_set_lexmin(
6947 __isl_take isl_basic_set *bset);
6948 __isl_give isl_set *isl_basic_set_lexmax(
6949 __isl_take isl_basic_set *bset);
6950 __isl_give isl_set *isl_set_lexmin(
6951 __isl_take isl_set *set);
6952 __isl_give isl_set *isl_set_lexmax(
6953 __isl_take isl_set *set);
6954 __isl_give isl_union_set *isl_union_set_lexmin(
6955 __isl_take isl_union_set *uset);
6956 __isl_give isl_union_set *isl_union_set_lexmax(
6957 __isl_take isl_union_set *uset);
6959 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
6960 the following functions
6961 compute a relation that maps each element of C<dom>
6962 to the single lexicographic minimum or maximum
6963 of the elements that are associated to that same
6964 element in C<map> (or C<bmap>).
6965 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
6966 that contains the elements in C<dom> that do not map
6967 to any elements in C<map> (or C<bmap>).
6968 In other words, the union of the domain of the result and of C<*empty>
6971 #include <isl/map.h>
6972 __isl_give isl_map *isl_basic_map_partial_lexmax(
6973 __isl_take isl_basic_map *bmap,
6974 __isl_take isl_basic_set *dom,
6975 __isl_give isl_set **empty);
6976 __isl_give isl_map *isl_basic_map_partial_lexmin(
6977 __isl_take isl_basic_map *bmap,
6978 __isl_take isl_basic_set *dom,
6979 __isl_give isl_set **empty);
6980 __isl_give isl_map *isl_map_partial_lexmax(
6981 __isl_take isl_map *map, __isl_take isl_set *dom,
6982 __isl_give isl_set **empty);
6983 __isl_give isl_map *isl_map_partial_lexmin(
6984 __isl_take isl_map *map, __isl_take isl_set *dom,
6985 __isl_give isl_set **empty);
6987 Given a (basic) map C<map> (or C<bmap>), the following functions simply
6988 return a map mapping each element in the domain of
6989 C<map> (or C<bmap>) to the lexicographic minimum or maximum
6990 of all elements associated to that element.
6991 In case of union relations, the optimum is computed per space.
6993 #include <isl/map.h>
6994 __isl_give isl_map *isl_basic_map_lexmin(
6995 __isl_take isl_basic_map *bmap);
6996 __isl_give isl_map *isl_basic_map_lexmax(
6997 __isl_take isl_basic_map *bmap);
6998 __isl_give isl_map *isl_map_lexmin(
6999 __isl_take isl_map *map);
7000 __isl_give isl_map *isl_map_lexmax(
7001 __isl_take isl_map *map);
7002 __isl_give isl_union_map *isl_union_map_lexmin(
7003 __isl_take isl_union_map *umap);
7004 __isl_give isl_union_map *isl_union_map_lexmax(
7005 __isl_take isl_union_map *umap);
7007 The following functions return their result in the form of
7008 a piecewise multi-affine expression,
7009 but are otherwise equivalent to the corresponding functions
7010 returning a basic set or relation.
7012 #include <isl/set.h>
7013 __isl_give isl_pw_multi_aff *
7014 isl_basic_set_partial_lexmin_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 *
7019 isl_basic_set_partial_lexmax_pw_multi_aff(
7020 __isl_take isl_basic_set *bset,
7021 __isl_take isl_basic_set *dom,
7022 __isl_give isl_set **empty);
7023 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
7024 __isl_take isl_set *set);
7025 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
7026 __isl_take isl_set *set);
7028 #include <isl/map.h>
7029 __isl_give isl_pw_multi_aff *
7030 isl_basic_map_lexmin_pw_multi_aff(
7031 __isl_take isl_basic_map *bmap);
7032 __isl_give isl_pw_multi_aff *
7033 isl_basic_map_partial_lexmin_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 *
7038 isl_basic_map_partial_lexmax_pw_multi_aff(
7039 __isl_take isl_basic_map *bmap,
7040 __isl_take isl_basic_set *dom,
7041 __isl_give isl_set **empty);
7042 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
7043 __isl_take isl_map *map);
7044 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
7045 __isl_take isl_map *map);
7047 The following functions return the lexicographic minimum or maximum
7048 on the shared domain of the inputs and the single defined function
7049 on those parts of the domain where only a single function is defined.
7051 #include <isl/aff.h>
7052 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
7053 __isl_take isl_pw_multi_aff *pma1,
7054 __isl_take isl_pw_multi_aff *pma2);
7055 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
7056 __isl_take isl_pw_multi_aff *pma1,
7057 __isl_take isl_pw_multi_aff *pma2);
7059 =head2 Ternary Operations
7061 #include <isl/aff.h>
7062 __isl_give isl_pw_aff *isl_pw_aff_cond(
7063 __isl_take isl_pw_aff *cond,
7064 __isl_take isl_pw_aff *pwaff_true,
7065 __isl_take isl_pw_aff *pwaff_false);
7067 The function C<isl_pw_aff_cond> performs a conditional operator
7068 and returns an expression that is equal to C<pwaff_true>
7069 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
7070 where C<cond> is zero.
7074 Lists are defined over several element types, including
7075 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_union_pw_aff>,
7076 C<isl_union_pw_multi_aff>, C<isl_constraint>,
7077 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
7078 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
7079 Here we take lists of C<isl_set>s as an example.
7080 Lists can be created, copied, modified and freed using the following functions.
7082 #include <isl/set.h>
7083 __isl_give isl_set_list *isl_set_list_from_set(
7084 __isl_take isl_set *el);
7085 __isl_give isl_set_list *isl_set_list_alloc(
7086 isl_ctx *ctx, int n);
7087 __isl_give isl_set_list *isl_set_list_copy(
7088 __isl_keep isl_set_list *list);
7089 __isl_give isl_set_list *isl_set_list_insert(
7090 __isl_take isl_set_list *list, unsigned pos,
7091 __isl_take isl_set *el);
7092 __isl_give isl_set_list *isl_set_list_add(
7093 __isl_take isl_set_list *list,
7094 __isl_take isl_set *el);
7095 __isl_give isl_set_list *isl_set_list_drop(
7096 __isl_take isl_set_list *list,
7097 unsigned first, unsigned n);
7098 __isl_give isl_set_list *isl_set_list_set_set(
7099 __isl_take isl_set_list *list, int index,
7100 __isl_take isl_set *set);
7101 __isl_give isl_set_list *isl_set_list_concat(
7102 __isl_take isl_set_list *list1,
7103 __isl_take isl_set_list *list2);
7104 __isl_give isl_set_list *isl_set_list_sort(
7105 __isl_take isl_set_list *list,
7106 int (*cmp)(__isl_keep isl_set *a,
7107 __isl_keep isl_set *b, void *user),
7109 __isl_null isl_set_list *isl_set_list_free(
7110 __isl_take isl_set_list *list);
7112 C<isl_set_list_alloc> creates an empty list with an initial capacity
7113 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
7114 add elements to a list, increasing its capacity as needed.
7115 C<isl_set_list_from_set> creates a list with a single element.
7117 Lists can be inspected using the following functions.
7119 #include <isl/set.h>
7120 int isl_set_list_n_set(__isl_keep isl_set_list *list);
7121 __isl_give isl_set *isl_set_list_get_set(
7122 __isl_keep isl_set_list *list, int index);
7123 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list,
7124 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7126 isl_stat isl_set_list_foreach_scc(
7127 __isl_keep isl_set_list *list,
7128 isl_bool (*follows)(__isl_keep isl_set *a,
7129 __isl_keep isl_set *b, void *user),
7131 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7134 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
7135 strongly connected components of the graph with as vertices the elements
7136 of C<list> and a directed edge from vertex C<b> to vertex C<a>
7137 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
7138 should return C<-1> on error.
7140 Lists can be printed using
7142 #include <isl/set.h>
7143 __isl_give isl_printer *isl_printer_print_set_list(
7144 __isl_take isl_printer *p,
7145 __isl_keep isl_set_list *list);
7147 =head2 Associative arrays
7149 Associative arrays map isl objects of a specific type to isl objects
7150 of some (other) specific type. They are defined for several pairs
7151 of types, including (C<isl_map>, C<isl_basic_set>),
7152 (C<isl_id>, C<isl_ast_expr>) and.
7153 (C<isl_id>, C<isl_pw_aff>).
7154 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
7157 Associative arrays can be created, copied and freed using
7158 the following functions.
7160 #include <isl/id_to_ast_expr.h>
7161 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
7162 isl_ctx *ctx, int min_size);
7163 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
7164 __isl_keep isl_id_to_ast_expr *id2expr);
7165 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
7166 __isl_take isl_id_to_ast_expr *id2expr);
7168 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
7169 to specify the expected size of the associative array.
7170 The associative array will be grown automatically as needed.
7172 Associative arrays can be inspected using the following functions.
7174 #include <isl/id_to_ast_expr.h>
7175 isl_bool isl_id_to_ast_expr_has(
7176 __isl_keep isl_id_to_ast_expr *id2expr,
7177 __isl_keep isl_id *key);
7178 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
7179 __isl_keep isl_id_to_ast_expr *id2expr,
7180 __isl_take isl_id *key);
7181 isl_stat isl_id_to_ast_expr_foreach(
7182 __isl_keep isl_id_to_ast_expr *id2expr,
7183 isl_stat (*fn)(__isl_take isl_id *key,
7184 __isl_take isl_ast_expr *val, void *user),
7187 They can be modified using the following function.
7189 #include <isl/id_to_ast_expr.h>
7190 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
7191 __isl_take isl_id_to_ast_expr *id2expr,
7192 __isl_take isl_id *key,
7193 __isl_take isl_ast_expr *val);
7194 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
7195 __isl_take isl_id_to_ast_expr *id2expr,
7196 __isl_take isl_id *key);
7198 Associative arrays can be printed using the following function.
7200 #include <isl/id_to_ast_expr.h>
7201 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
7202 __isl_take isl_printer *p,
7203 __isl_keep isl_id_to_ast_expr *id2expr);
7207 Vectors can be created, copied and freed using the following functions.
7209 #include <isl/vec.h>
7210 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
7212 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
7213 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
7215 Note that the elements of a newly created vector may have arbitrary values.
7216 The elements can be changed and inspected using the following functions.
7218 int isl_vec_size(__isl_keep isl_vec *vec);
7219 __isl_give isl_val *isl_vec_get_element_val(
7220 __isl_keep isl_vec *vec, int pos);
7221 __isl_give isl_vec *isl_vec_set_element_si(
7222 __isl_take isl_vec *vec, int pos, int v);
7223 __isl_give isl_vec *isl_vec_set_element_val(
7224 __isl_take isl_vec *vec, int pos,
7225 __isl_take isl_val *v);
7226 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
7228 __isl_give isl_vec *isl_vec_set_val(
7229 __isl_take isl_vec *vec, __isl_take isl_val *v);
7230 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
7231 __isl_keep isl_vec *vec2, int pos);
7233 C<isl_vec_get_element> will return a negative value if anything went wrong.
7234 In that case, the value of C<*v> is undefined.
7236 The following function can be used to concatenate two vectors.
7238 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
7239 __isl_take isl_vec *vec2);
7243 Matrices can be created, copied and freed using the following functions.
7245 #include <isl/mat.h>
7246 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
7247 unsigned n_row, unsigned n_col);
7248 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
7249 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
7251 Note that the elements of a newly created matrix may have arbitrary values.
7252 The elements can be changed and inspected using the following functions.
7254 int isl_mat_rows(__isl_keep isl_mat *mat);
7255 int isl_mat_cols(__isl_keep isl_mat *mat);
7256 __isl_give isl_val *isl_mat_get_element_val(
7257 __isl_keep isl_mat *mat, int row, int col);
7258 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
7259 int row, int col, int v);
7260 __isl_give isl_mat *isl_mat_set_element_val(
7261 __isl_take isl_mat *mat, int row, int col,
7262 __isl_take isl_val *v);
7264 C<isl_mat_get_element> will return a negative value if anything went wrong.
7265 In that case, the value of C<*v> is undefined.
7267 The following function can be used to compute the (right) inverse
7268 of a matrix, i.e., a matrix such that the product of the original
7269 and the inverse (in that order) is a multiple of the identity matrix.
7270 The input matrix is assumed to be of full row-rank.
7272 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
7274 The following function can be used to compute the (right) kernel
7275 (or null space) of a matrix, i.e., a matrix such that the product of
7276 the original and the kernel (in that order) is the zero matrix.
7278 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
7280 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
7282 The following functions determine
7283 an upper or lower bound on a quasipolynomial over its domain.
7285 __isl_give isl_pw_qpolynomial_fold *
7286 isl_pw_qpolynomial_bound(
7287 __isl_take isl_pw_qpolynomial *pwqp,
7288 enum isl_fold type, int *tight);
7290 __isl_give isl_union_pw_qpolynomial_fold *
7291 isl_union_pw_qpolynomial_bound(
7292 __isl_take isl_union_pw_qpolynomial *upwqp,
7293 enum isl_fold type, int *tight);
7295 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
7296 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
7297 is the returned bound is known be tight, i.e., for each value
7298 of the parameters there is at least
7299 one element in the domain that reaches the bound.
7300 If the domain of C<pwqp> is not wrapping, then the bound is computed
7301 over all elements in that domain and the result has a purely parametric
7302 domain. If the domain of C<pwqp> is wrapping, then the bound is
7303 computed over the range of the wrapped relation. The domain of the
7304 wrapped relation becomes the domain of the result.
7306 =head2 Parametric Vertex Enumeration
7308 The parametric vertex enumeration described in this section
7309 is mainly intended to be used internally and by the C<barvinok>
7312 #include <isl/vertices.h>
7313 __isl_give isl_vertices *isl_basic_set_compute_vertices(
7314 __isl_keep isl_basic_set *bset);
7316 The function C<isl_basic_set_compute_vertices> performs the
7317 actual computation of the parametric vertices and the chamber
7318 decomposition and store the result in an C<isl_vertices> object.
7319 This information can be queried by either iterating over all
7320 the vertices or iterating over all the chambers or cells
7321 and then iterating over all vertices that are active on the chamber.
7323 isl_stat isl_vertices_foreach_vertex(
7324 __isl_keep isl_vertices *vertices,
7325 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7326 void *user), void *user);
7328 isl_stat isl_vertices_foreach_cell(
7329 __isl_keep isl_vertices *vertices,
7330 isl_stat (*fn)(__isl_take isl_cell *cell,
7331 void *user), void *user);
7332 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
7333 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7334 void *user), void *user);
7336 Other operations that can be performed on an C<isl_vertices> object are
7339 int isl_vertices_get_n_vertices(
7340 __isl_keep isl_vertices *vertices);
7341 void isl_vertices_free(__isl_take isl_vertices *vertices);
7343 Vertices can be inspected and destroyed using the following functions.
7345 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
7346 __isl_give isl_basic_set *isl_vertex_get_domain(
7347 __isl_keep isl_vertex *vertex);
7348 __isl_give isl_multi_aff *isl_vertex_get_expr(
7349 __isl_keep isl_vertex *vertex);
7350 void isl_vertex_free(__isl_take isl_vertex *vertex);
7352 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
7353 describing the vertex in terms of the parameters,
7354 while C<isl_vertex_get_domain> returns the activity domain
7357 Chambers can be inspected and destroyed using the following functions.
7359 __isl_give isl_basic_set *isl_cell_get_domain(
7360 __isl_keep isl_cell *cell);
7361 void isl_cell_free(__isl_take isl_cell *cell);
7363 =head1 Polyhedral Compilation Library
7365 This section collects functionality in C<isl> that has been specifically
7366 designed for use during polyhedral compilation.
7368 =head2 Schedule Trees
7370 A schedule tree is a structured representation of a schedule,
7371 assigning a relative order to a set of domain elements.
7372 The relative order expressed by the schedule tree is
7373 defined recursively. In particular, the order between
7374 two domain elements is determined by the node that is closest
7375 to the root that refers to both elements and that orders them apart.
7376 Each node in the tree is of one of several types.
7377 The root node is always of type C<isl_schedule_node_domain>
7378 (or C<isl_schedule_node_extension>)
7379 and it describes the (extra) domain elements to which the schedule applies.
7380 The other types of nodes are as follows.
7384 =item C<isl_schedule_node_band>
7386 A band of schedule dimensions. Each schedule dimension is represented
7387 by a union piecewise quasi-affine expression. If this expression
7388 assigns a different value to two domain elements, while all previous
7389 schedule dimensions in the same band assign them the same value,
7390 then the two domain elements are ordered according to these two
7393 =item C<isl_schedule_node_expansion>
7395 An expansion node maps each of the domain elements that reach the node
7396 to one or more domain elements. The image of this mapping forms
7397 the set of domain elements that reach the child of the expansion node.
7398 The function that maps each of the expanded domain elements
7399 to the original domain element from which it was expanded
7400 is called the contraction.
7402 =item C<isl_schedule_node_filter>
7404 A filter node does not impose any ordering, but rather intersects
7405 the set of domain elements that the current subtree refers to
7406 with a given union set. The subtree of the filter node only
7407 refers to domain elements in the intersection.
7408 A filter node is typically only used a child of a sequence or
7411 =item C<isl_schedule_node_leaf>
7413 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
7415 =item C<isl_schedule_node_mark>
7417 A mark node can be used to attach any kind of information to a subtree
7418 of the schedule tree.
7420 =item C<isl_schedule_node_sequence>
7422 A sequence node has one or more children, each of which is a filter node.
7423 The filters on these filter nodes form a partition of
7424 the domain elements that the current subtree refers to.
7425 If two domain elements appear in distinct filters then the sequence
7426 node orders them according to the child positions of the corresponding
7429 =item C<isl_schedule_node_set>
7431 A set node is similar to a sequence node, except that
7432 it expresses that domain elements appearing in distinct filters
7433 may have any order. The order of the children of a set node
7434 is therefore also immaterial.
7438 The following node types are only supported by the AST generator.
7442 =item C<isl_schedule_node_context>
7444 The context describes constraints on the parameters and
7445 the schedule dimensions of outer
7446 bands that the AST generator may assume to hold. It is also the only
7447 kind of node that may introduce additional parameters.
7448 The space of the context is that of the flat product of the outer
7449 band nodes. In particular, if there are no outer band nodes, then
7450 this space is the unnamed zero-dimensional space.
7451 Since a context node references the outer band nodes, any tree
7452 containing a context node is considered to be anchored.
7454 =item C<isl_schedule_node_extension>
7456 An extension node instructs the AST generator to add additional
7457 domain elements that need to be scheduled.
7458 The additional domain elements are described by the range of
7459 the extension map in terms of the outer schedule dimensions,
7460 i.e., the flat product of the outer band nodes.
7461 Note that domain elements are added whenever the AST generator
7462 reaches the extension node, meaning that there are still some
7463 active domain elements for which an AST needs to be generated.
7464 The conditions under which some domain elements are still active
7465 may however not be completely described by the outer AST nodes
7466 generated at that point.
7468 An extension node may also appear as the root of a schedule tree,
7469 when it is intended to be inserted into another tree
7470 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
7471 In this case, the domain of the extension node should
7472 correspond to the flat product of the outer band nodes
7473 in this other schedule tree at the point where the extension tree
7476 =item C<isl_schedule_node_guard>
7478 The guard describes constraints on the parameters and
7479 the schedule dimensions of outer
7480 bands that need to be enforced by the outer nodes
7481 in the generated AST.
7482 The space of the guard is that of the flat product of the outer
7483 band nodes. In particular, if there are no outer band nodes, then
7484 this space is the unnamed zero-dimensional space.
7485 Since a guard node references the outer band nodes, any tree
7486 containing a guard node is considered to be anchored.
7490 Except for the C<isl_schedule_node_context> nodes,
7491 none of the nodes may introduce any parameters that were not
7492 already present in the root domain node.
7494 A schedule tree is encapsulated in an C<isl_schedule> object.
7495 The simplest such objects, those with a tree consisting of single domain node,
7496 can be created using the following functions with either an empty
7497 domain or a given domain.
7499 #include <isl/schedule.h>
7500 __isl_give isl_schedule *isl_schedule_empty(
7501 __isl_take isl_space *space);
7502 __isl_give isl_schedule *isl_schedule_from_domain(
7503 __isl_take isl_union_set *domain);
7505 The function C<isl_schedule_constraints_compute_schedule> described
7506 in L</"Scheduling"> can also be used to construct schedules.
7508 C<isl_schedule> objects may be copied and freed using the following functions.
7510 #include <isl/schedule.h>
7511 __isl_give isl_schedule *isl_schedule_copy(
7512 __isl_keep isl_schedule *sched);
7513 __isl_null isl_schedule *isl_schedule_free(
7514 __isl_take isl_schedule *sched);
7516 The following functions checks whether two C<isl_schedule> objects
7517 are obviously the same.
7519 #include <isl/schedule.h>
7520 isl_bool isl_schedule_plain_is_equal(
7521 __isl_keep isl_schedule *schedule1,
7522 __isl_keep isl_schedule *schedule2);
7524 The domain of the schedule, i.e., the domain described by the root node,
7525 can be obtained using the following function.
7527 #include <isl/schedule.h>
7528 __isl_give isl_union_set *isl_schedule_get_domain(
7529 __isl_keep isl_schedule *schedule);
7531 An extra top-level band node (right underneath the domain node) can
7532 be introduced into the schedule using the following function.
7533 The schedule tree is assumed not to have any anchored nodes.
7535 #include <isl/schedule.h>
7536 __isl_give isl_schedule *
7537 isl_schedule_insert_partial_schedule(
7538 __isl_take isl_schedule *schedule,
7539 __isl_take isl_multi_union_pw_aff *partial);
7541 A top-level context node (right underneath the domain node) can
7542 be introduced into the schedule using the following function.
7544 #include <isl/schedule.h>
7545 __isl_give isl_schedule *isl_schedule_insert_context(
7546 __isl_take isl_schedule *schedule,
7547 __isl_take isl_set *context)
7549 A top-level guard node (right underneath the domain node) can
7550 be introduced into the schedule using the following function.
7552 #include <isl/schedule.h>
7553 __isl_give isl_schedule *isl_schedule_insert_guard(
7554 __isl_take isl_schedule *schedule,
7555 __isl_take isl_set *guard)
7557 A schedule that combines two schedules either in the given
7558 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
7559 or an C<isl_schedule_node_set> node,
7560 can be created using the following functions.
7562 #include <isl/schedule.h>
7563 __isl_give isl_schedule *isl_schedule_sequence(
7564 __isl_take isl_schedule *schedule1,
7565 __isl_take isl_schedule *schedule2);
7566 __isl_give isl_schedule *isl_schedule_set(
7567 __isl_take isl_schedule *schedule1,
7568 __isl_take isl_schedule *schedule2);
7570 The domains of the two input schedules need to be disjoint.
7572 The following function can be used to restrict the domain
7573 of a schedule with a domain node as root to be a subset of the given union set.
7574 This operation may remove nodes in the tree that have become
7577 #include <isl/schedule.h>
7578 __isl_give isl_schedule *isl_schedule_intersect_domain(
7579 __isl_take isl_schedule *schedule,
7580 __isl_take isl_union_set *domain);
7582 The following function resets the user pointers on all parameter
7583 and tuple identifiers referenced by the nodes of the given schedule.
7585 #include <isl/schedule.h>
7586 __isl_give isl_schedule *isl_schedule_reset_user(
7587 __isl_take isl_schedule *schedule);
7589 The following function aligns the parameters of all nodes
7590 in the given schedule to the given space.
7592 #include <isl/schedule.h>
7593 __isl_give isl_schedule *isl_schedule_align_params(
7594 __isl_take isl_schedule *schedule,
7595 __isl_take isl_space *space);
7597 The following function allows the user to plug in a given function
7598 in the iteration domains. The input schedule is not allowed to contain
7599 any expansion nodes.
7601 #include <isl/schedule.h>
7602 __isl_give isl_schedule *
7603 isl_schedule_pullback_union_pw_multi_aff(
7604 __isl_take isl_schedule *schedule,
7605 __isl_take isl_union_pw_multi_aff *upma);
7607 An C<isl_union_map> representation of the schedule can be obtained
7608 from an C<isl_schedule> using the following function.
7610 #include <isl/schedule.h>
7611 __isl_give isl_union_map *isl_schedule_get_map(
7612 __isl_keep isl_schedule *sched);
7614 The resulting relation encodes the same relative ordering as
7615 the schedule by mapping the domain elements to a common schedule space.
7616 If the schedule_separate_components option is set, then the order
7617 of the children of a set node is explicitly encoded in the result.
7618 If the tree contains any expansion nodes, then the relation
7619 is formulated in terms of the expanded domain elements.
7621 Schedules can be read from input using the following functions.
7623 #include <isl/schedule.h>
7624 __isl_give isl_schedule *isl_schedule_read_from_file(
7625 isl_ctx *ctx, FILE *input);
7626 __isl_give isl_schedule *isl_schedule_read_from_str(
7627 isl_ctx *ctx, const char *str);
7629 A representation of the schedule can be printed using
7631 #include <isl/schedule.h>
7632 __isl_give isl_printer *isl_printer_print_schedule(
7633 __isl_take isl_printer *p,
7634 __isl_keep isl_schedule *schedule);
7636 The schedule tree can be traversed through the use of
7637 C<isl_schedule_node> objects that point to a particular
7638 position in the schedule tree. Whenever a C<isl_schedule_node>
7639 is use to modify a node in the schedule tree, the original schedule
7640 tree is left untouched and the modifications are performed to a copy
7641 of the tree. The returned C<isl_schedule_node> then points to
7642 this modified copy of the tree.
7644 The root of the schedule tree can be obtained using the following function.
7646 #include <isl/schedule.h>
7647 __isl_give isl_schedule_node *isl_schedule_get_root(
7648 __isl_keep isl_schedule *schedule);
7650 A pointer to a newly created schedule tree with a single domain
7651 node can be created using the following functions.
7653 #include <isl/schedule_node.h>
7654 __isl_give isl_schedule_node *
7655 isl_schedule_node_from_domain(
7656 __isl_take isl_union_set *domain);
7657 __isl_give isl_schedule_node *
7658 isl_schedule_node_from_extension(
7659 __isl_take isl_union_map *extension);
7661 C<isl_schedule_node_from_extension> creates a tree with an extension
7664 Schedule nodes can be copied and freed using the following functions.
7666 #include <isl/schedule_node.h>
7667 __isl_give isl_schedule_node *isl_schedule_node_copy(
7668 __isl_keep isl_schedule_node *node);
7669 __isl_null isl_schedule_node *isl_schedule_node_free(
7670 __isl_take isl_schedule_node *node);
7672 The following functions can be used to check if two schedule
7673 nodes point to the same position in the same schedule.
7675 #include <isl/schedule_node.h>
7676 isl_bool isl_schedule_node_is_equal(
7677 __isl_keep isl_schedule_node *node1,
7678 __isl_keep isl_schedule_node *node2);
7680 The following properties can be obtained from a schedule node.
7682 #include <isl/schedule_node.h>
7683 enum isl_schedule_node_type isl_schedule_node_get_type(
7684 __isl_keep isl_schedule_node *node);
7685 enum isl_schedule_node_type
7686 isl_schedule_node_get_parent_type(
7687 __isl_keep isl_schedule_node *node);
7688 __isl_give isl_schedule *isl_schedule_node_get_schedule(
7689 __isl_keep isl_schedule_node *node);
7691 The function C<isl_schedule_node_get_type> returns the type of
7692 the node, while C<isl_schedule_node_get_parent_type> returns
7693 type of the parent of the node, which is required to exist.
7694 The function C<isl_schedule_node_get_schedule> returns a copy
7695 to the schedule to which the node belongs.
7697 The following functions can be used to move the schedule node
7698 to a different position in the tree or to check if such a position
7701 #include <isl/schedule_node.h>
7702 isl_bool isl_schedule_node_has_parent(
7703 __isl_keep isl_schedule_node *node);
7704 __isl_give isl_schedule_node *isl_schedule_node_parent(
7705 __isl_take isl_schedule_node *node);
7706 __isl_give isl_schedule_node *isl_schedule_node_root(
7707 __isl_take isl_schedule_node *node);
7708 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
7709 __isl_take isl_schedule_node *node,
7711 int isl_schedule_node_n_children(
7712 __isl_keep isl_schedule_node *node);
7713 __isl_give isl_schedule_node *isl_schedule_node_child(
7714 __isl_take isl_schedule_node *node, int pos);
7715 isl_bool isl_schedule_node_has_children(
7716 __isl_keep isl_schedule_node *node);
7717 __isl_give isl_schedule_node *isl_schedule_node_first_child(
7718 __isl_take isl_schedule_node *node);
7719 isl_bool isl_schedule_node_has_previous_sibling(
7720 __isl_keep isl_schedule_node *node);
7721 __isl_give isl_schedule_node *
7722 isl_schedule_node_previous_sibling(
7723 __isl_take isl_schedule_node *node);
7724 isl_bool isl_schedule_node_has_next_sibling(
7725 __isl_keep isl_schedule_node *node);
7726 __isl_give isl_schedule_node *
7727 isl_schedule_node_next_sibling(
7728 __isl_take isl_schedule_node *node);
7730 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
7731 is the node itself, the ancestor of generation 1 is its parent and so on.
7733 It is also possible to query the number of ancestors of a node,
7734 the position of the current node
7735 within the children of its parent, the position of the subtree
7736 containing a node within the children of an ancestor
7737 or to obtain a copy of a given
7738 child without destroying the current node.
7739 Given two nodes that point to the same schedule, their closest
7740 shared ancestor can be obtained using
7741 C<isl_schedule_node_get_shared_ancestor>.
7743 #include <isl/schedule_node.h>
7744 int isl_schedule_node_get_tree_depth(
7745 __isl_keep isl_schedule_node *node);
7746 int isl_schedule_node_get_child_position(
7747 __isl_keep isl_schedule_node *node);
7748 int isl_schedule_node_get_ancestor_child_position(
7749 __isl_keep isl_schedule_node *node,
7750 __isl_keep isl_schedule_node *ancestor);
7751 __isl_give isl_schedule_node *isl_schedule_node_get_child(
7752 __isl_keep isl_schedule_node *node, int pos);
7753 __isl_give isl_schedule_node *
7754 isl_schedule_node_get_shared_ancestor(
7755 __isl_keep isl_schedule_node *node1,
7756 __isl_keep isl_schedule_node *node2);
7758 All nodes in a schedule tree or
7759 all descendants of a specific node (including the node) can be visited
7760 in depth-first pre-order using the following functions.
7762 #include <isl/schedule.h>
7763 isl_stat isl_schedule_foreach_schedule_node_top_down(
7764 __isl_keep isl_schedule *sched,
7765 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
7766 void *user), void *user);
7768 #include <isl/schedule_node.h>
7769 isl_stat isl_schedule_node_foreach_descendant_top_down(
7770 __isl_keep isl_schedule_node *node,
7771 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
7772 void *user), void *user);
7774 The callback function is slightly different from the usual
7775 callbacks in that it not only indicates success (non-negative result)
7776 or failure (negative result), but also indicates whether the children
7777 of the given node should be visited. In particular, if the callback
7778 returns a positive value, then the children are visited, but if
7779 the callback returns zero, then the children are not visited.
7781 The ancestors of a node in a schedule tree can be visited from
7782 the root down to and including the parent of the node using
7783 the following function.
7785 #include <isl/schedule_node.h>
7786 isl_stat isl_schedule_node_foreach_ancestor_top_down(
7787 __isl_keep isl_schedule_node *node,
7788 isl_stat (*fn)(__isl_keep isl_schedule_node *node,
7789 void *user), void *user);
7791 The following functions allows for a depth-first post-order
7792 traversal of the nodes in a schedule tree or
7793 of the descendants of a specific node (including the node
7794 itself), where the user callback is allowed to modify the
7797 #include <isl/schedule.h>
7798 __isl_give isl_schedule *
7799 isl_schedule_map_schedule_node_bottom_up(
7800 __isl_take isl_schedule *schedule,
7801 __isl_give isl_schedule_node *(*fn)(
7802 __isl_take isl_schedule_node *node,
7803 void *user), void *user);
7805 #include <isl/schedule_node.h>
7806 __isl_give isl_schedule_node *
7807 isl_schedule_node_map_descendant_bottom_up(
7808 __isl_take isl_schedule_node *node,
7809 __isl_give isl_schedule_node *(*fn)(
7810 __isl_take isl_schedule_node *node,
7811 void *user), void *user);
7813 The traversal continues from the node returned by the callback function.
7814 It is the responsibility of the user to ensure that this does not
7815 lead to an infinite loop. It is safest to always return a pointer
7816 to the same position (same ancestors and child positions) as the input node.
7818 The following function removes a node (along with its descendants)
7819 from a schedule tree and returns a pointer to the leaf at the
7820 same position in the updated tree.
7821 It is not allowed to remove the root of a schedule tree or
7822 a child of a set or sequence node.
7824 #include <isl/schedule_node.h>
7825 __isl_give isl_schedule_node *isl_schedule_node_cut(
7826 __isl_take isl_schedule_node *node);
7828 The following function removes a single node
7829 from a schedule tree and returns a pointer to the child
7830 of the node, now located at the position of the original node
7831 or to a leaf node at that position if there was no child.
7832 It is not allowed to remove the root of a schedule tree,
7833 a set or sequence node, a child of a set or sequence node or
7834 a band node with an anchored subtree.
7836 #include <isl/schedule_node.h>
7837 __isl_give isl_schedule_node *isl_schedule_node_delete(
7838 __isl_take isl_schedule_node *node);
7840 Most nodes in a schedule tree only contain local information.
7841 In some cases, however, a node may also refer to outer band nodes.
7842 This means that the position of the node within the tree should
7843 not be changed, or at least that no changes are performed to the
7844 outer band nodes. The following function can be used to test
7845 whether the subtree rooted at a given node contains any such nodes.
7847 #include <isl/schedule_node.h>
7848 isl_bool isl_schedule_node_is_subtree_anchored(
7849 __isl_keep isl_schedule_node *node);
7851 The following function resets the user pointers on all parameter
7852 and tuple identifiers referenced by the given schedule node.
7854 #include <isl/schedule_node.h>
7855 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
7856 __isl_take isl_schedule_node *node);
7858 The following function aligns the parameters of the given schedule
7859 node to the given space.
7861 #include <isl/schedule_node.h>
7862 __isl_give isl_schedule_node *
7863 isl_schedule_node_align_params(
7864 __isl_take isl_schedule_node *node,
7865 __isl_take isl_space *space);
7867 Several node types have their own functions for querying
7868 (and in some cases setting) some node type specific properties.
7870 #include <isl/schedule_node.h>
7871 __isl_give isl_space *isl_schedule_node_band_get_space(
7872 __isl_keep isl_schedule_node *node);
7873 __isl_give isl_multi_union_pw_aff *
7874 isl_schedule_node_band_get_partial_schedule(
7875 __isl_keep isl_schedule_node *node);
7876 __isl_give isl_union_map *
7877 isl_schedule_node_band_get_partial_schedule_union_map(
7878 __isl_keep isl_schedule_node *node);
7879 unsigned isl_schedule_node_band_n_member(
7880 __isl_keep isl_schedule_node *node);
7881 isl_bool isl_schedule_node_band_member_get_coincident(
7882 __isl_keep isl_schedule_node *node, int pos);
7883 __isl_give isl_schedule_node *
7884 isl_schedule_node_band_member_set_coincident(
7885 __isl_take isl_schedule_node *node, int pos,
7887 isl_bool isl_schedule_node_band_get_permutable(
7888 __isl_keep isl_schedule_node *node);
7889 __isl_give isl_schedule_node *
7890 isl_schedule_node_band_set_permutable(
7891 __isl_take isl_schedule_node *node, int permutable);
7892 enum isl_ast_loop_type
7893 isl_schedule_node_band_member_get_ast_loop_type(
7894 __isl_keep isl_schedule_node *node, int pos);
7895 __isl_give isl_schedule_node *
7896 isl_schedule_node_band_member_set_ast_loop_type(
7897 __isl_take isl_schedule_node *node, int pos,
7898 enum isl_ast_loop_type type);
7899 __isl_give isl_union_set *
7900 enum isl_ast_loop_type
7901 isl_schedule_node_band_member_get_isolate_ast_loop_type(
7902 __isl_keep isl_schedule_node *node, int pos);
7903 __isl_give isl_schedule_node *
7904 isl_schedule_node_band_member_set_isolate_ast_loop_type(
7905 __isl_take isl_schedule_node *node, int pos,
7906 enum isl_ast_loop_type type);
7907 isl_schedule_node_band_get_ast_build_options(
7908 __isl_keep isl_schedule_node *node);
7909 __isl_give isl_schedule_node *
7910 isl_schedule_node_band_set_ast_build_options(
7911 __isl_take isl_schedule_node *node,
7912 __isl_take isl_union_set *options);
7914 The function C<isl_schedule_node_band_get_space> returns the space
7915 of the partial schedule of the band.
7916 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
7917 returns a representation of the partial schedule of the band node
7918 in the form of an C<isl_union_map>.
7919 The coincident and permutable properties are set by
7920 C<isl_schedule_constraints_compute_schedule> on the schedule tree
7922 A scheduling dimension is considered to be ``coincident''
7923 if it satisfies the coincidence constraints within its band.
7924 That is, if the dependence distances of the coincidence
7925 constraints are all zero in that direction (for fixed
7926 iterations of outer bands).
7927 A band is marked permutable if it was produced using the Pluto-like scheduler.
7928 Note that the scheduler may have to resort to a Feautrier style scheduling
7929 step even if the default scheduler is used.
7930 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
7931 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
7932 For the meaning of these loop AST generation types and the difference
7933 between the regular loop AST generation type and the isolate
7934 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
7935 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
7936 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
7937 may return C<isl_ast_loop_error> if an error occurs.
7938 The AST build options govern how an AST is generated for
7939 the individual schedule dimensions during AST generation.
7940 See L</"AST Generation Options (Schedule Tree)">.
7942 #include <isl/schedule_node.h>
7943 __isl_give isl_set *
7944 isl_schedule_node_context_get_context(
7945 __isl_keep isl_schedule_node *node);
7947 #include <isl/schedule_node.h>
7948 __isl_give isl_union_set *
7949 isl_schedule_node_domain_get_domain(
7950 __isl_keep isl_schedule_node *node);
7952 #include <isl/schedule_node.h>
7953 __isl_give isl_union_map *
7954 isl_schedule_node_expansion_get_expansion(
7955 __isl_keep isl_schedule_node *node);
7956 __isl_give isl_union_pw_multi_aff *
7957 isl_schedule_node_expansion_get_contraction(
7958 __isl_keep isl_schedule_node *node);
7960 #include <isl/schedule_node.h>
7961 __isl_give isl_union_map *
7962 isl_schedule_node_extension_get_extension(
7963 __isl_keep isl_schedule_node *node);
7965 #include <isl/schedule_node.h>
7966 __isl_give isl_union_set *
7967 isl_schedule_node_filter_get_filter(
7968 __isl_keep isl_schedule_node *node);
7970 #include <isl/schedule_node.h>
7971 __isl_give isl_set *isl_schedule_node_guard_get_guard(
7972 __isl_keep isl_schedule_node *node);
7974 #include <isl/schedule_node.h>
7975 __isl_give isl_id *isl_schedule_node_mark_get_id(
7976 __isl_keep isl_schedule_node *node);
7978 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
7979 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
7980 partial schedules related to the node.
7982 #include <isl/schedule_node.h>
7983 __isl_give isl_multi_union_pw_aff *
7984 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
7985 __isl_keep isl_schedule_node *node);
7986 __isl_give isl_union_pw_multi_aff *
7987 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
7988 __isl_keep isl_schedule_node *node);
7989 __isl_give isl_union_map *
7990 isl_schedule_node_get_prefix_schedule_union_map(
7991 __isl_keep isl_schedule_node *node);
7992 __isl_give isl_union_map *
7993 isl_schedule_node_get_prefix_schedule_relation(
7994 __isl_keep isl_schedule_node *node);
7995 __isl_give isl_union_map *
7996 isl_schedule_node_get_subtree_schedule_union_map(
7997 __isl_keep isl_schedule_node *node);
7999 In particular, the functions
8000 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
8001 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
8002 and C<isl_schedule_node_get_prefix_schedule_union_map>
8003 return a relative ordering on the domain elements that reach the given
8004 node determined by its ancestors.
8005 The function C<isl_schedule_node_get_prefix_schedule_relation>
8006 additionally includes the domain constraints in the result.
8007 The function C<isl_schedule_node_get_subtree_schedule_union_map>
8008 returns a representation of the partial schedule defined by the
8009 subtree rooted at the given node.
8010 If the tree contains any expansion nodes, then the subtree schedule
8011 is formulated in terms of the expanded domain elements.
8012 The tree passed to functions returning a prefix schedule
8013 may only contain extension nodes if these would not affect
8014 the result of these functions. That is, if one of the ancestors
8015 is an extension node, then all of the domain elements that were
8016 added by the extension node need to have been filtered out
8017 by filter nodes between the extension node and the input node.
8018 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
8019 may not contain in extension nodes in the selected subtree.
8021 The expansion/contraction defined by an entire subtree, combining
8022 the expansions/contractions
8023 on the expansion nodes in the subtree, can be obtained using
8024 the following functions.
8026 #include <isl/schedule_node.h>
8027 __isl_give isl_union_map *
8028 isl_schedule_node_get_subtree_expansion(
8029 __isl_keep isl_schedule_node *node);
8030 __isl_give isl_union_pw_multi_aff *
8031 isl_schedule_node_get_subtree_contraction(
8032 __isl_keep isl_schedule_node *node);
8034 The total number of outer band members of given node, i.e.,
8035 the shared output dimension of the maps in the result
8036 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
8037 using the following function.
8039 #include <isl/schedule_node.h>
8040 int isl_schedule_node_get_schedule_depth(
8041 __isl_keep isl_schedule_node *node);
8043 The following functions return the elements that reach the given node
8044 or the union of universes in the spaces that contain these elements.
8046 #include <isl/schedule_node.h>
8047 __isl_give isl_union_set *
8048 isl_schedule_node_get_domain(
8049 __isl_keep isl_schedule_node *node);
8050 __isl_give isl_union_set *
8051 isl_schedule_node_get_universe_domain(
8052 __isl_keep isl_schedule_node *node);
8054 The input tree of C<isl_schedule_node_get_domain>
8055 may only contain extension nodes if these would not affect
8056 the result of this function. That is, if one of the ancestors
8057 is an extension node, then all of the domain elements that were
8058 added by the extension node need to have been filtered out
8059 by filter nodes between the extension node and the input node.
8061 The following functions can be used to introduce additional nodes
8062 in the schedule tree. The new node is introduced at the point
8063 in the tree where the C<isl_schedule_node> points to and
8064 the results points to the new node.
8066 #include <isl/schedule_node.h>
8067 __isl_give isl_schedule_node *
8068 isl_schedule_node_insert_partial_schedule(
8069 __isl_take isl_schedule_node *node,
8070 __isl_take isl_multi_union_pw_aff *schedule);
8072 This function inserts a new band node with (the greatest integer
8073 part of) the given partial schedule.
8074 The subtree rooted at the given node is assumed not to have
8077 #include <isl/schedule_node.h>
8078 __isl_give isl_schedule_node *
8079 isl_schedule_node_insert_context(
8080 __isl_take isl_schedule_node *node,
8081 __isl_take isl_set *context);
8083 This function inserts a new context node with the given context constraints.
8085 #include <isl/schedule_node.h>
8086 __isl_give isl_schedule_node *
8087 isl_schedule_node_insert_filter(
8088 __isl_take isl_schedule_node *node,
8089 __isl_take isl_union_set *filter);
8091 This function inserts a new filter node with the given filter.
8092 If the original node already pointed to a filter node, then the
8093 two filter nodes are merged into one.
8095 #include <isl/schedule_node.h>
8096 __isl_give isl_schedule_node *
8097 isl_schedule_node_insert_guard(
8098 __isl_take isl_schedule_node *node,
8099 __isl_take isl_set *guard);
8101 This function inserts a new guard node with the given guard constraints.
8103 #include <isl/schedule_node.h>
8104 __isl_give isl_schedule_node *
8105 isl_schedule_node_insert_mark(
8106 __isl_take isl_schedule_node *node,
8107 __isl_take isl_id *mark);
8109 This function inserts a new mark node with the give mark identifier.
8111 #include <isl/schedule_node.h>
8112 __isl_give isl_schedule_node *
8113 isl_schedule_node_insert_sequence(
8114 __isl_take isl_schedule_node *node,
8115 __isl_take isl_union_set_list *filters);
8116 __isl_give isl_schedule_node *
8117 isl_schedule_node_insert_set(
8118 __isl_take isl_schedule_node *node,
8119 __isl_take isl_union_set_list *filters);
8121 These functions insert a new sequence or set node with the given
8122 filters as children.
8124 #include <isl/schedule_node.h>
8125 __isl_give isl_schedule_node *isl_schedule_node_group(
8126 __isl_take isl_schedule_node *node,
8127 __isl_take isl_id *group_id);
8129 This function introduces an expansion node in between the current
8130 node and its parent that expands instances of a space with tuple
8131 identifier C<group_id> to the original domain elements that reach
8132 the node. The group instances are identified by the prefix schedule
8133 of those domain elements. The ancestors of the node are adjusted
8134 to refer to the group instances instead of the original domain
8135 elements. The return value points to the same node in the updated
8136 schedule tree as the input node, i.e., to the child of the newly
8137 introduced expansion node. Grouping instances of different statements
8138 ensures that they will be treated as a single statement by the
8139 AST generator up to the point of the expansion node.
8141 The partial schedule of a band node can be scaled (down) or reduced using
8142 the following functions.
8144 #include <isl/schedule_node.h>
8145 __isl_give isl_schedule_node *
8146 isl_schedule_node_band_scale(
8147 __isl_take isl_schedule_node *node,
8148 __isl_take isl_multi_val *mv);
8149 __isl_give isl_schedule_node *
8150 isl_schedule_node_band_scale_down(
8151 __isl_take isl_schedule_node *node,
8152 __isl_take isl_multi_val *mv);
8153 __isl_give isl_schedule_node *
8154 isl_schedule_node_band_mod(
8155 __isl_take isl_schedule_node *node,
8156 __isl_take isl_multi_val *mv);
8158 The spaces of the two arguments need to match.
8159 After scaling, the partial schedule is replaced by its greatest
8160 integer part to ensure that the schedule remains integral.
8162 The partial schedule of a band node can be shifted by an
8163 C<isl_multi_union_pw_aff> with a domain that is a superset
8164 of the domain of the partial schedule using
8165 the following function.
8167 #include <isl/schedule_node.h>
8168 __isl_give isl_schedule_node *
8169 isl_schedule_node_band_shift(
8170 __isl_take isl_schedule_node *node,
8171 __isl_take isl_multi_union_pw_aff *shift);
8173 A band node can be tiled using the following function.
8175 #include <isl/schedule_node.h>
8176 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
8177 __isl_take isl_schedule_node *node,
8178 __isl_take isl_multi_val *sizes);
8180 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
8182 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
8183 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
8185 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
8187 The C<isl_schedule_node_band_tile> function tiles
8188 the band using the given tile sizes inside its schedule.
8189 A new child band node is created to represent the point loops and it is
8190 inserted between the modified band and its children.
8191 The subtree rooted at the given node is assumed not to have
8193 The C<tile_scale_tile_loops> option specifies whether the tile
8194 loops iterators should be scaled by the tile sizes.
8195 If the C<tile_shift_point_loops> option is set, then the point loops
8196 are shifted to start at zero.
8198 A band node can be split into two nested band nodes
8199 using the following function.
8201 #include <isl/schedule_node.h>
8202 __isl_give isl_schedule_node *isl_schedule_node_band_split(
8203 __isl_take isl_schedule_node *node, int pos);
8205 The resulting outer band node contains the first C<pos> dimensions of
8206 the schedule of C<node> while the inner band contains the remaining dimensions.
8207 The schedules of the two band nodes live in anonymous spaces.
8209 A band node can be moved down to the leaves of the subtree rooted
8210 at the band node using the following function.
8212 #include <isl/schedule_node.h>
8213 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
8214 __isl_take isl_schedule_node *node);
8216 The subtree rooted at the given node is assumed not to have
8218 The result points to the node in the resulting tree that is in the same
8219 position as the node pointed to by C<node> in the original tree.
8221 #include <isl/schedule_node.h>
8222 __isl_give isl_schedule_node *
8223 isl_schedule_node_order_after(
8224 __isl_take isl_schedule_node *node,
8225 __isl_take isl_union_set *filter);
8227 This function splits the domain elements that reach C<node>
8228 into those that satisfy C<filter> and those that do not and
8229 arranges for the elements that do satisfy the filter to be
8230 executed after those that do not. The order is imposed by
8231 a sequence node, possibly reusing the grandparent of C<node>
8232 on two copies of the subtree attached to the original C<node>.
8233 Both copies are simplified with respect to their filter.
8235 Return a pointer to the copy of the subtree that does not
8236 satisfy C<filter>. If there is no such copy (because all
8237 reaching domain elements satisfy the filter), then return
8238 the original pointer.
8240 #include <isl/schedule_node.h>
8241 __isl_give isl_schedule_node *
8242 isl_schedule_node_graft_before(
8243 __isl_take isl_schedule_node *node,
8244 __isl_take isl_schedule_node *graft);
8245 __isl_give isl_schedule_node *
8246 isl_schedule_node_graft_after(
8247 __isl_take isl_schedule_node *node,
8248 __isl_take isl_schedule_node *graft);
8250 This function inserts the C<graft> tree into the tree containing C<node>
8251 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
8252 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
8253 The root node of C<graft>
8254 should be an extension node where the domain of the extension
8255 is the flat product of all outer band nodes of C<node>.
8256 The root node may also be a domain node.
8257 The elements of the domain or the range of the extension may not
8258 intersect with the domain elements that reach "node".
8259 The schedule tree of C<graft> may not be anchored.
8261 The schedule tree of C<node> is modified to include an extension node
8262 corresponding to the root node of C<graft> as a child of the original
8263 parent of C<node>. The original node that C<node> points to and the
8264 child of the root node of C<graft> are attached to this extension node
8265 through a sequence, with appropriate filters and with the child
8266 of C<graft> appearing before or after the original C<node>.
8268 If C<node> already appears inside a sequence that is the child of
8269 an extension node and if the spaces of the new domain elements
8270 do not overlap with those of the original domain elements,
8271 then that extension node is extended with the new extension
8272 rather than introducing a new segment of extension and sequence nodes.
8274 Return a pointer to the same node in the modified tree that
8275 C<node> pointed to in the original tree.
8277 A representation of the schedule node can be printed using
8279 #include <isl/schedule_node.h>
8280 __isl_give isl_printer *isl_printer_print_schedule_node(
8281 __isl_take isl_printer *p,
8282 __isl_keep isl_schedule_node *node);
8284 =head2 Dependence Analysis
8286 C<isl> contains specialized functionality for performing
8287 array dataflow analysis. That is, given a I<sink> access relation
8288 and a collection of possible I<source> access relations,
8289 C<isl> can compute relations that describe
8290 for each iteration of the sink access, which iteration
8291 of which of the source access relations was the last
8292 to access the same data element before the given iteration
8294 The resulting dependence relations map source iterations
8295 to the corresponding sink iterations.
8296 To compute standard flow dependences, the sink should be
8297 a read, while the sources should be writes.
8298 If any of the source accesses are marked as being I<may>
8299 accesses, then there will be a dependence from the last
8300 I<must> access B<and> from any I<may> access that follows
8301 this last I<must> access.
8302 In particular, if I<all> sources are I<may> accesses,
8303 then memory based dependence analysis is performed.
8304 If, on the other hand, all sources are I<must> accesses,
8305 then value based dependence analysis is performed.
8307 =head3 High-level Interface
8309 A high-level interface to dependence analysis is provided
8310 by the following function.
8312 #include <isl/flow.h>
8313 __isl_give isl_union_flow *
8314 isl_union_access_info_compute_flow(
8315 __isl_take isl_union_access_info *access);
8317 The input C<isl_union_access_info> object describes the sink
8318 access relations, the source access relations and a schedule,
8319 while the output C<isl_union_flow> object describes
8320 the resulting dependence relations and the subsets of the
8321 sink relations for which no source was found.
8323 An C<isl_union_access_info> is created, modified, copied and freed using
8324 the following functions.
8326 #include <isl/flow.h>
8327 __isl_give isl_union_access_info *
8328 isl_union_access_info_from_sink(
8329 __isl_take isl_union_map *sink);
8330 __isl_give isl_union_access_info *
8331 isl_union_access_info_set_must_source(
8332 __isl_take isl_union_access_info *access,
8333 __isl_take isl_union_map *must_source);
8334 __isl_give isl_union_access_info *
8335 isl_union_access_info_set_may_source(
8336 __isl_take isl_union_access_info *access,
8337 __isl_take isl_union_map *may_source);
8338 __isl_give isl_union_access_info *
8339 isl_union_access_info_set_schedule(
8340 __isl_take isl_union_access_info *access,
8341 __isl_take isl_schedule *schedule);
8342 __isl_give isl_union_access_info *
8343 isl_union_access_info_set_schedule_map(
8344 __isl_take isl_union_access_info *access,
8345 __isl_take isl_union_map *schedule_map);
8346 __isl_give isl_union_access_info *
8347 isl_union_access_info_copy(
8348 __isl_keep isl_union_access_info *access);
8349 __isl_null isl_union_access_info *
8350 isl_union_access_info_free(
8351 __isl_take isl_union_access_info *access);
8353 The may sources set by C<isl_union_access_info_set_may_source>
8354 do not need to include the must sources set by
8355 C<isl_union_access_info_set_must_source> as a subset.
8356 The user is free not to call one (or both) of these functions,
8357 in which case the corresponding set is kept to its empty default.
8358 Similarly, the default schedule initialized by
8359 C<isl_union_access_info_from_sink> is empty.
8360 The current schedule is determined by the last call to either
8361 C<isl_union_access_info_set_schedule> or
8362 C<isl_union_access_info_set_schedule_map>.
8363 The domain of the schedule corresponds to the domains of
8364 the access relations. In particular, the domains of the access
8365 relations are effectively intersected with the domain of the schedule
8366 and only the resulting accesses are considered by the dependence analysis.
8368 The output of C<isl_union_access_info_compute_flow> can be examined
8369 and freed using the following functions.
8371 #include <isl/flow.h>
8372 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
8373 __isl_keep isl_union_flow *flow);
8374 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
8375 __isl_keep isl_union_flow *flow);
8376 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
8377 __isl_keep isl_union_flow *flow);
8378 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
8379 __isl_keep isl_union_flow *flow);
8380 __isl_null isl_union_flow *isl_union_flow_free(
8381 __isl_take isl_union_flow *flow);
8383 The relation returned by C<isl_union_flow_get_must_dependence>
8384 relates domain elements of must sources to domain elements of the sink.
8385 The relation returned by C<isl_union_flow_get_may_dependence>
8386 relates domain elements of must or may sources to domain elements of the sink
8387 and includes the previous relation as a subset.
8388 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
8389 of the sink relation for which no dependences have been found.
8390 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
8391 of the sink relation for which no definite dependences have been found.
8392 That is, it contains those sink access that do not contribute to any
8393 of the elements in the relation returned
8394 by C<isl_union_flow_get_must_dependence>.
8396 =head3 Low-level Interface
8398 A lower-level interface is provided by the following functions.
8400 #include <isl/flow.h>
8402 typedef int (*isl_access_level_before)(void *first, void *second);
8404 __isl_give isl_access_info *isl_access_info_alloc(
8405 __isl_take isl_map *sink,
8406 void *sink_user, isl_access_level_before fn,
8408 __isl_give isl_access_info *isl_access_info_add_source(
8409 __isl_take isl_access_info *acc,
8410 __isl_take isl_map *source, int must,
8412 __isl_null isl_access_info *isl_access_info_free(
8413 __isl_take isl_access_info *acc);
8415 __isl_give isl_flow *isl_access_info_compute_flow(
8416 __isl_take isl_access_info *acc);
8418 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,
8419 isl_stat (*fn)(__isl_take isl_map *dep, int must,
8420 void *dep_user, void *user),
8422 __isl_give isl_map *isl_flow_get_no_source(
8423 __isl_keep isl_flow *deps, int must);
8424 void isl_flow_free(__isl_take isl_flow *deps);
8426 The function C<isl_access_info_compute_flow> performs the actual
8427 dependence analysis. The other functions are used to construct
8428 the input for this function or to read off the output.
8430 The input is collected in an C<isl_access_info>, which can
8431 be created through a call to C<isl_access_info_alloc>.
8432 The arguments to this functions are the sink access relation
8433 C<sink>, a token C<sink_user> used to identify the sink
8434 access to the user, a callback function for specifying the
8435 relative order of source and sink accesses, and the number
8436 of source access relations that will be added.
8437 The callback function has type C<int (*)(void *first, void *second)>.
8438 The function is called with two user supplied tokens identifying
8439 either a source or the sink and it should return the shared nesting
8440 level and the relative order of the two accesses.
8441 In particular, let I<n> be the number of loops shared by
8442 the two accesses. If C<first> precedes C<second> textually,
8443 then the function should return I<2 * n + 1>; otherwise,
8444 it should return I<2 * n>.
8445 The sources can be added to the C<isl_access_info> by performing
8446 (at most) C<max_source> calls to C<isl_access_info_add_source>.
8447 C<must> indicates whether the source is a I<must> access
8448 or a I<may> access. Note that a multi-valued access relation
8449 should only be marked I<must> if every iteration in the domain
8450 of the relation accesses I<all> elements in its image.
8451 The C<source_user> token is again used to identify
8452 the source access. The range of the source access relation
8453 C<source> should have the same dimension as the range
8454 of the sink access relation.
8455 The C<isl_access_info_free> function should usually not be
8456 called explicitly, because it is called implicitly by
8457 C<isl_access_info_compute_flow>.
8459 The result of the dependence analysis is collected in an
8460 C<isl_flow>. There may be elements of
8461 the sink access for which no preceding source access could be
8462 found or for which all preceding sources are I<may> accesses.
8463 The relations containing these elements can be obtained through
8464 calls to C<isl_flow_get_no_source>, the first with C<must> set
8465 and the second with C<must> unset.
8466 In the case of standard flow dependence analysis,
8467 with the sink a read and the sources I<must> writes,
8468 the first relation corresponds to the reads from uninitialized
8469 array elements and the second relation is empty.
8470 The actual flow dependences can be extracted using
8471 C<isl_flow_foreach>. This function will call the user-specified
8472 callback function C<fn> for each B<non-empty> dependence between
8473 a source and the sink. The callback function is called
8474 with four arguments, the actual flow dependence relation
8475 mapping source iterations to sink iterations, a boolean that
8476 indicates whether it is a I<must> or I<may> dependence, a token
8477 identifying the source and an additional C<void *> with value
8478 equal to the third argument of the C<isl_flow_foreach> call.
8479 A dependence is marked I<must> if it originates from a I<must>
8480 source and if it is not followed by any I<may> sources.
8482 After finishing with an C<isl_flow>, the user should call
8483 C<isl_flow_free> to free all associated memory.
8485 =head3 Interaction with the Low-level Interface
8487 During the dependence analysis, we frequently need to perform
8488 the following operation. Given a relation between sink iterations
8489 and potential source iterations from a particular source domain,
8490 what is the last potential source iteration corresponding to each
8491 sink iteration. It can sometimes be convenient to adjust
8492 the set of potential source iterations before or after each such operation.
8493 The prototypical example is fuzzy array dataflow analysis,
8494 where we need to analyze if, based on data-dependent constraints,
8495 the sink iteration can ever be executed without one or more of
8496 the corresponding potential source iterations being executed.
8497 If so, we can introduce extra parameters and select an unknown
8498 but fixed source iteration from the potential source iterations.
8499 To be able to perform such manipulations, C<isl> provides the following
8502 #include <isl/flow.h>
8504 typedef __isl_give isl_restriction *(*isl_access_restrict)(
8505 __isl_keep isl_map *source_map,
8506 __isl_keep isl_set *sink, void *source_user,
8508 __isl_give isl_access_info *isl_access_info_set_restrict(
8509 __isl_take isl_access_info *acc,
8510 isl_access_restrict fn, void *user);
8512 The function C<isl_access_info_set_restrict> should be called
8513 before calling C<isl_access_info_compute_flow> and registers a callback function
8514 that will be called any time C<isl> is about to compute the last
8515 potential source. The first argument is the (reverse) proto-dependence,
8516 mapping sink iterations to potential source iterations.
8517 The second argument represents the sink iterations for which
8518 we want to compute the last source iteration.
8519 The third argument is the token corresponding to the source
8520 and the final argument is the token passed to C<isl_access_info_set_restrict>.
8521 The callback is expected to return a restriction on either the input or
8522 the output of the operation computing the last potential source.
8523 If the input needs to be restricted then restrictions are needed
8524 for both the source and the sink iterations. The sink iterations
8525 and the potential source iterations will be intersected with these sets.
8526 If the output needs to be restricted then only a restriction on the source
8527 iterations is required.
8528 If any error occurs, the callback should return C<NULL>.
8529 An C<isl_restriction> object can be created, freed and inspected
8530 using the following functions.
8532 #include <isl/flow.h>
8534 __isl_give isl_restriction *isl_restriction_input(
8535 __isl_take isl_set *source_restr,
8536 __isl_take isl_set *sink_restr);
8537 __isl_give isl_restriction *isl_restriction_output(
8538 __isl_take isl_set *source_restr);
8539 __isl_give isl_restriction *isl_restriction_none(
8540 __isl_take isl_map *source_map);
8541 __isl_give isl_restriction *isl_restriction_empty(
8542 __isl_take isl_map *source_map);
8543 __isl_null isl_restriction *isl_restriction_free(
8544 __isl_take isl_restriction *restr);
8546 C<isl_restriction_none> and C<isl_restriction_empty> are special
8547 cases of C<isl_restriction_input>. C<isl_restriction_none>
8548 is essentially equivalent to
8550 isl_restriction_input(isl_set_universe(
8551 isl_space_range(isl_map_get_space(source_map))),
8553 isl_space_domain(isl_map_get_space(source_map))));
8555 whereas C<isl_restriction_empty> is essentially equivalent to
8557 isl_restriction_input(isl_set_empty(
8558 isl_space_range(isl_map_get_space(source_map))),
8560 isl_space_domain(isl_map_get_space(source_map))));
8564 B<The functionality described in this section is fairly new
8565 and may be subject to change.>
8567 #include <isl/schedule.h>
8568 __isl_give isl_schedule *
8569 isl_schedule_constraints_compute_schedule(
8570 __isl_take isl_schedule_constraints *sc);
8572 The function C<isl_schedule_constraints_compute_schedule> can be
8573 used to compute a schedule that satisfies the given schedule constraints.
8574 These schedule constraints include the iteration domain for which
8575 a schedule should be computed and dependences between pairs of
8576 iterations. In particular, these dependences include
8577 I<validity> dependences and I<proximity> dependences.
8578 By default, the algorithm used to construct the schedule is similar
8579 to that of C<Pluto>.
8580 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
8582 The generated schedule respects all validity dependences.
8583 That is, all dependence distances over these dependences in the
8584 scheduled space are lexicographically positive.
8586 The default algorithm tries to ensure that the dependence distances
8587 over coincidence constraints are zero and to minimize the
8588 dependence distances over proximity dependences.
8589 Moreover, it tries to obtain sequences (bands) of schedule dimensions
8590 for groups of domains where the dependence distances over validity
8591 dependences have only non-negative values.
8592 Note that when minimizing the maximal dependence distance
8593 over proximity dependences, a single affine expression in the parameters
8594 is constructed that bounds all dependence distances. If no such expression
8595 exists, then the algorithm will fail and resort to an alternative
8596 scheduling algorithm. In particular, this means that adding proximity
8597 dependences may eliminate valid solutions. A typical example where this
8598 phenomenon may occur is when some subset of the proximity dependences
8599 has no restriction on some parameter, forcing the coefficient of that
8600 parameter to be zero, while some other subset forces the dependence
8601 distance to depend on that parameter, requiring the same coefficient
8603 When using Feautrier's algorithm, the coincidence and proximity constraints
8604 are only taken into account during the extension to a
8605 full-dimensional schedule.
8607 An C<isl_schedule_constraints> object can be constructed
8608 and manipulated using the following functions.
8610 #include <isl/schedule.h>
8611 __isl_give isl_schedule_constraints *
8612 isl_schedule_constraints_copy(
8613 __isl_keep isl_schedule_constraints *sc);
8614 __isl_give isl_schedule_constraints *
8615 isl_schedule_constraints_on_domain(
8616 __isl_take isl_union_set *domain);
8617 __isl_give isl_schedule_constraints *
8618 isl_schedule_constraints_set_context(
8619 __isl_take isl_schedule_constraints *sc,
8620 __isl_take isl_set *context);
8621 __isl_give isl_schedule_constraints *
8622 isl_schedule_constraints_set_validity(
8623 __isl_take isl_schedule_constraints *sc,
8624 __isl_take isl_union_map *validity);
8625 __isl_give isl_schedule_constraints *
8626 isl_schedule_constraints_set_coincidence(
8627 __isl_take isl_schedule_constraints *sc,
8628 __isl_take isl_union_map *coincidence);
8629 __isl_give isl_schedule_constraints *
8630 isl_schedule_constraints_set_proximity(
8631 __isl_take isl_schedule_constraints *sc,
8632 __isl_take isl_union_map *proximity);
8633 __isl_give isl_schedule_constraints *
8634 isl_schedule_constraints_set_conditional_validity(
8635 __isl_take isl_schedule_constraints *sc,
8636 __isl_take isl_union_map *condition,
8637 __isl_take isl_union_map *validity);
8638 __isl_null isl_schedule_constraints *
8639 isl_schedule_constraints_free(
8640 __isl_take isl_schedule_constraints *sc);
8642 The initial C<isl_schedule_constraints> object created by
8643 C<isl_schedule_constraints_on_domain> does not impose any constraints.
8644 That is, it has an empty set of dependences.
8645 The function C<isl_schedule_constraints_set_context> allows the user
8646 to specify additional constraints on the parameters that may
8647 be assumed to hold during the construction of the schedule.
8648 The function C<isl_schedule_constraints_set_validity> replaces the
8649 validity dependences, mapping domain elements I<i> to domain
8650 elements that should be scheduled after I<i>.
8651 The function C<isl_schedule_constraints_set_coincidence> replaces the
8652 coincidence dependences, mapping domain elements I<i> to domain
8653 elements that should be scheduled together with I<I>, if possible.
8654 The function C<isl_schedule_constraints_set_proximity> replaces the
8655 proximity dependences, mapping domain elements I<i> to domain
8656 elements that should be scheduled either before I<I>
8657 or as early as possible after I<i>.
8659 The function C<isl_schedule_constraints_set_conditional_validity>
8660 replaces the conditional validity constraints.
8661 A conditional validity constraint is only imposed when any of the corresponding
8662 conditions is satisfied, i.e., when any of them is non-zero.
8663 That is, the scheduler ensures that within each band if the dependence
8664 distances over the condition constraints are not all zero
8665 then all corresponding conditional validity constraints are respected.
8666 A conditional validity constraint corresponds to a condition
8667 if the two are adjacent, i.e., if the domain of one relation intersect
8668 the range of the other relation.
8669 The typical use case of conditional validity constraints is
8670 to allow order constraints between live ranges to be violated
8671 as long as the live ranges themselves are local to the band.
8672 To allow more fine-grained control over which conditions correspond
8673 to which conditional validity constraints, the domains and ranges
8674 of these relations may include I<tags>. That is, the domains and
8675 ranges of those relation may themselves be wrapped relations
8676 where the iteration domain appears in the domain of those wrapped relations
8677 and the range of the wrapped relations can be arbitrarily chosen
8678 by the user. Conditions and conditional validity constraints are only
8679 considered adjacent to each other if the entire wrapped relation matches.
8680 In particular, a relation with a tag will never be considered adjacent
8681 to a relation without a tag.
8683 An C<isl_schedule_constraints> object can be inspected
8684 using the following functions.
8686 #include <isl/schedule.h>
8687 __isl_give isl_union_map *
8688 isl_schedule_constraints_get_validity(
8689 __isl_keep isl_schedule_constraints *sc);
8690 __isl_give isl_union_map *
8691 isl_schedule_constraints_get_coincidence(
8692 __isl_keep isl_schedule_constraints *sc);
8693 __isl_give isl_union_map *
8694 isl_schedule_constraints_get_conditional_validity(
8695 __isl_keep isl_schedule_constraints *sc);
8696 __isl_give isl_union_map *
8697 isl_schedule_constraints_get_conditional_validity_condition(
8698 __isl_keep isl_schedule_constraints *sc);
8700 The following function computes a schedule directly from
8701 an iteration domain and validity and proximity dependences
8702 and is implemented in terms of the functions described above.
8703 The use of C<isl_union_set_compute_schedule> is discouraged.
8705 #include <isl/schedule.h>
8706 __isl_give isl_schedule *isl_union_set_compute_schedule(
8707 __isl_take isl_union_set *domain,
8708 __isl_take isl_union_map *validity,
8709 __isl_take isl_union_map *proximity);
8711 The generated schedule represents a schedule tree.
8712 For more information on schedule trees, see
8713 L</"Schedule Trees">.
8717 #include <isl/schedule.h>
8718 isl_stat isl_options_set_schedule_max_coefficient(
8719 isl_ctx *ctx, int val);
8720 int isl_options_get_schedule_max_coefficient(
8722 isl_stat isl_options_set_schedule_max_constant_term(
8723 isl_ctx *ctx, int val);
8724 int isl_options_get_schedule_max_constant_term(
8726 isl_stat isl_options_set_schedule_serialize_sccs(
8727 isl_ctx *ctx, int val);
8728 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx);
8729 isl_stat isl_options_set_schedule_maximize_band_depth(
8730 isl_ctx *ctx, int val);
8731 int isl_options_get_schedule_maximize_band_depth(
8733 isl_stat isl_options_set_schedule_outer_coincidence(
8734 isl_ctx *ctx, int val);
8735 int isl_options_get_schedule_outer_coincidence(
8737 isl_stat isl_options_set_schedule_split_scaled(
8738 isl_ctx *ctx, int val);
8739 int isl_options_get_schedule_split_scaled(
8741 isl_stat isl_options_set_schedule_algorithm(
8742 isl_ctx *ctx, int val);
8743 int isl_options_get_schedule_algorithm(
8745 isl_stat isl_options_set_schedule_separate_components(
8746 isl_ctx *ctx, int val);
8747 int isl_options_get_schedule_separate_components(
8752 =item * schedule_max_coefficient
8754 This option enforces that the coefficients for variable and parameter
8755 dimensions in the calculated schedule are not larger than the specified value.
8756 This option can significantly increase the speed of the scheduling calculation
8757 and may also prevent fusing of unrelated dimensions. A value of -1 means that
8758 this option does not introduce bounds on the variable or parameter
8761 =item * schedule_max_constant_term
8763 This option enforces that the constant coefficients in the calculated schedule
8764 are not larger than the maximal constant term. This option can significantly
8765 increase the speed of the scheduling calculation and may also prevent fusing of
8766 unrelated dimensions. A value of -1 means that this option does not introduce
8767 bounds on the constant coefficients.
8769 =item * schedule_serialize_sccs
8771 If this option is set, then all strongly connected components
8772 in the dependence graph are serialized as soon as they are detected.
8773 This means in particular that instances of statements will only
8774 appear in the same band node if these statements belong
8775 to the same strongly connected component at the point where
8776 the band node is constructed.
8778 =item * schedule_maximize_band_depth
8780 If this option is set, we do not split bands at the point
8781 where we detect splitting is necessary. Instead, we
8782 backtrack and split bands as early as possible. This
8783 reduces the number of splits and maximizes the width of
8784 the bands. Wider bands give more possibilities for tiling.
8785 Note that if the C<schedule_serialize_sccs> options is set,
8786 then bands will be split as early as possible, even if there is no need.
8787 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
8789 =item * schedule_outer_coincidence
8791 If this option is set, then we try to construct schedules
8792 where the outermost scheduling dimension in each band
8793 satisfies the coincidence constraints.
8795 =item * schedule_split_scaled
8797 If this option is set, then we try to construct schedules in which the
8798 constant term is split off from the linear part if the linear parts of
8799 the scheduling rows for all nodes in the graphs have a common non-trivial
8801 The constant term is then placed in a separate band and the linear
8804 =item * schedule_algorithm
8806 Selects the scheduling algorithm to be used.
8807 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
8808 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
8810 =item * schedule_separate_components
8812 If this option is set then the function C<isl_schedule_get_map>
8813 will treat set nodes in the same way as sequence nodes.
8817 =head2 AST Generation
8819 This section describes the C<isl> functionality for generating
8820 ASTs that visit all the elements
8821 in a domain in an order specified by a schedule tree or
8823 In case the schedule given as a C<isl_union_map>, an AST is generated
8824 that visits all the elements in the domain of the C<isl_union_map>
8825 according to the lexicographic order of the corresponding image
8826 element(s). If the range of the C<isl_union_map> consists of
8827 elements in more than one space, then each of these spaces is handled
8828 separately in an arbitrary order.
8829 It should be noted that the schedule tree or the image elements
8830 in a schedule map only specify the I<order>
8831 in which the corresponding domain elements should be visited.
8832 No direct relation between the partial schedule values
8833 or the image elements on the one hand and the loop iterators
8834 in the generated AST on the other hand should be assumed.
8836 Each AST is generated within a build. The initial build
8837 simply specifies the constraints on the parameters (if any)
8838 and can be created, inspected, copied and freed using the following functions.
8840 #include <isl/ast_build.h>
8841 __isl_give isl_ast_build *isl_ast_build_alloc(
8843 __isl_give isl_ast_build *isl_ast_build_from_context(
8844 __isl_take isl_set *set);
8845 __isl_give isl_ast_build *isl_ast_build_copy(
8846 __isl_keep isl_ast_build *build);
8847 __isl_null isl_ast_build *isl_ast_build_free(
8848 __isl_take isl_ast_build *build);
8850 The C<set> argument is usually a parameter set with zero or more parameters.
8851 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
8852 this set is required to be a parameter set.
8853 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
8854 specify any parameter constraints.
8855 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
8856 and L</"Fine-grained Control over AST Generation">.
8857 Finally, the AST itself can be constructed using one of the following
8860 #include <isl/ast_build.h>
8861 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
8862 __isl_keep isl_ast_build *build,
8863 __isl_take isl_schedule *schedule);
8864 __isl_give isl_ast_node *
8865 isl_ast_build_node_from_schedule_map(
8866 __isl_keep isl_ast_build *build,
8867 __isl_take isl_union_map *schedule);
8869 =head3 Inspecting the AST
8871 The basic properties of an AST node can be obtained as follows.
8873 #include <isl/ast.h>
8874 enum isl_ast_node_type isl_ast_node_get_type(
8875 __isl_keep isl_ast_node *node);
8877 The type of an AST node is one of
8878 C<isl_ast_node_for>,
8880 C<isl_ast_node_block>,
8881 C<isl_ast_node_mark> or
8882 C<isl_ast_node_user>.
8883 An C<isl_ast_node_for> represents a for node.
8884 An C<isl_ast_node_if> represents an if node.
8885 An C<isl_ast_node_block> represents a compound node.
8886 An C<isl_ast_node_mark> introduces a mark in the AST.
8887 An C<isl_ast_node_user> represents an expression statement.
8888 An expression statement typically corresponds to a domain element, i.e.,
8889 one of the elements that is visited by the AST.
8891 Each type of node has its own additional properties.
8893 #include <isl/ast.h>
8894 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
8895 __isl_keep isl_ast_node *node);
8896 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
8897 __isl_keep isl_ast_node *node);
8898 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
8899 __isl_keep isl_ast_node *node);
8900 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
8901 __isl_keep isl_ast_node *node);
8902 __isl_give isl_ast_node *isl_ast_node_for_get_body(
8903 __isl_keep isl_ast_node *node);
8904 isl_bool isl_ast_node_for_is_degenerate(
8905 __isl_keep isl_ast_node *node);
8907 An C<isl_ast_for> is considered degenerate if it is known to execute
8910 #include <isl/ast.h>
8911 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
8912 __isl_keep isl_ast_node *node);
8913 __isl_give isl_ast_node *isl_ast_node_if_get_then(
8914 __isl_keep isl_ast_node *node);
8915 isl_bool isl_ast_node_if_has_else(
8916 __isl_keep isl_ast_node *node);
8917 __isl_give isl_ast_node *isl_ast_node_if_get_else(
8918 __isl_keep isl_ast_node *node);
8920 __isl_give isl_ast_node_list *
8921 isl_ast_node_block_get_children(
8922 __isl_keep isl_ast_node *node);
8924 __isl_give isl_id *isl_ast_node_mark_get_id(
8925 __isl_keep isl_ast_node *node);
8926 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
8927 __isl_keep isl_ast_node *node);
8929 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
8930 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
8932 #include <isl/ast.h>
8933 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
8934 __isl_keep isl_ast_node *node);
8936 Each of the returned C<isl_ast_expr>s can in turn be inspected using
8937 the following functions.
8939 #include <isl/ast.h>
8940 enum isl_ast_expr_type isl_ast_expr_get_type(
8941 __isl_keep isl_ast_expr *expr);
8943 The type of an AST expression is one of
8945 C<isl_ast_expr_id> or
8946 C<isl_ast_expr_int>.
8947 An C<isl_ast_expr_op> represents the result of an operation.
8948 An C<isl_ast_expr_id> represents an identifier.
8949 An C<isl_ast_expr_int> represents an integer value.
8951 Each type of expression has its own additional properties.
8953 #include <isl/ast.h>
8954 enum isl_ast_op_type isl_ast_expr_get_op_type(
8955 __isl_keep isl_ast_expr *expr);
8956 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
8957 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
8958 __isl_keep isl_ast_expr *expr, int pos);
8959 isl_stat isl_ast_node_foreach_ast_op_type(
8960 __isl_keep isl_ast_node *node,
8961 isl_stat (*fn)(enum isl_ast_op_type type,
8962 void *user), void *user);
8964 C<isl_ast_expr_get_op_type> returns the type of the operation
8965 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
8966 arguments. C<isl_ast_expr_get_op_arg> returns the specified
8968 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
8969 C<isl_ast_op_type> that appears in C<node>.
8970 The operation type is one of the following.
8974 =item C<isl_ast_op_and>
8976 Logical I<and> of two arguments.
8977 Both arguments can be evaluated.
8979 =item C<isl_ast_op_and_then>
8981 Logical I<and> of two arguments.
8982 The second argument can only be evaluated if the first evaluates to true.
8984 =item C<isl_ast_op_or>
8986 Logical I<or> of two arguments.
8987 Both arguments can be evaluated.
8989 =item C<isl_ast_op_or_else>
8991 Logical I<or> of two arguments.
8992 The second argument can only be evaluated if the first evaluates to false.
8994 =item C<isl_ast_op_max>
8996 Maximum of two or more arguments.
8998 =item C<isl_ast_op_min>
9000 Minimum of two or more arguments.
9002 =item C<isl_ast_op_minus>
9006 =item C<isl_ast_op_add>
9008 Sum of two arguments.
9010 =item C<isl_ast_op_sub>
9012 Difference of two arguments.
9014 =item C<isl_ast_op_mul>
9016 Product of two arguments.
9018 =item C<isl_ast_op_div>
9020 Exact division. That is, the result is known to be an integer.
9022 =item C<isl_ast_op_fdiv_q>
9024 Result of integer division, rounded towards negative
9027 =item C<isl_ast_op_pdiv_q>
9029 Result of integer division, where dividend is known to be non-negative.
9031 =item C<isl_ast_op_pdiv_r>
9033 Remainder of integer division, where dividend is known to be non-negative.
9035 =item C<isl_ast_op_zdiv_r>
9037 Equal to zero iff the remainder on integer division is zero.
9039 =item C<isl_ast_op_cond>
9041 Conditional operator defined on three arguments.
9042 If the first argument evaluates to true, then the result
9043 is equal to the second argument. Otherwise, the result
9044 is equal to the third argument.
9045 The second and third argument may only be evaluated if
9046 the first argument evaluates to true and false, respectively.
9047 Corresponds to C<a ? b : c> in C.
9049 =item C<isl_ast_op_select>
9051 Conditional operator defined on three arguments.
9052 If the first argument evaluates to true, then the result
9053 is equal to the second argument. Otherwise, the result
9054 is equal to the third argument.
9055 The second and third argument may be evaluated independently
9056 of the value of the first argument.
9057 Corresponds to C<a * b + (1 - a) * c> in C.
9059 =item C<isl_ast_op_eq>
9063 =item C<isl_ast_op_le>
9065 Less than or equal relation.
9067 =item C<isl_ast_op_lt>
9071 =item C<isl_ast_op_ge>
9073 Greater than or equal relation.
9075 =item C<isl_ast_op_gt>
9077 Greater than relation.
9079 =item C<isl_ast_op_call>
9082 The number of arguments of the C<isl_ast_expr> is one more than
9083 the number of arguments in the function call, the first argument
9084 representing the function being called.
9086 =item C<isl_ast_op_access>
9089 The number of arguments of the C<isl_ast_expr> is one more than
9090 the number of index expressions in the array access, the first argument
9091 representing the array being accessed.
9093 =item C<isl_ast_op_member>
9096 This operation has two arguments, a structure and the name of
9097 the member of the structure being accessed.
9101 #include <isl/ast.h>
9102 __isl_give isl_id *isl_ast_expr_get_id(
9103 __isl_keep isl_ast_expr *expr);
9105 Return the identifier represented by the AST expression.
9107 #include <isl/ast.h>
9108 __isl_give isl_val *isl_ast_expr_get_val(
9109 __isl_keep isl_ast_expr *expr);
9111 Return the integer represented by the AST expression.
9113 =head3 Properties of ASTs
9115 #include <isl/ast.h>
9116 isl_bool isl_ast_expr_is_equal(
9117 __isl_keep isl_ast_expr *expr1,
9118 __isl_keep isl_ast_expr *expr2);
9120 Check if two C<isl_ast_expr>s are equal to each other.
9122 =head3 Manipulating and printing the AST
9124 AST nodes can be copied and freed using the following functions.
9126 #include <isl/ast.h>
9127 __isl_give isl_ast_node *isl_ast_node_copy(
9128 __isl_keep isl_ast_node *node);
9129 __isl_null isl_ast_node *isl_ast_node_free(
9130 __isl_take isl_ast_node *node);
9132 AST expressions can be copied and freed using the following functions.
9134 #include <isl/ast.h>
9135 __isl_give isl_ast_expr *isl_ast_expr_copy(
9136 __isl_keep isl_ast_expr *expr);
9137 __isl_null isl_ast_expr *isl_ast_expr_free(
9138 __isl_take isl_ast_expr *expr);
9140 New AST expressions can be created either directly or within
9141 the context of an C<isl_ast_build>.
9143 #include <isl/ast.h>
9144 __isl_give isl_ast_expr *isl_ast_expr_from_val(
9145 __isl_take isl_val *v);
9146 __isl_give isl_ast_expr *isl_ast_expr_from_id(
9147 __isl_take isl_id *id);
9148 __isl_give isl_ast_expr *isl_ast_expr_neg(
9149 __isl_take isl_ast_expr *expr);
9150 __isl_give isl_ast_expr *isl_ast_expr_address_of(
9151 __isl_take isl_ast_expr *expr);
9152 __isl_give isl_ast_expr *isl_ast_expr_add(
9153 __isl_take isl_ast_expr *expr1,
9154 __isl_take isl_ast_expr *expr2);
9155 __isl_give isl_ast_expr *isl_ast_expr_sub(
9156 __isl_take isl_ast_expr *expr1,
9157 __isl_take isl_ast_expr *expr2);
9158 __isl_give isl_ast_expr *isl_ast_expr_mul(
9159 __isl_take isl_ast_expr *expr1,
9160 __isl_take isl_ast_expr *expr2);
9161 __isl_give isl_ast_expr *isl_ast_expr_div(
9162 __isl_take isl_ast_expr *expr1,
9163 __isl_take isl_ast_expr *expr2);
9164 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
9165 __isl_take isl_ast_expr *expr1,
9166 __isl_take isl_ast_expr *expr2);
9167 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
9168 __isl_take isl_ast_expr *expr1,
9169 __isl_take isl_ast_expr *expr2);
9170 __isl_give isl_ast_expr *isl_ast_expr_and(
9171 __isl_take isl_ast_expr *expr1,
9172 __isl_take isl_ast_expr *expr2)
9173 __isl_give isl_ast_expr *isl_ast_expr_and_then(
9174 __isl_take isl_ast_expr *expr1,
9175 __isl_take isl_ast_expr *expr2)
9176 __isl_give isl_ast_expr *isl_ast_expr_or(
9177 __isl_take isl_ast_expr *expr1,
9178 __isl_take isl_ast_expr *expr2)
9179 __isl_give isl_ast_expr *isl_ast_expr_or_else(
9180 __isl_take isl_ast_expr *expr1,
9181 __isl_take isl_ast_expr *expr2)
9182 __isl_give isl_ast_expr *isl_ast_expr_eq(
9183 __isl_take isl_ast_expr *expr1,
9184 __isl_take isl_ast_expr *expr2);
9185 __isl_give isl_ast_expr *isl_ast_expr_le(
9186 __isl_take isl_ast_expr *expr1,
9187 __isl_take isl_ast_expr *expr2);
9188 __isl_give isl_ast_expr *isl_ast_expr_lt(
9189 __isl_take isl_ast_expr *expr1,
9190 __isl_take isl_ast_expr *expr2);
9191 __isl_give isl_ast_expr *isl_ast_expr_ge(
9192 __isl_take isl_ast_expr *expr1,
9193 __isl_take isl_ast_expr *expr2);
9194 __isl_give isl_ast_expr *isl_ast_expr_gt(
9195 __isl_take isl_ast_expr *expr1,
9196 __isl_take isl_ast_expr *expr2);
9197 __isl_give isl_ast_expr *isl_ast_expr_access(
9198 __isl_take isl_ast_expr *array,
9199 __isl_take isl_ast_expr_list *indices);
9200 __isl_give isl_ast_expr *isl_ast_expr_call(
9201 __isl_take isl_ast_expr *function,
9202 __isl_take isl_ast_expr_list *arguments);
9204 The function C<isl_ast_expr_address_of> can be applied to an
9205 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
9206 to represent the address of the C<isl_ast_expr_access>. The function
9207 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
9208 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
9210 #include <isl/ast_build.h>
9211 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
9212 __isl_keep isl_ast_build *build,
9213 __isl_take isl_set *set);
9214 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
9215 __isl_keep isl_ast_build *build,
9216 __isl_take isl_pw_aff *pa);
9217 __isl_give isl_ast_expr *
9218 isl_ast_build_access_from_pw_multi_aff(
9219 __isl_keep isl_ast_build *build,
9220 __isl_take isl_pw_multi_aff *pma);
9221 __isl_give isl_ast_expr *
9222 isl_ast_build_access_from_multi_pw_aff(
9223 __isl_keep isl_ast_build *build,
9224 __isl_take isl_multi_pw_aff *mpa);
9225 __isl_give isl_ast_expr *
9226 isl_ast_build_call_from_pw_multi_aff(
9227 __isl_keep isl_ast_build *build,
9228 __isl_take isl_pw_multi_aff *pma);
9229 __isl_give isl_ast_expr *
9230 isl_ast_build_call_from_multi_pw_aff(
9231 __isl_keep isl_ast_build *build,
9232 __isl_take isl_multi_pw_aff *mpa);
9235 the domains of C<pa>, C<mpa> and C<pma> should correspond
9236 to the schedule space of C<build>.
9237 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
9238 the function being called.
9239 If the accessed space is a nested relation, then it is taken
9240 to represent an access of the member specified by the range
9241 of this nested relation of the structure specified by the domain
9242 of the nested relation.
9244 The following functions can be used to modify an C<isl_ast_expr>.
9246 #include <isl/ast.h>
9247 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
9248 __isl_take isl_ast_expr *expr, int pos,
9249 __isl_take isl_ast_expr *arg);
9251 Replace the argument of C<expr> at position C<pos> by C<arg>.
9253 #include <isl/ast.h>
9254 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
9255 __isl_take isl_ast_expr *expr,
9256 __isl_take isl_id_to_ast_expr *id2expr);
9258 The function C<isl_ast_expr_substitute_ids> replaces the
9259 subexpressions of C<expr> of type C<isl_ast_expr_id>
9260 by the corresponding expression in C<id2expr>, if there is any.
9263 User specified data can be attached to an C<isl_ast_node> and obtained
9264 from the same C<isl_ast_node> using the following functions.
9266 #include <isl/ast.h>
9267 __isl_give isl_ast_node *isl_ast_node_set_annotation(
9268 __isl_take isl_ast_node *node,
9269 __isl_take isl_id *annotation);
9270 __isl_give isl_id *isl_ast_node_get_annotation(
9271 __isl_keep isl_ast_node *node);
9273 Basic printing can be performed using the following functions.
9275 #include <isl/ast.h>
9276 __isl_give isl_printer *isl_printer_print_ast_expr(
9277 __isl_take isl_printer *p,
9278 __isl_keep isl_ast_expr *expr);
9279 __isl_give isl_printer *isl_printer_print_ast_node(
9280 __isl_take isl_printer *p,
9281 __isl_keep isl_ast_node *node);
9282 __isl_give char *isl_ast_expr_to_str(
9283 __isl_keep isl_ast_expr *expr);
9285 More advanced printing can be performed using the following functions.
9287 #include <isl/ast.h>
9288 __isl_give isl_printer *isl_ast_op_type_print_macro(
9289 enum isl_ast_op_type type,
9290 __isl_take isl_printer *p);
9291 __isl_give isl_printer *isl_ast_node_print_macros(
9292 __isl_keep isl_ast_node *node,
9293 __isl_take isl_printer *p);
9294 __isl_give isl_printer *isl_ast_node_print(
9295 __isl_keep isl_ast_node *node,
9296 __isl_take isl_printer *p,
9297 __isl_take isl_ast_print_options *options);
9298 __isl_give isl_printer *isl_ast_node_for_print(
9299 __isl_keep isl_ast_node *node,
9300 __isl_take isl_printer *p,
9301 __isl_take isl_ast_print_options *options);
9302 __isl_give isl_printer *isl_ast_node_if_print(
9303 __isl_keep isl_ast_node *node,
9304 __isl_take isl_printer *p,
9305 __isl_take isl_ast_print_options *options);
9307 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
9308 C<isl> may print out an AST that makes use of macros such
9309 as C<floord>, C<min> and C<max>.
9310 C<isl_ast_op_type_print_macro> prints out the macro
9311 corresponding to a specific C<isl_ast_op_type>.
9312 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
9313 for expressions where these macros would be used and prints
9314 out the required macro definitions.
9315 Essentially, C<isl_ast_node_print_macros> calls
9316 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
9317 as function argument.
9318 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
9319 C<isl_ast_node_if_print> print an C<isl_ast_node>
9320 in C<ISL_FORMAT_C>, but allow for some extra control
9321 through an C<isl_ast_print_options> object.
9322 This object can be created using the following functions.
9324 #include <isl/ast.h>
9325 __isl_give isl_ast_print_options *
9326 isl_ast_print_options_alloc(isl_ctx *ctx);
9327 __isl_give isl_ast_print_options *
9328 isl_ast_print_options_copy(
9329 __isl_keep isl_ast_print_options *options);
9330 __isl_null isl_ast_print_options *
9331 isl_ast_print_options_free(
9332 __isl_take isl_ast_print_options *options);
9334 __isl_give isl_ast_print_options *
9335 isl_ast_print_options_set_print_user(
9336 __isl_take isl_ast_print_options *options,
9337 __isl_give isl_printer *(*print_user)(
9338 __isl_take isl_printer *p,
9339 __isl_take isl_ast_print_options *options,
9340 __isl_keep isl_ast_node *node, void *user),
9342 __isl_give isl_ast_print_options *
9343 isl_ast_print_options_set_print_for(
9344 __isl_take isl_ast_print_options *options,
9345 __isl_give isl_printer *(*print_for)(
9346 __isl_take isl_printer *p,
9347 __isl_take isl_ast_print_options *options,
9348 __isl_keep isl_ast_node *node, void *user),
9351 The callback set by C<isl_ast_print_options_set_print_user>
9352 is called whenever a node of type C<isl_ast_node_user> needs to
9354 The callback set by C<isl_ast_print_options_set_print_for>
9355 is called whenever a node of type C<isl_ast_node_for> needs to
9357 Note that C<isl_ast_node_for_print> will I<not> call the
9358 callback set by C<isl_ast_print_options_set_print_for> on the node
9359 on which C<isl_ast_node_for_print> is called, but only on nested
9360 nodes of type C<isl_ast_node_for>. It is therefore safe to
9361 call C<isl_ast_node_for_print> from within the callback set by
9362 C<isl_ast_print_options_set_print_for>.
9364 The following option determines the type to be used for iterators
9365 while printing the AST.
9367 isl_stat isl_options_set_ast_iterator_type(
9368 isl_ctx *ctx, const char *val);
9369 const char *isl_options_get_ast_iterator_type(
9372 The AST printer only prints body nodes as blocks if these
9373 blocks cannot be safely omitted.
9374 For example, a C<for> node with one body node will not be
9375 surrounded with braces in C<ISL_FORMAT_C>.
9376 A block will always be printed by setting the following option.
9378 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx,
9380 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
9384 #include <isl/ast_build.h>
9385 isl_stat isl_options_set_ast_build_atomic_upper_bound(
9386 isl_ctx *ctx, int val);
9387 int isl_options_get_ast_build_atomic_upper_bound(
9389 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
9391 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
9392 isl_stat isl_options_set_ast_build_exploit_nested_bounds(
9393 isl_ctx *ctx, int val);
9394 int isl_options_get_ast_build_exploit_nested_bounds(
9396 isl_stat isl_options_set_ast_build_group_coscheduled(
9397 isl_ctx *ctx, int val);
9398 int isl_options_get_ast_build_group_coscheduled(
9400 isl_stat isl_options_set_ast_build_scale_strides(
9401 isl_ctx *ctx, int val);
9402 int isl_options_get_ast_build_scale_strides(
9404 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx,
9406 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
9407 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx,
9409 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
9413 =item * ast_build_atomic_upper_bound
9415 Generate loop upper bounds that consist of the current loop iterator,
9416 an operator and an expression not involving the iterator.
9417 If this option is not set, then the current loop iterator may appear
9418 several times in the upper bound.
9419 For example, when this option is turned off, AST generation
9422 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
9426 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
9429 When the option is turned on, the following AST is generated
9431 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
9434 =item * ast_build_prefer_pdiv
9436 If this option is turned off, then the AST generation will
9437 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
9438 operators, but no C<isl_ast_op_pdiv_q> or
9439 C<isl_ast_op_pdiv_r> operators.
9440 If this options is turned on, then C<isl> will try to convert
9441 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
9442 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
9444 =item * ast_build_exploit_nested_bounds
9446 Simplify conditions based on bounds of nested for loops.
9447 In particular, remove conditions that are implied by the fact
9448 that one or more nested loops have at least one iteration,
9449 meaning that the upper bound is at least as large as the lower bound.
9450 For example, when this option is turned off, AST generation
9453 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
9459 for (int c0 = 0; c0 <= N; c0 += 1)
9460 for (int c1 = 0; c1 <= M; c1 += 1)
9463 When the option is turned on, the following AST is generated
9465 for (int c0 = 0; c0 <= N; c0 += 1)
9466 for (int c1 = 0; c1 <= M; c1 += 1)
9469 =item * ast_build_group_coscheduled
9471 If two domain elements are assigned the same schedule point, then
9472 they may be executed in any order and they may even appear in different
9473 loops. If this options is set, then the AST generator will make
9474 sure that coscheduled domain elements do not appear in separate parts
9475 of the AST. This is useful in case of nested AST generation
9476 if the outer AST generation is given only part of a schedule
9477 and the inner AST generation should handle the domains that are
9478 coscheduled by this initial part of the schedule together.
9479 For example if an AST is generated for a schedule
9481 { A[i] -> [0]; B[i] -> [0] }
9483 then the C<isl_ast_build_set_create_leaf> callback described
9484 below may get called twice, once for each domain.
9485 Setting this option ensures that the callback is only called once
9486 on both domains together.
9488 =item * ast_build_separation_bounds
9490 This option specifies which bounds to use during separation.
9491 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
9492 then all (possibly implicit) bounds on the current dimension will
9493 be used during separation.
9494 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
9495 then only those bounds that are explicitly available will
9496 be used during separation.
9498 =item * ast_build_scale_strides
9500 This option specifies whether the AST generator is allowed
9501 to scale down iterators of strided loops.
9503 =item * ast_build_allow_else
9505 This option specifies whether the AST generator is allowed
9506 to construct if statements with else branches.
9508 =item * ast_build_allow_or
9510 This option specifies whether the AST generator is allowed
9511 to construct if conditions with disjunctions.
9515 =head3 AST Generation Options (Schedule Tree)
9517 In case of AST construction from a schedule tree, the options
9518 that control how an AST is created from the individual schedule
9519 dimensions are stored in the band nodes of the tree
9520 (see L</"Schedule Trees">).
9522 In particular, a schedule dimension can be handled in four
9523 different ways, atomic, separate, unroll or the default.
9524 This loop AST generation type can be set using
9525 C<isl_schedule_node_band_member_set_ast_loop_type>.
9527 the first three can be selected by including a one-dimensional
9528 element with as value the position of the schedule dimension
9529 within the band and as name one of C<atomic>, C<separate>
9530 or C<unroll> in the options
9531 set by C<isl_schedule_node_band_set_ast_build_options>.
9532 Only one of these three may be specified for
9533 any given schedule dimension within a band node.
9534 If none of these is specified, then the default
9535 is used. The meaning of the options is as follows.
9541 When this option is specified, the AST generator will make
9542 sure that a given domains space only appears in a single
9543 loop at the specified level.
9545 For example, for the schedule tree
9547 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
9549 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
9550 options: "{ atomic[x] }"
9552 the following AST will be generated
9554 for (int c0 = 0; c0 <= 10; c0 += 1) {
9561 On the other hand, for the schedule tree
9563 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
9565 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
9566 options: "{ separate[x] }"
9568 the following AST will be generated
9572 for (int c0 = 1; c0 <= 9; c0 += 1) {
9579 If neither C<atomic> nor C<separate> is specified, then the AST generator
9580 may produce either of these two results or some intermediate form.
9584 When this option is specified, the AST generator will
9585 split the domain of the specified schedule dimension
9586 into pieces with a fixed set of statements for which
9587 instances need to be executed by the iterations in
9588 the schedule domain part. This option tends to avoid
9589 the generation of guards inside the corresponding loops.
9590 See also the C<atomic> option.
9594 When this option is specified, the AST generator will
9595 I<completely> unroll the corresponding schedule dimension.
9596 It is the responsibility of the user to ensure that such
9597 unrolling is possible.
9598 To obtain a partial unrolling, the user should apply an additional
9599 strip-mining to the schedule and fully unroll the inner schedule
9604 The C<isolate> option is a bit more involved. It allows the user
9605 to isolate a range of schedule dimension values from smaller and
9606 greater values. Additionally, the user may specify a different
9607 atomic/separate/unroll choice for the isolated part and the remaining
9608 parts. The typical use case of the C<isolate> option is to isolate
9609 full tiles from partial tiles.
9610 The part that needs to be isolated may depend on outer schedule dimensions.
9611 The option therefore needs to be able to reference those outer schedule
9612 dimensions. In particular, the space of the C<isolate> option is that
9613 of a wrapped map with as domain the flat product of all outer band nodes
9614 and as range the space of the current band node.
9615 The atomic/separate/unroll choice for the isolated part is determined
9616 by an option that lives in an unnamed wrapped space with as domain
9617 a zero-dimensional C<isolate> space and as range the regular
9618 C<atomic>, C<separate> or C<unroll> space.
9619 This option may also be set directly using
9620 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
9621 The atomic/separate/unroll choice for the remaining part is determined
9622 by the regular C<atomic>, C<separate> or C<unroll> option.
9623 The use of the C<isolate> option causes any tree containing the node
9624 to be considered anchored.
9626 As an example, consider the isolation of full tiles from partial tiles
9627 in a tiling of a triangular domain. The original schedule is as follows.
9629 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
9631 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
9632 { A[i,j] -> [floor(j/10)] }, \
9633 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
9637 for (int c0 = 0; c0 <= 10; c0 += 1)
9638 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
9639 for (int c2 = 10 * c0;
9640 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
9641 for (int c3 = 10 * c1;
9642 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
9645 Isolating the full tiles, we have the following input
9647 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
9649 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
9650 { A[i,j] -> [floor(j/10)] }, \
9651 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
9652 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
9653 10a+9+10b+9 <= 100 }"
9658 for (int c0 = 0; c0 <= 8; c0 += 1) {
9659 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
9660 for (int c2 = 10 * c0;
9661 c2 <= 10 * c0 + 9; c2 += 1)
9662 for (int c3 = 10 * c1;
9663 c3 <= 10 * c1 + 9; c3 += 1)
9665 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
9666 for (int c2 = 10 * c0;
9667 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
9668 for (int c3 = 10 * c1;
9669 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
9672 for (int c0 = 9; c0 <= 10; c0 += 1)
9673 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
9674 for (int c2 = 10 * c0;
9675 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
9676 for (int c3 = 10 * c1;
9677 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
9681 We may then additionally unroll the innermost loop of the isolated part
9683 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
9685 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
9686 { A[i,j] -> [floor(j/10)] }, \
9687 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
9688 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
9689 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
9694 for (int c0 = 0; c0 <= 8; c0 += 1) {
9695 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
9696 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
9708 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
9709 for (int c2 = 10 * c0;
9710 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
9711 for (int c3 = 10 * c1;
9712 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
9715 for (int c0 = 9; c0 <= 10; c0 += 1)
9716 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
9717 for (int c2 = 10 * c0;
9718 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
9719 for (int c3 = 10 * c1;
9720 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
9725 =head3 AST Generation Options (Schedule Map)
9727 In case of AST construction using
9728 C<isl_ast_build_node_from_schedule_map>, the options
9729 that control how an AST is created from the individual schedule
9730 dimensions are stored in the C<isl_ast_build>.
9731 They can be set using the following function.
9733 #include <isl/ast_build.h>
9734 __isl_give isl_ast_build *
9735 isl_ast_build_set_options(
9736 __isl_take isl_ast_build *control,
9737 __isl_take isl_union_map *options);
9739 The options are encoded in an C<isl_union_map>.
9740 The domain of this union relation refers to the schedule domain,
9741 i.e., the range of the schedule passed
9742 to C<isl_ast_build_node_from_schedule_map>.
9743 In the case of nested AST generation (see L</"Nested AST Generation">),
9744 the domain of C<options> should refer to the extra piece of the schedule.
9745 That is, it should be equal to the range of the wrapped relation in the
9746 range of the schedule.
9747 The range of the options can consist of elements in one or more spaces,
9748 the names of which determine the effect of the option.
9749 The values of the range typically also refer to the schedule dimension
9750 to which the option applies. In case of nested AST generation
9751 (see L</"Nested AST Generation">), these values refer to the position
9752 of the schedule dimension within the innermost AST generation.
9753 The constraints on the domain elements of
9754 the option should only refer to this dimension and earlier dimensions.
9755 We consider the following spaces.
9759 =item C<separation_class>
9761 B<This option has been deprecated. Use the isolate option on
9762 schedule trees instead.>
9764 This space is a wrapped relation between two one dimensional spaces.
9765 The input space represents the schedule dimension to which the option
9766 applies and the output space represents the separation class.
9767 While constructing a loop corresponding to the specified schedule
9768 dimension(s), the AST generator will try to generate separate loops
9769 for domain elements that are assigned different classes.
9770 If only some of the elements are assigned a class, then those elements
9771 that are not assigned any class will be treated as belonging to a class
9772 that is separate from the explicitly assigned classes.
9773 The typical use case for this option is to separate full tiles from
9775 The other options, described below, are applied after the separation
9778 As an example, consider the separation into full and partial tiles
9779 of a tiling of a triangular domain.
9780 Take, for example, the domain
9782 { A[i,j] : 0 <= i,j and i + j <= 100 }
9784 and a tiling into tiles of 10 by 10. The input to the AST generator
9785 is then the schedule
9787 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
9790 Without any options, the following AST is generated
9792 for (int c0 = 0; c0 <= 10; c0 += 1)
9793 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
9794 for (int c2 = 10 * c0;
9795 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
9797 for (int c3 = 10 * c1;
9798 c3 <= min(10 * c1 + 9, -c2 + 100);
9802 Separation into full and partial tiles can be obtained by assigning
9803 a class, say C<0>, to the full tiles. The full tiles are represented by those
9804 values of the first and second schedule dimensions for which there are
9805 values of the third and fourth dimensions to cover an entire tile.
9806 That is, we need to specify the following option
9808 { [a,b,c,d] -> separation_class[[0]->[0]] :
9809 exists b': 0 <= 10a,10b' and
9810 10a+9+10b'+9 <= 100;
9811 [a,b,c,d] -> separation_class[[1]->[0]] :
9812 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
9816 { [a, b, c, d] -> separation_class[[1] -> [0]] :
9817 a >= 0 and b >= 0 and b <= 8 - a;
9818 [a, b, c, d] -> separation_class[[0] -> [0]] :
9821 With this option, the generated AST is as follows
9824 for (int c0 = 0; c0 <= 8; c0 += 1) {
9825 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
9826 for (int c2 = 10 * c0;
9827 c2 <= 10 * c0 + 9; c2 += 1)
9828 for (int c3 = 10 * c1;
9829 c3 <= 10 * c1 + 9; c3 += 1)
9831 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
9832 for (int c2 = 10 * c0;
9833 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
9835 for (int c3 = 10 * c1;
9836 c3 <= min(-c2 + 100, 10 * c1 + 9);
9840 for (int c0 = 9; c0 <= 10; c0 += 1)
9841 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
9842 for (int c2 = 10 * c0;
9843 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
9845 for (int c3 = 10 * c1;
9846 c3 <= min(10 * c1 + 9, -c2 + 100);
9853 This is a single-dimensional space representing the schedule dimension(s)
9854 to which ``separation'' should be applied. Separation tries to split
9855 a loop into several pieces if this can avoid the generation of guards
9857 See also the C<atomic> option.
9861 This is a single-dimensional space representing the schedule dimension(s)
9862 for which the domains should be considered ``atomic''. That is, the
9863 AST generator will make sure that any given domain space will only appear
9864 in a single loop at the specified level.
9866 Consider the following schedule
9868 { a[i] -> [i] : 0 <= i < 10;
9869 b[i] -> [i+1] : 0 <= i < 10 }
9871 If the following option is specified
9873 { [i] -> separate[x] }
9875 then the following AST will be generated
9879 for (int c0 = 1; c0 <= 9; c0 += 1) {
9886 If, on the other hand, the following option is specified
9888 { [i] -> atomic[x] }
9890 then the following AST will be generated
9892 for (int c0 = 0; c0 <= 10; c0 += 1) {
9899 If neither C<atomic> nor C<separate> is specified, then the AST generator
9900 may produce either of these two results or some intermediate form.
9904 This is a single-dimensional space representing the schedule dimension(s)
9905 that should be I<completely> unrolled.
9906 To obtain a partial unrolling, the user should apply an additional
9907 strip-mining to the schedule and fully unroll the inner loop.
9911 =head3 Fine-grained Control over AST Generation
9913 Besides specifying the constraints on the parameters,
9914 an C<isl_ast_build> object can be used to control
9915 various aspects of the AST generation process.
9916 In case of AST construction using
9917 C<isl_ast_build_node_from_schedule_map>,
9918 the most prominent way of control is through ``options'',
9921 Additional control is available through the following functions.
9923 #include <isl/ast_build.h>
9924 __isl_give isl_ast_build *
9925 isl_ast_build_set_iterators(
9926 __isl_take isl_ast_build *control,
9927 __isl_take isl_id_list *iterators);
9929 The function C<isl_ast_build_set_iterators> allows the user to
9930 specify a list of iterator C<isl_id>s to be used as iterators.
9931 If the input schedule is injective, then
9932 the number of elements in this list should be as large as the dimension
9933 of the schedule space, but no direct correspondence should be assumed
9934 between dimensions and elements.
9935 If the input schedule is not injective, then an additional number
9936 of C<isl_id>s equal to the largest dimension of the input domains
9938 If the number of provided C<isl_id>s is insufficient, then additional
9939 names are automatically generated.
9941 #include <isl/ast_build.h>
9942 __isl_give isl_ast_build *
9943 isl_ast_build_set_create_leaf(
9944 __isl_take isl_ast_build *control,
9945 __isl_give isl_ast_node *(*fn)(
9946 __isl_take isl_ast_build *build,
9947 void *user), void *user);
9950 C<isl_ast_build_set_create_leaf> function allows for the
9951 specification of a callback that should be called whenever the AST
9952 generator arrives at an element of the schedule domain.
9953 The callback should return an AST node that should be inserted
9954 at the corresponding position of the AST. The default action (when
9955 the callback is not set) is to continue generating parts of the AST to scan
9956 all the domain elements associated to the schedule domain element
9957 and to insert user nodes, ``calling'' the domain element, for each of them.
9958 The C<build> argument contains the current state of the C<isl_ast_build>.
9959 To ease nested AST generation (see L</"Nested AST Generation">),
9960 all control information that is
9961 specific to the current AST generation such as the options and
9962 the callbacks has been removed from this C<isl_ast_build>.
9963 The callback would typically return the result of a nested
9965 user defined node created using the following function.
9967 #include <isl/ast.h>
9968 __isl_give isl_ast_node *isl_ast_node_alloc_user(
9969 __isl_take isl_ast_expr *expr);
9971 #include <isl/ast_build.h>
9972 __isl_give isl_ast_build *
9973 isl_ast_build_set_at_each_domain(
9974 __isl_take isl_ast_build *build,
9975 __isl_give isl_ast_node *(*fn)(
9976 __isl_take isl_ast_node *node,
9977 __isl_keep isl_ast_build *build,
9978 void *user), void *user);
9979 __isl_give isl_ast_build *
9980 isl_ast_build_set_before_each_for(
9981 __isl_take isl_ast_build *build,
9982 __isl_give isl_id *(*fn)(
9983 __isl_keep isl_ast_build *build,
9984 void *user), void *user);
9985 __isl_give isl_ast_build *
9986 isl_ast_build_set_after_each_for(
9987 __isl_take isl_ast_build *build,
9988 __isl_give isl_ast_node *(*fn)(
9989 __isl_take isl_ast_node *node,
9990 __isl_keep isl_ast_build *build,
9991 void *user), void *user);
9992 __isl_give isl_ast_build *
9993 isl_ast_build_set_before_each_mark(
9994 __isl_take isl_ast_build *build,
9995 isl_stat (*fn)(__isl_keep isl_id *mark,
9996 __isl_keep isl_ast_build *build,
9997 void *user), void *user);
9998 __isl_give isl_ast_build *
9999 isl_ast_build_set_after_each_mark(
10000 __isl_take isl_ast_build *build,
10001 __isl_give isl_ast_node *(*fn)(
10002 __isl_take isl_ast_node *node,
10003 __isl_keep isl_ast_build *build,
10004 void *user), void *user);
10006 The callback set by C<isl_ast_build_set_at_each_domain> will
10007 be called for each domain AST node.
10008 The callbacks set by C<isl_ast_build_set_before_each_for>
10009 and C<isl_ast_build_set_after_each_for> will be called
10010 for each for AST node. The first will be called in depth-first
10011 pre-order, while the second will be called in depth-first post-order.
10012 Since C<isl_ast_build_set_before_each_for> is called before the for
10013 node is actually constructed, it is only passed an C<isl_ast_build>.
10014 The returned C<isl_id> will be added as an annotation (using
10015 C<isl_ast_node_set_annotation>) to the constructed for node.
10016 In particular, if the user has also specified an C<after_each_for>
10017 callback, then the annotation can be retrieved from the node passed to
10018 that callback using C<isl_ast_node_get_annotation>.
10019 The callbacks set by C<isl_ast_build_set_before_each_mark>
10020 and C<isl_ast_build_set_after_each_mark> will be called for each
10021 mark AST node that is created, i.e., for each mark schedule node
10022 in the input schedule tree. The first will be called in depth-first
10023 pre-order, while the second will be called in depth-first post-order.
10024 Since the callback set by C<isl_ast_build_set_before_each_mark>
10025 is called before the mark AST node is actually constructed, it is passed
10026 the identifier of the mark node.
10027 All callbacks should C<NULL> (or -1) on failure.
10028 The given C<isl_ast_build> can be used to create new
10029 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
10030 or C<isl_ast_build_call_from_pw_multi_aff>.
10032 =head3 Nested AST Generation
10034 C<isl> allows the user to create an AST within the context
10035 of another AST. These nested ASTs are created using the
10036 same C<isl_ast_build_node_from_schedule_map> function that is used to create
10037 the outer AST. The C<build> argument should be an C<isl_ast_build>
10038 passed to a callback set by
10039 C<isl_ast_build_set_create_leaf>.
10040 The space of the range of the C<schedule> argument should refer
10041 to this build. In particular, the space should be a wrapped
10042 relation and the domain of this wrapped relation should be the
10043 same as that of the range of the schedule returned by
10044 C<isl_ast_build_get_schedule> below.
10045 In practice, the new schedule is typically
10046 created by calling C<isl_union_map_range_product> on the old schedule
10047 and some extra piece of the schedule.
10048 The space of the schedule domain is also available from
10049 the C<isl_ast_build>.
10051 #include <isl/ast_build.h>
10052 __isl_give isl_union_map *isl_ast_build_get_schedule(
10053 __isl_keep isl_ast_build *build);
10054 __isl_give isl_space *isl_ast_build_get_schedule_space(
10055 __isl_keep isl_ast_build *build);
10056 __isl_give isl_ast_build *isl_ast_build_restrict(
10057 __isl_take isl_ast_build *build,
10058 __isl_take isl_set *set);
10060 The C<isl_ast_build_get_schedule> function returns a (partial)
10061 schedule for the domains elements for which part of the AST still needs to
10062 be generated in the current build.
10063 In particular, the domain elements are mapped to those iterations of the loops
10064 enclosing the current point of the AST generation inside which
10065 the domain elements are executed.
10066 No direct correspondence between
10067 the input schedule and this schedule should be assumed.
10068 The space obtained from C<isl_ast_build_get_schedule_space> can be used
10069 to create a set for C<isl_ast_build_restrict> to intersect
10070 with the current build. In particular, the set passed to
10071 C<isl_ast_build_restrict> can have additional parameters.
10072 The ids of the set dimensions in the space returned by
10073 C<isl_ast_build_get_schedule_space> correspond to the
10074 iterators of the already generated loops.
10075 The user should not rely on the ids of the output dimensions
10076 of the relations in the union relation returned by
10077 C<isl_ast_build_get_schedule> having any particular value.
10079 =head1 Applications
10081 Although C<isl> is mainly meant to be used as a library,
10082 it also contains some basic applications that use some
10083 of the functionality of C<isl>.
10084 The input may be specified in either the L<isl format>
10085 or the L<PolyLib format>.
10087 =head2 C<isl_polyhedron_sample>
10089 C<isl_polyhedron_sample> takes a polyhedron as input and prints
10090 an integer element of the polyhedron, if there is any.
10091 The first column in the output is the denominator and is always
10092 equal to 1. If the polyhedron contains no integer points,
10093 then a vector of length zero is printed.
10097 C<isl_pip> takes the same input as the C<example> program
10098 from the C<piplib> distribution, i.e., a set of constraints
10099 on the parameters, a line containing only -1 and finally a set
10100 of constraints on a parametric polyhedron.
10101 The coefficients of the parameters appear in the last columns
10102 (but before the final constant column).
10103 The output is the lexicographic minimum of the parametric polyhedron.
10104 As C<isl> currently does not have its own output format, the output
10105 is just a dump of the internal state.
10107 =head2 C<isl_polyhedron_minimize>
10109 C<isl_polyhedron_minimize> computes the minimum of some linear
10110 or affine objective function over the integer points in a polyhedron.
10111 If an affine objective function
10112 is given, then the constant should appear in the last column.
10114 =head2 C<isl_polytope_scan>
10116 Given a polytope, C<isl_polytope_scan> prints
10117 all integer points in the polytope.
10119 =head2 C<isl_codegen>
10121 Given a schedule, a context set and an options relation,
10122 C<isl_codegen> prints out an AST that scans the domain elements
10123 of the schedule in the order of their image(s) taking into account
10124 the constraints in the context set.