3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
8 using C<GMP> or C<imath>.
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
171 =head3 Changes since isl-0.10
175 =item * The functions C<isl_set_dim_has_lower_bound> and
176 C<isl_set_dim_has_upper_bound> have been renamed to
177 C<isl_set_dim_has_any_lower_bound> and
178 C<isl_set_dim_has_any_upper_bound>.
179 The new C<isl_set_dim_has_lower_bound> and
180 C<isl_set_dim_has_upper_bound> have slightly different meanings.
184 =head3 Changes since isl-0.12
188 =item * C<isl_int> has been replaced by C<isl_val>.
189 Some of the old functions are still available in C<isl/deprecated/*.h>
190 but they will be removed in the future.
192 =item * The functions C<isl_pw_qpolynomial_eval>,
193 C<isl_union_pw_qpolynomial_eval>, C<isl_pw_qpolynomial_fold_eval>
194 and C<isl_union_pw_qpolynomial_fold_eval> have been changed to return
195 an C<isl_val> instead of an C<isl_qpolynomial>.
197 =item * The function C<isl_band_member_is_zero_distance>
198 has been removed. Essentially the same functionality is available
199 through C<isl_band_member_is_coincident>, except that it requires
200 setting up coincidence constraints.
201 The option C<schedule_outer_zero_distance> has accordingly been
202 replaced by the option C<schedule_outer_coincidence>.
204 =item * The function C<isl_vertex_get_expr> has been changed
205 to return an C<isl_multi_aff> instead of a rational C<isl_basic_set>.
206 The function C<isl_vertex_get_domain> has been changed to return
207 a regular basic set, rather than a rational basic set.
211 =head3 Changes since isl-0.14
215 =item * The function C<isl_union_pw_multi_aff_add> now consistently
216 computes the sum on the shared definition domain.
217 The function C<isl_union_pw_multi_aff_union_add> has been added
218 to compute the sum on the union of definition domains.
219 The original behavior of C<isl_union_pw_multi_aff_add> was
220 confused and is no longer available.
222 =item * Band forests have been replaced by schedule trees.
224 =item * The function C<isl_union_map_compute_flow> has been
225 replaced by the function C<isl_union_access_info_compute_flow>.
226 Note that the may dependence relation returned by
227 C<isl_union_flow_get_may_dependence> is the union of
228 the two dependence relations returned by
229 C<isl_union_map_compute_flow>. Similarly for the no source relations.
230 The function C<isl_union_map_compute_flow> is still available
231 for backward compatibility, but it will be removed in the future.
233 =item * The function C<isl_basic_set_drop_constraint> has been
236 =item * The function C<isl_ast_build_ast_from_schedule> has been
237 renamed to C<isl_ast_build_node_from_schedule_map>.
238 The original name is still available
239 for backward compatibility, but it will be removed in the future.
241 =item * The C<separation_class> AST generation option has been
244 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
245 have been renamed to C<isl_constraint_alloc_equality> and
246 C<isl_constraint_alloc_inequality>. The original names have been
247 kept for backward compatibility, but they will be removed in the future.
249 =item * The C<schedule_fuse> option has been replaced
250 by the C<schedule_serialize_sccs> option. The effect
251 of setting the C<schedule_fuse> option to C<ISL_SCHEDULE_FUSE_MIN>
252 is now obtained by turning on the C<schedule_serialize_sccs> option.
256 =head3 Changes since isl-0.17
260 =item * The function C<isl_printer_print_ast_expr> no longer prints
261 in C format by default. To print in C format, the output format
262 of the printer needs to have been explicitly set to C<ISL_FORMAT_C>.
263 As a result, the function C<isl_ast_expr_to_str> no longer prints
264 the expression in C format. Use C<isl_ast_expr_to_C_str> instead.
266 =item * The functions C<isl_set_align_divs> and C<isl_map_align_divs>
267 have been deprecated. The function C<isl_set_lift> has an effect
268 that is similar to C<isl_set_align_divs> and could in some cases
269 be used as an alternative.
275 C<isl> is released under the MIT license.
279 Permission is hereby granted, free of charge, to any person obtaining a copy of
280 this software and associated documentation files (the "Software"), to deal in
281 the Software without restriction, including without limitation the rights to
282 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
283 of the Software, and to permit persons to whom the Software is furnished to do
284 so, subject to the following conditions:
286 The above copyright notice and this permission notice shall be included in all
287 copies or substantial portions of the Software.
289 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
290 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
291 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
292 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
293 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
294 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
299 Note that by default C<isl> requires C<GMP>, which is released
300 under the GNU Lesser General Public License (LGPL). This means
301 that code linked against C<isl> is also linked against LGPL code.
303 When configuring with C<--with-int=imath> or C<--with-int=imath-32>, C<isl>
304 will link against C<imath>, a library for exact integer arithmetic released
305 under the MIT license.
309 The source of C<isl> can be obtained either as a tarball
310 or from the git repository. Both are available from
311 L<http://isl.gforge.inria.fr/>.
312 The installation process depends on how you obtained
315 =head2 Installation from the git repository
319 =item 1 Clone or update the repository
321 The first time the source is obtained, you need to clone
324 git clone git://repo.or.cz/isl.git
326 To obtain updates, you need to pull in the latest changes
330 =item 2 Optionally get C<imath> submodule
332 To build C<isl> with C<imath>, you need to obtain the C<imath>
333 submodule by running in the git source tree of C<isl>
338 This will fetch the required version of C<imath> in a subdirectory of C<isl>.
340 =item 2 Generate C<configure>
346 After performing the above steps, continue
347 with the L<Common installation instructions>.
349 =head2 Common installation instructions
353 =item 1 Obtain C<GMP>
355 By default, building C<isl> requires C<GMP>, including its headers files.
356 Your distribution may not provide these header files by default
357 and you may need to install a package called C<gmp-devel> or something
358 similar. Alternatively, C<GMP> can be built from
359 source, available from L<http://gmplib.org/>.
360 C<GMP> is not needed if you build C<isl> with C<imath>.
364 C<isl> uses the standard C<autoconf> C<configure> script.
369 optionally followed by some configure options.
370 A complete list of options can be obtained by running
374 Below we discuss some of the more common options.
380 Installation prefix for C<isl>
382 =item C<--with-int=[gmp|imath|imath-32]>
384 Select the integer library to be used by C<isl>, the default is C<gmp>.
385 With C<imath-32>, C<isl> will use 32 bit integers, but fall back to C<imath>
386 for values out of the 32 bit range. In most applications, C<isl> will run
387 fastest with the C<imath-32> option, followed by C<gmp> and C<imath>, the
390 =item C<--with-gmp-prefix>
392 Installation prefix for C<GMP> (architecture-independent files).
394 =item C<--with-gmp-exec-prefix>
396 Installation prefix for C<GMP> (architecture-dependent files).
404 =item 4 Install (optional)
410 =head1 Integer Set Library
412 =head2 Memory Management
414 Since a high-level operation on isl objects usually involves
415 several substeps and since the user is usually not interested in
416 the intermediate results, most functions that return a new object
417 will also release all the objects passed as arguments.
418 If the user still wants to use one or more of these arguments
419 after the function call, she should pass along a copy of the
420 object rather than the object itself.
421 The user is then responsible for making sure that the original
422 object gets used somewhere else or is explicitly freed.
424 The arguments and return values of all documented functions are
425 annotated to make clear which arguments are released and which
426 arguments are preserved. In particular, the following annotations
433 C<__isl_give> means that a new object is returned.
434 The user should make sure that the returned pointer is
435 used exactly once as a value for an C<__isl_take> argument.
436 In between, it can be used as a value for as many
437 C<__isl_keep> arguments as the user likes.
438 There is one exception, and that is the case where the
439 pointer returned is C<NULL>. Is this case, the user
440 is free to use it as an C<__isl_take> argument or not.
441 When applied to a C<char *>, the returned pointer needs to be
446 C<__isl_null> means that a C<NULL> value is returned.
450 C<__isl_take> means that the object the argument points to
451 is taken over by the function and may no longer be used
452 by the user as an argument to any other function.
453 The pointer value must be one returned by a function
454 returning an C<__isl_give> pointer.
455 If the user passes in a C<NULL> value, then this will
456 be treated as an error in the sense that the function will
457 not perform its usual operation. However, it will still
458 make sure that all the other C<__isl_take> arguments
463 C<__isl_keep> means that the function will only use the object
464 temporarily. After the function has finished, the user
465 can still use it as an argument to other functions.
466 A C<NULL> value will be treated in the same way as
467 a C<NULL> value for an C<__isl_take> argument.
468 This annotation may also be used on return values of
469 type C<const char *>, in which case the returned pointer should
470 not be freed by the user and is only valid until the object
471 from which it was derived is updated or freed.
475 =head2 Initialization
477 All manipulations of integer sets and relations occur within
478 the context of an C<isl_ctx>.
479 A given C<isl_ctx> can only be used within a single thread.
480 All arguments of a function are required to have been allocated
481 within the same context.
482 There are currently no functions available for moving an object
483 from one C<isl_ctx> to another C<isl_ctx>. This means that
484 there is currently no way of safely moving an object from one
485 thread to another, unless the whole C<isl_ctx> is moved.
487 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
488 freed using C<isl_ctx_free>.
489 All objects allocated within an C<isl_ctx> should be freed
490 before the C<isl_ctx> itself is freed.
492 isl_ctx *isl_ctx_alloc();
493 void isl_ctx_free(isl_ctx *ctx);
495 The user can impose a bound on the number of low-level I<operations>
496 that can be performed by an C<isl_ctx>. This bound can be set and
497 retrieved using the following functions. A bound of zero means that
498 no bound is imposed. The number of operations performed can be
499 reset using C<isl_ctx_reset_operations>. Note that the number
500 of low-level operations needed to perform a high-level computation
501 may differ significantly across different versions
502 of C<isl>, but it should be the same across different platforms
503 for the same version of C<isl>.
505 Warning: This feature is experimental. C<isl> has good support to abort and
506 bail out during the computation, but this feature may exercise error code paths
507 that are normally not used that much. Consequently, it is not unlikely that
508 hidden bugs will be exposed.
510 void isl_ctx_set_max_operations(isl_ctx *ctx,
511 unsigned long max_operations);
512 unsigned long isl_ctx_get_max_operations(isl_ctx *ctx);
513 void isl_ctx_reset_operations(isl_ctx *ctx);
515 In order to be able to create an object in the same context
516 as another object, most object types (described later in
517 this document) provide a function to obtain the context
518 in which the object was created.
521 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
522 isl_ctx *isl_multi_val_get_ctx(
523 __isl_keep isl_multi_val *mv);
526 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
528 #include <isl/local_space.h>
529 isl_ctx *isl_local_space_get_ctx(
530 __isl_keep isl_local_space *ls);
533 isl_ctx *isl_set_list_get_ctx(
534 __isl_keep isl_set_list *list);
537 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
538 isl_ctx *isl_multi_aff_get_ctx(
539 __isl_keep isl_multi_aff *maff);
540 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pa);
541 isl_ctx *isl_pw_multi_aff_get_ctx(
542 __isl_keep isl_pw_multi_aff *pma);
543 isl_ctx *isl_multi_pw_aff_get_ctx(
544 __isl_keep isl_multi_pw_aff *mpa);
545 isl_ctx *isl_union_pw_aff_get_ctx(
546 __isl_keep isl_union_pw_aff *upa);
547 isl_ctx *isl_union_pw_multi_aff_get_ctx(
548 __isl_keep isl_union_pw_multi_aff *upma);
549 isl_ctx *isl_multi_union_pw_aff_get_ctx(
550 __isl_keep isl_multi_union_pw_aff *mupa);
552 #include <isl/id_to_ast_expr.h>
553 isl_ctx *isl_id_to_ast_expr_get_ctx(
554 __isl_keep isl_id_to_ast_expr *id2expr);
556 #include <isl/point.h>
557 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
560 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
563 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
565 #include <isl/vertices.h>
566 isl_ctx *isl_vertices_get_ctx(
567 __isl_keep isl_vertices *vertices);
568 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
569 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
571 #include <isl/flow.h>
572 isl_ctx *isl_restriction_get_ctx(
573 __isl_keep isl_restriction *restr);
574 isl_ctx *isl_union_access_info_get_ctx(
575 __isl_keep isl_union_access_info *access);
576 isl_ctx *isl_union_flow_get_ctx(
577 __isl_keep isl_union_flow *flow);
579 #include <isl/schedule.h>
580 isl_ctx *isl_schedule_get_ctx(
581 __isl_keep isl_schedule *sched);
582 isl_ctx *isl_schedule_constraints_get_ctx(
583 __isl_keep isl_schedule_constraints *sc);
585 #include <isl/schedule_node.h>
586 isl_ctx *isl_schedule_node_get_ctx(
587 __isl_keep isl_schedule_node *node);
589 #include <isl/ast_build.h>
590 isl_ctx *isl_ast_build_get_ctx(
591 __isl_keep isl_ast_build *build);
594 isl_ctx *isl_ast_expr_get_ctx(
595 __isl_keep isl_ast_expr *expr);
596 isl_ctx *isl_ast_node_get_ctx(
597 __isl_keep isl_ast_node *node);
601 C<isl> uses two special return types for functions that either return
602 a boolean or that in principle do not return anything.
603 In particular, the C<isl_bool> type has three possible values:
604 C<isl_bool_true> (a positive integer value), indicating I<true> or I<yes>;
605 C<isl_bool_false> (the integer value zero), indicating I<false> or I<no>; and
606 C<isl_bool_error> (a negative integer value), indicating that something
607 went wrong. The following function can be used to negate an C<isl_bool>,
608 where the negation of C<isl_bool_error> is C<isl_bool_error> again.
611 isl_bool isl_bool_not(isl_bool b);
613 The C<isl_stat> type has two possible values:
614 C<isl_stat_ok> (the integer value zero), indicating a successful
616 C<isl_stat_error> (a negative integer value), indicating that something
618 See L</"Error Handling"> for more information on
619 C<isl_bool_error> and C<isl_stat_error>.
623 An C<isl_val> represents an integer value, a rational value
624 or one of three special values, infinity, negative infinity and NaN.
625 Some predefined values can be created using the following functions.
628 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
629 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
630 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
631 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
632 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
633 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
635 Specific integer values can be created using the following functions.
638 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
640 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
642 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
643 size_t n, size_t size, const void *chunks);
645 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
646 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
647 The least significant digit is assumed to be stored first.
649 Value objects can be copied and freed using the following functions.
652 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
653 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
655 They can be inspected using the following functions.
658 long isl_val_get_num_si(__isl_keep isl_val *v);
659 long isl_val_get_den_si(__isl_keep isl_val *v);
660 __isl_give isl_val *isl_val_get_den_val(
661 __isl_keep isl_val *v);
662 double isl_val_get_d(__isl_keep isl_val *v);
663 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
665 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
666 size_t size, void *chunks);
668 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
669 of C<size> bytes needed to store the absolute value of the
671 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
672 which is assumed to have been preallocated by the caller.
673 The least significant digit is stored first.
674 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
675 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
676 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
678 An C<isl_val> can be modified using the following function.
681 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
684 The following unary properties are defined on C<isl_val>s.
687 int isl_val_sgn(__isl_keep isl_val *v);
688 isl_bool isl_val_is_zero(__isl_keep isl_val *v);
689 isl_bool isl_val_is_one(__isl_keep isl_val *v);
690 isl_bool isl_val_is_negone(__isl_keep isl_val *v);
691 isl_bool isl_val_is_nonneg(__isl_keep isl_val *v);
692 isl_bool isl_val_is_nonpos(__isl_keep isl_val *v);
693 isl_bool isl_val_is_pos(__isl_keep isl_val *v);
694 isl_bool isl_val_is_neg(__isl_keep isl_val *v);
695 isl_bool isl_val_is_int(__isl_keep isl_val *v);
696 isl_bool isl_val_is_rat(__isl_keep isl_val *v);
697 isl_bool isl_val_is_nan(__isl_keep isl_val *v);
698 isl_bool isl_val_is_infty(__isl_keep isl_val *v);
699 isl_bool isl_val_is_neginfty(__isl_keep isl_val *v);
701 Note that the sign of NaN is undefined.
703 The following binary properties are defined on pairs of C<isl_val>s.
706 isl_bool isl_val_lt(__isl_keep isl_val *v1,
707 __isl_keep isl_val *v2);
708 isl_bool isl_val_le(__isl_keep isl_val *v1,
709 __isl_keep isl_val *v2);
710 isl_bool isl_val_gt(__isl_keep isl_val *v1,
711 __isl_keep isl_val *v2);
712 isl_bool isl_val_ge(__isl_keep isl_val *v1,
713 __isl_keep isl_val *v2);
714 isl_bool isl_val_eq(__isl_keep isl_val *v1,
715 __isl_keep isl_val *v2);
716 isl_bool isl_val_ne(__isl_keep isl_val *v1,
717 __isl_keep isl_val *v2);
718 isl_bool isl_val_abs_eq(__isl_keep isl_val *v1,
719 __isl_keep isl_val *v2);
721 Comparisons to NaN always return false.
722 That is, a NaN is not considered to hold any relative position
723 with respect to any value. In particular, a NaN
724 is neither considered to be equal to nor to be different from
725 any value (including another NaN).
726 The function C<isl_val_abs_eq> checks whether its two arguments
727 are equal in absolute value.
729 For integer C<isl_val>s we additionally have the following binary property.
732 isl_bool isl_val_is_divisible_by(__isl_keep isl_val *v1,
733 __isl_keep isl_val *v2);
735 An C<isl_val> can also be compared to an integer using the following
736 function. The result is undefined for NaN.
739 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
741 The following unary operations are available on C<isl_val>s.
744 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
745 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
746 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
747 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
748 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
749 __isl_give isl_val *isl_val_inv(__isl_take isl_val *v);
750 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
752 The following binary operations are available on C<isl_val>s.
755 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
756 __isl_take isl_val *v2);
757 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
758 __isl_take isl_val *v2);
759 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
760 __isl_take isl_val *v2);
761 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
763 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
764 __isl_take isl_val *v2);
765 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
767 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
768 __isl_take isl_val *v2);
769 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
771 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
772 __isl_take isl_val *v2);
773 __isl_give isl_val *isl_val_div_ui(__isl_take isl_val *v1,
776 On integer values, we additionally have the following operations.
779 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
780 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
781 __isl_take isl_val *v2);
782 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
783 __isl_take isl_val *v2);
784 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
785 __isl_take isl_val *v2, __isl_give isl_val **x,
786 __isl_give isl_val **y);
788 The function C<isl_val_gcdext> returns the greatest common divisor g
789 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
790 that C<*x> * C<v1> + C<*y> * C<v2> = g.
792 =head3 GMP specific functions
794 These functions are only available if C<isl> has been compiled with C<GMP>
797 Specific integer and rational values can be created from C<GMP> values using
798 the following functions.
800 #include <isl/val_gmp.h>
801 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
803 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
804 const mpz_t n, const mpz_t d);
806 The numerator and denominator of a rational value can be extracted as
807 C<GMP> values using the following functions.
809 #include <isl/val_gmp.h>
810 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
811 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
813 =head2 Sets and Relations
815 C<isl> uses six types of objects for representing sets and relations,
816 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
817 C<isl_union_set> and C<isl_union_map>.
818 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
819 can be described as a conjunction of affine constraints, while
820 C<isl_set> and C<isl_map> represent unions of
821 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
822 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
823 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
824 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
825 where spaces are considered different if they have a different number
826 of dimensions and/or different names (see L<"Spaces">).
827 The difference between sets and relations (maps) is that sets have
828 one set of variables, while relations have two sets of variables,
829 input variables and output variables.
831 =head2 Error Handling
833 C<isl> supports different ways to react in case a runtime error is triggered.
834 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
835 with two maps that have incompatible spaces. There are three possible ways
836 to react on error: to warn, to continue or to abort.
838 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
839 the last error in the corresponding C<isl_ctx> and the function in which the
840 error was triggered returns a value indicating that some error has
841 occurred. In case of functions returning a pointer, this value is
842 C<NULL>. In case of functions returning an C<isl_bool> or an
843 C<isl_stat>, this value is C<isl_bool_error> or C<isl_stat_error>.
844 An error does not corrupt internal state,
845 such that isl can continue to be used. C<isl> also provides functions to
846 read the last error, including the specific error message,
847 the isl source file where the error occurred and the line number,
848 and to reset all information about the last error. The
849 last error is only stored for information purposes. Its presence does not
850 change the behavior of C<isl>. Hence, resetting an error is not required to
851 continue to use isl, but only to observe new errors.
854 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
855 const char *isl_ctx_last_error_msg(isl_ctx *ctx);
856 const char *isl_ctx_last_error_file(isl_ctx *ctx);
857 int isl_ctx_last_error_line(isl_ctx *ctx);
858 void isl_ctx_reset_error(isl_ctx *ctx);
860 If no error has occurred since the last call to C<isl_ctx_reset_error>,
861 then the functions C<isl_ctx_last_error_msg> and
862 C<isl_ctx_last_error_file> return C<NULL>.
864 Another option is to continue on error. This is similar to warn on error mode,
865 except that C<isl> does not print any warning. This allows a program to
866 implement its own error reporting.
868 The last option is to directly abort the execution of the program from within
869 the isl library. This makes it obviously impossible to recover from an error,
870 but it allows to directly spot the error location. By aborting on error,
871 debuggers break at the location the error occurred and can provide a stack
872 trace. Other tools that automatically provide stack traces on abort or that do
873 not want to continue execution after an error was triggered may also prefer to
876 The on error behavior of isl can be specified by calling
877 C<isl_options_set_on_error> or by setting the command line option
878 C<--isl-on-error>. Valid arguments for the function call are
879 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
880 choices for the command line option are C<warn>, C<continue> and C<abort>.
881 It is also possible to query the current error mode.
883 #include <isl/options.h>
884 isl_stat isl_options_set_on_error(isl_ctx *ctx, int val);
885 int isl_options_get_on_error(isl_ctx *ctx);
889 Identifiers are used to identify both individual dimensions
890 and tuples of dimensions. They consist of an optional name and an optional
891 user pointer. The name and the user pointer cannot both be C<NULL>, however.
892 Identifiers with the same name but different pointer values
893 are considered to be distinct.
894 Similarly, identifiers with different names but the same pointer value
895 are also considered to be distinct.
896 Equal identifiers are represented using the same object.
897 Pairs of identifiers can therefore be tested for equality using the
899 Identifiers can be constructed, copied, freed, inspected and printed
900 using the following functions.
903 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
904 __isl_keep const char *name, void *user);
905 __isl_give isl_id *isl_id_set_free_user(
906 __isl_take isl_id *id,
907 void (*free_user)(void *user));
908 __isl_give isl_id *isl_id_copy(isl_id *id);
909 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
911 void *isl_id_get_user(__isl_keep isl_id *id);
912 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
914 __isl_give isl_printer *isl_printer_print_id(
915 __isl_take isl_printer *p, __isl_keep isl_id *id);
917 The callback set by C<isl_id_set_free_user> is called on the user
918 pointer when the last reference to the C<isl_id> is freed.
919 Note that C<isl_id_get_name> returns a pointer to some internal
920 data structure, so the result can only be used while the
921 corresponding C<isl_id> is alive.
925 Whenever a new set, relation or similar object is created from scratch,
926 the space in which it lives needs to be specified using an C<isl_space>.
927 Each space involves zero or more parameters and zero, one or two
928 tuples of set or input/output dimensions. The parameters and dimensions
929 are identified by an C<isl_dim_type> and a position.
930 The type C<isl_dim_param> refers to parameters,
931 the type C<isl_dim_set> refers to set dimensions (for spaces
932 with a single tuple of dimensions) and the types C<isl_dim_in>
933 and C<isl_dim_out> refer to input and output dimensions
934 (for spaces with two tuples of dimensions).
935 Local spaces (see L</"Local Spaces">) also contain dimensions
936 of type C<isl_dim_div>.
937 Note that parameters are only identified by their position within
938 a given object. Across different objects, parameters are (usually)
939 identified by their names or identifiers. Only unnamed parameters
940 are identified by their positions across objects. The use of unnamed
941 parameters is discouraged.
943 #include <isl/space.h>
944 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
945 unsigned nparam, unsigned n_in, unsigned n_out);
946 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
948 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
949 unsigned nparam, unsigned dim);
950 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
951 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
953 The space used for creating a parameter domain
954 needs to be created using C<isl_space_params_alloc>.
955 For other sets, the space
956 needs to be created using C<isl_space_set_alloc>, while
957 for a relation, the space
958 needs to be created using C<isl_space_alloc>.
960 To check whether a given space is that of a set or a map
961 or whether it is a parameter space, use these functions:
963 #include <isl/space.h>
964 isl_bool isl_space_is_params(__isl_keep isl_space *space);
965 isl_bool isl_space_is_set(__isl_keep isl_space *space);
966 isl_bool isl_space_is_map(__isl_keep isl_space *space);
968 Spaces can be compared using the following functions:
970 #include <isl/space.h>
971 isl_bool isl_space_is_equal(__isl_keep isl_space *space1,
972 __isl_keep isl_space *space2);
973 isl_bool isl_space_has_equal_params(
974 __isl_keep isl_space *space1,
975 __isl_keep isl_space *space2);
976 isl_bool isl_space_has_equal_tuples(
977 __isl_keep isl_space *space1,
978 __isl_keep isl_space *space2);
979 isl_bool isl_space_is_domain(__isl_keep isl_space *space1,
980 __isl_keep isl_space *space2);
981 isl_bool isl_space_is_range(__isl_keep isl_space *space1,
982 __isl_keep isl_space *space2);
983 isl_bool isl_space_tuple_is_equal(
984 __isl_keep isl_space *space1,
985 enum isl_dim_type type1,
986 __isl_keep isl_space *space2,
987 enum isl_dim_type type2);
989 C<isl_space_is_domain> checks whether the first argument is equal
990 to the domain of the second argument. This requires in particular that
991 the first argument is a set space and that the second argument
992 is a map space. C<isl_space_tuple_is_equal> checks whether the given
993 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
994 spaces are the same. That is, it checks if they have the same
995 identifier (if any), the same dimension and the same internal structure
998 C<isl_space_has_equal_params> checks whether two spaces
999 have the same parameters in the same order.
1000 C<isl_space_has_equal_tuples> check whether two spaces have
1001 the same tuples. In contrast to C<isl_space_is_equal> below,
1002 it does not check the
1003 parameters. This is useful because many C<isl> functions align the
1004 parameters before they perform their operations, such that equivalence
1006 C<isl_space_is_equal> checks whether two spaces are identical,
1007 meaning that they have the same parameters and the same tuples.
1008 That is, it checks whether both C<isl_space_has_equal_params> and
1009 C<isl_space_has_equal_tuples> hold.
1011 It is often useful to create objects that live in the
1012 same space as some other object. This can be accomplished
1013 by creating the new objects
1014 (see L</"Creating New Sets and Relations"> or
1015 L</"Functions">) based on the space
1016 of the original object.
1018 #include <isl/set.h>
1019 __isl_give isl_space *isl_basic_set_get_space(
1020 __isl_keep isl_basic_set *bset);
1021 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
1023 #include <isl/union_set.h>
1024 __isl_give isl_space *isl_union_set_get_space(
1025 __isl_keep isl_union_set *uset);
1027 #include <isl/map.h>
1028 __isl_give isl_space *isl_basic_map_get_space(
1029 __isl_keep isl_basic_map *bmap);
1030 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
1032 #include <isl/union_map.h>
1033 __isl_give isl_space *isl_union_map_get_space(
1034 __isl_keep isl_union_map *umap);
1036 #include <isl/constraint.h>
1037 __isl_give isl_space *isl_constraint_get_space(
1038 __isl_keep isl_constraint *constraint);
1040 #include <isl/polynomial.h>
1041 __isl_give isl_space *isl_qpolynomial_get_domain_space(
1042 __isl_keep isl_qpolynomial *qp);
1043 __isl_give isl_space *isl_qpolynomial_get_space(
1044 __isl_keep isl_qpolynomial *qp);
1045 __isl_give isl_space *
1046 isl_qpolynomial_fold_get_domain_space(
1047 __isl_keep isl_qpolynomial_fold *fold);
1048 __isl_give isl_space *isl_qpolynomial_fold_get_space(
1049 __isl_keep isl_qpolynomial_fold *fold);
1050 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
1051 __isl_keep isl_pw_qpolynomial *pwqp);
1052 __isl_give isl_space *isl_pw_qpolynomial_get_space(
1053 __isl_keep isl_pw_qpolynomial *pwqp);
1054 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
1055 __isl_keep isl_pw_qpolynomial_fold *pwf);
1056 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
1057 __isl_keep isl_pw_qpolynomial_fold *pwf);
1058 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
1059 __isl_keep isl_union_pw_qpolynomial *upwqp);
1060 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
1061 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1063 #include <isl/val.h>
1064 __isl_give isl_space *isl_multi_val_get_space(
1065 __isl_keep isl_multi_val *mv);
1067 #include <isl/aff.h>
1068 __isl_give isl_space *isl_aff_get_domain_space(
1069 __isl_keep isl_aff *aff);
1070 __isl_give isl_space *isl_aff_get_space(
1071 __isl_keep isl_aff *aff);
1072 __isl_give isl_space *isl_pw_aff_get_domain_space(
1073 __isl_keep isl_pw_aff *pwaff);
1074 __isl_give isl_space *isl_pw_aff_get_space(
1075 __isl_keep isl_pw_aff *pwaff);
1076 __isl_give isl_space *isl_multi_aff_get_domain_space(
1077 __isl_keep isl_multi_aff *maff);
1078 __isl_give isl_space *isl_multi_aff_get_space(
1079 __isl_keep isl_multi_aff *maff);
1080 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
1081 __isl_keep isl_pw_multi_aff *pma);
1082 __isl_give isl_space *isl_pw_multi_aff_get_space(
1083 __isl_keep isl_pw_multi_aff *pma);
1084 __isl_give isl_space *isl_union_pw_aff_get_space(
1085 __isl_keep isl_union_pw_aff *upa);
1086 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
1087 __isl_keep isl_union_pw_multi_aff *upma);
1088 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
1089 __isl_keep isl_multi_pw_aff *mpa);
1090 __isl_give isl_space *isl_multi_pw_aff_get_space(
1091 __isl_keep isl_multi_pw_aff *mpa);
1092 __isl_give isl_space *
1093 isl_multi_union_pw_aff_get_domain_space(
1094 __isl_keep isl_multi_union_pw_aff *mupa);
1095 __isl_give isl_space *
1096 isl_multi_union_pw_aff_get_space(
1097 __isl_keep isl_multi_union_pw_aff *mupa);
1099 #include <isl/point.h>
1100 __isl_give isl_space *isl_point_get_space(
1101 __isl_keep isl_point *pnt);
1103 The number of dimensions of a given type of space
1104 may be read off from a space or an object that lives
1105 in a space using the following functions.
1106 In case of C<isl_space_dim>, type may be
1107 C<isl_dim_param>, C<isl_dim_in> (only for relations),
1108 C<isl_dim_out> (only for relations), C<isl_dim_set>
1109 (only for sets) or C<isl_dim_all>.
1111 #include <isl/space.h>
1112 unsigned isl_space_dim(__isl_keep isl_space *space,
1113 enum isl_dim_type type);
1115 #include <isl/local_space.h>
1116 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1117 enum isl_dim_type type);
1119 #include <isl/set.h>
1120 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1121 enum isl_dim_type type);
1122 unsigned isl_set_dim(__isl_keep isl_set *set,
1123 enum isl_dim_type type);
1125 #include <isl/union_set.h>
1126 unsigned isl_union_set_dim(__isl_keep isl_union_set *uset,
1127 enum isl_dim_type type);
1129 #include <isl/map.h>
1130 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1131 enum isl_dim_type type);
1132 unsigned isl_map_dim(__isl_keep isl_map *map,
1133 enum isl_dim_type type);
1135 #include <isl/union_map.h>
1136 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1137 enum isl_dim_type type);
1139 #include <isl/val.h>
1140 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
1141 enum isl_dim_type type);
1143 #include <isl/aff.h>
1144 int isl_aff_dim(__isl_keep isl_aff *aff,
1145 enum isl_dim_type type);
1146 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1147 enum isl_dim_type type);
1148 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1149 enum isl_dim_type type);
1150 unsigned isl_pw_multi_aff_dim(
1151 __isl_keep isl_pw_multi_aff *pma,
1152 enum isl_dim_type type);
1153 unsigned isl_multi_pw_aff_dim(
1154 __isl_keep isl_multi_pw_aff *mpa,
1155 enum isl_dim_type type);
1156 unsigned isl_union_pw_aff_dim(
1157 __isl_keep isl_union_pw_aff *upa,
1158 enum isl_dim_type type);
1159 unsigned isl_union_pw_multi_aff_dim(
1160 __isl_keep isl_union_pw_multi_aff *upma,
1161 enum isl_dim_type type);
1162 unsigned isl_multi_union_pw_aff_dim(
1163 __isl_keep isl_multi_union_pw_aff *mupa,
1164 enum isl_dim_type type);
1166 #include <isl/polynomial.h>
1167 unsigned isl_union_pw_qpolynomial_dim(
1168 __isl_keep isl_union_pw_qpolynomial *upwqp,
1169 enum isl_dim_type type);
1170 unsigned isl_union_pw_qpolynomial_fold_dim(
1171 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1172 enum isl_dim_type type);
1174 Note that an C<isl_union_set>, an C<isl_union_map>,
1175 an C<isl_union_pw_multi_aff>,
1176 an C<isl_union_pw_qpolynomial> and
1177 an C<isl_union_pw_qpolynomial_fold>
1178 only have parameters.
1180 Additional parameters can be added to a space using the following function.
1182 #include <isl/space.h>
1183 __isl_give isl_space *isl_space_add_param_id(
1184 __isl_take isl_space *space,
1185 __isl_take isl_id *id);
1187 If a parameter with the given identifier already appears in the space,
1188 then it is not added again.
1190 The identifiers or names of the individual dimensions of spaces
1191 may be set or read off using the following functions on spaces
1192 or objects that live in spaces.
1193 These functions are mostly useful to obtain the identifiers, positions
1194 or names of the parameters. Identifiers of individual dimensions are
1195 essentially only useful for printing. They are ignored by all other
1196 operations and may not be preserved across those operations.
1198 #include <isl/space.h>
1199 __isl_give isl_space *isl_space_set_dim_id(
1200 __isl_take isl_space *space,
1201 enum isl_dim_type type, unsigned pos,
1202 __isl_take isl_id *id);
1203 isl_bool isl_space_has_dim_id(__isl_keep isl_space *space,
1204 enum isl_dim_type type, unsigned pos);
1205 __isl_give isl_id *isl_space_get_dim_id(
1206 __isl_keep isl_space *space,
1207 enum isl_dim_type type, unsigned pos);
1208 __isl_give isl_space *isl_space_set_dim_name(
1209 __isl_take isl_space *space,
1210 enum isl_dim_type type, unsigned pos,
1211 __isl_keep const char *name);
1212 isl_bool isl_space_has_dim_name(__isl_keep isl_space *space,
1213 enum isl_dim_type type, unsigned pos);
1214 __isl_keep const char *isl_space_get_dim_name(
1215 __isl_keep isl_space *space,
1216 enum isl_dim_type type, unsigned pos);
1218 #include <isl/local_space.h>
1219 __isl_give isl_local_space *isl_local_space_set_dim_id(
1220 __isl_take isl_local_space *ls,
1221 enum isl_dim_type type, unsigned pos,
1222 __isl_take isl_id *id);
1223 isl_bool isl_local_space_has_dim_id(
1224 __isl_keep isl_local_space *ls,
1225 enum isl_dim_type type, unsigned pos);
1226 __isl_give isl_id *isl_local_space_get_dim_id(
1227 __isl_keep isl_local_space *ls,
1228 enum isl_dim_type type, unsigned pos);
1229 __isl_give isl_local_space *isl_local_space_set_dim_name(
1230 __isl_take isl_local_space *ls,
1231 enum isl_dim_type type, unsigned pos, const char *s);
1232 isl_bool isl_local_space_has_dim_name(
1233 __isl_keep isl_local_space *ls,
1234 enum isl_dim_type type, unsigned pos)
1235 const char *isl_local_space_get_dim_name(
1236 __isl_keep isl_local_space *ls,
1237 enum isl_dim_type type, unsigned pos);
1239 #include <isl/constraint.h>
1240 const char *isl_constraint_get_dim_name(
1241 __isl_keep isl_constraint *constraint,
1242 enum isl_dim_type type, unsigned pos);
1244 #include <isl/set.h>
1245 __isl_give isl_id *isl_basic_set_get_dim_id(
1246 __isl_keep isl_basic_set *bset,
1247 enum isl_dim_type type, unsigned pos);
1248 __isl_give isl_set *isl_set_set_dim_id(
1249 __isl_take isl_set *set, enum isl_dim_type type,
1250 unsigned pos, __isl_take isl_id *id);
1251 isl_bool isl_set_has_dim_id(__isl_keep isl_set *set,
1252 enum isl_dim_type type, unsigned pos);
1253 __isl_give isl_id *isl_set_get_dim_id(
1254 __isl_keep isl_set *set, enum isl_dim_type type,
1256 const char *isl_basic_set_get_dim_name(
1257 __isl_keep isl_basic_set *bset,
1258 enum isl_dim_type type, unsigned pos);
1259 isl_bool isl_set_has_dim_name(__isl_keep isl_set *set,
1260 enum isl_dim_type type, unsigned pos);
1261 const char *isl_set_get_dim_name(
1262 __isl_keep isl_set *set,
1263 enum isl_dim_type type, unsigned pos);
1265 #include <isl/map.h>
1266 __isl_give isl_map *isl_map_set_dim_id(
1267 __isl_take isl_map *map, enum isl_dim_type type,
1268 unsigned pos, __isl_take isl_id *id);
1269 isl_bool isl_basic_map_has_dim_id(
1270 __isl_keep isl_basic_map *bmap,
1271 enum isl_dim_type type, unsigned pos);
1272 isl_bool isl_map_has_dim_id(__isl_keep isl_map *map,
1273 enum isl_dim_type type, unsigned pos);
1274 __isl_give isl_id *isl_map_get_dim_id(
1275 __isl_keep isl_map *map, enum isl_dim_type type,
1277 __isl_give isl_id *isl_union_map_get_dim_id(
1278 __isl_keep isl_union_map *umap,
1279 enum isl_dim_type type, unsigned pos);
1280 const char *isl_basic_map_get_dim_name(
1281 __isl_keep isl_basic_map *bmap,
1282 enum isl_dim_type type, unsigned pos);
1283 isl_bool isl_map_has_dim_name(__isl_keep isl_map *map,
1284 enum isl_dim_type type, unsigned pos);
1285 const char *isl_map_get_dim_name(
1286 __isl_keep isl_map *map,
1287 enum isl_dim_type type, unsigned pos);
1289 #include <isl/val.h>
1290 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1291 __isl_take isl_multi_val *mv,
1292 enum isl_dim_type type, unsigned pos,
1293 __isl_take isl_id *id);
1294 __isl_give isl_id *isl_multi_val_get_dim_id(
1295 __isl_keep isl_multi_val *mv,
1296 enum isl_dim_type type, unsigned pos);
1297 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1298 __isl_take isl_multi_val *mv,
1299 enum isl_dim_type type, unsigned pos, const char *s);
1301 #include <isl/aff.h>
1302 __isl_give isl_aff *isl_aff_set_dim_id(
1303 __isl_take isl_aff *aff, enum isl_dim_type type,
1304 unsigned pos, __isl_take isl_id *id);
1305 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1306 __isl_take isl_multi_aff *maff,
1307 enum isl_dim_type type, unsigned pos,
1308 __isl_take isl_id *id);
1309 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1310 __isl_take isl_pw_aff *pma,
1311 enum isl_dim_type type, unsigned pos,
1312 __isl_take isl_id *id);
1313 __isl_give isl_multi_pw_aff *
1314 isl_multi_pw_aff_set_dim_id(
1315 __isl_take isl_multi_pw_aff *mpa,
1316 enum isl_dim_type type, unsigned pos,
1317 __isl_take isl_id *id);
1318 __isl_give isl_multi_union_pw_aff *
1319 isl_multi_union_pw_aff_set_dim_id(
1320 __isl_take isl_multi_union_pw_aff *mupa,
1321 enum isl_dim_type type, unsigned pos,
1322 __isl_take isl_id *id);
1323 __isl_give isl_id *isl_multi_aff_get_dim_id(
1324 __isl_keep isl_multi_aff *ma,
1325 enum isl_dim_type type, unsigned pos);
1326 isl_bool isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1327 enum isl_dim_type type, unsigned pos);
1328 __isl_give isl_id *isl_pw_aff_get_dim_id(
1329 __isl_keep isl_pw_aff *pa,
1330 enum isl_dim_type type, unsigned pos);
1331 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1332 __isl_keep isl_pw_multi_aff *pma,
1333 enum isl_dim_type type, unsigned pos);
1334 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1335 __isl_keep isl_multi_pw_aff *mpa,
1336 enum isl_dim_type type, unsigned pos);
1337 __isl_give isl_id *isl_multi_union_pw_aff_get_dim_id(
1338 __isl_keep isl_multi_union_pw_aff *mupa,
1339 enum isl_dim_type type, unsigned pos);
1340 __isl_give isl_aff *isl_aff_set_dim_name(
1341 __isl_take isl_aff *aff, enum isl_dim_type type,
1342 unsigned pos, const char *s);
1343 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1344 __isl_take isl_multi_aff *maff,
1345 enum isl_dim_type type, unsigned pos, const char *s);
1346 __isl_give isl_multi_pw_aff *
1347 isl_multi_pw_aff_set_dim_name(
1348 __isl_take isl_multi_pw_aff *mpa,
1349 enum isl_dim_type type, unsigned pos, const char *s);
1350 __isl_give isl_union_pw_aff *
1351 isl_union_pw_aff_set_dim_name(
1352 __isl_take isl_union_pw_aff *upa,
1353 enum isl_dim_type type, unsigned pos,
1355 __isl_give isl_union_pw_multi_aff *
1356 isl_union_pw_multi_aff_set_dim_name(
1357 __isl_take isl_union_pw_multi_aff *upma,
1358 enum isl_dim_type type, unsigned pos,
1360 __isl_give isl_multi_union_pw_aff *
1361 isl_multi_union_pw_aff_set_dim_name(
1362 __isl_take isl_multi_union_pw_aff *mupa,
1363 enum isl_dim_type type, unsigned pos,
1364 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1365 enum isl_dim_type type, unsigned pos);
1366 const char *isl_pw_aff_get_dim_name(
1367 __isl_keep isl_pw_aff *pa,
1368 enum isl_dim_type type, unsigned pos);
1369 const char *isl_pw_multi_aff_get_dim_name(
1370 __isl_keep isl_pw_multi_aff *pma,
1371 enum isl_dim_type type, unsigned pos);
1373 #include <isl/polynomial.h>
1374 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1375 __isl_take isl_qpolynomial *qp,
1376 enum isl_dim_type type, unsigned pos,
1378 __isl_give isl_pw_qpolynomial *
1379 isl_pw_qpolynomial_set_dim_name(
1380 __isl_take isl_pw_qpolynomial *pwqp,
1381 enum isl_dim_type type, unsigned pos,
1383 __isl_give isl_pw_qpolynomial_fold *
1384 isl_pw_qpolynomial_fold_set_dim_name(
1385 __isl_take isl_pw_qpolynomial_fold *pwf,
1386 enum isl_dim_type type, unsigned pos,
1388 __isl_give isl_union_pw_qpolynomial *
1389 isl_union_pw_qpolynomial_set_dim_name(
1390 __isl_take isl_union_pw_qpolynomial *upwqp,
1391 enum isl_dim_type type, unsigned pos,
1393 __isl_give isl_union_pw_qpolynomial_fold *
1394 isl_union_pw_qpolynomial_fold_set_dim_name(
1395 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1396 enum isl_dim_type type, unsigned pos,
1399 Note that C<isl_space_get_name> returns a pointer to some internal
1400 data structure, so the result can only be used while the
1401 corresponding C<isl_space> is alive.
1402 Also note that every function that operates on two sets or relations
1403 requires that both arguments have the same parameters. This also
1404 means that if one of the arguments has named parameters, then the
1405 other needs to have named parameters too and the names need to match.
1406 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1407 arguments may have different parameters (as long as they are named),
1408 in which case the result will have as parameters the union of the parameters of
1411 Given the identifier or name of a dimension (typically a parameter),
1412 its position can be obtained from the following functions.
1414 #include <isl/space.h>
1415 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1416 enum isl_dim_type type, __isl_keep isl_id *id);
1417 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1418 enum isl_dim_type type, const char *name);
1420 #include <isl/local_space.h>
1421 int isl_local_space_find_dim_by_name(
1422 __isl_keep isl_local_space *ls,
1423 enum isl_dim_type type, const char *name);
1425 #include <isl/val.h>
1426 int isl_multi_val_find_dim_by_id(
1427 __isl_keep isl_multi_val *mv,
1428 enum isl_dim_type type, __isl_keep isl_id *id);
1429 int isl_multi_val_find_dim_by_name(
1430 __isl_keep isl_multi_val *mv,
1431 enum isl_dim_type type, const char *name);
1433 #include <isl/set.h>
1434 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1435 enum isl_dim_type type, __isl_keep isl_id *id);
1436 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1437 enum isl_dim_type type, const char *name);
1439 #include <isl/map.h>
1440 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1441 enum isl_dim_type type, __isl_keep isl_id *id);
1442 int isl_basic_map_find_dim_by_name(
1443 __isl_keep isl_basic_map *bmap,
1444 enum isl_dim_type type, const char *name);
1445 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1446 enum isl_dim_type type, const char *name);
1447 int isl_union_map_find_dim_by_name(
1448 __isl_keep isl_union_map *umap,
1449 enum isl_dim_type type, const char *name);
1451 #include <isl/aff.h>
1452 int isl_multi_aff_find_dim_by_id(
1453 __isl_keep isl_multi_aff *ma,
1454 enum isl_dim_type type, __isl_keep isl_id *id);
1455 int isl_multi_pw_aff_find_dim_by_id(
1456 __isl_keep isl_multi_pw_aff *mpa,
1457 enum isl_dim_type type, __isl_keep isl_id *id);
1458 int isl_multi_union_pw_aff_find_dim_by_id(
1459 __isl_keep isl_union_multi_pw_aff *mupa,
1460 enum isl_dim_type type, __isl_keep isl_id *id);
1461 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff,
1462 enum isl_dim_type type, const char *name);
1463 int isl_multi_aff_find_dim_by_name(
1464 __isl_keep isl_multi_aff *ma,
1465 enum isl_dim_type type, const char *name);
1466 int isl_pw_aff_find_dim_by_name(__isl_keep isl_pw_aff *pa,
1467 enum isl_dim_type type, const char *name);
1468 int isl_multi_pw_aff_find_dim_by_name(
1469 __isl_keep isl_multi_pw_aff *mpa,
1470 enum isl_dim_type type, const char *name);
1471 int isl_pw_multi_aff_find_dim_by_name(
1472 __isl_keep isl_pw_multi_aff *pma,
1473 enum isl_dim_type type, const char *name);
1474 int isl_union_pw_aff_find_dim_by_name(
1475 __isl_keep isl_union_pw_aff *upa,
1476 enum isl_dim_type type, const char *name);
1477 int isl_union_pw_multi_aff_find_dim_by_name(
1478 __isl_keep isl_union_pw_multi_aff *upma,
1479 enum isl_dim_type type, const char *name);
1480 int isl_multi_union_pw_aff_find_dim_by_name(
1481 __isl_keep isl_multi_union_pw_aff *mupa,
1482 enum isl_dim_type type, const char *name);
1484 #include <isl/polynomial.h>
1485 int isl_pw_qpolynomial_find_dim_by_name(
1486 __isl_keep isl_pw_qpolynomial *pwqp,
1487 enum isl_dim_type type, const char *name);
1488 int isl_pw_qpolynomial_fold_find_dim_by_name(
1489 __isl_keep isl_pw_qpolynomial_fold *pwf,
1490 enum isl_dim_type type, const char *name);
1491 int isl_union_pw_qpolynomial_find_dim_by_name(
1492 __isl_keep isl_union_pw_qpolynomial *upwqp,
1493 enum isl_dim_type type, const char *name);
1494 int isl_union_pw_qpolynomial_fold_find_dim_by_name(
1495 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1496 enum isl_dim_type type, const char *name);
1498 The identifiers or names of entire spaces may be set or read off
1499 using the following functions.
1501 #include <isl/space.h>
1502 __isl_give isl_space *isl_space_set_tuple_id(
1503 __isl_take isl_space *space,
1504 enum isl_dim_type type, __isl_take isl_id *id);
1505 __isl_give isl_space *isl_space_reset_tuple_id(
1506 __isl_take isl_space *space, enum isl_dim_type type);
1507 isl_bool isl_space_has_tuple_id(
1508 __isl_keep isl_space *space,
1509 enum isl_dim_type type);
1510 __isl_give isl_id *isl_space_get_tuple_id(
1511 __isl_keep isl_space *space, enum isl_dim_type type);
1512 __isl_give isl_space *isl_space_set_tuple_name(
1513 __isl_take isl_space *space,
1514 enum isl_dim_type type, const char *s);
1515 isl_bool isl_space_has_tuple_name(
1516 __isl_keep isl_space *space,
1517 enum isl_dim_type type);
1518 __isl_keep const char *isl_space_get_tuple_name(
1519 __isl_keep isl_space *space,
1520 enum isl_dim_type type);
1522 #include <isl/local_space.h>
1523 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1524 __isl_take isl_local_space *ls,
1525 enum isl_dim_type type, __isl_take isl_id *id);
1527 #include <isl/set.h>
1528 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1529 __isl_take isl_basic_set *bset,
1530 __isl_take isl_id *id);
1531 __isl_give isl_set *isl_set_set_tuple_id(
1532 __isl_take isl_set *set, __isl_take isl_id *id);
1533 __isl_give isl_set *isl_set_reset_tuple_id(
1534 __isl_take isl_set *set);
1535 isl_bool isl_set_has_tuple_id(__isl_keep isl_set *set);
1536 __isl_give isl_id *isl_set_get_tuple_id(
1537 __isl_keep isl_set *set);
1538 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1539 __isl_take isl_basic_set *set, const char *s);
1540 __isl_give isl_set *isl_set_set_tuple_name(
1541 __isl_take isl_set *set, const char *s);
1542 const char *isl_basic_set_get_tuple_name(
1543 __isl_keep isl_basic_set *bset);
1544 isl_bool isl_set_has_tuple_name(__isl_keep isl_set *set);
1545 const char *isl_set_get_tuple_name(
1546 __isl_keep isl_set *set);
1548 #include <isl/map.h>
1549 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1550 __isl_take isl_basic_map *bmap,
1551 enum isl_dim_type type, __isl_take isl_id *id);
1552 __isl_give isl_map *isl_map_set_tuple_id(
1553 __isl_take isl_map *map, enum isl_dim_type type,
1554 __isl_take isl_id *id);
1555 __isl_give isl_map *isl_map_reset_tuple_id(
1556 __isl_take isl_map *map, enum isl_dim_type type);
1557 isl_bool isl_map_has_tuple_id(__isl_keep isl_map *map,
1558 enum isl_dim_type type);
1559 __isl_give isl_id *isl_map_get_tuple_id(
1560 __isl_keep isl_map *map, enum isl_dim_type type);
1561 __isl_give isl_map *isl_map_set_tuple_name(
1562 __isl_take isl_map *map,
1563 enum isl_dim_type type, const char *s);
1564 const char *isl_basic_map_get_tuple_name(
1565 __isl_keep isl_basic_map *bmap,
1566 enum isl_dim_type type);
1567 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1568 __isl_take isl_basic_map *bmap,
1569 enum isl_dim_type type, const char *s);
1570 isl_bool isl_map_has_tuple_name(__isl_keep isl_map *map,
1571 enum isl_dim_type type);
1572 const char *isl_map_get_tuple_name(
1573 __isl_keep isl_map *map,
1574 enum isl_dim_type type);
1576 #include <isl/val.h>
1577 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1578 __isl_take isl_multi_val *mv,
1579 enum isl_dim_type type, __isl_take isl_id *id);
1580 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1581 __isl_take isl_multi_val *mv,
1582 enum isl_dim_type type);
1583 isl_bool isl_multi_val_has_tuple_id(
1584 __isl_keep isl_multi_val *mv,
1585 enum isl_dim_type type);
1586 __isl_give isl_id *isl_multi_val_get_tuple_id(
1587 __isl_keep isl_multi_val *mv,
1588 enum isl_dim_type type);
1589 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1590 __isl_take isl_multi_val *mv,
1591 enum isl_dim_type type, const char *s);
1592 const char *isl_multi_val_get_tuple_name(
1593 __isl_keep isl_multi_val *mv,
1594 enum isl_dim_type type);
1596 #include <isl/aff.h>
1597 __isl_give isl_aff *isl_aff_set_tuple_id(
1598 __isl_take isl_aff *aff,
1599 enum isl_dim_type type, __isl_take isl_id *id);
1600 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1601 __isl_take isl_multi_aff *maff,
1602 enum isl_dim_type type, __isl_take isl_id *id);
1603 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1604 __isl_take isl_pw_aff *pwaff,
1605 enum isl_dim_type type, __isl_take isl_id *id);
1606 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1607 __isl_take isl_pw_multi_aff *pma,
1608 enum isl_dim_type type, __isl_take isl_id *id);
1609 __isl_give isl_multi_union_pw_aff *
1610 isl_multi_union_pw_aff_set_tuple_id(
1611 __isl_take isl_multi_union_pw_aff *mupa,
1612 enum isl_dim_type type, __isl_take isl_id *id);
1613 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1614 __isl_take isl_multi_aff *ma,
1615 enum isl_dim_type type);
1616 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1617 __isl_take isl_pw_aff *pa,
1618 enum isl_dim_type type);
1619 __isl_give isl_multi_pw_aff *
1620 isl_multi_pw_aff_reset_tuple_id(
1621 __isl_take isl_multi_pw_aff *mpa,
1622 enum isl_dim_type type);
1623 __isl_give isl_pw_multi_aff *
1624 isl_pw_multi_aff_reset_tuple_id(
1625 __isl_take isl_pw_multi_aff *pma,
1626 enum isl_dim_type type);
1627 __isl_give isl_multi_union_pw_aff *
1628 isl_multi_union_pw_aff_reset_tuple_id(
1629 __isl_take isl_multi_union_pw_aff *mupa,
1630 enum isl_dim_type type);
1631 isl_bool isl_multi_aff_has_tuple_id(
1632 __isl_keep isl_multi_aff *ma,
1633 enum isl_dim_type type);
1634 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1635 __isl_keep isl_multi_aff *ma,
1636 enum isl_dim_type type);
1637 isl_bool isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1638 enum isl_dim_type type);
1639 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1640 __isl_keep isl_pw_aff *pa,
1641 enum isl_dim_type type);
1642 isl_bool isl_pw_multi_aff_has_tuple_id(
1643 __isl_keep isl_pw_multi_aff *pma,
1644 enum isl_dim_type type);
1645 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1646 __isl_keep isl_pw_multi_aff *pma,
1647 enum isl_dim_type type);
1648 isl_bool isl_multi_pw_aff_has_tuple_id(
1649 __isl_keep isl_multi_pw_aff *mpa,
1650 enum isl_dim_type type);
1651 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1652 __isl_keep isl_multi_pw_aff *mpa,
1653 enum isl_dim_type type);
1654 isl_bool isl_multi_union_pw_aff_has_tuple_id(
1655 __isl_keep isl_multi_union_pw_aff *mupa,
1656 enum isl_dim_type type);
1657 __isl_give isl_id *isl_multi_union_pw_aff_get_tuple_id(
1658 __isl_keep isl_multi_union_pw_aff *mupa,
1659 enum isl_dim_type type);
1660 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1661 __isl_take isl_multi_aff *maff,
1662 enum isl_dim_type type, const char *s);
1663 __isl_give isl_multi_pw_aff *
1664 isl_multi_pw_aff_set_tuple_name(
1665 __isl_take isl_multi_pw_aff *mpa,
1666 enum isl_dim_type type, const char *s);
1667 __isl_give isl_multi_union_pw_aff *
1668 isl_multi_union_pw_aff_set_tuple_name(
1669 __isl_take isl_multi_union_pw_aff *mupa,
1670 enum isl_dim_type type, const char *s);
1671 const char *isl_multi_aff_get_tuple_name(
1672 __isl_keep isl_multi_aff *multi,
1673 enum isl_dim_type type);
1674 isl_bool isl_pw_multi_aff_has_tuple_name(
1675 __isl_keep isl_pw_multi_aff *pma,
1676 enum isl_dim_type type);
1677 const char *isl_pw_multi_aff_get_tuple_name(
1678 __isl_keep isl_pw_multi_aff *pma,
1679 enum isl_dim_type type);
1680 const char *isl_multi_union_pw_aff_get_tuple_name(
1681 __isl_keep isl_multi_union_pw_aff *mupa,
1682 enum isl_dim_type type);
1684 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1685 or C<isl_dim_set>. As with C<isl_space_get_name>,
1686 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1688 Binary operations require the corresponding spaces of their arguments
1689 to have the same name.
1691 To keep the names of all parameters and tuples, but reset the user pointers
1692 of all the corresponding identifiers, use the following function.
1694 #include <isl/space.h>
1695 __isl_give isl_space *isl_space_reset_user(
1696 __isl_take isl_space *space);
1698 #include <isl/set.h>
1699 __isl_give isl_set *isl_set_reset_user(
1700 __isl_take isl_set *set);
1702 #include <isl/map.h>
1703 __isl_give isl_map *isl_map_reset_user(
1704 __isl_take isl_map *map);
1706 #include <isl/union_set.h>
1707 __isl_give isl_union_set *isl_union_set_reset_user(
1708 __isl_take isl_union_set *uset);
1710 #include <isl/union_map.h>
1711 __isl_give isl_union_map *isl_union_map_reset_user(
1712 __isl_take isl_union_map *umap);
1714 #include <isl/val.h>
1715 __isl_give isl_multi_val *isl_multi_val_reset_user(
1716 __isl_take isl_multi_val *mv);
1718 #include <isl/aff.h>
1719 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1720 __isl_take isl_multi_aff *ma);
1721 __isl_give isl_pw_aff *isl_pw_aff_reset_user(
1722 __isl_take isl_pw_aff *pa);
1723 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1724 __isl_take isl_multi_pw_aff *mpa);
1725 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_reset_user(
1726 __isl_take isl_pw_multi_aff *pma);
1727 __isl_give isl_union_pw_aff *isl_union_pw_aff_reset_user(
1728 __isl_take isl_union_pw_aff *upa);
1729 __isl_give isl_multi_union_pw_aff *
1730 isl_multi_union_pw_aff_reset_user(
1731 __isl_take isl_multi_union_pw_aff *mupa);
1732 __isl_give isl_union_pw_multi_aff *
1733 isl_union_pw_multi_aff_reset_user(
1734 __isl_take isl_union_pw_multi_aff *upma);
1736 #include <isl/polynomial.h>
1737 __isl_give isl_pw_qpolynomial *
1738 isl_pw_qpolynomial_reset_user(
1739 __isl_take isl_pw_qpolynomial *pwqp);
1740 __isl_give isl_union_pw_qpolynomial *
1741 isl_union_pw_qpolynomial_reset_user(
1742 __isl_take isl_union_pw_qpolynomial *upwqp);
1743 __isl_give isl_pw_qpolynomial_fold *
1744 isl_pw_qpolynomial_fold_reset_user(
1745 __isl_take isl_pw_qpolynomial_fold *pwf);
1746 __isl_give isl_union_pw_qpolynomial_fold *
1747 isl_union_pw_qpolynomial_fold_reset_user(
1748 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1750 Spaces can be nested. In particular, the domain of a set or
1751 the domain or range of a relation can be a nested relation.
1752 This process is also called I<wrapping>.
1753 The functions for detecting, constructing and deconstructing
1754 such nested spaces can be found in the wrapping properties
1755 of L</"Unary Properties">, the wrapping operations
1756 of L</"Unary Operations"> and the Cartesian product operations
1757 of L</"Basic Operations">.
1759 Spaces can be created from other spaces
1760 using the functions described in L</"Unary Operations">
1761 and L</"Binary Operations">.
1765 A local space is essentially a space with
1766 zero or more existentially quantified variables.
1767 The local space of various objects can be obtained
1768 using the following functions.
1770 #include <isl/constraint.h>
1771 __isl_give isl_local_space *isl_constraint_get_local_space(
1772 __isl_keep isl_constraint *constraint);
1774 #include <isl/set.h>
1775 __isl_give isl_local_space *isl_basic_set_get_local_space(
1776 __isl_keep isl_basic_set *bset);
1778 #include <isl/map.h>
1779 __isl_give isl_local_space *isl_basic_map_get_local_space(
1780 __isl_keep isl_basic_map *bmap);
1782 #include <isl/aff.h>
1783 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1784 __isl_keep isl_aff *aff);
1785 __isl_give isl_local_space *isl_aff_get_local_space(
1786 __isl_keep isl_aff *aff);
1788 A new local space can be created from a space using
1790 #include <isl/local_space.h>
1791 __isl_give isl_local_space *isl_local_space_from_space(
1792 __isl_take isl_space *space);
1794 They can be inspected, modified, copied and freed using the following functions.
1796 #include <isl/local_space.h>
1797 isl_bool isl_local_space_is_params(
1798 __isl_keep isl_local_space *ls);
1799 isl_bool isl_local_space_is_set(
1800 __isl_keep isl_local_space *ls);
1801 __isl_give isl_space *isl_local_space_get_space(
1802 __isl_keep isl_local_space *ls);
1803 __isl_give isl_aff *isl_local_space_get_div(
1804 __isl_keep isl_local_space *ls, int pos);
1805 __isl_give isl_local_space *isl_local_space_copy(
1806 __isl_keep isl_local_space *ls);
1807 __isl_null isl_local_space *isl_local_space_free(
1808 __isl_take isl_local_space *ls);
1810 Note that C<isl_local_space_get_div> can only be used on local spaces
1813 Two local spaces can be compared using
1815 isl_bool isl_local_space_is_equal(
1816 __isl_keep isl_local_space *ls1,
1817 __isl_keep isl_local_space *ls2);
1819 Local spaces can be created from other local spaces
1820 using the functions described in L</"Unary Operations">
1821 and L</"Binary Operations">.
1823 =head2 Creating New Sets and Relations
1825 C<isl> has functions for creating some standard sets and relations.
1829 =item * Empty sets and relations
1831 __isl_give isl_basic_set *isl_basic_set_empty(
1832 __isl_take isl_space *space);
1833 __isl_give isl_basic_map *isl_basic_map_empty(
1834 __isl_take isl_space *space);
1835 __isl_give isl_set *isl_set_empty(
1836 __isl_take isl_space *space);
1837 __isl_give isl_map *isl_map_empty(
1838 __isl_take isl_space *space);
1839 __isl_give isl_union_set *isl_union_set_empty(
1840 __isl_take isl_space *space);
1841 __isl_give isl_union_map *isl_union_map_empty(
1842 __isl_take isl_space *space);
1844 For C<isl_union_set>s and C<isl_union_map>s, the space
1845 is only used to specify the parameters.
1847 =item * Universe sets and relations
1849 __isl_give isl_basic_set *isl_basic_set_universe(
1850 __isl_take isl_space *space);
1851 __isl_give isl_basic_map *isl_basic_map_universe(
1852 __isl_take isl_space *space);
1853 __isl_give isl_set *isl_set_universe(
1854 __isl_take isl_space *space);
1855 __isl_give isl_map *isl_map_universe(
1856 __isl_take isl_space *space);
1857 __isl_give isl_union_set *isl_union_set_universe(
1858 __isl_take isl_union_set *uset);
1859 __isl_give isl_union_map *isl_union_map_universe(
1860 __isl_take isl_union_map *umap);
1862 The sets and relations constructed by the functions above
1863 contain all integer values, while those constructed by the
1864 functions below only contain non-negative values.
1866 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1867 __isl_take isl_space *space);
1868 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1869 __isl_take isl_space *space);
1870 __isl_give isl_set *isl_set_nat_universe(
1871 __isl_take isl_space *space);
1872 __isl_give isl_map *isl_map_nat_universe(
1873 __isl_take isl_space *space);
1875 =item * Identity relations
1877 __isl_give isl_basic_map *isl_basic_map_identity(
1878 __isl_take isl_space *space);
1879 __isl_give isl_map *isl_map_identity(
1880 __isl_take isl_space *space);
1882 The number of input and output dimensions in C<space> needs
1885 =item * Lexicographic order
1887 __isl_give isl_map *isl_map_lex_lt(
1888 __isl_take isl_space *set_space);
1889 __isl_give isl_map *isl_map_lex_le(
1890 __isl_take isl_space *set_space);
1891 __isl_give isl_map *isl_map_lex_gt(
1892 __isl_take isl_space *set_space);
1893 __isl_give isl_map *isl_map_lex_ge(
1894 __isl_take isl_space *set_space);
1895 __isl_give isl_map *isl_map_lex_lt_first(
1896 __isl_take isl_space *space, unsigned n);
1897 __isl_give isl_map *isl_map_lex_le_first(
1898 __isl_take isl_space *space, unsigned n);
1899 __isl_give isl_map *isl_map_lex_gt_first(
1900 __isl_take isl_space *space, unsigned n);
1901 __isl_give isl_map *isl_map_lex_ge_first(
1902 __isl_take isl_space *space, unsigned n);
1904 The first four functions take a space for a B<set>
1905 and return relations that express that the elements in the domain
1906 are lexicographically less
1907 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1908 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1909 than the elements in the range.
1910 The last four functions take a space for a map
1911 and return relations that express that the first C<n> dimensions
1912 in the domain are lexicographically less
1913 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1914 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1915 than the first C<n> dimensions in the range.
1919 A basic set or relation can be converted to a set or relation
1920 using the following functions.
1922 __isl_give isl_set *isl_set_from_basic_set(
1923 __isl_take isl_basic_set *bset);
1924 __isl_give isl_map *isl_map_from_basic_map(
1925 __isl_take isl_basic_map *bmap);
1927 Sets and relations can be converted to union sets and relations
1928 using the following functions.
1930 __isl_give isl_union_set *isl_union_set_from_basic_set(
1931 __isl_take isl_basic_set *bset);
1932 __isl_give isl_union_map *isl_union_map_from_basic_map(
1933 __isl_take isl_basic_map *bmap);
1934 __isl_give isl_union_set *isl_union_set_from_set(
1935 __isl_take isl_set *set);
1936 __isl_give isl_union_map *isl_union_map_from_map(
1937 __isl_take isl_map *map);
1939 The inverse conversions below can only be used if the input
1940 union set or relation is known to contain elements in exactly one
1943 __isl_give isl_set *isl_set_from_union_set(
1944 __isl_take isl_union_set *uset);
1945 __isl_give isl_map *isl_map_from_union_map(
1946 __isl_take isl_union_map *umap);
1948 Sets and relations can be copied and freed again using the following
1951 __isl_give isl_basic_set *isl_basic_set_copy(
1952 __isl_keep isl_basic_set *bset);
1953 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1954 __isl_give isl_union_set *isl_union_set_copy(
1955 __isl_keep isl_union_set *uset);
1956 __isl_give isl_basic_map *isl_basic_map_copy(
1957 __isl_keep isl_basic_map *bmap);
1958 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1959 __isl_give isl_union_map *isl_union_map_copy(
1960 __isl_keep isl_union_map *umap);
1961 __isl_null isl_basic_set *isl_basic_set_free(
1962 __isl_take isl_basic_set *bset);
1963 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1964 __isl_null isl_union_set *isl_union_set_free(
1965 __isl_take isl_union_set *uset);
1966 __isl_null isl_basic_map *isl_basic_map_free(
1967 __isl_take isl_basic_map *bmap);
1968 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1969 __isl_null isl_union_map *isl_union_map_free(
1970 __isl_take isl_union_map *umap);
1972 Other sets and relations can be constructed by starting
1973 from a universe set or relation, adding equality and/or
1974 inequality constraints and then projecting out the
1975 existentially quantified variables, if any.
1976 Constraints can be constructed, manipulated and
1977 added to (or removed from) (basic) sets and relations
1978 using the following functions.
1980 #include <isl/constraint.h>
1981 __isl_give isl_constraint *isl_constraint_alloc_equality(
1982 __isl_take isl_local_space *ls);
1983 __isl_give isl_constraint *isl_constraint_alloc_inequality(
1984 __isl_take isl_local_space *ls);
1985 __isl_give isl_constraint *isl_constraint_set_constant_si(
1986 __isl_take isl_constraint *constraint, int v);
1987 __isl_give isl_constraint *isl_constraint_set_constant_val(
1988 __isl_take isl_constraint *constraint,
1989 __isl_take isl_val *v);
1990 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1991 __isl_take isl_constraint *constraint,
1992 enum isl_dim_type type, int pos, int v);
1993 __isl_give isl_constraint *
1994 isl_constraint_set_coefficient_val(
1995 __isl_take isl_constraint *constraint,
1996 enum isl_dim_type type, int pos,
1997 __isl_take isl_val *v);
1998 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1999 __isl_take isl_basic_map *bmap,
2000 __isl_take isl_constraint *constraint);
2001 __isl_give isl_basic_set *isl_basic_set_add_constraint(
2002 __isl_take isl_basic_set *bset,
2003 __isl_take isl_constraint *constraint);
2004 __isl_give isl_map *isl_map_add_constraint(
2005 __isl_take isl_map *map,
2006 __isl_take isl_constraint *constraint);
2007 __isl_give isl_set *isl_set_add_constraint(
2008 __isl_take isl_set *set,
2009 __isl_take isl_constraint *constraint);
2011 For example, to create a set containing the even integers
2012 between 10 and 42, you would use the following code.
2015 isl_local_space *ls;
2017 isl_basic_set *bset;
2019 space = isl_space_set_alloc(ctx, 0, 2);
2020 bset = isl_basic_set_universe(isl_space_copy(space));
2021 ls = isl_local_space_from_space(space);
2023 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
2024 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2025 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
2026 bset = isl_basic_set_add_constraint(bset, c);
2028 c = isl_constraint_alloc_inequality(isl_local_space_copy(ls));
2029 c = isl_constraint_set_constant_si(c, -10);
2030 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
2031 bset = isl_basic_set_add_constraint(bset, c);
2033 c = isl_constraint_alloc_inequality(ls);
2034 c = isl_constraint_set_constant_si(c, 42);
2035 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2036 bset = isl_basic_set_add_constraint(bset, c);
2038 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
2042 isl_basic_set *bset;
2043 bset = isl_basic_set_read_from_str(ctx,
2044 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
2046 A basic set or relation can also be constructed from two matrices
2047 describing the equalities and the inequalities.
2049 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
2050 __isl_take isl_space *space,
2051 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2052 enum isl_dim_type c1,
2053 enum isl_dim_type c2, enum isl_dim_type c3,
2054 enum isl_dim_type c4);
2055 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
2056 __isl_take isl_space *space,
2057 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2058 enum isl_dim_type c1,
2059 enum isl_dim_type c2, enum isl_dim_type c3,
2060 enum isl_dim_type c4, enum isl_dim_type c5);
2062 The C<isl_dim_type> arguments indicate the order in which
2063 different kinds of variables appear in the input matrices
2064 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
2065 C<isl_dim_set> and C<isl_dim_div> for sets and
2066 of C<isl_dim_cst>, C<isl_dim_param>,
2067 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
2069 A (basic or union) set or relation can also be constructed from a
2070 (union) (piecewise) (multiple) affine expression
2071 or a list of affine expressions
2072 (See L</"Functions">), provided these affine expressions do not
2075 __isl_give isl_basic_map *isl_basic_map_from_aff(
2076 __isl_take isl_aff *aff);
2077 __isl_give isl_map *isl_map_from_aff(
2078 __isl_take isl_aff *aff);
2079 __isl_give isl_set *isl_set_from_pw_aff(
2080 __isl_take isl_pw_aff *pwaff);
2081 __isl_give isl_map *isl_map_from_pw_aff(
2082 __isl_take isl_pw_aff *pwaff);
2083 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
2084 __isl_take isl_space *domain_space,
2085 __isl_take isl_aff_list *list);
2086 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
2087 __isl_take isl_multi_aff *maff)
2088 __isl_give isl_map *isl_map_from_multi_aff(
2089 __isl_take isl_multi_aff *maff)
2090 __isl_give isl_set *isl_set_from_pw_multi_aff(
2091 __isl_take isl_pw_multi_aff *pma);
2092 __isl_give isl_map *isl_map_from_pw_multi_aff(
2093 __isl_take isl_pw_multi_aff *pma);
2094 __isl_give isl_set *isl_set_from_multi_pw_aff(
2095 __isl_take isl_multi_pw_aff *mpa);
2096 __isl_give isl_map *isl_map_from_multi_pw_aff(
2097 __isl_take isl_multi_pw_aff *mpa);
2098 __isl_give isl_union_map *isl_union_map_from_union_pw_aff(
2099 __isl_take isl_union_pw_aff *upa);
2100 __isl_give isl_union_map *
2101 isl_union_map_from_union_pw_multi_aff(
2102 __isl_take isl_union_pw_multi_aff *upma);
2103 __isl_give isl_union_map *
2104 isl_union_map_from_multi_union_pw_aff(
2105 __isl_take isl_multi_union_pw_aff *mupa);
2107 The C<domain_space> argument describes the domain of the resulting
2108 basic relation. It is required because the C<list> may consist
2109 of zero affine expressions.
2110 The C<mupa> passed to C<isl_union_map_from_multi_union_pw_aff>
2111 is not allowed to be zero-dimensional. The domain of the result
2112 is the shared domain of the union piecewise affine elements.
2114 =head2 Inspecting Sets and Relations
2116 Usually, the user should not have to care about the actual constraints
2117 of the sets and maps, but should instead apply the abstract operations
2118 explained in the following sections.
2119 Occasionally, however, it may be required to inspect the individual
2120 coefficients of the constraints. This section explains how to do so.
2121 In these cases, it may also be useful to have C<isl> compute
2122 an explicit representation of the existentially quantified variables.
2124 __isl_give isl_set *isl_set_compute_divs(
2125 __isl_take isl_set *set);
2126 __isl_give isl_map *isl_map_compute_divs(
2127 __isl_take isl_map *map);
2128 __isl_give isl_union_set *isl_union_set_compute_divs(
2129 __isl_take isl_union_set *uset);
2130 __isl_give isl_union_map *isl_union_map_compute_divs(
2131 __isl_take isl_union_map *umap);
2133 This explicit representation defines the existentially quantified
2134 variables as integer divisions of the other variables, possibly
2135 including earlier existentially quantified variables.
2136 An explicitly represented existentially quantified variable therefore
2137 has a unique value when the values of the other variables are known.
2139 Alternatively, the existentially quantified variables can be removed
2140 using the following functions, which compute an overapproximation.
2142 #include <isl/set.h>
2143 __isl_give isl_basic_set *isl_basic_set_remove_divs(
2144 __isl_take isl_basic_set *bset);
2145 __isl_give isl_set *isl_set_remove_divs(
2146 __isl_take isl_set *set);
2148 #include <isl/map.h>
2149 __isl_give isl_basic_map *isl_basic_map_remove_divs(
2150 __isl_take isl_basic_map *bmap);
2151 __isl_give isl_map *isl_map_remove_divs(
2152 __isl_take isl_map *map);
2154 #include <isl/union_set.h>
2155 __isl_give isl_union_set *isl_union_set_remove_divs(
2156 __isl_take isl_union_set *bset);
2158 #include <isl/union_map.h>
2159 __isl_give isl_union_map *isl_union_map_remove_divs(
2160 __isl_take isl_union_map *bmap);
2162 It is also possible to only remove those divs that are defined
2163 in terms of a given range of dimensions or only those for which
2164 no explicit representation is known.
2166 __isl_give isl_basic_set *
2167 isl_basic_set_remove_divs_involving_dims(
2168 __isl_take isl_basic_set *bset,
2169 enum isl_dim_type type,
2170 unsigned first, unsigned n);
2171 __isl_give isl_basic_map *
2172 isl_basic_map_remove_divs_involving_dims(
2173 __isl_take isl_basic_map *bmap,
2174 enum isl_dim_type type,
2175 unsigned first, unsigned n);
2176 __isl_give isl_set *isl_set_remove_divs_involving_dims(
2177 __isl_take isl_set *set, enum isl_dim_type type,
2178 unsigned first, unsigned n);
2179 __isl_give isl_map *isl_map_remove_divs_involving_dims(
2180 __isl_take isl_map *map, enum isl_dim_type type,
2181 unsigned first, unsigned n);
2183 __isl_give isl_basic_set *
2184 isl_basic_set_remove_unknown_divs(
2185 __isl_take isl_basic_set *bset);
2186 __isl_give isl_set *isl_set_remove_unknown_divs(
2187 __isl_take isl_set *set);
2188 __isl_give isl_map *isl_map_remove_unknown_divs(
2189 __isl_take isl_map *map);
2191 To iterate over all the sets or maps in a union set or map, use
2193 #include <isl/union_set.h>
2194 isl_stat isl_union_set_foreach_set(
2195 __isl_keep isl_union_set *uset,
2196 isl_stat (*fn)(__isl_take isl_set *set, void *user),
2199 #include <isl/union_map.h>
2200 isl_stat isl_union_map_foreach_map(
2201 __isl_keep isl_union_map *umap,
2202 isl_stat (*fn)(__isl_take isl_map *map, void *user),
2204 isl_bool isl_union_map_every_map(
2205 __isl_keep isl_union_map *umap,
2206 isl_bool (*test)(__isl_keep isl_map *map,
2210 These functions call the callback function once for each
2211 (pair of) space(s) for which there are elements in the input.
2212 The argument to the callback contains all elements in the input
2213 with that (pair of) space(s).
2214 The C<isl_union_map_every_map> variant check whether each
2215 call to the callback returns true and stops checking as soon as one
2216 of these calls returns false.
2218 The number of sets or maps in a union set or map can be obtained
2221 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
2222 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
2224 To extract the set or map in a given space from a union, use
2226 __isl_give isl_set *isl_union_set_extract_set(
2227 __isl_keep isl_union_set *uset,
2228 __isl_take isl_space *space);
2229 __isl_give isl_map *isl_union_map_extract_map(
2230 __isl_keep isl_union_map *umap,
2231 __isl_take isl_space *space);
2233 To iterate over all the basic sets or maps in a set or map, use
2235 isl_stat isl_set_foreach_basic_set(__isl_keep isl_set *set,
2236 isl_stat (*fn)(__isl_take isl_basic_set *bset,
2239 isl_stat isl_map_foreach_basic_map(__isl_keep isl_map *map,
2240 isl_stat (*fn)(__isl_take isl_basic_map *bmap,
2244 The callback function C<fn> should return C<isl_stat_ok> if successful and
2245 C<isl_stat_error> if an error occurs. In the latter case, or if any other error
2246 occurs, the above functions will return C<isl_stat_error>.
2248 It should be noted that C<isl> does not guarantee that
2249 the basic sets or maps passed to C<fn> are disjoint.
2250 If this is required, then the user should call one of
2251 the following functions first.
2253 __isl_give isl_set *isl_set_make_disjoint(
2254 __isl_take isl_set *set);
2255 __isl_give isl_map *isl_map_make_disjoint(
2256 __isl_take isl_map *map);
2258 The number of basic sets in a set can be obtained
2259 or the number of basic maps in a map can be obtained
2262 #include <isl/set.h>
2263 int isl_set_n_basic_set(__isl_keep isl_set *set);
2265 #include <isl/map.h>
2266 int isl_map_n_basic_map(__isl_keep isl_map *map);
2268 It is also possible to obtain a list of basic sets from a set
2271 #include <isl/set.h>
2272 __isl_give isl_basic_set_list *isl_set_get_basic_set_list(
2273 __isl_keep isl_set *set);
2275 #include <isl/union_set.h>
2276 __isl_give isl_basic_set_list *
2277 isl_union_set_get_basic_set_list(
2278 __isl_keep isl_union_set *uset);
2280 The returned list can be manipulated using the functions in L<"Lists">.
2282 To iterate over the constraints of a basic set or map, use
2284 #include <isl/constraint.h>
2286 int isl_basic_set_n_constraint(
2287 __isl_keep isl_basic_set *bset);
2288 isl_stat isl_basic_set_foreach_constraint(
2289 __isl_keep isl_basic_set *bset,
2290 isl_stat (*fn)(__isl_take isl_constraint *c,
2293 int isl_basic_map_n_constraint(
2294 __isl_keep isl_basic_map *bmap);
2295 isl_stat isl_basic_map_foreach_constraint(
2296 __isl_keep isl_basic_map *bmap,
2297 isl_stat (*fn)(__isl_take isl_constraint *c,
2300 __isl_null isl_constraint *isl_constraint_free(
2301 __isl_take isl_constraint *c);
2303 Again, the callback function C<fn> should return C<isl_stat_ok>
2305 C<isl_stat_error> if an error occurs. In the latter case, or if any other error
2306 occurs, the above functions will return C<isl_stat_error>.
2307 The constraint C<c> represents either an equality or an inequality.
2308 Use the following function to find out whether a constraint
2309 represents an equality. If not, it represents an inequality.
2311 isl_bool isl_constraint_is_equality(
2312 __isl_keep isl_constraint *constraint);
2314 It is also possible to obtain a list of constraints from a basic
2317 #include <isl/constraint.h>
2318 __isl_give isl_constraint_list *
2319 isl_basic_map_get_constraint_list(
2320 __isl_keep isl_basic_map *bmap);
2321 __isl_give isl_constraint_list *
2322 isl_basic_set_get_constraint_list(
2323 __isl_keep isl_basic_set *bset);
2325 These functions require that all existentially quantified variables
2326 have an explicit representation.
2327 The returned list can be manipulated using the functions in L<"Lists">.
2329 The coefficients of the constraints can be inspected using
2330 the following functions.
2332 isl_bool isl_constraint_is_lower_bound(
2333 __isl_keep isl_constraint *constraint,
2334 enum isl_dim_type type, unsigned pos);
2335 isl_bool isl_constraint_is_upper_bound(
2336 __isl_keep isl_constraint *constraint,
2337 enum isl_dim_type type, unsigned pos);
2338 __isl_give isl_val *isl_constraint_get_constant_val(
2339 __isl_keep isl_constraint *constraint);
2340 __isl_give isl_val *isl_constraint_get_coefficient_val(
2341 __isl_keep isl_constraint *constraint,
2342 enum isl_dim_type type, int pos);
2344 The explicit representations of the existentially quantified
2345 variables can be inspected using the following function.
2346 Note that the user is only allowed to use this function
2347 if the inspected set or map is the result of a call
2348 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2349 The existentially quantified variable is equal to the floor
2350 of the returned affine expression. The affine expression
2351 itself can be inspected using the functions in
2354 __isl_give isl_aff *isl_constraint_get_div(
2355 __isl_keep isl_constraint *constraint, int pos);
2357 To obtain the constraints of a basic set or map in matrix
2358 form, use the following functions.
2360 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2361 __isl_keep isl_basic_set *bset,
2362 enum isl_dim_type c1, enum isl_dim_type c2,
2363 enum isl_dim_type c3, enum isl_dim_type c4);
2364 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2365 __isl_keep isl_basic_set *bset,
2366 enum isl_dim_type c1, enum isl_dim_type c2,
2367 enum isl_dim_type c3, enum isl_dim_type c4);
2368 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2369 __isl_keep isl_basic_map *bmap,
2370 enum isl_dim_type c1,
2371 enum isl_dim_type c2, enum isl_dim_type c3,
2372 enum isl_dim_type c4, enum isl_dim_type c5);
2373 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2374 __isl_keep isl_basic_map *bmap,
2375 enum isl_dim_type c1,
2376 enum isl_dim_type c2, enum isl_dim_type c3,
2377 enum isl_dim_type c4, enum isl_dim_type c5);
2379 The C<isl_dim_type> arguments dictate the order in which
2380 different kinds of variables appear in the resulting matrix.
2381 For set inputs, they should be a permutation of
2382 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
2383 For map inputs, they should be a permutation of
2384 C<isl_dim_cst>, C<isl_dim_param>,
2385 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2389 Points are elements of a set. They can be used to construct
2390 simple sets (boxes) or they can be used to represent the
2391 individual elements of a set.
2392 The zero point (the origin) can be created using
2394 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2396 The coordinates of a point can be inspected, set and changed
2399 __isl_give isl_val *isl_point_get_coordinate_val(
2400 __isl_keep isl_point *pnt,
2401 enum isl_dim_type type, int pos);
2402 __isl_give isl_point *isl_point_set_coordinate_val(
2403 __isl_take isl_point *pnt,
2404 enum isl_dim_type type, int pos,
2405 __isl_take isl_val *v);
2407 __isl_give isl_point *isl_point_add_ui(
2408 __isl_take isl_point *pnt,
2409 enum isl_dim_type type, int pos, unsigned val);
2410 __isl_give isl_point *isl_point_sub_ui(
2411 __isl_take isl_point *pnt,
2412 enum isl_dim_type type, int pos, unsigned val);
2414 Points can be copied or freed using
2416 __isl_give isl_point *isl_point_copy(
2417 __isl_keep isl_point *pnt);
2418 __isl_null isl_point *isl_point_free(
2419 __isl_take isl_point *pnt);
2421 A singleton set can be created from a point using
2423 __isl_give isl_basic_set *isl_basic_set_from_point(
2424 __isl_take isl_point *pnt);
2425 __isl_give isl_set *isl_set_from_point(
2426 __isl_take isl_point *pnt);
2427 __isl_give isl_union_set *isl_union_set_from_point(
2428 __isl_take isl_point *pnt);
2430 and a box can be created from two opposite extremal points using
2432 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2433 __isl_take isl_point *pnt1,
2434 __isl_take isl_point *pnt2);
2435 __isl_give isl_set *isl_set_box_from_points(
2436 __isl_take isl_point *pnt1,
2437 __isl_take isl_point *pnt2);
2439 All elements of a B<bounded> (union) set can be enumerated using
2440 the following functions.
2442 isl_stat isl_set_foreach_point(__isl_keep isl_set *set,
2443 isl_stat (*fn)(__isl_take isl_point *pnt,
2446 isl_stat isl_union_set_foreach_point(
2447 __isl_keep isl_union_set *uset,
2448 isl_stat (*fn)(__isl_take isl_point *pnt,
2452 The function C<fn> is called for each integer point in
2453 C<set> with as second argument the last argument of
2454 the C<isl_set_foreach_point> call. The function C<fn>
2455 should return C<isl_stat_ok> on success and C<isl_stat_error> on failure.
2456 In the latter case, C<isl_set_foreach_point> will stop
2457 enumerating and return C<isl_stat_error> as well.
2458 If the enumeration is performed successfully and to completion,
2459 then C<isl_set_foreach_point> returns C<isl_stat_ok>.
2461 To obtain a single point of a (basic or union) set, use
2463 __isl_give isl_point *isl_basic_set_sample_point(
2464 __isl_take isl_basic_set *bset);
2465 __isl_give isl_point *isl_set_sample_point(
2466 __isl_take isl_set *set);
2467 __isl_give isl_point *isl_union_set_sample_point(
2468 __isl_take isl_union_set *uset);
2470 If C<set> does not contain any (integer) points, then the
2471 resulting point will be ``void'', a property that can be
2474 isl_bool isl_point_is_void(__isl_keep isl_point *pnt);
2478 Besides sets and relation, C<isl> also supports various types of functions.
2479 Each of these types is derived from the value type (see L</"Values">)
2480 or from one of two primitive function types
2481 through the application of zero or more type constructors.
2482 We first describe the primitive type and then we describe
2483 the types derived from these primitive types.
2485 =head3 Primitive Functions
2487 C<isl> support two primitive function types, quasi-affine
2488 expressions and quasipolynomials.
2489 A quasi-affine expression is defined either over a parameter
2490 space or over a set and is composed of integer constants,
2491 parameters and set variables, addition, subtraction and
2492 integer division by an integer constant.
2493 For example, the quasi-affine expression
2495 [n] -> { [x] -> [2*floor((4 n + x)/9)] }
2497 maps C<x> to C<2*floor((4 n + x)/9>.
2498 A quasipolynomial is a polynomial expression in quasi-affine
2499 expression. That is, it additionally allows for multiplication.
2500 Note, though, that it is not allowed to construct an integer
2501 division of an expression involving multiplications.
2502 Here is an example of a quasipolynomial that is not
2503 quasi-affine expression
2505 [n] -> { [x] -> (n*floor((4 n + x)/9)) }
2507 Note that the external representations of quasi-affine expressions
2508 and quasipolynomials are different. Quasi-affine expressions
2509 use a notation with square brackets just like binary relations,
2510 while quasipolynomials do not. This might change at some point.
2512 If a primitive function is defined over a parameter space,
2513 then the space of the function itself is that of a set.
2514 If it is defined over a set, then the space of the function
2515 is that of a relation. In both cases, the set space (or
2516 the output space) is single-dimensional, anonymous and unstructured.
2517 To create functions with multiple dimensions or with other kinds
2518 of set or output spaces, use multiple expressions
2519 (see L</"Multiple Expressions">).
2523 =item * Quasi-affine Expressions
2525 Besides the expressions described above, a quasi-affine
2526 expression can also be set to NaN. Such expressions
2527 typically represent a failure to represent a result
2528 as a quasi-affine expression.
2530 The zero quasi affine expression or the quasi affine expression
2531 that is equal to a given value, parameter or
2532 a specified dimension on a given domain can be created using
2534 #include <isl/aff.h>
2535 __isl_give isl_aff *isl_aff_zero_on_domain(
2536 __isl_take isl_local_space *ls);
2537 __isl_give isl_aff *isl_aff_val_on_domain(
2538 __isl_take isl_local_space *ls,
2539 __isl_take isl_val *val);
2540 __isl_give isl_aff *isl_aff_param_on_domain_space_id(
2541 __isl_take isl_space *space,
2542 __isl_take isl_id *id);
2543 __isl_give isl_aff *isl_aff_var_on_domain(
2544 __isl_take isl_local_space *ls,
2545 enum isl_dim_type type, unsigned pos);
2546 __isl_give isl_aff *isl_aff_nan_on_domain(
2547 __isl_take isl_local_space *ls);
2549 The space passed to C<isl_aff_param_on_domain_space_id>
2550 is required to have a parameter with the given identifier.
2552 Quasi affine expressions can be copied and freed using
2554 #include <isl/aff.h>
2555 __isl_give isl_aff *isl_aff_copy(
2556 __isl_keep isl_aff *aff);
2557 __isl_null isl_aff *isl_aff_free(
2558 __isl_take isl_aff *aff);
2560 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2561 using the following function. The constraint is required to have
2562 a non-zero coefficient for the specified dimension.
2564 #include <isl/constraint.h>
2565 __isl_give isl_aff *isl_constraint_get_bound(
2566 __isl_keep isl_constraint *constraint,
2567 enum isl_dim_type type, int pos);
2569 The entire affine expression of the constraint can also be extracted
2570 using the following function.
2572 #include <isl/constraint.h>
2573 __isl_give isl_aff *isl_constraint_get_aff(
2574 __isl_keep isl_constraint *constraint);
2576 Conversely, an equality constraint equating
2577 the affine expression to zero or an inequality constraint enforcing
2578 the affine expression to be non-negative, can be constructed using
2580 __isl_give isl_constraint *isl_equality_from_aff(
2581 __isl_take isl_aff *aff);
2582 __isl_give isl_constraint *isl_inequality_from_aff(
2583 __isl_take isl_aff *aff);
2585 The coefficients and the integer divisions of an affine expression
2586 can be inspected using the following functions.
2588 #include <isl/aff.h>
2589 __isl_give isl_val *isl_aff_get_constant_val(
2590 __isl_keep isl_aff *aff);
2591 __isl_give isl_val *isl_aff_get_coefficient_val(
2592 __isl_keep isl_aff *aff,
2593 enum isl_dim_type type, int pos);
2594 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2595 enum isl_dim_type type, int pos);
2596 __isl_give isl_val *isl_aff_get_denominator_val(
2597 __isl_keep isl_aff *aff);
2598 __isl_give isl_aff *isl_aff_get_div(
2599 __isl_keep isl_aff *aff, int pos);
2601 They can be modified using the following functions.
2603 #include <isl/aff.h>
2604 __isl_give isl_aff *isl_aff_set_constant_si(
2605 __isl_take isl_aff *aff, int v);
2606 __isl_give isl_aff *isl_aff_set_constant_val(
2607 __isl_take isl_aff *aff, __isl_take isl_val *v);
2608 __isl_give isl_aff *isl_aff_set_coefficient_si(
2609 __isl_take isl_aff *aff,
2610 enum isl_dim_type type, int pos, int v);
2611 __isl_give isl_aff *isl_aff_set_coefficient_val(
2612 __isl_take isl_aff *aff,
2613 enum isl_dim_type type, int pos,
2614 __isl_take isl_val *v);
2616 __isl_give isl_aff *isl_aff_add_constant_si(
2617 __isl_take isl_aff *aff, int v);
2618 __isl_give isl_aff *isl_aff_add_constant_val(
2619 __isl_take isl_aff *aff, __isl_take isl_val *v);
2620 __isl_give isl_aff *isl_aff_add_constant_num_si(
2621 __isl_take isl_aff *aff, int v);
2622 __isl_give isl_aff *isl_aff_add_coefficient_si(
2623 __isl_take isl_aff *aff,
2624 enum isl_dim_type type, int pos, int v);
2625 __isl_give isl_aff *isl_aff_add_coefficient_val(
2626 __isl_take isl_aff *aff,
2627 enum isl_dim_type type, int pos,
2628 __isl_take isl_val *v);
2630 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
2631 set the I<numerator> of the constant or coefficient, while
2632 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
2633 the constant or coefficient as a whole.
2634 The C<add_constant> and C<add_coefficient> functions add an integer
2635 or rational value to
2636 the possibly rational constant or coefficient.
2637 The C<add_constant_num> functions add an integer value to
2640 =item * Quasipolynomials
2642 Some simple quasipolynomials can be created using the following functions.
2644 #include <isl/polynomial.h>
2645 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2646 __isl_take isl_space *domain);
2647 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2648 __isl_take isl_space *domain);
2649 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2650 __isl_take isl_space *domain);
2651 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2652 __isl_take isl_space *domain);
2653 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2654 __isl_take isl_space *domain);
2655 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2656 __isl_take isl_space *domain,
2657 __isl_take isl_val *val);
2658 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2659 __isl_take isl_space *domain,
2660 enum isl_dim_type type, unsigned pos);
2661 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2662 __isl_take isl_aff *aff);
2664 Recall that the space in which a quasipolynomial lives is a map space
2665 with a one-dimensional range. The C<domain> argument in some of
2666 the functions above corresponds to the domain of this map space.
2668 Quasipolynomials can be copied and freed again using the following
2671 #include <isl/polynomial.h>
2672 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2673 __isl_keep isl_qpolynomial *qp);
2674 __isl_null isl_qpolynomial *isl_qpolynomial_free(
2675 __isl_take isl_qpolynomial *qp);
2677 The constant term of a quasipolynomial can be extracted using
2679 __isl_give isl_val *isl_qpolynomial_get_constant_val(
2680 __isl_keep isl_qpolynomial *qp);
2682 To iterate over all terms in a quasipolynomial,
2685 isl_stat isl_qpolynomial_foreach_term(
2686 __isl_keep isl_qpolynomial *qp,
2687 isl_stat (*fn)(__isl_take isl_term *term,
2688 void *user), void *user);
2690 The terms themselves can be inspected and freed using
2693 unsigned isl_term_dim(__isl_keep isl_term *term,
2694 enum isl_dim_type type);
2695 __isl_give isl_val *isl_term_get_coefficient_val(
2696 __isl_keep isl_term *term);
2697 int isl_term_get_exp(__isl_keep isl_term *term,
2698 enum isl_dim_type type, unsigned pos);
2699 __isl_give isl_aff *isl_term_get_div(
2700 __isl_keep isl_term *term, unsigned pos);
2701 void isl_term_free(__isl_take isl_term *term);
2703 Each term is a product of parameters, set variables and
2704 integer divisions. The function C<isl_term_get_exp>
2705 returns the exponent of a given dimensions in the given term.
2711 A reduction represents a maximum or a minimum of its
2713 The only reduction type defined by C<isl> is
2714 C<isl_qpolynomial_fold>.
2716 There are currently no functions to directly create such
2717 objects, but they do appear in the piecewise quasipolynomial
2718 reductions returned by the C<isl_pw_qpolynomial_bound> function.
2720 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
2722 Reductions can be copied and freed using
2723 the following functions.
2725 #include <isl/polynomial.h>
2726 __isl_give isl_qpolynomial_fold *
2727 isl_qpolynomial_fold_copy(
2728 __isl_keep isl_qpolynomial_fold *fold);
2729 void isl_qpolynomial_fold_free(
2730 __isl_take isl_qpolynomial_fold *fold);
2732 To iterate over all quasipolynomials in a reduction, use
2734 isl_stat isl_qpolynomial_fold_foreach_qpolynomial(
2735 __isl_keep isl_qpolynomial_fold *fold,
2736 isl_stat (*fn)(__isl_take isl_qpolynomial *qp,
2737 void *user), void *user);
2739 =head3 Multiple Expressions
2741 A multiple expression represents a sequence of zero or
2742 more base expressions, all defined on the same domain space.
2743 The domain space of the multiple expression is the same
2744 as that of the base expressions, but the range space
2745 can be any space. In case the base expressions have
2746 a set space, the corresponding multiple expression
2747 also has a set space.
2748 Objects of the value type do not have an associated space.
2749 The space of a multiple value is therefore always a set space.
2750 Similarly, the space of a multiple union piecewise
2751 affine expression is always a set space.
2753 The multiple expression types defined by C<isl>
2754 are C<isl_multi_val>, C<isl_multi_aff>, C<isl_multi_pw_aff>,
2755 C<isl_multi_union_pw_aff>.
2757 A multiple expression with the value zero for
2758 each output (or set) dimension can be created
2759 using the following functions.
2761 #include <isl/val.h>
2762 __isl_give isl_multi_val *isl_multi_val_zero(
2763 __isl_take isl_space *space);
2765 #include <isl/aff.h>
2766 __isl_give isl_multi_aff *isl_multi_aff_zero(
2767 __isl_take isl_space *space);
2768 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
2769 __isl_take isl_space *space);
2770 __isl_give isl_multi_union_pw_aff *
2771 isl_multi_union_pw_aff_zero(
2772 __isl_take isl_space *space);
2774 Since there is no canonical way of representing a zero
2775 value of type C<isl_union_pw_aff>, the space passed
2776 to C<isl_multi_union_pw_aff_zero> needs to be zero-dimensional.
2778 An identity function can be created using the following
2779 functions. The space needs to be that of a relation
2780 with the same number of input and output dimensions.
2782 #include <isl/aff.h>
2783 __isl_give isl_multi_aff *isl_multi_aff_identity(
2784 __isl_take isl_space *space);
2785 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
2786 __isl_take isl_space *space);
2788 A function that performs a projection on a universe
2789 relation or set can be created using the following functions.
2790 See also the corresponding
2791 projection operations in L</"Unary Operations">.
2793 #include <isl/aff.h>
2794 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
2795 __isl_take isl_space *space);
2796 __isl_give isl_multi_aff *isl_multi_aff_range_map(
2797 __isl_take isl_space *space);
2798 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
2799 __isl_take isl_space *space,
2800 enum isl_dim_type type,
2801 unsigned first, unsigned n);
2803 A multiple expression can be created from a single
2804 base expression using the following functions.
2805 The space of the created multiple expression is the same
2806 as that of the base expression, except for
2807 C<isl_multi_union_pw_aff_from_union_pw_aff> where the input
2808 lives in a parameter space and the output lives
2809 in a single-dimensional set space.
2811 #include <isl/aff.h>
2812 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
2813 __isl_take isl_aff *aff);
2814 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
2815 __isl_take isl_pw_aff *pa);
2816 __isl_give isl_multi_union_pw_aff *
2817 isl_multi_union_pw_aff_from_union_pw_aff(
2818 __isl_take isl_union_pw_aff *upa);
2820 A multiple expression can be created from a list
2821 of base expression in a specified space.
2822 The domain of this space needs to be the same
2823 as the domains of the base expressions in the list.
2824 If the base expressions have a set space (or no associated space),
2825 then this space also needs to be a set space.
2827 #include <isl/val.h>
2828 __isl_give isl_multi_val *isl_multi_val_from_val_list(
2829 __isl_take isl_space *space,
2830 __isl_take isl_val_list *list);
2832 #include <isl/aff.h>
2833 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2834 __isl_take isl_space *space,
2835 __isl_take isl_aff_list *list);
2836 __isl_give isl_multi_pw_aff *
2837 isl_multi_pw_aff_from_pw_aff_list(
2838 __isl_take isl_space *space,
2839 __isl_take isl_pw_aff_list *list);
2840 __isl_give isl_multi_union_pw_aff *
2841 isl_multi_union_pw_aff_from_union_pw_aff_list(
2842 __isl_take isl_space *space,
2843 __isl_take isl_union_pw_aff_list *list);
2845 As a convenience, a multiple piecewise expression can
2846 also be created from a multiple expression.
2847 Each piecewise expression in the result has a single
2850 #include <isl/aff.h>
2851 __isl_give isl_multi_pw_aff *
2852 isl_multi_pw_aff_from_multi_aff(
2853 __isl_take isl_multi_aff *ma);
2855 Similarly, a multiple union expression can be
2856 created from a multiple expression.
2858 #include <isl/aff.h>
2859 __isl_give isl_multi_union_pw_aff *
2860 isl_multi_union_pw_aff_from_multi_aff(
2861 __isl_take isl_multi_aff *ma);
2862 __isl_give isl_multi_union_pw_aff *
2863 isl_multi_union_pw_aff_from_multi_pw_aff(
2864 __isl_take isl_multi_pw_aff *mpa);
2866 A multiple quasi-affine expression can be created from
2867 a multiple value with a given domain space using the following
2870 #include <isl/aff.h>
2871 __isl_give isl_multi_aff *
2872 isl_multi_aff_multi_val_on_space(
2873 __isl_take isl_space *space,
2874 __isl_take isl_multi_val *mv);
2877 a multiple union piecewise affine expression can be created from
2878 a multiple value with a given domain or
2879 a (piecewise) multiple affine expression with a given domain
2880 using the following functions.
2882 #include <isl/aff.h>
2883 __isl_give isl_multi_union_pw_aff *
2884 isl_multi_union_pw_aff_multi_val_on_domain(
2885 __isl_take isl_union_set *domain,
2886 __isl_take isl_multi_val *mv);
2887 __isl_give isl_multi_union_pw_aff *
2888 isl_multi_union_pw_aff_multi_aff_on_domain(
2889 __isl_take isl_union_set *domain,
2890 __isl_take isl_multi_aff *ma);
2891 __isl_give isl_multi_union_pw_aff *
2892 isl_multi_union_pw_aff_pw_multi_aff_on_domain(
2893 __isl_take isl_union_set *domain,
2894 __isl_take isl_pw_multi_aff *pma);
2896 Multiple expressions can be copied and freed using
2897 the following functions.
2899 #include <isl/val.h>
2900 __isl_give isl_multi_val *isl_multi_val_copy(
2901 __isl_keep isl_multi_val *mv);
2902 __isl_null isl_multi_val *isl_multi_val_free(
2903 __isl_take isl_multi_val *mv);
2905 #include <isl/aff.h>
2906 __isl_give isl_multi_aff *isl_multi_aff_copy(
2907 __isl_keep isl_multi_aff *maff);
2908 __isl_null isl_multi_aff *isl_multi_aff_free(
2909 __isl_take isl_multi_aff *maff);
2910 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
2911 __isl_keep isl_multi_pw_aff *mpa);
2912 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
2913 __isl_take isl_multi_pw_aff *mpa);
2914 __isl_give isl_multi_union_pw_aff *
2915 isl_multi_union_pw_aff_copy(
2916 __isl_keep isl_multi_union_pw_aff *mupa);
2917 __isl_null isl_multi_union_pw_aff *
2918 isl_multi_union_pw_aff_free(
2919 __isl_take isl_multi_union_pw_aff *mupa);
2921 The base expression at a given position of a multiple
2922 expression can be extracted using the following functions.
2924 #include <isl/val.h>
2925 __isl_give isl_val *isl_multi_val_get_val(
2926 __isl_keep isl_multi_val *mv, int pos);
2928 #include <isl/aff.h>
2929 __isl_give isl_aff *isl_multi_aff_get_aff(
2930 __isl_keep isl_multi_aff *multi, int pos);
2931 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
2932 __isl_keep isl_multi_pw_aff *mpa, int pos);
2933 __isl_give isl_union_pw_aff *
2934 isl_multi_union_pw_aff_get_union_pw_aff(
2935 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
2937 It can be replaced using the following functions.
2939 #include <isl/val.h>
2940 __isl_give isl_multi_val *isl_multi_val_set_val(
2941 __isl_take isl_multi_val *mv, int pos,
2942 __isl_take isl_val *val);
2944 #include <isl/aff.h>
2945 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
2946 __isl_take isl_multi_aff *multi, int pos,
2947 __isl_take isl_aff *aff);
2948 __isl_give isl_multi_union_pw_aff *
2949 isl_multi_union_pw_aff_set_union_pw_aff(
2950 __isl_take isl_multi_union_pw_aff *mupa, int pos,
2951 __isl_take isl_union_pw_aff *upa);
2953 As a convenience, a sequence of base expressions that have
2954 their domains in a given space can be extracted from a sequence
2955 of union expressions using the following function.
2957 #include <isl/aff.h>
2958 __isl_give isl_multi_pw_aff *
2959 isl_multi_union_pw_aff_extract_multi_pw_aff(
2960 __isl_keep isl_multi_union_pw_aff *mupa,
2961 __isl_take isl_space *space);
2963 Note that there is a difference between C<isl_multi_union_pw_aff>
2964 and C<isl_union_pw_multi_aff> objects. The first is a sequence
2965 of unions of piecewise expressions, while the second is a union
2966 of piecewise sequences. In particular, multiple affine expressions
2967 in an C<isl_union_pw_multi_aff> may live in different spaces,
2968 while there is only a single multiple expression in
2969 an C<isl_multi_union_pw_aff>, which can therefore only live
2970 in a single space. This means that not every
2971 C<isl_union_pw_multi_aff> can be converted to
2972 an C<isl_multi_union_pw_aff>. Conversely, a zero-dimensional
2973 C<isl_multi_union_pw_aff> carries no information
2974 about any possible domain and therefore cannot be converted
2975 to an C<isl_union_pw_multi_aff>. Moreover, the elements
2976 of an C<isl_multi_union_pw_aff> may be defined over different domains,
2977 while each multiple expression inside an C<isl_union_pw_multi_aff>
2978 has a single domain. The conversion of an C<isl_union_pw_multi_aff>
2979 of dimension greater than one may therefore not be exact.
2980 The following functions can
2981 be used to perform these conversions when they are possible.
2983 #include <isl/aff.h>
2984 __isl_give isl_multi_union_pw_aff *
2985 isl_multi_union_pw_aff_from_union_pw_multi_aff(
2986 __isl_take isl_union_pw_multi_aff *upma);
2987 __isl_give isl_union_pw_multi_aff *
2988 isl_union_pw_multi_aff_from_multi_union_pw_aff(
2989 __isl_take isl_multi_union_pw_aff *mupa);
2991 =head3 Piecewise Expressions
2993 A piecewise expression is an expression that is described
2994 using zero or more base expression defined over the same
2995 number of cells in the domain space of the base expressions.
2996 All base expressions are defined over the same
2997 domain space and the cells are disjoint.
2998 The space of a piecewise expression is the same as
2999 that of the base expressions.
3000 If the union of the cells is a strict subset of the domain
3001 space, then the value of the piecewise expression outside
3002 this union is different for types derived from quasi-affine
3003 expressions and those derived from quasipolynomials.
3004 Piecewise expressions derived from quasi-affine expressions
3005 are considered to be undefined outside the union of their cells.
3006 Piecewise expressions derived from quasipolynomials
3007 are considered to be zero outside the union of their cells.
3009 Piecewise quasipolynomials are mainly used by the C<barvinok>
3010 library for representing the number of elements in a parametric set or map.
3011 For example, the piecewise quasipolynomial
3013 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3015 represents the number of points in the map
3017 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3019 The piecewise expression types defined by C<isl>
3020 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
3021 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
3023 A piecewise expression with no cells can be created using
3024 the following functions.
3026 #include <isl/aff.h>
3027 __isl_give isl_pw_aff *isl_pw_aff_empty(
3028 __isl_take isl_space *space);
3029 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3030 __isl_take isl_space *space);
3032 A piecewise expression with a single universe cell can be
3033 created using the following functions.
3035 #include <isl/aff.h>
3036 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3037 __isl_take isl_aff *aff);
3038 __isl_give isl_pw_multi_aff *
3039 isl_pw_multi_aff_from_multi_aff(
3040 __isl_take isl_multi_aff *ma);
3042 #include <isl/polynomial.h>
3043 __isl_give isl_pw_qpolynomial *
3044 isl_pw_qpolynomial_from_qpolynomial(
3045 __isl_take isl_qpolynomial *qp);
3047 A piecewise expression with a single specified cell can be
3048 created using the following functions.
3050 #include <isl/aff.h>
3051 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3052 __isl_take isl_set *set, __isl_take isl_aff *aff);
3053 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3054 __isl_take isl_set *set,
3055 __isl_take isl_multi_aff *maff);
3057 #include <isl/polynomial.h>
3058 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3059 __isl_take isl_set *set,
3060 __isl_take isl_qpolynomial *qp);
3062 The following convenience functions first create a base expression and
3063 then create a piecewise expression over a universe domain.
3065 #include <isl/aff.h>
3066 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3067 __isl_take isl_local_space *ls);
3068 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3069 __isl_take isl_local_space *ls,
3070 enum isl_dim_type type, unsigned pos);
3071 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3072 __isl_take isl_local_space *ls);
3073 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
3074 __isl_take isl_space *space);
3075 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3076 __isl_take isl_space *space);
3077 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
3078 __isl_take isl_space *space);
3079 __isl_give isl_pw_multi_aff *
3080 isl_pw_multi_aff_project_out_map(
3081 __isl_take isl_space *space,
3082 enum isl_dim_type type,
3083 unsigned first, unsigned n);
3085 #include <isl/polynomial.h>
3086 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3087 __isl_take isl_space *space);
3089 The following convenience functions first create a base expression and
3090 then create a piecewise expression over a given domain.
3092 #include <isl/aff.h>
3093 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
3094 __isl_take isl_set *domain,
3095 __isl_take isl_val *v);
3096 __isl_give isl_pw_multi_aff *
3097 isl_pw_multi_aff_multi_val_on_domain(
3098 __isl_take isl_set *domain,
3099 __isl_take isl_multi_val *mv);
3101 As a convenience, a piecewise multiple expression can
3102 also be created from a piecewise expression.
3103 Each multiple expression in the result is derived
3104 from the corresponding base expression.
3106 #include <isl/aff.h>
3107 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
3108 __isl_take isl_pw_aff *pa);
3110 Similarly, a piecewise quasipolynomial can be
3111 created from a piecewise quasi-affine expression using
3112 the following function.
3114 #include <isl/polynomial.h>
3115 __isl_give isl_pw_qpolynomial *
3116 isl_pw_qpolynomial_from_pw_aff(
3117 __isl_take isl_pw_aff *pwaff);
3119 Piecewise expressions can be copied and freed using the following functions.
3121 #include <isl/aff.h>
3122 __isl_give isl_pw_aff *isl_pw_aff_copy(
3123 __isl_keep isl_pw_aff *pwaff);
3124 __isl_null isl_pw_aff *isl_pw_aff_free(
3125 __isl_take isl_pw_aff *pwaff);
3126 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3127 __isl_keep isl_pw_multi_aff *pma);
3128 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
3129 __isl_take isl_pw_multi_aff *pma);
3131 #include <isl/polynomial.h>
3132 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3133 __isl_keep isl_pw_qpolynomial *pwqp);
3134 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
3135 __isl_take isl_pw_qpolynomial *pwqp);
3136 __isl_give isl_pw_qpolynomial_fold *
3137 isl_pw_qpolynomial_fold_copy(
3138 __isl_keep isl_pw_qpolynomial_fold *pwf);
3139 __isl_null isl_pw_qpolynomial_fold *
3140 isl_pw_qpolynomial_fold_free(
3141 __isl_take isl_pw_qpolynomial_fold *pwf);
3143 To iterate over the different cells of a piecewise expression,
3144 use the following functions.
3146 #include <isl/aff.h>
3147 isl_bool isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3148 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3149 isl_stat isl_pw_aff_foreach_piece(
3150 __isl_keep isl_pw_aff *pwaff,
3151 isl_stat (*fn)(__isl_take isl_set *set,
3152 __isl_take isl_aff *aff,
3153 void *user), void *user);
3154 int isl_pw_multi_aff_n_piece(
3155 __isl_keep isl_pw_multi_aff *pma);
3156 isl_stat isl_pw_multi_aff_foreach_piece(
3157 __isl_keep isl_pw_multi_aff *pma,
3158 isl_stat (*fn)(__isl_take isl_set *set,
3159 __isl_take isl_multi_aff *maff,
3160 void *user), void *user);
3162 #include <isl/polynomial.h>
3163 int isl_pw_qpolynomial_n_piece(
3164 __isl_keep isl_pw_qpolynomial *pwqp);
3165 isl_stat isl_pw_qpolynomial_foreach_piece(
3166 __isl_keep isl_pw_qpolynomial *pwqp,
3167 isl_stat (*fn)(__isl_take isl_set *set,
3168 __isl_take isl_qpolynomial *qp,
3169 void *user), void *user);
3170 isl_stat isl_pw_qpolynomial_foreach_lifted_piece(
3171 __isl_keep isl_pw_qpolynomial *pwqp,
3172 isl_stat (*fn)(__isl_take isl_set *set,
3173 __isl_take isl_qpolynomial *qp,
3174 void *user), void *user);
3175 int isl_pw_qpolynomial_fold_n_piece(
3176 __isl_keep isl_pw_qpolynomial_fold *pwf);
3177 isl_stat isl_pw_qpolynomial_fold_foreach_piece(
3178 __isl_keep isl_pw_qpolynomial_fold *pwf,
3179 isl_stat (*fn)(__isl_take isl_set *set,
3180 __isl_take isl_qpolynomial_fold *fold,
3181 void *user), void *user);
3182 isl_stat isl_pw_qpolynomial_fold_foreach_lifted_piece(
3183 __isl_keep isl_pw_qpolynomial_fold *pwf,
3184 isl_stat (*fn)(__isl_take isl_set *set,
3185 __isl_take isl_qpolynomial_fold *fold,
3186 void *user), void *user);
3188 As usual, the function C<fn> should return C<isl_stat_ok> on success
3189 and C<isl_stat_error> on failure. The difference between
3190 C<isl_pw_qpolynomial_foreach_piece> and
3191 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3192 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3193 compute unique representations for all existentially quantified
3194 variables and then turn these existentially quantified variables
3195 into extra set variables, adapting the associated quasipolynomial
3196 accordingly. This means that the C<set> passed to C<fn>
3197 will not have any existentially quantified variables, but that
3198 the dimensions of the sets may be different for different
3199 invocations of C<fn>.
3200 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
3201 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
3203 A piecewise expression consisting of the expressions at a given
3204 position of a piecewise multiple expression can be extracted
3205 using the following function.
3207 #include <isl/aff.h>
3208 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3209 __isl_keep isl_pw_multi_aff *pma, int pos);
3211 These expressions can be replaced using the following function.
3213 #include <isl/aff.h>
3214 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3215 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3216 __isl_take isl_pw_aff *pa);
3218 Note that there is a difference between C<isl_multi_pw_aff> and
3219 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
3220 affine expressions, while the second is a piecewise sequence
3221 of affine expressions. In particular, each of the piecewise
3222 affine expressions in an C<isl_multi_pw_aff> may have a different
3223 domain, while all multiple expressions associated to a cell
3224 in an C<isl_pw_multi_aff> have the same domain.
3225 It is possible to convert between the two, but when converting
3226 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
3227 of the result is the intersection of the domains of the input.
3228 The reverse conversion is exact.
3230 #include <isl/aff.h>
3231 __isl_give isl_pw_multi_aff *
3232 isl_pw_multi_aff_from_multi_pw_aff(
3233 __isl_take isl_multi_pw_aff *mpa);
3234 __isl_give isl_multi_pw_aff *
3235 isl_multi_pw_aff_from_pw_multi_aff(
3236 __isl_take isl_pw_multi_aff *pma);
3238 =head3 Union Expressions
3240 A union expression collects base expressions defined
3241 over different domains. The space of a union expression
3242 is that of the shared parameter space.
3244 The union expression types defined by C<isl>
3245 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
3246 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
3248 C<isl_union_pw_aff>,
3249 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>,
3250 there can be at most one base expression for a given domain space.
3252 C<isl_union_pw_multi_aff>,
3253 there can be multiple such expressions for a given domain space,
3254 but the domains of these expressions need to be disjoint.
3256 An empty union expression can be created using the following functions.
3258 #include <isl/aff.h>
3259 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
3260 __isl_take isl_space *space);
3261 __isl_give isl_union_pw_multi_aff *
3262 isl_union_pw_multi_aff_empty(
3263 __isl_take isl_space *space);
3265 #include <isl/polynomial.h>
3266 __isl_give isl_union_pw_qpolynomial *
3267 isl_union_pw_qpolynomial_zero(
3268 __isl_take isl_space *space);
3270 A union expression containing a single base expression
3271 can be created using the following functions.
3273 #include <isl/aff.h>
3274 __isl_give isl_union_pw_aff *
3275 isl_union_pw_aff_from_pw_aff(
3276 __isl_take isl_pw_aff *pa);
3277 __isl_give isl_union_pw_multi_aff *
3278 isl_union_pw_multi_aff_from_aff(
3279 __isl_take isl_aff *aff);
3280 __isl_give isl_union_pw_multi_aff *
3281 isl_union_pw_multi_aff_from_pw_multi_aff(
3282 __isl_take isl_pw_multi_aff *pma);
3284 #include <isl/polynomial.h>
3285 __isl_give isl_union_pw_qpolynomial *
3286 isl_union_pw_qpolynomial_from_pw_qpolynomial(
3287 __isl_take isl_pw_qpolynomial *pwqp);
3289 The following functions create a base expression on each
3290 of the sets in the union set and collect the results.
3292 #include <isl/aff.h>
3293 __isl_give isl_union_pw_multi_aff *
3294 isl_union_pw_multi_aff_from_union_pw_aff(
3295 __isl_take isl_union_pw_aff *upa);
3296 __isl_give isl_union_pw_aff *
3297 isl_union_pw_multi_aff_get_union_pw_aff(
3298 __isl_keep isl_union_pw_multi_aff *upma, int pos);
3299 __isl_give isl_union_pw_aff *
3300 isl_union_pw_aff_val_on_domain(
3301 __isl_take isl_union_set *domain,
3302 __isl_take isl_val *v);
3303 __isl_give isl_union_pw_multi_aff *
3304 isl_union_pw_multi_aff_multi_val_on_domain(
3305 __isl_take isl_union_set *domain,
3306 __isl_take isl_multi_val *mv);
3307 __isl_give isl_union_pw_aff *
3308 isl_union_pw_aff_param_on_domain_id(
3309 __isl_take isl_union_set *domain,
3310 __isl_take isl_id *id);
3312 The C<id> argument of C<isl_union_pw_aff_param_on_domain_id>
3313 is the identifier of a parameter that may or may not already
3314 be present in C<domain>.
3316 An C<isl_union_pw_aff> that is equal to a (parametric) affine
3318 expression on a given domain can be created using the following
3321 #include <isl/aff.h>
3322 __isl_give isl_union_pw_aff *
3323 isl_union_pw_aff_aff_on_domain(
3324 __isl_take isl_union_set *domain,
3325 __isl_take isl_aff *aff);
3326 __isl_give isl_union_pw_aff *
3327 isl_union_pw_aff_pw_aff_on_domain(
3328 __isl_take isl_union_set *domain,
3329 __isl_take isl_pw_aff *pa);
3331 A base expression can be added to a union expression using
3332 the following functions.
3334 #include <isl/aff.h>
3335 __isl_give isl_union_pw_aff *
3336 isl_union_pw_aff_add_pw_aff(
3337 __isl_take isl_union_pw_aff *upa,
3338 __isl_take isl_pw_aff *pa);
3339 __isl_give isl_union_pw_multi_aff *
3340 isl_union_pw_multi_aff_add_pw_multi_aff(
3341 __isl_take isl_union_pw_multi_aff *upma,
3342 __isl_take isl_pw_multi_aff *pma);
3344 #include <isl/polynomial.h>
3345 __isl_give isl_union_pw_qpolynomial *
3346 isl_union_pw_qpolynomial_add_pw_qpolynomial(
3347 __isl_take isl_union_pw_qpolynomial *upwqp,
3348 __isl_take isl_pw_qpolynomial *pwqp);
3350 Union expressions can be copied and freed using
3351 the following functions.
3353 #include <isl/aff.h>
3354 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
3355 __isl_keep isl_union_pw_aff *upa);
3356 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
3357 __isl_take isl_union_pw_aff *upa);
3358 __isl_give isl_union_pw_multi_aff *
3359 isl_union_pw_multi_aff_copy(
3360 __isl_keep isl_union_pw_multi_aff *upma);
3361 __isl_null isl_union_pw_multi_aff *
3362 isl_union_pw_multi_aff_free(
3363 __isl_take isl_union_pw_multi_aff *upma);
3365 #include <isl/polynomial.h>
3366 __isl_give isl_union_pw_qpolynomial *
3367 isl_union_pw_qpolynomial_copy(
3368 __isl_keep isl_union_pw_qpolynomial *upwqp);
3369 __isl_null isl_union_pw_qpolynomial *
3370 isl_union_pw_qpolynomial_free(
3371 __isl_take isl_union_pw_qpolynomial *upwqp);
3372 __isl_give isl_union_pw_qpolynomial_fold *
3373 isl_union_pw_qpolynomial_fold_copy(
3374 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3375 __isl_null isl_union_pw_qpolynomial_fold *
3376 isl_union_pw_qpolynomial_fold_free(
3377 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3379 To iterate over the base expressions in a union expression,
3380 use the following functions.
3382 #include <isl/aff.h>
3383 int isl_union_pw_aff_n_pw_aff(
3384 __isl_keep isl_union_pw_aff *upa);
3385 isl_stat isl_union_pw_aff_foreach_pw_aff(
3386 __isl_keep isl_union_pw_aff *upa,
3387 isl_stat (*fn)(__isl_take isl_pw_aff *pa,
3388 void *user), void *user);
3389 int isl_union_pw_multi_aff_n_pw_multi_aff(
3390 __isl_keep isl_union_pw_multi_aff *upma);
3391 isl_stat isl_union_pw_multi_aff_foreach_pw_multi_aff(
3392 __isl_keep isl_union_pw_multi_aff *upma,
3393 isl_stat (*fn)(__isl_take isl_pw_multi_aff *pma,
3394 void *user), void *user);
3396 #include <isl/polynomial.h>
3397 int isl_union_pw_qpolynomial_n_pw_qpolynomial(
3398 __isl_keep isl_union_pw_qpolynomial *upwqp);
3399 isl_stat isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3400 __isl_keep isl_union_pw_qpolynomial *upwqp,
3401 isl_stat (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
3402 void *user), void *user);
3403 int isl_union_pw_qpolynomial_fold_n_pw_qpolynomial_fold(
3404 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3405 isl_stat isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3406 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3407 isl_stat (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3408 void *user), void *user);
3410 To extract the base expression in a given space from a union, use
3411 the following functions.
3413 #include <isl/aff.h>
3414 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
3415 __isl_keep isl_union_pw_aff *upa,
3416 __isl_take isl_space *space);
3417 __isl_give isl_pw_multi_aff *
3418 isl_union_pw_multi_aff_extract_pw_multi_aff(
3419 __isl_keep isl_union_pw_multi_aff *upma,
3420 __isl_take isl_space *space);
3422 #include <isl/polynomial.h>
3423 __isl_give isl_pw_qpolynomial *
3424 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3425 __isl_keep isl_union_pw_qpolynomial *upwqp,
3426 __isl_take isl_space *space);
3428 =head2 Input and Output
3430 For set and relation,
3431 C<isl> supports its own input/output format, which is similar
3432 to the C<Omega> format, but also supports the C<PolyLib> format
3434 For other object types, typically only an C<isl> format is supported.
3436 =head3 C<isl> format
3438 The C<isl> format is similar to that of C<Omega>, but has a different
3439 syntax for describing the parameters and allows for the definition
3440 of an existentially quantified variable as the integer division
3441 of an affine expression.
3442 For example, the set of integers C<i> between C<0> and C<n>
3443 such that C<i % 10 <= 6> can be described as
3445 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
3448 A set or relation can have several disjuncts, separated
3449 by the keyword C<or>. Each disjunct is either a conjunction
3450 of constraints or a projection (C<exists>) of a conjunction
3451 of constraints. The constraints are separated by the keyword
3454 =head3 C<PolyLib> format
3456 If the represented set is a union, then the first line
3457 contains a single number representing the number of disjuncts.
3458 Otherwise, a line containing the number C<1> is optional.
3460 Each disjunct is represented by a matrix of constraints.
3461 The first line contains two numbers representing
3462 the number of rows and columns,
3463 where the number of rows is equal to the number of constraints
3464 and the number of columns is equal to two plus the number of variables.
3465 The following lines contain the actual rows of the constraint matrix.
3466 In each row, the first column indicates whether the constraint
3467 is an equality (C<0>) or inequality (C<1>). The final column
3468 corresponds to the constant term.
3470 If the set is parametric, then the coefficients of the parameters
3471 appear in the last columns before the constant column.
3472 The coefficients of any existentially quantified variables appear
3473 between those of the set variables and those of the parameters.
3475 =head3 Extended C<PolyLib> format
3477 The extended C<PolyLib> format is nearly identical to the
3478 C<PolyLib> format. The only difference is that the line
3479 containing the number of rows and columns of a constraint matrix
3480 also contains four additional numbers:
3481 the number of output dimensions, the number of input dimensions,
3482 the number of local dimensions (i.e., the number of existentially
3483 quantified variables) and the number of parameters.
3484 For sets, the number of ``output'' dimensions is equal
3485 to the number of set dimensions, while the number of ``input''
3490 Objects can be read from input using the following functions.
3492 #include <isl/val.h>
3493 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
3495 __isl_give isl_multi_val *isl_multi_val_read_from_str(
3496 isl_ctx *ctx, const char *str);
3498 #include <isl/set.h>
3499 __isl_give isl_basic_set *isl_basic_set_read_from_file(
3500 isl_ctx *ctx, FILE *input);
3501 __isl_give isl_basic_set *isl_basic_set_read_from_str(
3502 isl_ctx *ctx, const char *str);
3503 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
3505 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
3508 #include <isl/map.h>
3509 __isl_give isl_basic_map *isl_basic_map_read_from_file(
3510 isl_ctx *ctx, FILE *input);
3511 __isl_give isl_basic_map *isl_basic_map_read_from_str(
3512 isl_ctx *ctx, const char *str);
3513 __isl_give isl_map *isl_map_read_from_file(
3514 isl_ctx *ctx, FILE *input);
3515 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
3518 #include <isl/union_set.h>
3519 __isl_give isl_union_set *isl_union_set_read_from_file(
3520 isl_ctx *ctx, FILE *input);
3521 __isl_give isl_union_set *isl_union_set_read_from_str(
3522 isl_ctx *ctx, const char *str);
3524 #include <isl/union_map.h>
3525 __isl_give isl_union_map *isl_union_map_read_from_file(
3526 isl_ctx *ctx, FILE *input);
3527 __isl_give isl_union_map *isl_union_map_read_from_str(
3528 isl_ctx *ctx, const char *str);
3530 #include <isl/aff.h>
3531 __isl_give isl_aff *isl_aff_read_from_str(
3532 isl_ctx *ctx, const char *str);
3533 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3534 isl_ctx *ctx, const char *str);
3535 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3536 isl_ctx *ctx, const char *str);
3537 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3538 isl_ctx *ctx, const char *str);
3539 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
3540 isl_ctx *ctx, const char *str);
3541 __isl_give isl_union_pw_aff *
3542 isl_union_pw_aff_read_from_str(
3543 isl_ctx *ctx, const char *str);
3544 __isl_give isl_union_pw_multi_aff *
3545 isl_union_pw_multi_aff_read_from_str(
3546 isl_ctx *ctx, const char *str);
3547 __isl_give isl_multi_union_pw_aff *
3548 isl_multi_union_pw_aff_read_from_str(
3549 isl_ctx *ctx, const char *str);
3551 #include <isl/polynomial.h>
3552 __isl_give isl_union_pw_qpolynomial *
3553 isl_union_pw_qpolynomial_read_from_str(
3554 isl_ctx *ctx, const char *str);
3556 For sets and relations,
3557 the input format is autodetected and may be either the C<PolyLib> format
3558 or the C<isl> format.
3562 Before anything can be printed, an C<isl_printer> needs to
3565 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
3567 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
3568 __isl_null isl_printer *isl_printer_free(
3569 __isl_take isl_printer *printer);
3571 C<isl_printer_to_file> prints to the given file, while
3572 C<isl_printer_to_str> prints to a string that can be extracted
3573 using the following function.
3575 #include <isl/printer.h>
3576 __isl_give char *isl_printer_get_str(
3577 __isl_keep isl_printer *printer);
3579 The printer can be inspected using the following functions.
3581 FILE *isl_printer_get_file(
3582 __isl_keep isl_printer *printer);
3583 int isl_printer_get_output_format(
3584 __isl_keep isl_printer *p);
3585 int isl_printer_get_yaml_style(__isl_keep isl_printer *p);
3587 The behavior of the printer can be modified in various ways
3589 __isl_give isl_printer *isl_printer_set_output_format(
3590 __isl_take isl_printer *p, int output_format);
3591 __isl_give isl_printer *isl_printer_set_indent(
3592 __isl_take isl_printer *p, int indent);
3593 __isl_give isl_printer *isl_printer_set_indent_prefix(
3594 __isl_take isl_printer *p, const char *prefix);
3595 __isl_give isl_printer *isl_printer_indent(
3596 __isl_take isl_printer *p, int indent);
3597 __isl_give isl_printer *isl_printer_set_prefix(
3598 __isl_take isl_printer *p, const char *prefix);
3599 __isl_give isl_printer *isl_printer_set_suffix(
3600 __isl_take isl_printer *p, const char *suffix);
3601 __isl_give isl_printer *isl_printer_set_yaml_style(
3602 __isl_take isl_printer *p, int yaml_style);
3604 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
3605 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
3606 and defaults to C<ISL_FORMAT_ISL>.
3607 Each line in the output is prefixed by C<indent_prefix>,
3608 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
3609 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
3610 In the C<PolyLib> format output,
3611 the coefficients of the existentially quantified variables
3612 appear between those of the set variables and those
3614 The function C<isl_printer_indent> increases the indentation
3615 by the specified amount (which may be negative).
3616 The YAML style may be either C<ISL_YAML_STYLE_BLOCK> or
3617 C<ISL_YAML_STYLE_FLOW> and when we are printing something
3620 To actually print something, use
3622 #include <isl/printer.h>
3623 __isl_give isl_printer *isl_printer_print_double(
3624 __isl_take isl_printer *p, double d);
3626 #include <isl/val.h>
3627 __isl_give isl_printer *isl_printer_print_val(
3628 __isl_take isl_printer *p, __isl_keep isl_val *v);
3630 #include <isl/set.h>
3631 __isl_give isl_printer *isl_printer_print_basic_set(
3632 __isl_take isl_printer *printer,
3633 __isl_keep isl_basic_set *bset);
3634 __isl_give isl_printer *isl_printer_print_set(
3635 __isl_take isl_printer *printer,
3636 __isl_keep isl_set *set);
3638 #include <isl/map.h>
3639 __isl_give isl_printer *isl_printer_print_basic_map(
3640 __isl_take isl_printer *printer,
3641 __isl_keep isl_basic_map *bmap);
3642 __isl_give isl_printer *isl_printer_print_map(
3643 __isl_take isl_printer *printer,
3644 __isl_keep isl_map *map);
3646 #include <isl/union_set.h>
3647 __isl_give isl_printer *isl_printer_print_union_set(
3648 __isl_take isl_printer *p,
3649 __isl_keep isl_union_set *uset);
3651 #include <isl/union_map.h>
3652 __isl_give isl_printer *isl_printer_print_union_map(
3653 __isl_take isl_printer *p,
3654 __isl_keep isl_union_map *umap);
3656 #include <isl/val.h>
3657 __isl_give isl_printer *isl_printer_print_multi_val(
3658 __isl_take isl_printer *p,
3659 __isl_keep isl_multi_val *mv);
3661 #include <isl/aff.h>
3662 __isl_give isl_printer *isl_printer_print_aff(
3663 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3664 __isl_give isl_printer *isl_printer_print_multi_aff(
3665 __isl_take isl_printer *p,
3666 __isl_keep isl_multi_aff *maff);
3667 __isl_give isl_printer *isl_printer_print_pw_aff(
3668 __isl_take isl_printer *p,
3669 __isl_keep isl_pw_aff *pwaff);
3670 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3671 __isl_take isl_printer *p,
3672 __isl_keep isl_pw_multi_aff *pma);
3673 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3674 __isl_take isl_printer *p,
3675 __isl_keep isl_multi_pw_aff *mpa);
3676 __isl_give isl_printer *isl_printer_print_union_pw_aff(
3677 __isl_take isl_printer *p,
3678 __isl_keep isl_union_pw_aff *upa);
3679 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3680 __isl_take isl_printer *p,
3681 __isl_keep isl_union_pw_multi_aff *upma);
3682 __isl_give isl_printer *
3683 isl_printer_print_multi_union_pw_aff(
3684 __isl_take isl_printer *p,
3685 __isl_keep isl_multi_union_pw_aff *mupa);
3687 #include <isl/polynomial.h>
3688 __isl_give isl_printer *isl_printer_print_qpolynomial(
3689 __isl_take isl_printer *p,
3690 __isl_keep isl_qpolynomial *qp);
3691 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3692 __isl_take isl_printer *p,
3693 __isl_keep isl_pw_qpolynomial *pwqp);
3694 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3695 __isl_take isl_printer *p,
3696 __isl_keep isl_union_pw_qpolynomial *upwqp);
3698 __isl_give isl_printer *
3699 isl_printer_print_pw_qpolynomial_fold(
3700 __isl_take isl_printer *p,
3701 __isl_keep isl_pw_qpolynomial_fold *pwf);
3702 __isl_give isl_printer *
3703 isl_printer_print_union_pw_qpolynomial_fold(
3704 __isl_take isl_printer *p,
3705 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3707 For C<isl_printer_print_qpolynomial>,
3708 C<isl_printer_print_pw_qpolynomial> and
3709 C<isl_printer_print_pw_qpolynomial_fold>,
3710 the output format of the printer
3711 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3712 For C<isl_printer_print_union_pw_qpolynomial> and
3713 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
3715 In case of printing in C<ISL_FORMAT_C>, the user may want
3716 to set the names of all dimensions first.
3718 C<isl> also provides limited support for printing YAML documents,
3719 just enough for the internal use for printing such documents.
3721 #include <isl/printer.h>
3722 __isl_give isl_printer *isl_printer_yaml_start_mapping(
3723 __isl_take isl_printer *p);
3724 __isl_give isl_printer *isl_printer_yaml_end_mapping(
3725 __isl_take isl_printer *p);
3726 __isl_give isl_printer *isl_printer_yaml_start_sequence(
3727 __isl_take isl_printer *p);
3728 __isl_give isl_printer *isl_printer_yaml_end_sequence(
3729 __isl_take isl_printer *p);
3730 __isl_give isl_printer *isl_printer_yaml_next(
3731 __isl_take isl_printer *p);
3733 A document is started by a call to either
3734 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3735 Anything printed to the printer after such a call belong to the
3736 first key of the mapping or the first element in the sequence.
3737 The function C<isl_printer_yaml_next> moves to the value if
3738 we are currently printing a mapping key, the next key if we
3739 are printing a value or the next element if we are printing
3740 an element in a sequence.
3741 Nested mappings and sequences are initiated by the same
3742 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3743 Each call to these functions needs to have a corresponding call to
3744 C<isl_printer_yaml_end_mapping> or C<isl_printer_yaml_end_sequence>.
3746 When called on a file printer, the following function flushes
3747 the file. When called on a string printer, the buffer is cleared.
3749 __isl_give isl_printer *isl_printer_flush(
3750 __isl_take isl_printer *p);
3752 The following functions allow the user to attach
3753 notes to a printer in order to keep track of additional state.
3755 #include <isl/printer.h>
3756 isl_bool isl_printer_has_note(__isl_keep isl_printer *p,
3757 __isl_keep isl_id *id);
3758 __isl_give isl_id *isl_printer_get_note(
3759 __isl_keep isl_printer *p, __isl_take isl_id *id);
3760 __isl_give isl_printer *isl_printer_set_note(
3761 __isl_take isl_printer *p,
3762 __isl_take isl_id *id, __isl_take isl_id *note);
3764 C<isl_printer_set_note> associates the given note to the given
3765 identifier in the printer.
3766 C<isl_printer_get_note> retrieves a note associated to an
3768 C<isl_printer_has_note> checks if there is such a note.
3769 C<isl_printer_get_note> fails if the requested note does not exist.
3771 Alternatively, a string representation can be obtained
3772 directly using the following functions, which always print
3776 __isl_give char *isl_id_to_str(
3777 __isl_keep isl_id *id);
3779 #include <isl/space.h>
3780 __isl_give char *isl_space_to_str(
3781 __isl_keep isl_space *space);
3783 #include <isl/val.h>
3784 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
3785 __isl_give char *isl_multi_val_to_str(
3786 __isl_keep isl_multi_val *mv);
3788 #include <isl/set.h>
3789 __isl_give char *isl_basic_set_to_str(
3790 __isl_keep isl_basic_set *bset);
3791 __isl_give char *isl_set_to_str(
3792 __isl_keep isl_set *set);
3794 #include <isl/union_set.h>
3795 __isl_give char *isl_union_set_to_str(
3796 __isl_keep isl_union_set *uset);
3798 #include <isl/map.h>
3799 __isl_give char *isl_basic_map_to_str(
3800 __isl_keep isl_basic_map *bmap);
3801 __isl_give char *isl_map_to_str(
3802 __isl_keep isl_map *map);
3804 #include <isl/union_map.h>
3805 __isl_give char *isl_union_map_to_str(
3806 __isl_keep isl_union_map *umap);
3808 #include <isl/aff.h>
3809 __isl_give char *isl_aff_to_str(__isl_keep isl_aff *aff);
3810 __isl_give char *isl_pw_aff_to_str(
3811 __isl_keep isl_pw_aff *pa);
3812 __isl_give char *isl_multi_aff_to_str(
3813 __isl_keep isl_multi_aff *ma);
3814 __isl_give char *isl_pw_multi_aff_to_str(
3815 __isl_keep isl_pw_multi_aff *pma);
3816 __isl_give char *isl_multi_pw_aff_to_str(
3817 __isl_keep isl_multi_pw_aff *mpa);
3818 __isl_give char *isl_union_pw_aff_to_str(
3819 __isl_keep isl_union_pw_aff *upa);
3820 __isl_give char *isl_union_pw_multi_aff_to_str(
3821 __isl_keep isl_union_pw_multi_aff *upma);
3822 __isl_give char *isl_multi_union_pw_aff_to_str(
3823 __isl_keep isl_multi_union_pw_aff *mupa);
3825 #include <isl/point.h>
3826 __isl_give char *isl_point_to_str(
3827 __isl_keep isl_point *pnt);
3829 #include <isl/polynomial.h>
3830 __isl_give char *isl_pw_qpolynomial_to_str(
3831 __isl_keep isl_pw_qpolynomial *pwqp);
3832 __isl_give char *isl_union_pw_qpolynomial_to_str(
3833 __isl_keep isl_union_pw_qpolynomial *upwqp);
3837 =head3 Unary Properties
3843 The following functions test whether the given set or relation
3844 contains any integer points. The ``plain'' variants do not perform
3845 any computations, but simply check if the given set or relation
3846 is already known to be empty.
3848 #include <isl/set.h>
3849 isl_bool isl_basic_set_plain_is_empty(
3850 __isl_keep isl_basic_set *bset);
3851 isl_bool isl_basic_set_is_empty(
3852 __isl_keep isl_basic_set *bset);
3853 isl_bool isl_set_plain_is_empty(
3854 __isl_keep isl_set *set);
3855 isl_bool isl_set_is_empty(__isl_keep isl_set *set);
3857 #include <isl/union_set.h>
3858 isl_bool isl_union_set_is_empty(
3859 __isl_keep isl_union_set *uset);
3861 #include <isl/map.h>
3862 isl_bool isl_basic_map_plain_is_empty(
3863 __isl_keep isl_basic_map *bmap);
3864 isl_bool isl_basic_map_is_empty(
3865 __isl_keep isl_basic_map *bmap);
3866 isl_bool isl_map_plain_is_empty(
3867 __isl_keep isl_map *map);
3868 isl_bool isl_map_is_empty(__isl_keep isl_map *map);
3870 #include <isl/union_map.h>
3871 isl_bool isl_union_map_plain_is_empty(
3872 __isl_keep isl_union_map *umap);
3873 isl_bool isl_union_map_is_empty(
3874 __isl_keep isl_union_map *umap);
3876 =item * Universality
3878 isl_bool isl_basic_set_plain_is_universe(
3879 __isl_keep isl_basic_set *bset);
3880 isl_bool isl_basic_set_is_universe(
3881 __isl_keep isl_basic_set *bset);
3882 isl_bool isl_basic_map_plain_is_universe(
3883 __isl_keep isl_basic_map *bmap);
3884 isl_bool isl_basic_map_is_universe(
3885 __isl_keep isl_basic_map *bmap);
3886 isl_bool isl_set_plain_is_universe(
3887 __isl_keep isl_set *set);
3888 isl_bool isl_map_plain_is_universe(
3889 __isl_keep isl_map *map);
3891 =item * Single-valuedness
3893 #include <isl/set.h>
3894 isl_bool isl_set_is_singleton(__isl_keep isl_set *set);
3896 #include <isl/map.h>
3897 isl_bool isl_basic_map_is_single_valued(
3898 __isl_keep isl_basic_map *bmap);
3899 isl_bool isl_map_plain_is_single_valued(
3900 __isl_keep isl_map *map);
3901 isl_bool isl_map_is_single_valued(__isl_keep isl_map *map);
3903 #include <isl/union_map.h>
3904 isl_bool isl_union_map_is_single_valued(
3905 __isl_keep isl_union_map *umap);
3909 isl_bool isl_map_plain_is_injective(
3910 __isl_keep isl_map *map);
3911 isl_bool isl_map_is_injective(
3912 __isl_keep isl_map *map);
3913 isl_bool isl_union_map_plain_is_injective(
3914 __isl_keep isl_union_map *umap);
3915 isl_bool isl_union_map_is_injective(
3916 __isl_keep isl_union_map *umap);
3920 isl_bool isl_map_is_bijective(
3921 __isl_keep isl_map *map);
3922 isl_bool isl_union_map_is_bijective(
3923 __isl_keep isl_union_map *umap);
3927 The following functions test whether the given relation
3928 only maps elements to themselves.
3930 #include <isl/map.h>
3931 isl_bool isl_map_is_identity(
3932 __isl_keep isl_map *map);
3934 #include <isl/union_map.h>
3935 isl_bool isl_union_map_is_identity(
3936 __isl_keep isl_union_map *umap);
3940 __isl_give isl_val *
3941 isl_basic_map_plain_get_val_if_fixed(
3942 __isl_keep isl_basic_map *bmap,
3943 enum isl_dim_type type, unsigned pos);
3944 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
3945 __isl_keep isl_set *set,
3946 enum isl_dim_type type, unsigned pos);
3947 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
3948 __isl_keep isl_map *map,
3949 enum isl_dim_type type, unsigned pos);
3951 If the set or relation obviously lies on a hyperplane where the given dimension
3952 has a fixed value, then return that value.
3953 Otherwise return NaN.
3957 isl_stat isl_set_dim_residue_class_val(
3958 __isl_keep isl_set *set,
3959 int pos, __isl_give isl_val **modulo,
3960 __isl_give isl_val **residue);
3962 Check if the values of the given set dimension are equal to a fixed
3963 value modulo some integer value. If so, assign the modulo to C<*modulo>
3964 and the fixed value to C<*residue>. If the given dimension attains only
3965 a single value, then assign C<0> to C<*modulo> and the fixed value to
3967 If the dimension does not attain only a single value and if no modulo
3968 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
3970 #include <isl/set.h>
3971 __isl_give isl_stride_info *isl_set_get_stride_info(
3972 __isl_keep isl_set *set, int pos);
3973 __isl_give isl_val *isl_set_get_stride(
3974 __isl_keep isl_set *set, int pos);
3976 Check if the values of the given set dimension are equal to
3977 some affine expression of the other dimensions (the offset)
3978 modulo some integer stride.
3979 If no more specific information can be found, then the stride
3980 is taken to be one and the offset is taken to be the zero expression.
3981 The function C<isl_set_get_stride_info> performs the same
3982 computation but only returns the stride.
3984 the stride and offset can be extracted from the returned object
3985 using the following functions.
3987 #include <isl/set.h>
3988 __isl_give isl_val *isl_stride_info_get_stride(
3989 __isl_keep isl_stride_info *si);
3990 __isl_give isl_aff *isl_stride_info_get_offset(
3991 __isl_keep isl_stride_info *si);
3993 The stride info object can be released using the following function.
3995 #include <isl/set.h>
3996 __isl_null isl_stride_info *isl_stride_info_free(
3997 __isl_take isl_stride_info *si);
4001 To check whether the description of a set, relation or function depends
4002 on one or more given dimensions,
4003 the following functions can be used.
4005 #include <isl/constraint.h>
4006 isl_bool isl_constraint_involves_dims(
4007 __isl_keep isl_constraint *constraint,
4008 enum isl_dim_type type, unsigned first, unsigned n);
4010 #include <isl/set.h>
4011 isl_bool isl_basic_set_involves_dims(
4012 __isl_keep isl_basic_set *bset,
4013 enum isl_dim_type type, unsigned first, unsigned n);
4014 isl_bool isl_set_involves_dims(__isl_keep isl_set *set,
4015 enum isl_dim_type type, unsigned first, unsigned n);
4017 #include <isl/map.h>
4018 isl_bool isl_basic_map_involves_dims(
4019 __isl_keep isl_basic_map *bmap,
4020 enum isl_dim_type type, unsigned first, unsigned n);
4021 isl_bool isl_map_involves_dims(__isl_keep isl_map *map,
4022 enum isl_dim_type type, unsigned first, unsigned n);
4024 #include <isl/union_map.h>
4025 isl_bool isl_union_map_involves_dims(
4026 __isl_keep isl_union_map *umap,
4027 enum isl_dim_type type, unsigned first, unsigned n);
4029 #include <isl/aff.h>
4030 isl_bool isl_aff_involves_dims(__isl_keep isl_aff *aff,
4031 enum isl_dim_type type, unsigned first, unsigned n);
4032 isl_bool isl_pw_aff_involves_dims(
4033 __isl_keep isl_pw_aff *pwaff,
4034 enum isl_dim_type type, unsigned first, unsigned n);
4035 isl_bool isl_multi_aff_involves_dims(
4036 __isl_keep isl_multi_aff *ma,
4037 enum isl_dim_type type, unsigned first, unsigned n);
4038 isl_bool isl_multi_pw_aff_involves_dims(
4039 __isl_keep isl_multi_pw_aff *mpa,
4040 enum isl_dim_type type, unsigned first, unsigned n);
4042 #include <isl/polynomial.h>
4043 isl_bool isl_qpolynomial_involves_dims(
4044 __isl_keep isl_qpolynomial *qp,
4045 enum isl_dim_type type, unsigned first, unsigned n);
4047 Similarly, the following functions can be used to check whether
4048 a given dimension is involved in any lower or upper bound.
4050 #include <isl/set.h>
4051 isl_bool isl_set_dim_has_any_lower_bound(
4052 __isl_keep isl_set *set,
4053 enum isl_dim_type type, unsigned pos);
4054 isl_bool isl_set_dim_has_any_upper_bound(
4055 __isl_keep isl_set *set,
4056 enum isl_dim_type type, unsigned pos);
4058 Note that these functions return true even if there is a bound on
4059 the dimension on only some of the basic sets of C<set>.
4060 To check if they have a bound for all of the basic sets in C<set>,
4061 use the following functions instead.
4063 #include <isl/set.h>
4064 isl_bool isl_set_dim_has_lower_bound(
4065 __isl_keep isl_set *set,
4066 enum isl_dim_type type, unsigned pos);
4067 isl_bool isl_set_dim_has_upper_bound(
4068 __isl_keep isl_set *set,
4069 enum isl_dim_type type, unsigned pos);
4073 To check whether a set is a parameter domain, use this function:
4075 isl_bool isl_set_is_params(__isl_keep isl_set *set);
4076 isl_bool isl_union_set_is_params(
4077 __isl_keep isl_union_set *uset);
4081 The following functions check whether the space of the given
4082 (basic) set or relation domain and/or range is a wrapped relation.
4084 #include <isl/space.h>
4085 isl_bool isl_space_is_wrapping(
4086 __isl_keep isl_space *space);
4087 isl_bool isl_space_domain_is_wrapping(
4088 __isl_keep isl_space *space);
4089 isl_bool isl_space_range_is_wrapping(
4090 __isl_keep isl_space *space);
4091 isl_bool isl_space_is_product(
4092 __isl_keep isl_space *space);
4094 #include <isl/set.h>
4095 isl_bool isl_basic_set_is_wrapping(
4096 __isl_keep isl_basic_set *bset);
4097 isl_bool isl_set_is_wrapping(__isl_keep isl_set *set);
4099 #include <isl/map.h>
4100 isl_bool isl_map_domain_is_wrapping(
4101 __isl_keep isl_map *map);
4102 isl_bool isl_map_range_is_wrapping(
4103 __isl_keep isl_map *map);
4104 isl_bool isl_map_is_product(__isl_keep isl_map *map);
4106 #include <isl/val.h>
4107 isl_bool isl_multi_val_range_is_wrapping(
4108 __isl_keep isl_multi_val *mv);
4110 #include <isl/aff.h>
4111 isl_bool isl_multi_aff_range_is_wrapping(
4112 __isl_keep isl_multi_aff *ma);
4113 isl_bool isl_multi_pw_aff_range_is_wrapping(
4114 __isl_keep isl_multi_pw_aff *mpa);
4115 isl_bool isl_multi_union_pw_aff_range_is_wrapping(
4116 __isl_keep isl_multi_union_pw_aff *mupa);
4118 The input to C<isl_space_is_wrapping> should
4119 be the space of a set, while that of
4120 C<isl_space_domain_is_wrapping> and
4121 C<isl_space_range_is_wrapping> should be the space of a relation.
4122 The input to C<isl_space_is_product> can be either the space
4123 of a set or that of a binary relation.
4124 In case the input is the space of a binary relation, it checks
4125 whether both domain and range are wrapping.
4127 =item * Internal Product
4129 isl_bool isl_basic_map_can_zip(
4130 __isl_keep isl_basic_map *bmap);
4131 isl_bool isl_map_can_zip(__isl_keep isl_map *map);
4133 Check whether the product of domain and range of the given relation
4135 i.e., whether both domain and range are nested relations.
4139 #include <isl/space.h>
4140 isl_bool isl_space_can_curry(
4141 __isl_keep isl_space *space);
4143 #include <isl/map.h>
4144 isl_bool isl_basic_map_can_curry(
4145 __isl_keep isl_basic_map *bmap);
4146 isl_bool isl_map_can_curry(__isl_keep isl_map *map);
4148 Check whether the domain of the (basic) relation is a wrapped relation.
4150 #include <isl/space.h>
4151 __isl_give isl_space *isl_space_uncurry(
4152 __isl_take isl_space *space);
4154 #include <isl/map.h>
4155 isl_bool isl_basic_map_can_uncurry(
4156 __isl_keep isl_basic_map *bmap);
4157 isl_bool isl_map_can_uncurry(__isl_keep isl_map *map);
4159 Check whether the range of the (basic) relation is a wrapped relation.
4161 #include <isl/space.h>
4162 isl_bool isl_space_can_range_curry(
4163 __isl_keep isl_space *space);
4165 #include <isl/map.h>
4166 isl_bool isl_map_can_range_curry(
4167 __isl_keep isl_map *map);
4169 Check whether the domain of the relation wrapped in the range of
4170 the input is itself a wrapped relation.
4172 =item * Special Values
4174 #include <isl/aff.h>
4175 isl_bool isl_aff_is_cst(__isl_keep isl_aff *aff);
4176 isl_bool isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
4177 isl_bool isl_multi_pw_aff_is_cst(
4178 __isl_keep isl_multi_pw_aff *mpa);
4180 Check whether the given expression is a constant.
4182 #include <isl/val.h>
4183 isl_bool isl_multi_val_involves_nan(
4184 __isl_keep isl_multi_val *mv);
4186 #include <isl/aff.h>
4187 isl_bool isl_aff_is_nan(__isl_keep isl_aff *aff);
4188 isl_bool isl_multi_aff_involves_nan(
4189 __isl_keep isl_multi_aff *ma);
4190 isl_bool isl_pw_aff_involves_nan(
4191 __isl_keep isl_pw_aff *pa);
4192 isl_bool isl_pw_multi_aff_involves_nan(
4193 __isl_keep isl_pw_multi_aff *pma);
4194 isl_bool isl_multi_pw_aff_involves_nan(
4195 __isl_keep isl_multi_pw_aff *mpa);
4196 isl_bool isl_union_pw_aff_involves_nan(
4197 __isl_keep isl_union_pw_aff *upa);
4198 isl_bool isl_union_pw_multi_aff_involves_nan(
4199 __isl_keep isl_union_pw_multi_aff *upma);
4200 isl_bool isl_multi_union_pw_aff_involves_nan(
4201 __isl_keep isl_multi_union_pw_aff *mupa);
4203 #include <isl/polynomial.h>
4204 isl_bool isl_qpolynomial_is_nan(
4205 __isl_keep isl_qpolynomial *qp);
4206 isl_bool isl_qpolynomial_fold_is_nan(
4207 __isl_keep isl_qpolynomial_fold *fold);
4208 isl_bool isl_pw_qpolynomial_involves_nan(
4209 __isl_keep isl_pw_qpolynomial *pwqp);
4210 isl_bool isl_pw_qpolynomial_fold_involves_nan(
4211 __isl_keep isl_pw_qpolynomial_fold *pwf);
4212 isl_bool isl_union_pw_qpolynomial_involves_nan(
4213 __isl_keep isl_union_pw_qpolynomial *upwqp);
4214 isl_bool isl_union_pw_qpolynomial_fold_involves_nan(
4215 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4217 Check whether the given expression is equal to or involves NaN.
4219 #include <isl/aff.h>
4220 isl_bool isl_aff_plain_is_zero(
4221 __isl_keep isl_aff *aff);
4223 Check whether the affine expression is obviously zero.
4227 =head3 Binary Properties
4233 The following functions check whether two objects
4234 represent the same set, relation or function.
4235 The C<plain> variants only return true if the objects
4236 are obviously the same. That is, they may return false
4237 even if the objects are the same, but they will never
4238 return true if the objects are not the same.
4240 #include <isl/set.h>
4241 isl_bool isl_basic_set_plain_is_equal(
4242 __isl_keep isl_basic_set *bset1,
4243 __isl_keep isl_basic_set *bset2);
4244 isl_bool isl_basic_set_is_equal(
4245 __isl_keep isl_basic_set *bset1,
4246 __isl_keep isl_basic_set *bset2);
4247 isl_bool isl_set_plain_is_equal(
4248 __isl_keep isl_set *set1,
4249 __isl_keep isl_set *set2);
4250 isl_bool isl_set_is_equal(__isl_keep isl_set *set1,
4251 __isl_keep isl_set *set2);
4253 #include <isl/map.h>
4254 isl_bool isl_basic_map_is_equal(
4255 __isl_keep isl_basic_map *bmap1,
4256 __isl_keep isl_basic_map *bmap2);
4257 isl_bool isl_map_is_equal(__isl_keep isl_map *map1,
4258 __isl_keep isl_map *map2);
4259 isl_bool isl_map_plain_is_equal(
4260 __isl_keep isl_map *map1,
4261 __isl_keep isl_map *map2);
4263 #include <isl/union_set.h>
4264 isl_bool isl_union_set_is_equal(
4265 __isl_keep isl_union_set *uset1,
4266 __isl_keep isl_union_set *uset2);
4268 #include <isl/union_map.h>
4269 isl_bool isl_union_map_is_equal(
4270 __isl_keep isl_union_map *umap1,
4271 __isl_keep isl_union_map *umap2);
4273 #include <isl/aff.h>
4274 isl_bool isl_aff_plain_is_equal(
4275 __isl_keep isl_aff *aff1,
4276 __isl_keep isl_aff *aff2);
4277 isl_bool isl_multi_aff_plain_is_equal(
4278 __isl_keep isl_multi_aff *maff1,
4279 __isl_keep isl_multi_aff *maff2);
4280 isl_bool isl_pw_aff_plain_is_equal(
4281 __isl_keep isl_pw_aff *pwaff1,
4282 __isl_keep isl_pw_aff *pwaff2);
4283 isl_bool isl_pw_aff_is_equal(
4284 __isl_keep isl_pw_aff *pa1,
4285 __isl_keep isl_pw_aff *pa2);
4286 isl_bool isl_pw_multi_aff_plain_is_equal(
4287 __isl_keep isl_pw_multi_aff *pma1,
4288 __isl_keep isl_pw_multi_aff *pma2);
4289 isl_bool isl_pw_multi_aff_is_equal(
4290 __isl_keep isl_pw_multi_aff *pma1,
4291 __isl_keep isl_pw_multi_aff *pma2);
4292 isl_bool isl_multi_pw_aff_plain_is_equal(
4293 __isl_keep isl_multi_pw_aff *mpa1,
4294 __isl_keep isl_multi_pw_aff *mpa2);
4295 isl_bool isl_multi_pw_aff_is_equal(
4296 __isl_keep isl_multi_pw_aff *mpa1,
4297 __isl_keep isl_multi_pw_aff *mpa2);
4298 isl_bool isl_union_pw_aff_plain_is_equal(
4299 __isl_keep isl_union_pw_aff *upa1,
4300 __isl_keep isl_union_pw_aff *upa2);
4301 isl_bool isl_union_pw_multi_aff_plain_is_equal(
4302 __isl_keep isl_union_pw_multi_aff *upma1,
4303 __isl_keep isl_union_pw_multi_aff *upma2);
4304 isl_bool isl_multi_union_pw_aff_plain_is_equal(
4305 __isl_keep isl_multi_union_pw_aff *mupa1,
4306 __isl_keep isl_multi_union_pw_aff *mupa2);
4308 #include <isl/polynomial.h>
4309 isl_bool isl_union_pw_qpolynomial_plain_is_equal(
4310 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4311 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4312 isl_bool isl_union_pw_qpolynomial_fold_plain_is_equal(
4313 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4314 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4316 =item * Disjointness
4318 #include <isl/set.h>
4319 isl_bool isl_basic_set_is_disjoint(
4320 __isl_keep isl_basic_set *bset1,
4321 __isl_keep isl_basic_set *bset2);
4322 isl_bool isl_set_plain_is_disjoint(
4323 __isl_keep isl_set *set1,
4324 __isl_keep isl_set *set2);
4325 isl_bool isl_set_is_disjoint(__isl_keep isl_set *set1,
4326 __isl_keep isl_set *set2);
4328 #include <isl/map.h>
4329 isl_bool isl_basic_map_is_disjoint(
4330 __isl_keep isl_basic_map *bmap1,
4331 __isl_keep isl_basic_map *bmap2);
4332 isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1,
4333 __isl_keep isl_map *map2);
4335 #include <isl/union_set.h>
4336 isl_bool isl_union_set_is_disjoint(
4337 __isl_keep isl_union_set *uset1,
4338 __isl_keep isl_union_set *uset2);
4340 #include <isl/union_map.h>
4341 isl_bool isl_union_map_is_disjoint(
4342 __isl_keep isl_union_map *umap1,
4343 __isl_keep isl_union_map *umap2);
4347 isl_bool isl_basic_set_is_subset(
4348 __isl_keep isl_basic_set *bset1,
4349 __isl_keep isl_basic_set *bset2);
4350 isl_bool isl_set_is_subset(__isl_keep isl_set *set1,
4351 __isl_keep isl_set *set2);
4352 isl_bool isl_set_is_strict_subset(
4353 __isl_keep isl_set *set1,
4354 __isl_keep isl_set *set2);
4355 isl_bool isl_union_set_is_subset(
4356 __isl_keep isl_union_set *uset1,
4357 __isl_keep isl_union_set *uset2);
4358 isl_bool isl_union_set_is_strict_subset(
4359 __isl_keep isl_union_set *uset1,
4360 __isl_keep isl_union_set *uset2);
4361 isl_bool isl_basic_map_is_subset(
4362 __isl_keep isl_basic_map *bmap1,
4363 __isl_keep isl_basic_map *bmap2);
4364 isl_bool isl_basic_map_is_strict_subset(
4365 __isl_keep isl_basic_map *bmap1,
4366 __isl_keep isl_basic_map *bmap2);
4367 isl_bool isl_map_is_subset(
4368 __isl_keep isl_map *map1,
4369 __isl_keep isl_map *map2);
4370 isl_bool isl_map_is_strict_subset(
4371 __isl_keep isl_map *map1,
4372 __isl_keep isl_map *map2);
4373 isl_bool isl_union_map_is_subset(
4374 __isl_keep isl_union_map *umap1,
4375 __isl_keep isl_union_map *umap2);
4376 isl_bool isl_union_map_is_strict_subset(
4377 __isl_keep isl_union_map *umap1,
4378 __isl_keep isl_union_map *umap2);
4380 Check whether the first argument is a (strict) subset of the
4385 Every comparison function returns a negative value if the first
4386 argument is considered smaller than the second, a positive value
4387 if the first argument is considered greater and zero if the two
4388 constraints are considered the same by the comparison criterion.
4390 #include <isl/constraint.h>
4391 int isl_constraint_plain_cmp(
4392 __isl_keep isl_constraint *c1,
4393 __isl_keep isl_constraint *c2);
4395 This function is useful for sorting C<isl_constraint>s.
4396 The order depends on the internal representation of the inputs.
4397 The order is fixed over different calls to the function (assuming
4398 the internal representation of the inputs has not changed), but may
4399 change over different versions of C<isl>.
4401 #include <isl/constraint.h>
4402 int isl_constraint_cmp_last_non_zero(
4403 __isl_keep isl_constraint *c1,
4404 __isl_keep isl_constraint *c2);
4406 This function can be used to sort constraints that live in the same
4407 local space. Constraints that involve ``earlier'' dimensions or
4408 that have a smaller coefficient for the shared latest dimension
4409 are considered smaller than other constraints.
4410 This function only defines a B<partial> order.
4412 #include <isl/set.h>
4413 int isl_set_plain_cmp(__isl_keep isl_set *set1,
4414 __isl_keep isl_set *set2);
4416 This function is useful for sorting C<isl_set>s.
4417 The order depends on the internal representation of the inputs.
4418 The order is fixed over different calls to the function (assuming
4419 the internal representation of the inputs has not changed), but may
4420 change over different versions of C<isl>.
4422 #include <isl/aff.h>
4423 int isl_multi_aff_plain_cmp(
4424 __isl_keep isl_multi_aff *ma1,
4425 __isl_keep isl_multi_aff *ma2);
4426 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4427 __isl_keep isl_pw_aff *pa2);
4429 The functions C<isl_multi_aff_plain_cmp> and
4430 C<isl_pw_aff_plain_cmp> can be used to sort C<isl_multi_aff>s and
4431 C<isl_pw_aff>s. The order is not strictly defined.
4432 The current order sorts expressions that only involve
4433 earlier dimensions before those that involve later dimensions.
4437 =head2 Unary Operations
4443 __isl_give isl_set *isl_set_complement(
4444 __isl_take isl_set *set);
4445 __isl_give isl_map *isl_map_complement(
4446 __isl_take isl_map *map);
4450 #include <isl/space.h>
4451 __isl_give isl_space *isl_space_reverse(
4452 __isl_take isl_space *space);
4454 #include <isl/map.h>
4455 __isl_give isl_basic_map *isl_basic_map_reverse(
4456 __isl_take isl_basic_map *bmap);
4457 __isl_give isl_map *isl_map_reverse(
4458 __isl_take isl_map *map);
4460 #include <isl/union_map.h>
4461 __isl_give isl_union_map *isl_union_map_reverse(
4462 __isl_take isl_union_map *umap);
4466 #include <isl/space.h>
4467 __isl_give isl_space *isl_space_domain(
4468 __isl_take isl_space *space);
4469 __isl_give isl_space *isl_space_range(
4470 __isl_take isl_space *space);
4471 __isl_give isl_space *isl_space_params(
4472 __isl_take isl_space *space);
4474 #include <isl/local_space.h>
4475 __isl_give isl_local_space *isl_local_space_domain(
4476 __isl_take isl_local_space *ls);
4477 __isl_give isl_local_space *isl_local_space_range(
4478 __isl_take isl_local_space *ls);
4480 #include <isl/set.h>
4481 __isl_give isl_basic_set *isl_basic_set_project_out(
4482 __isl_take isl_basic_set *bset,
4483 enum isl_dim_type type, unsigned first, unsigned n);
4484 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
4485 enum isl_dim_type type, unsigned first, unsigned n);
4486 __isl_give isl_map *isl_set_project_onto_map(
4487 __isl_take isl_set *set,
4488 enum isl_dim_type type, unsigned first,
4490 __isl_give isl_basic_set *isl_basic_set_params(
4491 __isl_take isl_basic_set *bset);
4492 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
4494 The function C<isl_set_project_onto_map> returns a relation
4495 that projects the input set onto the given set dimensions.
4497 #include <isl/map.h>
4498 __isl_give isl_basic_map *isl_basic_map_project_out(
4499 __isl_take isl_basic_map *bmap,
4500 enum isl_dim_type type, unsigned first, unsigned n);
4501 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
4502 enum isl_dim_type type, unsigned first, unsigned n);
4503 __isl_give isl_basic_set *isl_basic_map_domain(
4504 __isl_take isl_basic_map *bmap);
4505 __isl_give isl_basic_set *isl_basic_map_range(
4506 __isl_take isl_basic_map *bmap);
4507 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
4508 __isl_give isl_set *isl_map_domain(
4509 __isl_take isl_map *bmap);
4510 __isl_give isl_set *isl_map_range(
4511 __isl_take isl_map *map);
4513 #include <isl/union_set.h>
4514 __isl_give isl_union_set *isl_union_set_project_out(
4515 __isl_take isl_union_set *uset,
4516 enum isl_dim_type type,
4517 unsigned first, unsigned n);
4518 __isl_give isl_set *isl_union_set_params(
4519 __isl_take isl_union_set *uset);
4521 The function C<isl_union_set_project_out> can only project out
4524 #include <isl/union_map.h>
4525 __isl_give isl_union_map *isl_union_map_project_out(
4526 __isl_take isl_union_map *umap,
4527 enum isl_dim_type type, unsigned first, unsigned n);
4528 __isl_give isl_union_map *
4529 isl_union_map_project_out_all_params(
4530 __isl_take isl_union_map *umap);
4531 __isl_give isl_set *isl_union_map_params(
4532 __isl_take isl_union_map *umap);
4533 __isl_give isl_union_set *isl_union_map_domain(
4534 __isl_take isl_union_map *umap);
4535 __isl_give isl_union_set *isl_union_map_range(
4536 __isl_take isl_union_map *umap);
4538 The function C<isl_union_map_project_out> can only project out
4541 #include <isl/aff.h>
4542 __isl_give isl_aff *isl_aff_project_domain_on_params(
4543 __isl_take isl_aff *aff);
4544 __isl_give isl_multi_aff *
4545 isl_multi_aff_project_domain_on_params(
4546 __isl_take isl_multi_aff *ma);
4547 __isl_give isl_pw_aff *
4548 isl_pw_aff_project_domain_on_params(
4549 __isl_take isl_pw_aff *pa);
4550 __isl_give isl_multi_pw_aff *
4551 isl_multi_pw_aff_project_domain_on_params(
4552 __isl_take isl_multi_pw_aff *mpa);
4553 __isl_give isl_pw_multi_aff *
4554 isl_pw_multi_aff_project_domain_on_params(
4555 __isl_take isl_pw_multi_aff *pma);
4556 __isl_give isl_set *isl_pw_aff_domain(
4557 __isl_take isl_pw_aff *pwaff);
4558 __isl_give isl_set *isl_pw_multi_aff_domain(
4559 __isl_take isl_pw_multi_aff *pma);
4560 __isl_give isl_set *isl_multi_pw_aff_domain(
4561 __isl_take isl_multi_pw_aff *mpa);
4562 __isl_give isl_union_set *isl_union_pw_aff_domain(
4563 __isl_take isl_union_pw_aff *upa);
4564 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4565 __isl_take isl_union_pw_multi_aff *upma);
4566 __isl_give isl_union_set *
4567 isl_multi_union_pw_aff_domain(
4568 __isl_take isl_multi_union_pw_aff *mupa);
4569 __isl_give isl_set *isl_pw_aff_params(
4570 __isl_take isl_pw_aff *pwa);
4572 The function C<isl_multi_union_pw_aff_domain> requires its
4573 input to have at least one set dimension.
4575 #include <isl/polynomial.h>
4576 __isl_give isl_qpolynomial *
4577 isl_qpolynomial_project_domain_on_params(
4578 __isl_take isl_qpolynomial *qp);
4579 __isl_give isl_pw_qpolynomial *
4580 isl_pw_qpolynomial_project_domain_on_params(
4581 __isl_take isl_pw_qpolynomial *pwqp);
4582 __isl_give isl_pw_qpolynomial_fold *
4583 isl_pw_qpolynomial_fold_project_domain_on_params(
4584 __isl_take isl_pw_qpolynomial_fold *pwf);
4585 __isl_give isl_set *isl_pw_qpolynomial_domain(
4586 __isl_take isl_pw_qpolynomial *pwqp);
4587 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4588 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4589 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4590 __isl_take isl_union_pw_qpolynomial *upwqp);
4592 #include <isl/space.h>
4593 __isl_give isl_space *isl_space_domain_map(
4594 __isl_take isl_space *space);
4595 __isl_give isl_space *isl_space_range_map(
4596 __isl_take isl_space *space);
4598 #include <isl/map.h>
4599 __isl_give isl_map *isl_set_wrapped_domain_map(
4600 __isl_take isl_set *set);
4601 __isl_give isl_basic_map *isl_basic_map_domain_map(
4602 __isl_take isl_basic_map *bmap);
4603 __isl_give isl_basic_map *isl_basic_map_range_map(
4604 __isl_take isl_basic_map *bmap);
4605 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
4606 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
4608 #include <isl/union_map.h>
4609 __isl_give isl_union_map *isl_union_map_domain_map(
4610 __isl_take isl_union_map *umap);
4611 __isl_give isl_union_pw_multi_aff *
4612 isl_union_map_domain_map_union_pw_multi_aff(
4613 __isl_take isl_union_map *umap);
4614 __isl_give isl_union_map *isl_union_map_range_map(
4615 __isl_take isl_union_map *umap);
4616 __isl_give isl_union_map *
4617 isl_union_set_wrapped_domain_map(
4618 __isl_take isl_union_set *uset);
4620 The functions above construct a (basic, regular or union) relation
4621 that maps (a wrapped version of) the input relation to its domain or range.
4622 C<isl_set_wrapped_domain_map> maps the input set to the domain
4623 of its wrapped relation.
4627 __isl_give isl_basic_set *isl_basic_set_eliminate(
4628 __isl_take isl_basic_set *bset,
4629 enum isl_dim_type type,
4630 unsigned first, unsigned n);
4631 __isl_give isl_set *isl_set_eliminate(
4632 __isl_take isl_set *set, enum isl_dim_type type,
4633 unsigned first, unsigned n);
4634 __isl_give isl_basic_map *isl_basic_map_eliminate(
4635 __isl_take isl_basic_map *bmap,
4636 enum isl_dim_type type,
4637 unsigned first, unsigned n);
4638 __isl_give isl_map *isl_map_eliminate(
4639 __isl_take isl_map *map, enum isl_dim_type type,
4640 unsigned first, unsigned n);
4642 Eliminate the coefficients for the given dimensions from the constraints,
4643 without removing the dimensions.
4645 =item * Constructing a set from a parameter domain
4647 A zero-dimensional (local) space or (basic) set can be constructed
4648 on a given parameter domain using the following functions.
4650 #include <isl/space.h>
4651 __isl_give isl_space *isl_space_set_from_params(
4652 __isl_take isl_space *space);
4654 #include <isl/local_space.h>
4655 __isl_give isl_local_space *
4656 isl_local_space_set_from_params(
4657 __isl_take isl_local_space *ls);
4659 #include <isl/set.h>
4660 __isl_give isl_basic_set *isl_basic_set_from_params(
4661 __isl_take isl_basic_set *bset);
4662 __isl_give isl_set *isl_set_from_params(
4663 __isl_take isl_set *set);
4665 =item * Constructing a relation from one or two sets
4667 Create a relation with the given set(s) as domain and/or range.
4668 If only the domain or the range is specified, then
4669 the range or domain of the created relation is a zero-dimensional
4670 flat anonymous space.
4672 #include <isl/space.h>
4673 __isl_give isl_space *isl_space_from_domain(
4674 __isl_take isl_space *space);
4675 __isl_give isl_space *isl_space_from_range(
4676 __isl_take isl_space *space);
4677 __isl_give isl_space *isl_space_map_from_set(
4678 __isl_take isl_space *space);
4679 __isl_give isl_space *isl_space_map_from_domain_and_range(
4680 __isl_take isl_space *domain,
4681 __isl_take isl_space *range);
4683 #include <isl/local_space.h>
4684 __isl_give isl_local_space *isl_local_space_from_domain(
4685 __isl_take isl_local_space *ls);
4687 #include <isl/map.h>
4688 __isl_give isl_map *isl_map_from_domain(
4689 __isl_take isl_set *set);
4690 __isl_give isl_map *isl_map_from_range(
4691 __isl_take isl_set *set);
4693 #include <isl/union_map.h>
4694 __isl_give isl_union_map *isl_union_map_from_domain(
4695 __isl_take isl_union_set *uset);
4696 __isl_give isl_union_map *isl_union_map_from_range(
4697 __isl_take isl_union_set *uset);
4698 __isl_give isl_union_map *
4699 isl_union_map_from_domain_and_range(
4700 __isl_take isl_union_set *domain,
4701 __isl_take isl_union_set *range);
4703 #include <isl/val.h>
4704 __isl_give isl_multi_val *isl_multi_val_from_range(
4705 __isl_take isl_multi_val *mv);
4707 #include <isl/aff.h>
4708 __isl_give isl_aff *isl_aff_from_range(
4709 __isl_take isl_aff *aff);
4710 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4711 __isl_take isl_multi_aff *ma);
4712 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4713 __isl_take isl_pw_aff *pwa);
4714 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4715 __isl_take isl_multi_pw_aff *mpa);
4716 __isl_give isl_multi_union_pw_aff *
4717 isl_multi_union_pw_aff_from_range(
4718 __isl_take isl_multi_union_pw_aff *mupa);
4719 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4720 __isl_take isl_set *set);
4721 __isl_give isl_union_pw_multi_aff *
4722 isl_union_pw_multi_aff_from_domain(
4723 __isl_take isl_union_set *uset);
4725 #include <isl/polynomial.h>
4726 __isl_give isl_pw_qpolynomial *
4727 isl_pw_qpolynomial_from_range(
4728 __isl_take isl_pw_qpolynomial *pwqp);
4729 __isl_give isl_pw_qpolynomial_fold *
4730 isl_pw_qpolynomial_fold_from_range(
4731 __isl_take isl_pw_qpolynomial_fold *pwf);
4735 #include <isl/set.h>
4736 __isl_give isl_basic_set *isl_basic_set_fix_si(
4737 __isl_take isl_basic_set *bset,
4738 enum isl_dim_type type, unsigned pos, int value);
4739 __isl_give isl_basic_set *isl_basic_set_fix_val(
4740 __isl_take isl_basic_set *bset,
4741 enum isl_dim_type type, unsigned pos,
4742 __isl_take isl_val *v);
4743 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
4744 enum isl_dim_type type, unsigned pos, int value);
4745 __isl_give isl_set *isl_set_fix_val(
4746 __isl_take isl_set *set,
4747 enum isl_dim_type type, unsigned pos,
4748 __isl_take isl_val *v);
4750 #include <isl/map.h>
4751 __isl_give isl_basic_map *isl_basic_map_fix_si(
4752 __isl_take isl_basic_map *bmap,
4753 enum isl_dim_type type, unsigned pos, int value);
4754 __isl_give isl_basic_map *isl_basic_map_fix_val(
4755 __isl_take isl_basic_map *bmap,
4756 enum isl_dim_type type, unsigned pos,
4757 __isl_take isl_val *v);
4758 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
4759 enum isl_dim_type type, unsigned pos, int value);
4760 __isl_give isl_map *isl_map_fix_val(
4761 __isl_take isl_map *map,
4762 enum isl_dim_type type, unsigned pos,
4763 __isl_take isl_val *v);
4765 #include <isl/aff.h>
4766 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4767 __isl_take isl_pw_multi_aff *pma,
4768 enum isl_dim_type type, unsigned pos, int value);
4770 #include <isl/polynomial.h>
4771 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4772 __isl_take isl_pw_qpolynomial *pwqp,
4773 enum isl_dim_type type, unsigned n,
4774 __isl_take isl_val *v);
4775 __isl_give isl_pw_qpolynomial_fold *
4776 isl_pw_qpolynomial_fold_fix_val(
4777 __isl_take isl_pw_qpolynomial_fold *pwf,
4778 enum isl_dim_type type, unsigned n,
4779 __isl_take isl_val *v);
4781 Intersect the set, relation or function domain
4782 with the hyperplane where the given
4783 dimension has the fixed given value.
4785 #include <isl/set.h>
4786 __isl_give isl_basic_set *
4787 isl_basic_set_lower_bound_val(
4788 __isl_take isl_basic_set *bset,
4789 enum isl_dim_type type, unsigned pos,
4790 __isl_take isl_val *value);
4791 __isl_give isl_basic_set *
4792 isl_basic_set_upper_bound_val(
4793 __isl_take isl_basic_set *bset,
4794 enum isl_dim_type type, unsigned pos,
4795 __isl_take isl_val *value);
4796 __isl_give isl_set *isl_set_lower_bound_si(
4797 __isl_take isl_set *set,
4798 enum isl_dim_type type, unsigned pos, int value);
4799 __isl_give isl_set *isl_set_lower_bound_val(
4800 __isl_take isl_set *set,
4801 enum isl_dim_type type, unsigned pos,
4802 __isl_take isl_val *value);
4803 __isl_give isl_set *isl_set_upper_bound_si(
4804 __isl_take isl_set *set,
4805 enum isl_dim_type type, unsigned pos, int value);
4806 __isl_give isl_set *isl_set_upper_bound_val(
4807 __isl_take isl_set *set,
4808 enum isl_dim_type type, unsigned pos,
4809 __isl_take isl_val *value);
4811 #include <isl/map.h>
4812 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
4813 __isl_take isl_basic_map *bmap,
4814 enum isl_dim_type type, unsigned pos, int value);
4815 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
4816 __isl_take isl_basic_map *bmap,
4817 enum isl_dim_type type, unsigned pos, int value);
4818 __isl_give isl_map *isl_map_lower_bound_si(
4819 __isl_take isl_map *map,
4820 enum isl_dim_type type, unsigned pos, int value);
4821 __isl_give isl_map *isl_map_upper_bound_si(
4822 __isl_take isl_map *map,
4823 enum isl_dim_type type, unsigned pos, int value);
4825 Intersect the set or relation with the half-space where the given
4826 dimension has a value bounded by the fixed given integer value.
4828 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
4829 enum isl_dim_type type1, int pos1,
4830 enum isl_dim_type type2, int pos2);
4831 __isl_give isl_basic_map *isl_basic_map_equate(
4832 __isl_take isl_basic_map *bmap,
4833 enum isl_dim_type type1, int pos1,
4834 enum isl_dim_type type2, int pos2);
4835 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
4836 enum isl_dim_type type1, int pos1,
4837 enum isl_dim_type type2, int pos2);
4839 Intersect the set or relation with the hyperplane where the given
4840 dimensions are equal to each other.
4842 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
4843 enum isl_dim_type type1, int pos1,
4844 enum isl_dim_type type2, int pos2);
4846 Intersect the relation with the hyperplane where the given
4847 dimensions have opposite values.
4849 __isl_give isl_map *isl_map_order_le(
4850 __isl_take isl_map *map,
4851 enum isl_dim_type type1, int pos1,
4852 enum isl_dim_type type2, int pos2);
4853 __isl_give isl_basic_map *isl_basic_map_order_ge(
4854 __isl_take isl_basic_map *bmap,
4855 enum isl_dim_type type1, int pos1,
4856 enum isl_dim_type type2, int pos2);
4857 __isl_give isl_map *isl_map_order_ge(
4858 __isl_take isl_map *map,
4859 enum isl_dim_type type1, int pos1,
4860 enum isl_dim_type type2, int pos2);
4861 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
4862 enum isl_dim_type type1, int pos1,
4863 enum isl_dim_type type2, int pos2);
4864 __isl_give isl_basic_map *isl_basic_map_order_gt(
4865 __isl_take isl_basic_map *bmap,
4866 enum isl_dim_type type1, int pos1,
4867 enum isl_dim_type type2, int pos2);
4868 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
4869 enum isl_dim_type type1, int pos1,
4870 enum isl_dim_type type2, int pos2);
4872 Intersect the relation with the half-space where the given
4873 dimensions satisfy the given ordering.
4875 #include <isl/union_set.h>
4876 __isl_give isl_union_map *isl_union_map_remove_map_if(
4877 __isl_take isl_union_map *umap,
4878 isl_bool (*fn)(__isl_keep isl_map *map,
4879 void *user), void *user);
4881 This function calls the callback function once for each
4882 pair of spaces for which there are elements in the input.
4883 If the callback returns C<isl_bool_true>, then all those elements
4884 are removed from the result. The only remaining elements in the output
4885 are then those for which the callback returns C<isl_bool_false>.
4889 #include <isl/aff.h>
4890 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4891 __isl_take isl_aff *aff);
4892 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4893 __isl_take isl_aff *aff);
4894 __isl_give isl_set *isl_pw_aff_pos_set(
4895 __isl_take isl_pw_aff *pa);
4896 __isl_give isl_set *isl_pw_aff_nonneg_set(
4897 __isl_take isl_pw_aff *pwaff);
4898 __isl_give isl_set *isl_pw_aff_zero_set(
4899 __isl_take isl_pw_aff *pwaff);
4900 __isl_give isl_set *isl_pw_aff_non_zero_set(
4901 __isl_take isl_pw_aff *pwaff);
4902 __isl_give isl_union_set *
4903 isl_union_pw_aff_zero_union_set(
4904 __isl_take isl_union_pw_aff *upa);
4905 __isl_give isl_union_set *
4906 isl_multi_union_pw_aff_zero_union_set(
4907 __isl_take isl_multi_union_pw_aff *mupa);
4909 The function C<isl_aff_neg_basic_set> returns a basic set
4910 containing those elements in the domain space
4911 of C<aff> where C<aff> is negative.
4912 The function C<isl_pw_aff_nonneg_set> returns a set
4913 containing those elements in the domain
4914 of C<pwaff> where C<pwaff> is non-negative.
4915 The function C<isl_multi_union_pw_aff_zero_union_set>
4916 returns a union set containing those elements
4917 in the domains of its elements where they are all zero.
4921 __isl_give isl_map *isl_set_identity(
4922 __isl_take isl_set *set);
4923 __isl_give isl_union_map *isl_union_set_identity(
4924 __isl_take isl_union_set *uset);
4925 __isl_give isl_union_pw_multi_aff *
4926 isl_union_set_identity_union_pw_multi_aff(
4927 __isl_take isl_union_set *uset);
4929 Construct an identity relation on the given (union) set.
4931 =item * Function Extraction
4933 A piecewise quasi affine expression that is equal to 1 on a set
4934 and 0 outside the set can be created using the following function.
4936 #include <isl/aff.h>
4937 __isl_give isl_pw_aff *isl_set_indicator_function(
4938 __isl_take isl_set *set);
4940 A piecewise multiple quasi affine expression can be extracted
4941 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4942 and the C<isl_map> is single-valued.
4943 In case of a conversion from an C<isl_union_map>
4944 to an C<isl_union_pw_multi_aff>, these properties need to hold
4945 in each domain space.
4946 A conversion to a C<isl_multi_union_pw_aff> additionally
4947 requires that the input is non-empty and involves only a single
4950 #include <isl/aff.h>
4951 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4952 __isl_take isl_set *set);
4953 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4954 __isl_take isl_map *map);
4956 __isl_give isl_union_pw_multi_aff *
4957 isl_union_pw_multi_aff_from_union_set(
4958 __isl_take isl_union_set *uset);
4959 __isl_give isl_union_pw_multi_aff *
4960 isl_union_pw_multi_aff_from_union_map(
4961 __isl_take isl_union_map *umap);
4963 __isl_give isl_multi_union_pw_aff *
4964 isl_multi_union_pw_aff_from_union_map(
4965 __isl_take isl_union_map *umap);
4969 __isl_give isl_basic_set *isl_basic_map_deltas(
4970 __isl_take isl_basic_map *bmap);
4971 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
4972 __isl_give isl_union_set *isl_union_map_deltas(
4973 __isl_take isl_union_map *umap);
4975 These functions return a (basic) set containing the differences
4976 between image elements and corresponding domain elements in the input.
4978 __isl_give isl_basic_map *isl_basic_map_deltas_map(
4979 __isl_take isl_basic_map *bmap);
4980 __isl_give isl_map *isl_map_deltas_map(
4981 __isl_take isl_map *map);
4982 __isl_give isl_union_map *isl_union_map_deltas_map(
4983 __isl_take isl_union_map *umap);
4985 The functions above construct a (basic, regular or union) relation
4986 that maps (a wrapped version of) the input relation to its delta set.
4990 Simplify the representation of a set, relation or functions by trying
4991 to combine pairs of basic sets or relations into a single
4992 basic set or relation.
4994 #include <isl/set.h>
4995 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
4997 #include <isl/map.h>
4998 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
5000 #include <isl/union_set.h>
5001 __isl_give isl_union_set *isl_union_set_coalesce(
5002 __isl_take isl_union_set *uset);
5004 #include <isl/union_map.h>
5005 __isl_give isl_union_map *isl_union_map_coalesce(
5006 __isl_take isl_union_map *umap);
5008 #include <isl/aff.h>
5009 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
5010 __isl_take isl_pw_aff *pwqp);
5011 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
5012 __isl_take isl_pw_multi_aff *pma);
5013 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
5014 __isl_take isl_multi_pw_aff *mpa);
5015 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
5016 __isl_take isl_union_pw_aff *upa);
5017 __isl_give isl_union_pw_multi_aff *
5018 isl_union_pw_multi_aff_coalesce(
5019 __isl_take isl_union_pw_multi_aff *upma);
5020 __isl_give isl_multi_union_pw_aff *
5021 isl_multi_union_pw_aff_coalesce(
5022 __isl_take isl_multi_union_pw_aff *aff);
5024 #include <isl/polynomial.h>
5025 __isl_give isl_pw_qpolynomial_fold *
5026 isl_pw_qpolynomial_fold_coalesce(
5027 __isl_take isl_pw_qpolynomial_fold *pwf);
5028 __isl_give isl_union_pw_qpolynomial *
5029 isl_union_pw_qpolynomial_coalesce(
5030 __isl_take isl_union_pw_qpolynomial *upwqp);
5031 __isl_give isl_union_pw_qpolynomial_fold *
5032 isl_union_pw_qpolynomial_fold_coalesce(
5033 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5035 One of the methods for combining pairs of basic sets or relations
5036 can result in coefficients that are much larger than those that appear
5037 in the constraints of the input. By default, the coefficients are
5038 not allowed to grow larger, but this can be changed by unsetting
5039 the following option.
5041 isl_stat isl_options_set_coalesce_bounded_wrapping(
5042 isl_ctx *ctx, int val);
5043 int isl_options_get_coalesce_bounded_wrapping(
5046 =item * Detecting equalities
5048 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
5049 __isl_take isl_basic_set *bset);
5050 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
5051 __isl_take isl_basic_map *bmap);
5052 __isl_give isl_set *isl_set_detect_equalities(
5053 __isl_take isl_set *set);
5054 __isl_give isl_map *isl_map_detect_equalities(
5055 __isl_take isl_map *map);
5056 __isl_give isl_union_set *isl_union_set_detect_equalities(
5057 __isl_take isl_union_set *uset);
5058 __isl_give isl_union_map *isl_union_map_detect_equalities(
5059 __isl_take isl_union_map *umap);
5061 Simplify the representation of a set or relation by detecting implicit
5064 =item * Removing redundant constraints
5066 #include <isl/set.h>
5067 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
5068 __isl_take isl_basic_set *bset);
5069 __isl_give isl_set *isl_set_remove_redundancies(
5070 __isl_take isl_set *set);
5072 #include <isl/union_set.h>
5073 __isl_give isl_union_set *
5074 isl_union_set_remove_redundancies(
5075 __isl_take isl_union_set *uset);
5077 #include <isl/map.h>
5078 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
5079 __isl_take isl_basic_map *bmap);
5080 __isl_give isl_map *isl_map_remove_redundancies(
5081 __isl_take isl_map *map);
5083 #include <isl/union_map.h>
5084 __isl_give isl_union_map *
5085 isl_union_map_remove_redundancies(
5086 __isl_take isl_union_map *umap);
5090 __isl_give isl_basic_set *isl_set_convex_hull(
5091 __isl_take isl_set *set);
5092 __isl_give isl_basic_map *isl_map_convex_hull(
5093 __isl_take isl_map *map);
5095 If the input set or relation has any existentially quantified
5096 variables, then the result of these operations is currently undefined.
5100 #include <isl/set.h>
5101 __isl_give isl_basic_set *
5102 isl_set_unshifted_simple_hull(
5103 __isl_take isl_set *set);
5104 __isl_give isl_basic_set *isl_set_simple_hull(
5105 __isl_take isl_set *set);
5106 __isl_give isl_basic_set *
5107 isl_set_plain_unshifted_simple_hull(
5108 __isl_take isl_set *set);
5109 __isl_give isl_basic_set *
5110 isl_set_unshifted_simple_hull_from_set_list(
5111 __isl_take isl_set *set,
5112 __isl_take isl_set_list *list);
5114 #include <isl/map.h>
5115 __isl_give isl_basic_map *
5116 isl_map_unshifted_simple_hull(
5117 __isl_take isl_map *map);
5118 __isl_give isl_basic_map *isl_map_simple_hull(
5119 __isl_take isl_map *map);
5120 __isl_give isl_basic_map *
5121 isl_map_plain_unshifted_simple_hull(
5122 __isl_take isl_map *map);
5123 __isl_give isl_basic_map *
5124 isl_map_unshifted_simple_hull_from_map_list(
5125 __isl_take isl_map *map,
5126 __isl_take isl_map_list *list);
5128 #include <isl/union_map.h>
5129 __isl_give isl_union_map *isl_union_map_simple_hull(
5130 __isl_take isl_union_map *umap);
5132 These functions compute a single basic set or relation
5133 that contains the whole input set or relation.
5134 In particular, the output is described by translates
5135 of the constraints describing the basic sets or relations in the input.
5136 In case of C<isl_set_unshifted_simple_hull>, only the original
5137 constraints are used, without any translation.
5138 In case of C<isl_set_plain_unshifted_simple_hull> and
5139 C<isl_map_plain_unshifted_simple_hull>, the result is described
5140 by original constraints that are obviously satisfied
5141 by the entire input set or relation.
5142 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
5143 C<isl_map_unshifted_simple_hull_from_map_list>, the
5144 constraints are taken from the elements of the second argument.
5148 (See \autoref{s:simple hull}.)
5154 __isl_give isl_basic_set *isl_basic_set_affine_hull(
5155 __isl_take isl_basic_set *bset);
5156 __isl_give isl_basic_set *isl_set_affine_hull(
5157 __isl_take isl_set *set);
5158 __isl_give isl_union_set *isl_union_set_affine_hull(
5159 __isl_take isl_union_set *uset);
5160 __isl_give isl_basic_map *isl_basic_map_affine_hull(
5161 __isl_take isl_basic_map *bmap);
5162 __isl_give isl_basic_map *isl_map_affine_hull(
5163 __isl_take isl_map *map);
5164 __isl_give isl_union_map *isl_union_map_affine_hull(
5165 __isl_take isl_union_map *umap);
5167 In case of union sets and relations, the affine hull is computed
5170 =item * Polyhedral hull
5172 __isl_give isl_basic_set *isl_set_polyhedral_hull(
5173 __isl_take isl_set *set);
5174 __isl_give isl_basic_map *isl_map_polyhedral_hull(
5175 __isl_take isl_map *map);
5176 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
5177 __isl_take isl_union_set *uset);
5178 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
5179 __isl_take isl_union_map *umap);
5181 These functions compute a single basic set or relation
5182 not involving any existentially quantified variables
5183 that contains the whole input set or relation.
5184 In case of union sets and relations, the polyhedral hull is computed
5187 =item * Other approximations
5189 #include <isl/set.h>
5190 __isl_give isl_basic_set *
5191 isl_basic_set_drop_constraints_involving_dims(
5192 __isl_take isl_basic_set *bset,
5193 enum isl_dim_type type,
5194 unsigned first, unsigned n);
5195 __isl_give isl_basic_set *
5196 isl_basic_set_drop_constraints_not_involving_dims(
5197 __isl_take isl_basic_set *bset,
5198 enum isl_dim_type type,
5199 unsigned first, unsigned n);
5200 __isl_give isl_set *
5201 isl_set_drop_constraints_involving_dims(
5202 __isl_take isl_set *set,
5203 enum isl_dim_type type,
5204 unsigned first, unsigned n);
5205 __isl_give isl_set *
5206 isl_set_drop_constraints_not_involving_dims(
5207 __isl_take isl_set *set,
5208 enum isl_dim_type type,
5209 unsigned first, unsigned n);
5211 #include <isl/map.h>
5212 __isl_give isl_basic_map *
5213 isl_basic_map_drop_constraints_involving_dims(
5214 __isl_take isl_basic_map *bmap,
5215 enum isl_dim_type type,
5216 unsigned first, unsigned n);
5217 __isl_give isl_basic_map *
5218 isl_basic_map_drop_constraints_not_involving_dims(
5219 __isl_take isl_basic_map *bmap,
5220 enum isl_dim_type type,
5221 unsigned first, unsigned n);
5222 __isl_give isl_map *
5223 isl_map_drop_constraints_involving_dims(
5224 __isl_take isl_map *map,
5225 enum isl_dim_type type,
5226 unsigned first, unsigned n);
5227 __isl_give isl_map *
5228 isl_map_drop_constraints_not_involving_dims(
5229 __isl_take isl_map *map,
5230 enum isl_dim_type type,
5231 unsigned first, unsigned n);
5233 These functions drop any constraints (not) involving the specified dimensions.
5234 Note that the result depends on the representation of the input.
5236 #include <isl/polynomial.h>
5237 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5238 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5239 __isl_give isl_union_pw_qpolynomial *
5240 isl_union_pw_qpolynomial_to_polynomial(
5241 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5243 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5244 the polynomial will be an overapproximation. If C<sign> is negative,
5245 it will be an underapproximation. If C<sign> is zero, the approximation
5246 will lie somewhere in between.
5250 __isl_give isl_basic_set *isl_basic_set_sample(
5251 __isl_take isl_basic_set *bset);
5252 __isl_give isl_basic_set *isl_set_sample(
5253 __isl_take isl_set *set);
5254 __isl_give isl_basic_map *isl_basic_map_sample(
5255 __isl_take isl_basic_map *bmap);
5256 __isl_give isl_basic_map *isl_map_sample(
5257 __isl_take isl_map *map);
5259 If the input (basic) set or relation is non-empty, then return
5260 a singleton subset of the input. Otherwise, return an empty set.
5262 =item * Optimization
5264 #include <isl/ilp.h>
5265 __isl_give isl_val *isl_basic_set_max_val(
5266 __isl_keep isl_basic_set *bset,
5267 __isl_keep isl_aff *obj);
5268 __isl_give isl_val *isl_set_min_val(
5269 __isl_keep isl_set *set,
5270 __isl_keep isl_aff *obj);
5271 __isl_give isl_val *isl_set_max_val(
5272 __isl_keep isl_set *set,
5273 __isl_keep isl_aff *obj);
5274 __isl_give isl_multi_val *
5275 isl_union_set_min_multi_union_pw_aff(
5276 __isl_keep isl_union_set *set,
5277 __isl_keep isl_multi_union_pw_aff *obj);
5279 Compute the minimum or maximum of the integer affine expression C<obj>
5280 over the points in C<set>, returning the result in C<opt>.
5281 The result is C<NULL> in case of an error, the optimal value in case
5282 there is one, negative infinity or infinity if the problem is unbounded and
5283 NaN if the problem is empty.
5285 #include <isl/ilp.h>
5286 __isl_give isl_val *isl_basic_set_dim_max_val(
5287 __isl_take isl_basic_set *bset, int pos);
5289 Return the maximal value attained by the given set dimension,
5290 independently of the parameter values and of any other dimensions.
5291 The result is C<NULL> in case of an error, the optimal value in case
5292 there is one, infinity if the problem is unbounded and
5293 NaN if the input is empty.
5295 =item * Parametric optimization
5297 __isl_give isl_pw_aff *isl_set_dim_min(
5298 __isl_take isl_set *set, int pos);
5299 __isl_give isl_pw_aff *isl_set_dim_max(
5300 __isl_take isl_set *set, int pos);
5301 __isl_give isl_pw_aff *isl_map_dim_min(
5302 __isl_take isl_map *map, int pos);
5303 __isl_give isl_pw_aff *isl_map_dim_max(
5304 __isl_take isl_map *map, int pos);
5306 Compute the minimum or maximum of the given set or output dimension
5307 as a function of the parameters (and input dimensions), but independently
5308 of the other set or output dimensions.
5309 For lexicographic optimization, see L<"Lexicographic Optimization">.
5313 The following functions compute either the set of (rational) coefficient
5314 values of valid constraints for the given set or the set of (rational)
5315 values satisfying the constraints with coefficients from the given set.
5316 Internally, these two sets of functions perform essentially the
5317 same operations, except that the set of coefficients is assumed to
5318 be a cone, while the set of values may be any polyhedron.
5319 The current implementation is based on the Farkas lemma and
5320 Fourier-Motzkin elimination, but this may change or be made optional
5321 in future. In particular, future implementations may use different
5322 dualization algorithms or skip the elimination step.
5324 #include <isl/set.h>
5325 __isl_give isl_basic_set *isl_basic_set_coefficients(
5326 __isl_take isl_basic_set *bset);
5327 __isl_give isl_basic_set_list *
5328 isl_basic_set_list_coefficients(
5329 __isl_take isl_basic_set_list *list);
5330 __isl_give isl_basic_set *isl_set_coefficients(
5331 __isl_take isl_set *set);
5332 __isl_give isl_union_set *isl_union_set_coefficients(
5333 __isl_take isl_union_set *bset);
5334 __isl_give isl_basic_set *isl_basic_set_solutions(
5335 __isl_take isl_basic_set *bset);
5336 __isl_give isl_basic_set *isl_set_solutions(
5337 __isl_take isl_set *set);
5338 __isl_give isl_union_set *isl_union_set_solutions(
5339 __isl_take isl_union_set *bset);
5343 __isl_give isl_map *isl_map_fixed_power_val(
5344 __isl_take isl_map *map,
5345 __isl_take isl_val *exp);
5346 __isl_give isl_union_map *
5347 isl_union_map_fixed_power_val(
5348 __isl_take isl_union_map *umap,
5349 __isl_take isl_val *exp);
5351 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
5352 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
5353 of C<map> is computed.
5355 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
5357 __isl_give isl_union_map *isl_union_map_power(
5358 __isl_take isl_union_map *umap, int *exact);
5360 Compute a parametric representation for all positive powers I<k> of C<map>.
5361 The result maps I<k> to a nested relation corresponding to the
5362 I<k>th power of C<map>.
5363 The result may be an overapproximation. If the result is known to be exact,
5364 then C<*exact> is set to C<1>.
5366 =item * Transitive closure
5368 __isl_give isl_map *isl_map_transitive_closure(
5369 __isl_take isl_map *map, int *exact);
5370 __isl_give isl_union_map *isl_union_map_transitive_closure(
5371 __isl_take isl_union_map *umap, int *exact);
5373 Compute the transitive closure of C<map>.
5374 The result may be an overapproximation. If the result is known to be exact,
5375 then C<*exact> is set to C<1>.
5377 =item * Reaching path lengths
5379 __isl_give isl_map *isl_map_reaching_path_lengths(
5380 __isl_take isl_map *map, int *exact);
5382 Compute a relation that maps each element in the range of C<map>
5383 to the lengths of all paths composed of edges in C<map> that
5384 end up in the given element.
5385 The result may be an overapproximation. If the result is known to be exact,
5386 then C<*exact> is set to C<1>.
5387 To compute the I<maximal> path length, the resulting relation
5388 should be postprocessed by C<isl_map_lexmax>.
5389 In particular, if the input relation is a dependence relation
5390 (mapping sources to sinks), then the maximal path length corresponds
5391 to the free schedule.
5392 Note, however, that C<isl_map_lexmax> expects the maximum to be
5393 finite, so if the path lengths are unbounded (possibly due to
5394 the overapproximation), then you will get an error message.
5398 #include <isl/space.h>
5399 __isl_give isl_space *isl_space_wrap(
5400 __isl_take isl_space *space);
5401 __isl_give isl_space *isl_space_unwrap(
5402 __isl_take isl_space *space);
5404 #include <isl/local_space.h>
5405 __isl_give isl_local_space *isl_local_space_wrap(
5406 __isl_take isl_local_space *ls);
5408 #include <isl/set.h>
5409 __isl_give isl_basic_map *isl_basic_set_unwrap(
5410 __isl_take isl_basic_set *bset);
5411 __isl_give isl_map *isl_set_unwrap(
5412 __isl_take isl_set *set);
5414 #include <isl/map.h>
5415 __isl_give isl_basic_set *isl_basic_map_wrap(
5416 __isl_take isl_basic_map *bmap);
5417 __isl_give isl_set *isl_map_wrap(
5418 __isl_take isl_map *map);
5420 #include <isl/union_set.h>
5421 __isl_give isl_union_map *isl_union_set_unwrap(
5422 __isl_take isl_union_set *uset);
5424 #include <isl/union_map.h>
5425 __isl_give isl_union_set *isl_union_map_wrap(
5426 __isl_take isl_union_map *umap);
5428 The input to C<isl_space_unwrap> should
5429 be the space of a set, while that of
5430 C<isl_space_wrap> should be the space of a relation.
5431 Conversely, the output of C<isl_space_unwrap> is the space
5432 of a relation, while that of C<isl_space_wrap> is the space of a set.
5436 Remove any internal structure of domain (and range) of the given
5437 set or relation. If there is any such internal structure in the input,
5438 then the name of the space is also removed.
5440 #include <isl/space.h>
5441 __isl_give isl_space *isl_space_flatten_domain(
5442 __isl_take isl_space *space);
5443 __isl_give isl_space *isl_space_flatten_range(
5444 __isl_take isl_space *space);
5446 #include <isl/local_space.h>
5447 __isl_give isl_local_space *
5448 isl_local_space_flatten_domain(
5449 __isl_take isl_local_space *ls);
5450 __isl_give isl_local_space *
5451 isl_local_space_flatten_range(
5452 __isl_take isl_local_space *ls);
5454 #include <isl/set.h>
5455 __isl_give isl_basic_set *isl_basic_set_flatten(
5456 __isl_take isl_basic_set *bset);
5457 __isl_give isl_set *isl_set_flatten(
5458 __isl_take isl_set *set);
5460 #include <isl/map.h>
5461 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
5462 __isl_take isl_basic_map *bmap);
5463 __isl_give isl_basic_map *isl_basic_map_flatten_range(
5464 __isl_take isl_basic_map *bmap);
5465 __isl_give isl_map *isl_map_flatten_range(
5466 __isl_take isl_map *map);
5467 __isl_give isl_map *isl_map_flatten_domain(
5468 __isl_take isl_map *map);
5469 __isl_give isl_basic_map *isl_basic_map_flatten(
5470 __isl_take isl_basic_map *bmap);
5471 __isl_give isl_map *isl_map_flatten(
5472 __isl_take isl_map *map);
5474 #include <isl/val.h>
5475 __isl_give isl_multi_val *isl_multi_val_flatten_range(
5476 __isl_take isl_multi_val *mv);
5478 #include <isl/aff.h>
5479 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
5480 __isl_take isl_multi_aff *ma);
5481 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
5482 __isl_take isl_multi_aff *ma);
5483 __isl_give isl_multi_pw_aff *
5484 isl_multi_pw_aff_flatten_range(
5485 __isl_take isl_multi_pw_aff *mpa);
5486 __isl_give isl_multi_union_pw_aff *
5487 isl_multi_union_pw_aff_flatten_range(
5488 __isl_take isl_multi_union_pw_aff *mupa);
5490 #include <isl/map.h>
5491 __isl_give isl_map *isl_set_flatten_map(
5492 __isl_take isl_set *set);
5494 The function above constructs a relation
5495 that maps the input set to a flattened version of the set.
5499 Lift the input set to a space with extra dimensions corresponding
5500 to the existentially quantified variables in the input.
5501 In particular, the result lives in a wrapped map where the domain
5502 is the original space and the range corresponds to the original
5503 existentially quantified variables.
5505 #include <isl/set.h>
5506 __isl_give isl_basic_set *isl_basic_set_lift(
5507 __isl_take isl_basic_set *bset);
5508 __isl_give isl_set *isl_set_lift(
5509 __isl_take isl_set *set);
5510 __isl_give isl_union_set *isl_union_set_lift(
5511 __isl_take isl_union_set *uset);
5513 Given a local space that contains the existentially quantified
5514 variables of a set, a basic relation that, when applied to
5515 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
5516 can be constructed using the following function.
5518 #include <isl/local_space.h>
5519 __isl_give isl_basic_map *isl_local_space_lifting(
5520 __isl_take isl_local_space *ls);
5522 #include <isl/aff.h>
5523 __isl_give isl_multi_aff *isl_multi_aff_lift(
5524 __isl_take isl_multi_aff *maff,
5525 __isl_give isl_local_space **ls);
5527 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
5528 then it is assigned the local space that lies at the basis of
5529 the lifting applied.
5531 =item * Internal Product
5533 #include <isl/space.h>
5534 __isl_give isl_space *isl_space_zip(
5535 __isl_take isl_space *space);
5537 #include <isl/map.h>
5538 __isl_give isl_basic_map *isl_basic_map_zip(
5539 __isl_take isl_basic_map *bmap);
5540 __isl_give isl_map *isl_map_zip(
5541 __isl_take isl_map *map);
5543 #include <isl/union_map.h>
5544 __isl_give isl_union_map *isl_union_map_zip(
5545 __isl_take isl_union_map *umap);
5547 Given a relation with nested relations for domain and range,
5548 interchange the range of the domain with the domain of the range.
5552 #include <isl/space.h>
5553 __isl_give isl_space *isl_space_curry(
5554 __isl_take isl_space *space);
5555 __isl_give isl_space *isl_space_uncurry(
5556 __isl_take isl_space *space);
5558 #include <isl/map.h>
5559 __isl_give isl_basic_map *isl_basic_map_curry(
5560 __isl_take isl_basic_map *bmap);
5561 __isl_give isl_basic_map *isl_basic_map_uncurry(
5562 __isl_take isl_basic_map *bmap);
5563 __isl_give isl_map *isl_map_curry(
5564 __isl_take isl_map *map);
5565 __isl_give isl_map *isl_map_uncurry(
5566 __isl_take isl_map *map);
5568 #include <isl/union_map.h>
5569 __isl_give isl_union_map *isl_union_map_curry(
5570 __isl_take isl_union_map *umap);
5571 __isl_give isl_union_map *isl_union_map_uncurry(
5572 __isl_take isl_union_map *umap);
5574 Given a relation with a nested relation for domain,
5575 the C<curry> functions
5576 move the range of the nested relation out of the domain
5577 and use it as the domain of a nested relation in the range,
5578 with the original range as range of this nested relation.
5579 The C<uncurry> functions perform the inverse operation.
5581 #include <isl/space.h>
5582 __isl_give isl_space *isl_space_range_curry(
5583 __isl_take isl_space *space);
5585 #include <isl/map.h>
5586 __isl_give isl_map *isl_map_range_curry(
5587 __isl_take isl_map *map);
5589 #include <isl/union_map.h>
5590 __isl_give isl_union_map *isl_union_map_range_curry(
5591 __isl_take isl_union_map *umap);
5593 These functions apply the currying to the relation that
5594 is nested inside the range of the input.
5596 =item * Aligning parameters
5598 Change the order of the parameters of the given set, relation
5600 such that the first parameters match those of C<model>.
5601 This may involve the introduction of extra parameters.
5602 All parameters need to be named.
5604 #include <isl/space.h>
5605 __isl_give isl_space *isl_space_align_params(
5606 __isl_take isl_space *space1,
5607 __isl_take isl_space *space2)
5609 #include <isl/set.h>
5610 __isl_give isl_basic_set *isl_basic_set_align_params(
5611 __isl_take isl_basic_set *bset,
5612 __isl_take isl_space *model);
5613 __isl_give isl_set *isl_set_align_params(
5614 __isl_take isl_set *set,
5615 __isl_take isl_space *model);
5617 #include <isl/map.h>
5618 __isl_give isl_basic_map *isl_basic_map_align_params(
5619 __isl_take isl_basic_map *bmap,
5620 __isl_take isl_space *model);
5621 __isl_give isl_map *isl_map_align_params(
5622 __isl_take isl_map *map,
5623 __isl_take isl_space *model);
5625 #include <isl/val.h>
5626 __isl_give isl_multi_val *isl_multi_val_align_params(
5627 __isl_take isl_multi_val *mv,
5628 __isl_take isl_space *model);
5630 #include <isl/aff.h>
5631 __isl_give isl_aff *isl_aff_align_params(
5632 __isl_take isl_aff *aff,
5633 __isl_take isl_space *model);
5634 __isl_give isl_multi_aff *isl_multi_aff_align_params(
5635 __isl_take isl_multi_aff *multi,
5636 __isl_take isl_space *model);
5637 __isl_give isl_pw_aff *isl_pw_aff_align_params(
5638 __isl_take isl_pw_aff *pwaff,
5639 __isl_take isl_space *model);
5640 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
5641 __isl_take isl_pw_multi_aff *pma,
5642 __isl_take isl_space *model);
5643 __isl_give isl_union_pw_aff *
5644 isl_union_pw_aff_align_params(
5645 __isl_take isl_union_pw_aff *upa,
5646 __isl_take isl_space *model);
5647 __isl_give isl_union_pw_multi_aff *
5648 isl_union_pw_multi_aff_align_params(
5649 __isl_take isl_union_pw_multi_aff *upma,
5650 __isl_take isl_space *model);
5651 __isl_give isl_multi_union_pw_aff *
5652 isl_multi_union_pw_aff_align_params(
5653 __isl_take isl_multi_union_pw_aff *mupa,
5654 __isl_take isl_space *model);
5656 #include <isl/polynomial.h>
5657 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5658 __isl_take isl_qpolynomial *qp,
5659 __isl_take isl_space *model);
5661 =item * Unary Arithmetic Operations
5663 #include <isl/set.h>
5664 __isl_give isl_set *isl_set_neg(
5665 __isl_take isl_set *set);
5666 #include <isl/map.h>
5667 __isl_give isl_map *isl_map_neg(
5668 __isl_take isl_map *map);
5670 C<isl_set_neg> constructs a set containing the opposites of
5671 the elements in its argument.
5672 The domain of the result of C<isl_map_neg> is the same
5673 as the domain of its argument. The corresponding range
5674 elements are the opposites of the corresponding range
5675 elements in the argument.
5677 #include <isl/val.h>
5678 __isl_give isl_multi_val *isl_multi_val_neg(
5679 __isl_take isl_multi_val *mv);
5681 #include <isl/aff.h>
5682 __isl_give isl_aff *isl_aff_neg(
5683 __isl_take isl_aff *aff);
5684 __isl_give isl_multi_aff *isl_multi_aff_neg(
5685 __isl_take isl_multi_aff *ma);
5686 __isl_give isl_pw_aff *isl_pw_aff_neg(
5687 __isl_take isl_pw_aff *pwaff);
5688 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
5689 __isl_take isl_pw_multi_aff *pma);
5690 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
5691 __isl_take isl_multi_pw_aff *mpa);
5692 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
5693 __isl_take isl_union_pw_aff *upa);
5694 __isl_give isl_union_pw_multi_aff *
5695 isl_union_pw_multi_aff_neg(
5696 __isl_take isl_union_pw_multi_aff *upma);
5697 __isl_give isl_multi_union_pw_aff *
5698 isl_multi_union_pw_aff_neg(
5699 __isl_take isl_multi_union_pw_aff *mupa);
5700 __isl_give isl_aff *isl_aff_ceil(
5701 __isl_take isl_aff *aff);
5702 __isl_give isl_pw_aff *isl_pw_aff_ceil(
5703 __isl_take isl_pw_aff *pwaff);
5704 __isl_give isl_aff *isl_aff_floor(
5705 __isl_take isl_aff *aff);
5706 __isl_give isl_multi_aff *isl_multi_aff_floor(
5707 __isl_take isl_multi_aff *ma);
5708 __isl_give isl_pw_aff *isl_pw_aff_floor(
5709 __isl_take isl_pw_aff *pwaff);
5710 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
5711 __isl_take isl_union_pw_aff *upa);
5712 __isl_give isl_multi_union_pw_aff *
5713 isl_multi_union_pw_aff_floor(
5714 __isl_take isl_multi_union_pw_aff *mupa);
5716 #include <isl/aff.h>
5717 __isl_give isl_pw_aff *isl_pw_aff_list_min(
5718 __isl_take isl_pw_aff_list *list);
5719 __isl_give isl_pw_aff *isl_pw_aff_list_max(
5720 __isl_take isl_pw_aff_list *list);
5722 #include <isl/polynomial.h>
5723 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5724 __isl_take isl_qpolynomial *qp);
5725 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5726 __isl_take isl_pw_qpolynomial *pwqp);
5727 __isl_give isl_union_pw_qpolynomial *
5728 isl_union_pw_qpolynomial_neg(
5729 __isl_take isl_union_pw_qpolynomial *upwqp);
5730 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5731 __isl_take isl_qpolynomial *qp,
5733 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5734 __isl_take isl_pw_qpolynomial *pwqp,
5739 The following functions evaluate a function in a point.
5741 #include <isl/polynomial.h>
5742 __isl_give isl_val *isl_pw_qpolynomial_eval(
5743 __isl_take isl_pw_qpolynomial *pwqp,
5744 __isl_take isl_point *pnt);
5745 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5746 __isl_take isl_pw_qpolynomial_fold *pwf,
5747 __isl_take isl_point *pnt);
5748 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5749 __isl_take isl_union_pw_qpolynomial *upwqp,
5750 __isl_take isl_point *pnt);
5751 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5752 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5753 __isl_take isl_point *pnt);
5755 =item * Dimension manipulation
5757 It is usually not advisable to directly change the (input or output)
5758 space of a set or a relation as this removes the name and the internal
5759 structure of the space. However, the functions below can be useful
5760 to add new parameters, assuming
5761 C<isl_set_align_params> and C<isl_map_align_params>
5764 #include <isl/space.h>
5765 __isl_give isl_space *isl_space_add_dims(
5766 __isl_take isl_space *space,
5767 enum isl_dim_type type, unsigned n);
5768 __isl_give isl_space *isl_space_insert_dims(
5769 __isl_take isl_space *space,
5770 enum isl_dim_type type, unsigned pos, unsigned n);
5771 __isl_give isl_space *isl_space_drop_dims(
5772 __isl_take isl_space *space,
5773 enum isl_dim_type type, unsigned first, unsigned n);
5774 __isl_give isl_space *isl_space_move_dims(
5775 __isl_take isl_space *space,
5776 enum isl_dim_type dst_type, unsigned dst_pos,
5777 enum isl_dim_type src_type, unsigned src_pos,
5780 #include <isl/local_space.h>
5781 __isl_give isl_local_space *isl_local_space_add_dims(
5782 __isl_take isl_local_space *ls,
5783 enum isl_dim_type type, unsigned n);
5784 __isl_give isl_local_space *isl_local_space_insert_dims(
5785 __isl_take isl_local_space *ls,
5786 enum isl_dim_type type, unsigned first, unsigned n);
5787 __isl_give isl_local_space *isl_local_space_drop_dims(
5788 __isl_take isl_local_space *ls,
5789 enum isl_dim_type type, unsigned first, unsigned n);
5791 #include <isl/set.h>
5792 __isl_give isl_basic_set *isl_basic_set_add_dims(
5793 __isl_take isl_basic_set *bset,
5794 enum isl_dim_type type, unsigned n);
5795 __isl_give isl_set *isl_set_add_dims(
5796 __isl_take isl_set *set,
5797 enum isl_dim_type type, unsigned n);
5798 __isl_give isl_basic_set *isl_basic_set_insert_dims(
5799 __isl_take isl_basic_set *bset,
5800 enum isl_dim_type type, unsigned pos,
5802 __isl_give isl_set *isl_set_insert_dims(
5803 __isl_take isl_set *set,
5804 enum isl_dim_type type, unsigned pos, unsigned n);
5805 __isl_give isl_basic_set *isl_basic_set_move_dims(
5806 __isl_take isl_basic_set *bset,
5807 enum isl_dim_type dst_type, unsigned dst_pos,
5808 enum isl_dim_type src_type, unsigned src_pos,
5810 __isl_give isl_set *isl_set_move_dims(
5811 __isl_take isl_set *set,
5812 enum isl_dim_type dst_type, unsigned dst_pos,
5813 enum isl_dim_type src_type, unsigned src_pos,
5816 #include <isl/map.h>
5817 __isl_give isl_basic_map *isl_basic_map_add_dims(
5818 __isl_take isl_basic_map *bmap,
5819 enum isl_dim_type type, unsigned n);
5820 __isl_give isl_map *isl_map_add_dims(
5821 __isl_take isl_map *map,
5822 enum isl_dim_type type, unsigned n);
5823 __isl_give isl_basic_map *isl_basic_map_insert_dims(
5824 __isl_take isl_basic_map *bmap,
5825 enum isl_dim_type type, unsigned pos,
5827 __isl_give isl_map *isl_map_insert_dims(
5828 __isl_take isl_map *map,
5829 enum isl_dim_type type, unsigned pos, unsigned n);
5830 __isl_give isl_basic_map *isl_basic_map_move_dims(
5831 __isl_take isl_basic_map *bmap,
5832 enum isl_dim_type dst_type, unsigned dst_pos,
5833 enum isl_dim_type src_type, unsigned src_pos,
5835 __isl_give isl_map *isl_map_move_dims(
5836 __isl_take isl_map *map,
5837 enum isl_dim_type dst_type, unsigned dst_pos,
5838 enum isl_dim_type src_type, unsigned src_pos,
5841 #include <isl/val.h>
5842 __isl_give isl_multi_val *isl_multi_val_insert_dims(
5843 __isl_take isl_multi_val *mv,
5844 enum isl_dim_type type, unsigned first, unsigned n);
5845 __isl_give isl_multi_val *isl_multi_val_add_dims(
5846 __isl_take isl_multi_val *mv,
5847 enum isl_dim_type type, unsigned n);
5848 __isl_give isl_multi_val *isl_multi_val_drop_dims(
5849 __isl_take isl_multi_val *mv,
5850 enum isl_dim_type type, unsigned first, unsigned n);
5852 #include <isl/aff.h>
5853 __isl_give isl_aff *isl_aff_insert_dims(
5854 __isl_take isl_aff *aff,
5855 enum isl_dim_type type, unsigned first, unsigned n);
5856 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
5857 __isl_take isl_multi_aff *ma,
5858 enum isl_dim_type type, unsigned first, unsigned n);
5859 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
5860 __isl_take isl_pw_aff *pwaff,
5861 enum isl_dim_type type, unsigned first, unsigned n);
5862 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
5863 __isl_take isl_multi_pw_aff *mpa,
5864 enum isl_dim_type type, unsigned first, unsigned n);
5865 __isl_give isl_aff *isl_aff_add_dims(
5866 __isl_take isl_aff *aff,
5867 enum isl_dim_type type, unsigned n);
5868 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
5869 __isl_take isl_multi_aff *ma,
5870 enum isl_dim_type type, unsigned n);
5871 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
5872 __isl_take isl_pw_aff *pwaff,
5873 enum isl_dim_type type, unsigned n);
5874 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
5875 __isl_take isl_multi_pw_aff *mpa,
5876 enum isl_dim_type type, unsigned n);
5877 __isl_give isl_aff *isl_aff_drop_dims(
5878 __isl_take isl_aff *aff,
5879 enum isl_dim_type type, unsigned first, unsigned n);
5880 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
5881 __isl_take isl_multi_aff *maff,
5882 enum isl_dim_type type, unsigned first, unsigned n);
5883 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
5884 __isl_take isl_pw_aff *pwaff,
5885 enum isl_dim_type type, unsigned first, unsigned n);
5886 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
5887 __isl_take isl_pw_multi_aff *pma,
5888 enum isl_dim_type type, unsigned first, unsigned n);
5889 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
5890 __isl_take isl_union_pw_aff *upa,
5891 enum isl_dim_type type, unsigned first, unsigned n);
5892 __isl_give isl_union_pw_multi_aff *
5893 isl_union_pw_multi_aff_drop_dims(
5894 __isl_take isl_union_pw_multi_aff *upma,
5895 enum isl_dim_type type,
5896 unsigned first, unsigned n);
5897 __isl_give isl_multi_union_pw_aff *
5898 isl_multi_union_pw_aff_drop_dims(
5899 __isl_take isl_multi_union_pw_aff *mupa,
5900 enum isl_dim_type type, unsigned first,
5902 __isl_give isl_aff *isl_aff_move_dims(
5903 __isl_take isl_aff *aff,
5904 enum isl_dim_type dst_type, unsigned dst_pos,
5905 enum isl_dim_type src_type, unsigned src_pos,
5907 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
5908 __isl_take isl_multi_aff *ma,
5909 enum isl_dim_type dst_type, unsigned dst_pos,
5910 enum isl_dim_type src_type, unsigned src_pos,
5912 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
5913 __isl_take isl_pw_aff *pa,
5914 enum isl_dim_type dst_type, unsigned dst_pos,
5915 enum isl_dim_type src_type, unsigned src_pos,
5917 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
5918 __isl_take isl_multi_pw_aff *pma,
5919 enum isl_dim_type dst_type, unsigned dst_pos,
5920 enum isl_dim_type src_type, unsigned src_pos,
5923 #include <isl/polynomial.h>
5924 __isl_give isl_union_pw_qpolynomial *
5925 isl_union_pw_qpolynomial_drop_dims(
5926 __isl_take isl_union_pw_qpolynomial *upwqp,
5927 enum isl_dim_type type,
5928 unsigned first, unsigned n);
5929 __isl_give isl_union_pw_qpolynomial_fold *
5930 isl_union_pw_qpolynomial_fold_drop_dims(
5931 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5932 enum isl_dim_type type,
5933 unsigned first, unsigned n);
5935 The operations on union expressions can only manipulate parameters.
5939 =head2 Binary Operations
5941 The two arguments of a binary operation not only need to live
5942 in the same C<isl_ctx>, they currently also need to have
5943 the same (number of) parameters.
5945 =head3 Basic Operations
5949 =item * Intersection
5951 #include <isl/local_space.h>
5952 __isl_give isl_local_space *isl_local_space_intersect(
5953 __isl_take isl_local_space *ls1,
5954 __isl_take isl_local_space *ls2);
5956 #include <isl/set.h>
5957 __isl_give isl_basic_set *isl_basic_set_intersect_params(
5958 __isl_take isl_basic_set *bset1,
5959 __isl_take isl_basic_set *bset2);
5960 __isl_give isl_basic_set *isl_basic_set_intersect(
5961 __isl_take isl_basic_set *bset1,
5962 __isl_take isl_basic_set *bset2);
5963 __isl_give isl_basic_set *isl_basic_set_list_intersect(
5964 __isl_take struct isl_basic_set_list *list);
5965 __isl_give isl_set *isl_set_intersect_params(
5966 __isl_take isl_set *set,
5967 __isl_take isl_set *params);
5968 __isl_give isl_set *isl_set_intersect(
5969 __isl_take isl_set *set1,
5970 __isl_take isl_set *set2);
5972 #include <isl/map.h>
5973 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
5974 __isl_take isl_basic_map *bmap,
5975 __isl_take isl_basic_set *bset);
5976 __isl_give isl_basic_map *isl_basic_map_intersect_range(
5977 __isl_take isl_basic_map *bmap,
5978 __isl_take isl_basic_set *bset);
5979 __isl_give isl_basic_map *isl_basic_map_intersect(
5980 __isl_take isl_basic_map *bmap1,
5981 __isl_take isl_basic_map *bmap2);
5982 __isl_give isl_basic_map *isl_basic_map_list_intersect(
5983 __isl_take isl_basic_map_list *list);
5984 __isl_give isl_map *isl_map_intersect_params(
5985 __isl_take isl_map *map,
5986 __isl_take isl_set *params);
5987 __isl_give isl_map *isl_map_intersect_domain(
5988 __isl_take isl_map *map,
5989 __isl_take isl_set *set);
5990 __isl_give isl_map *isl_map_intersect_range(
5991 __isl_take isl_map *map,
5992 __isl_take isl_set *set);
5993 __isl_give isl_map *isl_map_intersect(
5994 __isl_take isl_map *map1,
5995 __isl_take isl_map *map2);
5996 __isl_give isl_map *
5997 isl_map_intersect_domain_factor_range(
5998 __isl_take isl_map *map,
5999 __isl_take isl_map *factor);
6000 __isl_give isl_map *
6001 isl_map_intersect_range_factor_range(
6002 __isl_take isl_map *map,
6003 __isl_take isl_map *factor);
6005 #include <isl/union_set.h>
6006 __isl_give isl_union_set *isl_union_set_intersect_params(
6007 __isl_take isl_union_set *uset,
6008 __isl_take isl_set *set);
6009 __isl_give isl_union_set *isl_union_set_intersect(
6010 __isl_take isl_union_set *uset1,
6011 __isl_take isl_union_set *uset2);
6013 #include <isl/union_map.h>
6014 __isl_give isl_union_map *isl_union_map_intersect_params(
6015 __isl_take isl_union_map *umap,
6016 __isl_take isl_set *set);
6017 __isl_give isl_union_map *isl_union_map_intersect_domain(
6018 __isl_take isl_union_map *umap,
6019 __isl_take isl_union_set *uset);
6020 __isl_give isl_union_map *isl_union_map_intersect_range(
6021 __isl_take isl_union_map *umap,
6022 __isl_take isl_union_set *uset);
6023 __isl_give isl_union_map *isl_union_map_intersect(
6024 __isl_take isl_union_map *umap1,
6025 __isl_take isl_union_map *umap2);
6026 __isl_give isl_union_map *
6027 isl_union_map_intersect_range_factor_range(
6028 __isl_take isl_union_map *umap,
6029 __isl_take isl_union_map *factor);
6031 #include <isl/aff.h>
6032 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
6033 __isl_take isl_pw_aff *pa,
6034 __isl_take isl_set *set);
6035 __isl_give isl_multi_pw_aff *
6036 isl_multi_pw_aff_intersect_domain(
6037 __isl_take isl_multi_pw_aff *mpa,
6038 __isl_take isl_set *domain);
6039 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
6040 __isl_take isl_pw_multi_aff *pma,
6041 __isl_take isl_set *set);
6042 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
6043 __isl_take isl_union_pw_aff *upa,
6044 __isl_take isl_union_set *uset);
6045 __isl_give isl_union_pw_multi_aff *
6046 isl_union_pw_multi_aff_intersect_domain(
6047 __isl_take isl_union_pw_multi_aff *upma,
6048 __isl_take isl_union_set *uset);
6049 __isl_give isl_multi_union_pw_aff *
6050 isl_multi_union_pw_aff_intersect_domain(
6051 __isl_take isl_multi_union_pw_aff *mupa,
6052 __isl_take isl_union_set *uset);
6053 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
6054 __isl_take isl_pw_aff *pa,
6055 __isl_take isl_set *set);
6056 __isl_give isl_multi_pw_aff *
6057 isl_multi_pw_aff_intersect_params(
6058 __isl_take isl_multi_pw_aff *mpa,
6059 __isl_take isl_set *set);
6060 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
6061 __isl_take isl_pw_multi_aff *pma,
6062 __isl_take isl_set *set);
6063 __isl_give isl_union_pw_aff *
6064 isl_union_pw_aff_intersect_params(
6065 __isl_take isl_union_pw_aff *upa,
6066 __isl_give isl_union_pw_multi_aff *
6067 isl_union_pw_multi_aff_intersect_params(
6068 __isl_take isl_union_pw_multi_aff *upma,
6069 __isl_take isl_set *set);
6070 __isl_give isl_multi_union_pw_aff *
6071 isl_multi_union_pw_aff_intersect_params(
6072 __isl_take isl_multi_union_pw_aff *mupa,
6073 __isl_take isl_set *params);
6074 isl_multi_union_pw_aff_intersect_range(
6075 __isl_take isl_multi_union_pw_aff *mupa,
6076 __isl_take isl_set *set);
6078 #include <isl/polynomial.h>
6079 __isl_give isl_pw_qpolynomial *
6080 isl_pw_qpolynomial_intersect_domain(
6081 __isl_take isl_pw_qpolynomial *pwpq,
6082 __isl_take isl_set *set);
6083 __isl_give isl_union_pw_qpolynomial *
6084 isl_union_pw_qpolynomial_intersect_domain(
6085 __isl_take isl_union_pw_qpolynomial *upwpq,
6086 __isl_take isl_union_set *uset);
6087 __isl_give isl_union_pw_qpolynomial_fold *
6088 isl_union_pw_qpolynomial_fold_intersect_domain(
6089 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6090 __isl_take isl_union_set *uset);
6091 __isl_give isl_pw_qpolynomial *
6092 isl_pw_qpolynomial_intersect_params(
6093 __isl_take isl_pw_qpolynomial *pwpq,
6094 __isl_take isl_set *set);
6095 __isl_give isl_pw_qpolynomial_fold *
6096 isl_pw_qpolynomial_fold_intersect_params(
6097 __isl_take isl_pw_qpolynomial_fold *pwf,
6098 __isl_take isl_set *set);
6099 __isl_give isl_union_pw_qpolynomial *
6100 isl_union_pw_qpolynomial_intersect_params(
6101 __isl_take isl_union_pw_qpolynomial *upwpq,
6102 __isl_take isl_set *set);
6103 __isl_give isl_union_pw_qpolynomial_fold *
6104 isl_union_pw_qpolynomial_fold_intersect_params(
6105 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6106 __isl_take isl_set *set);
6108 The second argument to the C<_params> functions needs to be
6109 a parametric (basic) set. For the other functions, a parametric set
6110 for either argument is only allowed if the other argument is
6111 a parametric set as well.
6112 The list passed to C<isl_basic_set_list_intersect> needs to have
6113 at least one element and all elements need to live in the same space.
6114 The function C<isl_multi_union_pw_aff_intersect_range>
6115 restricts the input function to those shared domain elements
6116 that map to the specified range.
6120 #include <isl/set.h>
6121 __isl_give isl_set *isl_basic_set_union(
6122 __isl_take isl_basic_set *bset1,
6123 __isl_take isl_basic_set *bset2);
6124 __isl_give isl_set *isl_set_union(
6125 __isl_take isl_set *set1,
6126 __isl_take isl_set *set2);
6127 __isl_give isl_set *isl_set_list_union(
6128 __isl_take isl_set_list *list);
6130 #include <isl/map.h>
6131 __isl_give isl_map *isl_basic_map_union(
6132 __isl_take isl_basic_map *bmap1,
6133 __isl_take isl_basic_map *bmap2);
6134 __isl_give isl_map *isl_map_union(
6135 __isl_take isl_map *map1,
6136 __isl_take isl_map *map2);
6138 #include <isl/union_set.h>
6139 __isl_give isl_union_set *isl_union_set_union(
6140 __isl_take isl_union_set *uset1,
6141 __isl_take isl_union_set *uset2);
6142 __isl_give isl_union_set *isl_union_set_list_union(
6143 __isl_take isl_union_set_list *list);
6145 #include <isl/union_map.h>
6146 __isl_give isl_union_map *isl_union_map_union(
6147 __isl_take isl_union_map *umap1,
6148 __isl_take isl_union_map *umap2);
6150 The list passed to C<isl_set_list_union> needs to have
6151 at least one element and all elements need to live in the same space.
6153 =item * Set difference
6155 #include <isl/set.h>
6156 __isl_give isl_set *isl_set_subtract(
6157 __isl_take isl_set *set1,
6158 __isl_take isl_set *set2);
6160 #include <isl/map.h>
6161 __isl_give isl_map *isl_map_subtract(
6162 __isl_take isl_map *map1,
6163 __isl_take isl_map *map2);
6164 __isl_give isl_map *isl_map_subtract_domain(
6165 __isl_take isl_map *map,
6166 __isl_take isl_set *dom);
6167 __isl_give isl_map *isl_map_subtract_range(
6168 __isl_take isl_map *map,
6169 __isl_take isl_set *dom);
6171 #include <isl/union_set.h>
6172 __isl_give isl_union_set *isl_union_set_subtract(
6173 __isl_take isl_union_set *uset1,
6174 __isl_take isl_union_set *uset2);
6176 #include <isl/union_map.h>
6177 __isl_give isl_union_map *isl_union_map_subtract(
6178 __isl_take isl_union_map *umap1,
6179 __isl_take isl_union_map *umap2);
6180 __isl_give isl_union_map *isl_union_map_subtract_domain(
6181 __isl_take isl_union_map *umap,
6182 __isl_take isl_union_set *dom);
6183 __isl_give isl_union_map *isl_union_map_subtract_range(
6184 __isl_take isl_union_map *umap,
6185 __isl_take isl_union_set *dom);
6187 #include <isl/aff.h>
6188 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
6189 __isl_take isl_pw_aff *pa,
6190 __isl_take isl_set *set);
6191 __isl_give isl_pw_multi_aff *
6192 isl_pw_multi_aff_subtract_domain(
6193 __isl_take isl_pw_multi_aff *pma,
6194 __isl_take isl_set *set);
6195 __isl_give isl_union_pw_aff *
6196 isl_union_pw_aff_subtract_domain(
6197 __isl_take isl_union_pw_aff *upa,
6198 __isl_take isl_union_set *uset);
6199 __isl_give isl_union_pw_multi_aff *
6200 isl_union_pw_multi_aff_subtract_domain(
6201 __isl_take isl_union_pw_multi_aff *upma,
6202 __isl_take isl_set *set);
6204 #include <isl/polynomial.h>
6205 __isl_give isl_pw_qpolynomial *
6206 isl_pw_qpolynomial_subtract_domain(
6207 __isl_take isl_pw_qpolynomial *pwpq,
6208 __isl_take isl_set *set);
6209 __isl_give isl_pw_qpolynomial_fold *
6210 isl_pw_qpolynomial_fold_subtract_domain(
6211 __isl_take isl_pw_qpolynomial_fold *pwf,
6212 __isl_take isl_set *set);
6213 __isl_give isl_union_pw_qpolynomial *
6214 isl_union_pw_qpolynomial_subtract_domain(
6215 __isl_take isl_union_pw_qpolynomial *upwpq,
6216 __isl_take isl_union_set *uset);
6217 __isl_give isl_union_pw_qpolynomial_fold *
6218 isl_union_pw_qpolynomial_fold_subtract_domain(
6219 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6220 __isl_take isl_union_set *uset);
6224 #include <isl/space.h>
6225 __isl_give isl_space *isl_space_join(
6226 __isl_take isl_space *left,
6227 __isl_take isl_space *right);
6229 #include <isl/map.h>
6230 __isl_give isl_basic_set *isl_basic_set_apply(
6231 __isl_take isl_basic_set *bset,
6232 __isl_take isl_basic_map *bmap);
6233 __isl_give isl_set *isl_set_apply(
6234 __isl_take isl_set *set,
6235 __isl_take isl_map *map);
6236 __isl_give isl_union_set *isl_union_set_apply(
6237 __isl_take isl_union_set *uset,
6238 __isl_take isl_union_map *umap);
6239 __isl_give isl_basic_map *isl_basic_map_apply_domain(
6240 __isl_take isl_basic_map *bmap1,
6241 __isl_take isl_basic_map *bmap2);
6242 __isl_give isl_basic_map *isl_basic_map_apply_range(
6243 __isl_take isl_basic_map *bmap1,
6244 __isl_take isl_basic_map *bmap2);
6245 __isl_give isl_map *isl_map_apply_domain(
6246 __isl_take isl_map *map1,
6247 __isl_take isl_map *map2);
6248 __isl_give isl_map *isl_map_apply_range(
6249 __isl_take isl_map *map1,
6250 __isl_take isl_map *map2);
6252 #include <isl/union_map.h>
6253 __isl_give isl_union_map *isl_union_map_apply_domain(
6254 __isl_take isl_union_map *umap1,
6255 __isl_take isl_union_map *umap2);
6256 __isl_give isl_union_map *isl_union_map_apply_range(
6257 __isl_take isl_union_map *umap1,
6258 __isl_take isl_union_map *umap2);
6260 #include <isl/aff.h>
6261 __isl_give isl_union_pw_aff *
6262 isl_multi_union_pw_aff_apply_aff(
6263 __isl_take isl_multi_union_pw_aff *mupa,
6264 __isl_take isl_aff *aff);
6265 __isl_give isl_union_pw_aff *
6266 isl_multi_union_pw_aff_apply_pw_aff(
6267 __isl_take isl_multi_union_pw_aff *mupa,
6268 __isl_take isl_pw_aff *pa);
6269 __isl_give isl_multi_union_pw_aff *
6270 isl_multi_union_pw_aff_apply_multi_aff(
6271 __isl_take isl_multi_union_pw_aff *mupa,
6272 __isl_take isl_multi_aff *ma);
6273 __isl_give isl_multi_union_pw_aff *
6274 isl_multi_union_pw_aff_apply_pw_multi_aff(
6275 __isl_take isl_multi_union_pw_aff *mupa,
6276 __isl_take isl_pw_multi_aff *pma);
6278 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
6279 over the shared domain of the elements of the input. The dimension is
6280 required to be greater than zero.
6281 The C<isl_multi_union_pw_aff> argument of
6282 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
6283 but only if the range of the C<isl_multi_aff> argument
6284 is also zero-dimensional.
6285 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
6287 #include <isl/polynomial.h>
6288 __isl_give isl_pw_qpolynomial_fold *
6289 isl_set_apply_pw_qpolynomial_fold(
6290 __isl_take isl_set *set,
6291 __isl_take isl_pw_qpolynomial_fold *pwf,
6293 __isl_give isl_pw_qpolynomial_fold *
6294 isl_map_apply_pw_qpolynomial_fold(
6295 __isl_take isl_map *map,
6296 __isl_take isl_pw_qpolynomial_fold *pwf,
6298 __isl_give isl_union_pw_qpolynomial_fold *
6299 isl_union_set_apply_union_pw_qpolynomial_fold(
6300 __isl_take isl_union_set *uset,
6301 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6303 __isl_give isl_union_pw_qpolynomial_fold *
6304 isl_union_map_apply_union_pw_qpolynomial_fold(
6305 __isl_take isl_union_map *umap,
6306 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6309 The functions taking a map
6310 compose the given map with the given piecewise quasipolynomial reduction.
6311 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
6312 over all elements in the intersection of the range of the map
6313 and the domain of the piecewise quasipolynomial reduction
6314 as a function of an element in the domain of the map.
6315 The functions taking a set compute a bound over all elements in the
6316 intersection of the set and the domain of the
6317 piecewise quasipolynomial reduction.
6321 #include <isl/set.h>
6322 __isl_give isl_basic_set *
6323 isl_basic_set_preimage_multi_aff(
6324 __isl_take isl_basic_set *bset,
6325 __isl_take isl_multi_aff *ma);
6326 __isl_give isl_set *isl_set_preimage_multi_aff(
6327 __isl_take isl_set *set,
6328 __isl_take isl_multi_aff *ma);
6329 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
6330 __isl_take isl_set *set,
6331 __isl_take isl_pw_multi_aff *pma);
6332 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
6333 __isl_take isl_set *set,
6334 __isl_take isl_multi_pw_aff *mpa);
6336 #include <isl/union_set.h>
6337 __isl_give isl_union_set *
6338 isl_union_set_preimage_multi_aff(
6339 __isl_take isl_union_set *uset,
6340 __isl_take isl_multi_aff *ma);
6341 __isl_give isl_union_set *
6342 isl_union_set_preimage_pw_multi_aff(
6343 __isl_take isl_union_set *uset,
6344 __isl_take isl_pw_multi_aff *pma);
6345 __isl_give isl_union_set *
6346 isl_union_set_preimage_union_pw_multi_aff(
6347 __isl_take isl_union_set *uset,
6348 __isl_take isl_union_pw_multi_aff *upma);
6350 #include <isl/map.h>
6351 __isl_give isl_basic_map *
6352 isl_basic_map_preimage_domain_multi_aff(
6353 __isl_take isl_basic_map *bmap,
6354 __isl_take isl_multi_aff *ma);
6355 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
6356 __isl_take isl_map *map,
6357 __isl_take isl_multi_aff *ma);
6358 __isl_give isl_map *isl_map_preimage_range_multi_aff(
6359 __isl_take isl_map *map,
6360 __isl_take isl_multi_aff *ma);
6361 __isl_give isl_map *
6362 isl_map_preimage_domain_pw_multi_aff(
6363 __isl_take isl_map *map,
6364 __isl_take isl_pw_multi_aff *pma);
6365 __isl_give isl_map *
6366 isl_map_preimage_range_pw_multi_aff(
6367 __isl_take isl_map *map,
6368 __isl_take isl_pw_multi_aff *pma);
6369 __isl_give isl_map *
6370 isl_map_preimage_domain_multi_pw_aff(
6371 __isl_take isl_map *map,
6372 __isl_take isl_multi_pw_aff *mpa);
6373 __isl_give isl_basic_map *
6374 isl_basic_map_preimage_range_multi_aff(
6375 __isl_take isl_basic_map *bmap,
6376 __isl_take isl_multi_aff *ma);
6378 #include <isl/union_map.h>
6379 __isl_give isl_union_map *
6380 isl_union_map_preimage_domain_multi_aff(
6381 __isl_take isl_union_map *umap,
6382 __isl_take isl_multi_aff *ma);
6383 __isl_give isl_union_map *
6384 isl_union_map_preimage_range_multi_aff(
6385 __isl_take isl_union_map *umap,
6386 __isl_take isl_multi_aff *ma);
6387 __isl_give isl_union_map *
6388 isl_union_map_preimage_domain_pw_multi_aff(
6389 __isl_take isl_union_map *umap,
6390 __isl_take isl_pw_multi_aff *pma);
6391 __isl_give isl_union_map *
6392 isl_union_map_preimage_range_pw_multi_aff(
6393 __isl_take isl_union_map *umap,
6394 __isl_take isl_pw_multi_aff *pma);
6395 __isl_give isl_union_map *
6396 isl_union_map_preimage_domain_union_pw_multi_aff(
6397 __isl_take isl_union_map *umap,
6398 __isl_take isl_union_pw_multi_aff *upma);
6399 __isl_give isl_union_map *
6400 isl_union_map_preimage_range_union_pw_multi_aff(
6401 __isl_take isl_union_map *umap,
6402 __isl_take isl_union_pw_multi_aff *upma);
6404 These functions compute the preimage of the given set or map domain/range under
6405 the given function. In other words, the expression is plugged
6406 into the set description or into the domain/range of the map.
6410 #include <isl/aff.h>
6411 __isl_give isl_aff *isl_aff_pullback_aff(
6412 __isl_take isl_aff *aff1,
6413 __isl_take isl_aff *aff2);
6414 __isl_give isl_aff *isl_aff_pullback_multi_aff(
6415 __isl_take isl_aff *aff,
6416 __isl_take isl_multi_aff *ma);
6417 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
6418 __isl_take isl_pw_aff *pa,
6419 __isl_take isl_multi_aff *ma);
6420 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
6421 __isl_take isl_pw_aff *pa,
6422 __isl_take isl_pw_multi_aff *pma);
6423 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
6424 __isl_take isl_pw_aff *pa,
6425 __isl_take isl_multi_pw_aff *mpa);
6426 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
6427 __isl_take isl_multi_aff *ma1,
6428 __isl_take isl_multi_aff *ma2);
6429 __isl_give isl_pw_multi_aff *
6430 isl_pw_multi_aff_pullback_multi_aff(
6431 __isl_take isl_pw_multi_aff *pma,
6432 __isl_take isl_multi_aff *ma);
6433 __isl_give isl_multi_pw_aff *
6434 isl_multi_pw_aff_pullback_multi_aff(
6435 __isl_take isl_multi_pw_aff *mpa,
6436 __isl_take isl_multi_aff *ma);
6437 __isl_give isl_pw_multi_aff *
6438 isl_pw_multi_aff_pullback_pw_multi_aff(
6439 __isl_take isl_pw_multi_aff *pma1,
6440 __isl_take isl_pw_multi_aff *pma2);
6441 __isl_give isl_multi_pw_aff *
6442 isl_multi_pw_aff_pullback_pw_multi_aff(
6443 __isl_take isl_multi_pw_aff *mpa,
6444 __isl_take isl_pw_multi_aff *pma);
6445 __isl_give isl_multi_pw_aff *
6446 isl_multi_pw_aff_pullback_multi_pw_aff(
6447 __isl_take isl_multi_pw_aff *mpa1,
6448 __isl_take isl_multi_pw_aff *mpa2);
6449 __isl_give isl_union_pw_aff *
6450 isl_union_pw_aff_pullback_union_pw_multi_aff(
6451 __isl_take isl_union_pw_aff *upa,
6452 __isl_take isl_union_pw_multi_aff *upma);
6453 __isl_give isl_union_pw_multi_aff *
6454 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
6455 __isl_take isl_union_pw_multi_aff *upma1,
6456 __isl_take isl_union_pw_multi_aff *upma2);
6457 __isl_give isl_multi_union_pw_aff *
6458 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
6459 __isl_take isl_multi_union_pw_aff *mupa,
6460 __isl_take isl_union_pw_multi_aff *upma);
6462 These functions precompose the first expression by the second function.
6463 In other words, the second function is plugged
6464 into the first expression.
6468 #include <isl/aff.h>
6469 __isl_give isl_basic_set *isl_aff_eq_basic_set(
6470 __isl_take isl_aff *aff1,
6471 __isl_take isl_aff *aff2);
6472 __isl_give isl_set *isl_aff_eq_set(
6473 __isl_take isl_aff *aff1,
6474 __isl_take isl_aff *aff2);
6475 __isl_give isl_set *isl_aff_ne_set(
6476 __isl_take isl_aff *aff1,
6477 __isl_take isl_aff *aff2);
6478 __isl_give isl_basic_set *isl_aff_le_basic_set(
6479 __isl_take isl_aff *aff1,
6480 __isl_take isl_aff *aff2);
6481 __isl_give isl_set *isl_aff_le_set(
6482 __isl_take isl_aff *aff1,
6483 __isl_take isl_aff *aff2);
6484 __isl_give isl_basic_set *isl_aff_lt_basic_set(
6485 __isl_take isl_aff *aff1,
6486 __isl_take isl_aff *aff2);
6487 __isl_give isl_set *isl_aff_lt_set(
6488 __isl_take isl_aff *aff1,
6489 __isl_take isl_aff *aff2);
6490 __isl_give isl_basic_set *isl_aff_ge_basic_set(
6491 __isl_take isl_aff *aff1,
6492 __isl_take isl_aff *aff2);
6493 __isl_give isl_set *isl_aff_ge_set(
6494 __isl_take isl_aff *aff1,
6495 __isl_take isl_aff *aff2);
6496 __isl_give isl_basic_set *isl_aff_gt_basic_set(
6497 __isl_take isl_aff *aff1,
6498 __isl_take isl_aff *aff2);
6499 __isl_give isl_set *isl_aff_gt_set(
6500 __isl_take isl_aff *aff1,
6501 __isl_take isl_aff *aff2);
6502 __isl_give isl_set *isl_pw_aff_eq_set(
6503 __isl_take isl_pw_aff *pwaff1,
6504 __isl_take isl_pw_aff *pwaff2);
6505 __isl_give isl_set *isl_pw_aff_ne_set(
6506 __isl_take isl_pw_aff *pwaff1,
6507 __isl_take isl_pw_aff *pwaff2);
6508 __isl_give isl_set *isl_pw_aff_le_set(
6509 __isl_take isl_pw_aff *pwaff1,
6510 __isl_take isl_pw_aff *pwaff2);
6511 __isl_give isl_set *isl_pw_aff_lt_set(
6512 __isl_take isl_pw_aff *pwaff1,
6513 __isl_take isl_pw_aff *pwaff2);
6514 __isl_give isl_set *isl_pw_aff_ge_set(
6515 __isl_take isl_pw_aff *pwaff1,
6516 __isl_take isl_pw_aff *pwaff2);
6517 __isl_give isl_set *isl_pw_aff_gt_set(
6518 __isl_take isl_pw_aff *pwaff1,
6519 __isl_take isl_pw_aff *pwaff2);
6521 __isl_give isl_set *isl_multi_aff_lex_le_set(
6522 __isl_take isl_multi_aff *ma1,
6523 __isl_take isl_multi_aff *ma2);
6524 __isl_give isl_set *isl_multi_aff_lex_lt_set(
6525 __isl_take isl_multi_aff *ma1,
6526 __isl_take isl_multi_aff *ma2);
6527 __isl_give isl_set *isl_multi_aff_lex_ge_set(
6528 __isl_take isl_multi_aff *ma1,
6529 __isl_take isl_multi_aff *ma2);
6530 __isl_give isl_set *isl_multi_aff_lex_gt_set(
6531 __isl_take isl_multi_aff *ma1,
6532 __isl_take isl_multi_aff *ma2);
6534 __isl_give isl_set *isl_pw_aff_list_eq_set(
6535 __isl_take isl_pw_aff_list *list1,
6536 __isl_take isl_pw_aff_list *list2);
6537 __isl_give isl_set *isl_pw_aff_list_ne_set(
6538 __isl_take isl_pw_aff_list *list1,
6539 __isl_take isl_pw_aff_list *list2);
6540 __isl_give isl_set *isl_pw_aff_list_le_set(
6541 __isl_take isl_pw_aff_list *list1,
6542 __isl_take isl_pw_aff_list *list2);
6543 __isl_give isl_set *isl_pw_aff_list_lt_set(
6544 __isl_take isl_pw_aff_list *list1,
6545 __isl_take isl_pw_aff_list *list2);
6546 __isl_give isl_set *isl_pw_aff_list_ge_set(
6547 __isl_take isl_pw_aff_list *list1,
6548 __isl_take isl_pw_aff_list *list2);
6549 __isl_give isl_set *isl_pw_aff_list_gt_set(
6550 __isl_take isl_pw_aff_list *list1,
6551 __isl_take isl_pw_aff_list *list2);
6553 The function C<isl_aff_ge_basic_set> returns a basic set
6554 containing those elements in the shared space
6555 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
6556 The function C<isl_pw_aff_ge_set> returns a set
6557 containing those elements in the shared domain
6558 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
6559 greater than or equal to C<pwaff2>.
6560 The function C<isl_multi_aff_lex_le_set> returns a set
6561 containing those elements in the shared domain space
6562 where C<ma1> is lexicographically smaller than or
6564 The functions operating on C<isl_pw_aff_list> apply the corresponding
6565 C<isl_pw_aff> function to each pair of elements in the two lists.
6567 #include <isl/aff.h>
6568 __isl_give isl_map *isl_pw_aff_eq_map(
6569 __isl_take isl_pw_aff *pa1,
6570 __isl_take isl_pw_aff *pa2);
6571 __isl_give isl_map *isl_pw_aff_lt_map(
6572 __isl_take isl_pw_aff *pa1,
6573 __isl_take isl_pw_aff *pa2);
6574 __isl_give isl_map *isl_pw_aff_gt_map(
6575 __isl_take isl_pw_aff *pa1,
6576 __isl_take isl_pw_aff *pa2);
6578 __isl_give isl_map *isl_multi_pw_aff_eq_map(
6579 __isl_take isl_multi_pw_aff *mpa1,
6580 __isl_take isl_multi_pw_aff *mpa2);
6581 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
6582 __isl_take isl_multi_pw_aff *mpa1,
6583 __isl_take isl_multi_pw_aff *mpa2);
6584 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
6585 __isl_take isl_multi_pw_aff *mpa1,
6586 __isl_take isl_multi_pw_aff *mpa2);
6588 These functions return a map between domain elements of the arguments
6589 where the function values satisfy the given relation.
6591 #include <isl/union_map.h>
6592 __isl_give isl_union_map *
6593 isl_union_map_eq_at_multi_union_pw_aff(
6594 __isl_take isl_union_map *umap,
6595 __isl_take isl_multi_union_pw_aff *mupa);
6596 __isl_give isl_union_map *
6597 isl_union_map_lex_lt_at_multi_union_pw_aff(
6598 __isl_take isl_union_map *umap,
6599 __isl_take isl_multi_union_pw_aff *mupa);
6600 __isl_give isl_union_map *
6601 isl_union_map_lex_gt_at_multi_union_pw_aff(
6602 __isl_take isl_union_map *umap,
6603 __isl_take isl_multi_union_pw_aff *mupa);
6605 These functions select the subset of elements in the union map
6606 that have an equal or lexicographically smaller function value.
6608 =item * Cartesian Product
6610 #include <isl/space.h>
6611 __isl_give isl_space *isl_space_product(
6612 __isl_take isl_space *space1,
6613 __isl_take isl_space *space2);
6614 __isl_give isl_space *isl_space_domain_product(
6615 __isl_take isl_space *space1,
6616 __isl_take isl_space *space2);
6617 __isl_give isl_space *isl_space_range_product(
6618 __isl_take isl_space *space1,
6619 __isl_take isl_space *space2);
6622 C<isl_space_product>, C<isl_space_domain_product>
6623 and C<isl_space_range_product> take pairs or relation spaces and
6624 produce a single relations space, where either the domain, the range
6625 or both domain and range are wrapped spaces of relations between
6626 the domains and/or ranges of the input spaces.
6627 If the product is only constructed over the domain or the range
6628 then the ranges or the domains of the inputs should be the same.
6629 The function C<isl_space_product> also accepts a pair of set spaces,
6630 in which case it returns a wrapped space of a relation between the
6633 #include <isl/set.h>
6634 __isl_give isl_set *isl_set_product(
6635 __isl_take isl_set *set1,
6636 __isl_take isl_set *set2);
6638 #include <isl/map.h>
6639 __isl_give isl_basic_map *isl_basic_map_domain_product(
6640 __isl_take isl_basic_map *bmap1,
6641 __isl_take isl_basic_map *bmap2);
6642 __isl_give isl_basic_map *isl_basic_map_range_product(
6643 __isl_take isl_basic_map *bmap1,
6644 __isl_take isl_basic_map *bmap2);
6645 __isl_give isl_basic_map *isl_basic_map_product(
6646 __isl_take isl_basic_map *bmap1,
6647 __isl_take isl_basic_map *bmap2);
6648 __isl_give isl_map *isl_map_domain_product(
6649 __isl_take isl_map *map1,
6650 __isl_take isl_map *map2);
6651 __isl_give isl_map *isl_map_range_product(
6652 __isl_take isl_map *map1,
6653 __isl_take isl_map *map2);
6654 __isl_give isl_map *isl_map_product(
6655 __isl_take isl_map *map1,
6656 __isl_take isl_map *map2);
6658 #include <isl/union_set.h>
6659 __isl_give isl_union_set *isl_union_set_product(
6660 __isl_take isl_union_set *uset1,
6661 __isl_take isl_union_set *uset2);
6663 #include <isl/union_map.h>
6664 __isl_give isl_union_map *isl_union_map_domain_product(
6665 __isl_take isl_union_map *umap1,
6666 __isl_take isl_union_map *umap2);
6667 __isl_give isl_union_map *isl_union_map_range_product(
6668 __isl_take isl_union_map *umap1,
6669 __isl_take isl_union_map *umap2);
6670 __isl_give isl_union_map *isl_union_map_product(
6671 __isl_take isl_union_map *umap1,
6672 __isl_take isl_union_map *umap2);
6674 #include <isl/val.h>
6675 __isl_give isl_multi_val *isl_multi_val_range_product(
6676 __isl_take isl_multi_val *mv1,
6677 __isl_take isl_multi_val *mv2);
6678 __isl_give isl_multi_val *isl_multi_val_product(
6679 __isl_take isl_multi_val *mv1,
6680 __isl_take isl_multi_val *mv2);
6682 #include <isl/aff.h>
6683 __isl_give isl_multi_aff *isl_multi_aff_range_product(
6684 __isl_take isl_multi_aff *ma1,
6685 __isl_take isl_multi_aff *ma2);
6686 __isl_give isl_multi_aff *isl_multi_aff_product(
6687 __isl_take isl_multi_aff *ma1,
6688 __isl_take isl_multi_aff *ma2);
6689 __isl_give isl_multi_pw_aff *
6690 isl_multi_pw_aff_range_product(
6691 __isl_take isl_multi_pw_aff *mpa1,
6692 __isl_take isl_multi_pw_aff *mpa2);
6693 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
6694 __isl_take isl_multi_pw_aff *mpa1,
6695 __isl_take isl_multi_pw_aff *mpa2);
6696 __isl_give isl_pw_multi_aff *
6697 isl_pw_multi_aff_range_product(
6698 __isl_take isl_pw_multi_aff *pma1,
6699 __isl_take isl_pw_multi_aff *pma2);
6700 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
6701 __isl_take isl_pw_multi_aff *pma1,
6702 __isl_take isl_pw_multi_aff *pma2);
6703 __isl_give isl_multi_union_pw_aff *
6704 isl_multi_union_pw_aff_range_product(
6705 __isl_take isl_multi_union_pw_aff *mupa1,
6706 __isl_take isl_multi_union_pw_aff *mupa2);
6708 The above functions compute the cross product of the given
6709 sets, relations or functions. The domains and ranges of the results
6710 are wrapped maps between domains and ranges of the inputs.
6711 To obtain a ``flat'' product, use the following functions
6714 #include <isl/set.h>
6715 __isl_give isl_basic_set *isl_basic_set_flat_product(
6716 __isl_take isl_basic_set *bset1,
6717 __isl_take isl_basic_set *bset2);
6718 __isl_give isl_set *isl_set_flat_product(
6719 __isl_take isl_set *set1,
6720 __isl_take isl_set *set2);
6722 #include <isl/map.h>
6723 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
6724 __isl_take isl_basic_map *bmap1,
6725 __isl_take isl_basic_map *bmap2);
6726 __isl_give isl_map *isl_map_flat_domain_product(
6727 __isl_take isl_map *map1,
6728 __isl_take isl_map *map2);
6729 __isl_give isl_map *isl_map_flat_range_product(
6730 __isl_take isl_map *map1,
6731 __isl_take isl_map *map2);
6732 __isl_give isl_basic_map *isl_basic_map_flat_product(
6733 __isl_take isl_basic_map *bmap1,
6734 __isl_take isl_basic_map *bmap2);
6735 __isl_give isl_map *isl_map_flat_product(
6736 __isl_take isl_map *map1,
6737 __isl_take isl_map *map2);
6739 #include <isl/union_map.h>
6740 __isl_give isl_union_map *
6741 isl_union_map_flat_domain_product(
6742 __isl_take isl_union_map *umap1,
6743 __isl_take isl_union_map *umap2);
6744 __isl_give isl_union_map *
6745 isl_union_map_flat_range_product(
6746 __isl_take isl_union_map *umap1,
6747 __isl_take isl_union_map *umap2);
6749 #include <isl/val.h>
6750 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
6751 __isl_take isl_multi_val *mv1,
6752 __isl_take isl_multi_aff *mv2);
6754 #include <isl/aff.h>
6755 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
6756 __isl_take isl_multi_aff *ma1,
6757 __isl_take isl_multi_aff *ma2);
6758 __isl_give isl_pw_multi_aff *
6759 isl_pw_multi_aff_flat_range_product(
6760 __isl_take isl_pw_multi_aff *pma1,
6761 __isl_take isl_pw_multi_aff *pma2);
6762 __isl_give isl_multi_pw_aff *
6763 isl_multi_pw_aff_flat_range_product(
6764 __isl_take isl_multi_pw_aff *mpa1,
6765 __isl_take isl_multi_pw_aff *mpa2);
6766 __isl_give isl_union_pw_multi_aff *
6767 isl_union_pw_multi_aff_flat_range_product(
6768 __isl_take isl_union_pw_multi_aff *upma1,
6769 __isl_take isl_union_pw_multi_aff *upma2);
6770 __isl_give isl_multi_union_pw_aff *
6771 isl_multi_union_pw_aff_flat_range_product(
6772 __isl_take isl_multi_union_pw_aff *mupa1,
6773 __isl_take isl_multi_union_pw_aff *mupa2);
6775 #include <isl/space.h>
6776 __isl_give isl_space *isl_space_factor_domain(
6777 __isl_take isl_space *space);
6778 __isl_give isl_space *isl_space_factor_range(
6779 __isl_take isl_space *space);
6780 __isl_give isl_space *isl_space_domain_factor_domain(
6781 __isl_take isl_space *space);
6782 __isl_give isl_space *isl_space_domain_factor_range(
6783 __isl_take isl_space *space);
6784 __isl_give isl_space *isl_space_range_factor_domain(
6785 __isl_take isl_space *space);
6786 __isl_give isl_space *isl_space_range_factor_range(
6787 __isl_take isl_space *space);
6789 The functions C<isl_space_range_factor_domain> and
6790 C<isl_space_range_factor_range> extract the two arguments from
6791 the result of a call to C<isl_space_range_product>.
6793 The arguments of a call to a product can be extracted
6794 from the result using the following functions.
6796 #include <isl/map.h>
6797 __isl_give isl_map *isl_map_factor_domain(
6798 __isl_take isl_map *map);
6799 __isl_give isl_map *isl_map_factor_range(
6800 __isl_take isl_map *map);
6801 __isl_give isl_map *isl_map_domain_factor_domain(
6802 __isl_take isl_map *map);
6803 __isl_give isl_map *isl_map_domain_factor_range(
6804 __isl_take isl_map *map);
6805 __isl_give isl_map *isl_map_range_factor_domain(
6806 __isl_take isl_map *map);
6807 __isl_give isl_map *isl_map_range_factor_range(
6808 __isl_take isl_map *map);
6810 #include <isl/union_map.h>
6811 __isl_give isl_union_map *isl_union_map_factor_domain(
6812 __isl_take isl_union_map *umap);
6813 __isl_give isl_union_map *isl_union_map_factor_range(
6814 __isl_take isl_union_map *umap);
6815 __isl_give isl_union_map *
6816 isl_union_map_domain_factor_domain(
6817 __isl_take isl_union_map *umap);
6818 __isl_give isl_union_map *
6819 isl_union_map_domain_factor_range(
6820 __isl_take isl_union_map *umap);
6821 __isl_give isl_union_map *
6822 isl_union_map_range_factor_domain(
6823 __isl_take isl_union_map *umap);
6824 __isl_give isl_union_map *
6825 isl_union_map_range_factor_range(
6826 __isl_take isl_union_map *umap);
6828 #include <isl/val.h>
6829 __isl_give isl_multi_val *isl_multi_val_factor_range(
6830 __isl_take isl_multi_val *mv);
6831 __isl_give isl_multi_val *
6832 isl_multi_val_range_factor_domain(
6833 __isl_take isl_multi_val *mv);
6834 __isl_give isl_multi_val *
6835 isl_multi_val_range_factor_range(
6836 __isl_take isl_multi_val *mv);
6838 #include <isl/aff.h>
6839 __isl_give isl_multi_aff *isl_multi_aff_factor_range(
6840 __isl_take isl_multi_aff *ma);
6841 __isl_give isl_multi_aff *
6842 isl_multi_aff_range_factor_domain(
6843 __isl_take isl_multi_aff *ma);
6844 __isl_give isl_multi_aff *
6845 isl_multi_aff_range_factor_range(
6846 __isl_take isl_multi_aff *ma);
6847 __isl_give isl_multi_pw_aff *
6848 isl_multi_pw_aff_factor_range(
6849 __isl_take isl_multi_pw_aff *mpa);
6850 __isl_give isl_multi_pw_aff *
6851 isl_multi_pw_aff_range_factor_domain(
6852 __isl_take isl_multi_pw_aff *mpa);
6853 __isl_give isl_multi_pw_aff *
6854 isl_multi_pw_aff_range_factor_range(
6855 __isl_take isl_multi_pw_aff *mpa);
6856 __isl_give isl_multi_union_pw_aff *
6857 isl_multi_union_pw_aff_factor_range(
6858 __isl_take isl_multi_union_pw_aff *mupa);
6859 __isl_give isl_multi_union_pw_aff *
6860 isl_multi_union_pw_aff_range_factor_domain(
6861 __isl_take isl_multi_union_pw_aff *mupa);
6862 __isl_give isl_multi_union_pw_aff *
6863 isl_multi_union_pw_aff_range_factor_range(
6864 __isl_take isl_multi_union_pw_aff *mupa);
6866 The splice functions are a generalization of the flat product functions,
6867 where the second argument may be inserted at any position inside
6868 the first argument rather than being placed at the end.
6869 The functions C<isl_multi_val_factor_range>,
6870 C<isl_multi_aff_factor_range>,
6871 C<isl_multi_pw_aff_factor_range> and
6872 C<isl_multi_union_pw_aff_factor_range>
6873 take functions that live in a set space.
6875 #include <isl/val.h>
6876 __isl_give isl_multi_val *isl_multi_val_range_splice(
6877 __isl_take isl_multi_val *mv1, unsigned pos,
6878 __isl_take isl_multi_val *mv2);
6880 #include <isl/aff.h>
6881 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
6882 __isl_take isl_multi_aff *ma1, unsigned pos,
6883 __isl_take isl_multi_aff *ma2);
6884 __isl_give isl_multi_aff *isl_multi_aff_splice(
6885 __isl_take isl_multi_aff *ma1,
6886 unsigned in_pos, unsigned out_pos,
6887 __isl_take isl_multi_aff *ma2);
6888 __isl_give isl_multi_pw_aff *
6889 isl_multi_pw_aff_range_splice(
6890 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
6891 __isl_take isl_multi_pw_aff *mpa2);
6892 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
6893 __isl_take isl_multi_pw_aff *mpa1,
6894 unsigned in_pos, unsigned out_pos,
6895 __isl_take isl_multi_pw_aff *mpa2);
6896 __isl_give isl_multi_union_pw_aff *
6897 isl_multi_union_pw_aff_range_splice(
6898 __isl_take isl_multi_union_pw_aff *mupa1,
6900 __isl_take isl_multi_union_pw_aff *mupa2);
6902 =item * Simplification
6904 When applied to a set or relation,
6905 the gist operation returns a set or relation that has the
6906 same intersection with the context as the input set or relation.
6907 Any implicit equality in the intersection is made explicit in the result,
6908 while all inequalities that are redundant with respect to the intersection
6910 In case of union sets and relations, the gist operation is performed
6913 When applied to a function,
6914 the gist operation applies the set gist operation to each of
6915 the cells in the domain of the input piecewise expression.
6916 The context is also exploited
6917 to simplify the expression associated to each cell.
6919 #include <isl/set.h>
6920 __isl_give isl_basic_set *isl_basic_set_gist(
6921 __isl_take isl_basic_set *bset,
6922 __isl_take isl_basic_set *context);
6923 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
6924 __isl_take isl_set *context);
6925 __isl_give isl_set *isl_set_gist_params(
6926 __isl_take isl_set *set,
6927 __isl_take isl_set *context);
6929 #include <isl/map.h>
6930 __isl_give isl_basic_map *isl_basic_map_gist(
6931 __isl_take isl_basic_map *bmap,
6932 __isl_take isl_basic_map *context);
6933 __isl_give isl_basic_map *isl_basic_map_gist_domain(
6934 __isl_take isl_basic_map *bmap,
6935 __isl_take isl_basic_set *context);
6936 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
6937 __isl_take isl_map *context);
6938 __isl_give isl_map *isl_map_gist_params(
6939 __isl_take isl_map *map,
6940 __isl_take isl_set *context);
6941 __isl_give isl_map *isl_map_gist_domain(
6942 __isl_take isl_map *map,
6943 __isl_take isl_set *context);
6944 __isl_give isl_map *isl_map_gist_range(
6945 __isl_take isl_map *map,
6946 __isl_take isl_set *context);
6948 #include <isl/union_set.h>
6949 __isl_give isl_union_set *isl_union_set_gist(
6950 __isl_take isl_union_set *uset,
6951 __isl_take isl_union_set *context);
6952 __isl_give isl_union_set *isl_union_set_gist_params(
6953 __isl_take isl_union_set *uset,
6954 __isl_take isl_set *set);
6956 #include <isl/union_map.h>
6957 __isl_give isl_union_map *isl_union_map_gist(
6958 __isl_take isl_union_map *umap,
6959 __isl_take isl_union_map *context);
6960 __isl_give isl_union_map *isl_union_map_gist_params(
6961 __isl_take isl_union_map *umap,
6962 __isl_take isl_set *set);
6963 __isl_give isl_union_map *isl_union_map_gist_domain(
6964 __isl_take isl_union_map *umap,
6965 __isl_take isl_union_set *uset);
6966 __isl_give isl_union_map *isl_union_map_gist_range(
6967 __isl_take isl_union_map *umap,
6968 __isl_take isl_union_set *uset);
6970 #include <isl/aff.h>
6971 __isl_give isl_aff *isl_aff_gist_params(
6972 __isl_take isl_aff *aff,
6973 __isl_take isl_set *context);
6974 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
6975 __isl_take isl_set *context);
6976 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
6977 __isl_take isl_multi_aff *maff,
6978 __isl_take isl_set *context);
6979 __isl_give isl_multi_aff *isl_multi_aff_gist(
6980 __isl_take isl_multi_aff *maff,
6981 __isl_take isl_set *context);
6982 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
6983 __isl_take isl_pw_aff *pwaff,
6984 __isl_take isl_set *context);
6985 __isl_give isl_pw_aff *isl_pw_aff_gist(
6986 __isl_take isl_pw_aff *pwaff,
6987 __isl_take isl_set *context);
6988 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
6989 __isl_take isl_pw_multi_aff *pma,
6990 __isl_take isl_set *set);
6991 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
6992 __isl_take isl_pw_multi_aff *pma,
6993 __isl_take isl_set *set);
6994 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
6995 __isl_take isl_multi_pw_aff *mpa,
6996 __isl_take isl_set *set);
6997 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
6998 __isl_take isl_multi_pw_aff *mpa,
6999 __isl_take isl_set *set);
7000 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
7001 __isl_take isl_union_pw_aff *upa,
7002 __isl_take isl_union_set *context);
7003 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
7004 __isl_take isl_union_pw_aff *upa,
7005 __isl_take isl_set *context);
7006 __isl_give isl_union_pw_multi_aff *
7007 isl_union_pw_multi_aff_gist_params(
7008 __isl_take isl_union_pw_multi_aff *upma,
7009 __isl_take isl_set *context);
7010 __isl_give isl_union_pw_multi_aff *
7011 isl_union_pw_multi_aff_gist(
7012 __isl_take isl_union_pw_multi_aff *upma,
7013 __isl_take isl_union_set *context);
7014 __isl_give isl_multi_union_pw_aff *
7015 isl_multi_union_pw_aff_gist_params(
7016 __isl_take isl_multi_union_pw_aff *aff,
7017 __isl_take isl_set *context);
7018 __isl_give isl_multi_union_pw_aff *
7019 isl_multi_union_pw_aff_gist(
7020 __isl_take isl_multi_union_pw_aff *aff,
7021 __isl_take isl_union_set *context);
7023 #include <isl/polynomial.h>
7024 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
7025 __isl_take isl_qpolynomial *qp,
7026 __isl_take isl_set *context);
7027 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
7028 __isl_take isl_qpolynomial *qp,
7029 __isl_take isl_set *context);
7030 __isl_give isl_qpolynomial_fold *
7031 isl_qpolynomial_fold_gist_params(
7032 __isl_take isl_qpolynomial_fold *fold,
7033 __isl_take isl_set *context);
7034 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
7035 __isl_take isl_qpolynomial_fold *fold,
7036 __isl_take isl_set *context);
7037 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
7038 __isl_take isl_pw_qpolynomial *pwqp,
7039 __isl_take isl_set *context);
7040 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
7041 __isl_take isl_pw_qpolynomial *pwqp,
7042 __isl_take isl_set *context);
7043 __isl_give isl_pw_qpolynomial_fold *
7044 isl_pw_qpolynomial_fold_gist(
7045 __isl_take isl_pw_qpolynomial_fold *pwf,
7046 __isl_take isl_set *context);
7047 __isl_give isl_pw_qpolynomial_fold *
7048 isl_pw_qpolynomial_fold_gist_params(
7049 __isl_take isl_pw_qpolynomial_fold *pwf,
7050 __isl_take isl_set *context);
7051 __isl_give isl_union_pw_qpolynomial *
7052 isl_union_pw_qpolynomial_gist_params(
7053 __isl_take isl_union_pw_qpolynomial *upwqp,
7054 __isl_take isl_set *context);
7055 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
7056 __isl_take isl_union_pw_qpolynomial *upwqp,
7057 __isl_take isl_union_set *context);
7058 __isl_give isl_union_pw_qpolynomial_fold *
7059 isl_union_pw_qpolynomial_fold_gist(
7060 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7061 __isl_take isl_union_set *context);
7062 __isl_give isl_union_pw_qpolynomial_fold *
7063 isl_union_pw_qpolynomial_fold_gist_params(
7064 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7065 __isl_take isl_set *context);
7067 =item * Binary Arithmetic Operations
7069 #include <isl/set.h>
7070 __isl_give isl_set *isl_set_sum(
7071 __isl_take isl_set *set1,
7072 __isl_take isl_set *set2);
7073 #include <isl/map.h>
7074 __isl_give isl_map *isl_map_sum(
7075 __isl_take isl_map *map1,
7076 __isl_take isl_map *map2);
7078 C<isl_set_sum> computes the Minkowski sum of its two arguments,
7079 i.e., the set containing the sums of pairs of elements from
7080 C<set1> and C<set2>.
7081 The domain of the result of C<isl_map_sum> is the intersection
7082 of the domains of its two arguments. The corresponding range
7083 elements are the sums of the corresponding range elements
7084 in the two arguments.
7086 #include <isl/val.h>
7087 __isl_give isl_multi_val *isl_multi_val_add(
7088 __isl_take isl_multi_val *mv1,
7089 __isl_take isl_multi_val *mv2);
7090 __isl_give isl_multi_val *isl_multi_val_sub(
7091 __isl_take isl_multi_val *mv1,
7092 __isl_take isl_multi_val *mv2);
7094 #include <isl/aff.h>
7095 __isl_give isl_aff *isl_aff_add(
7096 __isl_take isl_aff *aff1,
7097 __isl_take isl_aff *aff2);
7098 __isl_give isl_multi_aff *isl_multi_aff_add(
7099 __isl_take isl_multi_aff *maff1,
7100 __isl_take isl_multi_aff *maff2);
7101 __isl_give isl_pw_aff *isl_pw_aff_add(
7102 __isl_take isl_pw_aff *pwaff1,
7103 __isl_take isl_pw_aff *pwaff2);
7104 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add(
7105 __isl_take isl_multi_pw_aff *mpa1,
7106 __isl_take isl_multi_pw_aff *mpa2);
7107 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
7108 __isl_take isl_pw_multi_aff *pma1,
7109 __isl_take isl_pw_multi_aff *pma2);
7110 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
7111 __isl_take isl_union_pw_aff *upa1,
7112 __isl_take isl_union_pw_aff *upa2);
7113 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
7114 __isl_take isl_union_pw_multi_aff *upma1,
7115 __isl_take isl_union_pw_multi_aff *upma2);
7116 __isl_give isl_multi_union_pw_aff *
7117 isl_multi_union_pw_aff_add(
7118 __isl_take isl_multi_union_pw_aff *mupa1,
7119 __isl_take isl_multi_union_pw_aff *mupa2);
7120 __isl_give isl_pw_aff *isl_pw_aff_min(
7121 __isl_take isl_pw_aff *pwaff1,
7122 __isl_take isl_pw_aff *pwaff2);
7123 __isl_give isl_pw_aff *isl_pw_aff_max(
7124 __isl_take isl_pw_aff *pwaff1,
7125 __isl_take isl_pw_aff *pwaff2);
7126 __isl_give isl_aff *isl_aff_sub(
7127 __isl_take isl_aff *aff1,
7128 __isl_take isl_aff *aff2);
7129 __isl_give isl_multi_aff *isl_multi_aff_sub(
7130 __isl_take isl_multi_aff *ma1,
7131 __isl_take isl_multi_aff *ma2);
7132 __isl_give isl_pw_aff *isl_pw_aff_sub(
7133 __isl_take isl_pw_aff *pwaff1,
7134 __isl_take isl_pw_aff *pwaff2);
7135 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
7136 __isl_take isl_multi_pw_aff *mpa1,
7137 __isl_take isl_multi_pw_aff *mpa2);
7138 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
7139 __isl_take isl_pw_multi_aff *pma1,
7140 __isl_take isl_pw_multi_aff *pma2);
7141 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
7142 __isl_take isl_union_pw_aff *upa1,
7143 __isl_take isl_union_pw_aff *upa2);
7144 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
7145 __isl_take isl_union_pw_multi_aff *upma1,
7146 __isl_take isl_union_pw_multi_aff *upma2);
7147 __isl_give isl_multi_union_pw_aff *
7148 isl_multi_union_pw_aff_sub(
7149 __isl_take isl_multi_union_pw_aff *mupa1,
7150 __isl_take isl_multi_union_pw_aff *mupa2);
7152 C<isl_aff_sub> subtracts the second argument from the first.
7154 #include <isl/polynomial.h>
7155 __isl_give isl_qpolynomial *isl_qpolynomial_add(
7156 __isl_take isl_qpolynomial *qp1,
7157 __isl_take isl_qpolynomial *qp2);
7158 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
7159 __isl_take isl_pw_qpolynomial *pwqp1,
7160 __isl_take isl_pw_qpolynomial *pwqp2);
7161 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
7162 __isl_take isl_pw_qpolynomial *pwqp1,
7163 __isl_take isl_pw_qpolynomial *pwqp2);
7164 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
7165 __isl_take isl_pw_qpolynomial_fold *pwf1,
7166 __isl_take isl_pw_qpolynomial_fold *pwf2);
7167 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
7168 __isl_take isl_union_pw_qpolynomial *upwqp1,
7169 __isl_take isl_union_pw_qpolynomial *upwqp2);
7170 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
7171 __isl_take isl_qpolynomial *qp1,
7172 __isl_take isl_qpolynomial *qp2);
7173 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
7174 __isl_take isl_pw_qpolynomial *pwqp1,
7175 __isl_take isl_pw_qpolynomial *pwqp2);
7176 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
7177 __isl_take isl_union_pw_qpolynomial *upwqp1,
7178 __isl_take isl_union_pw_qpolynomial *upwqp2);
7179 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
7180 __isl_take isl_pw_qpolynomial_fold *pwf1,
7181 __isl_take isl_pw_qpolynomial_fold *pwf2);
7182 __isl_give isl_union_pw_qpolynomial_fold *
7183 isl_union_pw_qpolynomial_fold_fold(
7184 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
7185 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
7187 #include <isl/aff.h>
7188 __isl_give isl_pw_aff *isl_pw_aff_union_add(
7189 __isl_take isl_pw_aff *pwaff1,
7190 __isl_take isl_pw_aff *pwaff2);
7191 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
7192 __isl_take isl_pw_multi_aff *pma1,
7193 __isl_take isl_pw_multi_aff *pma2);
7194 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
7195 __isl_take isl_union_pw_aff *upa1,
7196 __isl_take isl_union_pw_aff *upa2);
7197 __isl_give isl_union_pw_multi_aff *
7198 isl_union_pw_multi_aff_union_add(
7199 __isl_take isl_union_pw_multi_aff *upma1,
7200 __isl_take isl_union_pw_multi_aff *upma2);
7201 __isl_give isl_multi_union_pw_aff *
7202 isl_multi_union_pw_aff_union_add(
7203 __isl_take isl_multi_union_pw_aff *mupa1,
7204 __isl_take isl_multi_union_pw_aff *mupa2);
7205 __isl_give isl_pw_aff *isl_pw_aff_union_min(
7206 __isl_take isl_pw_aff *pwaff1,
7207 __isl_take isl_pw_aff *pwaff2);
7208 __isl_give isl_pw_aff *isl_pw_aff_union_max(
7209 __isl_take isl_pw_aff *pwaff1,
7210 __isl_take isl_pw_aff *pwaff2);
7212 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
7213 expression with a domain that is the union of those of C<pwaff1> and
7214 C<pwaff2> and such that on each cell, the quasi-affine expression is
7215 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
7216 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
7217 associated expression is the defined one.
7218 This in contrast to the C<isl_pw_aff_max> function, which is
7219 only defined on the shared definition domain of the arguments.
7221 #include <isl/val.h>
7222 __isl_give isl_multi_val *isl_multi_val_add_val(
7223 __isl_take isl_multi_val *mv,
7224 __isl_take isl_val *v);
7225 __isl_give isl_multi_val *isl_multi_val_mod_val(
7226 __isl_take isl_multi_val *mv,
7227 __isl_take isl_val *v);
7228 __isl_give isl_multi_val *isl_multi_val_scale_val(
7229 __isl_take isl_multi_val *mv,
7230 __isl_take isl_val *v);
7231 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
7232 __isl_take isl_multi_val *mv,
7233 __isl_take isl_val *v);
7235 #include <isl/aff.h>
7236 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
7237 __isl_take isl_val *mod);
7238 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
7239 __isl_take isl_pw_aff *pa,
7240 __isl_take isl_val *mod);
7241 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
7242 __isl_take isl_union_pw_aff *upa,
7243 __isl_take isl_val *f);
7244 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
7245 __isl_take isl_val *v);
7246 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
7247 __isl_take isl_multi_aff *ma,
7248 __isl_take isl_val *v);
7249 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
7250 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
7251 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
7252 __isl_take isl_multi_pw_aff *mpa,
7253 __isl_take isl_val *v);
7254 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
7255 __isl_take isl_pw_multi_aff *pma,
7256 __isl_take isl_val *v);
7257 __isl_give isl_union_pw_multi_aff *
7258 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
7259 __isl_take isl_union_pw_aff *upa,
7260 __isl_take isl_val *f);
7261 isl_union_pw_multi_aff_scale_val(
7262 __isl_take isl_union_pw_multi_aff *upma,
7263 __isl_take isl_val *val);
7264 __isl_give isl_multi_union_pw_aff *
7265 isl_multi_union_pw_aff_scale_val(
7266 __isl_take isl_multi_union_pw_aff *mupa,
7267 __isl_take isl_val *v);
7268 __isl_give isl_aff *isl_aff_scale_down_ui(
7269 __isl_take isl_aff *aff, unsigned f);
7270 __isl_give isl_aff *isl_aff_scale_down_val(
7271 __isl_take isl_aff *aff, __isl_take isl_val *v);
7272 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
7273 __isl_take isl_multi_aff *ma,
7274 __isl_take isl_val *v);
7275 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
7276 __isl_take isl_pw_aff *pa,
7277 __isl_take isl_val *f);
7278 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
7279 __isl_take isl_multi_pw_aff *mpa,
7280 __isl_take isl_val *v);
7281 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
7282 __isl_take isl_pw_multi_aff *pma,
7283 __isl_take isl_val *v);
7284 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
7285 __isl_take isl_union_pw_aff *upa,
7286 __isl_take isl_val *v);
7287 __isl_give isl_union_pw_multi_aff *
7288 isl_union_pw_multi_aff_scale_down_val(
7289 __isl_take isl_union_pw_multi_aff *upma,
7290 __isl_take isl_val *val);
7291 __isl_give isl_multi_union_pw_aff *
7292 isl_multi_union_pw_aff_scale_down_val(
7293 __isl_take isl_multi_union_pw_aff *mupa,
7294 __isl_take isl_val *v);
7296 #include <isl/polynomial.h>
7297 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
7298 __isl_take isl_qpolynomial *qp,
7299 __isl_take isl_val *v);
7300 __isl_give isl_qpolynomial_fold *
7301 isl_qpolynomial_fold_scale_val(
7302 __isl_take isl_qpolynomial_fold *fold,
7303 __isl_take isl_val *v);
7304 __isl_give isl_pw_qpolynomial *
7305 isl_pw_qpolynomial_scale_val(
7306 __isl_take isl_pw_qpolynomial *pwqp,
7307 __isl_take isl_val *v);
7308 __isl_give isl_pw_qpolynomial_fold *
7309 isl_pw_qpolynomial_fold_scale_val(
7310 __isl_take isl_pw_qpolynomial_fold *pwf,
7311 __isl_take isl_val *v);
7312 __isl_give isl_union_pw_qpolynomial *
7313 isl_union_pw_qpolynomial_scale_val(
7314 __isl_take isl_union_pw_qpolynomial *upwqp,
7315 __isl_take isl_val *v);
7316 __isl_give isl_union_pw_qpolynomial_fold *
7317 isl_union_pw_qpolynomial_fold_scale_val(
7318 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7319 __isl_take isl_val *v);
7320 __isl_give isl_qpolynomial *
7321 isl_qpolynomial_scale_down_val(
7322 __isl_take isl_qpolynomial *qp,
7323 __isl_take isl_val *v);
7324 __isl_give isl_qpolynomial_fold *
7325 isl_qpolynomial_fold_scale_down_val(
7326 __isl_take isl_qpolynomial_fold *fold,
7327 __isl_take isl_val *v);
7328 __isl_give isl_pw_qpolynomial *
7329 isl_pw_qpolynomial_scale_down_val(
7330 __isl_take isl_pw_qpolynomial *pwqp,
7331 __isl_take isl_val *v);
7332 __isl_give isl_pw_qpolynomial_fold *
7333 isl_pw_qpolynomial_fold_scale_down_val(
7334 __isl_take isl_pw_qpolynomial_fold *pwf,
7335 __isl_take isl_val *v);
7336 __isl_give isl_union_pw_qpolynomial *
7337 isl_union_pw_qpolynomial_scale_down_val(
7338 __isl_take isl_union_pw_qpolynomial *upwqp,
7339 __isl_take isl_val *v);
7340 __isl_give isl_union_pw_qpolynomial_fold *
7341 isl_union_pw_qpolynomial_fold_scale_down_val(
7342 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7343 __isl_take isl_val *v);
7345 #include <isl/val.h>
7346 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
7347 __isl_take isl_multi_val *mv1,
7348 __isl_take isl_multi_val *mv2);
7349 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
7350 __isl_take isl_multi_val *mv1,
7351 __isl_take isl_multi_val *mv2);
7352 __isl_give isl_multi_val *
7353 isl_multi_val_scale_down_multi_val(
7354 __isl_take isl_multi_val *mv1,
7355 __isl_take isl_multi_val *mv2);
7357 #include <isl/aff.h>
7358 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
7359 __isl_take isl_multi_aff *ma,
7360 __isl_take isl_multi_val *mv);
7361 __isl_give isl_multi_union_pw_aff *
7362 isl_multi_union_pw_aff_mod_multi_val(
7363 __isl_take isl_multi_union_pw_aff *upma,
7364 __isl_take isl_multi_val *mv);
7365 __isl_give isl_multi_pw_aff *
7366 isl_multi_pw_aff_mod_multi_val(
7367 __isl_take isl_multi_pw_aff *mpa,
7368 __isl_take isl_multi_val *mv);
7369 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
7370 __isl_take isl_multi_aff *ma,
7371 __isl_take isl_multi_val *mv);
7372 __isl_give isl_pw_multi_aff *
7373 isl_pw_multi_aff_scale_multi_val(
7374 __isl_take isl_pw_multi_aff *pma,
7375 __isl_take isl_multi_val *mv);
7376 __isl_give isl_multi_pw_aff *
7377 isl_multi_pw_aff_scale_multi_val(
7378 __isl_take isl_multi_pw_aff *mpa,
7379 __isl_take isl_multi_val *mv);
7380 __isl_give isl_multi_union_pw_aff *
7381 isl_multi_union_pw_aff_scale_multi_val(
7382 __isl_take isl_multi_union_pw_aff *mupa,
7383 __isl_take isl_multi_val *mv);
7384 __isl_give isl_union_pw_multi_aff *
7385 isl_union_pw_multi_aff_scale_multi_val(
7386 __isl_take isl_union_pw_multi_aff *upma,
7387 __isl_take isl_multi_val *mv);
7388 __isl_give isl_multi_aff *
7389 isl_multi_aff_scale_down_multi_val(
7390 __isl_take isl_multi_aff *ma,
7391 __isl_take isl_multi_val *mv);
7392 __isl_give isl_multi_pw_aff *
7393 isl_multi_pw_aff_scale_down_multi_val(
7394 __isl_take isl_multi_pw_aff *mpa,
7395 __isl_take isl_multi_val *mv);
7396 __isl_give isl_multi_union_pw_aff *
7397 isl_multi_union_pw_aff_scale_down_multi_val(
7398 __isl_take isl_multi_union_pw_aff *mupa,
7399 __isl_take isl_multi_val *mv);
7401 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
7402 by the corresponding elements of C<mv>.
7404 #include <isl/aff.h>
7405 __isl_give isl_aff *isl_aff_mul(
7406 __isl_take isl_aff *aff1,
7407 __isl_take isl_aff *aff2);
7408 __isl_give isl_aff *isl_aff_div(
7409 __isl_take isl_aff *aff1,
7410 __isl_take isl_aff *aff2);
7411 __isl_give isl_pw_aff *isl_pw_aff_mul(
7412 __isl_take isl_pw_aff *pwaff1,
7413 __isl_take isl_pw_aff *pwaff2);
7414 __isl_give isl_pw_aff *isl_pw_aff_div(
7415 __isl_take isl_pw_aff *pa1,
7416 __isl_take isl_pw_aff *pa2);
7417 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
7418 __isl_take isl_pw_aff *pa1,
7419 __isl_take isl_pw_aff *pa2);
7420 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
7421 __isl_take isl_pw_aff *pa1,
7422 __isl_take isl_pw_aff *pa2);
7424 When multiplying two affine expressions, at least one of the two needs
7425 to be a constant. Similarly, when dividing an affine expression by another,
7426 the second expression needs to be a constant.
7427 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
7428 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
7431 #include <isl/polynomial.h>
7432 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
7433 __isl_take isl_qpolynomial *qp1,
7434 __isl_take isl_qpolynomial *qp2);
7435 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
7436 __isl_take isl_pw_qpolynomial *pwqp1,
7437 __isl_take isl_pw_qpolynomial *pwqp2);
7438 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
7439 __isl_take isl_union_pw_qpolynomial *upwqp1,
7440 __isl_take isl_union_pw_qpolynomial *upwqp2);
7444 =head3 Lexicographic Optimization
7446 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
7447 the following functions
7448 compute a set that contains the lexicographic minimum or maximum
7449 of the elements in C<set> (or C<bset>) for those values of the parameters
7450 that satisfy C<dom>.
7451 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7452 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
7454 In other words, the union of the parameter values
7455 for which the result is non-empty and of C<*empty>
7458 #include <isl/set.h>
7459 __isl_give isl_set *isl_basic_set_partial_lexmin(
7460 __isl_take isl_basic_set *bset,
7461 __isl_take isl_basic_set *dom,
7462 __isl_give isl_set **empty);
7463 __isl_give isl_set *isl_basic_set_partial_lexmax(
7464 __isl_take isl_basic_set *bset,
7465 __isl_take isl_basic_set *dom,
7466 __isl_give isl_set **empty);
7467 __isl_give isl_set *isl_set_partial_lexmin(
7468 __isl_take isl_set *set, __isl_take isl_set *dom,
7469 __isl_give isl_set **empty);
7470 __isl_give isl_set *isl_set_partial_lexmax(
7471 __isl_take isl_set *set, __isl_take isl_set *dom,
7472 __isl_give isl_set **empty);
7474 Given a (basic) set C<set> (or C<bset>), the following functions simply
7475 return a set containing the lexicographic minimum or maximum
7476 of the elements in C<set> (or C<bset>).
7477 In case of union sets, the optimum is computed per space.
7479 #include <isl/set.h>
7480 __isl_give isl_set *isl_basic_set_lexmin(
7481 __isl_take isl_basic_set *bset);
7482 __isl_give isl_set *isl_basic_set_lexmax(
7483 __isl_take isl_basic_set *bset);
7484 __isl_give isl_set *isl_set_lexmin(
7485 __isl_take isl_set *set);
7486 __isl_give isl_set *isl_set_lexmax(
7487 __isl_take isl_set *set);
7488 __isl_give isl_union_set *isl_union_set_lexmin(
7489 __isl_take isl_union_set *uset);
7490 __isl_give isl_union_set *isl_union_set_lexmax(
7491 __isl_take isl_union_set *uset);
7493 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
7494 the following functions
7495 compute a relation that maps each element of C<dom>
7496 to the single lexicographic minimum or maximum
7497 of the elements that are associated to that same
7498 element in C<map> (or C<bmap>).
7499 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7500 that contains the elements in C<dom> that do not map
7501 to any elements in C<map> (or C<bmap>).
7502 In other words, the union of the domain of the result and of C<*empty>
7505 #include <isl/map.h>
7506 __isl_give isl_map *isl_basic_map_partial_lexmax(
7507 __isl_take isl_basic_map *bmap,
7508 __isl_take isl_basic_set *dom,
7509 __isl_give isl_set **empty);
7510 __isl_give isl_map *isl_basic_map_partial_lexmin(
7511 __isl_take isl_basic_map *bmap,
7512 __isl_take isl_basic_set *dom,
7513 __isl_give isl_set **empty);
7514 __isl_give isl_map *isl_map_partial_lexmax(
7515 __isl_take isl_map *map, __isl_take isl_set *dom,
7516 __isl_give isl_set **empty);
7517 __isl_give isl_map *isl_map_partial_lexmin(
7518 __isl_take isl_map *map, __isl_take isl_set *dom,
7519 __isl_give isl_set **empty);
7521 Given a (basic) map C<map> (or C<bmap>), the following functions simply
7522 return a map mapping each element in the domain of
7523 C<map> (or C<bmap>) to the lexicographic minimum or maximum
7524 of all elements associated to that element.
7525 In case of union relations, the optimum is computed per space.
7527 #include <isl/map.h>
7528 __isl_give isl_map *isl_basic_map_lexmin(
7529 __isl_take isl_basic_map *bmap);
7530 __isl_give isl_map *isl_basic_map_lexmax(
7531 __isl_take isl_basic_map *bmap);
7532 __isl_give isl_map *isl_map_lexmin(
7533 __isl_take isl_map *map);
7534 __isl_give isl_map *isl_map_lexmax(
7535 __isl_take isl_map *map);
7536 __isl_give isl_union_map *isl_union_map_lexmin(
7537 __isl_take isl_union_map *umap);
7538 __isl_give isl_union_map *isl_union_map_lexmax(
7539 __isl_take isl_union_map *umap);
7541 The following functions return their result in the form of
7542 a piecewise multi-affine expression,
7543 but are otherwise equivalent to the corresponding functions
7544 returning a basic set or relation.
7546 #include <isl/set.h>
7547 __isl_give isl_pw_multi_aff *
7548 isl_basic_set_partial_lexmin_pw_multi_aff(
7549 __isl_take isl_basic_set *bset,
7550 __isl_take isl_basic_set *dom,
7551 __isl_give isl_set **empty);
7552 __isl_give isl_pw_multi_aff *
7553 isl_basic_set_partial_lexmax_pw_multi_aff(
7554 __isl_take isl_basic_set *bset,
7555 __isl_take isl_basic_set *dom,
7556 __isl_give isl_set **empty);
7557 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
7558 __isl_take isl_set *set);
7559 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
7560 __isl_take isl_set *set);
7562 #include <isl/map.h>
7563 __isl_give isl_pw_multi_aff *
7564 isl_basic_map_lexmin_pw_multi_aff(
7565 __isl_take isl_basic_map *bmap);
7566 __isl_give isl_pw_multi_aff *
7567 isl_basic_map_partial_lexmin_pw_multi_aff(
7568 __isl_take isl_basic_map *bmap,
7569 __isl_take isl_basic_set *dom,
7570 __isl_give isl_set **empty);
7571 __isl_give isl_pw_multi_aff *
7572 isl_basic_map_partial_lexmax_pw_multi_aff(
7573 __isl_take isl_basic_map *bmap,
7574 __isl_take isl_basic_set *dom,
7575 __isl_give isl_set **empty);
7576 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
7577 __isl_take isl_map *map);
7578 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
7579 __isl_take isl_map *map);
7581 The following functions return the lexicographic minimum or maximum
7582 on the shared domain of the inputs and the single defined function
7583 on those parts of the domain where only a single function is defined.
7585 #include <isl/aff.h>
7586 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
7587 __isl_take isl_pw_multi_aff *pma1,
7588 __isl_take isl_pw_multi_aff *pma2);
7589 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
7590 __isl_take isl_pw_multi_aff *pma1,
7591 __isl_take isl_pw_multi_aff *pma2);
7593 If the input to a lexicographic optimization problem has
7594 multiple constraints with the same coefficients for the optimized
7595 variables, then, by default, this symmetry is exploited by
7596 replacing those constraints by a single constraint with
7597 an abstract bound, which is in turn bounded by the corresponding terms
7598 in the original constraints.
7599 Without this optimization, the solver would typically consider
7600 all possible orderings of those original bounds, resulting in a needless
7601 decomposition of the domain.
7602 However, the optimization can also result in slowdowns since
7603 an extra parameter is introduced that may get used in additional
7605 The following option determines whether symmetry detection is applied
7606 during lexicographic optimization.
7608 #include <isl/options.h>
7609 isl_stat isl_options_set_pip_symmetry(isl_ctx *ctx,
7611 int isl_options_get_pip_symmetry(isl_ctx *ctx);
7615 See also \autoref{s:offline}.
7619 =head2 Ternary Operations
7621 #include <isl/aff.h>
7622 __isl_give isl_pw_aff *isl_pw_aff_cond(
7623 __isl_take isl_pw_aff *cond,
7624 __isl_take isl_pw_aff *pwaff_true,
7625 __isl_take isl_pw_aff *pwaff_false);
7627 The function C<isl_pw_aff_cond> performs a conditional operator
7628 and returns an expression that is equal to C<pwaff_true>
7629 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
7630 where C<cond> is zero.
7634 Lists are defined over several element types, including
7635 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_union_pw_aff>,
7636 C<isl_union_pw_multi_aff>, C<isl_constraint>,
7637 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
7638 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
7639 Here we take lists of C<isl_set>s as an example.
7640 Lists can be created, copied, modified and freed using the following functions.
7642 #include <isl/set.h>
7643 __isl_give isl_set_list *isl_set_list_from_set(
7644 __isl_take isl_set *el);
7645 __isl_give isl_set_list *isl_set_list_alloc(
7646 isl_ctx *ctx, int n);
7647 __isl_give isl_set_list *isl_set_list_copy(
7648 __isl_keep isl_set_list *list);
7649 __isl_give isl_set_list *isl_set_list_insert(
7650 __isl_take isl_set_list *list, unsigned pos,
7651 __isl_take isl_set *el);
7652 __isl_give isl_set_list *isl_set_list_add(
7653 __isl_take isl_set_list *list,
7654 __isl_take isl_set *el);
7655 __isl_give isl_set_list *isl_set_list_drop(
7656 __isl_take isl_set_list *list,
7657 unsigned first, unsigned n);
7658 __isl_give isl_set_list *isl_set_list_set_set(
7659 __isl_take isl_set_list *list, int index,
7660 __isl_take isl_set *set);
7661 __isl_give isl_set_list *isl_set_list_concat(
7662 __isl_take isl_set_list *list1,
7663 __isl_take isl_set_list *list2);
7664 __isl_give isl_set_list *isl_set_list_map(
7665 __isl_take isl_set_list *list,
7666 __isl_give isl_set *(*fn)(__isl_take isl_set *el,
7669 __isl_give isl_set_list *isl_set_list_sort(
7670 __isl_take isl_set_list *list,
7671 int (*cmp)(__isl_keep isl_set *a,
7672 __isl_keep isl_set *b, void *user),
7674 __isl_null isl_set_list *isl_set_list_free(
7675 __isl_take isl_set_list *list);
7677 C<isl_set_list_alloc> creates an empty list with an initial capacity
7678 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
7679 add elements to a list, increasing its capacity as needed.
7680 C<isl_set_list_from_set> creates a list with a single element.
7682 Lists can be inspected using the following functions.
7684 #include <isl/set.h>
7685 int isl_set_list_n_set(__isl_keep isl_set_list *list);
7686 __isl_give isl_set *isl_set_list_get_set(
7687 __isl_keep isl_set_list *list, int index);
7688 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list,
7689 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7691 isl_stat isl_set_list_foreach_scc(
7692 __isl_keep isl_set_list *list,
7693 isl_bool (*follows)(__isl_keep isl_set *a,
7694 __isl_keep isl_set *b, void *user),
7696 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7699 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
7700 strongly connected components of the graph with as vertices the elements
7701 of C<list> and a directed edge from vertex C<b> to vertex C<a>
7702 iff C<follows(a, b)> returns C<isl_bool_true>. The callbacks C<follows> and
7703 C<fn> should return C<isl_bool_error> or C<isl_stat_error> on error.
7705 Lists can be printed using
7707 #include <isl/set.h>
7708 __isl_give isl_printer *isl_printer_print_set_list(
7709 __isl_take isl_printer *p,
7710 __isl_keep isl_set_list *list);
7712 =head2 Associative arrays
7714 Associative arrays map isl objects of a specific type to isl objects
7715 of some (other) specific type. They are defined for several pairs
7716 of types, including (C<isl_map>, C<isl_basic_set>),
7717 (C<isl_id>, C<isl_ast_expr>),
7718 (C<isl_id>, C<isl_id>) and
7719 (C<isl_id>, C<isl_pw_aff>).
7720 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
7723 Associative arrays can be created, copied and freed using
7724 the following functions.
7726 #include <isl/id_to_ast_expr.h>
7727 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
7728 isl_ctx *ctx, int min_size);
7729 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
7730 __isl_keep isl_id_to_ast_expr *id2expr);
7731 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
7732 __isl_take isl_id_to_ast_expr *id2expr);
7734 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
7735 to specify the expected size of the associative array.
7736 The associative array will be grown automatically as needed.
7738 Associative arrays can be inspected using the following functions.
7740 #include <isl/id_to_ast_expr.h>
7741 __isl_give isl_maybe_isl_ast_expr
7742 isl_id_to_ast_expr_try_get(
7743 __isl_keep isl_id_to_ast_expr *id2expr,
7744 __isl_keep isl_id *key);
7745 isl_bool isl_id_to_ast_expr_has(
7746 __isl_keep isl_id_to_ast_expr *id2expr,
7747 __isl_keep isl_id *key);
7748 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
7749 __isl_keep isl_id_to_ast_expr *id2expr,
7750 __isl_take isl_id *key);
7751 isl_stat isl_id_to_ast_expr_foreach(
7752 __isl_keep isl_id_to_ast_expr *id2expr,
7753 isl_stat (*fn)(__isl_take isl_id *key,
7754 __isl_take isl_ast_expr *val, void *user),
7757 The function C<isl_id_to_ast_expr_try_get> returns a structure
7758 containing two elements, C<valid> and C<value>.
7759 If there is a value associated to the key, then C<valid>
7760 is set to C<isl_bool_true> and C<value> contains a copy of
7761 the associated value. Otherwise C<value> is C<NULL> and
7762 C<valid> may be C<isl_bool_error> or C<isl_bool_false> depending
7763 on whether some error has occurred or there simply is no associated value.
7764 The function C<isl_id_to_ast_expr_has> returns the C<valid> field
7765 in the structure and
7766 the function C<isl_id_to_ast_expr_get> returns the C<value> field.
7768 Associative arrays can be modified using the following functions.
7770 #include <isl/id_to_ast_expr.h>
7771 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
7772 __isl_take isl_id_to_ast_expr *id2expr,
7773 __isl_take isl_id *key,
7774 __isl_take isl_ast_expr *val);
7775 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
7776 __isl_take isl_id_to_ast_expr *id2expr,
7777 __isl_take isl_id *key);
7779 Associative arrays can be printed using the following function.
7781 #include <isl/id_to_ast_expr.h>
7782 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
7783 __isl_take isl_printer *p,
7784 __isl_keep isl_id_to_ast_expr *id2expr);
7788 Vectors can be created, copied and freed using the following functions.
7790 #include <isl/vec.h>
7791 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
7793 __isl_give isl_vec *isl_vec_zero(isl_ctx *ctx,
7795 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
7796 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
7798 Note that the elements of a vector created by C<isl_vec_alloc>
7799 may have arbitrary values.
7800 A vector created by C<isl_vec_zero> has elements with value zero.
7801 The elements can be changed and inspected using the following functions.
7803 int isl_vec_size(__isl_keep isl_vec *vec);
7804 __isl_give isl_val *isl_vec_get_element_val(
7805 __isl_keep isl_vec *vec, int pos);
7806 __isl_give isl_vec *isl_vec_set_element_si(
7807 __isl_take isl_vec *vec, int pos, int v);
7808 __isl_give isl_vec *isl_vec_set_element_val(
7809 __isl_take isl_vec *vec, int pos,
7810 __isl_take isl_val *v);
7811 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
7813 __isl_give isl_vec *isl_vec_set_val(
7814 __isl_take isl_vec *vec, __isl_take isl_val *v);
7815 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
7816 __isl_keep isl_vec *vec2, int pos);
7818 C<isl_vec_get_element> will return a negative value if anything went wrong.
7819 In that case, the value of C<*v> is undefined.
7821 The following function can be used to concatenate two vectors.
7823 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
7824 __isl_take isl_vec *vec2);
7828 Matrices can be created, copied and freed using the following functions.
7830 #include <isl/mat.h>
7831 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
7832 unsigned n_row, unsigned n_col);
7833 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
7834 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
7836 Note that the elements of a newly created matrix may have arbitrary values.
7837 The elements can be changed and inspected using the following functions.
7839 int isl_mat_rows(__isl_keep isl_mat *mat);
7840 int isl_mat_cols(__isl_keep isl_mat *mat);
7841 __isl_give isl_val *isl_mat_get_element_val(
7842 __isl_keep isl_mat *mat, int row, int col);
7843 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
7844 int row, int col, int v);
7845 __isl_give isl_mat *isl_mat_set_element_val(
7846 __isl_take isl_mat *mat, int row, int col,
7847 __isl_take isl_val *v);
7849 The following function computes the rank of a matrix.
7850 The return value may be -1 if some error occurred.
7852 #include <isl/mat.h>
7853 int isl_mat_rank(__isl_keep isl_mat *mat);
7855 The following function can be used to compute the (right) inverse
7856 of a matrix, i.e., a matrix such that the product of the original
7857 and the inverse (in that order) is a multiple of the identity matrix.
7858 The input matrix is assumed to be of full row-rank.
7860 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
7862 The following function can be used to compute the (right) kernel
7863 (or null space) of a matrix, i.e., a matrix such that the product of
7864 the original and the kernel (in that order) is the zero matrix.
7866 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
7868 The following function computes a basis for the space spanned
7869 by the rows of a matrix.
7871 __isl_give isl_mat *isl_mat_row_basis(
7872 __isl_take isl_mat *mat);
7874 The following function computes rows that extend a basis of C<mat1>
7875 to a basis that also covers C<mat2>.
7877 __isl_give isl_mat *isl_mat_row_basis_extension(
7878 __isl_take isl_mat *mat1,
7879 __isl_take isl_mat *mat2);
7881 The following function checks whether there is no linear dependence
7882 among the combined rows of "mat1" and "mat2" that is not already present
7883 in "mat1" or "mat2" individually.
7884 If "mat1" and "mat2" have linearly independent rows by themselves,
7885 then this means that there is no linear dependence among all rows together.
7887 isl_bool isl_mat_has_linearly_independent_rows(
7888 __isl_keep isl_mat *mat1,
7889 __isl_keep isl_mat *mat2);
7891 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
7893 The following functions determine
7894 an upper or lower bound on a quasipolynomial over its domain.
7896 __isl_give isl_pw_qpolynomial_fold *
7897 isl_pw_qpolynomial_bound(
7898 __isl_take isl_pw_qpolynomial *pwqp,
7899 enum isl_fold type, int *tight);
7901 __isl_give isl_union_pw_qpolynomial_fold *
7902 isl_union_pw_qpolynomial_bound(
7903 __isl_take isl_union_pw_qpolynomial *upwqp,
7904 enum isl_fold type, int *tight);
7906 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
7907 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
7908 is the returned bound is known be tight, i.e., for each value
7909 of the parameters there is at least
7910 one element in the domain that reaches the bound.
7911 If the domain of C<pwqp> is not wrapping, then the bound is computed
7912 over all elements in that domain and the result has a purely parametric
7913 domain. If the domain of C<pwqp> is wrapping, then the bound is
7914 computed over the range of the wrapped relation. The domain of the
7915 wrapped relation becomes the domain of the result.
7917 =head2 Parametric Vertex Enumeration
7919 The parametric vertex enumeration described in this section
7920 is mainly intended to be used internally and by the C<barvinok>
7923 #include <isl/vertices.h>
7924 __isl_give isl_vertices *isl_basic_set_compute_vertices(
7925 __isl_keep isl_basic_set *bset);
7927 The function C<isl_basic_set_compute_vertices> performs the
7928 actual computation of the parametric vertices and the chamber
7929 decomposition and stores the result in an C<isl_vertices> object.
7930 This information can be queried by either iterating over all
7931 the vertices or iterating over all the chambers or cells
7932 and then iterating over all vertices that are active on the chamber.
7934 isl_stat isl_vertices_foreach_vertex(
7935 __isl_keep isl_vertices *vertices,
7936 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7937 void *user), void *user);
7939 isl_stat isl_vertices_foreach_cell(
7940 __isl_keep isl_vertices *vertices,
7941 isl_stat (*fn)(__isl_take isl_cell *cell,
7942 void *user), void *user);
7943 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
7944 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7945 void *user), void *user);
7947 Other operations that can be performed on an C<isl_vertices> object are
7950 int isl_vertices_get_n_vertices(
7951 __isl_keep isl_vertices *vertices);
7952 __isl_null isl_vertices *isl_vertices_free(
7953 __isl_take isl_vertices *vertices);
7955 Vertices can be inspected and destroyed using the following functions.
7957 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
7958 __isl_give isl_basic_set *isl_vertex_get_domain(
7959 __isl_keep isl_vertex *vertex);
7960 __isl_give isl_multi_aff *isl_vertex_get_expr(
7961 __isl_keep isl_vertex *vertex);
7962 void isl_vertex_free(__isl_take isl_vertex *vertex);
7964 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
7965 describing the vertex in terms of the parameters,
7966 while C<isl_vertex_get_domain> returns the activity domain
7969 Chambers can be inspected and destroyed using the following functions.
7971 __isl_give isl_basic_set *isl_cell_get_domain(
7972 __isl_keep isl_cell *cell);
7973 void isl_cell_free(__isl_take isl_cell *cell);
7975 =head1 Polyhedral Compilation Library
7977 This section collects functionality in C<isl> that has been specifically
7978 designed for use during polyhedral compilation.
7980 =head2 Schedule Trees
7982 A schedule tree is a structured representation of a schedule,
7983 assigning a relative order to a set of domain elements.
7984 The relative order expressed by the schedule tree is
7985 defined recursively. In particular, the order between
7986 two domain elements is determined by the node that is closest
7987 to the root that refers to both elements and that orders them apart.
7988 Each node in the tree is of one of several types.
7989 The root node is always of type C<isl_schedule_node_domain>
7990 (or C<isl_schedule_node_extension>)
7991 and it describes the (extra) domain elements to which the schedule applies.
7992 The other types of nodes are as follows.
7996 =item C<isl_schedule_node_band>
7998 A band of schedule dimensions. Each schedule dimension is represented
7999 by a union piecewise quasi-affine expression. If this expression
8000 assigns a different value to two domain elements, while all previous
8001 schedule dimensions in the same band assign them the same value,
8002 then the two domain elements are ordered according to these two
8004 Each expression is required to be total in the domain elements
8005 that reach the band node.
8007 =item C<isl_schedule_node_expansion>
8009 An expansion node maps each of the domain elements that reach the node
8010 to one or more domain elements. The image of this mapping forms
8011 the set of domain elements that reach the child of the expansion node.
8012 The function that maps each of the expanded domain elements
8013 to the original domain element from which it was expanded
8014 is called the contraction.
8016 =item C<isl_schedule_node_filter>
8018 A filter node does not impose any ordering, but rather intersects
8019 the set of domain elements that the current subtree refers to
8020 with a given union set. The subtree of the filter node only
8021 refers to domain elements in the intersection.
8022 A filter node is typically only used as a child of a sequence or
8025 =item C<isl_schedule_node_leaf>
8027 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
8029 =item C<isl_schedule_node_mark>
8031 A mark node can be used to attach any kind of information to a subtree
8032 of the schedule tree.
8034 =item C<isl_schedule_node_sequence>
8036 A sequence node has one or more children, each of which is a filter node.
8037 The filters on these filter nodes form a partition of
8038 the domain elements that the current subtree refers to.
8039 If two domain elements appear in distinct filters then the sequence
8040 node orders them according to the child positions of the corresponding
8043 =item C<isl_schedule_node_set>
8045 A set node is similar to a sequence node, except that
8046 it expresses that domain elements appearing in distinct filters
8047 may have any order. The order of the children of a set node
8048 is therefore also immaterial.
8052 The following node types are only supported by the AST generator.
8056 =item C<isl_schedule_node_context>
8058 The context describes constraints on the parameters and
8059 the schedule dimensions of outer
8060 bands that the AST generator may assume to hold. It is also the only
8061 kind of node that may introduce additional parameters.
8062 The space of the context is that of the flat product of the outer
8063 band nodes. In particular, if there are no outer band nodes, then
8064 this space is the unnamed zero-dimensional space.
8065 Since a context node references the outer band nodes, any tree
8066 containing a context node is considered to be anchored.
8068 =item C<isl_schedule_node_extension>
8070 An extension node instructs the AST generator to add additional
8071 domain elements that need to be scheduled.
8072 The additional domain elements are described by the range of
8073 the extension map in terms of the outer schedule dimensions,
8074 i.e., the flat product of the outer band nodes.
8075 Note that domain elements are added whenever the AST generator
8076 reaches the extension node, meaning that there are still some
8077 active domain elements for which an AST needs to be generated.
8078 The conditions under which some domain elements are still active
8079 may however not be completely described by the outer AST nodes
8080 generated at that point.
8081 Since an extension node references the outer band nodes, any tree
8082 containing an extension node is considered to be anchored.
8084 An extension node may also appear as the root of a schedule tree,
8085 when it is intended to be inserted into another tree
8086 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
8087 In this case, the domain of the extension node should
8088 correspond to the flat product of the outer band nodes
8089 in this other schedule tree at the point where the extension tree
8092 =item C<isl_schedule_node_guard>
8094 The guard describes constraints on the parameters and
8095 the schedule dimensions of outer
8096 bands that need to be enforced by the outer nodes
8097 in the generated AST.
8098 That is, the part of the AST that is generated from descendants
8099 of the guard node can assume that these constraints are satisfied.
8100 The space of the guard is that of the flat product of the outer
8101 band nodes. In particular, if there are no outer band nodes, then
8102 this space is the unnamed zero-dimensional space.
8103 Since a guard node references the outer band nodes, any tree
8104 containing a guard node is considered to be anchored.
8108 Except for the C<isl_schedule_node_context> nodes,
8109 none of the nodes may introduce any parameters that were not
8110 already present in the root domain node.
8112 A schedule tree is encapsulated in an C<isl_schedule> object.
8113 The simplest such objects, those with a tree consisting of single domain node,
8114 can be created using the following functions with either an empty
8115 domain or a given domain.
8117 #include <isl/schedule.h>
8118 __isl_give isl_schedule *isl_schedule_empty(
8119 __isl_take isl_space *space);
8120 __isl_give isl_schedule *isl_schedule_from_domain(
8121 __isl_take isl_union_set *domain);
8123 The function C<isl_schedule_constraints_compute_schedule> described
8124 in L</"Scheduling"> can also be used to construct schedules.
8126 C<isl_schedule> objects may be copied and freed using the following functions.
8128 #include <isl/schedule.h>
8129 __isl_give isl_schedule *isl_schedule_copy(
8130 __isl_keep isl_schedule *sched);
8131 __isl_null isl_schedule *isl_schedule_free(
8132 __isl_take isl_schedule *sched);
8134 The following functions checks whether two C<isl_schedule> objects
8135 are obviously the same.
8137 #include <isl/schedule.h>
8138 isl_bool isl_schedule_plain_is_equal(
8139 __isl_keep isl_schedule *schedule1,
8140 __isl_keep isl_schedule *schedule2);
8142 The domain of the schedule, i.e., the domain described by the root node,
8143 can be obtained using the following function.
8145 #include <isl/schedule.h>
8146 __isl_give isl_union_set *isl_schedule_get_domain(
8147 __isl_keep isl_schedule *schedule);
8149 An extra top-level band node (right underneath the domain node) can
8150 be introduced into the schedule using the following function.
8151 The schedule tree is assumed not to have any anchored nodes.
8153 #include <isl/schedule.h>
8154 __isl_give isl_schedule *
8155 isl_schedule_insert_partial_schedule(
8156 __isl_take isl_schedule *schedule,
8157 __isl_take isl_multi_union_pw_aff *partial);
8159 A top-level context node (right underneath the domain node) can
8160 be introduced into the schedule using the following function.
8162 #include <isl/schedule.h>
8163 __isl_give isl_schedule *isl_schedule_insert_context(
8164 __isl_take isl_schedule *schedule,
8165 __isl_take isl_set *context)
8167 A top-level guard node (right underneath the domain node) can
8168 be introduced into the schedule using the following function.
8170 #include <isl/schedule.h>
8171 __isl_give isl_schedule *isl_schedule_insert_guard(
8172 __isl_take isl_schedule *schedule,
8173 __isl_take isl_set *guard)
8175 A schedule that combines two schedules either in the given
8176 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
8177 or an C<isl_schedule_node_set> node,
8178 can be created using the following functions.
8180 #include <isl/schedule.h>
8181 __isl_give isl_schedule *isl_schedule_sequence(
8182 __isl_take isl_schedule *schedule1,
8183 __isl_take isl_schedule *schedule2);
8184 __isl_give isl_schedule *isl_schedule_set(
8185 __isl_take isl_schedule *schedule1,
8186 __isl_take isl_schedule *schedule2);
8188 The domains of the two input schedules need to be disjoint.
8190 The following function can be used to restrict the domain
8191 of a schedule with a domain node as root to be a subset of the given union set.
8192 This operation may remove nodes in the tree that have become
8195 #include <isl/schedule.h>
8196 __isl_give isl_schedule *isl_schedule_intersect_domain(
8197 __isl_take isl_schedule *schedule,
8198 __isl_take isl_union_set *domain);
8200 The following function can be used to simplify the domain
8201 of a schedule with a domain node as root with respect to the given
8204 #include <isl/schedule.h>
8205 __isl_give isl_schedule *isl_schedule_gist_domain_params(
8206 __isl_take isl_schedule *schedule,
8207 __isl_take isl_set *context);
8209 The following function resets the user pointers on all parameter
8210 and tuple identifiers referenced by the nodes of the given schedule.
8212 #include <isl/schedule.h>
8213 __isl_give isl_schedule *isl_schedule_reset_user(
8214 __isl_take isl_schedule *schedule);
8216 The following function aligns the parameters of all nodes
8217 in the given schedule to the given space.
8219 #include <isl/schedule.h>
8220 __isl_give isl_schedule *isl_schedule_align_params(
8221 __isl_take isl_schedule *schedule,
8222 __isl_take isl_space *space);
8224 The following function allows the user to plug in a given function
8225 in the iteration domains. The input schedule is not allowed to contain
8226 any expansion nodes.
8228 #include <isl/schedule.h>
8229 __isl_give isl_schedule *
8230 isl_schedule_pullback_union_pw_multi_aff(
8231 __isl_take isl_schedule *schedule,
8232 __isl_take isl_union_pw_multi_aff *upma);
8234 The following function can be used to plug in the schedule C<expansion>
8235 in the leaves of C<schedule>, where C<contraction> describes how
8236 the domain elements of C<expansion> map to the domain elements
8237 at the original leaves of C<schedule>.
8238 The resulting schedule will contain expansion nodes, unless
8239 C<contraction> is an identity function.
8241 #include <isl/schedule.h>
8242 __isl_give isl_schedule *isl_schedule_expand(
8243 __isl_take isl_schedule *schedule,
8244 __isl_take isl_union_pw_multi_aff *contraction,
8245 __isl_take isl_schedule *expansion);
8247 An C<isl_union_map> representation of the schedule can be obtained
8248 from an C<isl_schedule> using the following function.
8250 #include <isl/schedule.h>
8251 __isl_give isl_union_map *isl_schedule_get_map(
8252 __isl_keep isl_schedule *sched);
8254 The resulting relation encodes the same relative ordering as
8255 the schedule by mapping the domain elements to a common schedule space.
8256 If the schedule_separate_components option is set, then the order
8257 of the children of a set node is explicitly encoded in the result.
8258 If the tree contains any expansion nodes, then the relation
8259 is formulated in terms of the expanded domain elements.
8261 Schedules can be read from input using the following functions.
8263 #include <isl/schedule.h>
8264 __isl_give isl_schedule *isl_schedule_read_from_file(
8265 isl_ctx *ctx, FILE *input);
8266 __isl_give isl_schedule *isl_schedule_read_from_str(
8267 isl_ctx *ctx, const char *str);
8269 A representation of the schedule can be printed using
8271 #include <isl/schedule.h>
8272 __isl_give isl_printer *isl_printer_print_schedule(
8273 __isl_take isl_printer *p,
8274 __isl_keep isl_schedule *schedule);
8275 __isl_give char *isl_schedule_to_str(
8276 __isl_keep isl_schedule *schedule);
8278 C<isl_schedule_to_str> prints the schedule in flow format.
8280 The schedule tree can be traversed through the use of
8281 C<isl_schedule_node> objects that point to a particular
8282 position in the schedule tree. Whenever a C<isl_schedule_node>
8283 is used to modify a node in the schedule tree, the original schedule
8284 tree is left untouched and the modifications are performed to a copy
8285 of the tree. The returned C<isl_schedule_node> then points to
8286 this modified copy of the tree.
8288 The root of the schedule tree can be obtained using the following function.
8290 #include <isl/schedule.h>
8291 __isl_give isl_schedule_node *isl_schedule_get_root(
8292 __isl_keep isl_schedule *schedule);
8294 A pointer to a newly created schedule tree with a single domain
8295 node can be created using the following functions.
8297 #include <isl/schedule_node.h>
8298 __isl_give isl_schedule_node *
8299 isl_schedule_node_from_domain(
8300 __isl_take isl_union_set *domain);
8301 __isl_give isl_schedule_node *
8302 isl_schedule_node_from_extension(
8303 __isl_take isl_union_map *extension);
8305 C<isl_schedule_node_from_extension> creates a tree with an extension
8308 Schedule nodes can be copied and freed using the following functions.
8310 #include <isl/schedule_node.h>
8311 __isl_give isl_schedule_node *isl_schedule_node_copy(
8312 __isl_keep isl_schedule_node *node);
8313 __isl_null isl_schedule_node *isl_schedule_node_free(
8314 __isl_take isl_schedule_node *node);
8316 The following functions can be used to check if two schedule
8317 nodes point to the same position in the same schedule.
8319 #include <isl/schedule_node.h>
8320 isl_bool isl_schedule_node_is_equal(
8321 __isl_keep isl_schedule_node *node1,
8322 __isl_keep isl_schedule_node *node2);
8324 The following properties can be obtained from a schedule node.
8326 #include <isl/schedule_node.h>
8327 enum isl_schedule_node_type isl_schedule_node_get_type(
8328 __isl_keep isl_schedule_node *node);
8329 enum isl_schedule_node_type
8330 isl_schedule_node_get_parent_type(
8331 __isl_keep isl_schedule_node *node);
8332 __isl_give isl_schedule *isl_schedule_node_get_schedule(
8333 __isl_keep isl_schedule_node *node);
8335 The function C<isl_schedule_node_get_type> returns the type of
8336 the node, while C<isl_schedule_node_get_parent_type> returns
8337 type of the parent of the node, which is required to exist.
8338 The function C<isl_schedule_node_get_schedule> returns a copy
8339 to the schedule to which the node belongs.
8341 The following functions can be used to move the schedule node
8342 to a different position in the tree or to check if such a position
8345 #include <isl/schedule_node.h>
8346 isl_bool isl_schedule_node_has_parent(
8347 __isl_keep isl_schedule_node *node);
8348 __isl_give isl_schedule_node *isl_schedule_node_parent(
8349 __isl_take isl_schedule_node *node);
8350 __isl_give isl_schedule_node *isl_schedule_node_root(
8351 __isl_take isl_schedule_node *node);
8352 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
8353 __isl_take isl_schedule_node *node,
8355 int isl_schedule_node_n_children(
8356 __isl_keep isl_schedule_node *node);
8357 __isl_give isl_schedule_node *isl_schedule_node_child(
8358 __isl_take isl_schedule_node *node, int pos);
8359 isl_bool isl_schedule_node_has_children(
8360 __isl_keep isl_schedule_node *node);
8361 __isl_give isl_schedule_node *isl_schedule_node_first_child(
8362 __isl_take isl_schedule_node *node);
8363 isl_bool isl_schedule_node_has_previous_sibling(
8364 __isl_keep isl_schedule_node *node);
8365 __isl_give isl_schedule_node *
8366 isl_schedule_node_previous_sibling(
8367 __isl_take isl_schedule_node *node);
8368 isl_bool isl_schedule_node_has_next_sibling(
8369 __isl_keep isl_schedule_node *node);
8370 __isl_give isl_schedule_node *
8371 isl_schedule_node_next_sibling(
8372 __isl_take isl_schedule_node *node);
8374 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
8375 is the node itself, the ancestor of generation 1 is its parent and so on.
8377 It is also possible to query the number of ancestors of a node,
8378 the position of the current node
8379 within the children of its parent, the position of the subtree
8380 containing a node within the children of an ancestor
8381 or to obtain a copy of a given
8382 child without destroying the current node.
8383 Given two nodes that point to the same schedule, their closest
8384 shared ancestor can be obtained using
8385 C<isl_schedule_node_get_shared_ancestor>.
8387 #include <isl/schedule_node.h>
8388 int isl_schedule_node_get_tree_depth(
8389 __isl_keep isl_schedule_node *node);
8390 int isl_schedule_node_get_child_position(
8391 __isl_keep isl_schedule_node *node);
8392 int isl_schedule_node_get_ancestor_child_position(
8393 __isl_keep isl_schedule_node *node,
8394 __isl_keep isl_schedule_node *ancestor);
8395 __isl_give isl_schedule_node *isl_schedule_node_get_child(
8396 __isl_keep isl_schedule_node *node, int pos);
8397 __isl_give isl_schedule_node *
8398 isl_schedule_node_get_shared_ancestor(
8399 __isl_keep isl_schedule_node *node1,
8400 __isl_keep isl_schedule_node *node2);
8402 All nodes in a schedule tree or
8403 all descendants of a specific node (including the node) can be visited
8404 in depth-first pre-order using the following functions.
8406 #include <isl/schedule.h>
8407 isl_stat isl_schedule_foreach_schedule_node_top_down(
8408 __isl_keep isl_schedule *sched,
8409 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8410 void *user), void *user);
8412 #include <isl/schedule_node.h>
8413 isl_stat isl_schedule_node_foreach_descendant_top_down(
8414 __isl_keep isl_schedule_node *node,
8415 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8416 void *user), void *user);
8418 The callback function is slightly different from the usual
8419 callbacks in that it not only indicates success (non-negative result)
8420 or failure (negative result), but also indicates whether the children
8421 of the given node should be visited. In particular, if the callback
8422 returns a positive value, then the children are visited, but if
8423 the callback returns zero, then the children are not visited.
8425 The following functions checks whether
8426 all descendants of a specific node (including the node itself)
8427 satisfy a user-specified test.
8429 #include <isl/schedule_node.h>
8430 isl_bool isl_schedule_node_every_descendant(
8431 __isl_keep isl_schedule_node *node,
8432 isl_bool (*test)(__isl_keep isl_schedule_node *node,
8433 void *user), void *user)
8435 The ancestors of a node in a schedule tree can be visited from
8436 the root down to and including the parent of the node using
8437 the following function.
8439 #include <isl/schedule_node.h>
8440 isl_stat isl_schedule_node_foreach_ancestor_top_down(
8441 __isl_keep isl_schedule_node *node,
8442 isl_stat (*fn)(__isl_keep isl_schedule_node *node,
8443 void *user), void *user);
8445 The following functions allows for a depth-first post-order
8446 traversal of the nodes in a schedule tree or
8447 of the descendants of a specific node (including the node
8448 itself), where the user callback is allowed to modify the
8451 #include <isl/schedule.h>
8452 __isl_give isl_schedule *
8453 isl_schedule_map_schedule_node_bottom_up(
8454 __isl_take isl_schedule *schedule,
8455 __isl_give isl_schedule_node *(*fn)(
8456 __isl_take isl_schedule_node *node,
8457 void *user), void *user);
8459 #include <isl/schedule_node.h>
8460 __isl_give isl_schedule_node *
8461 isl_schedule_node_map_descendant_bottom_up(
8462 __isl_take isl_schedule_node *node,
8463 __isl_give isl_schedule_node *(*fn)(
8464 __isl_take isl_schedule_node *node,
8465 void *user), void *user);
8467 The traversal continues from the node returned by the callback function.
8468 It is the responsibility of the user to ensure that this does not
8469 lead to an infinite loop. It is safest to always return a pointer
8470 to the same position (same ancestors and child positions) as the input node.
8472 The following function removes a node (along with its descendants)
8473 from a schedule tree and returns a pointer to the leaf at the
8474 same position in the updated tree.
8475 It is not allowed to remove the root of a schedule tree or
8476 a child of a set or sequence node.
8478 #include <isl/schedule_node.h>
8479 __isl_give isl_schedule_node *isl_schedule_node_cut(
8480 __isl_take isl_schedule_node *node);
8482 The following function removes a single node
8483 from a schedule tree and returns a pointer to the child
8484 of the node, now located at the position of the original node
8485 or to a leaf node at that position if there was no child.
8486 It is not allowed to remove the root of a schedule tree,
8487 a set or sequence node, a child of a set or sequence node or
8488 a band node with an anchored subtree.
8490 #include <isl/schedule_node.h>
8491 __isl_give isl_schedule_node *isl_schedule_node_delete(
8492 __isl_take isl_schedule_node *node);
8494 Most nodes in a schedule tree only contain local information.
8495 In some cases, however, a node may also refer to the schedule dimensions
8496 of its outer band nodes.
8497 This means that the position of the node within the tree should
8498 not be changed, or at least that no changes are performed to the
8499 outer band nodes. The following function can be used to test
8500 whether the subtree rooted at a given node contains any such nodes.
8502 #include <isl/schedule_node.h>
8503 isl_bool isl_schedule_node_is_subtree_anchored(
8504 __isl_keep isl_schedule_node *node);
8506 The following function resets the user pointers on all parameter
8507 and tuple identifiers referenced by the given schedule node.
8509 #include <isl/schedule_node.h>
8510 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
8511 __isl_take isl_schedule_node *node);
8513 The following function aligns the parameters of the given schedule
8514 node to the given space.
8516 #include <isl/schedule_node.h>
8517 __isl_give isl_schedule_node *
8518 isl_schedule_node_align_params(
8519 __isl_take isl_schedule_node *node,
8520 __isl_take isl_space *space);
8522 Several node types have their own functions for querying
8523 (and in some cases setting) some node type specific properties.
8525 #include <isl/schedule_node.h>
8526 __isl_give isl_space *isl_schedule_node_band_get_space(
8527 __isl_keep isl_schedule_node *node);
8528 __isl_give isl_multi_union_pw_aff *
8529 isl_schedule_node_band_get_partial_schedule(
8530 __isl_keep isl_schedule_node *node);
8531 __isl_give isl_union_map *
8532 isl_schedule_node_band_get_partial_schedule_union_map(
8533 __isl_keep isl_schedule_node *node);
8534 unsigned isl_schedule_node_band_n_member(
8535 __isl_keep isl_schedule_node *node);
8536 isl_bool isl_schedule_node_band_member_get_coincident(
8537 __isl_keep isl_schedule_node *node, int pos);
8538 __isl_give isl_schedule_node *
8539 isl_schedule_node_band_member_set_coincident(
8540 __isl_take isl_schedule_node *node, int pos,
8542 isl_bool isl_schedule_node_band_get_permutable(
8543 __isl_keep isl_schedule_node *node);
8544 __isl_give isl_schedule_node *
8545 isl_schedule_node_band_set_permutable(
8546 __isl_take isl_schedule_node *node, int permutable);
8547 enum isl_ast_loop_type
8548 isl_schedule_node_band_member_get_ast_loop_type(
8549 __isl_keep isl_schedule_node *node, int pos);
8550 __isl_give isl_schedule_node *
8551 isl_schedule_node_band_member_set_ast_loop_type(
8552 __isl_take isl_schedule_node *node, int pos,
8553 enum isl_ast_loop_type type);
8554 __isl_give isl_union_set *
8555 enum isl_ast_loop_type
8556 isl_schedule_node_band_member_get_isolate_ast_loop_type(
8557 __isl_keep isl_schedule_node *node, int pos);
8558 __isl_give isl_schedule_node *
8559 isl_schedule_node_band_member_set_isolate_ast_loop_type(
8560 __isl_take isl_schedule_node *node, int pos,
8561 enum isl_ast_loop_type type);
8562 isl_schedule_node_band_get_ast_build_options(
8563 __isl_keep isl_schedule_node *node);
8564 __isl_give isl_schedule_node *
8565 isl_schedule_node_band_set_ast_build_options(
8566 __isl_take isl_schedule_node *node,
8567 __isl_take isl_union_set *options);
8568 __isl_give isl_set *
8569 isl_schedule_node_band_get_ast_isolate_option(
8570 __isl_keep isl_schedule_node *node);
8572 The function C<isl_schedule_node_band_get_space> returns the space
8573 of the partial schedule of the band.
8574 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
8575 returns a representation of the partial schedule of the band node
8576 in the form of an C<isl_union_map>.
8577 The coincident and permutable properties are set by
8578 C<isl_schedule_constraints_compute_schedule> on the schedule tree
8580 A scheduling dimension is considered to be ``coincident''
8581 if it satisfies the coincidence constraints within its band.
8582 That is, if the dependence distances of the coincidence
8583 constraints are all zero in that direction (for fixed
8584 iterations of outer bands).
8585 A band is marked permutable if it was produced using the Pluto-like scheduler.
8586 Note that the scheduler may have to resort to a Feautrier style scheduling
8587 step even if the default scheduler is used.
8588 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
8589 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
8590 For the meaning of these loop AST generation types and the difference
8591 between the regular loop AST generation type and the isolate
8592 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
8593 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
8594 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
8595 may return C<isl_ast_loop_error> if an error occurs.
8596 The AST build options govern how an AST is generated for
8597 the individual schedule dimensions during AST generation.
8598 See L</"AST Generation Options (Schedule Tree)">.
8599 The isolate option for the given node can be extracted from these
8600 AST build options using the function
8601 C<isl_schedule_node_band_get_ast_isolate_option>.
8603 #include <isl/schedule_node.h>
8604 __isl_give isl_set *
8605 isl_schedule_node_context_get_context(
8606 __isl_keep isl_schedule_node *node);
8608 #include <isl/schedule_node.h>
8609 __isl_give isl_union_set *
8610 isl_schedule_node_domain_get_domain(
8611 __isl_keep isl_schedule_node *node);
8613 #include <isl/schedule_node.h>
8614 __isl_give isl_union_map *
8615 isl_schedule_node_expansion_get_expansion(
8616 __isl_keep isl_schedule_node *node);
8617 __isl_give isl_union_pw_multi_aff *
8618 isl_schedule_node_expansion_get_contraction(
8619 __isl_keep isl_schedule_node *node);
8621 #include <isl/schedule_node.h>
8622 __isl_give isl_union_map *
8623 isl_schedule_node_extension_get_extension(
8624 __isl_keep isl_schedule_node *node);
8626 #include <isl/schedule_node.h>
8627 __isl_give isl_union_set *
8628 isl_schedule_node_filter_get_filter(
8629 __isl_keep isl_schedule_node *node);
8631 #include <isl/schedule_node.h>
8632 __isl_give isl_set *isl_schedule_node_guard_get_guard(
8633 __isl_keep isl_schedule_node *node);
8635 #include <isl/schedule_node.h>
8636 __isl_give isl_id *isl_schedule_node_mark_get_id(
8637 __isl_keep isl_schedule_node *node);
8639 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
8640 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
8641 partial schedules related to the node.
8643 #include <isl/schedule_node.h>
8644 __isl_give isl_multi_union_pw_aff *
8645 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
8646 __isl_keep isl_schedule_node *node);
8647 __isl_give isl_union_pw_multi_aff *
8648 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
8649 __isl_keep isl_schedule_node *node);
8650 __isl_give isl_union_map *
8651 isl_schedule_node_get_prefix_schedule_union_map(
8652 __isl_keep isl_schedule_node *node);
8653 __isl_give isl_union_map *
8654 isl_schedule_node_get_prefix_schedule_relation(
8655 __isl_keep isl_schedule_node *node);
8656 __isl_give isl_union_map *
8657 isl_schedule_node_get_subtree_schedule_union_map(
8658 __isl_keep isl_schedule_node *node);
8660 In particular, the functions
8661 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
8662 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
8663 and C<isl_schedule_node_get_prefix_schedule_union_map>
8664 return a relative ordering on the domain elements that reach the given
8665 node determined by its ancestors.
8666 The function C<isl_schedule_node_get_prefix_schedule_relation>
8667 additionally includes the domain constraints in the result.
8668 The function C<isl_schedule_node_get_subtree_schedule_union_map>
8669 returns a representation of the partial schedule defined by the
8670 subtree rooted at the given node.
8671 If the tree contains any expansion nodes, then the subtree schedule
8672 is formulated in terms of the expanded domain elements.
8673 The tree passed to functions returning a prefix schedule
8674 may only contain extension nodes if these would not affect
8675 the result of these functions. That is, if one of the ancestors
8676 is an extension node, then all of the domain elements that were
8677 added by the extension node need to have been filtered out
8678 by filter nodes between the extension node and the input node.
8679 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
8680 may not contain in extension nodes in the selected subtree.
8682 The expansion/contraction defined by an entire subtree, combining
8683 the expansions/contractions
8684 on the expansion nodes in the subtree, can be obtained using
8685 the following functions.
8687 #include <isl/schedule_node.h>
8688 __isl_give isl_union_map *
8689 isl_schedule_node_get_subtree_expansion(
8690 __isl_keep isl_schedule_node *node);
8691 __isl_give isl_union_pw_multi_aff *
8692 isl_schedule_node_get_subtree_contraction(
8693 __isl_keep isl_schedule_node *node);
8695 The total number of outer band members of given node, i.e.,
8696 the shared output dimension of the maps in the result
8697 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
8698 using the following function.
8700 #include <isl/schedule_node.h>
8701 int isl_schedule_node_get_schedule_depth(
8702 __isl_keep isl_schedule_node *node);
8704 The following functions return the elements that reach the given node
8705 or the union of universes in the spaces that contain these elements.
8707 #include <isl/schedule_node.h>
8708 __isl_give isl_union_set *
8709 isl_schedule_node_get_domain(
8710 __isl_keep isl_schedule_node *node);
8711 __isl_give isl_union_set *
8712 isl_schedule_node_get_universe_domain(
8713 __isl_keep isl_schedule_node *node);
8715 The input tree of C<isl_schedule_node_get_domain>
8716 may only contain extension nodes if these would not affect
8717 the result of this function. That is, if one of the ancestors
8718 is an extension node, then all of the domain elements that were
8719 added by the extension node need to have been filtered out
8720 by filter nodes between the extension node and the input node.
8722 The following functions can be used to introduce additional nodes
8723 in the schedule tree. The new node is introduced at the point
8724 in the tree where the C<isl_schedule_node> points to and
8725 the results points to the new node.
8727 #include <isl/schedule_node.h>
8728 __isl_give isl_schedule_node *
8729 isl_schedule_node_insert_partial_schedule(
8730 __isl_take isl_schedule_node *node,
8731 __isl_take isl_multi_union_pw_aff *schedule);
8733 This function inserts a new band node with (the greatest integer
8734 part of) the given partial schedule.
8735 The subtree rooted at the given node is assumed not to have
8738 #include <isl/schedule_node.h>
8739 __isl_give isl_schedule_node *
8740 isl_schedule_node_insert_context(
8741 __isl_take isl_schedule_node *node,
8742 __isl_take isl_set *context);
8744 This function inserts a new context node with the given context constraints.
8746 #include <isl/schedule_node.h>
8747 __isl_give isl_schedule_node *
8748 isl_schedule_node_insert_filter(
8749 __isl_take isl_schedule_node *node,
8750 __isl_take isl_union_set *filter);
8752 This function inserts a new filter node with the given filter.
8753 If the original node already pointed to a filter node, then the
8754 two filter nodes are merged into one.
8756 #include <isl/schedule_node.h>
8757 __isl_give isl_schedule_node *
8758 isl_schedule_node_insert_guard(
8759 __isl_take isl_schedule_node *node,
8760 __isl_take isl_set *guard);
8762 This function inserts a new guard node with the given guard constraints.
8764 #include <isl/schedule_node.h>
8765 __isl_give isl_schedule_node *
8766 isl_schedule_node_insert_mark(
8767 __isl_take isl_schedule_node *node,
8768 __isl_take isl_id *mark);
8770 This function inserts a new mark node with the give mark identifier.
8772 #include <isl/schedule_node.h>
8773 __isl_give isl_schedule_node *
8774 isl_schedule_node_insert_sequence(
8775 __isl_take isl_schedule_node *node,
8776 __isl_take isl_union_set_list *filters);
8777 __isl_give isl_schedule_node *
8778 isl_schedule_node_insert_set(
8779 __isl_take isl_schedule_node *node,
8780 __isl_take isl_union_set_list *filters);
8782 These functions insert a new sequence or set node with the given
8783 filters as children.
8785 #include <isl/schedule_node.h>
8786 __isl_give isl_schedule_node *isl_schedule_node_group(
8787 __isl_take isl_schedule_node *node,
8788 __isl_take isl_id *group_id);
8790 This function introduces an expansion node in between the current
8791 node and its parent that expands instances of a space with tuple
8792 identifier C<group_id> to the original domain elements that reach
8793 the node. The group instances are identified by the prefix schedule
8794 of those domain elements. The ancestors of the node are adjusted
8795 to refer to the group instances instead of the original domain
8796 elements. The return value points to the same node in the updated
8797 schedule tree as the input node, i.e., to the child of the newly
8798 introduced expansion node. Grouping instances of different statements
8799 ensures that they will be treated as a single statement by the
8800 AST generator up to the point of the expansion node.
8802 The following function can be used to flatten a nested
8805 #include <isl/schedule_node.h>
8806 __isl_give isl_schedule_node *
8807 isl_schedule_node_sequence_splice_child(
8808 __isl_take isl_schedule_node *node, int pos);
8810 That is, given a sequence node C<node> that has another sequence node
8811 in its child at position C<pos> (in particular, the child of that filter
8812 node is a sequence node), attach the children of that other sequence
8813 node as children of C<node>, replacing the original child at position
8816 The partial schedule of a band node can be scaled (down) or reduced using
8817 the following functions.
8819 #include <isl/schedule_node.h>
8820 __isl_give isl_schedule_node *
8821 isl_schedule_node_band_scale(
8822 __isl_take isl_schedule_node *node,
8823 __isl_take isl_multi_val *mv);
8824 __isl_give isl_schedule_node *
8825 isl_schedule_node_band_scale_down(
8826 __isl_take isl_schedule_node *node,
8827 __isl_take isl_multi_val *mv);
8828 __isl_give isl_schedule_node *
8829 isl_schedule_node_band_mod(
8830 __isl_take isl_schedule_node *node,
8831 __isl_take isl_multi_val *mv);
8833 The spaces of the two arguments need to match.
8834 After scaling, the partial schedule is replaced by its greatest
8835 integer part to ensure that the schedule remains integral.
8837 The partial schedule of a band node can be shifted by an
8838 C<isl_multi_union_pw_aff> with a domain that is a superset
8839 of the domain of the partial schedule using
8840 the following function.
8842 #include <isl/schedule_node.h>
8843 __isl_give isl_schedule_node *
8844 isl_schedule_node_band_shift(
8845 __isl_take isl_schedule_node *node,
8846 __isl_take isl_multi_union_pw_aff *shift);
8848 A band node can be tiled using the following function.
8850 #include <isl/schedule_node.h>
8851 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
8852 __isl_take isl_schedule_node *node,
8853 __isl_take isl_multi_val *sizes);
8855 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
8857 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
8858 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
8860 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
8862 The C<isl_schedule_node_band_tile> function tiles
8863 the band using the given tile sizes inside its schedule.
8864 A new child band node is created to represent the point loops and it is
8865 inserted between the modified band and its children.
8866 The subtree rooted at the given node is assumed not to have
8868 The C<tile_scale_tile_loops> option specifies whether the tile
8869 loops iterators should be scaled by the tile sizes.
8870 If the C<tile_shift_point_loops> option is set, then the point loops
8871 are shifted to start at zero.
8873 A band node can be split into two nested band nodes
8874 using the following function.
8876 #include <isl/schedule_node.h>
8877 __isl_give isl_schedule_node *isl_schedule_node_band_split(
8878 __isl_take isl_schedule_node *node, int pos);
8880 The resulting outer band node contains the first C<pos> dimensions of
8881 the schedule of C<node> while the inner band contains the remaining dimensions.
8882 The schedules of the two band nodes live in anonymous spaces.
8883 The loop AST generation type options and the isolate option
8884 are split over the two band nodes.
8886 A band node can be moved down to the leaves of the subtree rooted
8887 at the band node using the following function.
8889 #include <isl/schedule_node.h>
8890 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
8891 __isl_take isl_schedule_node *node);
8893 The subtree rooted at the given node is assumed not to have
8895 The result points to the node in the resulting tree that is in the same
8896 position as the node pointed to by C<node> in the original tree.
8898 #include <isl/schedule_node.h>
8899 __isl_give isl_schedule_node *
8900 isl_schedule_node_order_before(
8901 __isl_take isl_schedule_node *node,
8902 __isl_take isl_union_set *filter);
8903 __isl_give isl_schedule_node *
8904 isl_schedule_node_order_after(
8905 __isl_take isl_schedule_node *node,
8906 __isl_take isl_union_set *filter);
8908 These functions split the domain elements that reach C<node>
8909 into those that satisfy C<filter> and those that do not and
8910 arranges for the elements that do satisfy the filter to be
8911 executed before (in case of C<isl_schedule_node_order_before>)
8912 or after (in case of C<isl_schedule_node_order_after>)
8913 those that do not. The order is imposed by
8914 a sequence node, possibly reusing the grandparent of C<node>
8915 on two copies of the subtree attached to the original C<node>.
8916 Both copies are simplified with respect to their filter.
8918 Return a pointer to the copy of the subtree that does not
8919 satisfy C<filter>. If there is no such copy (because all
8920 reaching domain elements satisfy the filter), then return
8921 the original pointer.
8923 #include <isl/schedule_node.h>
8924 __isl_give isl_schedule_node *
8925 isl_schedule_node_graft_before(
8926 __isl_take isl_schedule_node *node,
8927 __isl_take isl_schedule_node *graft);
8928 __isl_give isl_schedule_node *
8929 isl_schedule_node_graft_after(
8930 __isl_take isl_schedule_node *node,
8931 __isl_take isl_schedule_node *graft);
8933 This function inserts the C<graft> tree into the tree containing C<node>
8934 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
8935 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
8936 The root node of C<graft>
8937 should be an extension node where the domain of the extension
8938 is the flat product of all outer band nodes of C<node>.
8939 The root node may also be a domain node.
8940 The elements of the domain or the range of the extension may not
8941 intersect with the domain elements that reach "node".
8942 The schedule tree of C<graft> may not be anchored.
8944 The schedule tree of C<node> is modified to include an extension node
8945 corresponding to the root node of C<graft> as a child of the original
8946 parent of C<node>. The original node that C<node> points to and the
8947 child of the root node of C<graft> are attached to this extension node
8948 through a sequence, with appropriate filters and with the child
8949 of C<graft> appearing before or after the original C<node>.
8951 If C<node> already appears inside a sequence that is the child of
8952 an extension node and if the spaces of the new domain elements
8953 do not overlap with those of the original domain elements,
8954 then that extension node is extended with the new extension
8955 rather than introducing a new segment of extension and sequence nodes.
8957 Return a pointer to the same node in the modified tree that
8958 C<node> pointed to in the original tree.
8960 A representation of the schedule node can be printed using
8962 #include <isl/schedule_node.h>
8963 __isl_give isl_printer *isl_printer_print_schedule_node(
8964 __isl_take isl_printer *p,
8965 __isl_keep isl_schedule_node *node);
8966 __isl_give char *isl_schedule_node_to_str(
8967 __isl_keep isl_schedule_node *node);
8969 C<isl_schedule_node_to_str> prints the schedule node in block format.
8971 =head2 Dependence Analysis
8973 C<isl> contains specialized functionality for performing
8974 array dataflow analysis. That is, given a I<sink> access relation,
8975 a collection of possible I<source> accesses and
8976 a collection of I<kill> accesses,
8977 C<isl> can compute relations that describe
8978 for each iteration of the sink access, which iterations
8979 of which of the source access relations may have
8980 accessed the same data element before the given iteration
8981 of the sink access without any intermediate kill of that data element.
8982 The resulting dependence relations map source iterations
8983 to either the corresponding sink iterations or
8984 pairs of corresponding sink iterations and accessed data elements.
8985 To compute standard flow dependences, the sink should be
8986 a read, while the sources should be writes.
8987 If no kills are specified,
8988 then memory based dependence analysis is performed.
8989 If, on the other hand, all sources are also kills,
8990 then value based dependence analysis is performed.
8991 If any of the source accesses are marked as being I<must>
8992 accesses, then they are also treated as kills.
8993 Furthermore, the specification of must-sources results
8994 in the computation of must-dependences.
8995 Only dependences originating in a must access not coscheduled
8996 with any other access to the same element and without
8997 any may accesses between the must access and the sink access
8998 are considered to be must dependences.
9000 =head3 High-level Interface
9002 A high-level interface to dependence analysis is provided
9003 by the following function.
9005 #include <isl/flow.h>
9006 __isl_give isl_union_flow *
9007 isl_union_access_info_compute_flow(
9008 __isl_take isl_union_access_info *access);
9010 The input C<isl_union_access_info> object describes the sink
9011 access relations, the source access relations and a schedule,
9012 while the output C<isl_union_flow> object describes
9013 the resulting dependence relations and the subsets of the
9014 sink relations for which no source was found.
9016 An C<isl_union_access_info> is created, modified, copied and freed using
9017 the following functions.
9019 #include <isl/flow.h>
9020 __isl_give isl_union_access_info *
9021 isl_union_access_info_from_sink(
9022 __isl_take isl_union_map *sink);
9023 __isl_give isl_union_access_info *
9024 isl_union_access_info_set_kill(
9025 __isl_take isl_union_access_info *access,
9026 __isl_take isl_union_map *kill);
9027 __isl_give isl_union_access_info *
9028 isl_union_access_info_set_may_source(
9029 __isl_take isl_union_access_info *access,
9030 __isl_take isl_union_map *may_source);
9031 __isl_give isl_union_access_info *
9032 isl_union_access_info_set_must_source(
9033 __isl_take isl_union_access_info *access,
9034 __isl_take isl_union_map *must_source);
9035 __isl_give isl_union_access_info *
9036 isl_union_access_info_set_schedule(
9037 __isl_take isl_union_access_info *access,
9038 __isl_take isl_schedule *schedule);
9039 __isl_give isl_union_access_info *
9040 isl_union_access_info_set_schedule_map(
9041 __isl_take isl_union_access_info *access,
9042 __isl_take isl_union_map *schedule_map);
9043 __isl_give isl_union_access_info *
9044 isl_union_access_info_copy(
9045 __isl_keep isl_union_access_info *access);
9046 __isl_null isl_union_access_info *
9047 isl_union_access_info_free(
9048 __isl_take isl_union_access_info *access);
9050 The may sources set by C<isl_union_access_info_set_may_source>
9051 do not need to include the must sources set by
9052 C<isl_union_access_info_set_must_source> as a subset.
9053 The kills set by C<isl_union_access_info_set_kill> may overlap
9054 with the may-sources and/or must-sources.
9055 The user is free not to call one (or more) of these functions,
9056 in which case the corresponding set is kept to its empty default.
9057 Similarly, the default schedule initialized by
9058 C<isl_union_access_info_from_sink> is empty.
9059 The current schedule is determined by the last call to either
9060 C<isl_union_access_info_set_schedule> or
9061 C<isl_union_access_info_set_schedule_map>.
9062 The domain of the schedule corresponds to the domains of
9063 the access relations. In particular, the domains of the access
9064 relations are effectively intersected with the domain of the schedule
9065 and only the resulting accesses are considered by the dependence analysis.
9067 An C<isl_union_access_info> object can be read from input
9068 using the following function.
9070 #include <isl/flow.h>
9071 __isl_give isl_union_access_info *
9072 isl_union_access_info_read_from_file(isl_ctx *ctx,
9075 A representation of the information contained in an object
9076 of type C<isl_union_access_info> can be obtained using
9078 #include <isl/flow.h>
9079 __isl_give isl_printer *
9080 isl_printer_print_union_access_info(
9081 __isl_take isl_printer *p,
9082 __isl_keep isl_union_access_info *access);
9083 __isl_give char *isl_union_access_info_to_str(
9084 __isl_keep isl_union_access_info *access);
9086 C<isl_union_access_info_to_str> prints the information in flow format.
9088 The output of C<isl_union_access_info_compute_flow> can be examined,
9089 copied, and freed using the following functions.
9091 #include <isl/flow.h>
9092 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
9093 __isl_keep isl_union_flow *flow);
9094 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
9095 __isl_keep isl_union_flow *flow);
9096 __isl_give isl_union_map *
9097 isl_union_flow_get_full_must_dependence(
9098 __isl_keep isl_union_flow *flow);
9099 __isl_give isl_union_map *
9100 isl_union_flow_get_full_may_dependence(
9101 __isl_keep isl_union_flow *flow);
9102 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
9103 __isl_keep isl_union_flow *flow);
9104 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
9105 __isl_keep isl_union_flow *flow);
9106 __isl_give isl_union_flow *isl_union_flow_copy(
9107 __isl_keep isl_union_flow *flow);
9108 __isl_null isl_union_flow *isl_union_flow_free(
9109 __isl_take isl_union_flow *flow);
9111 The relation returned by C<isl_union_flow_get_must_dependence>
9112 relates domain elements of must sources to domain elements of the sink.
9113 The relation returned by C<isl_union_flow_get_may_dependence>
9114 relates domain elements of must or may sources to domain elements of the sink
9115 and includes the previous relation as a subset.
9116 The relation returned by C<isl_union_flow_get_full_must_dependence>
9117 relates domain elements of must sources to pairs of domain elements of the sink
9118 and accessed data elements.
9119 The relation returned by C<isl_union_flow_get_full_may_dependence>
9120 relates domain elements of must or may sources to pairs of
9121 domain elements of the sink and accessed data elements.
9122 This relation includes the previous relation as a subset.
9123 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
9124 of the sink relation for which no dependences have been found.
9125 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
9126 of the sink relation for which no definite dependences have been found.
9127 That is, it contains those sink access that do not contribute to any
9128 of the elements in the relation returned
9129 by C<isl_union_flow_get_must_dependence>.
9131 A representation of the information contained in an object
9132 of type C<isl_union_flow> can be obtained using
9134 #include <isl/flow.h>
9135 __isl_give isl_printer *isl_printer_print_union_flow(
9136 __isl_take isl_printer *p,
9137 __isl_keep isl_union_flow *flow);
9138 __isl_give char *isl_union_flow_to_str(
9139 __isl_keep isl_union_flow *flow);
9141 C<isl_union_flow_to_str> prints the information in flow format.
9143 =head3 Low-level Interface
9145 A lower-level interface is provided by the following functions.
9147 #include <isl/flow.h>
9149 typedef int (*isl_access_level_before)(void *first, void *second);
9151 __isl_give isl_access_info *isl_access_info_alloc(
9152 __isl_take isl_map *sink,
9153 void *sink_user, isl_access_level_before fn,
9155 __isl_give isl_access_info *isl_access_info_add_source(
9156 __isl_take isl_access_info *acc,
9157 __isl_take isl_map *source, int must,
9159 __isl_null isl_access_info *isl_access_info_free(
9160 __isl_take isl_access_info *acc);
9162 __isl_give isl_flow *isl_access_info_compute_flow(
9163 __isl_take isl_access_info *acc);
9165 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,
9166 isl_stat (*fn)(__isl_take isl_map *dep, int must,
9167 void *dep_user, void *user),
9169 __isl_give isl_map *isl_flow_get_no_source(
9170 __isl_keep isl_flow *deps, int must);
9171 void isl_flow_free(__isl_take isl_flow *deps);
9173 The function C<isl_access_info_compute_flow> performs the actual
9174 dependence analysis. The other functions are used to construct
9175 the input for this function or to read off the output.
9177 The input is collected in an C<isl_access_info>, which can
9178 be created through a call to C<isl_access_info_alloc>.
9179 The arguments to this functions are the sink access relation
9180 C<sink>, a token C<sink_user> used to identify the sink
9181 access to the user, a callback function for specifying the
9182 relative order of source and sink accesses, and the number
9183 of source access relations that will be added.
9185 The callback function has type C<int (*)(void *first, void *second)>.
9186 The function is called with two user supplied tokens identifying
9187 either a source or the sink and it should return the shared nesting
9188 level and the relative order of the two accesses.
9189 In particular, let I<n> be the number of loops shared by
9190 the two accesses. If C<first> precedes C<second> textually,
9191 then the function should return I<2 * n + 1>; otherwise,
9192 it should return I<2 * n>.
9193 The low-level interface assumes that no sources are coscheduled.
9194 If the information returned by the callback does not allow
9195 the relative order to be determined, then one of the sources
9196 is arbitrarily taken to be executed after the other(s).
9198 The sources can be added to the C<isl_access_info> object by performing
9199 (at most) C<max_source> calls to C<isl_access_info_add_source>.
9200 C<must> indicates whether the source is a I<must> access
9201 or a I<may> access. Note that a multi-valued access relation
9202 should only be marked I<must> if every iteration in the domain
9203 of the relation accesses I<all> elements in its image.
9204 The C<source_user> token is again used to identify
9205 the source access. The range of the source access relation
9206 C<source> should have the same dimension as the range
9207 of the sink access relation.
9208 The C<isl_access_info_free> function should usually not be
9209 called explicitly, because it is already called implicitly by
9210 C<isl_access_info_compute_flow>.
9212 The result of the dependence analysis is collected in an
9213 C<isl_flow>. There may be elements of
9214 the sink access for which no preceding source access could be
9215 found or for which all preceding sources are I<may> accesses.
9216 The relations containing these elements can be obtained through
9217 calls to C<isl_flow_get_no_source>, the first with C<must> set
9218 and the second with C<must> unset.
9219 In the case of standard flow dependence analysis,
9220 with the sink a read and the sources I<must> writes,
9221 the first relation corresponds to the reads from uninitialized
9222 array elements and the second relation is empty.
9223 The actual flow dependences can be extracted using
9224 C<isl_flow_foreach>. This function will call the user-specified
9225 callback function C<fn> for each B<non-empty> dependence between
9226 a source and the sink. The callback function is called
9227 with four arguments, the actual flow dependence relation
9228 mapping source iterations to sink iterations, a boolean that
9229 indicates whether it is a I<must> or I<may> dependence, a token
9230 identifying the source and an additional C<void *> with value
9231 equal to the third argument of the C<isl_flow_foreach> call.
9232 A dependence is marked I<must> if it originates from a I<must>
9233 source and if it is not followed by any I<may> sources.
9235 After finishing with an C<isl_flow>, the user should call
9236 C<isl_flow_free> to free all associated memory.
9238 =head3 Interaction with the Low-level Interface
9240 During the dependence analysis, we frequently need to perform
9241 the following operation. Given a relation between sink iterations
9242 and potential source iterations from a particular source domain,
9243 what is the last potential source iteration corresponding to each
9244 sink iteration. It can sometimes be convenient to adjust
9245 the set of potential source iterations before or after each such operation.
9246 The prototypical example is fuzzy array dataflow analysis,
9247 where we need to analyze if, based on data-dependent constraints,
9248 the sink iteration can ever be executed without one or more of
9249 the corresponding potential source iterations being executed.
9250 If so, we can introduce extra parameters and select an unknown
9251 but fixed source iteration from the potential source iterations.
9252 To be able to perform such manipulations, C<isl> provides the following
9255 #include <isl/flow.h>
9257 typedef __isl_give isl_restriction *(*isl_access_restrict)(
9258 __isl_keep isl_map *source_map,
9259 __isl_keep isl_set *sink, void *source_user,
9261 __isl_give isl_access_info *isl_access_info_set_restrict(
9262 __isl_take isl_access_info *acc,
9263 isl_access_restrict fn, void *user);
9265 The function C<isl_access_info_set_restrict> should be called
9266 before calling C<isl_access_info_compute_flow> and registers a callback function
9267 that will be called any time C<isl> is about to compute the last
9268 potential source. The first argument is the (reverse) proto-dependence,
9269 mapping sink iterations to potential source iterations.
9270 The second argument represents the sink iterations for which
9271 we want to compute the last source iteration.
9272 The third argument is the token corresponding to the source
9273 and the final argument is the token passed to C<isl_access_info_set_restrict>.
9274 The callback is expected to return a restriction on either the input or
9275 the output of the operation computing the last potential source.
9276 If the input needs to be restricted then restrictions are needed
9277 for both the source and the sink iterations. The sink iterations
9278 and the potential source iterations will be intersected with these sets.
9279 If the output needs to be restricted then only a restriction on the source
9280 iterations is required.
9281 If any error occurs, the callback should return C<NULL>.
9282 An C<isl_restriction> object can be created, freed and inspected
9283 using the following functions.
9285 #include <isl/flow.h>
9287 __isl_give isl_restriction *isl_restriction_input(
9288 __isl_take isl_set *source_restr,
9289 __isl_take isl_set *sink_restr);
9290 __isl_give isl_restriction *isl_restriction_output(
9291 __isl_take isl_set *source_restr);
9292 __isl_give isl_restriction *isl_restriction_none(
9293 __isl_take isl_map *source_map);
9294 __isl_give isl_restriction *isl_restriction_empty(
9295 __isl_take isl_map *source_map);
9296 __isl_null isl_restriction *isl_restriction_free(
9297 __isl_take isl_restriction *restr);
9299 C<isl_restriction_none> and C<isl_restriction_empty> are special
9300 cases of C<isl_restriction_input>. C<isl_restriction_none>
9301 is essentially equivalent to
9303 isl_restriction_input(isl_set_universe(
9304 isl_space_range(isl_map_get_space(source_map))),
9306 isl_space_domain(isl_map_get_space(source_map))));
9308 whereas C<isl_restriction_empty> is essentially equivalent to
9310 isl_restriction_input(isl_set_empty(
9311 isl_space_range(isl_map_get_space(source_map))),
9313 isl_space_domain(isl_map_get_space(source_map))));
9317 #include <isl/schedule.h>
9318 __isl_give isl_schedule *
9319 isl_schedule_constraints_compute_schedule(
9320 __isl_take isl_schedule_constraints *sc);
9322 The function C<isl_schedule_constraints_compute_schedule> can be
9323 used to compute a schedule that satisfies the given schedule constraints.
9324 These schedule constraints include the iteration domain for which
9325 a schedule should be computed and dependences between pairs of
9326 iterations. In particular, these dependences include
9327 I<validity> dependences and I<proximity> dependences.
9328 By default, the algorithm used to construct the schedule is similar
9329 to that of C<Pluto>.
9330 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
9332 The generated schedule respects all validity dependences.
9333 That is, all dependence distances over these dependences in the
9334 scheduled space are lexicographically positive.
9336 The default algorithm tries to ensure that the dependence distances
9337 over coincidence constraints are zero and to minimize the
9338 dependence distances over proximity dependences.
9339 Moreover, it tries to obtain sequences (bands) of schedule dimensions
9340 for groups of domains where the dependence distances over validity
9341 dependences have only non-negative values.
9342 Note that when minimizing the maximal dependence distance
9343 over proximity dependences, a single affine expression in the parameters
9344 is constructed that bounds all dependence distances. If no such expression
9345 exists, then the algorithm will fail and resort to an alternative
9346 scheduling algorithm. In particular, this means that adding proximity
9347 dependences may eliminate valid solutions. A typical example where this
9348 phenomenon may occur is when some subset of the proximity dependences
9349 has no restriction on some parameter, forcing the coefficient of that
9350 parameter to be zero, while some other subset forces the dependence
9351 distance to depend on that parameter, requiring the same coefficient
9353 When using Feautrier's algorithm, the coincidence and proximity constraints
9354 are only taken into account during the extension to a
9355 full-dimensional schedule.
9357 An C<isl_schedule_constraints> object can be constructed
9358 and manipulated using the following functions.
9360 #include <isl/schedule.h>
9361 __isl_give isl_schedule_constraints *
9362 isl_schedule_constraints_copy(
9363 __isl_keep isl_schedule_constraints *sc);
9364 __isl_give isl_schedule_constraints *
9365 isl_schedule_constraints_on_domain(
9366 __isl_take isl_union_set *domain);
9367 __isl_give isl_schedule_constraints *
9368 isl_schedule_constraints_set_context(
9369 __isl_take isl_schedule_constraints *sc,
9370 __isl_take isl_set *context);
9371 __isl_give isl_schedule_constraints *
9372 isl_schedule_constraints_set_validity(
9373 __isl_take isl_schedule_constraints *sc,
9374 __isl_take isl_union_map *validity);
9375 __isl_give isl_schedule_constraints *
9376 isl_schedule_constraints_set_coincidence(
9377 __isl_take isl_schedule_constraints *sc,
9378 __isl_take isl_union_map *coincidence);
9379 __isl_give isl_schedule_constraints *
9380 isl_schedule_constraints_set_proximity(
9381 __isl_take isl_schedule_constraints *sc,
9382 __isl_take isl_union_map *proximity);
9383 __isl_give isl_schedule_constraints *
9384 isl_schedule_constraints_set_conditional_validity(
9385 __isl_take isl_schedule_constraints *sc,
9386 __isl_take isl_union_map *condition,
9387 __isl_take isl_union_map *validity);
9388 __isl_give isl_schedule_constraints *
9389 isl_schedule_constraints_apply(
9390 __isl_take isl_schedule_constraints *sc,
9391 __isl_take isl_union_map *umap);
9392 __isl_null isl_schedule_constraints *
9393 isl_schedule_constraints_free(
9394 __isl_take isl_schedule_constraints *sc);
9396 The initial C<isl_schedule_constraints> object created by
9397 C<isl_schedule_constraints_on_domain> does not impose any constraints.
9398 That is, it has an empty set of dependences.
9399 The function C<isl_schedule_constraints_set_context> allows the user
9400 to specify additional constraints on the parameters that may
9401 be assumed to hold during the construction of the schedule.
9402 The function C<isl_schedule_constraints_set_validity> replaces the
9403 validity dependences, mapping domain elements I<i> to domain
9404 elements that should be scheduled after I<i>.
9405 The function C<isl_schedule_constraints_set_coincidence> replaces the
9406 coincidence dependences, mapping domain elements I<i> to domain
9407 elements that should be scheduled together with I<I>, if possible.
9408 The function C<isl_schedule_constraints_set_proximity> replaces the
9409 proximity dependences, mapping domain elements I<i> to domain
9410 elements that should be scheduled either before I<I>
9411 or as early as possible after I<i>.
9413 The function C<isl_schedule_constraints_set_conditional_validity>
9414 replaces the conditional validity constraints.
9415 A conditional validity constraint is only imposed when any of the corresponding
9416 conditions is satisfied, i.e., when any of them is non-zero.
9417 That is, the scheduler ensures that within each band if the dependence
9418 distances over the condition constraints are not all zero
9419 then all corresponding conditional validity constraints are respected.
9420 A conditional validity constraint corresponds to a condition
9421 if the two are adjacent, i.e., if the domain of one relation intersect
9422 the range of the other relation.
9423 The typical use case of conditional validity constraints is
9424 to allow order constraints between live ranges to be violated
9425 as long as the live ranges themselves are local to the band.
9426 To allow more fine-grained control over which conditions correspond
9427 to which conditional validity constraints, the domains and ranges
9428 of these relations may include I<tags>. That is, the domains and
9429 ranges of those relation may themselves be wrapped relations
9430 where the iteration domain appears in the domain of those wrapped relations
9431 and the range of the wrapped relations can be arbitrarily chosen
9432 by the user. Conditions and conditional validity constraints are only
9433 considered adjacent to each other if the entire wrapped relation matches.
9434 In particular, a relation with a tag will never be considered adjacent
9435 to a relation without a tag.
9437 The function C<isl_schedule_constraints_apply> takes
9438 schedule constraints that are defined on some set of domain elements
9439 and transforms them to schedule constraints on the elements
9440 to which these domain elements are mapped by the given transformation.
9442 An C<isl_schedule_constraints> object can be inspected
9443 using the following functions.
9445 #include <isl/schedule.h>
9446 __isl_give isl_union_set *
9447 isl_schedule_constraints_get_domain(
9448 __isl_keep isl_schedule_constraints *sc);
9449 __isl_give isl_set *isl_schedule_constraints_get_context(
9450 __isl_keep isl_schedule_constraints *sc);
9451 __isl_give isl_union_map *
9452 isl_schedule_constraints_get_validity(
9453 __isl_keep isl_schedule_constraints *sc);
9454 __isl_give isl_union_map *
9455 isl_schedule_constraints_get_coincidence(
9456 __isl_keep isl_schedule_constraints *sc);
9457 __isl_give isl_union_map *
9458 isl_schedule_constraints_get_proximity(
9459 __isl_keep isl_schedule_constraints *sc);
9460 __isl_give isl_union_map *
9461 isl_schedule_constraints_get_conditional_validity(
9462 __isl_keep isl_schedule_constraints *sc);
9463 __isl_give isl_union_map *
9464 isl_schedule_constraints_get_conditional_validity_condition(
9465 __isl_keep isl_schedule_constraints *sc);
9467 An C<isl_schedule_constraints> object can be read from input
9468 using the following functions.
9470 #include <isl/schedule.h>
9471 __isl_give isl_schedule_constraints *
9472 isl_schedule_constraints_read_from_str(isl_ctx *ctx,
9474 __isl_give isl_schedule_constraints *
9475 isl_schedule_constraints_read_from_file(isl_ctx *ctx,
9478 The contents of an C<isl_schedule_constraints> object can be printed
9479 using the following functions.
9481 #include <isl/schedule.h>
9482 __isl_give isl_printer *
9483 isl_printer_print_schedule_constraints(
9484 __isl_take isl_printer *p,
9485 __isl_keep isl_schedule_constraints *sc);
9486 __isl_give char *isl_schedule_constraints_to_str(
9487 __isl_keep isl_schedule_constraints *sc);
9489 The following function computes a schedule directly from
9490 an iteration domain and validity and proximity dependences
9491 and is implemented in terms of the functions described above.
9492 The use of C<isl_union_set_compute_schedule> is discouraged.
9494 #include <isl/schedule.h>
9495 __isl_give isl_schedule *isl_union_set_compute_schedule(
9496 __isl_take isl_union_set *domain,
9497 __isl_take isl_union_map *validity,
9498 __isl_take isl_union_map *proximity);
9500 The generated schedule represents a schedule tree.
9501 For more information on schedule trees, see
9502 L</"Schedule Trees">.
9506 #include <isl/schedule.h>
9507 isl_stat isl_options_set_schedule_max_coefficient(
9508 isl_ctx *ctx, int val);
9509 int isl_options_get_schedule_max_coefficient(
9511 isl_stat isl_options_set_schedule_max_constant_term(
9512 isl_ctx *ctx, int val);
9513 int isl_options_get_schedule_max_constant_term(
9515 isl_stat isl_options_set_schedule_serialize_sccs(
9516 isl_ctx *ctx, int val);
9517 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx);
9518 isl_stat isl_options_set_schedule_whole_component(
9519 isl_ctx *ctx, int val);
9520 int isl_options_get_schedule_whole_component(
9522 isl_stat isl_options_set_schedule_maximize_band_depth(
9523 isl_ctx *ctx, int val);
9524 int isl_options_get_schedule_maximize_band_depth(
9526 isl_stat isl_options_set_schedule_maximize_coincidence(
9527 isl_ctx *ctx, int val);
9528 int isl_options_get_schedule_maximize_coincidence(
9530 isl_stat isl_options_set_schedule_outer_coincidence(
9531 isl_ctx *ctx, int val);
9532 int isl_options_get_schedule_outer_coincidence(
9534 isl_stat isl_options_set_schedule_split_scaled(
9535 isl_ctx *ctx, int val);
9536 int isl_options_get_schedule_split_scaled(
9538 isl_stat isl_options_set_schedule_treat_coalescing(
9539 isl_ctx *ctx, int val);
9540 int isl_options_get_schedule_treat_coalescing(
9542 isl_stat isl_options_set_schedule_algorithm(
9543 isl_ctx *ctx, int val);
9544 int isl_options_get_schedule_algorithm(
9546 isl_stat isl_options_set_schedule_carry_self_first(
9547 isl_ctx *ctx, int val);
9548 int isl_options_get_schedule_carry_self_first(
9550 isl_stat isl_options_set_schedule_separate_components(
9551 isl_ctx *ctx, int val);
9552 int isl_options_get_schedule_separate_components(
9557 =item * schedule_max_coefficient
9559 This option enforces that the coefficients for variable and parameter
9560 dimensions in the calculated schedule are not larger than the specified value.
9561 This option can significantly increase the speed of the scheduling calculation
9562 and may also prevent fusing of unrelated dimensions. A value of -1 means that
9563 this option does not introduce bounds on the variable or parameter
9566 =item * schedule_max_constant_term
9568 This option enforces that the constant coefficients in the calculated schedule
9569 are not larger than the maximal constant term. This option can significantly
9570 increase the speed of the scheduling calculation and may also prevent fusing of
9571 unrelated dimensions. A value of -1 means that this option does not introduce
9572 bounds on the constant coefficients.
9574 =item * schedule_serialize_sccs
9576 If this option is set, then all strongly connected components
9577 in the dependence graph are serialized as soon as they are detected.
9578 This means in particular that instances of statements will only
9579 appear in the same band node if these statements belong
9580 to the same strongly connected component at the point where
9581 the band node is constructed.
9583 =item * schedule_whole_component
9585 If this option is set, then entire (weakly) connected
9586 components in the dependence graph are scheduled together
9588 Otherwise, each strongly connected component within
9589 such a weakly connected component is first scheduled separately
9590 and then combined with other strongly connected components.
9591 This option has no effect if C<schedule_serialize_sccs> is set.
9593 =item * schedule_maximize_band_depth
9595 If this option is set, then the scheduler tries to maximize
9596 the width of the bands. Wider bands give more possibilities for tiling.
9597 In particular, if the C<schedule_whole_component> option is set,
9598 then bands are split if this might result in wider bands.
9599 Otherwise, the effect of this option is to only allow
9600 strongly connected components to be combined if this does
9601 not reduce the width of the bands.
9602 Note that if the C<schedule_serialize_sccs> options is set, then
9603 the C<schedule_maximize_band_depth> option therefore has no effect.
9605 =item * schedule_maximize_coincidence
9607 This option is only effective if the C<schedule_whole_component>
9608 option is turned off.
9609 If the C<schedule_maximize_coincidence> option is set, then (clusters of)
9610 strongly connected components are only combined with each other
9611 if this does not reduce the number of coincident band members.
9613 =item * schedule_outer_coincidence
9615 If this option is set, then we try to construct schedules
9616 where the outermost scheduling dimension in each band
9617 satisfies the coincidence constraints.
9619 =item * schedule_algorithm
9621 Selects the scheduling algorithm to be used.
9622 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
9623 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
9625 =item * schedule_split_scaled
9627 If this option is set, then we try to construct schedules in which the
9628 constant term is split off from the linear part if the linear parts of
9629 the scheduling rows for all nodes in the graph have a common non-trivial
9631 The constant term is then dropped and the linear
9633 This option is only effective when the Feautrier style scheduler is
9634 being used, either as the main scheduler or as a fallback for the
9635 Pluto-like scheduler.
9637 =item * schedule_treat_coalescing
9639 If this option is set, then the scheduler will try and avoid
9640 producing schedules that perform loop coalescing.
9641 In particular, for the Pluto-like scheduler, this option places
9642 bounds on the schedule coefficients based on the sizes of the instance sets.
9643 For the Feautrier style scheduler, this option detects potentially
9644 coalescing schedules and then tries to adjust the schedule to avoid
9647 =item * schedule_carry_self_first
9649 If this option is set, then the Feautrier style scheduler
9650 (when used as a fallback for the Pluto-like scheduler) will
9651 first try to only carry self-dependences.
9653 =item * schedule_separate_components
9655 If this option is set then the function C<isl_schedule_get_map>
9656 will treat set nodes in the same way as sequence nodes.
9660 =head2 AST Generation
9662 This section describes the C<isl> functionality for generating
9663 ASTs that visit all the elements
9664 in a domain in an order specified by a schedule tree or
9666 In case the schedule given as a C<isl_union_map>, an AST is generated
9667 that visits all the elements in the domain of the C<isl_union_map>
9668 according to the lexicographic order of the corresponding image
9669 element(s). If the range of the C<isl_union_map> consists of
9670 elements in more than one space, then each of these spaces is handled
9671 separately in an arbitrary order.
9672 It should be noted that the schedule tree or the image elements
9673 in a schedule map only specify the I<order>
9674 in which the corresponding domain elements should be visited.
9675 No direct relation between the partial schedule values
9676 or the image elements on the one hand and the loop iterators
9677 in the generated AST on the other hand should be assumed.
9679 Each AST is generated within a build. The initial build
9680 simply specifies the constraints on the parameters (if any)
9681 and can be created, inspected, copied and freed using the following functions.
9683 #include <isl/ast_build.h>
9684 __isl_give isl_ast_build *isl_ast_build_alloc(
9686 __isl_give isl_ast_build *isl_ast_build_from_context(
9687 __isl_take isl_set *set);
9688 __isl_give isl_ast_build *isl_ast_build_copy(
9689 __isl_keep isl_ast_build *build);
9690 __isl_null isl_ast_build *isl_ast_build_free(
9691 __isl_take isl_ast_build *build);
9693 The C<set> argument is usually a parameter set with zero or more parameters.
9694 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
9695 this set is required to be a parameter set.
9696 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
9697 specify any parameter constraints.
9698 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
9699 and L</"Fine-grained Control over AST Generation">.
9700 Finally, the AST itself can be constructed using one of the following
9703 #include <isl/ast_build.h>
9704 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
9705 __isl_keep isl_ast_build *build,
9706 __isl_take isl_schedule *schedule);
9707 __isl_give isl_ast_node *
9708 isl_ast_build_node_from_schedule_map(
9709 __isl_keep isl_ast_build *build,
9710 __isl_take isl_union_map *schedule);
9712 =head3 Inspecting the AST
9714 The basic properties of an AST node can be obtained as follows.
9716 #include <isl/ast.h>
9717 enum isl_ast_node_type isl_ast_node_get_type(
9718 __isl_keep isl_ast_node *node);
9720 The type of an AST node is one of
9721 C<isl_ast_node_for>,
9723 C<isl_ast_node_block>,
9724 C<isl_ast_node_mark> or
9725 C<isl_ast_node_user>.
9726 An C<isl_ast_node_for> represents a for node.
9727 An C<isl_ast_node_if> represents an if node.
9728 An C<isl_ast_node_block> represents a compound node.
9729 An C<isl_ast_node_mark> introduces a mark in the AST.
9730 An C<isl_ast_node_user> represents an expression statement.
9731 An expression statement typically corresponds to a domain element, i.e.,
9732 one of the elements that is visited by the AST.
9734 Each type of node has its own additional properties.
9736 #include <isl/ast.h>
9737 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
9738 __isl_keep isl_ast_node *node);
9739 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
9740 __isl_keep isl_ast_node *node);
9741 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
9742 __isl_keep isl_ast_node *node);
9743 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
9744 __isl_keep isl_ast_node *node);
9745 __isl_give isl_ast_node *isl_ast_node_for_get_body(
9746 __isl_keep isl_ast_node *node);
9747 isl_bool isl_ast_node_for_is_degenerate(
9748 __isl_keep isl_ast_node *node);
9750 An C<isl_ast_for> is considered degenerate if it is known to execute
9753 #include <isl/ast.h>
9754 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
9755 __isl_keep isl_ast_node *node);
9756 __isl_give isl_ast_node *isl_ast_node_if_get_then(
9757 __isl_keep isl_ast_node *node);
9758 isl_bool isl_ast_node_if_has_else(
9759 __isl_keep isl_ast_node *node);
9760 __isl_give isl_ast_node *isl_ast_node_if_get_else(
9761 __isl_keep isl_ast_node *node);
9763 __isl_give isl_ast_node_list *
9764 isl_ast_node_block_get_children(
9765 __isl_keep isl_ast_node *node);
9767 __isl_give isl_id *isl_ast_node_mark_get_id(
9768 __isl_keep isl_ast_node *node);
9769 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
9770 __isl_keep isl_ast_node *node);
9772 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
9773 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
9775 #include <isl/ast.h>
9776 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
9777 __isl_keep isl_ast_node *node);
9779 All descendants of a specific node in the AST (including the node itself)
9781 in depth-first pre-order using the following function.
9783 #include <isl/ast.h>
9784 isl_stat isl_ast_node_foreach_descendant_top_down(
9785 __isl_keep isl_ast_node *node,
9786 isl_bool (*fn)(__isl_keep isl_ast_node *node,
9787 void *user), void *user);
9789 The callback function should return C<isl_bool_true> if the children
9790 of the given node should be visited and C<isl_bool_false> if they should not.
9791 It should return C<isl_bool_error> in case of failure, in which case
9792 the entire traversal is aborted.
9794 Each of the returned C<isl_ast_expr>s can in turn be inspected using
9795 the following functions.
9797 #include <isl/ast.h>
9798 enum isl_ast_expr_type isl_ast_expr_get_type(
9799 __isl_keep isl_ast_expr *expr);
9801 The type of an AST expression is one of
9803 C<isl_ast_expr_id> or
9804 C<isl_ast_expr_int>.
9805 An C<isl_ast_expr_op> represents the result of an operation.
9806 An C<isl_ast_expr_id> represents an identifier.
9807 An C<isl_ast_expr_int> represents an integer value.
9809 Each type of expression has its own additional properties.
9811 #include <isl/ast.h>
9812 enum isl_ast_op_type isl_ast_expr_get_op_type(
9813 __isl_keep isl_ast_expr *expr);
9814 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
9815 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
9816 __isl_keep isl_ast_expr *expr, int pos);
9817 isl_stat isl_ast_expr_foreach_ast_op_type(
9818 __isl_keep isl_ast_expr *expr,
9819 isl_stat (*fn)(enum isl_ast_op_type type,
9820 void *user), void *user);
9821 isl_stat isl_ast_node_foreach_ast_op_type(
9822 __isl_keep isl_ast_node *node,
9823 isl_stat (*fn)(enum isl_ast_op_type type,
9824 void *user), void *user);
9826 C<isl_ast_expr_get_op_type> returns the type of the operation
9827 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
9828 arguments. C<isl_ast_expr_get_op_arg> returns the specified
9830 C<isl_ast_expr_foreach_ast_op_type> calls C<fn> for each distinct
9831 C<isl_ast_op_type> that appears in C<expr>.
9832 C<isl_ast_node_foreach_ast_op_type> does the same for each distinct
9833 C<isl_ast_op_type> that appears in C<node>.
9834 The operation type is one of the following.
9838 =item C<isl_ast_op_and>
9840 Logical I<and> of two arguments.
9841 Both arguments can be evaluated.
9843 =item C<isl_ast_op_and_then>
9845 Logical I<and> of two arguments.
9846 The second argument can only be evaluated if the first evaluates to true.
9848 =item C<isl_ast_op_or>
9850 Logical I<or> of two arguments.
9851 Both arguments can be evaluated.
9853 =item C<isl_ast_op_or_else>
9855 Logical I<or> of two arguments.
9856 The second argument can only be evaluated if the first evaluates to false.
9858 =item C<isl_ast_op_max>
9860 Maximum of two or more arguments.
9862 =item C<isl_ast_op_min>
9864 Minimum of two or more arguments.
9866 =item C<isl_ast_op_minus>
9870 =item C<isl_ast_op_add>
9872 Sum of two arguments.
9874 =item C<isl_ast_op_sub>
9876 Difference of two arguments.
9878 =item C<isl_ast_op_mul>
9880 Product of two arguments.
9882 =item C<isl_ast_op_div>
9884 Exact division. That is, the result is known to be an integer.
9886 =item C<isl_ast_op_fdiv_q>
9888 Result of integer division, rounded towards negative
9891 =item C<isl_ast_op_pdiv_q>
9893 Result of integer division, where dividend is known to be non-negative.
9895 =item C<isl_ast_op_pdiv_r>
9897 Remainder of integer division, where dividend is known to be non-negative.
9899 =item C<isl_ast_op_zdiv_r>
9901 Equal to zero iff the remainder on integer division is zero.
9903 =item C<isl_ast_op_cond>
9905 Conditional operator defined on three arguments.
9906 If the first argument evaluates to true, then the result
9907 is equal to the second argument. Otherwise, the result
9908 is equal to the third argument.
9909 The second and third argument may only be evaluated if
9910 the first argument evaluates to true and false, respectively.
9911 Corresponds to C<a ? b : c> in C.
9913 =item C<isl_ast_op_select>
9915 Conditional operator defined on three arguments.
9916 If the first argument evaluates to true, then the result
9917 is equal to the second argument. Otherwise, the result
9918 is equal to the third argument.
9919 The second and third argument may be evaluated independently
9920 of the value of the first argument.
9921 Corresponds to C<a * b + (1 - a) * c> in C.
9923 =item C<isl_ast_op_eq>
9927 =item C<isl_ast_op_le>
9929 Less than or equal relation.
9931 =item C<isl_ast_op_lt>
9935 =item C<isl_ast_op_ge>
9937 Greater than or equal relation.
9939 =item C<isl_ast_op_gt>
9941 Greater than relation.
9943 =item C<isl_ast_op_call>
9946 The number of arguments of the C<isl_ast_expr> is one more than
9947 the number of arguments in the function call, the first argument
9948 representing the function being called.
9950 =item C<isl_ast_op_access>
9953 The number of arguments of the C<isl_ast_expr> is one more than
9954 the number of index expressions in the array access, the first argument
9955 representing the array being accessed.
9957 =item C<isl_ast_op_member>
9960 This operation has two arguments, a structure and the name of
9961 the member of the structure being accessed.
9965 #include <isl/ast.h>
9966 __isl_give isl_id *isl_ast_expr_get_id(
9967 __isl_keep isl_ast_expr *expr);
9969 Return the identifier represented by the AST expression.
9971 #include <isl/ast.h>
9972 __isl_give isl_val *isl_ast_expr_get_val(
9973 __isl_keep isl_ast_expr *expr);
9975 Return the integer represented by the AST expression.
9977 =head3 Properties of ASTs
9979 #include <isl/ast.h>
9980 isl_bool isl_ast_expr_is_equal(
9981 __isl_keep isl_ast_expr *expr1,
9982 __isl_keep isl_ast_expr *expr2);
9984 Check if two C<isl_ast_expr>s are equal to each other.
9986 =head3 Manipulating and printing the AST
9988 AST nodes can be copied and freed using the following functions.
9990 #include <isl/ast.h>
9991 __isl_give isl_ast_node *isl_ast_node_copy(
9992 __isl_keep isl_ast_node *node);
9993 __isl_null isl_ast_node *isl_ast_node_free(
9994 __isl_take isl_ast_node *node);
9996 AST expressions can be copied and freed using the following functions.
9998 #include <isl/ast.h>
9999 __isl_give isl_ast_expr *isl_ast_expr_copy(
10000 __isl_keep isl_ast_expr *expr);
10001 __isl_null isl_ast_expr *isl_ast_expr_free(
10002 __isl_take isl_ast_expr *expr);
10004 New AST expressions can be created either directly or within
10005 the context of an C<isl_ast_build>.
10007 #include <isl/ast.h>
10008 __isl_give isl_ast_expr *isl_ast_expr_from_val(
10009 __isl_take isl_val *v);
10010 __isl_give isl_ast_expr *isl_ast_expr_from_id(
10011 __isl_take isl_id *id);
10012 __isl_give isl_ast_expr *isl_ast_expr_neg(
10013 __isl_take isl_ast_expr *expr);
10014 __isl_give isl_ast_expr *isl_ast_expr_address_of(
10015 __isl_take isl_ast_expr *expr);
10016 __isl_give isl_ast_expr *isl_ast_expr_add(
10017 __isl_take isl_ast_expr *expr1,
10018 __isl_take isl_ast_expr *expr2);
10019 __isl_give isl_ast_expr *isl_ast_expr_sub(
10020 __isl_take isl_ast_expr *expr1,
10021 __isl_take isl_ast_expr *expr2);
10022 __isl_give isl_ast_expr *isl_ast_expr_mul(
10023 __isl_take isl_ast_expr *expr1,
10024 __isl_take isl_ast_expr *expr2);
10025 __isl_give isl_ast_expr *isl_ast_expr_div(
10026 __isl_take isl_ast_expr *expr1,
10027 __isl_take isl_ast_expr *expr2);
10028 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
10029 __isl_take isl_ast_expr *expr1,
10030 __isl_take isl_ast_expr *expr2);
10031 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
10032 __isl_take isl_ast_expr *expr1,
10033 __isl_take isl_ast_expr *expr2);
10034 __isl_give isl_ast_expr *isl_ast_expr_and(
10035 __isl_take isl_ast_expr *expr1,
10036 __isl_take isl_ast_expr *expr2)
10037 __isl_give isl_ast_expr *isl_ast_expr_and_then(
10038 __isl_take isl_ast_expr *expr1,
10039 __isl_take isl_ast_expr *expr2)
10040 __isl_give isl_ast_expr *isl_ast_expr_or(
10041 __isl_take isl_ast_expr *expr1,
10042 __isl_take isl_ast_expr *expr2)
10043 __isl_give isl_ast_expr *isl_ast_expr_or_else(
10044 __isl_take isl_ast_expr *expr1,
10045 __isl_take isl_ast_expr *expr2)
10046 __isl_give isl_ast_expr *isl_ast_expr_eq(
10047 __isl_take isl_ast_expr *expr1,
10048 __isl_take isl_ast_expr *expr2);
10049 __isl_give isl_ast_expr *isl_ast_expr_le(
10050 __isl_take isl_ast_expr *expr1,
10051 __isl_take isl_ast_expr *expr2);
10052 __isl_give isl_ast_expr *isl_ast_expr_lt(
10053 __isl_take isl_ast_expr *expr1,
10054 __isl_take isl_ast_expr *expr2);
10055 __isl_give isl_ast_expr *isl_ast_expr_ge(
10056 __isl_take isl_ast_expr *expr1,
10057 __isl_take isl_ast_expr *expr2);
10058 __isl_give isl_ast_expr *isl_ast_expr_gt(
10059 __isl_take isl_ast_expr *expr1,
10060 __isl_take isl_ast_expr *expr2);
10061 __isl_give isl_ast_expr *isl_ast_expr_access(
10062 __isl_take isl_ast_expr *array,
10063 __isl_take isl_ast_expr_list *indices);
10064 __isl_give isl_ast_expr *isl_ast_expr_call(
10065 __isl_take isl_ast_expr *function,
10066 __isl_take isl_ast_expr_list *arguments);
10068 The function C<isl_ast_expr_address_of> can be applied to an
10069 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
10070 to represent the address of the C<isl_ast_expr_access>. The function
10071 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
10072 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
10074 #include <isl/ast_build.h>
10075 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
10076 __isl_keep isl_ast_build *build,
10077 __isl_take isl_set *set);
10078 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
10079 __isl_keep isl_ast_build *build,
10080 __isl_take isl_pw_aff *pa);
10081 __isl_give isl_ast_expr *
10082 isl_ast_build_access_from_pw_multi_aff(
10083 __isl_keep isl_ast_build *build,
10084 __isl_take isl_pw_multi_aff *pma);
10085 __isl_give isl_ast_expr *
10086 isl_ast_build_access_from_multi_pw_aff(
10087 __isl_keep isl_ast_build *build,
10088 __isl_take isl_multi_pw_aff *mpa);
10089 __isl_give isl_ast_expr *
10090 isl_ast_build_call_from_pw_multi_aff(
10091 __isl_keep isl_ast_build *build,
10092 __isl_take isl_pw_multi_aff *pma);
10093 __isl_give isl_ast_expr *
10094 isl_ast_build_call_from_multi_pw_aff(
10095 __isl_keep isl_ast_build *build,
10096 __isl_take isl_multi_pw_aff *mpa);
10099 the domains of C<pa>, C<mpa> and C<pma> should correspond
10100 to the schedule space of C<build>.
10101 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
10102 the function being called.
10103 If the accessed space is a nested relation, then it is taken
10104 to represent an access of the member specified by the range
10105 of this nested relation of the structure specified by the domain
10106 of the nested relation.
10108 The following functions can be used to modify an C<isl_ast_expr>.
10110 #include <isl/ast.h>
10111 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
10112 __isl_take isl_ast_expr *expr, int pos,
10113 __isl_take isl_ast_expr *arg);
10115 Replace the argument of C<expr> at position C<pos> by C<arg>.
10117 #include <isl/ast.h>
10118 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
10119 __isl_take isl_ast_expr *expr,
10120 __isl_take isl_id_to_ast_expr *id2expr);
10122 The function C<isl_ast_expr_substitute_ids> replaces the
10123 subexpressions of C<expr> of type C<isl_ast_expr_id>
10124 by the corresponding expression in C<id2expr>, if there is any.
10127 User specified data can be attached to an C<isl_ast_node> and obtained
10128 from the same C<isl_ast_node> using the following functions.
10130 #include <isl/ast.h>
10131 __isl_give isl_ast_node *isl_ast_node_set_annotation(
10132 __isl_take isl_ast_node *node,
10133 __isl_take isl_id *annotation);
10134 __isl_give isl_id *isl_ast_node_get_annotation(
10135 __isl_keep isl_ast_node *node);
10137 Basic printing can be performed using the following functions.
10139 #include <isl/ast.h>
10140 __isl_give isl_printer *isl_printer_print_ast_expr(
10141 __isl_take isl_printer *p,
10142 __isl_keep isl_ast_expr *expr);
10143 __isl_give isl_printer *isl_printer_print_ast_node(
10144 __isl_take isl_printer *p,
10145 __isl_keep isl_ast_node *node);
10146 __isl_give char *isl_ast_expr_to_str(
10147 __isl_keep isl_ast_expr *expr);
10148 __isl_give char *isl_ast_node_to_str(
10149 __isl_keep isl_ast_node *node);
10150 __isl_give char *isl_ast_expr_to_C_str(
10151 __isl_keep isl_ast_expr *expr);
10152 __isl_give char *isl_ast_node_to_C_str(
10153 __isl_keep isl_ast_node *node);
10155 The functions C<isl_ast_expr_to_C_str> and
10156 C<isl_ast_node_to_C_str> are convenience functions
10157 that return a string representation of the input in C format.
10159 More advanced printing can be performed using the following functions.
10161 #include <isl/ast.h>
10162 __isl_give isl_printer *isl_ast_op_type_set_print_name(
10163 __isl_take isl_printer *p,
10164 enum isl_ast_op_type type,
10165 __isl_keep const char *name);
10166 isl_stat isl_options_set_ast_print_macro_once(
10167 isl_ctx *ctx, int val);
10168 int isl_options_get_ast_print_macro_once(isl_ctx *ctx);
10169 __isl_give isl_printer *isl_ast_op_type_print_macro(
10170 enum isl_ast_op_type type,
10171 __isl_take isl_printer *p);
10172 __isl_give isl_printer *isl_ast_expr_print_macros(
10173 __isl_keep isl_ast_expr *expr,
10174 __isl_take isl_printer *p);
10175 __isl_give isl_printer *isl_ast_node_print_macros(
10176 __isl_keep isl_ast_node *node,
10177 __isl_take isl_printer *p);
10178 __isl_give isl_printer *isl_ast_node_print(
10179 __isl_keep isl_ast_node *node,
10180 __isl_take isl_printer *p,
10181 __isl_take isl_ast_print_options *options);
10182 __isl_give isl_printer *isl_ast_node_for_print(
10183 __isl_keep isl_ast_node *node,
10184 __isl_take isl_printer *p,
10185 __isl_take isl_ast_print_options *options);
10186 __isl_give isl_printer *isl_ast_node_if_print(
10187 __isl_keep isl_ast_node *node,
10188 __isl_take isl_printer *p,
10189 __isl_take isl_ast_print_options *options);
10191 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
10192 C<isl> may print out an AST that makes use of macros such
10193 as C<floord>, C<min> and C<max>.
10194 The names of these macros may be modified by a call
10195 to C<isl_ast_op_type_set_print_name>. The user-specified
10196 names are associated to the printer object.
10197 C<isl_ast_op_type_print_macro> prints out the macro
10198 corresponding to a specific C<isl_ast_op_type>.
10199 If the print-macro-once option is set, then a given macro definition
10200 is only printed once to any given printer object.
10201 C<isl_ast_expr_print_macros> scans the C<isl_ast_expr>
10202 for subexpressions where these macros would be used and prints
10203 out the required macro definitions.
10204 Essentially, C<isl_ast_expr_print_macros> calls
10205 C<isl_ast_expr_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
10206 as function argument.
10207 C<isl_ast_node_print_macros> does the same
10208 for expressions in its C<isl_ast_node> argument.
10209 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
10210 C<isl_ast_node_if_print> print an C<isl_ast_node>
10211 in C<ISL_FORMAT_C>, but allow for some extra control
10212 through an C<isl_ast_print_options> object.
10213 This object can be created using the following functions.
10215 #include <isl/ast.h>
10216 __isl_give isl_ast_print_options *
10217 isl_ast_print_options_alloc(isl_ctx *ctx);
10218 __isl_give isl_ast_print_options *
10219 isl_ast_print_options_copy(
10220 __isl_keep isl_ast_print_options *options);
10221 __isl_null isl_ast_print_options *
10222 isl_ast_print_options_free(
10223 __isl_take isl_ast_print_options *options);
10225 __isl_give isl_ast_print_options *
10226 isl_ast_print_options_set_print_user(
10227 __isl_take isl_ast_print_options *options,
10228 __isl_give isl_printer *(*print_user)(
10229 __isl_take isl_printer *p,
10230 __isl_take isl_ast_print_options *options,
10231 __isl_keep isl_ast_node *node, void *user),
10233 __isl_give isl_ast_print_options *
10234 isl_ast_print_options_set_print_for(
10235 __isl_take isl_ast_print_options *options,
10236 __isl_give isl_printer *(*print_for)(
10237 __isl_take isl_printer *p,
10238 __isl_take isl_ast_print_options *options,
10239 __isl_keep isl_ast_node *node, void *user),
10242 The callback set by C<isl_ast_print_options_set_print_user>
10243 is called whenever a node of type C<isl_ast_node_user> needs to
10245 The callback set by C<isl_ast_print_options_set_print_for>
10246 is called whenever a node of type C<isl_ast_node_for> needs to
10248 Note that C<isl_ast_node_for_print> will I<not> call the
10249 callback set by C<isl_ast_print_options_set_print_for> on the node
10250 on which C<isl_ast_node_for_print> is called, but only on nested
10251 nodes of type C<isl_ast_node_for>. It is therefore safe to
10252 call C<isl_ast_node_for_print> from within the callback set by
10253 C<isl_ast_print_options_set_print_for>.
10255 The following option determines the type to be used for iterators
10256 while printing the AST.
10258 isl_stat isl_options_set_ast_iterator_type(
10259 isl_ctx *ctx, const char *val);
10260 const char *isl_options_get_ast_iterator_type(
10263 The AST printer only prints body nodes as blocks if these
10264 blocks cannot be safely omitted.
10265 For example, a C<for> node with one body node will not be
10266 surrounded with braces in C<ISL_FORMAT_C>.
10267 A block will always be printed by setting the following option.
10269 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx,
10271 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
10275 #include <isl/ast_build.h>
10276 isl_stat isl_options_set_ast_build_atomic_upper_bound(
10277 isl_ctx *ctx, int val);
10278 int isl_options_get_ast_build_atomic_upper_bound(
10280 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
10282 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
10283 isl_stat isl_options_set_ast_build_detect_min_max(
10284 isl_ctx *ctx, int val);
10285 int isl_options_get_ast_build_detect_min_max(
10287 isl_stat isl_options_set_ast_build_exploit_nested_bounds(
10288 isl_ctx *ctx, int val);
10289 int isl_options_get_ast_build_exploit_nested_bounds(
10291 isl_stat isl_options_set_ast_build_group_coscheduled(
10292 isl_ctx *ctx, int val);
10293 int isl_options_get_ast_build_group_coscheduled(
10295 isl_stat isl_options_set_ast_build_scale_strides(
10296 isl_ctx *ctx, int val);
10297 int isl_options_get_ast_build_scale_strides(
10299 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx,
10301 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
10302 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx,
10304 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
10308 =item * ast_build_atomic_upper_bound
10310 Generate loop upper bounds that consist of the current loop iterator,
10311 an operator and an expression not involving the iterator.
10312 If this option is not set, then the current loop iterator may appear
10313 several times in the upper bound.
10314 For example, when this option is turned off, AST generation
10317 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
10321 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
10324 When the option is turned on, the following AST is generated
10326 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
10329 =item * ast_build_prefer_pdiv
10331 If this option is turned off, then the AST generation will
10332 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
10333 operators, but no C<isl_ast_op_pdiv_q> or
10334 C<isl_ast_op_pdiv_r> operators.
10335 If this option is turned on, then C<isl> will try to convert
10336 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
10337 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
10339 =item * ast_build_detect_min_max
10341 If this option is turned on, then C<isl> will try and detect
10342 min or max-expressions when building AST expressions from
10343 piecewise affine expressions.
10345 =item * ast_build_exploit_nested_bounds
10347 Simplify conditions based on bounds of nested for loops.
10348 In particular, remove conditions that are implied by the fact
10349 that one or more nested loops have at least one iteration,
10350 meaning that the upper bound is at least as large as the lower bound.
10351 For example, when this option is turned off, AST generation
10354 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
10360 for (int c0 = 0; c0 <= N; c0 += 1)
10361 for (int c1 = 0; c1 <= M; c1 += 1)
10364 When the option is turned on, the following AST is generated
10366 for (int c0 = 0; c0 <= N; c0 += 1)
10367 for (int c1 = 0; c1 <= M; c1 += 1)
10370 =item * ast_build_group_coscheduled
10372 If two domain elements are assigned the same schedule point, then
10373 they may be executed in any order and they may even appear in different
10374 loops. If this options is set, then the AST generator will make
10375 sure that coscheduled domain elements do not appear in separate parts
10376 of the AST. This is useful in case of nested AST generation
10377 if the outer AST generation is given only part of a schedule
10378 and the inner AST generation should handle the domains that are
10379 coscheduled by this initial part of the schedule together.
10380 For example if an AST is generated for a schedule
10382 { A[i] -> [0]; B[i] -> [0] }
10384 then the C<isl_ast_build_set_create_leaf> callback described
10385 below may get called twice, once for each domain.
10386 Setting this option ensures that the callback is only called once
10387 on both domains together.
10389 =item * ast_build_separation_bounds
10391 This option specifies which bounds to use during separation.
10392 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
10393 then all (possibly implicit) bounds on the current dimension will
10394 be used during separation.
10395 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
10396 then only those bounds that are explicitly available will
10397 be used during separation.
10399 =item * ast_build_scale_strides
10401 This option specifies whether the AST generator is allowed
10402 to scale down iterators of strided loops.
10404 =item * ast_build_allow_else
10406 This option specifies whether the AST generator is allowed
10407 to construct if statements with else branches.
10409 =item * ast_build_allow_or
10411 This option specifies whether the AST generator is allowed
10412 to construct if conditions with disjunctions.
10416 =head3 AST Generation Options (Schedule Tree)
10418 In case of AST construction from a schedule tree, the options
10419 that control how an AST is created from the individual schedule
10420 dimensions are stored in the band nodes of the tree
10421 (see L</"Schedule Trees">).
10423 In particular, a schedule dimension can be handled in four
10424 different ways, atomic, separate, unroll or the default.
10425 This loop AST generation type can be set using
10426 C<isl_schedule_node_band_member_set_ast_loop_type>.
10428 the first three can be selected by including a one-dimensional
10429 element with as value the position of the schedule dimension
10430 within the band and as name one of C<atomic>, C<separate>
10431 or C<unroll> in the options
10432 set by C<isl_schedule_node_band_set_ast_build_options>.
10433 Only one of these three may be specified for
10434 any given schedule dimension within a band node.
10435 If none of these is specified, then the default
10436 is used. The meaning of the options is as follows.
10442 When this option is specified, the AST generator will make
10443 sure that a given domains space only appears in a single
10444 loop at the specified level.
10446 For example, for the schedule tree
10448 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10450 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10451 options: "{ atomic[x] }"
10453 the following AST will be generated
10455 for (int c0 = 0; c0 <= 10; c0 += 1) {
10462 On the other hand, for the schedule tree
10464 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10466 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10467 options: "{ separate[x] }"
10469 the following AST will be generated
10473 for (int c0 = 1; c0 <= 9; c0 += 1) {
10480 If neither C<atomic> nor C<separate> is specified, then the AST generator
10481 may produce either of these two results or some intermediate form.
10485 When this option is specified, the AST generator will
10486 split the domain of the specified schedule dimension
10487 into pieces with a fixed set of statements for which
10488 instances need to be executed by the iterations in
10489 the schedule domain part. This option tends to avoid
10490 the generation of guards inside the corresponding loops.
10491 See also the C<atomic> option.
10495 When this option is specified, the AST generator will
10496 I<completely> unroll the corresponding schedule dimension.
10497 It is the responsibility of the user to ensure that such
10498 unrolling is possible.
10499 To obtain a partial unrolling, the user should apply an additional
10500 strip-mining to the schedule and fully unroll the inner schedule
10505 The C<isolate> option is a bit more involved. It allows the user
10506 to isolate a range of schedule dimension values from smaller and
10507 greater values. Additionally, the user may specify a different
10508 atomic/separate/unroll choice for the isolated part and the remaining
10509 parts. The typical use case of the C<isolate> option is to isolate
10510 full tiles from partial tiles.
10511 The part that needs to be isolated may depend on outer schedule dimensions.
10512 The option therefore needs to be able to reference those outer schedule
10513 dimensions. In particular, the space of the C<isolate> option is that
10514 of a wrapped map with as domain the flat product of all outer band nodes
10515 and as range the space of the current band node.
10516 The atomic/separate/unroll choice for the isolated part is determined
10517 by an option that lives in an unnamed wrapped space with as domain
10518 a zero-dimensional C<isolate> space and as range the regular
10519 C<atomic>, C<separate> or C<unroll> space.
10520 This option may also be set directly using
10521 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
10522 The atomic/separate/unroll choice for the remaining part is determined
10523 by the regular C<atomic>, C<separate> or C<unroll> option.
10524 Since the C<isolate> option references outer schedule dimensions,
10525 its use in a band node causes any tree containing the node
10526 to be considered anchored.
10528 As an example, consider the isolation of full tiles from partial tiles
10529 in a tiling of a triangular domain. The original schedule is as follows.
10531 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10533 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10534 { A[i,j] -> [floor(j/10)] }, \
10535 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10539 for (int c0 = 0; c0 <= 10; c0 += 1)
10540 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10541 for (int c2 = 10 * c0;
10542 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10543 for (int c3 = 10 * c1;
10544 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10547 Isolating the full tiles, we have the following input
10549 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10551 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10552 { A[i,j] -> [floor(j/10)] }, \
10553 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10554 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10555 10a+9+10b+9 <= 100 }"
10560 for (int c0 = 0; c0 <= 8; c0 += 1) {
10561 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10562 for (int c2 = 10 * c0;
10563 c2 <= 10 * c0 + 9; c2 += 1)
10564 for (int c3 = 10 * c1;
10565 c3 <= 10 * c1 + 9; c3 += 1)
10567 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10568 for (int c2 = 10 * c0;
10569 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10570 for (int c3 = 10 * c1;
10571 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10574 for (int c0 = 9; c0 <= 10; c0 += 1)
10575 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10576 for (int c2 = 10 * c0;
10577 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10578 for (int c3 = 10 * c1;
10579 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10583 We may then additionally unroll the innermost loop of the isolated part
10585 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10587 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10588 { A[i,j] -> [floor(j/10)] }, \
10589 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10590 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10591 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
10596 for (int c0 = 0; c0 <= 8; c0 += 1) {
10597 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10598 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
10600 A(c2, 10 * c1 + 1);
10601 A(c2, 10 * c1 + 2);
10602 A(c2, 10 * c1 + 3);
10603 A(c2, 10 * c1 + 4);
10604 A(c2, 10 * c1 + 5);
10605 A(c2, 10 * c1 + 6);
10606 A(c2, 10 * c1 + 7);
10607 A(c2, 10 * c1 + 8);
10608 A(c2, 10 * c1 + 9);
10610 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10611 for (int c2 = 10 * c0;
10612 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10613 for (int c3 = 10 * c1;
10614 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10617 for (int c0 = 9; c0 <= 10; c0 += 1)
10618 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10619 for (int c2 = 10 * c0;
10620 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10621 for (int c3 = 10 * c1;
10622 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10627 =head3 AST Generation Options (Schedule Map)
10629 In case of AST construction using
10630 C<isl_ast_build_node_from_schedule_map>, the options
10631 that control how an AST is created from the individual schedule
10632 dimensions are stored in the C<isl_ast_build>.
10633 They can be set using the following function.
10635 #include <isl/ast_build.h>
10636 __isl_give isl_ast_build *
10637 isl_ast_build_set_options(
10638 __isl_take isl_ast_build *build,
10639 __isl_take isl_union_map *options);
10641 The options are encoded in an C<isl_union_map>.
10642 The domain of this union relation refers to the schedule domain,
10643 i.e., the range of the schedule passed
10644 to C<isl_ast_build_node_from_schedule_map>.
10645 In the case of nested AST generation (see L</"Nested AST Generation">),
10646 the domain of C<options> should refer to the extra piece of the schedule.
10647 That is, it should be equal to the range of the wrapped relation in the
10648 range of the schedule.
10649 The range of the options can consist of elements in one or more spaces,
10650 the names of which determine the effect of the option.
10651 The values of the range typically also refer to the schedule dimension
10652 to which the option applies. In case of nested AST generation
10653 (see L</"Nested AST Generation">), these values refer to the position
10654 of the schedule dimension within the innermost AST generation.
10655 The constraints on the domain elements of
10656 the option should only refer to this dimension and earlier dimensions.
10657 We consider the following spaces.
10661 =item C<separation_class>
10663 B<This option has been deprecated. Use the isolate option on
10664 schedule trees instead.>
10666 This space is a wrapped relation between two one dimensional spaces.
10667 The input space represents the schedule dimension to which the option
10668 applies and the output space represents the separation class.
10669 While constructing a loop corresponding to the specified schedule
10670 dimension(s), the AST generator will try to generate separate loops
10671 for domain elements that are assigned different classes.
10672 If only some of the elements are assigned a class, then those elements
10673 that are not assigned any class will be treated as belonging to a class
10674 that is separate from the explicitly assigned classes.
10675 The typical use case for this option is to separate full tiles from
10677 The other options, described below, are applied after the separation
10680 As an example, consider the separation into full and partial tiles
10681 of a tiling of a triangular domain.
10682 Take, for example, the domain
10684 { A[i,j] : 0 <= i,j and i + j <= 100 }
10686 and a tiling into tiles of 10 by 10. The input to the AST generator
10687 is then the schedule
10689 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
10692 Without any options, the following AST is generated
10694 for (int c0 = 0; c0 <= 10; c0 += 1)
10695 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10696 for (int c2 = 10 * c0;
10697 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10699 for (int c3 = 10 * c1;
10700 c3 <= min(10 * c1 + 9, -c2 + 100);
10704 Separation into full and partial tiles can be obtained by assigning
10705 a class, say C<0>, to the full tiles. The full tiles are represented by those
10706 values of the first and second schedule dimensions for which there are
10707 values of the third and fourth dimensions to cover an entire tile.
10708 That is, we need to specify the following option
10710 { [a,b,c,d] -> separation_class[[0]->[0]] :
10711 exists b': 0 <= 10a,10b' and
10712 10a+9+10b'+9 <= 100;
10713 [a,b,c,d] -> separation_class[[1]->[0]] :
10714 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
10716 which simplifies to
10718 { [a, b, c, d] -> separation_class[[1] -> [0]] :
10719 a >= 0 and b >= 0 and b <= 8 - a;
10720 [a, b, c, d] -> separation_class[[0] -> [0]] :
10721 a >= 0 and a <= 8 }
10723 With this option, the generated AST is as follows
10726 for (int c0 = 0; c0 <= 8; c0 += 1) {
10727 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10728 for (int c2 = 10 * c0;
10729 c2 <= 10 * c0 + 9; c2 += 1)
10730 for (int c3 = 10 * c1;
10731 c3 <= 10 * c1 + 9; c3 += 1)
10733 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10734 for (int c2 = 10 * c0;
10735 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10737 for (int c3 = 10 * c1;
10738 c3 <= min(-c2 + 100, 10 * c1 + 9);
10742 for (int c0 = 9; c0 <= 10; c0 += 1)
10743 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10744 for (int c2 = 10 * c0;
10745 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10747 for (int c3 = 10 * c1;
10748 c3 <= min(10 * c1 + 9, -c2 + 100);
10755 This is a single-dimensional space representing the schedule dimension(s)
10756 to which ``separation'' should be applied. Separation tries to split
10757 a loop into several pieces if this can avoid the generation of guards
10759 See also the C<atomic> option.
10763 This is a single-dimensional space representing the schedule dimension(s)
10764 for which the domains should be considered ``atomic''. That is, the
10765 AST generator will make sure that any given domain space will only appear
10766 in a single loop at the specified level.
10768 Consider the following schedule
10770 { a[i] -> [i] : 0 <= i < 10;
10771 b[i] -> [i+1] : 0 <= i < 10 }
10773 If the following option is specified
10775 { [i] -> separate[x] }
10777 then the following AST will be generated
10781 for (int c0 = 1; c0 <= 9; c0 += 1) {
10788 If, on the other hand, the following option is specified
10790 { [i] -> atomic[x] }
10792 then the following AST will be generated
10794 for (int c0 = 0; c0 <= 10; c0 += 1) {
10801 If neither C<atomic> nor C<separate> is specified, then the AST generator
10802 may produce either of these two results or some intermediate form.
10806 This is a single-dimensional space representing the schedule dimension(s)
10807 that should be I<completely> unrolled.
10808 To obtain a partial unrolling, the user should apply an additional
10809 strip-mining to the schedule and fully unroll the inner loop.
10813 =head3 Fine-grained Control over AST Generation
10815 Besides specifying the constraints on the parameters,
10816 an C<isl_ast_build> object can be used to control
10817 various aspects of the AST generation process.
10818 In case of AST construction using
10819 C<isl_ast_build_node_from_schedule_map>,
10820 the most prominent way of control is through ``options'',
10821 as explained above.
10823 Additional control is available through the following functions.
10825 #include <isl/ast_build.h>
10826 __isl_give isl_ast_build *
10827 isl_ast_build_set_iterators(
10828 __isl_take isl_ast_build *build,
10829 __isl_take isl_id_list *iterators);
10831 The function C<isl_ast_build_set_iterators> allows the user to
10832 specify a list of iterator C<isl_id>s to be used as iterators.
10833 If the input schedule is injective, then
10834 the number of elements in this list should be as large as the dimension
10835 of the schedule space, but no direct correspondence should be assumed
10836 between dimensions and elements.
10837 If the input schedule is not injective, then an additional number
10838 of C<isl_id>s equal to the largest dimension of the input domains
10840 If the number of provided C<isl_id>s is insufficient, then additional
10841 names are automatically generated.
10843 #include <isl/ast_build.h>
10844 __isl_give isl_ast_build *
10845 isl_ast_build_set_create_leaf(
10846 __isl_take isl_ast_build *build,
10847 __isl_give isl_ast_node *(*fn)(
10848 __isl_take isl_ast_build *build,
10849 void *user), void *user);
10852 C<isl_ast_build_set_create_leaf> function allows for the
10853 specification of a callback that should be called whenever the AST
10854 generator arrives at an element of the schedule domain.
10855 The callback should return an AST node that should be inserted
10856 at the corresponding position of the AST. The default action (when
10857 the callback is not set) is to continue generating parts of the AST to scan
10858 all the domain elements associated to the schedule domain element
10859 and to insert user nodes, ``calling'' the domain element, for each of them.
10860 The C<build> argument contains the current state of the C<isl_ast_build>.
10861 To ease nested AST generation (see L</"Nested AST Generation">),
10862 all control information that is
10863 specific to the current AST generation such as the options and
10864 the callbacks has been removed from this C<isl_ast_build>.
10865 The callback would typically return the result of a nested
10866 AST generation or a
10867 user defined node created using the following function.
10869 #include <isl/ast.h>
10870 __isl_give isl_ast_node *isl_ast_node_alloc_user(
10871 __isl_take isl_ast_expr *expr);
10873 #include <isl/ast_build.h>
10874 __isl_give isl_ast_build *
10875 isl_ast_build_set_at_each_domain(
10876 __isl_take isl_ast_build *build,
10877 __isl_give isl_ast_node *(*fn)(
10878 __isl_take isl_ast_node *node,
10879 __isl_keep isl_ast_build *build,
10880 void *user), void *user);
10881 __isl_give isl_ast_build *
10882 isl_ast_build_set_before_each_for(
10883 __isl_take isl_ast_build *build,
10884 __isl_give isl_id *(*fn)(
10885 __isl_keep isl_ast_build *build,
10886 void *user), void *user);
10887 __isl_give isl_ast_build *
10888 isl_ast_build_set_after_each_for(
10889 __isl_take isl_ast_build *build,
10890 __isl_give isl_ast_node *(*fn)(
10891 __isl_take isl_ast_node *node,
10892 __isl_keep isl_ast_build *build,
10893 void *user), void *user);
10894 __isl_give isl_ast_build *
10895 isl_ast_build_set_before_each_mark(
10896 __isl_take isl_ast_build *build,
10897 isl_stat (*fn)(__isl_keep isl_id *mark,
10898 __isl_keep isl_ast_build *build,
10899 void *user), void *user);
10900 __isl_give isl_ast_build *
10901 isl_ast_build_set_after_each_mark(
10902 __isl_take isl_ast_build *build,
10903 __isl_give isl_ast_node *(*fn)(
10904 __isl_take isl_ast_node *node,
10905 __isl_keep isl_ast_build *build,
10906 void *user), void *user);
10908 The callback set by C<isl_ast_build_set_at_each_domain> will
10909 be called for each domain AST node.
10910 The callbacks set by C<isl_ast_build_set_before_each_for>
10911 and C<isl_ast_build_set_after_each_for> will be called
10912 for each for AST node. The first will be called in depth-first
10913 pre-order, while the second will be called in depth-first post-order.
10914 Since C<isl_ast_build_set_before_each_for> is called before the for
10915 node is actually constructed, it is only passed an C<isl_ast_build>.
10916 The returned C<isl_id> will be added as an annotation (using
10917 C<isl_ast_node_set_annotation>) to the constructed for node.
10918 In particular, if the user has also specified an C<after_each_for>
10919 callback, then the annotation can be retrieved from the node passed to
10920 that callback using C<isl_ast_node_get_annotation>.
10921 The callbacks set by C<isl_ast_build_set_before_each_mark>
10922 and C<isl_ast_build_set_after_each_mark> will be called for each
10923 mark AST node that is created, i.e., for each mark schedule node
10924 in the input schedule tree. The first will be called in depth-first
10925 pre-order, while the second will be called in depth-first post-order.
10926 Since the callback set by C<isl_ast_build_set_before_each_mark>
10927 is called before the mark AST node is actually constructed, it is passed
10928 the identifier of the mark node.
10929 All callbacks should C<NULL> (or C<isl_stat_error>) on failure.
10930 The given C<isl_ast_build> can be used to create new
10931 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
10932 or C<isl_ast_build_call_from_pw_multi_aff>.
10934 =head3 Nested AST Generation
10936 C<isl> allows the user to create an AST within the context
10937 of another AST. These nested ASTs are created using the
10938 same C<isl_ast_build_node_from_schedule_map> function that is used to create
10939 the outer AST. The C<build> argument should be an C<isl_ast_build>
10940 passed to a callback set by
10941 C<isl_ast_build_set_create_leaf>.
10942 The space of the range of the C<schedule> argument should refer
10943 to this build. In particular, the space should be a wrapped
10944 relation and the domain of this wrapped relation should be the
10945 same as that of the range of the schedule returned by
10946 C<isl_ast_build_get_schedule> below.
10947 In practice, the new schedule is typically
10948 created by calling C<isl_union_map_range_product> on the old schedule
10949 and some extra piece of the schedule.
10950 The space of the schedule domain is also available from
10951 the C<isl_ast_build>.
10953 #include <isl/ast_build.h>
10954 __isl_give isl_union_map *isl_ast_build_get_schedule(
10955 __isl_keep isl_ast_build *build);
10956 __isl_give isl_space *isl_ast_build_get_schedule_space(
10957 __isl_keep isl_ast_build *build);
10958 __isl_give isl_ast_build *isl_ast_build_restrict(
10959 __isl_take isl_ast_build *build,
10960 __isl_take isl_set *set);
10962 The C<isl_ast_build_get_schedule> function returns a (partial)
10963 schedule for the domains elements for which part of the AST still needs to
10964 be generated in the current build.
10965 In particular, the domain elements are mapped to those iterations of the loops
10966 enclosing the current point of the AST generation inside which
10967 the domain elements are executed.
10968 No direct correspondence between
10969 the input schedule and this schedule should be assumed.
10970 The space obtained from C<isl_ast_build_get_schedule_space> can be used
10971 to create a set for C<isl_ast_build_restrict> to intersect
10972 with the current build. In particular, the set passed to
10973 C<isl_ast_build_restrict> can have additional parameters.
10974 The ids of the set dimensions in the space returned by
10975 C<isl_ast_build_get_schedule_space> correspond to the
10976 iterators of the already generated loops.
10977 The user should not rely on the ids of the output dimensions
10978 of the relations in the union relation returned by
10979 C<isl_ast_build_get_schedule> having any particular value.
10981 =head1 Applications
10983 Although C<isl> is mainly meant to be used as a library,
10984 it also contains some basic applications that use some
10985 of the functionality of C<isl>.
10986 For applications that take one or more polytopes or polyhedra
10987 as input, this input may be specified in either the L<isl format>
10988 or the L<PolyLib format>.
10990 =head2 C<isl_polyhedron_sample>
10992 C<isl_polyhedron_sample> takes a polyhedron as input and prints
10993 an integer element of the polyhedron, if there is any.
10994 The first column in the output is the denominator and is always
10995 equal to 1. If the polyhedron contains no integer points,
10996 then a vector of length zero is printed.
11000 C<isl_pip> takes the same input as the C<example> program
11001 from the C<piplib> distribution, i.e., a set of constraints
11002 on the parameters, a line containing only -1 and finally a set
11003 of constraints on a parametric polyhedron.
11004 The coefficients of the parameters appear in the last columns
11005 (but before the final constant column).
11006 The output is the lexicographic minimum of the parametric polyhedron.
11007 As C<isl> currently does not have its own output format, the output
11008 is just a dump of the internal state.
11010 =head2 C<isl_polyhedron_minimize>
11012 C<isl_polyhedron_minimize> computes the minimum of some linear
11013 or affine objective function over the integer points in a polyhedron.
11014 If an affine objective function
11015 is given, then the constant should appear in the last column.
11017 =head2 C<isl_polytope_scan>
11019 Given a polytope, C<isl_polytope_scan> prints
11020 all integer points in the polytope.
11024 Given an C<isl_union_access_info> object as input,
11025 C<isl_flow> prints out the corresponding dependences,
11026 as computed by C<isl_union_access_info_compute_flow>.
11028 =head2 C<isl_codegen>
11030 Given either a schedule tree or a sequence consisting of
11031 a schedule map, a context set and an options relation,
11032 C<isl_codegen> prints out an AST that scans the domain elements
11033 of the schedule in the order of their image(s) taking into account
11034 the constraints in the context set.
11036 =head2 C<isl_schedule>
11038 Given an C<isl_schedule_constraints> object as input,
11039 C<isl_schedule> prints out a schedule that satisfies the given