3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
8 using C<GMP> or C<imath>.
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
171 =head3 Changes since isl-0.10
175 =item * The functions C<isl_set_dim_has_lower_bound> and
176 C<isl_set_dim_has_upper_bound> have been renamed to
177 C<isl_set_dim_has_any_lower_bound> and
178 C<isl_set_dim_has_any_upper_bound>.
179 The new C<isl_set_dim_has_lower_bound> and
180 C<isl_set_dim_has_upper_bound> have slightly different meanings.
184 =head3 Changes since isl-0.12
188 =item * C<isl_int> has been replaced by C<isl_val>.
189 Some of the old functions are still available in C<isl/deprecated/*.h>
190 but they will be removed in the future.
192 =item * The functions C<isl_pw_qpolynomial_eval>,
193 C<isl_union_pw_qpolynomial_eval>, C<isl_pw_qpolynomial_fold_eval>
194 and C<isl_union_pw_qpolynomial_fold_eval> have been changed to return
195 an C<isl_val> instead of an C<isl_qpolynomial>.
197 =item * The function C<isl_band_member_is_zero_distance>
198 has been removed. Essentially the same functionality is available
199 through C<isl_band_member_is_coincident>, except that it requires
200 setting up coincidence constraints.
201 The option C<schedule_outer_zero_distance> has accordingly been
202 replaced by the option C<schedule_outer_coincidence>.
204 =item * The function C<isl_vertex_get_expr> has been changed
205 to return an C<isl_multi_aff> instead of a rational C<isl_basic_set>.
206 The function C<isl_vertex_get_domain> has been changed to return
207 a regular basic set, rather than a rational basic set.
211 =head3 Changes since isl-0.14
215 =item * The function C<isl_union_pw_multi_aff_add> now consistently
216 computes the sum on the shared definition domain.
217 The function C<isl_union_pw_multi_aff_union_add> has been added
218 to compute the sum on the union of definition domains.
219 The original behavior of C<isl_union_pw_multi_aff_add> was
220 confused and is no longer available.
222 =item * Band forests have been replaced by schedule trees.
224 =item * The function C<isl_union_map_compute_flow> has been
225 replaced by the function C<isl_union_access_info_compute_flow>.
226 Note that the may dependence relation returned by
227 C<isl_union_flow_get_may_dependence> is the union of
228 the two dependence relations returned by
229 C<isl_union_map_compute_flow>. Similarly for the no source relations.
230 The function C<isl_union_map_compute_flow> is still available
231 for backward compatibility, but it will be removed in the future.
233 =item * The function C<isl_basic_set_drop_constraint> has been
236 =item * The function C<isl_ast_build_ast_from_schedule> has been
237 renamed to C<isl_ast_build_node_from_schedule_map>.
238 The original name is still available
239 for backward compatibility, but it will be removed in the future.
241 =item * The C<separation_class> AST generation option has been
244 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
245 have been renamed to C<isl_constraint_alloc_equality> and
246 C<isl_constraint_alloc_inequality>. The original names have been
247 kept for backward compatibility, but they will be removed in the future.
249 =item * The C<schedule_fuse> option has been replaced
250 by the C<schedule_serialize_sccs> option. The effect
251 of setting the C<schedule_fuse> option to C<ISL_SCHEDULE_FUSE_MIN>
252 is now obtained by turning on the C<schedule_serialize_sccs> option.
256 =head3 Changes since isl-0.17
260 =item * The function C<isl_printer_print_ast_expr> no longer prints
261 in C format by default. To print in C format, the output format
262 of the printer needs to have been explicitly set to C<ISL_FORMAT_C>.
263 As a result, the function C<isl_ast_expr_to_str> no longer prints
264 the expression in C format. Use C<isl_ast_expr_to_C_str> instead.
266 =item * The functions C<isl_set_align_divs> and C<isl_map_align_divs>
267 have been deprecated. The function C<isl_set_lift> has an effect
268 that is similar to C<isl_set_align_divs> and could in some cases
269 be used as an alternative.
275 C<isl> is released under the MIT license.
279 Permission is hereby granted, free of charge, to any person obtaining a copy of
280 this software and associated documentation files (the "Software"), to deal in
281 the Software without restriction, including without limitation the rights to
282 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
283 of the Software, and to permit persons to whom the Software is furnished to do
284 so, subject to the following conditions:
286 The above copyright notice and this permission notice shall be included in all
287 copies or substantial portions of the Software.
289 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
290 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
291 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
292 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
293 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
294 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
299 Note that by default C<isl> requires C<GMP>, which is released
300 under the GNU Lesser General Public License (LGPL). This means
301 that code linked against C<isl> is also linked against LGPL code.
303 When configuring with C<--with-int=imath> or C<--with-int=imath-32>, C<isl>
304 will link against C<imath>, a library for exact integer arithmetic released
305 under the MIT license.
309 The source of C<isl> can be obtained either as a tarball
310 or from the git repository. Both are available from
311 L<http://isl.gforge.inria.fr/>.
312 The installation process depends on how you obtained
315 =head2 Installation from the git repository
319 =item 1 Clone or update the repository
321 The first time the source is obtained, you need to clone
324 git clone git://repo.or.cz/isl.git
326 To obtain updates, you need to pull in the latest changes
330 =item 2 Optionally get C<imath> submodule
332 To build C<isl> with C<imath>, you need to obtain the C<imath>
333 submodule by running in the git source tree of C<isl>
338 This will fetch the required version of C<imath> in a subdirectory of C<isl>.
340 =item 2 Generate C<configure>
346 After performing the above steps, continue
347 with the L<Common installation instructions>.
349 =head2 Common installation instructions
353 =item 1 Obtain C<GMP>
355 By default, building C<isl> requires C<GMP>, including its headers files.
356 Your distribution may not provide these header files by default
357 and you may need to install a package called C<gmp-devel> or something
358 similar. Alternatively, C<GMP> can be built from
359 source, available from L<http://gmplib.org/>.
360 C<GMP> is not needed if you build C<isl> with C<imath>.
364 C<isl> uses the standard C<autoconf> C<configure> script.
369 optionally followed by some configure options.
370 A complete list of options can be obtained by running
374 Below we discuss some of the more common options.
380 Installation prefix for C<isl>
382 =item C<--with-int=[gmp|imath|imath-32]>
384 Select the integer library to be used by C<isl>, the default is C<gmp>.
385 With C<imath-32>, C<isl> will use 32 bit integers, but fall back to C<imath>
386 for values out of the 32 bit range. In most applications, C<isl> will run
387 fastest with the C<imath-32> option, followed by C<gmp> and C<imath>, the
390 =item C<--with-gmp-prefix>
392 Installation prefix for C<GMP> (architecture-independent files).
394 =item C<--with-gmp-exec-prefix>
396 Installation prefix for C<GMP> (architecture-dependent files).
404 =item 4 Install (optional)
410 =head1 Integer Set Library
412 =head2 Memory Management
414 Since a high-level operation on isl objects usually involves
415 several substeps and since the user is usually not interested in
416 the intermediate results, most functions that return a new object
417 will also release all the objects passed as arguments.
418 If the user still wants to use one or more of these arguments
419 after the function call, she should pass along a copy of the
420 object rather than the object itself.
421 The user is then responsible for making sure that the original
422 object gets used somewhere else or is explicitly freed.
424 The arguments and return values of all documented functions are
425 annotated to make clear which arguments are released and which
426 arguments are preserved. In particular, the following annotations
433 C<__isl_give> means that a new object is returned.
434 The user should make sure that the returned pointer is
435 used exactly once as a value for an C<__isl_take> argument.
436 In between, it can be used as a value for as many
437 C<__isl_keep> arguments as the user likes.
438 There is one exception, and that is the case where the
439 pointer returned is C<NULL>. Is this case, the user
440 is free to use it as an C<__isl_take> argument or not.
441 When applied to a C<char *>, the returned pointer needs to be
446 C<__isl_null> means that a C<NULL> value is returned.
450 C<__isl_take> means that the object the argument points to
451 is taken over by the function and may no longer be used
452 by the user as an argument to any other function.
453 The pointer value must be one returned by a function
454 returning an C<__isl_give> pointer.
455 If the user passes in a C<NULL> value, then this will
456 be treated as an error in the sense that the function will
457 not perform its usual operation. However, it will still
458 make sure that all the other C<__isl_take> arguments
463 C<__isl_keep> means that the function will only use the object
464 temporarily. After the function has finished, the user
465 can still use it as an argument to other functions.
466 A C<NULL> value will be treated in the same way as
467 a C<NULL> value for an C<__isl_take> argument.
468 This annotation may also be used on return values of
469 type C<const char *>, in which case the returned pointer should
470 not be freed by the user and is only valid until the object
471 from which it was derived is updated or freed.
475 =head2 Initialization
477 All manipulations of integer sets and relations occur within
478 the context of an C<isl_ctx>.
479 A given C<isl_ctx> can only be used within a single thread.
480 All arguments of a function are required to have been allocated
481 within the same context.
482 There are currently no functions available for moving an object
483 from one C<isl_ctx> to another C<isl_ctx>. This means that
484 there is currently no way of safely moving an object from one
485 thread to another, unless the whole C<isl_ctx> is moved.
487 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
488 freed using C<isl_ctx_free>.
489 All objects allocated within an C<isl_ctx> should be freed
490 before the C<isl_ctx> itself is freed.
492 isl_ctx *isl_ctx_alloc();
493 void isl_ctx_free(isl_ctx *ctx);
495 The user can impose a bound on the number of low-level I<operations>
496 that can be performed by an C<isl_ctx>. This bound can be set and
497 retrieved using the following functions. A bound of zero means that
498 no bound is imposed. The number of operations performed can be
499 reset using C<isl_ctx_reset_operations>. Note that the number
500 of low-level operations needed to perform a high-level computation
501 may differ significantly across different versions
502 of C<isl>, but it should be the same across different platforms
503 for the same version of C<isl>.
505 Warning: This feature is experimental. C<isl> has good support to abort and
506 bail out during the computation, but this feature may exercise error code paths
507 that are normally not used that much. Consequently, it is not unlikely that
508 hidden bugs will be exposed.
510 void isl_ctx_set_max_operations(isl_ctx *ctx,
511 unsigned long max_operations);
512 unsigned long isl_ctx_get_max_operations(isl_ctx *ctx);
513 void isl_ctx_reset_operations(isl_ctx *ctx);
515 In order to be able to create an object in the same context
516 as another object, most object types (described later in
517 this document) provide a function to obtain the context
518 in which the object was created.
521 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
522 isl_ctx *isl_multi_val_get_ctx(
523 __isl_keep isl_multi_val *mv);
526 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
528 #include <isl/local_space.h>
529 isl_ctx *isl_local_space_get_ctx(
530 __isl_keep isl_local_space *ls);
533 isl_ctx *isl_set_list_get_ctx(
534 __isl_keep isl_set_list *list);
537 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
538 isl_ctx *isl_multi_aff_get_ctx(
539 __isl_keep isl_multi_aff *maff);
540 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pa);
541 isl_ctx *isl_pw_multi_aff_get_ctx(
542 __isl_keep isl_pw_multi_aff *pma);
543 isl_ctx *isl_multi_pw_aff_get_ctx(
544 __isl_keep isl_multi_pw_aff *mpa);
545 isl_ctx *isl_union_pw_aff_get_ctx(
546 __isl_keep isl_union_pw_aff *upa);
547 isl_ctx *isl_union_pw_multi_aff_get_ctx(
548 __isl_keep isl_union_pw_multi_aff *upma);
549 isl_ctx *isl_multi_union_pw_aff_get_ctx(
550 __isl_keep isl_multi_union_pw_aff *mupa);
552 #include <isl/id_to_ast_expr.h>
553 isl_ctx *isl_id_to_ast_expr_get_ctx(
554 __isl_keep isl_id_to_ast_expr *id2expr);
556 #include <isl/point.h>
557 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
560 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
563 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
565 #include <isl/vertices.h>
566 isl_ctx *isl_vertices_get_ctx(
567 __isl_keep isl_vertices *vertices);
568 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
569 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
571 #include <isl/flow.h>
572 isl_ctx *isl_restriction_get_ctx(
573 __isl_keep isl_restriction *restr);
574 isl_ctx *isl_union_access_info_get_ctx(
575 __isl_keep isl_union_access_info *access);
576 isl_ctx *isl_union_flow_get_ctx(
577 __isl_keep isl_union_flow *flow);
579 #include <isl/schedule.h>
580 isl_ctx *isl_schedule_get_ctx(
581 __isl_keep isl_schedule *sched);
582 isl_ctx *isl_schedule_constraints_get_ctx(
583 __isl_keep isl_schedule_constraints *sc);
585 #include <isl/schedule_node.h>
586 isl_ctx *isl_schedule_node_get_ctx(
587 __isl_keep isl_schedule_node *node);
589 #include <isl/band.h>
590 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
592 #include <isl/ast_build.h>
593 isl_ctx *isl_ast_build_get_ctx(
594 __isl_keep isl_ast_build *build);
597 isl_ctx *isl_ast_expr_get_ctx(
598 __isl_keep isl_ast_expr *expr);
599 isl_ctx *isl_ast_node_get_ctx(
600 __isl_keep isl_ast_node *node);
604 C<isl> uses two special return types for functions that either return
605 a boolean or that in principle do not return anything.
606 In particular, the C<isl_bool> type has three possible values:
607 C<isl_bool_true> (a positive integer value), indicating I<true> or I<yes>;
608 C<isl_bool_false> (the integer value zero), indicating I<false> or I<no>; and
609 C<isl_bool_error> (a negative integer value), indicating that something
610 went wrong. The following function can be used to negate an C<isl_bool>,
611 where the negation of C<isl_bool_error> is C<isl_bool_error> again.
614 isl_bool isl_bool_not(isl_bool b);
616 The C<isl_stat> type has two possible values:
617 C<isl_stat_ok> (the integer value zero), indicating a successful
619 C<isl_stat_error> (a negative integer value), indicating that something
621 See L</"Error Handling"> for more information on
622 C<isl_bool_error> and C<isl_stat_error>.
626 An C<isl_val> represents an integer value, a rational value
627 or one of three special values, infinity, negative infinity and NaN.
628 Some predefined values can be created using the following functions.
631 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
632 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
633 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
634 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
635 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
636 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
638 Specific integer values can be created using the following functions.
641 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
643 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
645 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
646 size_t n, size_t size, const void *chunks);
648 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
649 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
650 The least significant digit is assumed to be stored first.
652 Value objects can be copied and freed using the following functions.
655 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
656 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
658 They can be inspected using the following functions.
661 long isl_val_get_num_si(__isl_keep isl_val *v);
662 long isl_val_get_den_si(__isl_keep isl_val *v);
663 __isl_give isl_val *isl_val_get_den_val(
664 __isl_keep isl_val *v);
665 double isl_val_get_d(__isl_keep isl_val *v);
666 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
668 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
669 size_t size, void *chunks);
671 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
672 of C<size> bytes needed to store the absolute value of the
674 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
675 which is assumed to have been preallocated by the caller.
676 The least significant digit is stored first.
677 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
678 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
679 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
681 An C<isl_val> can be modified using the following function.
684 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
687 The following unary properties are defined on C<isl_val>s.
690 int isl_val_sgn(__isl_keep isl_val *v);
691 isl_bool isl_val_is_zero(__isl_keep isl_val *v);
692 isl_bool isl_val_is_one(__isl_keep isl_val *v);
693 isl_bool isl_val_is_negone(__isl_keep isl_val *v);
694 isl_bool isl_val_is_nonneg(__isl_keep isl_val *v);
695 isl_bool isl_val_is_nonpos(__isl_keep isl_val *v);
696 isl_bool isl_val_is_pos(__isl_keep isl_val *v);
697 isl_bool isl_val_is_neg(__isl_keep isl_val *v);
698 isl_bool isl_val_is_int(__isl_keep isl_val *v);
699 isl_bool isl_val_is_rat(__isl_keep isl_val *v);
700 isl_bool isl_val_is_nan(__isl_keep isl_val *v);
701 isl_bool isl_val_is_infty(__isl_keep isl_val *v);
702 isl_bool isl_val_is_neginfty(__isl_keep isl_val *v);
704 Note that the sign of NaN is undefined.
706 The following binary properties are defined on pairs of C<isl_val>s.
709 isl_bool isl_val_lt(__isl_keep isl_val *v1,
710 __isl_keep isl_val *v2);
711 isl_bool isl_val_le(__isl_keep isl_val *v1,
712 __isl_keep isl_val *v2);
713 isl_bool isl_val_gt(__isl_keep isl_val *v1,
714 __isl_keep isl_val *v2);
715 isl_bool isl_val_ge(__isl_keep isl_val *v1,
716 __isl_keep isl_val *v2);
717 isl_bool isl_val_eq(__isl_keep isl_val *v1,
718 __isl_keep isl_val *v2);
719 isl_bool isl_val_ne(__isl_keep isl_val *v1,
720 __isl_keep isl_val *v2);
721 isl_bool isl_val_abs_eq(__isl_keep isl_val *v1,
722 __isl_keep isl_val *v2);
724 The function C<isl_val_abs_eq> checks whether its two arguments
725 are equal in absolute value.
727 For integer C<isl_val>s we additionally have the following binary property.
730 isl_bool isl_val_is_divisible_by(__isl_keep isl_val *v1,
731 __isl_keep isl_val *v2);
733 An C<isl_val> can also be compared to an integer using the following
734 function. The result is undefined for NaN.
737 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
739 The following unary operations are available on C<isl_val>s.
742 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
743 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
744 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
745 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
746 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
747 __isl_give isl_val *isl_val_inv(__isl_take isl_val *v);
748 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
750 The following binary operations are available on C<isl_val>s.
753 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
754 __isl_take isl_val *v2);
755 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
756 __isl_take isl_val *v2);
757 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
758 __isl_take isl_val *v2);
759 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
761 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
762 __isl_take isl_val *v2);
763 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
765 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
766 __isl_take isl_val *v2);
767 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
769 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
770 __isl_take isl_val *v2);
772 On integer values, we additionally have the following operations.
775 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
776 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
777 __isl_take isl_val *v2);
778 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
779 __isl_take isl_val *v2);
780 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
781 __isl_take isl_val *v2, __isl_give isl_val **x,
782 __isl_give isl_val **y);
784 The function C<isl_val_gcdext> returns the greatest common divisor g
785 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
786 that C<*x> * C<v1> + C<*y> * C<v2> = g.
788 =head3 GMP specific functions
790 These functions are only available if C<isl> has been compiled with C<GMP>
793 Specific integer and rational values can be created from C<GMP> values using
794 the following functions.
796 #include <isl/val_gmp.h>
797 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
799 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
800 const mpz_t n, const mpz_t d);
802 The numerator and denominator of a rational value can be extracted as
803 C<GMP> values using the following functions.
805 #include <isl/val_gmp.h>
806 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
807 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
809 =head2 Sets and Relations
811 C<isl> uses six types of objects for representing sets and relations,
812 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
813 C<isl_union_set> and C<isl_union_map>.
814 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
815 can be described as a conjunction of affine constraints, while
816 C<isl_set> and C<isl_map> represent unions of
817 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
818 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
819 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
820 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
821 where spaces are considered different if they have a different number
822 of dimensions and/or different names (see L<"Spaces">).
823 The difference between sets and relations (maps) is that sets have
824 one set of variables, while relations have two sets of variables,
825 input variables and output variables.
827 =head2 Error Handling
829 C<isl> supports different ways to react in case a runtime error is triggered.
830 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
831 with two maps that have incompatible spaces. There are three possible ways
832 to react on error: to warn, to continue or to abort.
834 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
835 the last error in the corresponding C<isl_ctx> and the function in which the
836 error was triggered returns a value indicating that some error has
837 occurred. In case of functions returning a pointer, this value is
838 C<NULL>. In case of functions returning an C<isl_bool> or an
839 C<isl_stat>, this valus is C<isl_bool_error> or C<isl_stat_error>.
840 An error does not corrupt internal state,
841 such that isl can continue to be used. C<isl> also provides functions to
842 read the last error and to reset the memory that stores the last error. The
843 last error is only stored for information purposes. Its presence does not
844 change the behavior of C<isl>. Hence, resetting an error is not required to
845 continue to use isl, but only to observe new errors.
848 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
849 void isl_ctx_reset_error(isl_ctx *ctx);
851 Another option is to continue on error. This is similar to warn on error mode,
852 except that C<isl> does not print any warning. This allows a program to
853 implement its own error reporting.
855 The last option is to directly abort the execution of the program from within
856 the isl library. This makes it obviously impossible to recover from an error,
857 but it allows to directly spot the error location. By aborting on error,
858 debuggers break at the location the error occurred and can provide a stack
859 trace. Other tools that automatically provide stack traces on abort or that do
860 not want to continue execution after an error was triggered may also prefer to
863 The on error behavior of isl can be specified by calling
864 C<isl_options_set_on_error> or by setting the command line option
865 C<--isl-on-error>. Valid arguments for the function call are
866 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
867 choices for the command line option are C<warn>, C<continue> and C<abort>.
868 It is also possible to query the current error mode.
870 #include <isl/options.h>
871 isl_stat isl_options_set_on_error(isl_ctx *ctx, int val);
872 int isl_options_get_on_error(isl_ctx *ctx);
876 Identifiers are used to identify both individual dimensions
877 and tuples of dimensions. They consist of an optional name and an optional
878 user pointer. The name and the user pointer cannot both be C<NULL>, however.
879 Identifiers with the same name but different pointer values
880 are considered to be distinct.
881 Similarly, identifiers with different names but the same pointer value
882 are also considered to be distinct.
883 Equal identifiers are represented using the same object.
884 Pairs of identifiers can therefore be tested for equality using the
886 Identifiers can be constructed, copied, freed, inspected and printed
887 using the following functions.
890 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
891 __isl_keep const char *name, void *user);
892 __isl_give isl_id *isl_id_set_free_user(
893 __isl_take isl_id *id,
894 void (*free_user)(void *user));
895 __isl_give isl_id *isl_id_copy(isl_id *id);
896 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
898 void *isl_id_get_user(__isl_keep isl_id *id);
899 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
901 __isl_give isl_printer *isl_printer_print_id(
902 __isl_take isl_printer *p, __isl_keep isl_id *id);
904 The callback set by C<isl_id_set_free_user> is called on the user
905 pointer when the last reference to the C<isl_id> is freed.
906 Note that C<isl_id_get_name> returns a pointer to some internal
907 data structure, so the result can only be used while the
908 corresponding C<isl_id> is alive.
912 Whenever a new set, relation or similar object is created from scratch,
913 the space in which it lives needs to be specified using an C<isl_space>.
914 Each space involves zero or more parameters and zero, one or two
915 tuples of set or input/output dimensions. The parameters and dimensions
916 are identified by an C<isl_dim_type> and a position.
917 The type C<isl_dim_param> refers to parameters,
918 the type C<isl_dim_set> refers to set dimensions (for spaces
919 with a single tuple of dimensions) and the types C<isl_dim_in>
920 and C<isl_dim_out> refer to input and output dimensions
921 (for spaces with two tuples of dimensions).
922 Local spaces (see L</"Local Spaces">) also contain dimensions
923 of type C<isl_dim_div>.
924 Note that parameters are only identified by their position within
925 a given object. Across different objects, parameters are (usually)
926 identified by their names or identifiers. Only unnamed parameters
927 are identified by their positions across objects. The use of unnamed
928 parameters is discouraged.
930 #include <isl/space.h>
931 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
932 unsigned nparam, unsigned n_in, unsigned n_out);
933 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
935 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
936 unsigned nparam, unsigned dim);
937 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
938 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
940 The space used for creating a parameter domain
941 needs to be created using C<isl_space_params_alloc>.
942 For other sets, the space
943 needs to be created using C<isl_space_set_alloc>, while
944 for a relation, the space
945 needs to be created using C<isl_space_alloc>.
947 To check whether a given space is that of a set or a map
948 or whether it is a parameter space, use these functions:
950 #include <isl/space.h>
951 isl_bool isl_space_is_params(__isl_keep isl_space *space);
952 isl_bool isl_space_is_set(__isl_keep isl_space *space);
953 isl_bool isl_space_is_map(__isl_keep isl_space *space);
955 Spaces can be compared using the following functions:
957 #include <isl/space.h>
958 isl_bool isl_space_is_equal(__isl_keep isl_space *space1,
959 __isl_keep isl_space *space2);
960 isl_bool isl_space_has_equal_tuples(
961 __isl_keep isl_space *space1,
962 __isl_keep isl_space *space2);
963 isl_bool isl_space_is_domain(__isl_keep isl_space *space1,
964 __isl_keep isl_space *space2);
965 isl_bool isl_space_is_range(__isl_keep isl_space *space1,
966 __isl_keep isl_space *space2);
967 isl_bool isl_space_tuple_is_equal(
968 __isl_keep isl_space *space1,
969 enum isl_dim_type type1,
970 __isl_keep isl_space *space2,
971 enum isl_dim_type type2);
973 C<isl_space_is_domain> checks whether the first argument is equal
974 to the domain of the second argument. This requires in particular that
975 the first argument is a set space and that the second argument
976 is a map space. C<isl_space_tuple_is_equal> checks whether the given
977 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
978 spaces are the same. That is, it checks if they have the same
979 identifier (if any), the same dimension and the same internal structure
981 C<isl_space_is_equal> checks whether two spaces are identical.
982 In particular, it checks whether they have the same type
983 (parameter, set or map space), the same tuples
984 (if they are not parameter spaces) in the sense
985 of C<isl_space_tuple_is_equal> and the same parameters
987 C<isl_space_has_equal_tuples> check whether two spaces have
988 the same tuples. In contrast to C<isl_space_is_equal>, it does not check the
989 parameters. This is useful because many C<isl> functions align the
990 parameters before they perform their operations, such that equivalence
993 It is often useful to create objects that live in the
994 same space as some other object. This can be accomplished
995 by creating the new objects
996 (see L</"Creating New Sets and Relations"> or
997 L</"Functions">) based on the space
998 of the original object.
1000 #include <isl/set.h>
1001 __isl_give isl_space *isl_basic_set_get_space(
1002 __isl_keep isl_basic_set *bset);
1003 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
1005 #include <isl/union_set.h>
1006 __isl_give isl_space *isl_union_set_get_space(
1007 __isl_keep isl_union_set *uset);
1009 #include <isl/map.h>
1010 __isl_give isl_space *isl_basic_map_get_space(
1011 __isl_keep isl_basic_map *bmap);
1012 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
1014 #include <isl/union_map.h>
1015 __isl_give isl_space *isl_union_map_get_space(
1016 __isl_keep isl_union_map *umap);
1018 #include <isl/constraint.h>
1019 __isl_give isl_space *isl_constraint_get_space(
1020 __isl_keep isl_constraint *constraint);
1022 #include <isl/polynomial.h>
1023 __isl_give isl_space *isl_qpolynomial_get_domain_space(
1024 __isl_keep isl_qpolynomial *qp);
1025 __isl_give isl_space *isl_qpolynomial_get_space(
1026 __isl_keep isl_qpolynomial *qp);
1027 __isl_give isl_space *
1028 isl_qpolynomial_fold_get_domain_space(
1029 __isl_keep isl_qpolynomial_fold *fold);
1030 __isl_give isl_space *isl_qpolynomial_fold_get_space(
1031 __isl_keep isl_qpolynomial_fold *fold);
1032 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
1033 __isl_keep isl_pw_qpolynomial *pwqp);
1034 __isl_give isl_space *isl_pw_qpolynomial_get_space(
1035 __isl_keep isl_pw_qpolynomial *pwqp);
1036 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
1037 __isl_keep isl_pw_qpolynomial_fold *pwf);
1038 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
1039 __isl_keep isl_pw_qpolynomial_fold *pwf);
1040 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
1041 __isl_keep isl_union_pw_qpolynomial *upwqp);
1042 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
1043 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1045 #include <isl/val.h>
1046 __isl_give isl_space *isl_multi_val_get_space(
1047 __isl_keep isl_multi_val *mv);
1049 #include <isl/aff.h>
1050 __isl_give isl_space *isl_aff_get_domain_space(
1051 __isl_keep isl_aff *aff);
1052 __isl_give isl_space *isl_aff_get_space(
1053 __isl_keep isl_aff *aff);
1054 __isl_give isl_space *isl_pw_aff_get_domain_space(
1055 __isl_keep isl_pw_aff *pwaff);
1056 __isl_give isl_space *isl_pw_aff_get_space(
1057 __isl_keep isl_pw_aff *pwaff);
1058 __isl_give isl_space *isl_multi_aff_get_domain_space(
1059 __isl_keep isl_multi_aff *maff);
1060 __isl_give isl_space *isl_multi_aff_get_space(
1061 __isl_keep isl_multi_aff *maff);
1062 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
1063 __isl_keep isl_pw_multi_aff *pma);
1064 __isl_give isl_space *isl_pw_multi_aff_get_space(
1065 __isl_keep isl_pw_multi_aff *pma);
1066 __isl_give isl_space *isl_union_pw_aff_get_space(
1067 __isl_keep isl_union_pw_aff *upa);
1068 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
1069 __isl_keep isl_union_pw_multi_aff *upma);
1070 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
1071 __isl_keep isl_multi_pw_aff *mpa);
1072 __isl_give isl_space *isl_multi_pw_aff_get_space(
1073 __isl_keep isl_multi_pw_aff *mpa);
1074 __isl_give isl_space *
1075 isl_multi_union_pw_aff_get_domain_space(
1076 __isl_keep isl_multi_union_pw_aff *mupa);
1077 __isl_give isl_space *
1078 isl_multi_union_pw_aff_get_space(
1079 __isl_keep isl_multi_union_pw_aff *mupa);
1081 #include <isl/point.h>
1082 __isl_give isl_space *isl_point_get_space(
1083 __isl_keep isl_point *pnt);
1085 The number of dimensions of a given type of space
1086 may be read off from a space or an object that lives
1087 in a space using the following functions.
1088 In case of C<isl_space_dim>, type may be
1089 C<isl_dim_param>, C<isl_dim_in> (only for relations),
1090 C<isl_dim_out> (only for relations), C<isl_dim_set>
1091 (only for sets) or C<isl_dim_all>.
1093 #include <isl/space.h>
1094 unsigned isl_space_dim(__isl_keep isl_space *space,
1095 enum isl_dim_type type);
1097 #include <isl/local_space.h>
1098 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1099 enum isl_dim_type type);
1101 #include <isl/set.h>
1102 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1103 enum isl_dim_type type);
1104 unsigned isl_set_dim(__isl_keep isl_set *set,
1105 enum isl_dim_type type);
1107 #include <isl/union_set.h>
1108 unsigned isl_union_set_dim(__isl_keep isl_union_set *uset,
1109 enum isl_dim_type type);
1111 #include <isl/map.h>
1112 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1113 enum isl_dim_type type);
1114 unsigned isl_map_dim(__isl_keep isl_map *map,
1115 enum isl_dim_type type);
1117 #include <isl/union_map.h>
1118 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1119 enum isl_dim_type type);
1121 #include <isl/val.h>
1122 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
1123 enum isl_dim_type type);
1125 #include <isl/aff.h>
1126 int isl_aff_dim(__isl_keep isl_aff *aff,
1127 enum isl_dim_type type);
1128 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1129 enum isl_dim_type type);
1130 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1131 enum isl_dim_type type);
1132 unsigned isl_pw_multi_aff_dim(
1133 __isl_keep isl_pw_multi_aff *pma,
1134 enum isl_dim_type type);
1135 unsigned isl_multi_pw_aff_dim(
1136 __isl_keep isl_multi_pw_aff *mpa,
1137 enum isl_dim_type type);
1138 unsigned isl_union_pw_aff_dim(
1139 __isl_keep isl_union_pw_aff *upa,
1140 enum isl_dim_type type);
1141 unsigned isl_union_pw_multi_aff_dim(
1142 __isl_keep isl_union_pw_multi_aff *upma,
1143 enum isl_dim_type type);
1144 unsigned isl_multi_union_pw_aff_dim(
1145 __isl_keep isl_multi_union_pw_aff *mupa,
1146 enum isl_dim_type type);
1148 #include <isl/polynomial.h>
1149 unsigned isl_union_pw_qpolynomial_dim(
1150 __isl_keep isl_union_pw_qpolynomial *upwqp,
1151 enum isl_dim_type type);
1152 unsigned isl_union_pw_qpolynomial_fold_dim(
1153 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1154 enum isl_dim_type type);
1156 Note that an C<isl_union_set>, an C<isl_union_map>,
1157 an C<isl_union_pw_multi_aff>,
1158 an C<isl_union_pw_qpolynomial> and
1159 an C<isl_union_pw_qpolynomial_fold>
1160 only have parameters.
1162 The identifiers or names of the individual dimensions of spaces
1163 may be set or read off using the following functions on spaces
1164 or objects that live in spaces.
1165 These functions are mostly useful to obtain the identifiers, positions
1166 or names of the parameters. Identifiers of individual dimensions are
1167 essentially only useful for printing. They are ignored by all other
1168 operations and may not be preserved across those operations.
1170 #include <isl/space.h>
1171 __isl_give isl_space *isl_space_set_dim_id(
1172 __isl_take isl_space *space,
1173 enum isl_dim_type type, unsigned pos,
1174 __isl_take isl_id *id);
1175 isl_bool isl_space_has_dim_id(__isl_keep isl_space *space,
1176 enum isl_dim_type type, unsigned pos);
1177 __isl_give isl_id *isl_space_get_dim_id(
1178 __isl_keep isl_space *space,
1179 enum isl_dim_type type, unsigned pos);
1180 __isl_give isl_space *isl_space_set_dim_name(
1181 __isl_take isl_space *space,
1182 enum isl_dim_type type, unsigned pos,
1183 __isl_keep const char *name);
1184 isl_bool isl_space_has_dim_name(__isl_keep isl_space *space,
1185 enum isl_dim_type type, unsigned pos);
1186 __isl_keep const char *isl_space_get_dim_name(
1187 __isl_keep isl_space *space,
1188 enum isl_dim_type type, unsigned pos);
1190 #include <isl/local_space.h>
1191 __isl_give isl_local_space *isl_local_space_set_dim_id(
1192 __isl_take isl_local_space *ls,
1193 enum isl_dim_type type, unsigned pos,
1194 __isl_take isl_id *id);
1195 isl_bool isl_local_space_has_dim_id(
1196 __isl_keep isl_local_space *ls,
1197 enum isl_dim_type type, unsigned pos);
1198 __isl_give isl_id *isl_local_space_get_dim_id(
1199 __isl_keep isl_local_space *ls,
1200 enum isl_dim_type type, unsigned pos);
1201 __isl_give isl_local_space *isl_local_space_set_dim_name(
1202 __isl_take isl_local_space *ls,
1203 enum isl_dim_type type, unsigned pos, const char *s);
1204 isl_bool isl_local_space_has_dim_name(
1205 __isl_keep isl_local_space *ls,
1206 enum isl_dim_type type, unsigned pos)
1207 const char *isl_local_space_get_dim_name(
1208 __isl_keep isl_local_space *ls,
1209 enum isl_dim_type type, unsigned pos);
1211 #include <isl/constraint.h>
1212 const char *isl_constraint_get_dim_name(
1213 __isl_keep isl_constraint *constraint,
1214 enum isl_dim_type type, unsigned pos);
1216 #include <isl/set.h>
1217 __isl_give isl_id *isl_basic_set_get_dim_id(
1218 __isl_keep isl_basic_set *bset,
1219 enum isl_dim_type type, unsigned pos);
1220 __isl_give isl_set *isl_set_set_dim_id(
1221 __isl_take isl_set *set, enum isl_dim_type type,
1222 unsigned pos, __isl_take isl_id *id);
1223 isl_bool isl_set_has_dim_id(__isl_keep isl_set *set,
1224 enum isl_dim_type type, unsigned pos);
1225 __isl_give isl_id *isl_set_get_dim_id(
1226 __isl_keep isl_set *set, enum isl_dim_type type,
1228 const char *isl_basic_set_get_dim_name(
1229 __isl_keep isl_basic_set *bset,
1230 enum isl_dim_type type, unsigned pos);
1231 isl_bool isl_set_has_dim_name(__isl_keep isl_set *set,
1232 enum isl_dim_type type, unsigned pos);
1233 const char *isl_set_get_dim_name(
1234 __isl_keep isl_set *set,
1235 enum isl_dim_type type, unsigned pos);
1237 #include <isl/map.h>
1238 __isl_give isl_map *isl_map_set_dim_id(
1239 __isl_take isl_map *map, enum isl_dim_type type,
1240 unsigned pos, __isl_take isl_id *id);
1241 isl_bool isl_basic_map_has_dim_id(
1242 __isl_keep isl_basic_map *bmap,
1243 enum isl_dim_type type, unsigned pos);
1244 isl_bool isl_map_has_dim_id(__isl_keep isl_map *map,
1245 enum isl_dim_type type, unsigned pos);
1246 __isl_give isl_id *isl_map_get_dim_id(
1247 __isl_keep isl_map *map, enum isl_dim_type type,
1249 __isl_give isl_id *isl_union_map_get_dim_id(
1250 __isl_keep isl_union_map *umap,
1251 enum isl_dim_type type, unsigned pos);
1252 const char *isl_basic_map_get_dim_name(
1253 __isl_keep isl_basic_map *bmap,
1254 enum isl_dim_type type, unsigned pos);
1255 isl_bool isl_map_has_dim_name(__isl_keep isl_map *map,
1256 enum isl_dim_type type, unsigned pos);
1257 const char *isl_map_get_dim_name(
1258 __isl_keep isl_map *map,
1259 enum isl_dim_type type, unsigned pos);
1261 #include <isl/val.h>
1262 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1263 __isl_take isl_multi_val *mv,
1264 enum isl_dim_type type, unsigned pos,
1265 __isl_take isl_id *id);
1266 __isl_give isl_id *isl_multi_val_get_dim_id(
1267 __isl_keep isl_multi_val *mv,
1268 enum isl_dim_type type, unsigned pos);
1269 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1270 __isl_take isl_multi_val *mv,
1271 enum isl_dim_type type, unsigned pos, const char *s);
1273 #include <isl/aff.h>
1274 __isl_give isl_aff *isl_aff_set_dim_id(
1275 __isl_take isl_aff *aff, enum isl_dim_type type,
1276 unsigned pos, __isl_take isl_id *id);
1277 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1278 __isl_take isl_multi_aff *maff,
1279 enum isl_dim_type type, unsigned pos,
1280 __isl_take isl_id *id);
1281 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1282 __isl_take isl_pw_aff *pma,
1283 enum isl_dim_type type, unsigned pos,
1284 __isl_take isl_id *id);
1285 __isl_give isl_multi_pw_aff *
1286 isl_multi_pw_aff_set_dim_id(
1287 __isl_take isl_multi_pw_aff *mpa,
1288 enum isl_dim_type type, unsigned pos,
1289 __isl_take isl_id *id);
1290 __isl_give isl_multi_union_pw_aff *
1291 isl_multi_union_pw_aff_set_dim_id(
1292 __isl_take isl_multi_union_pw_aff *mupa,
1293 enum isl_dim_type type, unsigned pos,
1294 __isl_take isl_id *id);
1295 __isl_give isl_id *isl_multi_aff_get_dim_id(
1296 __isl_keep isl_multi_aff *ma,
1297 enum isl_dim_type type, unsigned pos);
1298 isl_bool isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1299 enum isl_dim_type type, unsigned pos);
1300 __isl_give isl_id *isl_pw_aff_get_dim_id(
1301 __isl_keep isl_pw_aff *pa,
1302 enum isl_dim_type type, unsigned pos);
1303 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1304 __isl_keep isl_pw_multi_aff *pma,
1305 enum isl_dim_type type, unsigned pos);
1306 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1307 __isl_keep isl_multi_pw_aff *mpa,
1308 enum isl_dim_type type, unsigned pos);
1309 __isl_give isl_id *isl_multi_union_pw_aff_get_dim_id(
1310 __isl_keep isl_multi_union_pw_aff *mupa,
1311 enum isl_dim_type type, unsigned pos);
1312 __isl_give isl_aff *isl_aff_set_dim_name(
1313 __isl_take isl_aff *aff, enum isl_dim_type type,
1314 unsigned pos, const char *s);
1315 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1316 __isl_take isl_multi_aff *maff,
1317 enum isl_dim_type type, unsigned pos, const char *s);
1318 __isl_give isl_multi_pw_aff *
1319 isl_multi_pw_aff_set_dim_name(
1320 __isl_take isl_multi_pw_aff *mpa,
1321 enum isl_dim_type type, unsigned pos, const char *s);
1322 __isl_give isl_union_pw_aff *
1323 isl_union_pw_aff_set_dim_name(
1324 __isl_take isl_union_pw_aff *upa,
1325 enum isl_dim_type type, unsigned pos,
1327 __isl_give isl_union_pw_multi_aff *
1328 isl_union_pw_multi_aff_set_dim_name(
1329 __isl_take isl_union_pw_multi_aff *upma,
1330 enum isl_dim_type type, unsigned pos,
1332 __isl_give isl_multi_union_pw_aff *
1333 isl_multi_union_pw_aff_set_dim_name(
1334 __isl_take isl_multi_union_pw_aff *mupa,
1335 enum isl_dim_type type, unsigned pos,
1336 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1337 enum isl_dim_type type, unsigned pos);
1338 const char *isl_pw_aff_get_dim_name(
1339 __isl_keep isl_pw_aff *pa,
1340 enum isl_dim_type type, unsigned pos);
1341 const char *isl_pw_multi_aff_get_dim_name(
1342 __isl_keep isl_pw_multi_aff *pma,
1343 enum isl_dim_type type, unsigned pos);
1345 #include <isl/polynomial.h>
1346 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1347 __isl_take isl_qpolynomial *qp,
1348 enum isl_dim_type type, unsigned pos,
1350 __isl_give isl_pw_qpolynomial *
1351 isl_pw_qpolynomial_set_dim_name(
1352 __isl_take isl_pw_qpolynomial *pwqp,
1353 enum isl_dim_type type, unsigned pos,
1355 __isl_give isl_pw_qpolynomial_fold *
1356 isl_pw_qpolynomial_fold_set_dim_name(
1357 __isl_take isl_pw_qpolynomial_fold *pwf,
1358 enum isl_dim_type type, unsigned pos,
1360 __isl_give isl_union_pw_qpolynomial *
1361 isl_union_pw_qpolynomial_set_dim_name(
1362 __isl_take isl_union_pw_qpolynomial *upwqp,
1363 enum isl_dim_type type, unsigned pos,
1365 __isl_give isl_union_pw_qpolynomial_fold *
1366 isl_union_pw_qpolynomial_fold_set_dim_name(
1367 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1368 enum isl_dim_type type, unsigned pos,
1371 Note that C<isl_space_get_name> returns a pointer to some internal
1372 data structure, so the result can only be used while the
1373 corresponding C<isl_space> is alive.
1374 Also note that every function that operates on two sets or relations
1375 requires that both arguments have the same parameters. This also
1376 means that if one of the arguments has named parameters, then the
1377 other needs to have named parameters too and the names need to match.
1378 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1379 arguments may have different parameters (as long as they are named),
1380 in which case the result will have as parameters the union of the parameters of
1383 Given the identifier or name of a dimension (typically a parameter),
1384 its position can be obtained from the following functions.
1386 #include <isl/space.h>
1387 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1388 enum isl_dim_type type, __isl_keep isl_id *id);
1389 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1390 enum isl_dim_type type, const char *name);
1392 #include <isl/local_space.h>
1393 int isl_local_space_find_dim_by_name(
1394 __isl_keep isl_local_space *ls,
1395 enum isl_dim_type type, const char *name);
1397 #include <isl/val.h>
1398 int isl_multi_val_find_dim_by_id(
1399 __isl_keep isl_multi_val *mv,
1400 enum isl_dim_type type, __isl_keep isl_id *id);
1401 int isl_multi_val_find_dim_by_name(
1402 __isl_keep isl_multi_val *mv,
1403 enum isl_dim_type type, const char *name);
1405 #include <isl/set.h>
1406 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1407 enum isl_dim_type type, __isl_keep isl_id *id);
1408 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1409 enum isl_dim_type type, const char *name);
1411 #include <isl/map.h>
1412 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1413 enum isl_dim_type type, __isl_keep isl_id *id);
1414 int isl_basic_map_find_dim_by_name(
1415 __isl_keep isl_basic_map *bmap,
1416 enum isl_dim_type type, const char *name);
1417 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1418 enum isl_dim_type type, const char *name);
1419 int isl_union_map_find_dim_by_name(
1420 __isl_keep isl_union_map *umap,
1421 enum isl_dim_type type, const char *name);
1423 #include <isl/aff.h>
1424 int isl_multi_aff_find_dim_by_id(
1425 __isl_keep isl_multi_aff *ma,
1426 enum isl_dim_type type, __isl_keep isl_id *id);
1427 int isl_multi_pw_aff_find_dim_by_id(
1428 __isl_keep isl_multi_pw_aff *mpa,
1429 enum isl_dim_type type, __isl_keep isl_id *id);
1430 int isl_multi_union_pw_aff_find_dim_by_id(
1431 __isl_keep isl_union_multi_pw_aff *mupa,
1432 enum isl_dim_type type, __isl_keep isl_id *id);
1433 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff,
1434 enum isl_dim_type type, const char *name);
1435 int isl_multi_aff_find_dim_by_name(
1436 __isl_keep isl_multi_aff *ma,
1437 enum isl_dim_type type, const char *name);
1438 int isl_pw_aff_find_dim_by_name(__isl_keep isl_pw_aff *pa,
1439 enum isl_dim_type type, const char *name);
1440 int isl_multi_pw_aff_find_dim_by_name(
1441 __isl_keep isl_multi_pw_aff *mpa,
1442 enum isl_dim_type type, const char *name);
1443 int isl_pw_multi_aff_find_dim_by_name(
1444 __isl_keep isl_pw_multi_aff *pma,
1445 enum isl_dim_type type, const char *name);
1446 int isl_union_pw_aff_find_dim_by_name(
1447 __isl_keep isl_union_pw_aff *upa,
1448 enum isl_dim_type type, const char *name);
1449 int isl_union_pw_multi_aff_find_dim_by_name(
1450 __isl_keep isl_union_pw_multi_aff *upma,
1451 enum isl_dim_type type, const char *name);
1452 int isl_multi_union_pw_aff_find_dim_by_name(
1453 __isl_keep isl_multi_union_pw_aff *mupa,
1454 enum isl_dim_type type, const char *name);
1456 #include <isl/polynomial.h>
1457 int isl_pw_qpolynomial_find_dim_by_name(
1458 __isl_keep isl_pw_qpolynomial *pwqp,
1459 enum isl_dim_type type, const char *name);
1460 int isl_pw_qpolynomial_fold_find_dim_by_name(
1461 __isl_keep isl_pw_qpolynomial_fold *pwf,
1462 enum isl_dim_type type, const char *name);
1463 int isl_union_pw_qpolynomial_find_dim_by_name(
1464 __isl_keep isl_union_pw_qpolynomial *upwqp,
1465 enum isl_dim_type type, const char *name);
1466 int isl_union_pw_qpolynomial_fold_find_dim_by_name(
1467 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1468 enum isl_dim_type type, const char *name);
1470 The identifiers or names of entire spaces may be set or read off
1471 using the following functions.
1473 #include <isl/space.h>
1474 __isl_give isl_space *isl_space_set_tuple_id(
1475 __isl_take isl_space *space,
1476 enum isl_dim_type type, __isl_take isl_id *id);
1477 __isl_give isl_space *isl_space_reset_tuple_id(
1478 __isl_take isl_space *space, enum isl_dim_type type);
1479 isl_bool isl_space_has_tuple_id(
1480 __isl_keep isl_space *space,
1481 enum isl_dim_type type);
1482 __isl_give isl_id *isl_space_get_tuple_id(
1483 __isl_keep isl_space *space, enum isl_dim_type type);
1484 __isl_give isl_space *isl_space_set_tuple_name(
1485 __isl_take isl_space *space,
1486 enum isl_dim_type type, const char *s);
1487 isl_bool isl_space_has_tuple_name(
1488 __isl_keep isl_space *space,
1489 enum isl_dim_type type);
1490 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
1491 enum isl_dim_type type);
1493 #include <isl/local_space.h>
1494 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1495 __isl_take isl_local_space *ls,
1496 enum isl_dim_type type, __isl_take isl_id *id);
1498 #include <isl/set.h>
1499 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1500 __isl_take isl_basic_set *bset,
1501 __isl_take isl_id *id);
1502 __isl_give isl_set *isl_set_set_tuple_id(
1503 __isl_take isl_set *set, __isl_take isl_id *id);
1504 __isl_give isl_set *isl_set_reset_tuple_id(
1505 __isl_take isl_set *set);
1506 isl_bool isl_set_has_tuple_id(__isl_keep isl_set *set);
1507 __isl_give isl_id *isl_set_get_tuple_id(
1508 __isl_keep isl_set *set);
1509 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1510 __isl_take isl_basic_set *set, const char *s);
1511 __isl_give isl_set *isl_set_set_tuple_name(
1512 __isl_take isl_set *set, const char *s);
1513 const char *isl_basic_set_get_tuple_name(
1514 __isl_keep isl_basic_set *bset);
1515 isl_bool isl_set_has_tuple_name(__isl_keep isl_set *set);
1516 const char *isl_set_get_tuple_name(
1517 __isl_keep isl_set *set);
1519 #include <isl/map.h>
1520 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1521 __isl_take isl_basic_map *bmap,
1522 enum isl_dim_type type, __isl_take isl_id *id);
1523 __isl_give isl_map *isl_map_set_tuple_id(
1524 __isl_take isl_map *map, enum isl_dim_type type,
1525 __isl_take isl_id *id);
1526 __isl_give isl_map *isl_map_reset_tuple_id(
1527 __isl_take isl_map *map, enum isl_dim_type type);
1528 isl_bool isl_map_has_tuple_id(__isl_keep isl_map *map,
1529 enum isl_dim_type type);
1530 __isl_give isl_id *isl_map_get_tuple_id(
1531 __isl_keep isl_map *map, enum isl_dim_type type);
1532 __isl_give isl_map *isl_map_set_tuple_name(
1533 __isl_take isl_map *map,
1534 enum isl_dim_type type, const char *s);
1535 const char *isl_basic_map_get_tuple_name(
1536 __isl_keep isl_basic_map *bmap,
1537 enum isl_dim_type type);
1538 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1539 __isl_take isl_basic_map *bmap,
1540 enum isl_dim_type type, const char *s);
1541 isl_bool isl_map_has_tuple_name(__isl_keep isl_map *map,
1542 enum isl_dim_type type);
1543 const char *isl_map_get_tuple_name(
1544 __isl_keep isl_map *map,
1545 enum isl_dim_type type);
1547 #include <isl/val.h>
1548 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1549 __isl_take isl_multi_val *mv,
1550 enum isl_dim_type type, __isl_take isl_id *id);
1551 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1552 __isl_take isl_multi_val *mv,
1553 enum isl_dim_type type);
1554 isl_bool isl_multi_val_has_tuple_id(
1555 __isl_keep isl_multi_val *mv,
1556 enum isl_dim_type type);
1557 __isl_give isl_id *isl_multi_val_get_tuple_id(
1558 __isl_keep isl_multi_val *mv,
1559 enum isl_dim_type type);
1560 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1561 __isl_take isl_multi_val *mv,
1562 enum isl_dim_type type, const char *s);
1563 const char *isl_multi_val_get_tuple_name(
1564 __isl_keep isl_multi_val *mv,
1565 enum isl_dim_type type);
1567 #include <isl/aff.h>
1568 __isl_give isl_aff *isl_aff_set_tuple_id(
1569 __isl_take isl_aff *aff,
1570 enum isl_dim_type type, __isl_take isl_id *id);
1571 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1572 __isl_take isl_multi_aff *maff,
1573 enum isl_dim_type type, __isl_take isl_id *id);
1574 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1575 __isl_take isl_pw_aff *pwaff,
1576 enum isl_dim_type type, __isl_take isl_id *id);
1577 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1578 __isl_take isl_pw_multi_aff *pma,
1579 enum isl_dim_type type, __isl_take isl_id *id);
1580 __isl_give isl_multi_union_pw_aff *
1581 isl_multi_union_pw_aff_set_tuple_id(
1582 __isl_take isl_multi_union_pw_aff *mupa,
1583 enum isl_dim_type type, __isl_take isl_id *id);
1584 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1585 __isl_take isl_multi_aff *ma,
1586 enum isl_dim_type type);
1587 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1588 __isl_take isl_pw_aff *pa,
1589 enum isl_dim_type type);
1590 __isl_give isl_multi_pw_aff *
1591 isl_multi_pw_aff_reset_tuple_id(
1592 __isl_take isl_multi_pw_aff *mpa,
1593 enum isl_dim_type type);
1594 __isl_give isl_pw_multi_aff *
1595 isl_pw_multi_aff_reset_tuple_id(
1596 __isl_take isl_pw_multi_aff *pma,
1597 enum isl_dim_type type);
1598 __isl_give isl_multi_union_pw_aff *
1599 isl_multi_union_pw_aff_reset_tuple_id(
1600 __isl_take isl_multi_union_pw_aff *mupa,
1601 enum isl_dim_type type);
1602 isl_bool isl_multi_aff_has_tuple_id(
1603 __isl_keep isl_multi_aff *ma,
1604 enum isl_dim_type type);
1605 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1606 __isl_keep isl_multi_aff *ma,
1607 enum isl_dim_type type);
1608 isl_bool isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1609 enum isl_dim_type type);
1610 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1611 __isl_keep isl_pw_aff *pa,
1612 enum isl_dim_type type);
1613 isl_bool isl_pw_multi_aff_has_tuple_id(
1614 __isl_keep isl_pw_multi_aff *pma,
1615 enum isl_dim_type type);
1616 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1617 __isl_keep isl_pw_multi_aff *pma,
1618 enum isl_dim_type type);
1619 isl_bool isl_multi_pw_aff_has_tuple_id(
1620 __isl_keep isl_multi_pw_aff *mpa,
1621 enum isl_dim_type type);
1622 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1623 __isl_keep isl_multi_pw_aff *mpa,
1624 enum isl_dim_type type);
1625 isl_bool isl_multi_union_pw_aff_has_tuple_id(
1626 __isl_keep isl_multi_union_pw_aff *mupa,
1627 enum isl_dim_type type);
1628 __isl_give isl_id *isl_multi_union_pw_aff_get_tuple_id(
1629 __isl_keep isl_multi_union_pw_aff *mupa,
1630 enum isl_dim_type type);
1631 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1632 __isl_take isl_multi_aff *maff,
1633 enum isl_dim_type type, const char *s);
1634 __isl_give isl_multi_pw_aff *
1635 isl_multi_pw_aff_set_tuple_name(
1636 __isl_take isl_multi_pw_aff *mpa,
1637 enum isl_dim_type type, const char *s);
1638 __isl_give isl_multi_union_pw_aff *
1639 isl_multi_union_pw_aff_set_tuple_name(
1640 __isl_take isl_multi_union_pw_aff *mupa,
1641 enum isl_dim_type type, const char *s);
1642 const char *isl_multi_aff_get_tuple_name(
1643 __isl_keep isl_multi_aff *multi,
1644 enum isl_dim_type type);
1645 isl_bool isl_pw_multi_aff_has_tuple_name(
1646 __isl_keep isl_pw_multi_aff *pma,
1647 enum isl_dim_type type);
1648 const char *isl_pw_multi_aff_get_tuple_name(
1649 __isl_keep isl_pw_multi_aff *pma,
1650 enum isl_dim_type type);
1651 const char *isl_multi_union_pw_aff_get_tuple_name(
1652 __isl_keep isl_multi_union_pw_aff *mupa,
1653 enum isl_dim_type type);
1655 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1656 or C<isl_dim_set>. As with C<isl_space_get_name>,
1657 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1659 Binary operations require the corresponding spaces of their arguments
1660 to have the same name.
1662 To keep the names of all parameters and tuples, but reset the user pointers
1663 of all the corresponding identifiers, use the following function.
1665 #include <isl/space.h>
1666 __isl_give isl_space *isl_space_reset_user(
1667 __isl_take isl_space *space);
1669 #include <isl/set.h>
1670 __isl_give isl_set *isl_set_reset_user(
1671 __isl_take isl_set *set);
1673 #include <isl/map.h>
1674 __isl_give isl_map *isl_map_reset_user(
1675 __isl_take isl_map *map);
1677 #include <isl/union_set.h>
1678 __isl_give isl_union_set *isl_union_set_reset_user(
1679 __isl_take isl_union_set *uset);
1681 #include <isl/union_map.h>
1682 __isl_give isl_union_map *isl_union_map_reset_user(
1683 __isl_take isl_union_map *umap);
1685 #include <isl/val.h>
1686 __isl_give isl_multi_val *isl_multi_val_reset_user(
1687 __isl_take isl_multi_val *mv);
1689 #include <isl/aff.h>
1690 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1691 __isl_take isl_multi_aff *ma);
1692 __isl_give isl_pw_aff *isl_pw_aff_reset_user(
1693 __isl_take isl_pw_aff *pa);
1694 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1695 __isl_take isl_multi_pw_aff *mpa);
1696 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_reset_user(
1697 __isl_take isl_pw_multi_aff *pma);
1698 __isl_give isl_union_pw_aff *isl_union_pw_aff_reset_user(
1699 __isl_take isl_union_pw_aff *upa);
1700 __isl_give isl_multi_union_pw_aff *
1701 isl_multi_union_pw_aff_reset_user(
1702 __isl_take isl_multi_union_pw_aff *mupa);
1703 __isl_give isl_union_pw_multi_aff *
1704 isl_union_pw_multi_aff_reset_user(
1705 __isl_take isl_union_pw_multi_aff *upma);
1707 #include <isl/polynomial.h>
1708 __isl_give isl_pw_qpolynomial *
1709 isl_pw_qpolynomial_reset_user(
1710 __isl_take isl_pw_qpolynomial *pwqp);
1711 __isl_give isl_union_pw_qpolynomial *
1712 isl_union_pw_qpolynomial_reset_user(
1713 __isl_take isl_union_pw_qpolynomial *upwqp);
1714 __isl_give isl_pw_qpolynomial_fold *
1715 isl_pw_qpolynomial_fold_reset_user(
1716 __isl_take isl_pw_qpolynomial_fold *pwf);
1717 __isl_give isl_union_pw_qpolynomial_fold *
1718 isl_union_pw_qpolynomial_fold_reset_user(
1719 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1721 Spaces can be nested. In particular, the domain of a set or
1722 the domain or range of a relation can be a nested relation.
1723 This process is also called I<wrapping>.
1724 The functions for detecting, constructing and deconstructing
1725 such nested spaces can be found in the wrapping properties
1726 of L</"Unary Properties">, the wrapping operations
1727 of L</"Unary Operations"> and the Cartesian product operations
1728 of L</"Basic Operations">.
1730 Spaces can be created from other spaces
1731 using the functions described in L</"Unary Operations">
1732 and L</"Binary Operations">.
1736 A local space is essentially a space with
1737 zero or more existentially quantified variables.
1738 The local space of various objects can be obtained
1739 using the following functions.
1741 #include <isl/constraint.h>
1742 __isl_give isl_local_space *isl_constraint_get_local_space(
1743 __isl_keep isl_constraint *constraint);
1745 #include <isl/set.h>
1746 __isl_give isl_local_space *isl_basic_set_get_local_space(
1747 __isl_keep isl_basic_set *bset);
1749 #include <isl/map.h>
1750 __isl_give isl_local_space *isl_basic_map_get_local_space(
1751 __isl_keep isl_basic_map *bmap);
1753 #include <isl/aff.h>
1754 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1755 __isl_keep isl_aff *aff);
1756 __isl_give isl_local_space *isl_aff_get_local_space(
1757 __isl_keep isl_aff *aff);
1759 A new local space can be created from a space using
1761 #include <isl/local_space.h>
1762 __isl_give isl_local_space *isl_local_space_from_space(
1763 __isl_take isl_space *space);
1765 They can be inspected, modified, copied and freed using the following functions.
1767 #include <isl/local_space.h>
1768 isl_bool isl_local_space_is_params(
1769 __isl_keep isl_local_space *ls);
1770 isl_bool isl_local_space_is_set(
1771 __isl_keep isl_local_space *ls);
1772 __isl_give isl_space *isl_local_space_get_space(
1773 __isl_keep isl_local_space *ls);
1774 __isl_give isl_aff *isl_local_space_get_div(
1775 __isl_keep isl_local_space *ls, int pos);
1776 __isl_give isl_local_space *isl_local_space_copy(
1777 __isl_keep isl_local_space *ls);
1778 __isl_null isl_local_space *isl_local_space_free(
1779 __isl_take isl_local_space *ls);
1781 Note that C<isl_local_space_get_div> can only be used on local spaces
1784 Two local spaces can be compared using
1786 isl_bool isl_local_space_is_equal(
1787 __isl_keep isl_local_space *ls1,
1788 __isl_keep isl_local_space *ls2);
1790 Local spaces can be created from other local spaces
1791 using the functions described in L</"Unary Operations">
1792 and L</"Binary Operations">.
1794 =head2 Creating New Sets and Relations
1796 C<isl> has functions for creating some standard sets and relations.
1800 =item * Empty sets and relations
1802 __isl_give isl_basic_set *isl_basic_set_empty(
1803 __isl_take isl_space *space);
1804 __isl_give isl_basic_map *isl_basic_map_empty(
1805 __isl_take isl_space *space);
1806 __isl_give isl_set *isl_set_empty(
1807 __isl_take isl_space *space);
1808 __isl_give isl_map *isl_map_empty(
1809 __isl_take isl_space *space);
1810 __isl_give isl_union_set *isl_union_set_empty(
1811 __isl_take isl_space *space);
1812 __isl_give isl_union_map *isl_union_map_empty(
1813 __isl_take isl_space *space);
1815 For C<isl_union_set>s and C<isl_union_map>s, the space
1816 is only used to specify the parameters.
1818 =item * Universe sets and relations
1820 __isl_give isl_basic_set *isl_basic_set_universe(
1821 __isl_take isl_space *space);
1822 __isl_give isl_basic_map *isl_basic_map_universe(
1823 __isl_take isl_space *space);
1824 __isl_give isl_set *isl_set_universe(
1825 __isl_take isl_space *space);
1826 __isl_give isl_map *isl_map_universe(
1827 __isl_take isl_space *space);
1828 __isl_give isl_union_set *isl_union_set_universe(
1829 __isl_take isl_union_set *uset);
1830 __isl_give isl_union_map *isl_union_map_universe(
1831 __isl_take isl_union_map *umap);
1833 The sets and relations constructed by the functions above
1834 contain all integer values, while those constructed by the
1835 functions below only contain non-negative values.
1837 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1838 __isl_take isl_space *space);
1839 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1840 __isl_take isl_space *space);
1841 __isl_give isl_set *isl_set_nat_universe(
1842 __isl_take isl_space *space);
1843 __isl_give isl_map *isl_map_nat_universe(
1844 __isl_take isl_space *space);
1846 =item * Identity relations
1848 __isl_give isl_basic_map *isl_basic_map_identity(
1849 __isl_take isl_space *space);
1850 __isl_give isl_map *isl_map_identity(
1851 __isl_take isl_space *space);
1853 The number of input and output dimensions in C<space> needs
1856 =item * Lexicographic order
1858 __isl_give isl_map *isl_map_lex_lt(
1859 __isl_take isl_space *set_space);
1860 __isl_give isl_map *isl_map_lex_le(
1861 __isl_take isl_space *set_space);
1862 __isl_give isl_map *isl_map_lex_gt(
1863 __isl_take isl_space *set_space);
1864 __isl_give isl_map *isl_map_lex_ge(
1865 __isl_take isl_space *set_space);
1866 __isl_give isl_map *isl_map_lex_lt_first(
1867 __isl_take isl_space *space, unsigned n);
1868 __isl_give isl_map *isl_map_lex_le_first(
1869 __isl_take isl_space *space, unsigned n);
1870 __isl_give isl_map *isl_map_lex_gt_first(
1871 __isl_take isl_space *space, unsigned n);
1872 __isl_give isl_map *isl_map_lex_ge_first(
1873 __isl_take isl_space *space, unsigned n);
1875 The first four functions take a space for a B<set>
1876 and return relations that express that the elements in the domain
1877 are lexicographically less
1878 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1879 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1880 than the elements in the range.
1881 The last four functions take a space for a map
1882 and return relations that express that the first C<n> dimensions
1883 in the domain are lexicographically less
1884 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1885 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1886 than the first C<n> dimensions in the range.
1890 A basic set or relation can be converted to a set or relation
1891 using the following functions.
1893 __isl_give isl_set *isl_set_from_basic_set(
1894 __isl_take isl_basic_set *bset);
1895 __isl_give isl_map *isl_map_from_basic_map(
1896 __isl_take isl_basic_map *bmap);
1898 Sets and relations can be converted to union sets and relations
1899 using the following functions.
1901 __isl_give isl_union_set *isl_union_set_from_basic_set(
1902 __isl_take isl_basic_set *bset);
1903 __isl_give isl_union_map *isl_union_map_from_basic_map(
1904 __isl_take isl_basic_map *bmap);
1905 __isl_give isl_union_set *isl_union_set_from_set(
1906 __isl_take isl_set *set);
1907 __isl_give isl_union_map *isl_union_map_from_map(
1908 __isl_take isl_map *map);
1910 The inverse conversions below can only be used if the input
1911 union set or relation is known to contain elements in exactly one
1914 __isl_give isl_set *isl_set_from_union_set(
1915 __isl_take isl_union_set *uset);
1916 __isl_give isl_map *isl_map_from_union_map(
1917 __isl_take isl_union_map *umap);
1919 Sets and relations can be copied and freed again using the following
1922 __isl_give isl_basic_set *isl_basic_set_copy(
1923 __isl_keep isl_basic_set *bset);
1924 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1925 __isl_give isl_union_set *isl_union_set_copy(
1926 __isl_keep isl_union_set *uset);
1927 __isl_give isl_basic_map *isl_basic_map_copy(
1928 __isl_keep isl_basic_map *bmap);
1929 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1930 __isl_give isl_union_map *isl_union_map_copy(
1931 __isl_keep isl_union_map *umap);
1932 __isl_null isl_basic_set *isl_basic_set_free(
1933 __isl_take isl_basic_set *bset);
1934 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1935 __isl_null isl_union_set *isl_union_set_free(
1936 __isl_take isl_union_set *uset);
1937 __isl_null isl_basic_map *isl_basic_map_free(
1938 __isl_take isl_basic_map *bmap);
1939 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1940 __isl_null isl_union_map *isl_union_map_free(
1941 __isl_take isl_union_map *umap);
1943 Other sets and relations can be constructed by starting
1944 from a universe set or relation, adding equality and/or
1945 inequality constraints and then projecting out the
1946 existentially quantified variables, if any.
1947 Constraints can be constructed, manipulated and
1948 added to (or removed from) (basic) sets and relations
1949 using the following functions.
1951 #include <isl/constraint.h>
1952 __isl_give isl_constraint *isl_constraint_alloc_equality(
1953 __isl_take isl_local_space *ls);
1954 __isl_give isl_constraint *isl_constraint_alloc_inequality(
1955 __isl_take isl_local_space *ls);
1956 __isl_give isl_constraint *isl_constraint_set_constant_si(
1957 __isl_take isl_constraint *constraint, int v);
1958 __isl_give isl_constraint *isl_constraint_set_constant_val(
1959 __isl_take isl_constraint *constraint,
1960 __isl_take isl_val *v);
1961 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1962 __isl_take isl_constraint *constraint,
1963 enum isl_dim_type type, int pos, int v);
1964 __isl_give isl_constraint *
1965 isl_constraint_set_coefficient_val(
1966 __isl_take isl_constraint *constraint,
1967 enum isl_dim_type type, int pos,
1968 __isl_take isl_val *v);
1969 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1970 __isl_take isl_basic_map *bmap,
1971 __isl_take isl_constraint *constraint);
1972 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1973 __isl_take isl_basic_set *bset,
1974 __isl_take isl_constraint *constraint);
1975 __isl_give isl_map *isl_map_add_constraint(
1976 __isl_take isl_map *map,
1977 __isl_take isl_constraint *constraint);
1978 __isl_give isl_set *isl_set_add_constraint(
1979 __isl_take isl_set *set,
1980 __isl_take isl_constraint *constraint);
1982 For example, to create a set containing the even integers
1983 between 10 and 42, you would use the following code.
1986 isl_local_space *ls;
1988 isl_basic_set *bset;
1990 space = isl_space_set_alloc(ctx, 0, 2);
1991 bset = isl_basic_set_universe(isl_space_copy(space));
1992 ls = isl_local_space_from_space(space);
1994 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
1995 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1996 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1997 bset = isl_basic_set_add_constraint(bset, c);
1999 c = isl_constraint_alloc_inequality(isl_local_space_copy(ls));
2000 c = isl_constraint_set_constant_si(c, -10);
2001 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
2002 bset = isl_basic_set_add_constraint(bset, c);
2004 c = isl_constraint_alloc_inequality(ls);
2005 c = isl_constraint_set_constant_si(c, 42);
2006 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2007 bset = isl_basic_set_add_constraint(bset, c);
2009 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
2013 isl_basic_set *bset;
2014 bset = isl_basic_set_read_from_str(ctx,
2015 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
2017 A basic set or relation can also be constructed from two matrices
2018 describing the equalities and the inequalities.
2020 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
2021 __isl_take isl_space *space,
2022 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2023 enum isl_dim_type c1,
2024 enum isl_dim_type c2, enum isl_dim_type c3,
2025 enum isl_dim_type c4);
2026 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
2027 __isl_take isl_space *space,
2028 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2029 enum isl_dim_type c1,
2030 enum isl_dim_type c2, enum isl_dim_type c3,
2031 enum isl_dim_type c4, enum isl_dim_type c5);
2033 The C<isl_dim_type> arguments indicate the order in which
2034 different kinds of variables appear in the input matrices
2035 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
2036 C<isl_dim_set> and C<isl_dim_div> for sets and
2037 of C<isl_dim_cst>, C<isl_dim_param>,
2038 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
2040 A (basic or union) set or relation can also be constructed from a
2041 (union) (piecewise) (multiple) affine expression
2042 or a list of affine expressions
2043 (See L</"Functions">), provided these affine expressions do not
2046 __isl_give isl_basic_map *isl_basic_map_from_aff(
2047 __isl_take isl_aff *aff);
2048 __isl_give isl_map *isl_map_from_aff(
2049 __isl_take isl_aff *aff);
2050 __isl_give isl_set *isl_set_from_pw_aff(
2051 __isl_take isl_pw_aff *pwaff);
2052 __isl_give isl_map *isl_map_from_pw_aff(
2053 __isl_take isl_pw_aff *pwaff);
2054 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
2055 __isl_take isl_space *domain_space,
2056 __isl_take isl_aff_list *list);
2057 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
2058 __isl_take isl_multi_aff *maff)
2059 __isl_give isl_map *isl_map_from_multi_aff(
2060 __isl_take isl_multi_aff *maff)
2061 __isl_give isl_set *isl_set_from_pw_multi_aff(
2062 __isl_take isl_pw_multi_aff *pma);
2063 __isl_give isl_map *isl_map_from_pw_multi_aff(
2064 __isl_take isl_pw_multi_aff *pma);
2065 __isl_give isl_set *isl_set_from_multi_pw_aff(
2066 __isl_take isl_multi_pw_aff *mpa);
2067 __isl_give isl_map *isl_map_from_multi_pw_aff(
2068 __isl_take isl_multi_pw_aff *mpa);
2069 __isl_give isl_union_map *isl_union_map_from_union_pw_aff(
2070 __isl_take isl_union_pw_aff *upa);
2071 __isl_give isl_union_map *
2072 isl_union_map_from_union_pw_multi_aff(
2073 __isl_take isl_union_pw_multi_aff *upma);
2074 __isl_give isl_union_map *
2075 isl_union_map_from_multi_union_pw_aff(
2076 __isl_take isl_multi_union_pw_aff *mupa);
2078 The C<domain_space> argument describes the domain of the resulting
2079 basic relation. It is required because the C<list> may consist
2080 of zero affine expressions.
2081 The C<mupa> passed to C<isl_union_map_from_multi_union_pw_aff>
2082 is not allowed to be zero-dimensional. The domain of the result
2083 is the shared domain of the union piecewise affine elements.
2085 =head2 Inspecting Sets and Relations
2087 Usually, the user should not have to care about the actual constraints
2088 of the sets and maps, but should instead apply the abstract operations
2089 explained in the following sections.
2090 Occasionally, however, it may be required to inspect the individual
2091 coefficients of the constraints. This section explains how to do so.
2092 In these cases, it may also be useful to have C<isl> compute
2093 an explicit representation of the existentially quantified variables.
2095 __isl_give isl_set *isl_set_compute_divs(
2096 __isl_take isl_set *set);
2097 __isl_give isl_map *isl_map_compute_divs(
2098 __isl_take isl_map *map);
2099 __isl_give isl_union_set *isl_union_set_compute_divs(
2100 __isl_take isl_union_set *uset);
2101 __isl_give isl_union_map *isl_union_map_compute_divs(
2102 __isl_take isl_union_map *umap);
2104 This explicit representation defines the existentially quantified
2105 variables as integer divisions of the other variables, possibly
2106 including earlier existentially quantified variables.
2107 An explicitly represented existentially quantified variable therefore
2108 has a unique value when the values of the other variables are known.
2110 Alternatively, the existentially quantified variables can be removed
2111 using the following functions, which compute an overapproximation.
2113 __isl_give isl_basic_set *isl_basic_set_remove_divs(
2114 __isl_take isl_basic_set *bset);
2115 __isl_give isl_basic_map *isl_basic_map_remove_divs(
2116 __isl_take isl_basic_map *bmap);
2117 __isl_give isl_set *isl_set_remove_divs(
2118 __isl_take isl_set *set);
2119 __isl_give isl_map *isl_map_remove_divs(
2120 __isl_take isl_map *map);
2122 It is also possible to only remove those divs that are defined
2123 in terms of a given range of dimensions or only those for which
2124 no explicit representation is known.
2126 __isl_give isl_basic_set *
2127 isl_basic_set_remove_divs_involving_dims(
2128 __isl_take isl_basic_set *bset,
2129 enum isl_dim_type type,
2130 unsigned first, unsigned n);
2131 __isl_give isl_basic_map *
2132 isl_basic_map_remove_divs_involving_dims(
2133 __isl_take isl_basic_map *bmap,
2134 enum isl_dim_type type,
2135 unsigned first, unsigned n);
2136 __isl_give isl_set *isl_set_remove_divs_involving_dims(
2137 __isl_take isl_set *set, enum isl_dim_type type,
2138 unsigned first, unsigned n);
2139 __isl_give isl_map *isl_map_remove_divs_involving_dims(
2140 __isl_take isl_map *map, enum isl_dim_type type,
2141 unsigned first, unsigned n);
2143 __isl_give isl_basic_set *
2144 isl_basic_set_remove_unknown_divs(
2145 __isl_take isl_basic_set *bset);
2146 __isl_give isl_set *isl_set_remove_unknown_divs(
2147 __isl_take isl_set *set);
2148 __isl_give isl_map *isl_map_remove_unknown_divs(
2149 __isl_take isl_map *map);
2151 To iterate over all the sets or maps in a union set or map, use
2153 isl_stat isl_union_set_foreach_set(
2154 __isl_keep isl_union_set *uset,
2155 isl_stat (*fn)(__isl_take isl_set *set, void *user),
2157 isl_stat isl_union_map_foreach_map(
2158 __isl_keep isl_union_map *umap,
2159 isl_stat (*fn)(__isl_take isl_map *map, void *user),
2162 These functions call the callback function once for each
2163 (pair of) space(s) for which there are elements in the input.
2164 The argument to the callback contains all elements in the input
2165 with that (pair of) space(s).
2167 The number of sets or maps in a union set or map can be obtained
2170 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
2171 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
2173 To extract the set or map in a given space from a union, use
2175 __isl_give isl_set *isl_union_set_extract_set(
2176 __isl_keep isl_union_set *uset,
2177 __isl_take isl_space *space);
2178 __isl_give isl_map *isl_union_map_extract_map(
2179 __isl_keep isl_union_map *umap,
2180 __isl_take isl_space *space);
2182 To iterate over all the basic sets or maps in a set or map, use
2184 isl_stat isl_set_foreach_basic_set(__isl_keep isl_set *set,
2185 isl_stat (*fn)(__isl_take isl_basic_set *bset,
2188 isl_stat isl_map_foreach_basic_map(__isl_keep isl_map *map,
2189 isl_stat (*fn)(__isl_take isl_basic_map *bmap,
2193 The callback function C<fn> should return 0 if successful and
2194 -1 if an error occurs. In the latter case, or if any other error
2195 occurs, the above functions will return -1.
2197 It should be noted that C<isl> does not guarantee that
2198 the basic sets or maps passed to C<fn> are disjoint.
2199 If this is required, then the user should call one of
2200 the following functions first.
2202 __isl_give isl_set *isl_set_make_disjoint(
2203 __isl_take isl_set *set);
2204 __isl_give isl_map *isl_map_make_disjoint(
2205 __isl_take isl_map *map);
2207 The number of basic sets in a set can be obtained
2208 or the number of basic maps in a map can be obtained
2211 #include <isl/set.h>
2212 int isl_set_n_basic_set(__isl_keep isl_set *set);
2214 #include <isl/map.h>
2215 int isl_map_n_basic_map(__isl_keep isl_map *map);
2217 It is also possible to obtain a list of basic sets from a set
2219 #include <isl/set.h>
2220 __isl_give isl_basic_set_list *isl_set_get_basic_set_list(
2221 __isl_keep isl_set *set);
2223 The returned list can be manipulated using the functions in L<"Lists">.
2225 To iterate over the constraints of a basic set or map, use
2227 #include <isl/constraint.h>
2229 int isl_basic_set_n_constraint(
2230 __isl_keep isl_basic_set *bset);
2231 isl_stat isl_basic_set_foreach_constraint(
2232 __isl_keep isl_basic_set *bset,
2233 isl_stat (*fn)(__isl_take isl_constraint *c,
2236 int isl_basic_map_n_constraint(
2237 __isl_keep isl_basic_map *bmap);
2238 isl_stat isl_basic_map_foreach_constraint(
2239 __isl_keep isl_basic_map *bmap,
2240 isl_stat (*fn)(__isl_take isl_constraint *c,
2243 __isl_null isl_constraint *isl_constraint_free(
2244 __isl_take isl_constraint *c);
2246 Again, the callback function C<fn> should return 0 if successful and
2247 -1 if an error occurs. In the latter case, or if any other error
2248 occurs, the above functions will return -1.
2249 The constraint C<c> represents either an equality or an inequality.
2250 Use the following function to find out whether a constraint
2251 represents an equality. If not, it represents an inequality.
2253 isl_bool isl_constraint_is_equality(
2254 __isl_keep isl_constraint *constraint);
2256 It is also possible to obtain a list of constraints from a basic
2259 #include <isl/constraint.h>
2260 __isl_give isl_constraint_list *
2261 isl_basic_map_get_constraint_list(
2262 __isl_keep isl_basic_map *bmap);
2263 __isl_give isl_constraint_list *
2264 isl_basic_set_get_constraint_list(
2265 __isl_keep isl_basic_set *bset);
2267 These functions require that all existentially quantified variables
2268 have an explicit representation.
2269 The returned list can be manipulated using the functions in L<"Lists">.
2271 The coefficients of the constraints can be inspected using
2272 the following functions.
2274 isl_bool isl_constraint_is_lower_bound(
2275 __isl_keep isl_constraint *constraint,
2276 enum isl_dim_type type, unsigned pos);
2277 isl_bool isl_constraint_is_upper_bound(
2278 __isl_keep isl_constraint *constraint,
2279 enum isl_dim_type type, unsigned pos);
2280 __isl_give isl_val *isl_constraint_get_constant_val(
2281 __isl_keep isl_constraint *constraint);
2282 __isl_give isl_val *isl_constraint_get_coefficient_val(
2283 __isl_keep isl_constraint *constraint,
2284 enum isl_dim_type type, int pos);
2286 The explicit representations of the existentially quantified
2287 variables can be inspected using the following function.
2288 Note that the user is only allowed to use this function
2289 if the inspected set or map is the result of a call
2290 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2291 The existentially quantified variable is equal to the floor
2292 of the returned affine expression. The affine expression
2293 itself can be inspected using the functions in
2296 __isl_give isl_aff *isl_constraint_get_div(
2297 __isl_keep isl_constraint *constraint, int pos);
2299 To obtain the constraints of a basic set or map in matrix
2300 form, use the following functions.
2302 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2303 __isl_keep isl_basic_set *bset,
2304 enum isl_dim_type c1, enum isl_dim_type c2,
2305 enum isl_dim_type c3, enum isl_dim_type c4);
2306 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2307 __isl_keep isl_basic_set *bset,
2308 enum isl_dim_type c1, enum isl_dim_type c2,
2309 enum isl_dim_type c3, enum isl_dim_type c4);
2310 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2311 __isl_keep isl_basic_map *bmap,
2312 enum isl_dim_type c1,
2313 enum isl_dim_type c2, enum isl_dim_type c3,
2314 enum isl_dim_type c4, enum isl_dim_type c5);
2315 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2316 __isl_keep isl_basic_map *bmap,
2317 enum isl_dim_type c1,
2318 enum isl_dim_type c2, enum isl_dim_type c3,
2319 enum isl_dim_type c4, enum isl_dim_type c5);
2321 The C<isl_dim_type> arguments dictate the order in which
2322 different kinds of variables appear in the resulting matrix.
2323 For set inputs, they should be a permutation of
2324 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
2325 For map inputs, they should be a permutation of
2326 C<isl_dim_cst>, C<isl_dim_param>,
2327 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2331 Points are elements of a set. They can be used to construct
2332 simple sets (boxes) or they can be used to represent the
2333 individual elements of a set.
2334 The zero point (the origin) can be created using
2336 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2338 The coordinates of a point can be inspected, set and changed
2341 __isl_give isl_val *isl_point_get_coordinate_val(
2342 __isl_keep isl_point *pnt,
2343 enum isl_dim_type type, int pos);
2344 __isl_give isl_point *isl_point_set_coordinate_val(
2345 __isl_take isl_point *pnt,
2346 enum isl_dim_type type, int pos,
2347 __isl_take isl_val *v);
2349 __isl_give isl_point *isl_point_add_ui(
2350 __isl_take isl_point *pnt,
2351 enum isl_dim_type type, int pos, unsigned val);
2352 __isl_give isl_point *isl_point_sub_ui(
2353 __isl_take isl_point *pnt,
2354 enum isl_dim_type type, int pos, unsigned val);
2356 Points can be copied or freed using
2358 __isl_give isl_point *isl_point_copy(
2359 __isl_keep isl_point *pnt);
2360 void isl_point_free(__isl_take isl_point *pnt);
2362 A singleton set can be created from a point using
2364 __isl_give isl_basic_set *isl_basic_set_from_point(
2365 __isl_take isl_point *pnt);
2366 __isl_give isl_set *isl_set_from_point(
2367 __isl_take isl_point *pnt);
2368 __isl_give isl_union_set *isl_union_set_from_point(
2369 __isl_take isl_point *pnt);
2371 and a box can be created from two opposite extremal points using
2373 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2374 __isl_take isl_point *pnt1,
2375 __isl_take isl_point *pnt2);
2376 __isl_give isl_set *isl_set_box_from_points(
2377 __isl_take isl_point *pnt1,
2378 __isl_take isl_point *pnt2);
2380 All elements of a B<bounded> (union) set can be enumerated using
2381 the following functions.
2383 isl_stat isl_set_foreach_point(__isl_keep isl_set *set,
2384 isl_stat (*fn)(__isl_take isl_point *pnt,
2387 isl_stat isl_union_set_foreach_point(
2388 __isl_keep isl_union_set *uset,
2389 isl_stat (*fn)(__isl_take isl_point *pnt,
2393 The function C<fn> is called for each integer point in
2394 C<set> with as second argument the last argument of
2395 the C<isl_set_foreach_point> call. The function C<fn>
2396 should return C<0> on success and C<-1> on failure.
2397 In the latter case, C<isl_set_foreach_point> will stop
2398 enumerating and return C<-1> as well.
2399 If the enumeration is performed successfully and to completion,
2400 then C<isl_set_foreach_point> returns C<0>.
2402 To obtain a single point of a (basic or union) set, use
2404 __isl_give isl_point *isl_basic_set_sample_point(
2405 __isl_take isl_basic_set *bset);
2406 __isl_give isl_point *isl_set_sample_point(
2407 __isl_take isl_set *set);
2408 __isl_give isl_point *isl_union_set_sample_point(
2409 __isl_take isl_union_set *uset);
2411 If C<set> does not contain any (integer) points, then the
2412 resulting point will be ``void'', a property that can be
2415 isl_bool isl_point_is_void(__isl_keep isl_point *pnt);
2419 Besides sets and relation, C<isl> also supports various types of functions.
2420 Each of these types is derived from the value type (see L</"Values">)
2421 or from one of two primitive function types
2422 through the application of zero or more type constructors.
2423 We first describe the primitive type and then we describe
2424 the types derived from these primitive types.
2426 =head3 Primitive Functions
2428 C<isl> support two primitive function types, quasi-affine
2429 expressions and quasipolynomials.
2430 A quasi-affine expression is defined either over a parameter
2431 space or over a set and is composed of integer constants,
2432 parameters and set variables, addition, subtraction and
2433 integer division by an integer constant.
2434 For example, the quasi-affine expression
2436 [n] -> { [x] -> [2*floor((4 n + x)/9] }
2438 maps C<x> to C<2*floor((4 n + x)/9>.
2439 A quasipolynomial is a polynomial expression in quasi-affine
2440 expression. That is, it additionally allows for multiplication.
2441 Note, though, that it is not allowed to construct an integer
2442 division of an expression involving multiplications.
2443 Here is an example of a quasipolynomial that is not
2444 quasi-affine expression
2446 [n] -> { [x] -> (n*floor((4 n + x)/9) }
2448 Note that the external representations of quasi-affine expressions
2449 and quasipolynomials are different. Quasi-affine expressions
2450 use a notation with square brackets just like binary relations,
2451 while quasipolynomials do not. This might change at some point.
2453 If a primitive function is defined over a parameter space,
2454 then the space of the function itself is that of a set.
2455 If it is defined over a set, then the space of the function
2456 is that of a relation. In both cases, the set space (or
2457 the output space) is single-dimensional, anonymous and unstructured.
2458 To create functions with multiple dimensions or with other kinds
2459 of set or output spaces, use multiple expressions
2460 (see L</"Multiple Expressions">).
2464 =item * Quasi-affine Expressions
2466 Besides the expressions described above, a quasi-affine
2467 expression can also be set to NaN. Such expressions
2468 typically represent a failure to represent a result
2469 as a quasi-affine expression.
2471 The zero quasi affine expression or the quasi affine expression
2472 that is equal to a given value or
2473 a specified dimension on a given domain can be created using
2475 #include <isl/aff.h>
2476 __isl_give isl_aff *isl_aff_zero_on_domain(
2477 __isl_take isl_local_space *ls);
2478 __isl_give isl_aff *isl_aff_val_on_domain(
2479 __isl_take isl_local_space *ls,
2480 __isl_take isl_val *val);
2481 __isl_give isl_aff *isl_aff_var_on_domain(
2482 __isl_take isl_local_space *ls,
2483 enum isl_dim_type type, unsigned pos);
2484 __isl_give isl_aff *isl_aff_nan_on_domain(
2485 __isl_take isl_local_space *ls);
2487 Quasi affine expressions can be copied and freed using
2489 #include <isl/aff.h>
2490 __isl_give isl_aff *isl_aff_copy(
2491 __isl_keep isl_aff *aff);
2492 __isl_null isl_aff *isl_aff_free(
2493 __isl_take isl_aff *aff);
2495 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2496 using the following function. The constraint is required to have
2497 a non-zero coefficient for the specified dimension.
2499 #include <isl/constraint.h>
2500 __isl_give isl_aff *isl_constraint_get_bound(
2501 __isl_keep isl_constraint *constraint,
2502 enum isl_dim_type type, int pos);
2504 The entire affine expression of the constraint can also be extracted
2505 using the following function.
2507 #include <isl/constraint.h>
2508 __isl_give isl_aff *isl_constraint_get_aff(
2509 __isl_keep isl_constraint *constraint);
2511 Conversely, an equality constraint equating
2512 the affine expression to zero or an inequality constraint enforcing
2513 the affine expression to be non-negative, can be constructed using
2515 __isl_give isl_constraint *isl_equality_from_aff(
2516 __isl_take isl_aff *aff);
2517 __isl_give isl_constraint *isl_inequality_from_aff(
2518 __isl_take isl_aff *aff);
2520 The coefficients and the integer divisions of an affine expression
2521 can be inspected using the following functions.
2523 #include <isl/aff.h>
2524 __isl_give isl_val *isl_aff_get_constant_val(
2525 __isl_keep isl_aff *aff);
2526 __isl_give isl_val *isl_aff_get_coefficient_val(
2527 __isl_keep isl_aff *aff,
2528 enum isl_dim_type type, int pos);
2529 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2530 enum isl_dim_type type, int pos);
2531 __isl_give isl_val *isl_aff_get_denominator_val(
2532 __isl_keep isl_aff *aff);
2533 __isl_give isl_aff *isl_aff_get_div(
2534 __isl_keep isl_aff *aff, int pos);
2536 They can be modified using the following functions.
2538 #include <isl/aff.h>
2539 __isl_give isl_aff *isl_aff_set_constant_si(
2540 __isl_take isl_aff *aff, int v);
2541 __isl_give isl_aff *isl_aff_set_constant_val(
2542 __isl_take isl_aff *aff, __isl_take isl_val *v);
2543 __isl_give isl_aff *isl_aff_set_coefficient_si(
2544 __isl_take isl_aff *aff,
2545 enum isl_dim_type type, int pos, int v);
2546 __isl_give isl_aff *isl_aff_set_coefficient_val(
2547 __isl_take isl_aff *aff,
2548 enum isl_dim_type type, int pos,
2549 __isl_take isl_val *v);
2551 __isl_give isl_aff *isl_aff_add_constant_si(
2552 __isl_take isl_aff *aff, int v);
2553 __isl_give isl_aff *isl_aff_add_constant_val(
2554 __isl_take isl_aff *aff, __isl_take isl_val *v);
2555 __isl_give isl_aff *isl_aff_add_constant_num_si(
2556 __isl_take isl_aff *aff, int v);
2557 __isl_give isl_aff *isl_aff_add_coefficient_si(
2558 __isl_take isl_aff *aff,
2559 enum isl_dim_type type, int pos, int v);
2560 __isl_give isl_aff *isl_aff_add_coefficient_val(
2561 __isl_take isl_aff *aff,
2562 enum isl_dim_type type, int pos,
2563 __isl_take isl_val *v);
2565 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
2566 set the I<numerator> of the constant or coefficient, while
2567 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
2568 the constant or coefficient as a whole.
2569 The C<add_constant> and C<add_coefficient> functions add an integer
2570 or rational value to
2571 the possibly rational constant or coefficient.
2572 The C<add_constant_num> functions add an integer value to
2575 =item * Quasipolynomials
2577 Some simple quasipolynomials can be created using the following functions.
2579 #include <isl/polynomial.h>
2580 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2581 __isl_take isl_space *domain);
2582 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2583 __isl_take isl_space *domain);
2584 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2585 __isl_take isl_space *domain);
2586 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2587 __isl_take isl_space *domain);
2588 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2589 __isl_take isl_space *domain);
2590 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2591 __isl_take isl_space *domain,
2592 __isl_take isl_val *val);
2593 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2594 __isl_take isl_space *domain,
2595 enum isl_dim_type type, unsigned pos);
2596 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2597 __isl_take isl_aff *aff);
2599 Recall that the space in which a quasipolynomial lives is a map space
2600 with a one-dimensional range. The C<domain> argument in some of
2601 the functions above corresponds to the domain of this map space.
2603 Quasipolynomials can be copied and freed again using the following
2606 #include <isl/polynomial.h>
2607 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2608 __isl_keep isl_qpolynomial *qp);
2609 __isl_null isl_qpolynomial *isl_qpolynomial_free(
2610 __isl_take isl_qpolynomial *qp);
2612 The constant term of a quasipolynomial can be extracted using
2614 __isl_give isl_val *isl_qpolynomial_get_constant_val(
2615 __isl_keep isl_qpolynomial *qp);
2617 To iterate over all terms in a quasipolynomial,
2620 isl_stat isl_qpolynomial_foreach_term(
2621 __isl_keep isl_qpolynomial *qp,
2622 isl_stat (*fn)(__isl_take isl_term *term,
2623 void *user), void *user);
2625 The terms themselves can be inspected and freed using
2628 unsigned isl_term_dim(__isl_keep isl_term *term,
2629 enum isl_dim_type type);
2630 __isl_give isl_val *isl_term_get_coefficient_val(
2631 __isl_keep isl_term *term);
2632 int isl_term_get_exp(__isl_keep isl_term *term,
2633 enum isl_dim_type type, unsigned pos);
2634 __isl_give isl_aff *isl_term_get_div(
2635 __isl_keep isl_term *term, unsigned pos);
2636 void isl_term_free(__isl_take isl_term *term);
2638 Each term is a product of parameters, set variables and
2639 integer divisions. The function C<isl_term_get_exp>
2640 returns the exponent of a given dimensions in the given term.
2646 A reduction represents a maximum or a minimum of its
2648 The only reduction type defined by C<isl> is
2649 C<isl_qpolynomial_fold>.
2651 There are currently no functions to directly create such
2652 objects, but they do appear in the piecewise quasipolynomial
2653 reductions returned by the C<isl_pw_qpolynomial_bound> function.
2655 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
2657 Reductions can be copied and freed using
2658 the following functions.
2660 #include <isl/polynomial.h>
2661 __isl_give isl_qpolynomial_fold *
2662 isl_qpolynomial_fold_copy(
2663 __isl_keep isl_qpolynomial_fold *fold);
2664 void isl_qpolynomial_fold_free(
2665 __isl_take isl_qpolynomial_fold *fold);
2667 To iterate over all quasipolynomials in a reduction, use
2669 isl_stat isl_qpolynomial_fold_foreach_qpolynomial(
2670 __isl_keep isl_qpolynomial_fold *fold,
2671 isl_stat (*fn)(__isl_take isl_qpolynomial *qp,
2672 void *user), void *user);
2674 =head3 Multiple Expressions
2676 A multiple expression represents a sequence of zero or
2677 more base expressions, all defined on the same domain space.
2678 The domain space of the multiple expression is the same
2679 as that of the base expressions, but the range space
2680 can be any space. In case the base expressions have
2681 a set space, the corresponding multiple expression
2682 also has a set space.
2683 Objects of the value type do not have an associated space.
2684 The space of a multiple value is therefore always a set space.
2685 Similarly, the space of a multiple union piecewise
2686 affine expression is always a set space.
2688 The multiple expression types defined by C<isl>
2689 are C<isl_multi_val>, C<isl_multi_aff>, C<isl_multi_pw_aff>,
2690 C<isl_multi_union_pw_aff>.
2692 A multiple expression with the value zero for
2693 each output (or set) dimension can be created
2694 using the following functions.
2696 #include <isl/val.h>
2697 __isl_give isl_multi_val *isl_multi_val_zero(
2698 __isl_take isl_space *space);
2700 #include <isl/aff.h>
2701 __isl_give isl_multi_aff *isl_multi_aff_zero(
2702 __isl_take isl_space *space);
2703 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
2704 __isl_take isl_space *space);
2705 __isl_give isl_multi_union_pw_aff *
2706 isl_multi_union_pw_aff_zero(
2707 __isl_take isl_space *space);
2709 Since there is no canonical way of representing a zero
2710 value of type C<isl_union_pw_aff>, the space passed
2711 to C<isl_multi_union_pw_aff_zero> needs to be zero-dimensional.
2713 An identity function can be created using the following
2714 functions. The space needs to be that of a relation
2715 with the same number of input and output dimensions.
2717 #include <isl/aff.h>
2718 __isl_give isl_multi_aff *isl_multi_aff_identity(
2719 __isl_take isl_space *space);
2720 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
2721 __isl_take isl_space *space);
2723 A function that performs a projection on a universe
2724 relation or set can be created using the following functions.
2725 See also the corresponding
2726 projection operations in L</"Unary Operations">.
2728 #include <isl/aff.h>
2729 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
2730 __isl_take isl_space *space);
2731 __isl_give isl_multi_aff *isl_multi_aff_range_map(
2732 __isl_take isl_space *space);
2733 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
2734 __isl_take isl_space *space,
2735 enum isl_dim_type type,
2736 unsigned first, unsigned n);
2738 A multiple expression can be created from a single
2739 base expression using the following functions.
2740 The space of the created multiple expression is the same
2741 as that of the base expression, except for
2742 C<isl_multi_union_pw_aff_from_union_pw_aff> where the input
2743 lives in a parameter space and the output lives
2744 in a single-dimensional set space.
2746 #include <isl/aff.h>
2747 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
2748 __isl_take isl_aff *aff);
2749 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
2750 __isl_take isl_pw_aff *pa);
2751 __isl_give isl_multi_union_pw_aff *
2752 isl_multi_union_pw_aff_from_union_pw_aff(
2753 __isl_take isl_union_pw_aff *upa);
2755 A multiple expression can be created from a list
2756 of base expression in a specified space.
2757 The domain of this space needs to be the same
2758 as the domains of the base expressions in the list.
2759 If the base expressions have a set space (or no associated space),
2760 then this space also needs to be a set space.
2762 #include <isl/val.h>
2763 __isl_give isl_multi_val *isl_multi_val_from_val_list(
2764 __isl_take isl_space *space,
2765 __isl_take isl_val_list *list);
2767 #include <isl/aff.h>
2768 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2769 __isl_take isl_space *space,
2770 __isl_take isl_aff_list *list);
2771 __isl_give isl_multi_pw_aff *
2772 isl_multi_pw_aff_from_pw_aff_list(
2773 __isl_take isl_space *space,
2774 __isl_take isl_pw_aff_list *list);
2775 __isl_give isl_multi_union_pw_aff *
2776 isl_multi_union_pw_aff_from_union_pw_aff_list(
2777 __isl_take isl_space *space,
2778 __isl_take isl_union_pw_aff_list *list);
2780 As a convenience, a multiple piecewise expression can
2781 also be created from a multiple expression.
2782 Each piecewise expression in the result has a single
2785 #include <isl/aff.h>
2786 __isl_give isl_multi_pw_aff *
2787 isl_multi_pw_aff_from_multi_aff(
2788 __isl_take isl_multi_aff *ma);
2790 Similarly, a multiple union expression can be
2791 created from a multiple expression.
2793 #include <isl/aff.h>
2794 __isl_give isl_multi_union_pw_aff *
2795 isl_multi_union_pw_aff_from_multi_aff(
2796 __isl_take isl_multi_aff *ma);
2797 __isl_give isl_multi_union_pw_aff *
2798 isl_multi_union_pw_aff_from_multi_pw_aff(
2799 __isl_take isl_multi_pw_aff *mpa);
2801 A multiple quasi-affine expression can be created from
2802 a multiple value with a given domain space using the following
2805 #include <isl/aff.h>
2806 __isl_give isl_multi_aff *
2807 isl_multi_aff_multi_val_on_space(
2808 __isl_take isl_space *space,
2809 __isl_take isl_multi_val *mv);
2812 a multiple union piecewise affine expression can be created from
2813 a multiple value with a given domain or
2814 a multiple affine expression with a given domain
2815 using the following functions.
2817 #include <isl/aff.h>
2818 __isl_give isl_multi_union_pw_aff *
2819 isl_multi_union_pw_aff_multi_val_on_domain(
2820 __isl_take isl_union_set *domain,
2821 __isl_take isl_multi_val *mv);
2822 __isl_give isl_multi_union_pw_aff *
2823 isl_multi_union_pw_aff_multi_aff_on_domain(
2824 __isl_take isl_union_set *domain,
2825 __isl_take isl_multi_aff *ma);
2827 Multiple expressions can be copied and freed using
2828 the following functions.
2830 #include <isl/val.h>
2831 __isl_give isl_multi_val *isl_multi_val_copy(
2832 __isl_keep isl_multi_val *mv);
2833 __isl_null isl_multi_val *isl_multi_val_free(
2834 __isl_take isl_multi_val *mv);
2836 #include <isl/aff.h>
2837 __isl_give isl_multi_aff *isl_multi_aff_copy(
2838 __isl_keep isl_multi_aff *maff);
2839 __isl_null isl_multi_aff *isl_multi_aff_free(
2840 __isl_take isl_multi_aff *maff);
2841 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
2842 __isl_keep isl_multi_pw_aff *mpa);
2843 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
2844 __isl_take isl_multi_pw_aff *mpa);
2845 __isl_give isl_multi_union_pw_aff *
2846 isl_multi_union_pw_aff_copy(
2847 __isl_keep isl_multi_union_pw_aff *mupa);
2848 __isl_null isl_multi_union_pw_aff *
2849 isl_multi_union_pw_aff_free(
2850 __isl_take isl_multi_union_pw_aff *mupa);
2852 The base expression at a given position of a multiple
2853 expression can be extracted using the following functions.
2855 #include <isl/val.h>
2856 __isl_give isl_val *isl_multi_val_get_val(
2857 __isl_keep isl_multi_val *mv, int pos);
2859 #include <isl/aff.h>
2860 __isl_give isl_aff *isl_multi_aff_get_aff(
2861 __isl_keep isl_multi_aff *multi, int pos);
2862 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
2863 __isl_keep isl_multi_pw_aff *mpa, int pos);
2864 __isl_give isl_union_pw_aff *
2865 isl_multi_union_pw_aff_get_union_pw_aff(
2866 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
2868 It can be replaced using the following functions.
2870 #include <isl/val.h>
2871 __isl_give isl_multi_val *isl_multi_val_set_val(
2872 __isl_take isl_multi_val *mv, int pos,
2873 __isl_take isl_val *val);
2875 #include <isl/aff.h>
2876 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
2877 __isl_take isl_multi_aff *multi, int pos,
2878 __isl_take isl_aff *aff);
2879 __isl_give isl_multi_union_pw_aff *
2880 isl_multi_union_pw_aff_set_union_pw_aff(
2881 __isl_take isl_multi_union_pw_aff *mupa, int pos,
2882 __isl_take isl_union_pw_aff *upa);
2884 As a convenience, a sequence of base expressions that have
2885 their domains in a given space can be extracted from a sequence
2886 of union expressions using the following function.
2888 #include <isl/aff.h>
2889 __isl_give isl_multi_pw_aff *
2890 isl_multi_union_pw_aff_extract_multi_pw_aff(
2891 __isl_keep isl_multi_union_pw_aff *mupa,
2892 __isl_take isl_space *space);
2894 Note that there is a difference between C<isl_multi_union_pw_aff>
2895 and C<isl_union_pw_multi_aff> objects. The first is a sequence
2896 of unions of piecewise expressions, while the second is a union
2897 of piecewise sequences. In particular, multiple affine expressions
2898 in an C<isl_union_pw_multi_aff> may live in different spaces,
2899 while there is only a single multiple expression in
2900 an C<isl_multi_union_pw_aff>, which can therefore only live
2901 in a single space. This means that not every
2902 C<isl_union_pw_multi_aff> can be converted to
2903 an C<isl_multi_union_pw_aff>. Conversely, a zero-dimensional
2904 C<isl_multi_union_pw_aff> carries no information
2905 about any possible domain and therefore cannot be converted
2906 to an C<isl_union_pw_multi_aff>. Moreover, the elements
2907 of an C<isl_multi_union_pw_aff> may be defined over different domains,
2908 while each multiple expression inside an C<isl_union_pw_multi_aff>
2909 has a single domain. The conversion of an C<isl_union_pw_multi_aff>
2910 of dimension greater than one may therefore not be exact.
2911 The following functions can
2912 be used to perform these conversions when they are possible.
2914 #include <isl/aff.h>
2915 __isl_give isl_multi_union_pw_aff *
2916 isl_multi_union_pw_aff_from_union_pw_multi_aff(
2917 __isl_take isl_union_pw_multi_aff *upma);
2918 __isl_give isl_union_pw_multi_aff *
2919 isl_union_pw_multi_aff_from_multi_union_pw_aff(
2920 __isl_take isl_multi_union_pw_aff *mupa);
2922 =head3 Piecewise Expressions
2924 A piecewise expression is an expression that is described
2925 using zero or more base expression defined over the same
2926 number of cells in the domain space of the base expressions.
2927 All base expressions are defined over the same
2928 domain space and the cells are disjoint.
2929 The space of a piecewise expression is the same as
2930 that of the base expressions.
2931 If the union of the cells is a strict subset of the domain
2932 space, then the value of the piecewise expression outside
2933 this union is different for types derived from quasi-affine
2934 expressions and those derived from quasipolynomials.
2935 Piecewise expressions derived from quasi-affine expressions
2936 are considered to be undefined outside the union of their cells.
2937 Piecewise expressions derived from quasipolynomials
2938 are considered to be zero outside the union of their cells.
2940 Piecewise quasipolynomials are mainly used by the C<barvinok>
2941 library for representing the number of elements in a parametric set or map.
2942 For example, the piecewise quasipolynomial
2944 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2946 represents the number of points in the map
2948 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2950 The piecewise expression types defined by C<isl>
2951 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
2952 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
2954 A piecewise expression with no cells can be created using
2955 the following functions.
2957 #include <isl/aff.h>
2958 __isl_give isl_pw_aff *isl_pw_aff_empty(
2959 __isl_take isl_space *space);
2960 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
2961 __isl_take isl_space *space);
2963 A piecewise expression with a single universe cell can be
2964 created using the following functions.
2966 #include <isl/aff.h>
2967 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2968 __isl_take isl_aff *aff);
2969 __isl_give isl_pw_multi_aff *
2970 isl_pw_multi_aff_from_multi_aff(
2971 __isl_take isl_multi_aff *ma);
2973 #include <isl/polynomial.h>
2974 __isl_give isl_pw_qpolynomial *
2975 isl_pw_qpolynomial_from_qpolynomial(
2976 __isl_take isl_qpolynomial *qp);
2978 A piecewise expression with a single specified cell can be
2979 created using the following functions.
2981 #include <isl/aff.h>
2982 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2983 __isl_take isl_set *set, __isl_take isl_aff *aff);
2984 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
2985 __isl_take isl_set *set,
2986 __isl_take isl_multi_aff *maff);
2988 #include <isl/polynomial.h>
2989 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2990 __isl_take isl_set *set,
2991 __isl_take isl_qpolynomial *qp);
2993 The following convenience functions first create a base expression and
2994 then create a piecewise expression over a universe domain.
2996 #include <isl/aff.h>
2997 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
2998 __isl_take isl_local_space *ls);
2999 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3000 __isl_take isl_local_space *ls,
3001 enum isl_dim_type type, unsigned pos);
3002 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3003 __isl_take isl_local_space *ls);
3004 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
3005 __isl_take isl_space *space);
3006 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3007 __isl_take isl_space *space);
3008 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
3009 __isl_take isl_space *space);
3010 __isl_give isl_pw_multi_aff *
3011 isl_pw_multi_aff_project_out_map(
3012 __isl_take isl_space *space,
3013 enum isl_dim_type type,
3014 unsigned first, unsigned n);
3016 #include <isl/polynomial.h>
3017 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3018 __isl_take isl_space *space);
3020 The following convenience functions first create a base expression and
3021 then create a piecewise expression over a given domain.
3023 #include <isl/aff.h>
3024 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
3025 __isl_take isl_set *domain,
3026 __isl_take isl_val *v);
3027 __isl_give isl_pw_multi_aff *
3028 isl_pw_multi_aff_multi_val_on_domain(
3029 __isl_take isl_set *domain,
3030 __isl_take isl_multi_val *mv);
3032 As a convenience, a piecewise multiple expression can
3033 also be created from a piecewise expression.
3034 Each multiple expression in the result is derived
3035 from the corresponding base expression.
3037 #include <isl/aff.h>
3038 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
3039 __isl_take isl_pw_aff *pa);
3041 Similarly, a piecewise quasipolynomial can be
3042 created from a piecewise quasi-affine expression using
3043 the following function.
3045 #include <isl/polynomial.h>
3046 __isl_give isl_pw_qpolynomial *
3047 isl_pw_qpolynomial_from_pw_aff(
3048 __isl_take isl_pw_aff *pwaff);
3050 Piecewise expressions can be copied and freed using the following functions.
3052 #include <isl/aff.h>
3053 __isl_give isl_pw_aff *isl_pw_aff_copy(
3054 __isl_keep isl_pw_aff *pwaff);
3055 __isl_null isl_pw_aff *isl_pw_aff_free(
3056 __isl_take isl_pw_aff *pwaff);
3057 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3058 __isl_keep isl_pw_multi_aff *pma);
3059 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
3060 __isl_take isl_pw_multi_aff *pma);
3062 #include <isl/polynomial.h>
3063 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3064 __isl_keep isl_pw_qpolynomial *pwqp);
3065 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
3066 __isl_take isl_pw_qpolynomial *pwqp);
3067 __isl_give isl_pw_qpolynomial_fold *
3068 isl_pw_qpolynomial_fold_copy(
3069 __isl_keep isl_pw_qpolynomial_fold *pwf);
3070 __isl_null isl_pw_qpolynomial_fold *
3071 isl_pw_qpolynomial_fold_free(
3072 __isl_take isl_pw_qpolynomial_fold *pwf);
3074 To iterate over the different cells of a piecewise expression,
3075 use the following functions.
3077 #include <isl/aff.h>
3078 isl_bool isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3079 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3080 isl_stat isl_pw_aff_foreach_piece(
3081 __isl_keep isl_pw_aff *pwaff,
3082 isl_stat (*fn)(__isl_take isl_set *set,
3083 __isl_take isl_aff *aff,
3084 void *user), void *user);
3085 isl_stat isl_pw_multi_aff_foreach_piece(
3086 __isl_keep isl_pw_multi_aff *pma,
3087 isl_stat (*fn)(__isl_take isl_set *set,
3088 __isl_take isl_multi_aff *maff,
3089 void *user), void *user);
3091 #include <isl/polynomial.h>
3092 isl_stat isl_pw_qpolynomial_foreach_piece(
3093 __isl_keep isl_pw_qpolynomial *pwqp,
3094 isl_stat (*fn)(__isl_take isl_set *set,
3095 __isl_take isl_qpolynomial *qp,
3096 void *user), void *user);
3097 isl_stat isl_pw_qpolynomial_foreach_lifted_piece(
3098 __isl_keep isl_pw_qpolynomial *pwqp,
3099 isl_stat (*fn)(__isl_take isl_set *set,
3100 __isl_take isl_qpolynomial *qp,
3101 void *user), void *user);
3102 isl_stat isl_pw_qpolynomial_fold_foreach_piece(
3103 __isl_keep isl_pw_qpolynomial_fold *pwf,
3104 isl_stat (*fn)(__isl_take isl_set *set,
3105 __isl_take isl_qpolynomial_fold *fold,
3106 void *user), void *user);
3107 isl_stat isl_pw_qpolynomial_fold_foreach_lifted_piece(
3108 __isl_keep isl_pw_qpolynomial_fold *pwf,
3109 isl_stat (*fn)(__isl_take isl_set *set,
3110 __isl_take isl_qpolynomial_fold *fold,
3111 void *user), void *user);
3113 As usual, the function C<fn> should return C<0> on success
3114 and C<-1> on failure. The difference between
3115 C<isl_pw_qpolynomial_foreach_piece> and
3116 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3117 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3118 compute unique representations for all existentially quantified
3119 variables and then turn these existentially quantified variables
3120 into extra set variables, adapting the associated quasipolynomial
3121 accordingly. This means that the C<set> passed to C<fn>
3122 will not have any existentially quantified variables, but that
3123 the dimensions of the sets may be different for different
3124 invocations of C<fn>.
3125 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
3126 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
3128 A piecewise expression consisting of the expressions at a given
3129 position of a piecewise multiple expression can be extracted
3130 using the following function.
3132 #include <isl/aff.h>
3133 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3134 __isl_keep isl_pw_multi_aff *pma, int pos);
3136 These expressions can be replaced using the following function.
3138 #include <isl/aff.h>
3139 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3140 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3141 __isl_take isl_pw_aff *pa);
3143 Note that there is a difference between C<isl_multi_pw_aff> and
3144 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
3145 affine expressions, while the second is a piecewise sequence
3146 of affine expressions. In particular, each of the piecewise
3147 affine expressions in an C<isl_multi_pw_aff> may have a different
3148 domain, while all multiple expressions associated to a cell
3149 in an C<isl_pw_multi_aff> have the same domain.
3150 It is possible to convert between the two, but when converting
3151 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
3152 of the result is the intersection of the domains of the input.
3153 The reverse conversion is exact.
3155 #include <isl/aff.h>
3156 __isl_give isl_pw_multi_aff *
3157 isl_pw_multi_aff_from_multi_pw_aff(
3158 __isl_take isl_multi_pw_aff *mpa);
3159 __isl_give isl_multi_pw_aff *
3160 isl_multi_pw_aff_from_pw_multi_aff(
3161 __isl_take isl_pw_multi_aff *pma);
3163 =head3 Union Expressions
3165 A union expression collects base expressions defined
3166 over different domains. The space of a union expression
3167 is that of the shared parameter space.
3169 The union expression types defined by C<isl>
3170 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
3171 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
3173 C<isl_union_pw_aff>,
3174 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>,
3175 there can be at most one base expression for a given domain space.
3177 C<isl_union_pw_multi_aff>,
3178 there can be multiple such expressions for a given domain space,
3179 but the domains of these expressions need to be disjoint.
3181 An empty union expression can be created using the following functions.
3183 #include <isl/aff.h>
3184 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
3185 __isl_take isl_space *space);
3186 __isl_give isl_union_pw_multi_aff *
3187 isl_union_pw_multi_aff_empty(
3188 __isl_take isl_space *space);
3190 #include <isl/polynomial.h>
3191 __isl_give isl_union_pw_qpolynomial *
3192 isl_union_pw_qpolynomial_zero(
3193 __isl_take isl_space *space);
3195 A union expression containing a single base expression
3196 can be created using the following functions.
3198 #include <isl/aff.h>
3199 __isl_give isl_union_pw_aff *
3200 isl_union_pw_aff_from_pw_aff(
3201 __isl_take isl_pw_aff *pa);
3202 __isl_give isl_union_pw_multi_aff *
3203 isl_union_pw_multi_aff_from_aff(
3204 __isl_take isl_aff *aff);
3205 __isl_give isl_union_pw_multi_aff *
3206 isl_union_pw_multi_aff_from_pw_multi_aff(
3207 __isl_take isl_pw_multi_aff *pma);
3209 #include <isl/polynomial.h>
3210 __isl_give isl_union_pw_qpolynomial *
3211 isl_union_pw_qpolynomial_from_pw_qpolynomial(
3212 __isl_take isl_pw_qpolynomial *pwqp);
3214 The following functions create a base expression on each
3215 of the sets in the union set and collect the results.
3217 #include <isl/aff.h>
3218 __isl_give isl_union_pw_multi_aff *
3219 isl_union_pw_multi_aff_from_union_pw_aff(
3220 __isl_take isl_union_pw_aff *upa);
3221 __isl_give isl_union_pw_aff *
3222 isl_union_pw_multi_aff_get_union_pw_aff(
3223 __isl_keep isl_union_pw_multi_aff *upma, int pos);
3224 __isl_give isl_union_pw_aff *
3225 isl_union_pw_aff_val_on_domain(
3226 __isl_take isl_union_set *domain,
3227 __isl_take isl_val *v);
3228 __isl_give isl_union_pw_multi_aff *
3229 isl_union_pw_multi_aff_multi_val_on_domain(
3230 __isl_take isl_union_set *domain,
3231 __isl_take isl_multi_val *mv);
3233 An C<isl_union_pw_aff> that is equal to a (parametric) affine
3234 expression on a given domain can be created using the following
3237 #include <isl/aff.h>
3238 __isl_give isl_union_pw_aff *
3239 isl_union_pw_aff_aff_on_domain(
3240 __isl_take isl_union_set *domain,
3241 __isl_take isl_aff *aff);
3243 A base expression can be added to a union expression using
3244 the following functions.
3246 #include <isl/aff.h>
3247 __isl_give isl_union_pw_aff *
3248 isl_union_pw_aff_add_pw_aff(
3249 __isl_take isl_union_pw_aff *upa,
3250 __isl_take isl_pw_aff *pa);
3251 __isl_give isl_union_pw_multi_aff *
3252 isl_union_pw_multi_aff_add_pw_multi_aff(
3253 __isl_take isl_union_pw_multi_aff *upma,
3254 __isl_take isl_pw_multi_aff *pma);
3256 #include <isl/polynomial.h>
3257 __isl_give isl_union_pw_qpolynomial *
3258 isl_union_pw_qpolynomial_add_pw_qpolynomial(
3259 __isl_take isl_union_pw_qpolynomial *upwqp,
3260 __isl_take isl_pw_qpolynomial *pwqp);
3262 Union expressions can be copied and freed using
3263 the following functions.
3265 #include <isl/aff.h>
3266 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
3267 __isl_keep isl_union_pw_aff *upa);
3268 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
3269 __isl_take isl_union_pw_aff *upa);
3270 __isl_give isl_union_pw_multi_aff *
3271 isl_union_pw_multi_aff_copy(
3272 __isl_keep isl_union_pw_multi_aff *upma);
3273 __isl_null isl_union_pw_multi_aff *
3274 isl_union_pw_multi_aff_free(
3275 __isl_take isl_union_pw_multi_aff *upma);
3277 #include <isl/polynomial.h>
3278 __isl_give isl_union_pw_qpolynomial *
3279 isl_union_pw_qpolynomial_copy(
3280 __isl_keep isl_union_pw_qpolynomial *upwqp);
3281 __isl_null isl_union_pw_qpolynomial *
3282 isl_union_pw_qpolynomial_free(
3283 __isl_take isl_union_pw_qpolynomial *upwqp);
3284 __isl_give isl_union_pw_qpolynomial_fold *
3285 isl_union_pw_qpolynomial_fold_copy(
3286 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3287 __isl_null isl_union_pw_qpolynomial_fold *
3288 isl_union_pw_qpolynomial_fold_free(
3289 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3291 To iterate over the base expressions in a union expression,
3292 use the following functions.
3294 #include <isl/aff.h>
3295 int isl_union_pw_aff_n_pw_aff(
3296 __isl_keep isl_union_pw_aff *upa);
3297 isl_stat isl_union_pw_aff_foreach_pw_aff(
3298 __isl_keep isl_union_pw_aff *upa,
3299 isl_stat (*fn)(__isl_take isl_pw_aff *pa,
3300 void *user), void *user);
3301 int isl_union_pw_multi_aff_n_pw_multi_aff(
3302 __isl_keep isl_union_pw_multi_aff *upma);
3303 isl_stat isl_union_pw_multi_aff_foreach_pw_multi_aff(
3304 __isl_keep isl_union_pw_multi_aff *upma,
3305 isl_stat (*fn)(__isl_take isl_pw_multi_aff *pma,
3306 void *user), void *user);
3308 #include <isl/polynomial.h>
3309 int isl_union_pw_qpolynomial_n_pw_qpolynomial(
3310 __isl_keep isl_union_pw_qpolynomial *upwqp);
3311 isl_stat isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3312 __isl_keep isl_union_pw_qpolynomial *upwqp,
3313 isl_stat (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
3314 void *user), void *user);
3315 int isl_union_pw_qpolynomial_fold_n_pw_qpolynomial_fold(
3316 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3317 isl_stat isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3318 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3319 isl_stat (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3320 void *user), void *user);
3322 To extract the base expression in a given space from a union, use
3323 the following functions.
3325 #include <isl/aff.h>
3326 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
3327 __isl_keep isl_union_pw_aff *upa,
3328 __isl_take isl_space *space);
3329 __isl_give isl_pw_multi_aff *
3330 isl_union_pw_multi_aff_extract_pw_multi_aff(
3331 __isl_keep isl_union_pw_multi_aff *upma,
3332 __isl_take isl_space *space);
3334 #include <isl/polynomial.h>
3335 __isl_give isl_pw_qpolynomial *
3336 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3337 __isl_keep isl_union_pw_qpolynomial *upwqp,
3338 __isl_take isl_space *space);
3340 =head2 Input and Output
3342 For set and relation,
3343 C<isl> supports its own input/output format, which is similar
3344 to the C<Omega> format, but also supports the C<PolyLib> format
3346 For other object types, typically only an C<isl> format is supported.
3348 =head3 C<isl> format
3350 The C<isl> format is similar to that of C<Omega>, but has a different
3351 syntax for describing the parameters and allows for the definition
3352 of an existentially quantified variable as the integer division
3353 of an affine expression.
3354 For example, the set of integers C<i> between C<0> and C<n>
3355 such that C<i % 10 <= 6> can be described as
3357 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
3360 A set or relation can have several disjuncts, separated
3361 by the keyword C<or>. Each disjunct is either a conjunction
3362 of constraints or a projection (C<exists>) of a conjunction
3363 of constraints. The constraints are separated by the keyword
3366 =head3 C<PolyLib> format
3368 If the represented set is a union, then the first line
3369 contains a single number representing the number of disjuncts.
3370 Otherwise, a line containing the number C<1> is optional.
3372 Each disjunct is represented by a matrix of constraints.
3373 The first line contains two numbers representing
3374 the number of rows and columns,
3375 where the number of rows is equal to the number of constraints
3376 and the number of columns is equal to two plus the number of variables.
3377 The following lines contain the actual rows of the constraint matrix.
3378 In each row, the first column indicates whether the constraint
3379 is an equality (C<0>) or inequality (C<1>). The final column
3380 corresponds to the constant term.
3382 If the set is parametric, then the coefficients of the parameters
3383 appear in the last columns before the constant column.
3384 The coefficients of any existentially quantified variables appear
3385 between those of the set variables and those of the parameters.
3387 =head3 Extended C<PolyLib> format
3389 The extended C<PolyLib> format is nearly identical to the
3390 C<PolyLib> format. The only difference is that the line
3391 containing the number of rows and columns of a constraint matrix
3392 also contains four additional numbers:
3393 the number of output dimensions, the number of input dimensions,
3394 the number of local dimensions (i.e., the number of existentially
3395 quantified variables) and the number of parameters.
3396 For sets, the number of ``output'' dimensions is equal
3397 to the number of set dimensions, while the number of ``input''
3402 Objects can be read from input using the following functions.
3404 #include <isl/val.h>
3405 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
3407 __isl_give isl_multi_val *isl_multi_val_read_from_str(
3408 isl_ctx *ctx, const char *str);
3410 #include <isl/set.h>
3411 __isl_give isl_basic_set *isl_basic_set_read_from_file(
3412 isl_ctx *ctx, FILE *input);
3413 __isl_give isl_basic_set *isl_basic_set_read_from_str(
3414 isl_ctx *ctx, const char *str);
3415 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
3417 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
3420 #include <isl/map.h>
3421 __isl_give isl_basic_map *isl_basic_map_read_from_file(
3422 isl_ctx *ctx, FILE *input);
3423 __isl_give isl_basic_map *isl_basic_map_read_from_str(
3424 isl_ctx *ctx, const char *str);
3425 __isl_give isl_map *isl_map_read_from_file(
3426 isl_ctx *ctx, FILE *input);
3427 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
3430 #include <isl/union_set.h>
3431 __isl_give isl_union_set *isl_union_set_read_from_file(
3432 isl_ctx *ctx, FILE *input);
3433 __isl_give isl_union_set *isl_union_set_read_from_str(
3434 isl_ctx *ctx, const char *str);
3436 #include <isl/union_map.h>
3437 __isl_give isl_union_map *isl_union_map_read_from_file(
3438 isl_ctx *ctx, FILE *input);
3439 __isl_give isl_union_map *isl_union_map_read_from_str(
3440 isl_ctx *ctx, const char *str);
3442 #include <isl/aff.h>
3443 __isl_give isl_aff *isl_aff_read_from_str(
3444 isl_ctx *ctx, const char *str);
3445 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3446 isl_ctx *ctx, const char *str);
3447 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3448 isl_ctx *ctx, const char *str);
3449 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3450 isl_ctx *ctx, const char *str);
3451 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
3452 isl_ctx *ctx, const char *str);
3453 __isl_give isl_union_pw_aff *
3454 isl_union_pw_aff_read_from_str(
3455 isl_ctx *ctx, const char *str);
3456 __isl_give isl_union_pw_multi_aff *
3457 isl_union_pw_multi_aff_read_from_str(
3458 isl_ctx *ctx, const char *str);
3459 __isl_give isl_multi_union_pw_aff *
3460 isl_multi_union_pw_aff_read_from_str(
3461 isl_ctx *ctx, const char *str);
3463 #include <isl/polynomial.h>
3464 __isl_give isl_union_pw_qpolynomial *
3465 isl_union_pw_qpolynomial_read_from_str(
3466 isl_ctx *ctx, const char *str);
3468 For sets and relations,
3469 the input format is autodetected and may be either the C<PolyLib> format
3470 or the C<isl> format.
3474 Before anything can be printed, an C<isl_printer> needs to
3477 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
3479 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
3480 __isl_null isl_printer *isl_printer_free(
3481 __isl_take isl_printer *printer);
3483 C<isl_printer_to_file> prints to the given file, while
3484 C<isl_printer_to_str> prints to a string that can be extracted
3485 using the following function.
3487 #include <isl/printer.h>
3488 __isl_give char *isl_printer_get_str(
3489 __isl_keep isl_printer *printer);
3491 The printer can be inspected using the following functions.
3493 FILE *isl_printer_get_file(
3494 __isl_keep isl_printer *printer);
3495 int isl_printer_get_output_format(
3496 __isl_keep isl_printer *p);
3497 int isl_printer_get_yaml_style(__isl_keep isl_printer *p);
3499 The behavior of the printer can be modified in various ways
3501 __isl_give isl_printer *isl_printer_set_output_format(
3502 __isl_take isl_printer *p, int output_format);
3503 __isl_give isl_printer *isl_printer_set_indent(
3504 __isl_take isl_printer *p, int indent);
3505 __isl_give isl_printer *isl_printer_set_indent_prefix(
3506 __isl_take isl_printer *p, const char *prefix);
3507 __isl_give isl_printer *isl_printer_indent(
3508 __isl_take isl_printer *p, int indent);
3509 __isl_give isl_printer *isl_printer_set_prefix(
3510 __isl_take isl_printer *p, const char *prefix);
3511 __isl_give isl_printer *isl_printer_set_suffix(
3512 __isl_take isl_printer *p, const char *suffix);
3513 __isl_give isl_printer *isl_printer_set_yaml_style(
3514 __isl_take isl_printer *p, int yaml_style);
3516 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
3517 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
3518 and defaults to C<ISL_FORMAT_ISL>.
3519 Each line in the output is prefixed by C<indent_prefix>,
3520 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
3521 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
3522 In the C<PolyLib> format output,
3523 the coefficients of the existentially quantified variables
3524 appear between those of the set variables and those
3526 The function C<isl_printer_indent> increases the indentation
3527 by the specified amount (which may be negative).
3528 The YAML style may be either C<ISL_YAML_STYLE_BLOCK> or
3529 C<ISL_YAML_STYLE_FLOW> and when we are printing something
3532 To actually print something, use
3534 #include <isl/printer.h>
3535 __isl_give isl_printer *isl_printer_print_double(
3536 __isl_take isl_printer *p, double d);
3538 #include <isl/val.h>
3539 __isl_give isl_printer *isl_printer_print_val(
3540 __isl_take isl_printer *p, __isl_keep isl_val *v);
3542 #include <isl/set.h>
3543 __isl_give isl_printer *isl_printer_print_basic_set(
3544 __isl_take isl_printer *printer,
3545 __isl_keep isl_basic_set *bset);
3546 __isl_give isl_printer *isl_printer_print_set(
3547 __isl_take isl_printer *printer,
3548 __isl_keep isl_set *set);
3550 #include <isl/map.h>
3551 __isl_give isl_printer *isl_printer_print_basic_map(
3552 __isl_take isl_printer *printer,
3553 __isl_keep isl_basic_map *bmap);
3554 __isl_give isl_printer *isl_printer_print_map(
3555 __isl_take isl_printer *printer,
3556 __isl_keep isl_map *map);
3558 #include <isl/union_set.h>
3559 __isl_give isl_printer *isl_printer_print_union_set(
3560 __isl_take isl_printer *p,
3561 __isl_keep isl_union_set *uset);
3563 #include <isl/union_map.h>
3564 __isl_give isl_printer *isl_printer_print_union_map(
3565 __isl_take isl_printer *p,
3566 __isl_keep isl_union_map *umap);
3568 #include <isl/val.h>
3569 __isl_give isl_printer *isl_printer_print_multi_val(
3570 __isl_take isl_printer *p,
3571 __isl_keep isl_multi_val *mv);
3573 #include <isl/aff.h>
3574 __isl_give isl_printer *isl_printer_print_aff(
3575 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3576 __isl_give isl_printer *isl_printer_print_multi_aff(
3577 __isl_take isl_printer *p,
3578 __isl_keep isl_multi_aff *maff);
3579 __isl_give isl_printer *isl_printer_print_pw_aff(
3580 __isl_take isl_printer *p,
3581 __isl_keep isl_pw_aff *pwaff);
3582 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3583 __isl_take isl_printer *p,
3584 __isl_keep isl_pw_multi_aff *pma);
3585 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3586 __isl_take isl_printer *p,
3587 __isl_keep isl_multi_pw_aff *mpa);
3588 __isl_give isl_printer *isl_printer_print_union_pw_aff(
3589 __isl_take isl_printer *p,
3590 __isl_keep isl_union_pw_aff *upa);
3591 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3592 __isl_take isl_printer *p,
3593 __isl_keep isl_union_pw_multi_aff *upma);
3594 __isl_give isl_printer *
3595 isl_printer_print_multi_union_pw_aff(
3596 __isl_take isl_printer *p,
3597 __isl_keep isl_multi_union_pw_aff *mupa);
3599 #include <isl/polynomial.h>
3600 __isl_give isl_printer *isl_printer_print_qpolynomial(
3601 __isl_take isl_printer *p,
3602 __isl_keep isl_qpolynomial *qp);
3603 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3604 __isl_take isl_printer *p,
3605 __isl_keep isl_pw_qpolynomial *pwqp);
3606 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3607 __isl_take isl_printer *p,
3608 __isl_keep isl_union_pw_qpolynomial *upwqp);
3610 __isl_give isl_printer *
3611 isl_printer_print_pw_qpolynomial_fold(
3612 __isl_take isl_printer *p,
3613 __isl_keep isl_pw_qpolynomial_fold *pwf);
3614 __isl_give isl_printer *
3615 isl_printer_print_union_pw_qpolynomial_fold(
3616 __isl_take isl_printer *p,
3617 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3619 For C<isl_printer_print_qpolynomial>,
3620 C<isl_printer_print_pw_qpolynomial> and
3621 C<isl_printer_print_pw_qpolynomial_fold>,
3622 the output format of the printer
3623 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3624 For C<isl_printer_print_union_pw_qpolynomial> and
3625 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
3627 In case of printing in C<ISL_FORMAT_C>, the user may want
3628 to set the names of all dimensions first.
3630 C<isl> also provides limited support for printing YAML documents,
3631 just enough for the internal use for printing such documents.
3633 #include <isl/printer.h>
3634 __isl_give isl_printer *isl_printer_yaml_start_mapping(
3635 __isl_take isl_printer *p);
3636 __isl_give isl_printer *isl_printer_yaml_end_mapping(
3637 __isl_take isl_printer *p);
3638 __isl_give isl_printer *isl_printer_yaml_start_sequence(
3639 __isl_take isl_printer *p);
3640 __isl_give isl_printer *isl_printer_yaml_end_sequence(
3641 __isl_take isl_printer *p);
3642 __isl_give isl_printer *isl_printer_yaml_next(
3643 __isl_take isl_printer *p);
3645 A document is started by a call to either
3646 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3647 Anything printed to the printer after such a call belong to the
3648 first key of the mapping or the first element in the sequence.
3649 The function C<isl_printer_yaml_next> moves to the value if
3650 we are currently printing a mapping key, the next key if we
3651 are printing a value or the next element if we are printing
3652 an element in a sequence.
3653 Nested mappings and sequences are initiated by the same
3654 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3655 Each call to these functions needs to have a corresponding call to
3656 C<isl_printer_yaml_end_mapping> or C<isl_printer_yaml_end_sequence>.
3658 When called on a file printer, the following function flushes
3659 the file. When called on a string printer, the buffer is cleared.
3661 __isl_give isl_printer *isl_printer_flush(
3662 __isl_take isl_printer *p);
3664 The following functions allow the user to attach
3665 notes to a printer in order to keep track of additional state.
3667 #include <isl/printer.h>
3668 isl_bool isl_printer_has_note(__isl_keep isl_printer *p,
3669 __isl_keep isl_id *id);
3670 __isl_give isl_id *isl_printer_get_note(
3671 __isl_keep isl_printer *p, __isl_take isl_id *id);
3672 __isl_give isl_printer *isl_printer_set_note(
3673 __isl_take isl_printer *p,
3674 __isl_take isl_id *id, __isl_take isl_id *note);
3676 C<isl_printer_set_note> associates the given note to the given
3677 identifier in the printer.
3678 C<isl_printer_get_note> retrieves a note associated to an
3680 C<isl_printer_has_note> checks if there is such a note.
3681 C<isl_printer_get_note> fails if the requested note does not exist.
3683 Alternatively, a string representation can be obtained
3684 directly using the following functions, which always print
3688 __isl_give char *isl_id_to_str(
3689 __isl_keep isl_id *id);
3691 #include <isl/space.h>
3692 __isl_give char *isl_space_to_str(
3693 __isl_keep isl_space *space);
3695 #include <isl/val.h>
3696 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
3697 __isl_give char *isl_multi_val_to_str(
3698 __isl_keep isl_multi_val *mv);
3700 #include <isl/set.h>
3701 __isl_give char *isl_basic_set_to_str(
3702 __isl_keep isl_basic_set *bset);
3703 __isl_give char *isl_set_to_str(
3704 __isl_keep isl_set *set);
3706 #include <isl/union_set.h>
3707 __isl_give char *isl_union_set_to_str(
3708 __isl_keep isl_union_set *uset);
3710 #include <isl/map.h>
3711 __isl_give char *isl_basic_map_to_str(
3712 __isl_keep isl_basic_map *bmap);
3713 __isl_give char *isl_map_to_str(
3714 __isl_keep isl_map *map);
3716 #include <isl/union_map.h>
3717 __isl_give char *isl_union_map_to_str(
3718 __isl_keep isl_union_map *umap);
3720 #include <isl/aff.h>
3721 __isl_give char *isl_aff_to_str(__isl_keep isl_aff *aff);
3722 __isl_give char *isl_pw_aff_to_str(
3723 __isl_keep isl_pw_aff *pa);
3724 __isl_give char *isl_multi_aff_to_str(
3725 __isl_keep isl_multi_aff *ma);
3726 __isl_give char *isl_pw_multi_aff_to_str(
3727 __isl_keep isl_pw_multi_aff *pma);
3728 __isl_give char *isl_multi_pw_aff_to_str(
3729 __isl_keep isl_multi_pw_aff *mpa);
3730 __isl_give char *isl_union_pw_aff_to_str(
3731 __isl_keep isl_union_pw_aff *upa);
3732 __isl_give char *isl_union_pw_multi_aff_to_str(
3733 __isl_keep isl_union_pw_multi_aff *upma);
3734 __isl_give char *isl_multi_union_pw_aff_to_str(
3735 __isl_keep isl_multi_union_pw_aff *mupa);
3737 #include <isl/point.h>
3738 __isl_give char *isl_point_to_str(
3739 __isl_keep isl_point *pnt);
3741 #include <isl/polynomial.h>
3742 __isl_give char *isl_pw_qpolynomial_to_str(
3743 __isl_keep isl_pw_qpolynomial *pwqp);
3744 __isl_give char *isl_union_pw_qpolynomial_to_str(
3745 __isl_keep isl_union_pw_qpolynomial *upwqp);
3749 =head3 Unary Properties
3755 The following functions test whether the given set or relation
3756 contains any integer points. The ``plain'' variants do not perform
3757 any computations, but simply check if the given set or relation
3758 is already known to be empty.
3760 isl_bool isl_basic_set_plain_is_empty(
3761 __isl_keep isl_basic_set *bset);
3762 isl_bool isl_basic_set_is_empty(
3763 __isl_keep isl_basic_set *bset);
3764 isl_bool isl_set_plain_is_empty(
3765 __isl_keep isl_set *set);
3766 isl_bool isl_set_is_empty(__isl_keep isl_set *set);
3767 isl_bool isl_union_set_is_empty(
3768 __isl_keep isl_union_set *uset);
3769 isl_bool isl_basic_map_plain_is_empty(
3770 __isl_keep isl_basic_map *bmap);
3771 isl_bool isl_basic_map_is_empty(
3772 __isl_keep isl_basic_map *bmap);
3773 isl_bool isl_map_plain_is_empty(
3774 __isl_keep isl_map *map);
3775 isl_bool isl_map_is_empty(__isl_keep isl_map *map);
3776 isl_bool isl_union_map_is_empty(
3777 __isl_keep isl_union_map *umap);
3779 =item * Universality
3781 isl_bool isl_basic_set_plain_is_universe(
3782 __isl_keep isl_basic_set *bset);
3783 isl_bool isl_basic_set_is_universe(
3784 __isl_keep isl_basic_set *bset);
3785 isl_bool isl_basic_map_plain_is_universe(
3786 __isl_keep isl_basic_map *bmap);
3787 isl_bool isl_basic_map_is_universe(
3788 __isl_keep isl_basic_map *bmap);
3789 isl_bool isl_set_plain_is_universe(
3790 __isl_keep isl_set *set);
3791 isl_bool isl_map_plain_is_universe(
3792 __isl_keep isl_map *map);
3794 =item * Single-valuedness
3796 #include <isl/set.h>
3797 isl_bool isl_set_is_singleton(__isl_keep isl_set *set);
3799 #include <isl/map.h>
3800 isl_bool isl_basic_map_is_single_valued(
3801 __isl_keep isl_basic_map *bmap);
3802 isl_bool isl_map_plain_is_single_valued(
3803 __isl_keep isl_map *map);
3804 isl_bool isl_map_is_single_valued(__isl_keep isl_map *map);
3806 #include <isl/union_map.h>
3807 isl_bool isl_union_map_is_single_valued(
3808 __isl_keep isl_union_map *umap);
3812 isl_bool isl_map_plain_is_injective(
3813 __isl_keep isl_map *map);
3814 isl_bool isl_map_is_injective(
3815 __isl_keep isl_map *map);
3816 isl_bool isl_union_map_plain_is_injective(
3817 __isl_keep isl_union_map *umap);
3818 isl_bool isl_union_map_is_injective(
3819 __isl_keep isl_union_map *umap);
3823 isl_bool isl_map_is_bijective(
3824 __isl_keep isl_map *map);
3825 isl_bool isl_union_map_is_bijective(
3826 __isl_keep isl_union_map *umap);
3830 The following functions test whether the given relation
3831 only maps elements to themselves.
3833 #include <isl/map.h>
3834 isl_bool isl_map_is_identity(
3835 __isl_keep isl_map *map);
3837 #include <isl/union_map.h>
3838 isl_bool isl_union_map_is_identity(
3839 __isl_keep isl_union_map *umap);
3843 __isl_give isl_val *
3844 isl_basic_map_plain_get_val_if_fixed(
3845 __isl_keep isl_basic_map *bmap,
3846 enum isl_dim_type type, unsigned pos);
3847 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
3848 __isl_keep isl_set *set,
3849 enum isl_dim_type type, unsigned pos);
3850 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
3851 __isl_keep isl_map *map,
3852 enum isl_dim_type type, unsigned pos);
3854 If the set or relation obviously lies on a hyperplane where the given dimension
3855 has a fixed value, then return that value.
3856 Otherwise return NaN.
3860 isl_stat isl_set_dim_residue_class_val(
3861 __isl_keep isl_set *set,
3862 int pos, __isl_give isl_val **modulo,
3863 __isl_give isl_val **residue);
3865 Check if the values of the given set dimension are equal to a fixed
3866 value modulo some integer value. If so, assign the modulo to C<*modulo>
3867 and the fixed value to C<*residue>. If the given dimension attains only
3868 a single value, then assign C<0> to C<*modulo> and the fixed value to
3870 If the dimension does not attain only a single value and if no modulo
3871 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
3875 To check whether the description of a set, relation or function depends
3876 on one or more given dimensions,
3877 the following functions can be used.
3879 #include <isl/constraint.h>
3880 isl_bool isl_constraint_involves_dims(
3881 __isl_keep isl_constraint *constraint,
3882 enum isl_dim_type type, unsigned first, unsigned n);
3884 #include <isl/set.h>
3885 isl_bool isl_basic_set_involves_dims(
3886 __isl_keep isl_basic_set *bset,
3887 enum isl_dim_type type, unsigned first, unsigned n);
3888 isl_bool isl_set_involves_dims(__isl_keep isl_set *set,
3889 enum isl_dim_type type, unsigned first, unsigned n);
3891 #include <isl/map.h>
3892 isl_bool isl_basic_map_involves_dims(
3893 __isl_keep isl_basic_map *bmap,
3894 enum isl_dim_type type, unsigned first, unsigned n);
3895 isl_bool isl_map_involves_dims(__isl_keep isl_map *map,
3896 enum isl_dim_type type, unsigned first, unsigned n);
3898 #include <isl/union_map.h>
3899 isl_bool isl_union_map_involves_dims(
3900 __isl_keep isl_union_map *umap,
3901 enum isl_dim_type type, unsigned first, unsigned n);
3903 #include <isl/aff.h>
3904 isl_bool isl_aff_involves_dims(__isl_keep isl_aff *aff,
3905 enum isl_dim_type type, unsigned first, unsigned n);
3906 isl_bool isl_pw_aff_involves_dims(
3907 __isl_keep isl_pw_aff *pwaff,
3908 enum isl_dim_type type, unsigned first, unsigned n);
3909 isl_bool isl_multi_aff_involves_dims(
3910 __isl_keep isl_multi_aff *ma,
3911 enum isl_dim_type type, unsigned first, unsigned n);
3912 isl_bool isl_multi_pw_aff_involves_dims(
3913 __isl_keep isl_multi_pw_aff *mpa,
3914 enum isl_dim_type type, unsigned first, unsigned n);
3916 #include <isl/polynomial.h>
3917 isl_bool isl_qpolynomial_involves_dims(
3918 __isl_keep isl_qpolynomial *qp,
3919 enum isl_dim_type type, unsigned first, unsigned n);
3921 Similarly, the following functions can be used to check whether
3922 a given dimension is involved in any lower or upper bound.
3924 #include <isl/set.h>
3925 isl_bool isl_set_dim_has_any_lower_bound(
3926 __isl_keep isl_set *set,
3927 enum isl_dim_type type, unsigned pos);
3928 isl_bool isl_set_dim_has_any_upper_bound(
3929 __isl_keep isl_set *set,
3930 enum isl_dim_type type, unsigned pos);
3932 Note that these functions return true even if there is a bound on
3933 the dimension on only some of the basic sets of C<set>.
3934 To check if they have a bound for all of the basic sets in C<set>,
3935 use the following functions instead.
3937 #include <isl/set.h>
3938 isl_bool isl_set_dim_has_lower_bound(
3939 __isl_keep isl_set *set,
3940 enum isl_dim_type type, unsigned pos);
3941 isl_bool isl_set_dim_has_upper_bound(
3942 __isl_keep isl_set *set,
3943 enum isl_dim_type type, unsigned pos);
3947 To check whether a set is a parameter domain, use this function:
3949 isl_bool isl_set_is_params(__isl_keep isl_set *set);
3950 isl_bool isl_union_set_is_params(
3951 __isl_keep isl_union_set *uset);
3955 The following functions check whether the space of the given
3956 (basic) set or relation range is a wrapped relation.
3958 #include <isl/space.h>
3959 isl_bool isl_space_is_wrapping(
3960 __isl_keep isl_space *space);
3961 isl_bool isl_space_domain_is_wrapping(
3962 __isl_keep isl_space *space);
3963 isl_bool isl_space_range_is_wrapping(
3964 __isl_keep isl_space *space);
3966 #include <isl/set.h>
3967 isl_bool isl_basic_set_is_wrapping(
3968 __isl_keep isl_basic_set *bset);
3969 isl_bool isl_set_is_wrapping(__isl_keep isl_set *set);
3971 #include <isl/map.h>
3972 isl_bool isl_map_domain_is_wrapping(
3973 __isl_keep isl_map *map);
3974 isl_bool isl_map_range_is_wrapping(
3975 __isl_keep isl_map *map);
3977 #include <isl/val.h>
3978 isl_bool isl_multi_val_range_is_wrapping(
3979 __isl_keep isl_multi_val *mv);
3981 #include <isl/aff.h>
3982 isl_bool isl_multi_aff_range_is_wrapping(
3983 __isl_keep isl_multi_aff *ma);
3984 isl_bool isl_multi_pw_aff_range_is_wrapping(
3985 __isl_keep isl_multi_pw_aff *mpa);
3986 isl_bool isl_multi_union_pw_aff_range_is_wrapping(
3987 __isl_keep isl_multi_union_pw_aff *mupa);
3989 The input to C<isl_space_is_wrapping> should
3990 be the space of a set, while that of
3991 C<isl_space_domain_is_wrapping> and
3992 C<isl_space_range_is_wrapping> should be the space of a relation.
3994 =item * Internal Product
3996 isl_bool isl_basic_map_can_zip(
3997 __isl_keep isl_basic_map *bmap);
3998 isl_bool isl_map_can_zip(__isl_keep isl_map *map);
4000 Check whether the product of domain and range of the given relation
4002 i.e., whether both domain and range are nested relations.
4006 #include <isl/space.h>
4007 isl_bool isl_space_can_curry(
4008 __isl_keep isl_space *space);
4010 #include <isl/map.h>
4011 isl_bool isl_basic_map_can_curry(
4012 __isl_keep isl_basic_map *bmap);
4013 isl_bool isl_map_can_curry(__isl_keep isl_map *map);
4015 Check whether the domain of the (basic) relation is a wrapped relation.
4017 #include <isl/space.h>
4018 __isl_give isl_space *isl_space_uncurry(
4019 __isl_take isl_space *space);
4021 #include <isl/map.h>
4022 isl_bool isl_basic_map_can_uncurry(
4023 __isl_keep isl_basic_map *bmap);
4024 isl_bool isl_map_can_uncurry(__isl_keep isl_map *map);
4026 Check whether the range of the (basic) relation is a wrapped relation.
4028 #include <isl/space.h>
4029 isl_bool isl_space_can_range_curry(
4030 __isl_keep isl_space *space);
4032 #include <isl/map.h>
4033 isl_bool isl_map_can_range_curry(
4034 __isl_keep isl_map *map);
4036 Check whether the domain of the relation wrapped in the range of
4037 the input is itself a wrapped relation.
4039 =item * Special Values
4041 #include <isl/aff.h>
4042 isl_bool isl_aff_is_cst(__isl_keep isl_aff *aff);
4043 isl_bool isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
4044 isl_bool isl_multi_pw_aff_is_cst(
4045 __isl_keep isl_multi_pw_aff *mpa);
4047 Check whether the given expression is a constant.
4049 #include <isl/aff.h>
4050 isl_bool isl_aff_is_nan(__isl_keep isl_aff *aff);
4051 isl_bool isl_pw_aff_involves_nan(
4052 __isl_keep isl_pw_aff *pa);
4054 #include <isl/polynomial.h>
4055 isl_bool isl_qpolynomial_is_nan(
4056 __isl_keep isl_qpolynomial *qp);
4057 isl_bool isl_qpolynomial_fold_is_nan(
4058 __isl_keep isl_qpolynomial_fold *fold);
4060 Check whether the given expression is equal to or involves NaN.
4062 #include <isl/aff.h>
4063 isl_bool isl_aff_plain_is_zero(
4064 __isl_keep isl_aff *aff);
4066 Check whether the affine expression is obviously zero.
4070 =head3 Binary Properties
4076 The following functions check whether two objects
4077 represent the same set, relation or function.
4078 The C<plain> variants only return true if the objects
4079 are obviously the same. That is, they may return false
4080 even if the objects are the same, but they will never
4081 return true if the objects are not the same.
4083 #include <isl/set.h>
4084 isl_bool isl_basic_set_plain_is_equal(
4085 __isl_keep isl_basic_set *bset1,
4086 __isl_keep isl_basic_set *bset2);
4087 isl_bool isl_basic_set_is_equal(
4088 __isl_keep isl_basic_set *bset1,
4089 __isl_keep isl_basic_set *bset2);
4090 isl_bool isl_set_plain_is_equal(
4091 __isl_keep isl_set *set1,
4092 __isl_keep isl_set *set2);
4093 isl_bool isl_set_is_equal(__isl_keep isl_set *set1,
4094 __isl_keep isl_set *set2);
4096 #include <isl/map.h>
4097 isl_bool isl_basic_map_is_equal(
4098 __isl_keep isl_basic_map *bmap1,
4099 __isl_keep isl_basic_map *bmap2);
4100 isl_bool isl_map_is_equal(__isl_keep isl_map *map1,
4101 __isl_keep isl_map *map2);
4102 isl_bool isl_map_plain_is_equal(
4103 __isl_keep isl_map *map1,
4104 __isl_keep isl_map *map2);
4106 #include <isl/union_set.h>
4107 isl_bool isl_union_set_is_equal(
4108 __isl_keep isl_union_set *uset1,
4109 __isl_keep isl_union_set *uset2);
4111 #include <isl/union_map.h>
4112 isl_bool isl_union_map_is_equal(
4113 __isl_keep isl_union_map *umap1,
4114 __isl_keep isl_union_map *umap2);
4116 #include <isl/aff.h>
4117 isl_bool isl_aff_plain_is_equal(
4118 __isl_keep isl_aff *aff1,
4119 __isl_keep isl_aff *aff2);
4120 isl_bool isl_multi_aff_plain_is_equal(
4121 __isl_keep isl_multi_aff *maff1,
4122 __isl_keep isl_multi_aff *maff2);
4123 isl_bool isl_pw_aff_plain_is_equal(
4124 __isl_keep isl_pw_aff *pwaff1,
4125 __isl_keep isl_pw_aff *pwaff2);
4126 isl_bool isl_pw_multi_aff_plain_is_equal(
4127 __isl_keep isl_pw_multi_aff *pma1,
4128 __isl_keep isl_pw_multi_aff *pma2);
4129 isl_bool isl_multi_pw_aff_plain_is_equal(
4130 __isl_keep isl_multi_pw_aff *mpa1,
4131 __isl_keep isl_multi_pw_aff *mpa2);
4132 isl_bool isl_multi_pw_aff_is_equal(
4133 __isl_keep isl_multi_pw_aff *mpa1,
4134 __isl_keep isl_multi_pw_aff *mpa2);
4135 isl_bool isl_union_pw_aff_plain_is_equal(
4136 __isl_keep isl_union_pw_aff *upa1,
4137 __isl_keep isl_union_pw_aff *upa2);
4138 isl_bool isl_union_pw_multi_aff_plain_is_equal(
4139 __isl_keep isl_union_pw_multi_aff *upma1,
4140 __isl_keep isl_union_pw_multi_aff *upma2);
4141 isl_bool isl_multi_union_pw_aff_plain_is_equal(
4142 __isl_keep isl_multi_union_pw_aff *mupa1,
4143 __isl_keep isl_multi_union_pw_aff *mupa2);
4145 #include <isl/polynomial.h>
4146 isl_bool isl_union_pw_qpolynomial_plain_is_equal(
4147 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4148 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4149 isl_bool isl_union_pw_qpolynomial_fold_plain_is_equal(
4150 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4151 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4153 =item * Disjointness
4155 #include <isl/set.h>
4156 isl_bool isl_basic_set_is_disjoint(
4157 __isl_keep isl_basic_set *bset1,
4158 __isl_keep isl_basic_set *bset2);
4159 isl_bool isl_set_plain_is_disjoint(
4160 __isl_keep isl_set *set1,
4161 __isl_keep isl_set *set2);
4162 isl_bool isl_set_is_disjoint(__isl_keep isl_set *set1,
4163 __isl_keep isl_set *set2);
4165 #include <isl/map.h>
4166 isl_bool isl_basic_map_is_disjoint(
4167 __isl_keep isl_basic_map *bmap1,
4168 __isl_keep isl_basic_map *bmap2);
4169 isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1,
4170 __isl_keep isl_map *map2);
4172 #include <isl/union_set.h>
4173 isl_bool isl_union_set_is_disjoint(
4174 __isl_keep isl_union_set *uset1,
4175 __isl_keep isl_union_set *uset2);
4177 #include <isl/union_map.h>
4178 isl_bool isl_union_map_is_disjoint(
4179 __isl_keep isl_union_map *umap1,
4180 __isl_keep isl_union_map *umap2);
4184 isl_bool isl_basic_set_is_subset(
4185 __isl_keep isl_basic_set *bset1,
4186 __isl_keep isl_basic_set *bset2);
4187 isl_bool isl_set_is_subset(__isl_keep isl_set *set1,
4188 __isl_keep isl_set *set2);
4189 isl_bool isl_set_is_strict_subset(
4190 __isl_keep isl_set *set1,
4191 __isl_keep isl_set *set2);
4192 isl_bool isl_union_set_is_subset(
4193 __isl_keep isl_union_set *uset1,
4194 __isl_keep isl_union_set *uset2);
4195 isl_bool isl_union_set_is_strict_subset(
4196 __isl_keep isl_union_set *uset1,
4197 __isl_keep isl_union_set *uset2);
4198 isl_bool isl_basic_map_is_subset(
4199 __isl_keep isl_basic_map *bmap1,
4200 __isl_keep isl_basic_map *bmap2);
4201 isl_bool isl_basic_map_is_strict_subset(
4202 __isl_keep isl_basic_map *bmap1,
4203 __isl_keep isl_basic_map *bmap2);
4204 isl_bool isl_map_is_subset(
4205 __isl_keep isl_map *map1,
4206 __isl_keep isl_map *map2);
4207 isl_bool isl_map_is_strict_subset(
4208 __isl_keep isl_map *map1,
4209 __isl_keep isl_map *map2);
4210 isl_bool isl_union_map_is_subset(
4211 __isl_keep isl_union_map *umap1,
4212 __isl_keep isl_union_map *umap2);
4213 isl_bool isl_union_map_is_strict_subset(
4214 __isl_keep isl_union_map *umap1,
4215 __isl_keep isl_union_map *umap2);
4217 Check whether the first argument is a (strict) subset of the
4222 Every comparison function returns a negative value if the first
4223 argument is considered smaller than the second, a positive value
4224 if the first argument is considered greater and zero if the two
4225 constraints are considered the same by the comparison criterion.
4227 #include <isl/constraint.h>
4228 int isl_constraint_plain_cmp(
4229 __isl_keep isl_constraint *c1,
4230 __isl_keep isl_constraint *c2);
4232 This function is useful for sorting C<isl_constraint>s.
4233 The order depends on the internal representation of the inputs.
4234 The order is fixed over different calls to the function (assuming
4235 the internal representation of the inputs has not changed), but may
4236 change over different versions of C<isl>.
4238 #include <isl/constraint.h>
4239 int isl_constraint_cmp_last_non_zero(
4240 __isl_keep isl_constraint *c1,
4241 __isl_keep isl_constraint *c2);
4243 This function can be used to sort constraints that live in the same
4244 local space. Constraints that involve ``earlier'' dimensions or
4245 that have a smaller coefficient for the shared latest dimension
4246 are considered smaller than other constraints.
4247 This function only defines a B<partial> order.
4249 #include <isl/set.h>
4250 int isl_set_plain_cmp(__isl_keep isl_set *set1,
4251 __isl_keep isl_set *set2);
4253 This function is useful for sorting C<isl_set>s.
4254 The order depends on the internal representation of the inputs.
4255 The order is fixed over different calls to the function (assuming
4256 the internal representation of the inputs has not changed), but may
4257 change over different versions of C<isl>.
4259 #include <isl/aff.h>
4260 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4261 __isl_keep isl_pw_aff *pa2);
4263 The function C<isl_pw_aff_plain_cmp> can be used to sort
4264 C<isl_pw_aff>s. The order is not strictly defined.
4265 The current order sorts expressions that only involve
4266 earlier dimensions before those that involve later dimensions.
4270 =head2 Unary Operations
4276 __isl_give isl_set *isl_set_complement(
4277 __isl_take isl_set *set);
4278 __isl_give isl_map *isl_map_complement(
4279 __isl_take isl_map *map);
4283 #include <isl/space.h>
4284 __isl_give isl_space *isl_space_reverse(
4285 __isl_take isl_space *space);
4287 #include <isl/map.h>
4288 __isl_give isl_basic_map *isl_basic_map_reverse(
4289 __isl_take isl_basic_map *bmap);
4290 __isl_give isl_map *isl_map_reverse(
4291 __isl_take isl_map *map);
4293 #include <isl/union_map.h>
4294 __isl_give isl_union_map *isl_union_map_reverse(
4295 __isl_take isl_union_map *umap);
4299 #include <isl/space.h>
4300 __isl_give isl_space *isl_space_domain(
4301 __isl_take isl_space *space);
4302 __isl_give isl_space *isl_space_range(
4303 __isl_take isl_space *space);
4304 __isl_give isl_space *isl_space_params(
4305 __isl_take isl_space *space);
4307 #include <isl/local_space.h>
4308 __isl_give isl_local_space *isl_local_space_domain(
4309 __isl_take isl_local_space *ls);
4310 __isl_give isl_local_space *isl_local_space_range(
4311 __isl_take isl_local_space *ls);
4313 #include <isl/set.h>
4314 __isl_give isl_basic_set *isl_basic_set_project_out(
4315 __isl_take isl_basic_set *bset,
4316 enum isl_dim_type type, unsigned first, unsigned n);
4317 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
4318 enum isl_dim_type type, unsigned first, unsigned n);
4319 __isl_give isl_map *isl_set_project_onto_map(
4320 __isl_take isl_set *set,
4321 enum isl_dim_type type, unsigned first,
4323 __isl_give isl_basic_set *isl_basic_set_params(
4324 __isl_take isl_basic_set *bset);
4325 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
4327 The function C<isl_set_project_onto_map> returns a relation
4328 that projects the input set onto the given set dimensions.
4330 #include <isl/map.h>
4331 __isl_give isl_basic_map *isl_basic_map_project_out(
4332 __isl_take isl_basic_map *bmap,
4333 enum isl_dim_type type, unsigned first, unsigned n);
4334 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
4335 enum isl_dim_type type, unsigned first, unsigned n);
4336 __isl_give isl_basic_set *isl_basic_map_domain(
4337 __isl_take isl_basic_map *bmap);
4338 __isl_give isl_basic_set *isl_basic_map_range(
4339 __isl_take isl_basic_map *bmap);
4340 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
4341 __isl_give isl_set *isl_map_domain(
4342 __isl_take isl_map *bmap);
4343 __isl_give isl_set *isl_map_range(
4344 __isl_take isl_map *map);
4346 #include <isl/union_set.h>
4347 __isl_give isl_union_set *isl_union_set_project_out(
4348 __isl_take isl_union_set *uset,
4349 enum isl_dim_type type,
4350 unsigned first, unsigned n);
4351 __isl_give isl_set *isl_union_set_params(
4352 __isl_take isl_union_set *uset);
4354 The function C<isl_union_set_project_out> can only project out
4357 #include <isl/union_map.h>
4358 __isl_give isl_union_map *isl_union_map_project_out(
4359 __isl_take isl_union_map *umap,
4360 enum isl_dim_type type, unsigned first, unsigned n);
4361 __isl_give isl_set *isl_union_map_params(
4362 __isl_take isl_union_map *umap);
4363 __isl_give isl_union_set *isl_union_map_domain(
4364 __isl_take isl_union_map *umap);
4365 __isl_give isl_union_set *isl_union_map_range(
4366 __isl_take isl_union_map *umap);
4368 The function C<isl_union_map_project_out> can only project out
4371 #include <isl/aff.h>
4372 __isl_give isl_aff *isl_aff_project_domain_on_params(
4373 __isl_take isl_aff *aff);
4374 __isl_give isl_pw_multi_aff *
4375 isl_pw_multi_aff_project_domain_on_params(
4376 __isl_take isl_pw_multi_aff *pma);
4377 __isl_give isl_set *isl_pw_aff_domain(
4378 __isl_take isl_pw_aff *pwaff);
4379 __isl_give isl_set *isl_pw_multi_aff_domain(
4380 __isl_take isl_pw_multi_aff *pma);
4381 __isl_give isl_set *isl_multi_pw_aff_domain(
4382 __isl_take isl_multi_pw_aff *mpa);
4383 __isl_give isl_union_set *isl_union_pw_aff_domain(
4384 __isl_take isl_union_pw_aff *upa);
4385 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4386 __isl_take isl_union_pw_multi_aff *upma);
4387 __isl_give isl_union_set *
4388 isl_multi_union_pw_aff_domain(
4389 __isl_take isl_multi_union_pw_aff *mupa);
4390 __isl_give isl_set *isl_pw_aff_params(
4391 __isl_take isl_pw_aff *pwa);
4393 The function C<isl_multi_union_pw_aff_domain> requires its
4394 input to have at least one set dimension.
4396 #include <isl/polynomial.h>
4397 __isl_give isl_qpolynomial *
4398 isl_qpolynomial_project_domain_on_params(
4399 __isl_take isl_qpolynomial *qp);
4400 __isl_give isl_pw_qpolynomial *
4401 isl_pw_qpolynomial_project_domain_on_params(
4402 __isl_take isl_pw_qpolynomial *pwqp);
4403 __isl_give isl_pw_qpolynomial_fold *
4404 isl_pw_qpolynomial_fold_project_domain_on_params(
4405 __isl_take isl_pw_qpolynomial_fold *pwf);
4406 __isl_give isl_set *isl_pw_qpolynomial_domain(
4407 __isl_take isl_pw_qpolynomial *pwqp);
4408 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4409 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4410 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4411 __isl_take isl_union_pw_qpolynomial *upwqp);
4413 #include <isl/space.h>
4414 __isl_give isl_space *isl_space_domain_map(
4415 __isl_take isl_space *space);
4416 __isl_give isl_space *isl_space_range_map(
4417 __isl_take isl_space *space);
4419 #include <isl/map.h>
4420 __isl_give isl_map *isl_set_wrapped_domain_map(
4421 __isl_take isl_set *set);
4422 __isl_give isl_basic_map *isl_basic_map_domain_map(
4423 __isl_take isl_basic_map *bmap);
4424 __isl_give isl_basic_map *isl_basic_map_range_map(
4425 __isl_take isl_basic_map *bmap);
4426 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
4427 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
4429 #include <isl/union_map.h>
4430 __isl_give isl_union_map *isl_union_map_domain_map(
4431 __isl_take isl_union_map *umap);
4432 __isl_give isl_union_pw_multi_aff *
4433 isl_union_map_domain_map_union_pw_multi_aff(
4434 __isl_take isl_union_map *umap);
4435 __isl_give isl_union_map *isl_union_map_range_map(
4436 __isl_take isl_union_map *umap);
4437 __isl_give isl_union_map *
4438 isl_union_set_wrapped_domain_map(
4439 __isl_take isl_union_set *uset);
4441 The functions above construct a (basic, regular or union) relation
4442 that maps (a wrapped version of) the input relation to its domain or range.
4443 C<isl_set_wrapped_domain_map> maps the input set to the domain
4444 of its wrapped relation.
4448 __isl_give isl_basic_set *isl_basic_set_eliminate(
4449 __isl_take isl_basic_set *bset,
4450 enum isl_dim_type type,
4451 unsigned first, unsigned n);
4452 __isl_give isl_set *isl_set_eliminate(
4453 __isl_take isl_set *set, enum isl_dim_type type,
4454 unsigned first, unsigned n);
4455 __isl_give isl_basic_map *isl_basic_map_eliminate(
4456 __isl_take isl_basic_map *bmap,
4457 enum isl_dim_type type,
4458 unsigned first, unsigned n);
4459 __isl_give isl_map *isl_map_eliminate(
4460 __isl_take isl_map *map, enum isl_dim_type type,
4461 unsigned first, unsigned n);
4463 Eliminate the coefficients for the given dimensions from the constraints,
4464 without removing the dimensions.
4466 =item * Constructing a set from a parameter domain
4468 A zero-dimensional space or (basic) set can be constructed
4469 on a given parameter domain using the following functions.
4471 #include <isl/space.h>
4472 __isl_give isl_space *isl_space_set_from_params(
4473 __isl_take isl_space *space);
4475 #include <isl/set.h>
4476 __isl_give isl_basic_set *isl_basic_set_from_params(
4477 __isl_take isl_basic_set *bset);
4478 __isl_give isl_set *isl_set_from_params(
4479 __isl_take isl_set *set);
4481 =item * Constructing a relation from one or two sets
4483 Create a relation with the given set(s) as domain and/or range.
4484 If only the domain or the range is specified, then
4485 the range or domain of the created relation is a zero-dimensional
4486 flat anonymous space.
4488 #include <isl/space.h>
4489 __isl_give isl_space *isl_space_from_domain(
4490 __isl_take isl_space *space);
4491 __isl_give isl_space *isl_space_from_range(
4492 __isl_take isl_space *space);
4493 __isl_give isl_space *isl_space_map_from_set(
4494 __isl_take isl_space *space);
4495 __isl_give isl_space *isl_space_map_from_domain_and_range(
4496 __isl_take isl_space *domain,
4497 __isl_take isl_space *range);
4499 #include <isl/local_space.h>
4500 __isl_give isl_local_space *isl_local_space_from_domain(
4501 __isl_take isl_local_space *ls);
4503 #include <isl/map.h>
4504 __isl_give isl_map *isl_map_from_domain(
4505 __isl_take isl_set *set);
4506 __isl_give isl_map *isl_map_from_range(
4507 __isl_take isl_set *set);
4509 #include <isl/union_map.h>
4510 __isl_give isl_union_map *
4511 isl_union_map_from_domain_and_range(
4512 __isl_take isl_union_set *domain,
4513 __isl_take isl_union_set *range);
4515 #include <isl/val.h>
4516 __isl_give isl_multi_val *isl_multi_val_from_range(
4517 __isl_take isl_multi_val *mv);
4519 #include <isl/aff.h>
4520 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4521 __isl_take isl_multi_aff *ma);
4522 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4523 __isl_take isl_pw_aff *pwa);
4524 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4525 __isl_take isl_multi_pw_aff *mpa);
4526 __isl_give isl_multi_union_pw_aff *
4527 isl_multi_union_pw_aff_from_range(
4528 __isl_take isl_multi_union_pw_aff *mupa);
4529 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4530 __isl_take isl_set *set);
4531 __isl_give isl_union_pw_multi_aff *
4532 isl_union_pw_multi_aff_from_domain(
4533 __isl_take isl_union_set *uset);
4537 #include <isl/set.h>
4538 __isl_give isl_basic_set *isl_basic_set_fix_si(
4539 __isl_take isl_basic_set *bset,
4540 enum isl_dim_type type, unsigned pos, int value);
4541 __isl_give isl_basic_set *isl_basic_set_fix_val(
4542 __isl_take isl_basic_set *bset,
4543 enum isl_dim_type type, unsigned pos,
4544 __isl_take isl_val *v);
4545 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
4546 enum isl_dim_type type, unsigned pos, int value);
4547 __isl_give isl_set *isl_set_fix_val(
4548 __isl_take isl_set *set,
4549 enum isl_dim_type type, unsigned pos,
4550 __isl_take isl_val *v);
4552 #include <isl/map.h>
4553 __isl_give isl_basic_map *isl_basic_map_fix_si(
4554 __isl_take isl_basic_map *bmap,
4555 enum isl_dim_type type, unsigned pos, int value);
4556 __isl_give isl_basic_map *isl_basic_map_fix_val(
4557 __isl_take isl_basic_map *bmap,
4558 enum isl_dim_type type, unsigned pos,
4559 __isl_take isl_val *v);
4560 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
4561 enum isl_dim_type type, unsigned pos, int value);
4562 __isl_give isl_map *isl_map_fix_val(
4563 __isl_take isl_map *map,
4564 enum isl_dim_type type, unsigned pos,
4565 __isl_take isl_val *v);
4567 #include <isl/aff.h>
4568 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4569 __isl_take isl_pw_multi_aff *pma,
4570 enum isl_dim_type type, unsigned pos, int value);
4572 #include <isl/polynomial.h>
4573 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4574 __isl_take isl_pw_qpolynomial *pwqp,
4575 enum isl_dim_type type, unsigned n,
4576 __isl_take isl_val *v);
4578 Intersect the set, relation or function domain
4579 with the hyperplane where the given
4580 dimension has the fixed given value.
4582 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
4583 __isl_take isl_basic_map *bmap,
4584 enum isl_dim_type type, unsigned pos, int value);
4585 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
4586 __isl_take isl_basic_map *bmap,
4587 enum isl_dim_type type, unsigned pos, int value);
4588 __isl_give isl_set *isl_set_lower_bound_si(
4589 __isl_take isl_set *set,
4590 enum isl_dim_type type, unsigned pos, int value);
4591 __isl_give isl_set *isl_set_lower_bound_val(
4592 __isl_take isl_set *set,
4593 enum isl_dim_type type, unsigned pos,
4594 __isl_take isl_val *value);
4595 __isl_give isl_map *isl_map_lower_bound_si(
4596 __isl_take isl_map *map,
4597 enum isl_dim_type type, unsigned pos, int value);
4598 __isl_give isl_set *isl_set_upper_bound_si(
4599 __isl_take isl_set *set,
4600 enum isl_dim_type type, unsigned pos, int value);
4601 __isl_give isl_set *isl_set_upper_bound_val(
4602 __isl_take isl_set *set,
4603 enum isl_dim_type type, unsigned pos,
4604 __isl_take isl_val *value);
4605 __isl_give isl_map *isl_map_upper_bound_si(
4606 __isl_take isl_map *map,
4607 enum isl_dim_type type, unsigned pos, int value);
4609 Intersect the set or relation with the half-space where the given
4610 dimension has a value bounded by the fixed given integer value.
4612 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
4613 enum isl_dim_type type1, int pos1,
4614 enum isl_dim_type type2, int pos2);
4615 __isl_give isl_basic_map *isl_basic_map_equate(
4616 __isl_take isl_basic_map *bmap,
4617 enum isl_dim_type type1, int pos1,
4618 enum isl_dim_type type2, int pos2);
4619 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
4620 enum isl_dim_type type1, int pos1,
4621 enum isl_dim_type type2, int pos2);
4623 Intersect the set or relation with the hyperplane where the given
4624 dimensions are equal to each other.
4626 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
4627 enum isl_dim_type type1, int pos1,
4628 enum isl_dim_type type2, int pos2);
4630 Intersect the relation with the hyperplane where the given
4631 dimensions have opposite values.
4633 __isl_give isl_map *isl_map_order_le(
4634 __isl_take isl_map *map,
4635 enum isl_dim_type type1, int pos1,
4636 enum isl_dim_type type2, int pos2);
4637 __isl_give isl_basic_map *isl_basic_map_order_ge(
4638 __isl_take isl_basic_map *bmap,
4639 enum isl_dim_type type1, int pos1,
4640 enum isl_dim_type type2, int pos2);
4641 __isl_give isl_map *isl_map_order_ge(
4642 __isl_take isl_map *map,
4643 enum isl_dim_type type1, int pos1,
4644 enum isl_dim_type type2, int pos2);
4645 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
4646 enum isl_dim_type type1, int pos1,
4647 enum isl_dim_type type2, int pos2);
4648 __isl_give isl_basic_map *isl_basic_map_order_gt(
4649 __isl_take isl_basic_map *bmap,
4650 enum isl_dim_type type1, int pos1,
4651 enum isl_dim_type type2, int pos2);
4652 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
4653 enum isl_dim_type type1, int pos1,
4654 enum isl_dim_type type2, int pos2);
4656 Intersect the relation with the half-space where the given
4657 dimensions satisfy the given ordering.
4661 #include <isl/aff.h>
4662 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4663 __isl_take isl_aff *aff);
4664 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4665 __isl_take isl_aff *aff);
4666 __isl_give isl_set *isl_pw_aff_pos_set(
4667 __isl_take isl_pw_aff *pa);
4668 __isl_give isl_set *isl_pw_aff_nonneg_set(
4669 __isl_take isl_pw_aff *pwaff);
4670 __isl_give isl_set *isl_pw_aff_zero_set(
4671 __isl_take isl_pw_aff *pwaff);
4672 __isl_give isl_set *isl_pw_aff_non_zero_set(
4673 __isl_take isl_pw_aff *pwaff);
4674 __isl_give isl_union_set *
4675 isl_union_pw_aff_zero_union_set(
4676 __isl_take isl_union_pw_aff *upa);
4677 __isl_give isl_union_set *
4678 isl_multi_union_pw_aff_zero_union_set(
4679 __isl_take isl_multi_union_pw_aff *mupa);
4681 The function C<isl_aff_neg_basic_set> returns a basic set
4682 containing those elements in the domain space
4683 of C<aff> where C<aff> is negative.
4684 The function C<isl_pw_aff_nonneg_set> returns a set
4685 containing those elements in the domain
4686 of C<pwaff> where C<pwaff> is non-negative.
4687 The function C<isl_multi_union_pw_aff_zero_union_set>
4688 returns a union set containing those elements
4689 in the domains of its elements where they are all zero.
4693 __isl_give isl_map *isl_set_identity(
4694 __isl_take isl_set *set);
4695 __isl_give isl_union_map *isl_union_set_identity(
4696 __isl_take isl_union_set *uset);
4697 __isl_give isl_union_pw_multi_aff *
4698 isl_union_set_identity_union_pw_multi_aff(
4699 __isl_take isl_union_set *uset);
4701 Construct an identity relation on the given (union) set.
4703 =item * Function Extraction
4705 A piecewise quasi affine expression that is equal to 1 on a set
4706 and 0 outside the set can be created using the following function.
4708 #include <isl/aff.h>
4709 __isl_give isl_pw_aff *isl_set_indicator_function(
4710 __isl_take isl_set *set);
4712 A piecewise multiple quasi affine expression can be extracted
4713 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4714 and the C<isl_map> is single-valued.
4715 In case of a conversion from an C<isl_union_map>
4716 to an C<isl_union_pw_multi_aff>, these properties need to hold
4717 in each domain space.
4718 A conversion to a C<isl_multi_union_pw_aff> additionally
4719 requires that the input is non-empty and involves only a single
4722 #include <isl/aff.h>
4723 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4724 __isl_take isl_set *set);
4725 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4726 __isl_take isl_map *map);
4728 __isl_give isl_union_pw_multi_aff *
4729 isl_union_pw_multi_aff_from_union_set(
4730 __isl_take isl_union_set *uset);
4731 __isl_give isl_union_pw_multi_aff *
4732 isl_union_pw_multi_aff_from_union_map(
4733 __isl_take isl_union_map *umap);
4735 __isl_give isl_multi_union_pw_aff *
4736 isl_multi_union_pw_aff_from_union_map(
4737 __isl_take isl_union_map *umap);
4741 __isl_give isl_basic_set *isl_basic_map_deltas(
4742 __isl_take isl_basic_map *bmap);
4743 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
4744 __isl_give isl_union_set *isl_union_map_deltas(
4745 __isl_take isl_union_map *umap);
4747 These functions return a (basic) set containing the differences
4748 between image elements and corresponding domain elements in the input.
4750 __isl_give isl_basic_map *isl_basic_map_deltas_map(
4751 __isl_take isl_basic_map *bmap);
4752 __isl_give isl_map *isl_map_deltas_map(
4753 __isl_take isl_map *map);
4754 __isl_give isl_union_map *isl_union_map_deltas_map(
4755 __isl_take isl_union_map *umap);
4757 The functions above construct a (basic, regular or union) relation
4758 that maps (a wrapped version of) the input relation to its delta set.
4762 Simplify the representation of a set, relation or functions by trying
4763 to combine pairs of basic sets or relations into a single
4764 basic set or relation.
4766 #include <isl/set.h>
4767 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
4769 #include <isl/map.h>
4770 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
4772 #include <isl/union_set.h>
4773 __isl_give isl_union_set *isl_union_set_coalesce(
4774 __isl_take isl_union_set *uset);
4776 #include <isl/union_map.h>
4777 __isl_give isl_union_map *isl_union_map_coalesce(
4778 __isl_take isl_union_map *umap);
4780 #include <isl/aff.h>
4781 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4782 __isl_take isl_pw_aff *pwqp);
4783 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4784 __isl_take isl_pw_multi_aff *pma);
4785 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4786 __isl_take isl_multi_pw_aff *mpa);
4787 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
4788 __isl_take isl_union_pw_aff *upa);
4789 __isl_give isl_union_pw_multi_aff *
4790 isl_union_pw_multi_aff_coalesce(
4791 __isl_take isl_union_pw_multi_aff *upma);
4792 __isl_give isl_multi_union_pw_aff *
4793 isl_multi_union_pw_aff_coalesce(
4794 __isl_take isl_multi_union_pw_aff *aff);
4796 #include <isl/polynomial.h>
4797 __isl_give isl_pw_qpolynomial_fold *
4798 isl_pw_qpolynomial_fold_coalesce(
4799 __isl_take isl_pw_qpolynomial_fold *pwf);
4800 __isl_give isl_union_pw_qpolynomial *
4801 isl_union_pw_qpolynomial_coalesce(
4802 __isl_take isl_union_pw_qpolynomial *upwqp);
4803 __isl_give isl_union_pw_qpolynomial_fold *
4804 isl_union_pw_qpolynomial_fold_coalesce(
4805 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4807 One of the methods for combining pairs of basic sets or relations
4808 can result in coefficients that are much larger than those that appear
4809 in the constraints of the input. By default, the coefficients are
4810 not allowed to grow larger, but this can be changed by unsetting
4811 the following option.
4813 isl_stat isl_options_set_coalesce_bounded_wrapping(
4814 isl_ctx *ctx, int val);
4815 int isl_options_get_coalesce_bounded_wrapping(
4818 =item * Detecting equalities
4820 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
4821 __isl_take isl_basic_set *bset);
4822 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
4823 __isl_take isl_basic_map *bmap);
4824 __isl_give isl_set *isl_set_detect_equalities(
4825 __isl_take isl_set *set);
4826 __isl_give isl_map *isl_map_detect_equalities(
4827 __isl_take isl_map *map);
4828 __isl_give isl_union_set *isl_union_set_detect_equalities(
4829 __isl_take isl_union_set *uset);
4830 __isl_give isl_union_map *isl_union_map_detect_equalities(
4831 __isl_take isl_union_map *umap);
4833 Simplify the representation of a set or relation by detecting implicit
4836 =item * Removing redundant constraints
4838 #include <isl/set.h>
4839 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
4840 __isl_take isl_basic_set *bset);
4841 __isl_give isl_set *isl_set_remove_redundancies(
4842 __isl_take isl_set *set);
4844 #include <isl/union_set.h>
4845 __isl_give isl_union_set *
4846 isl_union_set_remove_redundancies(
4847 __isl_take isl_union_set *uset);
4849 #include <isl/map.h>
4850 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
4851 __isl_take isl_basic_map *bmap);
4852 __isl_give isl_map *isl_map_remove_redundancies(
4853 __isl_take isl_map *map);
4855 #include <isl/union_map.h>
4856 __isl_give isl_union_map *
4857 isl_union_map_remove_redundancies(
4858 __isl_take isl_union_map *umap);
4862 __isl_give isl_basic_set *isl_set_convex_hull(
4863 __isl_take isl_set *set);
4864 __isl_give isl_basic_map *isl_map_convex_hull(
4865 __isl_take isl_map *map);
4867 If the input set or relation has any existentially quantified
4868 variables, then the result of these operations is currently undefined.
4872 #include <isl/set.h>
4873 __isl_give isl_basic_set *
4874 isl_set_unshifted_simple_hull(
4875 __isl_take isl_set *set);
4876 __isl_give isl_basic_set *isl_set_simple_hull(
4877 __isl_take isl_set *set);
4878 __isl_give isl_basic_set *
4879 isl_set_plain_unshifted_simple_hull(
4880 __isl_take isl_set *set);
4881 __isl_give isl_basic_set *
4882 isl_set_unshifted_simple_hull_from_set_list(
4883 __isl_take isl_set *set,
4884 __isl_take isl_set_list *list);
4886 #include <isl/map.h>
4887 __isl_give isl_basic_map *
4888 isl_map_unshifted_simple_hull(
4889 __isl_take isl_map *map);
4890 __isl_give isl_basic_map *isl_map_simple_hull(
4891 __isl_take isl_map *map);
4892 __isl_give isl_basic_map *
4893 isl_map_plain_unshifted_simple_hull(
4894 __isl_take isl_map *map);
4895 __isl_give isl_basic_map *
4896 isl_map_unshifted_simple_hull_from_map_list(
4897 __isl_take isl_map *map,
4898 __isl_take isl_map_list *list);
4900 #include <isl/union_map.h>
4901 __isl_give isl_union_map *isl_union_map_simple_hull(
4902 __isl_take isl_union_map *umap);
4904 These functions compute a single basic set or relation
4905 that contains the whole input set or relation.
4906 In particular, the output is described by translates
4907 of the constraints describing the basic sets or relations in the input.
4908 In case of C<isl_set_unshifted_simple_hull>, only the original
4909 constraints are used, without any translation.
4910 In case of C<isl_set_plain_unshifted_simple_hull> and
4911 C<isl_map_plain_unshifted_simple_hull>, the result is described
4912 by original constraints that are obviously satisfied
4913 by the entire input set or relation.
4914 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
4915 C<isl_map_unshifted_simple_hull_from_map_list>, the
4916 constraints are taken from the elements of the second argument.
4920 (See \autoref{s:simple hull}.)
4926 __isl_give isl_basic_set *isl_basic_set_affine_hull(
4927 __isl_take isl_basic_set *bset);
4928 __isl_give isl_basic_set *isl_set_affine_hull(
4929 __isl_take isl_set *set);
4930 __isl_give isl_union_set *isl_union_set_affine_hull(
4931 __isl_take isl_union_set *uset);
4932 __isl_give isl_basic_map *isl_basic_map_affine_hull(
4933 __isl_take isl_basic_map *bmap);
4934 __isl_give isl_basic_map *isl_map_affine_hull(
4935 __isl_take isl_map *map);
4936 __isl_give isl_union_map *isl_union_map_affine_hull(
4937 __isl_take isl_union_map *umap);
4939 In case of union sets and relations, the affine hull is computed
4942 =item * Polyhedral hull
4944 __isl_give isl_basic_set *isl_set_polyhedral_hull(
4945 __isl_take isl_set *set);
4946 __isl_give isl_basic_map *isl_map_polyhedral_hull(
4947 __isl_take isl_map *map);
4948 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
4949 __isl_take isl_union_set *uset);
4950 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
4951 __isl_take isl_union_map *umap);
4953 These functions compute a single basic set or relation
4954 not involving any existentially quantified variables
4955 that contains the whole input set or relation.
4956 In case of union sets and relations, the polyhedral hull is computed
4959 =item * Other approximations
4961 #include <isl/set.h>
4962 __isl_give isl_basic_set *
4963 isl_basic_set_drop_constraints_involving_dims(
4964 __isl_take isl_basic_set *bset,
4965 enum isl_dim_type type,
4966 unsigned first, unsigned n);
4967 __isl_give isl_basic_set *
4968 isl_basic_set_drop_constraints_not_involving_dims(
4969 __isl_take isl_basic_set *bset,
4970 enum isl_dim_type type,
4971 unsigned first, unsigned n);
4972 __isl_give isl_set *
4973 isl_set_drop_constraints_involving_dims(
4974 __isl_take isl_set *set,
4975 enum isl_dim_type type,
4976 unsigned first, unsigned n);
4977 __isl_give isl_set *
4978 isl_set_drop_constraints_not_involving_dims(
4979 __isl_take isl_set *set,
4980 enum isl_dim_type type,
4981 unsigned first, unsigned n);
4983 #include <isl/map.h>
4984 __isl_give isl_basic_map *
4985 isl_basic_map_drop_constraints_involving_dims(
4986 __isl_take isl_basic_map *bmap,
4987 enum isl_dim_type type,
4988 unsigned first, unsigned n);
4989 __isl_give isl_basic_map *
4990 isl_basic_map_drop_constraints_not_involving_dims(
4991 __isl_take isl_basic_map *bmap,
4992 enum isl_dim_type type,
4993 unsigned first, unsigned n);
4994 __isl_give isl_map *
4995 isl_map_drop_constraints_involving_dims(
4996 __isl_take isl_map *map,
4997 enum isl_dim_type type,
4998 unsigned first, unsigned n);
4999 __isl_give isl_map *
5000 isl_map_drop_constraints_not_involving_dims(
5001 __isl_take isl_map *map,
5002 enum isl_dim_type type,
5003 unsigned first, unsigned n);
5005 These functions drop any constraints (not) involving the specified dimensions.
5006 Note that the result depends on the representation of the input.
5008 #include <isl/polynomial.h>
5009 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5010 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5011 __isl_give isl_union_pw_qpolynomial *
5012 isl_union_pw_qpolynomial_to_polynomial(
5013 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5015 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5016 the polynomial will be an overapproximation. If C<sign> is negative,
5017 it will be an underapproximation. If C<sign> is zero, the approximation
5018 will lie somewhere in between.
5022 __isl_give isl_basic_set *isl_basic_set_sample(
5023 __isl_take isl_basic_set *bset);
5024 __isl_give isl_basic_set *isl_set_sample(
5025 __isl_take isl_set *set);
5026 __isl_give isl_basic_map *isl_basic_map_sample(
5027 __isl_take isl_basic_map *bmap);
5028 __isl_give isl_basic_map *isl_map_sample(
5029 __isl_take isl_map *map);
5031 If the input (basic) set or relation is non-empty, then return
5032 a singleton subset of the input. Otherwise, return an empty set.
5034 =item * Optimization
5036 #include <isl/ilp.h>
5037 __isl_give isl_val *isl_basic_set_max_val(
5038 __isl_keep isl_basic_set *bset,
5039 __isl_keep isl_aff *obj);
5040 __isl_give isl_val *isl_set_min_val(
5041 __isl_keep isl_set *set,
5042 __isl_keep isl_aff *obj);
5043 __isl_give isl_val *isl_set_max_val(
5044 __isl_keep isl_set *set,
5045 __isl_keep isl_aff *obj);
5046 __isl_give isl_multi_val *
5047 isl_union_set_min_multi_union_pw_aff(
5048 __isl_keep isl_union_set *set,
5049 __isl_keep isl_multi_union_pw_aff *obj);
5051 Compute the minimum or maximum of the integer affine expression C<obj>
5052 over the points in C<set>, returning the result in C<opt>.
5053 The result is C<NULL> in case of an error, the optimal value in case
5054 there is one, negative infinity or infinity if the problem is unbounded and
5055 NaN if the problem is empty.
5057 =item * Parametric optimization
5059 __isl_give isl_pw_aff *isl_set_dim_min(
5060 __isl_take isl_set *set, int pos);
5061 __isl_give isl_pw_aff *isl_set_dim_max(
5062 __isl_take isl_set *set, int pos);
5063 __isl_give isl_pw_aff *isl_map_dim_min(
5064 __isl_take isl_map *map, int pos);
5065 __isl_give isl_pw_aff *isl_map_dim_max(
5066 __isl_take isl_map *map, int pos);
5068 Compute the minimum or maximum of the given set or output dimension
5069 as a function of the parameters (and input dimensions), but independently
5070 of the other set or output dimensions.
5071 For lexicographic optimization, see L<"Lexicographic Optimization">.
5075 The following functions compute either the set of (rational) coefficient
5076 values of valid constraints for the given set or the set of (rational)
5077 values satisfying the constraints with coefficients from the given set.
5078 Internally, these two sets of functions perform essentially the
5079 same operations, except that the set of coefficients is assumed to
5080 be a cone, while the set of values may be any polyhedron.
5081 The current implementation is based on the Farkas lemma and
5082 Fourier-Motzkin elimination, but this may change or be made optional
5083 in future. In particular, future implementations may use different
5084 dualization algorithms or skip the elimination step.
5086 __isl_give isl_basic_set *isl_basic_set_coefficients(
5087 __isl_take isl_basic_set *bset);
5088 __isl_give isl_basic_set *isl_set_coefficients(
5089 __isl_take isl_set *set);
5090 __isl_give isl_union_set *isl_union_set_coefficients(
5091 __isl_take isl_union_set *bset);
5092 __isl_give isl_basic_set *isl_basic_set_solutions(
5093 __isl_take isl_basic_set *bset);
5094 __isl_give isl_basic_set *isl_set_solutions(
5095 __isl_take isl_set *set);
5096 __isl_give isl_union_set *isl_union_set_solutions(
5097 __isl_take isl_union_set *bset);
5101 __isl_give isl_map *isl_map_fixed_power_val(
5102 __isl_take isl_map *map,
5103 __isl_take isl_val *exp);
5104 __isl_give isl_union_map *
5105 isl_union_map_fixed_power_val(
5106 __isl_take isl_union_map *umap,
5107 __isl_take isl_val *exp);
5109 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
5110 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
5111 of C<map> is computed.
5113 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
5115 __isl_give isl_union_map *isl_union_map_power(
5116 __isl_take isl_union_map *umap, int *exact);
5118 Compute a parametric representation for all positive powers I<k> of C<map>.
5119 The result maps I<k> to a nested relation corresponding to the
5120 I<k>th power of C<map>.
5121 The result may be an overapproximation. If the result is known to be exact,
5122 then C<*exact> is set to C<1>.
5124 =item * Transitive closure
5126 __isl_give isl_map *isl_map_transitive_closure(
5127 __isl_take isl_map *map, int *exact);
5128 __isl_give isl_union_map *isl_union_map_transitive_closure(
5129 __isl_take isl_union_map *umap, int *exact);
5131 Compute the transitive closure of C<map>.
5132 The result may be an overapproximation. If the result is known to be exact,
5133 then C<*exact> is set to C<1>.
5135 =item * Reaching path lengths
5137 __isl_give isl_map *isl_map_reaching_path_lengths(
5138 __isl_take isl_map *map, int *exact);
5140 Compute a relation that maps each element in the range of C<map>
5141 to the lengths of all paths composed of edges in C<map> that
5142 end up in the given element.
5143 The result may be an overapproximation. If the result is known to be exact,
5144 then C<*exact> is set to C<1>.
5145 To compute the I<maximal> path length, the resulting relation
5146 should be postprocessed by C<isl_map_lexmax>.
5147 In particular, if the input relation is a dependence relation
5148 (mapping sources to sinks), then the maximal path length corresponds
5149 to the free schedule.
5150 Note, however, that C<isl_map_lexmax> expects the maximum to be
5151 finite, so if the path lengths are unbounded (possibly due to
5152 the overapproximation), then you will get an error message.
5156 #include <isl/space.h>
5157 __isl_give isl_space *isl_space_wrap(
5158 __isl_take isl_space *space);
5159 __isl_give isl_space *isl_space_unwrap(
5160 __isl_take isl_space *space);
5162 #include <isl/local_space.h>
5163 __isl_give isl_local_space *isl_local_space_wrap(
5164 __isl_take isl_local_space *ls);
5166 #include <isl/set.h>
5167 __isl_give isl_basic_map *isl_basic_set_unwrap(
5168 __isl_take isl_basic_set *bset);
5169 __isl_give isl_map *isl_set_unwrap(
5170 __isl_take isl_set *set);
5172 #include <isl/map.h>
5173 __isl_give isl_basic_set *isl_basic_map_wrap(
5174 __isl_take isl_basic_map *bmap);
5175 __isl_give isl_set *isl_map_wrap(
5176 __isl_take isl_map *map);
5178 #include <isl/union_set.h>
5179 __isl_give isl_union_map *isl_union_set_unwrap(
5180 __isl_take isl_union_set *uset);
5182 #include <isl/union_map.h>
5183 __isl_give isl_union_set *isl_union_map_wrap(
5184 __isl_take isl_union_map *umap);
5186 The input to C<isl_space_unwrap> should
5187 be the space of a set, while that of
5188 C<isl_space_wrap> should be the space of a relation.
5189 Conversely, the output of C<isl_space_unwrap> is the space
5190 of a relation, while that of C<isl_space_wrap> is the space of a set.
5194 Remove any internal structure of domain (and range) of the given
5195 set or relation. If there is any such internal structure in the input,
5196 then the name of the space is also removed.
5198 #include <isl/local_space.h>
5199 __isl_give isl_local_space *
5200 isl_local_space_flatten_domain(
5201 __isl_take isl_local_space *ls);
5202 __isl_give isl_local_space *
5203 isl_local_space_flatten_range(
5204 __isl_take isl_local_space *ls);
5206 #include <isl/set.h>
5207 __isl_give isl_basic_set *isl_basic_set_flatten(
5208 __isl_take isl_basic_set *bset);
5209 __isl_give isl_set *isl_set_flatten(
5210 __isl_take isl_set *set);
5212 #include <isl/map.h>
5213 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
5214 __isl_take isl_basic_map *bmap);
5215 __isl_give isl_basic_map *isl_basic_map_flatten_range(
5216 __isl_take isl_basic_map *bmap);
5217 __isl_give isl_map *isl_map_flatten_range(
5218 __isl_take isl_map *map);
5219 __isl_give isl_map *isl_map_flatten_domain(
5220 __isl_take isl_map *map);
5221 __isl_give isl_basic_map *isl_basic_map_flatten(
5222 __isl_take isl_basic_map *bmap);
5223 __isl_give isl_map *isl_map_flatten(
5224 __isl_take isl_map *map);
5226 #include <isl/val.h>
5227 __isl_give isl_multi_val *isl_multi_val_flatten_range(
5228 __isl_take isl_multi_val *mv);
5230 #include <isl/aff.h>
5231 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
5232 __isl_take isl_multi_aff *ma);
5233 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
5234 __isl_take isl_multi_aff *ma);
5235 __isl_give isl_multi_pw_aff *
5236 isl_multi_pw_aff_flatten_range(
5237 __isl_take isl_multi_pw_aff *mpa);
5238 __isl_give isl_multi_union_pw_aff *
5239 isl_multi_union_pw_aff_flatten_range(
5240 __isl_take isl_multi_union_pw_aff *mupa);
5242 #include <isl/map.h>
5243 __isl_give isl_map *isl_set_flatten_map(
5244 __isl_take isl_set *set);
5246 The function above constructs a relation
5247 that maps the input set to a flattened version of the set.
5251 Lift the input set to a space with extra dimensions corresponding
5252 to the existentially quantified variables in the input.
5253 In particular, the result lives in a wrapped map where the domain
5254 is the original space and the range corresponds to the original
5255 existentially quantified variables.
5257 #include <isl/set.h>
5258 __isl_give isl_basic_set *isl_basic_set_lift(
5259 __isl_take isl_basic_set *bset);
5260 __isl_give isl_set *isl_set_lift(
5261 __isl_take isl_set *set);
5262 __isl_give isl_union_set *isl_union_set_lift(
5263 __isl_take isl_union_set *uset);
5265 Given a local space that contains the existentially quantified
5266 variables of a set, a basic relation that, when applied to
5267 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
5268 can be constructed using the following function.
5270 #include <isl/local_space.h>
5271 __isl_give isl_basic_map *isl_local_space_lifting(
5272 __isl_take isl_local_space *ls);
5274 #include <isl/aff.h>
5275 __isl_give isl_multi_aff *isl_multi_aff_lift(
5276 __isl_take isl_multi_aff *maff,
5277 __isl_give isl_local_space **ls);
5279 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
5280 then it is assigned the local space that lies at the basis of
5281 the lifting applied.
5283 =item * Internal Product
5285 #include <isl/space.h>
5286 __isl_give isl_space *isl_space_zip(
5287 __isl_take isl_space *space);
5289 #include <isl/map.h>
5290 __isl_give isl_basic_map *isl_basic_map_zip(
5291 __isl_take isl_basic_map *bmap);
5292 __isl_give isl_map *isl_map_zip(
5293 __isl_take isl_map *map);
5295 #include <isl/union_map.h>
5296 __isl_give isl_union_map *isl_union_map_zip(
5297 __isl_take isl_union_map *umap);
5299 Given a relation with nested relations for domain and range,
5300 interchange the range of the domain with the domain of the range.
5304 #include <isl/space.h>
5305 __isl_give isl_space *isl_space_curry(
5306 __isl_take isl_space *space);
5307 __isl_give isl_space *isl_space_uncurry(
5308 __isl_take isl_space *space);
5310 #include <isl/map.h>
5311 __isl_give isl_basic_map *isl_basic_map_curry(
5312 __isl_take isl_basic_map *bmap);
5313 __isl_give isl_basic_map *isl_basic_map_uncurry(
5314 __isl_take isl_basic_map *bmap);
5315 __isl_give isl_map *isl_map_curry(
5316 __isl_take isl_map *map);
5317 __isl_give isl_map *isl_map_uncurry(
5318 __isl_take isl_map *map);
5320 #include <isl/union_map.h>
5321 __isl_give isl_union_map *isl_union_map_curry(
5322 __isl_take isl_union_map *umap);
5323 __isl_give isl_union_map *isl_union_map_uncurry(
5324 __isl_take isl_union_map *umap);
5326 Given a relation with a nested relation for domain,
5327 the C<curry> functions
5328 move the range of the nested relation out of the domain
5329 and use it as the domain of a nested relation in the range,
5330 with the original range as range of this nested relation.
5331 The C<uncurry> functions perform the inverse operation.
5333 #include <isl/space.h>
5334 __isl_give isl_space *isl_space_range_curry(
5335 __isl_take isl_space *space);
5337 #include <isl/map.h>
5338 __isl_give isl_map *isl_map_range_curry(
5339 __isl_take isl_map *map);
5341 #include <isl/union_map.h>
5342 __isl_give isl_union_map *isl_union_map_range_curry(
5343 __isl_take isl_union_map *umap);
5345 These functions apply the currying to the relation that
5346 is nested inside the range of the input.
5348 =item * Aligning parameters
5350 Change the order of the parameters of the given set, relation
5352 such that the first parameters match those of C<model>.
5353 This may involve the introduction of extra parameters.
5354 All parameters need to be named.
5356 #include <isl/space.h>
5357 __isl_give isl_space *isl_space_align_params(
5358 __isl_take isl_space *space1,
5359 __isl_take isl_space *space2)
5361 #include <isl/set.h>
5362 __isl_give isl_basic_set *isl_basic_set_align_params(
5363 __isl_take isl_basic_set *bset,
5364 __isl_take isl_space *model);
5365 __isl_give isl_set *isl_set_align_params(
5366 __isl_take isl_set *set,
5367 __isl_take isl_space *model);
5369 #include <isl/map.h>
5370 __isl_give isl_basic_map *isl_basic_map_align_params(
5371 __isl_take isl_basic_map *bmap,
5372 __isl_take isl_space *model);
5373 __isl_give isl_map *isl_map_align_params(
5374 __isl_take isl_map *map,
5375 __isl_take isl_space *model);
5377 #include <isl/val.h>
5378 __isl_give isl_multi_val *isl_multi_val_align_params(
5379 __isl_take isl_multi_val *mv,
5380 __isl_take isl_space *model);
5382 #include <isl/aff.h>
5383 __isl_give isl_aff *isl_aff_align_params(
5384 __isl_take isl_aff *aff,
5385 __isl_take isl_space *model);
5386 __isl_give isl_multi_aff *isl_multi_aff_align_params(
5387 __isl_take isl_multi_aff *multi,
5388 __isl_take isl_space *model);
5389 __isl_give isl_pw_aff *isl_pw_aff_align_params(
5390 __isl_take isl_pw_aff *pwaff,
5391 __isl_take isl_space *model);
5392 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
5393 __isl_take isl_pw_multi_aff *pma,
5394 __isl_take isl_space *model);
5395 __isl_give isl_union_pw_aff *
5396 isl_union_pw_aff_align_params(
5397 __isl_take isl_union_pw_aff *upa,
5398 __isl_take isl_space *model);
5399 __isl_give isl_union_pw_multi_aff *
5400 isl_union_pw_multi_aff_align_params(
5401 __isl_take isl_union_pw_multi_aff *upma,
5402 __isl_take isl_space *model);
5403 __isl_give isl_multi_union_pw_aff *
5404 isl_multi_union_pw_aff_align_params(
5405 __isl_take isl_multi_union_pw_aff *mupa,
5406 __isl_take isl_space *model);
5408 #include <isl/polynomial.h>
5409 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5410 __isl_take isl_qpolynomial *qp,
5411 __isl_take isl_space *model);
5413 =item * Unary Arithmetic Operations
5415 #include <isl/set.h>
5416 __isl_give isl_set *isl_set_neg(
5417 __isl_take isl_set *set);
5418 #include <isl/map.h>
5419 __isl_give isl_map *isl_map_neg(
5420 __isl_take isl_map *map);
5422 C<isl_set_neg> constructs a set containing the opposites of
5423 the elements in its argument.
5424 The domain of the result of C<isl_map_neg> is the same
5425 as the domain of its argument. The corresponding range
5426 elements are the opposites of the corresponding range
5427 elements in the argument.
5429 #include <isl/val.h>
5430 __isl_give isl_multi_val *isl_multi_val_neg(
5431 __isl_take isl_multi_val *mv);
5433 #include <isl/aff.h>
5434 __isl_give isl_aff *isl_aff_neg(
5435 __isl_take isl_aff *aff);
5436 __isl_give isl_multi_aff *isl_multi_aff_neg(
5437 __isl_take isl_multi_aff *ma);
5438 __isl_give isl_pw_aff *isl_pw_aff_neg(
5439 __isl_take isl_pw_aff *pwaff);
5440 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
5441 __isl_take isl_pw_multi_aff *pma);
5442 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
5443 __isl_take isl_multi_pw_aff *mpa);
5444 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
5445 __isl_take isl_union_pw_aff *upa);
5446 __isl_give isl_union_pw_multi_aff *
5447 isl_union_pw_multi_aff_neg(
5448 __isl_take isl_union_pw_multi_aff *upma);
5449 __isl_give isl_multi_union_pw_aff *
5450 isl_multi_union_pw_aff_neg(
5451 __isl_take isl_multi_union_pw_aff *mupa);
5452 __isl_give isl_aff *isl_aff_ceil(
5453 __isl_take isl_aff *aff);
5454 __isl_give isl_pw_aff *isl_pw_aff_ceil(
5455 __isl_take isl_pw_aff *pwaff);
5456 __isl_give isl_aff *isl_aff_floor(
5457 __isl_take isl_aff *aff);
5458 __isl_give isl_multi_aff *isl_multi_aff_floor(
5459 __isl_take isl_multi_aff *ma);
5460 __isl_give isl_pw_aff *isl_pw_aff_floor(
5461 __isl_take isl_pw_aff *pwaff);
5462 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
5463 __isl_take isl_union_pw_aff *upa);
5464 __isl_give isl_multi_union_pw_aff *
5465 isl_multi_union_pw_aff_floor(
5466 __isl_take isl_multi_union_pw_aff *mupa);
5468 #include <isl/aff.h>
5469 __isl_give isl_pw_aff *isl_pw_aff_list_min(
5470 __isl_take isl_pw_aff_list *list);
5471 __isl_give isl_pw_aff *isl_pw_aff_list_max(
5472 __isl_take isl_pw_aff_list *list);
5474 #include <isl/polynomial.h>
5475 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5476 __isl_take isl_qpolynomial *qp);
5477 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5478 __isl_take isl_pw_qpolynomial *pwqp);
5479 __isl_give isl_union_pw_qpolynomial *
5480 isl_union_pw_qpolynomial_neg(
5481 __isl_take isl_union_pw_qpolynomial *upwqp);
5482 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5483 __isl_take isl_qpolynomial *qp,
5485 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5486 __isl_take isl_pw_qpolynomial *pwqp,
5491 The following functions evaluate a function in a point.
5493 #include <isl/polynomial.h>
5494 __isl_give isl_val *isl_pw_qpolynomial_eval(
5495 __isl_take isl_pw_qpolynomial *pwqp,
5496 __isl_take isl_point *pnt);
5497 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5498 __isl_take isl_pw_qpolynomial_fold *pwf,
5499 __isl_take isl_point *pnt);
5500 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5501 __isl_take isl_union_pw_qpolynomial *upwqp,
5502 __isl_take isl_point *pnt);
5503 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5504 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5505 __isl_take isl_point *pnt);
5507 =item * Dimension manipulation
5509 It is usually not advisable to directly change the (input or output)
5510 space of a set or a relation as this removes the name and the internal
5511 structure of the space. However, the functions below can be useful
5512 to add new parameters, assuming
5513 C<isl_set_align_params> and C<isl_map_align_params>
5516 #include <isl/space.h>
5517 __isl_give isl_space *isl_space_add_dims(
5518 __isl_take isl_space *space,
5519 enum isl_dim_type type, unsigned n);
5520 __isl_give isl_space *isl_space_insert_dims(
5521 __isl_take isl_space *space,
5522 enum isl_dim_type type, unsigned pos, unsigned n);
5523 __isl_give isl_space *isl_space_drop_dims(
5524 __isl_take isl_space *space,
5525 enum isl_dim_type type, unsigned first, unsigned n);
5526 __isl_give isl_space *isl_space_move_dims(
5527 __isl_take isl_space *space,
5528 enum isl_dim_type dst_type, unsigned dst_pos,
5529 enum isl_dim_type src_type, unsigned src_pos,
5532 #include <isl/local_space.h>
5533 __isl_give isl_local_space *isl_local_space_add_dims(
5534 __isl_take isl_local_space *ls,
5535 enum isl_dim_type type, unsigned n);
5536 __isl_give isl_local_space *isl_local_space_insert_dims(
5537 __isl_take isl_local_space *ls,
5538 enum isl_dim_type type, unsigned first, unsigned n);
5539 __isl_give isl_local_space *isl_local_space_drop_dims(
5540 __isl_take isl_local_space *ls,
5541 enum isl_dim_type type, unsigned first, unsigned n);
5543 #include <isl/set.h>
5544 __isl_give isl_basic_set *isl_basic_set_add_dims(
5545 __isl_take isl_basic_set *bset,
5546 enum isl_dim_type type, unsigned n);
5547 __isl_give isl_set *isl_set_add_dims(
5548 __isl_take isl_set *set,
5549 enum isl_dim_type type, unsigned n);
5550 __isl_give isl_basic_set *isl_basic_set_insert_dims(
5551 __isl_take isl_basic_set *bset,
5552 enum isl_dim_type type, unsigned pos,
5554 __isl_give isl_set *isl_set_insert_dims(
5555 __isl_take isl_set *set,
5556 enum isl_dim_type type, unsigned pos, unsigned n);
5557 __isl_give isl_basic_set *isl_basic_set_move_dims(
5558 __isl_take isl_basic_set *bset,
5559 enum isl_dim_type dst_type, unsigned dst_pos,
5560 enum isl_dim_type src_type, unsigned src_pos,
5562 __isl_give isl_set *isl_set_move_dims(
5563 __isl_take isl_set *set,
5564 enum isl_dim_type dst_type, unsigned dst_pos,
5565 enum isl_dim_type src_type, unsigned src_pos,
5568 #include <isl/map.h>
5569 __isl_give isl_basic_map *isl_basic_map_add_dims(
5570 __isl_take isl_basic_map *bmap,
5571 enum isl_dim_type type, unsigned n);
5572 __isl_give isl_map *isl_map_add_dims(
5573 __isl_take isl_map *map,
5574 enum isl_dim_type type, unsigned n);
5575 __isl_give isl_basic_map *isl_basic_map_insert_dims(
5576 __isl_take isl_basic_map *bmap,
5577 enum isl_dim_type type, unsigned pos,
5579 __isl_give isl_map *isl_map_insert_dims(
5580 __isl_take isl_map *map,
5581 enum isl_dim_type type, unsigned pos, unsigned n);
5582 __isl_give isl_basic_map *isl_basic_map_move_dims(
5583 __isl_take isl_basic_map *bmap,
5584 enum isl_dim_type dst_type, unsigned dst_pos,
5585 enum isl_dim_type src_type, unsigned src_pos,
5587 __isl_give isl_map *isl_map_move_dims(
5588 __isl_take isl_map *map,
5589 enum isl_dim_type dst_type, unsigned dst_pos,
5590 enum isl_dim_type src_type, unsigned src_pos,
5593 #include <isl/val.h>
5594 __isl_give isl_multi_val *isl_multi_val_insert_dims(
5595 __isl_take isl_multi_val *mv,
5596 enum isl_dim_type type, unsigned first, unsigned n);
5597 __isl_give isl_multi_val *isl_multi_val_add_dims(
5598 __isl_take isl_multi_val *mv,
5599 enum isl_dim_type type, unsigned n);
5600 __isl_give isl_multi_val *isl_multi_val_drop_dims(
5601 __isl_take isl_multi_val *mv,
5602 enum isl_dim_type type, unsigned first, unsigned n);
5604 #include <isl/aff.h>
5605 __isl_give isl_aff *isl_aff_insert_dims(
5606 __isl_take isl_aff *aff,
5607 enum isl_dim_type type, unsigned first, unsigned n);
5608 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
5609 __isl_take isl_multi_aff *ma,
5610 enum isl_dim_type type, unsigned first, unsigned n);
5611 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
5612 __isl_take isl_pw_aff *pwaff,
5613 enum isl_dim_type type, unsigned first, unsigned n);
5614 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
5615 __isl_take isl_multi_pw_aff *mpa,
5616 enum isl_dim_type type, unsigned first, unsigned n);
5617 __isl_give isl_aff *isl_aff_add_dims(
5618 __isl_take isl_aff *aff,
5619 enum isl_dim_type type, unsigned n);
5620 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
5621 __isl_take isl_multi_aff *ma,
5622 enum isl_dim_type type, unsigned n);
5623 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
5624 __isl_take isl_pw_aff *pwaff,
5625 enum isl_dim_type type, unsigned n);
5626 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
5627 __isl_take isl_multi_pw_aff *mpa,
5628 enum isl_dim_type type, unsigned n);
5629 __isl_give isl_aff *isl_aff_drop_dims(
5630 __isl_take isl_aff *aff,
5631 enum isl_dim_type type, unsigned first, unsigned n);
5632 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
5633 __isl_take isl_multi_aff *maff,
5634 enum isl_dim_type type, unsigned first, unsigned n);
5635 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
5636 __isl_take isl_pw_aff *pwaff,
5637 enum isl_dim_type type, unsigned first, unsigned n);
5638 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
5639 __isl_take isl_pw_multi_aff *pma,
5640 enum isl_dim_type type, unsigned first, unsigned n);
5641 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
5642 __isl_take isl_union_pw_aff *upa,
5643 enum isl_dim_type type, unsigned first, unsigned n);
5644 __isl_give isl_union_pw_multi_aff *
5645 isl_union_pw_multi_aff_drop_dims(
5646 __isl_take isl_union_pw_multi_aff *upma,
5647 enum isl_dim_type type,
5648 unsigned first, unsigned n);
5649 __isl_give isl_multi_union_pw_aff *
5650 isl_multi_union_pw_aff_drop_dims(
5651 __isl_take isl_multi_union_pw_aff *mupa,
5652 enum isl_dim_type type, unsigned first,
5654 __isl_give isl_aff *isl_aff_move_dims(
5655 __isl_take isl_aff *aff,
5656 enum isl_dim_type dst_type, unsigned dst_pos,
5657 enum isl_dim_type src_type, unsigned src_pos,
5659 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
5660 __isl_take isl_multi_aff *ma,
5661 enum isl_dim_type dst_type, unsigned dst_pos,
5662 enum isl_dim_type src_type, unsigned src_pos,
5664 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
5665 __isl_take isl_pw_aff *pa,
5666 enum isl_dim_type dst_type, unsigned dst_pos,
5667 enum isl_dim_type src_type, unsigned src_pos,
5669 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
5670 __isl_take isl_multi_pw_aff *pma,
5671 enum isl_dim_type dst_type, unsigned dst_pos,
5672 enum isl_dim_type src_type, unsigned src_pos,
5675 #include <isl/polynomial.h>
5676 __isl_give isl_union_pw_qpolynomial *
5677 isl_union_pw_qpolynomial_drop_dims(
5678 __isl_take isl_union_pw_qpolynomial *upwqp,
5679 enum isl_dim_type type,
5680 unsigned first, unsigned n);
5681 __isl_give isl_union_pw_qpolynomial_fold *
5682 isl_union_pw_qpolynomial_fold_drop_dims(
5683 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5684 enum isl_dim_type type,
5685 unsigned first, unsigned n);
5687 The operations on union expressions can only manipulate parameters.
5691 =head2 Binary Operations
5693 The two arguments of a binary operation not only need to live
5694 in the same C<isl_ctx>, they currently also need to have
5695 the same (number of) parameters.
5697 =head3 Basic Operations
5701 =item * Intersection
5703 #include <isl/local_space.h>
5704 __isl_give isl_local_space *isl_local_space_intersect(
5705 __isl_take isl_local_space *ls1,
5706 __isl_take isl_local_space *ls2);
5708 #include <isl/set.h>
5709 __isl_give isl_basic_set *isl_basic_set_intersect_params(
5710 __isl_take isl_basic_set *bset1,
5711 __isl_take isl_basic_set *bset2);
5712 __isl_give isl_basic_set *isl_basic_set_intersect(
5713 __isl_take isl_basic_set *bset1,
5714 __isl_take isl_basic_set *bset2);
5715 __isl_give isl_basic_set *isl_basic_set_list_intersect(
5716 __isl_take struct isl_basic_set_list *list);
5717 __isl_give isl_set *isl_set_intersect_params(
5718 __isl_take isl_set *set,
5719 __isl_take isl_set *params);
5720 __isl_give isl_set *isl_set_intersect(
5721 __isl_take isl_set *set1,
5722 __isl_take isl_set *set2);
5724 #include <isl/map.h>
5725 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
5726 __isl_take isl_basic_map *bmap,
5727 __isl_take isl_basic_set *bset);
5728 __isl_give isl_basic_map *isl_basic_map_intersect_range(
5729 __isl_take isl_basic_map *bmap,
5730 __isl_take isl_basic_set *bset);
5731 __isl_give isl_basic_map *isl_basic_map_intersect(
5732 __isl_take isl_basic_map *bmap1,
5733 __isl_take isl_basic_map *bmap2);
5734 __isl_give isl_basic_map *isl_basic_map_list_intersect(
5735 __isl_take isl_basic_map_list *list);
5736 __isl_give isl_map *isl_map_intersect_params(
5737 __isl_take isl_map *map,
5738 __isl_take isl_set *params);
5739 __isl_give isl_map *isl_map_intersect_domain(
5740 __isl_take isl_map *map,
5741 __isl_take isl_set *set);
5742 __isl_give isl_map *isl_map_intersect_range(
5743 __isl_take isl_map *map,
5744 __isl_take isl_set *set);
5745 __isl_give isl_map *isl_map_intersect(
5746 __isl_take isl_map *map1,
5747 __isl_take isl_map *map2);
5749 #include <isl/union_set.h>
5750 __isl_give isl_union_set *isl_union_set_intersect_params(
5751 __isl_take isl_union_set *uset,
5752 __isl_take isl_set *set);
5753 __isl_give isl_union_set *isl_union_set_intersect(
5754 __isl_take isl_union_set *uset1,
5755 __isl_take isl_union_set *uset2);
5757 #include <isl/union_map.h>
5758 __isl_give isl_union_map *isl_union_map_intersect_params(
5759 __isl_take isl_union_map *umap,
5760 __isl_take isl_set *set);
5761 __isl_give isl_union_map *isl_union_map_intersect_domain(
5762 __isl_take isl_union_map *umap,
5763 __isl_take isl_union_set *uset);
5764 __isl_give isl_union_map *isl_union_map_intersect_range(
5765 __isl_take isl_union_map *umap,
5766 __isl_take isl_union_set *uset);
5767 __isl_give isl_union_map *isl_union_map_intersect(
5768 __isl_take isl_union_map *umap1,
5769 __isl_take isl_union_map *umap2);
5771 #include <isl/aff.h>
5772 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
5773 __isl_take isl_pw_aff *pa,
5774 __isl_take isl_set *set);
5775 __isl_give isl_multi_pw_aff *
5776 isl_multi_pw_aff_intersect_domain(
5777 __isl_take isl_multi_pw_aff *mpa,
5778 __isl_take isl_set *domain);
5779 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
5780 __isl_take isl_pw_multi_aff *pma,
5781 __isl_take isl_set *set);
5782 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
5783 __isl_take isl_union_pw_aff *upa,
5784 __isl_take isl_union_set *uset);
5785 __isl_give isl_union_pw_multi_aff *
5786 isl_union_pw_multi_aff_intersect_domain(
5787 __isl_take isl_union_pw_multi_aff *upma,
5788 __isl_take isl_union_set *uset);
5789 __isl_give isl_multi_union_pw_aff *
5790 isl_multi_union_pw_aff_intersect_domain(
5791 __isl_take isl_multi_union_pw_aff *mupa,
5792 __isl_take isl_union_set *uset);
5793 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
5794 __isl_take isl_pw_aff *pa,
5795 __isl_take isl_set *set);
5796 __isl_give isl_multi_pw_aff *
5797 isl_multi_pw_aff_intersect_params(
5798 __isl_take isl_multi_pw_aff *mpa,
5799 __isl_take isl_set *set);
5800 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
5801 __isl_take isl_pw_multi_aff *pma,
5802 __isl_take isl_set *set);
5803 __isl_give isl_union_pw_aff *
5804 isl_union_pw_aff_intersect_params(
5805 __isl_take isl_union_pw_aff *upa,
5806 __isl_give isl_union_pw_multi_aff *
5807 isl_union_pw_multi_aff_intersect_params(
5808 __isl_take isl_union_pw_multi_aff *upma,
5809 __isl_take isl_set *set);
5810 __isl_give isl_multi_union_pw_aff *
5811 isl_multi_union_pw_aff_intersect_params(
5812 __isl_take isl_multi_union_pw_aff *mupa,
5813 __isl_take isl_set *params);
5814 isl_multi_union_pw_aff_intersect_range(
5815 __isl_take isl_multi_union_pw_aff *mupa,
5816 __isl_take isl_set *set);
5818 #include <isl/polynomial.h>
5819 __isl_give isl_pw_qpolynomial *
5820 isl_pw_qpolynomial_intersect_domain(
5821 __isl_take isl_pw_qpolynomial *pwpq,
5822 __isl_take isl_set *set);
5823 __isl_give isl_union_pw_qpolynomial *
5824 isl_union_pw_qpolynomial_intersect_domain(
5825 __isl_take isl_union_pw_qpolynomial *upwpq,
5826 __isl_take isl_union_set *uset);
5827 __isl_give isl_union_pw_qpolynomial_fold *
5828 isl_union_pw_qpolynomial_fold_intersect_domain(
5829 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5830 __isl_take isl_union_set *uset);
5831 __isl_give isl_pw_qpolynomial *
5832 isl_pw_qpolynomial_intersect_params(
5833 __isl_take isl_pw_qpolynomial *pwpq,
5834 __isl_take isl_set *set);
5835 __isl_give isl_pw_qpolynomial_fold *
5836 isl_pw_qpolynomial_fold_intersect_params(
5837 __isl_take isl_pw_qpolynomial_fold *pwf,
5838 __isl_take isl_set *set);
5839 __isl_give isl_union_pw_qpolynomial *
5840 isl_union_pw_qpolynomial_intersect_params(
5841 __isl_take isl_union_pw_qpolynomial *upwpq,
5842 __isl_take isl_set *set);
5843 __isl_give isl_union_pw_qpolynomial_fold *
5844 isl_union_pw_qpolynomial_fold_intersect_params(
5845 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5846 __isl_take isl_set *set);
5848 The second argument to the C<_params> functions needs to be
5849 a parametric (basic) set. For the other functions, a parametric set
5850 for either argument is only allowed if the other argument is
5851 a parametric set as well.
5852 The list passed to C<isl_basic_set_list_intersect> needs to have
5853 at least one element and all elements need to live in the same space.
5854 The function C<isl_multi_union_pw_aff_intersect_range>
5855 restricts the input function to those shared domain elements
5856 that map to the specified range.
5860 #include <isl/set.h>
5861 __isl_give isl_set *isl_basic_set_union(
5862 __isl_take isl_basic_set *bset1,
5863 __isl_take isl_basic_set *bset2);
5864 __isl_give isl_set *isl_set_union(
5865 __isl_take isl_set *set1,
5866 __isl_take isl_set *set2);
5867 __isl_give isl_set *isl_set_list_union(
5868 __isl_take isl_set_list *list);
5870 #include <isl/map.h>
5871 __isl_give isl_map *isl_basic_map_union(
5872 __isl_take isl_basic_map *bmap1,
5873 __isl_take isl_basic_map *bmap2);
5874 __isl_give isl_map *isl_map_union(
5875 __isl_take isl_map *map1,
5876 __isl_take isl_map *map2);
5878 #include <isl/union_set.h>
5879 __isl_give isl_union_set *isl_union_set_union(
5880 __isl_take isl_union_set *uset1,
5881 __isl_take isl_union_set *uset2);
5882 __isl_give isl_union_set *isl_union_set_list_union(
5883 __isl_take isl_union_set_list *list);
5885 #include <isl/union_map.h>
5886 __isl_give isl_union_map *isl_union_map_union(
5887 __isl_take isl_union_map *umap1,
5888 __isl_take isl_union_map *umap2);
5890 The list passed to C<isl_set_list_union> needs to have
5891 at least one element and all elements need to live in the same space.
5893 =item * Set difference
5895 #include <isl/set.h>
5896 __isl_give isl_set *isl_set_subtract(
5897 __isl_take isl_set *set1,
5898 __isl_take isl_set *set2);
5900 #include <isl/map.h>
5901 __isl_give isl_map *isl_map_subtract(
5902 __isl_take isl_map *map1,
5903 __isl_take isl_map *map2);
5904 __isl_give isl_map *isl_map_subtract_domain(
5905 __isl_take isl_map *map,
5906 __isl_take isl_set *dom);
5907 __isl_give isl_map *isl_map_subtract_range(
5908 __isl_take isl_map *map,
5909 __isl_take isl_set *dom);
5911 #include <isl/union_set.h>
5912 __isl_give isl_union_set *isl_union_set_subtract(
5913 __isl_take isl_union_set *uset1,
5914 __isl_take isl_union_set *uset2);
5916 #include <isl/union_map.h>
5917 __isl_give isl_union_map *isl_union_map_subtract(
5918 __isl_take isl_union_map *umap1,
5919 __isl_take isl_union_map *umap2);
5920 __isl_give isl_union_map *isl_union_map_subtract_domain(
5921 __isl_take isl_union_map *umap,
5922 __isl_take isl_union_set *dom);
5923 __isl_give isl_union_map *isl_union_map_subtract_range(
5924 __isl_take isl_union_map *umap,
5925 __isl_take isl_union_set *dom);
5927 #include <isl/aff.h>
5928 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
5929 __isl_take isl_pw_aff *pa,
5930 __isl_take isl_set *set);
5931 __isl_give isl_pw_multi_aff *
5932 isl_pw_multi_aff_subtract_domain(
5933 __isl_take isl_pw_multi_aff *pma,
5934 __isl_take isl_set *set);
5935 __isl_give isl_union_pw_aff *
5936 isl_union_pw_aff_subtract_domain(
5937 __isl_take isl_union_pw_aff *upa,
5938 __isl_take isl_union_set *uset);
5939 __isl_give isl_union_pw_multi_aff *
5940 isl_union_pw_multi_aff_subtract_domain(
5941 __isl_take isl_union_pw_multi_aff *upma,
5942 __isl_take isl_set *set);
5944 #include <isl/polynomial.h>
5945 __isl_give isl_pw_qpolynomial *
5946 isl_pw_qpolynomial_subtract_domain(
5947 __isl_take isl_pw_qpolynomial *pwpq,
5948 __isl_take isl_set *set);
5949 __isl_give isl_pw_qpolynomial_fold *
5950 isl_pw_qpolynomial_fold_subtract_domain(
5951 __isl_take isl_pw_qpolynomial_fold *pwf,
5952 __isl_take isl_set *set);
5953 __isl_give isl_union_pw_qpolynomial *
5954 isl_union_pw_qpolynomial_subtract_domain(
5955 __isl_take isl_union_pw_qpolynomial *upwpq,
5956 __isl_take isl_union_set *uset);
5957 __isl_give isl_union_pw_qpolynomial_fold *
5958 isl_union_pw_qpolynomial_fold_subtract_domain(
5959 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5960 __isl_take isl_union_set *uset);
5964 #include <isl/space.h>
5965 __isl_give isl_space *isl_space_join(
5966 __isl_take isl_space *left,
5967 __isl_take isl_space *right);
5969 #include <isl/map.h>
5970 __isl_give isl_basic_set *isl_basic_set_apply(
5971 __isl_take isl_basic_set *bset,
5972 __isl_take isl_basic_map *bmap);
5973 __isl_give isl_set *isl_set_apply(
5974 __isl_take isl_set *set,
5975 __isl_take isl_map *map);
5976 __isl_give isl_union_set *isl_union_set_apply(
5977 __isl_take isl_union_set *uset,
5978 __isl_take isl_union_map *umap);
5979 __isl_give isl_basic_map *isl_basic_map_apply_domain(
5980 __isl_take isl_basic_map *bmap1,
5981 __isl_take isl_basic_map *bmap2);
5982 __isl_give isl_basic_map *isl_basic_map_apply_range(
5983 __isl_take isl_basic_map *bmap1,
5984 __isl_take isl_basic_map *bmap2);
5985 __isl_give isl_map *isl_map_apply_domain(
5986 __isl_take isl_map *map1,
5987 __isl_take isl_map *map2);
5988 __isl_give isl_map *isl_map_apply_range(
5989 __isl_take isl_map *map1,
5990 __isl_take isl_map *map2);
5992 #include <isl/union_map.h>
5993 __isl_give isl_union_map *isl_union_map_apply_domain(
5994 __isl_take isl_union_map *umap1,
5995 __isl_take isl_union_map *umap2);
5996 __isl_give isl_union_map *isl_union_map_apply_range(
5997 __isl_take isl_union_map *umap1,
5998 __isl_take isl_union_map *umap2);
6000 #include <isl/aff.h>
6001 __isl_give isl_union_pw_aff *
6002 isl_multi_union_pw_aff_apply_aff(
6003 __isl_take isl_multi_union_pw_aff *mupa,
6004 __isl_take isl_aff *aff);
6005 __isl_give isl_union_pw_aff *
6006 isl_multi_union_pw_aff_apply_pw_aff(
6007 __isl_take isl_multi_union_pw_aff *mupa,
6008 __isl_take isl_pw_aff *pa);
6009 __isl_give isl_multi_union_pw_aff *
6010 isl_multi_union_pw_aff_apply_multi_aff(
6011 __isl_take isl_multi_union_pw_aff *mupa,
6012 __isl_take isl_multi_aff *ma);
6013 __isl_give isl_multi_union_pw_aff *
6014 isl_multi_union_pw_aff_apply_pw_multi_aff(
6015 __isl_take isl_multi_union_pw_aff *mupa,
6016 __isl_take isl_pw_multi_aff *pma);
6018 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
6019 over the shared domain of the elements of the input. The dimension is
6020 required to be greater than zero.
6021 The C<isl_multi_union_pw_aff> argument of
6022 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
6023 but only if the range of the C<isl_multi_aff> argument
6024 is also zero-dimensional.
6025 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
6027 #include <isl/polynomial.h>
6028 __isl_give isl_pw_qpolynomial_fold *
6029 isl_set_apply_pw_qpolynomial_fold(
6030 __isl_take isl_set *set,
6031 __isl_take isl_pw_qpolynomial_fold *pwf,
6033 __isl_give isl_pw_qpolynomial_fold *
6034 isl_map_apply_pw_qpolynomial_fold(
6035 __isl_take isl_map *map,
6036 __isl_take isl_pw_qpolynomial_fold *pwf,
6038 __isl_give isl_union_pw_qpolynomial_fold *
6039 isl_union_set_apply_union_pw_qpolynomial_fold(
6040 __isl_take isl_union_set *uset,
6041 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6043 __isl_give isl_union_pw_qpolynomial_fold *
6044 isl_union_map_apply_union_pw_qpolynomial_fold(
6045 __isl_take isl_union_map *umap,
6046 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6049 The functions taking a map
6050 compose the given map with the given piecewise quasipolynomial reduction.
6051 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
6052 over all elements in the intersection of the range of the map
6053 and the domain of the piecewise quasipolynomial reduction
6054 as a function of an element in the domain of the map.
6055 The functions taking a set compute a bound over all elements in the
6056 intersection of the set and the domain of the
6057 piecewise quasipolynomial reduction.
6061 #include <isl/set.h>
6062 __isl_give isl_basic_set *
6063 isl_basic_set_preimage_multi_aff(
6064 __isl_take isl_basic_set *bset,
6065 __isl_take isl_multi_aff *ma);
6066 __isl_give isl_set *isl_set_preimage_multi_aff(
6067 __isl_take isl_set *set,
6068 __isl_take isl_multi_aff *ma);
6069 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
6070 __isl_take isl_set *set,
6071 __isl_take isl_pw_multi_aff *pma);
6072 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
6073 __isl_take isl_set *set,
6074 __isl_take isl_multi_pw_aff *mpa);
6076 #include <isl/union_set.h>
6077 __isl_give isl_union_set *
6078 isl_union_set_preimage_multi_aff(
6079 __isl_take isl_union_set *uset,
6080 __isl_take isl_multi_aff *ma);
6081 __isl_give isl_union_set *
6082 isl_union_set_preimage_pw_multi_aff(
6083 __isl_take isl_union_set *uset,
6084 __isl_take isl_pw_multi_aff *pma);
6085 __isl_give isl_union_set *
6086 isl_union_set_preimage_union_pw_multi_aff(
6087 __isl_take isl_union_set *uset,
6088 __isl_take isl_union_pw_multi_aff *upma);
6090 #include <isl/map.h>
6091 __isl_give isl_basic_map *
6092 isl_basic_map_preimage_domain_multi_aff(
6093 __isl_take isl_basic_map *bmap,
6094 __isl_take isl_multi_aff *ma);
6095 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
6096 __isl_take isl_map *map,
6097 __isl_take isl_multi_aff *ma);
6098 __isl_give isl_map *isl_map_preimage_range_multi_aff(
6099 __isl_take isl_map *map,
6100 __isl_take isl_multi_aff *ma);
6101 __isl_give isl_map *
6102 isl_map_preimage_domain_pw_multi_aff(
6103 __isl_take isl_map *map,
6104 __isl_take isl_pw_multi_aff *pma);
6105 __isl_give isl_map *
6106 isl_map_preimage_range_pw_multi_aff(
6107 __isl_take isl_map *map,
6108 __isl_take isl_pw_multi_aff *pma);
6109 __isl_give isl_map *
6110 isl_map_preimage_domain_multi_pw_aff(
6111 __isl_take isl_map *map,
6112 __isl_take isl_multi_pw_aff *mpa);
6113 __isl_give isl_basic_map *
6114 isl_basic_map_preimage_range_multi_aff(
6115 __isl_take isl_basic_map *bmap,
6116 __isl_take isl_multi_aff *ma);
6118 #include <isl/union_map.h>
6119 __isl_give isl_union_map *
6120 isl_union_map_preimage_domain_multi_aff(
6121 __isl_take isl_union_map *umap,
6122 __isl_take isl_multi_aff *ma);
6123 __isl_give isl_union_map *
6124 isl_union_map_preimage_range_multi_aff(
6125 __isl_take isl_union_map *umap,
6126 __isl_take isl_multi_aff *ma);
6127 __isl_give isl_union_map *
6128 isl_union_map_preimage_domain_pw_multi_aff(
6129 __isl_take isl_union_map *umap,
6130 __isl_take isl_pw_multi_aff *pma);
6131 __isl_give isl_union_map *
6132 isl_union_map_preimage_range_pw_multi_aff(
6133 __isl_take isl_union_map *umap,
6134 __isl_take isl_pw_multi_aff *pma);
6135 __isl_give isl_union_map *
6136 isl_union_map_preimage_domain_union_pw_multi_aff(
6137 __isl_take isl_union_map *umap,
6138 __isl_take isl_union_pw_multi_aff *upma);
6139 __isl_give isl_union_map *
6140 isl_union_map_preimage_range_union_pw_multi_aff(
6141 __isl_take isl_union_map *umap,
6142 __isl_take isl_union_pw_multi_aff *upma);
6144 These functions compute the preimage of the given set or map domain/range under
6145 the given function. In other words, the expression is plugged
6146 into the set description or into the domain/range of the map.
6150 #include <isl/aff.h>
6151 __isl_give isl_aff *isl_aff_pullback_aff(
6152 __isl_take isl_aff *aff1,
6153 __isl_take isl_aff *aff2);
6154 __isl_give isl_aff *isl_aff_pullback_multi_aff(
6155 __isl_take isl_aff *aff,
6156 __isl_take isl_multi_aff *ma);
6157 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
6158 __isl_take isl_pw_aff *pa,
6159 __isl_take isl_multi_aff *ma);
6160 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
6161 __isl_take isl_pw_aff *pa,
6162 __isl_take isl_pw_multi_aff *pma);
6163 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
6164 __isl_take isl_pw_aff *pa,
6165 __isl_take isl_multi_pw_aff *mpa);
6166 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
6167 __isl_take isl_multi_aff *ma1,
6168 __isl_take isl_multi_aff *ma2);
6169 __isl_give isl_pw_multi_aff *
6170 isl_pw_multi_aff_pullback_multi_aff(
6171 __isl_take isl_pw_multi_aff *pma,
6172 __isl_take isl_multi_aff *ma);
6173 __isl_give isl_multi_pw_aff *
6174 isl_multi_pw_aff_pullback_multi_aff(
6175 __isl_take isl_multi_pw_aff *mpa,
6176 __isl_take isl_multi_aff *ma);
6177 __isl_give isl_pw_multi_aff *
6178 isl_pw_multi_aff_pullback_pw_multi_aff(
6179 __isl_take isl_pw_multi_aff *pma1,
6180 __isl_take isl_pw_multi_aff *pma2);
6181 __isl_give isl_multi_pw_aff *
6182 isl_multi_pw_aff_pullback_pw_multi_aff(
6183 __isl_take isl_multi_pw_aff *mpa,
6184 __isl_take isl_pw_multi_aff *pma);
6185 __isl_give isl_multi_pw_aff *
6186 isl_multi_pw_aff_pullback_multi_pw_aff(
6187 __isl_take isl_multi_pw_aff *mpa1,
6188 __isl_take isl_multi_pw_aff *mpa2);
6189 __isl_give isl_union_pw_aff *
6190 isl_union_pw_aff_pullback_union_pw_multi_aff(
6191 __isl_take isl_union_pw_aff *upa,
6192 __isl_take isl_union_pw_multi_aff *upma);
6193 __isl_give isl_union_pw_multi_aff *
6194 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
6195 __isl_take isl_union_pw_multi_aff *upma1,
6196 __isl_take isl_union_pw_multi_aff *upma2);
6197 __isl_give isl_multi_union_pw_aff *
6198 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
6199 __isl_take isl_multi_union_pw_aff *mupa,
6200 __isl_take isl_union_pw_multi_aff *upma);
6202 These functions precompose the first expression by the second function.
6203 In other words, the second function is plugged
6204 into the first expression.
6208 #include <isl/aff.h>
6209 __isl_give isl_basic_set *isl_aff_eq_basic_set(
6210 __isl_take isl_aff *aff1,
6211 __isl_take isl_aff *aff2);
6212 __isl_give isl_set *isl_aff_eq_set(
6213 __isl_take isl_aff *aff1,
6214 __isl_take isl_aff *aff2);
6215 __isl_give isl_basic_set *isl_aff_le_basic_set(
6216 __isl_take isl_aff *aff1,
6217 __isl_take isl_aff *aff2);
6218 __isl_give isl_set *isl_aff_le_set(
6219 __isl_take isl_aff *aff1,
6220 __isl_take isl_aff *aff2);
6221 __isl_give isl_basic_set *isl_aff_ge_basic_set(
6222 __isl_take isl_aff *aff1,
6223 __isl_take isl_aff *aff2);
6224 __isl_give isl_set *isl_aff_ge_set(
6225 __isl_take isl_aff *aff1,
6226 __isl_take isl_aff *aff2);
6227 __isl_give isl_set *isl_pw_aff_eq_set(
6228 __isl_take isl_pw_aff *pwaff1,
6229 __isl_take isl_pw_aff *pwaff2);
6230 __isl_give isl_set *isl_pw_aff_ne_set(
6231 __isl_take isl_pw_aff *pwaff1,
6232 __isl_take isl_pw_aff *pwaff2);
6233 __isl_give isl_set *isl_pw_aff_le_set(
6234 __isl_take isl_pw_aff *pwaff1,
6235 __isl_take isl_pw_aff *pwaff2);
6236 __isl_give isl_set *isl_pw_aff_lt_set(
6237 __isl_take isl_pw_aff *pwaff1,
6238 __isl_take isl_pw_aff *pwaff2);
6239 __isl_give isl_set *isl_pw_aff_ge_set(
6240 __isl_take isl_pw_aff *pwaff1,
6241 __isl_take isl_pw_aff *pwaff2);
6242 __isl_give isl_set *isl_pw_aff_gt_set(
6243 __isl_take isl_pw_aff *pwaff1,
6244 __isl_take isl_pw_aff *pwaff2);
6246 __isl_give isl_set *isl_multi_aff_lex_le_set(
6247 __isl_take isl_multi_aff *ma1,
6248 __isl_take isl_multi_aff *ma2);
6249 __isl_give isl_set *isl_multi_aff_lex_lt_set(
6250 __isl_take isl_multi_aff *ma1,
6251 __isl_take isl_multi_aff *ma2);
6252 __isl_give isl_set *isl_multi_aff_lex_ge_set(
6253 __isl_take isl_multi_aff *ma1,
6254 __isl_take isl_multi_aff *ma2);
6255 __isl_give isl_set *isl_multi_aff_lex_gt_set(
6256 __isl_take isl_multi_aff *ma1,
6257 __isl_take isl_multi_aff *ma2);
6259 __isl_give isl_set *isl_pw_aff_list_eq_set(
6260 __isl_take isl_pw_aff_list *list1,
6261 __isl_take isl_pw_aff_list *list2);
6262 __isl_give isl_set *isl_pw_aff_list_ne_set(
6263 __isl_take isl_pw_aff_list *list1,
6264 __isl_take isl_pw_aff_list *list2);
6265 __isl_give isl_set *isl_pw_aff_list_le_set(
6266 __isl_take isl_pw_aff_list *list1,
6267 __isl_take isl_pw_aff_list *list2);
6268 __isl_give isl_set *isl_pw_aff_list_lt_set(
6269 __isl_take isl_pw_aff_list *list1,
6270 __isl_take isl_pw_aff_list *list2);
6271 __isl_give isl_set *isl_pw_aff_list_ge_set(
6272 __isl_take isl_pw_aff_list *list1,
6273 __isl_take isl_pw_aff_list *list2);
6274 __isl_give isl_set *isl_pw_aff_list_gt_set(
6275 __isl_take isl_pw_aff_list *list1,
6276 __isl_take isl_pw_aff_list *list2);
6278 The function C<isl_aff_ge_basic_set> returns a basic set
6279 containing those elements in the shared space
6280 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
6281 The function C<isl_pw_aff_ge_set> returns a set
6282 containing those elements in the shared domain
6283 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
6284 greater than or equal to C<pwaff2>.
6285 The function C<isl_multi_aff_lex_le_set> returns a set
6286 containing those elements in the shared domain space
6287 where C<ma1> is lexicographically smaller than or
6289 The functions operating on C<isl_pw_aff_list> apply the corresponding
6290 C<isl_pw_aff> function to each pair of elements in the two lists.
6292 #include <isl/aff.h>
6293 __isl_give isl_map *isl_pw_aff_eq_map(
6294 __isl_take isl_pw_aff *pa1,
6295 __isl_take isl_pw_aff *pa2);
6296 __isl_give isl_map *isl_pw_aff_lt_map(
6297 __isl_take isl_pw_aff *pa1,
6298 __isl_take isl_pw_aff *pa2);
6299 __isl_give isl_map *isl_pw_aff_gt_map(
6300 __isl_take isl_pw_aff *pa1,
6301 __isl_take isl_pw_aff *pa2);
6303 __isl_give isl_map *isl_multi_pw_aff_eq_map(
6304 __isl_take isl_multi_pw_aff *mpa1,
6305 __isl_take isl_multi_pw_aff *mpa2);
6306 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
6307 __isl_take isl_multi_pw_aff *mpa1,
6308 __isl_take isl_multi_pw_aff *mpa2);
6309 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
6310 __isl_take isl_multi_pw_aff *mpa1,
6311 __isl_take isl_multi_pw_aff *mpa2);
6313 These functions return a map between domain elements of the arguments
6314 where the function values satisfy the given relation.
6316 #include <isl/union_map.h>
6317 __isl_give isl_union_map *
6318 isl_union_map_eq_at_multi_union_pw_aff(
6319 __isl_take isl_union_map *umap,
6320 __isl_take isl_multi_union_pw_aff *mupa);
6321 __isl_give isl_union_map *
6322 isl_union_map_lex_lt_at_multi_union_pw_aff(
6323 __isl_take isl_union_map *umap,
6324 __isl_take isl_multi_union_pw_aff *mupa);
6325 __isl_give isl_union_map *
6326 isl_union_map_lex_gt_at_multi_union_pw_aff(
6327 __isl_take isl_union_map *umap,
6328 __isl_take isl_multi_union_pw_aff *mupa);
6330 These functions select the subset of elements in the union map
6331 that have an equal or lexicographically smaller function value.
6333 =item * Cartesian Product
6335 #include <isl/space.h>
6336 __isl_give isl_space *isl_space_product(
6337 __isl_take isl_space *space1,
6338 __isl_take isl_space *space2);
6339 __isl_give isl_space *isl_space_domain_product(
6340 __isl_take isl_space *space1,
6341 __isl_take isl_space *space2);
6342 __isl_give isl_space *isl_space_range_product(
6343 __isl_take isl_space *space1,
6344 __isl_take isl_space *space2);
6347 C<isl_space_product>, C<isl_space_domain_product>
6348 and C<isl_space_range_product> take pairs or relation spaces and
6349 produce a single relations space, where either the domain, the range
6350 or both domain and range are wrapped spaces of relations between
6351 the domains and/or ranges of the input spaces.
6352 If the product is only constructed over the domain or the range
6353 then the ranges or the domains of the inputs should be the same.
6354 The function C<isl_space_product> also accepts a pair of set spaces,
6355 in which case it returns a wrapped space of a relation between the
6358 #include <isl/set.h>
6359 __isl_give isl_set *isl_set_product(
6360 __isl_take isl_set *set1,
6361 __isl_take isl_set *set2);
6363 #include <isl/map.h>
6364 __isl_give isl_basic_map *isl_basic_map_domain_product(
6365 __isl_take isl_basic_map *bmap1,
6366 __isl_take isl_basic_map *bmap2);
6367 __isl_give isl_basic_map *isl_basic_map_range_product(
6368 __isl_take isl_basic_map *bmap1,
6369 __isl_take isl_basic_map *bmap2);
6370 __isl_give isl_basic_map *isl_basic_map_product(
6371 __isl_take isl_basic_map *bmap1,
6372 __isl_take isl_basic_map *bmap2);
6373 __isl_give isl_map *isl_map_domain_product(
6374 __isl_take isl_map *map1,
6375 __isl_take isl_map *map2);
6376 __isl_give isl_map *isl_map_range_product(
6377 __isl_take isl_map *map1,
6378 __isl_take isl_map *map2);
6379 __isl_give isl_map *isl_map_product(
6380 __isl_take isl_map *map1,
6381 __isl_take isl_map *map2);
6383 #include <isl/union_set.h>
6384 __isl_give isl_union_set *isl_union_set_product(
6385 __isl_take isl_union_set *uset1,
6386 __isl_take isl_union_set *uset2);
6388 #include <isl/union_map.h>
6389 __isl_give isl_union_map *isl_union_map_domain_product(
6390 __isl_take isl_union_map *umap1,
6391 __isl_take isl_union_map *umap2);
6392 __isl_give isl_union_map *isl_union_map_range_product(
6393 __isl_take isl_union_map *umap1,
6394 __isl_take isl_union_map *umap2);
6395 __isl_give isl_union_map *isl_union_map_product(
6396 __isl_take isl_union_map *umap1,
6397 __isl_take isl_union_map *umap2);
6399 #include <isl/val.h>
6400 __isl_give isl_multi_val *isl_multi_val_range_product(
6401 __isl_take isl_multi_val *mv1,
6402 __isl_take isl_multi_val *mv2);
6403 __isl_give isl_multi_val *isl_multi_val_product(
6404 __isl_take isl_multi_val *mv1,
6405 __isl_take isl_multi_val *mv2);
6407 #include <isl/aff.h>
6408 __isl_give isl_multi_aff *isl_multi_aff_range_product(
6409 __isl_take isl_multi_aff *ma1,
6410 __isl_take isl_multi_aff *ma2);
6411 __isl_give isl_multi_aff *isl_multi_aff_product(
6412 __isl_take isl_multi_aff *ma1,
6413 __isl_take isl_multi_aff *ma2);
6414 __isl_give isl_multi_pw_aff *
6415 isl_multi_pw_aff_range_product(
6416 __isl_take isl_multi_pw_aff *mpa1,
6417 __isl_take isl_multi_pw_aff *mpa2);
6418 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
6419 __isl_take isl_multi_pw_aff *mpa1,
6420 __isl_take isl_multi_pw_aff *mpa2);
6421 __isl_give isl_pw_multi_aff *
6422 isl_pw_multi_aff_range_product(
6423 __isl_take isl_pw_multi_aff *pma1,
6424 __isl_take isl_pw_multi_aff *pma2);
6425 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
6426 __isl_take isl_pw_multi_aff *pma1,
6427 __isl_take isl_pw_multi_aff *pma2);
6428 __isl_give isl_multi_union_pw_aff *
6429 isl_multi_union_pw_aff_range_product(
6430 __isl_take isl_multi_union_pw_aff *mupa1,
6431 __isl_take isl_multi_union_pw_aff *mupa2);
6433 The above functions compute the cross product of the given
6434 sets, relations or functions. The domains and ranges of the results
6435 are wrapped maps between domains and ranges of the inputs.
6436 To obtain a ``flat'' product, use the following functions
6439 #include <isl/set.h>
6440 __isl_give isl_basic_set *isl_basic_set_flat_product(
6441 __isl_take isl_basic_set *bset1,
6442 __isl_take isl_basic_set *bset2);
6443 __isl_give isl_set *isl_set_flat_product(
6444 __isl_take isl_set *set1,
6445 __isl_take isl_set *set2);
6447 #include <isl/map.h>
6448 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
6449 __isl_take isl_basic_map *bmap1,
6450 __isl_take isl_basic_map *bmap2);
6451 __isl_give isl_map *isl_map_flat_domain_product(
6452 __isl_take isl_map *map1,
6453 __isl_take isl_map *map2);
6454 __isl_give isl_map *isl_map_flat_range_product(
6455 __isl_take isl_map *map1,
6456 __isl_take isl_map *map2);
6457 __isl_give isl_basic_map *isl_basic_map_flat_product(
6458 __isl_take isl_basic_map *bmap1,
6459 __isl_take isl_basic_map *bmap2);
6460 __isl_give isl_map *isl_map_flat_product(
6461 __isl_take isl_map *map1,
6462 __isl_take isl_map *map2);
6464 #include <isl/union_map.h>
6465 __isl_give isl_union_map *
6466 isl_union_map_flat_domain_product(
6467 __isl_take isl_union_map *umap1,
6468 __isl_take isl_union_map *umap2);
6469 __isl_give isl_union_map *
6470 isl_union_map_flat_range_product(
6471 __isl_take isl_union_map *umap1,
6472 __isl_take isl_union_map *umap2);
6474 #include <isl/val.h>
6475 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
6476 __isl_take isl_multi_val *mv1,
6477 __isl_take isl_multi_aff *mv2);
6479 #include <isl/aff.h>
6480 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
6481 __isl_take isl_multi_aff *ma1,
6482 __isl_take isl_multi_aff *ma2);
6483 __isl_give isl_pw_multi_aff *
6484 isl_pw_multi_aff_flat_range_product(
6485 __isl_take isl_pw_multi_aff *pma1,
6486 __isl_take isl_pw_multi_aff *pma2);
6487 __isl_give isl_multi_pw_aff *
6488 isl_multi_pw_aff_flat_range_product(
6489 __isl_take isl_multi_pw_aff *mpa1,
6490 __isl_take isl_multi_pw_aff *mpa2);
6491 __isl_give isl_union_pw_multi_aff *
6492 isl_union_pw_multi_aff_flat_range_product(
6493 __isl_take isl_union_pw_multi_aff *upma1,
6494 __isl_take isl_union_pw_multi_aff *upma2);
6495 __isl_give isl_multi_union_pw_aff *
6496 isl_multi_union_pw_aff_flat_range_product(
6497 __isl_take isl_multi_union_pw_aff *mupa1,
6498 __isl_take isl_multi_union_pw_aff *mupa2);
6500 #include <isl/space.h>
6501 __isl_give isl_space *isl_space_factor_domain(
6502 __isl_take isl_space *space);
6503 __isl_give isl_space *isl_space_factor_range(
6504 __isl_take isl_space *space);
6505 __isl_give isl_space *isl_space_domain_factor_domain(
6506 __isl_take isl_space *space);
6507 __isl_give isl_space *isl_space_domain_factor_range(
6508 __isl_take isl_space *space);
6509 __isl_give isl_space *isl_space_range_factor_domain(
6510 __isl_take isl_space *space);
6511 __isl_give isl_space *isl_space_range_factor_range(
6512 __isl_take isl_space *space);
6514 The functions C<isl_space_range_factor_domain> and
6515 C<isl_space_range_factor_range> extract the two arguments from
6516 the result of a call to C<isl_space_range_product>.
6518 The arguments of a call to a product can be extracted
6519 from the result using the following functions.
6521 #include <isl/map.h>
6522 __isl_give isl_map *isl_map_factor_domain(
6523 __isl_take isl_map *map);
6524 __isl_give isl_map *isl_map_factor_range(
6525 __isl_take isl_map *map);
6526 __isl_give isl_map *isl_map_domain_factor_domain(
6527 __isl_take isl_map *map);
6528 __isl_give isl_map *isl_map_domain_factor_range(
6529 __isl_take isl_map *map);
6530 __isl_give isl_map *isl_map_range_factor_domain(
6531 __isl_take isl_map *map);
6532 __isl_give isl_map *isl_map_range_factor_range(
6533 __isl_take isl_map *map);
6535 #include <isl/union_map.h>
6536 __isl_give isl_union_map *isl_union_map_factor_domain(
6537 __isl_take isl_union_map *umap);
6538 __isl_give isl_union_map *isl_union_map_factor_range(
6539 __isl_take isl_union_map *umap);
6540 __isl_give isl_union_map *
6541 isl_union_map_domain_factor_domain(
6542 __isl_take isl_union_map *umap);
6543 __isl_give isl_union_map *
6544 isl_union_map_domain_factor_range(
6545 __isl_take isl_union_map *umap);
6546 __isl_give isl_union_map *
6547 isl_union_map_range_factor_domain(
6548 __isl_take isl_union_map *umap);
6549 __isl_give isl_union_map *
6550 isl_union_map_range_factor_range(
6551 __isl_take isl_union_map *umap);
6553 #include <isl/val.h>
6554 __isl_give isl_multi_val *isl_multi_val_factor_range(
6555 __isl_take isl_multi_val *mv);
6556 __isl_give isl_multi_val *
6557 isl_multi_val_range_factor_domain(
6558 __isl_take isl_multi_val *mv);
6559 __isl_give isl_multi_val *
6560 isl_multi_val_range_factor_range(
6561 __isl_take isl_multi_val *mv);
6563 #include <isl/aff.h>
6564 __isl_give isl_multi_aff *isl_multi_aff_factor_range(
6565 __isl_take isl_multi_aff *ma);
6566 __isl_give isl_multi_aff *
6567 isl_multi_aff_range_factor_domain(
6568 __isl_take isl_multi_aff *ma);
6569 __isl_give isl_multi_aff *
6570 isl_multi_aff_range_factor_range(
6571 __isl_take isl_multi_aff *ma);
6572 __isl_give isl_multi_pw_aff *
6573 isl_multi_pw_aff_factor_range(
6574 __isl_take isl_multi_pw_aff *mpa);
6575 __isl_give isl_multi_pw_aff *
6576 isl_multi_pw_aff_range_factor_domain(
6577 __isl_take isl_multi_pw_aff *mpa);
6578 __isl_give isl_multi_pw_aff *
6579 isl_multi_pw_aff_range_factor_range(
6580 __isl_take isl_multi_pw_aff *mpa);
6581 __isl_give isl_multi_union_pw_aff *
6582 isl_multi_union_pw_aff_factor_range(
6583 __isl_take isl_multi_union_pw_aff *mupa);
6584 __isl_give isl_multi_union_pw_aff *
6585 isl_multi_union_pw_aff_range_factor_domain(
6586 __isl_take isl_multi_union_pw_aff *mupa);
6587 __isl_give isl_multi_union_pw_aff *
6588 isl_multi_union_pw_aff_range_factor_range(
6589 __isl_take isl_multi_union_pw_aff *mupa);
6591 The splice functions are a generalization of the flat product functions,
6592 where the second argument may be inserted at any position inside
6593 the first argument rather than being placed at the end.
6594 The functions C<isl_multi_val_factor_range>,
6595 C<isl_multi_aff_factor_range>,
6596 C<isl_multi_pw_aff_factor_range> and
6597 C<isl_multi_union_pw_aff_factor_range>
6598 take functions that live in a set space.
6600 #include <isl/val.h>
6601 __isl_give isl_multi_val *isl_multi_val_range_splice(
6602 __isl_take isl_multi_val *mv1, unsigned pos,
6603 __isl_take isl_multi_val *mv2);
6605 #include <isl/aff.h>
6606 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
6607 __isl_take isl_multi_aff *ma1, unsigned pos,
6608 __isl_take isl_multi_aff *ma2);
6609 __isl_give isl_multi_aff *isl_multi_aff_splice(
6610 __isl_take isl_multi_aff *ma1,
6611 unsigned in_pos, unsigned out_pos,
6612 __isl_take isl_multi_aff *ma2);
6613 __isl_give isl_multi_pw_aff *
6614 isl_multi_pw_aff_range_splice(
6615 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
6616 __isl_take isl_multi_pw_aff *mpa2);
6617 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
6618 __isl_take isl_multi_pw_aff *mpa1,
6619 unsigned in_pos, unsigned out_pos,
6620 __isl_take isl_multi_pw_aff *mpa2);
6621 __isl_give isl_multi_union_pw_aff *
6622 isl_multi_union_pw_aff_range_splice(
6623 __isl_take isl_multi_union_pw_aff *mupa1,
6625 __isl_take isl_multi_union_pw_aff *mupa2);
6627 =item * Simplification
6629 When applied to a set or relation,
6630 the gist operation returns a set or relation that has the
6631 same intersection with the context as the input set or relation.
6632 Any implicit equality in the intersection is made explicit in the result,
6633 while all inequalities that are redundant with respect to the intersection
6635 In case of union sets and relations, the gist operation is performed
6638 When applied to a function,
6639 the gist operation applies the set gist operation to each of
6640 the cells in the domain of the input piecewise expression.
6641 The context is also exploited
6642 to simplify the expression associated to each cell.
6644 #include <isl/set.h>
6645 __isl_give isl_basic_set *isl_basic_set_gist(
6646 __isl_take isl_basic_set *bset,
6647 __isl_take isl_basic_set *context);
6648 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
6649 __isl_take isl_set *context);
6650 __isl_give isl_set *isl_set_gist_params(
6651 __isl_take isl_set *set,
6652 __isl_take isl_set *context);
6654 #include <isl/map.h>
6655 __isl_give isl_basic_map *isl_basic_map_gist(
6656 __isl_take isl_basic_map *bmap,
6657 __isl_take isl_basic_map *context);
6658 __isl_give isl_basic_map *isl_basic_map_gist_domain(
6659 __isl_take isl_basic_map *bmap,
6660 __isl_take isl_basic_set *context);
6661 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
6662 __isl_take isl_map *context);
6663 __isl_give isl_map *isl_map_gist_params(
6664 __isl_take isl_map *map,
6665 __isl_take isl_set *context);
6666 __isl_give isl_map *isl_map_gist_domain(
6667 __isl_take isl_map *map,
6668 __isl_take isl_set *context);
6669 __isl_give isl_map *isl_map_gist_range(
6670 __isl_take isl_map *map,
6671 __isl_take isl_set *context);
6673 #include <isl/union_set.h>
6674 __isl_give isl_union_set *isl_union_set_gist(
6675 __isl_take isl_union_set *uset,
6676 __isl_take isl_union_set *context);
6677 __isl_give isl_union_set *isl_union_set_gist_params(
6678 __isl_take isl_union_set *uset,
6679 __isl_take isl_set *set);
6681 #include <isl/union_map.h>
6682 __isl_give isl_union_map *isl_union_map_gist(
6683 __isl_take isl_union_map *umap,
6684 __isl_take isl_union_map *context);
6685 __isl_give isl_union_map *isl_union_map_gist_params(
6686 __isl_take isl_union_map *umap,
6687 __isl_take isl_set *set);
6688 __isl_give isl_union_map *isl_union_map_gist_domain(
6689 __isl_take isl_union_map *umap,
6690 __isl_take isl_union_set *uset);
6691 __isl_give isl_union_map *isl_union_map_gist_range(
6692 __isl_take isl_union_map *umap,
6693 __isl_take isl_union_set *uset);
6695 #include <isl/aff.h>
6696 __isl_give isl_aff *isl_aff_gist_params(
6697 __isl_take isl_aff *aff,
6698 __isl_take isl_set *context);
6699 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
6700 __isl_take isl_set *context);
6701 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
6702 __isl_take isl_multi_aff *maff,
6703 __isl_take isl_set *context);
6704 __isl_give isl_multi_aff *isl_multi_aff_gist(
6705 __isl_take isl_multi_aff *maff,
6706 __isl_take isl_set *context);
6707 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
6708 __isl_take isl_pw_aff *pwaff,
6709 __isl_take isl_set *context);
6710 __isl_give isl_pw_aff *isl_pw_aff_gist(
6711 __isl_take isl_pw_aff *pwaff,
6712 __isl_take isl_set *context);
6713 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
6714 __isl_take isl_pw_multi_aff *pma,
6715 __isl_take isl_set *set);
6716 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
6717 __isl_take isl_pw_multi_aff *pma,
6718 __isl_take isl_set *set);
6719 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
6720 __isl_take isl_multi_pw_aff *mpa,
6721 __isl_take isl_set *set);
6722 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
6723 __isl_take isl_multi_pw_aff *mpa,
6724 __isl_take isl_set *set);
6725 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
6726 __isl_take isl_union_pw_aff *upa,
6727 __isl_take isl_union_set *context);
6728 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
6729 __isl_take isl_union_pw_aff *upa,
6730 __isl_take isl_set *context);
6731 __isl_give isl_union_pw_multi_aff *
6732 isl_union_pw_multi_aff_gist_params(
6733 __isl_take isl_union_pw_multi_aff *upma,
6734 __isl_take isl_set *context);
6735 __isl_give isl_union_pw_multi_aff *
6736 isl_union_pw_multi_aff_gist(
6737 __isl_take isl_union_pw_multi_aff *upma,
6738 __isl_take isl_union_set *context);
6739 __isl_give isl_multi_union_pw_aff *
6740 isl_multi_union_pw_aff_gist_params(
6741 __isl_take isl_multi_union_pw_aff *aff,
6742 __isl_take isl_set *context);
6743 __isl_give isl_multi_union_pw_aff *
6744 isl_multi_union_pw_aff_gist(
6745 __isl_take isl_multi_union_pw_aff *aff,
6746 __isl_take isl_union_set *context);
6748 #include <isl/polynomial.h>
6749 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
6750 __isl_take isl_qpolynomial *qp,
6751 __isl_take isl_set *context);
6752 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
6753 __isl_take isl_qpolynomial *qp,
6754 __isl_take isl_set *context);
6755 __isl_give isl_qpolynomial_fold *
6756 isl_qpolynomial_fold_gist_params(
6757 __isl_take isl_qpolynomial_fold *fold,
6758 __isl_take isl_set *context);
6759 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
6760 __isl_take isl_qpolynomial_fold *fold,
6761 __isl_take isl_set *context);
6762 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
6763 __isl_take isl_pw_qpolynomial *pwqp,
6764 __isl_take isl_set *context);
6765 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
6766 __isl_take isl_pw_qpolynomial *pwqp,
6767 __isl_take isl_set *context);
6768 __isl_give isl_pw_qpolynomial_fold *
6769 isl_pw_qpolynomial_fold_gist(
6770 __isl_take isl_pw_qpolynomial_fold *pwf,
6771 __isl_take isl_set *context);
6772 __isl_give isl_pw_qpolynomial_fold *
6773 isl_pw_qpolynomial_fold_gist_params(
6774 __isl_take isl_pw_qpolynomial_fold *pwf,
6775 __isl_take isl_set *context);
6776 __isl_give isl_union_pw_qpolynomial *
6777 isl_union_pw_qpolynomial_gist_params(
6778 __isl_take isl_union_pw_qpolynomial *upwqp,
6779 __isl_take isl_set *context);
6780 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
6781 __isl_take isl_union_pw_qpolynomial *upwqp,
6782 __isl_take isl_union_set *context);
6783 __isl_give isl_union_pw_qpolynomial_fold *
6784 isl_union_pw_qpolynomial_fold_gist(
6785 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6786 __isl_take isl_union_set *context);
6787 __isl_give isl_union_pw_qpolynomial_fold *
6788 isl_union_pw_qpolynomial_fold_gist_params(
6789 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6790 __isl_take isl_set *context);
6792 =item * Binary Arithmetic Operations
6794 #include <isl/set.h>
6795 __isl_give isl_set *isl_set_sum(
6796 __isl_take isl_set *set1,
6797 __isl_take isl_set *set2);
6798 #include <isl/map.h>
6799 __isl_give isl_map *isl_map_sum(
6800 __isl_take isl_map *map1,
6801 __isl_take isl_map *map2);
6803 C<isl_set_sum> computes the Minkowski sum of its two arguments,
6804 i.e., the set containing the sums of pairs of elements from
6805 C<set1> and C<set2>.
6806 The domain of the result of C<isl_map_sum> is the intersection
6807 of the domains of its two arguments. The corresponding range
6808 elements are the sums of the corresponding range elements
6809 in the two arguments.
6811 #include <isl/val.h>
6812 __isl_give isl_multi_val *isl_multi_val_add(
6813 __isl_take isl_multi_val *mv1,
6814 __isl_take isl_multi_val *mv2);
6815 __isl_give isl_multi_val *isl_multi_val_sub(
6816 __isl_take isl_multi_val *mv1,
6817 __isl_take isl_multi_val *mv2);
6819 #include <isl/aff.h>
6820 __isl_give isl_aff *isl_aff_add(
6821 __isl_take isl_aff *aff1,
6822 __isl_take isl_aff *aff2);
6823 __isl_give isl_multi_aff *isl_multi_aff_add(
6824 __isl_take isl_multi_aff *maff1,
6825 __isl_take isl_multi_aff *maff2);
6826 __isl_give isl_pw_aff *isl_pw_aff_add(
6827 __isl_take isl_pw_aff *pwaff1,
6828 __isl_take isl_pw_aff *pwaff2);
6829 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add(
6830 __isl_take isl_multi_pw_aff *mpa1,
6831 __isl_take isl_multi_pw_aff *mpa2);
6832 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
6833 __isl_take isl_pw_multi_aff *pma1,
6834 __isl_take isl_pw_multi_aff *pma2);
6835 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
6836 __isl_take isl_union_pw_aff *upa1,
6837 __isl_take isl_union_pw_aff *upa2);
6838 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
6839 __isl_take isl_union_pw_multi_aff *upma1,
6840 __isl_take isl_union_pw_multi_aff *upma2);
6841 __isl_give isl_multi_union_pw_aff *
6842 isl_multi_union_pw_aff_add(
6843 __isl_take isl_multi_union_pw_aff *mupa1,
6844 __isl_take isl_multi_union_pw_aff *mupa2);
6845 __isl_give isl_pw_aff *isl_pw_aff_min(
6846 __isl_take isl_pw_aff *pwaff1,
6847 __isl_take isl_pw_aff *pwaff2);
6848 __isl_give isl_pw_aff *isl_pw_aff_max(
6849 __isl_take isl_pw_aff *pwaff1,
6850 __isl_take isl_pw_aff *pwaff2);
6851 __isl_give isl_aff *isl_aff_sub(
6852 __isl_take isl_aff *aff1,
6853 __isl_take isl_aff *aff2);
6854 __isl_give isl_multi_aff *isl_multi_aff_sub(
6855 __isl_take isl_multi_aff *ma1,
6856 __isl_take isl_multi_aff *ma2);
6857 __isl_give isl_pw_aff *isl_pw_aff_sub(
6858 __isl_take isl_pw_aff *pwaff1,
6859 __isl_take isl_pw_aff *pwaff2);
6860 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
6861 __isl_take isl_multi_pw_aff *mpa1,
6862 __isl_take isl_multi_pw_aff *mpa2);
6863 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
6864 __isl_take isl_pw_multi_aff *pma1,
6865 __isl_take isl_pw_multi_aff *pma2);
6866 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
6867 __isl_take isl_union_pw_aff *upa1,
6868 __isl_take isl_union_pw_aff *upa2);
6869 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
6870 __isl_take isl_union_pw_multi_aff *upma1,
6871 __isl_take isl_union_pw_multi_aff *upma2);
6872 __isl_give isl_multi_union_pw_aff *
6873 isl_multi_union_pw_aff_sub(
6874 __isl_take isl_multi_union_pw_aff *mupa1,
6875 __isl_take isl_multi_union_pw_aff *mupa2);
6877 C<isl_aff_sub> subtracts the second argument from the first.
6879 #include <isl/polynomial.h>
6880 __isl_give isl_qpolynomial *isl_qpolynomial_add(
6881 __isl_take isl_qpolynomial *qp1,
6882 __isl_take isl_qpolynomial *qp2);
6883 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
6884 __isl_take isl_pw_qpolynomial *pwqp1,
6885 __isl_take isl_pw_qpolynomial *pwqp2);
6886 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
6887 __isl_take isl_pw_qpolynomial *pwqp1,
6888 __isl_take isl_pw_qpolynomial *pwqp2);
6889 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
6890 __isl_take isl_pw_qpolynomial_fold *pwf1,
6891 __isl_take isl_pw_qpolynomial_fold *pwf2);
6892 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
6893 __isl_take isl_union_pw_qpolynomial *upwqp1,
6894 __isl_take isl_union_pw_qpolynomial *upwqp2);
6895 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
6896 __isl_take isl_qpolynomial *qp1,
6897 __isl_take isl_qpolynomial *qp2);
6898 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
6899 __isl_take isl_pw_qpolynomial *pwqp1,
6900 __isl_take isl_pw_qpolynomial *pwqp2);
6901 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
6902 __isl_take isl_union_pw_qpolynomial *upwqp1,
6903 __isl_take isl_union_pw_qpolynomial *upwqp2);
6904 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
6905 __isl_take isl_pw_qpolynomial_fold *pwf1,
6906 __isl_take isl_pw_qpolynomial_fold *pwf2);
6907 __isl_give isl_union_pw_qpolynomial_fold *
6908 isl_union_pw_qpolynomial_fold_fold(
6909 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
6910 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
6912 #include <isl/aff.h>
6913 __isl_give isl_pw_aff *isl_pw_aff_union_add(
6914 __isl_take isl_pw_aff *pwaff1,
6915 __isl_take isl_pw_aff *pwaff2);
6916 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
6917 __isl_take isl_pw_multi_aff *pma1,
6918 __isl_take isl_pw_multi_aff *pma2);
6919 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
6920 __isl_take isl_union_pw_aff *upa1,
6921 __isl_take isl_union_pw_aff *upa2);
6922 __isl_give isl_union_pw_multi_aff *
6923 isl_union_pw_multi_aff_union_add(
6924 __isl_take isl_union_pw_multi_aff *upma1,
6925 __isl_take isl_union_pw_multi_aff *upma2);
6926 __isl_give isl_multi_union_pw_aff *
6927 isl_multi_union_pw_aff_union_add(
6928 __isl_take isl_multi_union_pw_aff *mupa1,
6929 __isl_take isl_multi_union_pw_aff *mupa2);
6930 __isl_give isl_pw_aff *isl_pw_aff_union_min(
6931 __isl_take isl_pw_aff *pwaff1,
6932 __isl_take isl_pw_aff *pwaff2);
6933 __isl_give isl_pw_aff *isl_pw_aff_union_max(
6934 __isl_take isl_pw_aff *pwaff1,
6935 __isl_take isl_pw_aff *pwaff2);
6937 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
6938 expression with a domain that is the union of those of C<pwaff1> and
6939 C<pwaff2> and such that on each cell, the quasi-affine expression is
6940 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
6941 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
6942 associated expression is the defined one.
6943 This in contrast to the C<isl_pw_aff_max> function, which is
6944 only defined on the shared definition domain of the arguments.
6946 #include <isl/val.h>
6947 __isl_give isl_multi_val *isl_multi_val_add_val(
6948 __isl_take isl_multi_val *mv,
6949 __isl_take isl_val *v);
6950 __isl_give isl_multi_val *isl_multi_val_mod_val(
6951 __isl_take isl_multi_val *mv,
6952 __isl_take isl_val *v);
6953 __isl_give isl_multi_val *isl_multi_val_scale_val(
6954 __isl_take isl_multi_val *mv,
6955 __isl_take isl_val *v);
6956 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
6957 __isl_take isl_multi_val *mv,
6958 __isl_take isl_val *v);
6960 #include <isl/aff.h>
6961 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
6962 __isl_take isl_val *mod);
6963 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
6964 __isl_take isl_pw_aff *pa,
6965 __isl_take isl_val *mod);
6966 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
6967 __isl_take isl_union_pw_aff *upa,
6968 __isl_take isl_val *f);
6969 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
6970 __isl_take isl_val *v);
6971 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
6972 __isl_take isl_multi_aff *ma,
6973 __isl_take isl_val *v);
6974 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
6975 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
6976 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
6977 __isl_take isl_multi_pw_aff *mpa,
6978 __isl_take isl_val *v);
6979 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
6980 __isl_take isl_pw_multi_aff *pma,
6981 __isl_take isl_val *v);
6982 __isl_give isl_union_pw_multi_aff *
6983 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
6984 __isl_take isl_union_pw_aff *upa,
6985 __isl_take isl_val *f);
6986 isl_union_pw_multi_aff_scale_val(
6987 __isl_take isl_union_pw_multi_aff *upma,
6988 __isl_take isl_val *val);
6989 __isl_give isl_multi_union_pw_aff *
6990 isl_multi_union_pw_aff_scale_val(
6991 __isl_take isl_multi_union_pw_aff *mupa,
6992 __isl_take isl_val *v);
6993 __isl_give isl_aff *isl_aff_scale_down_ui(
6994 __isl_take isl_aff *aff, unsigned f);
6995 __isl_give isl_aff *isl_aff_scale_down_val(
6996 __isl_take isl_aff *aff, __isl_take isl_val *v);
6997 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
6998 __isl_take isl_multi_aff *ma,
6999 __isl_take isl_val *v);
7000 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
7001 __isl_take isl_pw_aff *pa,
7002 __isl_take isl_val *f);
7003 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
7004 __isl_take isl_multi_pw_aff *mpa,
7005 __isl_take isl_val *v);
7006 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
7007 __isl_take isl_pw_multi_aff *pma,
7008 __isl_take isl_val *v);
7009 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
7010 __isl_take isl_union_pw_aff *upa,
7011 __isl_take isl_val *v);
7012 __isl_give isl_union_pw_multi_aff *
7013 isl_union_pw_multi_aff_scale_down_val(
7014 __isl_take isl_union_pw_multi_aff *upma,
7015 __isl_take isl_val *val);
7016 __isl_give isl_multi_union_pw_aff *
7017 isl_multi_union_pw_aff_scale_down_val(
7018 __isl_take isl_multi_union_pw_aff *mupa,
7019 __isl_take isl_val *v);
7021 #include <isl/polynomial.h>
7022 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
7023 __isl_take isl_qpolynomial *qp,
7024 __isl_take isl_val *v);
7025 __isl_give isl_qpolynomial_fold *
7026 isl_qpolynomial_fold_scale_val(
7027 __isl_take isl_qpolynomial_fold *fold,
7028 __isl_take isl_val *v);
7029 __isl_give isl_pw_qpolynomial *
7030 isl_pw_qpolynomial_scale_val(
7031 __isl_take isl_pw_qpolynomial *pwqp,
7032 __isl_take isl_val *v);
7033 __isl_give isl_pw_qpolynomial_fold *
7034 isl_pw_qpolynomial_fold_scale_val(
7035 __isl_take isl_pw_qpolynomial_fold *pwf,
7036 __isl_take isl_val *v);
7037 __isl_give isl_union_pw_qpolynomial *
7038 isl_union_pw_qpolynomial_scale_val(
7039 __isl_take isl_union_pw_qpolynomial *upwqp,
7040 __isl_take isl_val *v);
7041 __isl_give isl_union_pw_qpolynomial_fold *
7042 isl_union_pw_qpolynomial_fold_scale_val(
7043 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7044 __isl_take isl_val *v);
7045 __isl_give isl_qpolynomial *
7046 isl_qpolynomial_scale_down_val(
7047 __isl_take isl_qpolynomial *qp,
7048 __isl_take isl_val *v);
7049 __isl_give isl_qpolynomial_fold *
7050 isl_qpolynomial_fold_scale_down_val(
7051 __isl_take isl_qpolynomial_fold *fold,
7052 __isl_take isl_val *v);
7053 __isl_give isl_pw_qpolynomial *
7054 isl_pw_qpolynomial_scale_down_val(
7055 __isl_take isl_pw_qpolynomial *pwqp,
7056 __isl_take isl_val *v);
7057 __isl_give isl_pw_qpolynomial_fold *
7058 isl_pw_qpolynomial_fold_scale_down_val(
7059 __isl_take isl_pw_qpolynomial_fold *pwf,
7060 __isl_take isl_val *v);
7061 __isl_give isl_union_pw_qpolynomial *
7062 isl_union_pw_qpolynomial_scale_down_val(
7063 __isl_take isl_union_pw_qpolynomial *upwqp,
7064 __isl_take isl_val *v);
7065 __isl_give isl_union_pw_qpolynomial_fold *
7066 isl_union_pw_qpolynomial_fold_scale_down_val(
7067 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7068 __isl_take isl_val *v);
7070 #include <isl/val.h>
7071 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
7072 __isl_take isl_multi_val *mv1,
7073 __isl_take isl_multi_val *mv2);
7074 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
7075 __isl_take isl_multi_val *mv1,
7076 __isl_take isl_multi_val *mv2);
7077 __isl_give isl_multi_val *
7078 isl_multi_val_scale_down_multi_val(
7079 __isl_take isl_multi_val *mv1,
7080 __isl_take isl_multi_val *mv2);
7082 #include <isl/aff.h>
7083 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
7084 __isl_take isl_multi_aff *ma,
7085 __isl_take isl_multi_val *mv);
7086 __isl_give isl_multi_union_pw_aff *
7087 isl_multi_union_pw_aff_mod_multi_val(
7088 __isl_take isl_multi_union_pw_aff *upma,
7089 __isl_take isl_multi_val *mv);
7090 __isl_give isl_multi_pw_aff *
7091 isl_multi_pw_aff_mod_multi_val(
7092 __isl_take isl_multi_pw_aff *mpa,
7093 __isl_take isl_multi_val *mv);
7094 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
7095 __isl_take isl_multi_aff *ma,
7096 __isl_take isl_multi_val *mv);
7097 __isl_give isl_pw_multi_aff *
7098 isl_pw_multi_aff_scale_multi_val(
7099 __isl_take isl_pw_multi_aff *pma,
7100 __isl_take isl_multi_val *mv);
7101 __isl_give isl_multi_pw_aff *
7102 isl_multi_pw_aff_scale_multi_val(
7103 __isl_take isl_multi_pw_aff *mpa,
7104 __isl_take isl_multi_val *mv);
7105 __isl_give isl_multi_union_pw_aff *
7106 isl_multi_union_pw_aff_scale_multi_val(
7107 __isl_take isl_multi_union_pw_aff *mupa,
7108 __isl_take isl_multi_val *mv);
7109 __isl_give isl_union_pw_multi_aff *
7110 isl_union_pw_multi_aff_scale_multi_val(
7111 __isl_take isl_union_pw_multi_aff *upma,
7112 __isl_take isl_multi_val *mv);
7113 __isl_give isl_multi_aff *
7114 isl_multi_aff_scale_down_multi_val(
7115 __isl_take isl_multi_aff *ma,
7116 __isl_take isl_multi_val *mv);
7117 __isl_give isl_multi_pw_aff *
7118 isl_multi_pw_aff_scale_down_multi_val(
7119 __isl_take isl_multi_pw_aff *mpa,
7120 __isl_take isl_multi_val *mv);
7121 __isl_give isl_multi_union_pw_aff *
7122 isl_multi_union_pw_aff_scale_down_multi_val(
7123 __isl_take isl_multi_union_pw_aff *mupa,
7124 __isl_take isl_multi_val *mv);
7126 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
7127 by the corresponding elements of C<mv>.
7129 #include <isl/aff.h>
7130 __isl_give isl_aff *isl_aff_mul(
7131 __isl_take isl_aff *aff1,
7132 __isl_take isl_aff *aff2);
7133 __isl_give isl_aff *isl_aff_div(
7134 __isl_take isl_aff *aff1,
7135 __isl_take isl_aff *aff2);
7136 __isl_give isl_pw_aff *isl_pw_aff_mul(
7137 __isl_take isl_pw_aff *pwaff1,
7138 __isl_take isl_pw_aff *pwaff2);
7139 __isl_give isl_pw_aff *isl_pw_aff_div(
7140 __isl_take isl_pw_aff *pa1,
7141 __isl_take isl_pw_aff *pa2);
7142 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
7143 __isl_take isl_pw_aff *pa1,
7144 __isl_take isl_pw_aff *pa2);
7145 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
7146 __isl_take isl_pw_aff *pa1,
7147 __isl_take isl_pw_aff *pa2);
7149 When multiplying two affine expressions, at least one of the two needs
7150 to be a constant. Similarly, when dividing an affine expression by another,
7151 the second expression needs to be a constant.
7152 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
7153 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
7156 #include <isl/polynomial.h>
7157 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
7158 __isl_take isl_qpolynomial *qp1,
7159 __isl_take isl_qpolynomial *qp2);
7160 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
7161 __isl_take isl_pw_qpolynomial *pwqp1,
7162 __isl_take isl_pw_qpolynomial *pwqp2);
7163 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
7164 __isl_take isl_union_pw_qpolynomial *upwqp1,
7165 __isl_take isl_union_pw_qpolynomial *upwqp2);
7169 =head3 Lexicographic Optimization
7171 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
7172 the following functions
7173 compute a set that contains the lexicographic minimum or maximum
7174 of the elements in C<set> (or C<bset>) for those values of the parameters
7175 that satisfy C<dom>.
7176 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7177 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
7179 In other words, the union of the parameter values
7180 for which the result is non-empty and of C<*empty>
7183 #include <isl/set.h>
7184 __isl_give isl_set *isl_basic_set_partial_lexmin(
7185 __isl_take isl_basic_set *bset,
7186 __isl_take isl_basic_set *dom,
7187 __isl_give isl_set **empty);
7188 __isl_give isl_set *isl_basic_set_partial_lexmax(
7189 __isl_take isl_basic_set *bset,
7190 __isl_take isl_basic_set *dom,
7191 __isl_give isl_set **empty);
7192 __isl_give isl_set *isl_set_partial_lexmin(
7193 __isl_take isl_set *set, __isl_take isl_set *dom,
7194 __isl_give isl_set **empty);
7195 __isl_give isl_set *isl_set_partial_lexmax(
7196 __isl_take isl_set *set, __isl_take isl_set *dom,
7197 __isl_give isl_set **empty);
7199 Given a (basic) set C<set> (or C<bset>), the following functions simply
7200 return a set containing the lexicographic minimum or maximum
7201 of the elements in C<set> (or C<bset>).
7202 In case of union sets, the optimum is computed per space.
7204 #include <isl/set.h>
7205 __isl_give isl_set *isl_basic_set_lexmin(
7206 __isl_take isl_basic_set *bset);
7207 __isl_give isl_set *isl_basic_set_lexmax(
7208 __isl_take isl_basic_set *bset);
7209 __isl_give isl_set *isl_set_lexmin(
7210 __isl_take isl_set *set);
7211 __isl_give isl_set *isl_set_lexmax(
7212 __isl_take isl_set *set);
7213 __isl_give isl_union_set *isl_union_set_lexmin(
7214 __isl_take isl_union_set *uset);
7215 __isl_give isl_union_set *isl_union_set_lexmax(
7216 __isl_take isl_union_set *uset);
7218 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
7219 the following functions
7220 compute a relation that maps each element of C<dom>
7221 to the single lexicographic minimum or maximum
7222 of the elements that are associated to that same
7223 element in C<map> (or C<bmap>).
7224 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7225 that contains the elements in C<dom> that do not map
7226 to any elements in C<map> (or C<bmap>).
7227 In other words, the union of the domain of the result and of C<*empty>
7230 #include <isl/map.h>
7231 __isl_give isl_map *isl_basic_map_partial_lexmax(
7232 __isl_take isl_basic_map *bmap,
7233 __isl_take isl_basic_set *dom,
7234 __isl_give isl_set **empty);
7235 __isl_give isl_map *isl_basic_map_partial_lexmin(
7236 __isl_take isl_basic_map *bmap,
7237 __isl_take isl_basic_set *dom,
7238 __isl_give isl_set **empty);
7239 __isl_give isl_map *isl_map_partial_lexmax(
7240 __isl_take isl_map *map, __isl_take isl_set *dom,
7241 __isl_give isl_set **empty);
7242 __isl_give isl_map *isl_map_partial_lexmin(
7243 __isl_take isl_map *map, __isl_take isl_set *dom,
7244 __isl_give isl_set **empty);
7246 Given a (basic) map C<map> (or C<bmap>), the following functions simply
7247 return a map mapping each element in the domain of
7248 C<map> (or C<bmap>) to the lexicographic minimum or maximum
7249 of all elements associated to that element.
7250 In case of union relations, the optimum is computed per space.
7252 #include <isl/map.h>
7253 __isl_give isl_map *isl_basic_map_lexmin(
7254 __isl_take isl_basic_map *bmap);
7255 __isl_give isl_map *isl_basic_map_lexmax(
7256 __isl_take isl_basic_map *bmap);
7257 __isl_give isl_map *isl_map_lexmin(
7258 __isl_take isl_map *map);
7259 __isl_give isl_map *isl_map_lexmax(
7260 __isl_take isl_map *map);
7261 __isl_give isl_union_map *isl_union_map_lexmin(
7262 __isl_take isl_union_map *umap);
7263 __isl_give isl_union_map *isl_union_map_lexmax(
7264 __isl_take isl_union_map *umap);
7266 The following functions return their result in the form of
7267 a piecewise multi-affine expression,
7268 but are otherwise equivalent to the corresponding functions
7269 returning a basic set or relation.
7271 #include <isl/set.h>
7272 __isl_give isl_pw_multi_aff *
7273 isl_basic_set_partial_lexmin_pw_multi_aff(
7274 __isl_take isl_basic_set *bset,
7275 __isl_take isl_basic_set *dom,
7276 __isl_give isl_set **empty);
7277 __isl_give isl_pw_multi_aff *
7278 isl_basic_set_partial_lexmax_pw_multi_aff(
7279 __isl_take isl_basic_set *bset,
7280 __isl_take isl_basic_set *dom,
7281 __isl_give isl_set **empty);
7282 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
7283 __isl_take isl_set *set);
7284 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
7285 __isl_take isl_set *set);
7287 #include <isl/map.h>
7288 __isl_give isl_pw_multi_aff *
7289 isl_basic_map_lexmin_pw_multi_aff(
7290 __isl_take isl_basic_map *bmap);
7291 __isl_give isl_pw_multi_aff *
7292 isl_basic_map_partial_lexmin_pw_multi_aff(
7293 __isl_take isl_basic_map *bmap,
7294 __isl_take isl_basic_set *dom,
7295 __isl_give isl_set **empty);
7296 __isl_give isl_pw_multi_aff *
7297 isl_basic_map_partial_lexmax_pw_multi_aff(
7298 __isl_take isl_basic_map *bmap,
7299 __isl_take isl_basic_set *dom,
7300 __isl_give isl_set **empty);
7301 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
7302 __isl_take isl_map *map);
7303 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
7304 __isl_take isl_map *map);
7306 The following functions return the lexicographic minimum or maximum
7307 on the shared domain of the inputs and the single defined function
7308 on those parts of the domain where only a single function is defined.
7310 #include <isl/aff.h>
7311 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
7312 __isl_take isl_pw_multi_aff *pma1,
7313 __isl_take isl_pw_multi_aff *pma2);
7314 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
7315 __isl_take isl_pw_multi_aff *pma1,
7316 __isl_take isl_pw_multi_aff *pma2);
7318 If the input to a lexicographic optimization problem has
7319 multiple constraints with the same coefficients for the optimized
7320 variables, then, by default, this symmetry is exploited by
7321 replacing those constraints by a single constraint with
7322 an abstract bound, which is in turn bounded by the corresponding terms
7323 in the original constraints.
7324 Without this optimization, the solver would typically consider
7325 all possible orderings of those original bounds, resulting in a needless
7326 decomposition of the domain.
7327 However, the optimization can also result in slowdowns since
7328 an extra parameter is introduced that may get used in additional
7330 The following option determines whether symmetry detection is applied
7331 during lexicographic optimization.
7333 #include <isl/options.h>
7334 isl_stat isl_options_set_pip_symmetry(isl_ctx *ctx,
7336 int isl_options_get_pip_symmetry(isl_ctx *ctx);
7340 See also \autoref{s:offline}.
7344 =head2 Ternary Operations
7346 #include <isl/aff.h>
7347 __isl_give isl_pw_aff *isl_pw_aff_cond(
7348 __isl_take isl_pw_aff *cond,
7349 __isl_take isl_pw_aff *pwaff_true,
7350 __isl_take isl_pw_aff *pwaff_false);
7352 The function C<isl_pw_aff_cond> performs a conditional operator
7353 and returns an expression that is equal to C<pwaff_true>
7354 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
7355 where C<cond> is zero.
7359 Lists are defined over several element types, including
7360 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_union_pw_aff>,
7361 C<isl_union_pw_multi_aff>, C<isl_constraint>,
7362 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
7363 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
7364 Here we take lists of C<isl_set>s as an example.
7365 Lists can be created, copied, modified and freed using the following functions.
7367 #include <isl/set.h>
7368 __isl_give isl_set_list *isl_set_list_from_set(
7369 __isl_take isl_set *el);
7370 __isl_give isl_set_list *isl_set_list_alloc(
7371 isl_ctx *ctx, int n);
7372 __isl_give isl_set_list *isl_set_list_copy(
7373 __isl_keep isl_set_list *list);
7374 __isl_give isl_set_list *isl_set_list_insert(
7375 __isl_take isl_set_list *list, unsigned pos,
7376 __isl_take isl_set *el);
7377 __isl_give isl_set_list *isl_set_list_add(
7378 __isl_take isl_set_list *list,
7379 __isl_take isl_set *el);
7380 __isl_give isl_set_list *isl_set_list_drop(
7381 __isl_take isl_set_list *list,
7382 unsigned first, unsigned n);
7383 __isl_give isl_set_list *isl_set_list_set_set(
7384 __isl_take isl_set_list *list, int index,
7385 __isl_take isl_set *set);
7386 __isl_give isl_set_list *isl_set_list_concat(
7387 __isl_take isl_set_list *list1,
7388 __isl_take isl_set_list *list2);
7389 __isl_give isl_set_list *isl_set_list_sort(
7390 __isl_take isl_set_list *list,
7391 int (*cmp)(__isl_keep isl_set *a,
7392 __isl_keep isl_set *b, void *user),
7394 __isl_null isl_set_list *isl_set_list_free(
7395 __isl_take isl_set_list *list);
7397 C<isl_set_list_alloc> creates an empty list with an initial capacity
7398 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
7399 add elements to a list, increasing its capacity as needed.
7400 C<isl_set_list_from_set> creates a list with a single element.
7402 Lists can be inspected using the following functions.
7404 #include <isl/set.h>
7405 int isl_set_list_n_set(__isl_keep isl_set_list *list);
7406 __isl_give isl_set *isl_set_list_get_set(
7407 __isl_keep isl_set_list *list, int index);
7408 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list,
7409 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7411 isl_stat isl_set_list_foreach_scc(
7412 __isl_keep isl_set_list *list,
7413 isl_bool (*follows)(__isl_keep isl_set *a,
7414 __isl_keep isl_set *b, void *user),
7416 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7419 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
7420 strongly connected components of the graph with as vertices the elements
7421 of C<list> and a directed edge from vertex C<b> to vertex C<a>
7422 iff C<follows(a, b)> returns C<isl_bool_true>. The callbacks C<follows> and
7423 C<fn> should return C<isl_bool_error> or C<isl_stat_error> on error.
7425 Lists can be printed using
7427 #include <isl/set.h>
7428 __isl_give isl_printer *isl_printer_print_set_list(
7429 __isl_take isl_printer *p,
7430 __isl_keep isl_set_list *list);
7432 =head2 Associative arrays
7434 Associative arrays map isl objects of a specific type to isl objects
7435 of some (other) specific type. They are defined for several pairs
7436 of types, including (C<isl_map>, C<isl_basic_set>),
7437 (C<isl_id>, C<isl_ast_expr>),
7438 (C<isl_id>, C<isl_id>) and
7439 (C<isl_id>, C<isl_pw_aff>).
7440 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
7443 Associative arrays can be created, copied and freed using
7444 the following functions.
7446 #include <isl/id_to_ast_expr.h>
7447 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
7448 isl_ctx *ctx, int min_size);
7449 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
7450 __isl_keep isl_id_to_ast_expr *id2expr);
7451 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
7452 __isl_take isl_id_to_ast_expr *id2expr);
7454 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
7455 to specify the expected size of the associative array.
7456 The associative array will be grown automatically as needed.
7458 Associative arrays can be inspected using the following functions.
7460 #include <isl/id_to_ast_expr.h>
7461 __isl_give isl_maybe_isl_ast_expr
7462 isl_id_to_ast_expr_try_get(
7463 __isl_keep isl_id_to_ast_expr *id2expr,
7464 __isl_keep isl_id *key);
7465 isl_bool isl_id_to_ast_expr_has(
7466 __isl_keep isl_id_to_ast_expr *id2expr,
7467 __isl_keep isl_id *key);
7468 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
7469 __isl_keep isl_id_to_ast_expr *id2expr,
7470 __isl_take isl_id *key);
7471 isl_stat isl_id_to_ast_expr_foreach(
7472 __isl_keep isl_id_to_ast_expr *id2expr,
7473 isl_stat (*fn)(__isl_take isl_id *key,
7474 __isl_take isl_ast_expr *val, void *user),
7477 The function C<isl_id_to_ast_expr_try_get> returns a structure
7478 containing two elements, C<valid> and C<value>.
7479 If there is a value associated to the key, then C<valid>
7480 is set to C<isl_bool_true> and C<value> contains a copy of
7481 the associated value. Otherwise C<value> is C<NULL> and
7482 C<valid> may be C<isl_bool_error> or C<isl_bool_false> depending
7483 on whether some error has occurred or there simply is no associated value.
7484 The function C<isl_id_to_ast_expr_has> returns the C<valid> field
7485 in the structure and
7486 the function C<isl_id_to_ast_expr_get> returns the C<value> field.
7488 Associative arrays can be modified using the following functions.
7490 #include <isl/id_to_ast_expr.h>
7491 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
7492 __isl_take isl_id_to_ast_expr *id2expr,
7493 __isl_take isl_id *key,
7494 __isl_take isl_ast_expr *val);
7495 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
7496 __isl_take isl_id_to_ast_expr *id2expr,
7497 __isl_take isl_id *key);
7499 Associative arrays can be printed using the following function.
7501 #include <isl/id_to_ast_expr.h>
7502 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
7503 __isl_take isl_printer *p,
7504 __isl_keep isl_id_to_ast_expr *id2expr);
7508 Vectors can be created, copied and freed using the following functions.
7510 #include <isl/vec.h>
7511 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
7513 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
7514 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
7516 Note that the elements of a newly created vector may have arbitrary values.
7517 The elements can be changed and inspected using the following functions.
7519 int isl_vec_size(__isl_keep isl_vec *vec);
7520 __isl_give isl_val *isl_vec_get_element_val(
7521 __isl_keep isl_vec *vec, int pos);
7522 __isl_give isl_vec *isl_vec_set_element_si(
7523 __isl_take isl_vec *vec, int pos, int v);
7524 __isl_give isl_vec *isl_vec_set_element_val(
7525 __isl_take isl_vec *vec, int pos,
7526 __isl_take isl_val *v);
7527 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
7529 __isl_give isl_vec *isl_vec_set_val(
7530 __isl_take isl_vec *vec, __isl_take isl_val *v);
7531 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
7532 __isl_keep isl_vec *vec2, int pos);
7534 C<isl_vec_get_element> will return a negative value if anything went wrong.
7535 In that case, the value of C<*v> is undefined.
7537 The following function can be used to concatenate two vectors.
7539 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
7540 __isl_take isl_vec *vec2);
7544 Matrices can be created, copied and freed using the following functions.
7546 #include <isl/mat.h>
7547 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
7548 unsigned n_row, unsigned n_col);
7549 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
7550 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
7552 Note that the elements of a newly created matrix may have arbitrary values.
7553 The elements can be changed and inspected using the following functions.
7555 int isl_mat_rows(__isl_keep isl_mat *mat);
7556 int isl_mat_cols(__isl_keep isl_mat *mat);
7557 __isl_give isl_val *isl_mat_get_element_val(
7558 __isl_keep isl_mat *mat, int row, int col);
7559 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
7560 int row, int col, int v);
7561 __isl_give isl_mat *isl_mat_set_element_val(
7562 __isl_take isl_mat *mat, int row, int col,
7563 __isl_take isl_val *v);
7565 C<isl_mat_get_element> will return a negative value if anything went wrong.
7566 In that case, the value of C<*v> is undefined.
7568 The following function can be used to compute the (right) inverse
7569 of a matrix, i.e., a matrix such that the product of the original
7570 and the inverse (in that order) is a multiple of the identity matrix.
7571 The input matrix is assumed to be of full row-rank.
7573 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
7575 The following function can be used to compute the (right) kernel
7576 (or null space) of a matrix, i.e., a matrix such that the product of
7577 the original and the kernel (in that order) is the zero matrix.
7579 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
7581 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
7583 The following functions determine
7584 an upper or lower bound on a quasipolynomial over its domain.
7586 __isl_give isl_pw_qpolynomial_fold *
7587 isl_pw_qpolynomial_bound(
7588 __isl_take isl_pw_qpolynomial *pwqp,
7589 enum isl_fold type, int *tight);
7591 __isl_give isl_union_pw_qpolynomial_fold *
7592 isl_union_pw_qpolynomial_bound(
7593 __isl_take isl_union_pw_qpolynomial *upwqp,
7594 enum isl_fold type, int *tight);
7596 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
7597 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
7598 is the returned bound is known be tight, i.e., for each value
7599 of the parameters there is at least
7600 one element in the domain that reaches the bound.
7601 If the domain of C<pwqp> is not wrapping, then the bound is computed
7602 over all elements in that domain and the result has a purely parametric
7603 domain. If the domain of C<pwqp> is wrapping, then the bound is
7604 computed over the range of the wrapped relation. The domain of the
7605 wrapped relation becomes the domain of the result.
7607 =head2 Parametric Vertex Enumeration
7609 The parametric vertex enumeration described in this section
7610 is mainly intended to be used internally and by the C<barvinok>
7613 #include <isl/vertices.h>
7614 __isl_give isl_vertices *isl_basic_set_compute_vertices(
7615 __isl_keep isl_basic_set *bset);
7617 The function C<isl_basic_set_compute_vertices> performs the
7618 actual computation of the parametric vertices and the chamber
7619 decomposition and stores the result in an C<isl_vertices> object.
7620 This information can be queried by either iterating over all
7621 the vertices or iterating over all the chambers or cells
7622 and then iterating over all vertices that are active on the chamber.
7624 isl_stat isl_vertices_foreach_vertex(
7625 __isl_keep isl_vertices *vertices,
7626 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7627 void *user), void *user);
7629 isl_stat isl_vertices_foreach_cell(
7630 __isl_keep isl_vertices *vertices,
7631 isl_stat (*fn)(__isl_take isl_cell *cell,
7632 void *user), void *user);
7633 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
7634 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7635 void *user), void *user);
7637 Other operations that can be performed on an C<isl_vertices> object are
7640 int isl_vertices_get_n_vertices(
7641 __isl_keep isl_vertices *vertices);
7642 void isl_vertices_free(__isl_take isl_vertices *vertices);
7644 Vertices can be inspected and destroyed using the following functions.
7646 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
7647 __isl_give isl_basic_set *isl_vertex_get_domain(
7648 __isl_keep isl_vertex *vertex);
7649 __isl_give isl_multi_aff *isl_vertex_get_expr(
7650 __isl_keep isl_vertex *vertex);
7651 void isl_vertex_free(__isl_take isl_vertex *vertex);
7653 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
7654 describing the vertex in terms of the parameters,
7655 while C<isl_vertex_get_domain> returns the activity domain
7658 Chambers can be inspected and destroyed using the following functions.
7660 __isl_give isl_basic_set *isl_cell_get_domain(
7661 __isl_keep isl_cell *cell);
7662 void isl_cell_free(__isl_take isl_cell *cell);
7664 =head1 Polyhedral Compilation Library
7666 This section collects functionality in C<isl> that has been specifically
7667 designed for use during polyhedral compilation.
7669 =head2 Schedule Trees
7671 A schedule tree is a structured representation of a schedule,
7672 assigning a relative order to a set of domain elements.
7673 The relative order expressed by the schedule tree is
7674 defined recursively. In particular, the order between
7675 two domain elements is determined by the node that is closest
7676 to the root that refers to both elements and that orders them apart.
7677 Each node in the tree is of one of several types.
7678 The root node is always of type C<isl_schedule_node_domain>
7679 (or C<isl_schedule_node_extension>)
7680 and it describes the (extra) domain elements to which the schedule applies.
7681 The other types of nodes are as follows.
7685 =item C<isl_schedule_node_band>
7687 A band of schedule dimensions. Each schedule dimension is represented
7688 by a union piecewise quasi-affine expression. If this expression
7689 assigns a different value to two domain elements, while all previous
7690 schedule dimensions in the same band assign them the same value,
7691 then the two domain elements are ordered according to these two
7693 Each expression is required to be total in the domain elements
7694 that reach the band node.
7696 =item C<isl_schedule_node_expansion>
7698 An expansion node maps each of the domain elements that reach the node
7699 to one or more domain elements. The image of this mapping forms
7700 the set of domain elements that reach the child of the expansion node.
7701 The function that maps each of the expanded domain elements
7702 to the original domain element from which it was expanded
7703 is called the contraction.
7705 =item C<isl_schedule_node_filter>
7707 A filter node does not impose any ordering, but rather intersects
7708 the set of domain elements that the current subtree refers to
7709 with a given union set. The subtree of the filter node only
7710 refers to domain elements in the intersection.
7711 A filter node is typically only used as a child of a sequence or
7714 =item C<isl_schedule_node_leaf>
7716 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
7718 =item C<isl_schedule_node_mark>
7720 A mark node can be used to attach any kind of information to a subtree
7721 of the schedule tree.
7723 =item C<isl_schedule_node_sequence>
7725 A sequence node has one or more children, each of which is a filter node.
7726 The filters on these filter nodes form a partition of
7727 the domain elements that the current subtree refers to.
7728 If two domain elements appear in distinct filters then the sequence
7729 node orders them according to the child positions of the corresponding
7732 =item C<isl_schedule_node_set>
7734 A set node is similar to a sequence node, except that
7735 it expresses that domain elements appearing in distinct filters
7736 may have any order. The order of the children of a set node
7737 is therefore also immaterial.
7741 The following node types are only supported by the AST generator.
7745 =item C<isl_schedule_node_context>
7747 The context describes constraints on the parameters and
7748 the schedule dimensions of outer
7749 bands that the AST generator may assume to hold. It is also the only
7750 kind of node that may introduce additional parameters.
7751 The space of the context is that of the flat product of the outer
7752 band nodes. In particular, if there are no outer band nodes, then
7753 this space is the unnamed zero-dimensional space.
7754 Since a context node references the outer band nodes, any tree
7755 containing a context node is considered to be anchored.
7757 =item C<isl_schedule_node_extension>
7759 An extension node instructs the AST generator to add additional
7760 domain elements that need to be scheduled.
7761 The additional domain elements are described by the range of
7762 the extension map in terms of the outer schedule dimensions,
7763 i.e., the flat product of the outer band nodes.
7764 Note that domain elements are added whenever the AST generator
7765 reaches the extension node, meaning that there are still some
7766 active domain elements for which an AST needs to be generated.
7767 The conditions under which some domain elements are still active
7768 may however not be completely described by the outer AST nodes
7769 generated at that point.
7771 An extension node may also appear as the root of a schedule tree,
7772 when it is intended to be inserted into another tree
7773 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
7774 In this case, the domain of the extension node should
7775 correspond to the flat product of the outer band nodes
7776 in this other schedule tree at the point where the extension tree
7779 =item C<isl_schedule_node_guard>
7781 The guard describes constraints on the parameters and
7782 the schedule dimensions of outer
7783 bands that need to be enforced by the outer nodes
7784 in the generated AST.
7785 The space of the guard is that of the flat product of the outer
7786 band nodes. In particular, if there are no outer band nodes, then
7787 this space is the unnamed zero-dimensional space.
7788 Since a guard node references the outer band nodes, any tree
7789 containing a guard node is considered to be anchored.
7793 Except for the C<isl_schedule_node_context> nodes,
7794 none of the nodes may introduce any parameters that were not
7795 already present in the root domain node.
7797 A schedule tree is encapsulated in an C<isl_schedule> object.
7798 The simplest such objects, those with a tree consisting of single domain node,
7799 can be created using the following functions with either an empty
7800 domain or a given domain.
7802 #include <isl/schedule.h>
7803 __isl_give isl_schedule *isl_schedule_empty(
7804 __isl_take isl_space *space);
7805 __isl_give isl_schedule *isl_schedule_from_domain(
7806 __isl_take isl_union_set *domain);
7808 The function C<isl_schedule_constraints_compute_schedule> described
7809 in L</"Scheduling"> can also be used to construct schedules.
7811 C<isl_schedule> objects may be copied and freed using the following functions.
7813 #include <isl/schedule.h>
7814 __isl_give isl_schedule *isl_schedule_copy(
7815 __isl_keep isl_schedule *sched);
7816 __isl_null isl_schedule *isl_schedule_free(
7817 __isl_take isl_schedule *sched);
7819 The following functions checks whether two C<isl_schedule> objects
7820 are obviously the same.
7822 #include <isl/schedule.h>
7823 isl_bool isl_schedule_plain_is_equal(
7824 __isl_keep isl_schedule *schedule1,
7825 __isl_keep isl_schedule *schedule2);
7827 The domain of the schedule, i.e., the domain described by the root node,
7828 can be obtained using the following function.
7830 #include <isl/schedule.h>
7831 __isl_give isl_union_set *isl_schedule_get_domain(
7832 __isl_keep isl_schedule *schedule);
7834 An extra top-level band node (right underneath the domain node) can
7835 be introduced into the schedule using the following function.
7836 The schedule tree is assumed not to have any anchored nodes.
7838 #include <isl/schedule.h>
7839 __isl_give isl_schedule *
7840 isl_schedule_insert_partial_schedule(
7841 __isl_take isl_schedule *schedule,
7842 __isl_take isl_multi_union_pw_aff *partial);
7844 A top-level context node (right underneath the domain node) can
7845 be introduced into the schedule using the following function.
7847 #include <isl/schedule.h>
7848 __isl_give isl_schedule *isl_schedule_insert_context(
7849 __isl_take isl_schedule *schedule,
7850 __isl_take isl_set *context)
7852 A top-level guard node (right underneath the domain node) can
7853 be introduced into the schedule using the following function.
7855 #include <isl/schedule.h>
7856 __isl_give isl_schedule *isl_schedule_insert_guard(
7857 __isl_take isl_schedule *schedule,
7858 __isl_take isl_set *guard)
7860 A schedule that combines two schedules either in the given
7861 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
7862 or an C<isl_schedule_node_set> node,
7863 can be created using the following functions.
7865 #include <isl/schedule.h>
7866 __isl_give isl_schedule *isl_schedule_sequence(
7867 __isl_take isl_schedule *schedule1,
7868 __isl_take isl_schedule *schedule2);
7869 __isl_give isl_schedule *isl_schedule_set(
7870 __isl_take isl_schedule *schedule1,
7871 __isl_take isl_schedule *schedule2);
7873 The domains of the two input schedules need to be disjoint.
7875 The following function can be used to restrict the domain
7876 of a schedule with a domain node as root to be a subset of the given union set.
7877 This operation may remove nodes in the tree that have become
7880 #include <isl/schedule.h>
7881 __isl_give isl_schedule *isl_schedule_intersect_domain(
7882 __isl_take isl_schedule *schedule,
7883 __isl_take isl_union_set *domain);
7885 The following function can be used to simplify the domain
7886 of a schedule with a domain node as root with respect to the given
7889 #include <isl/schedule.h>
7890 __isl_give isl_schedule *isl_schedule_gist_domain_params(
7891 __isl_take isl_schedule *schedule,
7892 __isl_take isl_set *context);
7894 The following function resets the user pointers on all parameter
7895 and tuple identifiers referenced by the nodes of the given schedule.
7897 #include <isl/schedule.h>
7898 __isl_give isl_schedule *isl_schedule_reset_user(
7899 __isl_take isl_schedule *schedule);
7901 The following function aligns the parameters of all nodes
7902 in the given schedule to the given space.
7904 #include <isl/schedule.h>
7905 __isl_give isl_schedule *isl_schedule_align_params(
7906 __isl_take isl_schedule *schedule,
7907 __isl_take isl_space *space);
7909 The following function allows the user to plug in a given function
7910 in the iteration domains. The input schedule is not allowed to contain
7911 any expansion nodes.
7913 #include <isl/schedule.h>
7914 __isl_give isl_schedule *
7915 isl_schedule_pullback_union_pw_multi_aff(
7916 __isl_take isl_schedule *schedule,
7917 __isl_take isl_union_pw_multi_aff *upma);
7919 The following function can be used to plug in the schedule C<expansion>
7920 in the leaves of C<schedule>, where C<contraction> describes how
7921 the domain elements of C<expansion> map to the domain elements
7922 at the original leaves of C<schedule>.
7923 The resulting schedule will contain expansion nodes, unless
7924 C<contraction> is an identity function.
7926 #include <isl/schedule.h>
7927 __isl_give isl_schedule *isl_schedule_expand(
7928 __isl_take isl_schedule *schedule,
7929 __isl_take isl_union_pw_multi_aff *contraction,
7930 __isl_take isl_schedule *expansion);
7932 An C<isl_union_map> representation of the schedule can be obtained
7933 from an C<isl_schedule> using the following function.
7935 #include <isl/schedule.h>
7936 __isl_give isl_union_map *isl_schedule_get_map(
7937 __isl_keep isl_schedule *sched);
7939 The resulting relation encodes the same relative ordering as
7940 the schedule by mapping the domain elements to a common schedule space.
7941 If the schedule_separate_components option is set, then the order
7942 of the children of a set node is explicitly encoded in the result.
7943 If the tree contains any expansion nodes, then the relation
7944 is formulated in terms of the expanded domain elements.
7946 Schedules can be read from input using the following functions.
7948 #include <isl/schedule.h>
7949 __isl_give isl_schedule *isl_schedule_read_from_file(
7950 isl_ctx *ctx, FILE *input);
7951 __isl_give isl_schedule *isl_schedule_read_from_str(
7952 isl_ctx *ctx, const char *str);
7954 A representation of the schedule can be printed using
7956 #include <isl/schedule.h>
7957 __isl_give isl_printer *isl_printer_print_schedule(
7958 __isl_take isl_printer *p,
7959 __isl_keep isl_schedule *schedule);
7960 __isl_give char *isl_schedule_to_str(
7961 __isl_keep isl_schedule *schedule);
7963 C<isl_schedule_to_str> prints the schedule in flow format.
7965 The schedule tree can be traversed through the use of
7966 C<isl_schedule_node> objects that point to a particular
7967 position in the schedule tree. Whenever a C<isl_schedule_node>
7968 is use to modify a node in the schedule tree, the original schedule
7969 tree is left untouched and the modifications are performed to a copy
7970 of the tree. The returned C<isl_schedule_node> then points to
7971 this modified copy of the tree.
7973 The root of the schedule tree can be obtained using the following function.
7975 #include <isl/schedule.h>
7976 __isl_give isl_schedule_node *isl_schedule_get_root(
7977 __isl_keep isl_schedule *schedule);
7979 A pointer to a newly created schedule tree with a single domain
7980 node can be created using the following functions.
7982 #include <isl/schedule_node.h>
7983 __isl_give isl_schedule_node *
7984 isl_schedule_node_from_domain(
7985 __isl_take isl_union_set *domain);
7986 __isl_give isl_schedule_node *
7987 isl_schedule_node_from_extension(
7988 __isl_take isl_union_map *extension);
7990 C<isl_schedule_node_from_extension> creates a tree with an extension
7993 Schedule nodes can be copied and freed using the following functions.
7995 #include <isl/schedule_node.h>
7996 __isl_give isl_schedule_node *isl_schedule_node_copy(
7997 __isl_keep isl_schedule_node *node);
7998 __isl_null isl_schedule_node *isl_schedule_node_free(
7999 __isl_take isl_schedule_node *node);
8001 The following functions can be used to check if two schedule
8002 nodes point to the same position in the same schedule.
8004 #include <isl/schedule_node.h>
8005 isl_bool isl_schedule_node_is_equal(
8006 __isl_keep isl_schedule_node *node1,
8007 __isl_keep isl_schedule_node *node2);
8009 The following properties can be obtained from a schedule node.
8011 #include <isl/schedule_node.h>
8012 enum isl_schedule_node_type isl_schedule_node_get_type(
8013 __isl_keep isl_schedule_node *node);
8014 enum isl_schedule_node_type
8015 isl_schedule_node_get_parent_type(
8016 __isl_keep isl_schedule_node *node);
8017 __isl_give isl_schedule *isl_schedule_node_get_schedule(
8018 __isl_keep isl_schedule_node *node);
8020 The function C<isl_schedule_node_get_type> returns the type of
8021 the node, while C<isl_schedule_node_get_parent_type> returns
8022 type of the parent of the node, which is required to exist.
8023 The function C<isl_schedule_node_get_schedule> returns a copy
8024 to the schedule to which the node belongs.
8026 The following functions can be used to move the schedule node
8027 to a different position in the tree or to check if such a position
8030 #include <isl/schedule_node.h>
8031 isl_bool isl_schedule_node_has_parent(
8032 __isl_keep isl_schedule_node *node);
8033 __isl_give isl_schedule_node *isl_schedule_node_parent(
8034 __isl_take isl_schedule_node *node);
8035 __isl_give isl_schedule_node *isl_schedule_node_root(
8036 __isl_take isl_schedule_node *node);
8037 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
8038 __isl_take isl_schedule_node *node,
8040 int isl_schedule_node_n_children(
8041 __isl_keep isl_schedule_node *node);
8042 __isl_give isl_schedule_node *isl_schedule_node_child(
8043 __isl_take isl_schedule_node *node, int pos);
8044 isl_bool isl_schedule_node_has_children(
8045 __isl_keep isl_schedule_node *node);
8046 __isl_give isl_schedule_node *isl_schedule_node_first_child(
8047 __isl_take isl_schedule_node *node);
8048 isl_bool isl_schedule_node_has_previous_sibling(
8049 __isl_keep isl_schedule_node *node);
8050 __isl_give isl_schedule_node *
8051 isl_schedule_node_previous_sibling(
8052 __isl_take isl_schedule_node *node);
8053 isl_bool isl_schedule_node_has_next_sibling(
8054 __isl_keep isl_schedule_node *node);
8055 __isl_give isl_schedule_node *
8056 isl_schedule_node_next_sibling(
8057 __isl_take isl_schedule_node *node);
8059 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
8060 is the node itself, the ancestor of generation 1 is its parent and so on.
8062 It is also possible to query the number of ancestors of a node,
8063 the position of the current node
8064 within the children of its parent, the position of the subtree
8065 containing a node within the children of an ancestor
8066 or to obtain a copy of a given
8067 child without destroying the current node.
8068 Given two nodes that point to the same schedule, their closest
8069 shared ancestor can be obtained using
8070 C<isl_schedule_node_get_shared_ancestor>.
8072 #include <isl/schedule_node.h>
8073 int isl_schedule_node_get_tree_depth(
8074 __isl_keep isl_schedule_node *node);
8075 int isl_schedule_node_get_child_position(
8076 __isl_keep isl_schedule_node *node);
8077 int isl_schedule_node_get_ancestor_child_position(
8078 __isl_keep isl_schedule_node *node,
8079 __isl_keep isl_schedule_node *ancestor);
8080 __isl_give isl_schedule_node *isl_schedule_node_get_child(
8081 __isl_keep isl_schedule_node *node, int pos);
8082 __isl_give isl_schedule_node *
8083 isl_schedule_node_get_shared_ancestor(
8084 __isl_keep isl_schedule_node *node1,
8085 __isl_keep isl_schedule_node *node2);
8087 All nodes in a schedule tree or
8088 all descendants of a specific node (including the node) can be visited
8089 in depth-first pre-order using the following functions.
8091 #include <isl/schedule.h>
8092 isl_stat isl_schedule_foreach_schedule_node_top_down(
8093 __isl_keep isl_schedule *sched,
8094 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8095 void *user), void *user);
8097 #include <isl/schedule_node.h>
8098 isl_stat isl_schedule_node_foreach_descendant_top_down(
8099 __isl_keep isl_schedule_node *node,
8100 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8101 void *user), void *user);
8103 The callback function is slightly different from the usual
8104 callbacks in that it not only indicates success (non-negative result)
8105 or failure (negative result), but also indicates whether the children
8106 of the given node should be visited. In particular, if the callback
8107 returns a positive value, then the children are visited, but if
8108 the callback returns zero, then the children are not visited.
8110 The ancestors of a node in a schedule tree can be visited from
8111 the root down to and including the parent of the node using
8112 the following function.
8114 #include <isl/schedule_node.h>
8115 isl_stat isl_schedule_node_foreach_ancestor_top_down(
8116 __isl_keep isl_schedule_node *node,
8117 isl_stat (*fn)(__isl_keep isl_schedule_node *node,
8118 void *user), void *user);
8120 The following functions allows for a depth-first post-order
8121 traversal of the nodes in a schedule tree or
8122 of the descendants of a specific node (including the node
8123 itself), where the user callback is allowed to modify the
8126 #include <isl/schedule.h>
8127 __isl_give isl_schedule *
8128 isl_schedule_map_schedule_node_bottom_up(
8129 __isl_take isl_schedule *schedule,
8130 __isl_give isl_schedule_node *(*fn)(
8131 __isl_take isl_schedule_node *node,
8132 void *user), void *user);
8134 #include <isl/schedule_node.h>
8135 __isl_give isl_schedule_node *
8136 isl_schedule_node_map_descendant_bottom_up(
8137 __isl_take isl_schedule_node *node,
8138 __isl_give isl_schedule_node *(*fn)(
8139 __isl_take isl_schedule_node *node,
8140 void *user), void *user);
8142 The traversal continues from the node returned by the callback function.
8143 It is the responsibility of the user to ensure that this does not
8144 lead to an infinite loop. It is safest to always return a pointer
8145 to the same position (same ancestors and child positions) as the input node.
8147 The following function removes a node (along with its descendants)
8148 from a schedule tree and returns a pointer to the leaf at the
8149 same position in the updated tree.
8150 It is not allowed to remove the root of a schedule tree or
8151 a child of a set or sequence node.
8153 #include <isl/schedule_node.h>
8154 __isl_give isl_schedule_node *isl_schedule_node_cut(
8155 __isl_take isl_schedule_node *node);
8157 The following function removes a single node
8158 from a schedule tree and returns a pointer to the child
8159 of the node, now located at the position of the original node
8160 or to a leaf node at that position if there was no child.
8161 It is not allowed to remove the root of a schedule tree,
8162 a set or sequence node, a child of a set or sequence node or
8163 a band node with an anchored subtree.
8165 #include <isl/schedule_node.h>
8166 __isl_give isl_schedule_node *isl_schedule_node_delete(
8167 __isl_take isl_schedule_node *node);
8169 Most nodes in a schedule tree only contain local information.
8170 In some cases, however, a node may also refer to the schedule dimensions
8171 of its outer band nodes.
8172 This means that the position of the node within the tree should
8173 not be changed, or at least that no changes are performed to the
8174 outer band nodes. The following function can be used to test
8175 whether the subtree rooted at a given node contains any such nodes.
8177 #include <isl/schedule_node.h>
8178 isl_bool isl_schedule_node_is_subtree_anchored(
8179 __isl_keep isl_schedule_node *node);
8181 The following function resets the user pointers on all parameter
8182 and tuple identifiers referenced by the given schedule node.
8184 #include <isl/schedule_node.h>
8185 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
8186 __isl_take isl_schedule_node *node);
8188 The following function aligns the parameters of the given schedule
8189 node to the given space.
8191 #include <isl/schedule_node.h>
8192 __isl_give isl_schedule_node *
8193 isl_schedule_node_align_params(
8194 __isl_take isl_schedule_node *node,
8195 __isl_take isl_space *space);
8197 Several node types have their own functions for querying
8198 (and in some cases setting) some node type specific properties.
8200 #include <isl/schedule_node.h>
8201 __isl_give isl_space *isl_schedule_node_band_get_space(
8202 __isl_keep isl_schedule_node *node);
8203 __isl_give isl_multi_union_pw_aff *
8204 isl_schedule_node_band_get_partial_schedule(
8205 __isl_keep isl_schedule_node *node);
8206 __isl_give isl_union_map *
8207 isl_schedule_node_band_get_partial_schedule_union_map(
8208 __isl_keep isl_schedule_node *node);
8209 unsigned isl_schedule_node_band_n_member(
8210 __isl_keep isl_schedule_node *node);
8211 isl_bool isl_schedule_node_band_member_get_coincident(
8212 __isl_keep isl_schedule_node *node, int pos);
8213 __isl_give isl_schedule_node *
8214 isl_schedule_node_band_member_set_coincident(
8215 __isl_take isl_schedule_node *node, int pos,
8217 isl_bool isl_schedule_node_band_get_permutable(
8218 __isl_keep isl_schedule_node *node);
8219 __isl_give isl_schedule_node *
8220 isl_schedule_node_band_set_permutable(
8221 __isl_take isl_schedule_node *node, int permutable);
8222 enum isl_ast_loop_type
8223 isl_schedule_node_band_member_get_ast_loop_type(
8224 __isl_keep isl_schedule_node *node, int pos);
8225 __isl_give isl_schedule_node *
8226 isl_schedule_node_band_member_set_ast_loop_type(
8227 __isl_take isl_schedule_node *node, int pos,
8228 enum isl_ast_loop_type type);
8229 __isl_give isl_union_set *
8230 enum isl_ast_loop_type
8231 isl_schedule_node_band_member_get_isolate_ast_loop_type(
8232 __isl_keep isl_schedule_node *node, int pos);
8233 __isl_give isl_schedule_node *
8234 isl_schedule_node_band_member_set_isolate_ast_loop_type(
8235 __isl_take isl_schedule_node *node, int pos,
8236 enum isl_ast_loop_type type);
8237 isl_schedule_node_band_get_ast_build_options(
8238 __isl_keep isl_schedule_node *node);
8239 __isl_give isl_schedule_node *
8240 isl_schedule_node_band_set_ast_build_options(
8241 __isl_take isl_schedule_node *node,
8242 __isl_take isl_union_set *options);
8243 __isl_give isl_set *
8244 isl_schedule_node_band_get_ast_isolate_option(
8245 __isl_keep isl_schedule_node *node);
8247 The function C<isl_schedule_node_band_get_space> returns the space
8248 of the partial schedule of the band.
8249 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
8250 returns a representation of the partial schedule of the band node
8251 in the form of an C<isl_union_map>.
8252 The coincident and permutable properties are set by
8253 C<isl_schedule_constraints_compute_schedule> on the schedule tree
8255 A scheduling dimension is considered to be ``coincident''
8256 if it satisfies the coincidence constraints within its band.
8257 That is, if the dependence distances of the coincidence
8258 constraints are all zero in that direction (for fixed
8259 iterations of outer bands).
8260 A band is marked permutable if it was produced using the Pluto-like scheduler.
8261 Note that the scheduler may have to resort to a Feautrier style scheduling
8262 step even if the default scheduler is used.
8263 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
8264 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
8265 For the meaning of these loop AST generation types and the difference
8266 between the regular loop AST generation type and the isolate
8267 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
8268 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
8269 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
8270 may return C<isl_ast_loop_error> if an error occurs.
8271 The AST build options govern how an AST is generated for
8272 the individual schedule dimensions during AST generation.
8273 See L</"AST Generation Options (Schedule Tree)">.
8274 The isolate option for the given node can be extracted from these
8275 AST build options using the function
8276 C<isl_schedule_node_band_get_ast_isolate_option>.
8278 #include <isl/schedule_node.h>
8279 __isl_give isl_set *
8280 isl_schedule_node_context_get_context(
8281 __isl_keep isl_schedule_node *node);
8283 #include <isl/schedule_node.h>
8284 __isl_give isl_union_set *
8285 isl_schedule_node_domain_get_domain(
8286 __isl_keep isl_schedule_node *node);
8288 #include <isl/schedule_node.h>
8289 __isl_give isl_union_map *
8290 isl_schedule_node_expansion_get_expansion(
8291 __isl_keep isl_schedule_node *node);
8292 __isl_give isl_union_pw_multi_aff *
8293 isl_schedule_node_expansion_get_contraction(
8294 __isl_keep isl_schedule_node *node);
8296 #include <isl/schedule_node.h>
8297 __isl_give isl_union_map *
8298 isl_schedule_node_extension_get_extension(
8299 __isl_keep isl_schedule_node *node);
8301 #include <isl/schedule_node.h>
8302 __isl_give isl_union_set *
8303 isl_schedule_node_filter_get_filter(
8304 __isl_keep isl_schedule_node *node);
8306 #include <isl/schedule_node.h>
8307 __isl_give isl_set *isl_schedule_node_guard_get_guard(
8308 __isl_keep isl_schedule_node *node);
8310 #include <isl/schedule_node.h>
8311 __isl_give isl_id *isl_schedule_node_mark_get_id(
8312 __isl_keep isl_schedule_node *node);
8314 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
8315 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
8316 partial schedules related to the node.
8318 #include <isl/schedule_node.h>
8319 __isl_give isl_multi_union_pw_aff *
8320 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
8321 __isl_keep isl_schedule_node *node);
8322 __isl_give isl_union_pw_multi_aff *
8323 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
8324 __isl_keep isl_schedule_node *node);
8325 __isl_give isl_union_map *
8326 isl_schedule_node_get_prefix_schedule_union_map(
8327 __isl_keep isl_schedule_node *node);
8328 __isl_give isl_union_map *
8329 isl_schedule_node_get_prefix_schedule_relation(
8330 __isl_keep isl_schedule_node *node);
8331 __isl_give isl_union_map *
8332 isl_schedule_node_get_subtree_schedule_union_map(
8333 __isl_keep isl_schedule_node *node);
8335 In particular, the functions
8336 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
8337 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
8338 and C<isl_schedule_node_get_prefix_schedule_union_map>
8339 return a relative ordering on the domain elements that reach the given
8340 node determined by its ancestors.
8341 The function C<isl_schedule_node_get_prefix_schedule_relation>
8342 additionally includes the domain constraints in the result.
8343 The function C<isl_schedule_node_get_subtree_schedule_union_map>
8344 returns a representation of the partial schedule defined by the
8345 subtree rooted at the given node.
8346 If the tree contains any expansion nodes, then the subtree schedule
8347 is formulated in terms of the expanded domain elements.
8348 The tree passed to functions returning a prefix schedule
8349 may only contain extension nodes if these would not affect
8350 the result of these functions. That is, if one of the ancestors
8351 is an extension node, then all of the domain elements that were
8352 added by the extension node need to have been filtered out
8353 by filter nodes between the extension node and the input node.
8354 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
8355 may not contain in extension nodes in the selected subtree.
8357 The expansion/contraction defined by an entire subtree, combining
8358 the expansions/contractions
8359 on the expansion nodes in the subtree, can be obtained using
8360 the following functions.
8362 #include <isl/schedule_node.h>
8363 __isl_give isl_union_map *
8364 isl_schedule_node_get_subtree_expansion(
8365 __isl_keep isl_schedule_node *node);
8366 __isl_give isl_union_pw_multi_aff *
8367 isl_schedule_node_get_subtree_contraction(
8368 __isl_keep isl_schedule_node *node);
8370 The total number of outer band members of given node, i.e.,
8371 the shared output dimension of the maps in the result
8372 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
8373 using the following function.
8375 #include <isl/schedule_node.h>
8376 int isl_schedule_node_get_schedule_depth(
8377 __isl_keep isl_schedule_node *node);
8379 The following functions return the elements that reach the given node
8380 or the union of universes in the spaces that contain these elements.
8382 #include <isl/schedule_node.h>
8383 __isl_give isl_union_set *
8384 isl_schedule_node_get_domain(
8385 __isl_keep isl_schedule_node *node);
8386 __isl_give isl_union_set *
8387 isl_schedule_node_get_universe_domain(
8388 __isl_keep isl_schedule_node *node);
8390 The input tree of C<isl_schedule_node_get_domain>
8391 may only contain extension nodes if these would not affect
8392 the result of this function. That is, if one of the ancestors
8393 is an extension node, then all of the domain elements that were
8394 added by the extension node need to have been filtered out
8395 by filter nodes between the extension node and the input node.
8397 The following functions can be used to introduce additional nodes
8398 in the schedule tree. The new node is introduced at the point
8399 in the tree where the C<isl_schedule_node> points to and
8400 the results points to the new node.
8402 #include <isl/schedule_node.h>
8403 __isl_give isl_schedule_node *
8404 isl_schedule_node_insert_partial_schedule(
8405 __isl_take isl_schedule_node *node,
8406 __isl_take isl_multi_union_pw_aff *schedule);
8408 This function inserts a new band node with (the greatest integer
8409 part of) the given partial schedule.
8410 The subtree rooted at the given node is assumed not to have
8413 #include <isl/schedule_node.h>
8414 __isl_give isl_schedule_node *
8415 isl_schedule_node_insert_context(
8416 __isl_take isl_schedule_node *node,
8417 __isl_take isl_set *context);
8419 This function inserts a new context node with the given context constraints.
8421 #include <isl/schedule_node.h>
8422 __isl_give isl_schedule_node *
8423 isl_schedule_node_insert_filter(
8424 __isl_take isl_schedule_node *node,
8425 __isl_take isl_union_set *filter);
8427 This function inserts a new filter node with the given filter.
8428 If the original node already pointed to a filter node, then the
8429 two filter nodes are merged into one.
8431 #include <isl/schedule_node.h>
8432 __isl_give isl_schedule_node *
8433 isl_schedule_node_insert_guard(
8434 __isl_take isl_schedule_node *node,
8435 __isl_take isl_set *guard);
8437 This function inserts a new guard node with the given guard constraints.
8439 #include <isl/schedule_node.h>
8440 __isl_give isl_schedule_node *
8441 isl_schedule_node_insert_mark(
8442 __isl_take isl_schedule_node *node,
8443 __isl_take isl_id *mark);
8445 This function inserts a new mark node with the give mark identifier.
8447 #include <isl/schedule_node.h>
8448 __isl_give isl_schedule_node *
8449 isl_schedule_node_insert_sequence(
8450 __isl_take isl_schedule_node *node,
8451 __isl_take isl_union_set_list *filters);
8452 __isl_give isl_schedule_node *
8453 isl_schedule_node_insert_set(
8454 __isl_take isl_schedule_node *node,
8455 __isl_take isl_union_set_list *filters);
8457 These functions insert a new sequence or set node with the given
8458 filters as children.
8460 #include <isl/schedule_node.h>
8461 __isl_give isl_schedule_node *isl_schedule_node_group(
8462 __isl_take isl_schedule_node *node,
8463 __isl_take isl_id *group_id);
8465 This function introduces an expansion node in between the current
8466 node and its parent that expands instances of a space with tuple
8467 identifier C<group_id> to the original domain elements that reach
8468 the node. The group instances are identified by the prefix schedule
8469 of those domain elements. The ancestors of the node are adjusted
8470 to refer to the group instances instead of the original domain
8471 elements. The return value points to the same node in the updated
8472 schedule tree as the input node, i.e., to the child of the newly
8473 introduced expansion node. Grouping instances of different statements
8474 ensures that they will be treated as a single statement by the
8475 AST generator up to the point of the expansion node.
8477 The following function can be used to flatten a nested
8480 #include <isl/schedule_node.h>
8481 __isl_give isl_schedule_node *
8482 isl_schedule_node_sequence_splice_child(
8483 __isl_take isl_schedule_node *node, int pos);
8485 That is, given a sequence node C<node> that has another sequence node
8486 in its child at position C<pos> (in particular, the child of that filter
8487 node is a sequence node), attach the children of that other sequence
8488 node as children of C<node>, replacing the original child at position
8491 The partial schedule of a band node can be scaled (down) or reduced using
8492 the following functions.
8494 #include <isl/schedule_node.h>
8495 __isl_give isl_schedule_node *
8496 isl_schedule_node_band_scale(
8497 __isl_take isl_schedule_node *node,
8498 __isl_take isl_multi_val *mv);
8499 __isl_give isl_schedule_node *
8500 isl_schedule_node_band_scale_down(
8501 __isl_take isl_schedule_node *node,
8502 __isl_take isl_multi_val *mv);
8503 __isl_give isl_schedule_node *
8504 isl_schedule_node_band_mod(
8505 __isl_take isl_schedule_node *node,
8506 __isl_take isl_multi_val *mv);
8508 The spaces of the two arguments need to match.
8509 After scaling, the partial schedule is replaced by its greatest
8510 integer part to ensure that the schedule remains integral.
8512 The partial schedule of a band node can be shifted by an
8513 C<isl_multi_union_pw_aff> with a domain that is a superset
8514 of the domain of the partial schedule using
8515 the following function.
8517 #include <isl/schedule_node.h>
8518 __isl_give isl_schedule_node *
8519 isl_schedule_node_band_shift(
8520 __isl_take isl_schedule_node *node,
8521 __isl_take isl_multi_union_pw_aff *shift);
8523 A band node can be tiled using the following function.
8525 #include <isl/schedule_node.h>
8526 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
8527 __isl_take isl_schedule_node *node,
8528 __isl_take isl_multi_val *sizes);
8530 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
8532 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
8533 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
8535 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
8537 The C<isl_schedule_node_band_tile> function tiles
8538 the band using the given tile sizes inside its schedule.
8539 A new child band node is created to represent the point loops and it is
8540 inserted between the modified band and its children.
8541 The subtree rooted at the given node is assumed not to have
8543 The C<tile_scale_tile_loops> option specifies whether the tile
8544 loops iterators should be scaled by the tile sizes.
8545 If the C<tile_shift_point_loops> option is set, then the point loops
8546 are shifted to start at zero.
8548 A band node can be split into two nested band nodes
8549 using the following function.
8551 #include <isl/schedule_node.h>
8552 __isl_give isl_schedule_node *isl_schedule_node_band_split(
8553 __isl_take isl_schedule_node *node, int pos);
8555 The resulting outer band node contains the first C<pos> dimensions of
8556 the schedule of C<node> while the inner band contains the remaining dimensions.
8557 The schedules of the two band nodes live in anonymous spaces.
8558 The loop AST generation type options and the isolate option
8559 are split over the the two band nodes.
8561 A band node can be moved down to the leaves of the subtree rooted
8562 at the band node using the following function.
8564 #include <isl/schedule_node.h>
8565 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
8566 __isl_take isl_schedule_node *node);
8568 The subtree rooted at the given node is assumed not to have
8570 The result points to the node in the resulting tree that is in the same
8571 position as the node pointed to by C<node> in the original tree.
8573 #include <isl/schedule_node.h>
8574 __isl_give isl_schedule_node *
8575 isl_schedule_node_order_before(
8576 __isl_take isl_schedule_node *node,
8577 __isl_take isl_union_set *filter);
8578 __isl_give isl_schedule_node *
8579 isl_schedule_node_order_after(
8580 __isl_take isl_schedule_node *node,
8581 __isl_take isl_union_set *filter);
8583 These functions split the domain elements that reach C<node>
8584 into those that satisfy C<filter> and those that do not and
8585 arranges for the elements that do satisfy the filter to be
8586 executed before (in case of C<isl_schedule_node_order_before>)
8587 or after (in case of C<isl_schedule_node_order_after>)
8588 those that do not. The order is imposed by
8589 a sequence node, possibly reusing the grandparent of C<node>
8590 on two copies of the subtree attached to the original C<node>.
8591 Both copies are simplified with respect to their filter.
8593 Return a pointer to the copy of the subtree that does not
8594 satisfy C<filter>. If there is no such copy (because all
8595 reaching domain elements satisfy the filter), then return
8596 the original pointer.
8598 #include <isl/schedule_node.h>
8599 __isl_give isl_schedule_node *
8600 isl_schedule_node_graft_before(
8601 __isl_take isl_schedule_node *node,
8602 __isl_take isl_schedule_node *graft);
8603 __isl_give isl_schedule_node *
8604 isl_schedule_node_graft_after(
8605 __isl_take isl_schedule_node *node,
8606 __isl_take isl_schedule_node *graft);
8608 This function inserts the C<graft> tree into the tree containing C<node>
8609 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
8610 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
8611 The root node of C<graft>
8612 should be an extension node where the domain of the extension
8613 is the flat product of all outer band nodes of C<node>.
8614 The root node may also be a domain node.
8615 The elements of the domain or the range of the extension may not
8616 intersect with the domain elements that reach "node".
8617 The schedule tree of C<graft> may not be anchored.
8619 The schedule tree of C<node> is modified to include an extension node
8620 corresponding to the root node of C<graft> as a child of the original
8621 parent of C<node>. The original node that C<node> points to and the
8622 child of the root node of C<graft> are attached to this extension node
8623 through a sequence, with appropriate filters and with the child
8624 of C<graft> appearing before or after the original C<node>.
8626 If C<node> already appears inside a sequence that is the child of
8627 an extension node and if the spaces of the new domain elements
8628 do not overlap with those of the original domain elements,
8629 then that extension node is extended with the new extension
8630 rather than introducing a new segment of extension and sequence nodes.
8632 Return a pointer to the same node in the modified tree that
8633 C<node> pointed to in the original tree.
8635 A representation of the schedule node can be printed using
8637 #include <isl/schedule_node.h>
8638 __isl_give isl_printer *isl_printer_print_schedule_node(
8639 __isl_take isl_printer *p,
8640 __isl_keep isl_schedule_node *node);
8641 __isl_give char *isl_schedule_node_to_str(
8642 __isl_keep isl_schedule_node *node);
8644 C<isl_schedule_node_to_str> prints the schedule node in block format.
8646 =head2 Dependence Analysis
8648 C<isl> contains specialized functionality for performing
8649 array dataflow analysis. That is, given a I<sink> access relation
8650 and a collection of possible I<source> access relations,
8651 C<isl> can compute relations that describe
8652 for each iteration of the sink access, which iteration
8653 of which of the source access relations was the last
8654 to access the same data element before the given iteration
8656 The resulting dependence relations map source iterations
8657 to either the corresponding sink iterations or
8658 pairs of corresponding sink iterations and accessed data elements.
8659 To compute standard flow dependences, the sink should be
8660 a read, while the sources should be writes.
8661 If any of the source accesses are marked as being I<may>
8662 accesses, then there will be a dependence from the last
8663 I<must> access B<and> from any I<may> access that follows
8664 this last I<must> access.
8665 In particular, if I<all> sources are I<may> accesses,
8666 then memory based dependence analysis is performed.
8667 If, on the other hand, all sources are I<must> accesses,
8668 then value based dependence analysis is performed.
8670 =head3 High-level Interface
8672 A high-level interface to dependence analysis is provided
8673 by the following function.
8675 #include <isl/flow.h>
8676 __isl_give isl_union_flow *
8677 isl_union_access_info_compute_flow(
8678 __isl_take isl_union_access_info *access);
8680 The input C<isl_union_access_info> object describes the sink
8681 access relations, the source access relations and a schedule,
8682 while the output C<isl_union_flow> object describes
8683 the resulting dependence relations and the subsets of the
8684 sink relations for which no source was found.
8686 An C<isl_union_access_info> is created, modified, copied and freed using
8687 the following functions.
8689 #include <isl/flow.h>
8690 __isl_give isl_union_access_info *
8691 isl_union_access_info_from_sink(
8692 __isl_take isl_union_map *sink);
8693 __isl_give isl_union_access_info *
8694 isl_union_access_info_set_must_source(
8695 __isl_take isl_union_access_info *access,
8696 __isl_take isl_union_map *must_source);
8697 __isl_give isl_union_access_info *
8698 isl_union_access_info_set_may_source(
8699 __isl_take isl_union_access_info *access,
8700 __isl_take isl_union_map *may_source);
8701 __isl_give isl_union_access_info *
8702 isl_union_access_info_set_schedule(
8703 __isl_take isl_union_access_info *access,
8704 __isl_take isl_schedule *schedule);
8705 __isl_give isl_union_access_info *
8706 isl_union_access_info_set_schedule_map(
8707 __isl_take isl_union_access_info *access,
8708 __isl_take isl_union_map *schedule_map);
8709 __isl_give isl_union_access_info *
8710 isl_union_access_info_copy(
8711 __isl_keep isl_union_access_info *access);
8712 __isl_null isl_union_access_info *
8713 isl_union_access_info_free(
8714 __isl_take isl_union_access_info *access);
8716 The may sources set by C<isl_union_access_info_set_may_source>
8717 do not need to include the must sources set by
8718 C<isl_union_access_info_set_must_source> as a subset.
8719 The user is free not to call one (or both) of these functions,
8720 in which case the corresponding set is kept to its empty default.
8721 Similarly, the default schedule initialized by
8722 C<isl_union_access_info_from_sink> is empty.
8723 The current schedule is determined by the last call to either
8724 C<isl_union_access_info_set_schedule> or
8725 C<isl_union_access_info_set_schedule_map>.
8726 The domain of the schedule corresponds to the domains of
8727 the access relations. In particular, the domains of the access
8728 relations are effectively intersected with the domain of the schedule
8729 and only the resulting accesses are considered by the dependence analysis.
8731 A representation of the information contained in an object
8732 of type C<isl_union_access_info> can be obtained using
8734 #include <isl/flow.h>
8735 __isl_give isl_printer *
8736 isl_printer_print_union_access_info(
8737 __isl_take isl_printer *p,
8738 __isl_keep isl_union_access_info *access);
8739 __isl_give char *isl_union_access_info_to_str(
8740 __isl_keep isl_union_access_info *access);
8742 C<isl_union_access_info_to_str> prints the information in flow format.
8744 The output of C<isl_union_access_info_compute_flow> can be examined,
8745 copied, and freed using the following functions.
8747 #include <isl/flow.h>
8748 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
8749 __isl_keep isl_union_flow *flow);
8750 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
8751 __isl_keep isl_union_flow *flow);
8752 __isl_give isl_union_map *
8753 isl_union_flow_get_full_must_dependence(
8754 __isl_keep isl_union_flow *flow);
8755 __isl_give isl_union_map *
8756 isl_union_flow_get_full_may_dependence(
8757 __isl_keep isl_union_flow *flow);
8758 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
8759 __isl_keep isl_union_flow *flow);
8760 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
8761 __isl_keep isl_union_flow *flow);
8762 __isl_give isl_union_flow *isl_union_flow_copy(
8763 __isl_keep isl_union_flow *flow);
8764 __isl_null isl_union_flow *isl_union_flow_free(
8765 __isl_take isl_union_flow *flow);
8767 The relation returned by C<isl_union_flow_get_must_dependence>
8768 relates domain elements of must sources to domain elements of the sink.
8769 The relation returned by C<isl_union_flow_get_may_dependence>
8770 relates domain elements of must or may sources to domain elements of the sink
8771 and includes the previous relation as a subset.
8772 The relation returned by C<isl_union_flow_get_full_must_dependence>
8773 relates domain elements of must sources to pairs of domain elements of the sink
8774 and accessed data elements.
8775 The relation returned by C<isl_union_flow_get_full_may_dependence>
8776 relates domain elements of must or may sources to pairs of
8777 domain elements of the sink and accessed data elements.
8778 This relation includes the previous relation as a subset.
8779 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
8780 of the sink relation for which no dependences have been found.
8781 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
8782 of the sink relation for which no definite dependences have been found.
8783 That is, it contains those sink access that do not contribute to any
8784 of the elements in the relation returned
8785 by C<isl_union_flow_get_must_dependence>.
8787 A representation of the information contained in an object
8788 of type C<isl_union_flow> can be obtained using
8790 #include <isl/flow.h>
8791 __isl_give isl_printer *isl_printer_print_union_flow(
8792 __isl_take isl_printer *p,
8793 __isl_keep isl_union_flow *flow);
8794 __isl_give char *isl_union_flow_to_str(
8795 __isl_keep isl_union_flow *flow);
8797 C<isl_union_flow_to_str> prints the information in flow format.
8799 =head3 Low-level Interface
8801 A lower-level interface is provided by the following functions.
8803 #include <isl/flow.h>
8805 typedef int (*isl_access_level_before)(void *first, void *second);
8807 __isl_give isl_access_info *isl_access_info_alloc(
8808 __isl_take isl_map *sink,
8809 void *sink_user, isl_access_level_before fn,
8811 __isl_give isl_access_info *isl_access_info_add_source(
8812 __isl_take isl_access_info *acc,
8813 __isl_take isl_map *source, int must,
8815 __isl_null isl_access_info *isl_access_info_free(
8816 __isl_take isl_access_info *acc);
8818 __isl_give isl_flow *isl_access_info_compute_flow(
8819 __isl_take isl_access_info *acc);
8821 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,
8822 isl_stat (*fn)(__isl_take isl_map *dep, int must,
8823 void *dep_user, void *user),
8825 __isl_give isl_map *isl_flow_get_no_source(
8826 __isl_keep isl_flow *deps, int must);
8827 void isl_flow_free(__isl_take isl_flow *deps);
8829 The function C<isl_access_info_compute_flow> performs the actual
8830 dependence analysis. The other functions are used to construct
8831 the input for this function or to read off the output.
8833 The input is collected in an C<isl_access_info>, which can
8834 be created through a call to C<isl_access_info_alloc>.
8835 The arguments to this functions are the sink access relation
8836 C<sink>, a token C<sink_user> used to identify the sink
8837 access to the user, a callback function for specifying the
8838 relative order of source and sink accesses, and the number
8839 of source access relations that will be added.
8840 The callback function has type C<int (*)(void *first, void *second)>.
8841 The function is called with two user supplied tokens identifying
8842 either a source or the sink and it should return the shared nesting
8843 level and the relative order of the two accesses.
8844 In particular, let I<n> be the number of loops shared by
8845 the two accesses. If C<first> precedes C<second> textually,
8846 then the function should return I<2 * n + 1>; otherwise,
8847 it should return I<2 * n>.
8848 The sources can be added to the C<isl_access_info> by performing
8849 (at most) C<max_source> calls to C<isl_access_info_add_source>.
8850 C<must> indicates whether the source is a I<must> access
8851 or a I<may> access. Note that a multi-valued access relation
8852 should only be marked I<must> if every iteration in the domain
8853 of the relation accesses I<all> elements in its image.
8854 The C<source_user> token is again used to identify
8855 the source access. The range of the source access relation
8856 C<source> should have the same dimension as the range
8857 of the sink access relation.
8858 The C<isl_access_info_free> function should usually not be
8859 called explicitly, because it is called implicitly by
8860 C<isl_access_info_compute_flow>.
8862 The result of the dependence analysis is collected in an
8863 C<isl_flow>. There may be elements of
8864 the sink access for which no preceding source access could be
8865 found or for which all preceding sources are I<may> accesses.
8866 The relations containing these elements can be obtained through
8867 calls to C<isl_flow_get_no_source>, the first with C<must> set
8868 and the second with C<must> unset.
8869 In the case of standard flow dependence analysis,
8870 with the sink a read and the sources I<must> writes,
8871 the first relation corresponds to the reads from uninitialized
8872 array elements and the second relation is empty.
8873 The actual flow dependences can be extracted using
8874 C<isl_flow_foreach>. This function will call the user-specified
8875 callback function C<fn> for each B<non-empty> dependence between
8876 a source and the sink. The callback function is called
8877 with four arguments, the actual flow dependence relation
8878 mapping source iterations to sink iterations, a boolean that
8879 indicates whether it is a I<must> or I<may> dependence, a token
8880 identifying the source and an additional C<void *> with value
8881 equal to the third argument of the C<isl_flow_foreach> call.
8882 A dependence is marked I<must> if it originates from a I<must>
8883 source and if it is not followed by any I<may> sources.
8885 After finishing with an C<isl_flow>, the user should call
8886 C<isl_flow_free> to free all associated memory.
8888 =head3 Interaction with the Low-level Interface
8890 During the dependence analysis, we frequently need to perform
8891 the following operation. Given a relation between sink iterations
8892 and potential source iterations from a particular source domain,
8893 what is the last potential source iteration corresponding to each
8894 sink iteration. It can sometimes be convenient to adjust
8895 the set of potential source iterations before or after each such operation.
8896 The prototypical example is fuzzy array dataflow analysis,
8897 where we need to analyze if, based on data-dependent constraints,
8898 the sink iteration can ever be executed without one or more of
8899 the corresponding potential source iterations being executed.
8900 If so, we can introduce extra parameters and select an unknown
8901 but fixed source iteration from the potential source iterations.
8902 To be able to perform such manipulations, C<isl> provides the following
8905 #include <isl/flow.h>
8907 typedef __isl_give isl_restriction *(*isl_access_restrict)(
8908 __isl_keep isl_map *source_map,
8909 __isl_keep isl_set *sink, void *source_user,
8911 __isl_give isl_access_info *isl_access_info_set_restrict(
8912 __isl_take isl_access_info *acc,
8913 isl_access_restrict fn, void *user);
8915 The function C<isl_access_info_set_restrict> should be called
8916 before calling C<isl_access_info_compute_flow> and registers a callback function
8917 that will be called any time C<isl> is about to compute the last
8918 potential source. The first argument is the (reverse) proto-dependence,
8919 mapping sink iterations to potential source iterations.
8920 The second argument represents the sink iterations for which
8921 we want to compute the last source iteration.
8922 The third argument is the token corresponding to the source
8923 and the final argument is the token passed to C<isl_access_info_set_restrict>.
8924 The callback is expected to return a restriction on either the input or
8925 the output of the operation computing the last potential source.
8926 If the input needs to be restricted then restrictions are needed
8927 for both the source and the sink iterations. The sink iterations
8928 and the potential source iterations will be intersected with these sets.
8929 If the output needs to be restricted then only a restriction on the source
8930 iterations is required.
8931 If any error occurs, the callback should return C<NULL>.
8932 An C<isl_restriction> object can be created, freed and inspected
8933 using the following functions.
8935 #include <isl/flow.h>
8937 __isl_give isl_restriction *isl_restriction_input(
8938 __isl_take isl_set *source_restr,
8939 __isl_take isl_set *sink_restr);
8940 __isl_give isl_restriction *isl_restriction_output(
8941 __isl_take isl_set *source_restr);
8942 __isl_give isl_restriction *isl_restriction_none(
8943 __isl_take isl_map *source_map);
8944 __isl_give isl_restriction *isl_restriction_empty(
8945 __isl_take isl_map *source_map);
8946 __isl_null isl_restriction *isl_restriction_free(
8947 __isl_take isl_restriction *restr);
8949 C<isl_restriction_none> and C<isl_restriction_empty> are special
8950 cases of C<isl_restriction_input>. C<isl_restriction_none>
8951 is essentially equivalent to
8953 isl_restriction_input(isl_set_universe(
8954 isl_space_range(isl_map_get_space(source_map))),
8956 isl_space_domain(isl_map_get_space(source_map))));
8958 whereas C<isl_restriction_empty> is essentially equivalent to
8960 isl_restriction_input(isl_set_empty(
8961 isl_space_range(isl_map_get_space(source_map))),
8963 isl_space_domain(isl_map_get_space(source_map))));
8967 #include <isl/schedule.h>
8968 __isl_give isl_schedule *
8969 isl_schedule_constraints_compute_schedule(
8970 __isl_take isl_schedule_constraints *sc);
8972 The function C<isl_schedule_constraints_compute_schedule> can be
8973 used to compute a schedule that satisfies the given schedule constraints.
8974 These schedule constraints include the iteration domain for which
8975 a schedule should be computed and dependences between pairs of
8976 iterations. In particular, these dependences include
8977 I<validity> dependences and I<proximity> dependences.
8978 By default, the algorithm used to construct the schedule is similar
8979 to that of C<Pluto>.
8980 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
8982 The generated schedule respects all validity dependences.
8983 That is, all dependence distances over these dependences in the
8984 scheduled space are lexicographically positive.
8986 The default algorithm tries to ensure that the dependence distances
8987 over coincidence constraints are zero and to minimize the
8988 dependence distances over proximity dependences.
8989 Moreover, it tries to obtain sequences (bands) of schedule dimensions
8990 for groups of domains where the dependence distances over validity
8991 dependences have only non-negative values.
8992 Note that when minimizing the maximal dependence distance
8993 over proximity dependences, a single affine expression in the parameters
8994 is constructed that bounds all dependence distances. If no such expression
8995 exists, then the algorithm will fail and resort to an alternative
8996 scheduling algorithm. In particular, this means that adding proximity
8997 dependences may eliminate valid solutions. A typical example where this
8998 phenomenon may occur is when some subset of the proximity dependences
8999 has no restriction on some parameter, forcing the coefficient of that
9000 parameter to be zero, while some other subset forces the dependence
9001 distance to depend on that parameter, requiring the same coefficient
9003 When using Feautrier's algorithm, the coincidence and proximity constraints
9004 are only taken into account during the extension to a
9005 full-dimensional schedule.
9007 An C<isl_schedule_constraints> object can be constructed
9008 and manipulated using the following functions.
9010 #include <isl/schedule.h>
9011 __isl_give isl_schedule_constraints *
9012 isl_schedule_constraints_copy(
9013 __isl_keep isl_schedule_constraints *sc);
9014 __isl_give isl_schedule_constraints *
9015 isl_schedule_constraints_on_domain(
9016 __isl_take isl_union_set *domain);
9017 __isl_give isl_schedule_constraints *
9018 isl_schedule_constraints_set_context(
9019 __isl_take isl_schedule_constraints *sc,
9020 __isl_take isl_set *context);
9021 __isl_give isl_schedule_constraints *
9022 isl_schedule_constraints_set_validity(
9023 __isl_take isl_schedule_constraints *sc,
9024 __isl_take isl_union_map *validity);
9025 __isl_give isl_schedule_constraints *
9026 isl_schedule_constraints_set_coincidence(
9027 __isl_take isl_schedule_constraints *sc,
9028 __isl_take isl_union_map *coincidence);
9029 __isl_give isl_schedule_constraints *
9030 isl_schedule_constraints_set_proximity(
9031 __isl_take isl_schedule_constraints *sc,
9032 __isl_take isl_union_map *proximity);
9033 __isl_give isl_schedule_constraints *
9034 isl_schedule_constraints_set_conditional_validity(
9035 __isl_take isl_schedule_constraints *sc,
9036 __isl_take isl_union_map *condition,
9037 __isl_take isl_union_map *validity);
9038 __isl_give isl_schedule_constraints *
9039 isl_schedule_constraints_apply(
9040 __isl_take isl_schedule_constraints *sc,
9041 __isl_take isl_union_map *umap);
9042 __isl_null isl_schedule_constraints *
9043 isl_schedule_constraints_free(
9044 __isl_take isl_schedule_constraints *sc);
9046 The initial C<isl_schedule_constraints> object created by
9047 C<isl_schedule_constraints_on_domain> does not impose any constraints.
9048 That is, it has an empty set of dependences.
9049 The function C<isl_schedule_constraints_set_context> allows the user
9050 to specify additional constraints on the parameters that may
9051 be assumed to hold during the construction of the schedule.
9052 The function C<isl_schedule_constraints_set_validity> replaces the
9053 validity dependences, mapping domain elements I<i> to domain
9054 elements that should be scheduled after I<i>.
9055 The function C<isl_schedule_constraints_set_coincidence> replaces the
9056 coincidence dependences, mapping domain elements I<i> to domain
9057 elements that should be scheduled together with I<I>, if possible.
9058 The function C<isl_schedule_constraints_set_proximity> replaces the
9059 proximity dependences, mapping domain elements I<i> to domain
9060 elements that should be scheduled either before I<I>
9061 or as early as possible after I<i>.
9063 The function C<isl_schedule_constraints_set_conditional_validity>
9064 replaces the conditional validity constraints.
9065 A conditional validity constraint is only imposed when any of the corresponding
9066 conditions is satisfied, i.e., when any of them is non-zero.
9067 That is, the scheduler ensures that within each band if the dependence
9068 distances over the condition constraints are not all zero
9069 then all corresponding conditional validity constraints are respected.
9070 A conditional validity constraint corresponds to a condition
9071 if the two are adjacent, i.e., if the domain of one relation intersect
9072 the range of the other relation.
9073 The typical use case of conditional validity constraints is
9074 to allow order constraints between live ranges to be violated
9075 as long as the live ranges themselves are local to the band.
9076 To allow more fine-grained control over which conditions correspond
9077 to which conditional validity constraints, the domains and ranges
9078 of these relations may include I<tags>. That is, the domains and
9079 ranges of those relation may themselves be wrapped relations
9080 where the iteration domain appears in the domain of those wrapped relations
9081 and the range of the wrapped relations can be arbitrarily chosen
9082 by the user. Conditions and conditional validity constraints are only
9083 considered adjacent to each other if the entire wrapped relation matches.
9084 In particular, a relation with a tag will never be considered adjacent
9085 to a relation without a tag.
9087 The function C<isl_schedule_constraints_compute_schedule> takes
9088 schedule constraints that are defined on some set of domain elements
9089 and transforms them to schedule constraints on the elements
9090 to which these domain elements are mapped by the given transformation.
9092 An C<isl_schedule_constraints> object can be inspected
9093 using the following functions.
9095 #include <isl/schedule.h>
9096 __isl_give isl_union_set *
9097 isl_schedule_constraints_get_domain(
9098 __isl_keep isl_schedule_constraints *sc);
9099 __isl_give isl_set *isl_schedule_constraints_get_context(
9100 __isl_keep isl_schedule_constraints *sc);
9101 __isl_give isl_union_map *
9102 isl_schedule_constraints_get_validity(
9103 __isl_keep isl_schedule_constraints *sc);
9104 __isl_give isl_union_map *
9105 isl_schedule_constraints_get_coincidence(
9106 __isl_keep isl_schedule_constraints *sc);
9107 __isl_give isl_union_map *
9108 isl_schedule_constraints_get_proximity(
9109 __isl_keep isl_schedule_constraints *sc);
9110 __isl_give isl_union_map *
9111 isl_schedule_constraints_get_conditional_validity(
9112 __isl_keep isl_schedule_constraints *sc);
9113 __isl_give isl_union_map *
9114 isl_schedule_constraints_get_conditional_validity_condition(
9115 __isl_keep isl_schedule_constraints *sc);
9117 An C<isl_schedule_constraints> object can be read from input
9118 using the following functions.
9120 #include <isl/schedule.h>
9121 __isl_give isl_schedule_constraints *
9122 isl_schedule_constraints_read_from_str(isl_ctx *ctx,
9124 __isl_give isl_schedule_constraints *
9125 isl_schedule_constraints_read_from_file(isl_ctx *ctx,
9128 The contents of an C<isl_schedule_constraints> object can be printed
9129 using the following functions.
9131 #include <isl/schedule.h>
9132 __isl_give isl_printer *
9133 isl_printer_print_schedule_constraints(
9134 __isl_take isl_printer *p,
9135 __isl_keep isl_schedule_constraints *sc);
9136 __isl_give char *isl_schedule_constraints_to_str(
9137 __isl_keep isl_schedule_constraints *sc);
9139 The following function computes a schedule directly from
9140 an iteration domain and validity and proximity dependences
9141 and is implemented in terms of the functions described above.
9142 The use of C<isl_union_set_compute_schedule> is discouraged.
9144 #include <isl/schedule.h>
9145 __isl_give isl_schedule *isl_union_set_compute_schedule(
9146 __isl_take isl_union_set *domain,
9147 __isl_take isl_union_map *validity,
9148 __isl_take isl_union_map *proximity);
9150 The generated schedule represents a schedule tree.
9151 For more information on schedule trees, see
9152 L</"Schedule Trees">.
9156 #include <isl/schedule.h>
9157 isl_stat isl_options_set_schedule_max_coefficient(
9158 isl_ctx *ctx, int val);
9159 int isl_options_get_schedule_max_coefficient(
9161 isl_stat isl_options_set_schedule_max_constant_term(
9162 isl_ctx *ctx, int val);
9163 int isl_options_get_schedule_max_constant_term(
9165 isl_stat isl_options_set_schedule_serialize_sccs(
9166 isl_ctx *ctx, int val);
9167 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx);
9168 isl_stat isl_options_set_schedule_whole_component(
9169 isl_ctx *ctx, int val);
9170 int isl_options_get_schedule_whole_component(
9172 isl_stat isl_options_set_schedule_maximize_band_depth(
9173 isl_ctx *ctx, int val);
9174 int isl_options_get_schedule_maximize_band_depth(
9176 isl_stat isl_options_set_schedule_maximize_coincidence(
9177 isl_ctx *ctx, int val);
9178 int isl_options_get_schedule_maximize_coincidence(
9180 isl_stat isl_options_set_schedule_outer_coincidence(
9181 isl_ctx *ctx, int val);
9182 int isl_options_get_schedule_outer_coincidence(
9184 isl_stat isl_options_set_schedule_split_scaled(
9185 isl_ctx *ctx, int val);
9186 int isl_options_get_schedule_split_scaled(
9188 isl_stat isl_options_set_schedule_treat_coalescing(
9189 isl_ctx *ctx, int val);
9190 int isl_options_get_schedule_treat_coalescing(
9192 isl_stat isl_options_set_schedule_algorithm(
9193 isl_ctx *ctx, int val);
9194 int isl_options_get_schedule_algorithm(
9196 isl_stat isl_options_set_schedule_separate_components(
9197 isl_ctx *ctx, int val);
9198 int isl_options_get_schedule_separate_components(
9203 =item * schedule_max_coefficient
9205 This option enforces that the coefficients for variable and parameter
9206 dimensions in the calculated schedule are not larger than the specified value.
9207 This option can significantly increase the speed of the scheduling calculation
9208 and may also prevent fusing of unrelated dimensions. A value of -1 means that
9209 this option does not introduce bounds on the variable or parameter
9212 =item * schedule_max_constant_term
9214 This option enforces that the constant coefficients in the calculated schedule
9215 are not larger than the maximal constant term. This option can significantly
9216 increase the speed of the scheduling calculation and may also prevent fusing of
9217 unrelated dimensions. A value of -1 means that this option does not introduce
9218 bounds on the constant coefficients.
9220 =item * schedule_serialize_sccs
9222 If this option is set, then all strongly connected components
9223 in the dependence graph are serialized as soon as they are detected.
9224 This means in particular that instances of statements will only
9225 appear in the same band node if these statements belong
9226 to the same strongly connected component at the point where
9227 the band node is constructed.
9229 =item * schedule_whole_component
9231 If this option is set, then entire (weakly) connected
9232 components in the dependence graph are scheduled together
9234 Otherwise, each strongly connected component within
9235 such a weakly connected component is first scheduled separately
9236 and then combined with other strongly connected components.
9237 This option has no effect if C<schedule_serialize_sccs> is set.
9239 =item * schedule_maximize_band_depth
9241 If this option is set, then the scheduler tries to maximize
9242 the width of the bands. Wider bands give more possibilities for tiling.
9243 In particular, if the C<schedule_whole_component> option is set,
9244 then bands are split if this might result in wider bands.
9245 Otherwise, the effect of this option is to only allow
9246 strongly connected components to be combined if this does
9247 not reduce the width of the bands.
9248 Note that if the C<schedule_serialize_sccs> options is set, then
9249 the C<schedule_maximize_band_depth> option therefore has no effect.
9251 =item * schedule_maximize_coincidence
9253 This option is only effective if the C<schedule_whole_component>
9254 option is turned off.
9255 If the C<schedule_maximize_coincidence> option is set, then (clusters of)
9256 strongly connected components are only combined with each other
9257 if this does not reduce the number of coincident band members.
9259 =item * schedule_outer_coincidence
9261 If this option is set, then we try to construct schedules
9262 where the outermost scheduling dimension in each band
9263 satisfies the coincidence constraints.
9265 =item * schedule_algorithm
9267 Selects the scheduling algorithm to be used.
9268 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
9269 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
9271 =item * schedule_split_scaled
9273 If this option is set, then we try to construct schedules in which the
9274 constant term is split off from the linear part if the linear parts of
9275 the scheduling rows for all nodes in the graphs have a common non-trivial
9277 The constant term is then placed in a separate band and the linear
9279 This option is only effective when the Feautrier style scheduler is
9280 being used, either as the main scheduler or as a fallback for the
9281 Pluto-like scheduler.
9283 =item * schedule_treat_coalescing
9285 If this option is set, then the scheduler will try and avoid
9286 producing schedules that perform loop coalescing.
9287 In particular, for the Pluto-like scheduler, this option places
9288 bounds on the schedule coefficients based on the sizes of the instance sets.
9289 For the Feautrier style scheduler, this option detects potentially
9290 coalescing schedules and then tries to adjust the schedule to avoid
9293 =item * schedule_separate_components
9295 If this option is set then the function C<isl_schedule_get_map>
9296 will treat set nodes in the same way as sequence nodes.
9300 =head2 AST Generation
9302 This section describes the C<isl> functionality for generating
9303 ASTs that visit all the elements
9304 in a domain in an order specified by a schedule tree or
9306 In case the schedule given as a C<isl_union_map>, an AST is generated
9307 that visits all the elements in the domain of the C<isl_union_map>
9308 according to the lexicographic order of the corresponding image
9309 element(s). If the range of the C<isl_union_map> consists of
9310 elements in more than one space, then each of these spaces is handled
9311 separately in an arbitrary order.
9312 It should be noted that the schedule tree or the image elements
9313 in a schedule map only specify the I<order>
9314 in which the corresponding domain elements should be visited.
9315 No direct relation between the partial schedule values
9316 or the image elements on the one hand and the loop iterators
9317 in the generated AST on the other hand should be assumed.
9319 Each AST is generated within a build. The initial build
9320 simply specifies the constraints on the parameters (if any)
9321 and can be created, inspected, copied and freed using the following functions.
9323 #include <isl/ast_build.h>
9324 __isl_give isl_ast_build *isl_ast_build_alloc(
9326 __isl_give isl_ast_build *isl_ast_build_from_context(
9327 __isl_take isl_set *set);
9328 __isl_give isl_ast_build *isl_ast_build_copy(
9329 __isl_keep isl_ast_build *build);
9330 __isl_null isl_ast_build *isl_ast_build_free(
9331 __isl_take isl_ast_build *build);
9333 The C<set> argument is usually a parameter set with zero or more parameters.
9334 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
9335 this set is required to be a parameter set.
9336 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
9337 specify any parameter constraints.
9338 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
9339 and L</"Fine-grained Control over AST Generation">.
9340 Finally, the AST itself can be constructed using one of the following
9343 #include <isl/ast_build.h>
9344 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
9345 __isl_keep isl_ast_build *build,
9346 __isl_take isl_schedule *schedule);
9347 __isl_give isl_ast_node *
9348 isl_ast_build_node_from_schedule_map(
9349 __isl_keep isl_ast_build *build,
9350 __isl_take isl_union_map *schedule);
9352 =head3 Inspecting the AST
9354 The basic properties of an AST node can be obtained as follows.
9356 #include <isl/ast.h>
9357 enum isl_ast_node_type isl_ast_node_get_type(
9358 __isl_keep isl_ast_node *node);
9360 The type of an AST node is one of
9361 C<isl_ast_node_for>,
9363 C<isl_ast_node_block>,
9364 C<isl_ast_node_mark> or
9365 C<isl_ast_node_user>.
9366 An C<isl_ast_node_for> represents a for node.
9367 An C<isl_ast_node_if> represents an if node.
9368 An C<isl_ast_node_block> represents a compound node.
9369 An C<isl_ast_node_mark> introduces a mark in the AST.
9370 An C<isl_ast_node_user> represents an expression statement.
9371 An expression statement typically corresponds to a domain element, i.e.,
9372 one of the elements that is visited by the AST.
9374 Each type of node has its own additional properties.
9376 #include <isl/ast.h>
9377 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
9378 __isl_keep isl_ast_node *node);
9379 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
9380 __isl_keep isl_ast_node *node);
9381 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
9382 __isl_keep isl_ast_node *node);
9383 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
9384 __isl_keep isl_ast_node *node);
9385 __isl_give isl_ast_node *isl_ast_node_for_get_body(
9386 __isl_keep isl_ast_node *node);
9387 isl_bool isl_ast_node_for_is_degenerate(
9388 __isl_keep isl_ast_node *node);
9390 An C<isl_ast_for> is considered degenerate if it is known to execute
9393 #include <isl/ast.h>
9394 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
9395 __isl_keep isl_ast_node *node);
9396 __isl_give isl_ast_node *isl_ast_node_if_get_then(
9397 __isl_keep isl_ast_node *node);
9398 isl_bool isl_ast_node_if_has_else(
9399 __isl_keep isl_ast_node *node);
9400 __isl_give isl_ast_node *isl_ast_node_if_get_else(
9401 __isl_keep isl_ast_node *node);
9403 __isl_give isl_ast_node_list *
9404 isl_ast_node_block_get_children(
9405 __isl_keep isl_ast_node *node);
9407 __isl_give isl_id *isl_ast_node_mark_get_id(
9408 __isl_keep isl_ast_node *node);
9409 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
9410 __isl_keep isl_ast_node *node);
9412 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
9413 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
9415 #include <isl/ast.h>
9416 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
9417 __isl_keep isl_ast_node *node);
9419 All descendants of a specific node in the AST (including the node itself)
9421 in depth-first pre-order using the following function.
9423 #include <isl/ast.h>
9424 isl_stat isl_ast_node_foreach_descendant_top_down(
9425 __isl_keep isl_ast_node *node,
9426 isl_bool (*fn)(__isl_keep isl_ast_node *node,
9427 void *user), void *user);
9429 The callback function should return C<isl_bool_true> if the children
9430 of the given node should be visited and C<isl_bool_false> if they should not.
9431 It should return C<isl_bool_error> in case of failure, in which case
9432 the entire traversal is aborted.
9434 Each of the returned C<isl_ast_expr>s can in turn be inspected using
9435 the following functions.
9437 #include <isl/ast.h>
9438 enum isl_ast_expr_type isl_ast_expr_get_type(
9439 __isl_keep isl_ast_expr *expr);
9441 The type of an AST expression is one of
9443 C<isl_ast_expr_id> or
9444 C<isl_ast_expr_int>.
9445 An C<isl_ast_expr_op> represents the result of an operation.
9446 An C<isl_ast_expr_id> represents an identifier.
9447 An C<isl_ast_expr_int> represents an integer value.
9449 Each type of expression has its own additional properties.
9451 #include <isl/ast.h>
9452 enum isl_ast_op_type isl_ast_expr_get_op_type(
9453 __isl_keep isl_ast_expr *expr);
9454 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
9455 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
9456 __isl_keep isl_ast_expr *expr, int pos);
9457 isl_stat isl_ast_expr_foreach_ast_op_type(
9458 __isl_keep isl_ast_expr *expr,
9459 isl_stat (*fn)(enum isl_ast_op_type type,
9460 void *user), void *user);
9461 isl_stat isl_ast_node_foreach_ast_op_type(
9462 __isl_keep isl_ast_node *node,
9463 isl_stat (*fn)(enum isl_ast_op_type type,
9464 void *user), void *user);
9466 C<isl_ast_expr_get_op_type> returns the type of the operation
9467 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
9468 arguments. C<isl_ast_expr_get_op_arg> returns the specified
9470 C<isl_ast_expr_foreach_ast_op_type> calls C<fn> for each distinct
9471 C<isl_ast_op_type> that appears in C<expr>.
9472 C<isl_ast_node_foreach_ast_op_type> does the same for each distinct
9473 C<isl_ast_op_type> that appears in C<node>.
9474 The operation type is one of the following.
9478 =item C<isl_ast_op_and>
9480 Logical I<and> of two arguments.
9481 Both arguments can be evaluated.
9483 =item C<isl_ast_op_and_then>
9485 Logical I<and> of two arguments.
9486 The second argument can only be evaluated if the first evaluates to true.
9488 =item C<isl_ast_op_or>
9490 Logical I<or> of two arguments.
9491 Both arguments can be evaluated.
9493 =item C<isl_ast_op_or_else>
9495 Logical I<or> of two arguments.
9496 The second argument can only be evaluated if the first evaluates to false.
9498 =item C<isl_ast_op_max>
9500 Maximum of two or more arguments.
9502 =item C<isl_ast_op_min>
9504 Minimum of two or more arguments.
9506 =item C<isl_ast_op_minus>
9510 =item C<isl_ast_op_add>
9512 Sum of two arguments.
9514 =item C<isl_ast_op_sub>
9516 Difference of two arguments.
9518 =item C<isl_ast_op_mul>
9520 Product of two arguments.
9522 =item C<isl_ast_op_div>
9524 Exact division. That is, the result is known to be an integer.
9526 =item C<isl_ast_op_fdiv_q>
9528 Result of integer division, rounded towards negative
9531 =item C<isl_ast_op_pdiv_q>
9533 Result of integer division, where dividend is known to be non-negative.
9535 =item C<isl_ast_op_pdiv_r>
9537 Remainder of integer division, where dividend is known to be non-negative.
9539 =item C<isl_ast_op_zdiv_r>
9541 Equal to zero iff the remainder on integer division is zero.
9543 =item C<isl_ast_op_cond>
9545 Conditional operator defined on three arguments.
9546 If the first argument evaluates to true, then the result
9547 is equal to the second argument. Otherwise, the result
9548 is equal to the third argument.
9549 The second and third argument may only be evaluated if
9550 the first argument evaluates to true and false, respectively.
9551 Corresponds to C<a ? b : c> in C.
9553 =item C<isl_ast_op_select>
9555 Conditional operator defined on three arguments.
9556 If the first argument evaluates to true, then the result
9557 is equal to the second argument. Otherwise, the result
9558 is equal to the third argument.
9559 The second and third argument may be evaluated independently
9560 of the value of the first argument.
9561 Corresponds to C<a * b + (1 - a) * c> in C.
9563 =item C<isl_ast_op_eq>
9567 =item C<isl_ast_op_le>
9569 Less than or equal relation.
9571 =item C<isl_ast_op_lt>
9575 =item C<isl_ast_op_ge>
9577 Greater than or equal relation.
9579 =item C<isl_ast_op_gt>
9581 Greater than relation.
9583 =item C<isl_ast_op_call>
9586 The number of arguments of the C<isl_ast_expr> is one more than
9587 the number of arguments in the function call, the first argument
9588 representing the function being called.
9590 =item C<isl_ast_op_access>
9593 The number of arguments of the C<isl_ast_expr> is one more than
9594 the number of index expressions in the array access, the first argument
9595 representing the array being accessed.
9597 =item C<isl_ast_op_member>
9600 This operation has two arguments, a structure and the name of
9601 the member of the structure being accessed.
9605 #include <isl/ast.h>
9606 __isl_give isl_id *isl_ast_expr_get_id(
9607 __isl_keep isl_ast_expr *expr);
9609 Return the identifier represented by the AST expression.
9611 #include <isl/ast.h>
9612 __isl_give isl_val *isl_ast_expr_get_val(
9613 __isl_keep isl_ast_expr *expr);
9615 Return the integer represented by the AST expression.
9617 =head3 Properties of ASTs
9619 #include <isl/ast.h>
9620 isl_bool isl_ast_expr_is_equal(
9621 __isl_keep isl_ast_expr *expr1,
9622 __isl_keep isl_ast_expr *expr2);
9624 Check if two C<isl_ast_expr>s are equal to each other.
9626 =head3 Manipulating and printing the AST
9628 AST nodes can be copied and freed using the following functions.
9630 #include <isl/ast.h>
9631 __isl_give isl_ast_node *isl_ast_node_copy(
9632 __isl_keep isl_ast_node *node);
9633 __isl_null isl_ast_node *isl_ast_node_free(
9634 __isl_take isl_ast_node *node);
9636 AST expressions can be copied and freed using the following functions.
9638 #include <isl/ast.h>
9639 __isl_give isl_ast_expr *isl_ast_expr_copy(
9640 __isl_keep isl_ast_expr *expr);
9641 __isl_null isl_ast_expr *isl_ast_expr_free(
9642 __isl_take isl_ast_expr *expr);
9644 New AST expressions can be created either directly or within
9645 the context of an C<isl_ast_build>.
9647 #include <isl/ast.h>
9648 __isl_give isl_ast_expr *isl_ast_expr_from_val(
9649 __isl_take isl_val *v);
9650 __isl_give isl_ast_expr *isl_ast_expr_from_id(
9651 __isl_take isl_id *id);
9652 __isl_give isl_ast_expr *isl_ast_expr_neg(
9653 __isl_take isl_ast_expr *expr);
9654 __isl_give isl_ast_expr *isl_ast_expr_address_of(
9655 __isl_take isl_ast_expr *expr);
9656 __isl_give isl_ast_expr *isl_ast_expr_add(
9657 __isl_take isl_ast_expr *expr1,
9658 __isl_take isl_ast_expr *expr2);
9659 __isl_give isl_ast_expr *isl_ast_expr_sub(
9660 __isl_take isl_ast_expr *expr1,
9661 __isl_take isl_ast_expr *expr2);
9662 __isl_give isl_ast_expr *isl_ast_expr_mul(
9663 __isl_take isl_ast_expr *expr1,
9664 __isl_take isl_ast_expr *expr2);
9665 __isl_give isl_ast_expr *isl_ast_expr_div(
9666 __isl_take isl_ast_expr *expr1,
9667 __isl_take isl_ast_expr *expr2);
9668 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
9669 __isl_take isl_ast_expr *expr1,
9670 __isl_take isl_ast_expr *expr2);
9671 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
9672 __isl_take isl_ast_expr *expr1,
9673 __isl_take isl_ast_expr *expr2);
9674 __isl_give isl_ast_expr *isl_ast_expr_and(
9675 __isl_take isl_ast_expr *expr1,
9676 __isl_take isl_ast_expr *expr2)
9677 __isl_give isl_ast_expr *isl_ast_expr_and_then(
9678 __isl_take isl_ast_expr *expr1,
9679 __isl_take isl_ast_expr *expr2)
9680 __isl_give isl_ast_expr *isl_ast_expr_or(
9681 __isl_take isl_ast_expr *expr1,
9682 __isl_take isl_ast_expr *expr2)
9683 __isl_give isl_ast_expr *isl_ast_expr_or_else(
9684 __isl_take isl_ast_expr *expr1,
9685 __isl_take isl_ast_expr *expr2)
9686 __isl_give isl_ast_expr *isl_ast_expr_eq(
9687 __isl_take isl_ast_expr *expr1,
9688 __isl_take isl_ast_expr *expr2);
9689 __isl_give isl_ast_expr *isl_ast_expr_le(
9690 __isl_take isl_ast_expr *expr1,
9691 __isl_take isl_ast_expr *expr2);
9692 __isl_give isl_ast_expr *isl_ast_expr_lt(
9693 __isl_take isl_ast_expr *expr1,
9694 __isl_take isl_ast_expr *expr2);
9695 __isl_give isl_ast_expr *isl_ast_expr_ge(
9696 __isl_take isl_ast_expr *expr1,
9697 __isl_take isl_ast_expr *expr2);
9698 __isl_give isl_ast_expr *isl_ast_expr_gt(
9699 __isl_take isl_ast_expr *expr1,
9700 __isl_take isl_ast_expr *expr2);
9701 __isl_give isl_ast_expr *isl_ast_expr_access(
9702 __isl_take isl_ast_expr *array,
9703 __isl_take isl_ast_expr_list *indices);
9704 __isl_give isl_ast_expr *isl_ast_expr_call(
9705 __isl_take isl_ast_expr *function,
9706 __isl_take isl_ast_expr_list *arguments);
9708 The function C<isl_ast_expr_address_of> can be applied to an
9709 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
9710 to represent the address of the C<isl_ast_expr_access>. The function
9711 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
9712 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
9714 #include <isl/ast_build.h>
9715 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
9716 __isl_keep isl_ast_build *build,
9717 __isl_take isl_set *set);
9718 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
9719 __isl_keep isl_ast_build *build,
9720 __isl_take isl_pw_aff *pa);
9721 __isl_give isl_ast_expr *
9722 isl_ast_build_access_from_pw_multi_aff(
9723 __isl_keep isl_ast_build *build,
9724 __isl_take isl_pw_multi_aff *pma);
9725 __isl_give isl_ast_expr *
9726 isl_ast_build_access_from_multi_pw_aff(
9727 __isl_keep isl_ast_build *build,
9728 __isl_take isl_multi_pw_aff *mpa);
9729 __isl_give isl_ast_expr *
9730 isl_ast_build_call_from_pw_multi_aff(
9731 __isl_keep isl_ast_build *build,
9732 __isl_take isl_pw_multi_aff *pma);
9733 __isl_give isl_ast_expr *
9734 isl_ast_build_call_from_multi_pw_aff(
9735 __isl_keep isl_ast_build *build,
9736 __isl_take isl_multi_pw_aff *mpa);
9739 the domains of C<pa>, C<mpa> and C<pma> should correspond
9740 to the schedule space of C<build>.
9741 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
9742 the function being called.
9743 If the accessed space is a nested relation, then it is taken
9744 to represent an access of the member specified by the range
9745 of this nested relation of the structure specified by the domain
9746 of the nested relation.
9748 The following functions can be used to modify an C<isl_ast_expr>.
9750 #include <isl/ast.h>
9751 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
9752 __isl_take isl_ast_expr *expr, int pos,
9753 __isl_take isl_ast_expr *arg);
9755 Replace the argument of C<expr> at position C<pos> by C<arg>.
9757 #include <isl/ast.h>
9758 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
9759 __isl_take isl_ast_expr *expr,
9760 __isl_take isl_id_to_ast_expr *id2expr);
9762 The function C<isl_ast_expr_substitute_ids> replaces the
9763 subexpressions of C<expr> of type C<isl_ast_expr_id>
9764 by the corresponding expression in C<id2expr>, if there is any.
9767 User specified data can be attached to an C<isl_ast_node> and obtained
9768 from the same C<isl_ast_node> using the following functions.
9770 #include <isl/ast.h>
9771 __isl_give isl_ast_node *isl_ast_node_set_annotation(
9772 __isl_take isl_ast_node *node,
9773 __isl_take isl_id *annotation);
9774 __isl_give isl_id *isl_ast_node_get_annotation(
9775 __isl_keep isl_ast_node *node);
9777 Basic printing can be performed using the following functions.
9779 #include <isl/ast.h>
9780 __isl_give isl_printer *isl_printer_print_ast_expr(
9781 __isl_take isl_printer *p,
9782 __isl_keep isl_ast_expr *expr);
9783 __isl_give isl_printer *isl_printer_print_ast_node(
9784 __isl_take isl_printer *p,
9785 __isl_keep isl_ast_node *node);
9786 __isl_give char *isl_ast_expr_to_str(
9787 __isl_keep isl_ast_expr *expr);
9788 __isl_give char *isl_ast_node_to_str(
9789 __isl_keep isl_ast_node *node);
9790 __isl_give char *isl_ast_expr_to_C_str(
9791 __isl_keep isl_ast_expr *expr);
9792 __isl_give char *isl_ast_node_to_C_str(
9793 __isl_keep isl_ast_node *node);
9795 The functions C<isl_ast_expr_to_C_str> and
9796 C<isl_ast_node_to_C_str> are convenience functions
9797 that return a string representation of the input in C format.
9799 More advanced printing can be performed using the following functions.
9801 #include <isl/ast.h>
9802 __isl_give isl_printer *isl_ast_op_type_set_print_name(
9803 __isl_take isl_printer *p,
9804 enum isl_ast_op_type type,
9805 __isl_keep const char *name);
9806 isl_stat isl_options_set_ast_print_macro_once(
9807 isl_ctx *ctx, int val);
9808 int isl_options_get_ast_print_macro_once(isl_ctx *ctx);
9809 __isl_give isl_printer *isl_ast_op_type_print_macro(
9810 enum isl_ast_op_type type,
9811 __isl_take isl_printer *p);
9812 __isl_give isl_printer *isl_ast_expr_print_macros(
9813 __isl_keep isl_ast_expr *expr,
9814 __isl_take isl_printer *p);
9815 __isl_give isl_printer *isl_ast_node_print_macros(
9816 __isl_keep isl_ast_node *node,
9817 __isl_take isl_printer *p);
9818 __isl_give isl_printer *isl_ast_node_print(
9819 __isl_keep isl_ast_node *node,
9820 __isl_take isl_printer *p,
9821 __isl_take isl_ast_print_options *options);
9822 __isl_give isl_printer *isl_ast_node_for_print(
9823 __isl_keep isl_ast_node *node,
9824 __isl_take isl_printer *p,
9825 __isl_take isl_ast_print_options *options);
9826 __isl_give isl_printer *isl_ast_node_if_print(
9827 __isl_keep isl_ast_node *node,
9828 __isl_take isl_printer *p,
9829 __isl_take isl_ast_print_options *options);
9831 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
9832 C<isl> may print out an AST that makes use of macros such
9833 as C<floord>, C<min> and C<max>.
9834 The names of these macros may be modified by a call
9835 to C<isl_ast_op_type_set_print_name>. The user-specified
9836 names are associated to the printer object.
9837 C<isl_ast_op_type_print_macro> prints out the macro
9838 corresponding to a specific C<isl_ast_op_type>.
9839 If the print-macro-once option is set, then a given macro definition
9840 is only printed once to any given printer object.
9841 C<isl_ast_expr_print_macros> scans the C<isl_ast_expr>
9842 for subexpressions where these macros would be used and prints
9843 out the required macro definitions.
9844 Essentially, C<isl_ast_expr_print_macros> calls
9845 C<isl_ast_expr_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
9846 as function argument.
9847 C<isl_ast_node_print_macros> does the same
9848 for expressions in its C<isl_ast_node> argument.
9849 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
9850 C<isl_ast_node_if_print> print an C<isl_ast_node>
9851 in C<ISL_FORMAT_C>, but allow for some extra control
9852 through an C<isl_ast_print_options> object.
9853 This object can be created using the following functions.
9855 #include <isl/ast.h>
9856 __isl_give isl_ast_print_options *
9857 isl_ast_print_options_alloc(isl_ctx *ctx);
9858 __isl_give isl_ast_print_options *
9859 isl_ast_print_options_copy(
9860 __isl_keep isl_ast_print_options *options);
9861 __isl_null isl_ast_print_options *
9862 isl_ast_print_options_free(
9863 __isl_take isl_ast_print_options *options);
9865 __isl_give isl_ast_print_options *
9866 isl_ast_print_options_set_print_user(
9867 __isl_take isl_ast_print_options *options,
9868 __isl_give isl_printer *(*print_user)(
9869 __isl_take isl_printer *p,
9870 __isl_take isl_ast_print_options *options,
9871 __isl_keep isl_ast_node *node, void *user),
9873 __isl_give isl_ast_print_options *
9874 isl_ast_print_options_set_print_for(
9875 __isl_take isl_ast_print_options *options,
9876 __isl_give isl_printer *(*print_for)(
9877 __isl_take isl_printer *p,
9878 __isl_take isl_ast_print_options *options,
9879 __isl_keep isl_ast_node *node, void *user),
9882 The callback set by C<isl_ast_print_options_set_print_user>
9883 is called whenever a node of type C<isl_ast_node_user> needs to
9885 The callback set by C<isl_ast_print_options_set_print_for>
9886 is called whenever a node of type C<isl_ast_node_for> needs to
9888 Note that C<isl_ast_node_for_print> will I<not> call the
9889 callback set by C<isl_ast_print_options_set_print_for> on the node
9890 on which C<isl_ast_node_for_print> is called, but only on nested
9891 nodes of type C<isl_ast_node_for>. It is therefore safe to
9892 call C<isl_ast_node_for_print> from within the callback set by
9893 C<isl_ast_print_options_set_print_for>.
9895 The following option determines the type to be used for iterators
9896 while printing the AST.
9898 isl_stat isl_options_set_ast_iterator_type(
9899 isl_ctx *ctx, const char *val);
9900 const char *isl_options_get_ast_iterator_type(
9903 The AST printer only prints body nodes as blocks if these
9904 blocks cannot be safely omitted.
9905 For example, a C<for> node with one body node will not be
9906 surrounded with braces in C<ISL_FORMAT_C>.
9907 A block will always be printed by setting the following option.
9909 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx,
9911 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
9915 #include <isl/ast_build.h>
9916 isl_stat isl_options_set_ast_build_atomic_upper_bound(
9917 isl_ctx *ctx, int val);
9918 int isl_options_get_ast_build_atomic_upper_bound(
9920 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
9922 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
9923 isl_stat isl_options_set_ast_build_detect_min_max(
9924 isl_ctx *ctx, int val);
9925 int isl_options_get_ast_build_detect_min_max(
9927 isl_stat isl_options_set_ast_build_exploit_nested_bounds(
9928 isl_ctx *ctx, int val);
9929 int isl_options_get_ast_build_exploit_nested_bounds(
9931 isl_stat isl_options_set_ast_build_group_coscheduled(
9932 isl_ctx *ctx, int val);
9933 int isl_options_get_ast_build_group_coscheduled(
9935 isl_stat isl_options_set_ast_build_scale_strides(
9936 isl_ctx *ctx, int val);
9937 int isl_options_get_ast_build_scale_strides(
9939 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx,
9941 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
9942 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx,
9944 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
9948 =item * ast_build_atomic_upper_bound
9950 Generate loop upper bounds that consist of the current loop iterator,
9951 an operator and an expression not involving the iterator.
9952 If this option is not set, then the current loop iterator may appear
9953 several times in the upper bound.
9954 For example, when this option is turned off, AST generation
9957 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
9961 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
9964 When the option is turned on, the following AST is generated
9966 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
9969 =item * ast_build_prefer_pdiv
9971 If this option is turned off, then the AST generation will
9972 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
9973 operators, but no C<isl_ast_op_pdiv_q> or
9974 C<isl_ast_op_pdiv_r> operators.
9975 If this option is turned on, then C<isl> will try to convert
9976 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
9977 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
9979 =item * ast_build_detect_min_max
9981 If this option is turned on, then C<isl> will try and detect
9982 min or max-expressions when building AST expressions from
9983 piecewise affine expressions.
9985 =item * ast_build_exploit_nested_bounds
9987 Simplify conditions based on bounds of nested for loops.
9988 In particular, remove conditions that are implied by the fact
9989 that one or more nested loops have at least one iteration,
9990 meaning that the upper bound is at least as large as the lower bound.
9991 For example, when this option is turned off, AST generation
9994 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
10000 for (int c0 = 0; c0 <= N; c0 += 1)
10001 for (int c1 = 0; c1 <= M; c1 += 1)
10004 When the option is turned on, the following AST is generated
10006 for (int c0 = 0; c0 <= N; c0 += 1)
10007 for (int c1 = 0; c1 <= M; c1 += 1)
10010 =item * ast_build_group_coscheduled
10012 If two domain elements are assigned the same schedule point, then
10013 they may be executed in any order and they may even appear in different
10014 loops. If this options is set, then the AST generator will make
10015 sure that coscheduled domain elements do not appear in separate parts
10016 of the AST. This is useful in case of nested AST generation
10017 if the outer AST generation is given only part of a schedule
10018 and the inner AST generation should handle the domains that are
10019 coscheduled by this initial part of the schedule together.
10020 For example if an AST is generated for a schedule
10022 { A[i] -> [0]; B[i] -> [0] }
10024 then the C<isl_ast_build_set_create_leaf> callback described
10025 below may get called twice, once for each domain.
10026 Setting this option ensures that the callback is only called once
10027 on both domains together.
10029 =item * ast_build_separation_bounds
10031 This option specifies which bounds to use during separation.
10032 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
10033 then all (possibly implicit) bounds on the current dimension will
10034 be used during separation.
10035 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
10036 then only those bounds that are explicitly available will
10037 be used during separation.
10039 =item * ast_build_scale_strides
10041 This option specifies whether the AST generator is allowed
10042 to scale down iterators of strided loops.
10044 =item * ast_build_allow_else
10046 This option specifies whether the AST generator is allowed
10047 to construct if statements with else branches.
10049 =item * ast_build_allow_or
10051 This option specifies whether the AST generator is allowed
10052 to construct if conditions with disjunctions.
10056 =head3 AST Generation Options (Schedule Tree)
10058 In case of AST construction from a schedule tree, the options
10059 that control how an AST is created from the individual schedule
10060 dimensions are stored in the band nodes of the tree
10061 (see L</"Schedule Trees">).
10063 In particular, a schedule dimension can be handled in four
10064 different ways, atomic, separate, unroll or the default.
10065 This loop AST generation type can be set using
10066 C<isl_schedule_node_band_member_set_ast_loop_type>.
10068 the first three can be selected by including a one-dimensional
10069 element with as value the position of the schedule dimension
10070 within the band and as name one of C<atomic>, C<separate>
10071 or C<unroll> in the options
10072 set by C<isl_schedule_node_band_set_ast_build_options>.
10073 Only one of these three may be specified for
10074 any given schedule dimension within a band node.
10075 If none of these is specified, then the default
10076 is used. The meaning of the options is as follows.
10082 When this option is specified, the AST generator will make
10083 sure that a given domains space only appears in a single
10084 loop at the specified level.
10086 For example, for the schedule tree
10088 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10090 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10091 options: "{ atomic[x] }"
10093 the following AST will be generated
10095 for (int c0 = 0; c0 <= 10; c0 += 1) {
10102 On the other hand, for the schedule tree
10104 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10106 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10107 options: "{ separate[x] }"
10109 the following AST will be generated
10113 for (int c0 = 1; c0 <= 9; c0 += 1) {
10120 If neither C<atomic> nor C<separate> is specified, then the AST generator
10121 may produce either of these two results or some intermediate form.
10125 When this option is specified, the AST generator will
10126 split the domain of the specified schedule dimension
10127 into pieces with a fixed set of statements for which
10128 instances need to be executed by the iterations in
10129 the schedule domain part. This option tends to avoid
10130 the generation of guards inside the corresponding loops.
10131 See also the C<atomic> option.
10135 When this option is specified, the AST generator will
10136 I<completely> unroll the corresponding schedule dimension.
10137 It is the responsibility of the user to ensure that such
10138 unrolling is possible.
10139 To obtain a partial unrolling, the user should apply an additional
10140 strip-mining to the schedule and fully unroll the inner schedule
10145 The C<isolate> option is a bit more involved. It allows the user
10146 to isolate a range of schedule dimension values from smaller and
10147 greater values. Additionally, the user may specify a different
10148 atomic/separate/unroll choice for the isolated part and the remaining
10149 parts. The typical use case of the C<isolate> option is to isolate
10150 full tiles from partial tiles.
10151 The part that needs to be isolated may depend on outer schedule dimensions.
10152 The option therefore needs to be able to reference those outer schedule
10153 dimensions. In particular, the space of the C<isolate> option is that
10154 of a wrapped map with as domain the flat product of all outer band nodes
10155 and as range the space of the current band node.
10156 The atomic/separate/unroll choice for the isolated part is determined
10157 by an option that lives in an unnamed wrapped space with as domain
10158 a zero-dimensional C<isolate> space and as range the regular
10159 C<atomic>, C<separate> or C<unroll> space.
10160 This option may also be set directly using
10161 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
10162 The atomic/separate/unroll choice for the remaining part is determined
10163 by the regular C<atomic>, C<separate> or C<unroll> option.
10164 Since the C<isolate> option references outer schedule dimensions,
10165 its use in a band node causes any tree containing the node
10166 to be considered anchored.
10168 As an example, consider the isolation of full tiles from partial tiles
10169 in a tiling of a triangular domain. The original schedule is as follows.
10171 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10173 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10174 { A[i,j] -> [floor(j/10)] }, \
10175 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10179 for (int c0 = 0; c0 <= 10; c0 += 1)
10180 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10181 for (int c2 = 10 * c0;
10182 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10183 for (int c3 = 10 * c1;
10184 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10187 Isolating the full tiles, we have the following input
10189 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10191 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10192 { A[i,j] -> [floor(j/10)] }, \
10193 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10194 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10195 10a+9+10b+9 <= 100 }"
10200 for (int c0 = 0; c0 <= 8; c0 += 1) {
10201 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10202 for (int c2 = 10 * c0;
10203 c2 <= 10 * c0 + 9; c2 += 1)
10204 for (int c3 = 10 * c1;
10205 c3 <= 10 * c1 + 9; c3 += 1)
10207 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10208 for (int c2 = 10 * c0;
10209 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10210 for (int c3 = 10 * c1;
10211 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10214 for (int c0 = 9; c0 <= 10; c0 += 1)
10215 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10216 for (int c2 = 10 * c0;
10217 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10218 for (int c3 = 10 * c1;
10219 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10223 We may then additionally unroll the innermost loop of the isolated part
10225 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10227 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10228 { A[i,j] -> [floor(j/10)] }, \
10229 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10230 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10231 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
10236 for (int c0 = 0; c0 <= 8; c0 += 1) {
10237 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10238 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
10240 A(c2, 10 * c1 + 1);
10241 A(c2, 10 * c1 + 2);
10242 A(c2, 10 * c1 + 3);
10243 A(c2, 10 * c1 + 4);
10244 A(c2, 10 * c1 + 5);
10245 A(c2, 10 * c1 + 6);
10246 A(c2, 10 * c1 + 7);
10247 A(c2, 10 * c1 + 8);
10248 A(c2, 10 * c1 + 9);
10250 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10251 for (int c2 = 10 * c0;
10252 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10253 for (int c3 = 10 * c1;
10254 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10257 for (int c0 = 9; c0 <= 10; c0 += 1)
10258 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10259 for (int c2 = 10 * c0;
10260 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10261 for (int c3 = 10 * c1;
10262 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10267 =head3 AST Generation Options (Schedule Map)
10269 In case of AST construction using
10270 C<isl_ast_build_node_from_schedule_map>, the options
10271 that control how an AST is created from the individual schedule
10272 dimensions are stored in the C<isl_ast_build>.
10273 They can be set using the following function.
10275 #include <isl/ast_build.h>
10276 __isl_give isl_ast_build *
10277 isl_ast_build_set_options(
10278 __isl_take isl_ast_build *control,
10279 __isl_take isl_union_map *options);
10281 The options are encoded in an C<isl_union_map>.
10282 The domain of this union relation refers to the schedule domain,
10283 i.e., the range of the schedule passed
10284 to C<isl_ast_build_node_from_schedule_map>.
10285 In the case of nested AST generation (see L</"Nested AST Generation">),
10286 the domain of C<options> should refer to the extra piece of the schedule.
10287 That is, it should be equal to the range of the wrapped relation in the
10288 range of the schedule.
10289 The range of the options can consist of elements in one or more spaces,
10290 the names of which determine the effect of the option.
10291 The values of the range typically also refer to the schedule dimension
10292 to which the option applies. In case of nested AST generation
10293 (see L</"Nested AST Generation">), these values refer to the position
10294 of the schedule dimension within the innermost AST generation.
10295 The constraints on the domain elements of
10296 the option should only refer to this dimension and earlier dimensions.
10297 We consider the following spaces.
10301 =item C<separation_class>
10303 B<This option has been deprecated. Use the isolate option on
10304 schedule trees instead.>
10306 This space is a wrapped relation between two one dimensional spaces.
10307 The input space represents the schedule dimension to which the option
10308 applies and the output space represents the separation class.
10309 While constructing a loop corresponding to the specified schedule
10310 dimension(s), the AST generator will try to generate separate loops
10311 for domain elements that are assigned different classes.
10312 If only some of the elements are assigned a class, then those elements
10313 that are not assigned any class will be treated as belonging to a class
10314 that is separate from the explicitly assigned classes.
10315 The typical use case for this option is to separate full tiles from
10317 The other options, described below, are applied after the separation
10320 As an example, consider the separation into full and partial tiles
10321 of a tiling of a triangular domain.
10322 Take, for example, the domain
10324 { A[i,j] : 0 <= i,j and i + j <= 100 }
10326 and a tiling into tiles of 10 by 10. The input to the AST generator
10327 is then the schedule
10329 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
10332 Without any options, the following AST is generated
10334 for (int c0 = 0; c0 <= 10; c0 += 1)
10335 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10336 for (int c2 = 10 * c0;
10337 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10339 for (int c3 = 10 * c1;
10340 c3 <= min(10 * c1 + 9, -c2 + 100);
10344 Separation into full and partial tiles can be obtained by assigning
10345 a class, say C<0>, to the full tiles. The full tiles are represented by those
10346 values of the first and second schedule dimensions for which there are
10347 values of the third and fourth dimensions to cover an entire tile.
10348 That is, we need to specify the following option
10350 { [a,b,c,d] -> separation_class[[0]->[0]] :
10351 exists b': 0 <= 10a,10b' and
10352 10a+9+10b'+9 <= 100;
10353 [a,b,c,d] -> separation_class[[1]->[0]] :
10354 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
10356 which simplifies to
10358 { [a, b, c, d] -> separation_class[[1] -> [0]] :
10359 a >= 0 and b >= 0 and b <= 8 - a;
10360 [a, b, c, d] -> separation_class[[0] -> [0]] :
10361 a >= 0 and a <= 8 }
10363 With this option, the generated AST is as follows
10366 for (int c0 = 0; c0 <= 8; c0 += 1) {
10367 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10368 for (int c2 = 10 * c0;
10369 c2 <= 10 * c0 + 9; c2 += 1)
10370 for (int c3 = 10 * c1;
10371 c3 <= 10 * c1 + 9; c3 += 1)
10373 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10374 for (int c2 = 10 * c0;
10375 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10377 for (int c3 = 10 * c1;
10378 c3 <= min(-c2 + 100, 10 * c1 + 9);
10382 for (int c0 = 9; c0 <= 10; c0 += 1)
10383 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10384 for (int c2 = 10 * c0;
10385 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10387 for (int c3 = 10 * c1;
10388 c3 <= min(10 * c1 + 9, -c2 + 100);
10395 This is a single-dimensional space representing the schedule dimension(s)
10396 to which ``separation'' should be applied. Separation tries to split
10397 a loop into several pieces if this can avoid the generation of guards
10399 See also the C<atomic> option.
10403 This is a single-dimensional space representing the schedule dimension(s)
10404 for which the domains should be considered ``atomic''. That is, the
10405 AST generator will make sure that any given domain space will only appear
10406 in a single loop at the specified level.
10408 Consider the following schedule
10410 { a[i] -> [i] : 0 <= i < 10;
10411 b[i] -> [i+1] : 0 <= i < 10 }
10413 If the following option is specified
10415 { [i] -> separate[x] }
10417 then the following AST will be generated
10421 for (int c0 = 1; c0 <= 9; c0 += 1) {
10428 If, on the other hand, the following option is specified
10430 { [i] -> atomic[x] }
10432 then the following AST will be generated
10434 for (int c0 = 0; c0 <= 10; c0 += 1) {
10441 If neither C<atomic> nor C<separate> is specified, then the AST generator
10442 may produce either of these two results or some intermediate form.
10446 This is a single-dimensional space representing the schedule dimension(s)
10447 that should be I<completely> unrolled.
10448 To obtain a partial unrolling, the user should apply an additional
10449 strip-mining to the schedule and fully unroll the inner loop.
10453 =head3 Fine-grained Control over AST Generation
10455 Besides specifying the constraints on the parameters,
10456 an C<isl_ast_build> object can be used to control
10457 various aspects of the AST generation process.
10458 In case of AST construction using
10459 C<isl_ast_build_node_from_schedule_map>,
10460 the most prominent way of control is through ``options'',
10461 as explained above.
10463 Additional control is available through the following functions.
10465 #include <isl/ast_build.h>
10466 __isl_give isl_ast_build *
10467 isl_ast_build_set_iterators(
10468 __isl_take isl_ast_build *control,
10469 __isl_take isl_id_list *iterators);
10471 The function C<isl_ast_build_set_iterators> allows the user to
10472 specify a list of iterator C<isl_id>s to be used as iterators.
10473 If the input schedule is injective, then
10474 the number of elements in this list should be as large as the dimension
10475 of the schedule space, but no direct correspondence should be assumed
10476 between dimensions and elements.
10477 If the input schedule is not injective, then an additional number
10478 of C<isl_id>s equal to the largest dimension of the input domains
10480 If the number of provided C<isl_id>s is insufficient, then additional
10481 names are automatically generated.
10483 #include <isl/ast_build.h>
10484 __isl_give isl_ast_build *
10485 isl_ast_build_set_create_leaf(
10486 __isl_take isl_ast_build *control,
10487 __isl_give isl_ast_node *(*fn)(
10488 __isl_take isl_ast_build *build,
10489 void *user), void *user);
10492 C<isl_ast_build_set_create_leaf> function allows for the
10493 specification of a callback that should be called whenever the AST
10494 generator arrives at an element of the schedule domain.
10495 The callback should return an AST node that should be inserted
10496 at the corresponding position of the AST. The default action (when
10497 the callback is not set) is to continue generating parts of the AST to scan
10498 all the domain elements associated to the schedule domain element
10499 and to insert user nodes, ``calling'' the domain element, for each of them.
10500 The C<build> argument contains the current state of the C<isl_ast_build>.
10501 To ease nested AST generation (see L</"Nested AST Generation">),
10502 all control information that is
10503 specific to the current AST generation such as the options and
10504 the callbacks has been removed from this C<isl_ast_build>.
10505 The callback would typically return the result of a nested
10506 AST generation or a
10507 user defined node created using the following function.
10509 #include <isl/ast.h>
10510 __isl_give isl_ast_node *isl_ast_node_alloc_user(
10511 __isl_take isl_ast_expr *expr);
10513 #include <isl/ast_build.h>
10514 __isl_give isl_ast_build *
10515 isl_ast_build_set_at_each_domain(
10516 __isl_take isl_ast_build *build,
10517 __isl_give isl_ast_node *(*fn)(
10518 __isl_take isl_ast_node *node,
10519 __isl_keep isl_ast_build *build,
10520 void *user), void *user);
10521 __isl_give isl_ast_build *
10522 isl_ast_build_set_before_each_for(
10523 __isl_take isl_ast_build *build,
10524 __isl_give isl_id *(*fn)(
10525 __isl_keep isl_ast_build *build,
10526 void *user), void *user);
10527 __isl_give isl_ast_build *
10528 isl_ast_build_set_after_each_for(
10529 __isl_take isl_ast_build *build,
10530 __isl_give isl_ast_node *(*fn)(
10531 __isl_take isl_ast_node *node,
10532 __isl_keep isl_ast_build *build,
10533 void *user), void *user);
10534 __isl_give isl_ast_build *
10535 isl_ast_build_set_before_each_mark(
10536 __isl_take isl_ast_build *build,
10537 isl_stat (*fn)(__isl_keep isl_id *mark,
10538 __isl_keep isl_ast_build *build,
10539 void *user), void *user);
10540 __isl_give isl_ast_build *
10541 isl_ast_build_set_after_each_mark(
10542 __isl_take isl_ast_build *build,
10543 __isl_give isl_ast_node *(*fn)(
10544 __isl_take isl_ast_node *node,
10545 __isl_keep isl_ast_build *build,
10546 void *user), void *user);
10548 The callback set by C<isl_ast_build_set_at_each_domain> will
10549 be called for each domain AST node.
10550 The callbacks set by C<isl_ast_build_set_before_each_for>
10551 and C<isl_ast_build_set_after_each_for> will be called
10552 for each for AST node. The first will be called in depth-first
10553 pre-order, while the second will be called in depth-first post-order.
10554 Since C<isl_ast_build_set_before_each_for> is called before the for
10555 node is actually constructed, it is only passed an C<isl_ast_build>.
10556 The returned C<isl_id> will be added as an annotation (using
10557 C<isl_ast_node_set_annotation>) to the constructed for node.
10558 In particular, if the user has also specified an C<after_each_for>
10559 callback, then the annotation can be retrieved from the node passed to
10560 that callback using C<isl_ast_node_get_annotation>.
10561 The callbacks set by C<isl_ast_build_set_before_each_mark>
10562 and C<isl_ast_build_set_after_each_mark> will be called for each
10563 mark AST node that is created, i.e., for each mark schedule node
10564 in the input schedule tree. The first will be called in depth-first
10565 pre-order, while the second will be called in depth-first post-order.
10566 Since the callback set by C<isl_ast_build_set_before_each_mark>
10567 is called before the mark AST node is actually constructed, it is passed
10568 the identifier of the mark node.
10569 All callbacks should C<NULL> (or -1) on failure.
10570 The given C<isl_ast_build> can be used to create new
10571 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
10572 or C<isl_ast_build_call_from_pw_multi_aff>.
10574 =head3 Nested AST Generation
10576 C<isl> allows the user to create an AST within the context
10577 of another AST. These nested ASTs are created using the
10578 same C<isl_ast_build_node_from_schedule_map> function that is used to create
10579 the outer AST. The C<build> argument should be an C<isl_ast_build>
10580 passed to a callback set by
10581 C<isl_ast_build_set_create_leaf>.
10582 The space of the range of the C<schedule> argument should refer
10583 to this build. In particular, the space should be a wrapped
10584 relation and the domain of this wrapped relation should be the
10585 same as that of the range of the schedule returned by
10586 C<isl_ast_build_get_schedule> below.
10587 In practice, the new schedule is typically
10588 created by calling C<isl_union_map_range_product> on the old schedule
10589 and some extra piece of the schedule.
10590 The space of the schedule domain is also available from
10591 the C<isl_ast_build>.
10593 #include <isl/ast_build.h>
10594 __isl_give isl_union_map *isl_ast_build_get_schedule(
10595 __isl_keep isl_ast_build *build);
10596 __isl_give isl_space *isl_ast_build_get_schedule_space(
10597 __isl_keep isl_ast_build *build);
10598 __isl_give isl_ast_build *isl_ast_build_restrict(
10599 __isl_take isl_ast_build *build,
10600 __isl_take isl_set *set);
10602 The C<isl_ast_build_get_schedule> function returns a (partial)
10603 schedule for the domains elements for which part of the AST still needs to
10604 be generated in the current build.
10605 In particular, the domain elements are mapped to those iterations of the loops
10606 enclosing the current point of the AST generation inside which
10607 the domain elements are executed.
10608 No direct correspondence between
10609 the input schedule and this schedule should be assumed.
10610 The space obtained from C<isl_ast_build_get_schedule_space> can be used
10611 to create a set for C<isl_ast_build_restrict> to intersect
10612 with the current build. In particular, the set passed to
10613 C<isl_ast_build_restrict> can have additional parameters.
10614 The ids of the set dimensions in the space returned by
10615 C<isl_ast_build_get_schedule_space> correspond to the
10616 iterators of the already generated loops.
10617 The user should not rely on the ids of the output dimensions
10618 of the relations in the union relation returned by
10619 C<isl_ast_build_get_schedule> having any particular value.
10621 =head1 Applications
10623 Although C<isl> is mainly meant to be used as a library,
10624 it also contains some basic applications that use some
10625 of the functionality of C<isl>.
10626 For applications that take one or more polytopes or polyhedra
10627 as input, this input may be specified in either the L<isl format>
10628 or the L<PolyLib format>.
10630 =head2 C<isl_polyhedron_sample>
10632 C<isl_polyhedron_sample> takes a polyhedron as input and prints
10633 an integer element of the polyhedron, if there is any.
10634 The first column in the output is the denominator and is always
10635 equal to 1. If the polyhedron contains no integer points,
10636 then a vector of length zero is printed.
10640 C<isl_pip> takes the same input as the C<example> program
10641 from the C<piplib> distribution, i.e., a set of constraints
10642 on the parameters, a line containing only -1 and finally a set
10643 of constraints on a parametric polyhedron.
10644 The coefficients of the parameters appear in the last columns
10645 (but before the final constant column).
10646 The output is the lexicographic minimum of the parametric polyhedron.
10647 As C<isl> currently does not have its own output format, the output
10648 is just a dump of the internal state.
10650 =head2 C<isl_polyhedron_minimize>
10652 C<isl_polyhedron_minimize> computes the minimum of some linear
10653 or affine objective function over the integer points in a polyhedron.
10654 If an affine objective function
10655 is given, then the constant should appear in the last column.
10657 =head2 C<isl_polytope_scan>
10659 Given a polytope, C<isl_polytope_scan> prints
10660 all integer points in the polytope.
10662 =head2 C<isl_codegen>
10664 Given either a schedule tree or a sequence consisting of
10665 a schedule map, a context set and an options relation,
10666 C<isl_codegen> prints out an AST that scans the domain elements
10667 of the schedule in the order of their image(s) taking into account
10668 the constraints in the context set.
10670 =head2 C<isl_schedule>
10672 Given an C<isl_schedule_constraints> object as input,
10673 C<isl_schedule> prints out a schedule that satisfies the given