3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
8 using C<GMP> or C<imath>.
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
171 =head3 Changes since isl-0.10
175 =item * The functions C<isl_set_dim_has_lower_bound> and
176 C<isl_set_dim_has_upper_bound> have been renamed to
177 C<isl_set_dim_has_any_lower_bound> and
178 C<isl_set_dim_has_any_upper_bound>.
179 The new C<isl_set_dim_has_lower_bound> and
180 C<isl_set_dim_has_upper_bound> have slightly different meanings.
184 =head3 Changes since isl-0.12
188 =item * C<isl_int> has been replaced by C<isl_val>.
189 Some of the old functions are still available in C<isl/deprecated/*.h>
190 but they will be removed in the future.
192 =item * The functions C<isl_pw_qpolynomial_eval>,
193 C<isl_union_pw_qpolynomial_eval>, C<isl_pw_qpolynomial_fold_eval>
194 and C<isl_union_pw_qpolynomial_fold_eval> have been changed to return
195 an C<isl_val> instead of an C<isl_qpolynomial>.
197 =item * The function C<isl_band_member_is_zero_distance>
198 has been removed. Essentially the same functionality is available
199 through C<isl_band_member_is_coincident>, except that it requires
200 setting up coincidence constraints.
201 The option C<schedule_outer_zero_distance> has accordingly been
202 replaced by the option C<schedule_outer_coincidence>.
204 =item * The function C<isl_vertex_get_expr> has been changed
205 to return an C<isl_multi_aff> instead of a rational C<isl_basic_set>.
206 The function C<isl_vertex_get_domain> has been changed to return
207 a regular basic set, rather than a rational basic set.
211 =head3 Changes since isl-0.14
215 =item * The function C<isl_union_pw_multi_aff_add> now consistently
216 computes the sum on the shared definition domain.
217 The function C<isl_union_pw_multi_aff_union_add> has been added
218 to compute the sum on the union of definition domains.
219 The original behavior of C<isl_union_pw_multi_aff_add> was
220 confused and is no longer available.
222 =item * Band forests have been replaced by schedule trees.
224 =item * The function C<isl_union_map_compute_flow> has been
225 replaced by the function C<isl_union_access_info_compute_flow>.
226 Note that the may dependence relation returned by
227 C<isl_union_flow_get_may_dependence> is the union of
228 the two dependence relations returned by
229 C<isl_union_map_compute_flow>. Similarly for the no source relations.
230 The function C<isl_union_map_compute_flow> is still available
231 for backward compatibility, but it will be removed in the future.
233 =item * The function C<isl_basic_set_drop_constraint> has been
236 =item * The function C<isl_ast_build_ast_from_schedule> has been
237 renamed to C<isl_ast_build_node_from_schedule_map>.
238 The original name is still available
239 for backward compatibility, but it will be removed in the future.
241 =item * The C<separation_class> AST generation option has been
244 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
245 have been renamed to C<isl_constraint_alloc_equality> and
246 C<isl_constraint_alloc_inequality>. The original names have been
247 kept for backward compatibility, but they will be removed in the future.
249 =item * The C<schedule_fuse> option has been replaced
250 by the C<schedule_serialize_sccs> option. The effect
251 of setting the C<schedule_fuse> option to C<ISL_SCHEDULE_FUSE_MIN>
252 is now obtained by turning on the C<schedule_serialize_sccs> option.
256 =head3 Changes since isl-0.17
260 =item * The function C<isl_printer_print_ast_expr> no longer prints
261 in C format by default. To print in C format, the output format
262 of the printer needs to have been explicitly set to C<ISL_FORMAT_C>.
263 As a result, the function C<isl_ast_expr_to_str> no longer prints
264 the expression in C format. Use C<isl_ast_expr_to_C_str> instead.
266 =item * The functions C<isl_set_align_divs> and C<isl_map_align_divs>
267 have been deprecated. The function C<isl_set_lift> has an effect
268 that is similar to C<isl_set_align_divs> and could in some cases
269 be used as an alternative.
275 C<isl> is released under the MIT license.
279 Permission is hereby granted, free of charge, to any person obtaining a copy of
280 this software and associated documentation files (the "Software"), to deal in
281 the Software without restriction, including without limitation the rights to
282 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
283 of the Software, and to permit persons to whom the Software is furnished to do
284 so, subject to the following conditions:
286 The above copyright notice and this permission notice shall be included in all
287 copies or substantial portions of the Software.
289 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
290 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
291 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
292 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
293 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
294 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
299 Note that by default C<isl> requires C<GMP>, which is released
300 under the GNU Lesser General Public License (LGPL). This means
301 that code linked against C<isl> is also linked against LGPL code.
303 When configuring with C<--with-int=imath> or C<--with-int=imath-32>, C<isl>
304 will link against C<imath>, a library for exact integer arithmetic released
305 under the MIT license.
309 The source of C<isl> can be obtained either as a tarball
310 or from the git repository. Both are available from
311 L<http://isl.gforge.inria.fr/>.
312 The installation process depends on how you obtained
315 =head2 Installation from the git repository
319 =item 1 Clone or update the repository
321 The first time the source is obtained, you need to clone
324 git clone git://repo.or.cz/isl.git
326 To obtain updates, you need to pull in the latest changes
330 =item 2 Optionally get C<imath> submodule
332 To build C<isl> with C<imath>, you need to obtain the C<imath>
333 submodule by running in the git source tree of C<isl>
338 This will fetch the required version of C<imath> in a subdirectory of C<isl>.
340 =item 2 Generate C<configure>
346 After performing the above steps, continue
347 with the L<Common installation instructions>.
349 =head2 Common installation instructions
353 =item 1 Obtain C<GMP>
355 By default, building C<isl> requires C<GMP>, including its headers files.
356 Your distribution may not provide these header files by default
357 and you may need to install a package called C<gmp-devel> or something
358 similar. Alternatively, C<GMP> can be built from
359 source, available from L<http://gmplib.org/>.
360 C<GMP> is not needed if you build C<isl> with C<imath>.
364 C<isl> uses the standard C<autoconf> C<configure> script.
369 optionally followed by some configure options.
370 A complete list of options can be obtained by running
374 Below we discuss some of the more common options.
380 Installation prefix for C<isl>
382 =item C<--with-int=[gmp|imath|imath-32]>
384 Select the integer library to be used by C<isl>, the default is C<gmp>.
385 With C<imath-32>, C<isl> will use 32 bit integers, but fall back to C<imath>
386 for values out of the 32 bit range. In most applications, C<isl> will run
387 fastest with the C<imath-32> option, followed by C<gmp> and C<imath>, the
390 =item C<--with-gmp-prefix>
392 Installation prefix for C<GMP> (architecture-independent files).
394 =item C<--with-gmp-exec-prefix>
396 Installation prefix for C<GMP> (architecture-dependent files).
404 =item 4 Install (optional)
410 =head1 Integer Set Library
412 =head2 Memory Management
414 Since a high-level operation on isl objects usually involves
415 several substeps and since the user is usually not interested in
416 the intermediate results, most functions that return a new object
417 will also release all the objects passed as arguments.
418 If the user still wants to use one or more of these arguments
419 after the function call, she should pass along a copy of the
420 object rather than the object itself.
421 The user is then responsible for making sure that the original
422 object gets used somewhere else or is explicitly freed.
424 The arguments and return values of all documented functions are
425 annotated to make clear which arguments are released and which
426 arguments are preserved. In particular, the following annotations
433 C<__isl_give> means that a new object is returned.
434 The user should make sure that the returned pointer is
435 used exactly once as a value for an C<__isl_take> argument.
436 In between, it can be used as a value for as many
437 C<__isl_keep> arguments as the user likes.
438 There is one exception, and that is the case where the
439 pointer returned is C<NULL>. Is this case, the user
440 is free to use it as an C<__isl_take> argument or not.
441 When applied to a C<char *>, the returned pointer needs to be
446 C<__isl_null> means that a C<NULL> value is returned.
450 C<__isl_take> means that the object the argument points to
451 is taken over by the function and may no longer be used
452 by the user as an argument to any other function.
453 The pointer value must be one returned by a function
454 returning an C<__isl_give> pointer.
455 If the user passes in a C<NULL> value, then this will
456 be treated as an error in the sense that the function will
457 not perform its usual operation. However, it will still
458 make sure that all the other C<__isl_take> arguments
463 C<__isl_keep> means that the function will only use the object
464 temporarily. After the function has finished, the user
465 can still use it as an argument to other functions.
466 A C<NULL> value will be treated in the same way as
467 a C<NULL> value for an C<__isl_take> argument.
468 This annotation may also be used on return values of
469 type C<const char *>, in which case the returned pointer should
470 not be freed by the user and is only valid until the object
471 from which it was derived is updated or freed.
475 =head2 Initialization
477 All manipulations of integer sets and relations occur within
478 the context of an C<isl_ctx>.
479 A given C<isl_ctx> can only be used within a single thread.
480 All arguments of a function are required to have been allocated
481 within the same context.
482 There are currently no functions available for moving an object
483 from one C<isl_ctx> to another C<isl_ctx>. This means that
484 there is currently no way of safely moving an object from one
485 thread to another, unless the whole C<isl_ctx> is moved.
487 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
488 freed using C<isl_ctx_free>.
489 All objects allocated within an C<isl_ctx> should be freed
490 before the C<isl_ctx> itself is freed.
492 isl_ctx *isl_ctx_alloc();
493 void isl_ctx_free(isl_ctx *ctx);
495 The user can impose a bound on the number of low-level I<operations>
496 that can be performed by an C<isl_ctx>. This bound can be set and
497 retrieved using the following functions. A bound of zero means that
498 no bound is imposed. The number of operations performed can be
499 reset using C<isl_ctx_reset_operations>. Note that the number
500 of low-level operations needed to perform a high-level computation
501 may differ significantly across different versions
502 of C<isl>, but it should be the same across different platforms
503 for the same version of C<isl>.
505 Warning: This feature is experimental. C<isl> has good support to abort and
506 bail out during the computation, but this feature may exercise error code paths
507 that are normally not used that much. Consequently, it is not unlikely that
508 hidden bugs will be exposed.
510 void isl_ctx_set_max_operations(isl_ctx *ctx,
511 unsigned long max_operations);
512 unsigned long isl_ctx_get_max_operations(isl_ctx *ctx);
513 void isl_ctx_reset_operations(isl_ctx *ctx);
515 In order to be able to create an object in the same context
516 as another object, most object types (described later in
517 this document) provide a function to obtain the context
518 in which the object was created.
521 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
522 isl_ctx *isl_multi_val_get_ctx(
523 __isl_keep isl_multi_val *mv);
526 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
528 #include <isl/local_space.h>
529 isl_ctx *isl_local_space_get_ctx(
530 __isl_keep isl_local_space *ls);
533 isl_ctx *isl_set_list_get_ctx(
534 __isl_keep isl_set_list *list);
537 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
538 isl_ctx *isl_multi_aff_get_ctx(
539 __isl_keep isl_multi_aff *maff);
540 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pa);
541 isl_ctx *isl_pw_multi_aff_get_ctx(
542 __isl_keep isl_pw_multi_aff *pma);
543 isl_ctx *isl_multi_pw_aff_get_ctx(
544 __isl_keep isl_multi_pw_aff *mpa);
545 isl_ctx *isl_union_pw_aff_get_ctx(
546 __isl_keep isl_union_pw_aff *upa);
547 isl_ctx *isl_union_pw_multi_aff_get_ctx(
548 __isl_keep isl_union_pw_multi_aff *upma);
549 isl_ctx *isl_multi_union_pw_aff_get_ctx(
550 __isl_keep isl_multi_union_pw_aff *mupa);
552 #include <isl/id_to_ast_expr.h>
553 isl_ctx *isl_id_to_ast_expr_get_ctx(
554 __isl_keep isl_id_to_ast_expr *id2expr);
556 #include <isl/point.h>
557 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
560 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
563 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
565 #include <isl/vertices.h>
566 isl_ctx *isl_vertices_get_ctx(
567 __isl_keep isl_vertices *vertices);
568 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
569 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
571 #include <isl/flow.h>
572 isl_ctx *isl_restriction_get_ctx(
573 __isl_keep isl_restriction *restr);
574 isl_ctx *isl_union_access_info_get_ctx(
575 __isl_keep isl_union_access_info *access);
576 isl_ctx *isl_union_flow_get_ctx(
577 __isl_keep isl_union_flow *flow);
579 #include <isl/schedule.h>
580 isl_ctx *isl_schedule_get_ctx(
581 __isl_keep isl_schedule *sched);
582 isl_ctx *isl_schedule_constraints_get_ctx(
583 __isl_keep isl_schedule_constraints *sc);
585 #include <isl/schedule_node.h>
586 isl_ctx *isl_schedule_node_get_ctx(
587 __isl_keep isl_schedule_node *node);
589 #include <isl/ast_build.h>
590 isl_ctx *isl_ast_build_get_ctx(
591 __isl_keep isl_ast_build *build);
594 isl_ctx *isl_ast_expr_get_ctx(
595 __isl_keep isl_ast_expr *expr);
596 isl_ctx *isl_ast_node_get_ctx(
597 __isl_keep isl_ast_node *node);
601 C<isl> uses two special return types for functions that either return
602 a boolean or that in principle do not return anything.
603 In particular, the C<isl_bool> type has three possible values:
604 C<isl_bool_true> (a positive integer value), indicating I<true> or I<yes>;
605 C<isl_bool_false> (the integer value zero), indicating I<false> or I<no>; and
606 C<isl_bool_error> (a negative integer value), indicating that something
607 went wrong. The following function can be used to negate an C<isl_bool>,
608 where the negation of C<isl_bool_error> is C<isl_bool_error> again.
611 isl_bool isl_bool_not(isl_bool b);
613 The C<isl_stat> type has two possible values:
614 C<isl_stat_ok> (the integer value zero), indicating a successful
616 C<isl_stat_error> (a negative integer value), indicating that something
618 See L</"Error Handling"> for more information on
619 C<isl_bool_error> and C<isl_stat_error>.
623 An C<isl_val> represents an integer value, a rational value
624 or one of three special values, infinity, negative infinity and NaN.
625 Some predefined values can be created using the following functions.
628 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
629 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
630 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
631 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
632 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
633 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
635 Specific integer values can be created using the following functions.
638 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
640 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
642 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
643 size_t n, size_t size, const void *chunks);
645 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
646 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
647 The least significant digit is assumed to be stored first.
649 Value objects can be copied and freed using the following functions.
652 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
653 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
655 They can be inspected using the following functions.
658 long isl_val_get_num_si(__isl_keep isl_val *v);
659 long isl_val_get_den_si(__isl_keep isl_val *v);
660 __isl_give isl_val *isl_val_get_den_val(
661 __isl_keep isl_val *v);
662 double isl_val_get_d(__isl_keep isl_val *v);
663 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
665 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
666 size_t size, void *chunks);
668 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
669 of C<size> bytes needed to store the absolute value of the
671 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
672 which is assumed to have been preallocated by the caller.
673 The least significant digit is stored first.
674 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
675 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
676 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
678 An C<isl_val> can be modified using the following function.
681 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
684 The following unary properties are defined on C<isl_val>s.
687 int isl_val_sgn(__isl_keep isl_val *v);
688 isl_bool isl_val_is_zero(__isl_keep isl_val *v);
689 isl_bool isl_val_is_one(__isl_keep isl_val *v);
690 isl_bool isl_val_is_negone(__isl_keep isl_val *v);
691 isl_bool isl_val_is_nonneg(__isl_keep isl_val *v);
692 isl_bool isl_val_is_nonpos(__isl_keep isl_val *v);
693 isl_bool isl_val_is_pos(__isl_keep isl_val *v);
694 isl_bool isl_val_is_neg(__isl_keep isl_val *v);
695 isl_bool isl_val_is_int(__isl_keep isl_val *v);
696 isl_bool isl_val_is_rat(__isl_keep isl_val *v);
697 isl_bool isl_val_is_nan(__isl_keep isl_val *v);
698 isl_bool isl_val_is_infty(__isl_keep isl_val *v);
699 isl_bool isl_val_is_neginfty(__isl_keep isl_val *v);
701 Note that the sign of NaN is undefined.
703 The following binary properties are defined on pairs of C<isl_val>s.
706 isl_bool isl_val_lt(__isl_keep isl_val *v1,
707 __isl_keep isl_val *v2);
708 isl_bool isl_val_le(__isl_keep isl_val *v1,
709 __isl_keep isl_val *v2);
710 isl_bool isl_val_gt(__isl_keep isl_val *v1,
711 __isl_keep isl_val *v2);
712 isl_bool isl_val_ge(__isl_keep isl_val *v1,
713 __isl_keep isl_val *v2);
714 isl_bool isl_val_eq(__isl_keep isl_val *v1,
715 __isl_keep isl_val *v2);
716 isl_bool isl_val_ne(__isl_keep isl_val *v1,
717 __isl_keep isl_val *v2);
718 isl_bool isl_val_abs_eq(__isl_keep isl_val *v1,
719 __isl_keep isl_val *v2);
721 Comparisons to NaN always return false.
722 That is, a NaN is not considered to hold any relative position
723 with respect to any value. In particular, a NaN
724 is neither considered to be equal to nor to be different from
725 any value (including another NaN).
726 The function C<isl_val_abs_eq> checks whether its two arguments
727 are equal in absolute value.
729 For integer C<isl_val>s we additionally have the following binary property.
732 isl_bool isl_val_is_divisible_by(__isl_keep isl_val *v1,
733 __isl_keep isl_val *v2);
735 An C<isl_val> can also be compared to an integer using the following
736 function. The result is undefined for NaN.
739 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
741 The following unary operations are available on C<isl_val>s.
744 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
745 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
746 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
747 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
748 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
749 __isl_give isl_val *isl_val_inv(__isl_take isl_val *v);
750 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
752 The following binary operations are available on C<isl_val>s.
755 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
756 __isl_take isl_val *v2);
757 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
758 __isl_take isl_val *v2);
759 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
760 __isl_take isl_val *v2);
761 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
763 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
764 __isl_take isl_val *v2);
765 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
767 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
768 __isl_take isl_val *v2);
769 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
771 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
772 __isl_take isl_val *v2);
773 __isl_give isl_val *isl_val_div_ui(__isl_take isl_val *v1,
776 On integer values, we additionally have the following operations.
779 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
780 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
781 __isl_take isl_val *v2);
782 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
783 __isl_take isl_val *v2);
784 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
785 __isl_take isl_val *v2, __isl_give isl_val **x,
786 __isl_give isl_val **y);
788 The function C<isl_val_gcdext> returns the greatest common divisor g
789 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
790 that C<*x> * C<v1> + C<*y> * C<v2> = g.
792 =head3 GMP specific functions
794 These functions are only available if C<isl> has been compiled with C<GMP>
797 Specific integer and rational values can be created from C<GMP> values using
798 the following functions.
800 #include <isl/val_gmp.h>
801 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
803 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
804 const mpz_t n, const mpz_t d);
806 The numerator and denominator of a rational value can be extracted as
807 C<GMP> values using the following functions.
809 #include <isl/val_gmp.h>
810 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
811 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
813 =head2 Sets and Relations
815 C<isl> uses six types of objects for representing sets and relations,
816 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
817 C<isl_union_set> and C<isl_union_map>.
818 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
819 can be described as a conjunction of affine constraints, while
820 C<isl_set> and C<isl_map> represent unions of
821 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
822 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
823 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
824 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
825 where spaces are considered different if they have a different number
826 of dimensions and/or different names (see L<"Spaces">).
827 The difference between sets and relations (maps) is that sets have
828 one set of variables, while relations have two sets of variables,
829 input variables and output variables.
831 =head2 Error Handling
833 C<isl> supports different ways to react in case a runtime error is triggered.
834 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
835 with two maps that have incompatible spaces. There are three possible ways
836 to react on error: to warn, to continue or to abort.
838 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
839 the last error in the corresponding C<isl_ctx> and the function in which the
840 error was triggered returns a value indicating that some error has
841 occurred. In case of functions returning a pointer, this value is
842 C<NULL>. In case of functions returning an C<isl_bool> or an
843 C<isl_stat>, this value is C<isl_bool_error> or C<isl_stat_error>.
844 An error does not corrupt internal state,
845 such that isl can continue to be used. C<isl> also provides functions to
846 read the last error, including the specific error message,
847 the isl source file where the error occurred and the line number,
848 and to reset all information about the last error. The
849 last error is only stored for information purposes. Its presence does not
850 change the behavior of C<isl>. Hence, resetting an error is not required to
851 continue to use isl, but only to observe new errors.
854 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
855 const char *isl_ctx_last_error_msg(isl_ctx *ctx);
856 const char *isl_ctx_last_error_file(isl_ctx *ctx);
857 int isl_ctx_last_error_line(isl_ctx *ctx);
858 void isl_ctx_reset_error(isl_ctx *ctx);
860 If no error has occurred since the last call to C<isl_ctx_reset_error>,
861 then the functions C<isl_ctx_last_error_msg> and
862 C<isl_ctx_last_error_file> return C<NULL>.
864 Another option is to continue on error. This is similar to warn on error mode,
865 except that C<isl> does not print any warning. This allows a program to
866 implement its own error reporting.
868 The last option is to directly abort the execution of the program from within
869 the isl library. This makes it obviously impossible to recover from an error,
870 but it allows to directly spot the error location. By aborting on error,
871 debuggers break at the location the error occurred and can provide a stack
872 trace. Other tools that automatically provide stack traces on abort or that do
873 not want to continue execution after an error was triggered may also prefer to
876 The on error behavior of isl can be specified by calling
877 C<isl_options_set_on_error> or by setting the command line option
878 C<--isl-on-error>. Valid arguments for the function call are
879 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
880 choices for the command line option are C<warn>, C<continue> and C<abort>.
881 It is also possible to query the current error mode.
883 #include <isl/options.h>
884 isl_stat isl_options_set_on_error(isl_ctx *ctx, int val);
885 int isl_options_get_on_error(isl_ctx *ctx);
889 Identifiers are used to identify both individual dimensions
890 and tuples of dimensions. They consist of an optional name and an optional
891 user pointer. The name and the user pointer cannot both be C<NULL>, however.
892 Identifiers with the same name but different pointer values
893 are considered to be distinct.
894 Similarly, identifiers with different names but the same pointer value
895 are also considered to be distinct.
896 Equal identifiers are represented using the same object.
897 Pairs of identifiers can therefore be tested for equality using the
899 Identifiers can be constructed, copied, freed, inspected and printed
900 using the following functions.
903 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
904 __isl_keep const char *name, void *user);
905 __isl_give isl_id *isl_id_set_free_user(
906 __isl_take isl_id *id,
907 void (*free_user)(void *user));
908 __isl_give isl_id *isl_id_copy(isl_id *id);
909 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
911 void *isl_id_get_user(__isl_keep isl_id *id);
912 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
914 __isl_give isl_printer *isl_printer_print_id(
915 __isl_take isl_printer *p, __isl_keep isl_id *id);
917 The callback set by C<isl_id_set_free_user> is called on the user
918 pointer when the last reference to the C<isl_id> is freed.
919 Note that C<isl_id_get_name> returns a pointer to some internal
920 data structure, so the result can only be used while the
921 corresponding C<isl_id> is alive.
925 Whenever a new set, relation or similar object is created from scratch,
926 the space in which it lives needs to be specified using an C<isl_space>.
927 Each space involves zero or more parameters and zero, one or two
928 tuples of set or input/output dimensions. The parameters and dimensions
929 are identified by an C<isl_dim_type> and a position.
930 The type C<isl_dim_param> refers to parameters,
931 the type C<isl_dim_set> refers to set dimensions (for spaces
932 with a single tuple of dimensions) and the types C<isl_dim_in>
933 and C<isl_dim_out> refer to input and output dimensions
934 (for spaces with two tuples of dimensions).
935 Local spaces (see L</"Local Spaces">) also contain dimensions
936 of type C<isl_dim_div>.
937 Note that parameters are only identified by their position within
938 a given object. Across different objects, parameters are (usually)
939 identified by their names or identifiers. Only unnamed parameters
940 are identified by their positions across objects. The use of unnamed
941 parameters is discouraged.
943 #include <isl/space.h>
944 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
945 unsigned nparam, unsigned n_in, unsigned n_out);
946 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
948 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
949 unsigned nparam, unsigned dim);
950 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
951 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
953 The space used for creating a parameter domain
954 needs to be created using C<isl_space_params_alloc>.
955 For other sets, the space
956 needs to be created using C<isl_space_set_alloc>, while
957 for a relation, the space
958 needs to be created using C<isl_space_alloc>.
960 To check whether a given space is that of a set or a map
961 or whether it is a parameter space, use these functions:
963 #include <isl/space.h>
964 isl_bool isl_space_is_params(__isl_keep isl_space *space);
965 isl_bool isl_space_is_set(__isl_keep isl_space *space);
966 isl_bool isl_space_is_map(__isl_keep isl_space *space);
968 Spaces can be compared using the following functions:
970 #include <isl/space.h>
971 isl_bool isl_space_is_equal(__isl_keep isl_space *space1,
972 __isl_keep isl_space *space2);
973 isl_bool isl_space_has_equal_params(
974 __isl_keep isl_space *space1,
975 __isl_keep isl_space *space2);
976 isl_bool isl_space_has_equal_tuples(
977 __isl_keep isl_space *space1,
978 __isl_keep isl_space *space2);
979 isl_bool isl_space_is_domain(__isl_keep isl_space *space1,
980 __isl_keep isl_space *space2);
981 isl_bool isl_space_is_range(__isl_keep isl_space *space1,
982 __isl_keep isl_space *space2);
983 isl_bool isl_space_tuple_is_equal(
984 __isl_keep isl_space *space1,
985 enum isl_dim_type type1,
986 __isl_keep isl_space *space2,
987 enum isl_dim_type type2);
989 C<isl_space_is_domain> checks whether the first argument is equal
990 to the domain of the second argument. This requires in particular that
991 the first argument is a set space and that the second argument
992 is a map space. C<isl_space_tuple_is_equal> checks whether the given
993 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
994 spaces are the same. That is, it checks if they have the same
995 identifier (if any), the same dimension and the same internal structure
998 C<isl_space_has_equal_params> checks whether two spaces
999 have the same parameters in the same order.
1000 C<isl_space_has_equal_tuples> check whether two spaces have
1001 the same tuples. In contrast to C<isl_space_is_equal> below,
1002 it does not check the
1003 parameters. This is useful because many C<isl> functions align the
1004 parameters before they perform their operations, such that equivalence
1006 C<isl_space_is_equal> checks whether two spaces are identical,
1007 meaning that they have the same parameters and the same tuples.
1008 That is, it checks whether both C<isl_space_has_equal_params> and
1009 C<isl_space_has_equal_tuples> hold.
1011 It is often useful to create objects that live in the
1012 same space as some other object. This can be accomplished
1013 by creating the new objects
1014 (see L</"Creating New Sets and Relations"> or
1015 L</"Functions">) based on the space
1016 of the original object.
1018 #include <isl/set.h>
1019 __isl_give isl_space *isl_basic_set_get_space(
1020 __isl_keep isl_basic_set *bset);
1021 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
1023 #include <isl/union_set.h>
1024 __isl_give isl_space *isl_union_set_get_space(
1025 __isl_keep isl_union_set *uset);
1027 #include <isl/map.h>
1028 __isl_give isl_space *isl_basic_map_get_space(
1029 __isl_keep isl_basic_map *bmap);
1030 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
1032 #include <isl/union_map.h>
1033 __isl_give isl_space *isl_union_map_get_space(
1034 __isl_keep isl_union_map *umap);
1036 #include <isl/constraint.h>
1037 __isl_give isl_space *isl_constraint_get_space(
1038 __isl_keep isl_constraint *constraint);
1040 #include <isl/polynomial.h>
1041 __isl_give isl_space *isl_qpolynomial_get_domain_space(
1042 __isl_keep isl_qpolynomial *qp);
1043 __isl_give isl_space *isl_qpolynomial_get_space(
1044 __isl_keep isl_qpolynomial *qp);
1045 __isl_give isl_space *
1046 isl_qpolynomial_fold_get_domain_space(
1047 __isl_keep isl_qpolynomial_fold *fold);
1048 __isl_give isl_space *isl_qpolynomial_fold_get_space(
1049 __isl_keep isl_qpolynomial_fold *fold);
1050 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
1051 __isl_keep isl_pw_qpolynomial *pwqp);
1052 __isl_give isl_space *isl_pw_qpolynomial_get_space(
1053 __isl_keep isl_pw_qpolynomial *pwqp);
1054 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
1055 __isl_keep isl_pw_qpolynomial_fold *pwf);
1056 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
1057 __isl_keep isl_pw_qpolynomial_fold *pwf);
1058 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
1059 __isl_keep isl_union_pw_qpolynomial *upwqp);
1060 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
1061 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1063 #include <isl/val.h>
1064 __isl_give isl_space *isl_multi_val_get_space(
1065 __isl_keep isl_multi_val *mv);
1067 #include <isl/aff.h>
1068 __isl_give isl_space *isl_aff_get_domain_space(
1069 __isl_keep isl_aff *aff);
1070 __isl_give isl_space *isl_aff_get_space(
1071 __isl_keep isl_aff *aff);
1072 __isl_give isl_space *isl_pw_aff_get_domain_space(
1073 __isl_keep isl_pw_aff *pwaff);
1074 __isl_give isl_space *isl_pw_aff_get_space(
1075 __isl_keep isl_pw_aff *pwaff);
1076 __isl_give isl_space *isl_multi_aff_get_domain_space(
1077 __isl_keep isl_multi_aff *maff);
1078 __isl_give isl_space *isl_multi_aff_get_space(
1079 __isl_keep isl_multi_aff *maff);
1080 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
1081 __isl_keep isl_pw_multi_aff *pma);
1082 __isl_give isl_space *isl_pw_multi_aff_get_space(
1083 __isl_keep isl_pw_multi_aff *pma);
1084 __isl_give isl_space *isl_union_pw_aff_get_space(
1085 __isl_keep isl_union_pw_aff *upa);
1086 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
1087 __isl_keep isl_union_pw_multi_aff *upma);
1088 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
1089 __isl_keep isl_multi_pw_aff *mpa);
1090 __isl_give isl_space *isl_multi_pw_aff_get_space(
1091 __isl_keep isl_multi_pw_aff *mpa);
1092 __isl_give isl_space *
1093 isl_multi_union_pw_aff_get_domain_space(
1094 __isl_keep isl_multi_union_pw_aff *mupa);
1095 __isl_give isl_space *
1096 isl_multi_union_pw_aff_get_space(
1097 __isl_keep isl_multi_union_pw_aff *mupa);
1099 #include <isl/point.h>
1100 __isl_give isl_space *isl_point_get_space(
1101 __isl_keep isl_point *pnt);
1103 The number of dimensions of a given type of space
1104 may be read off from a space or an object that lives
1105 in a space using the following functions.
1106 In case of C<isl_space_dim>, type may be
1107 C<isl_dim_param>, C<isl_dim_in> (only for relations),
1108 C<isl_dim_out> (only for relations), C<isl_dim_set>
1109 (only for sets) or C<isl_dim_all>.
1111 #include <isl/space.h>
1112 unsigned isl_space_dim(__isl_keep isl_space *space,
1113 enum isl_dim_type type);
1115 #include <isl/local_space.h>
1116 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1117 enum isl_dim_type type);
1119 #include <isl/set.h>
1120 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1121 enum isl_dim_type type);
1122 unsigned isl_set_dim(__isl_keep isl_set *set,
1123 enum isl_dim_type type);
1125 #include <isl/union_set.h>
1126 unsigned isl_union_set_dim(__isl_keep isl_union_set *uset,
1127 enum isl_dim_type type);
1129 #include <isl/map.h>
1130 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1131 enum isl_dim_type type);
1132 unsigned isl_map_dim(__isl_keep isl_map *map,
1133 enum isl_dim_type type);
1135 #include <isl/union_map.h>
1136 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1137 enum isl_dim_type type);
1139 #include <isl/val.h>
1140 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
1141 enum isl_dim_type type);
1143 #include <isl/aff.h>
1144 int isl_aff_dim(__isl_keep isl_aff *aff,
1145 enum isl_dim_type type);
1146 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1147 enum isl_dim_type type);
1148 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1149 enum isl_dim_type type);
1150 unsigned isl_pw_multi_aff_dim(
1151 __isl_keep isl_pw_multi_aff *pma,
1152 enum isl_dim_type type);
1153 unsigned isl_multi_pw_aff_dim(
1154 __isl_keep isl_multi_pw_aff *mpa,
1155 enum isl_dim_type type);
1156 unsigned isl_union_pw_aff_dim(
1157 __isl_keep isl_union_pw_aff *upa,
1158 enum isl_dim_type type);
1159 unsigned isl_union_pw_multi_aff_dim(
1160 __isl_keep isl_union_pw_multi_aff *upma,
1161 enum isl_dim_type type);
1162 unsigned isl_multi_union_pw_aff_dim(
1163 __isl_keep isl_multi_union_pw_aff *mupa,
1164 enum isl_dim_type type);
1166 #include <isl/polynomial.h>
1167 unsigned isl_union_pw_qpolynomial_dim(
1168 __isl_keep isl_union_pw_qpolynomial *upwqp,
1169 enum isl_dim_type type);
1170 unsigned isl_union_pw_qpolynomial_fold_dim(
1171 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1172 enum isl_dim_type type);
1174 Note that an C<isl_union_set>, an C<isl_union_map>,
1175 an C<isl_union_pw_multi_aff>,
1176 an C<isl_union_pw_qpolynomial> and
1177 an C<isl_union_pw_qpolynomial_fold>
1178 only have parameters.
1180 Additional parameters can be added to a space using the following function.
1182 #include <isl/space.h>
1183 __isl_give isl_space *isl_space_add_param_id(
1184 __isl_take isl_space *space,
1185 __isl_take isl_id *id);
1187 If a parameter with the given identifier already appears in the space,
1188 then it is not added again.
1190 The identifiers or names of the individual dimensions of spaces
1191 may be set or read off using the following functions on spaces
1192 or objects that live in spaces.
1193 These functions are mostly useful to obtain the identifiers, positions
1194 or names of the parameters. Identifiers of individual dimensions are
1195 essentially only useful for printing. They are ignored by all other
1196 operations and may not be preserved across those operations.
1198 #include <isl/space.h>
1199 __isl_give isl_space *isl_space_set_dim_id(
1200 __isl_take isl_space *space,
1201 enum isl_dim_type type, unsigned pos,
1202 __isl_take isl_id *id);
1203 isl_bool isl_space_has_dim_id(__isl_keep isl_space *space,
1204 enum isl_dim_type type, unsigned pos);
1205 __isl_give isl_id *isl_space_get_dim_id(
1206 __isl_keep isl_space *space,
1207 enum isl_dim_type type, unsigned pos);
1208 __isl_give isl_space *isl_space_set_dim_name(
1209 __isl_take isl_space *space,
1210 enum isl_dim_type type, unsigned pos,
1211 __isl_keep const char *name);
1212 isl_bool isl_space_has_dim_name(__isl_keep isl_space *space,
1213 enum isl_dim_type type, unsigned pos);
1214 __isl_keep const char *isl_space_get_dim_name(
1215 __isl_keep isl_space *space,
1216 enum isl_dim_type type, unsigned pos);
1218 #include <isl/local_space.h>
1219 __isl_give isl_local_space *isl_local_space_set_dim_id(
1220 __isl_take isl_local_space *ls,
1221 enum isl_dim_type type, unsigned pos,
1222 __isl_take isl_id *id);
1223 isl_bool isl_local_space_has_dim_id(
1224 __isl_keep isl_local_space *ls,
1225 enum isl_dim_type type, unsigned pos);
1226 __isl_give isl_id *isl_local_space_get_dim_id(
1227 __isl_keep isl_local_space *ls,
1228 enum isl_dim_type type, unsigned pos);
1229 __isl_give isl_local_space *isl_local_space_set_dim_name(
1230 __isl_take isl_local_space *ls,
1231 enum isl_dim_type type, unsigned pos, const char *s);
1232 isl_bool isl_local_space_has_dim_name(
1233 __isl_keep isl_local_space *ls,
1234 enum isl_dim_type type, unsigned pos)
1235 const char *isl_local_space_get_dim_name(
1236 __isl_keep isl_local_space *ls,
1237 enum isl_dim_type type, unsigned pos);
1239 #include <isl/constraint.h>
1240 const char *isl_constraint_get_dim_name(
1241 __isl_keep isl_constraint *constraint,
1242 enum isl_dim_type type, unsigned pos);
1244 #include <isl/set.h>
1245 __isl_give isl_id *isl_basic_set_get_dim_id(
1246 __isl_keep isl_basic_set *bset,
1247 enum isl_dim_type type, unsigned pos);
1248 __isl_give isl_set *isl_set_set_dim_id(
1249 __isl_take isl_set *set, enum isl_dim_type type,
1250 unsigned pos, __isl_take isl_id *id);
1251 isl_bool isl_set_has_dim_id(__isl_keep isl_set *set,
1252 enum isl_dim_type type, unsigned pos);
1253 __isl_give isl_id *isl_set_get_dim_id(
1254 __isl_keep isl_set *set, enum isl_dim_type type,
1256 const char *isl_basic_set_get_dim_name(
1257 __isl_keep isl_basic_set *bset,
1258 enum isl_dim_type type, unsigned pos);
1259 isl_bool isl_set_has_dim_name(__isl_keep isl_set *set,
1260 enum isl_dim_type type, unsigned pos);
1261 const char *isl_set_get_dim_name(
1262 __isl_keep isl_set *set,
1263 enum isl_dim_type type, unsigned pos);
1265 #include <isl/map.h>
1266 __isl_give isl_map *isl_map_set_dim_id(
1267 __isl_take isl_map *map, enum isl_dim_type type,
1268 unsigned pos, __isl_take isl_id *id);
1269 isl_bool isl_basic_map_has_dim_id(
1270 __isl_keep isl_basic_map *bmap,
1271 enum isl_dim_type type, unsigned pos);
1272 isl_bool isl_map_has_dim_id(__isl_keep isl_map *map,
1273 enum isl_dim_type type, unsigned pos);
1274 __isl_give isl_id *isl_map_get_dim_id(
1275 __isl_keep isl_map *map, enum isl_dim_type type,
1277 __isl_give isl_id *isl_union_map_get_dim_id(
1278 __isl_keep isl_union_map *umap,
1279 enum isl_dim_type type, unsigned pos);
1280 const char *isl_basic_map_get_dim_name(
1281 __isl_keep isl_basic_map *bmap,
1282 enum isl_dim_type type, unsigned pos);
1283 isl_bool isl_map_has_dim_name(__isl_keep isl_map *map,
1284 enum isl_dim_type type, unsigned pos);
1285 const char *isl_map_get_dim_name(
1286 __isl_keep isl_map *map,
1287 enum isl_dim_type type, unsigned pos);
1289 #include <isl/val.h>
1290 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1291 __isl_take isl_multi_val *mv,
1292 enum isl_dim_type type, unsigned pos,
1293 __isl_take isl_id *id);
1294 __isl_give isl_id *isl_multi_val_get_dim_id(
1295 __isl_keep isl_multi_val *mv,
1296 enum isl_dim_type type, unsigned pos);
1297 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1298 __isl_take isl_multi_val *mv,
1299 enum isl_dim_type type, unsigned pos, const char *s);
1301 #include <isl/aff.h>
1302 __isl_give isl_aff *isl_aff_set_dim_id(
1303 __isl_take isl_aff *aff, enum isl_dim_type type,
1304 unsigned pos, __isl_take isl_id *id);
1305 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1306 __isl_take isl_multi_aff *maff,
1307 enum isl_dim_type type, unsigned pos,
1308 __isl_take isl_id *id);
1309 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1310 __isl_take isl_pw_aff *pma,
1311 enum isl_dim_type type, unsigned pos,
1312 __isl_take isl_id *id);
1313 __isl_give isl_multi_pw_aff *
1314 isl_multi_pw_aff_set_dim_id(
1315 __isl_take isl_multi_pw_aff *mpa,
1316 enum isl_dim_type type, unsigned pos,
1317 __isl_take isl_id *id);
1318 __isl_give isl_multi_union_pw_aff *
1319 isl_multi_union_pw_aff_set_dim_id(
1320 __isl_take isl_multi_union_pw_aff *mupa,
1321 enum isl_dim_type type, unsigned pos,
1322 __isl_take isl_id *id);
1323 __isl_give isl_id *isl_multi_aff_get_dim_id(
1324 __isl_keep isl_multi_aff *ma,
1325 enum isl_dim_type type, unsigned pos);
1326 isl_bool isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1327 enum isl_dim_type type, unsigned pos);
1328 __isl_give isl_id *isl_pw_aff_get_dim_id(
1329 __isl_keep isl_pw_aff *pa,
1330 enum isl_dim_type type, unsigned pos);
1331 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1332 __isl_keep isl_pw_multi_aff *pma,
1333 enum isl_dim_type type, unsigned pos);
1334 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1335 __isl_keep isl_multi_pw_aff *mpa,
1336 enum isl_dim_type type, unsigned pos);
1337 __isl_give isl_id *isl_multi_union_pw_aff_get_dim_id(
1338 __isl_keep isl_multi_union_pw_aff *mupa,
1339 enum isl_dim_type type, unsigned pos);
1340 __isl_give isl_aff *isl_aff_set_dim_name(
1341 __isl_take isl_aff *aff, enum isl_dim_type type,
1342 unsigned pos, const char *s);
1343 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1344 __isl_take isl_multi_aff *maff,
1345 enum isl_dim_type type, unsigned pos, const char *s);
1346 __isl_give isl_multi_pw_aff *
1347 isl_multi_pw_aff_set_dim_name(
1348 __isl_take isl_multi_pw_aff *mpa,
1349 enum isl_dim_type type, unsigned pos, const char *s);
1350 __isl_give isl_union_pw_aff *
1351 isl_union_pw_aff_set_dim_name(
1352 __isl_take isl_union_pw_aff *upa,
1353 enum isl_dim_type type, unsigned pos,
1355 __isl_give isl_union_pw_multi_aff *
1356 isl_union_pw_multi_aff_set_dim_name(
1357 __isl_take isl_union_pw_multi_aff *upma,
1358 enum isl_dim_type type, unsigned pos,
1360 __isl_give isl_multi_union_pw_aff *
1361 isl_multi_union_pw_aff_set_dim_name(
1362 __isl_take isl_multi_union_pw_aff *mupa,
1363 enum isl_dim_type type, unsigned pos,
1364 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1365 enum isl_dim_type type, unsigned pos);
1366 const char *isl_pw_aff_get_dim_name(
1367 __isl_keep isl_pw_aff *pa,
1368 enum isl_dim_type type, unsigned pos);
1369 const char *isl_pw_multi_aff_get_dim_name(
1370 __isl_keep isl_pw_multi_aff *pma,
1371 enum isl_dim_type type, unsigned pos);
1373 #include <isl/polynomial.h>
1374 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1375 __isl_take isl_qpolynomial *qp,
1376 enum isl_dim_type type, unsigned pos,
1378 __isl_give isl_pw_qpolynomial *
1379 isl_pw_qpolynomial_set_dim_name(
1380 __isl_take isl_pw_qpolynomial *pwqp,
1381 enum isl_dim_type type, unsigned pos,
1383 __isl_give isl_pw_qpolynomial_fold *
1384 isl_pw_qpolynomial_fold_set_dim_name(
1385 __isl_take isl_pw_qpolynomial_fold *pwf,
1386 enum isl_dim_type type, unsigned pos,
1388 __isl_give isl_union_pw_qpolynomial *
1389 isl_union_pw_qpolynomial_set_dim_name(
1390 __isl_take isl_union_pw_qpolynomial *upwqp,
1391 enum isl_dim_type type, unsigned pos,
1393 __isl_give isl_union_pw_qpolynomial_fold *
1394 isl_union_pw_qpolynomial_fold_set_dim_name(
1395 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1396 enum isl_dim_type type, unsigned pos,
1399 Note that C<isl_space_get_name> returns a pointer to some internal
1400 data structure, so the result can only be used while the
1401 corresponding C<isl_space> is alive.
1402 Also note that every function that operates on two sets or relations
1403 requires that both arguments have the same parameters. This also
1404 means that if one of the arguments has named parameters, then the
1405 other needs to have named parameters too and the names need to match.
1406 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1407 arguments may have different parameters (as long as they are named),
1408 in which case the result will have as parameters the union of the parameters of
1411 Given the identifier or name of a dimension (typically a parameter),
1412 its position can be obtained from the following functions.
1414 #include <isl/space.h>
1415 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1416 enum isl_dim_type type, __isl_keep isl_id *id);
1417 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1418 enum isl_dim_type type, const char *name);
1420 #include <isl/local_space.h>
1421 int isl_local_space_find_dim_by_name(
1422 __isl_keep isl_local_space *ls,
1423 enum isl_dim_type type, const char *name);
1425 #include <isl/val.h>
1426 int isl_multi_val_find_dim_by_id(
1427 __isl_keep isl_multi_val *mv,
1428 enum isl_dim_type type, __isl_keep isl_id *id);
1429 int isl_multi_val_find_dim_by_name(
1430 __isl_keep isl_multi_val *mv,
1431 enum isl_dim_type type, const char *name);
1433 #include <isl/set.h>
1434 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1435 enum isl_dim_type type, __isl_keep isl_id *id);
1436 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1437 enum isl_dim_type type, const char *name);
1439 #include <isl/map.h>
1440 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1441 enum isl_dim_type type, __isl_keep isl_id *id);
1442 int isl_basic_map_find_dim_by_name(
1443 __isl_keep isl_basic_map *bmap,
1444 enum isl_dim_type type, const char *name);
1445 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1446 enum isl_dim_type type, const char *name);
1447 int isl_union_map_find_dim_by_name(
1448 __isl_keep isl_union_map *umap,
1449 enum isl_dim_type type, const char *name);
1451 #include <isl/aff.h>
1452 int isl_multi_aff_find_dim_by_id(
1453 __isl_keep isl_multi_aff *ma,
1454 enum isl_dim_type type, __isl_keep isl_id *id);
1455 int isl_multi_pw_aff_find_dim_by_id(
1456 __isl_keep isl_multi_pw_aff *mpa,
1457 enum isl_dim_type type, __isl_keep isl_id *id);
1458 int isl_multi_union_pw_aff_find_dim_by_id(
1459 __isl_keep isl_union_multi_pw_aff *mupa,
1460 enum isl_dim_type type, __isl_keep isl_id *id);
1461 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff,
1462 enum isl_dim_type type, const char *name);
1463 int isl_multi_aff_find_dim_by_name(
1464 __isl_keep isl_multi_aff *ma,
1465 enum isl_dim_type type, const char *name);
1466 int isl_pw_aff_find_dim_by_name(__isl_keep isl_pw_aff *pa,
1467 enum isl_dim_type type, const char *name);
1468 int isl_multi_pw_aff_find_dim_by_name(
1469 __isl_keep isl_multi_pw_aff *mpa,
1470 enum isl_dim_type type, const char *name);
1471 int isl_pw_multi_aff_find_dim_by_name(
1472 __isl_keep isl_pw_multi_aff *pma,
1473 enum isl_dim_type type, const char *name);
1474 int isl_union_pw_aff_find_dim_by_name(
1475 __isl_keep isl_union_pw_aff *upa,
1476 enum isl_dim_type type, const char *name);
1477 int isl_union_pw_multi_aff_find_dim_by_name(
1478 __isl_keep isl_union_pw_multi_aff *upma,
1479 enum isl_dim_type type, const char *name);
1480 int isl_multi_union_pw_aff_find_dim_by_name(
1481 __isl_keep isl_multi_union_pw_aff *mupa,
1482 enum isl_dim_type type, const char *name);
1484 #include <isl/polynomial.h>
1485 int isl_pw_qpolynomial_find_dim_by_name(
1486 __isl_keep isl_pw_qpolynomial *pwqp,
1487 enum isl_dim_type type, const char *name);
1488 int isl_pw_qpolynomial_fold_find_dim_by_name(
1489 __isl_keep isl_pw_qpolynomial_fold *pwf,
1490 enum isl_dim_type type, const char *name);
1491 int isl_union_pw_qpolynomial_find_dim_by_name(
1492 __isl_keep isl_union_pw_qpolynomial *upwqp,
1493 enum isl_dim_type type, const char *name);
1494 int isl_union_pw_qpolynomial_fold_find_dim_by_name(
1495 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1496 enum isl_dim_type type, const char *name);
1498 The identifiers or names of entire spaces may be set or read off
1499 using the following functions.
1501 #include <isl/space.h>
1502 __isl_give isl_space *isl_space_set_tuple_id(
1503 __isl_take isl_space *space,
1504 enum isl_dim_type type, __isl_take isl_id *id);
1505 __isl_give isl_space *isl_space_reset_tuple_id(
1506 __isl_take isl_space *space, enum isl_dim_type type);
1507 isl_bool isl_space_has_tuple_id(
1508 __isl_keep isl_space *space,
1509 enum isl_dim_type type);
1510 __isl_give isl_id *isl_space_get_tuple_id(
1511 __isl_keep isl_space *space, enum isl_dim_type type);
1512 __isl_give isl_space *isl_space_set_tuple_name(
1513 __isl_take isl_space *space,
1514 enum isl_dim_type type, const char *s);
1515 isl_bool isl_space_has_tuple_name(
1516 __isl_keep isl_space *space,
1517 enum isl_dim_type type);
1518 __isl_keep const char *isl_space_get_tuple_name(
1519 __isl_keep isl_space *space,
1520 enum isl_dim_type type);
1522 #include <isl/local_space.h>
1523 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1524 __isl_take isl_local_space *ls,
1525 enum isl_dim_type type, __isl_take isl_id *id);
1527 #include <isl/set.h>
1528 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1529 __isl_take isl_basic_set *bset,
1530 __isl_take isl_id *id);
1531 __isl_give isl_set *isl_set_set_tuple_id(
1532 __isl_take isl_set *set, __isl_take isl_id *id);
1533 __isl_give isl_set *isl_set_reset_tuple_id(
1534 __isl_take isl_set *set);
1535 isl_bool isl_set_has_tuple_id(__isl_keep isl_set *set);
1536 __isl_give isl_id *isl_set_get_tuple_id(
1537 __isl_keep isl_set *set);
1538 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1539 __isl_take isl_basic_set *set, const char *s);
1540 __isl_give isl_set *isl_set_set_tuple_name(
1541 __isl_take isl_set *set, const char *s);
1542 const char *isl_basic_set_get_tuple_name(
1543 __isl_keep isl_basic_set *bset);
1544 isl_bool isl_set_has_tuple_name(__isl_keep isl_set *set);
1545 const char *isl_set_get_tuple_name(
1546 __isl_keep isl_set *set);
1548 #include <isl/map.h>
1549 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1550 __isl_take isl_basic_map *bmap,
1551 enum isl_dim_type type, __isl_take isl_id *id);
1552 __isl_give isl_map *isl_map_set_tuple_id(
1553 __isl_take isl_map *map, enum isl_dim_type type,
1554 __isl_take isl_id *id);
1555 __isl_give isl_map *isl_map_reset_tuple_id(
1556 __isl_take isl_map *map, enum isl_dim_type type);
1557 isl_bool isl_map_has_tuple_id(__isl_keep isl_map *map,
1558 enum isl_dim_type type);
1559 __isl_give isl_id *isl_map_get_tuple_id(
1560 __isl_keep isl_map *map, enum isl_dim_type type);
1561 __isl_give isl_map *isl_map_set_tuple_name(
1562 __isl_take isl_map *map,
1563 enum isl_dim_type type, const char *s);
1564 const char *isl_basic_map_get_tuple_name(
1565 __isl_keep isl_basic_map *bmap,
1566 enum isl_dim_type type);
1567 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1568 __isl_take isl_basic_map *bmap,
1569 enum isl_dim_type type, const char *s);
1570 isl_bool isl_map_has_tuple_name(__isl_keep isl_map *map,
1571 enum isl_dim_type type);
1572 const char *isl_map_get_tuple_name(
1573 __isl_keep isl_map *map,
1574 enum isl_dim_type type);
1576 #include <isl/val.h>
1577 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1578 __isl_take isl_multi_val *mv,
1579 enum isl_dim_type type, __isl_take isl_id *id);
1580 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1581 __isl_take isl_multi_val *mv,
1582 enum isl_dim_type type);
1583 isl_bool isl_multi_val_has_tuple_id(
1584 __isl_keep isl_multi_val *mv,
1585 enum isl_dim_type type);
1586 __isl_give isl_id *isl_multi_val_get_tuple_id(
1587 __isl_keep isl_multi_val *mv,
1588 enum isl_dim_type type);
1589 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1590 __isl_take isl_multi_val *mv,
1591 enum isl_dim_type type, const char *s);
1592 const char *isl_multi_val_get_tuple_name(
1593 __isl_keep isl_multi_val *mv,
1594 enum isl_dim_type type);
1596 #include <isl/aff.h>
1597 __isl_give isl_aff *isl_aff_set_tuple_id(
1598 __isl_take isl_aff *aff,
1599 enum isl_dim_type type, __isl_take isl_id *id);
1600 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1601 __isl_take isl_multi_aff *maff,
1602 enum isl_dim_type type, __isl_take isl_id *id);
1603 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1604 __isl_take isl_pw_aff *pwaff,
1605 enum isl_dim_type type, __isl_take isl_id *id);
1606 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1607 __isl_take isl_pw_multi_aff *pma,
1608 enum isl_dim_type type, __isl_take isl_id *id);
1609 __isl_give isl_multi_union_pw_aff *
1610 isl_multi_union_pw_aff_set_tuple_id(
1611 __isl_take isl_multi_union_pw_aff *mupa,
1612 enum isl_dim_type type, __isl_take isl_id *id);
1613 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1614 __isl_take isl_multi_aff *ma,
1615 enum isl_dim_type type);
1616 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1617 __isl_take isl_pw_aff *pa,
1618 enum isl_dim_type type);
1619 __isl_give isl_multi_pw_aff *
1620 isl_multi_pw_aff_reset_tuple_id(
1621 __isl_take isl_multi_pw_aff *mpa,
1622 enum isl_dim_type type);
1623 __isl_give isl_pw_multi_aff *
1624 isl_pw_multi_aff_reset_tuple_id(
1625 __isl_take isl_pw_multi_aff *pma,
1626 enum isl_dim_type type);
1627 __isl_give isl_multi_union_pw_aff *
1628 isl_multi_union_pw_aff_reset_tuple_id(
1629 __isl_take isl_multi_union_pw_aff *mupa,
1630 enum isl_dim_type type);
1631 isl_bool isl_multi_aff_has_tuple_id(
1632 __isl_keep isl_multi_aff *ma,
1633 enum isl_dim_type type);
1634 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1635 __isl_keep isl_multi_aff *ma,
1636 enum isl_dim_type type);
1637 isl_bool isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1638 enum isl_dim_type type);
1639 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1640 __isl_keep isl_pw_aff *pa,
1641 enum isl_dim_type type);
1642 isl_bool isl_pw_multi_aff_has_tuple_id(
1643 __isl_keep isl_pw_multi_aff *pma,
1644 enum isl_dim_type type);
1645 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1646 __isl_keep isl_pw_multi_aff *pma,
1647 enum isl_dim_type type);
1648 isl_bool isl_multi_pw_aff_has_tuple_id(
1649 __isl_keep isl_multi_pw_aff *mpa,
1650 enum isl_dim_type type);
1651 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1652 __isl_keep isl_multi_pw_aff *mpa,
1653 enum isl_dim_type type);
1654 isl_bool isl_multi_union_pw_aff_has_tuple_id(
1655 __isl_keep isl_multi_union_pw_aff *mupa,
1656 enum isl_dim_type type);
1657 __isl_give isl_id *isl_multi_union_pw_aff_get_tuple_id(
1658 __isl_keep isl_multi_union_pw_aff *mupa,
1659 enum isl_dim_type type);
1660 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1661 __isl_take isl_multi_aff *maff,
1662 enum isl_dim_type type, const char *s);
1663 __isl_give isl_multi_pw_aff *
1664 isl_multi_pw_aff_set_tuple_name(
1665 __isl_take isl_multi_pw_aff *mpa,
1666 enum isl_dim_type type, const char *s);
1667 __isl_give isl_multi_union_pw_aff *
1668 isl_multi_union_pw_aff_set_tuple_name(
1669 __isl_take isl_multi_union_pw_aff *mupa,
1670 enum isl_dim_type type, const char *s);
1671 const char *isl_multi_aff_get_tuple_name(
1672 __isl_keep isl_multi_aff *multi,
1673 enum isl_dim_type type);
1674 isl_bool isl_pw_multi_aff_has_tuple_name(
1675 __isl_keep isl_pw_multi_aff *pma,
1676 enum isl_dim_type type);
1677 const char *isl_pw_multi_aff_get_tuple_name(
1678 __isl_keep isl_pw_multi_aff *pma,
1679 enum isl_dim_type type);
1680 const char *isl_multi_union_pw_aff_get_tuple_name(
1681 __isl_keep isl_multi_union_pw_aff *mupa,
1682 enum isl_dim_type type);
1684 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1685 or C<isl_dim_set>. As with C<isl_space_get_name>,
1686 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1688 Binary operations require the corresponding spaces of their arguments
1689 to have the same name.
1691 To keep the names of all parameters and tuples, but reset the user pointers
1692 of all the corresponding identifiers, use the following function.
1694 #include <isl/space.h>
1695 __isl_give isl_space *isl_space_reset_user(
1696 __isl_take isl_space *space);
1698 #include <isl/set.h>
1699 __isl_give isl_set *isl_set_reset_user(
1700 __isl_take isl_set *set);
1702 #include <isl/map.h>
1703 __isl_give isl_map *isl_map_reset_user(
1704 __isl_take isl_map *map);
1706 #include <isl/union_set.h>
1707 __isl_give isl_union_set *isl_union_set_reset_user(
1708 __isl_take isl_union_set *uset);
1710 #include <isl/union_map.h>
1711 __isl_give isl_union_map *isl_union_map_reset_user(
1712 __isl_take isl_union_map *umap);
1714 #include <isl/val.h>
1715 __isl_give isl_multi_val *isl_multi_val_reset_user(
1716 __isl_take isl_multi_val *mv);
1718 #include <isl/aff.h>
1719 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1720 __isl_take isl_multi_aff *ma);
1721 __isl_give isl_pw_aff *isl_pw_aff_reset_user(
1722 __isl_take isl_pw_aff *pa);
1723 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1724 __isl_take isl_multi_pw_aff *mpa);
1725 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_reset_user(
1726 __isl_take isl_pw_multi_aff *pma);
1727 __isl_give isl_union_pw_aff *isl_union_pw_aff_reset_user(
1728 __isl_take isl_union_pw_aff *upa);
1729 __isl_give isl_multi_union_pw_aff *
1730 isl_multi_union_pw_aff_reset_user(
1731 __isl_take isl_multi_union_pw_aff *mupa);
1732 __isl_give isl_union_pw_multi_aff *
1733 isl_union_pw_multi_aff_reset_user(
1734 __isl_take isl_union_pw_multi_aff *upma);
1736 #include <isl/polynomial.h>
1737 __isl_give isl_pw_qpolynomial *
1738 isl_pw_qpolynomial_reset_user(
1739 __isl_take isl_pw_qpolynomial *pwqp);
1740 __isl_give isl_union_pw_qpolynomial *
1741 isl_union_pw_qpolynomial_reset_user(
1742 __isl_take isl_union_pw_qpolynomial *upwqp);
1743 __isl_give isl_pw_qpolynomial_fold *
1744 isl_pw_qpolynomial_fold_reset_user(
1745 __isl_take isl_pw_qpolynomial_fold *pwf);
1746 __isl_give isl_union_pw_qpolynomial_fold *
1747 isl_union_pw_qpolynomial_fold_reset_user(
1748 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1750 Spaces can be nested. In particular, the domain of a set or
1751 the domain or range of a relation can be a nested relation.
1752 This process is also called I<wrapping>.
1753 The functions for detecting, constructing and deconstructing
1754 such nested spaces can be found in the wrapping properties
1755 of L</"Unary Properties">, the wrapping operations
1756 of L</"Unary Operations"> and the Cartesian product operations
1757 of L</"Basic Operations">.
1759 Spaces can be created from other spaces
1760 using the functions described in L</"Unary Operations">
1761 and L</"Binary Operations">.
1765 A local space is essentially a space with
1766 zero or more existentially quantified variables.
1767 The local space of various objects can be obtained
1768 using the following functions.
1770 #include <isl/constraint.h>
1771 __isl_give isl_local_space *isl_constraint_get_local_space(
1772 __isl_keep isl_constraint *constraint);
1774 #include <isl/set.h>
1775 __isl_give isl_local_space *isl_basic_set_get_local_space(
1776 __isl_keep isl_basic_set *bset);
1778 #include <isl/map.h>
1779 __isl_give isl_local_space *isl_basic_map_get_local_space(
1780 __isl_keep isl_basic_map *bmap);
1782 #include <isl/aff.h>
1783 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1784 __isl_keep isl_aff *aff);
1785 __isl_give isl_local_space *isl_aff_get_local_space(
1786 __isl_keep isl_aff *aff);
1788 A new local space can be created from a space using
1790 #include <isl/local_space.h>
1791 __isl_give isl_local_space *isl_local_space_from_space(
1792 __isl_take isl_space *space);
1794 They can be inspected, modified, copied and freed using the following functions.
1796 #include <isl/local_space.h>
1797 isl_bool isl_local_space_is_params(
1798 __isl_keep isl_local_space *ls);
1799 isl_bool isl_local_space_is_set(
1800 __isl_keep isl_local_space *ls);
1801 __isl_give isl_space *isl_local_space_get_space(
1802 __isl_keep isl_local_space *ls);
1803 __isl_give isl_aff *isl_local_space_get_div(
1804 __isl_keep isl_local_space *ls, int pos);
1805 __isl_give isl_local_space *isl_local_space_copy(
1806 __isl_keep isl_local_space *ls);
1807 __isl_null isl_local_space *isl_local_space_free(
1808 __isl_take isl_local_space *ls);
1810 Note that C<isl_local_space_get_div> can only be used on local spaces
1813 Two local spaces can be compared using
1815 isl_bool isl_local_space_is_equal(
1816 __isl_keep isl_local_space *ls1,
1817 __isl_keep isl_local_space *ls2);
1819 Local spaces can be created from other local spaces
1820 using the functions described in L</"Unary Operations">
1821 and L</"Binary Operations">.
1823 =head2 Creating New Sets and Relations
1825 C<isl> has functions for creating some standard sets and relations.
1829 =item * Empty sets and relations
1831 __isl_give isl_basic_set *isl_basic_set_empty(
1832 __isl_take isl_space *space);
1833 __isl_give isl_basic_map *isl_basic_map_empty(
1834 __isl_take isl_space *space);
1835 __isl_give isl_set *isl_set_empty(
1836 __isl_take isl_space *space);
1837 __isl_give isl_map *isl_map_empty(
1838 __isl_take isl_space *space);
1839 __isl_give isl_union_set *isl_union_set_empty(
1840 __isl_take isl_space *space);
1841 __isl_give isl_union_map *isl_union_map_empty(
1842 __isl_take isl_space *space);
1844 For C<isl_union_set>s and C<isl_union_map>s, the space
1845 is only used to specify the parameters.
1847 =item * Universe sets and relations
1849 __isl_give isl_basic_set *isl_basic_set_universe(
1850 __isl_take isl_space *space);
1851 __isl_give isl_basic_map *isl_basic_map_universe(
1852 __isl_take isl_space *space);
1853 __isl_give isl_set *isl_set_universe(
1854 __isl_take isl_space *space);
1855 __isl_give isl_map *isl_map_universe(
1856 __isl_take isl_space *space);
1857 __isl_give isl_union_set *isl_union_set_universe(
1858 __isl_take isl_union_set *uset);
1859 __isl_give isl_union_map *isl_union_map_universe(
1860 __isl_take isl_union_map *umap);
1862 The sets and relations constructed by the functions above
1863 contain all integer values, while those constructed by the
1864 functions below only contain non-negative values.
1866 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1867 __isl_take isl_space *space);
1868 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1869 __isl_take isl_space *space);
1870 __isl_give isl_set *isl_set_nat_universe(
1871 __isl_take isl_space *space);
1872 __isl_give isl_map *isl_map_nat_universe(
1873 __isl_take isl_space *space);
1875 =item * Identity relations
1877 __isl_give isl_basic_map *isl_basic_map_identity(
1878 __isl_take isl_space *space);
1879 __isl_give isl_map *isl_map_identity(
1880 __isl_take isl_space *space);
1882 The number of input and output dimensions in C<space> needs
1885 =item * Lexicographic order
1887 __isl_give isl_map *isl_map_lex_lt(
1888 __isl_take isl_space *set_space);
1889 __isl_give isl_map *isl_map_lex_le(
1890 __isl_take isl_space *set_space);
1891 __isl_give isl_map *isl_map_lex_gt(
1892 __isl_take isl_space *set_space);
1893 __isl_give isl_map *isl_map_lex_ge(
1894 __isl_take isl_space *set_space);
1895 __isl_give isl_map *isl_map_lex_lt_first(
1896 __isl_take isl_space *space, unsigned n);
1897 __isl_give isl_map *isl_map_lex_le_first(
1898 __isl_take isl_space *space, unsigned n);
1899 __isl_give isl_map *isl_map_lex_gt_first(
1900 __isl_take isl_space *space, unsigned n);
1901 __isl_give isl_map *isl_map_lex_ge_first(
1902 __isl_take isl_space *space, unsigned n);
1904 The first four functions take a space for a B<set>
1905 and return relations that express that the elements in the domain
1906 are lexicographically less
1907 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1908 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1909 than the elements in the range.
1910 The last four functions take a space for a map
1911 and return relations that express that the first C<n> dimensions
1912 in the domain are lexicographically less
1913 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1914 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1915 than the first C<n> dimensions in the range.
1919 A basic set or relation can be converted to a set or relation
1920 using the following functions.
1922 __isl_give isl_set *isl_set_from_basic_set(
1923 __isl_take isl_basic_set *bset);
1924 __isl_give isl_map *isl_map_from_basic_map(
1925 __isl_take isl_basic_map *bmap);
1927 Sets and relations can be converted to union sets and relations
1928 using the following functions.
1930 __isl_give isl_union_set *isl_union_set_from_basic_set(
1931 __isl_take isl_basic_set *bset);
1932 __isl_give isl_union_map *isl_union_map_from_basic_map(
1933 __isl_take isl_basic_map *bmap);
1934 __isl_give isl_union_set *isl_union_set_from_set(
1935 __isl_take isl_set *set);
1936 __isl_give isl_union_map *isl_union_map_from_map(
1937 __isl_take isl_map *map);
1939 The inverse conversions below can only be used if the input
1940 union set or relation is known to contain elements in exactly one
1943 __isl_give isl_set *isl_set_from_union_set(
1944 __isl_take isl_union_set *uset);
1945 __isl_give isl_map *isl_map_from_union_map(
1946 __isl_take isl_union_map *umap);
1948 Sets and relations can be copied and freed again using the following
1951 __isl_give isl_basic_set *isl_basic_set_copy(
1952 __isl_keep isl_basic_set *bset);
1953 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1954 __isl_give isl_union_set *isl_union_set_copy(
1955 __isl_keep isl_union_set *uset);
1956 __isl_give isl_basic_map *isl_basic_map_copy(
1957 __isl_keep isl_basic_map *bmap);
1958 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1959 __isl_give isl_union_map *isl_union_map_copy(
1960 __isl_keep isl_union_map *umap);
1961 __isl_null isl_basic_set *isl_basic_set_free(
1962 __isl_take isl_basic_set *bset);
1963 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1964 __isl_null isl_union_set *isl_union_set_free(
1965 __isl_take isl_union_set *uset);
1966 __isl_null isl_basic_map *isl_basic_map_free(
1967 __isl_take isl_basic_map *bmap);
1968 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1969 __isl_null isl_union_map *isl_union_map_free(
1970 __isl_take isl_union_map *umap);
1972 Other sets and relations can be constructed by starting
1973 from a universe set or relation, adding equality and/or
1974 inequality constraints and then projecting out the
1975 existentially quantified variables, if any.
1976 Constraints can be constructed, manipulated and
1977 added to (or removed from) (basic) sets and relations
1978 using the following functions.
1980 #include <isl/constraint.h>
1981 __isl_give isl_constraint *isl_constraint_alloc_equality(
1982 __isl_take isl_local_space *ls);
1983 __isl_give isl_constraint *isl_constraint_alloc_inequality(
1984 __isl_take isl_local_space *ls);
1985 __isl_give isl_constraint *isl_constraint_set_constant_si(
1986 __isl_take isl_constraint *constraint, int v);
1987 __isl_give isl_constraint *isl_constraint_set_constant_val(
1988 __isl_take isl_constraint *constraint,
1989 __isl_take isl_val *v);
1990 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1991 __isl_take isl_constraint *constraint,
1992 enum isl_dim_type type, int pos, int v);
1993 __isl_give isl_constraint *
1994 isl_constraint_set_coefficient_val(
1995 __isl_take isl_constraint *constraint,
1996 enum isl_dim_type type, int pos,
1997 __isl_take isl_val *v);
1998 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1999 __isl_take isl_basic_map *bmap,
2000 __isl_take isl_constraint *constraint);
2001 __isl_give isl_basic_set *isl_basic_set_add_constraint(
2002 __isl_take isl_basic_set *bset,
2003 __isl_take isl_constraint *constraint);
2004 __isl_give isl_map *isl_map_add_constraint(
2005 __isl_take isl_map *map,
2006 __isl_take isl_constraint *constraint);
2007 __isl_give isl_set *isl_set_add_constraint(
2008 __isl_take isl_set *set,
2009 __isl_take isl_constraint *constraint);
2011 For example, to create a set containing the even integers
2012 between 10 and 42, you would use the following code.
2015 isl_local_space *ls;
2017 isl_basic_set *bset;
2019 space = isl_space_set_alloc(ctx, 0, 2);
2020 bset = isl_basic_set_universe(isl_space_copy(space));
2021 ls = isl_local_space_from_space(space);
2023 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
2024 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2025 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
2026 bset = isl_basic_set_add_constraint(bset, c);
2028 c = isl_constraint_alloc_inequality(isl_local_space_copy(ls));
2029 c = isl_constraint_set_constant_si(c, -10);
2030 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
2031 bset = isl_basic_set_add_constraint(bset, c);
2033 c = isl_constraint_alloc_inequality(ls);
2034 c = isl_constraint_set_constant_si(c, 42);
2035 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2036 bset = isl_basic_set_add_constraint(bset, c);
2038 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
2042 isl_basic_set *bset;
2043 bset = isl_basic_set_read_from_str(ctx,
2044 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
2046 A basic set or relation can also be constructed from two matrices
2047 describing the equalities and the inequalities.
2049 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
2050 __isl_take isl_space *space,
2051 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2052 enum isl_dim_type c1,
2053 enum isl_dim_type c2, enum isl_dim_type c3,
2054 enum isl_dim_type c4);
2055 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
2056 __isl_take isl_space *space,
2057 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2058 enum isl_dim_type c1,
2059 enum isl_dim_type c2, enum isl_dim_type c3,
2060 enum isl_dim_type c4, enum isl_dim_type c5);
2062 The C<isl_dim_type> arguments indicate the order in which
2063 different kinds of variables appear in the input matrices
2064 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
2065 C<isl_dim_set> and C<isl_dim_div> for sets and
2066 of C<isl_dim_cst>, C<isl_dim_param>,
2067 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
2069 A (basic or union) set or relation can also be constructed from a
2070 (union) (piecewise) (multiple) affine expression
2071 or a list of affine expressions
2072 (See L</"Functions">), provided these affine expressions do not
2075 __isl_give isl_basic_map *isl_basic_map_from_aff(
2076 __isl_take isl_aff *aff);
2077 __isl_give isl_map *isl_map_from_aff(
2078 __isl_take isl_aff *aff);
2079 __isl_give isl_set *isl_set_from_pw_aff(
2080 __isl_take isl_pw_aff *pwaff);
2081 __isl_give isl_map *isl_map_from_pw_aff(
2082 __isl_take isl_pw_aff *pwaff);
2083 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
2084 __isl_take isl_space *domain_space,
2085 __isl_take isl_aff_list *list);
2086 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
2087 __isl_take isl_multi_aff *maff)
2088 __isl_give isl_map *isl_map_from_multi_aff(
2089 __isl_take isl_multi_aff *maff)
2090 __isl_give isl_set *isl_set_from_pw_multi_aff(
2091 __isl_take isl_pw_multi_aff *pma);
2092 __isl_give isl_map *isl_map_from_pw_multi_aff(
2093 __isl_take isl_pw_multi_aff *pma);
2094 __isl_give isl_set *isl_set_from_multi_pw_aff(
2095 __isl_take isl_multi_pw_aff *mpa);
2096 __isl_give isl_map *isl_map_from_multi_pw_aff(
2097 __isl_take isl_multi_pw_aff *mpa);
2098 __isl_give isl_union_map *isl_union_map_from_union_pw_aff(
2099 __isl_take isl_union_pw_aff *upa);
2100 __isl_give isl_union_map *
2101 isl_union_map_from_union_pw_multi_aff(
2102 __isl_take isl_union_pw_multi_aff *upma);
2103 __isl_give isl_union_map *
2104 isl_union_map_from_multi_union_pw_aff(
2105 __isl_take isl_multi_union_pw_aff *mupa);
2107 The C<domain_space> argument describes the domain of the resulting
2108 basic relation. It is required because the C<list> may consist
2109 of zero affine expressions.
2110 The C<mupa> passed to C<isl_union_map_from_multi_union_pw_aff>
2111 is not allowed to be zero-dimensional. The domain of the result
2112 is the shared domain of the union piecewise affine elements.
2114 =head2 Inspecting Sets and Relations
2116 Usually, the user should not have to care about the actual constraints
2117 of the sets and maps, but should instead apply the abstract operations
2118 explained in the following sections.
2119 Occasionally, however, it may be required to inspect the individual
2120 coefficients of the constraints. This section explains how to do so.
2121 In these cases, it may also be useful to have C<isl> compute
2122 an explicit representation of the existentially quantified variables.
2124 __isl_give isl_set *isl_set_compute_divs(
2125 __isl_take isl_set *set);
2126 __isl_give isl_map *isl_map_compute_divs(
2127 __isl_take isl_map *map);
2128 __isl_give isl_union_set *isl_union_set_compute_divs(
2129 __isl_take isl_union_set *uset);
2130 __isl_give isl_union_map *isl_union_map_compute_divs(
2131 __isl_take isl_union_map *umap);
2133 This explicit representation defines the existentially quantified
2134 variables as integer divisions of the other variables, possibly
2135 including earlier existentially quantified variables.
2136 An explicitly represented existentially quantified variable therefore
2137 has a unique value when the values of the other variables are known.
2139 Alternatively, the existentially quantified variables can be removed
2140 using the following functions, which compute an overapproximation.
2142 #include <isl/set.h>
2143 __isl_give isl_basic_set *isl_basic_set_remove_divs(
2144 __isl_take isl_basic_set *bset);
2145 __isl_give isl_set *isl_set_remove_divs(
2146 __isl_take isl_set *set);
2148 #include <isl/map.h>
2149 __isl_give isl_basic_map *isl_basic_map_remove_divs(
2150 __isl_take isl_basic_map *bmap);
2151 __isl_give isl_map *isl_map_remove_divs(
2152 __isl_take isl_map *map);
2154 #include <isl/union_set.h>
2155 __isl_give isl_union_set *isl_union_set_remove_divs(
2156 __isl_take isl_union_set *bset);
2158 #include <isl/union_map.h>
2159 __isl_give isl_union_map *isl_union_map_remove_divs(
2160 __isl_take isl_union_map *bmap);
2162 It is also possible to only remove those divs that are defined
2163 in terms of a given range of dimensions or only those for which
2164 no explicit representation is known.
2166 __isl_give isl_basic_set *
2167 isl_basic_set_remove_divs_involving_dims(
2168 __isl_take isl_basic_set *bset,
2169 enum isl_dim_type type,
2170 unsigned first, unsigned n);
2171 __isl_give isl_basic_map *
2172 isl_basic_map_remove_divs_involving_dims(
2173 __isl_take isl_basic_map *bmap,
2174 enum isl_dim_type type,
2175 unsigned first, unsigned n);
2176 __isl_give isl_set *isl_set_remove_divs_involving_dims(
2177 __isl_take isl_set *set, enum isl_dim_type type,
2178 unsigned first, unsigned n);
2179 __isl_give isl_map *isl_map_remove_divs_involving_dims(
2180 __isl_take isl_map *map, enum isl_dim_type type,
2181 unsigned first, unsigned n);
2183 __isl_give isl_basic_set *
2184 isl_basic_set_remove_unknown_divs(
2185 __isl_take isl_basic_set *bset);
2186 __isl_give isl_set *isl_set_remove_unknown_divs(
2187 __isl_take isl_set *set);
2188 __isl_give isl_map *isl_map_remove_unknown_divs(
2189 __isl_take isl_map *map);
2191 To iterate over all the sets or maps in a union set or map, use
2193 #include <isl/union_set.h>
2194 isl_stat isl_union_set_foreach_set(
2195 __isl_keep isl_union_set *uset,
2196 isl_stat (*fn)(__isl_take isl_set *set, void *user),
2199 #include <isl/union_map.h>
2200 isl_stat isl_union_map_foreach_map(
2201 __isl_keep isl_union_map *umap,
2202 isl_stat (*fn)(__isl_take isl_map *map, void *user),
2204 isl_bool isl_union_map_every_map(
2205 __isl_keep isl_union_map *umap,
2206 isl_bool (*test)(__isl_keep isl_map *map,
2210 These functions call the callback function once for each
2211 (pair of) space(s) for which there are elements in the input.
2212 The argument to the callback contains all elements in the input
2213 with that (pair of) space(s).
2214 The C<isl_union_map_every_map> variant check whether each
2215 call to the callback returns true and stops checking as soon as one
2216 of these calls returns false.
2218 The number of sets or maps in a union set or map can be obtained
2221 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
2222 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
2224 To extract the set or map in a given space from a union, use
2226 __isl_give isl_set *isl_union_set_extract_set(
2227 __isl_keep isl_union_set *uset,
2228 __isl_take isl_space *space);
2229 __isl_give isl_map *isl_union_map_extract_map(
2230 __isl_keep isl_union_map *umap,
2231 __isl_take isl_space *space);
2233 To iterate over all the basic sets or maps in a set or map, use
2235 isl_stat isl_set_foreach_basic_set(__isl_keep isl_set *set,
2236 isl_stat (*fn)(__isl_take isl_basic_set *bset,
2239 isl_stat isl_map_foreach_basic_map(__isl_keep isl_map *map,
2240 isl_stat (*fn)(__isl_take isl_basic_map *bmap,
2244 The callback function C<fn> should return C<isl_stat_ok> if successful and
2245 C<isl_stat_error> if an error occurs. In the latter case, or if any other error
2246 occurs, the above functions will return C<isl_stat_error>.
2248 It should be noted that C<isl> does not guarantee that
2249 the basic sets or maps passed to C<fn> are disjoint.
2250 If this is required, then the user should call one of
2251 the following functions first.
2253 __isl_give isl_set *isl_set_make_disjoint(
2254 __isl_take isl_set *set);
2255 __isl_give isl_map *isl_map_make_disjoint(
2256 __isl_take isl_map *map);
2258 The number of basic sets in a set can be obtained
2259 or the number of basic maps in a map can be obtained
2262 #include <isl/set.h>
2263 int isl_set_n_basic_set(__isl_keep isl_set *set);
2265 #include <isl/map.h>
2266 int isl_map_n_basic_map(__isl_keep isl_map *map);
2268 It is also possible to obtain a list of basic sets from a set
2271 #include <isl/set.h>
2272 __isl_give isl_basic_set_list *isl_set_get_basic_set_list(
2273 __isl_keep isl_set *set);
2275 #include <isl/union_set.h>
2276 __isl_give isl_basic_set_list *
2277 isl_union_set_get_basic_set_list(
2278 __isl_keep isl_union_set *uset);
2280 The returned list can be manipulated using the functions in L<"Lists">.
2282 To iterate over the constraints of a basic set or map, use
2284 #include <isl/constraint.h>
2286 int isl_basic_set_n_constraint(
2287 __isl_keep isl_basic_set *bset);
2288 isl_stat isl_basic_set_foreach_constraint(
2289 __isl_keep isl_basic_set *bset,
2290 isl_stat (*fn)(__isl_take isl_constraint *c,
2293 int isl_basic_map_n_constraint(
2294 __isl_keep isl_basic_map *bmap);
2295 isl_stat isl_basic_map_foreach_constraint(
2296 __isl_keep isl_basic_map *bmap,
2297 isl_stat (*fn)(__isl_take isl_constraint *c,
2300 __isl_null isl_constraint *isl_constraint_free(
2301 __isl_take isl_constraint *c);
2303 Again, the callback function C<fn> should return C<isl_stat_ok>
2305 C<isl_stat_error> if an error occurs. In the latter case, or if any other error
2306 occurs, the above functions will return C<isl_stat_error>.
2307 The constraint C<c> represents either an equality or an inequality.
2308 Use the following function to find out whether a constraint
2309 represents an equality. If not, it represents an inequality.
2311 isl_bool isl_constraint_is_equality(
2312 __isl_keep isl_constraint *constraint);
2314 It is also possible to obtain a list of constraints from a basic
2317 #include <isl/constraint.h>
2318 __isl_give isl_constraint_list *
2319 isl_basic_map_get_constraint_list(
2320 __isl_keep isl_basic_map *bmap);
2321 __isl_give isl_constraint_list *
2322 isl_basic_set_get_constraint_list(
2323 __isl_keep isl_basic_set *bset);
2325 These functions require that all existentially quantified variables
2326 have an explicit representation.
2327 The returned list can be manipulated using the functions in L<"Lists">.
2329 The coefficients of the constraints can be inspected using
2330 the following functions.
2332 isl_bool isl_constraint_is_lower_bound(
2333 __isl_keep isl_constraint *constraint,
2334 enum isl_dim_type type, unsigned pos);
2335 isl_bool isl_constraint_is_upper_bound(
2336 __isl_keep isl_constraint *constraint,
2337 enum isl_dim_type type, unsigned pos);
2338 __isl_give isl_val *isl_constraint_get_constant_val(
2339 __isl_keep isl_constraint *constraint);
2340 __isl_give isl_val *isl_constraint_get_coefficient_val(
2341 __isl_keep isl_constraint *constraint,
2342 enum isl_dim_type type, int pos);
2344 The explicit representations of the existentially quantified
2345 variables can be inspected using the following function.
2346 Note that the user is only allowed to use this function
2347 if the inspected set or map is the result of a call
2348 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2349 The existentially quantified variable is equal to the floor
2350 of the returned affine expression. The affine expression
2351 itself can be inspected using the functions in
2354 __isl_give isl_aff *isl_constraint_get_div(
2355 __isl_keep isl_constraint *constraint, int pos);
2357 To obtain the constraints of a basic set or map in matrix
2358 form, use the following functions.
2360 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2361 __isl_keep isl_basic_set *bset,
2362 enum isl_dim_type c1, enum isl_dim_type c2,
2363 enum isl_dim_type c3, enum isl_dim_type c4);
2364 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2365 __isl_keep isl_basic_set *bset,
2366 enum isl_dim_type c1, enum isl_dim_type c2,
2367 enum isl_dim_type c3, enum isl_dim_type c4);
2368 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2369 __isl_keep isl_basic_map *bmap,
2370 enum isl_dim_type c1,
2371 enum isl_dim_type c2, enum isl_dim_type c3,
2372 enum isl_dim_type c4, enum isl_dim_type c5);
2373 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2374 __isl_keep isl_basic_map *bmap,
2375 enum isl_dim_type c1,
2376 enum isl_dim_type c2, enum isl_dim_type c3,
2377 enum isl_dim_type c4, enum isl_dim_type c5);
2379 The C<isl_dim_type> arguments dictate the order in which
2380 different kinds of variables appear in the resulting matrix.
2381 For set inputs, they should be a permutation of
2382 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
2383 For map inputs, they should be a permutation of
2384 C<isl_dim_cst>, C<isl_dim_param>,
2385 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2389 Points are elements of a set. They can be used to construct
2390 simple sets (boxes) or they can be used to represent the
2391 individual elements of a set.
2392 The zero point (the origin) can be created using
2394 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2396 The coordinates of a point can be inspected, set and changed
2399 __isl_give isl_val *isl_point_get_coordinate_val(
2400 __isl_keep isl_point *pnt,
2401 enum isl_dim_type type, int pos);
2402 __isl_give isl_point *isl_point_set_coordinate_val(
2403 __isl_take isl_point *pnt,
2404 enum isl_dim_type type, int pos,
2405 __isl_take isl_val *v);
2407 __isl_give isl_point *isl_point_add_ui(
2408 __isl_take isl_point *pnt,
2409 enum isl_dim_type type, int pos, unsigned val);
2410 __isl_give isl_point *isl_point_sub_ui(
2411 __isl_take isl_point *pnt,
2412 enum isl_dim_type type, int pos, unsigned val);
2414 Points can be copied or freed using
2416 __isl_give isl_point *isl_point_copy(
2417 __isl_keep isl_point *pnt);
2418 __isl_null isl_point *isl_point_free(
2419 __isl_take isl_point *pnt);
2421 A singleton set can be created from a point using
2423 __isl_give isl_basic_set *isl_basic_set_from_point(
2424 __isl_take isl_point *pnt);
2425 __isl_give isl_set *isl_set_from_point(
2426 __isl_take isl_point *pnt);
2427 __isl_give isl_union_set *isl_union_set_from_point(
2428 __isl_take isl_point *pnt);
2430 and a box can be created from two opposite extremal points using
2432 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2433 __isl_take isl_point *pnt1,
2434 __isl_take isl_point *pnt2);
2435 __isl_give isl_set *isl_set_box_from_points(
2436 __isl_take isl_point *pnt1,
2437 __isl_take isl_point *pnt2);
2439 All elements of a B<bounded> (union) set can be enumerated using
2440 the following functions.
2442 isl_stat isl_set_foreach_point(__isl_keep isl_set *set,
2443 isl_stat (*fn)(__isl_take isl_point *pnt,
2446 isl_stat isl_union_set_foreach_point(
2447 __isl_keep isl_union_set *uset,
2448 isl_stat (*fn)(__isl_take isl_point *pnt,
2452 The function C<fn> is called for each integer point in
2453 C<set> with as second argument the last argument of
2454 the C<isl_set_foreach_point> call. The function C<fn>
2455 should return C<isl_stat_ok> on success and C<isl_stat_error> on failure.
2456 In the latter case, C<isl_set_foreach_point> will stop
2457 enumerating and return C<isl_stat_error> as well.
2458 If the enumeration is performed successfully and to completion,
2459 then C<isl_set_foreach_point> returns C<isl_stat_ok>.
2461 To obtain a single point of a (basic or union) set, use
2463 __isl_give isl_point *isl_basic_set_sample_point(
2464 __isl_take isl_basic_set *bset);
2465 __isl_give isl_point *isl_set_sample_point(
2466 __isl_take isl_set *set);
2467 __isl_give isl_point *isl_union_set_sample_point(
2468 __isl_take isl_union_set *uset);
2470 If C<set> does not contain any (integer) points, then the
2471 resulting point will be ``void'', a property that can be
2474 isl_bool isl_point_is_void(__isl_keep isl_point *pnt);
2478 Besides sets and relation, C<isl> also supports various types of functions.
2479 Each of these types is derived from the value type (see L</"Values">)
2480 or from one of two primitive function types
2481 through the application of zero or more type constructors.
2482 We first describe the primitive type and then we describe
2483 the types derived from these primitive types.
2485 =head3 Primitive Functions
2487 C<isl> support two primitive function types, quasi-affine
2488 expressions and quasipolynomials.
2489 A quasi-affine expression is defined either over a parameter
2490 space or over a set and is composed of integer constants,
2491 parameters and set variables, addition, subtraction and
2492 integer division by an integer constant.
2493 For example, the quasi-affine expression
2495 [n] -> { [x] -> [2*floor((4 n + x)/9)] }
2497 maps C<x> to C<2*floor((4 n + x)/9>.
2498 A quasipolynomial is a polynomial expression in quasi-affine
2499 expression. That is, it additionally allows for multiplication.
2500 Note, though, that it is not allowed to construct an integer
2501 division of an expression involving multiplications.
2502 Here is an example of a quasipolynomial that is not
2503 quasi-affine expression
2505 [n] -> { [x] -> (n*floor((4 n + x)/9)) }
2507 Note that the external representations of quasi-affine expressions
2508 and quasipolynomials are different. Quasi-affine expressions
2509 use a notation with square brackets just like binary relations,
2510 while quasipolynomials do not. This might change at some point.
2512 If a primitive function is defined over a parameter space,
2513 then the space of the function itself is that of a set.
2514 If it is defined over a set, then the space of the function
2515 is that of a relation. In both cases, the set space (or
2516 the output space) is single-dimensional, anonymous and unstructured.
2517 To create functions with multiple dimensions or with other kinds
2518 of set or output spaces, use multiple expressions
2519 (see L</"Multiple Expressions">).
2523 =item * Quasi-affine Expressions
2525 Besides the expressions described above, a quasi-affine
2526 expression can also be set to NaN. Such expressions
2527 typically represent a failure to represent a result
2528 as a quasi-affine expression.
2530 The zero quasi affine expression or the quasi affine expression
2531 that is equal to a given value, parameter or
2532 a specified dimension on a given domain can be created using
2534 #include <isl/aff.h>
2535 __isl_give isl_aff *isl_aff_zero_on_domain(
2536 __isl_take isl_local_space *ls);
2537 __isl_give isl_aff *isl_aff_val_on_domain(
2538 __isl_take isl_local_space *ls,
2539 __isl_take isl_val *val);
2540 __isl_give isl_aff *isl_aff_param_on_domain_space_id(
2541 __isl_take isl_space *space,
2542 __isl_take isl_id *id);
2543 __isl_give isl_aff *isl_aff_var_on_domain(
2544 __isl_take isl_local_space *ls,
2545 enum isl_dim_type type, unsigned pos);
2546 __isl_give isl_aff *isl_aff_nan_on_domain(
2547 __isl_take isl_local_space *ls);
2549 The space passed to C<isl_aff_param_on_domain_space_id>
2550 is required to have a parameter with the given identifier.
2552 Quasi affine expressions can be copied and freed using
2554 #include <isl/aff.h>
2555 __isl_give isl_aff *isl_aff_copy(
2556 __isl_keep isl_aff *aff);
2557 __isl_null isl_aff *isl_aff_free(
2558 __isl_take isl_aff *aff);
2560 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2561 using the following function. The constraint is required to have
2562 a non-zero coefficient for the specified dimension.
2564 #include <isl/constraint.h>
2565 __isl_give isl_aff *isl_constraint_get_bound(
2566 __isl_keep isl_constraint *constraint,
2567 enum isl_dim_type type, int pos);
2569 The entire affine expression of the constraint can also be extracted
2570 using the following function.
2572 #include <isl/constraint.h>
2573 __isl_give isl_aff *isl_constraint_get_aff(
2574 __isl_keep isl_constraint *constraint);
2576 Conversely, an equality constraint equating
2577 the affine expression to zero or an inequality constraint enforcing
2578 the affine expression to be non-negative, can be constructed using
2580 __isl_give isl_constraint *isl_equality_from_aff(
2581 __isl_take isl_aff *aff);
2582 __isl_give isl_constraint *isl_inequality_from_aff(
2583 __isl_take isl_aff *aff);
2585 The coefficients and the integer divisions of an affine expression
2586 can be inspected using the following functions.
2588 #include <isl/aff.h>
2589 __isl_give isl_val *isl_aff_get_constant_val(
2590 __isl_keep isl_aff *aff);
2591 __isl_give isl_val *isl_aff_get_coefficient_val(
2592 __isl_keep isl_aff *aff,
2593 enum isl_dim_type type, int pos);
2594 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2595 enum isl_dim_type type, int pos);
2596 __isl_give isl_val *isl_aff_get_denominator_val(
2597 __isl_keep isl_aff *aff);
2598 __isl_give isl_aff *isl_aff_get_div(
2599 __isl_keep isl_aff *aff, int pos);
2601 They can be modified using the following functions.
2603 #include <isl/aff.h>
2604 __isl_give isl_aff *isl_aff_set_constant_si(
2605 __isl_take isl_aff *aff, int v);
2606 __isl_give isl_aff *isl_aff_set_constant_val(
2607 __isl_take isl_aff *aff, __isl_take isl_val *v);
2608 __isl_give isl_aff *isl_aff_set_coefficient_si(
2609 __isl_take isl_aff *aff,
2610 enum isl_dim_type type, int pos, int v);
2611 __isl_give isl_aff *isl_aff_set_coefficient_val(
2612 __isl_take isl_aff *aff,
2613 enum isl_dim_type type, int pos,
2614 __isl_take isl_val *v);
2616 __isl_give isl_aff *isl_aff_add_constant_si(
2617 __isl_take isl_aff *aff, int v);
2618 __isl_give isl_aff *isl_aff_add_constant_val(
2619 __isl_take isl_aff *aff, __isl_take isl_val *v);
2620 __isl_give isl_aff *isl_aff_add_constant_num_si(
2621 __isl_take isl_aff *aff, int v);
2622 __isl_give isl_aff *isl_aff_add_coefficient_si(
2623 __isl_take isl_aff *aff,
2624 enum isl_dim_type type, int pos, int v);
2625 __isl_give isl_aff *isl_aff_add_coefficient_val(
2626 __isl_take isl_aff *aff,
2627 enum isl_dim_type type, int pos,
2628 __isl_take isl_val *v);
2630 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
2631 set the I<numerator> of the constant or coefficient, while
2632 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
2633 the constant or coefficient as a whole.
2634 The C<add_constant> and C<add_coefficient> functions add an integer
2635 or rational value to
2636 the possibly rational constant or coefficient.
2637 The C<add_constant_num> functions add an integer value to
2640 =item * Quasipolynomials
2642 Some simple quasipolynomials can be created using the following functions.
2644 #include <isl/polynomial.h>
2645 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2646 __isl_take isl_space *domain);
2647 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2648 __isl_take isl_space *domain);
2649 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2650 __isl_take isl_space *domain);
2651 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2652 __isl_take isl_space *domain);
2653 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2654 __isl_take isl_space *domain);
2655 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2656 __isl_take isl_space *domain,
2657 __isl_take isl_val *val);
2658 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2659 __isl_take isl_space *domain,
2660 enum isl_dim_type type, unsigned pos);
2661 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2662 __isl_take isl_aff *aff);
2664 Recall that the space in which a quasipolynomial lives is a map space
2665 with a one-dimensional range. The C<domain> argument in some of
2666 the functions above corresponds to the domain of this map space.
2668 Quasipolynomials can be copied and freed again using the following
2671 #include <isl/polynomial.h>
2672 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2673 __isl_keep isl_qpolynomial *qp);
2674 __isl_null isl_qpolynomial *isl_qpolynomial_free(
2675 __isl_take isl_qpolynomial *qp);
2677 The constant term of a quasipolynomial can be extracted using
2679 __isl_give isl_val *isl_qpolynomial_get_constant_val(
2680 __isl_keep isl_qpolynomial *qp);
2682 To iterate over all terms in a quasipolynomial,
2685 isl_stat isl_qpolynomial_foreach_term(
2686 __isl_keep isl_qpolynomial *qp,
2687 isl_stat (*fn)(__isl_take isl_term *term,
2688 void *user), void *user);
2690 The terms themselves can be inspected and freed using
2693 unsigned isl_term_dim(__isl_keep isl_term *term,
2694 enum isl_dim_type type);
2695 __isl_give isl_val *isl_term_get_coefficient_val(
2696 __isl_keep isl_term *term);
2697 int isl_term_get_exp(__isl_keep isl_term *term,
2698 enum isl_dim_type type, unsigned pos);
2699 __isl_give isl_aff *isl_term_get_div(
2700 __isl_keep isl_term *term, unsigned pos);
2701 void isl_term_free(__isl_take isl_term *term);
2703 Each term is a product of parameters, set variables and
2704 integer divisions. The function C<isl_term_get_exp>
2705 returns the exponent of a given dimensions in the given term.
2711 A reduction represents a maximum or a minimum of its
2713 The only reduction type defined by C<isl> is
2714 C<isl_qpolynomial_fold>.
2716 There are currently no functions to directly create such
2717 objects, but they do appear in the piecewise quasipolynomial
2718 reductions returned by the C<isl_pw_qpolynomial_bound> function.
2720 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
2722 Reductions can be copied and freed using
2723 the following functions.
2725 #include <isl/polynomial.h>
2726 __isl_give isl_qpolynomial_fold *
2727 isl_qpolynomial_fold_copy(
2728 __isl_keep isl_qpolynomial_fold *fold);
2729 void isl_qpolynomial_fold_free(
2730 __isl_take isl_qpolynomial_fold *fold);
2732 To iterate over all quasipolynomials in a reduction, use
2734 isl_stat isl_qpolynomial_fold_foreach_qpolynomial(
2735 __isl_keep isl_qpolynomial_fold *fold,
2736 isl_stat (*fn)(__isl_take isl_qpolynomial *qp,
2737 void *user), void *user);
2739 =head3 Multiple Expressions
2741 A multiple expression represents a sequence of zero or
2742 more base expressions, all defined on the same domain space.
2743 The domain space of the multiple expression is the same
2744 as that of the base expressions, but the range space
2745 can be any space. In case the base expressions have
2746 a set space, the corresponding multiple expression
2747 also has a set space.
2748 Objects of the value type do not have an associated space.
2749 The space of a multiple value is therefore always a set space.
2750 Similarly, the space of a multiple union piecewise
2751 affine expression is always a set space.
2753 The multiple expression types defined by C<isl>
2754 are C<isl_multi_val>, C<isl_multi_aff>, C<isl_multi_pw_aff>,
2755 C<isl_multi_union_pw_aff>.
2757 A multiple expression with the value zero for
2758 each output (or set) dimension can be created
2759 using the following functions.
2761 #include <isl/val.h>
2762 __isl_give isl_multi_val *isl_multi_val_zero(
2763 __isl_take isl_space *space);
2765 #include <isl/aff.h>
2766 __isl_give isl_multi_aff *isl_multi_aff_zero(
2767 __isl_take isl_space *space);
2768 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
2769 __isl_take isl_space *space);
2770 __isl_give isl_multi_union_pw_aff *
2771 isl_multi_union_pw_aff_zero(
2772 __isl_take isl_space *space);
2774 Since there is no canonical way of representing a zero
2775 value of type C<isl_union_pw_aff>, the space passed
2776 to C<isl_multi_union_pw_aff_zero> needs to be zero-dimensional.
2778 An identity function can be created using the following
2779 functions. The space needs to be that of a relation
2780 with the same number of input and output dimensions.
2782 #include <isl/aff.h>
2783 __isl_give isl_multi_aff *isl_multi_aff_identity(
2784 __isl_take isl_space *space);
2785 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
2786 __isl_take isl_space *space);
2788 A function that performs a projection on a universe
2789 relation or set can be created using the following functions.
2790 See also the corresponding
2791 projection operations in L</"Unary Operations">.
2793 #include <isl/aff.h>
2794 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
2795 __isl_take isl_space *space);
2796 __isl_give isl_multi_aff *isl_multi_aff_range_map(
2797 __isl_take isl_space *space);
2798 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
2799 __isl_take isl_space *space,
2800 enum isl_dim_type type,
2801 unsigned first, unsigned n);
2803 A multiple expression can be created from a single
2804 base expression using the following functions.
2805 The space of the created multiple expression is the same
2806 as that of the base expression, except for
2807 C<isl_multi_union_pw_aff_from_union_pw_aff> where the input
2808 lives in a parameter space and the output lives
2809 in a single-dimensional set space.
2811 #include <isl/aff.h>
2812 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
2813 __isl_take isl_aff *aff);
2814 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
2815 __isl_take isl_pw_aff *pa);
2816 __isl_give isl_multi_union_pw_aff *
2817 isl_multi_union_pw_aff_from_union_pw_aff(
2818 __isl_take isl_union_pw_aff *upa);
2820 A multiple expression can be created from a list
2821 of base expression in a specified space.
2822 The domain of this space needs to be the same
2823 as the domains of the base expressions in the list.
2824 If the base expressions have a set space (or no associated space),
2825 then this space also needs to be a set space.
2827 #include <isl/val.h>
2828 __isl_give isl_multi_val *isl_multi_val_from_val_list(
2829 __isl_take isl_space *space,
2830 __isl_take isl_val_list *list);
2832 #include <isl/aff.h>
2833 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2834 __isl_take isl_space *space,
2835 __isl_take isl_aff_list *list);
2836 __isl_give isl_multi_pw_aff *
2837 isl_multi_pw_aff_from_pw_aff_list(
2838 __isl_take isl_space *space,
2839 __isl_take isl_pw_aff_list *list);
2840 __isl_give isl_multi_union_pw_aff *
2841 isl_multi_union_pw_aff_from_union_pw_aff_list(
2842 __isl_take isl_space *space,
2843 __isl_take isl_union_pw_aff_list *list);
2845 As a convenience, a multiple piecewise expression can
2846 also be created from a multiple expression.
2847 Each piecewise expression in the result has a single
2850 #include <isl/aff.h>
2851 __isl_give isl_multi_pw_aff *
2852 isl_multi_pw_aff_from_multi_aff(
2853 __isl_take isl_multi_aff *ma);
2855 Similarly, a multiple union expression can be
2856 created from a multiple expression.
2858 #include <isl/aff.h>
2859 __isl_give isl_multi_union_pw_aff *
2860 isl_multi_union_pw_aff_from_multi_aff(
2861 __isl_take isl_multi_aff *ma);
2862 __isl_give isl_multi_union_pw_aff *
2863 isl_multi_union_pw_aff_from_multi_pw_aff(
2864 __isl_take isl_multi_pw_aff *mpa);
2866 A multiple quasi-affine expression can be created from
2867 a multiple value with a given domain space using the following
2870 #include <isl/aff.h>
2871 __isl_give isl_multi_aff *
2872 isl_multi_aff_multi_val_on_space(
2873 __isl_take isl_space *space,
2874 __isl_take isl_multi_val *mv);
2877 a multiple union piecewise affine expression can be created from
2878 a multiple value with a given domain or
2879 a (piecewise) multiple affine expression with a given domain
2880 using the following functions.
2882 #include <isl/aff.h>
2883 __isl_give isl_multi_union_pw_aff *
2884 isl_multi_union_pw_aff_multi_val_on_domain(
2885 __isl_take isl_union_set *domain,
2886 __isl_take isl_multi_val *mv);
2887 __isl_give isl_multi_union_pw_aff *
2888 isl_multi_union_pw_aff_multi_aff_on_domain(
2889 __isl_take isl_union_set *domain,
2890 __isl_take isl_multi_aff *ma);
2891 __isl_give isl_multi_union_pw_aff *
2892 isl_multi_union_pw_aff_pw_multi_aff_on_domain(
2893 __isl_take isl_union_set *domain,
2894 __isl_take isl_pw_multi_aff *pma);
2896 Multiple expressions can be copied and freed using
2897 the following functions.
2899 #include <isl/val.h>
2900 __isl_give isl_multi_val *isl_multi_val_copy(
2901 __isl_keep isl_multi_val *mv);
2902 __isl_null isl_multi_val *isl_multi_val_free(
2903 __isl_take isl_multi_val *mv);
2905 #include <isl/aff.h>
2906 __isl_give isl_multi_aff *isl_multi_aff_copy(
2907 __isl_keep isl_multi_aff *maff);
2908 __isl_null isl_multi_aff *isl_multi_aff_free(
2909 __isl_take isl_multi_aff *maff);
2910 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
2911 __isl_keep isl_multi_pw_aff *mpa);
2912 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
2913 __isl_take isl_multi_pw_aff *mpa);
2914 __isl_give isl_multi_union_pw_aff *
2915 isl_multi_union_pw_aff_copy(
2916 __isl_keep isl_multi_union_pw_aff *mupa);
2917 __isl_null isl_multi_union_pw_aff *
2918 isl_multi_union_pw_aff_free(
2919 __isl_take isl_multi_union_pw_aff *mupa);
2921 The base expression at a given position of a multiple
2922 expression can be extracted using the following functions.
2924 #include <isl/val.h>
2925 __isl_give isl_val *isl_multi_val_get_val(
2926 __isl_keep isl_multi_val *mv, int pos);
2928 #include <isl/aff.h>
2929 __isl_give isl_aff *isl_multi_aff_get_aff(
2930 __isl_keep isl_multi_aff *multi, int pos);
2931 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
2932 __isl_keep isl_multi_pw_aff *mpa, int pos);
2933 __isl_give isl_union_pw_aff *
2934 isl_multi_union_pw_aff_get_union_pw_aff(
2935 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
2937 It can be replaced using the following functions.
2939 #include <isl/val.h>
2940 __isl_give isl_multi_val *isl_multi_val_set_val(
2941 __isl_take isl_multi_val *mv, int pos,
2942 __isl_take isl_val *val);
2944 #include <isl/aff.h>
2945 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
2946 __isl_take isl_multi_aff *multi, int pos,
2947 __isl_take isl_aff *aff);
2948 __isl_give isl_multi_union_pw_aff *
2949 isl_multi_union_pw_aff_set_union_pw_aff(
2950 __isl_take isl_multi_union_pw_aff *mupa, int pos,
2951 __isl_take isl_union_pw_aff *upa);
2953 As a convenience, a sequence of base expressions that have
2954 their domains in a given space can be extracted from a sequence
2955 of union expressions using the following function.
2957 #include <isl/aff.h>
2958 __isl_give isl_multi_pw_aff *
2959 isl_multi_union_pw_aff_extract_multi_pw_aff(
2960 __isl_keep isl_multi_union_pw_aff *mupa,
2961 __isl_take isl_space *space);
2963 Note that there is a difference between C<isl_multi_union_pw_aff>
2964 and C<isl_union_pw_multi_aff> objects. The first is a sequence
2965 of unions of piecewise expressions, while the second is a union
2966 of piecewise sequences. In particular, multiple affine expressions
2967 in an C<isl_union_pw_multi_aff> may live in different spaces,
2968 while there is only a single multiple expression in
2969 an C<isl_multi_union_pw_aff>, which can therefore only live
2970 in a single space. This means that not every
2971 C<isl_union_pw_multi_aff> can be converted to
2972 an C<isl_multi_union_pw_aff>. Conversely, a zero-dimensional
2973 C<isl_multi_union_pw_aff> carries no information
2974 about any possible domain and therefore cannot be converted
2975 to an C<isl_union_pw_multi_aff>. Moreover, the elements
2976 of an C<isl_multi_union_pw_aff> may be defined over different domains,
2977 while each multiple expression inside an C<isl_union_pw_multi_aff>
2978 has a single domain. The conversion of an C<isl_union_pw_multi_aff>
2979 of dimension greater than one may therefore not be exact.
2980 The following functions can
2981 be used to perform these conversions when they are possible.
2983 #include <isl/aff.h>
2984 __isl_give isl_multi_union_pw_aff *
2985 isl_multi_union_pw_aff_from_union_pw_multi_aff(
2986 __isl_take isl_union_pw_multi_aff *upma);
2987 __isl_give isl_union_pw_multi_aff *
2988 isl_union_pw_multi_aff_from_multi_union_pw_aff(
2989 __isl_take isl_multi_union_pw_aff *mupa);
2991 =head3 Piecewise Expressions
2993 A piecewise expression is an expression that is described
2994 using zero or more base expression defined over the same
2995 number of cells in the domain space of the base expressions.
2996 All base expressions are defined over the same
2997 domain space and the cells are disjoint.
2998 The space of a piecewise expression is the same as
2999 that of the base expressions.
3000 If the union of the cells is a strict subset of the domain
3001 space, then the value of the piecewise expression outside
3002 this union is different for types derived from quasi-affine
3003 expressions and those derived from quasipolynomials.
3004 Piecewise expressions derived from quasi-affine expressions
3005 are considered to be undefined outside the union of their cells.
3006 Piecewise expressions derived from quasipolynomials
3007 are considered to be zero outside the union of their cells.
3009 Piecewise quasipolynomials are mainly used by the C<barvinok>
3010 library for representing the number of elements in a parametric set or map.
3011 For example, the piecewise quasipolynomial
3013 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3015 represents the number of points in the map
3017 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3019 The piecewise expression types defined by C<isl>
3020 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
3021 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
3023 A piecewise expression with no cells can be created using
3024 the following functions.
3026 #include <isl/aff.h>
3027 __isl_give isl_pw_aff *isl_pw_aff_empty(
3028 __isl_take isl_space *space);
3029 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3030 __isl_take isl_space *space);
3032 A piecewise expression with a single universe cell can be
3033 created using the following functions.
3035 #include <isl/aff.h>
3036 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3037 __isl_take isl_aff *aff);
3038 __isl_give isl_pw_multi_aff *
3039 isl_pw_multi_aff_from_multi_aff(
3040 __isl_take isl_multi_aff *ma);
3042 #include <isl/polynomial.h>
3043 __isl_give isl_pw_qpolynomial *
3044 isl_pw_qpolynomial_from_qpolynomial(
3045 __isl_take isl_qpolynomial *qp);
3047 A piecewise expression with a single specified cell can be
3048 created using the following functions.
3050 #include <isl/aff.h>
3051 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3052 __isl_take isl_set *set, __isl_take isl_aff *aff);
3053 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3054 __isl_take isl_set *set,
3055 __isl_take isl_multi_aff *maff);
3057 #include <isl/polynomial.h>
3058 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3059 __isl_take isl_set *set,
3060 __isl_take isl_qpolynomial *qp);
3062 The following convenience functions first create a base expression and
3063 then create a piecewise expression over a universe domain.
3065 #include <isl/aff.h>
3066 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3067 __isl_take isl_local_space *ls);
3068 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3069 __isl_take isl_local_space *ls,
3070 enum isl_dim_type type, unsigned pos);
3071 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3072 __isl_take isl_local_space *ls);
3073 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
3074 __isl_take isl_space *space);
3075 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3076 __isl_take isl_space *space);
3077 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
3078 __isl_take isl_space *space);
3079 __isl_give isl_pw_multi_aff *
3080 isl_pw_multi_aff_project_out_map(
3081 __isl_take isl_space *space,
3082 enum isl_dim_type type,
3083 unsigned first, unsigned n);
3085 #include <isl/polynomial.h>
3086 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3087 __isl_take isl_space *space);
3089 The following convenience functions first create a base expression and
3090 then create a piecewise expression over a given domain.
3092 #include <isl/aff.h>
3093 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
3094 __isl_take isl_set *domain,
3095 __isl_take isl_val *v);
3096 __isl_give isl_pw_multi_aff *
3097 isl_pw_multi_aff_multi_val_on_domain(
3098 __isl_take isl_set *domain,
3099 __isl_take isl_multi_val *mv);
3101 As a convenience, a piecewise multiple expression can
3102 also be created from a piecewise expression.
3103 Each multiple expression in the result is derived
3104 from the corresponding base expression.
3106 #include <isl/aff.h>
3107 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
3108 __isl_take isl_pw_aff *pa);
3110 Similarly, a piecewise quasipolynomial can be
3111 created from a piecewise quasi-affine expression using
3112 the following function.
3114 #include <isl/polynomial.h>
3115 __isl_give isl_pw_qpolynomial *
3116 isl_pw_qpolynomial_from_pw_aff(
3117 __isl_take isl_pw_aff *pwaff);
3119 Piecewise expressions can be copied and freed using the following functions.
3121 #include <isl/aff.h>
3122 __isl_give isl_pw_aff *isl_pw_aff_copy(
3123 __isl_keep isl_pw_aff *pwaff);
3124 __isl_null isl_pw_aff *isl_pw_aff_free(
3125 __isl_take isl_pw_aff *pwaff);
3126 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3127 __isl_keep isl_pw_multi_aff *pma);
3128 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
3129 __isl_take isl_pw_multi_aff *pma);
3131 #include <isl/polynomial.h>
3132 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3133 __isl_keep isl_pw_qpolynomial *pwqp);
3134 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
3135 __isl_take isl_pw_qpolynomial *pwqp);
3136 __isl_give isl_pw_qpolynomial_fold *
3137 isl_pw_qpolynomial_fold_copy(
3138 __isl_keep isl_pw_qpolynomial_fold *pwf);
3139 __isl_null isl_pw_qpolynomial_fold *
3140 isl_pw_qpolynomial_fold_free(
3141 __isl_take isl_pw_qpolynomial_fold *pwf);
3143 To iterate over the different cells of a piecewise expression,
3144 use the following functions.
3146 #include <isl/aff.h>
3147 isl_bool isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3148 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3149 isl_stat isl_pw_aff_foreach_piece(
3150 __isl_keep isl_pw_aff *pwaff,
3151 isl_stat (*fn)(__isl_take isl_set *set,
3152 __isl_take isl_aff *aff,
3153 void *user), void *user);
3154 int isl_pw_multi_aff_n_piece(
3155 __isl_keep isl_pw_multi_aff *pma);
3156 isl_stat isl_pw_multi_aff_foreach_piece(
3157 __isl_keep isl_pw_multi_aff *pma,
3158 isl_stat (*fn)(__isl_take isl_set *set,
3159 __isl_take isl_multi_aff *maff,
3160 void *user), void *user);
3162 #include <isl/polynomial.h>
3163 int isl_pw_qpolynomial_n_piece(
3164 __isl_keep isl_pw_qpolynomial *pwqp);
3165 isl_stat isl_pw_qpolynomial_foreach_piece(
3166 __isl_keep isl_pw_qpolynomial *pwqp,
3167 isl_stat (*fn)(__isl_take isl_set *set,
3168 __isl_take isl_qpolynomial *qp,
3169 void *user), void *user);
3170 isl_stat isl_pw_qpolynomial_foreach_lifted_piece(
3171 __isl_keep isl_pw_qpolynomial *pwqp,
3172 isl_stat (*fn)(__isl_take isl_set *set,
3173 __isl_take isl_qpolynomial *qp,
3174 void *user), void *user);
3175 int isl_pw_qpolynomial_fold_n_piece(
3176 __isl_keep isl_pw_qpolynomial_fold *pwf);
3177 isl_stat isl_pw_qpolynomial_fold_foreach_piece(
3178 __isl_keep isl_pw_qpolynomial_fold *pwf,
3179 isl_stat (*fn)(__isl_take isl_set *set,
3180 __isl_take isl_qpolynomial_fold *fold,
3181 void *user), void *user);
3182 isl_stat isl_pw_qpolynomial_fold_foreach_lifted_piece(
3183 __isl_keep isl_pw_qpolynomial_fold *pwf,
3184 isl_stat (*fn)(__isl_take isl_set *set,
3185 __isl_take isl_qpolynomial_fold *fold,
3186 void *user), void *user);
3188 As usual, the function C<fn> should return C<isl_stat_ok> on success
3189 and C<isl_stat_error> on failure. The difference between
3190 C<isl_pw_qpolynomial_foreach_piece> and
3191 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3192 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3193 compute unique representations for all existentially quantified
3194 variables and then turn these existentially quantified variables
3195 into extra set variables, adapting the associated quasipolynomial
3196 accordingly. This means that the C<set> passed to C<fn>
3197 will not have any existentially quantified variables, but that
3198 the dimensions of the sets may be different for different
3199 invocations of C<fn>.
3200 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
3201 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
3203 A piecewise expression consisting of the expressions at a given
3204 position of a piecewise multiple expression can be extracted
3205 using the following function.
3207 #include <isl/aff.h>
3208 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3209 __isl_keep isl_pw_multi_aff *pma, int pos);
3211 These expressions can be replaced using the following function.
3213 #include <isl/aff.h>
3214 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3215 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3216 __isl_take isl_pw_aff *pa);
3218 Note that there is a difference between C<isl_multi_pw_aff> and
3219 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
3220 affine expressions, while the second is a piecewise sequence
3221 of affine expressions. In particular, each of the piecewise
3222 affine expressions in an C<isl_multi_pw_aff> may have a different
3223 domain, while all multiple expressions associated to a cell
3224 in an C<isl_pw_multi_aff> have the same domain.
3225 It is possible to convert between the two, but when converting
3226 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
3227 of the result is the intersection of the domains of the input.
3228 The reverse conversion is exact.
3230 #include <isl/aff.h>
3231 __isl_give isl_pw_multi_aff *
3232 isl_pw_multi_aff_from_multi_pw_aff(
3233 __isl_take isl_multi_pw_aff *mpa);
3234 __isl_give isl_multi_pw_aff *
3235 isl_multi_pw_aff_from_pw_multi_aff(
3236 __isl_take isl_pw_multi_aff *pma);
3238 =head3 Union Expressions
3240 A union expression collects base expressions defined
3241 over different domains. The space of a union expression
3242 is that of the shared parameter space.
3244 The union expression types defined by C<isl>
3245 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
3246 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
3248 C<isl_union_pw_aff>,
3249 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>,
3250 there can be at most one base expression for a given domain space.
3252 C<isl_union_pw_multi_aff>,
3253 there can be multiple such expressions for a given domain space,
3254 but the domains of these expressions need to be disjoint.
3256 An empty union expression can be created using the following functions.
3258 #include <isl/aff.h>
3259 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
3260 __isl_take isl_space *space);
3261 __isl_give isl_union_pw_multi_aff *
3262 isl_union_pw_multi_aff_empty(
3263 __isl_take isl_space *space);
3265 #include <isl/polynomial.h>
3266 __isl_give isl_union_pw_qpolynomial *
3267 isl_union_pw_qpolynomial_zero(
3268 __isl_take isl_space *space);
3270 A union expression containing a single base expression
3271 can be created using the following functions.
3273 #include <isl/aff.h>
3274 __isl_give isl_union_pw_aff *
3275 isl_union_pw_aff_from_pw_aff(
3276 __isl_take isl_pw_aff *pa);
3277 __isl_give isl_union_pw_multi_aff *
3278 isl_union_pw_multi_aff_from_aff(
3279 __isl_take isl_aff *aff);
3280 __isl_give isl_union_pw_multi_aff *
3281 isl_union_pw_multi_aff_from_pw_multi_aff(
3282 __isl_take isl_pw_multi_aff *pma);
3284 #include <isl/polynomial.h>
3285 __isl_give isl_union_pw_qpolynomial *
3286 isl_union_pw_qpolynomial_from_pw_qpolynomial(
3287 __isl_take isl_pw_qpolynomial *pwqp);
3289 The following functions create a base expression on each
3290 of the sets in the union set and collect the results.
3292 #include <isl/aff.h>
3293 __isl_give isl_union_pw_multi_aff *
3294 isl_union_pw_multi_aff_from_union_pw_aff(
3295 __isl_take isl_union_pw_aff *upa);
3296 __isl_give isl_union_pw_aff *
3297 isl_union_pw_multi_aff_get_union_pw_aff(
3298 __isl_keep isl_union_pw_multi_aff *upma, int pos);
3299 __isl_give isl_union_pw_aff *
3300 isl_union_pw_aff_val_on_domain(
3301 __isl_take isl_union_set *domain,
3302 __isl_take isl_val *v);
3303 __isl_give isl_union_pw_multi_aff *
3304 isl_union_pw_multi_aff_multi_val_on_domain(
3305 __isl_take isl_union_set *domain,
3306 __isl_take isl_multi_val *mv);
3307 __isl_give isl_union_pw_aff *
3308 isl_union_pw_aff_param_on_domain_id(
3309 __isl_take isl_union_set *domain,
3310 __isl_take isl_id *id);
3312 The C<id> argument of C<isl_union_pw_aff_param_on_domain_id>
3313 is the identifier of a parameter that may or may not already
3314 be present in C<domain>.
3316 An C<isl_union_pw_aff> that is equal to a (parametric) affine
3318 expression on a given domain can be created using the following
3321 #include <isl/aff.h>
3322 __isl_give isl_union_pw_aff *
3323 isl_union_pw_aff_aff_on_domain(
3324 __isl_take isl_union_set *domain,
3325 __isl_take isl_aff *aff);
3326 __isl_give isl_union_pw_aff *
3327 isl_union_pw_aff_pw_aff_on_domain(
3328 __isl_take isl_union_set *domain,
3329 __isl_take isl_pw_aff *pa);
3331 A base expression can be added to a union expression using
3332 the following functions.
3334 #include <isl/aff.h>
3335 __isl_give isl_union_pw_aff *
3336 isl_union_pw_aff_add_pw_aff(
3337 __isl_take isl_union_pw_aff *upa,
3338 __isl_take isl_pw_aff *pa);
3339 __isl_give isl_union_pw_multi_aff *
3340 isl_union_pw_multi_aff_add_pw_multi_aff(
3341 __isl_take isl_union_pw_multi_aff *upma,
3342 __isl_take isl_pw_multi_aff *pma);
3344 #include <isl/polynomial.h>
3345 __isl_give isl_union_pw_qpolynomial *
3346 isl_union_pw_qpolynomial_add_pw_qpolynomial(
3347 __isl_take isl_union_pw_qpolynomial *upwqp,
3348 __isl_take isl_pw_qpolynomial *pwqp);
3350 Union expressions can be copied and freed using
3351 the following functions.
3353 #include <isl/aff.h>
3354 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
3355 __isl_keep isl_union_pw_aff *upa);
3356 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
3357 __isl_take isl_union_pw_aff *upa);
3358 __isl_give isl_union_pw_multi_aff *
3359 isl_union_pw_multi_aff_copy(
3360 __isl_keep isl_union_pw_multi_aff *upma);
3361 __isl_null isl_union_pw_multi_aff *
3362 isl_union_pw_multi_aff_free(
3363 __isl_take isl_union_pw_multi_aff *upma);
3365 #include <isl/polynomial.h>
3366 __isl_give isl_union_pw_qpolynomial *
3367 isl_union_pw_qpolynomial_copy(
3368 __isl_keep isl_union_pw_qpolynomial *upwqp);
3369 __isl_null isl_union_pw_qpolynomial *
3370 isl_union_pw_qpolynomial_free(
3371 __isl_take isl_union_pw_qpolynomial *upwqp);
3372 __isl_give isl_union_pw_qpolynomial_fold *
3373 isl_union_pw_qpolynomial_fold_copy(
3374 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3375 __isl_null isl_union_pw_qpolynomial_fold *
3376 isl_union_pw_qpolynomial_fold_free(
3377 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3379 To iterate over the base expressions in a union expression,
3380 use the following functions.
3382 #include <isl/aff.h>
3383 int isl_union_pw_aff_n_pw_aff(
3384 __isl_keep isl_union_pw_aff *upa);
3385 isl_stat isl_union_pw_aff_foreach_pw_aff(
3386 __isl_keep isl_union_pw_aff *upa,
3387 isl_stat (*fn)(__isl_take isl_pw_aff *pa,
3388 void *user), void *user);
3389 int isl_union_pw_multi_aff_n_pw_multi_aff(
3390 __isl_keep isl_union_pw_multi_aff *upma);
3391 isl_stat isl_union_pw_multi_aff_foreach_pw_multi_aff(
3392 __isl_keep isl_union_pw_multi_aff *upma,
3393 isl_stat (*fn)(__isl_take isl_pw_multi_aff *pma,
3394 void *user), void *user);
3396 #include <isl/polynomial.h>
3397 int isl_union_pw_qpolynomial_n_pw_qpolynomial(
3398 __isl_keep isl_union_pw_qpolynomial *upwqp);
3399 isl_stat isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3400 __isl_keep isl_union_pw_qpolynomial *upwqp,
3401 isl_stat (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
3402 void *user), void *user);
3403 int isl_union_pw_qpolynomial_fold_n_pw_qpolynomial_fold(
3404 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3405 isl_stat isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3406 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3407 isl_stat (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3408 void *user), void *user);
3410 To extract the base expression in a given space from a union, use
3411 the following functions.
3413 #include <isl/aff.h>
3414 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
3415 __isl_keep isl_union_pw_aff *upa,
3416 __isl_take isl_space *space);
3417 __isl_give isl_pw_multi_aff *
3418 isl_union_pw_multi_aff_extract_pw_multi_aff(
3419 __isl_keep isl_union_pw_multi_aff *upma,
3420 __isl_take isl_space *space);
3422 #include <isl/polynomial.h>
3423 __isl_give isl_pw_qpolynomial *
3424 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3425 __isl_keep isl_union_pw_qpolynomial *upwqp,
3426 __isl_take isl_space *space);
3428 =head2 Input and Output
3430 For set and relation,
3431 C<isl> supports its own input/output format, which is similar
3432 to the C<Omega> format, but also supports the C<PolyLib> format
3434 For other object types, typically only an C<isl> format is supported.
3436 =head3 C<isl> format
3438 The C<isl> format is similar to that of C<Omega>, but has a different
3439 syntax for describing the parameters and allows for the definition
3440 of an existentially quantified variable as the integer division
3441 of an affine expression.
3442 For example, the set of integers C<i> between C<0> and C<n>
3443 such that C<i % 10 <= 6> can be described as
3445 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
3448 A set or relation can have several disjuncts, separated
3449 by the keyword C<or>. Each disjunct is either a conjunction
3450 of constraints or a projection (C<exists>) of a conjunction
3451 of constraints. The constraints are separated by the keyword
3454 =head3 C<PolyLib> format
3456 If the represented set is a union, then the first line
3457 contains a single number representing the number of disjuncts.
3458 Otherwise, a line containing the number C<1> is optional.
3460 Each disjunct is represented by a matrix of constraints.
3461 The first line contains two numbers representing
3462 the number of rows and columns,
3463 where the number of rows is equal to the number of constraints
3464 and the number of columns is equal to two plus the number of variables.
3465 The following lines contain the actual rows of the constraint matrix.
3466 In each row, the first column indicates whether the constraint
3467 is an equality (C<0>) or inequality (C<1>). The final column
3468 corresponds to the constant term.
3470 If the set is parametric, then the coefficients of the parameters
3471 appear in the last columns before the constant column.
3472 The coefficients of any existentially quantified variables appear
3473 between those of the set variables and those of the parameters.
3475 =head3 Extended C<PolyLib> format
3477 The extended C<PolyLib> format is nearly identical to the
3478 C<PolyLib> format. The only difference is that the line
3479 containing the number of rows and columns of a constraint matrix
3480 also contains four additional numbers:
3481 the number of output dimensions, the number of input dimensions,
3482 the number of local dimensions (i.e., the number of existentially
3483 quantified variables) and the number of parameters.
3484 For sets, the number of ``output'' dimensions is equal
3485 to the number of set dimensions, while the number of ``input''
3490 Objects can be read from input using the following functions.
3492 #include <isl/val.h>
3493 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
3495 __isl_give isl_multi_val *isl_multi_val_read_from_str(
3496 isl_ctx *ctx, const char *str);
3498 #include <isl/set.h>
3499 __isl_give isl_basic_set *isl_basic_set_read_from_file(
3500 isl_ctx *ctx, FILE *input);
3501 __isl_give isl_basic_set *isl_basic_set_read_from_str(
3502 isl_ctx *ctx, const char *str);
3503 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
3505 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
3508 #include <isl/map.h>
3509 __isl_give isl_basic_map *isl_basic_map_read_from_file(
3510 isl_ctx *ctx, FILE *input);
3511 __isl_give isl_basic_map *isl_basic_map_read_from_str(
3512 isl_ctx *ctx, const char *str);
3513 __isl_give isl_map *isl_map_read_from_file(
3514 isl_ctx *ctx, FILE *input);
3515 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
3518 #include <isl/union_set.h>
3519 __isl_give isl_union_set *isl_union_set_read_from_file(
3520 isl_ctx *ctx, FILE *input);
3521 __isl_give isl_union_set *isl_union_set_read_from_str(
3522 isl_ctx *ctx, const char *str);
3524 #include <isl/union_map.h>
3525 __isl_give isl_union_map *isl_union_map_read_from_file(
3526 isl_ctx *ctx, FILE *input);
3527 __isl_give isl_union_map *isl_union_map_read_from_str(
3528 isl_ctx *ctx, const char *str);
3530 #include <isl/aff.h>
3531 __isl_give isl_aff *isl_aff_read_from_str(
3532 isl_ctx *ctx, const char *str);
3533 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3534 isl_ctx *ctx, const char *str);
3535 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3536 isl_ctx *ctx, const char *str);
3537 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3538 isl_ctx *ctx, const char *str);
3539 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
3540 isl_ctx *ctx, const char *str);
3541 __isl_give isl_union_pw_aff *
3542 isl_union_pw_aff_read_from_str(
3543 isl_ctx *ctx, const char *str);
3544 __isl_give isl_union_pw_multi_aff *
3545 isl_union_pw_multi_aff_read_from_str(
3546 isl_ctx *ctx, const char *str);
3547 __isl_give isl_multi_union_pw_aff *
3548 isl_multi_union_pw_aff_read_from_str(
3549 isl_ctx *ctx, const char *str);
3551 #include <isl/polynomial.h>
3552 __isl_give isl_union_pw_qpolynomial *
3553 isl_union_pw_qpolynomial_read_from_str(
3554 isl_ctx *ctx, const char *str);
3556 For sets and relations,
3557 the input format is autodetected and may be either the C<PolyLib> format
3558 or the C<isl> format.
3562 Before anything can be printed, an C<isl_printer> needs to
3565 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
3567 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
3568 __isl_null isl_printer *isl_printer_free(
3569 __isl_take isl_printer *printer);
3571 C<isl_printer_to_file> prints to the given file, while
3572 C<isl_printer_to_str> prints to a string that can be extracted
3573 using the following function.
3575 #include <isl/printer.h>
3576 __isl_give char *isl_printer_get_str(
3577 __isl_keep isl_printer *printer);
3579 The printer can be inspected using the following functions.
3581 FILE *isl_printer_get_file(
3582 __isl_keep isl_printer *printer);
3583 int isl_printer_get_output_format(
3584 __isl_keep isl_printer *p);
3585 int isl_printer_get_yaml_style(__isl_keep isl_printer *p);
3587 The behavior of the printer can be modified in various ways
3589 __isl_give isl_printer *isl_printer_set_output_format(
3590 __isl_take isl_printer *p, int output_format);
3591 __isl_give isl_printer *isl_printer_set_indent(
3592 __isl_take isl_printer *p, int indent);
3593 __isl_give isl_printer *isl_printer_set_indent_prefix(
3594 __isl_take isl_printer *p, const char *prefix);
3595 __isl_give isl_printer *isl_printer_indent(
3596 __isl_take isl_printer *p, int indent);
3597 __isl_give isl_printer *isl_printer_set_prefix(
3598 __isl_take isl_printer *p, const char *prefix);
3599 __isl_give isl_printer *isl_printer_set_suffix(
3600 __isl_take isl_printer *p, const char *suffix);
3601 __isl_give isl_printer *isl_printer_set_yaml_style(
3602 __isl_take isl_printer *p, int yaml_style);
3604 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
3605 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
3606 and defaults to C<ISL_FORMAT_ISL>.
3607 Each line in the output is prefixed by C<indent_prefix>,
3608 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
3609 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
3610 In the C<PolyLib> format output,
3611 the coefficients of the existentially quantified variables
3612 appear between those of the set variables and those
3614 The function C<isl_printer_indent> increases the indentation
3615 by the specified amount (which may be negative).
3616 The YAML style may be either C<ISL_YAML_STYLE_BLOCK> or
3617 C<ISL_YAML_STYLE_FLOW> and when we are printing something
3620 To actually print something, use
3622 #include <isl/printer.h>
3623 __isl_give isl_printer *isl_printer_print_double(
3624 __isl_take isl_printer *p, double d);
3626 #include <isl/val.h>
3627 __isl_give isl_printer *isl_printer_print_val(
3628 __isl_take isl_printer *p, __isl_keep isl_val *v);
3630 #include <isl/set.h>
3631 __isl_give isl_printer *isl_printer_print_basic_set(
3632 __isl_take isl_printer *printer,
3633 __isl_keep isl_basic_set *bset);
3634 __isl_give isl_printer *isl_printer_print_set(
3635 __isl_take isl_printer *printer,
3636 __isl_keep isl_set *set);
3638 #include <isl/map.h>
3639 __isl_give isl_printer *isl_printer_print_basic_map(
3640 __isl_take isl_printer *printer,
3641 __isl_keep isl_basic_map *bmap);
3642 __isl_give isl_printer *isl_printer_print_map(
3643 __isl_take isl_printer *printer,
3644 __isl_keep isl_map *map);
3646 #include <isl/union_set.h>
3647 __isl_give isl_printer *isl_printer_print_union_set(
3648 __isl_take isl_printer *p,
3649 __isl_keep isl_union_set *uset);
3651 #include <isl/union_map.h>
3652 __isl_give isl_printer *isl_printer_print_union_map(
3653 __isl_take isl_printer *p,
3654 __isl_keep isl_union_map *umap);
3656 #include <isl/val.h>
3657 __isl_give isl_printer *isl_printer_print_multi_val(
3658 __isl_take isl_printer *p,
3659 __isl_keep isl_multi_val *mv);
3661 #include <isl/aff.h>
3662 __isl_give isl_printer *isl_printer_print_aff(
3663 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3664 __isl_give isl_printer *isl_printer_print_multi_aff(
3665 __isl_take isl_printer *p,
3666 __isl_keep isl_multi_aff *maff);
3667 __isl_give isl_printer *isl_printer_print_pw_aff(
3668 __isl_take isl_printer *p,
3669 __isl_keep isl_pw_aff *pwaff);
3670 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3671 __isl_take isl_printer *p,
3672 __isl_keep isl_pw_multi_aff *pma);
3673 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3674 __isl_take isl_printer *p,
3675 __isl_keep isl_multi_pw_aff *mpa);
3676 __isl_give isl_printer *isl_printer_print_union_pw_aff(
3677 __isl_take isl_printer *p,
3678 __isl_keep isl_union_pw_aff *upa);
3679 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3680 __isl_take isl_printer *p,
3681 __isl_keep isl_union_pw_multi_aff *upma);
3682 __isl_give isl_printer *
3683 isl_printer_print_multi_union_pw_aff(
3684 __isl_take isl_printer *p,
3685 __isl_keep isl_multi_union_pw_aff *mupa);
3687 #include <isl/polynomial.h>
3688 __isl_give isl_printer *isl_printer_print_qpolynomial(
3689 __isl_take isl_printer *p,
3690 __isl_keep isl_qpolynomial *qp);
3691 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3692 __isl_take isl_printer *p,
3693 __isl_keep isl_pw_qpolynomial *pwqp);
3694 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3695 __isl_take isl_printer *p,
3696 __isl_keep isl_union_pw_qpolynomial *upwqp);
3698 __isl_give isl_printer *
3699 isl_printer_print_pw_qpolynomial_fold(
3700 __isl_take isl_printer *p,
3701 __isl_keep isl_pw_qpolynomial_fold *pwf);
3702 __isl_give isl_printer *
3703 isl_printer_print_union_pw_qpolynomial_fold(
3704 __isl_take isl_printer *p,
3705 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3707 For C<isl_printer_print_qpolynomial>,
3708 C<isl_printer_print_pw_qpolynomial> and
3709 C<isl_printer_print_pw_qpolynomial_fold>,
3710 the output format of the printer
3711 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3712 For C<isl_printer_print_union_pw_qpolynomial> and
3713 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
3715 In case of printing in C<ISL_FORMAT_C>, the user may want
3716 to set the names of all dimensions first.
3718 C<isl> also provides limited support for printing YAML documents,
3719 just enough for the internal use for printing such documents.
3721 #include <isl/printer.h>
3722 __isl_give isl_printer *isl_printer_yaml_start_mapping(
3723 __isl_take isl_printer *p);
3724 __isl_give isl_printer *isl_printer_yaml_end_mapping(
3725 __isl_take isl_printer *p);
3726 __isl_give isl_printer *isl_printer_yaml_start_sequence(
3727 __isl_take isl_printer *p);
3728 __isl_give isl_printer *isl_printer_yaml_end_sequence(
3729 __isl_take isl_printer *p);
3730 __isl_give isl_printer *isl_printer_yaml_next(
3731 __isl_take isl_printer *p);
3733 A document is started by a call to either
3734 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3735 Anything printed to the printer after such a call belong to the
3736 first key of the mapping or the first element in the sequence.
3737 The function C<isl_printer_yaml_next> moves to the value if
3738 we are currently printing a mapping key, the next key if we
3739 are printing a value or the next element if we are printing
3740 an element in a sequence.
3741 Nested mappings and sequences are initiated by the same
3742 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3743 Each call to these functions needs to have a corresponding call to
3744 C<isl_printer_yaml_end_mapping> or C<isl_printer_yaml_end_sequence>.
3746 When called on a file printer, the following function flushes
3747 the file. When called on a string printer, the buffer is cleared.
3749 __isl_give isl_printer *isl_printer_flush(
3750 __isl_take isl_printer *p);
3752 The following functions allow the user to attach
3753 notes to a printer in order to keep track of additional state.
3755 #include <isl/printer.h>
3756 isl_bool isl_printer_has_note(__isl_keep isl_printer *p,
3757 __isl_keep isl_id *id);
3758 __isl_give isl_id *isl_printer_get_note(
3759 __isl_keep isl_printer *p, __isl_take isl_id *id);
3760 __isl_give isl_printer *isl_printer_set_note(
3761 __isl_take isl_printer *p,
3762 __isl_take isl_id *id, __isl_take isl_id *note);
3764 C<isl_printer_set_note> associates the given note to the given
3765 identifier in the printer.
3766 C<isl_printer_get_note> retrieves a note associated to an
3768 C<isl_printer_has_note> checks if there is such a note.
3769 C<isl_printer_get_note> fails if the requested note does not exist.
3771 Alternatively, a string representation can be obtained
3772 directly using the following functions, which always print
3776 __isl_give char *isl_id_to_str(
3777 __isl_keep isl_id *id);
3779 #include <isl/space.h>
3780 __isl_give char *isl_space_to_str(
3781 __isl_keep isl_space *space);
3783 #include <isl/val.h>
3784 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
3785 __isl_give char *isl_multi_val_to_str(
3786 __isl_keep isl_multi_val *mv);
3788 #include <isl/set.h>
3789 __isl_give char *isl_basic_set_to_str(
3790 __isl_keep isl_basic_set *bset);
3791 __isl_give char *isl_set_to_str(
3792 __isl_keep isl_set *set);
3794 #include <isl/union_set.h>
3795 __isl_give char *isl_union_set_to_str(
3796 __isl_keep isl_union_set *uset);
3798 #include <isl/map.h>
3799 __isl_give char *isl_basic_map_to_str(
3800 __isl_keep isl_basic_map *bmap);
3801 __isl_give char *isl_map_to_str(
3802 __isl_keep isl_map *map);
3804 #include <isl/union_map.h>
3805 __isl_give char *isl_union_map_to_str(
3806 __isl_keep isl_union_map *umap);
3808 #include <isl/aff.h>
3809 __isl_give char *isl_aff_to_str(__isl_keep isl_aff *aff);
3810 __isl_give char *isl_pw_aff_to_str(
3811 __isl_keep isl_pw_aff *pa);
3812 __isl_give char *isl_multi_aff_to_str(
3813 __isl_keep isl_multi_aff *ma);
3814 __isl_give char *isl_pw_multi_aff_to_str(
3815 __isl_keep isl_pw_multi_aff *pma);
3816 __isl_give char *isl_multi_pw_aff_to_str(
3817 __isl_keep isl_multi_pw_aff *mpa);
3818 __isl_give char *isl_union_pw_aff_to_str(
3819 __isl_keep isl_union_pw_aff *upa);
3820 __isl_give char *isl_union_pw_multi_aff_to_str(
3821 __isl_keep isl_union_pw_multi_aff *upma);
3822 __isl_give char *isl_multi_union_pw_aff_to_str(
3823 __isl_keep isl_multi_union_pw_aff *mupa);
3825 #include <isl/point.h>
3826 __isl_give char *isl_point_to_str(
3827 __isl_keep isl_point *pnt);
3829 #include <isl/polynomial.h>
3830 __isl_give char *isl_pw_qpolynomial_to_str(
3831 __isl_keep isl_pw_qpolynomial *pwqp);
3832 __isl_give char *isl_union_pw_qpolynomial_to_str(
3833 __isl_keep isl_union_pw_qpolynomial *upwqp);
3837 =head3 Unary Properties
3843 The following functions test whether the given set or relation
3844 contains any integer points. The ``plain'' variants do not perform
3845 any computations, but simply check if the given set or relation
3846 is already known to be empty.
3848 #include <isl/set.h>
3849 isl_bool isl_basic_set_plain_is_empty(
3850 __isl_keep isl_basic_set *bset);
3851 isl_bool isl_basic_set_is_empty(
3852 __isl_keep isl_basic_set *bset);
3853 isl_bool isl_set_plain_is_empty(
3854 __isl_keep isl_set *set);
3855 isl_bool isl_set_is_empty(__isl_keep isl_set *set);
3857 #include <isl/union_set.h>
3858 isl_bool isl_union_set_is_empty(
3859 __isl_keep isl_union_set *uset);
3861 #include <isl/map.h>
3862 isl_bool isl_basic_map_plain_is_empty(
3863 __isl_keep isl_basic_map *bmap);
3864 isl_bool isl_basic_map_is_empty(
3865 __isl_keep isl_basic_map *bmap);
3866 isl_bool isl_map_plain_is_empty(
3867 __isl_keep isl_map *map);
3868 isl_bool isl_map_is_empty(__isl_keep isl_map *map);
3870 #include <isl/union_map.h>
3871 isl_bool isl_union_map_plain_is_empty(
3872 __isl_keep isl_union_map *umap);
3873 isl_bool isl_union_map_is_empty(
3874 __isl_keep isl_union_map *umap);
3876 =item * Universality
3878 isl_bool isl_basic_set_plain_is_universe(
3879 __isl_keep isl_basic_set *bset);
3880 isl_bool isl_basic_set_is_universe(
3881 __isl_keep isl_basic_set *bset);
3882 isl_bool isl_basic_map_plain_is_universe(
3883 __isl_keep isl_basic_map *bmap);
3884 isl_bool isl_basic_map_is_universe(
3885 __isl_keep isl_basic_map *bmap);
3886 isl_bool isl_set_plain_is_universe(
3887 __isl_keep isl_set *set);
3888 isl_bool isl_map_plain_is_universe(
3889 __isl_keep isl_map *map);
3891 =item * Single-valuedness
3893 #include <isl/set.h>
3894 isl_bool isl_set_is_singleton(__isl_keep isl_set *set);
3896 #include <isl/map.h>
3897 isl_bool isl_basic_map_is_single_valued(
3898 __isl_keep isl_basic_map *bmap);
3899 isl_bool isl_map_plain_is_single_valued(
3900 __isl_keep isl_map *map);
3901 isl_bool isl_map_is_single_valued(__isl_keep isl_map *map);
3903 #include <isl/union_map.h>
3904 isl_bool isl_union_map_is_single_valued(
3905 __isl_keep isl_union_map *umap);
3909 isl_bool isl_map_plain_is_injective(
3910 __isl_keep isl_map *map);
3911 isl_bool isl_map_is_injective(
3912 __isl_keep isl_map *map);
3913 isl_bool isl_union_map_plain_is_injective(
3914 __isl_keep isl_union_map *umap);
3915 isl_bool isl_union_map_is_injective(
3916 __isl_keep isl_union_map *umap);
3920 isl_bool isl_map_is_bijective(
3921 __isl_keep isl_map *map);
3922 isl_bool isl_union_map_is_bijective(
3923 __isl_keep isl_union_map *umap);
3927 The following functions test whether the given relation
3928 only maps elements to themselves.
3930 #include <isl/map.h>
3931 isl_bool isl_map_is_identity(
3932 __isl_keep isl_map *map);
3934 #include <isl/union_map.h>
3935 isl_bool isl_union_map_is_identity(
3936 __isl_keep isl_union_map *umap);
3940 __isl_give isl_val *
3941 isl_basic_map_plain_get_val_if_fixed(
3942 __isl_keep isl_basic_map *bmap,
3943 enum isl_dim_type type, unsigned pos);
3944 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
3945 __isl_keep isl_set *set,
3946 enum isl_dim_type type, unsigned pos);
3947 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
3948 __isl_keep isl_map *map,
3949 enum isl_dim_type type, unsigned pos);
3951 If the set or relation obviously lies on a hyperplane where the given dimension
3952 has a fixed value, then return that value.
3953 Otherwise return NaN.
3957 isl_stat isl_set_dim_residue_class_val(
3958 __isl_keep isl_set *set,
3959 int pos, __isl_give isl_val **modulo,
3960 __isl_give isl_val **residue);
3962 Check if the values of the given set dimension are equal to a fixed
3963 value modulo some integer value. If so, assign the modulo to C<*modulo>
3964 and the fixed value to C<*residue>. If the given dimension attains only
3965 a single value, then assign C<0> to C<*modulo> and the fixed value to
3967 If the dimension does not attain only a single value and if no modulo
3968 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
3970 #include <isl/set.h>
3971 __isl_give isl_stride_info *isl_set_get_stride_info(
3972 __isl_keep isl_set *set, int pos);
3973 __isl_give isl_val *isl_set_get_stride(
3974 __isl_keep isl_set *set, int pos);
3976 Check if the values of the given set dimension are equal to
3977 some affine expression of the other dimensions (the offset)
3978 modulo some integer stride.
3979 If no more specific information can be found, then the stride
3980 is taken to be one and the offset is taken to be the zero expression.
3981 The function C<isl_set_get_stride_info> performs the same
3982 computation but only returns the stride.
3984 the stride and offset can be extracted from the returned object
3985 using the following functions.
3987 #include <isl/set.h>
3988 __isl_give isl_val *isl_stride_info_get_stride(
3989 __isl_keep isl_stride_info *si);
3990 __isl_give isl_aff *isl_stride_info_get_offset(
3991 __isl_keep isl_stride_info *si);
3993 The stride info object can be released using the following function.
3995 #include <isl/set.h>
3996 __isl_null isl_stride_info *isl_stride_info_free(
3997 __isl_take isl_stride_info *si);
4001 To check whether the description of a set, relation or function depends
4002 on one or more given dimensions,
4003 the following functions can be used.
4005 #include <isl/constraint.h>
4006 isl_bool isl_constraint_involves_dims(
4007 __isl_keep isl_constraint *constraint,
4008 enum isl_dim_type type, unsigned first, unsigned n);
4010 #include <isl/set.h>
4011 isl_bool isl_basic_set_involves_dims(
4012 __isl_keep isl_basic_set *bset,
4013 enum isl_dim_type type, unsigned first, unsigned n);
4014 isl_bool isl_set_involves_dims(__isl_keep isl_set *set,
4015 enum isl_dim_type type, unsigned first, unsigned n);
4017 #include <isl/map.h>
4018 isl_bool isl_basic_map_involves_dims(
4019 __isl_keep isl_basic_map *bmap,
4020 enum isl_dim_type type, unsigned first, unsigned n);
4021 isl_bool isl_map_involves_dims(__isl_keep isl_map *map,
4022 enum isl_dim_type type, unsigned first, unsigned n);
4024 #include <isl/union_map.h>
4025 isl_bool isl_union_map_involves_dims(
4026 __isl_keep isl_union_map *umap,
4027 enum isl_dim_type type, unsigned first, unsigned n);
4029 #include <isl/aff.h>
4030 isl_bool isl_aff_involves_dims(__isl_keep isl_aff *aff,
4031 enum isl_dim_type type, unsigned first, unsigned n);
4032 isl_bool isl_pw_aff_involves_dims(
4033 __isl_keep isl_pw_aff *pwaff,
4034 enum isl_dim_type type, unsigned first, unsigned n);
4035 isl_bool isl_multi_aff_involves_dims(
4036 __isl_keep isl_multi_aff *ma,
4037 enum isl_dim_type type, unsigned first, unsigned n);
4038 isl_bool isl_multi_pw_aff_involves_dims(
4039 __isl_keep isl_multi_pw_aff *mpa,
4040 enum isl_dim_type type, unsigned first, unsigned n);
4042 #include <isl/polynomial.h>
4043 isl_bool isl_qpolynomial_involves_dims(
4044 __isl_keep isl_qpolynomial *qp,
4045 enum isl_dim_type type, unsigned first, unsigned n);
4047 Similarly, the following functions can be used to check whether
4048 a given dimension is involved in any lower or upper bound.
4050 #include <isl/set.h>
4051 isl_bool isl_set_dim_has_any_lower_bound(
4052 __isl_keep isl_set *set,
4053 enum isl_dim_type type, unsigned pos);
4054 isl_bool isl_set_dim_has_any_upper_bound(
4055 __isl_keep isl_set *set,
4056 enum isl_dim_type type, unsigned pos);
4058 Note that these functions return true even if there is a bound on
4059 the dimension on only some of the basic sets of C<set>.
4060 To check if they have a bound for all of the basic sets in C<set>,
4061 use the following functions instead.
4063 #include <isl/set.h>
4064 isl_bool isl_set_dim_has_lower_bound(
4065 __isl_keep isl_set *set,
4066 enum isl_dim_type type, unsigned pos);
4067 isl_bool isl_set_dim_has_upper_bound(
4068 __isl_keep isl_set *set,
4069 enum isl_dim_type type, unsigned pos);
4073 To check whether a set is a parameter domain, use this function:
4075 isl_bool isl_set_is_params(__isl_keep isl_set *set);
4076 isl_bool isl_union_set_is_params(
4077 __isl_keep isl_union_set *uset);
4081 The following functions check whether the space of the given
4082 (basic) set or relation domain and/or range is a wrapped relation.
4084 #include <isl/space.h>
4085 isl_bool isl_space_is_wrapping(
4086 __isl_keep isl_space *space);
4087 isl_bool isl_space_domain_is_wrapping(
4088 __isl_keep isl_space *space);
4089 isl_bool isl_space_range_is_wrapping(
4090 __isl_keep isl_space *space);
4091 isl_bool isl_space_is_product(
4092 __isl_keep isl_space *space);
4094 #include <isl/set.h>
4095 isl_bool isl_basic_set_is_wrapping(
4096 __isl_keep isl_basic_set *bset);
4097 isl_bool isl_set_is_wrapping(__isl_keep isl_set *set);
4099 #include <isl/map.h>
4100 isl_bool isl_map_domain_is_wrapping(
4101 __isl_keep isl_map *map);
4102 isl_bool isl_map_range_is_wrapping(
4103 __isl_keep isl_map *map);
4104 isl_bool isl_map_is_product(__isl_keep isl_map *map);
4106 #include <isl/val.h>
4107 isl_bool isl_multi_val_range_is_wrapping(
4108 __isl_keep isl_multi_val *mv);
4110 #include <isl/aff.h>
4111 isl_bool isl_multi_aff_range_is_wrapping(
4112 __isl_keep isl_multi_aff *ma);
4113 isl_bool isl_multi_pw_aff_range_is_wrapping(
4114 __isl_keep isl_multi_pw_aff *mpa);
4115 isl_bool isl_multi_union_pw_aff_range_is_wrapping(
4116 __isl_keep isl_multi_union_pw_aff *mupa);
4118 The input to C<isl_space_is_wrapping> should
4119 be the space of a set, while that of
4120 C<isl_space_domain_is_wrapping> and
4121 C<isl_space_range_is_wrapping> should be the space of a relation.
4122 The input to C<isl_space_is_product> can be either the space
4123 of a set or that of a binary relation.
4124 In case the input is the space of a binary relation, it checks
4125 whether both domain and range are wrapping.
4127 =item * Internal Product
4129 isl_bool isl_basic_map_can_zip(
4130 __isl_keep isl_basic_map *bmap);
4131 isl_bool isl_map_can_zip(__isl_keep isl_map *map);
4133 Check whether the product of domain and range of the given relation
4135 i.e., whether both domain and range are nested relations.
4139 #include <isl/space.h>
4140 isl_bool isl_space_can_curry(
4141 __isl_keep isl_space *space);
4143 #include <isl/map.h>
4144 isl_bool isl_basic_map_can_curry(
4145 __isl_keep isl_basic_map *bmap);
4146 isl_bool isl_map_can_curry(__isl_keep isl_map *map);
4148 Check whether the domain of the (basic) relation is a wrapped relation.
4150 #include <isl/space.h>
4151 __isl_give isl_space *isl_space_uncurry(
4152 __isl_take isl_space *space);
4154 #include <isl/map.h>
4155 isl_bool isl_basic_map_can_uncurry(
4156 __isl_keep isl_basic_map *bmap);
4157 isl_bool isl_map_can_uncurry(__isl_keep isl_map *map);
4159 Check whether the range of the (basic) relation is a wrapped relation.
4161 #include <isl/space.h>
4162 isl_bool isl_space_can_range_curry(
4163 __isl_keep isl_space *space);
4165 #include <isl/map.h>
4166 isl_bool isl_map_can_range_curry(
4167 __isl_keep isl_map *map);
4169 Check whether the domain of the relation wrapped in the range of
4170 the input is itself a wrapped relation.
4172 =item * Special Values
4174 #include <isl/aff.h>
4175 isl_bool isl_aff_is_cst(__isl_keep isl_aff *aff);
4176 isl_bool isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
4177 isl_bool isl_multi_pw_aff_is_cst(
4178 __isl_keep isl_multi_pw_aff *mpa);
4180 Check whether the given expression is a constant.
4182 #include <isl/val.h>
4183 isl_bool isl_multi_val_involves_nan(
4184 __isl_keep isl_multi_val *mv);
4186 #include <isl/aff.h>
4187 isl_bool isl_aff_is_nan(__isl_keep isl_aff *aff);
4188 isl_bool isl_multi_aff_involves_nan(
4189 __isl_keep isl_multi_aff *ma);
4190 isl_bool isl_pw_aff_involves_nan(
4191 __isl_keep isl_pw_aff *pa);
4192 isl_bool isl_pw_multi_aff_involves_nan(
4193 __isl_keep isl_pw_multi_aff *pma);
4194 isl_bool isl_multi_pw_aff_involves_nan(
4195 __isl_keep isl_multi_pw_aff *mpa);
4196 isl_bool isl_union_pw_aff_involves_nan(
4197 __isl_keep isl_union_pw_aff *upa);
4198 isl_bool isl_union_pw_multi_aff_involves_nan(
4199 __isl_keep isl_union_pw_multi_aff *upma);
4200 isl_bool isl_multi_union_pw_aff_involves_nan(
4201 __isl_keep isl_multi_union_pw_aff *mupa);
4203 #include <isl/polynomial.h>
4204 isl_bool isl_qpolynomial_is_nan(
4205 __isl_keep isl_qpolynomial *qp);
4206 isl_bool isl_qpolynomial_fold_is_nan(
4207 __isl_keep isl_qpolynomial_fold *fold);
4208 isl_bool isl_pw_qpolynomial_involves_nan(
4209 __isl_keep isl_pw_qpolynomial *pwqp);
4210 isl_bool isl_pw_qpolynomial_fold_involves_nan(
4211 __isl_keep isl_pw_qpolynomial_fold *pwf);
4212 isl_bool isl_union_pw_qpolynomial_involves_nan(
4213 __isl_keep isl_union_pw_qpolynomial *upwqp);
4214 isl_bool isl_union_pw_qpolynomial_fold_involves_nan(
4215 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4217 Check whether the given expression is equal to or involves NaN.
4219 #include <isl/aff.h>
4220 isl_bool isl_aff_plain_is_zero(
4221 __isl_keep isl_aff *aff);
4223 Check whether the affine expression is obviously zero.
4227 =head3 Binary Properties
4233 The following functions check whether two objects
4234 represent the same set, relation or function.
4235 The C<plain> variants only return true if the objects
4236 are obviously the same. That is, they may return false
4237 even if the objects are the same, but they will never
4238 return true if the objects are not the same.
4240 #include <isl/set.h>
4241 isl_bool isl_basic_set_plain_is_equal(
4242 __isl_keep isl_basic_set *bset1,
4243 __isl_keep isl_basic_set *bset2);
4244 isl_bool isl_basic_set_is_equal(
4245 __isl_keep isl_basic_set *bset1,
4246 __isl_keep isl_basic_set *bset2);
4247 isl_bool isl_set_plain_is_equal(
4248 __isl_keep isl_set *set1,
4249 __isl_keep isl_set *set2);
4250 isl_bool isl_set_is_equal(__isl_keep isl_set *set1,
4251 __isl_keep isl_set *set2);
4253 #include <isl/map.h>
4254 isl_bool isl_basic_map_is_equal(
4255 __isl_keep isl_basic_map *bmap1,
4256 __isl_keep isl_basic_map *bmap2);
4257 isl_bool isl_map_is_equal(__isl_keep isl_map *map1,
4258 __isl_keep isl_map *map2);
4259 isl_bool isl_map_plain_is_equal(
4260 __isl_keep isl_map *map1,
4261 __isl_keep isl_map *map2);
4263 #include <isl/union_set.h>
4264 isl_bool isl_union_set_is_equal(
4265 __isl_keep isl_union_set *uset1,
4266 __isl_keep isl_union_set *uset2);
4268 #include <isl/union_map.h>
4269 isl_bool isl_union_map_is_equal(
4270 __isl_keep isl_union_map *umap1,
4271 __isl_keep isl_union_map *umap2);
4273 #include <isl/aff.h>
4274 isl_bool isl_aff_plain_is_equal(
4275 __isl_keep isl_aff *aff1,
4276 __isl_keep isl_aff *aff2);
4277 isl_bool isl_multi_aff_plain_is_equal(
4278 __isl_keep isl_multi_aff *maff1,
4279 __isl_keep isl_multi_aff *maff2);
4280 isl_bool isl_pw_aff_plain_is_equal(
4281 __isl_keep isl_pw_aff *pwaff1,
4282 __isl_keep isl_pw_aff *pwaff2);
4283 isl_bool isl_pw_aff_is_equal(
4284 __isl_keep isl_pw_aff *pa1,
4285 __isl_keep isl_pw_aff *pa2);
4286 isl_bool isl_pw_multi_aff_plain_is_equal(
4287 __isl_keep isl_pw_multi_aff *pma1,
4288 __isl_keep isl_pw_multi_aff *pma2);
4289 isl_bool isl_pw_multi_aff_is_equal(
4290 __isl_keep isl_pw_multi_aff *pma1,
4291 __isl_keep isl_pw_multi_aff *pma2);
4292 isl_bool isl_multi_pw_aff_plain_is_equal(
4293 __isl_keep isl_multi_pw_aff *mpa1,
4294 __isl_keep isl_multi_pw_aff *mpa2);
4295 isl_bool isl_multi_pw_aff_is_equal(
4296 __isl_keep isl_multi_pw_aff *mpa1,
4297 __isl_keep isl_multi_pw_aff *mpa2);
4298 isl_bool isl_union_pw_aff_plain_is_equal(
4299 __isl_keep isl_union_pw_aff *upa1,
4300 __isl_keep isl_union_pw_aff *upa2);
4301 isl_bool isl_union_pw_multi_aff_plain_is_equal(
4302 __isl_keep isl_union_pw_multi_aff *upma1,
4303 __isl_keep isl_union_pw_multi_aff *upma2);
4304 isl_bool isl_multi_union_pw_aff_plain_is_equal(
4305 __isl_keep isl_multi_union_pw_aff *mupa1,
4306 __isl_keep isl_multi_union_pw_aff *mupa2);
4308 #include <isl/polynomial.h>
4309 isl_bool isl_union_pw_qpolynomial_plain_is_equal(
4310 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4311 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4312 isl_bool isl_union_pw_qpolynomial_fold_plain_is_equal(
4313 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4314 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4316 =item * Disjointness
4318 #include <isl/set.h>
4319 isl_bool isl_basic_set_is_disjoint(
4320 __isl_keep isl_basic_set *bset1,
4321 __isl_keep isl_basic_set *bset2);
4322 isl_bool isl_set_plain_is_disjoint(
4323 __isl_keep isl_set *set1,
4324 __isl_keep isl_set *set2);
4325 isl_bool isl_set_is_disjoint(__isl_keep isl_set *set1,
4326 __isl_keep isl_set *set2);
4328 #include <isl/map.h>
4329 isl_bool isl_basic_map_is_disjoint(
4330 __isl_keep isl_basic_map *bmap1,
4331 __isl_keep isl_basic_map *bmap2);
4332 isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1,
4333 __isl_keep isl_map *map2);
4335 #include <isl/union_set.h>
4336 isl_bool isl_union_set_is_disjoint(
4337 __isl_keep isl_union_set *uset1,
4338 __isl_keep isl_union_set *uset2);
4340 #include <isl/union_map.h>
4341 isl_bool isl_union_map_is_disjoint(
4342 __isl_keep isl_union_map *umap1,
4343 __isl_keep isl_union_map *umap2);
4347 isl_bool isl_basic_set_is_subset(
4348 __isl_keep isl_basic_set *bset1,
4349 __isl_keep isl_basic_set *bset2);
4350 isl_bool isl_set_is_subset(__isl_keep isl_set *set1,
4351 __isl_keep isl_set *set2);
4352 isl_bool isl_set_is_strict_subset(
4353 __isl_keep isl_set *set1,
4354 __isl_keep isl_set *set2);
4355 isl_bool isl_union_set_is_subset(
4356 __isl_keep isl_union_set *uset1,
4357 __isl_keep isl_union_set *uset2);
4358 isl_bool isl_union_set_is_strict_subset(
4359 __isl_keep isl_union_set *uset1,
4360 __isl_keep isl_union_set *uset2);
4361 isl_bool isl_basic_map_is_subset(
4362 __isl_keep isl_basic_map *bmap1,
4363 __isl_keep isl_basic_map *bmap2);
4364 isl_bool isl_basic_map_is_strict_subset(
4365 __isl_keep isl_basic_map *bmap1,
4366 __isl_keep isl_basic_map *bmap2);
4367 isl_bool isl_map_is_subset(
4368 __isl_keep isl_map *map1,
4369 __isl_keep isl_map *map2);
4370 isl_bool isl_map_is_strict_subset(
4371 __isl_keep isl_map *map1,
4372 __isl_keep isl_map *map2);
4373 isl_bool isl_union_map_is_subset(
4374 __isl_keep isl_union_map *umap1,
4375 __isl_keep isl_union_map *umap2);
4376 isl_bool isl_union_map_is_strict_subset(
4377 __isl_keep isl_union_map *umap1,
4378 __isl_keep isl_union_map *umap2);
4380 Check whether the first argument is a (strict) subset of the
4385 Every comparison function returns a negative value if the first
4386 argument is considered smaller than the second, a positive value
4387 if the first argument is considered greater and zero if the two
4388 constraints are considered the same by the comparison criterion.
4390 #include <isl/constraint.h>
4391 int isl_constraint_plain_cmp(
4392 __isl_keep isl_constraint *c1,
4393 __isl_keep isl_constraint *c2);
4395 This function is useful for sorting C<isl_constraint>s.
4396 The order depends on the internal representation of the inputs.
4397 The order is fixed over different calls to the function (assuming
4398 the internal representation of the inputs has not changed), but may
4399 change over different versions of C<isl>.
4401 #include <isl/constraint.h>
4402 int isl_constraint_cmp_last_non_zero(
4403 __isl_keep isl_constraint *c1,
4404 __isl_keep isl_constraint *c2);
4406 This function can be used to sort constraints that live in the same
4407 local space. Constraints that involve ``earlier'' dimensions or
4408 that have a smaller coefficient for the shared latest dimension
4409 are considered smaller than other constraints.
4410 This function only defines a B<partial> order.
4412 #include <isl/set.h>
4413 int isl_set_plain_cmp(__isl_keep isl_set *set1,
4414 __isl_keep isl_set *set2);
4416 This function is useful for sorting C<isl_set>s.
4417 The order depends on the internal representation of the inputs.
4418 The order is fixed over different calls to the function (assuming
4419 the internal representation of the inputs has not changed), but may
4420 change over different versions of C<isl>.
4422 #include <isl/aff.h>
4423 int isl_multi_aff_plain_cmp(
4424 __isl_keep isl_multi_aff *ma1,
4425 __isl_keep isl_multi_aff *ma2);
4426 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4427 __isl_keep isl_pw_aff *pa2);
4429 The functions C<isl_multi_aff_plain_cmp> and
4430 C<isl_pw_aff_plain_cmp> can be used to sort C<isl_multi_aff>s and
4431 C<isl_pw_aff>s. The order is not strictly defined.
4432 The current order sorts expressions that only involve
4433 earlier dimensions before those that involve later dimensions.
4437 =head2 Unary Operations
4443 __isl_give isl_set *isl_set_complement(
4444 __isl_take isl_set *set);
4445 __isl_give isl_map *isl_map_complement(
4446 __isl_take isl_map *map);
4450 #include <isl/space.h>
4451 __isl_give isl_space *isl_space_reverse(
4452 __isl_take isl_space *space);
4454 #include <isl/map.h>
4455 __isl_give isl_basic_map *isl_basic_map_reverse(
4456 __isl_take isl_basic_map *bmap);
4457 __isl_give isl_map *isl_map_reverse(
4458 __isl_take isl_map *map);
4460 #include <isl/union_map.h>
4461 __isl_give isl_union_map *isl_union_map_reverse(
4462 __isl_take isl_union_map *umap);
4466 #include <isl/space.h>
4467 __isl_give isl_space *isl_space_domain(
4468 __isl_take isl_space *space);
4469 __isl_give isl_space *isl_space_range(
4470 __isl_take isl_space *space);
4471 __isl_give isl_space *isl_space_params(
4472 __isl_take isl_space *space);
4474 #include <isl/local_space.h>
4475 __isl_give isl_local_space *isl_local_space_domain(
4476 __isl_take isl_local_space *ls);
4477 __isl_give isl_local_space *isl_local_space_range(
4478 __isl_take isl_local_space *ls);
4480 #include <isl/set.h>
4481 __isl_give isl_basic_set *isl_basic_set_project_out(
4482 __isl_take isl_basic_set *bset,
4483 enum isl_dim_type type, unsigned first, unsigned n);
4484 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
4485 enum isl_dim_type type, unsigned first, unsigned n);
4486 __isl_give isl_map *isl_set_project_onto_map(
4487 __isl_take isl_set *set,
4488 enum isl_dim_type type, unsigned first,
4490 __isl_give isl_basic_set *isl_basic_set_params(
4491 __isl_take isl_basic_set *bset);
4492 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
4494 The function C<isl_set_project_onto_map> returns a relation
4495 that projects the input set onto the given set dimensions.
4497 #include <isl/map.h>
4498 __isl_give isl_basic_map *isl_basic_map_project_out(
4499 __isl_take isl_basic_map *bmap,
4500 enum isl_dim_type type, unsigned first, unsigned n);
4501 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
4502 enum isl_dim_type type, unsigned first, unsigned n);
4503 __isl_give isl_basic_set *isl_basic_map_domain(
4504 __isl_take isl_basic_map *bmap);
4505 __isl_give isl_basic_set *isl_basic_map_range(
4506 __isl_take isl_basic_map *bmap);
4507 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
4508 __isl_give isl_set *isl_map_domain(
4509 __isl_take isl_map *bmap);
4510 __isl_give isl_set *isl_map_range(
4511 __isl_take isl_map *map);
4513 #include <isl/union_set.h>
4514 __isl_give isl_union_set *isl_union_set_project_out(
4515 __isl_take isl_union_set *uset,
4516 enum isl_dim_type type,
4517 unsigned first, unsigned n);
4518 __isl_give isl_set *isl_union_set_params(
4519 __isl_take isl_union_set *uset);
4521 The function C<isl_union_set_project_out> can only project out
4524 #include <isl/union_map.h>
4525 __isl_give isl_union_map *isl_union_map_project_out(
4526 __isl_take isl_union_map *umap,
4527 enum isl_dim_type type, unsigned first, unsigned n);
4528 __isl_give isl_union_map *
4529 isl_union_map_project_out_all_params(
4530 __isl_take isl_union_map *umap);
4531 __isl_give isl_set *isl_union_map_params(
4532 __isl_take isl_union_map *umap);
4533 __isl_give isl_union_set *isl_union_map_domain(
4534 __isl_take isl_union_map *umap);
4535 __isl_give isl_union_set *isl_union_map_range(
4536 __isl_take isl_union_map *umap);
4538 The function C<isl_union_map_project_out> can only project out
4541 #include <isl/aff.h>
4542 __isl_give isl_aff *isl_aff_project_domain_on_params(
4543 __isl_take isl_aff *aff);
4544 __isl_give isl_multi_aff *
4545 isl_multi_aff_project_domain_on_params(
4546 __isl_take isl_multi_aff *ma);
4547 __isl_give isl_pw_aff *
4548 isl_pw_aff_project_domain_on_params(
4549 __isl_take isl_pw_aff *pa);
4550 __isl_give isl_multi_pw_aff *
4551 isl_multi_pw_aff_project_domain_on_params(
4552 __isl_take isl_multi_pw_aff *mpa);
4553 __isl_give isl_pw_multi_aff *
4554 isl_pw_multi_aff_project_domain_on_params(
4555 __isl_take isl_pw_multi_aff *pma);
4556 __isl_give isl_set *isl_pw_aff_domain(
4557 __isl_take isl_pw_aff *pwaff);
4558 __isl_give isl_set *isl_pw_multi_aff_domain(
4559 __isl_take isl_pw_multi_aff *pma);
4560 __isl_give isl_set *isl_multi_pw_aff_domain(
4561 __isl_take isl_multi_pw_aff *mpa);
4562 __isl_give isl_union_set *isl_union_pw_aff_domain(
4563 __isl_take isl_union_pw_aff *upa);
4564 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4565 __isl_take isl_union_pw_multi_aff *upma);
4566 __isl_give isl_union_set *
4567 isl_multi_union_pw_aff_domain(
4568 __isl_take isl_multi_union_pw_aff *mupa);
4569 __isl_give isl_set *isl_pw_aff_params(
4570 __isl_take isl_pw_aff *pwa);
4572 The function C<isl_multi_union_pw_aff_domain> requires its
4573 input to have at least one set dimension.
4575 #include <isl/polynomial.h>
4576 __isl_give isl_qpolynomial *
4577 isl_qpolynomial_project_domain_on_params(
4578 __isl_take isl_qpolynomial *qp);
4579 __isl_give isl_pw_qpolynomial *
4580 isl_pw_qpolynomial_project_domain_on_params(
4581 __isl_take isl_pw_qpolynomial *pwqp);
4582 __isl_give isl_pw_qpolynomial_fold *
4583 isl_pw_qpolynomial_fold_project_domain_on_params(
4584 __isl_take isl_pw_qpolynomial_fold *pwf);
4585 __isl_give isl_set *isl_pw_qpolynomial_domain(
4586 __isl_take isl_pw_qpolynomial *pwqp);
4587 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4588 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4589 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4590 __isl_take isl_union_pw_qpolynomial *upwqp);
4592 #include <isl/space.h>
4593 __isl_give isl_space *isl_space_domain_map(
4594 __isl_take isl_space *space);
4595 __isl_give isl_space *isl_space_range_map(
4596 __isl_take isl_space *space);
4598 #include <isl/map.h>
4599 __isl_give isl_map *isl_set_wrapped_domain_map(
4600 __isl_take isl_set *set);
4601 __isl_give isl_basic_map *isl_basic_map_domain_map(
4602 __isl_take isl_basic_map *bmap);
4603 __isl_give isl_basic_map *isl_basic_map_range_map(
4604 __isl_take isl_basic_map *bmap);
4605 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
4606 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
4608 #include <isl/union_map.h>
4609 __isl_give isl_union_map *isl_union_map_domain_map(
4610 __isl_take isl_union_map *umap);
4611 __isl_give isl_union_pw_multi_aff *
4612 isl_union_map_domain_map_union_pw_multi_aff(
4613 __isl_take isl_union_map *umap);
4614 __isl_give isl_union_map *isl_union_map_range_map(
4615 __isl_take isl_union_map *umap);
4616 __isl_give isl_union_map *
4617 isl_union_set_wrapped_domain_map(
4618 __isl_take isl_union_set *uset);
4620 The functions above construct a (basic, regular or union) relation
4621 that maps (a wrapped version of) the input relation to its domain or range.
4622 C<isl_set_wrapped_domain_map> maps the input set to the domain
4623 of its wrapped relation.
4627 __isl_give isl_basic_set *isl_basic_set_eliminate(
4628 __isl_take isl_basic_set *bset,
4629 enum isl_dim_type type,
4630 unsigned first, unsigned n);
4631 __isl_give isl_set *isl_set_eliminate(
4632 __isl_take isl_set *set, enum isl_dim_type type,
4633 unsigned first, unsigned n);
4634 __isl_give isl_basic_map *isl_basic_map_eliminate(
4635 __isl_take isl_basic_map *bmap,
4636 enum isl_dim_type type,
4637 unsigned first, unsigned n);
4638 __isl_give isl_map *isl_map_eliminate(
4639 __isl_take isl_map *map, enum isl_dim_type type,
4640 unsigned first, unsigned n);
4642 Eliminate the coefficients for the given dimensions from the constraints,
4643 without removing the dimensions.
4645 =item * Constructing a set from a parameter domain
4647 A zero-dimensional (local) space or (basic) set can be constructed
4648 on a given parameter domain using the following functions.
4650 #include <isl/space.h>
4651 __isl_give isl_space *isl_space_set_from_params(
4652 __isl_take isl_space *space);
4654 #include <isl/local_space.h>
4655 __isl_give isl_local_space *
4656 isl_local_space_set_from_params(
4657 __isl_take isl_local_space *ls);
4659 #include <isl/set.h>
4660 __isl_give isl_basic_set *isl_basic_set_from_params(
4661 __isl_take isl_basic_set *bset);
4662 __isl_give isl_set *isl_set_from_params(
4663 __isl_take isl_set *set);
4665 =item * Constructing a relation from one or two sets
4667 Create a relation with the given set(s) as domain and/or range.
4668 If only the domain or the range is specified, then
4669 the range or domain of the created relation is a zero-dimensional
4670 flat anonymous space.
4672 #include <isl/space.h>
4673 __isl_give isl_space *isl_space_from_domain(
4674 __isl_take isl_space *space);
4675 __isl_give isl_space *isl_space_from_range(
4676 __isl_take isl_space *space);
4677 __isl_give isl_space *isl_space_map_from_set(
4678 __isl_take isl_space *space);
4679 __isl_give isl_space *isl_space_map_from_domain_and_range(
4680 __isl_take isl_space *domain,
4681 __isl_take isl_space *range);
4683 #include <isl/local_space.h>
4684 __isl_give isl_local_space *isl_local_space_from_domain(
4685 __isl_take isl_local_space *ls);
4687 #include <isl/map.h>
4688 __isl_give isl_map *isl_map_from_domain(
4689 __isl_take isl_set *set);
4690 __isl_give isl_map *isl_map_from_range(
4691 __isl_take isl_set *set);
4693 #include <isl/union_map.h>
4694 __isl_give isl_union_map *isl_union_map_from_domain(
4695 __isl_take isl_union_set *uset);
4696 __isl_give isl_union_map *isl_union_map_from_range(
4697 __isl_take isl_union_set *uset);
4698 __isl_give isl_union_map *
4699 isl_union_map_from_domain_and_range(
4700 __isl_take isl_union_set *domain,
4701 __isl_take isl_union_set *range);
4703 #include <isl/val.h>
4704 __isl_give isl_multi_val *isl_multi_val_from_range(
4705 __isl_take isl_multi_val *mv);
4707 #include <isl/aff.h>
4708 __isl_give isl_aff *isl_aff_from_range(
4709 __isl_take isl_aff *aff);
4710 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4711 __isl_take isl_multi_aff *ma);
4712 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4713 __isl_take isl_pw_aff *pwa);
4714 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4715 __isl_take isl_multi_pw_aff *mpa);
4716 __isl_give isl_multi_union_pw_aff *
4717 isl_multi_union_pw_aff_from_range(
4718 __isl_take isl_multi_union_pw_aff *mupa);
4719 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4720 __isl_take isl_set *set);
4721 __isl_give isl_union_pw_multi_aff *
4722 isl_union_pw_multi_aff_from_domain(
4723 __isl_take isl_union_set *uset);
4725 #include <isl/polynomial.h>
4726 __isl_give isl_pw_qpolynomial *
4727 isl_pw_qpolynomial_from_range(
4728 __isl_take isl_pw_qpolynomial *pwqp);
4729 __isl_give isl_pw_qpolynomial_fold *
4730 isl_pw_qpolynomial_fold_from_range(
4731 __isl_take isl_pw_qpolynomial_fold *pwf);
4735 #include <isl/set.h>
4736 __isl_give isl_basic_set *isl_basic_set_fix_si(
4737 __isl_take isl_basic_set *bset,
4738 enum isl_dim_type type, unsigned pos, int value);
4739 __isl_give isl_basic_set *isl_basic_set_fix_val(
4740 __isl_take isl_basic_set *bset,
4741 enum isl_dim_type type, unsigned pos,
4742 __isl_take isl_val *v);
4743 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
4744 enum isl_dim_type type, unsigned pos, int value);
4745 __isl_give isl_set *isl_set_fix_val(
4746 __isl_take isl_set *set,
4747 enum isl_dim_type type, unsigned pos,
4748 __isl_take isl_val *v);
4750 #include <isl/map.h>
4751 __isl_give isl_basic_map *isl_basic_map_fix_si(
4752 __isl_take isl_basic_map *bmap,
4753 enum isl_dim_type type, unsigned pos, int value);
4754 __isl_give isl_basic_map *isl_basic_map_fix_val(
4755 __isl_take isl_basic_map *bmap,
4756 enum isl_dim_type type, unsigned pos,
4757 __isl_take isl_val *v);
4758 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
4759 enum isl_dim_type type, unsigned pos, int value);
4760 __isl_give isl_map *isl_map_fix_val(
4761 __isl_take isl_map *map,
4762 enum isl_dim_type type, unsigned pos,
4763 __isl_take isl_val *v);
4765 #include <isl/aff.h>
4766 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4767 __isl_take isl_pw_multi_aff *pma,
4768 enum isl_dim_type type, unsigned pos, int value);
4770 #include <isl/polynomial.h>
4771 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4772 __isl_take isl_pw_qpolynomial *pwqp,
4773 enum isl_dim_type type, unsigned n,
4774 __isl_take isl_val *v);
4775 __isl_give isl_pw_qpolynomial_fold *
4776 isl_pw_qpolynomial_fold_fix_val(
4777 __isl_take isl_pw_qpolynomial_fold *pwf,
4778 enum isl_dim_type type, unsigned n,
4779 __isl_take isl_val *v);
4781 Intersect the set, relation or function domain
4782 with the hyperplane where the given
4783 dimension has the fixed given value.
4785 #include <isl/set.h>
4786 __isl_give isl_basic_set *
4787 isl_basic_set_lower_bound_val(
4788 __isl_take isl_basic_set *bset,
4789 enum isl_dim_type type, unsigned pos,
4790 __isl_take isl_val *value);
4791 __isl_give isl_basic_set *
4792 isl_basic_set_upper_bound_val(
4793 __isl_take isl_basic_set *bset,
4794 enum isl_dim_type type, unsigned pos,
4795 __isl_take isl_val *value);
4796 __isl_give isl_set *isl_set_lower_bound_si(
4797 __isl_take isl_set *set,
4798 enum isl_dim_type type, unsigned pos, int value);
4799 __isl_give isl_set *isl_set_lower_bound_val(
4800 __isl_take isl_set *set,
4801 enum isl_dim_type type, unsigned pos,
4802 __isl_take isl_val *value);
4803 __isl_give isl_set *isl_set_upper_bound_si(
4804 __isl_take isl_set *set,
4805 enum isl_dim_type type, unsigned pos, int value);
4806 __isl_give isl_set *isl_set_upper_bound_val(
4807 __isl_take isl_set *set,
4808 enum isl_dim_type type, unsigned pos,
4809 __isl_take isl_val *value);
4811 #include <isl/map.h>
4812 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
4813 __isl_take isl_basic_map *bmap,
4814 enum isl_dim_type type, unsigned pos, int value);
4815 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
4816 __isl_take isl_basic_map *bmap,
4817 enum isl_dim_type type, unsigned pos, int value);
4818 __isl_give isl_map *isl_map_lower_bound_si(
4819 __isl_take isl_map *map,
4820 enum isl_dim_type type, unsigned pos, int value);
4821 __isl_give isl_map *isl_map_upper_bound_si(
4822 __isl_take isl_map *map,
4823 enum isl_dim_type type, unsigned pos, int value);
4825 Intersect the set or relation with the half-space where the given
4826 dimension has a value bounded by the fixed given integer value.
4828 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
4829 enum isl_dim_type type1, int pos1,
4830 enum isl_dim_type type2, int pos2);
4831 __isl_give isl_basic_map *isl_basic_map_equate(
4832 __isl_take isl_basic_map *bmap,
4833 enum isl_dim_type type1, int pos1,
4834 enum isl_dim_type type2, int pos2);
4835 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
4836 enum isl_dim_type type1, int pos1,
4837 enum isl_dim_type type2, int pos2);
4839 Intersect the set or relation with the hyperplane where the given
4840 dimensions are equal to each other.
4842 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
4843 enum isl_dim_type type1, int pos1,
4844 enum isl_dim_type type2, int pos2);
4846 Intersect the relation with the hyperplane where the given
4847 dimensions have opposite values.
4849 __isl_give isl_map *isl_map_order_le(
4850 __isl_take isl_map *map,
4851 enum isl_dim_type type1, int pos1,
4852 enum isl_dim_type type2, int pos2);
4853 __isl_give isl_basic_map *isl_basic_map_order_ge(
4854 __isl_take isl_basic_map *bmap,
4855 enum isl_dim_type type1, int pos1,
4856 enum isl_dim_type type2, int pos2);
4857 __isl_give isl_map *isl_map_order_ge(
4858 __isl_take isl_map *map,
4859 enum isl_dim_type type1, int pos1,
4860 enum isl_dim_type type2, int pos2);
4861 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
4862 enum isl_dim_type type1, int pos1,
4863 enum isl_dim_type type2, int pos2);
4864 __isl_give isl_basic_map *isl_basic_map_order_gt(
4865 __isl_take isl_basic_map *bmap,
4866 enum isl_dim_type type1, int pos1,
4867 enum isl_dim_type type2, int pos2);
4868 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
4869 enum isl_dim_type type1, int pos1,
4870 enum isl_dim_type type2, int pos2);
4872 Intersect the relation with the half-space where the given
4873 dimensions satisfy the given ordering.
4875 #include <isl/union_set.h>
4876 __isl_give isl_union_map *isl_union_map_remove_map_if(
4877 __isl_take isl_union_map *umap,
4878 isl_bool (*fn)(__isl_keep isl_map *map,
4879 void *user), void *user);
4881 This function calls the callback function once for each
4882 pair of spaces for which there are elements in the input.
4883 If the callback returns C<isl_bool_true>, then all those elements
4884 are removed from the result. The only remaining elements in the output
4885 are then those for which the callback returns C<isl_bool_false>.
4889 #include <isl/aff.h>
4890 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4891 __isl_take isl_aff *aff);
4892 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4893 __isl_take isl_aff *aff);
4894 __isl_give isl_set *isl_pw_aff_pos_set(
4895 __isl_take isl_pw_aff *pa);
4896 __isl_give isl_set *isl_pw_aff_nonneg_set(
4897 __isl_take isl_pw_aff *pwaff);
4898 __isl_give isl_set *isl_pw_aff_zero_set(
4899 __isl_take isl_pw_aff *pwaff);
4900 __isl_give isl_set *isl_pw_aff_non_zero_set(
4901 __isl_take isl_pw_aff *pwaff);
4902 __isl_give isl_union_set *
4903 isl_union_pw_aff_zero_union_set(
4904 __isl_take isl_union_pw_aff *upa);
4905 __isl_give isl_union_set *
4906 isl_multi_union_pw_aff_zero_union_set(
4907 __isl_take isl_multi_union_pw_aff *mupa);
4909 The function C<isl_aff_neg_basic_set> returns a basic set
4910 containing those elements in the domain space
4911 of C<aff> where C<aff> is negative.
4912 The function C<isl_pw_aff_nonneg_set> returns a set
4913 containing those elements in the domain
4914 of C<pwaff> where C<pwaff> is non-negative.
4915 The function C<isl_multi_union_pw_aff_zero_union_set>
4916 returns a union set containing those elements
4917 in the domains of its elements where they are all zero.
4921 __isl_give isl_map *isl_set_identity(
4922 __isl_take isl_set *set);
4923 __isl_give isl_union_map *isl_union_set_identity(
4924 __isl_take isl_union_set *uset);
4925 __isl_give isl_union_pw_multi_aff *
4926 isl_union_set_identity_union_pw_multi_aff(
4927 __isl_take isl_union_set *uset);
4929 Construct an identity relation on the given (union) set.
4931 =item * Function Extraction
4933 A piecewise quasi affine expression that is equal to 1 on a set
4934 and 0 outside the set can be created using the following function.
4936 #include <isl/aff.h>
4937 __isl_give isl_pw_aff *isl_set_indicator_function(
4938 __isl_take isl_set *set);
4940 A piecewise multiple quasi affine expression can be extracted
4941 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4942 and the C<isl_map> is single-valued.
4943 In case of a conversion from an C<isl_union_map>
4944 to an C<isl_union_pw_multi_aff>, these properties need to hold
4945 in each domain space.
4946 A conversion to a C<isl_multi_union_pw_aff> additionally
4947 requires that the input is non-empty and involves only a single
4950 #include <isl/aff.h>
4951 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4952 __isl_take isl_set *set);
4953 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4954 __isl_take isl_map *map);
4956 __isl_give isl_union_pw_multi_aff *
4957 isl_union_pw_multi_aff_from_union_set(
4958 __isl_take isl_union_set *uset);
4959 __isl_give isl_union_pw_multi_aff *
4960 isl_union_pw_multi_aff_from_union_map(
4961 __isl_take isl_union_map *umap);
4963 __isl_give isl_multi_union_pw_aff *
4964 isl_multi_union_pw_aff_from_union_map(
4965 __isl_take isl_union_map *umap);
4969 __isl_give isl_basic_set *isl_basic_map_deltas(
4970 __isl_take isl_basic_map *bmap);
4971 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
4972 __isl_give isl_union_set *isl_union_map_deltas(
4973 __isl_take isl_union_map *umap);
4975 These functions return a (basic) set containing the differences
4976 between image elements and corresponding domain elements in the input.
4978 __isl_give isl_basic_map *isl_basic_map_deltas_map(
4979 __isl_take isl_basic_map *bmap);
4980 __isl_give isl_map *isl_map_deltas_map(
4981 __isl_take isl_map *map);
4982 __isl_give isl_union_map *isl_union_map_deltas_map(
4983 __isl_take isl_union_map *umap);
4985 The functions above construct a (basic, regular or union) relation
4986 that maps (a wrapped version of) the input relation to its delta set.
4990 Simplify the representation of a set, relation or functions by trying
4991 to combine pairs of basic sets or relations into a single
4992 basic set or relation.
4994 #include <isl/set.h>
4995 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
4997 #include <isl/map.h>
4998 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
5000 #include <isl/union_set.h>
5001 __isl_give isl_union_set *isl_union_set_coalesce(
5002 __isl_take isl_union_set *uset);
5004 #include <isl/union_map.h>
5005 __isl_give isl_union_map *isl_union_map_coalesce(
5006 __isl_take isl_union_map *umap);
5008 #include <isl/aff.h>
5009 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
5010 __isl_take isl_pw_aff *pwqp);
5011 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
5012 __isl_take isl_pw_multi_aff *pma);
5013 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
5014 __isl_take isl_multi_pw_aff *mpa);
5015 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
5016 __isl_take isl_union_pw_aff *upa);
5017 __isl_give isl_union_pw_multi_aff *
5018 isl_union_pw_multi_aff_coalesce(
5019 __isl_take isl_union_pw_multi_aff *upma);
5020 __isl_give isl_multi_union_pw_aff *
5021 isl_multi_union_pw_aff_coalesce(
5022 __isl_take isl_multi_union_pw_aff *aff);
5024 #include <isl/polynomial.h>
5025 __isl_give isl_pw_qpolynomial_fold *
5026 isl_pw_qpolynomial_fold_coalesce(
5027 __isl_take isl_pw_qpolynomial_fold *pwf);
5028 __isl_give isl_union_pw_qpolynomial *
5029 isl_union_pw_qpolynomial_coalesce(
5030 __isl_take isl_union_pw_qpolynomial *upwqp);
5031 __isl_give isl_union_pw_qpolynomial_fold *
5032 isl_union_pw_qpolynomial_fold_coalesce(
5033 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5035 One of the methods for combining pairs of basic sets or relations
5036 can result in coefficients that are much larger than those that appear
5037 in the constraints of the input. By default, the coefficients are
5038 not allowed to grow larger, but this can be changed by unsetting
5039 the following option.
5041 isl_stat isl_options_set_coalesce_bounded_wrapping(
5042 isl_ctx *ctx, int val);
5043 int isl_options_get_coalesce_bounded_wrapping(
5046 =item * Detecting equalities
5048 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
5049 __isl_take isl_basic_set *bset);
5050 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
5051 __isl_take isl_basic_map *bmap);
5052 __isl_give isl_set *isl_set_detect_equalities(
5053 __isl_take isl_set *set);
5054 __isl_give isl_map *isl_map_detect_equalities(
5055 __isl_take isl_map *map);
5056 __isl_give isl_union_set *isl_union_set_detect_equalities(
5057 __isl_take isl_union_set *uset);
5058 __isl_give isl_union_map *isl_union_map_detect_equalities(
5059 __isl_take isl_union_map *umap);
5061 Simplify the representation of a set or relation by detecting implicit
5064 =item * Removing redundant constraints
5066 #include <isl/set.h>
5067 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
5068 __isl_take isl_basic_set *bset);
5069 __isl_give isl_set *isl_set_remove_redundancies(
5070 __isl_take isl_set *set);
5072 #include <isl/union_set.h>
5073 __isl_give isl_union_set *
5074 isl_union_set_remove_redundancies(
5075 __isl_take isl_union_set *uset);
5077 #include <isl/map.h>
5078 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
5079 __isl_take isl_basic_map *bmap);
5080 __isl_give isl_map *isl_map_remove_redundancies(
5081 __isl_take isl_map *map);
5083 #include <isl/union_map.h>
5084 __isl_give isl_union_map *
5085 isl_union_map_remove_redundancies(
5086 __isl_take isl_union_map *umap);
5090 __isl_give isl_basic_set *isl_set_convex_hull(
5091 __isl_take isl_set *set);
5092 __isl_give isl_basic_map *isl_map_convex_hull(
5093 __isl_take isl_map *map);
5095 If the input set or relation has any existentially quantified
5096 variables, then the result of these operations is currently undefined.
5100 #include <isl/set.h>
5101 __isl_give isl_basic_set *
5102 isl_set_unshifted_simple_hull(
5103 __isl_take isl_set *set);
5104 __isl_give isl_basic_set *isl_set_simple_hull(
5105 __isl_take isl_set *set);
5106 __isl_give isl_basic_set *
5107 isl_set_plain_unshifted_simple_hull(
5108 __isl_take isl_set *set);
5109 __isl_give isl_basic_set *
5110 isl_set_unshifted_simple_hull_from_set_list(
5111 __isl_take isl_set *set,
5112 __isl_take isl_set_list *list);
5114 #include <isl/map.h>
5115 __isl_give isl_basic_map *
5116 isl_map_unshifted_simple_hull(
5117 __isl_take isl_map *map);
5118 __isl_give isl_basic_map *isl_map_simple_hull(
5119 __isl_take isl_map *map);
5120 __isl_give isl_basic_map *
5121 isl_map_plain_unshifted_simple_hull(
5122 __isl_take isl_map *map);
5123 __isl_give isl_basic_map *
5124 isl_map_unshifted_simple_hull_from_map_list(
5125 __isl_take isl_map *map,
5126 __isl_take isl_map_list *list);
5128 #include <isl/union_map.h>
5129 __isl_give isl_union_map *isl_union_map_simple_hull(
5130 __isl_take isl_union_map *umap);
5132 These functions compute a single basic set or relation
5133 that contains the whole input set or relation.
5134 In particular, the output is described by translates
5135 of the constraints describing the basic sets or relations in the input.
5136 In case of C<isl_set_unshifted_simple_hull>, only the original
5137 constraints are used, without any translation.
5138 In case of C<isl_set_plain_unshifted_simple_hull> and
5139 C<isl_map_plain_unshifted_simple_hull>, the result is described
5140 by original constraints that are obviously satisfied
5141 by the entire input set or relation.
5142 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
5143 C<isl_map_unshifted_simple_hull_from_map_list>, the
5144 constraints are taken from the elements of the second argument.
5148 (See \autoref{s:simple hull}.)
5154 __isl_give isl_basic_set *isl_basic_set_affine_hull(
5155 __isl_take isl_basic_set *bset);
5156 __isl_give isl_basic_set *isl_set_affine_hull(
5157 __isl_take isl_set *set);
5158 __isl_give isl_union_set *isl_union_set_affine_hull(
5159 __isl_take isl_union_set *uset);
5160 __isl_give isl_basic_map *isl_basic_map_affine_hull(
5161 __isl_take isl_basic_map *bmap);
5162 __isl_give isl_basic_map *isl_map_affine_hull(
5163 __isl_take isl_map *map);
5164 __isl_give isl_union_map *isl_union_map_affine_hull(
5165 __isl_take isl_union_map *umap);
5167 In case of union sets and relations, the affine hull is computed
5170 =item * Polyhedral hull
5172 __isl_give isl_basic_set *isl_set_polyhedral_hull(
5173 __isl_take isl_set *set);
5174 __isl_give isl_basic_map *isl_map_polyhedral_hull(
5175 __isl_take isl_map *map);
5176 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
5177 __isl_take isl_union_set *uset);
5178 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
5179 __isl_take isl_union_map *umap);
5181 These functions compute a single basic set or relation
5182 not involving any existentially quantified variables
5183 that contains the whole input set or relation.
5184 In case of union sets and relations, the polyhedral hull is computed
5187 =item * Other approximations
5189 #include <isl/set.h>
5190 __isl_give isl_basic_set *
5191 isl_basic_set_drop_constraints_involving_dims(
5192 __isl_take isl_basic_set *bset,
5193 enum isl_dim_type type,
5194 unsigned first, unsigned n);
5195 __isl_give isl_basic_set *
5196 isl_basic_set_drop_constraints_not_involving_dims(
5197 __isl_take isl_basic_set *bset,
5198 enum isl_dim_type type,
5199 unsigned first, unsigned n);
5200 __isl_give isl_set *
5201 isl_set_drop_constraints_involving_dims(
5202 __isl_take isl_set *set,
5203 enum isl_dim_type type,
5204 unsigned first, unsigned n);
5205 __isl_give isl_set *
5206 isl_set_drop_constraints_not_involving_dims(
5207 __isl_take isl_set *set,
5208 enum isl_dim_type type,
5209 unsigned first, unsigned n);
5211 #include <isl/map.h>
5212 __isl_give isl_basic_map *
5213 isl_basic_map_drop_constraints_involving_dims(
5214 __isl_take isl_basic_map *bmap,
5215 enum isl_dim_type type,
5216 unsigned first, unsigned n);
5217 __isl_give isl_basic_map *
5218 isl_basic_map_drop_constraints_not_involving_dims(
5219 __isl_take isl_basic_map *bmap,
5220 enum isl_dim_type type,
5221 unsigned first, unsigned n);
5222 __isl_give isl_map *
5223 isl_map_drop_constraints_involving_dims(
5224 __isl_take isl_map *map,
5225 enum isl_dim_type type,
5226 unsigned first, unsigned n);
5227 __isl_give isl_map *
5228 isl_map_drop_constraints_not_involving_dims(
5229 __isl_take isl_map *map,
5230 enum isl_dim_type type,
5231 unsigned first, unsigned n);
5233 These functions drop any constraints (not) involving the specified dimensions.
5234 Note that the result depends on the representation of the input.
5236 #include <isl/polynomial.h>
5237 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5238 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5239 __isl_give isl_union_pw_qpolynomial *
5240 isl_union_pw_qpolynomial_to_polynomial(
5241 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5243 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5244 the polynomial will be an overapproximation. If C<sign> is negative,
5245 it will be an underapproximation. If C<sign> is zero, the approximation
5246 will lie somewhere in between.
5250 __isl_give isl_basic_set *isl_basic_set_sample(
5251 __isl_take isl_basic_set *bset);
5252 __isl_give isl_basic_set *isl_set_sample(
5253 __isl_take isl_set *set);
5254 __isl_give isl_basic_map *isl_basic_map_sample(
5255 __isl_take isl_basic_map *bmap);
5256 __isl_give isl_basic_map *isl_map_sample(
5257 __isl_take isl_map *map);
5259 If the input (basic) set or relation is non-empty, then return
5260 a singleton subset of the input. Otherwise, return an empty set.
5262 =item * Optimization
5264 #include <isl/ilp.h>
5265 __isl_give isl_val *isl_basic_set_max_val(
5266 __isl_keep isl_basic_set *bset,
5267 __isl_keep isl_aff *obj);
5268 __isl_give isl_val *isl_set_min_val(
5269 __isl_keep isl_set *set,
5270 __isl_keep isl_aff *obj);
5271 __isl_give isl_val *isl_set_max_val(
5272 __isl_keep isl_set *set,
5273 __isl_keep isl_aff *obj);
5274 __isl_give isl_multi_val *
5275 isl_union_set_min_multi_union_pw_aff(
5276 __isl_keep isl_union_set *set,
5277 __isl_keep isl_multi_union_pw_aff *obj);
5279 Compute the minimum or maximum of the integer affine expression C<obj>
5280 over the points in C<set>, returning the result in C<opt>.
5281 The result is C<NULL> in case of an error, the optimal value in case
5282 there is one, negative infinity or infinity if the problem is unbounded and
5283 NaN if the problem is empty.
5285 #include <isl/ilp.h>
5286 __isl_give isl_val *isl_basic_set_dim_max_val(
5287 __isl_take isl_basic_set *bset, int pos);
5289 Return the maximal value attained by the given set dimension,
5290 independently of the parameter values and of any other dimensions.
5291 The result is C<NULL> in case of an error, the optimal value in case
5292 there is one, infinity if the problem is unbounded and
5293 NaN if the input is empty.
5295 =item * Parametric optimization
5297 __isl_give isl_pw_aff *isl_set_dim_min(
5298 __isl_take isl_set *set, int pos);
5299 __isl_give isl_pw_aff *isl_set_dim_max(
5300 __isl_take isl_set *set, int pos);
5301 __isl_give isl_pw_aff *isl_map_dim_min(
5302 __isl_take isl_map *map, int pos);
5303 __isl_give isl_pw_aff *isl_map_dim_max(
5304 __isl_take isl_map *map, int pos);
5306 Compute the minimum or maximum of the given set or output dimension
5307 as a function of the parameters (and input dimensions), but independently
5308 of the other set or output dimensions.
5309 For lexicographic optimization, see L<"Lexicographic Optimization">.
5313 The following functions compute either the set of (rational) coefficient
5314 values of valid constraints for the given set or the set of (rational)
5315 values satisfying the constraints with coefficients from the given set.
5316 Internally, these two sets of functions perform essentially the
5317 same operations, except that the set of coefficients is assumed to
5318 be a cone, while the set of values may be any polyhedron.
5319 The current implementation is based on the Farkas lemma and
5320 Fourier-Motzkin elimination, but this may change or be made optional
5321 in future. In particular, future implementations may use different
5322 dualization algorithms or skip the elimination step.
5324 #include <isl/set.h>
5325 __isl_give isl_basic_set *isl_basic_set_coefficients(
5326 __isl_take isl_basic_set *bset);
5327 __isl_give isl_basic_set_list *
5328 isl_basic_set_list_coefficients(
5329 __isl_take isl_basic_set_list *list);
5330 __isl_give isl_basic_set *isl_set_coefficients(
5331 __isl_take isl_set *set);
5332 __isl_give isl_union_set *isl_union_set_coefficients(
5333 __isl_take isl_union_set *bset);
5334 __isl_give isl_basic_set *isl_basic_set_solutions(
5335 __isl_take isl_basic_set *bset);
5336 __isl_give isl_basic_set *isl_set_solutions(
5337 __isl_take isl_set *set);
5338 __isl_give isl_union_set *isl_union_set_solutions(
5339 __isl_take isl_union_set *bset);
5343 __isl_give isl_map *isl_map_fixed_power_val(
5344 __isl_take isl_map *map,
5345 __isl_take isl_val *exp);
5346 __isl_give isl_union_map *
5347 isl_union_map_fixed_power_val(
5348 __isl_take isl_union_map *umap,
5349 __isl_take isl_val *exp);
5351 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
5352 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
5353 of C<map> is computed.
5355 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
5357 __isl_give isl_union_map *isl_union_map_power(
5358 __isl_take isl_union_map *umap, int *exact);
5360 Compute a parametric representation for all positive powers I<k> of C<map>.
5361 The result maps I<k> to a nested relation corresponding to the
5362 I<k>th power of C<map>.
5363 The result may be an overapproximation. If the result is known to be exact,
5364 then C<*exact> is set to C<1>.
5366 =item * Transitive closure
5368 __isl_give isl_map *isl_map_transitive_closure(
5369 __isl_take isl_map *map, int *exact);
5370 __isl_give isl_union_map *isl_union_map_transitive_closure(
5371 __isl_take isl_union_map *umap, int *exact);
5373 Compute the transitive closure of C<map>.
5374 The result may be an overapproximation. If the result is known to be exact,
5375 then C<*exact> is set to C<1>.
5377 =item * Reaching path lengths
5379 __isl_give isl_map *isl_map_reaching_path_lengths(
5380 __isl_take isl_map *map, int *exact);
5382 Compute a relation that maps each element in the range of C<map>
5383 to the lengths of all paths composed of edges in C<map> that
5384 end up in the given element.
5385 The result may be an overapproximation. If the result is known to be exact,
5386 then C<*exact> is set to C<1>.
5387 To compute the I<maximal> path length, the resulting relation
5388 should be postprocessed by C<isl_map_lexmax>.
5389 In particular, if the input relation is a dependence relation
5390 (mapping sources to sinks), then the maximal path length corresponds
5391 to the free schedule.
5392 Note, however, that C<isl_map_lexmax> expects the maximum to be
5393 finite, so if the path lengths are unbounded (possibly due to
5394 the overapproximation), then you will get an error message.
5398 #include <isl/space.h>
5399 __isl_give isl_space *isl_space_wrap(
5400 __isl_take isl_space *space);
5401 __isl_give isl_space *isl_space_unwrap(
5402 __isl_take isl_space *space);
5404 #include <isl/local_space.h>
5405 __isl_give isl_local_space *isl_local_space_wrap(
5406 __isl_take isl_local_space *ls);
5408 #include <isl/set.h>
5409 __isl_give isl_basic_map *isl_basic_set_unwrap(
5410 __isl_take isl_basic_set *bset);
5411 __isl_give isl_map *isl_set_unwrap(
5412 __isl_take isl_set *set);
5414 #include <isl/map.h>
5415 __isl_give isl_basic_set *isl_basic_map_wrap(
5416 __isl_take isl_basic_map *bmap);
5417 __isl_give isl_set *isl_map_wrap(
5418 __isl_take isl_map *map);
5420 #include <isl/union_set.h>
5421 __isl_give isl_union_map *isl_union_set_unwrap(
5422 __isl_take isl_union_set *uset);
5424 #include <isl/union_map.h>
5425 __isl_give isl_union_set *isl_union_map_wrap(
5426 __isl_take isl_union_map *umap);
5428 The input to C<isl_space_unwrap> should
5429 be the space of a set, while that of
5430 C<isl_space_wrap> should be the space of a relation.
5431 Conversely, the output of C<isl_space_unwrap> is the space
5432 of a relation, while that of C<isl_space_wrap> is the space of a set.
5436 Remove any internal structure of domain (and range) of the given
5437 set or relation. If there is any such internal structure in the input,
5438 then the name of the space is also removed.
5440 #include <isl/space.h>
5441 __isl_give isl_space *isl_space_flatten_domain(
5442 __isl_take isl_space *space);
5443 __isl_give isl_space *isl_space_flatten_range(
5444 __isl_take isl_space *space);
5446 #include <isl/local_space.h>
5447 __isl_give isl_local_space *
5448 isl_local_space_flatten_domain(
5449 __isl_take isl_local_space *ls);
5450 __isl_give isl_local_space *
5451 isl_local_space_flatten_range(
5452 __isl_take isl_local_space *ls);
5454 #include <isl/set.h>
5455 __isl_give isl_basic_set *isl_basic_set_flatten(
5456 __isl_take isl_basic_set *bset);
5457 __isl_give isl_set *isl_set_flatten(
5458 __isl_take isl_set *set);
5460 #include <isl/map.h>
5461 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
5462 __isl_take isl_basic_map *bmap);
5463 __isl_give isl_basic_map *isl_basic_map_flatten_range(
5464 __isl_take isl_basic_map *bmap);
5465 __isl_give isl_map *isl_map_flatten_range(
5466 __isl_take isl_map *map);
5467 __isl_give isl_map *isl_map_flatten_domain(
5468 __isl_take isl_map *map);
5469 __isl_give isl_basic_map *isl_basic_map_flatten(
5470 __isl_take isl_basic_map *bmap);
5471 __isl_give isl_map *isl_map_flatten(
5472 __isl_take isl_map *map);
5474 #include <isl/val.h>
5475 __isl_give isl_multi_val *isl_multi_val_flatten_range(
5476 __isl_take isl_multi_val *mv);
5478 #include <isl/aff.h>
5479 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
5480 __isl_take isl_multi_aff *ma);
5481 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
5482 __isl_take isl_multi_aff *ma);
5483 __isl_give isl_multi_pw_aff *
5484 isl_multi_pw_aff_flatten_range(
5485 __isl_take isl_multi_pw_aff *mpa);
5486 __isl_give isl_multi_union_pw_aff *
5487 isl_multi_union_pw_aff_flatten_range(
5488 __isl_take isl_multi_union_pw_aff *mupa);
5490 #include <isl/map.h>
5491 __isl_give isl_map *isl_set_flatten_map(
5492 __isl_take isl_set *set);
5494 The function above constructs a relation
5495 that maps the input set to a flattened version of the set.
5499 Lift the input set to a space with extra dimensions corresponding
5500 to the existentially quantified variables in the input.
5501 In particular, the result lives in a wrapped map where the domain
5502 is the original space and the range corresponds to the original
5503 existentially quantified variables.
5505 #include <isl/set.h>
5506 __isl_give isl_basic_set *isl_basic_set_lift(
5507 __isl_take isl_basic_set *bset);
5508 __isl_give isl_set *isl_set_lift(
5509 __isl_take isl_set *set);
5510 __isl_give isl_union_set *isl_union_set_lift(
5511 __isl_take isl_union_set *uset);
5513 Given a local space that contains the existentially quantified
5514 variables of a set, a basic relation that, when applied to
5515 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
5516 can be constructed using the following function.
5518 #include <isl/local_space.h>
5519 __isl_give isl_basic_map *isl_local_space_lifting(
5520 __isl_take isl_local_space *ls);
5522 #include <isl/aff.h>
5523 __isl_give isl_multi_aff *isl_multi_aff_lift(
5524 __isl_take isl_multi_aff *maff,
5525 __isl_give isl_local_space **ls);
5527 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
5528 then it is assigned the local space that lies at the basis of
5529 the lifting applied.
5531 =item * Internal Product
5533 #include <isl/space.h>
5534 __isl_give isl_space *isl_space_zip(
5535 __isl_take isl_space *space);
5537 #include <isl/map.h>
5538 __isl_give isl_basic_map *isl_basic_map_zip(
5539 __isl_take isl_basic_map *bmap);
5540 __isl_give isl_map *isl_map_zip(
5541 __isl_take isl_map *map);
5543 #include <isl/union_map.h>
5544 __isl_give isl_union_map *isl_union_map_zip(
5545 __isl_take isl_union_map *umap);
5547 Given a relation with nested relations for domain and range,
5548 interchange the range of the domain with the domain of the range.
5552 #include <isl/space.h>
5553 __isl_give isl_space *isl_space_curry(
5554 __isl_take isl_space *space);
5555 __isl_give isl_space *isl_space_uncurry(
5556 __isl_take isl_space *space);
5558 #include <isl/map.h>
5559 __isl_give isl_basic_map *isl_basic_map_curry(
5560 __isl_take isl_basic_map *bmap);
5561 __isl_give isl_basic_map *isl_basic_map_uncurry(
5562 __isl_take isl_basic_map *bmap);
5563 __isl_give isl_map *isl_map_curry(
5564 __isl_take isl_map *map);
5565 __isl_give isl_map *isl_map_uncurry(
5566 __isl_take isl_map *map);
5568 #include <isl/union_map.h>
5569 __isl_give isl_union_map *isl_union_map_curry(
5570 __isl_take isl_union_map *umap);
5571 __isl_give isl_union_map *isl_union_map_uncurry(
5572 __isl_take isl_union_map *umap);
5574 Given a relation with a nested relation for domain,
5575 the C<curry> functions
5576 move the range of the nested relation out of the domain
5577 and use it as the domain of a nested relation in the range,
5578 with the original range as range of this nested relation.
5579 The C<uncurry> functions perform the inverse operation.
5581 #include <isl/space.h>
5582 __isl_give isl_space *isl_space_range_curry(
5583 __isl_take isl_space *space);
5585 #include <isl/map.h>
5586 __isl_give isl_map *isl_map_range_curry(
5587 __isl_take isl_map *map);
5589 #include <isl/union_map.h>
5590 __isl_give isl_union_map *isl_union_map_range_curry(
5591 __isl_take isl_union_map *umap);
5593 These functions apply the currying to the relation that
5594 is nested inside the range of the input.
5596 =item * Aligning parameters
5598 Change the order of the parameters of the given set, relation
5600 such that the first parameters match those of C<model>.
5601 This may involve the introduction of extra parameters.
5602 All parameters need to be named.
5604 #include <isl/space.h>
5605 __isl_give isl_space *isl_space_align_params(
5606 __isl_take isl_space *space1,
5607 __isl_take isl_space *space2)
5609 #include <isl/set.h>
5610 __isl_give isl_basic_set *isl_basic_set_align_params(
5611 __isl_take isl_basic_set *bset,
5612 __isl_take isl_space *model);
5613 __isl_give isl_set *isl_set_align_params(
5614 __isl_take isl_set *set,
5615 __isl_take isl_space *model);
5617 #include <isl/map.h>
5618 __isl_give isl_basic_map *isl_basic_map_align_params(
5619 __isl_take isl_basic_map *bmap,
5620 __isl_take isl_space *model);
5621 __isl_give isl_map *isl_map_align_params(
5622 __isl_take isl_map *map,
5623 __isl_take isl_space *model);
5625 #include <isl/val.h>
5626 __isl_give isl_multi_val *isl_multi_val_align_params(
5627 __isl_take isl_multi_val *mv,
5628 __isl_take isl_space *model);
5630 #include <isl/aff.h>
5631 __isl_give isl_aff *isl_aff_align_params(
5632 __isl_take isl_aff *aff,
5633 __isl_take isl_space *model);
5634 __isl_give isl_multi_aff *isl_multi_aff_align_params(
5635 __isl_take isl_multi_aff *multi,
5636 __isl_take isl_space *model);
5637 __isl_give isl_pw_aff *isl_pw_aff_align_params(
5638 __isl_take isl_pw_aff *pwaff,
5639 __isl_take isl_space *model);
5640 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
5641 __isl_take isl_pw_multi_aff *pma,
5642 __isl_take isl_space *model);
5643 __isl_give isl_union_pw_aff *
5644 isl_union_pw_aff_align_params(
5645 __isl_take isl_union_pw_aff *upa,
5646 __isl_take isl_space *model);
5647 __isl_give isl_union_pw_multi_aff *
5648 isl_union_pw_multi_aff_align_params(
5649 __isl_take isl_union_pw_multi_aff *upma,
5650 __isl_take isl_space *model);
5651 __isl_give isl_multi_union_pw_aff *
5652 isl_multi_union_pw_aff_align_params(
5653 __isl_take isl_multi_union_pw_aff *mupa,
5654 __isl_take isl_space *model);
5656 #include <isl/polynomial.h>
5657 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5658 __isl_take isl_qpolynomial *qp,
5659 __isl_take isl_space *model);
5661 =item * Unary Arithmetic Operations
5663 #include <isl/set.h>
5664 __isl_give isl_set *isl_set_neg(
5665 __isl_take isl_set *set);
5666 #include <isl/map.h>
5667 __isl_give isl_map *isl_map_neg(
5668 __isl_take isl_map *map);
5670 C<isl_set_neg> constructs a set containing the opposites of
5671 the elements in its argument.
5672 The domain of the result of C<isl_map_neg> is the same
5673 as the domain of its argument. The corresponding range
5674 elements are the opposites of the corresponding range
5675 elements in the argument.
5677 #include <isl/val.h>
5678 __isl_give isl_multi_val *isl_multi_val_neg(
5679 __isl_take isl_multi_val *mv);
5681 #include <isl/aff.h>
5682 __isl_give isl_aff *isl_aff_neg(
5683 __isl_take isl_aff *aff);
5684 __isl_give isl_multi_aff *isl_multi_aff_neg(
5685 __isl_take isl_multi_aff *ma);
5686 __isl_give isl_pw_aff *isl_pw_aff_neg(
5687 __isl_take isl_pw_aff *pwaff);
5688 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
5689 __isl_take isl_pw_multi_aff *pma);
5690 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
5691 __isl_take isl_multi_pw_aff *mpa);
5692 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
5693 __isl_take isl_union_pw_aff *upa);
5694 __isl_give isl_union_pw_multi_aff *
5695 isl_union_pw_multi_aff_neg(
5696 __isl_take isl_union_pw_multi_aff *upma);
5697 __isl_give isl_multi_union_pw_aff *
5698 isl_multi_union_pw_aff_neg(
5699 __isl_take isl_multi_union_pw_aff *mupa);
5700 __isl_give isl_aff *isl_aff_ceil(
5701 __isl_take isl_aff *aff);
5702 __isl_give isl_pw_aff *isl_pw_aff_ceil(
5703 __isl_take isl_pw_aff *pwaff);
5704 __isl_give isl_aff *isl_aff_floor(
5705 __isl_take isl_aff *aff);
5706 __isl_give isl_multi_aff *isl_multi_aff_floor(
5707 __isl_take isl_multi_aff *ma);
5708 __isl_give isl_pw_aff *isl_pw_aff_floor(
5709 __isl_take isl_pw_aff *pwaff);
5710 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
5711 __isl_take isl_union_pw_aff *upa);
5712 __isl_give isl_multi_union_pw_aff *
5713 isl_multi_union_pw_aff_floor(
5714 __isl_take isl_multi_union_pw_aff *mupa);
5716 #include <isl/aff.h>
5717 __isl_give isl_pw_aff *isl_pw_aff_list_min(
5718 __isl_take isl_pw_aff_list *list);
5719 __isl_give isl_pw_aff *isl_pw_aff_list_max(
5720 __isl_take isl_pw_aff_list *list);
5722 #include <isl/polynomial.h>
5723 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5724 __isl_take isl_qpolynomial *qp);
5725 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5726 __isl_take isl_pw_qpolynomial *pwqp);
5727 __isl_give isl_union_pw_qpolynomial *
5728 isl_union_pw_qpolynomial_neg(
5729 __isl_take isl_union_pw_qpolynomial *upwqp);
5730 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5731 __isl_take isl_qpolynomial *qp,
5733 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5734 __isl_take isl_pw_qpolynomial *pwqp,
5739 The following functions evaluate a function in a point.
5741 #include <isl/polynomial.h>
5742 __isl_give isl_val *isl_pw_qpolynomial_eval(
5743 __isl_take isl_pw_qpolynomial *pwqp,
5744 __isl_take isl_point *pnt);
5745 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5746 __isl_take isl_pw_qpolynomial_fold *pwf,
5747 __isl_take isl_point *pnt);
5748 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5749 __isl_take isl_union_pw_qpolynomial *upwqp,
5750 __isl_take isl_point *pnt);
5751 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5752 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5753 __isl_take isl_point *pnt);
5755 These functions return NaN when evaluated at a void point.
5757 =item * Dimension manipulation
5759 It is usually not advisable to directly change the (input or output)
5760 space of a set or a relation as this removes the name and the internal
5761 structure of the space. However, the functions below can be useful
5762 to add new parameters, assuming
5763 C<isl_set_align_params> and C<isl_map_align_params>
5766 #include <isl/space.h>
5767 __isl_give isl_space *isl_space_add_dims(
5768 __isl_take isl_space *space,
5769 enum isl_dim_type type, unsigned n);
5770 __isl_give isl_space *isl_space_insert_dims(
5771 __isl_take isl_space *space,
5772 enum isl_dim_type type, unsigned pos, unsigned n);
5773 __isl_give isl_space *isl_space_drop_dims(
5774 __isl_take isl_space *space,
5775 enum isl_dim_type type, unsigned first, unsigned n);
5776 __isl_give isl_space *isl_space_move_dims(
5777 __isl_take isl_space *space,
5778 enum isl_dim_type dst_type, unsigned dst_pos,
5779 enum isl_dim_type src_type, unsigned src_pos,
5782 #include <isl/local_space.h>
5783 __isl_give isl_local_space *isl_local_space_add_dims(
5784 __isl_take isl_local_space *ls,
5785 enum isl_dim_type type, unsigned n);
5786 __isl_give isl_local_space *isl_local_space_insert_dims(
5787 __isl_take isl_local_space *ls,
5788 enum isl_dim_type type, unsigned first, unsigned n);
5789 __isl_give isl_local_space *isl_local_space_drop_dims(
5790 __isl_take isl_local_space *ls,
5791 enum isl_dim_type type, unsigned first, unsigned n);
5793 #include <isl/set.h>
5794 __isl_give isl_basic_set *isl_basic_set_add_dims(
5795 __isl_take isl_basic_set *bset,
5796 enum isl_dim_type type, unsigned n);
5797 __isl_give isl_set *isl_set_add_dims(
5798 __isl_take isl_set *set,
5799 enum isl_dim_type type, unsigned n);
5800 __isl_give isl_basic_set *isl_basic_set_insert_dims(
5801 __isl_take isl_basic_set *bset,
5802 enum isl_dim_type type, unsigned pos,
5804 __isl_give isl_set *isl_set_insert_dims(
5805 __isl_take isl_set *set,
5806 enum isl_dim_type type, unsigned pos, unsigned n);
5807 __isl_give isl_basic_set *isl_basic_set_move_dims(
5808 __isl_take isl_basic_set *bset,
5809 enum isl_dim_type dst_type, unsigned dst_pos,
5810 enum isl_dim_type src_type, unsigned src_pos,
5812 __isl_give isl_set *isl_set_move_dims(
5813 __isl_take isl_set *set,
5814 enum isl_dim_type dst_type, unsigned dst_pos,
5815 enum isl_dim_type src_type, unsigned src_pos,
5818 #include <isl/map.h>
5819 __isl_give isl_basic_map *isl_basic_map_add_dims(
5820 __isl_take isl_basic_map *bmap,
5821 enum isl_dim_type type, unsigned n);
5822 __isl_give isl_map *isl_map_add_dims(
5823 __isl_take isl_map *map,
5824 enum isl_dim_type type, unsigned n);
5825 __isl_give isl_basic_map *isl_basic_map_insert_dims(
5826 __isl_take isl_basic_map *bmap,
5827 enum isl_dim_type type, unsigned pos,
5829 __isl_give isl_map *isl_map_insert_dims(
5830 __isl_take isl_map *map,
5831 enum isl_dim_type type, unsigned pos, unsigned n);
5832 __isl_give isl_basic_map *isl_basic_map_move_dims(
5833 __isl_take isl_basic_map *bmap,
5834 enum isl_dim_type dst_type, unsigned dst_pos,
5835 enum isl_dim_type src_type, unsigned src_pos,
5837 __isl_give isl_map *isl_map_move_dims(
5838 __isl_take isl_map *map,
5839 enum isl_dim_type dst_type, unsigned dst_pos,
5840 enum isl_dim_type src_type, unsigned src_pos,
5843 #include <isl/val.h>
5844 __isl_give isl_multi_val *isl_multi_val_insert_dims(
5845 __isl_take isl_multi_val *mv,
5846 enum isl_dim_type type, unsigned first, unsigned n);
5847 __isl_give isl_multi_val *isl_multi_val_add_dims(
5848 __isl_take isl_multi_val *mv,
5849 enum isl_dim_type type, unsigned n);
5850 __isl_give isl_multi_val *isl_multi_val_drop_dims(
5851 __isl_take isl_multi_val *mv,
5852 enum isl_dim_type type, unsigned first, unsigned n);
5854 #include <isl/aff.h>
5855 __isl_give isl_aff *isl_aff_insert_dims(
5856 __isl_take isl_aff *aff,
5857 enum isl_dim_type type, unsigned first, unsigned n);
5858 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
5859 __isl_take isl_multi_aff *ma,
5860 enum isl_dim_type type, unsigned first, unsigned n);
5861 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
5862 __isl_take isl_pw_aff *pwaff,
5863 enum isl_dim_type type, unsigned first, unsigned n);
5864 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
5865 __isl_take isl_multi_pw_aff *mpa,
5866 enum isl_dim_type type, unsigned first, unsigned n);
5867 __isl_give isl_aff *isl_aff_add_dims(
5868 __isl_take isl_aff *aff,
5869 enum isl_dim_type type, unsigned n);
5870 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
5871 __isl_take isl_multi_aff *ma,
5872 enum isl_dim_type type, unsigned n);
5873 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
5874 __isl_take isl_pw_aff *pwaff,
5875 enum isl_dim_type type, unsigned n);
5876 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
5877 __isl_take isl_multi_pw_aff *mpa,
5878 enum isl_dim_type type, unsigned n);
5879 __isl_give isl_aff *isl_aff_drop_dims(
5880 __isl_take isl_aff *aff,
5881 enum isl_dim_type type, unsigned first, unsigned n);
5882 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
5883 __isl_take isl_multi_aff *maff,
5884 enum isl_dim_type type, unsigned first, unsigned n);
5885 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
5886 __isl_take isl_pw_aff *pwaff,
5887 enum isl_dim_type type, unsigned first, unsigned n);
5888 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
5889 __isl_take isl_pw_multi_aff *pma,
5890 enum isl_dim_type type, unsigned first, unsigned n);
5891 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
5892 __isl_take isl_union_pw_aff *upa,
5893 enum isl_dim_type type, unsigned first, unsigned n);
5894 __isl_give isl_union_pw_multi_aff *
5895 isl_union_pw_multi_aff_drop_dims(
5896 __isl_take isl_union_pw_multi_aff *upma,
5897 enum isl_dim_type type,
5898 unsigned first, unsigned n);
5899 __isl_give isl_multi_union_pw_aff *
5900 isl_multi_union_pw_aff_drop_dims(
5901 __isl_take isl_multi_union_pw_aff *mupa,
5902 enum isl_dim_type type, unsigned first,
5904 __isl_give isl_aff *isl_aff_move_dims(
5905 __isl_take isl_aff *aff,
5906 enum isl_dim_type dst_type, unsigned dst_pos,
5907 enum isl_dim_type src_type, unsigned src_pos,
5909 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
5910 __isl_take isl_multi_aff *ma,
5911 enum isl_dim_type dst_type, unsigned dst_pos,
5912 enum isl_dim_type src_type, unsigned src_pos,
5914 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
5915 __isl_take isl_pw_aff *pa,
5916 enum isl_dim_type dst_type, unsigned dst_pos,
5917 enum isl_dim_type src_type, unsigned src_pos,
5919 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
5920 __isl_take isl_multi_pw_aff *pma,
5921 enum isl_dim_type dst_type, unsigned dst_pos,
5922 enum isl_dim_type src_type, unsigned src_pos,
5925 #include <isl/polynomial.h>
5926 __isl_give isl_union_pw_qpolynomial *
5927 isl_union_pw_qpolynomial_drop_dims(
5928 __isl_take isl_union_pw_qpolynomial *upwqp,
5929 enum isl_dim_type type,
5930 unsigned first, unsigned n);
5931 __isl_give isl_union_pw_qpolynomial_fold *
5932 isl_union_pw_qpolynomial_fold_drop_dims(
5933 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5934 enum isl_dim_type type,
5935 unsigned first, unsigned n);
5937 The operations on union expressions can only manipulate parameters.
5941 =head2 Binary Operations
5943 The two arguments of a binary operation not only need to live
5944 in the same C<isl_ctx>, they currently also need to have
5945 the same (number of) parameters.
5947 =head3 Basic Operations
5951 =item * Intersection
5953 #include <isl/local_space.h>
5954 __isl_give isl_local_space *isl_local_space_intersect(
5955 __isl_take isl_local_space *ls1,
5956 __isl_take isl_local_space *ls2);
5958 #include <isl/set.h>
5959 __isl_give isl_basic_set *isl_basic_set_intersect_params(
5960 __isl_take isl_basic_set *bset1,
5961 __isl_take isl_basic_set *bset2);
5962 __isl_give isl_basic_set *isl_basic_set_intersect(
5963 __isl_take isl_basic_set *bset1,
5964 __isl_take isl_basic_set *bset2);
5965 __isl_give isl_basic_set *isl_basic_set_list_intersect(
5966 __isl_take struct isl_basic_set_list *list);
5967 __isl_give isl_set *isl_set_intersect_params(
5968 __isl_take isl_set *set,
5969 __isl_take isl_set *params);
5970 __isl_give isl_set *isl_set_intersect(
5971 __isl_take isl_set *set1,
5972 __isl_take isl_set *set2);
5974 #include <isl/map.h>
5975 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
5976 __isl_take isl_basic_map *bmap,
5977 __isl_take isl_basic_set *bset);
5978 __isl_give isl_basic_map *isl_basic_map_intersect_range(
5979 __isl_take isl_basic_map *bmap,
5980 __isl_take isl_basic_set *bset);
5981 __isl_give isl_basic_map *isl_basic_map_intersect(
5982 __isl_take isl_basic_map *bmap1,
5983 __isl_take isl_basic_map *bmap2);
5984 __isl_give isl_basic_map *isl_basic_map_list_intersect(
5985 __isl_take isl_basic_map_list *list);
5986 __isl_give isl_map *isl_map_intersect_params(
5987 __isl_take isl_map *map,
5988 __isl_take isl_set *params);
5989 __isl_give isl_map *isl_map_intersect_domain(
5990 __isl_take isl_map *map,
5991 __isl_take isl_set *set);
5992 __isl_give isl_map *isl_map_intersect_range(
5993 __isl_take isl_map *map,
5994 __isl_take isl_set *set);
5995 __isl_give isl_map *isl_map_intersect(
5996 __isl_take isl_map *map1,
5997 __isl_take isl_map *map2);
5998 __isl_give isl_map *
5999 isl_map_intersect_domain_factor_range(
6000 __isl_take isl_map *map,
6001 __isl_take isl_map *factor);
6002 __isl_give isl_map *
6003 isl_map_intersect_range_factor_range(
6004 __isl_take isl_map *map,
6005 __isl_take isl_map *factor);
6007 #include <isl/union_set.h>
6008 __isl_give isl_union_set *isl_union_set_intersect_params(
6009 __isl_take isl_union_set *uset,
6010 __isl_take isl_set *set);
6011 __isl_give isl_union_set *isl_union_set_intersect(
6012 __isl_take isl_union_set *uset1,
6013 __isl_take isl_union_set *uset2);
6015 #include <isl/union_map.h>
6016 __isl_give isl_union_map *isl_union_map_intersect_params(
6017 __isl_take isl_union_map *umap,
6018 __isl_take isl_set *set);
6019 __isl_give isl_union_map *isl_union_map_intersect_domain(
6020 __isl_take isl_union_map *umap,
6021 __isl_take isl_union_set *uset);
6022 __isl_give isl_union_map *isl_union_map_intersect_range(
6023 __isl_take isl_union_map *umap,
6024 __isl_take isl_union_set *uset);
6025 __isl_give isl_union_map *isl_union_map_intersect(
6026 __isl_take isl_union_map *umap1,
6027 __isl_take isl_union_map *umap2);
6028 __isl_give isl_union_map *
6029 isl_union_map_intersect_range_factor_range(
6030 __isl_take isl_union_map *umap,
6031 __isl_take isl_union_map *factor);
6033 #include <isl/aff.h>
6034 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
6035 __isl_take isl_pw_aff *pa,
6036 __isl_take isl_set *set);
6037 __isl_give isl_multi_pw_aff *
6038 isl_multi_pw_aff_intersect_domain(
6039 __isl_take isl_multi_pw_aff *mpa,
6040 __isl_take isl_set *domain);
6041 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
6042 __isl_take isl_pw_multi_aff *pma,
6043 __isl_take isl_set *set);
6044 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
6045 __isl_take isl_union_pw_aff *upa,
6046 __isl_take isl_union_set *uset);
6047 __isl_give isl_union_pw_multi_aff *
6048 isl_union_pw_multi_aff_intersect_domain(
6049 __isl_take isl_union_pw_multi_aff *upma,
6050 __isl_take isl_union_set *uset);
6051 __isl_give isl_multi_union_pw_aff *
6052 isl_multi_union_pw_aff_intersect_domain(
6053 __isl_take isl_multi_union_pw_aff *mupa,
6054 __isl_take isl_union_set *uset);
6055 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
6056 __isl_take isl_pw_aff *pa,
6057 __isl_take isl_set *set);
6058 __isl_give isl_multi_pw_aff *
6059 isl_multi_pw_aff_intersect_params(
6060 __isl_take isl_multi_pw_aff *mpa,
6061 __isl_take isl_set *set);
6062 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
6063 __isl_take isl_pw_multi_aff *pma,
6064 __isl_take isl_set *set);
6065 __isl_give isl_union_pw_aff *
6066 isl_union_pw_aff_intersect_params(
6067 __isl_take isl_union_pw_aff *upa,
6068 __isl_give isl_union_pw_multi_aff *
6069 isl_union_pw_multi_aff_intersect_params(
6070 __isl_take isl_union_pw_multi_aff *upma,
6071 __isl_take isl_set *set);
6072 __isl_give isl_multi_union_pw_aff *
6073 isl_multi_union_pw_aff_intersect_params(
6074 __isl_take isl_multi_union_pw_aff *mupa,
6075 __isl_take isl_set *params);
6076 isl_multi_union_pw_aff_intersect_range(
6077 __isl_take isl_multi_union_pw_aff *mupa,
6078 __isl_take isl_set *set);
6080 #include <isl/polynomial.h>
6081 __isl_give isl_pw_qpolynomial *
6082 isl_pw_qpolynomial_intersect_domain(
6083 __isl_take isl_pw_qpolynomial *pwpq,
6084 __isl_take isl_set *set);
6085 __isl_give isl_union_pw_qpolynomial *
6086 isl_union_pw_qpolynomial_intersect_domain(
6087 __isl_take isl_union_pw_qpolynomial *upwpq,
6088 __isl_take isl_union_set *uset);
6089 __isl_give isl_union_pw_qpolynomial_fold *
6090 isl_union_pw_qpolynomial_fold_intersect_domain(
6091 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6092 __isl_take isl_union_set *uset);
6093 __isl_give isl_pw_qpolynomial *
6094 isl_pw_qpolynomial_intersect_params(
6095 __isl_take isl_pw_qpolynomial *pwpq,
6096 __isl_take isl_set *set);
6097 __isl_give isl_pw_qpolynomial_fold *
6098 isl_pw_qpolynomial_fold_intersect_params(
6099 __isl_take isl_pw_qpolynomial_fold *pwf,
6100 __isl_take isl_set *set);
6101 __isl_give isl_union_pw_qpolynomial *
6102 isl_union_pw_qpolynomial_intersect_params(
6103 __isl_take isl_union_pw_qpolynomial *upwpq,
6104 __isl_take isl_set *set);
6105 __isl_give isl_union_pw_qpolynomial_fold *
6106 isl_union_pw_qpolynomial_fold_intersect_params(
6107 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6108 __isl_take isl_set *set);
6110 The second argument to the C<_params> functions needs to be
6111 a parametric (basic) set. For the other functions, a parametric set
6112 for either argument is only allowed if the other argument is
6113 a parametric set as well.
6114 The list passed to C<isl_basic_set_list_intersect> needs to have
6115 at least one element and all elements need to live in the same space.
6116 The function C<isl_multi_union_pw_aff_intersect_range>
6117 restricts the input function to those shared domain elements
6118 that map to the specified range.
6122 #include <isl/set.h>
6123 __isl_give isl_set *isl_basic_set_union(
6124 __isl_take isl_basic_set *bset1,
6125 __isl_take isl_basic_set *bset2);
6126 __isl_give isl_set *isl_set_union(
6127 __isl_take isl_set *set1,
6128 __isl_take isl_set *set2);
6129 __isl_give isl_set *isl_set_list_union(
6130 __isl_take isl_set_list *list);
6132 #include <isl/map.h>
6133 __isl_give isl_map *isl_basic_map_union(
6134 __isl_take isl_basic_map *bmap1,
6135 __isl_take isl_basic_map *bmap2);
6136 __isl_give isl_map *isl_map_union(
6137 __isl_take isl_map *map1,
6138 __isl_take isl_map *map2);
6140 #include <isl/union_set.h>
6141 __isl_give isl_union_set *isl_union_set_union(
6142 __isl_take isl_union_set *uset1,
6143 __isl_take isl_union_set *uset2);
6144 __isl_give isl_union_set *isl_union_set_list_union(
6145 __isl_take isl_union_set_list *list);
6147 #include <isl/union_map.h>
6148 __isl_give isl_union_map *isl_union_map_union(
6149 __isl_take isl_union_map *umap1,
6150 __isl_take isl_union_map *umap2);
6152 The list passed to C<isl_set_list_union> needs to have
6153 at least one element and all elements need to live in the same space.
6155 =item * Set difference
6157 #include <isl/set.h>
6158 __isl_give isl_set *isl_set_subtract(
6159 __isl_take isl_set *set1,
6160 __isl_take isl_set *set2);
6162 #include <isl/map.h>
6163 __isl_give isl_map *isl_map_subtract(
6164 __isl_take isl_map *map1,
6165 __isl_take isl_map *map2);
6166 __isl_give isl_map *isl_map_subtract_domain(
6167 __isl_take isl_map *map,
6168 __isl_take isl_set *dom);
6169 __isl_give isl_map *isl_map_subtract_range(
6170 __isl_take isl_map *map,
6171 __isl_take isl_set *dom);
6173 #include <isl/union_set.h>
6174 __isl_give isl_union_set *isl_union_set_subtract(
6175 __isl_take isl_union_set *uset1,
6176 __isl_take isl_union_set *uset2);
6178 #include <isl/union_map.h>
6179 __isl_give isl_union_map *isl_union_map_subtract(
6180 __isl_take isl_union_map *umap1,
6181 __isl_take isl_union_map *umap2);
6182 __isl_give isl_union_map *isl_union_map_subtract_domain(
6183 __isl_take isl_union_map *umap,
6184 __isl_take isl_union_set *dom);
6185 __isl_give isl_union_map *isl_union_map_subtract_range(
6186 __isl_take isl_union_map *umap,
6187 __isl_take isl_union_set *dom);
6189 #include <isl/aff.h>
6190 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
6191 __isl_take isl_pw_aff *pa,
6192 __isl_take isl_set *set);
6193 __isl_give isl_pw_multi_aff *
6194 isl_pw_multi_aff_subtract_domain(
6195 __isl_take isl_pw_multi_aff *pma,
6196 __isl_take isl_set *set);
6197 __isl_give isl_union_pw_aff *
6198 isl_union_pw_aff_subtract_domain(
6199 __isl_take isl_union_pw_aff *upa,
6200 __isl_take isl_union_set *uset);
6201 __isl_give isl_union_pw_multi_aff *
6202 isl_union_pw_multi_aff_subtract_domain(
6203 __isl_take isl_union_pw_multi_aff *upma,
6204 __isl_take isl_set *set);
6206 #include <isl/polynomial.h>
6207 __isl_give isl_pw_qpolynomial *
6208 isl_pw_qpolynomial_subtract_domain(
6209 __isl_take isl_pw_qpolynomial *pwpq,
6210 __isl_take isl_set *set);
6211 __isl_give isl_pw_qpolynomial_fold *
6212 isl_pw_qpolynomial_fold_subtract_domain(
6213 __isl_take isl_pw_qpolynomial_fold *pwf,
6214 __isl_take isl_set *set);
6215 __isl_give isl_union_pw_qpolynomial *
6216 isl_union_pw_qpolynomial_subtract_domain(
6217 __isl_take isl_union_pw_qpolynomial *upwpq,
6218 __isl_take isl_union_set *uset);
6219 __isl_give isl_union_pw_qpolynomial_fold *
6220 isl_union_pw_qpolynomial_fold_subtract_domain(
6221 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6222 __isl_take isl_union_set *uset);
6226 #include <isl/space.h>
6227 __isl_give isl_space *isl_space_join(
6228 __isl_take isl_space *left,
6229 __isl_take isl_space *right);
6231 #include <isl/map.h>
6232 __isl_give isl_basic_set *isl_basic_set_apply(
6233 __isl_take isl_basic_set *bset,
6234 __isl_take isl_basic_map *bmap);
6235 __isl_give isl_set *isl_set_apply(
6236 __isl_take isl_set *set,
6237 __isl_take isl_map *map);
6238 __isl_give isl_union_set *isl_union_set_apply(
6239 __isl_take isl_union_set *uset,
6240 __isl_take isl_union_map *umap);
6241 __isl_give isl_basic_map *isl_basic_map_apply_domain(
6242 __isl_take isl_basic_map *bmap1,
6243 __isl_take isl_basic_map *bmap2);
6244 __isl_give isl_basic_map *isl_basic_map_apply_range(
6245 __isl_take isl_basic_map *bmap1,
6246 __isl_take isl_basic_map *bmap2);
6247 __isl_give isl_map *isl_map_apply_domain(
6248 __isl_take isl_map *map1,
6249 __isl_take isl_map *map2);
6250 __isl_give isl_map *isl_map_apply_range(
6251 __isl_take isl_map *map1,
6252 __isl_take isl_map *map2);
6254 #include <isl/union_map.h>
6255 __isl_give isl_union_map *isl_union_map_apply_domain(
6256 __isl_take isl_union_map *umap1,
6257 __isl_take isl_union_map *umap2);
6258 __isl_give isl_union_map *isl_union_map_apply_range(
6259 __isl_take isl_union_map *umap1,
6260 __isl_take isl_union_map *umap2);
6262 #include <isl/aff.h>
6263 __isl_give isl_union_pw_aff *
6264 isl_multi_union_pw_aff_apply_aff(
6265 __isl_take isl_multi_union_pw_aff *mupa,
6266 __isl_take isl_aff *aff);
6267 __isl_give isl_union_pw_aff *
6268 isl_multi_union_pw_aff_apply_pw_aff(
6269 __isl_take isl_multi_union_pw_aff *mupa,
6270 __isl_take isl_pw_aff *pa);
6271 __isl_give isl_multi_union_pw_aff *
6272 isl_multi_union_pw_aff_apply_multi_aff(
6273 __isl_take isl_multi_union_pw_aff *mupa,
6274 __isl_take isl_multi_aff *ma);
6275 __isl_give isl_multi_union_pw_aff *
6276 isl_multi_union_pw_aff_apply_pw_multi_aff(
6277 __isl_take isl_multi_union_pw_aff *mupa,
6278 __isl_take isl_pw_multi_aff *pma);
6280 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
6281 over the shared domain of the elements of the input. The dimension is
6282 required to be greater than zero.
6283 The C<isl_multi_union_pw_aff> argument of
6284 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
6285 but only if the range of the C<isl_multi_aff> argument
6286 is also zero-dimensional.
6287 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
6289 #include <isl/polynomial.h>
6290 __isl_give isl_pw_qpolynomial_fold *
6291 isl_set_apply_pw_qpolynomial_fold(
6292 __isl_take isl_set *set,
6293 __isl_take isl_pw_qpolynomial_fold *pwf,
6295 __isl_give isl_pw_qpolynomial_fold *
6296 isl_map_apply_pw_qpolynomial_fold(
6297 __isl_take isl_map *map,
6298 __isl_take isl_pw_qpolynomial_fold *pwf,
6300 __isl_give isl_union_pw_qpolynomial_fold *
6301 isl_union_set_apply_union_pw_qpolynomial_fold(
6302 __isl_take isl_union_set *uset,
6303 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6305 __isl_give isl_union_pw_qpolynomial_fold *
6306 isl_union_map_apply_union_pw_qpolynomial_fold(
6307 __isl_take isl_union_map *umap,
6308 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6311 The functions taking a map
6312 compose the given map with the given piecewise quasipolynomial reduction.
6313 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
6314 over all elements in the intersection of the range of the map
6315 and the domain of the piecewise quasipolynomial reduction
6316 as a function of an element in the domain of the map.
6317 The functions taking a set compute a bound over all elements in the
6318 intersection of the set and the domain of the
6319 piecewise quasipolynomial reduction.
6323 #include <isl/set.h>
6324 __isl_give isl_basic_set *
6325 isl_basic_set_preimage_multi_aff(
6326 __isl_take isl_basic_set *bset,
6327 __isl_take isl_multi_aff *ma);
6328 __isl_give isl_set *isl_set_preimage_multi_aff(
6329 __isl_take isl_set *set,
6330 __isl_take isl_multi_aff *ma);
6331 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
6332 __isl_take isl_set *set,
6333 __isl_take isl_pw_multi_aff *pma);
6334 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
6335 __isl_take isl_set *set,
6336 __isl_take isl_multi_pw_aff *mpa);
6338 #include <isl/union_set.h>
6339 __isl_give isl_union_set *
6340 isl_union_set_preimage_multi_aff(
6341 __isl_take isl_union_set *uset,
6342 __isl_take isl_multi_aff *ma);
6343 __isl_give isl_union_set *
6344 isl_union_set_preimage_pw_multi_aff(
6345 __isl_take isl_union_set *uset,
6346 __isl_take isl_pw_multi_aff *pma);
6347 __isl_give isl_union_set *
6348 isl_union_set_preimage_union_pw_multi_aff(
6349 __isl_take isl_union_set *uset,
6350 __isl_take isl_union_pw_multi_aff *upma);
6352 #include <isl/map.h>
6353 __isl_give isl_basic_map *
6354 isl_basic_map_preimage_domain_multi_aff(
6355 __isl_take isl_basic_map *bmap,
6356 __isl_take isl_multi_aff *ma);
6357 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
6358 __isl_take isl_map *map,
6359 __isl_take isl_multi_aff *ma);
6360 __isl_give isl_map *isl_map_preimage_range_multi_aff(
6361 __isl_take isl_map *map,
6362 __isl_take isl_multi_aff *ma);
6363 __isl_give isl_map *
6364 isl_map_preimage_domain_pw_multi_aff(
6365 __isl_take isl_map *map,
6366 __isl_take isl_pw_multi_aff *pma);
6367 __isl_give isl_map *
6368 isl_map_preimage_range_pw_multi_aff(
6369 __isl_take isl_map *map,
6370 __isl_take isl_pw_multi_aff *pma);
6371 __isl_give isl_map *
6372 isl_map_preimage_domain_multi_pw_aff(
6373 __isl_take isl_map *map,
6374 __isl_take isl_multi_pw_aff *mpa);
6375 __isl_give isl_basic_map *
6376 isl_basic_map_preimage_range_multi_aff(
6377 __isl_take isl_basic_map *bmap,
6378 __isl_take isl_multi_aff *ma);
6380 #include <isl/union_map.h>
6381 __isl_give isl_union_map *
6382 isl_union_map_preimage_domain_multi_aff(
6383 __isl_take isl_union_map *umap,
6384 __isl_take isl_multi_aff *ma);
6385 __isl_give isl_union_map *
6386 isl_union_map_preimage_range_multi_aff(
6387 __isl_take isl_union_map *umap,
6388 __isl_take isl_multi_aff *ma);
6389 __isl_give isl_union_map *
6390 isl_union_map_preimage_domain_pw_multi_aff(
6391 __isl_take isl_union_map *umap,
6392 __isl_take isl_pw_multi_aff *pma);
6393 __isl_give isl_union_map *
6394 isl_union_map_preimage_range_pw_multi_aff(
6395 __isl_take isl_union_map *umap,
6396 __isl_take isl_pw_multi_aff *pma);
6397 __isl_give isl_union_map *
6398 isl_union_map_preimage_domain_union_pw_multi_aff(
6399 __isl_take isl_union_map *umap,
6400 __isl_take isl_union_pw_multi_aff *upma);
6401 __isl_give isl_union_map *
6402 isl_union_map_preimage_range_union_pw_multi_aff(
6403 __isl_take isl_union_map *umap,
6404 __isl_take isl_union_pw_multi_aff *upma);
6406 These functions compute the preimage of the given set or map domain/range under
6407 the given function. In other words, the expression is plugged
6408 into the set description or into the domain/range of the map.
6412 #include <isl/aff.h>
6413 __isl_give isl_aff *isl_aff_pullback_aff(
6414 __isl_take isl_aff *aff1,
6415 __isl_take isl_aff *aff2);
6416 __isl_give isl_aff *isl_aff_pullback_multi_aff(
6417 __isl_take isl_aff *aff,
6418 __isl_take isl_multi_aff *ma);
6419 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
6420 __isl_take isl_pw_aff *pa,
6421 __isl_take isl_multi_aff *ma);
6422 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
6423 __isl_take isl_pw_aff *pa,
6424 __isl_take isl_pw_multi_aff *pma);
6425 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
6426 __isl_take isl_pw_aff *pa,
6427 __isl_take isl_multi_pw_aff *mpa);
6428 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
6429 __isl_take isl_multi_aff *ma1,
6430 __isl_take isl_multi_aff *ma2);
6431 __isl_give isl_pw_multi_aff *
6432 isl_pw_multi_aff_pullback_multi_aff(
6433 __isl_take isl_pw_multi_aff *pma,
6434 __isl_take isl_multi_aff *ma);
6435 __isl_give isl_multi_pw_aff *
6436 isl_multi_pw_aff_pullback_multi_aff(
6437 __isl_take isl_multi_pw_aff *mpa,
6438 __isl_take isl_multi_aff *ma);
6439 __isl_give isl_pw_multi_aff *
6440 isl_pw_multi_aff_pullback_pw_multi_aff(
6441 __isl_take isl_pw_multi_aff *pma1,
6442 __isl_take isl_pw_multi_aff *pma2);
6443 __isl_give isl_multi_pw_aff *
6444 isl_multi_pw_aff_pullback_pw_multi_aff(
6445 __isl_take isl_multi_pw_aff *mpa,
6446 __isl_take isl_pw_multi_aff *pma);
6447 __isl_give isl_multi_pw_aff *
6448 isl_multi_pw_aff_pullback_multi_pw_aff(
6449 __isl_take isl_multi_pw_aff *mpa1,
6450 __isl_take isl_multi_pw_aff *mpa2);
6451 __isl_give isl_union_pw_aff *
6452 isl_union_pw_aff_pullback_union_pw_multi_aff(
6453 __isl_take isl_union_pw_aff *upa,
6454 __isl_take isl_union_pw_multi_aff *upma);
6455 __isl_give isl_union_pw_multi_aff *
6456 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
6457 __isl_take isl_union_pw_multi_aff *upma1,
6458 __isl_take isl_union_pw_multi_aff *upma2);
6459 __isl_give isl_multi_union_pw_aff *
6460 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
6461 __isl_take isl_multi_union_pw_aff *mupa,
6462 __isl_take isl_union_pw_multi_aff *upma);
6464 These functions precompose the first expression by the second function.
6465 In other words, the second function is plugged
6466 into the first expression.
6470 #include <isl/aff.h>
6471 __isl_give isl_basic_set *isl_aff_eq_basic_set(
6472 __isl_take isl_aff *aff1,
6473 __isl_take isl_aff *aff2);
6474 __isl_give isl_set *isl_aff_eq_set(
6475 __isl_take isl_aff *aff1,
6476 __isl_take isl_aff *aff2);
6477 __isl_give isl_set *isl_aff_ne_set(
6478 __isl_take isl_aff *aff1,
6479 __isl_take isl_aff *aff2);
6480 __isl_give isl_basic_set *isl_aff_le_basic_set(
6481 __isl_take isl_aff *aff1,
6482 __isl_take isl_aff *aff2);
6483 __isl_give isl_set *isl_aff_le_set(
6484 __isl_take isl_aff *aff1,
6485 __isl_take isl_aff *aff2);
6486 __isl_give isl_basic_set *isl_aff_lt_basic_set(
6487 __isl_take isl_aff *aff1,
6488 __isl_take isl_aff *aff2);
6489 __isl_give isl_set *isl_aff_lt_set(
6490 __isl_take isl_aff *aff1,
6491 __isl_take isl_aff *aff2);
6492 __isl_give isl_basic_set *isl_aff_ge_basic_set(
6493 __isl_take isl_aff *aff1,
6494 __isl_take isl_aff *aff2);
6495 __isl_give isl_set *isl_aff_ge_set(
6496 __isl_take isl_aff *aff1,
6497 __isl_take isl_aff *aff2);
6498 __isl_give isl_basic_set *isl_aff_gt_basic_set(
6499 __isl_take isl_aff *aff1,
6500 __isl_take isl_aff *aff2);
6501 __isl_give isl_set *isl_aff_gt_set(
6502 __isl_take isl_aff *aff1,
6503 __isl_take isl_aff *aff2);
6504 __isl_give isl_set *isl_pw_aff_eq_set(
6505 __isl_take isl_pw_aff *pwaff1,
6506 __isl_take isl_pw_aff *pwaff2);
6507 __isl_give isl_set *isl_pw_aff_ne_set(
6508 __isl_take isl_pw_aff *pwaff1,
6509 __isl_take isl_pw_aff *pwaff2);
6510 __isl_give isl_set *isl_pw_aff_le_set(
6511 __isl_take isl_pw_aff *pwaff1,
6512 __isl_take isl_pw_aff *pwaff2);
6513 __isl_give isl_set *isl_pw_aff_lt_set(
6514 __isl_take isl_pw_aff *pwaff1,
6515 __isl_take isl_pw_aff *pwaff2);
6516 __isl_give isl_set *isl_pw_aff_ge_set(
6517 __isl_take isl_pw_aff *pwaff1,
6518 __isl_take isl_pw_aff *pwaff2);
6519 __isl_give isl_set *isl_pw_aff_gt_set(
6520 __isl_take isl_pw_aff *pwaff1,
6521 __isl_take isl_pw_aff *pwaff2);
6523 __isl_give isl_set *isl_multi_aff_lex_le_set(
6524 __isl_take isl_multi_aff *ma1,
6525 __isl_take isl_multi_aff *ma2);
6526 __isl_give isl_set *isl_multi_aff_lex_lt_set(
6527 __isl_take isl_multi_aff *ma1,
6528 __isl_take isl_multi_aff *ma2);
6529 __isl_give isl_set *isl_multi_aff_lex_ge_set(
6530 __isl_take isl_multi_aff *ma1,
6531 __isl_take isl_multi_aff *ma2);
6532 __isl_give isl_set *isl_multi_aff_lex_gt_set(
6533 __isl_take isl_multi_aff *ma1,
6534 __isl_take isl_multi_aff *ma2);
6536 __isl_give isl_set *isl_pw_aff_list_eq_set(
6537 __isl_take isl_pw_aff_list *list1,
6538 __isl_take isl_pw_aff_list *list2);
6539 __isl_give isl_set *isl_pw_aff_list_ne_set(
6540 __isl_take isl_pw_aff_list *list1,
6541 __isl_take isl_pw_aff_list *list2);
6542 __isl_give isl_set *isl_pw_aff_list_le_set(
6543 __isl_take isl_pw_aff_list *list1,
6544 __isl_take isl_pw_aff_list *list2);
6545 __isl_give isl_set *isl_pw_aff_list_lt_set(
6546 __isl_take isl_pw_aff_list *list1,
6547 __isl_take isl_pw_aff_list *list2);
6548 __isl_give isl_set *isl_pw_aff_list_ge_set(
6549 __isl_take isl_pw_aff_list *list1,
6550 __isl_take isl_pw_aff_list *list2);
6551 __isl_give isl_set *isl_pw_aff_list_gt_set(
6552 __isl_take isl_pw_aff_list *list1,
6553 __isl_take isl_pw_aff_list *list2);
6555 The function C<isl_aff_ge_basic_set> returns a basic set
6556 containing those elements in the shared space
6557 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
6558 The function C<isl_pw_aff_ge_set> returns a set
6559 containing those elements in the shared domain
6560 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
6561 greater than or equal to C<pwaff2>.
6562 The function C<isl_multi_aff_lex_le_set> returns a set
6563 containing those elements in the shared domain space
6564 where C<ma1> is lexicographically smaller than or
6566 The functions operating on C<isl_pw_aff_list> apply the corresponding
6567 C<isl_pw_aff> function to each pair of elements in the two lists.
6569 #include <isl/aff.h>
6570 __isl_give isl_map *isl_pw_aff_eq_map(
6571 __isl_take isl_pw_aff *pa1,
6572 __isl_take isl_pw_aff *pa2);
6573 __isl_give isl_map *isl_pw_aff_lt_map(
6574 __isl_take isl_pw_aff *pa1,
6575 __isl_take isl_pw_aff *pa2);
6576 __isl_give isl_map *isl_pw_aff_gt_map(
6577 __isl_take isl_pw_aff *pa1,
6578 __isl_take isl_pw_aff *pa2);
6580 __isl_give isl_map *isl_multi_pw_aff_eq_map(
6581 __isl_take isl_multi_pw_aff *mpa1,
6582 __isl_take isl_multi_pw_aff *mpa2);
6583 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
6584 __isl_take isl_multi_pw_aff *mpa1,
6585 __isl_take isl_multi_pw_aff *mpa2);
6586 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
6587 __isl_take isl_multi_pw_aff *mpa1,
6588 __isl_take isl_multi_pw_aff *mpa2);
6590 These functions return a map between domain elements of the arguments
6591 where the function values satisfy the given relation.
6593 #include <isl/union_map.h>
6594 __isl_give isl_union_map *
6595 isl_union_map_eq_at_multi_union_pw_aff(
6596 __isl_take isl_union_map *umap,
6597 __isl_take isl_multi_union_pw_aff *mupa);
6598 __isl_give isl_union_map *
6599 isl_union_map_lex_lt_at_multi_union_pw_aff(
6600 __isl_take isl_union_map *umap,
6601 __isl_take isl_multi_union_pw_aff *mupa);
6602 __isl_give isl_union_map *
6603 isl_union_map_lex_gt_at_multi_union_pw_aff(
6604 __isl_take isl_union_map *umap,
6605 __isl_take isl_multi_union_pw_aff *mupa);
6607 These functions select the subset of elements in the union map
6608 that have an equal or lexicographically smaller function value.
6610 =item * Cartesian Product
6612 #include <isl/space.h>
6613 __isl_give isl_space *isl_space_product(
6614 __isl_take isl_space *space1,
6615 __isl_take isl_space *space2);
6616 __isl_give isl_space *isl_space_domain_product(
6617 __isl_take isl_space *space1,
6618 __isl_take isl_space *space2);
6619 __isl_give isl_space *isl_space_range_product(
6620 __isl_take isl_space *space1,
6621 __isl_take isl_space *space2);
6624 C<isl_space_product>, C<isl_space_domain_product>
6625 and C<isl_space_range_product> take pairs or relation spaces and
6626 produce a single relations space, where either the domain, the range
6627 or both domain and range are wrapped spaces of relations between
6628 the domains and/or ranges of the input spaces.
6629 If the product is only constructed over the domain or the range
6630 then the ranges or the domains of the inputs should be the same.
6631 The function C<isl_space_product> also accepts a pair of set spaces,
6632 in which case it returns a wrapped space of a relation between the
6635 #include <isl/set.h>
6636 __isl_give isl_set *isl_set_product(
6637 __isl_take isl_set *set1,
6638 __isl_take isl_set *set2);
6640 #include <isl/map.h>
6641 __isl_give isl_basic_map *isl_basic_map_domain_product(
6642 __isl_take isl_basic_map *bmap1,
6643 __isl_take isl_basic_map *bmap2);
6644 __isl_give isl_basic_map *isl_basic_map_range_product(
6645 __isl_take isl_basic_map *bmap1,
6646 __isl_take isl_basic_map *bmap2);
6647 __isl_give isl_basic_map *isl_basic_map_product(
6648 __isl_take isl_basic_map *bmap1,
6649 __isl_take isl_basic_map *bmap2);
6650 __isl_give isl_map *isl_map_domain_product(
6651 __isl_take isl_map *map1,
6652 __isl_take isl_map *map2);
6653 __isl_give isl_map *isl_map_range_product(
6654 __isl_take isl_map *map1,
6655 __isl_take isl_map *map2);
6656 __isl_give isl_map *isl_map_product(
6657 __isl_take isl_map *map1,
6658 __isl_take isl_map *map2);
6660 #include <isl/union_set.h>
6661 __isl_give isl_union_set *isl_union_set_product(
6662 __isl_take isl_union_set *uset1,
6663 __isl_take isl_union_set *uset2);
6665 #include <isl/union_map.h>
6666 __isl_give isl_union_map *isl_union_map_domain_product(
6667 __isl_take isl_union_map *umap1,
6668 __isl_take isl_union_map *umap2);
6669 __isl_give isl_union_map *isl_union_map_range_product(
6670 __isl_take isl_union_map *umap1,
6671 __isl_take isl_union_map *umap2);
6672 __isl_give isl_union_map *isl_union_map_product(
6673 __isl_take isl_union_map *umap1,
6674 __isl_take isl_union_map *umap2);
6676 #include <isl/val.h>
6677 __isl_give isl_multi_val *isl_multi_val_range_product(
6678 __isl_take isl_multi_val *mv1,
6679 __isl_take isl_multi_val *mv2);
6680 __isl_give isl_multi_val *isl_multi_val_product(
6681 __isl_take isl_multi_val *mv1,
6682 __isl_take isl_multi_val *mv2);
6684 #include <isl/aff.h>
6685 __isl_give isl_multi_aff *isl_multi_aff_range_product(
6686 __isl_take isl_multi_aff *ma1,
6687 __isl_take isl_multi_aff *ma2);
6688 __isl_give isl_multi_aff *isl_multi_aff_product(
6689 __isl_take isl_multi_aff *ma1,
6690 __isl_take isl_multi_aff *ma2);
6691 __isl_give isl_multi_pw_aff *
6692 isl_multi_pw_aff_range_product(
6693 __isl_take isl_multi_pw_aff *mpa1,
6694 __isl_take isl_multi_pw_aff *mpa2);
6695 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
6696 __isl_take isl_multi_pw_aff *mpa1,
6697 __isl_take isl_multi_pw_aff *mpa2);
6698 __isl_give isl_pw_multi_aff *
6699 isl_pw_multi_aff_range_product(
6700 __isl_take isl_pw_multi_aff *pma1,
6701 __isl_take isl_pw_multi_aff *pma2);
6702 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
6703 __isl_take isl_pw_multi_aff *pma1,
6704 __isl_take isl_pw_multi_aff *pma2);
6705 __isl_give isl_multi_union_pw_aff *
6706 isl_multi_union_pw_aff_range_product(
6707 __isl_take isl_multi_union_pw_aff *mupa1,
6708 __isl_take isl_multi_union_pw_aff *mupa2);
6710 The above functions compute the cross product of the given
6711 sets, relations or functions. The domains and ranges of the results
6712 are wrapped maps between domains and ranges of the inputs.
6713 To obtain a ``flat'' product, use the following functions
6716 #include <isl/set.h>
6717 __isl_give isl_basic_set *isl_basic_set_flat_product(
6718 __isl_take isl_basic_set *bset1,
6719 __isl_take isl_basic_set *bset2);
6720 __isl_give isl_set *isl_set_flat_product(
6721 __isl_take isl_set *set1,
6722 __isl_take isl_set *set2);
6724 #include <isl/map.h>
6725 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
6726 __isl_take isl_basic_map *bmap1,
6727 __isl_take isl_basic_map *bmap2);
6728 __isl_give isl_map *isl_map_flat_domain_product(
6729 __isl_take isl_map *map1,
6730 __isl_take isl_map *map2);
6731 __isl_give isl_map *isl_map_flat_range_product(
6732 __isl_take isl_map *map1,
6733 __isl_take isl_map *map2);
6734 __isl_give isl_basic_map *isl_basic_map_flat_product(
6735 __isl_take isl_basic_map *bmap1,
6736 __isl_take isl_basic_map *bmap2);
6737 __isl_give isl_map *isl_map_flat_product(
6738 __isl_take isl_map *map1,
6739 __isl_take isl_map *map2);
6741 #include <isl/union_map.h>
6742 __isl_give isl_union_map *
6743 isl_union_map_flat_domain_product(
6744 __isl_take isl_union_map *umap1,
6745 __isl_take isl_union_map *umap2);
6746 __isl_give isl_union_map *
6747 isl_union_map_flat_range_product(
6748 __isl_take isl_union_map *umap1,
6749 __isl_take isl_union_map *umap2);
6751 #include <isl/val.h>
6752 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
6753 __isl_take isl_multi_val *mv1,
6754 __isl_take isl_multi_aff *mv2);
6756 #include <isl/aff.h>
6757 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
6758 __isl_take isl_multi_aff *ma1,
6759 __isl_take isl_multi_aff *ma2);
6760 __isl_give isl_pw_multi_aff *
6761 isl_pw_multi_aff_flat_range_product(
6762 __isl_take isl_pw_multi_aff *pma1,
6763 __isl_take isl_pw_multi_aff *pma2);
6764 __isl_give isl_multi_pw_aff *
6765 isl_multi_pw_aff_flat_range_product(
6766 __isl_take isl_multi_pw_aff *mpa1,
6767 __isl_take isl_multi_pw_aff *mpa2);
6768 __isl_give isl_union_pw_multi_aff *
6769 isl_union_pw_multi_aff_flat_range_product(
6770 __isl_take isl_union_pw_multi_aff *upma1,
6771 __isl_take isl_union_pw_multi_aff *upma2);
6772 __isl_give isl_multi_union_pw_aff *
6773 isl_multi_union_pw_aff_flat_range_product(
6774 __isl_take isl_multi_union_pw_aff *mupa1,
6775 __isl_take isl_multi_union_pw_aff *mupa2);
6777 #include <isl/space.h>
6778 __isl_give isl_space *isl_space_factor_domain(
6779 __isl_take isl_space *space);
6780 __isl_give isl_space *isl_space_factor_range(
6781 __isl_take isl_space *space);
6782 __isl_give isl_space *isl_space_domain_factor_domain(
6783 __isl_take isl_space *space);
6784 __isl_give isl_space *isl_space_domain_factor_range(
6785 __isl_take isl_space *space);
6786 __isl_give isl_space *isl_space_range_factor_domain(
6787 __isl_take isl_space *space);
6788 __isl_give isl_space *isl_space_range_factor_range(
6789 __isl_take isl_space *space);
6791 The functions C<isl_space_range_factor_domain> and
6792 C<isl_space_range_factor_range> extract the two arguments from
6793 the result of a call to C<isl_space_range_product>.
6795 The arguments of a call to a product can be extracted
6796 from the result using the following functions.
6798 #include <isl/map.h>
6799 __isl_give isl_map *isl_map_factor_domain(
6800 __isl_take isl_map *map);
6801 __isl_give isl_map *isl_map_factor_range(
6802 __isl_take isl_map *map);
6803 __isl_give isl_map *isl_map_domain_factor_domain(
6804 __isl_take isl_map *map);
6805 __isl_give isl_map *isl_map_domain_factor_range(
6806 __isl_take isl_map *map);
6807 __isl_give isl_map *isl_map_range_factor_domain(
6808 __isl_take isl_map *map);
6809 __isl_give isl_map *isl_map_range_factor_range(
6810 __isl_take isl_map *map);
6812 #include <isl/union_map.h>
6813 __isl_give isl_union_map *isl_union_map_factor_domain(
6814 __isl_take isl_union_map *umap);
6815 __isl_give isl_union_map *isl_union_map_factor_range(
6816 __isl_take isl_union_map *umap);
6817 __isl_give isl_union_map *
6818 isl_union_map_domain_factor_domain(
6819 __isl_take isl_union_map *umap);
6820 __isl_give isl_union_map *
6821 isl_union_map_domain_factor_range(
6822 __isl_take isl_union_map *umap);
6823 __isl_give isl_union_map *
6824 isl_union_map_range_factor_domain(
6825 __isl_take isl_union_map *umap);
6826 __isl_give isl_union_map *
6827 isl_union_map_range_factor_range(
6828 __isl_take isl_union_map *umap);
6830 #include <isl/val.h>
6831 __isl_give isl_multi_val *isl_multi_val_factor_range(
6832 __isl_take isl_multi_val *mv);
6833 __isl_give isl_multi_val *
6834 isl_multi_val_range_factor_domain(
6835 __isl_take isl_multi_val *mv);
6836 __isl_give isl_multi_val *
6837 isl_multi_val_range_factor_range(
6838 __isl_take isl_multi_val *mv);
6840 #include <isl/aff.h>
6841 __isl_give isl_multi_aff *isl_multi_aff_factor_range(
6842 __isl_take isl_multi_aff *ma);
6843 __isl_give isl_multi_aff *
6844 isl_multi_aff_range_factor_domain(
6845 __isl_take isl_multi_aff *ma);
6846 __isl_give isl_multi_aff *
6847 isl_multi_aff_range_factor_range(
6848 __isl_take isl_multi_aff *ma);
6849 __isl_give isl_multi_pw_aff *
6850 isl_multi_pw_aff_factor_range(
6851 __isl_take isl_multi_pw_aff *mpa);
6852 __isl_give isl_multi_pw_aff *
6853 isl_multi_pw_aff_range_factor_domain(
6854 __isl_take isl_multi_pw_aff *mpa);
6855 __isl_give isl_multi_pw_aff *
6856 isl_multi_pw_aff_range_factor_range(
6857 __isl_take isl_multi_pw_aff *mpa);
6858 __isl_give isl_multi_union_pw_aff *
6859 isl_multi_union_pw_aff_factor_range(
6860 __isl_take isl_multi_union_pw_aff *mupa);
6861 __isl_give isl_multi_union_pw_aff *
6862 isl_multi_union_pw_aff_range_factor_domain(
6863 __isl_take isl_multi_union_pw_aff *mupa);
6864 __isl_give isl_multi_union_pw_aff *
6865 isl_multi_union_pw_aff_range_factor_range(
6866 __isl_take isl_multi_union_pw_aff *mupa);
6868 The splice functions are a generalization of the flat product functions,
6869 where the second argument may be inserted at any position inside
6870 the first argument rather than being placed at the end.
6871 The functions C<isl_multi_val_factor_range>,
6872 C<isl_multi_aff_factor_range>,
6873 C<isl_multi_pw_aff_factor_range> and
6874 C<isl_multi_union_pw_aff_factor_range>
6875 take functions that live in a set space.
6877 #include <isl/val.h>
6878 __isl_give isl_multi_val *isl_multi_val_range_splice(
6879 __isl_take isl_multi_val *mv1, unsigned pos,
6880 __isl_take isl_multi_val *mv2);
6882 #include <isl/aff.h>
6883 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
6884 __isl_take isl_multi_aff *ma1, unsigned pos,
6885 __isl_take isl_multi_aff *ma2);
6886 __isl_give isl_multi_aff *isl_multi_aff_splice(
6887 __isl_take isl_multi_aff *ma1,
6888 unsigned in_pos, unsigned out_pos,
6889 __isl_take isl_multi_aff *ma2);
6890 __isl_give isl_multi_pw_aff *
6891 isl_multi_pw_aff_range_splice(
6892 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
6893 __isl_take isl_multi_pw_aff *mpa2);
6894 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
6895 __isl_take isl_multi_pw_aff *mpa1,
6896 unsigned in_pos, unsigned out_pos,
6897 __isl_take isl_multi_pw_aff *mpa2);
6898 __isl_give isl_multi_union_pw_aff *
6899 isl_multi_union_pw_aff_range_splice(
6900 __isl_take isl_multi_union_pw_aff *mupa1,
6902 __isl_take isl_multi_union_pw_aff *mupa2);
6904 =item * Simplification
6906 When applied to a set or relation,
6907 the gist operation returns a set or relation that has the
6908 same intersection with the context as the input set or relation.
6909 Any implicit equality in the intersection is made explicit in the result,
6910 while all inequalities that are redundant with respect to the intersection
6912 In case of union sets and relations, the gist operation is performed
6915 When applied to a function,
6916 the gist operation applies the set gist operation to each of
6917 the cells in the domain of the input piecewise expression.
6918 The context is also exploited
6919 to simplify the expression associated to each cell.
6921 #include <isl/set.h>
6922 __isl_give isl_basic_set *isl_basic_set_gist(
6923 __isl_take isl_basic_set *bset,
6924 __isl_take isl_basic_set *context);
6925 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
6926 __isl_take isl_set *context);
6927 __isl_give isl_set *isl_set_gist_params(
6928 __isl_take isl_set *set,
6929 __isl_take isl_set *context);
6931 #include <isl/map.h>
6932 __isl_give isl_basic_map *isl_basic_map_gist(
6933 __isl_take isl_basic_map *bmap,
6934 __isl_take isl_basic_map *context);
6935 __isl_give isl_basic_map *isl_basic_map_gist_domain(
6936 __isl_take isl_basic_map *bmap,
6937 __isl_take isl_basic_set *context);
6938 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
6939 __isl_take isl_map *context);
6940 __isl_give isl_map *isl_map_gist_params(
6941 __isl_take isl_map *map,
6942 __isl_take isl_set *context);
6943 __isl_give isl_map *isl_map_gist_domain(
6944 __isl_take isl_map *map,
6945 __isl_take isl_set *context);
6946 __isl_give isl_map *isl_map_gist_range(
6947 __isl_take isl_map *map,
6948 __isl_take isl_set *context);
6950 #include <isl/union_set.h>
6951 __isl_give isl_union_set *isl_union_set_gist(
6952 __isl_take isl_union_set *uset,
6953 __isl_take isl_union_set *context);
6954 __isl_give isl_union_set *isl_union_set_gist_params(
6955 __isl_take isl_union_set *uset,
6956 __isl_take isl_set *set);
6958 #include <isl/union_map.h>
6959 __isl_give isl_union_map *isl_union_map_gist(
6960 __isl_take isl_union_map *umap,
6961 __isl_take isl_union_map *context);
6962 __isl_give isl_union_map *isl_union_map_gist_params(
6963 __isl_take isl_union_map *umap,
6964 __isl_take isl_set *set);
6965 __isl_give isl_union_map *isl_union_map_gist_domain(
6966 __isl_take isl_union_map *umap,
6967 __isl_take isl_union_set *uset);
6968 __isl_give isl_union_map *isl_union_map_gist_range(
6969 __isl_take isl_union_map *umap,
6970 __isl_take isl_union_set *uset);
6972 #include <isl/aff.h>
6973 __isl_give isl_aff *isl_aff_gist_params(
6974 __isl_take isl_aff *aff,
6975 __isl_take isl_set *context);
6976 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
6977 __isl_take isl_set *context);
6978 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
6979 __isl_take isl_multi_aff *maff,
6980 __isl_take isl_set *context);
6981 __isl_give isl_multi_aff *isl_multi_aff_gist(
6982 __isl_take isl_multi_aff *maff,
6983 __isl_take isl_set *context);
6984 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
6985 __isl_take isl_pw_aff *pwaff,
6986 __isl_take isl_set *context);
6987 __isl_give isl_pw_aff *isl_pw_aff_gist(
6988 __isl_take isl_pw_aff *pwaff,
6989 __isl_take isl_set *context);
6990 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
6991 __isl_take isl_pw_multi_aff *pma,
6992 __isl_take isl_set *set);
6993 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
6994 __isl_take isl_pw_multi_aff *pma,
6995 __isl_take isl_set *set);
6996 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
6997 __isl_take isl_multi_pw_aff *mpa,
6998 __isl_take isl_set *set);
6999 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
7000 __isl_take isl_multi_pw_aff *mpa,
7001 __isl_take isl_set *set);
7002 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
7003 __isl_take isl_union_pw_aff *upa,
7004 __isl_take isl_union_set *context);
7005 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
7006 __isl_take isl_union_pw_aff *upa,
7007 __isl_take isl_set *context);
7008 __isl_give isl_union_pw_multi_aff *
7009 isl_union_pw_multi_aff_gist_params(
7010 __isl_take isl_union_pw_multi_aff *upma,
7011 __isl_take isl_set *context);
7012 __isl_give isl_union_pw_multi_aff *
7013 isl_union_pw_multi_aff_gist(
7014 __isl_take isl_union_pw_multi_aff *upma,
7015 __isl_take isl_union_set *context);
7016 __isl_give isl_multi_union_pw_aff *
7017 isl_multi_union_pw_aff_gist_params(
7018 __isl_take isl_multi_union_pw_aff *aff,
7019 __isl_take isl_set *context);
7020 __isl_give isl_multi_union_pw_aff *
7021 isl_multi_union_pw_aff_gist(
7022 __isl_take isl_multi_union_pw_aff *aff,
7023 __isl_take isl_union_set *context);
7025 #include <isl/polynomial.h>
7026 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
7027 __isl_take isl_qpolynomial *qp,
7028 __isl_take isl_set *context);
7029 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
7030 __isl_take isl_qpolynomial *qp,
7031 __isl_take isl_set *context);
7032 __isl_give isl_qpolynomial_fold *
7033 isl_qpolynomial_fold_gist_params(
7034 __isl_take isl_qpolynomial_fold *fold,
7035 __isl_take isl_set *context);
7036 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
7037 __isl_take isl_qpolynomial_fold *fold,
7038 __isl_take isl_set *context);
7039 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
7040 __isl_take isl_pw_qpolynomial *pwqp,
7041 __isl_take isl_set *context);
7042 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
7043 __isl_take isl_pw_qpolynomial *pwqp,
7044 __isl_take isl_set *context);
7045 __isl_give isl_pw_qpolynomial_fold *
7046 isl_pw_qpolynomial_fold_gist(
7047 __isl_take isl_pw_qpolynomial_fold *pwf,
7048 __isl_take isl_set *context);
7049 __isl_give isl_pw_qpolynomial_fold *
7050 isl_pw_qpolynomial_fold_gist_params(
7051 __isl_take isl_pw_qpolynomial_fold *pwf,
7052 __isl_take isl_set *context);
7053 __isl_give isl_union_pw_qpolynomial *
7054 isl_union_pw_qpolynomial_gist_params(
7055 __isl_take isl_union_pw_qpolynomial *upwqp,
7056 __isl_take isl_set *context);
7057 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
7058 __isl_take isl_union_pw_qpolynomial *upwqp,
7059 __isl_take isl_union_set *context);
7060 __isl_give isl_union_pw_qpolynomial_fold *
7061 isl_union_pw_qpolynomial_fold_gist(
7062 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7063 __isl_take isl_union_set *context);
7064 __isl_give isl_union_pw_qpolynomial_fold *
7065 isl_union_pw_qpolynomial_fold_gist_params(
7066 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7067 __isl_take isl_set *context);
7069 =item * Binary Arithmetic Operations
7071 #include <isl/set.h>
7072 __isl_give isl_set *isl_set_sum(
7073 __isl_take isl_set *set1,
7074 __isl_take isl_set *set2);
7075 #include <isl/map.h>
7076 __isl_give isl_map *isl_map_sum(
7077 __isl_take isl_map *map1,
7078 __isl_take isl_map *map2);
7080 C<isl_set_sum> computes the Minkowski sum of its two arguments,
7081 i.e., the set containing the sums of pairs of elements from
7082 C<set1> and C<set2>.
7083 The domain of the result of C<isl_map_sum> is the intersection
7084 of the domains of its two arguments. The corresponding range
7085 elements are the sums of the corresponding range elements
7086 in the two arguments.
7088 #include <isl/val.h>
7089 __isl_give isl_multi_val *isl_multi_val_add(
7090 __isl_take isl_multi_val *mv1,
7091 __isl_take isl_multi_val *mv2);
7092 __isl_give isl_multi_val *isl_multi_val_sub(
7093 __isl_take isl_multi_val *mv1,
7094 __isl_take isl_multi_val *mv2);
7096 #include <isl/aff.h>
7097 __isl_give isl_aff *isl_aff_add(
7098 __isl_take isl_aff *aff1,
7099 __isl_take isl_aff *aff2);
7100 __isl_give isl_multi_aff *isl_multi_aff_add(
7101 __isl_take isl_multi_aff *maff1,
7102 __isl_take isl_multi_aff *maff2);
7103 __isl_give isl_pw_aff *isl_pw_aff_add(
7104 __isl_take isl_pw_aff *pwaff1,
7105 __isl_take isl_pw_aff *pwaff2);
7106 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add(
7107 __isl_take isl_multi_pw_aff *mpa1,
7108 __isl_take isl_multi_pw_aff *mpa2);
7109 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
7110 __isl_take isl_pw_multi_aff *pma1,
7111 __isl_take isl_pw_multi_aff *pma2);
7112 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
7113 __isl_take isl_union_pw_aff *upa1,
7114 __isl_take isl_union_pw_aff *upa2);
7115 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
7116 __isl_take isl_union_pw_multi_aff *upma1,
7117 __isl_take isl_union_pw_multi_aff *upma2);
7118 __isl_give isl_multi_union_pw_aff *
7119 isl_multi_union_pw_aff_add(
7120 __isl_take isl_multi_union_pw_aff *mupa1,
7121 __isl_take isl_multi_union_pw_aff *mupa2);
7122 __isl_give isl_pw_aff *isl_pw_aff_min(
7123 __isl_take isl_pw_aff *pwaff1,
7124 __isl_take isl_pw_aff *pwaff2);
7125 __isl_give isl_pw_aff *isl_pw_aff_max(
7126 __isl_take isl_pw_aff *pwaff1,
7127 __isl_take isl_pw_aff *pwaff2);
7128 __isl_give isl_aff *isl_aff_sub(
7129 __isl_take isl_aff *aff1,
7130 __isl_take isl_aff *aff2);
7131 __isl_give isl_multi_aff *isl_multi_aff_sub(
7132 __isl_take isl_multi_aff *ma1,
7133 __isl_take isl_multi_aff *ma2);
7134 __isl_give isl_pw_aff *isl_pw_aff_sub(
7135 __isl_take isl_pw_aff *pwaff1,
7136 __isl_take isl_pw_aff *pwaff2);
7137 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
7138 __isl_take isl_multi_pw_aff *mpa1,
7139 __isl_take isl_multi_pw_aff *mpa2);
7140 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
7141 __isl_take isl_pw_multi_aff *pma1,
7142 __isl_take isl_pw_multi_aff *pma2);
7143 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
7144 __isl_take isl_union_pw_aff *upa1,
7145 __isl_take isl_union_pw_aff *upa2);
7146 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
7147 __isl_take isl_union_pw_multi_aff *upma1,
7148 __isl_take isl_union_pw_multi_aff *upma2);
7149 __isl_give isl_multi_union_pw_aff *
7150 isl_multi_union_pw_aff_sub(
7151 __isl_take isl_multi_union_pw_aff *mupa1,
7152 __isl_take isl_multi_union_pw_aff *mupa2);
7154 C<isl_aff_sub> subtracts the second argument from the first.
7156 #include <isl/polynomial.h>
7157 __isl_give isl_qpolynomial *isl_qpolynomial_add(
7158 __isl_take isl_qpolynomial *qp1,
7159 __isl_take isl_qpolynomial *qp2);
7160 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
7161 __isl_take isl_pw_qpolynomial *pwqp1,
7162 __isl_take isl_pw_qpolynomial *pwqp2);
7163 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
7164 __isl_take isl_pw_qpolynomial *pwqp1,
7165 __isl_take isl_pw_qpolynomial *pwqp2);
7166 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
7167 __isl_take isl_pw_qpolynomial_fold *pwf1,
7168 __isl_take isl_pw_qpolynomial_fold *pwf2);
7169 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
7170 __isl_take isl_union_pw_qpolynomial *upwqp1,
7171 __isl_take isl_union_pw_qpolynomial *upwqp2);
7172 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
7173 __isl_take isl_qpolynomial *qp1,
7174 __isl_take isl_qpolynomial *qp2);
7175 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
7176 __isl_take isl_pw_qpolynomial *pwqp1,
7177 __isl_take isl_pw_qpolynomial *pwqp2);
7178 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
7179 __isl_take isl_union_pw_qpolynomial *upwqp1,
7180 __isl_take isl_union_pw_qpolynomial *upwqp2);
7181 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
7182 __isl_take isl_pw_qpolynomial_fold *pwf1,
7183 __isl_take isl_pw_qpolynomial_fold *pwf2);
7184 __isl_give isl_union_pw_qpolynomial_fold *
7185 isl_union_pw_qpolynomial_fold_fold(
7186 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
7187 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
7189 #include <isl/aff.h>
7190 __isl_give isl_pw_aff *isl_pw_aff_union_add(
7191 __isl_take isl_pw_aff *pwaff1,
7192 __isl_take isl_pw_aff *pwaff2);
7193 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
7194 __isl_take isl_pw_multi_aff *pma1,
7195 __isl_take isl_pw_multi_aff *pma2);
7196 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
7197 __isl_take isl_union_pw_aff *upa1,
7198 __isl_take isl_union_pw_aff *upa2);
7199 __isl_give isl_union_pw_multi_aff *
7200 isl_union_pw_multi_aff_union_add(
7201 __isl_take isl_union_pw_multi_aff *upma1,
7202 __isl_take isl_union_pw_multi_aff *upma2);
7203 __isl_give isl_multi_union_pw_aff *
7204 isl_multi_union_pw_aff_union_add(
7205 __isl_take isl_multi_union_pw_aff *mupa1,
7206 __isl_take isl_multi_union_pw_aff *mupa2);
7207 __isl_give isl_pw_aff *isl_pw_aff_union_min(
7208 __isl_take isl_pw_aff *pwaff1,
7209 __isl_take isl_pw_aff *pwaff2);
7210 __isl_give isl_pw_aff *isl_pw_aff_union_max(
7211 __isl_take isl_pw_aff *pwaff1,
7212 __isl_take isl_pw_aff *pwaff2);
7214 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
7215 expression with a domain that is the union of those of C<pwaff1> and
7216 C<pwaff2> and such that on each cell, the quasi-affine expression is
7217 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
7218 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
7219 associated expression is the defined one.
7220 This in contrast to the C<isl_pw_aff_max> function, which is
7221 only defined on the shared definition domain of the arguments.
7223 #include <isl/val.h>
7224 __isl_give isl_multi_val *isl_multi_val_add_val(
7225 __isl_take isl_multi_val *mv,
7226 __isl_take isl_val *v);
7227 __isl_give isl_multi_val *isl_multi_val_mod_val(
7228 __isl_take isl_multi_val *mv,
7229 __isl_take isl_val *v);
7230 __isl_give isl_multi_val *isl_multi_val_scale_val(
7231 __isl_take isl_multi_val *mv,
7232 __isl_take isl_val *v);
7233 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
7234 __isl_take isl_multi_val *mv,
7235 __isl_take isl_val *v);
7237 #include <isl/aff.h>
7238 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
7239 __isl_take isl_val *mod);
7240 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
7241 __isl_take isl_pw_aff *pa,
7242 __isl_take isl_val *mod);
7243 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
7244 __isl_take isl_union_pw_aff *upa,
7245 __isl_take isl_val *f);
7246 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
7247 __isl_take isl_val *v);
7248 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
7249 __isl_take isl_multi_aff *ma,
7250 __isl_take isl_val *v);
7251 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
7252 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
7253 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
7254 __isl_take isl_multi_pw_aff *mpa,
7255 __isl_take isl_val *v);
7256 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
7257 __isl_take isl_pw_multi_aff *pma,
7258 __isl_take isl_val *v);
7259 __isl_give isl_union_pw_multi_aff *
7260 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
7261 __isl_take isl_union_pw_aff *upa,
7262 __isl_take isl_val *f);
7263 isl_union_pw_multi_aff_scale_val(
7264 __isl_take isl_union_pw_multi_aff *upma,
7265 __isl_take isl_val *val);
7266 __isl_give isl_multi_union_pw_aff *
7267 isl_multi_union_pw_aff_scale_val(
7268 __isl_take isl_multi_union_pw_aff *mupa,
7269 __isl_take isl_val *v);
7270 __isl_give isl_aff *isl_aff_scale_down_ui(
7271 __isl_take isl_aff *aff, unsigned f);
7272 __isl_give isl_aff *isl_aff_scale_down_val(
7273 __isl_take isl_aff *aff, __isl_take isl_val *v);
7274 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
7275 __isl_take isl_multi_aff *ma,
7276 __isl_take isl_val *v);
7277 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
7278 __isl_take isl_pw_aff *pa,
7279 __isl_take isl_val *f);
7280 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
7281 __isl_take isl_multi_pw_aff *mpa,
7282 __isl_take isl_val *v);
7283 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
7284 __isl_take isl_pw_multi_aff *pma,
7285 __isl_take isl_val *v);
7286 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
7287 __isl_take isl_union_pw_aff *upa,
7288 __isl_take isl_val *v);
7289 __isl_give isl_union_pw_multi_aff *
7290 isl_union_pw_multi_aff_scale_down_val(
7291 __isl_take isl_union_pw_multi_aff *upma,
7292 __isl_take isl_val *val);
7293 __isl_give isl_multi_union_pw_aff *
7294 isl_multi_union_pw_aff_scale_down_val(
7295 __isl_take isl_multi_union_pw_aff *mupa,
7296 __isl_take isl_val *v);
7298 #include <isl/polynomial.h>
7299 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
7300 __isl_take isl_qpolynomial *qp,
7301 __isl_take isl_val *v);
7302 __isl_give isl_qpolynomial_fold *
7303 isl_qpolynomial_fold_scale_val(
7304 __isl_take isl_qpolynomial_fold *fold,
7305 __isl_take isl_val *v);
7306 __isl_give isl_pw_qpolynomial *
7307 isl_pw_qpolynomial_scale_val(
7308 __isl_take isl_pw_qpolynomial *pwqp,
7309 __isl_take isl_val *v);
7310 __isl_give isl_pw_qpolynomial_fold *
7311 isl_pw_qpolynomial_fold_scale_val(
7312 __isl_take isl_pw_qpolynomial_fold *pwf,
7313 __isl_take isl_val *v);
7314 __isl_give isl_union_pw_qpolynomial *
7315 isl_union_pw_qpolynomial_scale_val(
7316 __isl_take isl_union_pw_qpolynomial *upwqp,
7317 __isl_take isl_val *v);
7318 __isl_give isl_union_pw_qpolynomial_fold *
7319 isl_union_pw_qpolynomial_fold_scale_val(
7320 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7321 __isl_take isl_val *v);
7322 __isl_give isl_qpolynomial *
7323 isl_qpolynomial_scale_down_val(
7324 __isl_take isl_qpolynomial *qp,
7325 __isl_take isl_val *v);
7326 __isl_give isl_qpolynomial_fold *
7327 isl_qpolynomial_fold_scale_down_val(
7328 __isl_take isl_qpolynomial_fold *fold,
7329 __isl_take isl_val *v);
7330 __isl_give isl_pw_qpolynomial *
7331 isl_pw_qpolynomial_scale_down_val(
7332 __isl_take isl_pw_qpolynomial *pwqp,
7333 __isl_take isl_val *v);
7334 __isl_give isl_pw_qpolynomial_fold *
7335 isl_pw_qpolynomial_fold_scale_down_val(
7336 __isl_take isl_pw_qpolynomial_fold *pwf,
7337 __isl_take isl_val *v);
7338 __isl_give isl_union_pw_qpolynomial *
7339 isl_union_pw_qpolynomial_scale_down_val(
7340 __isl_take isl_union_pw_qpolynomial *upwqp,
7341 __isl_take isl_val *v);
7342 __isl_give isl_union_pw_qpolynomial_fold *
7343 isl_union_pw_qpolynomial_fold_scale_down_val(
7344 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7345 __isl_take isl_val *v);
7347 #include <isl/val.h>
7348 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
7349 __isl_take isl_multi_val *mv1,
7350 __isl_take isl_multi_val *mv2);
7351 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
7352 __isl_take isl_multi_val *mv1,
7353 __isl_take isl_multi_val *mv2);
7354 __isl_give isl_multi_val *
7355 isl_multi_val_scale_down_multi_val(
7356 __isl_take isl_multi_val *mv1,
7357 __isl_take isl_multi_val *mv2);
7359 #include <isl/aff.h>
7360 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
7361 __isl_take isl_multi_aff *ma,
7362 __isl_take isl_multi_val *mv);
7363 __isl_give isl_multi_union_pw_aff *
7364 isl_multi_union_pw_aff_mod_multi_val(
7365 __isl_take isl_multi_union_pw_aff *upma,
7366 __isl_take isl_multi_val *mv);
7367 __isl_give isl_multi_pw_aff *
7368 isl_multi_pw_aff_mod_multi_val(
7369 __isl_take isl_multi_pw_aff *mpa,
7370 __isl_take isl_multi_val *mv);
7371 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
7372 __isl_take isl_multi_aff *ma,
7373 __isl_take isl_multi_val *mv);
7374 __isl_give isl_pw_multi_aff *
7375 isl_pw_multi_aff_scale_multi_val(
7376 __isl_take isl_pw_multi_aff *pma,
7377 __isl_take isl_multi_val *mv);
7378 __isl_give isl_multi_pw_aff *
7379 isl_multi_pw_aff_scale_multi_val(
7380 __isl_take isl_multi_pw_aff *mpa,
7381 __isl_take isl_multi_val *mv);
7382 __isl_give isl_multi_union_pw_aff *
7383 isl_multi_union_pw_aff_scale_multi_val(
7384 __isl_take isl_multi_union_pw_aff *mupa,
7385 __isl_take isl_multi_val *mv);
7386 __isl_give isl_union_pw_multi_aff *
7387 isl_union_pw_multi_aff_scale_multi_val(
7388 __isl_take isl_union_pw_multi_aff *upma,
7389 __isl_take isl_multi_val *mv);
7390 __isl_give isl_multi_aff *
7391 isl_multi_aff_scale_down_multi_val(
7392 __isl_take isl_multi_aff *ma,
7393 __isl_take isl_multi_val *mv);
7394 __isl_give isl_multi_pw_aff *
7395 isl_multi_pw_aff_scale_down_multi_val(
7396 __isl_take isl_multi_pw_aff *mpa,
7397 __isl_take isl_multi_val *mv);
7398 __isl_give isl_multi_union_pw_aff *
7399 isl_multi_union_pw_aff_scale_down_multi_val(
7400 __isl_take isl_multi_union_pw_aff *mupa,
7401 __isl_take isl_multi_val *mv);
7403 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
7404 by the corresponding elements of C<mv>.
7406 #include <isl/aff.h>
7407 __isl_give isl_aff *isl_aff_mul(
7408 __isl_take isl_aff *aff1,
7409 __isl_take isl_aff *aff2);
7410 __isl_give isl_aff *isl_aff_div(
7411 __isl_take isl_aff *aff1,
7412 __isl_take isl_aff *aff2);
7413 __isl_give isl_pw_aff *isl_pw_aff_mul(
7414 __isl_take isl_pw_aff *pwaff1,
7415 __isl_take isl_pw_aff *pwaff2);
7416 __isl_give isl_pw_aff *isl_pw_aff_div(
7417 __isl_take isl_pw_aff *pa1,
7418 __isl_take isl_pw_aff *pa2);
7419 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
7420 __isl_take isl_pw_aff *pa1,
7421 __isl_take isl_pw_aff *pa2);
7422 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
7423 __isl_take isl_pw_aff *pa1,
7424 __isl_take isl_pw_aff *pa2);
7426 When multiplying two affine expressions, at least one of the two needs
7427 to be a constant. Similarly, when dividing an affine expression by another,
7428 the second expression needs to be a constant.
7429 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
7430 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
7433 #include <isl/polynomial.h>
7434 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
7435 __isl_take isl_qpolynomial *qp1,
7436 __isl_take isl_qpolynomial *qp2);
7437 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
7438 __isl_take isl_pw_qpolynomial *pwqp1,
7439 __isl_take isl_pw_qpolynomial *pwqp2);
7440 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
7441 __isl_take isl_union_pw_qpolynomial *upwqp1,
7442 __isl_take isl_union_pw_qpolynomial *upwqp2);
7446 =head3 Lexicographic Optimization
7448 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
7449 the following functions
7450 compute a set that contains the lexicographic minimum or maximum
7451 of the elements in C<set> (or C<bset>) for those values of the parameters
7452 that satisfy C<dom>.
7453 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7454 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
7456 In other words, the union of the parameter values
7457 for which the result is non-empty and of C<*empty>
7460 #include <isl/set.h>
7461 __isl_give isl_set *isl_basic_set_partial_lexmin(
7462 __isl_take isl_basic_set *bset,
7463 __isl_take isl_basic_set *dom,
7464 __isl_give isl_set **empty);
7465 __isl_give isl_set *isl_basic_set_partial_lexmax(
7466 __isl_take isl_basic_set *bset,
7467 __isl_take isl_basic_set *dom,
7468 __isl_give isl_set **empty);
7469 __isl_give isl_set *isl_set_partial_lexmin(
7470 __isl_take isl_set *set, __isl_take isl_set *dom,
7471 __isl_give isl_set **empty);
7472 __isl_give isl_set *isl_set_partial_lexmax(
7473 __isl_take isl_set *set, __isl_take isl_set *dom,
7474 __isl_give isl_set **empty);
7476 Given a (basic) set C<set> (or C<bset>), the following functions simply
7477 return a set containing the lexicographic minimum or maximum
7478 of the elements in C<set> (or C<bset>).
7479 In case of union sets, the optimum is computed per space.
7481 #include <isl/set.h>
7482 __isl_give isl_set *isl_basic_set_lexmin(
7483 __isl_take isl_basic_set *bset);
7484 __isl_give isl_set *isl_basic_set_lexmax(
7485 __isl_take isl_basic_set *bset);
7486 __isl_give isl_set *isl_set_lexmin(
7487 __isl_take isl_set *set);
7488 __isl_give isl_set *isl_set_lexmax(
7489 __isl_take isl_set *set);
7490 __isl_give isl_union_set *isl_union_set_lexmin(
7491 __isl_take isl_union_set *uset);
7492 __isl_give isl_union_set *isl_union_set_lexmax(
7493 __isl_take isl_union_set *uset);
7495 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
7496 the following functions
7497 compute a relation that maps each element of C<dom>
7498 to the single lexicographic minimum or maximum
7499 of the elements that are associated to that same
7500 element in C<map> (or C<bmap>).
7501 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7502 that contains the elements in C<dom> that do not map
7503 to any elements in C<map> (or C<bmap>).
7504 In other words, the union of the domain of the result and of C<*empty>
7507 #include <isl/map.h>
7508 __isl_give isl_map *isl_basic_map_partial_lexmax(
7509 __isl_take isl_basic_map *bmap,
7510 __isl_take isl_basic_set *dom,
7511 __isl_give isl_set **empty);
7512 __isl_give isl_map *isl_basic_map_partial_lexmin(
7513 __isl_take isl_basic_map *bmap,
7514 __isl_take isl_basic_set *dom,
7515 __isl_give isl_set **empty);
7516 __isl_give isl_map *isl_map_partial_lexmax(
7517 __isl_take isl_map *map, __isl_take isl_set *dom,
7518 __isl_give isl_set **empty);
7519 __isl_give isl_map *isl_map_partial_lexmin(
7520 __isl_take isl_map *map, __isl_take isl_set *dom,
7521 __isl_give isl_set **empty);
7523 Given a (basic) map C<map> (or C<bmap>), the following functions simply
7524 return a map mapping each element in the domain of
7525 C<map> (or C<bmap>) to the lexicographic minimum or maximum
7526 of all elements associated to that element.
7527 In case of union relations, the optimum is computed per space.
7529 #include <isl/map.h>
7530 __isl_give isl_map *isl_basic_map_lexmin(
7531 __isl_take isl_basic_map *bmap);
7532 __isl_give isl_map *isl_basic_map_lexmax(
7533 __isl_take isl_basic_map *bmap);
7534 __isl_give isl_map *isl_map_lexmin(
7535 __isl_take isl_map *map);
7536 __isl_give isl_map *isl_map_lexmax(
7537 __isl_take isl_map *map);
7538 __isl_give isl_union_map *isl_union_map_lexmin(
7539 __isl_take isl_union_map *umap);
7540 __isl_give isl_union_map *isl_union_map_lexmax(
7541 __isl_take isl_union_map *umap);
7543 The following functions return their result in the form of
7544 a piecewise multi-affine expression,
7545 but are otherwise equivalent to the corresponding functions
7546 returning a basic set or relation.
7548 #include <isl/set.h>
7549 __isl_give isl_pw_multi_aff *
7550 isl_basic_set_partial_lexmin_pw_multi_aff(
7551 __isl_take isl_basic_set *bset,
7552 __isl_take isl_basic_set *dom,
7553 __isl_give isl_set **empty);
7554 __isl_give isl_pw_multi_aff *
7555 isl_basic_set_partial_lexmax_pw_multi_aff(
7556 __isl_take isl_basic_set *bset,
7557 __isl_take isl_basic_set *dom,
7558 __isl_give isl_set **empty);
7559 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
7560 __isl_take isl_set *set);
7561 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
7562 __isl_take isl_set *set);
7564 #include <isl/map.h>
7565 __isl_give isl_pw_multi_aff *
7566 isl_basic_map_lexmin_pw_multi_aff(
7567 __isl_take isl_basic_map *bmap);
7568 __isl_give isl_pw_multi_aff *
7569 isl_basic_map_partial_lexmin_pw_multi_aff(
7570 __isl_take isl_basic_map *bmap,
7571 __isl_take isl_basic_set *dom,
7572 __isl_give isl_set **empty);
7573 __isl_give isl_pw_multi_aff *
7574 isl_basic_map_partial_lexmax_pw_multi_aff(
7575 __isl_take isl_basic_map *bmap,
7576 __isl_take isl_basic_set *dom,
7577 __isl_give isl_set **empty);
7578 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
7579 __isl_take isl_map *map);
7580 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
7581 __isl_take isl_map *map);
7583 The following functions return the lexicographic minimum or maximum
7584 on the shared domain of the inputs and the single defined function
7585 on those parts of the domain where only a single function is defined.
7587 #include <isl/aff.h>
7588 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
7589 __isl_take isl_pw_multi_aff *pma1,
7590 __isl_take isl_pw_multi_aff *pma2);
7591 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
7592 __isl_take isl_pw_multi_aff *pma1,
7593 __isl_take isl_pw_multi_aff *pma2);
7595 If the input to a lexicographic optimization problem has
7596 multiple constraints with the same coefficients for the optimized
7597 variables, then, by default, this symmetry is exploited by
7598 replacing those constraints by a single constraint with
7599 an abstract bound, which is in turn bounded by the corresponding terms
7600 in the original constraints.
7601 Without this optimization, the solver would typically consider
7602 all possible orderings of those original bounds, resulting in a needless
7603 decomposition of the domain.
7604 However, the optimization can also result in slowdowns since
7605 an extra parameter is introduced that may get used in additional
7607 The following option determines whether symmetry detection is applied
7608 during lexicographic optimization.
7610 #include <isl/options.h>
7611 isl_stat isl_options_set_pip_symmetry(isl_ctx *ctx,
7613 int isl_options_get_pip_symmetry(isl_ctx *ctx);
7617 See also \autoref{s:offline}.
7621 =head2 Ternary Operations
7623 #include <isl/aff.h>
7624 __isl_give isl_pw_aff *isl_pw_aff_cond(
7625 __isl_take isl_pw_aff *cond,
7626 __isl_take isl_pw_aff *pwaff_true,
7627 __isl_take isl_pw_aff *pwaff_false);
7629 The function C<isl_pw_aff_cond> performs a conditional operator
7630 and returns an expression that is equal to C<pwaff_true>
7631 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
7632 where C<cond> is zero.
7636 Lists are defined over several element types, including
7637 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_union_pw_aff>,
7638 C<isl_union_pw_multi_aff>, C<isl_constraint>,
7639 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
7640 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
7641 Here we take lists of C<isl_set>s as an example.
7642 Lists can be created, copied, modified and freed using the following functions.
7644 #include <isl/set.h>
7645 __isl_give isl_set_list *isl_set_list_from_set(
7646 __isl_take isl_set *el);
7647 __isl_give isl_set_list *isl_set_list_alloc(
7648 isl_ctx *ctx, int n);
7649 __isl_give isl_set_list *isl_set_list_copy(
7650 __isl_keep isl_set_list *list);
7651 __isl_give isl_set_list *isl_set_list_insert(
7652 __isl_take isl_set_list *list, unsigned pos,
7653 __isl_take isl_set *el);
7654 __isl_give isl_set_list *isl_set_list_add(
7655 __isl_take isl_set_list *list,
7656 __isl_take isl_set *el);
7657 __isl_give isl_set_list *isl_set_list_drop(
7658 __isl_take isl_set_list *list,
7659 unsigned first, unsigned n);
7660 __isl_give isl_set_list *isl_set_list_set_set(
7661 __isl_take isl_set_list *list, int index,
7662 __isl_take isl_set *set);
7663 __isl_give isl_set_list *isl_set_list_concat(
7664 __isl_take isl_set_list *list1,
7665 __isl_take isl_set_list *list2);
7666 __isl_give isl_set_list *isl_set_list_map(
7667 __isl_take isl_set_list *list,
7668 __isl_give isl_set *(*fn)(__isl_take isl_set *el,
7671 __isl_give isl_set_list *isl_set_list_sort(
7672 __isl_take isl_set_list *list,
7673 int (*cmp)(__isl_keep isl_set *a,
7674 __isl_keep isl_set *b, void *user),
7676 __isl_null isl_set_list *isl_set_list_free(
7677 __isl_take isl_set_list *list);
7679 C<isl_set_list_alloc> creates an empty list with an initial capacity
7680 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
7681 add elements to a list, increasing its capacity as needed.
7682 C<isl_set_list_from_set> creates a list with a single element.
7684 Lists can be inspected using the following functions.
7686 #include <isl/set.h>
7687 int isl_set_list_n_set(__isl_keep isl_set_list *list);
7688 __isl_give isl_set *isl_set_list_get_set(
7689 __isl_keep isl_set_list *list, int index);
7690 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list,
7691 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7693 isl_stat isl_set_list_foreach_scc(
7694 __isl_keep isl_set_list *list,
7695 isl_bool (*follows)(__isl_keep isl_set *a,
7696 __isl_keep isl_set *b, void *user),
7698 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7701 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
7702 strongly connected components of the graph with as vertices the elements
7703 of C<list> and a directed edge from vertex C<b> to vertex C<a>
7704 iff C<follows(a, b)> returns C<isl_bool_true>. The callbacks C<follows> and
7705 C<fn> should return C<isl_bool_error> or C<isl_stat_error> on error.
7707 Lists can be printed using
7709 #include <isl/set.h>
7710 __isl_give isl_printer *isl_printer_print_set_list(
7711 __isl_take isl_printer *p,
7712 __isl_keep isl_set_list *list);
7714 =head2 Associative arrays
7716 Associative arrays map isl objects of a specific type to isl objects
7717 of some (other) specific type. They are defined for several pairs
7718 of types, including (C<isl_map>, C<isl_basic_set>),
7719 (C<isl_id>, C<isl_ast_expr>),
7720 (C<isl_id>, C<isl_id>) and
7721 (C<isl_id>, C<isl_pw_aff>).
7722 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
7725 Associative arrays can be created, copied and freed using
7726 the following functions.
7728 #include <isl/id_to_ast_expr.h>
7729 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
7730 isl_ctx *ctx, int min_size);
7731 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
7732 __isl_keep isl_id_to_ast_expr *id2expr);
7733 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
7734 __isl_take isl_id_to_ast_expr *id2expr);
7736 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
7737 to specify the expected size of the associative array.
7738 The associative array will be grown automatically as needed.
7740 Associative arrays can be inspected using the following functions.
7742 #include <isl/id_to_ast_expr.h>
7743 __isl_give isl_maybe_isl_ast_expr
7744 isl_id_to_ast_expr_try_get(
7745 __isl_keep isl_id_to_ast_expr *id2expr,
7746 __isl_keep isl_id *key);
7747 isl_bool isl_id_to_ast_expr_has(
7748 __isl_keep isl_id_to_ast_expr *id2expr,
7749 __isl_keep isl_id *key);
7750 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
7751 __isl_keep isl_id_to_ast_expr *id2expr,
7752 __isl_take isl_id *key);
7753 isl_stat isl_id_to_ast_expr_foreach(
7754 __isl_keep isl_id_to_ast_expr *id2expr,
7755 isl_stat (*fn)(__isl_take isl_id *key,
7756 __isl_take isl_ast_expr *val, void *user),
7759 The function C<isl_id_to_ast_expr_try_get> returns a structure
7760 containing two elements, C<valid> and C<value>.
7761 If there is a value associated to the key, then C<valid>
7762 is set to C<isl_bool_true> and C<value> contains a copy of
7763 the associated value. Otherwise C<value> is C<NULL> and
7764 C<valid> may be C<isl_bool_error> or C<isl_bool_false> depending
7765 on whether some error has occurred or there simply is no associated value.
7766 The function C<isl_id_to_ast_expr_has> returns the C<valid> field
7767 in the structure and
7768 the function C<isl_id_to_ast_expr_get> returns the C<value> field.
7770 Associative arrays can be modified using the following functions.
7772 #include <isl/id_to_ast_expr.h>
7773 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
7774 __isl_take isl_id_to_ast_expr *id2expr,
7775 __isl_take isl_id *key,
7776 __isl_take isl_ast_expr *val);
7777 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
7778 __isl_take isl_id_to_ast_expr *id2expr,
7779 __isl_take isl_id *key);
7781 Associative arrays can be printed using the following function.
7783 #include <isl/id_to_ast_expr.h>
7784 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
7785 __isl_take isl_printer *p,
7786 __isl_keep isl_id_to_ast_expr *id2expr);
7790 Vectors can be created, copied and freed using the following functions.
7792 #include <isl/vec.h>
7793 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
7795 __isl_give isl_vec *isl_vec_zero(isl_ctx *ctx,
7797 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
7798 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
7800 Note that the elements of a vector created by C<isl_vec_alloc>
7801 may have arbitrary values.
7802 A vector created by C<isl_vec_zero> has elements with value zero.
7803 The elements can be changed and inspected using the following functions.
7805 int isl_vec_size(__isl_keep isl_vec *vec);
7806 __isl_give isl_val *isl_vec_get_element_val(
7807 __isl_keep isl_vec *vec, int pos);
7808 __isl_give isl_vec *isl_vec_set_element_si(
7809 __isl_take isl_vec *vec, int pos, int v);
7810 __isl_give isl_vec *isl_vec_set_element_val(
7811 __isl_take isl_vec *vec, int pos,
7812 __isl_take isl_val *v);
7813 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
7815 __isl_give isl_vec *isl_vec_set_val(
7816 __isl_take isl_vec *vec, __isl_take isl_val *v);
7817 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
7818 __isl_keep isl_vec *vec2, int pos);
7820 C<isl_vec_get_element> will return a negative value if anything went wrong.
7821 In that case, the value of C<*v> is undefined.
7823 The following function can be used to concatenate two vectors.
7825 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
7826 __isl_take isl_vec *vec2);
7830 Matrices can be created, copied and freed using the following functions.
7832 #include <isl/mat.h>
7833 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
7834 unsigned n_row, unsigned n_col);
7835 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
7836 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
7838 Note that the elements of a newly created matrix may have arbitrary values.
7839 The elements can be changed and inspected using the following functions.
7841 int isl_mat_rows(__isl_keep isl_mat *mat);
7842 int isl_mat_cols(__isl_keep isl_mat *mat);
7843 __isl_give isl_val *isl_mat_get_element_val(
7844 __isl_keep isl_mat *mat, int row, int col);
7845 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
7846 int row, int col, int v);
7847 __isl_give isl_mat *isl_mat_set_element_val(
7848 __isl_take isl_mat *mat, int row, int col,
7849 __isl_take isl_val *v);
7851 The following function computes the rank of a matrix.
7852 The return value may be -1 if some error occurred.
7854 #include <isl/mat.h>
7855 int isl_mat_rank(__isl_keep isl_mat *mat);
7857 The following function can be used to compute the (right) inverse
7858 of a matrix, i.e., a matrix such that the product of the original
7859 and the inverse (in that order) is a multiple of the identity matrix.
7860 The input matrix is assumed to be of full row-rank.
7862 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
7864 The following function can be used to compute the (right) kernel
7865 (or null space) of a matrix, i.e., a matrix such that the product of
7866 the original and the kernel (in that order) is the zero matrix.
7868 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
7870 The following function computes a basis for the space spanned
7871 by the rows of a matrix.
7873 __isl_give isl_mat *isl_mat_row_basis(
7874 __isl_take isl_mat *mat);
7876 The following function computes rows that extend a basis of C<mat1>
7877 to a basis that also covers C<mat2>.
7879 __isl_give isl_mat *isl_mat_row_basis_extension(
7880 __isl_take isl_mat *mat1,
7881 __isl_take isl_mat *mat2);
7883 The following function checks whether there is no linear dependence
7884 among the combined rows of "mat1" and "mat2" that is not already present
7885 in "mat1" or "mat2" individually.
7886 If "mat1" and "mat2" have linearly independent rows by themselves,
7887 then this means that there is no linear dependence among all rows together.
7889 isl_bool isl_mat_has_linearly_independent_rows(
7890 __isl_keep isl_mat *mat1,
7891 __isl_keep isl_mat *mat2);
7893 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
7895 The following functions determine
7896 an upper or lower bound on a quasipolynomial over its domain.
7898 __isl_give isl_pw_qpolynomial_fold *
7899 isl_pw_qpolynomial_bound(
7900 __isl_take isl_pw_qpolynomial *pwqp,
7901 enum isl_fold type, int *tight);
7903 __isl_give isl_union_pw_qpolynomial_fold *
7904 isl_union_pw_qpolynomial_bound(
7905 __isl_take isl_union_pw_qpolynomial *upwqp,
7906 enum isl_fold type, int *tight);
7908 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
7909 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
7910 is the returned bound is known be tight, i.e., for each value
7911 of the parameters there is at least
7912 one element in the domain that reaches the bound.
7913 If the domain of C<pwqp> is not wrapping, then the bound is computed
7914 over all elements in that domain and the result has a purely parametric
7915 domain. If the domain of C<pwqp> is wrapping, then the bound is
7916 computed over the range of the wrapped relation. The domain of the
7917 wrapped relation becomes the domain of the result.
7919 =head2 Parametric Vertex Enumeration
7921 The parametric vertex enumeration described in this section
7922 is mainly intended to be used internally and by the C<barvinok>
7925 #include <isl/vertices.h>
7926 __isl_give isl_vertices *isl_basic_set_compute_vertices(
7927 __isl_keep isl_basic_set *bset);
7929 The function C<isl_basic_set_compute_vertices> performs the
7930 actual computation of the parametric vertices and the chamber
7931 decomposition and stores the result in an C<isl_vertices> object.
7932 This information can be queried by either iterating over all
7933 the vertices or iterating over all the chambers or cells
7934 and then iterating over all vertices that are active on the chamber.
7936 isl_stat isl_vertices_foreach_vertex(
7937 __isl_keep isl_vertices *vertices,
7938 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7939 void *user), void *user);
7941 isl_stat isl_vertices_foreach_cell(
7942 __isl_keep isl_vertices *vertices,
7943 isl_stat (*fn)(__isl_take isl_cell *cell,
7944 void *user), void *user);
7945 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
7946 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7947 void *user), void *user);
7949 Other operations that can be performed on an C<isl_vertices> object are
7952 int isl_vertices_get_n_vertices(
7953 __isl_keep isl_vertices *vertices);
7954 __isl_null isl_vertices *isl_vertices_free(
7955 __isl_take isl_vertices *vertices);
7957 Vertices can be inspected and destroyed using the following functions.
7959 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
7960 __isl_give isl_basic_set *isl_vertex_get_domain(
7961 __isl_keep isl_vertex *vertex);
7962 __isl_give isl_multi_aff *isl_vertex_get_expr(
7963 __isl_keep isl_vertex *vertex);
7964 void isl_vertex_free(__isl_take isl_vertex *vertex);
7966 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
7967 describing the vertex in terms of the parameters,
7968 while C<isl_vertex_get_domain> returns the activity domain
7971 Chambers can be inspected and destroyed using the following functions.
7973 __isl_give isl_basic_set *isl_cell_get_domain(
7974 __isl_keep isl_cell *cell);
7975 void isl_cell_free(__isl_take isl_cell *cell);
7977 =head1 Polyhedral Compilation Library
7979 This section collects functionality in C<isl> that has been specifically
7980 designed for use during polyhedral compilation.
7982 =head2 Schedule Trees
7984 A schedule tree is a structured representation of a schedule,
7985 assigning a relative order to a set of domain elements.
7986 The relative order expressed by the schedule tree is
7987 defined recursively. In particular, the order between
7988 two domain elements is determined by the node that is closest
7989 to the root that refers to both elements and that orders them apart.
7990 Each node in the tree is of one of several types.
7991 The root node is always of type C<isl_schedule_node_domain>
7992 (or C<isl_schedule_node_extension>)
7993 and it describes the (extra) domain elements to which the schedule applies.
7994 The other types of nodes are as follows.
7998 =item C<isl_schedule_node_band>
8000 A band of schedule dimensions. Each schedule dimension is represented
8001 by a union piecewise quasi-affine expression. If this expression
8002 assigns a different value to two domain elements, while all previous
8003 schedule dimensions in the same band assign them the same value,
8004 then the two domain elements are ordered according to these two
8006 Each expression is required to be total in the domain elements
8007 that reach the band node.
8009 =item C<isl_schedule_node_expansion>
8011 An expansion node maps each of the domain elements that reach the node
8012 to one or more domain elements. The image of this mapping forms
8013 the set of domain elements that reach the child of the expansion node.
8014 The function that maps each of the expanded domain elements
8015 to the original domain element from which it was expanded
8016 is called the contraction.
8018 =item C<isl_schedule_node_filter>
8020 A filter node does not impose any ordering, but rather intersects
8021 the set of domain elements that the current subtree refers to
8022 with a given union set. The subtree of the filter node only
8023 refers to domain elements in the intersection.
8024 A filter node is typically only used as a child of a sequence or
8027 =item C<isl_schedule_node_leaf>
8029 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
8031 =item C<isl_schedule_node_mark>
8033 A mark node can be used to attach any kind of information to a subtree
8034 of the schedule tree.
8036 =item C<isl_schedule_node_sequence>
8038 A sequence node has one or more children, each of which is a filter node.
8039 The filters on these filter nodes form a partition of
8040 the domain elements that the current subtree refers to.
8041 If two domain elements appear in distinct filters then the sequence
8042 node orders them according to the child positions of the corresponding
8045 =item C<isl_schedule_node_set>
8047 A set node is similar to a sequence node, except that
8048 it expresses that domain elements appearing in distinct filters
8049 may have any order. The order of the children of a set node
8050 is therefore also immaterial.
8054 The following node types are only supported by the AST generator.
8058 =item C<isl_schedule_node_context>
8060 The context describes constraints on the parameters and
8061 the schedule dimensions of outer
8062 bands that the AST generator may assume to hold. It is also the only
8063 kind of node that may introduce additional parameters.
8064 The space of the context is that of the flat product of the outer
8065 band nodes. In particular, if there are no outer band nodes, then
8066 this space is the unnamed zero-dimensional space.
8067 Since a context node references the outer band nodes, any tree
8068 containing a context node is considered to be anchored.
8070 =item C<isl_schedule_node_extension>
8072 An extension node instructs the AST generator to add additional
8073 domain elements that need to be scheduled.
8074 The additional domain elements are described by the range of
8075 the extension map in terms of the outer schedule dimensions,
8076 i.e., the flat product of the outer band nodes.
8077 Note that domain elements are added whenever the AST generator
8078 reaches the extension node, meaning that there are still some
8079 active domain elements for which an AST needs to be generated.
8080 The conditions under which some domain elements are still active
8081 may however not be completely described by the outer AST nodes
8082 generated at that point.
8083 Since an extension node references the outer band nodes, any tree
8084 containing an extension node is considered to be anchored.
8086 An extension node may also appear as the root of a schedule tree,
8087 when it is intended to be inserted into another tree
8088 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
8089 In this case, the domain of the extension node should
8090 correspond to the flat product of the outer band nodes
8091 in this other schedule tree at the point where the extension tree
8094 =item C<isl_schedule_node_guard>
8096 The guard describes constraints on the parameters and
8097 the schedule dimensions of outer
8098 bands that need to be enforced by the outer nodes
8099 in the generated AST.
8100 That is, the part of the AST that is generated from descendants
8101 of the guard node can assume that these constraints are satisfied.
8102 The space of the guard is that of the flat product of the outer
8103 band nodes. In particular, if there are no outer band nodes, then
8104 this space is the unnamed zero-dimensional space.
8105 Since a guard node references the outer band nodes, any tree
8106 containing a guard node is considered to be anchored.
8110 Except for the C<isl_schedule_node_context> nodes,
8111 none of the nodes may introduce any parameters that were not
8112 already present in the root domain node.
8114 A schedule tree is encapsulated in an C<isl_schedule> object.
8115 The simplest such objects, those with a tree consisting of single domain node,
8116 can be created using the following functions with either an empty
8117 domain or a given domain.
8119 #include <isl/schedule.h>
8120 __isl_give isl_schedule *isl_schedule_empty(
8121 __isl_take isl_space *space);
8122 __isl_give isl_schedule *isl_schedule_from_domain(
8123 __isl_take isl_union_set *domain);
8125 The function C<isl_schedule_constraints_compute_schedule> described
8126 in L</"Scheduling"> can also be used to construct schedules.
8128 C<isl_schedule> objects may be copied and freed using the following functions.
8130 #include <isl/schedule.h>
8131 __isl_give isl_schedule *isl_schedule_copy(
8132 __isl_keep isl_schedule *sched);
8133 __isl_null isl_schedule *isl_schedule_free(
8134 __isl_take isl_schedule *sched);
8136 The following functions checks whether two C<isl_schedule> objects
8137 are obviously the same.
8139 #include <isl/schedule.h>
8140 isl_bool isl_schedule_plain_is_equal(
8141 __isl_keep isl_schedule *schedule1,
8142 __isl_keep isl_schedule *schedule2);
8144 The domain of the schedule, i.e., the domain described by the root node,
8145 can be obtained using the following function.
8147 #include <isl/schedule.h>
8148 __isl_give isl_union_set *isl_schedule_get_domain(
8149 __isl_keep isl_schedule *schedule);
8151 An extra top-level band node (right underneath the domain node) can
8152 be introduced into the schedule using the following function.
8153 The schedule tree is assumed not to have any anchored nodes.
8155 #include <isl/schedule.h>
8156 __isl_give isl_schedule *
8157 isl_schedule_insert_partial_schedule(
8158 __isl_take isl_schedule *schedule,
8159 __isl_take isl_multi_union_pw_aff *partial);
8161 A top-level context node (right underneath the domain node) can
8162 be introduced into the schedule using the following function.
8164 #include <isl/schedule.h>
8165 __isl_give isl_schedule *isl_schedule_insert_context(
8166 __isl_take isl_schedule *schedule,
8167 __isl_take isl_set *context)
8169 A top-level guard node (right underneath the domain node) can
8170 be introduced into the schedule using the following function.
8172 #include <isl/schedule.h>
8173 __isl_give isl_schedule *isl_schedule_insert_guard(
8174 __isl_take isl_schedule *schedule,
8175 __isl_take isl_set *guard)
8177 A schedule that combines two schedules either in the given
8178 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
8179 or an C<isl_schedule_node_set> node,
8180 can be created using the following functions.
8182 #include <isl/schedule.h>
8183 __isl_give isl_schedule *isl_schedule_sequence(
8184 __isl_take isl_schedule *schedule1,
8185 __isl_take isl_schedule *schedule2);
8186 __isl_give isl_schedule *isl_schedule_set(
8187 __isl_take isl_schedule *schedule1,
8188 __isl_take isl_schedule *schedule2);
8190 The domains of the two input schedules need to be disjoint.
8192 The following function can be used to restrict the domain
8193 of a schedule with a domain node as root to be a subset of the given union set.
8194 This operation may remove nodes in the tree that have become
8197 #include <isl/schedule.h>
8198 __isl_give isl_schedule *isl_schedule_intersect_domain(
8199 __isl_take isl_schedule *schedule,
8200 __isl_take isl_union_set *domain);
8202 The following function can be used to simplify the domain
8203 of a schedule with a domain node as root with respect to the given
8206 #include <isl/schedule.h>
8207 __isl_give isl_schedule *isl_schedule_gist_domain_params(
8208 __isl_take isl_schedule *schedule,
8209 __isl_take isl_set *context);
8211 The following function resets the user pointers on all parameter
8212 and tuple identifiers referenced by the nodes of the given schedule.
8214 #include <isl/schedule.h>
8215 __isl_give isl_schedule *isl_schedule_reset_user(
8216 __isl_take isl_schedule *schedule);
8218 The following function aligns the parameters of all nodes
8219 in the given schedule to the given space.
8221 #include <isl/schedule.h>
8222 __isl_give isl_schedule *isl_schedule_align_params(
8223 __isl_take isl_schedule *schedule,
8224 __isl_take isl_space *space);
8226 The following function allows the user to plug in a given function
8227 in the iteration domains. The input schedule is not allowed to contain
8228 any expansion nodes.
8230 #include <isl/schedule.h>
8231 __isl_give isl_schedule *
8232 isl_schedule_pullback_union_pw_multi_aff(
8233 __isl_take isl_schedule *schedule,
8234 __isl_take isl_union_pw_multi_aff *upma);
8236 The following function can be used to plug in the schedule C<expansion>
8237 in the leaves of C<schedule>, where C<contraction> describes how
8238 the domain elements of C<expansion> map to the domain elements
8239 at the original leaves of C<schedule>.
8240 The resulting schedule will contain expansion nodes, unless
8241 C<contraction> is an identity function.
8243 #include <isl/schedule.h>
8244 __isl_give isl_schedule *isl_schedule_expand(
8245 __isl_take isl_schedule *schedule,
8246 __isl_take isl_union_pw_multi_aff *contraction,
8247 __isl_take isl_schedule *expansion);
8249 An C<isl_union_map> representation of the schedule can be obtained
8250 from an C<isl_schedule> using the following function.
8252 #include <isl/schedule.h>
8253 __isl_give isl_union_map *isl_schedule_get_map(
8254 __isl_keep isl_schedule *sched);
8256 The resulting relation encodes the same relative ordering as
8257 the schedule by mapping the domain elements to a common schedule space.
8258 If the schedule_separate_components option is set, then the order
8259 of the children of a set node is explicitly encoded in the result.
8260 If the tree contains any expansion nodes, then the relation
8261 is formulated in terms of the expanded domain elements.
8263 Schedules can be read from input using the following functions.
8265 #include <isl/schedule.h>
8266 __isl_give isl_schedule *isl_schedule_read_from_file(
8267 isl_ctx *ctx, FILE *input);
8268 __isl_give isl_schedule *isl_schedule_read_from_str(
8269 isl_ctx *ctx, const char *str);
8271 A representation of the schedule can be printed using
8273 #include <isl/schedule.h>
8274 __isl_give isl_printer *isl_printer_print_schedule(
8275 __isl_take isl_printer *p,
8276 __isl_keep isl_schedule *schedule);
8277 __isl_give char *isl_schedule_to_str(
8278 __isl_keep isl_schedule *schedule);
8280 C<isl_schedule_to_str> prints the schedule in flow format.
8282 The schedule tree can be traversed through the use of
8283 C<isl_schedule_node> objects that point to a particular
8284 position in the schedule tree. Whenever a C<isl_schedule_node>
8285 is used to modify a node in the schedule tree, the original schedule
8286 tree is left untouched and the modifications are performed to a copy
8287 of the tree. The returned C<isl_schedule_node> then points to
8288 this modified copy of the tree.
8290 The root of the schedule tree can be obtained using the following function.
8292 #include <isl/schedule.h>
8293 __isl_give isl_schedule_node *isl_schedule_get_root(
8294 __isl_keep isl_schedule *schedule);
8296 A pointer to a newly created schedule tree with a single domain
8297 node can be created using the following functions.
8299 #include <isl/schedule_node.h>
8300 __isl_give isl_schedule_node *
8301 isl_schedule_node_from_domain(
8302 __isl_take isl_union_set *domain);
8303 __isl_give isl_schedule_node *
8304 isl_schedule_node_from_extension(
8305 __isl_take isl_union_map *extension);
8307 C<isl_schedule_node_from_extension> creates a tree with an extension
8310 Schedule nodes can be copied and freed using the following functions.
8312 #include <isl/schedule_node.h>
8313 __isl_give isl_schedule_node *isl_schedule_node_copy(
8314 __isl_keep isl_schedule_node *node);
8315 __isl_null isl_schedule_node *isl_schedule_node_free(
8316 __isl_take isl_schedule_node *node);
8318 The following functions can be used to check if two schedule
8319 nodes point to the same position in the same schedule.
8321 #include <isl/schedule_node.h>
8322 isl_bool isl_schedule_node_is_equal(
8323 __isl_keep isl_schedule_node *node1,
8324 __isl_keep isl_schedule_node *node2);
8326 The following properties can be obtained from a schedule node.
8328 #include <isl/schedule_node.h>
8329 enum isl_schedule_node_type isl_schedule_node_get_type(
8330 __isl_keep isl_schedule_node *node);
8331 enum isl_schedule_node_type
8332 isl_schedule_node_get_parent_type(
8333 __isl_keep isl_schedule_node *node);
8334 __isl_give isl_schedule *isl_schedule_node_get_schedule(
8335 __isl_keep isl_schedule_node *node);
8337 The function C<isl_schedule_node_get_type> returns the type of
8338 the node, while C<isl_schedule_node_get_parent_type> returns
8339 type of the parent of the node, which is required to exist.
8340 The function C<isl_schedule_node_get_schedule> returns a copy
8341 to the schedule to which the node belongs.
8343 The following functions can be used to move the schedule node
8344 to a different position in the tree or to check if such a position
8347 #include <isl/schedule_node.h>
8348 isl_bool isl_schedule_node_has_parent(
8349 __isl_keep isl_schedule_node *node);
8350 __isl_give isl_schedule_node *isl_schedule_node_parent(
8351 __isl_take isl_schedule_node *node);
8352 __isl_give isl_schedule_node *isl_schedule_node_root(
8353 __isl_take isl_schedule_node *node);
8354 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
8355 __isl_take isl_schedule_node *node,
8357 int isl_schedule_node_n_children(
8358 __isl_keep isl_schedule_node *node);
8359 __isl_give isl_schedule_node *isl_schedule_node_child(
8360 __isl_take isl_schedule_node *node, int pos);
8361 isl_bool isl_schedule_node_has_children(
8362 __isl_keep isl_schedule_node *node);
8363 __isl_give isl_schedule_node *isl_schedule_node_first_child(
8364 __isl_take isl_schedule_node *node);
8365 isl_bool isl_schedule_node_has_previous_sibling(
8366 __isl_keep isl_schedule_node *node);
8367 __isl_give isl_schedule_node *
8368 isl_schedule_node_previous_sibling(
8369 __isl_take isl_schedule_node *node);
8370 isl_bool isl_schedule_node_has_next_sibling(
8371 __isl_keep isl_schedule_node *node);
8372 __isl_give isl_schedule_node *
8373 isl_schedule_node_next_sibling(
8374 __isl_take isl_schedule_node *node);
8376 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
8377 is the node itself, the ancestor of generation 1 is its parent and so on.
8379 It is also possible to query the number of ancestors of a node,
8380 the position of the current node
8381 within the children of its parent, the position of the subtree
8382 containing a node within the children of an ancestor
8383 or to obtain a copy of a given
8384 child without destroying the current node.
8385 Given two nodes that point to the same schedule, their closest
8386 shared ancestor can be obtained using
8387 C<isl_schedule_node_get_shared_ancestor>.
8389 #include <isl/schedule_node.h>
8390 int isl_schedule_node_get_tree_depth(
8391 __isl_keep isl_schedule_node *node);
8392 int isl_schedule_node_get_child_position(
8393 __isl_keep isl_schedule_node *node);
8394 int isl_schedule_node_get_ancestor_child_position(
8395 __isl_keep isl_schedule_node *node,
8396 __isl_keep isl_schedule_node *ancestor);
8397 __isl_give isl_schedule_node *isl_schedule_node_get_child(
8398 __isl_keep isl_schedule_node *node, int pos);
8399 __isl_give isl_schedule_node *
8400 isl_schedule_node_get_shared_ancestor(
8401 __isl_keep isl_schedule_node *node1,
8402 __isl_keep isl_schedule_node *node2);
8404 All nodes in a schedule tree or
8405 all descendants of a specific node (including the node) can be visited
8406 in depth-first pre-order using the following functions.
8408 #include <isl/schedule.h>
8409 isl_stat isl_schedule_foreach_schedule_node_top_down(
8410 __isl_keep isl_schedule *sched,
8411 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8412 void *user), void *user);
8414 #include <isl/schedule_node.h>
8415 isl_stat isl_schedule_node_foreach_descendant_top_down(
8416 __isl_keep isl_schedule_node *node,
8417 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8418 void *user), void *user);
8420 The callback function is slightly different from the usual
8421 callbacks in that it not only indicates success (non-negative result)
8422 or failure (negative result), but also indicates whether the children
8423 of the given node should be visited. In particular, if the callback
8424 returns a positive value, then the children are visited, but if
8425 the callback returns zero, then the children are not visited.
8427 The following functions checks whether
8428 all descendants of a specific node (including the node itself)
8429 satisfy a user-specified test.
8431 #include <isl/schedule_node.h>
8432 isl_bool isl_schedule_node_every_descendant(
8433 __isl_keep isl_schedule_node *node,
8434 isl_bool (*test)(__isl_keep isl_schedule_node *node,
8435 void *user), void *user)
8437 The ancestors of a node in a schedule tree can be visited from
8438 the root down to and including the parent of the node using
8439 the following function.
8441 #include <isl/schedule_node.h>
8442 isl_stat isl_schedule_node_foreach_ancestor_top_down(
8443 __isl_keep isl_schedule_node *node,
8444 isl_stat (*fn)(__isl_keep isl_schedule_node *node,
8445 void *user), void *user);
8447 The following functions allows for a depth-first post-order
8448 traversal of the nodes in a schedule tree or
8449 of the descendants of a specific node (including the node
8450 itself), where the user callback is allowed to modify the
8453 #include <isl/schedule.h>
8454 __isl_give isl_schedule *
8455 isl_schedule_map_schedule_node_bottom_up(
8456 __isl_take isl_schedule *schedule,
8457 __isl_give isl_schedule_node *(*fn)(
8458 __isl_take isl_schedule_node *node,
8459 void *user), void *user);
8461 #include <isl/schedule_node.h>
8462 __isl_give isl_schedule_node *
8463 isl_schedule_node_map_descendant_bottom_up(
8464 __isl_take isl_schedule_node *node,
8465 __isl_give isl_schedule_node *(*fn)(
8466 __isl_take isl_schedule_node *node,
8467 void *user), void *user);
8469 The traversal continues from the node returned by the callback function.
8470 It is the responsibility of the user to ensure that this does not
8471 lead to an infinite loop. It is safest to always return a pointer
8472 to the same position (same ancestors and child positions) as the input node.
8474 The following function removes a node (along with its descendants)
8475 from a schedule tree and returns a pointer to the leaf at the
8476 same position in the updated tree.
8477 It is not allowed to remove the root of a schedule tree or
8478 a child of a set or sequence node.
8480 #include <isl/schedule_node.h>
8481 __isl_give isl_schedule_node *isl_schedule_node_cut(
8482 __isl_take isl_schedule_node *node);
8484 The following function removes a single node
8485 from a schedule tree and returns a pointer to the child
8486 of the node, now located at the position of the original node
8487 or to a leaf node at that position if there was no child.
8488 It is not allowed to remove the root of a schedule tree,
8489 a set or sequence node, a child of a set or sequence node or
8490 a band node with an anchored subtree.
8492 #include <isl/schedule_node.h>
8493 __isl_give isl_schedule_node *isl_schedule_node_delete(
8494 __isl_take isl_schedule_node *node);
8496 Most nodes in a schedule tree only contain local information.
8497 In some cases, however, a node may also refer to the schedule dimensions
8498 of its outer band nodes.
8499 This means that the position of the node within the tree should
8500 not be changed, or at least that no changes are performed to the
8501 outer band nodes. The following function can be used to test
8502 whether the subtree rooted at a given node contains any such nodes.
8504 #include <isl/schedule_node.h>
8505 isl_bool isl_schedule_node_is_subtree_anchored(
8506 __isl_keep isl_schedule_node *node);
8508 The following function resets the user pointers on all parameter
8509 and tuple identifiers referenced by the given schedule node.
8511 #include <isl/schedule_node.h>
8512 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
8513 __isl_take isl_schedule_node *node);
8515 The following function aligns the parameters of the given schedule
8516 node to the given space.
8518 #include <isl/schedule_node.h>
8519 __isl_give isl_schedule_node *
8520 isl_schedule_node_align_params(
8521 __isl_take isl_schedule_node *node,
8522 __isl_take isl_space *space);
8524 Several node types have their own functions for querying
8525 (and in some cases setting) some node type specific properties.
8527 #include <isl/schedule_node.h>
8528 __isl_give isl_space *isl_schedule_node_band_get_space(
8529 __isl_keep isl_schedule_node *node);
8530 __isl_give isl_multi_union_pw_aff *
8531 isl_schedule_node_band_get_partial_schedule(
8532 __isl_keep isl_schedule_node *node);
8533 __isl_give isl_union_map *
8534 isl_schedule_node_band_get_partial_schedule_union_map(
8535 __isl_keep isl_schedule_node *node);
8536 unsigned isl_schedule_node_band_n_member(
8537 __isl_keep isl_schedule_node *node);
8538 isl_bool isl_schedule_node_band_member_get_coincident(
8539 __isl_keep isl_schedule_node *node, int pos);
8540 __isl_give isl_schedule_node *
8541 isl_schedule_node_band_member_set_coincident(
8542 __isl_take isl_schedule_node *node, int pos,
8544 isl_bool isl_schedule_node_band_get_permutable(
8545 __isl_keep isl_schedule_node *node);
8546 __isl_give isl_schedule_node *
8547 isl_schedule_node_band_set_permutable(
8548 __isl_take isl_schedule_node *node, int permutable);
8549 enum isl_ast_loop_type
8550 isl_schedule_node_band_member_get_ast_loop_type(
8551 __isl_keep isl_schedule_node *node, int pos);
8552 __isl_give isl_schedule_node *
8553 isl_schedule_node_band_member_set_ast_loop_type(
8554 __isl_take isl_schedule_node *node, int pos,
8555 enum isl_ast_loop_type type);
8556 __isl_give isl_union_set *
8557 enum isl_ast_loop_type
8558 isl_schedule_node_band_member_get_isolate_ast_loop_type(
8559 __isl_keep isl_schedule_node *node, int pos);
8560 __isl_give isl_schedule_node *
8561 isl_schedule_node_band_member_set_isolate_ast_loop_type(
8562 __isl_take isl_schedule_node *node, int pos,
8563 enum isl_ast_loop_type type);
8564 isl_schedule_node_band_get_ast_build_options(
8565 __isl_keep isl_schedule_node *node);
8566 __isl_give isl_schedule_node *
8567 isl_schedule_node_band_set_ast_build_options(
8568 __isl_take isl_schedule_node *node,
8569 __isl_take isl_union_set *options);
8570 __isl_give isl_set *
8571 isl_schedule_node_band_get_ast_isolate_option(
8572 __isl_keep isl_schedule_node *node);
8574 The function C<isl_schedule_node_band_get_space> returns the space
8575 of the partial schedule of the band.
8576 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
8577 returns a representation of the partial schedule of the band node
8578 in the form of an C<isl_union_map>.
8579 The coincident and permutable properties are set by
8580 C<isl_schedule_constraints_compute_schedule> on the schedule tree
8582 A scheduling dimension is considered to be ``coincident''
8583 if it satisfies the coincidence constraints within its band.
8584 That is, if the dependence distances of the coincidence
8585 constraints are all zero in that direction (for fixed
8586 iterations of outer bands).
8587 A band is marked permutable if it was produced using the Pluto-like scheduler.
8588 Note that the scheduler may have to resort to a Feautrier style scheduling
8589 step even if the default scheduler is used.
8590 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
8591 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
8592 For the meaning of these loop AST generation types and the difference
8593 between the regular loop AST generation type and the isolate
8594 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
8595 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
8596 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
8597 may return C<isl_ast_loop_error> if an error occurs.
8598 The AST build options govern how an AST is generated for
8599 the individual schedule dimensions during AST generation.
8600 See L</"AST Generation Options (Schedule Tree)">.
8601 The isolate option for the given node can be extracted from these
8602 AST build options using the function
8603 C<isl_schedule_node_band_get_ast_isolate_option>.
8605 #include <isl/schedule_node.h>
8606 __isl_give isl_set *
8607 isl_schedule_node_context_get_context(
8608 __isl_keep isl_schedule_node *node);
8610 #include <isl/schedule_node.h>
8611 __isl_give isl_union_set *
8612 isl_schedule_node_domain_get_domain(
8613 __isl_keep isl_schedule_node *node);
8615 #include <isl/schedule_node.h>
8616 __isl_give isl_union_map *
8617 isl_schedule_node_expansion_get_expansion(
8618 __isl_keep isl_schedule_node *node);
8619 __isl_give isl_union_pw_multi_aff *
8620 isl_schedule_node_expansion_get_contraction(
8621 __isl_keep isl_schedule_node *node);
8623 #include <isl/schedule_node.h>
8624 __isl_give isl_union_map *
8625 isl_schedule_node_extension_get_extension(
8626 __isl_keep isl_schedule_node *node);
8628 #include <isl/schedule_node.h>
8629 __isl_give isl_union_set *
8630 isl_schedule_node_filter_get_filter(
8631 __isl_keep isl_schedule_node *node);
8633 #include <isl/schedule_node.h>
8634 __isl_give isl_set *isl_schedule_node_guard_get_guard(
8635 __isl_keep isl_schedule_node *node);
8637 #include <isl/schedule_node.h>
8638 __isl_give isl_id *isl_schedule_node_mark_get_id(
8639 __isl_keep isl_schedule_node *node);
8641 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
8642 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
8643 partial schedules related to the node.
8645 #include <isl/schedule_node.h>
8646 __isl_give isl_multi_union_pw_aff *
8647 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
8648 __isl_keep isl_schedule_node *node);
8649 __isl_give isl_union_pw_multi_aff *
8650 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
8651 __isl_keep isl_schedule_node *node);
8652 __isl_give isl_union_map *
8653 isl_schedule_node_get_prefix_schedule_union_map(
8654 __isl_keep isl_schedule_node *node);
8655 __isl_give isl_union_map *
8656 isl_schedule_node_get_prefix_schedule_relation(
8657 __isl_keep isl_schedule_node *node);
8658 __isl_give isl_union_map *
8659 isl_schedule_node_get_subtree_schedule_union_map(
8660 __isl_keep isl_schedule_node *node);
8662 In particular, the functions
8663 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
8664 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
8665 and C<isl_schedule_node_get_prefix_schedule_union_map>
8666 return a relative ordering on the domain elements that reach the given
8667 node determined by its ancestors.
8668 The function C<isl_schedule_node_get_prefix_schedule_relation>
8669 additionally includes the domain constraints in the result.
8670 The function C<isl_schedule_node_get_subtree_schedule_union_map>
8671 returns a representation of the partial schedule defined by the
8672 subtree rooted at the given node.
8673 If the tree contains any expansion nodes, then the subtree schedule
8674 is formulated in terms of the expanded domain elements.
8675 The tree passed to functions returning a prefix schedule
8676 may only contain extension nodes if these would not affect
8677 the result of these functions. That is, if one of the ancestors
8678 is an extension node, then all of the domain elements that were
8679 added by the extension node need to have been filtered out
8680 by filter nodes between the extension node and the input node.
8681 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
8682 may not contain in extension nodes in the selected subtree.
8684 The expansion/contraction defined by an entire subtree, combining
8685 the expansions/contractions
8686 on the expansion nodes in the subtree, can be obtained using
8687 the following functions.
8689 #include <isl/schedule_node.h>
8690 __isl_give isl_union_map *
8691 isl_schedule_node_get_subtree_expansion(
8692 __isl_keep isl_schedule_node *node);
8693 __isl_give isl_union_pw_multi_aff *
8694 isl_schedule_node_get_subtree_contraction(
8695 __isl_keep isl_schedule_node *node);
8697 The total number of outer band members of given node, i.e.,
8698 the shared output dimension of the maps in the result
8699 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
8700 using the following function.
8702 #include <isl/schedule_node.h>
8703 int isl_schedule_node_get_schedule_depth(
8704 __isl_keep isl_schedule_node *node);
8706 The following functions return the elements that reach the given node
8707 or the union of universes in the spaces that contain these elements.
8709 #include <isl/schedule_node.h>
8710 __isl_give isl_union_set *
8711 isl_schedule_node_get_domain(
8712 __isl_keep isl_schedule_node *node);
8713 __isl_give isl_union_set *
8714 isl_schedule_node_get_universe_domain(
8715 __isl_keep isl_schedule_node *node);
8717 The input tree of C<isl_schedule_node_get_domain>
8718 may only contain extension nodes if these would not affect
8719 the result of this function. That is, if one of the ancestors
8720 is an extension node, then all of the domain elements that were
8721 added by the extension node need to have been filtered out
8722 by filter nodes between the extension node and the input node.
8724 The following functions can be used to introduce additional nodes
8725 in the schedule tree. The new node is introduced at the point
8726 in the tree where the C<isl_schedule_node> points to and
8727 the results points to the new node.
8729 #include <isl/schedule_node.h>
8730 __isl_give isl_schedule_node *
8731 isl_schedule_node_insert_partial_schedule(
8732 __isl_take isl_schedule_node *node,
8733 __isl_take isl_multi_union_pw_aff *schedule);
8735 This function inserts a new band node with (the greatest integer
8736 part of) the given partial schedule.
8737 The subtree rooted at the given node is assumed not to have
8740 #include <isl/schedule_node.h>
8741 __isl_give isl_schedule_node *
8742 isl_schedule_node_insert_context(
8743 __isl_take isl_schedule_node *node,
8744 __isl_take isl_set *context);
8746 This function inserts a new context node with the given context constraints.
8748 #include <isl/schedule_node.h>
8749 __isl_give isl_schedule_node *
8750 isl_schedule_node_insert_filter(
8751 __isl_take isl_schedule_node *node,
8752 __isl_take isl_union_set *filter);
8754 This function inserts a new filter node with the given filter.
8755 If the original node already pointed to a filter node, then the
8756 two filter nodes are merged into one.
8758 #include <isl/schedule_node.h>
8759 __isl_give isl_schedule_node *
8760 isl_schedule_node_insert_guard(
8761 __isl_take isl_schedule_node *node,
8762 __isl_take isl_set *guard);
8764 This function inserts a new guard node with the given guard constraints.
8766 #include <isl/schedule_node.h>
8767 __isl_give isl_schedule_node *
8768 isl_schedule_node_insert_mark(
8769 __isl_take isl_schedule_node *node,
8770 __isl_take isl_id *mark);
8772 This function inserts a new mark node with the give mark identifier.
8774 #include <isl/schedule_node.h>
8775 __isl_give isl_schedule_node *
8776 isl_schedule_node_insert_sequence(
8777 __isl_take isl_schedule_node *node,
8778 __isl_take isl_union_set_list *filters);
8779 __isl_give isl_schedule_node *
8780 isl_schedule_node_insert_set(
8781 __isl_take isl_schedule_node *node,
8782 __isl_take isl_union_set_list *filters);
8784 These functions insert a new sequence or set node with the given
8785 filters as children.
8787 #include <isl/schedule_node.h>
8788 __isl_give isl_schedule_node *isl_schedule_node_group(
8789 __isl_take isl_schedule_node *node,
8790 __isl_take isl_id *group_id);
8792 This function introduces an expansion node in between the current
8793 node and its parent that expands instances of a space with tuple
8794 identifier C<group_id> to the original domain elements that reach
8795 the node. The group instances are identified by the prefix schedule
8796 of those domain elements. The ancestors of the node are adjusted
8797 to refer to the group instances instead of the original domain
8798 elements. The return value points to the same node in the updated
8799 schedule tree as the input node, i.e., to the child of the newly
8800 introduced expansion node. Grouping instances of different statements
8801 ensures that they will be treated as a single statement by the
8802 AST generator up to the point of the expansion node.
8804 The following function can be used to flatten a nested
8807 #include <isl/schedule_node.h>
8808 __isl_give isl_schedule_node *
8809 isl_schedule_node_sequence_splice_child(
8810 __isl_take isl_schedule_node *node, int pos);
8812 That is, given a sequence node C<node> that has another sequence node
8813 in its child at position C<pos> (in particular, the child of that filter
8814 node is a sequence node), attach the children of that other sequence
8815 node as children of C<node>, replacing the original child at position
8818 The partial schedule of a band node can be scaled (down) or reduced using
8819 the following functions.
8821 #include <isl/schedule_node.h>
8822 __isl_give isl_schedule_node *
8823 isl_schedule_node_band_scale(
8824 __isl_take isl_schedule_node *node,
8825 __isl_take isl_multi_val *mv);
8826 __isl_give isl_schedule_node *
8827 isl_schedule_node_band_scale_down(
8828 __isl_take isl_schedule_node *node,
8829 __isl_take isl_multi_val *mv);
8830 __isl_give isl_schedule_node *
8831 isl_schedule_node_band_mod(
8832 __isl_take isl_schedule_node *node,
8833 __isl_take isl_multi_val *mv);
8835 The spaces of the two arguments need to match.
8836 After scaling, the partial schedule is replaced by its greatest
8837 integer part to ensure that the schedule remains integral.
8839 The partial schedule of a band node can be shifted by an
8840 C<isl_multi_union_pw_aff> with a domain that is a superset
8841 of the domain of the partial schedule using
8842 the following function.
8844 #include <isl/schedule_node.h>
8845 __isl_give isl_schedule_node *
8846 isl_schedule_node_band_shift(
8847 __isl_take isl_schedule_node *node,
8848 __isl_take isl_multi_union_pw_aff *shift);
8850 A band node can be tiled using the following function.
8852 #include <isl/schedule_node.h>
8853 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
8854 __isl_take isl_schedule_node *node,
8855 __isl_take isl_multi_val *sizes);
8857 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
8859 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
8860 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
8862 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
8864 The C<isl_schedule_node_band_tile> function tiles
8865 the band using the given tile sizes inside its schedule.
8866 A new child band node is created to represent the point loops and it is
8867 inserted between the modified band and its children.
8868 The subtree rooted at the given node is assumed not to have
8870 The C<tile_scale_tile_loops> option specifies whether the tile
8871 loops iterators should be scaled by the tile sizes.
8872 If the C<tile_shift_point_loops> option is set, then the point loops
8873 are shifted to start at zero.
8875 A band node can be split into two nested band nodes
8876 using the following function.
8878 #include <isl/schedule_node.h>
8879 __isl_give isl_schedule_node *isl_schedule_node_band_split(
8880 __isl_take isl_schedule_node *node, int pos);
8882 The resulting outer band node contains the first C<pos> dimensions of
8883 the schedule of C<node> while the inner band contains the remaining dimensions.
8884 The schedules of the two band nodes live in anonymous spaces.
8885 The loop AST generation type options and the isolate option
8886 are split over the two band nodes.
8888 A band node can be moved down to the leaves of the subtree rooted
8889 at the band node using the following function.
8891 #include <isl/schedule_node.h>
8892 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
8893 __isl_take isl_schedule_node *node);
8895 The subtree rooted at the given node is assumed not to have
8897 The result points to the node in the resulting tree that is in the same
8898 position as the node pointed to by C<node> in the original tree.
8900 #include <isl/schedule_node.h>
8901 __isl_give isl_schedule_node *
8902 isl_schedule_node_order_before(
8903 __isl_take isl_schedule_node *node,
8904 __isl_take isl_union_set *filter);
8905 __isl_give isl_schedule_node *
8906 isl_schedule_node_order_after(
8907 __isl_take isl_schedule_node *node,
8908 __isl_take isl_union_set *filter);
8910 These functions split the domain elements that reach C<node>
8911 into those that satisfy C<filter> and those that do not and
8912 arranges for the elements that do satisfy the filter to be
8913 executed before (in case of C<isl_schedule_node_order_before>)
8914 or after (in case of C<isl_schedule_node_order_after>)
8915 those that do not. The order is imposed by
8916 a sequence node, possibly reusing the grandparent of C<node>
8917 on two copies of the subtree attached to the original C<node>.
8918 Both copies are simplified with respect to their filter.
8920 Return a pointer to the copy of the subtree that does not
8921 satisfy C<filter>. If there is no such copy (because all
8922 reaching domain elements satisfy the filter), then return
8923 the original pointer.
8925 #include <isl/schedule_node.h>
8926 __isl_give isl_schedule_node *
8927 isl_schedule_node_graft_before(
8928 __isl_take isl_schedule_node *node,
8929 __isl_take isl_schedule_node *graft);
8930 __isl_give isl_schedule_node *
8931 isl_schedule_node_graft_after(
8932 __isl_take isl_schedule_node *node,
8933 __isl_take isl_schedule_node *graft);
8935 This function inserts the C<graft> tree into the tree containing C<node>
8936 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
8937 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
8938 The root node of C<graft>
8939 should be an extension node where the domain of the extension
8940 is the flat product of all outer band nodes of C<node>.
8941 The root node may also be a domain node.
8942 The elements of the domain or the range of the extension may not
8943 intersect with the domain elements that reach "node".
8944 The schedule tree of C<graft> may not be anchored.
8946 The schedule tree of C<node> is modified to include an extension node
8947 corresponding to the root node of C<graft> as a child of the original
8948 parent of C<node>. The original node that C<node> points to and the
8949 child of the root node of C<graft> are attached to this extension node
8950 through a sequence, with appropriate filters and with the child
8951 of C<graft> appearing before or after the original C<node>.
8953 If C<node> already appears inside a sequence that is the child of
8954 an extension node and if the spaces of the new domain elements
8955 do not overlap with those of the original domain elements,
8956 then that extension node is extended with the new extension
8957 rather than introducing a new segment of extension and sequence nodes.
8959 Return a pointer to the same node in the modified tree that
8960 C<node> pointed to in the original tree.
8962 A representation of the schedule node can be printed using
8964 #include <isl/schedule_node.h>
8965 __isl_give isl_printer *isl_printer_print_schedule_node(
8966 __isl_take isl_printer *p,
8967 __isl_keep isl_schedule_node *node);
8968 __isl_give char *isl_schedule_node_to_str(
8969 __isl_keep isl_schedule_node *node);
8971 C<isl_schedule_node_to_str> prints the schedule node in block format.
8973 =head2 Dependence Analysis
8975 C<isl> contains specialized functionality for performing
8976 array dataflow analysis. That is, given a I<sink> access relation,
8977 a collection of possible I<source> accesses and
8978 a collection of I<kill> accesses,
8979 C<isl> can compute relations that describe
8980 for each iteration of the sink access, which iterations
8981 of which of the source access relations may have
8982 accessed the same data element before the given iteration
8983 of the sink access without any intermediate kill of that data element.
8984 The resulting dependence relations map source iterations
8985 to either the corresponding sink iterations or
8986 pairs of corresponding sink iterations and accessed data elements.
8987 To compute standard flow dependences, the sink should be
8988 a read, while the sources should be writes.
8989 If no kills are specified,
8990 then memory based dependence analysis is performed.
8991 If, on the other hand, all sources are also kills,
8992 then value based dependence analysis is performed.
8993 If any of the source accesses are marked as being I<must>
8994 accesses, then they are also treated as kills.
8995 Furthermore, the specification of must-sources results
8996 in the computation of must-dependences.
8997 Only dependences originating in a must access not coscheduled
8998 with any other access to the same element and without
8999 any may accesses between the must access and the sink access
9000 are considered to be must dependences.
9002 =head3 High-level Interface
9004 A high-level interface to dependence analysis is provided
9005 by the following function.
9007 #include <isl/flow.h>
9008 __isl_give isl_union_flow *
9009 isl_union_access_info_compute_flow(
9010 __isl_take isl_union_access_info *access);
9012 The input C<isl_union_access_info> object describes the sink
9013 access relations, the source access relations and a schedule,
9014 while the output C<isl_union_flow> object describes
9015 the resulting dependence relations and the subsets of the
9016 sink relations for which no source was found.
9018 An C<isl_union_access_info> is created, modified, copied and freed using
9019 the following functions.
9021 #include <isl/flow.h>
9022 __isl_give isl_union_access_info *
9023 isl_union_access_info_from_sink(
9024 __isl_take isl_union_map *sink);
9025 __isl_give isl_union_access_info *
9026 isl_union_access_info_set_kill(
9027 __isl_take isl_union_access_info *access,
9028 __isl_take isl_union_map *kill);
9029 __isl_give isl_union_access_info *
9030 isl_union_access_info_set_may_source(
9031 __isl_take isl_union_access_info *access,
9032 __isl_take isl_union_map *may_source);
9033 __isl_give isl_union_access_info *
9034 isl_union_access_info_set_must_source(
9035 __isl_take isl_union_access_info *access,
9036 __isl_take isl_union_map *must_source);
9037 __isl_give isl_union_access_info *
9038 isl_union_access_info_set_schedule(
9039 __isl_take isl_union_access_info *access,
9040 __isl_take isl_schedule *schedule);
9041 __isl_give isl_union_access_info *
9042 isl_union_access_info_set_schedule_map(
9043 __isl_take isl_union_access_info *access,
9044 __isl_take isl_union_map *schedule_map);
9045 __isl_give isl_union_access_info *
9046 isl_union_access_info_copy(
9047 __isl_keep isl_union_access_info *access);
9048 __isl_null isl_union_access_info *
9049 isl_union_access_info_free(
9050 __isl_take isl_union_access_info *access);
9052 The may sources set by C<isl_union_access_info_set_may_source>
9053 do not need to include the must sources set by
9054 C<isl_union_access_info_set_must_source> as a subset.
9055 The kills set by C<isl_union_access_info_set_kill> may overlap
9056 with the may-sources and/or must-sources.
9057 The user is free not to call one (or more) of these functions,
9058 in which case the corresponding set is kept to its empty default.
9059 Similarly, the default schedule initialized by
9060 C<isl_union_access_info_from_sink> is empty.
9061 The current schedule is determined by the last call to either
9062 C<isl_union_access_info_set_schedule> or
9063 C<isl_union_access_info_set_schedule_map>.
9064 The domain of the schedule corresponds to the domains of
9065 the access relations. In particular, the domains of the access
9066 relations are effectively intersected with the domain of the schedule
9067 and only the resulting accesses are considered by the dependence analysis.
9069 An C<isl_union_access_info> object can be read from input
9070 using the following function.
9072 #include <isl/flow.h>
9073 __isl_give isl_union_access_info *
9074 isl_union_access_info_read_from_file(isl_ctx *ctx,
9077 A representation of the information contained in an object
9078 of type C<isl_union_access_info> can be obtained using
9080 #include <isl/flow.h>
9081 __isl_give isl_printer *
9082 isl_printer_print_union_access_info(
9083 __isl_take isl_printer *p,
9084 __isl_keep isl_union_access_info *access);
9085 __isl_give char *isl_union_access_info_to_str(
9086 __isl_keep isl_union_access_info *access);
9088 C<isl_union_access_info_to_str> prints the information in flow format.
9090 The output of C<isl_union_access_info_compute_flow> can be examined,
9091 copied, and freed using the following functions.
9093 #include <isl/flow.h>
9094 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
9095 __isl_keep isl_union_flow *flow);
9096 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
9097 __isl_keep isl_union_flow *flow);
9098 __isl_give isl_union_map *
9099 isl_union_flow_get_full_must_dependence(
9100 __isl_keep isl_union_flow *flow);
9101 __isl_give isl_union_map *
9102 isl_union_flow_get_full_may_dependence(
9103 __isl_keep isl_union_flow *flow);
9104 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
9105 __isl_keep isl_union_flow *flow);
9106 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
9107 __isl_keep isl_union_flow *flow);
9108 __isl_give isl_union_flow *isl_union_flow_copy(
9109 __isl_keep isl_union_flow *flow);
9110 __isl_null isl_union_flow *isl_union_flow_free(
9111 __isl_take isl_union_flow *flow);
9113 The relation returned by C<isl_union_flow_get_must_dependence>
9114 relates domain elements of must sources to domain elements of the sink.
9115 The relation returned by C<isl_union_flow_get_may_dependence>
9116 relates domain elements of must or may sources to domain elements of the sink
9117 and includes the previous relation as a subset.
9118 The relation returned by C<isl_union_flow_get_full_must_dependence>
9119 relates domain elements of must sources to pairs of domain elements of the sink
9120 and accessed data elements.
9121 The relation returned by C<isl_union_flow_get_full_may_dependence>
9122 relates domain elements of must or may sources to pairs of
9123 domain elements of the sink and accessed data elements.
9124 This relation includes the previous relation as a subset.
9125 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
9126 of the sink relation for which no dependences have been found.
9127 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
9128 of the sink relation for which no definite dependences have been found.
9129 That is, it contains those sink access that do not contribute to any
9130 of the elements in the relation returned
9131 by C<isl_union_flow_get_must_dependence>.
9133 A representation of the information contained in an object
9134 of type C<isl_union_flow> can be obtained using
9136 #include <isl/flow.h>
9137 __isl_give isl_printer *isl_printer_print_union_flow(
9138 __isl_take isl_printer *p,
9139 __isl_keep isl_union_flow *flow);
9140 __isl_give char *isl_union_flow_to_str(
9141 __isl_keep isl_union_flow *flow);
9143 C<isl_union_flow_to_str> prints the information in flow format.
9145 =head3 Low-level Interface
9147 A lower-level interface is provided by the following functions.
9149 #include <isl/flow.h>
9151 typedef int (*isl_access_level_before)(void *first, void *second);
9153 __isl_give isl_access_info *isl_access_info_alloc(
9154 __isl_take isl_map *sink,
9155 void *sink_user, isl_access_level_before fn,
9157 __isl_give isl_access_info *isl_access_info_add_source(
9158 __isl_take isl_access_info *acc,
9159 __isl_take isl_map *source, int must,
9161 __isl_null isl_access_info *isl_access_info_free(
9162 __isl_take isl_access_info *acc);
9164 __isl_give isl_flow *isl_access_info_compute_flow(
9165 __isl_take isl_access_info *acc);
9167 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,
9168 isl_stat (*fn)(__isl_take isl_map *dep, int must,
9169 void *dep_user, void *user),
9171 __isl_give isl_map *isl_flow_get_no_source(
9172 __isl_keep isl_flow *deps, int must);
9173 void isl_flow_free(__isl_take isl_flow *deps);
9175 The function C<isl_access_info_compute_flow> performs the actual
9176 dependence analysis. The other functions are used to construct
9177 the input for this function or to read off the output.
9179 The input is collected in an C<isl_access_info>, which can
9180 be created through a call to C<isl_access_info_alloc>.
9181 The arguments to this functions are the sink access relation
9182 C<sink>, a token C<sink_user> used to identify the sink
9183 access to the user, a callback function for specifying the
9184 relative order of source and sink accesses, and the number
9185 of source access relations that will be added.
9187 The callback function has type C<int (*)(void *first, void *second)>.
9188 The function is called with two user supplied tokens identifying
9189 either a source or the sink and it should return the shared nesting
9190 level and the relative order of the two accesses.
9191 In particular, let I<n> be the number of loops shared by
9192 the two accesses. If C<first> precedes C<second> textually,
9193 then the function should return I<2 * n + 1>; otherwise,
9194 it should return I<2 * n>.
9195 The low-level interface assumes that no sources are coscheduled.
9196 If the information returned by the callback does not allow
9197 the relative order to be determined, then one of the sources
9198 is arbitrarily taken to be executed after the other(s).
9200 The sources can be added to the C<isl_access_info> object by performing
9201 (at most) C<max_source> calls to C<isl_access_info_add_source>.
9202 C<must> indicates whether the source is a I<must> access
9203 or a I<may> access. Note that a multi-valued access relation
9204 should only be marked I<must> if every iteration in the domain
9205 of the relation accesses I<all> elements in its image.
9206 The C<source_user> token is again used to identify
9207 the source access. The range of the source access relation
9208 C<source> should have the same dimension as the range
9209 of the sink access relation.
9210 The C<isl_access_info_free> function should usually not be
9211 called explicitly, because it is already called implicitly by
9212 C<isl_access_info_compute_flow>.
9214 The result of the dependence analysis is collected in an
9215 C<isl_flow>. There may be elements of
9216 the sink access for which no preceding source access could be
9217 found or for which all preceding sources are I<may> accesses.
9218 The relations containing these elements can be obtained through
9219 calls to C<isl_flow_get_no_source>, the first with C<must> set
9220 and the second with C<must> unset.
9221 In the case of standard flow dependence analysis,
9222 with the sink a read and the sources I<must> writes,
9223 the first relation corresponds to the reads from uninitialized
9224 array elements and the second relation is empty.
9225 The actual flow dependences can be extracted using
9226 C<isl_flow_foreach>. This function will call the user-specified
9227 callback function C<fn> for each B<non-empty> dependence between
9228 a source and the sink. The callback function is called
9229 with four arguments, the actual flow dependence relation
9230 mapping source iterations to sink iterations, a boolean that
9231 indicates whether it is a I<must> or I<may> dependence, a token
9232 identifying the source and an additional C<void *> with value
9233 equal to the third argument of the C<isl_flow_foreach> call.
9234 A dependence is marked I<must> if it originates from a I<must>
9235 source and if it is not followed by any I<may> sources.
9237 After finishing with an C<isl_flow>, the user should call
9238 C<isl_flow_free> to free all associated memory.
9240 =head3 Interaction with the Low-level Interface
9242 During the dependence analysis, we frequently need to perform
9243 the following operation. Given a relation between sink iterations
9244 and potential source iterations from a particular source domain,
9245 what is the last potential source iteration corresponding to each
9246 sink iteration. It can sometimes be convenient to adjust
9247 the set of potential source iterations before or after each such operation.
9248 The prototypical example is fuzzy array dataflow analysis,
9249 where we need to analyze if, based on data-dependent constraints,
9250 the sink iteration can ever be executed without one or more of
9251 the corresponding potential source iterations being executed.
9252 If so, we can introduce extra parameters and select an unknown
9253 but fixed source iteration from the potential source iterations.
9254 To be able to perform such manipulations, C<isl> provides the following
9257 #include <isl/flow.h>
9259 typedef __isl_give isl_restriction *(*isl_access_restrict)(
9260 __isl_keep isl_map *source_map,
9261 __isl_keep isl_set *sink, void *source_user,
9263 __isl_give isl_access_info *isl_access_info_set_restrict(
9264 __isl_take isl_access_info *acc,
9265 isl_access_restrict fn, void *user);
9267 The function C<isl_access_info_set_restrict> should be called
9268 before calling C<isl_access_info_compute_flow> and registers a callback function
9269 that will be called any time C<isl> is about to compute the last
9270 potential source. The first argument is the (reverse) proto-dependence,
9271 mapping sink iterations to potential source iterations.
9272 The second argument represents the sink iterations for which
9273 we want to compute the last source iteration.
9274 The third argument is the token corresponding to the source
9275 and the final argument is the token passed to C<isl_access_info_set_restrict>.
9276 The callback is expected to return a restriction on either the input or
9277 the output of the operation computing the last potential source.
9278 If the input needs to be restricted then restrictions are needed
9279 for both the source and the sink iterations. The sink iterations
9280 and the potential source iterations will be intersected with these sets.
9281 If the output needs to be restricted then only a restriction on the source
9282 iterations is required.
9283 If any error occurs, the callback should return C<NULL>.
9284 An C<isl_restriction> object can be created, freed and inspected
9285 using the following functions.
9287 #include <isl/flow.h>
9289 __isl_give isl_restriction *isl_restriction_input(
9290 __isl_take isl_set *source_restr,
9291 __isl_take isl_set *sink_restr);
9292 __isl_give isl_restriction *isl_restriction_output(
9293 __isl_take isl_set *source_restr);
9294 __isl_give isl_restriction *isl_restriction_none(
9295 __isl_take isl_map *source_map);
9296 __isl_give isl_restriction *isl_restriction_empty(
9297 __isl_take isl_map *source_map);
9298 __isl_null isl_restriction *isl_restriction_free(
9299 __isl_take isl_restriction *restr);
9301 C<isl_restriction_none> and C<isl_restriction_empty> are special
9302 cases of C<isl_restriction_input>. C<isl_restriction_none>
9303 is essentially equivalent to
9305 isl_restriction_input(isl_set_universe(
9306 isl_space_range(isl_map_get_space(source_map))),
9308 isl_space_domain(isl_map_get_space(source_map))));
9310 whereas C<isl_restriction_empty> is essentially equivalent to
9312 isl_restriction_input(isl_set_empty(
9313 isl_space_range(isl_map_get_space(source_map))),
9315 isl_space_domain(isl_map_get_space(source_map))));
9319 #include <isl/schedule.h>
9320 __isl_give isl_schedule *
9321 isl_schedule_constraints_compute_schedule(
9322 __isl_take isl_schedule_constraints *sc);
9324 The function C<isl_schedule_constraints_compute_schedule> can be
9325 used to compute a schedule that satisfies the given schedule constraints.
9326 These schedule constraints include the iteration domain for which
9327 a schedule should be computed and dependences between pairs of
9328 iterations. In particular, these dependences include
9329 I<validity> dependences and I<proximity> dependences.
9330 By default, the algorithm used to construct the schedule is similar
9331 to that of C<Pluto>.
9332 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
9334 The generated schedule respects all validity dependences.
9335 That is, all dependence distances over these dependences in the
9336 scheduled space are lexicographically positive.
9338 The default algorithm tries to ensure that the dependence distances
9339 over coincidence constraints are zero and to minimize the
9340 dependence distances over proximity dependences.
9341 Moreover, it tries to obtain sequences (bands) of schedule dimensions
9342 for groups of domains where the dependence distances over validity
9343 dependences have only non-negative values.
9344 Note that when minimizing the maximal dependence distance
9345 over proximity dependences, a single affine expression in the parameters
9346 is constructed that bounds all dependence distances. If no such expression
9347 exists, then the algorithm will fail and resort to an alternative
9348 scheduling algorithm. In particular, this means that adding proximity
9349 dependences may eliminate valid solutions. A typical example where this
9350 phenomenon may occur is when some subset of the proximity dependences
9351 has no restriction on some parameter, forcing the coefficient of that
9352 parameter to be zero, while some other subset forces the dependence
9353 distance to depend on that parameter, requiring the same coefficient
9355 When using Feautrier's algorithm, the coincidence and proximity constraints
9356 are only taken into account during the extension to a
9357 full-dimensional schedule.
9359 An C<isl_schedule_constraints> object can be constructed
9360 and manipulated using the following functions.
9362 #include <isl/schedule.h>
9363 __isl_give isl_schedule_constraints *
9364 isl_schedule_constraints_copy(
9365 __isl_keep isl_schedule_constraints *sc);
9366 __isl_give isl_schedule_constraints *
9367 isl_schedule_constraints_on_domain(
9368 __isl_take isl_union_set *domain);
9369 __isl_give isl_schedule_constraints *
9370 isl_schedule_constraints_set_context(
9371 __isl_take isl_schedule_constraints *sc,
9372 __isl_take isl_set *context);
9373 __isl_give isl_schedule_constraints *
9374 isl_schedule_constraints_set_validity(
9375 __isl_take isl_schedule_constraints *sc,
9376 __isl_take isl_union_map *validity);
9377 __isl_give isl_schedule_constraints *
9378 isl_schedule_constraints_set_coincidence(
9379 __isl_take isl_schedule_constraints *sc,
9380 __isl_take isl_union_map *coincidence);
9381 __isl_give isl_schedule_constraints *
9382 isl_schedule_constraints_set_proximity(
9383 __isl_take isl_schedule_constraints *sc,
9384 __isl_take isl_union_map *proximity);
9385 __isl_give isl_schedule_constraints *
9386 isl_schedule_constraints_set_conditional_validity(
9387 __isl_take isl_schedule_constraints *sc,
9388 __isl_take isl_union_map *condition,
9389 __isl_take isl_union_map *validity);
9390 __isl_give isl_schedule_constraints *
9391 isl_schedule_constraints_apply(
9392 __isl_take isl_schedule_constraints *sc,
9393 __isl_take isl_union_map *umap);
9394 __isl_null isl_schedule_constraints *
9395 isl_schedule_constraints_free(
9396 __isl_take isl_schedule_constraints *sc);
9398 The initial C<isl_schedule_constraints> object created by
9399 C<isl_schedule_constraints_on_domain> does not impose any constraints.
9400 That is, it has an empty set of dependences.
9401 The function C<isl_schedule_constraints_set_context> allows the user
9402 to specify additional constraints on the parameters that may
9403 be assumed to hold during the construction of the schedule.
9404 The function C<isl_schedule_constraints_set_validity> replaces the
9405 validity dependences, mapping domain elements I<i> to domain
9406 elements that should be scheduled after I<i>.
9407 The function C<isl_schedule_constraints_set_coincidence> replaces the
9408 coincidence dependences, mapping domain elements I<i> to domain
9409 elements that should be scheduled together with I<I>, if possible.
9410 The function C<isl_schedule_constraints_set_proximity> replaces the
9411 proximity dependences, mapping domain elements I<i> to domain
9412 elements that should be scheduled either before I<I>
9413 or as early as possible after I<i>.
9415 The function C<isl_schedule_constraints_set_conditional_validity>
9416 replaces the conditional validity constraints.
9417 A conditional validity constraint is only imposed when any of the corresponding
9418 conditions is satisfied, i.e., when any of them is non-zero.
9419 That is, the scheduler ensures that within each band if the dependence
9420 distances over the condition constraints are not all zero
9421 then all corresponding conditional validity constraints are respected.
9422 A conditional validity constraint corresponds to a condition
9423 if the two are adjacent, i.e., if the domain of one relation intersect
9424 the range of the other relation.
9425 The typical use case of conditional validity constraints is
9426 to allow order constraints between live ranges to be violated
9427 as long as the live ranges themselves are local to the band.
9428 To allow more fine-grained control over which conditions correspond
9429 to which conditional validity constraints, the domains and ranges
9430 of these relations may include I<tags>. That is, the domains and
9431 ranges of those relation may themselves be wrapped relations
9432 where the iteration domain appears in the domain of those wrapped relations
9433 and the range of the wrapped relations can be arbitrarily chosen
9434 by the user. Conditions and conditional validity constraints are only
9435 considered adjacent to each other if the entire wrapped relation matches.
9436 In particular, a relation with a tag will never be considered adjacent
9437 to a relation without a tag.
9439 The function C<isl_schedule_constraints_apply> takes
9440 schedule constraints that are defined on some set of domain elements
9441 and transforms them to schedule constraints on the elements
9442 to which these domain elements are mapped by the given transformation.
9444 An C<isl_schedule_constraints> object can be inspected
9445 using the following functions.
9447 #include <isl/schedule.h>
9448 __isl_give isl_union_set *
9449 isl_schedule_constraints_get_domain(
9450 __isl_keep isl_schedule_constraints *sc);
9451 __isl_give isl_set *isl_schedule_constraints_get_context(
9452 __isl_keep isl_schedule_constraints *sc);
9453 __isl_give isl_union_map *
9454 isl_schedule_constraints_get_validity(
9455 __isl_keep isl_schedule_constraints *sc);
9456 __isl_give isl_union_map *
9457 isl_schedule_constraints_get_coincidence(
9458 __isl_keep isl_schedule_constraints *sc);
9459 __isl_give isl_union_map *
9460 isl_schedule_constraints_get_proximity(
9461 __isl_keep isl_schedule_constraints *sc);
9462 __isl_give isl_union_map *
9463 isl_schedule_constraints_get_conditional_validity(
9464 __isl_keep isl_schedule_constraints *sc);
9465 __isl_give isl_union_map *
9466 isl_schedule_constraints_get_conditional_validity_condition(
9467 __isl_keep isl_schedule_constraints *sc);
9469 An C<isl_schedule_constraints> object can be read from input
9470 using the following functions.
9472 #include <isl/schedule.h>
9473 __isl_give isl_schedule_constraints *
9474 isl_schedule_constraints_read_from_str(isl_ctx *ctx,
9476 __isl_give isl_schedule_constraints *
9477 isl_schedule_constraints_read_from_file(isl_ctx *ctx,
9480 The contents of an C<isl_schedule_constraints> object can be printed
9481 using the following functions.
9483 #include <isl/schedule.h>
9484 __isl_give isl_printer *
9485 isl_printer_print_schedule_constraints(
9486 __isl_take isl_printer *p,
9487 __isl_keep isl_schedule_constraints *sc);
9488 __isl_give char *isl_schedule_constraints_to_str(
9489 __isl_keep isl_schedule_constraints *sc);
9491 The following function computes a schedule directly from
9492 an iteration domain and validity and proximity dependences
9493 and is implemented in terms of the functions described above.
9494 The use of C<isl_union_set_compute_schedule> is discouraged.
9496 #include <isl/schedule.h>
9497 __isl_give isl_schedule *isl_union_set_compute_schedule(
9498 __isl_take isl_union_set *domain,
9499 __isl_take isl_union_map *validity,
9500 __isl_take isl_union_map *proximity);
9502 The generated schedule represents a schedule tree.
9503 For more information on schedule trees, see
9504 L</"Schedule Trees">.
9508 #include <isl/schedule.h>
9509 isl_stat isl_options_set_schedule_max_coefficient(
9510 isl_ctx *ctx, int val);
9511 int isl_options_get_schedule_max_coefficient(
9513 isl_stat isl_options_set_schedule_max_constant_term(
9514 isl_ctx *ctx, int val);
9515 int isl_options_get_schedule_max_constant_term(
9517 isl_stat isl_options_set_schedule_serialize_sccs(
9518 isl_ctx *ctx, int val);
9519 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx);
9520 isl_stat isl_options_set_schedule_whole_component(
9521 isl_ctx *ctx, int val);
9522 int isl_options_get_schedule_whole_component(
9524 isl_stat isl_options_set_schedule_maximize_band_depth(
9525 isl_ctx *ctx, int val);
9526 int isl_options_get_schedule_maximize_band_depth(
9528 isl_stat isl_options_set_schedule_maximize_coincidence(
9529 isl_ctx *ctx, int val);
9530 int isl_options_get_schedule_maximize_coincidence(
9532 isl_stat isl_options_set_schedule_outer_coincidence(
9533 isl_ctx *ctx, int val);
9534 int isl_options_get_schedule_outer_coincidence(
9536 isl_stat isl_options_set_schedule_split_scaled(
9537 isl_ctx *ctx, int val);
9538 int isl_options_get_schedule_split_scaled(
9540 isl_stat isl_options_set_schedule_treat_coalescing(
9541 isl_ctx *ctx, int val);
9542 int isl_options_get_schedule_treat_coalescing(
9544 isl_stat isl_options_set_schedule_algorithm(
9545 isl_ctx *ctx, int val);
9546 int isl_options_get_schedule_algorithm(
9548 isl_stat isl_options_set_schedule_carry_self_first(
9549 isl_ctx *ctx, int val);
9550 int isl_options_get_schedule_carry_self_first(
9552 isl_stat isl_options_set_schedule_separate_components(
9553 isl_ctx *ctx, int val);
9554 int isl_options_get_schedule_separate_components(
9559 =item * schedule_max_coefficient
9561 This option enforces that the coefficients for variable and parameter
9562 dimensions in the calculated schedule are not larger than the specified value.
9563 This option can significantly increase the speed of the scheduling calculation
9564 and may also prevent fusing of unrelated dimensions. A value of -1 means that
9565 this option does not introduce bounds on the variable or parameter
9568 =item * schedule_max_constant_term
9570 This option enforces that the constant coefficients in the calculated schedule
9571 are not larger than the maximal constant term. This option can significantly
9572 increase the speed of the scheduling calculation and may also prevent fusing of
9573 unrelated dimensions. A value of -1 means that this option does not introduce
9574 bounds on the constant coefficients.
9576 =item * schedule_serialize_sccs
9578 If this option is set, then all strongly connected components
9579 in the dependence graph are serialized as soon as they are detected.
9580 This means in particular that instances of statements will only
9581 appear in the same band node if these statements belong
9582 to the same strongly connected component at the point where
9583 the band node is constructed.
9585 =item * schedule_whole_component
9587 If this option is set, then entire (weakly) connected
9588 components in the dependence graph are scheduled together
9590 Otherwise, each strongly connected component within
9591 such a weakly connected component is first scheduled separately
9592 and then combined with other strongly connected components.
9593 This option has no effect if C<schedule_serialize_sccs> is set.
9595 =item * schedule_maximize_band_depth
9597 If this option is set, then the scheduler tries to maximize
9598 the width of the bands. Wider bands give more possibilities for tiling.
9599 In particular, if the C<schedule_whole_component> option is set,
9600 then bands are split if this might result in wider bands.
9601 Otherwise, the effect of this option is to only allow
9602 strongly connected components to be combined if this does
9603 not reduce the width of the bands.
9604 Note that if the C<schedule_serialize_sccs> options is set, then
9605 the C<schedule_maximize_band_depth> option therefore has no effect.
9607 =item * schedule_maximize_coincidence
9609 This option is only effective if the C<schedule_whole_component>
9610 option is turned off.
9611 If the C<schedule_maximize_coincidence> option is set, then (clusters of)
9612 strongly connected components are only combined with each other
9613 if this does not reduce the number of coincident band members.
9615 =item * schedule_outer_coincidence
9617 If this option is set, then we try to construct schedules
9618 where the outermost scheduling dimension in each band
9619 satisfies the coincidence constraints.
9621 =item * schedule_algorithm
9623 Selects the scheduling algorithm to be used.
9624 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
9625 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
9627 =item * schedule_split_scaled
9629 If this option is set, then we try to construct schedules in which the
9630 constant term is split off from the linear part if the linear parts of
9631 the scheduling rows for all nodes in the graph have a common non-trivial
9633 The constant term is then dropped and the linear
9635 This option is only effective when the Feautrier style scheduler is
9636 being used, either as the main scheduler or as a fallback for the
9637 Pluto-like scheduler.
9639 =item * schedule_treat_coalescing
9641 If this option is set, then the scheduler will try and avoid
9642 producing schedules that perform loop coalescing.
9643 In particular, for the Pluto-like scheduler, this option places
9644 bounds on the schedule coefficients based on the sizes of the instance sets.
9645 For the Feautrier style scheduler, this option detects potentially
9646 coalescing schedules and then tries to adjust the schedule to avoid
9649 =item * schedule_carry_self_first
9651 If this option is set, then the Feautrier style scheduler
9652 (when used as a fallback for the Pluto-like scheduler) will
9653 first try to only carry self-dependences.
9655 =item * schedule_separate_components
9657 If this option is set then the function C<isl_schedule_get_map>
9658 will treat set nodes in the same way as sequence nodes.
9662 =head2 AST Generation
9664 This section describes the C<isl> functionality for generating
9665 ASTs that visit all the elements
9666 in a domain in an order specified by a schedule tree or
9668 In case the schedule given as a C<isl_union_map>, an AST is generated
9669 that visits all the elements in the domain of the C<isl_union_map>
9670 according to the lexicographic order of the corresponding image
9671 element(s). If the range of the C<isl_union_map> consists of
9672 elements in more than one space, then each of these spaces is handled
9673 separately in an arbitrary order.
9674 It should be noted that the schedule tree or the image elements
9675 in a schedule map only specify the I<order>
9676 in which the corresponding domain elements should be visited.
9677 No direct relation between the partial schedule values
9678 or the image elements on the one hand and the loop iterators
9679 in the generated AST on the other hand should be assumed.
9681 Each AST is generated within a build. The initial build
9682 simply specifies the constraints on the parameters (if any)
9683 and can be created, inspected, copied and freed using the following functions.
9685 #include <isl/ast_build.h>
9686 __isl_give isl_ast_build *isl_ast_build_alloc(
9688 __isl_give isl_ast_build *isl_ast_build_from_context(
9689 __isl_take isl_set *set);
9690 __isl_give isl_ast_build *isl_ast_build_copy(
9691 __isl_keep isl_ast_build *build);
9692 __isl_null isl_ast_build *isl_ast_build_free(
9693 __isl_take isl_ast_build *build);
9695 The C<set> argument is usually a parameter set with zero or more parameters.
9696 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
9697 this set is required to be a parameter set.
9698 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
9699 specify any parameter constraints.
9700 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
9701 and L</"Fine-grained Control over AST Generation">.
9702 Finally, the AST itself can be constructed using one of the following
9705 #include <isl/ast_build.h>
9706 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
9707 __isl_keep isl_ast_build *build,
9708 __isl_take isl_schedule *schedule);
9709 __isl_give isl_ast_node *
9710 isl_ast_build_node_from_schedule_map(
9711 __isl_keep isl_ast_build *build,
9712 __isl_take isl_union_map *schedule);
9714 =head3 Inspecting the AST
9716 The basic properties of an AST node can be obtained as follows.
9718 #include <isl/ast.h>
9719 enum isl_ast_node_type isl_ast_node_get_type(
9720 __isl_keep isl_ast_node *node);
9722 The type of an AST node is one of
9723 C<isl_ast_node_for>,
9725 C<isl_ast_node_block>,
9726 C<isl_ast_node_mark> or
9727 C<isl_ast_node_user>.
9728 An C<isl_ast_node_for> represents a for node.
9729 An C<isl_ast_node_if> represents an if node.
9730 An C<isl_ast_node_block> represents a compound node.
9731 An C<isl_ast_node_mark> introduces a mark in the AST.
9732 An C<isl_ast_node_user> represents an expression statement.
9733 An expression statement typically corresponds to a domain element, i.e.,
9734 one of the elements that is visited by the AST.
9736 Each type of node has its own additional properties.
9738 #include <isl/ast.h>
9739 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
9740 __isl_keep isl_ast_node *node);
9741 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
9742 __isl_keep isl_ast_node *node);
9743 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
9744 __isl_keep isl_ast_node *node);
9745 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
9746 __isl_keep isl_ast_node *node);
9747 __isl_give isl_ast_node *isl_ast_node_for_get_body(
9748 __isl_keep isl_ast_node *node);
9749 isl_bool isl_ast_node_for_is_degenerate(
9750 __isl_keep isl_ast_node *node);
9752 An C<isl_ast_for> is considered degenerate if it is known to execute
9755 #include <isl/ast.h>
9756 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
9757 __isl_keep isl_ast_node *node);
9758 __isl_give isl_ast_node *isl_ast_node_if_get_then(
9759 __isl_keep isl_ast_node *node);
9760 isl_bool isl_ast_node_if_has_else(
9761 __isl_keep isl_ast_node *node);
9762 __isl_give isl_ast_node *isl_ast_node_if_get_else(
9763 __isl_keep isl_ast_node *node);
9765 __isl_give isl_ast_node_list *
9766 isl_ast_node_block_get_children(
9767 __isl_keep isl_ast_node *node);
9769 __isl_give isl_id *isl_ast_node_mark_get_id(
9770 __isl_keep isl_ast_node *node);
9771 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
9772 __isl_keep isl_ast_node *node);
9774 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
9775 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
9777 #include <isl/ast.h>
9778 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
9779 __isl_keep isl_ast_node *node);
9781 All descendants of a specific node in the AST (including the node itself)
9783 in depth-first pre-order using the following function.
9785 #include <isl/ast.h>
9786 isl_stat isl_ast_node_foreach_descendant_top_down(
9787 __isl_keep isl_ast_node *node,
9788 isl_bool (*fn)(__isl_keep isl_ast_node *node,
9789 void *user), void *user);
9791 The callback function should return C<isl_bool_true> if the children
9792 of the given node should be visited and C<isl_bool_false> if they should not.
9793 It should return C<isl_bool_error> in case of failure, in which case
9794 the entire traversal is aborted.
9796 Each of the returned C<isl_ast_expr>s can in turn be inspected using
9797 the following functions.
9799 #include <isl/ast.h>
9800 enum isl_ast_expr_type isl_ast_expr_get_type(
9801 __isl_keep isl_ast_expr *expr);
9803 The type of an AST expression is one of
9805 C<isl_ast_expr_id> or
9806 C<isl_ast_expr_int>.
9807 An C<isl_ast_expr_op> represents the result of an operation.
9808 An C<isl_ast_expr_id> represents an identifier.
9809 An C<isl_ast_expr_int> represents an integer value.
9811 Each type of expression has its own additional properties.
9813 #include <isl/ast.h>
9814 enum isl_ast_op_type isl_ast_expr_get_op_type(
9815 __isl_keep isl_ast_expr *expr);
9816 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
9817 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
9818 __isl_keep isl_ast_expr *expr, int pos);
9819 isl_stat isl_ast_expr_foreach_ast_op_type(
9820 __isl_keep isl_ast_expr *expr,
9821 isl_stat (*fn)(enum isl_ast_op_type type,
9822 void *user), void *user);
9823 isl_stat isl_ast_node_foreach_ast_op_type(
9824 __isl_keep isl_ast_node *node,
9825 isl_stat (*fn)(enum isl_ast_op_type type,
9826 void *user), void *user);
9828 C<isl_ast_expr_get_op_type> returns the type of the operation
9829 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
9830 arguments. C<isl_ast_expr_get_op_arg> returns the specified
9832 C<isl_ast_expr_foreach_ast_op_type> calls C<fn> for each distinct
9833 C<isl_ast_op_type> that appears in C<expr>.
9834 C<isl_ast_node_foreach_ast_op_type> does the same for each distinct
9835 C<isl_ast_op_type> that appears in C<node>.
9836 The operation type is one of the following.
9840 =item C<isl_ast_op_and>
9842 Logical I<and> of two arguments.
9843 Both arguments can be evaluated.
9845 =item C<isl_ast_op_and_then>
9847 Logical I<and> of two arguments.
9848 The second argument can only be evaluated if the first evaluates to true.
9850 =item C<isl_ast_op_or>
9852 Logical I<or> of two arguments.
9853 Both arguments can be evaluated.
9855 =item C<isl_ast_op_or_else>
9857 Logical I<or> of two arguments.
9858 The second argument can only be evaluated if the first evaluates to false.
9860 =item C<isl_ast_op_max>
9862 Maximum of two or more arguments.
9864 =item C<isl_ast_op_min>
9866 Minimum of two or more arguments.
9868 =item C<isl_ast_op_minus>
9872 =item C<isl_ast_op_add>
9874 Sum of two arguments.
9876 =item C<isl_ast_op_sub>
9878 Difference of two arguments.
9880 =item C<isl_ast_op_mul>
9882 Product of two arguments.
9884 =item C<isl_ast_op_div>
9886 Exact division. That is, the result is known to be an integer.
9888 =item C<isl_ast_op_fdiv_q>
9890 Result of integer division, rounded towards negative
9893 =item C<isl_ast_op_pdiv_q>
9895 Result of integer division, where dividend is known to be non-negative.
9897 =item C<isl_ast_op_pdiv_r>
9899 Remainder of integer division, where dividend is known to be non-negative.
9901 =item C<isl_ast_op_zdiv_r>
9903 Equal to zero iff the remainder on integer division is zero.
9905 =item C<isl_ast_op_cond>
9907 Conditional operator defined on three arguments.
9908 If the first argument evaluates to true, then the result
9909 is equal to the second argument. Otherwise, the result
9910 is equal to the third argument.
9911 The second and third argument may only be evaluated if
9912 the first argument evaluates to true and false, respectively.
9913 Corresponds to C<a ? b : c> in C.
9915 =item C<isl_ast_op_select>
9917 Conditional operator defined on three arguments.
9918 If the first argument evaluates to true, then the result
9919 is equal to the second argument. Otherwise, the result
9920 is equal to the third argument.
9921 The second and third argument may be evaluated independently
9922 of the value of the first argument.
9923 Corresponds to C<a * b + (1 - a) * c> in C.
9925 =item C<isl_ast_op_eq>
9929 =item C<isl_ast_op_le>
9931 Less than or equal relation.
9933 =item C<isl_ast_op_lt>
9937 =item C<isl_ast_op_ge>
9939 Greater than or equal relation.
9941 =item C<isl_ast_op_gt>
9943 Greater than relation.
9945 =item C<isl_ast_op_call>
9948 The number of arguments of the C<isl_ast_expr> is one more than
9949 the number of arguments in the function call, the first argument
9950 representing the function being called.
9952 =item C<isl_ast_op_access>
9955 The number of arguments of the C<isl_ast_expr> is one more than
9956 the number of index expressions in the array access, the first argument
9957 representing the array being accessed.
9959 =item C<isl_ast_op_member>
9962 This operation has two arguments, a structure and the name of
9963 the member of the structure being accessed.
9967 #include <isl/ast.h>
9968 __isl_give isl_id *isl_ast_expr_get_id(
9969 __isl_keep isl_ast_expr *expr);
9971 Return the identifier represented by the AST expression.
9973 #include <isl/ast.h>
9974 __isl_give isl_val *isl_ast_expr_get_val(
9975 __isl_keep isl_ast_expr *expr);
9977 Return the integer represented by the AST expression.
9979 =head3 Properties of ASTs
9981 #include <isl/ast.h>
9982 isl_bool isl_ast_expr_is_equal(
9983 __isl_keep isl_ast_expr *expr1,
9984 __isl_keep isl_ast_expr *expr2);
9986 Check if two C<isl_ast_expr>s are equal to each other.
9988 =head3 Manipulating and printing the AST
9990 AST nodes can be copied and freed using the following functions.
9992 #include <isl/ast.h>
9993 __isl_give isl_ast_node *isl_ast_node_copy(
9994 __isl_keep isl_ast_node *node);
9995 __isl_null isl_ast_node *isl_ast_node_free(
9996 __isl_take isl_ast_node *node);
9998 AST expressions can be copied and freed using the following functions.
10000 #include <isl/ast.h>
10001 __isl_give isl_ast_expr *isl_ast_expr_copy(
10002 __isl_keep isl_ast_expr *expr);
10003 __isl_null isl_ast_expr *isl_ast_expr_free(
10004 __isl_take isl_ast_expr *expr);
10006 New AST expressions can be created either directly or within
10007 the context of an C<isl_ast_build>.
10009 #include <isl/ast.h>
10010 __isl_give isl_ast_expr *isl_ast_expr_from_val(
10011 __isl_take isl_val *v);
10012 __isl_give isl_ast_expr *isl_ast_expr_from_id(
10013 __isl_take isl_id *id);
10014 __isl_give isl_ast_expr *isl_ast_expr_neg(
10015 __isl_take isl_ast_expr *expr);
10016 __isl_give isl_ast_expr *isl_ast_expr_address_of(
10017 __isl_take isl_ast_expr *expr);
10018 __isl_give isl_ast_expr *isl_ast_expr_add(
10019 __isl_take isl_ast_expr *expr1,
10020 __isl_take isl_ast_expr *expr2);
10021 __isl_give isl_ast_expr *isl_ast_expr_sub(
10022 __isl_take isl_ast_expr *expr1,
10023 __isl_take isl_ast_expr *expr2);
10024 __isl_give isl_ast_expr *isl_ast_expr_mul(
10025 __isl_take isl_ast_expr *expr1,
10026 __isl_take isl_ast_expr *expr2);
10027 __isl_give isl_ast_expr *isl_ast_expr_div(
10028 __isl_take isl_ast_expr *expr1,
10029 __isl_take isl_ast_expr *expr2);
10030 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
10031 __isl_take isl_ast_expr *expr1,
10032 __isl_take isl_ast_expr *expr2);
10033 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
10034 __isl_take isl_ast_expr *expr1,
10035 __isl_take isl_ast_expr *expr2);
10036 __isl_give isl_ast_expr *isl_ast_expr_and(
10037 __isl_take isl_ast_expr *expr1,
10038 __isl_take isl_ast_expr *expr2)
10039 __isl_give isl_ast_expr *isl_ast_expr_and_then(
10040 __isl_take isl_ast_expr *expr1,
10041 __isl_take isl_ast_expr *expr2)
10042 __isl_give isl_ast_expr *isl_ast_expr_or(
10043 __isl_take isl_ast_expr *expr1,
10044 __isl_take isl_ast_expr *expr2)
10045 __isl_give isl_ast_expr *isl_ast_expr_or_else(
10046 __isl_take isl_ast_expr *expr1,
10047 __isl_take isl_ast_expr *expr2)
10048 __isl_give isl_ast_expr *isl_ast_expr_eq(
10049 __isl_take isl_ast_expr *expr1,
10050 __isl_take isl_ast_expr *expr2);
10051 __isl_give isl_ast_expr *isl_ast_expr_le(
10052 __isl_take isl_ast_expr *expr1,
10053 __isl_take isl_ast_expr *expr2);
10054 __isl_give isl_ast_expr *isl_ast_expr_lt(
10055 __isl_take isl_ast_expr *expr1,
10056 __isl_take isl_ast_expr *expr2);
10057 __isl_give isl_ast_expr *isl_ast_expr_ge(
10058 __isl_take isl_ast_expr *expr1,
10059 __isl_take isl_ast_expr *expr2);
10060 __isl_give isl_ast_expr *isl_ast_expr_gt(
10061 __isl_take isl_ast_expr *expr1,
10062 __isl_take isl_ast_expr *expr2);
10063 __isl_give isl_ast_expr *isl_ast_expr_access(
10064 __isl_take isl_ast_expr *array,
10065 __isl_take isl_ast_expr_list *indices);
10066 __isl_give isl_ast_expr *isl_ast_expr_call(
10067 __isl_take isl_ast_expr *function,
10068 __isl_take isl_ast_expr_list *arguments);
10070 The function C<isl_ast_expr_address_of> can be applied to an
10071 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
10072 to represent the address of the C<isl_ast_expr_access>. The function
10073 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
10074 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
10076 #include <isl/ast_build.h>
10077 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
10078 __isl_keep isl_ast_build *build,
10079 __isl_take isl_set *set);
10080 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
10081 __isl_keep isl_ast_build *build,
10082 __isl_take isl_pw_aff *pa);
10083 __isl_give isl_ast_expr *
10084 isl_ast_build_access_from_pw_multi_aff(
10085 __isl_keep isl_ast_build *build,
10086 __isl_take isl_pw_multi_aff *pma);
10087 __isl_give isl_ast_expr *
10088 isl_ast_build_access_from_multi_pw_aff(
10089 __isl_keep isl_ast_build *build,
10090 __isl_take isl_multi_pw_aff *mpa);
10091 __isl_give isl_ast_expr *
10092 isl_ast_build_call_from_pw_multi_aff(
10093 __isl_keep isl_ast_build *build,
10094 __isl_take isl_pw_multi_aff *pma);
10095 __isl_give isl_ast_expr *
10096 isl_ast_build_call_from_multi_pw_aff(
10097 __isl_keep isl_ast_build *build,
10098 __isl_take isl_multi_pw_aff *mpa);
10101 the domains of C<pa>, C<mpa> and C<pma> should correspond
10102 to the schedule space of C<build>.
10103 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
10104 the function being called.
10105 If the accessed space is a nested relation, then it is taken
10106 to represent an access of the member specified by the range
10107 of this nested relation of the structure specified by the domain
10108 of the nested relation.
10110 The following functions can be used to modify an C<isl_ast_expr>.
10112 #include <isl/ast.h>
10113 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
10114 __isl_take isl_ast_expr *expr, int pos,
10115 __isl_take isl_ast_expr *arg);
10117 Replace the argument of C<expr> at position C<pos> by C<arg>.
10119 #include <isl/ast.h>
10120 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
10121 __isl_take isl_ast_expr *expr,
10122 __isl_take isl_id_to_ast_expr *id2expr);
10124 The function C<isl_ast_expr_substitute_ids> replaces the
10125 subexpressions of C<expr> of type C<isl_ast_expr_id>
10126 by the corresponding expression in C<id2expr>, if there is any.
10129 User specified data can be attached to an C<isl_ast_node> and obtained
10130 from the same C<isl_ast_node> using the following functions.
10132 #include <isl/ast.h>
10133 __isl_give isl_ast_node *isl_ast_node_set_annotation(
10134 __isl_take isl_ast_node *node,
10135 __isl_take isl_id *annotation);
10136 __isl_give isl_id *isl_ast_node_get_annotation(
10137 __isl_keep isl_ast_node *node);
10139 Basic printing can be performed using the following functions.
10141 #include <isl/ast.h>
10142 __isl_give isl_printer *isl_printer_print_ast_expr(
10143 __isl_take isl_printer *p,
10144 __isl_keep isl_ast_expr *expr);
10145 __isl_give isl_printer *isl_printer_print_ast_node(
10146 __isl_take isl_printer *p,
10147 __isl_keep isl_ast_node *node);
10148 __isl_give char *isl_ast_expr_to_str(
10149 __isl_keep isl_ast_expr *expr);
10150 __isl_give char *isl_ast_node_to_str(
10151 __isl_keep isl_ast_node *node);
10152 __isl_give char *isl_ast_expr_to_C_str(
10153 __isl_keep isl_ast_expr *expr);
10154 __isl_give char *isl_ast_node_to_C_str(
10155 __isl_keep isl_ast_node *node);
10157 The functions C<isl_ast_expr_to_C_str> and
10158 C<isl_ast_node_to_C_str> are convenience functions
10159 that return a string representation of the input in C format.
10161 More advanced printing can be performed using the following functions.
10163 #include <isl/ast.h>
10164 __isl_give isl_printer *isl_ast_op_type_set_print_name(
10165 __isl_take isl_printer *p,
10166 enum isl_ast_op_type type,
10167 __isl_keep const char *name);
10168 isl_stat isl_options_set_ast_print_macro_once(
10169 isl_ctx *ctx, int val);
10170 int isl_options_get_ast_print_macro_once(isl_ctx *ctx);
10171 __isl_give isl_printer *isl_ast_op_type_print_macro(
10172 enum isl_ast_op_type type,
10173 __isl_take isl_printer *p);
10174 __isl_give isl_printer *isl_ast_expr_print_macros(
10175 __isl_keep isl_ast_expr *expr,
10176 __isl_take isl_printer *p);
10177 __isl_give isl_printer *isl_ast_node_print_macros(
10178 __isl_keep isl_ast_node *node,
10179 __isl_take isl_printer *p);
10180 __isl_give isl_printer *isl_ast_node_print(
10181 __isl_keep isl_ast_node *node,
10182 __isl_take isl_printer *p,
10183 __isl_take isl_ast_print_options *options);
10184 __isl_give isl_printer *isl_ast_node_for_print(
10185 __isl_keep isl_ast_node *node,
10186 __isl_take isl_printer *p,
10187 __isl_take isl_ast_print_options *options);
10188 __isl_give isl_printer *isl_ast_node_if_print(
10189 __isl_keep isl_ast_node *node,
10190 __isl_take isl_printer *p,
10191 __isl_take isl_ast_print_options *options);
10193 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
10194 C<isl> may print out an AST that makes use of macros such
10195 as C<floord>, C<min> and C<max>.
10196 The names of these macros may be modified by a call
10197 to C<isl_ast_op_type_set_print_name>. The user-specified
10198 names are associated to the printer object.
10199 C<isl_ast_op_type_print_macro> prints out the macro
10200 corresponding to a specific C<isl_ast_op_type>.
10201 If the print-macro-once option is set, then a given macro definition
10202 is only printed once to any given printer object.
10203 C<isl_ast_expr_print_macros> scans the C<isl_ast_expr>
10204 for subexpressions where these macros would be used and prints
10205 out the required macro definitions.
10206 Essentially, C<isl_ast_expr_print_macros> calls
10207 C<isl_ast_expr_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
10208 as function argument.
10209 C<isl_ast_node_print_macros> does the same
10210 for expressions in its C<isl_ast_node> argument.
10211 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
10212 C<isl_ast_node_if_print> print an C<isl_ast_node>
10213 in C<ISL_FORMAT_C>, but allow for some extra control
10214 through an C<isl_ast_print_options> object.
10215 This object can be created using the following functions.
10217 #include <isl/ast.h>
10218 __isl_give isl_ast_print_options *
10219 isl_ast_print_options_alloc(isl_ctx *ctx);
10220 __isl_give isl_ast_print_options *
10221 isl_ast_print_options_copy(
10222 __isl_keep isl_ast_print_options *options);
10223 __isl_null isl_ast_print_options *
10224 isl_ast_print_options_free(
10225 __isl_take isl_ast_print_options *options);
10227 __isl_give isl_ast_print_options *
10228 isl_ast_print_options_set_print_user(
10229 __isl_take isl_ast_print_options *options,
10230 __isl_give isl_printer *(*print_user)(
10231 __isl_take isl_printer *p,
10232 __isl_take isl_ast_print_options *options,
10233 __isl_keep isl_ast_node *node, void *user),
10235 __isl_give isl_ast_print_options *
10236 isl_ast_print_options_set_print_for(
10237 __isl_take isl_ast_print_options *options,
10238 __isl_give isl_printer *(*print_for)(
10239 __isl_take isl_printer *p,
10240 __isl_take isl_ast_print_options *options,
10241 __isl_keep isl_ast_node *node, void *user),
10244 The callback set by C<isl_ast_print_options_set_print_user>
10245 is called whenever a node of type C<isl_ast_node_user> needs to
10247 The callback set by C<isl_ast_print_options_set_print_for>
10248 is called whenever a node of type C<isl_ast_node_for> needs to
10250 Note that C<isl_ast_node_for_print> will I<not> call the
10251 callback set by C<isl_ast_print_options_set_print_for> on the node
10252 on which C<isl_ast_node_for_print> is called, but only on nested
10253 nodes of type C<isl_ast_node_for>. It is therefore safe to
10254 call C<isl_ast_node_for_print> from within the callback set by
10255 C<isl_ast_print_options_set_print_for>.
10257 The following option determines the type to be used for iterators
10258 while printing the AST.
10260 isl_stat isl_options_set_ast_iterator_type(
10261 isl_ctx *ctx, const char *val);
10262 const char *isl_options_get_ast_iterator_type(
10265 The AST printer only prints body nodes as blocks if these
10266 blocks cannot be safely omitted.
10267 For example, a C<for> node with one body node will not be
10268 surrounded with braces in C<ISL_FORMAT_C>.
10269 A block will always be printed by setting the following option.
10271 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx,
10273 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
10277 #include <isl/ast_build.h>
10278 isl_stat isl_options_set_ast_build_atomic_upper_bound(
10279 isl_ctx *ctx, int val);
10280 int isl_options_get_ast_build_atomic_upper_bound(
10282 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
10284 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
10285 isl_stat isl_options_set_ast_build_detect_min_max(
10286 isl_ctx *ctx, int val);
10287 int isl_options_get_ast_build_detect_min_max(
10289 isl_stat isl_options_set_ast_build_exploit_nested_bounds(
10290 isl_ctx *ctx, int val);
10291 int isl_options_get_ast_build_exploit_nested_bounds(
10293 isl_stat isl_options_set_ast_build_group_coscheduled(
10294 isl_ctx *ctx, int val);
10295 int isl_options_get_ast_build_group_coscheduled(
10297 isl_stat isl_options_set_ast_build_scale_strides(
10298 isl_ctx *ctx, int val);
10299 int isl_options_get_ast_build_scale_strides(
10301 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx,
10303 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
10304 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx,
10306 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
10310 =item * ast_build_atomic_upper_bound
10312 Generate loop upper bounds that consist of the current loop iterator,
10313 an operator and an expression not involving the iterator.
10314 If this option is not set, then the current loop iterator may appear
10315 several times in the upper bound.
10316 For example, when this option is turned off, AST generation
10319 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
10323 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
10326 When the option is turned on, the following AST is generated
10328 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
10331 =item * ast_build_prefer_pdiv
10333 If this option is turned off, then the AST generation will
10334 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
10335 operators, but no C<isl_ast_op_pdiv_q> or
10336 C<isl_ast_op_pdiv_r> operators.
10337 If this option is turned on, then C<isl> will try to convert
10338 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
10339 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
10341 =item * ast_build_detect_min_max
10343 If this option is turned on, then C<isl> will try and detect
10344 min or max-expressions when building AST expressions from
10345 piecewise affine expressions.
10347 =item * ast_build_exploit_nested_bounds
10349 Simplify conditions based on bounds of nested for loops.
10350 In particular, remove conditions that are implied by the fact
10351 that one or more nested loops have at least one iteration,
10352 meaning that the upper bound is at least as large as the lower bound.
10353 For example, when this option is turned off, AST generation
10356 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
10362 for (int c0 = 0; c0 <= N; c0 += 1)
10363 for (int c1 = 0; c1 <= M; c1 += 1)
10366 When the option is turned on, the following AST is generated
10368 for (int c0 = 0; c0 <= N; c0 += 1)
10369 for (int c1 = 0; c1 <= M; c1 += 1)
10372 =item * ast_build_group_coscheduled
10374 If two domain elements are assigned the same schedule point, then
10375 they may be executed in any order and they may even appear in different
10376 loops. If this options is set, then the AST generator will make
10377 sure that coscheduled domain elements do not appear in separate parts
10378 of the AST. This is useful in case of nested AST generation
10379 if the outer AST generation is given only part of a schedule
10380 and the inner AST generation should handle the domains that are
10381 coscheduled by this initial part of the schedule together.
10382 For example if an AST is generated for a schedule
10384 { A[i] -> [0]; B[i] -> [0] }
10386 then the C<isl_ast_build_set_create_leaf> callback described
10387 below may get called twice, once for each domain.
10388 Setting this option ensures that the callback is only called once
10389 on both domains together.
10391 =item * ast_build_separation_bounds
10393 This option specifies which bounds to use during separation.
10394 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
10395 then all (possibly implicit) bounds on the current dimension will
10396 be used during separation.
10397 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
10398 then only those bounds that are explicitly available will
10399 be used during separation.
10401 =item * ast_build_scale_strides
10403 This option specifies whether the AST generator is allowed
10404 to scale down iterators of strided loops.
10406 =item * ast_build_allow_else
10408 This option specifies whether the AST generator is allowed
10409 to construct if statements with else branches.
10411 =item * ast_build_allow_or
10413 This option specifies whether the AST generator is allowed
10414 to construct if conditions with disjunctions.
10418 =head3 AST Generation Options (Schedule Tree)
10420 In case of AST construction from a schedule tree, the options
10421 that control how an AST is created from the individual schedule
10422 dimensions are stored in the band nodes of the tree
10423 (see L</"Schedule Trees">).
10425 In particular, a schedule dimension can be handled in four
10426 different ways, atomic, separate, unroll or the default.
10427 This loop AST generation type can be set using
10428 C<isl_schedule_node_band_member_set_ast_loop_type>.
10430 the first three can be selected by including a one-dimensional
10431 element with as value the position of the schedule dimension
10432 within the band and as name one of C<atomic>, C<separate>
10433 or C<unroll> in the options
10434 set by C<isl_schedule_node_band_set_ast_build_options>.
10435 Only one of these three may be specified for
10436 any given schedule dimension within a band node.
10437 If none of these is specified, then the default
10438 is used. The meaning of the options is as follows.
10444 When this option is specified, the AST generator will make
10445 sure that a given domains space only appears in a single
10446 loop at the specified level.
10448 For example, for the schedule tree
10450 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10452 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10453 options: "{ atomic[x] }"
10455 the following AST will be generated
10457 for (int c0 = 0; c0 <= 10; c0 += 1) {
10464 On the other hand, for the schedule tree
10466 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10468 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10469 options: "{ separate[x] }"
10471 the following AST will be generated
10475 for (int c0 = 1; c0 <= 9; c0 += 1) {
10482 If neither C<atomic> nor C<separate> is specified, then the AST generator
10483 may produce either of these two results or some intermediate form.
10487 When this option is specified, the AST generator will
10488 split the domain of the specified schedule dimension
10489 into pieces with a fixed set of statements for which
10490 instances need to be executed by the iterations in
10491 the schedule domain part. This option tends to avoid
10492 the generation of guards inside the corresponding loops.
10493 See also the C<atomic> option.
10497 When this option is specified, the AST generator will
10498 I<completely> unroll the corresponding schedule dimension.
10499 It is the responsibility of the user to ensure that such
10500 unrolling is possible.
10501 To obtain a partial unrolling, the user should apply an additional
10502 strip-mining to the schedule and fully unroll the inner schedule
10507 The C<isolate> option is a bit more involved. It allows the user
10508 to isolate a range of schedule dimension values from smaller and
10509 greater values. Additionally, the user may specify a different
10510 atomic/separate/unroll choice for the isolated part and the remaining
10511 parts. The typical use case of the C<isolate> option is to isolate
10512 full tiles from partial tiles.
10513 The part that needs to be isolated may depend on outer schedule dimensions.
10514 The option therefore needs to be able to reference those outer schedule
10515 dimensions. In particular, the space of the C<isolate> option is that
10516 of a wrapped map with as domain the flat product of all outer band nodes
10517 and as range the space of the current band node.
10518 The atomic/separate/unroll choice for the isolated part is determined
10519 by an option that lives in an unnamed wrapped space with as domain
10520 a zero-dimensional C<isolate> space and as range the regular
10521 C<atomic>, C<separate> or C<unroll> space.
10522 This option may also be set directly using
10523 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
10524 The atomic/separate/unroll choice for the remaining part is determined
10525 by the regular C<atomic>, C<separate> or C<unroll> option.
10526 Since the C<isolate> option references outer schedule dimensions,
10527 its use in a band node causes any tree containing the node
10528 to be considered anchored.
10530 As an example, consider the isolation of full tiles from partial tiles
10531 in a tiling of a triangular domain. The original schedule is as follows.
10533 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10535 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10536 { A[i,j] -> [floor(j/10)] }, \
10537 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10541 for (int c0 = 0; c0 <= 10; c0 += 1)
10542 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10543 for (int c2 = 10 * c0;
10544 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10545 for (int c3 = 10 * c1;
10546 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10549 Isolating the full tiles, we have the following input
10551 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10553 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10554 { A[i,j] -> [floor(j/10)] }, \
10555 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10556 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10557 10a+9+10b+9 <= 100 }"
10562 for (int c0 = 0; c0 <= 8; c0 += 1) {
10563 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10564 for (int c2 = 10 * c0;
10565 c2 <= 10 * c0 + 9; c2 += 1)
10566 for (int c3 = 10 * c1;
10567 c3 <= 10 * c1 + 9; c3 += 1)
10569 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10570 for (int c2 = 10 * c0;
10571 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10572 for (int c3 = 10 * c1;
10573 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10576 for (int c0 = 9; c0 <= 10; c0 += 1)
10577 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10578 for (int c2 = 10 * c0;
10579 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10580 for (int c3 = 10 * c1;
10581 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10585 We may then additionally unroll the innermost loop of the isolated part
10587 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10589 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10590 { A[i,j] -> [floor(j/10)] }, \
10591 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10592 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10593 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
10598 for (int c0 = 0; c0 <= 8; c0 += 1) {
10599 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10600 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
10602 A(c2, 10 * c1 + 1);
10603 A(c2, 10 * c1 + 2);
10604 A(c2, 10 * c1 + 3);
10605 A(c2, 10 * c1 + 4);
10606 A(c2, 10 * c1 + 5);
10607 A(c2, 10 * c1 + 6);
10608 A(c2, 10 * c1 + 7);
10609 A(c2, 10 * c1 + 8);
10610 A(c2, 10 * c1 + 9);
10612 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10613 for (int c2 = 10 * c0;
10614 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10615 for (int c3 = 10 * c1;
10616 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10619 for (int c0 = 9; c0 <= 10; c0 += 1)
10620 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10621 for (int c2 = 10 * c0;
10622 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10623 for (int c3 = 10 * c1;
10624 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10629 =head3 AST Generation Options (Schedule Map)
10631 In case of AST construction using
10632 C<isl_ast_build_node_from_schedule_map>, the options
10633 that control how an AST is created from the individual schedule
10634 dimensions are stored in the C<isl_ast_build>.
10635 They can be set using the following function.
10637 #include <isl/ast_build.h>
10638 __isl_give isl_ast_build *
10639 isl_ast_build_set_options(
10640 __isl_take isl_ast_build *build,
10641 __isl_take isl_union_map *options);
10643 The options are encoded in an C<isl_union_map>.
10644 The domain of this union relation refers to the schedule domain,
10645 i.e., the range of the schedule passed
10646 to C<isl_ast_build_node_from_schedule_map>.
10647 In the case of nested AST generation (see L</"Nested AST Generation">),
10648 the domain of C<options> should refer to the extra piece of the schedule.
10649 That is, it should be equal to the range of the wrapped relation in the
10650 range of the schedule.
10651 The range of the options can consist of elements in one or more spaces,
10652 the names of which determine the effect of the option.
10653 The values of the range typically also refer to the schedule dimension
10654 to which the option applies. In case of nested AST generation
10655 (see L</"Nested AST Generation">), these values refer to the position
10656 of the schedule dimension within the innermost AST generation.
10657 The constraints on the domain elements of
10658 the option should only refer to this dimension and earlier dimensions.
10659 We consider the following spaces.
10663 =item C<separation_class>
10665 B<This option has been deprecated. Use the isolate option on
10666 schedule trees instead.>
10668 This space is a wrapped relation between two one dimensional spaces.
10669 The input space represents the schedule dimension to which the option
10670 applies and the output space represents the separation class.
10671 While constructing a loop corresponding to the specified schedule
10672 dimension(s), the AST generator will try to generate separate loops
10673 for domain elements that are assigned different classes.
10674 If only some of the elements are assigned a class, then those elements
10675 that are not assigned any class will be treated as belonging to a class
10676 that is separate from the explicitly assigned classes.
10677 The typical use case for this option is to separate full tiles from
10679 The other options, described below, are applied after the separation
10682 As an example, consider the separation into full and partial tiles
10683 of a tiling of a triangular domain.
10684 Take, for example, the domain
10686 { A[i,j] : 0 <= i,j and i + j <= 100 }
10688 and a tiling into tiles of 10 by 10. The input to the AST generator
10689 is then the schedule
10691 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
10694 Without any options, the following AST is generated
10696 for (int c0 = 0; c0 <= 10; c0 += 1)
10697 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10698 for (int c2 = 10 * c0;
10699 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10701 for (int c3 = 10 * c1;
10702 c3 <= min(10 * c1 + 9, -c2 + 100);
10706 Separation into full and partial tiles can be obtained by assigning
10707 a class, say C<0>, to the full tiles. The full tiles are represented by those
10708 values of the first and second schedule dimensions for which there are
10709 values of the third and fourth dimensions to cover an entire tile.
10710 That is, we need to specify the following option
10712 { [a,b,c,d] -> separation_class[[0]->[0]] :
10713 exists b': 0 <= 10a,10b' and
10714 10a+9+10b'+9 <= 100;
10715 [a,b,c,d] -> separation_class[[1]->[0]] :
10716 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
10718 which simplifies to
10720 { [a, b, c, d] -> separation_class[[1] -> [0]] :
10721 a >= 0 and b >= 0 and b <= 8 - a;
10722 [a, b, c, d] -> separation_class[[0] -> [0]] :
10723 a >= 0 and a <= 8 }
10725 With this option, the generated AST is as follows
10728 for (int c0 = 0; c0 <= 8; c0 += 1) {
10729 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10730 for (int c2 = 10 * c0;
10731 c2 <= 10 * c0 + 9; c2 += 1)
10732 for (int c3 = 10 * c1;
10733 c3 <= 10 * c1 + 9; c3 += 1)
10735 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10736 for (int c2 = 10 * c0;
10737 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10739 for (int c3 = 10 * c1;
10740 c3 <= min(-c2 + 100, 10 * c1 + 9);
10744 for (int c0 = 9; c0 <= 10; c0 += 1)
10745 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10746 for (int c2 = 10 * c0;
10747 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10749 for (int c3 = 10 * c1;
10750 c3 <= min(10 * c1 + 9, -c2 + 100);
10757 This is a single-dimensional space representing the schedule dimension(s)
10758 to which ``separation'' should be applied. Separation tries to split
10759 a loop into several pieces if this can avoid the generation of guards
10761 See also the C<atomic> option.
10765 This is a single-dimensional space representing the schedule dimension(s)
10766 for which the domains should be considered ``atomic''. That is, the
10767 AST generator will make sure that any given domain space will only appear
10768 in a single loop at the specified level.
10770 Consider the following schedule
10772 { a[i] -> [i] : 0 <= i < 10;
10773 b[i] -> [i+1] : 0 <= i < 10 }
10775 If the following option is specified
10777 { [i] -> separate[x] }
10779 then the following AST will be generated
10783 for (int c0 = 1; c0 <= 9; c0 += 1) {
10790 If, on the other hand, the following option is specified
10792 { [i] -> atomic[x] }
10794 then the following AST will be generated
10796 for (int c0 = 0; c0 <= 10; c0 += 1) {
10803 If neither C<atomic> nor C<separate> is specified, then the AST generator
10804 may produce either of these two results or some intermediate form.
10808 This is a single-dimensional space representing the schedule dimension(s)
10809 that should be I<completely> unrolled.
10810 To obtain a partial unrolling, the user should apply an additional
10811 strip-mining to the schedule and fully unroll the inner loop.
10815 =head3 Fine-grained Control over AST Generation
10817 Besides specifying the constraints on the parameters,
10818 an C<isl_ast_build> object can be used to control
10819 various aspects of the AST generation process.
10820 In case of AST construction using
10821 C<isl_ast_build_node_from_schedule_map>,
10822 the most prominent way of control is through ``options'',
10823 as explained above.
10825 Additional control is available through the following functions.
10827 #include <isl/ast_build.h>
10828 __isl_give isl_ast_build *
10829 isl_ast_build_set_iterators(
10830 __isl_take isl_ast_build *build,
10831 __isl_take isl_id_list *iterators);
10833 The function C<isl_ast_build_set_iterators> allows the user to
10834 specify a list of iterator C<isl_id>s to be used as iterators.
10835 If the input schedule is injective, then
10836 the number of elements in this list should be as large as the dimension
10837 of the schedule space, but no direct correspondence should be assumed
10838 between dimensions and elements.
10839 If the input schedule is not injective, then an additional number
10840 of C<isl_id>s equal to the largest dimension of the input domains
10842 If the number of provided C<isl_id>s is insufficient, then additional
10843 names are automatically generated.
10845 #include <isl/ast_build.h>
10846 __isl_give isl_ast_build *
10847 isl_ast_build_set_create_leaf(
10848 __isl_take isl_ast_build *build,
10849 __isl_give isl_ast_node *(*fn)(
10850 __isl_take isl_ast_build *build,
10851 void *user), void *user);
10854 C<isl_ast_build_set_create_leaf> function allows for the
10855 specification of a callback that should be called whenever the AST
10856 generator arrives at an element of the schedule domain.
10857 The callback should return an AST node that should be inserted
10858 at the corresponding position of the AST. The default action (when
10859 the callback is not set) is to continue generating parts of the AST to scan
10860 all the domain elements associated to the schedule domain element
10861 and to insert user nodes, ``calling'' the domain element, for each of them.
10862 The C<build> argument contains the current state of the C<isl_ast_build>.
10863 To ease nested AST generation (see L</"Nested AST Generation">),
10864 all control information that is
10865 specific to the current AST generation such as the options and
10866 the callbacks has been removed from this C<isl_ast_build>.
10867 The callback would typically return the result of a nested
10868 AST generation or a
10869 user defined node created using the following function.
10871 #include <isl/ast.h>
10872 __isl_give isl_ast_node *isl_ast_node_alloc_user(
10873 __isl_take isl_ast_expr *expr);
10875 #include <isl/ast_build.h>
10876 __isl_give isl_ast_build *
10877 isl_ast_build_set_at_each_domain(
10878 __isl_take isl_ast_build *build,
10879 __isl_give isl_ast_node *(*fn)(
10880 __isl_take isl_ast_node *node,
10881 __isl_keep isl_ast_build *build,
10882 void *user), void *user);
10883 __isl_give isl_ast_build *
10884 isl_ast_build_set_before_each_for(
10885 __isl_take isl_ast_build *build,
10886 __isl_give isl_id *(*fn)(
10887 __isl_keep isl_ast_build *build,
10888 void *user), void *user);
10889 __isl_give isl_ast_build *
10890 isl_ast_build_set_after_each_for(
10891 __isl_take isl_ast_build *build,
10892 __isl_give isl_ast_node *(*fn)(
10893 __isl_take isl_ast_node *node,
10894 __isl_keep isl_ast_build *build,
10895 void *user), void *user);
10896 __isl_give isl_ast_build *
10897 isl_ast_build_set_before_each_mark(
10898 __isl_take isl_ast_build *build,
10899 isl_stat (*fn)(__isl_keep isl_id *mark,
10900 __isl_keep isl_ast_build *build,
10901 void *user), void *user);
10902 __isl_give isl_ast_build *
10903 isl_ast_build_set_after_each_mark(
10904 __isl_take isl_ast_build *build,
10905 __isl_give isl_ast_node *(*fn)(
10906 __isl_take isl_ast_node *node,
10907 __isl_keep isl_ast_build *build,
10908 void *user), void *user);
10910 The callback set by C<isl_ast_build_set_at_each_domain> will
10911 be called for each domain AST node.
10912 The callbacks set by C<isl_ast_build_set_before_each_for>
10913 and C<isl_ast_build_set_after_each_for> will be called
10914 for each for AST node. The first will be called in depth-first
10915 pre-order, while the second will be called in depth-first post-order.
10916 Since C<isl_ast_build_set_before_each_for> is called before the for
10917 node is actually constructed, it is only passed an C<isl_ast_build>.
10918 The returned C<isl_id> will be added as an annotation (using
10919 C<isl_ast_node_set_annotation>) to the constructed for node.
10920 In particular, if the user has also specified an C<after_each_for>
10921 callback, then the annotation can be retrieved from the node passed to
10922 that callback using C<isl_ast_node_get_annotation>.
10923 The callbacks set by C<isl_ast_build_set_before_each_mark>
10924 and C<isl_ast_build_set_after_each_mark> will be called for each
10925 mark AST node that is created, i.e., for each mark schedule node
10926 in the input schedule tree. The first will be called in depth-first
10927 pre-order, while the second will be called in depth-first post-order.
10928 Since the callback set by C<isl_ast_build_set_before_each_mark>
10929 is called before the mark AST node is actually constructed, it is passed
10930 the identifier of the mark node.
10931 All callbacks should C<NULL> (or C<isl_stat_error>) on failure.
10932 The given C<isl_ast_build> can be used to create new
10933 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
10934 or C<isl_ast_build_call_from_pw_multi_aff>.
10936 =head3 Nested AST Generation
10938 C<isl> allows the user to create an AST within the context
10939 of another AST. These nested ASTs are created using the
10940 same C<isl_ast_build_node_from_schedule_map> function that is used to create
10941 the outer AST. The C<build> argument should be an C<isl_ast_build>
10942 passed to a callback set by
10943 C<isl_ast_build_set_create_leaf>.
10944 The space of the range of the C<schedule> argument should refer
10945 to this build. In particular, the space should be a wrapped
10946 relation and the domain of this wrapped relation should be the
10947 same as that of the range of the schedule returned by
10948 C<isl_ast_build_get_schedule> below.
10949 In practice, the new schedule is typically
10950 created by calling C<isl_union_map_range_product> on the old schedule
10951 and some extra piece of the schedule.
10952 The space of the schedule domain is also available from
10953 the C<isl_ast_build>.
10955 #include <isl/ast_build.h>
10956 __isl_give isl_union_map *isl_ast_build_get_schedule(
10957 __isl_keep isl_ast_build *build);
10958 __isl_give isl_space *isl_ast_build_get_schedule_space(
10959 __isl_keep isl_ast_build *build);
10960 __isl_give isl_ast_build *isl_ast_build_restrict(
10961 __isl_take isl_ast_build *build,
10962 __isl_take isl_set *set);
10964 The C<isl_ast_build_get_schedule> function returns a (partial)
10965 schedule for the domains elements for which part of the AST still needs to
10966 be generated in the current build.
10967 In particular, the domain elements are mapped to those iterations of the loops
10968 enclosing the current point of the AST generation inside which
10969 the domain elements are executed.
10970 No direct correspondence between
10971 the input schedule and this schedule should be assumed.
10972 The space obtained from C<isl_ast_build_get_schedule_space> can be used
10973 to create a set for C<isl_ast_build_restrict> to intersect
10974 with the current build. In particular, the set passed to
10975 C<isl_ast_build_restrict> can have additional parameters.
10976 The ids of the set dimensions in the space returned by
10977 C<isl_ast_build_get_schedule_space> correspond to the
10978 iterators of the already generated loops.
10979 The user should not rely on the ids of the output dimensions
10980 of the relations in the union relation returned by
10981 C<isl_ast_build_get_schedule> having any particular value.
10983 =head1 Applications
10985 Although C<isl> is mainly meant to be used as a library,
10986 it also contains some basic applications that use some
10987 of the functionality of C<isl>.
10988 For applications that take one or more polytopes or polyhedra
10989 as input, this input may be specified in either the L<isl format>
10990 or the L<PolyLib format>.
10992 =head2 C<isl_polyhedron_sample>
10994 C<isl_polyhedron_sample> takes a polyhedron as input and prints
10995 an integer element of the polyhedron, if there is any.
10996 The first column in the output is the denominator and is always
10997 equal to 1. If the polyhedron contains no integer points,
10998 then a vector of length zero is printed.
11002 C<isl_pip> takes the same input as the C<example> program
11003 from the C<piplib> distribution, i.e., a set of constraints
11004 on the parameters, a line containing only -1 and finally a set
11005 of constraints on a parametric polyhedron.
11006 The coefficients of the parameters appear in the last columns
11007 (but before the final constant column).
11008 The output is the lexicographic minimum of the parametric polyhedron.
11009 As C<isl> currently does not have its own output format, the output
11010 is just a dump of the internal state.
11012 =head2 C<isl_polyhedron_minimize>
11014 C<isl_polyhedron_minimize> computes the minimum of some linear
11015 or affine objective function over the integer points in a polyhedron.
11016 If an affine objective function
11017 is given, then the constant should appear in the last column.
11019 =head2 C<isl_polytope_scan>
11021 Given a polytope, C<isl_polytope_scan> prints
11022 all integer points in the polytope.
11026 Given an C<isl_union_access_info> object as input,
11027 C<isl_flow> prints out the corresponding dependences,
11028 as computed by C<isl_union_access_info_compute_flow>.
11030 =head2 C<isl_codegen>
11032 Given either a schedule tree or a sequence consisting of
11033 a schedule map, a context set and an options relation,
11034 C<isl_codegen> prints out an AST that scans the domain elements
11035 of the schedule in the order of their image(s) taking into account
11036 the constraints in the context set.
11038 =head2 C<isl_schedule>
11040 Given an C<isl_schedule_constraints> object as input,
11041 C<isl_schedule> prints out a schedule that satisfies the given