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 and to reset the memory that stores the last error. The
847 last error is only stored for information purposes. Its presence does not
848 change the behavior of C<isl>. Hence, resetting an error is not required to
849 continue to use isl, but only to observe new errors.
852 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
853 void isl_ctx_reset_error(isl_ctx *ctx);
855 Another option is to continue on error. This is similar to warn on error mode,
856 except that C<isl> does not print any warning. This allows a program to
857 implement its own error reporting.
859 The last option is to directly abort the execution of the program from within
860 the isl library. This makes it obviously impossible to recover from an error,
861 but it allows to directly spot the error location. By aborting on error,
862 debuggers break at the location the error occurred and can provide a stack
863 trace. Other tools that automatically provide stack traces on abort or that do
864 not want to continue execution after an error was triggered may also prefer to
867 The on error behavior of isl can be specified by calling
868 C<isl_options_set_on_error> or by setting the command line option
869 C<--isl-on-error>. Valid arguments for the function call are
870 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
871 choices for the command line option are C<warn>, C<continue> and C<abort>.
872 It is also possible to query the current error mode.
874 #include <isl/options.h>
875 isl_stat isl_options_set_on_error(isl_ctx *ctx, int val);
876 int isl_options_get_on_error(isl_ctx *ctx);
880 Identifiers are used to identify both individual dimensions
881 and tuples of dimensions. They consist of an optional name and an optional
882 user pointer. The name and the user pointer cannot both be C<NULL>, however.
883 Identifiers with the same name but different pointer values
884 are considered to be distinct.
885 Similarly, identifiers with different names but the same pointer value
886 are also considered to be distinct.
887 Equal identifiers are represented using the same object.
888 Pairs of identifiers can therefore be tested for equality using the
890 Identifiers can be constructed, copied, freed, inspected and printed
891 using the following functions.
894 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
895 __isl_keep const char *name, void *user);
896 __isl_give isl_id *isl_id_set_free_user(
897 __isl_take isl_id *id,
898 void (*free_user)(void *user));
899 __isl_give isl_id *isl_id_copy(isl_id *id);
900 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
902 void *isl_id_get_user(__isl_keep isl_id *id);
903 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
905 __isl_give isl_printer *isl_printer_print_id(
906 __isl_take isl_printer *p, __isl_keep isl_id *id);
908 The callback set by C<isl_id_set_free_user> is called on the user
909 pointer when the last reference to the C<isl_id> is freed.
910 Note that C<isl_id_get_name> returns a pointer to some internal
911 data structure, so the result can only be used while the
912 corresponding C<isl_id> is alive.
916 Whenever a new set, relation or similar object is created from scratch,
917 the space in which it lives needs to be specified using an C<isl_space>.
918 Each space involves zero or more parameters and zero, one or two
919 tuples of set or input/output dimensions. The parameters and dimensions
920 are identified by an C<isl_dim_type> and a position.
921 The type C<isl_dim_param> refers to parameters,
922 the type C<isl_dim_set> refers to set dimensions (for spaces
923 with a single tuple of dimensions) and the types C<isl_dim_in>
924 and C<isl_dim_out> refer to input and output dimensions
925 (for spaces with two tuples of dimensions).
926 Local spaces (see L</"Local Spaces">) also contain dimensions
927 of type C<isl_dim_div>.
928 Note that parameters are only identified by their position within
929 a given object. Across different objects, parameters are (usually)
930 identified by their names or identifiers. Only unnamed parameters
931 are identified by their positions across objects. The use of unnamed
932 parameters is discouraged.
934 #include <isl/space.h>
935 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
936 unsigned nparam, unsigned n_in, unsigned n_out);
937 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
939 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
940 unsigned nparam, unsigned dim);
941 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
942 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
944 The space used for creating a parameter domain
945 needs to be created using C<isl_space_params_alloc>.
946 For other sets, the space
947 needs to be created using C<isl_space_set_alloc>, while
948 for a relation, the space
949 needs to be created using C<isl_space_alloc>.
951 To check whether a given space is that of a set or a map
952 or whether it is a parameter space, use these functions:
954 #include <isl/space.h>
955 isl_bool isl_space_is_params(__isl_keep isl_space *space);
956 isl_bool isl_space_is_set(__isl_keep isl_space *space);
957 isl_bool isl_space_is_map(__isl_keep isl_space *space);
959 Spaces can be compared using the following functions:
961 #include <isl/space.h>
962 isl_bool isl_space_is_equal(__isl_keep isl_space *space1,
963 __isl_keep isl_space *space2);
964 isl_bool isl_space_has_equal_params(
965 __isl_keep isl_space *space1,
966 __isl_keep isl_space *space2);
967 isl_bool isl_space_has_equal_tuples(
968 __isl_keep isl_space *space1,
969 __isl_keep isl_space *space2);
970 isl_bool isl_space_is_domain(__isl_keep isl_space *space1,
971 __isl_keep isl_space *space2);
972 isl_bool isl_space_is_range(__isl_keep isl_space *space1,
973 __isl_keep isl_space *space2);
974 isl_bool isl_space_tuple_is_equal(
975 __isl_keep isl_space *space1,
976 enum isl_dim_type type1,
977 __isl_keep isl_space *space2,
978 enum isl_dim_type type2);
980 C<isl_space_is_domain> checks whether the first argument is equal
981 to the domain of the second argument. This requires in particular that
982 the first argument is a set space and that the second argument
983 is a map space. C<isl_space_tuple_is_equal> checks whether the given
984 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
985 spaces are the same. That is, it checks if they have the same
986 identifier (if any), the same dimension and the same internal structure
989 C<isl_space_has_equal_params> checks whether two spaces
990 have the same parameters in the same order.
991 C<isl_space_has_equal_tuples> check whether two spaces have
992 the same tuples. In contrast to C<isl_space_is_equal> below,
993 it does not check the
994 parameters. This is useful because many C<isl> functions align the
995 parameters before they perform their operations, such that equivalence
997 C<isl_space_is_equal> checks whether two spaces are identical,
998 meaning that they have the same parameters and the same tuples.
999 That is, it checks whether both C<isl_space_has_equal_params> and
1000 C<isl_space_has_equal_tuples> hold.
1002 It is often useful to create objects that live in the
1003 same space as some other object. This can be accomplished
1004 by creating the new objects
1005 (see L</"Creating New Sets and Relations"> or
1006 L</"Functions">) based on the space
1007 of the original object.
1009 #include <isl/set.h>
1010 __isl_give isl_space *isl_basic_set_get_space(
1011 __isl_keep isl_basic_set *bset);
1012 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
1014 #include <isl/union_set.h>
1015 __isl_give isl_space *isl_union_set_get_space(
1016 __isl_keep isl_union_set *uset);
1018 #include <isl/map.h>
1019 __isl_give isl_space *isl_basic_map_get_space(
1020 __isl_keep isl_basic_map *bmap);
1021 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
1023 #include <isl/union_map.h>
1024 __isl_give isl_space *isl_union_map_get_space(
1025 __isl_keep isl_union_map *umap);
1027 #include <isl/constraint.h>
1028 __isl_give isl_space *isl_constraint_get_space(
1029 __isl_keep isl_constraint *constraint);
1031 #include <isl/polynomial.h>
1032 __isl_give isl_space *isl_qpolynomial_get_domain_space(
1033 __isl_keep isl_qpolynomial *qp);
1034 __isl_give isl_space *isl_qpolynomial_get_space(
1035 __isl_keep isl_qpolynomial *qp);
1036 __isl_give isl_space *
1037 isl_qpolynomial_fold_get_domain_space(
1038 __isl_keep isl_qpolynomial_fold *fold);
1039 __isl_give isl_space *isl_qpolynomial_fold_get_space(
1040 __isl_keep isl_qpolynomial_fold *fold);
1041 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
1042 __isl_keep isl_pw_qpolynomial *pwqp);
1043 __isl_give isl_space *isl_pw_qpolynomial_get_space(
1044 __isl_keep isl_pw_qpolynomial *pwqp);
1045 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
1046 __isl_keep isl_pw_qpolynomial_fold *pwf);
1047 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
1048 __isl_keep isl_pw_qpolynomial_fold *pwf);
1049 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
1050 __isl_keep isl_union_pw_qpolynomial *upwqp);
1051 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
1052 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1054 #include <isl/val.h>
1055 __isl_give isl_space *isl_multi_val_get_space(
1056 __isl_keep isl_multi_val *mv);
1058 #include <isl/aff.h>
1059 __isl_give isl_space *isl_aff_get_domain_space(
1060 __isl_keep isl_aff *aff);
1061 __isl_give isl_space *isl_aff_get_space(
1062 __isl_keep isl_aff *aff);
1063 __isl_give isl_space *isl_pw_aff_get_domain_space(
1064 __isl_keep isl_pw_aff *pwaff);
1065 __isl_give isl_space *isl_pw_aff_get_space(
1066 __isl_keep isl_pw_aff *pwaff);
1067 __isl_give isl_space *isl_multi_aff_get_domain_space(
1068 __isl_keep isl_multi_aff *maff);
1069 __isl_give isl_space *isl_multi_aff_get_space(
1070 __isl_keep isl_multi_aff *maff);
1071 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
1072 __isl_keep isl_pw_multi_aff *pma);
1073 __isl_give isl_space *isl_pw_multi_aff_get_space(
1074 __isl_keep isl_pw_multi_aff *pma);
1075 __isl_give isl_space *isl_union_pw_aff_get_space(
1076 __isl_keep isl_union_pw_aff *upa);
1077 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
1078 __isl_keep isl_union_pw_multi_aff *upma);
1079 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
1080 __isl_keep isl_multi_pw_aff *mpa);
1081 __isl_give isl_space *isl_multi_pw_aff_get_space(
1082 __isl_keep isl_multi_pw_aff *mpa);
1083 __isl_give isl_space *
1084 isl_multi_union_pw_aff_get_domain_space(
1085 __isl_keep isl_multi_union_pw_aff *mupa);
1086 __isl_give isl_space *
1087 isl_multi_union_pw_aff_get_space(
1088 __isl_keep isl_multi_union_pw_aff *mupa);
1090 #include <isl/point.h>
1091 __isl_give isl_space *isl_point_get_space(
1092 __isl_keep isl_point *pnt);
1094 The number of dimensions of a given type of space
1095 may be read off from a space or an object that lives
1096 in a space using the following functions.
1097 In case of C<isl_space_dim>, type may be
1098 C<isl_dim_param>, C<isl_dim_in> (only for relations),
1099 C<isl_dim_out> (only for relations), C<isl_dim_set>
1100 (only for sets) or C<isl_dim_all>.
1102 #include <isl/space.h>
1103 unsigned isl_space_dim(__isl_keep isl_space *space,
1104 enum isl_dim_type type);
1106 #include <isl/local_space.h>
1107 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1108 enum isl_dim_type type);
1110 #include <isl/set.h>
1111 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1112 enum isl_dim_type type);
1113 unsigned isl_set_dim(__isl_keep isl_set *set,
1114 enum isl_dim_type type);
1116 #include <isl/union_set.h>
1117 unsigned isl_union_set_dim(__isl_keep isl_union_set *uset,
1118 enum isl_dim_type type);
1120 #include <isl/map.h>
1121 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1122 enum isl_dim_type type);
1123 unsigned isl_map_dim(__isl_keep isl_map *map,
1124 enum isl_dim_type type);
1126 #include <isl/union_map.h>
1127 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1128 enum isl_dim_type type);
1130 #include <isl/val.h>
1131 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
1132 enum isl_dim_type type);
1134 #include <isl/aff.h>
1135 int isl_aff_dim(__isl_keep isl_aff *aff,
1136 enum isl_dim_type type);
1137 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1138 enum isl_dim_type type);
1139 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1140 enum isl_dim_type type);
1141 unsigned isl_pw_multi_aff_dim(
1142 __isl_keep isl_pw_multi_aff *pma,
1143 enum isl_dim_type type);
1144 unsigned isl_multi_pw_aff_dim(
1145 __isl_keep isl_multi_pw_aff *mpa,
1146 enum isl_dim_type type);
1147 unsigned isl_union_pw_aff_dim(
1148 __isl_keep isl_union_pw_aff *upa,
1149 enum isl_dim_type type);
1150 unsigned isl_union_pw_multi_aff_dim(
1151 __isl_keep isl_union_pw_multi_aff *upma,
1152 enum isl_dim_type type);
1153 unsigned isl_multi_union_pw_aff_dim(
1154 __isl_keep isl_multi_union_pw_aff *mupa,
1155 enum isl_dim_type type);
1157 #include <isl/polynomial.h>
1158 unsigned isl_union_pw_qpolynomial_dim(
1159 __isl_keep isl_union_pw_qpolynomial *upwqp,
1160 enum isl_dim_type type);
1161 unsigned isl_union_pw_qpolynomial_fold_dim(
1162 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1163 enum isl_dim_type type);
1165 Note that an C<isl_union_set>, an C<isl_union_map>,
1166 an C<isl_union_pw_multi_aff>,
1167 an C<isl_union_pw_qpolynomial> and
1168 an C<isl_union_pw_qpolynomial_fold>
1169 only have parameters.
1171 The identifiers or names of the individual dimensions of spaces
1172 may be set or read off using the following functions on spaces
1173 or objects that live in spaces.
1174 These functions are mostly useful to obtain the identifiers, positions
1175 or names of the parameters. Identifiers of individual dimensions are
1176 essentially only useful for printing. They are ignored by all other
1177 operations and may not be preserved across those operations.
1179 #include <isl/space.h>
1180 __isl_give isl_space *isl_space_set_dim_id(
1181 __isl_take isl_space *space,
1182 enum isl_dim_type type, unsigned pos,
1183 __isl_take isl_id *id);
1184 isl_bool isl_space_has_dim_id(__isl_keep isl_space *space,
1185 enum isl_dim_type type, unsigned pos);
1186 __isl_give isl_id *isl_space_get_dim_id(
1187 __isl_keep isl_space *space,
1188 enum isl_dim_type type, unsigned pos);
1189 __isl_give isl_space *isl_space_set_dim_name(
1190 __isl_take isl_space *space,
1191 enum isl_dim_type type, unsigned pos,
1192 __isl_keep const char *name);
1193 isl_bool isl_space_has_dim_name(__isl_keep isl_space *space,
1194 enum isl_dim_type type, unsigned pos);
1195 __isl_keep const char *isl_space_get_dim_name(
1196 __isl_keep isl_space *space,
1197 enum isl_dim_type type, unsigned pos);
1199 #include <isl/local_space.h>
1200 __isl_give isl_local_space *isl_local_space_set_dim_id(
1201 __isl_take isl_local_space *ls,
1202 enum isl_dim_type type, unsigned pos,
1203 __isl_take isl_id *id);
1204 isl_bool isl_local_space_has_dim_id(
1205 __isl_keep isl_local_space *ls,
1206 enum isl_dim_type type, unsigned pos);
1207 __isl_give isl_id *isl_local_space_get_dim_id(
1208 __isl_keep isl_local_space *ls,
1209 enum isl_dim_type type, unsigned pos);
1210 __isl_give isl_local_space *isl_local_space_set_dim_name(
1211 __isl_take isl_local_space *ls,
1212 enum isl_dim_type type, unsigned pos, const char *s);
1213 isl_bool isl_local_space_has_dim_name(
1214 __isl_keep isl_local_space *ls,
1215 enum isl_dim_type type, unsigned pos)
1216 const char *isl_local_space_get_dim_name(
1217 __isl_keep isl_local_space *ls,
1218 enum isl_dim_type type, unsigned pos);
1220 #include <isl/constraint.h>
1221 const char *isl_constraint_get_dim_name(
1222 __isl_keep isl_constraint *constraint,
1223 enum isl_dim_type type, unsigned pos);
1225 #include <isl/set.h>
1226 __isl_give isl_id *isl_basic_set_get_dim_id(
1227 __isl_keep isl_basic_set *bset,
1228 enum isl_dim_type type, unsigned pos);
1229 __isl_give isl_set *isl_set_set_dim_id(
1230 __isl_take isl_set *set, enum isl_dim_type type,
1231 unsigned pos, __isl_take isl_id *id);
1232 isl_bool isl_set_has_dim_id(__isl_keep isl_set *set,
1233 enum isl_dim_type type, unsigned pos);
1234 __isl_give isl_id *isl_set_get_dim_id(
1235 __isl_keep isl_set *set, enum isl_dim_type type,
1237 const char *isl_basic_set_get_dim_name(
1238 __isl_keep isl_basic_set *bset,
1239 enum isl_dim_type type, unsigned pos);
1240 isl_bool isl_set_has_dim_name(__isl_keep isl_set *set,
1241 enum isl_dim_type type, unsigned pos);
1242 const char *isl_set_get_dim_name(
1243 __isl_keep isl_set *set,
1244 enum isl_dim_type type, unsigned pos);
1246 #include <isl/map.h>
1247 __isl_give isl_map *isl_map_set_dim_id(
1248 __isl_take isl_map *map, enum isl_dim_type type,
1249 unsigned pos, __isl_take isl_id *id);
1250 isl_bool isl_basic_map_has_dim_id(
1251 __isl_keep isl_basic_map *bmap,
1252 enum isl_dim_type type, unsigned pos);
1253 isl_bool isl_map_has_dim_id(__isl_keep isl_map *map,
1254 enum isl_dim_type type, unsigned pos);
1255 __isl_give isl_id *isl_map_get_dim_id(
1256 __isl_keep isl_map *map, enum isl_dim_type type,
1258 __isl_give isl_id *isl_union_map_get_dim_id(
1259 __isl_keep isl_union_map *umap,
1260 enum isl_dim_type type, unsigned pos);
1261 const char *isl_basic_map_get_dim_name(
1262 __isl_keep isl_basic_map *bmap,
1263 enum isl_dim_type type, unsigned pos);
1264 isl_bool isl_map_has_dim_name(__isl_keep isl_map *map,
1265 enum isl_dim_type type, unsigned pos);
1266 const char *isl_map_get_dim_name(
1267 __isl_keep isl_map *map,
1268 enum isl_dim_type type, unsigned pos);
1270 #include <isl/val.h>
1271 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1272 __isl_take isl_multi_val *mv,
1273 enum isl_dim_type type, unsigned pos,
1274 __isl_take isl_id *id);
1275 __isl_give isl_id *isl_multi_val_get_dim_id(
1276 __isl_keep isl_multi_val *mv,
1277 enum isl_dim_type type, unsigned pos);
1278 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1279 __isl_take isl_multi_val *mv,
1280 enum isl_dim_type type, unsigned pos, const char *s);
1282 #include <isl/aff.h>
1283 __isl_give isl_aff *isl_aff_set_dim_id(
1284 __isl_take isl_aff *aff, enum isl_dim_type type,
1285 unsigned pos, __isl_take isl_id *id);
1286 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1287 __isl_take isl_multi_aff *maff,
1288 enum isl_dim_type type, unsigned pos,
1289 __isl_take isl_id *id);
1290 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1291 __isl_take isl_pw_aff *pma,
1292 enum isl_dim_type type, unsigned pos,
1293 __isl_take isl_id *id);
1294 __isl_give isl_multi_pw_aff *
1295 isl_multi_pw_aff_set_dim_id(
1296 __isl_take isl_multi_pw_aff *mpa,
1297 enum isl_dim_type type, unsigned pos,
1298 __isl_take isl_id *id);
1299 __isl_give isl_multi_union_pw_aff *
1300 isl_multi_union_pw_aff_set_dim_id(
1301 __isl_take isl_multi_union_pw_aff *mupa,
1302 enum isl_dim_type type, unsigned pos,
1303 __isl_take isl_id *id);
1304 __isl_give isl_id *isl_multi_aff_get_dim_id(
1305 __isl_keep isl_multi_aff *ma,
1306 enum isl_dim_type type, unsigned pos);
1307 isl_bool isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1308 enum isl_dim_type type, unsigned pos);
1309 __isl_give isl_id *isl_pw_aff_get_dim_id(
1310 __isl_keep isl_pw_aff *pa,
1311 enum isl_dim_type type, unsigned pos);
1312 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1313 __isl_keep isl_pw_multi_aff *pma,
1314 enum isl_dim_type type, unsigned pos);
1315 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1316 __isl_keep isl_multi_pw_aff *mpa,
1317 enum isl_dim_type type, unsigned pos);
1318 __isl_give isl_id *isl_multi_union_pw_aff_get_dim_id(
1319 __isl_keep isl_multi_union_pw_aff *mupa,
1320 enum isl_dim_type type, unsigned pos);
1321 __isl_give isl_aff *isl_aff_set_dim_name(
1322 __isl_take isl_aff *aff, enum isl_dim_type type,
1323 unsigned pos, const char *s);
1324 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1325 __isl_take isl_multi_aff *maff,
1326 enum isl_dim_type type, unsigned pos, const char *s);
1327 __isl_give isl_multi_pw_aff *
1328 isl_multi_pw_aff_set_dim_name(
1329 __isl_take isl_multi_pw_aff *mpa,
1330 enum isl_dim_type type, unsigned pos, const char *s);
1331 __isl_give isl_union_pw_aff *
1332 isl_union_pw_aff_set_dim_name(
1333 __isl_take isl_union_pw_aff *upa,
1334 enum isl_dim_type type, unsigned pos,
1336 __isl_give isl_union_pw_multi_aff *
1337 isl_union_pw_multi_aff_set_dim_name(
1338 __isl_take isl_union_pw_multi_aff *upma,
1339 enum isl_dim_type type, unsigned pos,
1341 __isl_give isl_multi_union_pw_aff *
1342 isl_multi_union_pw_aff_set_dim_name(
1343 __isl_take isl_multi_union_pw_aff *mupa,
1344 enum isl_dim_type type, unsigned pos,
1345 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1346 enum isl_dim_type type, unsigned pos);
1347 const char *isl_pw_aff_get_dim_name(
1348 __isl_keep isl_pw_aff *pa,
1349 enum isl_dim_type type, unsigned pos);
1350 const char *isl_pw_multi_aff_get_dim_name(
1351 __isl_keep isl_pw_multi_aff *pma,
1352 enum isl_dim_type type, unsigned pos);
1354 #include <isl/polynomial.h>
1355 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1356 __isl_take isl_qpolynomial *qp,
1357 enum isl_dim_type type, unsigned pos,
1359 __isl_give isl_pw_qpolynomial *
1360 isl_pw_qpolynomial_set_dim_name(
1361 __isl_take isl_pw_qpolynomial *pwqp,
1362 enum isl_dim_type type, unsigned pos,
1364 __isl_give isl_pw_qpolynomial_fold *
1365 isl_pw_qpolynomial_fold_set_dim_name(
1366 __isl_take isl_pw_qpolynomial_fold *pwf,
1367 enum isl_dim_type type, unsigned pos,
1369 __isl_give isl_union_pw_qpolynomial *
1370 isl_union_pw_qpolynomial_set_dim_name(
1371 __isl_take isl_union_pw_qpolynomial *upwqp,
1372 enum isl_dim_type type, unsigned pos,
1374 __isl_give isl_union_pw_qpolynomial_fold *
1375 isl_union_pw_qpolynomial_fold_set_dim_name(
1376 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1377 enum isl_dim_type type, unsigned pos,
1380 Note that C<isl_space_get_name> returns a pointer to some internal
1381 data structure, so the result can only be used while the
1382 corresponding C<isl_space> is alive.
1383 Also note that every function that operates on two sets or relations
1384 requires that both arguments have the same parameters. This also
1385 means that if one of the arguments has named parameters, then the
1386 other needs to have named parameters too and the names need to match.
1387 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1388 arguments may have different parameters (as long as they are named),
1389 in which case the result will have as parameters the union of the parameters of
1392 Given the identifier or name of a dimension (typically a parameter),
1393 its position can be obtained from the following functions.
1395 #include <isl/space.h>
1396 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1397 enum isl_dim_type type, __isl_keep isl_id *id);
1398 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1399 enum isl_dim_type type, const char *name);
1401 #include <isl/local_space.h>
1402 int isl_local_space_find_dim_by_name(
1403 __isl_keep isl_local_space *ls,
1404 enum isl_dim_type type, const char *name);
1406 #include <isl/val.h>
1407 int isl_multi_val_find_dim_by_id(
1408 __isl_keep isl_multi_val *mv,
1409 enum isl_dim_type type, __isl_keep isl_id *id);
1410 int isl_multi_val_find_dim_by_name(
1411 __isl_keep isl_multi_val *mv,
1412 enum isl_dim_type type, const char *name);
1414 #include <isl/set.h>
1415 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1416 enum isl_dim_type type, __isl_keep isl_id *id);
1417 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1418 enum isl_dim_type type, const char *name);
1420 #include <isl/map.h>
1421 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1422 enum isl_dim_type type, __isl_keep isl_id *id);
1423 int isl_basic_map_find_dim_by_name(
1424 __isl_keep isl_basic_map *bmap,
1425 enum isl_dim_type type, const char *name);
1426 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1427 enum isl_dim_type type, const char *name);
1428 int isl_union_map_find_dim_by_name(
1429 __isl_keep isl_union_map *umap,
1430 enum isl_dim_type type, const char *name);
1432 #include <isl/aff.h>
1433 int isl_multi_aff_find_dim_by_id(
1434 __isl_keep isl_multi_aff *ma,
1435 enum isl_dim_type type, __isl_keep isl_id *id);
1436 int isl_multi_pw_aff_find_dim_by_id(
1437 __isl_keep isl_multi_pw_aff *mpa,
1438 enum isl_dim_type type, __isl_keep isl_id *id);
1439 int isl_multi_union_pw_aff_find_dim_by_id(
1440 __isl_keep isl_union_multi_pw_aff *mupa,
1441 enum isl_dim_type type, __isl_keep isl_id *id);
1442 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff,
1443 enum isl_dim_type type, const char *name);
1444 int isl_multi_aff_find_dim_by_name(
1445 __isl_keep isl_multi_aff *ma,
1446 enum isl_dim_type type, const char *name);
1447 int isl_pw_aff_find_dim_by_name(__isl_keep isl_pw_aff *pa,
1448 enum isl_dim_type type, const char *name);
1449 int isl_multi_pw_aff_find_dim_by_name(
1450 __isl_keep isl_multi_pw_aff *mpa,
1451 enum isl_dim_type type, const char *name);
1452 int isl_pw_multi_aff_find_dim_by_name(
1453 __isl_keep isl_pw_multi_aff *pma,
1454 enum isl_dim_type type, const char *name);
1455 int isl_union_pw_aff_find_dim_by_name(
1456 __isl_keep isl_union_pw_aff *upa,
1457 enum isl_dim_type type, const char *name);
1458 int isl_union_pw_multi_aff_find_dim_by_name(
1459 __isl_keep isl_union_pw_multi_aff *upma,
1460 enum isl_dim_type type, const char *name);
1461 int isl_multi_union_pw_aff_find_dim_by_name(
1462 __isl_keep isl_multi_union_pw_aff *mupa,
1463 enum isl_dim_type type, const char *name);
1465 #include <isl/polynomial.h>
1466 int isl_pw_qpolynomial_find_dim_by_name(
1467 __isl_keep isl_pw_qpolynomial *pwqp,
1468 enum isl_dim_type type, const char *name);
1469 int isl_pw_qpolynomial_fold_find_dim_by_name(
1470 __isl_keep isl_pw_qpolynomial_fold *pwf,
1471 enum isl_dim_type type, const char *name);
1472 int isl_union_pw_qpolynomial_find_dim_by_name(
1473 __isl_keep isl_union_pw_qpolynomial *upwqp,
1474 enum isl_dim_type type, const char *name);
1475 int isl_union_pw_qpolynomial_fold_find_dim_by_name(
1476 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1477 enum isl_dim_type type, const char *name);
1479 The identifiers or names of entire spaces may be set or read off
1480 using the following functions.
1482 #include <isl/space.h>
1483 __isl_give isl_space *isl_space_set_tuple_id(
1484 __isl_take isl_space *space,
1485 enum isl_dim_type type, __isl_take isl_id *id);
1486 __isl_give isl_space *isl_space_reset_tuple_id(
1487 __isl_take isl_space *space, enum isl_dim_type type);
1488 isl_bool isl_space_has_tuple_id(
1489 __isl_keep isl_space *space,
1490 enum isl_dim_type type);
1491 __isl_give isl_id *isl_space_get_tuple_id(
1492 __isl_keep isl_space *space, enum isl_dim_type type);
1493 __isl_give isl_space *isl_space_set_tuple_name(
1494 __isl_take isl_space *space,
1495 enum isl_dim_type type, const char *s);
1496 isl_bool isl_space_has_tuple_name(
1497 __isl_keep isl_space *space,
1498 enum isl_dim_type type);
1499 __isl_keep const char *isl_space_get_tuple_name(
1500 __isl_keep isl_space *space,
1501 enum isl_dim_type type);
1503 #include <isl/local_space.h>
1504 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1505 __isl_take isl_local_space *ls,
1506 enum isl_dim_type type, __isl_take isl_id *id);
1508 #include <isl/set.h>
1509 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1510 __isl_take isl_basic_set *bset,
1511 __isl_take isl_id *id);
1512 __isl_give isl_set *isl_set_set_tuple_id(
1513 __isl_take isl_set *set, __isl_take isl_id *id);
1514 __isl_give isl_set *isl_set_reset_tuple_id(
1515 __isl_take isl_set *set);
1516 isl_bool isl_set_has_tuple_id(__isl_keep isl_set *set);
1517 __isl_give isl_id *isl_set_get_tuple_id(
1518 __isl_keep isl_set *set);
1519 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1520 __isl_take isl_basic_set *set, const char *s);
1521 __isl_give isl_set *isl_set_set_tuple_name(
1522 __isl_take isl_set *set, const char *s);
1523 const char *isl_basic_set_get_tuple_name(
1524 __isl_keep isl_basic_set *bset);
1525 isl_bool isl_set_has_tuple_name(__isl_keep isl_set *set);
1526 const char *isl_set_get_tuple_name(
1527 __isl_keep isl_set *set);
1529 #include <isl/map.h>
1530 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1531 __isl_take isl_basic_map *bmap,
1532 enum isl_dim_type type, __isl_take isl_id *id);
1533 __isl_give isl_map *isl_map_set_tuple_id(
1534 __isl_take isl_map *map, enum isl_dim_type type,
1535 __isl_take isl_id *id);
1536 __isl_give isl_map *isl_map_reset_tuple_id(
1537 __isl_take isl_map *map, enum isl_dim_type type);
1538 isl_bool isl_map_has_tuple_id(__isl_keep isl_map *map,
1539 enum isl_dim_type type);
1540 __isl_give isl_id *isl_map_get_tuple_id(
1541 __isl_keep isl_map *map, enum isl_dim_type type);
1542 __isl_give isl_map *isl_map_set_tuple_name(
1543 __isl_take isl_map *map,
1544 enum isl_dim_type type, const char *s);
1545 const char *isl_basic_map_get_tuple_name(
1546 __isl_keep isl_basic_map *bmap,
1547 enum isl_dim_type type);
1548 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1549 __isl_take isl_basic_map *bmap,
1550 enum isl_dim_type type, const char *s);
1551 isl_bool isl_map_has_tuple_name(__isl_keep isl_map *map,
1552 enum isl_dim_type type);
1553 const char *isl_map_get_tuple_name(
1554 __isl_keep isl_map *map,
1555 enum isl_dim_type type);
1557 #include <isl/val.h>
1558 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1559 __isl_take isl_multi_val *mv,
1560 enum isl_dim_type type, __isl_take isl_id *id);
1561 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1562 __isl_take isl_multi_val *mv,
1563 enum isl_dim_type type);
1564 isl_bool isl_multi_val_has_tuple_id(
1565 __isl_keep isl_multi_val *mv,
1566 enum isl_dim_type type);
1567 __isl_give isl_id *isl_multi_val_get_tuple_id(
1568 __isl_keep isl_multi_val *mv,
1569 enum isl_dim_type type);
1570 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1571 __isl_take isl_multi_val *mv,
1572 enum isl_dim_type type, const char *s);
1573 const char *isl_multi_val_get_tuple_name(
1574 __isl_keep isl_multi_val *mv,
1575 enum isl_dim_type type);
1577 #include <isl/aff.h>
1578 __isl_give isl_aff *isl_aff_set_tuple_id(
1579 __isl_take isl_aff *aff,
1580 enum isl_dim_type type, __isl_take isl_id *id);
1581 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1582 __isl_take isl_multi_aff *maff,
1583 enum isl_dim_type type, __isl_take isl_id *id);
1584 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1585 __isl_take isl_pw_aff *pwaff,
1586 enum isl_dim_type type, __isl_take isl_id *id);
1587 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1588 __isl_take isl_pw_multi_aff *pma,
1589 enum isl_dim_type type, __isl_take isl_id *id);
1590 __isl_give isl_multi_union_pw_aff *
1591 isl_multi_union_pw_aff_set_tuple_id(
1592 __isl_take isl_multi_union_pw_aff *mupa,
1593 enum isl_dim_type type, __isl_take isl_id *id);
1594 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1595 __isl_take isl_multi_aff *ma,
1596 enum isl_dim_type type);
1597 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1598 __isl_take isl_pw_aff *pa,
1599 enum isl_dim_type type);
1600 __isl_give isl_multi_pw_aff *
1601 isl_multi_pw_aff_reset_tuple_id(
1602 __isl_take isl_multi_pw_aff *mpa,
1603 enum isl_dim_type type);
1604 __isl_give isl_pw_multi_aff *
1605 isl_pw_multi_aff_reset_tuple_id(
1606 __isl_take isl_pw_multi_aff *pma,
1607 enum isl_dim_type type);
1608 __isl_give isl_multi_union_pw_aff *
1609 isl_multi_union_pw_aff_reset_tuple_id(
1610 __isl_take isl_multi_union_pw_aff *mupa,
1611 enum isl_dim_type type);
1612 isl_bool isl_multi_aff_has_tuple_id(
1613 __isl_keep isl_multi_aff *ma,
1614 enum isl_dim_type type);
1615 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1616 __isl_keep isl_multi_aff *ma,
1617 enum isl_dim_type type);
1618 isl_bool isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1619 enum isl_dim_type type);
1620 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1621 __isl_keep isl_pw_aff *pa,
1622 enum isl_dim_type type);
1623 isl_bool isl_pw_multi_aff_has_tuple_id(
1624 __isl_keep isl_pw_multi_aff *pma,
1625 enum isl_dim_type type);
1626 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1627 __isl_keep isl_pw_multi_aff *pma,
1628 enum isl_dim_type type);
1629 isl_bool isl_multi_pw_aff_has_tuple_id(
1630 __isl_keep isl_multi_pw_aff *mpa,
1631 enum isl_dim_type type);
1632 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1633 __isl_keep isl_multi_pw_aff *mpa,
1634 enum isl_dim_type type);
1635 isl_bool isl_multi_union_pw_aff_has_tuple_id(
1636 __isl_keep isl_multi_union_pw_aff *mupa,
1637 enum isl_dim_type type);
1638 __isl_give isl_id *isl_multi_union_pw_aff_get_tuple_id(
1639 __isl_keep isl_multi_union_pw_aff *mupa,
1640 enum isl_dim_type type);
1641 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1642 __isl_take isl_multi_aff *maff,
1643 enum isl_dim_type type, const char *s);
1644 __isl_give isl_multi_pw_aff *
1645 isl_multi_pw_aff_set_tuple_name(
1646 __isl_take isl_multi_pw_aff *mpa,
1647 enum isl_dim_type type, const char *s);
1648 __isl_give isl_multi_union_pw_aff *
1649 isl_multi_union_pw_aff_set_tuple_name(
1650 __isl_take isl_multi_union_pw_aff *mupa,
1651 enum isl_dim_type type, const char *s);
1652 const char *isl_multi_aff_get_tuple_name(
1653 __isl_keep isl_multi_aff *multi,
1654 enum isl_dim_type type);
1655 isl_bool isl_pw_multi_aff_has_tuple_name(
1656 __isl_keep isl_pw_multi_aff *pma,
1657 enum isl_dim_type type);
1658 const char *isl_pw_multi_aff_get_tuple_name(
1659 __isl_keep isl_pw_multi_aff *pma,
1660 enum isl_dim_type type);
1661 const char *isl_multi_union_pw_aff_get_tuple_name(
1662 __isl_keep isl_multi_union_pw_aff *mupa,
1663 enum isl_dim_type type);
1665 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1666 or C<isl_dim_set>. As with C<isl_space_get_name>,
1667 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1669 Binary operations require the corresponding spaces of their arguments
1670 to have the same name.
1672 To keep the names of all parameters and tuples, but reset the user pointers
1673 of all the corresponding identifiers, use the following function.
1675 #include <isl/space.h>
1676 __isl_give isl_space *isl_space_reset_user(
1677 __isl_take isl_space *space);
1679 #include <isl/set.h>
1680 __isl_give isl_set *isl_set_reset_user(
1681 __isl_take isl_set *set);
1683 #include <isl/map.h>
1684 __isl_give isl_map *isl_map_reset_user(
1685 __isl_take isl_map *map);
1687 #include <isl/union_set.h>
1688 __isl_give isl_union_set *isl_union_set_reset_user(
1689 __isl_take isl_union_set *uset);
1691 #include <isl/union_map.h>
1692 __isl_give isl_union_map *isl_union_map_reset_user(
1693 __isl_take isl_union_map *umap);
1695 #include <isl/val.h>
1696 __isl_give isl_multi_val *isl_multi_val_reset_user(
1697 __isl_take isl_multi_val *mv);
1699 #include <isl/aff.h>
1700 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1701 __isl_take isl_multi_aff *ma);
1702 __isl_give isl_pw_aff *isl_pw_aff_reset_user(
1703 __isl_take isl_pw_aff *pa);
1704 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1705 __isl_take isl_multi_pw_aff *mpa);
1706 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_reset_user(
1707 __isl_take isl_pw_multi_aff *pma);
1708 __isl_give isl_union_pw_aff *isl_union_pw_aff_reset_user(
1709 __isl_take isl_union_pw_aff *upa);
1710 __isl_give isl_multi_union_pw_aff *
1711 isl_multi_union_pw_aff_reset_user(
1712 __isl_take isl_multi_union_pw_aff *mupa);
1713 __isl_give isl_union_pw_multi_aff *
1714 isl_union_pw_multi_aff_reset_user(
1715 __isl_take isl_union_pw_multi_aff *upma);
1717 #include <isl/polynomial.h>
1718 __isl_give isl_pw_qpolynomial *
1719 isl_pw_qpolynomial_reset_user(
1720 __isl_take isl_pw_qpolynomial *pwqp);
1721 __isl_give isl_union_pw_qpolynomial *
1722 isl_union_pw_qpolynomial_reset_user(
1723 __isl_take isl_union_pw_qpolynomial *upwqp);
1724 __isl_give isl_pw_qpolynomial_fold *
1725 isl_pw_qpolynomial_fold_reset_user(
1726 __isl_take isl_pw_qpolynomial_fold *pwf);
1727 __isl_give isl_union_pw_qpolynomial_fold *
1728 isl_union_pw_qpolynomial_fold_reset_user(
1729 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1731 Spaces can be nested. In particular, the domain of a set or
1732 the domain or range of a relation can be a nested relation.
1733 This process is also called I<wrapping>.
1734 The functions for detecting, constructing and deconstructing
1735 such nested spaces can be found in the wrapping properties
1736 of L</"Unary Properties">, the wrapping operations
1737 of L</"Unary Operations"> and the Cartesian product operations
1738 of L</"Basic Operations">.
1740 Spaces can be created from other spaces
1741 using the functions described in L</"Unary Operations">
1742 and L</"Binary Operations">.
1746 A local space is essentially a space with
1747 zero or more existentially quantified variables.
1748 The local space of various objects can be obtained
1749 using the following functions.
1751 #include <isl/constraint.h>
1752 __isl_give isl_local_space *isl_constraint_get_local_space(
1753 __isl_keep isl_constraint *constraint);
1755 #include <isl/set.h>
1756 __isl_give isl_local_space *isl_basic_set_get_local_space(
1757 __isl_keep isl_basic_set *bset);
1759 #include <isl/map.h>
1760 __isl_give isl_local_space *isl_basic_map_get_local_space(
1761 __isl_keep isl_basic_map *bmap);
1763 #include <isl/aff.h>
1764 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1765 __isl_keep isl_aff *aff);
1766 __isl_give isl_local_space *isl_aff_get_local_space(
1767 __isl_keep isl_aff *aff);
1769 A new local space can be created from a space using
1771 #include <isl/local_space.h>
1772 __isl_give isl_local_space *isl_local_space_from_space(
1773 __isl_take isl_space *space);
1775 They can be inspected, modified, copied and freed using the following functions.
1777 #include <isl/local_space.h>
1778 isl_bool isl_local_space_is_params(
1779 __isl_keep isl_local_space *ls);
1780 isl_bool isl_local_space_is_set(
1781 __isl_keep isl_local_space *ls);
1782 __isl_give isl_space *isl_local_space_get_space(
1783 __isl_keep isl_local_space *ls);
1784 __isl_give isl_aff *isl_local_space_get_div(
1785 __isl_keep isl_local_space *ls, int pos);
1786 __isl_give isl_local_space *isl_local_space_copy(
1787 __isl_keep isl_local_space *ls);
1788 __isl_null isl_local_space *isl_local_space_free(
1789 __isl_take isl_local_space *ls);
1791 Note that C<isl_local_space_get_div> can only be used on local spaces
1794 Two local spaces can be compared using
1796 isl_bool isl_local_space_is_equal(
1797 __isl_keep isl_local_space *ls1,
1798 __isl_keep isl_local_space *ls2);
1800 Local spaces can be created from other local spaces
1801 using the functions described in L</"Unary Operations">
1802 and L</"Binary Operations">.
1804 =head2 Creating New Sets and Relations
1806 C<isl> has functions for creating some standard sets and relations.
1810 =item * Empty sets and relations
1812 __isl_give isl_basic_set *isl_basic_set_empty(
1813 __isl_take isl_space *space);
1814 __isl_give isl_basic_map *isl_basic_map_empty(
1815 __isl_take isl_space *space);
1816 __isl_give isl_set *isl_set_empty(
1817 __isl_take isl_space *space);
1818 __isl_give isl_map *isl_map_empty(
1819 __isl_take isl_space *space);
1820 __isl_give isl_union_set *isl_union_set_empty(
1821 __isl_take isl_space *space);
1822 __isl_give isl_union_map *isl_union_map_empty(
1823 __isl_take isl_space *space);
1825 For C<isl_union_set>s and C<isl_union_map>s, the space
1826 is only used to specify the parameters.
1828 =item * Universe sets and relations
1830 __isl_give isl_basic_set *isl_basic_set_universe(
1831 __isl_take isl_space *space);
1832 __isl_give isl_basic_map *isl_basic_map_universe(
1833 __isl_take isl_space *space);
1834 __isl_give isl_set *isl_set_universe(
1835 __isl_take isl_space *space);
1836 __isl_give isl_map *isl_map_universe(
1837 __isl_take isl_space *space);
1838 __isl_give isl_union_set *isl_union_set_universe(
1839 __isl_take isl_union_set *uset);
1840 __isl_give isl_union_map *isl_union_map_universe(
1841 __isl_take isl_union_map *umap);
1843 The sets and relations constructed by the functions above
1844 contain all integer values, while those constructed by the
1845 functions below only contain non-negative values.
1847 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1848 __isl_take isl_space *space);
1849 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1850 __isl_take isl_space *space);
1851 __isl_give isl_set *isl_set_nat_universe(
1852 __isl_take isl_space *space);
1853 __isl_give isl_map *isl_map_nat_universe(
1854 __isl_take isl_space *space);
1856 =item * Identity relations
1858 __isl_give isl_basic_map *isl_basic_map_identity(
1859 __isl_take isl_space *space);
1860 __isl_give isl_map *isl_map_identity(
1861 __isl_take isl_space *space);
1863 The number of input and output dimensions in C<space> needs
1866 =item * Lexicographic order
1868 __isl_give isl_map *isl_map_lex_lt(
1869 __isl_take isl_space *set_space);
1870 __isl_give isl_map *isl_map_lex_le(
1871 __isl_take isl_space *set_space);
1872 __isl_give isl_map *isl_map_lex_gt(
1873 __isl_take isl_space *set_space);
1874 __isl_give isl_map *isl_map_lex_ge(
1875 __isl_take isl_space *set_space);
1876 __isl_give isl_map *isl_map_lex_lt_first(
1877 __isl_take isl_space *space, unsigned n);
1878 __isl_give isl_map *isl_map_lex_le_first(
1879 __isl_take isl_space *space, unsigned n);
1880 __isl_give isl_map *isl_map_lex_gt_first(
1881 __isl_take isl_space *space, unsigned n);
1882 __isl_give isl_map *isl_map_lex_ge_first(
1883 __isl_take isl_space *space, unsigned n);
1885 The first four functions take a space for a B<set>
1886 and return relations that express that the elements in the domain
1887 are lexicographically less
1888 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1889 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1890 than the elements in the range.
1891 The last four functions take a space for a map
1892 and return relations that express that the first C<n> dimensions
1893 in the domain are lexicographically less
1894 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1895 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1896 than the first C<n> dimensions in the range.
1900 A basic set or relation can be converted to a set or relation
1901 using the following functions.
1903 __isl_give isl_set *isl_set_from_basic_set(
1904 __isl_take isl_basic_set *bset);
1905 __isl_give isl_map *isl_map_from_basic_map(
1906 __isl_take isl_basic_map *bmap);
1908 Sets and relations can be converted to union sets and relations
1909 using the following functions.
1911 __isl_give isl_union_set *isl_union_set_from_basic_set(
1912 __isl_take isl_basic_set *bset);
1913 __isl_give isl_union_map *isl_union_map_from_basic_map(
1914 __isl_take isl_basic_map *bmap);
1915 __isl_give isl_union_set *isl_union_set_from_set(
1916 __isl_take isl_set *set);
1917 __isl_give isl_union_map *isl_union_map_from_map(
1918 __isl_take isl_map *map);
1920 The inverse conversions below can only be used if the input
1921 union set or relation is known to contain elements in exactly one
1924 __isl_give isl_set *isl_set_from_union_set(
1925 __isl_take isl_union_set *uset);
1926 __isl_give isl_map *isl_map_from_union_map(
1927 __isl_take isl_union_map *umap);
1929 Sets and relations can be copied and freed again using the following
1932 __isl_give isl_basic_set *isl_basic_set_copy(
1933 __isl_keep isl_basic_set *bset);
1934 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1935 __isl_give isl_union_set *isl_union_set_copy(
1936 __isl_keep isl_union_set *uset);
1937 __isl_give isl_basic_map *isl_basic_map_copy(
1938 __isl_keep isl_basic_map *bmap);
1939 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1940 __isl_give isl_union_map *isl_union_map_copy(
1941 __isl_keep isl_union_map *umap);
1942 __isl_null isl_basic_set *isl_basic_set_free(
1943 __isl_take isl_basic_set *bset);
1944 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1945 __isl_null isl_union_set *isl_union_set_free(
1946 __isl_take isl_union_set *uset);
1947 __isl_null isl_basic_map *isl_basic_map_free(
1948 __isl_take isl_basic_map *bmap);
1949 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1950 __isl_null isl_union_map *isl_union_map_free(
1951 __isl_take isl_union_map *umap);
1953 Other sets and relations can be constructed by starting
1954 from a universe set or relation, adding equality and/or
1955 inequality constraints and then projecting out the
1956 existentially quantified variables, if any.
1957 Constraints can be constructed, manipulated and
1958 added to (or removed from) (basic) sets and relations
1959 using the following functions.
1961 #include <isl/constraint.h>
1962 __isl_give isl_constraint *isl_constraint_alloc_equality(
1963 __isl_take isl_local_space *ls);
1964 __isl_give isl_constraint *isl_constraint_alloc_inequality(
1965 __isl_take isl_local_space *ls);
1966 __isl_give isl_constraint *isl_constraint_set_constant_si(
1967 __isl_take isl_constraint *constraint, int v);
1968 __isl_give isl_constraint *isl_constraint_set_constant_val(
1969 __isl_take isl_constraint *constraint,
1970 __isl_take isl_val *v);
1971 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1972 __isl_take isl_constraint *constraint,
1973 enum isl_dim_type type, int pos, int v);
1974 __isl_give isl_constraint *
1975 isl_constraint_set_coefficient_val(
1976 __isl_take isl_constraint *constraint,
1977 enum isl_dim_type type, int pos,
1978 __isl_take isl_val *v);
1979 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1980 __isl_take isl_basic_map *bmap,
1981 __isl_take isl_constraint *constraint);
1982 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1983 __isl_take isl_basic_set *bset,
1984 __isl_take isl_constraint *constraint);
1985 __isl_give isl_map *isl_map_add_constraint(
1986 __isl_take isl_map *map,
1987 __isl_take isl_constraint *constraint);
1988 __isl_give isl_set *isl_set_add_constraint(
1989 __isl_take isl_set *set,
1990 __isl_take isl_constraint *constraint);
1992 For example, to create a set containing the even integers
1993 between 10 and 42, you would use the following code.
1996 isl_local_space *ls;
1998 isl_basic_set *bset;
2000 space = isl_space_set_alloc(ctx, 0, 2);
2001 bset = isl_basic_set_universe(isl_space_copy(space));
2002 ls = isl_local_space_from_space(space);
2004 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
2005 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2006 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
2007 bset = isl_basic_set_add_constraint(bset, c);
2009 c = isl_constraint_alloc_inequality(isl_local_space_copy(ls));
2010 c = isl_constraint_set_constant_si(c, -10);
2011 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
2012 bset = isl_basic_set_add_constraint(bset, c);
2014 c = isl_constraint_alloc_inequality(ls);
2015 c = isl_constraint_set_constant_si(c, 42);
2016 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2017 bset = isl_basic_set_add_constraint(bset, c);
2019 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
2023 isl_basic_set *bset;
2024 bset = isl_basic_set_read_from_str(ctx,
2025 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
2027 A basic set or relation can also be constructed from two matrices
2028 describing the equalities and the inequalities.
2030 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
2031 __isl_take isl_space *space,
2032 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2033 enum isl_dim_type c1,
2034 enum isl_dim_type c2, enum isl_dim_type c3,
2035 enum isl_dim_type c4);
2036 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
2037 __isl_take isl_space *space,
2038 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2039 enum isl_dim_type c1,
2040 enum isl_dim_type c2, enum isl_dim_type c3,
2041 enum isl_dim_type c4, enum isl_dim_type c5);
2043 The C<isl_dim_type> arguments indicate the order in which
2044 different kinds of variables appear in the input matrices
2045 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
2046 C<isl_dim_set> and C<isl_dim_div> for sets and
2047 of C<isl_dim_cst>, C<isl_dim_param>,
2048 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
2050 A (basic or union) set or relation can also be constructed from a
2051 (union) (piecewise) (multiple) affine expression
2052 or a list of affine expressions
2053 (See L</"Functions">), provided these affine expressions do not
2056 __isl_give isl_basic_map *isl_basic_map_from_aff(
2057 __isl_take isl_aff *aff);
2058 __isl_give isl_map *isl_map_from_aff(
2059 __isl_take isl_aff *aff);
2060 __isl_give isl_set *isl_set_from_pw_aff(
2061 __isl_take isl_pw_aff *pwaff);
2062 __isl_give isl_map *isl_map_from_pw_aff(
2063 __isl_take isl_pw_aff *pwaff);
2064 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
2065 __isl_take isl_space *domain_space,
2066 __isl_take isl_aff_list *list);
2067 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
2068 __isl_take isl_multi_aff *maff)
2069 __isl_give isl_map *isl_map_from_multi_aff(
2070 __isl_take isl_multi_aff *maff)
2071 __isl_give isl_set *isl_set_from_pw_multi_aff(
2072 __isl_take isl_pw_multi_aff *pma);
2073 __isl_give isl_map *isl_map_from_pw_multi_aff(
2074 __isl_take isl_pw_multi_aff *pma);
2075 __isl_give isl_set *isl_set_from_multi_pw_aff(
2076 __isl_take isl_multi_pw_aff *mpa);
2077 __isl_give isl_map *isl_map_from_multi_pw_aff(
2078 __isl_take isl_multi_pw_aff *mpa);
2079 __isl_give isl_union_map *isl_union_map_from_union_pw_aff(
2080 __isl_take isl_union_pw_aff *upa);
2081 __isl_give isl_union_map *
2082 isl_union_map_from_union_pw_multi_aff(
2083 __isl_take isl_union_pw_multi_aff *upma);
2084 __isl_give isl_union_map *
2085 isl_union_map_from_multi_union_pw_aff(
2086 __isl_take isl_multi_union_pw_aff *mupa);
2088 The C<domain_space> argument describes the domain of the resulting
2089 basic relation. It is required because the C<list> may consist
2090 of zero affine expressions.
2091 The C<mupa> passed to C<isl_union_map_from_multi_union_pw_aff>
2092 is not allowed to be zero-dimensional. The domain of the result
2093 is the shared domain of the union piecewise affine elements.
2095 =head2 Inspecting Sets and Relations
2097 Usually, the user should not have to care about the actual constraints
2098 of the sets and maps, but should instead apply the abstract operations
2099 explained in the following sections.
2100 Occasionally, however, it may be required to inspect the individual
2101 coefficients of the constraints. This section explains how to do so.
2102 In these cases, it may also be useful to have C<isl> compute
2103 an explicit representation of the existentially quantified variables.
2105 __isl_give isl_set *isl_set_compute_divs(
2106 __isl_take isl_set *set);
2107 __isl_give isl_map *isl_map_compute_divs(
2108 __isl_take isl_map *map);
2109 __isl_give isl_union_set *isl_union_set_compute_divs(
2110 __isl_take isl_union_set *uset);
2111 __isl_give isl_union_map *isl_union_map_compute_divs(
2112 __isl_take isl_union_map *umap);
2114 This explicit representation defines the existentially quantified
2115 variables as integer divisions of the other variables, possibly
2116 including earlier existentially quantified variables.
2117 An explicitly represented existentially quantified variable therefore
2118 has a unique value when the values of the other variables are known.
2120 Alternatively, the existentially quantified variables can be removed
2121 using the following functions, which compute an overapproximation.
2123 #include <isl/set.h>
2124 __isl_give isl_basic_set *isl_basic_set_remove_divs(
2125 __isl_take isl_basic_set *bset);
2126 __isl_give isl_set *isl_set_remove_divs(
2127 __isl_take isl_set *set);
2129 #include <isl/map.h>
2130 __isl_give isl_basic_map *isl_basic_map_remove_divs(
2131 __isl_take isl_basic_map *bmap);
2132 __isl_give isl_map *isl_map_remove_divs(
2133 __isl_take isl_map *map);
2135 #include <isl/union_set.h>
2136 __isl_give isl_union_set *isl_union_set_remove_divs(
2137 __isl_take isl_union_set *bset);
2139 #include <isl/union_map.h>
2140 __isl_give isl_union_map *isl_union_map_remove_divs(
2141 __isl_take isl_union_map *bmap);
2143 It is also possible to only remove those divs that are defined
2144 in terms of a given range of dimensions or only those for which
2145 no explicit representation is known.
2147 __isl_give isl_basic_set *
2148 isl_basic_set_remove_divs_involving_dims(
2149 __isl_take isl_basic_set *bset,
2150 enum isl_dim_type type,
2151 unsigned first, unsigned n);
2152 __isl_give isl_basic_map *
2153 isl_basic_map_remove_divs_involving_dims(
2154 __isl_take isl_basic_map *bmap,
2155 enum isl_dim_type type,
2156 unsigned first, unsigned n);
2157 __isl_give isl_set *isl_set_remove_divs_involving_dims(
2158 __isl_take isl_set *set, enum isl_dim_type type,
2159 unsigned first, unsigned n);
2160 __isl_give isl_map *isl_map_remove_divs_involving_dims(
2161 __isl_take isl_map *map, enum isl_dim_type type,
2162 unsigned first, unsigned n);
2164 __isl_give isl_basic_set *
2165 isl_basic_set_remove_unknown_divs(
2166 __isl_take isl_basic_set *bset);
2167 __isl_give isl_set *isl_set_remove_unknown_divs(
2168 __isl_take isl_set *set);
2169 __isl_give isl_map *isl_map_remove_unknown_divs(
2170 __isl_take isl_map *map);
2172 To iterate over all the sets or maps in a union set or map, use
2174 #include <isl/union_set.h>
2175 isl_stat isl_union_set_foreach_set(
2176 __isl_keep isl_union_set *uset,
2177 isl_stat (*fn)(__isl_take isl_set *set, void *user),
2180 #include <isl/union_map.h>
2181 isl_stat isl_union_map_foreach_map(
2182 __isl_keep isl_union_map *umap,
2183 isl_stat (*fn)(__isl_take isl_map *map, void *user),
2185 isl_bool isl_union_map_every_map(
2186 __isl_keep isl_union_map *umap,
2187 isl_bool (*test)(__isl_keep isl_map *map,
2191 These functions call the callback function once for each
2192 (pair of) space(s) for which there are elements in the input.
2193 The argument to the callback contains all elements in the input
2194 with that (pair of) space(s).
2195 The C<isl_union_map_every_map> variant check whether each
2196 call to the callback returns true and stops checking as soon as one
2197 of these calls returns false.
2199 The number of sets or maps in a union set or map can be obtained
2202 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
2203 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
2205 To extract the set or map in a given space from a union, use
2207 __isl_give isl_set *isl_union_set_extract_set(
2208 __isl_keep isl_union_set *uset,
2209 __isl_take isl_space *space);
2210 __isl_give isl_map *isl_union_map_extract_map(
2211 __isl_keep isl_union_map *umap,
2212 __isl_take isl_space *space);
2214 To iterate over all the basic sets or maps in a set or map, use
2216 isl_stat isl_set_foreach_basic_set(__isl_keep isl_set *set,
2217 isl_stat (*fn)(__isl_take isl_basic_set *bset,
2220 isl_stat isl_map_foreach_basic_map(__isl_keep isl_map *map,
2221 isl_stat (*fn)(__isl_take isl_basic_map *bmap,
2225 The callback function C<fn> should return C<isl_stat_ok> if successful and
2226 C<isl_stat_error> if an error occurs. In the latter case, or if any other error
2227 occurs, the above functions will return C<isl_stat_error>.
2229 It should be noted that C<isl> does not guarantee that
2230 the basic sets or maps passed to C<fn> are disjoint.
2231 If this is required, then the user should call one of
2232 the following functions first.
2234 __isl_give isl_set *isl_set_make_disjoint(
2235 __isl_take isl_set *set);
2236 __isl_give isl_map *isl_map_make_disjoint(
2237 __isl_take isl_map *map);
2239 The number of basic sets in a set can be obtained
2240 or the number of basic maps in a map can be obtained
2243 #include <isl/set.h>
2244 int isl_set_n_basic_set(__isl_keep isl_set *set);
2246 #include <isl/map.h>
2247 int isl_map_n_basic_map(__isl_keep isl_map *map);
2249 It is also possible to obtain a list of basic sets from a set
2252 #include <isl/set.h>
2253 __isl_give isl_basic_set_list *isl_set_get_basic_set_list(
2254 __isl_keep isl_set *set);
2256 #include <isl/union_set.h>
2257 __isl_give isl_basic_set_list *
2258 isl_union_set_get_basic_set_list(
2259 __isl_keep isl_union_set *uset);
2261 The returned list can be manipulated using the functions in L<"Lists">.
2263 To iterate over the constraints of a basic set or map, use
2265 #include <isl/constraint.h>
2267 int isl_basic_set_n_constraint(
2268 __isl_keep isl_basic_set *bset);
2269 isl_stat isl_basic_set_foreach_constraint(
2270 __isl_keep isl_basic_set *bset,
2271 isl_stat (*fn)(__isl_take isl_constraint *c,
2274 int isl_basic_map_n_constraint(
2275 __isl_keep isl_basic_map *bmap);
2276 isl_stat isl_basic_map_foreach_constraint(
2277 __isl_keep isl_basic_map *bmap,
2278 isl_stat (*fn)(__isl_take isl_constraint *c,
2281 __isl_null isl_constraint *isl_constraint_free(
2282 __isl_take isl_constraint *c);
2284 Again, the callback function C<fn> should return C<isl_stat_ok>
2286 C<isl_stat_error> if an error occurs. In the latter case, or if any other error
2287 occurs, the above functions will return C<isl_stat_error>.
2288 The constraint C<c> represents either an equality or an inequality.
2289 Use the following function to find out whether a constraint
2290 represents an equality. If not, it represents an inequality.
2292 isl_bool isl_constraint_is_equality(
2293 __isl_keep isl_constraint *constraint);
2295 It is also possible to obtain a list of constraints from a basic
2298 #include <isl/constraint.h>
2299 __isl_give isl_constraint_list *
2300 isl_basic_map_get_constraint_list(
2301 __isl_keep isl_basic_map *bmap);
2302 __isl_give isl_constraint_list *
2303 isl_basic_set_get_constraint_list(
2304 __isl_keep isl_basic_set *bset);
2306 These functions require that all existentially quantified variables
2307 have an explicit representation.
2308 The returned list can be manipulated using the functions in L<"Lists">.
2310 The coefficients of the constraints can be inspected using
2311 the following functions.
2313 isl_bool isl_constraint_is_lower_bound(
2314 __isl_keep isl_constraint *constraint,
2315 enum isl_dim_type type, unsigned pos);
2316 isl_bool isl_constraint_is_upper_bound(
2317 __isl_keep isl_constraint *constraint,
2318 enum isl_dim_type type, unsigned pos);
2319 __isl_give isl_val *isl_constraint_get_constant_val(
2320 __isl_keep isl_constraint *constraint);
2321 __isl_give isl_val *isl_constraint_get_coefficient_val(
2322 __isl_keep isl_constraint *constraint,
2323 enum isl_dim_type type, int pos);
2325 The explicit representations of the existentially quantified
2326 variables can be inspected using the following function.
2327 Note that the user is only allowed to use this function
2328 if the inspected set or map is the result of a call
2329 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2330 The existentially quantified variable is equal to the floor
2331 of the returned affine expression. The affine expression
2332 itself can be inspected using the functions in
2335 __isl_give isl_aff *isl_constraint_get_div(
2336 __isl_keep isl_constraint *constraint, int pos);
2338 To obtain the constraints of a basic set or map in matrix
2339 form, use the following functions.
2341 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2342 __isl_keep isl_basic_set *bset,
2343 enum isl_dim_type c1, enum isl_dim_type c2,
2344 enum isl_dim_type c3, enum isl_dim_type c4);
2345 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2346 __isl_keep isl_basic_set *bset,
2347 enum isl_dim_type c1, enum isl_dim_type c2,
2348 enum isl_dim_type c3, enum isl_dim_type c4);
2349 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2350 __isl_keep isl_basic_map *bmap,
2351 enum isl_dim_type c1,
2352 enum isl_dim_type c2, enum isl_dim_type c3,
2353 enum isl_dim_type c4, enum isl_dim_type c5);
2354 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2355 __isl_keep isl_basic_map *bmap,
2356 enum isl_dim_type c1,
2357 enum isl_dim_type c2, enum isl_dim_type c3,
2358 enum isl_dim_type c4, enum isl_dim_type c5);
2360 The C<isl_dim_type> arguments dictate the order in which
2361 different kinds of variables appear in the resulting matrix.
2362 For set inputs, they should be a permutation of
2363 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
2364 For map inputs, they should be a permutation of
2365 C<isl_dim_cst>, C<isl_dim_param>,
2366 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2370 Points are elements of a set. They can be used to construct
2371 simple sets (boxes) or they can be used to represent the
2372 individual elements of a set.
2373 The zero point (the origin) can be created using
2375 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2377 The coordinates of a point can be inspected, set and changed
2380 __isl_give isl_val *isl_point_get_coordinate_val(
2381 __isl_keep isl_point *pnt,
2382 enum isl_dim_type type, int pos);
2383 __isl_give isl_point *isl_point_set_coordinate_val(
2384 __isl_take isl_point *pnt,
2385 enum isl_dim_type type, int pos,
2386 __isl_take isl_val *v);
2388 __isl_give isl_point *isl_point_add_ui(
2389 __isl_take isl_point *pnt,
2390 enum isl_dim_type type, int pos, unsigned val);
2391 __isl_give isl_point *isl_point_sub_ui(
2392 __isl_take isl_point *pnt,
2393 enum isl_dim_type type, int pos, unsigned val);
2395 Points can be copied or freed using
2397 __isl_give isl_point *isl_point_copy(
2398 __isl_keep isl_point *pnt);
2399 __isl_null isl_point *isl_point_free(
2400 __isl_take isl_point *pnt);
2402 A singleton set can be created from a point using
2404 __isl_give isl_basic_set *isl_basic_set_from_point(
2405 __isl_take isl_point *pnt);
2406 __isl_give isl_set *isl_set_from_point(
2407 __isl_take isl_point *pnt);
2408 __isl_give isl_union_set *isl_union_set_from_point(
2409 __isl_take isl_point *pnt);
2411 and a box can be created from two opposite extremal points using
2413 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2414 __isl_take isl_point *pnt1,
2415 __isl_take isl_point *pnt2);
2416 __isl_give isl_set *isl_set_box_from_points(
2417 __isl_take isl_point *pnt1,
2418 __isl_take isl_point *pnt2);
2420 All elements of a B<bounded> (union) set can be enumerated using
2421 the following functions.
2423 isl_stat isl_set_foreach_point(__isl_keep isl_set *set,
2424 isl_stat (*fn)(__isl_take isl_point *pnt,
2427 isl_stat isl_union_set_foreach_point(
2428 __isl_keep isl_union_set *uset,
2429 isl_stat (*fn)(__isl_take isl_point *pnt,
2433 The function C<fn> is called for each integer point in
2434 C<set> with as second argument the last argument of
2435 the C<isl_set_foreach_point> call. The function C<fn>
2436 should return C<isl_stat_ok> on success and C<isl_stat_error> on failure.
2437 In the latter case, C<isl_set_foreach_point> will stop
2438 enumerating and return C<isl_stat_error> as well.
2439 If the enumeration is performed successfully and to completion,
2440 then C<isl_set_foreach_point> returns C<isl_stat_ok>.
2442 To obtain a single point of a (basic or union) set, use
2444 __isl_give isl_point *isl_basic_set_sample_point(
2445 __isl_take isl_basic_set *bset);
2446 __isl_give isl_point *isl_set_sample_point(
2447 __isl_take isl_set *set);
2448 __isl_give isl_point *isl_union_set_sample_point(
2449 __isl_take isl_union_set *uset);
2451 If C<set> does not contain any (integer) points, then the
2452 resulting point will be ``void'', a property that can be
2455 isl_bool isl_point_is_void(__isl_keep isl_point *pnt);
2459 Besides sets and relation, C<isl> also supports various types of functions.
2460 Each of these types is derived from the value type (see L</"Values">)
2461 or from one of two primitive function types
2462 through the application of zero or more type constructors.
2463 We first describe the primitive type and then we describe
2464 the types derived from these primitive types.
2466 =head3 Primitive Functions
2468 C<isl> support two primitive function types, quasi-affine
2469 expressions and quasipolynomials.
2470 A quasi-affine expression is defined either over a parameter
2471 space or over a set and is composed of integer constants,
2472 parameters and set variables, addition, subtraction and
2473 integer division by an integer constant.
2474 For example, the quasi-affine expression
2476 [n] -> { [x] -> [2*floor((4 n + x)/9)] }
2478 maps C<x> to C<2*floor((4 n + x)/9>.
2479 A quasipolynomial is a polynomial expression in quasi-affine
2480 expression. That is, it additionally allows for multiplication.
2481 Note, though, that it is not allowed to construct an integer
2482 division of an expression involving multiplications.
2483 Here is an example of a quasipolynomial that is not
2484 quasi-affine expression
2486 [n] -> { [x] -> (n*floor((4 n + x)/9)) }
2488 Note that the external representations of quasi-affine expressions
2489 and quasipolynomials are different. Quasi-affine expressions
2490 use a notation with square brackets just like binary relations,
2491 while quasipolynomials do not. This might change at some point.
2493 If a primitive function is defined over a parameter space,
2494 then the space of the function itself is that of a set.
2495 If it is defined over a set, then the space of the function
2496 is that of a relation. In both cases, the set space (or
2497 the output space) is single-dimensional, anonymous and unstructured.
2498 To create functions with multiple dimensions or with other kinds
2499 of set or output spaces, use multiple expressions
2500 (see L</"Multiple Expressions">).
2504 =item * Quasi-affine Expressions
2506 Besides the expressions described above, a quasi-affine
2507 expression can also be set to NaN. Such expressions
2508 typically represent a failure to represent a result
2509 as a quasi-affine expression.
2511 The zero quasi affine expression or the quasi affine expression
2512 that is equal to a given value or
2513 a specified dimension on a given domain can be created using
2515 #include <isl/aff.h>
2516 __isl_give isl_aff *isl_aff_zero_on_domain(
2517 __isl_take isl_local_space *ls);
2518 __isl_give isl_aff *isl_aff_val_on_domain(
2519 __isl_take isl_local_space *ls,
2520 __isl_take isl_val *val);
2521 __isl_give isl_aff *isl_aff_var_on_domain(
2522 __isl_take isl_local_space *ls,
2523 enum isl_dim_type type, unsigned pos);
2524 __isl_give isl_aff *isl_aff_nan_on_domain(
2525 __isl_take isl_local_space *ls);
2527 Quasi affine expressions can be copied and freed using
2529 #include <isl/aff.h>
2530 __isl_give isl_aff *isl_aff_copy(
2531 __isl_keep isl_aff *aff);
2532 __isl_null isl_aff *isl_aff_free(
2533 __isl_take isl_aff *aff);
2535 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2536 using the following function. The constraint is required to have
2537 a non-zero coefficient for the specified dimension.
2539 #include <isl/constraint.h>
2540 __isl_give isl_aff *isl_constraint_get_bound(
2541 __isl_keep isl_constraint *constraint,
2542 enum isl_dim_type type, int pos);
2544 The entire affine expression of the constraint can also be extracted
2545 using the following function.
2547 #include <isl/constraint.h>
2548 __isl_give isl_aff *isl_constraint_get_aff(
2549 __isl_keep isl_constraint *constraint);
2551 Conversely, an equality constraint equating
2552 the affine expression to zero or an inequality constraint enforcing
2553 the affine expression to be non-negative, can be constructed using
2555 __isl_give isl_constraint *isl_equality_from_aff(
2556 __isl_take isl_aff *aff);
2557 __isl_give isl_constraint *isl_inequality_from_aff(
2558 __isl_take isl_aff *aff);
2560 The coefficients and the integer divisions of an affine expression
2561 can be inspected using the following functions.
2563 #include <isl/aff.h>
2564 __isl_give isl_val *isl_aff_get_constant_val(
2565 __isl_keep isl_aff *aff);
2566 __isl_give isl_val *isl_aff_get_coefficient_val(
2567 __isl_keep isl_aff *aff,
2568 enum isl_dim_type type, int pos);
2569 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2570 enum isl_dim_type type, int pos);
2571 __isl_give isl_val *isl_aff_get_denominator_val(
2572 __isl_keep isl_aff *aff);
2573 __isl_give isl_aff *isl_aff_get_div(
2574 __isl_keep isl_aff *aff, int pos);
2576 They can be modified using the following functions.
2578 #include <isl/aff.h>
2579 __isl_give isl_aff *isl_aff_set_constant_si(
2580 __isl_take isl_aff *aff, int v);
2581 __isl_give isl_aff *isl_aff_set_constant_val(
2582 __isl_take isl_aff *aff, __isl_take isl_val *v);
2583 __isl_give isl_aff *isl_aff_set_coefficient_si(
2584 __isl_take isl_aff *aff,
2585 enum isl_dim_type type, int pos, int v);
2586 __isl_give isl_aff *isl_aff_set_coefficient_val(
2587 __isl_take isl_aff *aff,
2588 enum isl_dim_type type, int pos,
2589 __isl_take isl_val *v);
2591 __isl_give isl_aff *isl_aff_add_constant_si(
2592 __isl_take isl_aff *aff, int v);
2593 __isl_give isl_aff *isl_aff_add_constant_val(
2594 __isl_take isl_aff *aff, __isl_take isl_val *v);
2595 __isl_give isl_aff *isl_aff_add_constant_num_si(
2596 __isl_take isl_aff *aff, int v);
2597 __isl_give isl_aff *isl_aff_add_coefficient_si(
2598 __isl_take isl_aff *aff,
2599 enum isl_dim_type type, int pos, int v);
2600 __isl_give isl_aff *isl_aff_add_coefficient_val(
2601 __isl_take isl_aff *aff,
2602 enum isl_dim_type type, int pos,
2603 __isl_take isl_val *v);
2605 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
2606 set the I<numerator> of the constant or coefficient, while
2607 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
2608 the constant or coefficient as a whole.
2609 The C<add_constant> and C<add_coefficient> functions add an integer
2610 or rational value to
2611 the possibly rational constant or coefficient.
2612 The C<add_constant_num> functions add an integer value to
2615 =item * Quasipolynomials
2617 Some simple quasipolynomials can be created using the following functions.
2619 #include <isl/polynomial.h>
2620 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2621 __isl_take isl_space *domain);
2622 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2623 __isl_take isl_space *domain);
2624 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2625 __isl_take isl_space *domain);
2626 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2627 __isl_take isl_space *domain);
2628 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2629 __isl_take isl_space *domain);
2630 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2631 __isl_take isl_space *domain,
2632 __isl_take isl_val *val);
2633 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2634 __isl_take isl_space *domain,
2635 enum isl_dim_type type, unsigned pos);
2636 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2637 __isl_take isl_aff *aff);
2639 Recall that the space in which a quasipolynomial lives is a map space
2640 with a one-dimensional range. The C<domain> argument in some of
2641 the functions above corresponds to the domain of this map space.
2643 Quasipolynomials can be copied and freed again using the following
2646 #include <isl/polynomial.h>
2647 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2648 __isl_keep isl_qpolynomial *qp);
2649 __isl_null isl_qpolynomial *isl_qpolynomial_free(
2650 __isl_take isl_qpolynomial *qp);
2652 The constant term of a quasipolynomial can be extracted using
2654 __isl_give isl_val *isl_qpolynomial_get_constant_val(
2655 __isl_keep isl_qpolynomial *qp);
2657 To iterate over all terms in a quasipolynomial,
2660 isl_stat isl_qpolynomial_foreach_term(
2661 __isl_keep isl_qpolynomial *qp,
2662 isl_stat (*fn)(__isl_take isl_term *term,
2663 void *user), void *user);
2665 The terms themselves can be inspected and freed using
2668 unsigned isl_term_dim(__isl_keep isl_term *term,
2669 enum isl_dim_type type);
2670 __isl_give isl_val *isl_term_get_coefficient_val(
2671 __isl_keep isl_term *term);
2672 int isl_term_get_exp(__isl_keep isl_term *term,
2673 enum isl_dim_type type, unsigned pos);
2674 __isl_give isl_aff *isl_term_get_div(
2675 __isl_keep isl_term *term, unsigned pos);
2676 void isl_term_free(__isl_take isl_term *term);
2678 Each term is a product of parameters, set variables and
2679 integer divisions. The function C<isl_term_get_exp>
2680 returns the exponent of a given dimensions in the given term.
2686 A reduction represents a maximum or a minimum of its
2688 The only reduction type defined by C<isl> is
2689 C<isl_qpolynomial_fold>.
2691 There are currently no functions to directly create such
2692 objects, but they do appear in the piecewise quasipolynomial
2693 reductions returned by the C<isl_pw_qpolynomial_bound> function.
2695 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
2697 Reductions can be copied and freed using
2698 the following functions.
2700 #include <isl/polynomial.h>
2701 __isl_give isl_qpolynomial_fold *
2702 isl_qpolynomial_fold_copy(
2703 __isl_keep isl_qpolynomial_fold *fold);
2704 void isl_qpolynomial_fold_free(
2705 __isl_take isl_qpolynomial_fold *fold);
2707 To iterate over all quasipolynomials in a reduction, use
2709 isl_stat isl_qpolynomial_fold_foreach_qpolynomial(
2710 __isl_keep isl_qpolynomial_fold *fold,
2711 isl_stat (*fn)(__isl_take isl_qpolynomial *qp,
2712 void *user), void *user);
2714 =head3 Multiple Expressions
2716 A multiple expression represents a sequence of zero or
2717 more base expressions, all defined on the same domain space.
2718 The domain space of the multiple expression is the same
2719 as that of the base expressions, but the range space
2720 can be any space. In case the base expressions have
2721 a set space, the corresponding multiple expression
2722 also has a set space.
2723 Objects of the value type do not have an associated space.
2724 The space of a multiple value is therefore always a set space.
2725 Similarly, the space of a multiple union piecewise
2726 affine expression is always a set space.
2728 The multiple expression types defined by C<isl>
2729 are C<isl_multi_val>, C<isl_multi_aff>, C<isl_multi_pw_aff>,
2730 C<isl_multi_union_pw_aff>.
2732 A multiple expression with the value zero for
2733 each output (or set) dimension can be created
2734 using the following functions.
2736 #include <isl/val.h>
2737 __isl_give isl_multi_val *isl_multi_val_zero(
2738 __isl_take isl_space *space);
2740 #include <isl/aff.h>
2741 __isl_give isl_multi_aff *isl_multi_aff_zero(
2742 __isl_take isl_space *space);
2743 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
2744 __isl_take isl_space *space);
2745 __isl_give isl_multi_union_pw_aff *
2746 isl_multi_union_pw_aff_zero(
2747 __isl_take isl_space *space);
2749 Since there is no canonical way of representing a zero
2750 value of type C<isl_union_pw_aff>, the space passed
2751 to C<isl_multi_union_pw_aff_zero> needs to be zero-dimensional.
2753 An identity function can be created using the following
2754 functions. The space needs to be that of a relation
2755 with the same number of input and output dimensions.
2757 #include <isl/aff.h>
2758 __isl_give isl_multi_aff *isl_multi_aff_identity(
2759 __isl_take isl_space *space);
2760 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
2761 __isl_take isl_space *space);
2763 A function that performs a projection on a universe
2764 relation or set can be created using the following functions.
2765 See also the corresponding
2766 projection operations in L</"Unary Operations">.
2768 #include <isl/aff.h>
2769 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
2770 __isl_take isl_space *space);
2771 __isl_give isl_multi_aff *isl_multi_aff_range_map(
2772 __isl_take isl_space *space);
2773 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
2774 __isl_take isl_space *space,
2775 enum isl_dim_type type,
2776 unsigned first, unsigned n);
2778 A multiple expression can be created from a single
2779 base expression using the following functions.
2780 The space of the created multiple expression is the same
2781 as that of the base expression, except for
2782 C<isl_multi_union_pw_aff_from_union_pw_aff> where the input
2783 lives in a parameter space and the output lives
2784 in a single-dimensional set space.
2786 #include <isl/aff.h>
2787 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
2788 __isl_take isl_aff *aff);
2789 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
2790 __isl_take isl_pw_aff *pa);
2791 __isl_give isl_multi_union_pw_aff *
2792 isl_multi_union_pw_aff_from_union_pw_aff(
2793 __isl_take isl_union_pw_aff *upa);
2795 A multiple expression can be created from a list
2796 of base expression in a specified space.
2797 The domain of this space needs to be the same
2798 as the domains of the base expressions in the list.
2799 If the base expressions have a set space (or no associated space),
2800 then this space also needs to be a set space.
2802 #include <isl/val.h>
2803 __isl_give isl_multi_val *isl_multi_val_from_val_list(
2804 __isl_take isl_space *space,
2805 __isl_take isl_val_list *list);
2807 #include <isl/aff.h>
2808 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2809 __isl_take isl_space *space,
2810 __isl_take isl_aff_list *list);
2811 __isl_give isl_multi_pw_aff *
2812 isl_multi_pw_aff_from_pw_aff_list(
2813 __isl_take isl_space *space,
2814 __isl_take isl_pw_aff_list *list);
2815 __isl_give isl_multi_union_pw_aff *
2816 isl_multi_union_pw_aff_from_union_pw_aff_list(
2817 __isl_take isl_space *space,
2818 __isl_take isl_union_pw_aff_list *list);
2820 As a convenience, a multiple piecewise expression can
2821 also be created from a multiple expression.
2822 Each piecewise expression in the result has a single
2825 #include <isl/aff.h>
2826 __isl_give isl_multi_pw_aff *
2827 isl_multi_pw_aff_from_multi_aff(
2828 __isl_take isl_multi_aff *ma);
2830 Similarly, a multiple union expression can be
2831 created from a multiple expression.
2833 #include <isl/aff.h>
2834 __isl_give isl_multi_union_pw_aff *
2835 isl_multi_union_pw_aff_from_multi_aff(
2836 __isl_take isl_multi_aff *ma);
2837 __isl_give isl_multi_union_pw_aff *
2838 isl_multi_union_pw_aff_from_multi_pw_aff(
2839 __isl_take isl_multi_pw_aff *mpa);
2841 A multiple quasi-affine expression can be created from
2842 a multiple value with a given domain space using the following
2845 #include <isl/aff.h>
2846 __isl_give isl_multi_aff *
2847 isl_multi_aff_multi_val_on_space(
2848 __isl_take isl_space *space,
2849 __isl_take isl_multi_val *mv);
2852 a multiple union piecewise affine expression can be created from
2853 a multiple value with a given domain or
2854 a (piecewise) multiple affine expression with a given domain
2855 using the following functions.
2857 #include <isl/aff.h>
2858 __isl_give isl_multi_union_pw_aff *
2859 isl_multi_union_pw_aff_multi_val_on_domain(
2860 __isl_take isl_union_set *domain,
2861 __isl_take isl_multi_val *mv);
2862 __isl_give isl_multi_union_pw_aff *
2863 isl_multi_union_pw_aff_multi_aff_on_domain(
2864 __isl_take isl_union_set *domain,
2865 __isl_take isl_multi_aff *ma);
2866 __isl_give isl_multi_union_pw_aff *
2867 isl_multi_union_pw_aff_pw_multi_aff_on_domain(
2868 __isl_take isl_union_set *domain,
2869 __isl_take isl_pw_multi_aff *pma);
2871 Multiple expressions can be copied and freed using
2872 the following functions.
2874 #include <isl/val.h>
2875 __isl_give isl_multi_val *isl_multi_val_copy(
2876 __isl_keep isl_multi_val *mv);
2877 __isl_null isl_multi_val *isl_multi_val_free(
2878 __isl_take isl_multi_val *mv);
2880 #include <isl/aff.h>
2881 __isl_give isl_multi_aff *isl_multi_aff_copy(
2882 __isl_keep isl_multi_aff *maff);
2883 __isl_null isl_multi_aff *isl_multi_aff_free(
2884 __isl_take isl_multi_aff *maff);
2885 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
2886 __isl_keep isl_multi_pw_aff *mpa);
2887 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
2888 __isl_take isl_multi_pw_aff *mpa);
2889 __isl_give isl_multi_union_pw_aff *
2890 isl_multi_union_pw_aff_copy(
2891 __isl_keep isl_multi_union_pw_aff *mupa);
2892 __isl_null isl_multi_union_pw_aff *
2893 isl_multi_union_pw_aff_free(
2894 __isl_take isl_multi_union_pw_aff *mupa);
2896 The base expression at a given position of a multiple
2897 expression can be extracted using the following functions.
2899 #include <isl/val.h>
2900 __isl_give isl_val *isl_multi_val_get_val(
2901 __isl_keep isl_multi_val *mv, int pos);
2903 #include <isl/aff.h>
2904 __isl_give isl_aff *isl_multi_aff_get_aff(
2905 __isl_keep isl_multi_aff *multi, int pos);
2906 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
2907 __isl_keep isl_multi_pw_aff *mpa, int pos);
2908 __isl_give isl_union_pw_aff *
2909 isl_multi_union_pw_aff_get_union_pw_aff(
2910 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
2912 It can be replaced using the following functions.
2914 #include <isl/val.h>
2915 __isl_give isl_multi_val *isl_multi_val_set_val(
2916 __isl_take isl_multi_val *mv, int pos,
2917 __isl_take isl_val *val);
2919 #include <isl/aff.h>
2920 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
2921 __isl_take isl_multi_aff *multi, int pos,
2922 __isl_take isl_aff *aff);
2923 __isl_give isl_multi_union_pw_aff *
2924 isl_multi_union_pw_aff_set_union_pw_aff(
2925 __isl_take isl_multi_union_pw_aff *mupa, int pos,
2926 __isl_take isl_union_pw_aff *upa);
2928 As a convenience, a sequence of base expressions that have
2929 their domains in a given space can be extracted from a sequence
2930 of union expressions using the following function.
2932 #include <isl/aff.h>
2933 __isl_give isl_multi_pw_aff *
2934 isl_multi_union_pw_aff_extract_multi_pw_aff(
2935 __isl_keep isl_multi_union_pw_aff *mupa,
2936 __isl_take isl_space *space);
2938 Note that there is a difference between C<isl_multi_union_pw_aff>
2939 and C<isl_union_pw_multi_aff> objects. The first is a sequence
2940 of unions of piecewise expressions, while the second is a union
2941 of piecewise sequences. In particular, multiple affine expressions
2942 in an C<isl_union_pw_multi_aff> may live in different spaces,
2943 while there is only a single multiple expression in
2944 an C<isl_multi_union_pw_aff>, which can therefore only live
2945 in a single space. This means that not every
2946 C<isl_union_pw_multi_aff> can be converted to
2947 an C<isl_multi_union_pw_aff>. Conversely, a zero-dimensional
2948 C<isl_multi_union_pw_aff> carries no information
2949 about any possible domain and therefore cannot be converted
2950 to an C<isl_union_pw_multi_aff>. Moreover, the elements
2951 of an C<isl_multi_union_pw_aff> may be defined over different domains,
2952 while each multiple expression inside an C<isl_union_pw_multi_aff>
2953 has a single domain. The conversion of an C<isl_union_pw_multi_aff>
2954 of dimension greater than one may therefore not be exact.
2955 The following functions can
2956 be used to perform these conversions when they are possible.
2958 #include <isl/aff.h>
2959 __isl_give isl_multi_union_pw_aff *
2960 isl_multi_union_pw_aff_from_union_pw_multi_aff(
2961 __isl_take isl_union_pw_multi_aff *upma);
2962 __isl_give isl_union_pw_multi_aff *
2963 isl_union_pw_multi_aff_from_multi_union_pw_aff(
2964 __isl_take isl_multi_union_pw_aff *mupa);
2966 =head3 Piecewise Expressions
2968 A piecewise expression is an expression that is described
2969 using zero or more base expression defined over the same
2970 number of cells in the domain space of the base expressions.
2971 All base expressions are defined over the same
2972 domain space and the cells are disjoint.
2973 The space of a piecewise expression is the same as
2974 that of the base expressions.
2975 If the union of the cells is a strict subset of the domain
2976 space, then the value of the piecewise expression outside
2977 this union is different for types derived from quasi-affine
2978 expressions and those derived from quasipolynomials.
2979 Piecewise expressions derived from quasi-affine expressions
2980 are considered to be undefined outside the union of their cells.
2981 Piecewise expressions derived from quasipolynomials
2982 are considered to be zero outside the union of their cells.
2984 Piecewise quasipolynomials are mainly used by the C<barvinok>
2985 library for representing the number of elements in a parametric set or map.
2986 For example, the piecewise quasipolynomial
2988 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2990 represents the number of points in the map
2992 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2994 The piecewise expression types defined by C<isl>
2995 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
2996 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
2998 A piecewise expression with no cells can be created using
2999 the following functions.
3001 #include <isl/aff.h>
3002 __isl_give isl_pw_aff *isl_pw_aff_empty(
3003 __isl_take isl_space *space);
3004 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3005 __isl_take isl_space *space);
3007 A piecewise expression with a single universe cell can be
3008 created using the following functions.
3010 #include <isl/aff.h>
3011 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3012 __isl_take isl_aff *aff);
3013 __isl_give isl_pw_multi_aff *
3014 isl_pw_multi_aff_from_multi_aff(
3015 __isl_take isl_multi_aff *ma);
3017 #include <isl/polynomial.h>
3018 __isl_give isl_pw_qpolynomial *
3019 isl_pw_qpolynomial_from_qpolynomial(
3020 __isl_take isl_qpolynomial *qp);
3022 A piecewise expression with a single specified cell can be
3023 created using the following functions.
3025 #include <isl/aff.h>
3026 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3027 __isl_take isl_set *set, __isl_take isl_aff *aff);
3028 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3029 __isl_take isl_set *set,
3030 __isl_take isl_multi_aff *maff);
3032 #include <isl/polynomial.h>
3033 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3034 __isl_take isl_set *set,
3035 __isl_take isl_qpolynomial *qp);
3037 The following convenience functions first create a base expression and
3038 then create a piecewise expression over a universe domain.
3040 #include <isl/aff.h>
3041 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3042 __isl_take isl_local_space *ls);
3043 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3044 __isl_take isl_local_space *ls,
3045 enum isl_dim_type type, unsigned pos);
3046 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3047 __isl_take isl_local_space *ls);
3048 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
3049 __isl_take isl_space *space);
3050 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3051 __isl_take isl_space *space);
3052 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
3053 __isl_take isl_space *space);
3054 __isl_give isl_pw_multi_aff *
3055 isl_pw_multi_aff_project_out_map(
3056 __isl_take isl_space *space,
3057 enum isl_dim_type type,
3058 unsigned first, unsigned n);
3060 #include <isl/polynomial.h>
3061 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3062 __isl_take isl_space *space);
3064 The following convenience functions first create a base expression and
3065 then create a piecewise expression over a given domain.
3067 #include <isl/aff.h>
3068 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
3069 __isl_take isl_set *domain,
3070 __isl_take isl_val *v);
3071 __isl_give isl_pw_multi_aff *
3072 isl_pw_multi_aff_multi_val_on_domain(
3073 __isl_take isl_set *domain,
3074 __isl_take isl_multi_val *mv);
3076 As a convenience, a piecewise multiple expression can
3077 also be created from a piecewise expression.
3078 Each multiple expression in the result is derived
3079 from the corresponding base expression.
3081 #include <isl/aff.h>
3082 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
3083 __isl_take isl_pw_aff *pa);
3085 Similarly, a piecewise quasipolynomial can be
3086 created from a piecewise quasi-affine expression using
3087 the following function.
3089 #include <isl/polynomial.h>
3090 __isl_give isl_pw_qpolynomial *
3091 isl_pw_qpolynomial_from_pw_aff(
3092 __isl_take isl_pw_aff *pwaff);
3094 Piecewise expressions can be copied and freed using the following functions.
3096 #include <isl/aff.h>
3097 __isl_give isl_pw_aff *isl_pw_aff_copy(
3098 __isl_keep isl_pw_aff *pwaff);
3099 __isl_null isl_pw_aff *isl_pw_aff_free(
3100 __isl_take isl_pw_aff *pwaff);
3101 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3102 __isl_keep isl_pw_multi_aff *pma);
3103 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
3104 __isl_take isl_pw_multi_aff *pma);
3106 #include <isl/polynomial.h>
3107 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3108 __isl_keep isl_pw_qpolynomial *pwqp);
3109 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
3110 __isl_take isl_pw_qpolynomial *pwqp);
3111 __isl_give isl_pw_qpolynomial_fold *
3112 isl_pw_qpolynomial_fold_copy(
3113 __isl_keep isl_pw_qpolynomial_fold *pwf);
3114 __isl_null isl_pw_qpolynomial_fold *
3115 isl_pw_qpolynomial_fold_free(
3116 __isl_take isl_pw_qpolynomial_fold *pwf);
3118 To iterate over the different cells of a piecewise expression,
3119 use the following functions.
3121 #include <isl/aff.h>
3122 isl_bool isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3123 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3124 isl_stat isl_pw_aff_foreach_piece(
3125 __isl_keep isl_pw_aff *pwaff,
3126 isl_stat (*fn)(__isl_take isl_set *set,
3127 __isl_take isl_aff *aff,
3128 void *user), void *user);
3129 int isl_pw_multi_aff_n_piece(
3130 __isl_keep isl_pw_multi_aff *pma);
3131 isl_stat isl_pw_multi_aff_foreach_piece(
3132 __isl_keep isl_pw_multi_aff *pma,
3133 isl_stat (*fn)(__isl_take isl_set *set,
3134 __isl_take isl_multi_aff *maff,
3135 void *user), void *user);
3137 #include <isl/polynomial.h>
3138 int isl_pw_qpolynomial_n_piece(
3139 __isl_keep isl_pw_qpolynomial *pwqp);
3140 isl_stat isl_pw_qpolynomial_foreach_piece(
3141 __isl_keep isl_pw_qpolynomial *pwqp,
3142 isl_stat (*fn)(__isl_take isl_set *set,
3143 __isl_take isl_qpolynomial *qp,
3144 void *user), void *user);
3145 isl_stat isl_pw_qpolynomial_foreach_lifted_piece(
3146 __isl_keep isl_pw_qpolynomial *pwqp,
3147 isl_stat (*fn)(__isl_take isl_set *set,
3148 __isl_take isl_qpolynomial *qp,
3149 void *user), void *user);
3150 int isl_pw_qpolynomial_fold_n_piece(
3151 __isl_keep isl_pw_qpolynomial_fold *pwf);
3152 isl_stat isl_pw_qpolynomial_fold_foreach_piece(
3153 __isl_keep isl_pw_qpolynomial_fold *pwf,
3154 isl_stat (*fn)(__isl_take isl_set *set,
3155 __isl_take isl_qpolynomial_fold *fold,
3156 void *user), void *user);
3157 isl_stat isl_pw_qpolynomial_fold_foreach_lifted_piece(
3158 __isl_keep isl_pw_qpolynomial_fold *pwf,
3159 isl_stat (*fn)(__isl_take isl_set *set,
3160 __isl_take isl_qpolynomial_fold *fold,
3161 void *user), void *user);
3163 As usual, the function C<fn> should return C<isl_stat_ok> on success
3164 and C<isl_stat_error> on failure. The difference between
3165 C<isl_pw_qpolynomial_foreach_piece> and
3166 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3167 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3168 compute unique representations for all existentially quantified
3169 variables and then turn these existentially quantified variables
3170 into extra set variables, adapting the associated quasipolynomial
3171 accordingly. This means that the C<set> passed to C<fn>
3172 will not have any existentially quantified variables, but that
3173 the dimensions of the sets may be different for different
3174 invocations of C<fn>.
3175 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
3176 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
3178 A piecewise expression consisting of the expressions at a given
3179 position of a piecewise multiple expression can be extracted
3180 using the following function.
3182 #include <isl/aff.h>
3183 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3184 __isl_keep isl_pw_multi_aff *pma, int pos);
3186 These expressions can be replaced using the following function.
3188 #include <isl/aff.h>
3189 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3190 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3191 __isl_take isl_pw_aff *pa);
3193 Note that there is a difference between C<isl_multi_pw_aff> and
3194 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
3195 affine expressions, while the second is a piecewise sequence
3196 of affine expressions. In particular, each of the piecewise
3197 affine expressions in an C<isl_multi_pw_aff> may have a different
3198 domain, while all multiple expressions associated to a cell
3199 in an C<isl_pw_multi_aff> have the same domain.
3200 It is possible to convert between the two, but when converting
3201 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
3202 of the result is the intersection of the domains of the input.
3203 The reverse conversion is exact.
3205 #include <isl/aff.h>
3206 __isl_give isl_pw_multi_aff *
3207 isl_pw_multi_aff_from_multi_pw_aff(
3208 __isl_take isl_multi_pw_aff *mpa);
3209 __isl_give isl_multi_pw_aff *
3210 isl_multi_pw_aff_from_pw_multi_aff(
3211 __isl_take isl_pw_multi_aff *pma);
3213 =head3 Union Expressions
3215 A union expression collects base expressions defined
3216 over different domains. The space of a union expression
3217 is that of the shared parameter space.
3219 The union expression types defined by C<isl>
3220 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
3221 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
3223 C<isl_union_pw_aff>,
3224 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>,
3225 there can be at most one base expression for a given domain space.
3227 C<isl_union_pw_multi_aff>,
3228 there can be multiple such expressions for a given domain space,
3229 but the domains of these expressions need to be disjoint.
3231 An empty union expression can be created using the following functions.
3233 #include <isl/aff.h>
3234 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
3235 __isl_take isl_space *space);
3236 __isl_give isl_union_pw_multi_aff *
3237 isl_union_pw_multi_aff_empty(
3238 __isl_take isl_space *space);
3240 #include <isl/polynomial.h>
3241 __isl_give isl_union_pw_qpolynomial *
3242 isl_union_pw_qpolynomial_zero(
3243 __isl_take isl_space *space);
3245 A union expression containing a single base expression
3246 can be created using the following functions.
3248 #include <isl/aff.h>
3249 __isl_give isl_union_pw_aff *
3250 isl_union_pw_aff_from_pw_aff(
3251 __isl_take isl_pw_aff *pa);
3252 __isl_give isl_union_pw_multi_aff *
3253 isl_union_pw_multi_aff_from_aff(
3254 __isl_take isl_aff *aff);
3255 __isl_give isl_union_pw_multi_aff *
3256 isl_union_pw_multi_aff_from_pw_multi_aff(
3257 __isl_take isl_pw_multi_aff *pma);
3259 #include <isl/polynomial.h>
3260 __isl_give isl_union_pw_qpolynomial *
3261 isl_union_pw_qpolynomial_from_pw_qpolynomial(
3262 __isl_take isl_pw_qpolynomial *pwqp);
3264 The following functions create a base expression on each
3265 of the sets in the union set and collect the results.
3267 #include <isl/aff.h>
3268 __isl_give isl_union_pw_multi_aff *
3269 isl_union_pw_multi_aff_from_union_pw_aff(
3270 __isl_take isl_union_pw_aff *upa);
3271 __isl_give isl_union_pw_aff *
3272 isl_union_pw_multi_aff_get_union_pw_aff(
3273 __isl_keep isl_union_pw_multi_aff *upma, int pos);
3274 __isl_give isl_union_pw_aff *
3275 isl_union_pw_aff_val_on_domain(
3276 __isl_take isl_union_set *domain,
3277 __isl_take isl_val *v);
3278 __isl_give isl_union_pw_multi_aff *
3279 isl_union_pw_multi_aff_multi_val_on_domain(
3280 __isl_take isl_union_set *domain,
3281 __isl_take isl_multi_val *mv);
3283 An C<isl_union_pw_aff> that is equal to a (parametric) affine
3285 expression on a given domain can be created using the following
3288 #include <isl/aff.h>
3289 __isl_give isl_union_pw_aff *
3290 isl_union_pw_aff_aff_on_domain(
3291 __isl_take isl_union_set *domain,
3292 __isl_take isl_aff *aff);
3293 __isl_give isl_union_pw_aff *
3294 isl_union_pw_aff_pw_aff_on_domain(
3295 __isl_take isl_union_set *domain,
3296 __isl_take isl_pw_aff *pa);
3298 A base expression can be added to a union expression using
3299 the following functions.
3301 #include <isl/aff.h>
3302 __isl_give isl_union_pw_aff *
3303 isl_union_pw_aff_add_pw_aff(
3304 __isl_take isl_union_pw_aff *upa,
3305 __isl_take isl_pw_aff *pa);
3306 __isl_give isl_union_pw_multi_aff *
3307 isl_union_pw_multi_aff_add_pw_multi_aff(
3308 __isl_take isl_union_pw_multi_aff *upma,
3309 __isl_take isl_pw_multi_aff *pma);
3311 #include <isl/polynomial.h>
3312 __isl_give isl_union_pw_qpolynomial *
3313 isl_union_pw_qpolynomial_add_pw_qpolynomial(
3314 __isl_take isl_union_pw_qpolynomial *upwqp,
3315 __isl_take isl_pw_qpolynomial *pwqp);
3317 Union expressions can be copied and freed using
3318 the following functions.
3320 #include <isl/aff.h>
3321 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
3322 __isl_keep isl_union_pw_aff *upa);
3323 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
3324 __isl_take isl_union_pw_aff *upa);
3325 __isl_give isl_union_pw_multi_aff *
3326 isl_union_pw_multi_aff_copy(
3327 __isl_keep isl_union_pw_multi_aff *upma);
3328 __isl_null isl_union_pw_multi_aff *
3329 isl_union_pw_multi_aff_free(
3330 __isl_take isl_union_pw_multi_aff *upma);
3332 #include <isl/polynomial.h>
3333 __isl_give isl_union_pw_qpolynomial *
3334 isl_union_pw_qpolynomial_copy(
3335 __isl_keep isl_union_pw_qpolynomial *upwqp);
3336 __isl_null isl_union_pw_qpolynomial *
3337 isl_union_pw_qpolynomial_free(
3338 __isl_take isl_union_pw_qpolynomial *upwqp);
3339 __isl_give isl_union_pw_qpolynomial_fold *
3340 isl_union_pw_qpolynomial_fold_copy(
3341 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3342 __isl_null isl_union_pw_qpolynomial_fold *
3343 isl_union_pw_qpolynomial_fold_free(
3344 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3346 To iterate over the base expressions in a union expression,
3347 use the following functions.
3349 #include <isl/aff.h>
3350 int isl_union_pw_aff_n_pw_aff(
3351 __isl_keep isl_union_pw_aff *upa);
3352 isl_stat isl_union_pw_aff_foreach_pw_aff(
3353 __isl_keep isl_union_pw_aff *upa,
3354 isl_stat (*fn)(__isl_take isl_pw_aff *pa,
3355 void *user), void *user);
3356 int isl_union_pw_multi_aff_n_pw_multi_aff(
3357 __isl_keep isl_union_pw_multi_aff *upma);
3358 isl_stat isl_union_pw_multi_aff_foreach_pw_multi_aff(
3359 __isl_keep isl_union_pw_multi_aff *upma,
3360 isl_stat (*fn)(__isl_take isl_pw_multi_aff *pma,
3361 void *user), void *user);
3363 #include <isl/polynomial.h>
3364 int isl_union_pw_qpolynomial_n_pw_qpolynomial(
3365 __isl_keep isl_union_pw_qpolynomial *upwqp);
3366 isl_stat isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3367 __isl_keep isl_union_pw_qpolynomial *upwqp,
3368 isl_stat (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
3369 void *user), void *user);
3370 int isl_union_pw_qpolynomial_fold_n_pw_qpolynomial_fold(
3371 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3372 isl_stat isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3373 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3374 isl_stat (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3375 void *user), void *user);
3377 To extract the base expression in a given space from a union, use
3378 the following functions.
3380 #include <isl/aff.h>
3381 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
3382 __isl_keep isl_union_pw_aff *upa,
3383 __isl_take isl_space *space);
3384 __isl_give isl_pw_multi_aff *
3385 isl_union_pw_multi_aff_extract_pw_multi_aff(
3386 __isl_keep isl_union_pw_multi_aff *upma,
3387 __isl_take isl_space *space);
3389 #include <isl/polynomial.h>
3390 __isl_give isl_pw_qpolynomial *
3391 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3392 __isl_keep isl_union_pw_qpolynomial *upwqp,
3393 __isl_take isl_space *space);
3395 =head2 Input and Output
3397 For set and relation,
3398 C<isl> supports its own input/output format, which is similar
3399 to the C<Omega> format, but also supports the C<PolyLib> format
3401 For other object types, typically only an C<isl> format is supported.
3403 =head3 C<isl> format
3405 The C<isl> format is similar to that of C<Omega>, but has a different
3406 syntax for describing the parameters and allows for the definition
3407 of an existentially quantified variable as the integer division
3408 of an affine expression.
3409 For example, the set of integers C<i> between C<0> and C<n>
3410 such that C<i % 10 <= 6> can be described as
3412 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
3415 A set or relation can have several disjuncts, separated
3416 by the keyword C<or>. Each disjunct is either a conjunction
3417 of constraints or a projection (C<exists>) of a conjunction
3418 of constraints. The constraints are separated by the keyword
3421 =head3 C<PolyLib> format
3423 If the represented set is a union, then the first line
3424 contains a single number representing the number of disjuncts.
3425 Otherwise, a line containing the number C<1> is optional.
3427 Each disjunct is represented by a matrix of constraints.
3428 The first line contains two numbers representing
3429 the number of rows and columns,
3430 where the number of rows is equal to the number of constraints
3431 and the number of columns is equal to two plus the number of variables.
3432 The following lines contain the actual rows of the constraint matrix.
3433 In each row, the first column indicates whether the constraint
3434 is an equality (C<0>) or inequality (C<1>). The final column
3435 corresponds to the constant term.
3437 If the set is parametric, then the coefficients of the parameters
3438 appear in the last columns before the constant column.
3439 The coefficients of any existentially quantified variables appear
3440 between those of the set variables and those of the parameters.
3442 =head3 Extended C<PolyLib> format
3444 The extended C<PolyLib> format is nearly identical to the
3445 C<PolyLib> format. The only difference is that the line
3446 containing the number of rows and columns of a constraint matrix
3447 also contains four additional numbers:
3448 the number of output dimensions, the number of input dimensions,
3449 the number of local dimensions (i.e., the number of existentially
3450 quantified variables) and the number of parameters.
3451 For sets, the number of ``output'' dimensions is equal
3452 to the number of set dimensions, while the number of ``input''
3457 Objects can be read from input using the following functions.
3459 #include <isl/val.h>
3460 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
3462 __isl_give isl_multi_val *isl_multi_val_read_from_str(
3463 isl_ctx *ctx, const char *str);
3465 #include <isl/set.h>
3466 __isl_give isl_basic_set *isl_basic_set_read_from_file(
3467 isl_ctx *ctx, FILE *input);
3468 __isl_give isl_basic_set *isl_basic_set_read_from_str(
3469 isl_ctx *ctx, const char *str);
3470 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
3472 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
3475 #include <isl/map.h>
3476 __isl_give isl_basic_map *isl_basic_map_read_from_file(
3477 isl_ctx *ctx, FILE *input);
3478 __isl_give isl_basic_map *isl_basic_map_read_from_str(
3479 isl_ctx *ctx, const char *str);
3480 __isl_give isl_map *isl_map_read_from_file(
3481 isl_ctx *ctx, FILE *input);
3482 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
3485 #include <isl/union_set.h>
3486 __isl_give isl_union_set *isl_union_set_read_from_file(
3487 isl_ctx *ctx, FILE *input);
3488 __isl_give isl_union_set *isl_union_set_read_from_str(
3489 isl_ctx *ctx, const char *str);
3491 #include <isl/union_map.h>
3492 __isl_give isl_union_map *isl_union_map_read_from_file(
3493 isl_ctx *ctx, FILE *input);
3494 __isl_give isl_union_map *isl_union_map_read_from_str(
3495 isl_ctx *ctx, const char *str);
3497 #include <isl/aff.h>
3498 __isl_give isl_aff *isl_aff_read_from_str(
3499 isl_ctx *ctx, const char *str);
3500 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3501 isl_ctx *ctx, const char *str);
3502 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3503 isl_ctx *ctx, const char *str);
3504 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3505 isl_ctx *ctx, const char *str);
3506 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
3507 isl_ctx *ctx, const char *str);
3508 __isl_give isl_union_pw_aff *
3509 isl_union_pw_aff_read_from_str(
3510 isl_ctx *ctx, const char *str);
3511 __isl_give isl_union_pw_multi_aff *
3512 isl_union_pw_multi_aff_read_from_str(
3513 isl_ctx *ctx, const char *str);
3514 __isl_give isl_multi_union_pw_aff *
3515 isl_multi_union_pw_aff_read_from_str(
3516 isl_ctx *ctx, const char *str);
3518 #include <isl/polynomial.h>
3519 __isl_give isl_union_pw_qpolynomial *
3520 isl_union_pw_qpolynomial_read_from_str(
3521 isl_ctx *ctx, const char *str);
3523 For sets and relations,
3524 the input format is autodetected and may be either the C<PolyLib> format
3525 or the C<isl> format.
3529 Before anything can be printed, an C<isl_printer> needs to
3532 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
3534 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
3535 __isl_null isl_printer *isl_printer_free(
3536 __isl_take isl_printer *printer);
3538 C<isl_printer_to_file> prints to the given file, while
3539 C<isl_printer_to_str> prints to a string that can be extracted
3540 using the following function.
3542 #include <isl/printer.h>
3543 __isl_give char *isl_printer_get_str(
3544 __isl_keep isl_printer *printer);
3546 The printer can be inspected using the following functions.
3548 FILE *isl_printer_get_file(
3549 __isl_keep isl_printer *printer);
3550 int isl_printer_get_output_format(
3551 __isl_keep isl_printer *p);
3552 int isl_printer_get_yaml_style(__isl_keep isl_printer *p);
3554 The behavior of the printer can be modified in various ways
3556 __isl_give isl_printer *isl_printer_set_output_format(
3557 __isl_take isl_printer *p, int output_format);
3558 __isl_give isl_printer *isl_printer_set_indent(
3559 __isl_take isl_printer *p, int indent);
3560 __isl_give isl_printer *isl_printer_set_indent_prefix(
3561 __isl_take isl_printer *p, const char *prefix);
3562 __isl_give isl_printer *isl_printer_indent(
3563 __isl_take isl_printer *p, int indent);
3564 __isl_give isl_printer *isl_printer_set_prefix(
3565 __isl_take isl_printer *p, const char *prefix);
3566 __isl_give isl_printer *isl_printer_set_suffix(
3567 __isl_take isl_printer *p, const char *suffix);
3568 __isl_give isl_printer *isl_printer_set_yaml_style(
3569 __isl_take isl_printer *p, int yaml_style);
3571 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
3572 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
3573 and defaults to C<ISL_FORMAT_ISL>.
3574 Each line in the output is prefixed by C<indent_prefix>,
3575 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
3576 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
3577 In the C<PolyLib> format output,
3578 the coefficients of the existentially quantified variables
3579 appear between those of the set variables and those
3581 The function C<isl_printer_indent> increases the indentation
3582 by the specified amount (which may be negative).
3583 The YAML style may be either C<ISL_YAML_STYLE_BLOCK> or
3584 C<ISL_YAML_STYLE_FLOW> and when we are printing something
3587 To actually print something, use
3589 #include <isl/printer.h>
3590 __isl_give isl_printer *isl_printer_print_double(
3591 __isl_take isl_printer *p, double d);
3593 #include <isl/val.h>
3594 __isl_give isl_printer *isl_printer_print_val(
3595 __isl_take isl_printer *p, __isl_keep isl_val *v);
3597 #include <isl/set.h>
3598 __isl_give isl_printer *isl_printer_print_basic_set(
3599 __isl_take isl_printer *printer,
3600 __isl_keep isl_basic_set *bset);
3601 __isl_give isl_printer *isl_printer_print_set(
3602 __isl_take isl_printer *printer,
3603 __isl_keep isl_set *set);
3605 #include <isl/map.h>
3606 __isl_give isl_printer *isl_printer_print_basic_map(
3607 __isl_take isl_printer *printer,
3608 __isl_keep isl_basic_map *bmap);
3609 __isl_give isl_printer *isl_printer_print_map(
3610 __isl_take isl_printer *printer,
3611 __isl_keep isl_map *map);
3613 #include <isl/union_set.h>
3614 __isl_give isl_printer *isl_printer_print_union_set(
3615 __isl_take isl_printer *p,
3616 __isl_keep isl_union_set *uset);
3618 #include <isl/union_map.h>
3619 __isl_give isl_printer *isl_printer_print_union_map(
3620 __isl_take isl_printer *p,
3621 __isl_keep isl_union_map *umap);
3623 #include <isl/val.h>
3624 __isl_give isl_printer *isl_printer_print_multi_val(
3625 __isl_take isl_printer *p,
3626 __isl_keep isl_multi_val *mv);
3628 #include <isl/aff.h>
3629 __isl_give isl_printer *isl_printer_print_aff(
3630 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3631 __isl_give isl_printer *isl_printer_print_multi_aff(
3632 __isl_take isl_printer *p,
3633 __isl_keep isl_multi_aff *maff);
3634 __isl_give isl_printer *isl_printer_print_pw_aff(
3635 __isl_take isl_printer *p,
3636 __isl_keep isl_pw_aff *pwaff);
3637 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3638 __isl_take isl_printer *p,
3639 __isl_keep isl_pw_multi_aff *pma);
3640 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3641 __isl_take isl_printer *p,
3642 __isl_keep isl_multi_pw_aff *mpa);
3643 __isl_give isl_printer *isl_printer_print_union_pw_aff(
3644 __isl_take isl_printer *p,
3645 __isl_keep isl_union_pw_aff *upa);
3646 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3647 __isl_take isl_printer *p,
3648 __isl_keep isl_union_pw_multi_aff *upma);
3649 __isl_give isl_printer *
3650 isl_printer_print_multi_union_pw_aff(
3651 __isl_take isl_printer *p,
3652 __isl_keep isl_multi_union_pw_aff *mupa);
3654 #include <isl/polynomial.h>
3655 __isl_give isl_printer *isl_printer_print_qpolynomial(
3656 __isl_take isl_printer *p,
3657 __isl_keep isl_qpolynomial *qp);
3658 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3659 __isl_take isl_printer *p,
3660 __isl_keep isl_pw_qpolynomial *pwqp);
3661 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3662 __isl_take isl_printer *p,
3663 __isl_keep isl_union_pw_qpolynomial *upwqp);
3665 __isl_give isl_printer *
3666 isl_printer_print_pw_qpolynomial_fold(
3667 __isl_take isl_printer *p,
3668 __isl_keep isl_pw_qpolynomial_fold *pwf);
3669 __isl_give isl_printer *
3670 isl_printer_print_union_pw_qpolynomial_fold(
3671 __isl_take isl_printer *p,
3672 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3674 For C<isl_printer_print_qpolynomial>,
3675 C<isl_printer_print_pw_qpolynomial> and
3676 C<isl_printer_print_pw_qpolynomial_fold>,
3677 the output format of the printer
3678 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3679 For C<isl_printer_print_union_pw_qpolynomial> and
3680 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
3682 In case of printing in C<ISL_FORMAT_C>, the user may want
3683 to set the names of all dimensions first.
3685 C<isl> also provides limited support for printing YAML documents,
3686 just enough for the internal use for printing such documents.
3688 #include <isl/printer.h>
3689 __isl_give isl_printer *isl_printer_yaml_start_mapping(
3690 __isl_take isl_printer *p);
3691 __isl_give isl_printer *isl_printer_yaml_end_mapping(
3692 __isl_take isl_printer *p);
3693 __isl_give isl_printer *isl_printer_yaml_start_sequence(
3694 __isl_take isl_printer *p);
3695 __isl_give isl_printer *isl_printer_yaml_end_sequence(
3696 __isl_take isl_printer *p);
3697 __isl_give isl_printer *isl_printer_yaml_next(
3698 __isl_take isl_printer *p);
3700 A document is started by a call to either
3701 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3702 Anything printed to the printer after such a call belong to the
3703 first key of the mapping or the first element in the sequence.
3704 The function C<isl_printer_yaml_next> moves to the value if
3705 we are currently printing a mapping key, the next key if we
3706 are printing a value or the next element if we are printing
3707 an element in a sequence.
3708 Nested mappings and sequences are initiated by the same
3709 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3710 Each call to these functions needs to have a corresponding call to
3711 C<isl_printer_yaml_end_mapping> or C<isl_printer_yaml_end_sequence>.
3713 When called on a file printer, the following function flushes
3714 the file. When called on a string printer, the buffer is cleared.
3716 __isl_give isl_printer *isl_printer_flush(
3717 __isl_take isl_printer *p);
3719 The following functions allow the user to attach
3720 notes to a printer in order to keep track of additional state.
3722 #include <isl/printer.h>
3723 isl_bool isl_printer_has_note(__isl_keep isl_printer *p,
3724 __isl_keep isl_id *id);
3725 __isl_give isl_id *isl_printer_get_note(
3726 __isl_keep isl_printer *p, __isl_take isl_id *id);
3727 __isl_give isl_printer *isl_printer_set_note(
3728 __isl_take isl_printer *p,
3729 __isl_take isl_id *id, __isl_take isl_id *note);
3731 C<isl_printer_set_note> associates the given note to the given
3732 identifier in the printer.
3733 C<isl_printer_get_note> retrieves a note associated to an
3735 C<isl_printer_has_note> checks if there is such a note.
3736 C<isl_printer_get_note> fails if the requested note does not exist.
3738 Alternatively, a string representation can be obtained
3739 directly using the following functions, which always print
3743 __isl_give char *isl_id_to_str(
3744 __isl_keep isl_id *id);
3746 #include <isl/space.h>
3747 __isl_give char *isl_space_to_str(
3748 __isl_keep isl_space *space);
3750 #include <isl/val.h>
3751 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
3752 __isl_give char *isl_multi_val_to_str(
3753 __isl_keep isl_multi_val *mv);
3755 #include <isl/set.h>
3756 __isl_give char *isl_basic_set_to_str(
3757 __isl_keep isl_basic_set *bset);
3758 __isl_give char *isl_set_to_str(
3759 __isl_keep isl_set *set);
3761 #include <isl/union_set.h>
3762 __isl_give char *isl_union_set_to_str(
3763 __isl_keep isl_union_set *uset);
3765 #include <isl/map.h>
3766 __isl_give char *isl_basic_map_to_str(
3767 __isl_keep isl_basic_map *bmap);
3768 __isl_give char *isl_map_to_str(
3769 __isl_keep isl_map *map);
3771 #include <isl/union_map.h>
3772 __isl_give char *isl_union_map_to_str(
3773 __isl_keep isl_union_map *umap);
3775 #include <isl/aff.h>
3776 __isl_give char *isl_aff_to_str(__isl_keep isl_aff *aff);
3777 __isl_give char *isl_pw_aff_to_str(
3778 __isl_keep isl_pw_aff *pa);
3779 __isl_give char *isl_multi_aff_to_str(
3780 __isl_keep isl_multi_aff *ma);
3781 __isl_give char *isl_pw_multi_aff_to_str(
3782 __isl_keep isl_pw_multi_aff *pma);
3783 __isl_give char *isl_multi_pw_aff_to_str(
3784 __isl_keep isl_multi_pw_aff *mpa);
3785 __isl_give char *isl_union_pw_aff_to_str(
3786 __isl_keep isl_union_pw_aff *upa);
3787 __isl_give char *isl_union_pw_multi_aff_to_str(
3788 __isl_keep isl_union_pw_multi_aff *upma);
3789 __isl_give char *isl_multi_union_pw_aff_to_str(
3790 __isl_keep isl_multi_union_pw_aff *mupa);
3792 #include <isl/point.h>
3793 __isl_give char *isl_point_to_str(
3794 __isl_keep isl_point *pnt);
3796 #include <isl/polynomial.h>
3797 __isl_give char *isl_pw_qpolynomial_to_str(
3798 __isl_keep isl_pw_qpolynomial *pwqp);
3799 __isl_give char *isl_union_pw_qpolynomial_to_str(
3800 __isl_keep isl_union_pw_qpolynomial *upwqp);
3804 =head3 Unary Properties
3810 The following functions test whether the given set or relation
3811 contains any integer points. The ``plain'' variants do not perform
3812 any computations, but simply check if the given set or relation
3813 is already known to be empty.
3815 #include <isl/set.h>
3816 isl_bool isl_basic_set_plain_is_empty(
3817 __isl_keep isl_basic_set *bset);
3818 isl_bool isl_basic_set_is_empty(
3819 __isl_keep isl_basic_set *bset);
3820 isl_bool isl_set_plain_is_empty(
3821 __isl_keep isl_set *set);
3822 isl_bool isl_set_is_empty(__isl_keep isl_set *set);
3824 #include <isl/union_set.h>
3825 isl_bool isl_union_set_is_empty(
3826 __isl_keep isl_union_set *uset);
3828 #include <isl/map.h>
3829 isl_bool isl_basic_map_plain_is_empty(
3830 __isl_keep isl_basic_map *bmap);
3831 isl_bool isl_basic_map_is_empty(
3832 __isl_keep isl_basic_map *bmap);
3833 isl_bool isl_map_plain_is_empty(
3834 __isl_keep isl_map *map);
3835 isl_bool isl_map_is_empty(__isl_keep isl_map *map);
3837 #include <isl/union_map.h>
3838 isl_bool isl_union_map_plain_is_empty(
3839 __isl_keep isl_union_map *umap);
3840 isl_bool isl_union_map_is_empty(
3841 __isl_keep isl_union_map *umap);
3843 =item * Universality
3845 isl_bool isl_basic_set_plain_is_universe(
3846 __isl_keep isl_basic_set *bset);
3847 isl_bool isl_basic_set_is_universe(
3848 __isl_keep isl_basic_set *bset);
3849 isl_bool isl_basic_map_plain_is_universe(
3850 __isl_keep isl_basic_map *bmap);
3851 isl_bool isl_basic_map_is_universe(
3852 __isl_keep isl_basic_map *bmap);
3853 isl_bool isl_set_plain_is_universe(
3854 __isl_keep isl_set *set);
3855 isl_bool isl_map_plain_is_universe(
3856 __isl_keep isl_map *map);
3858 =item * Single-valuedness
3860 #include <isl/set.h>
3861 isl_bool isl_set_is_singleton(__isl_keep isl_set *set);
3863 #include <isl/map.h>
3864 isl_bool isl_basic_map_is_single_valued(
3865 __isl_keep isl_basic_map *bmap);
3866 isl_bool isl_map_plain_is_single_valued(
3867 __isl_keep isl_map *map);
3868 isl_bool isl_map_is_single_valued(__isl_keep isl_map *map);
3870 #include <isl/union_map.h>
3871 isl_bool isl_union_map_is_single_valued(
3872 __isl_keep isl_union_map *umap);
3876 isl_bool isl_map_plain_is_injective(
3877 __isl_keep isl_map *map);
3878 isl_bool isl_map_is_injective(
3879 __isl_keep isl_map *map);
3880 isl_bool isl_union_map_plain_is_injective(
3881 __isl_keep isl_union_map *umap);
3882 isl_bool isl_union_map_is_injective(
3883 __isl_keep isl_union_map *umap);
3887 isl_bool isl_map_is_bijective(
3888 __isl_keep isl_map *map);
3889 isl_bool isl_union_map_is_bijective(
3890 __isl_keep isl_union_map *umap);
3894 The following functions test whether the given relation
3895 only maps elements to themselves.
3897 #include <isl/map.h>
3898 isl_bool isl_map_is_identity(
3899 __isl_keep isl_map *map);
3901 #include <isl/union_map.h>
3902 isl_bool isl_union_map_is_identity(
3903 __isl_keep isl_union_map *umap);
3907 __isl_give isl_val *
3908 isl_basic_map_plain_get_val_if_fixed(
3909 __isl_keep isl_basic_map *bmap,
3910 enum isl_dim_type type, unsigned pos);
3911 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
3912 __isl_keep isl_set *set,
3913 enum isl_dim_type type, unsigned pos);
3914 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
3915 __isl_keep isl_map *map,
3916 enum isl_dim_type type, unsigned pos);
3918 If the set or relation obviously lies on a hyperplane where the given dimension
3919 has a fixed value, then return that value.
3920 Otherwise return NaN.
3924 isl_stat isl_set_dim_residue_class_val(
3925 __isl_keep isl_set *set,
3926 int pos, __isl_give isl_val **modulo,
3927 __isl_give isl_val **residue);
3929 Check if the values of the given set dimension are equal to a fixed
3930 value modulo some integer value. If so, assign the modulo to C<*modulo>
3931 and the fixed value to C<*residue>. If the given dimension attains only
3932 a single value, then assign C<0> to C<*modulo> and the fixed value to
3934 If the dimension does not attain only a single value and if no modulo
3935 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
3937 #include <isl/set.h>
3938 __isl_give isl_stride_info *isl_set_get_stride_info(
3939 __isl_keep isl_set *set, int pos);
3940 __isl_give isl_val *isl_set_get_stride(
3941 __isl_keep isl_set *set, int pos);
3943 Check if the values of the given set dimension are equal to
3944 some affine expression of the other dimensions (the offset)
3945 modulo some integer stride.
3946 If no more specific information can be found, then the stride
3947 is taken to be one and the offset is taken to be the zero expression.
3948 The function C<isl_set_get_stride_info> performs the same
3949 computation but only returns the stride.
3951 the stride and offset can be extracted from the returned object
3952 using the following functions.
3954 #include <isl/set.h>
3955 __isl_give isl_val *isl_stride_info_get_stride(
3956 __isl_keep isl_stride_info *si);
3957 __isl_give isl_aff *isl_stride_info_get_offset(
3958 __isl_keep isl_stride_info *si);
3960 The stride info object can be released using the following function.
3962 #include <isl/set.h>
3963 __isl_null isl_stride_info *isl_stride_info_free(
3964 __isl_take isl_stride_info *si);
3968 To check whether the description of a set, relation or function depends
3969 on one or more given dimensions,
3970 the following functions can be used.
3972 #include <isl/constraint.h>
3973 isl_bool isl_constraint_involves_dims(
3974 __isl_keep isl_constraint *constraint,
3975 enum isl_dim_type type, unsigned first, unsigned n);
3977 #include <isl/set.h>
3978 isl_bool isl_basic_set_involves_dims(
3979 __isl_keep isl_basic_set *bset,
3980 enum isl_dim_type type, unsigned first, unsigned n);
3981 isl_bool isl_set_involves_dims(__isl_keep isl_set *set,
3982 enum isl_dim_type type, unsigned first, unsigned n);
3984 #include <isl/map.h>
3985 isl_bool isl_basic_map_involves_dims(
3986 __isl_keep isl_basic_map *bmap,
3987 enum isl_dim_type type, unsigned first, unsigned n);
3988 isl_bool isl_map_involves_dims(__isl_keep isl_map *map,
3989 enum isl_dim_type type, unsigned first, unsigned n);
3991 #include <isl/union_map.h>
3992 isl_bool isl_union_map_involves_dims(
3993 __isl_keep isl_union_map *umap,
3994 enum isl_dim_type type, unsigned first, unsigned n);
3996 #include <isl/aff.h>
3997 isl_bool isl_aff_involves_dims(__isl_keep isl_aff *aff,
3998 enum isl_dim_type type, unsigned first, unsigned n);
3999 isl_bool isl_pw_aff_involves_dims(
4000 __isl_keep isl_pw_aff *pwaff,
4001 enum isl_dim_type type, unsigned first, unsigned n);
4002 isl_bool isl_multi_aff_involves_dims(
4003 __isl_keep isl_multi_aff *ma,
4004 enum isl_dim_type type, unsigned first, unsigned n);
4005 isl_bool isl_multi_pw_aff_involves_dims(
4006 __isl_keep isl_multi_pw_aff *mpa,
4007 enum isl_dim_type type, unsigned first, unsigned n);
4009 #include <isl/polynomial.h>
4010 isl_bool isl_qpolynomial_involves_dims(
4011 __isl_keep isl_qpolynomial *qp,
4012 enum isl_dim_type type, unsigned first, unsigned n);
4014 Similarly, the following functions can be used to check whether
4015 a given dimension is involved in any lower or upper bound.
4017 #include <isl/set.h>
4018 isl_bool isl_set_dim_has_any_lower_bound(
4019 __isl_keep isl_set *set,
4020 enum isl_dim_type type, unsigned pos);
4021 isl_bool isl_set_dim_has_any_upper_bound(
4022 __isl_keep isl_set *set,
4023 enum isl_dim_type type, unsigned pos);
4025 Note that these functions return true even if there is a bound on
4026 the dimension on only some of the basic sets of C<set>.
4027 To check if they have a bound for all of the basic sets in C<set>,
4028 use the following functions instead.
4030 #include <isl/set.h>
4031 isl_bool isl_set_dim_has_lower_bound(
4032 __isl_keep isl_set *set,
4033 enum isl_dim_type type, unsigned pos);
4034 isl_bool isl_set_dim_has_upper_bound(
4035 __isl_keep isl_set *set,
4036 enum isl_dim_type type, unsigned pos);
4040 To check whether a set is a parameter domain, use this function:
4042 isl_bool isl_set_is_params(__isl_keep isl_set *set);
4043 isl_bool isl_union_set_is_params(
4044 __isl_keep isl_union_set *uset);
4048 The following functions check whether the space of the given
4049 (basic) set or relation domain and/or range is a wrapped relation.
4051 #include <isl/space.h>
4052 isl_bool isl_space_is_wrapping(
4053 __isl_keep isl_space *space);
4054 isl_bool isl_space_domain_is_wrapping(
4055 __isl_keep isl_space *space);
4056 isl_bool isl_space_range_is_wrapping(
4057 __isl_keep isl_space *space);
4058 isl_bool isl_space_is_product(
4059 __isl_keep isl_space *space);
4061 #include <isl/set.h>
4062 isl_bool isl_basic_set_is_wrapping(
4063 __isl_keep isl_basic_set *bset);
4064 isl_bool isl_set_is_wrapping(__isl_keep isl_set *set);
4066 #include <isl/map.h>
4067 isl_bool isl_map_domain_is_wrapping(
4068 __isl_keep isl_map *map);
4069 isl_bool isl_map_range_is_wrapping(
4070 __isl_keep isl_map *map);
4071 isl_bool isl_map_is_product(__isl_keep isl_map *map);
4073 #include <isl/val.h>
4074 isl_bool isl_multi_val_range_is_wrapping(
4075 __isl_keep isl_multi_val *mv);
4077 #include <isl/aff.h>
4078 isl_bool isl_multi_aff_range_is_wrapping(
4079 __isl_keep isl_multi_aff *ma);
4080 isl_bool isl_multi_pw_aff_range_is_wrapping(
4081 __isl_keep isl_multi_pw_aff *mpa);
4082 isl_bool isl_multi_union_pw_aff_range_is_wrapping(
4083 __isl_keep isl_multi_union_pw_aff *mupa);
4085 The input to C<isl_space_is_wrapping> should
4086 be the space of a set, while that of
4087 C<isl_space_domain_is_wrapping> and
4088 C<isl_space_range_is_wrapping> should be the space of a relation.
4089 The input to C<isl_space_is_product> can be either the space
4090 of a set or that of a binary relation.
4091 In case the input is the space of a binary relation, it checks
4092 whether both domain and range are wrapping.
4094 =item * Internal Product
4096 isl_bool isl_basic_map_can_zip(
4097 __isl_keep isl_basic_map *bmap);
4098 isl_bool isl_map_can_zip(__isl_keep isl_map *map);
4100 Check whether the product of domain and range of the given relation
4102 i.e., whether both domain and range are nested relations.
4106 #include <isl/space.h>
4107 isl_bool isl_space_can_curry(
4108 __isl_keep isl_space *space);
4110 #include <isl/map.h>
4111 isl_bool isl_basic_map_can_curry(
4112 __isl_keep isl_basic_map *bmap);
4113 isl_bool isl_map_can_curry(__isl_keep isl_map *map);
4115 Check whether the domain of the (basic) relation is a wrapped relation.
4117 #include <isl/space.h>
4118 __isl_give isl_space *isl_space_uncurry(
4119 __isl_take isl_space *space);
4121 #include <isl/map.h>
4122 isl_bool isl_basic_map_can_uncurry(
4123 __isl_keep isl_basic_map *bmap);
4124 isl_bool isl_map_can_uncurry(__isl_keep isl_map *map);
4126 Check whether the range of the (basic) relation is a wrapped relation.
4128 #include <isl/space.h>
4129 isl_bool isl_space_can_range_curry(
4130 __isl_keep isl_space *space);
4132 #include <isl/map.h>
4133 isl_bool isl_map_can_range_curry(
4134 __isl_keep isl_map *map);
4136 Check whether the domain of the relation wrapped in the range of
4137 the input is itself a wrapped relation.
4139 =item * Special Values
4141 #include <isl/aff.h>
4142 isl_bool isl_aff_is_cst(__isl_keep isl_aff *aff);
4143 isl_bool isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
4144 isl_bool isl_multi_pw_aff_is_cst(
4145 __isl_keep isl_multi_pw_aff *mpa);
4147 Check whether the given expression is a constant.
4149 #include <isl/val.h>
4150 isl_bool isl_multi_val_involves_nan(
4151 __isl_keep isl_multi_val *mv);
4153 #include <isl/aff.h>
4154 isl_bool isl_aff_is_nan(__isl_keep isl_aff *aff);
4155 isl_bool isl_multi_aff_involves_nan(
4156 __isl_keep isl_multi_aff *ma);
4157 isl_bool isl_pw_aff_involves_nan(
4158 __isl_keep isl_pw_aff *pa);
4159 isl_bool isl_pw_multi_aff_involves_nan(
4160 __isl_keep isl_pw_multi_aff *pma);
4161 isl_bool isl_multi_pw_aff_involves_nan(
4162 __isl_keep isl_multi_pw_aff *mpa);
4163 isl_bool isl_union_pw_aff_involves_nan(
4164 __isl_keep isl_union_pw_aff *upa);
4165 isl_bool isl_union_pw_multi_aff_involves_nan(
4166 __isl_keep isl_union_pw_multi_aff *upma);
4167 isl_bool isl_multi_union_pw_aff_involves_nan(
4168 __isl_keep isl_multi_union_pw_aff *mupa);
4170 #include <isl/polynomial.h>
4171 isl_bool isl_qpolynomial_is_nan(
4172 __isl_keep isl_qpolynomial *qp);
4173 isl_bool isl_qpolynomial_fold_is_nan(
4174 __isl_keep isl_qpolynomial_fold *fold);
4175 isl_bool isl_pw_qpolynomial_involves_nan(
4176 __isl_keep isl_pw_qpolynomial *pwqp);
4177 isl_bool isl_pw_qpolynomial_fold_involves_nan(
4178 __isl_keep isl_pw_qpolynomial_fold *pwf);
4179 isl_bool isl_union_pw_qpolynomial_involves_nan(
4180 __isl_keep isl_union_pw_qpolynomial *upwqp);
4181 isl_bool isl_union_pw_qpolynomial_fold_involves_nan(
4182 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4184 Check whether the given expression is equal to or involves NaN.
4186 #include <isl/aff.h>
4187 isl_bool isl_aff_plain_is_zero(
4188 __isl_keep isl_aff *aff);
4190 Check whether the affine expression is obviously zero.
4194 =head3 Binary Properties
4200 The following functions check whether two objects
4201 represent the same set, relation or function.
4202 The C<plain> variants only return true if the objects
4203 are obviously the same. That is, they may return false
4204 even if the objects are the same, but they will never
4205 return true if the objects are not the same.
4207 #include <isl/set.h>
4208 isl_bool isl_basic_set_plain_is_equal(
4209 __isl_keep isl_basic_set *bset1,
4210 __isl_keep isl_basic_set *bset2);
4211 isl_bool isl_basic_set_is_equal(
4212 __isl_keep isl_basic_set *bset1,
4213 __isl_keep isl_basic_set *bset2);
4214 isl_bool isl_set_plain_is_equal(
4215 __isl_keep isl_set *set1,
4216 __isl_keep isl_set *set2);
4217 isl_bool isl_set_is_equal(__isl_keep isl_set *set1,
4218 __isl_keep isl_set *set2);
4220 #include <isl/map.h>
4221 isl_bool isl_basic_map_is_equal(
4222 __isl_keep isl_basic_map *bmap1,
4223 __isl_keep isl_basic_map *bmap2);
4224 isl_bool isl_map_is_equal(__isl_keep isl_map *map1,
4225 __isl_keep isl_map *map2);
4226 isl_bool isl_map_plain_is_equal(
4227 __isl_keep isl_map *map1,
4228 __isl_keep isl_map *map2);
4230 #include <isl/union_set.h>
4231 isl_bool isl_union_set_is_equal(
4232 __isl_keep isl_union_set *uset1,
4233 __isl_keep isl_union_set *uset2);
4235 #include <isl/union_map.h>
4236 isl_bool isl_union_map_is_equal(
4237 __isl_keep isl_union_map *umap1,
4238 __isl_keep isl_union_map *umap2);
4240 #include <isl/aff.h>
4241 isl_bool isl_aff_plain_is_equal(
4242 __isl_keep isl_aff *aff1,
4243 __isl_keep isl_aff *aff2);
4244 isl_bool isl_multi_aff_plain_is_equal(
4245 __isl_keep isl_multi_aff *maff1,
4246 __isl_keep isl_multi_aff *maff2);
4247 isl_bool isl_pw_aff_plain_is_equal(
4248 __isl_keep isl_pw_aff *pwaff1,
4249 __isl_keep isl_pw_aff *pwaff2);
4250 isl_bool isl_pw_aff_is_equal(
4251 __isl_keep isl_pw_aff *pa1,
4252 __isl_keep isl_pw_aff *pa2);
4253 isl_bool isl_pw_multi_aff_plain_is_equal(
4254 __isl_keep isl_pw_multi_aff *pma1,
4255 __isl_keep isl_pw_multi_aff *pma2);
4256 isl_bool isl_pw_multi_aff_is_equal(
4257 __isl_keep isl_pw_multi_aff *pma1,
4258 __isl_keep isl_pw_multi_aff *pma2);
4259 isl_bool isl_multi_pw_aff_plain_is_equal(
4260 __isl_keep isl_multi_pw_aff *mpa1,
4261 __isl_keep isl_multi_pw_aff *mpa2);
4262 isl_bool isl_multi_pw_aff_is_equal(
4263 __isl_keep isl_multi_pw_aff *mpa1,
4264 __isl_keep isl_multi_pw_aff *mpa2);
4265 isl_bool isl_union_pw_aff_plain_is_equal(
4266 __isl_keep isl_union_pw_aff *upa1,
4267 __isl_keep isl_union_pw_aff *upa2);
4268 isl_bool isl_union_pw_multi_aff_plain_is_equal(
4269 __isl_keep isl_union_pw_multi_aff *upma1,
4270 __isl_keep isl_union_pw_multi_aff *upma2);
4271 isl_bool isl_multi_union_pw_aff_plain_is_equal(
4272 __isl_keep isl_multi_union_pw_aff *mupa1,
4273 __isl_keep isl_multi_union_pw_aff *mupa2);
4275 #include <isl/polynomial.h>
4276 isl_bool isl_union_pw_qpolynomial_plain_is_equal(
4277 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4278 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4279 isl_bool isl_union_pw_qpolynomial_fold_plain_is_equal(
4280 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4281 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4283 =item * Disjointness
4285 #include <isl/set.h>
4286 isl_bool isl_basic_set_is_disjoint(
4287 __isl_keep isl_basic_set *bset1,
4288 __isl_keep isl_basic_set *bset2);
4289 isl_bool isl_set_plain_is_disjoint(
4290 __isl_keep isl_set *set1,
4291 __isl_keep isl_set *set2);
4292 isl_bool isl_set_is_disjoint(__isl_keep isl_set *set1,
4293 __isl_keep isl_set *set2);
4295 #include <isl/map.h>
4296 isl_bool isl_basic_map_is_disjoint(
4297 __isl_keep isl_basic_map *bmap1,
4298 __isl_keep isl_basic_map *bmap2);
4299 isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1,
4300 __isl_keep isl_map *map2);
4302 #include <isl/union_set.h>
4303 isl_bool isl_union_set_is_disjoint(
4304 __isl_keep isl_union_set *uset1,
4305 __isl_keep isl_union_set *uset2);
4307 #include <isl/union_map.h>
4308 isl_bool isl_union_map_is_disjoint(
4309 __isl_keep isl_union_map *umap1,
4310 __isl_keep isl_union_map *umap2);
4314 isl_bool isl_basic_set_is_subset(
4315 __isl_keep isl_basic_set *bset1,
4316 __isl_keep isl_basic_set *bset2);
4317 isl_bool isl_set_is_subset(__isl_keep isl_set *set1,
4318 __isl_keep isl_set *set2);
4319 isl_bool isl_set_is_strict_subset(
4320 __isl_keep isl_set *set1,
4321 __isl_keep isl_set *set2);
4322 isl_bool isl_union_set_is_subset(
4323 __isl_keep isl_union_set *uset1,
4324 __isl_keep isl_union_set *uset2);
4325 isl_bool isl_union_set_is_strict_subset(
4326 __isl_keep isl_union_set *uset1,
4327 __isl_keep isl_union_set *uset2);
4328 isl_bool isl_basic_map_is_subset(
4329 __isl_keep isl_basic_map *bmap1,
4330 __isl_keep isl_basic_map *bmap2);
4331 isl_bool isl_basic_map_is_strict_subset(
4332 __isl_keep isl_basic_map *bmap1,
4333 __isl_keep isl_basic_map *bmap2);
4334 isl_bool isl_map_is_subset(
4335 __isl_keep isl_map *map1,
4336 __isl_keep isl_map *map2);
4337 isl_bool isl_map_is_strict_subset(
4338 __isl_keep isl_map *map1,
4339 __isl_keep isl_map *map2);
4340 isl_bool isl_union_map_is_subset(
4341 __isl_keep isl_union_map *umap1,
4342 __isl_keep isl_union_map *umap2);
4343 isl_bool isl_union_map_is_strict_subset(
4344 __isl_keep isl_union_map *umap1,
4345 __isl_keep isl_union_map *umap2);
4347 Check whether the first argument is a (strict) subset of the
4352 Every comparison function returns a negative value if the first
4353 argument is considered smaller than the second, a positive value
4354 if the first argument is considered greater and zero if the two
4355 constraints are considered the same by the comparison criterion.
4357 #include <isl/constraint.h>
4358 int isl_constraint_plain_cmp(
4359 __isl_keep isl_constraint *c1,
4360 __isl_keep isl_constraint *c2);
4362 This function is useful for sorting C<isl_constraint>s.
4363 The order depends on the internal representation of the inputs.
4364 The order is fixed over different calls to the function (assuming
4365 the internal representation of the inputs has not changed), but may
4366 change over different versions of C<isl>.
4368 #include <isl/constraint.h>
4369 int isl_constraint_cmp_last_non_zero(
4370 __isl_keep isl_constraint *c1,
4371 __isl_keep isl_constraint *c2);
4373 This function can be used to sort constraints that live in the same
4374 local space. Constraints that involve ``earlier'' dimensions or
4375 that have a smaller coefficient for the shared latest dimension
4376 are considered smaller than other constraints.
4377 This function only defines a B<partial> order.
4379 #include <isl/set.h>
4380 int isl_set_plain_cmp(__isl_keep isl_set *set1,
4381 __isl_keep isl_set *set2);
4383 This function is useful for sorting C<isl_set>s.
4384 The order depends on the internal representation of the inputs.
4385 The order is fixed over different calls to the function (assuming
4386 the internal representation of the inputs has not changed), but may
4387 change over different versions of C<isl>.
4389 #include <isl/aff.h>
4390 int isl_multi_aff_plain_cmp(
4391 __isl_keep isl_multi_aff *ma1,
4392 __isl_keep isl_multi_aff *ma2);
4393 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4394 __isl_keep isl_pw_aff *pa2);
4396 The functions C<isl_multi_aff_plain_cmp> and
4397 C<isl_pw_aff_plain_cmp> can be used to sort C<isl_multi_aff>s and
4398 C<isl_pw_aff>s. The order is not strictly defined.
4399 The current order sorts expressions that only involve
4400 earlier dimensions before those that involve later dimensions.
4404 =head2 Unary Operations
4410 __isl_give isl_set *isl_set_complement(
4411 __isl_take isl_set *set);
4412 __isl_give isl_map *isl_map_complement(
4413 __isl_take isl_map *map);
4417 #include <isl/space.h>
4418 __isl_give isl_space *isl_space_reverse(
4419 __isl_take isl_space *space);
4421 #include <isl/map.h>
4422 __isl_give isl_basic_map *isl_basic_map_reverse(
4423 __isl_take isl_basic_map *bmap);
4424 __isl_give isl_map *isl_map_reverse(
4425 __isl_take isl_map *map);
4427 #include <isl/union_map.h>
4428 __isl_give isl_union_map *isl_union_map_reverse(
4429 __isl_take isl_union_map *umap);
4433 #include <isl/space.h>
4434 __isl_give isl_space *isl_space_domain(
4435 __isl_take isl_space *space);
4436 __isl_give isl_space *isl_space_range(
4437 __isl_take isl_space *space);
4438 __isl_give isl_space *isl_space_params(
4439 __isl_take isl_space *space);
4441 #include <isl/local_space.h>
4442 __isl_give isl_local_space *isl_local_space_domain(
4443 __isl_take isl_local_space *ls);
4444 __isl_give isl_local_space *isl_local_space_range(
4445 __isl_take isl_local_space *ls);
4447 #include <isl/set.h>
4448 __isl_give isl_basic_set *isl_basic_set_project_out(
4449 __isl_take isl_basic_set *bset,
4450 enum isl_dim_type type, unsigned first, unsigned n);
4451 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
4452 enum isl_dim_type type, unsigned first, unsigned n);
4453 __isl_give isl_map *isl_set_project_onto_map(
4454 __isl_take isl_set *set,
4455 enum isl_dim_type type, unsigned first,
4457 __isl_give isl_basic_set *isl_basic_set_params(
4458 __isl_take isl_basic_set *bset);
4459 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
4461 The function C<isl_set_project_onto_map> returns a relation
4462 that projects the input set onto the given set dimensions.
4464 #include <isl/map.h>
4465 __isl_give isl_basic_map *isl_basic_map_project_out(
4466 __isl_take isl_basic_map *bmap,
4467 enum isl_dim_type type, unsigned first, unsigned n);
4468 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
4469 enum isl_dim_type type, unsigned first, unsigned n);
4470 __isl_give isl_basic_set *isl_basic_map_domain(
4471 __isl_take isl_basic_map *bmap);
4472 __isl_give isl_basic_set *isl_basic_map_range(
4473 __isl_take isl_basic_map *bmap);
4474 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
4475 __isl_give isl_set *isl_map_domain(
4476 __isl_take isl_map *bmap);
4477 __isl_give isl_set *isl_map_range(
4478 __isl_take isl_map *map);
4480 #include <isl/union_set.h>
4481 __isl_give isl_union_set *isl_union_set_project_out(
4482 __isl_take isl_union_set *uset,
4483 enum isl_dim_type type,
4484 unsigned first, unsigned n);
4485 __isl_give isl_set *isl_union_set_params(
4486 __isl_take isl_union_set *uset);
4488 The function C<isl_union_set_project_out> can only project out
4491 #include <isl/union_map.h>
4492 __isl_give isl_union_map *isl_union_map_project_out(
4493 __isl_take isl_union_map *umap,
4494 enum isl_dim_type type, unsigned first, unsigned n);
4495 __isl_give isl_union_map *
4496 isl_union_map_project_out_all_params(
4497 __isl_take isl_union_map *umap);
4498 __isl_give isl_set *isl_union_map_params(
4499 __isl_take isl_union_map *umap);
4500 __isl_give isl_union_set *isl_union_map_domain(
4501 __isl_take isl_union_map *umap);
4502 __isl_give isl_union_set *isl_union_map_range(
4503 __isl_take isl_union_map *umap);
4505 The function C<isl_union_map_project_out> can only project out
4508 #include <isl/aff.h>
4509 __isl_give isl_aff *isl_aff_project_domain_on_params(
4510 __isl_take isl_aff *aff);
4511 __isl_give isl_multi_aff *
4512 isl_multi_aff_project_domain_on_params(
4513 __isl_take isl_multi_aff *ma);
4514 __isl_give isl_pw_aff *
4515 isl_pw_aff_project_domain_on_params(
4516 __isl_take isl_pw_aff *pa);
4517 __isl_give isl_multi_pw_aff *
4518 isl_multi_pw_aff_project_domain_on_params(
4519 __isl_take isl_multi_pw_aff *mpa);
4520 __isl_give isl_pw_multi_aff *
4521 isl_pw_multi_aff_project_domain_on_params(
4522 __isl_take isl_pw_multi_aff *pma);
4523 __isl_give isl_set *isl_pw_aff_domain(
4524 __isl_take isl_pw_aff *pwaff);
4525 __isl_give isl_set *isl_pw_multi_aff_domain(
4526 __isl_take isl_pw_multi_aff *pma);
4527 __isl_give isl_set *isl_multi_pw_aff_domain(
4528 __isl_take isl_multi_pw_aff *mpa);
4529 __isl_give isl_union_set *isl_union_pw_aff_domain(
4530 __isl_take isl_union_pw_aff *upa);
4531 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4532 __isl_take isl_union_pw_multi_aff *upma);
4533 __isl_give isl_union_set *
4534 isl_multi_union_pw_aff_domain(
4535 __isl_take isl_multi_union_pw_aff *mupa);
4536 __isl_give isl_set *isl_pw_aff_params(
4537 __isl_take isl_pw_aff *pwa);
4539 The function C<isl_multi_union_pw_aff_domain> requires its
4540 input to have at least one set dimension.
4542 #include <isl/polynomial.h>
4543 __isl_give isl_qpolynomial *
4544 isl_qpolynomial_project_domain_on_params(
4545 __isl_take isl_qpolynomial *qp);
4546 __isl_give isl_pw_qpolynomial *
4547 isl_pw_qpolynomial_project_domain_on_params(
4548 __isl_take isl_pw_qpolynomial *pwqp);
4549 __isl_give isl_pw_qpolynomial_fold *
4550 isl_pw_qpolynomial_fold_project_domain_on_params(
4551 __isl_take isl_pw_qpolynomial_fold *pwf);
4552 __isl_give isl_set *isl_pw_qpolynomial_domain(
4553 __isl_take isl_pw_qpolynomial *pwqp);
4554 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4555 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4556 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4557 __isl_take isl_union_pw_qpolynomial *upwqp);
4559 #include <isl/space.h>
4560 __isl_give isl_space *isl_space_domain_map(
4561 __isl_take isl_space *space);
4562 __isl_give isl_space *isl_space_range_map(
4563 __isl_take isl_space *space);
4565 #include <isl/map.h>
4566 __isl_give isl_map *isl_set_wrapped_domain_map(
4567 __isl_take isl_set *set);
4568 __isl_give isl_basic_map *isl_basic_map_domain_map(
4569 __isl_take isl_basic_map *bmap);
4570 __isl_give isl_basic_map *isl_basic_map_range_map(
4571 __isl_take isl_basic_map *bmap);
4572 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
4573 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
4575 #include <isl/union_map.h>
4576 __isl_give isl_union_map *isl_union_map_domain_map(
4577 __isl_take isl_union_map *umap);
4578 __isl_give isl_union_pw_multi_aff *
4579 isl_union_map_domain_map_union_pw_multi_aff(
4580 __isl_take isl_union_map *umap);
4581 __isl_give isl_union_map *isl_union_map_range_map(
4582 __isl_take isl_union_map *umap);
4583 __isl_give isl_union_map *
4584 isl_union_set_wrapped_domain_map(
4585 __isl_take isl_union_set *uset);
4587 The functions above construct a (basic, regular or union) relation
4588 that maps (a wrapped version of) the input relation to its domain or range.
4589 C<isl_set_wrapped_domain_map> maps the input set to the domain
4590 of its wrapped relation.
4594 __isl_give isl_basic_set *isl_basic_set_eliminate(
4595 __isl_take isl_basic_set *bset,
4596 enum isl_dim_type type,
4597 unsigned first, unsigned n);
4598 __isl_give isl_set *isl_set_eliminate(
4599 __isl_take isl_set *set, enum isl_dim_type type,
4600 unsigned first, unsigned n);
4601 __isl_give isl_basic_map *isl_basic_map_eliminate(
4602 __isl_take isl_basic_map *bmap,
4603 enum isl_dim_type type,
4604 unsigned first, unsigned n);
4605 __isl_give isl_map *isl_map_eliminate(
4606 __isl_take isl_map *map, enum isl_dim_type type,
4607 unsigned first, unsigned n);
4609 Eliminate the coefficients for the given dimensions from the constraints,
4610 without removing the dimensions.
4612 =item * Constructing a set from a parameter domain
4614 A zero-dimensional (local) space or (basic) set can be constructed
4615 on a given parameter domain using the following functions.
4617 #include <isl/space.h>
4618 __isl_give isl_space *isl_space_set_from_params(
4619 __isl_take isl_space *space);
4621 #include <isl/local_space.h>
4622 __isl_give isl_local_space *
4623 isl_local_space_set_from_params(
4624 __isl_take isl_local_space *ls);
4626 #include <isl/set.h>
4627 __isl_give isl_basic_set *isl_basic_set_from_params(
4628 __isl_take isl_basic_set *bset);
4629 __isl_give isl_set *isl_set_from_params(
4630 __isl_take isl_set *set);
4632 =item * Constructing a relation from one or two sets
4634 Create a relation with the given set(s) as domain and/or range.
4635 If only the domain or the range is specified, then
4636 the range or domain of the created relation is a zero-dimensional
4637 flat anonymous space.
4639 #include <isl/space.h>
4640 __isl_give isl_space *isl_space_from_domain(
4641 __isl_take isl_space *space);
4642 __isl_give isl_space *isl_space_from_range(
4643 __isl_take isl_space *space);
4644 __isl_give isl_space *isl_space_map_from_set(
4645 __isl_take isl_space *space);
4646 __isl_give isl_space *isl_space_map_from_domain_and_range(
4647 __isl_take isl_space *domain,
4648 __isl_take isl_space *range);
4650 #include <isl/local_space.h>
4651 __isl_give isl_local_space *isl_local_space_from_domain(
4652 __isl_take isl_local_space *ls);
4654 #include <isl/map.h>
4655 __isl_give isl_map *isl_map_from_domain(
4656 __isl_take isl_set *set);
4657 __isl_give isl_map *isl_map_from_range(
4658 __isl_take isl_set *set);
4660 #include <isl/union_map.h>
4661 __isl_give isl_union_map *isl_union_map_from_domain(
4662 __isl_take isl_union_set *uset);
4663 __isl_give isl_union_map *isl_union_map_from_range(
4664 __isl_take isl_union_set *uset);
4665 __isl_give isl_union_map *
4666 isl_union_map_from_domain_and_range(
4667 __isl_take isl_union_set *domain,
4668 __isl_take isl_union_set *range);
4670 #include <isl/val.h>
4671 __isl_give isl_multi_val *isl_multi_val_from_range(
4672 __isl_take isl_multi_val *mv);
4674 #include <isl/aff.h>
4675 __isl_give isl_aff *isl_aff_from_range(
4676 __isl_take isl_aff *aff);
4677 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4678 __isl_take isl_multi_aff *ma);
4679 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4680 __isl_take isl_pw_aff *pwa);
4681 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4682 __isl_take isl_multi_pw_aff *mpa);
4683 __isl_give isl_multi_union_pw_aff *
4684 isl_multi_union_pw_aff_from_range(
4685 __isl_take isl_multi_union_pw_aff *mupa);
4686 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4687 __isl_take isl_set *set);
4688 __isl_give isl_union_pw_multi_aff *
4689 isl_union_pw_multi_aff_from_domain(
4690 __isl_take isl_union_set *uset);
4692 #include <isl/polynomial.h>
4693 __isl_give isl_pw_qpolynomial *
4694 isl_pw_qpolynomial_from_range(
4695 __isl_take isl_pw_qpolynomial *pwqp);
4696 __isl_give isl_pw_qpolynomial_fold *
4697 isl_pw_qpolynomial_fold_from_range(
4698 __isl_take isl_pw_qpolynomial_fold *pwf);
4702 #include <isl/set.h>
4703 __isl_give isl_basic_set *isl_basic_set_fix_si(
4704 __isl_take isl_basic_set *bset,
4705 enum isl_dim_type type, unsigned pos, int value);
4706 __isl_give isl_basic_set *isl_basic_set_fix_val(
4707 __isl_take isl_basic_set *bset,
4708 enum isl_dim_type type, unsigned pos,
4709 __isl_take isl_val *v);
4710 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
4711 enum isl_dim_type type, unsigned pos, int value);
4712 __isl_give isl_set *isl_set_fix_val(
4713 __isl_take isl_set *set,
4714 enum isl_dim_type type, unsigned pos,
4715 __isl_take isl_val *v);
4717 #include <isl/map.h>
4718 __isl_give isl_basic_map *isl_basic_map_fix_si(
4719 __isl_take isl_basic_map *bmap,
4720 enum isl_dim_type type, unsigned pos, int value);
4721 __isl_give isl_basic_map *isl_basic_map_fix_val(
4722 __isl_take isl_basic_map *bmap,
4723 enum isl_dim_type type, unsigned pos,
4724 __isl_take isl_val *v);
4725 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
4726 enum isl_dim_type type, unsigned pos, int value);
4727 __isl_give isl_map *isl_map_fix_val(
4728 __isl_take isl_map *map,
4729 enum isl_dim_type type, unsigned pos,
4730 __isl_take isl_val *v);
4732 #include <isl/aff.h>
4733 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4734 __isl_take isl_pw_multi_aff *pma,
4735 enum isl_dim_type type, unsigned pos, int value);
4737 #include <isl/polynomial.h>
4738 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4739 __isl_take isl_pw_qpolynomial *pwqp,
4740 enum isl_dim_type type, unsigned n,
4741 __isl_take isl_val *v);
4742 __isl_give isl_pw_qpolynomial_fold *
4743 isl_pw_qpolynomial_fold_fix_val(
4744 __isl_take isl_pw_qpolynomial_fold *pwf,
4745 enum isl_dim_type type, unsigned n,
4746 __isl_take isl_val *v);
4748 Intersect the set, relation or function domain
4749 with the hyperplane where the given
4750 dimension has the fixed given value.
4752 #include <isl/set.h>
4753 __isl_give isl_basic_set *
4754 isl_basic_set_lower_bound_val(
4755 __isl_take isl_basic_set *bset,
4756 enum isl_dim_type type, unsigned pos,
4757 __isl_take isl_val *value);
4758 __isl_give isl_basic_set *
4759 isl_basic_set_upper_bound_val(
4760 __isl_take isl_basic_set *bset,
4761 enum isl_dim_type type, unsigned pos,
4762 __isl_take isl_val *value);
4763 __isl_give isl_set *isl_set_lower_bound_si(
4764 __isl_take isl_set *set,
4765 enum isl_dim_type type, unsigned pos, int value);
4766 __isl_give isl_set *isl_set_lower_bound_val(
4767 __isl_take isl_set *set,
4768 enum isl_dim_type type, unsigned pos,
4769 __isl_take isl_val *value);
4770 __isl_give isl_set *isl_set_upper_bound_si(
4771 __isl_take isl_set *set,
4772 enum isl_dim_type type, unsigned pos, int value);
4773 __isl_give isl_set *isl_set_upper_bound_val(
4774 __isl_take isl_set *set,
4775 enum isl_dim_type type, unsigned pos,
4776 __isl_take isl_val *value);
4778 #include <isl/map.h>
4779 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
4780 __isl_take isl_basic_map *bmap,
4781 enum isl_dim_type type, unsigned pos, int value);
4782 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
4783 __isl_take isl_basic_map *bmap,
4784 enum isl_dim_type type, unsigned pos, int value);
4785 __isl_give isl_map *isl_map_lower_bound_si(
4786 __isl_take isl_map *map,
4787 enum isl_dim_type type, unsigned pos, int value);
4788 __isl_give isl_map *isl_map_upper_bound_si(
4789 __isl_take isl_map *map,
4790 enum isl_dim_type type, unsigned pos, int value);
4792 Intersect the set or relation with the half-space where the given
4793 dimension has a value bounded by the fixed given integer value.
4795 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
4796 enum isl_dim_type type1, int pos1,
4797 enum isl_dim_type type2, int pos2);
4798 __isl_give isl_basic_map *isl_basic_map_equate(
4799 __isl_take isl_basic_map *bmap,
4800 enum isl_dim_type type1, int pos1,
4801 enum isl_dim_type type2, int pos2);
4802 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
4803 enum isl_dim_type type1, int pos1,
4804 enum isl_dim_type type2, int pos2);
4806 Intersect the set or relation with the hyperplane where the given
4807 dimensions are equal to each other.
4809 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
4810 enum isl_dim_type type1, int pos1,
4811 enum isl_dim_type type2, int pos2);
4813 Intersect the relation with the hyperplane where the given
4814 dimensions have opposite values.
4816 __isl_give isl_map *isl_map_order_le(
4817 __isl_take isl_map *map,
4818 enum isl_dim_type type1, int pos1,
4819 enum isl_dim_type type2, int pos2);
4820 __isl_give isl_basic_map *isl_basic_map_order_ge(
4821 __isl_take isl_basic_map *bmap,
4822 enum isl_dim_type type1, int pos1,
4823 enum isl_dim_type type2, int pos2);
4824 __isl_give isl_map *isl_map_order_ge(
4825 __isl_take isl_map *map,
4826 enum isl_dim_type type1, int pos1,
4827 enum isl_dim_type type2, int pos2);
4828 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
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_order_gt(
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_order_gt(__isl_take isl_map *map,
4836 enum isl_dim_type type1, int pos1,
4837 enum isl_dim_type type2, int pos2);
4839 Intersect the relation with the half-space where the given
4840 dimensions satisfy the given ordering.
4842 #include <isl/union_set.h>
4843 __isl_give isl_union_map *isl_union_map_remove_map_if(
4844 __isl_take isl_union_map *umap,
4845 isl_bool (*fn)(__isl_keep isl_map *map,
4846 void *user), void *user);
4848 This function calls the callback function once for each
4849 pair of spaces for which there are elements in the input.
4850 If the callback returns C<isl_bool_true>, then all those elements
4851 are removed from the result. The only remaining elements in the output
4852 are then those for which the callback returns C<isl_bool_false>.
4856 #include <isl/aff.h>
4857 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4858 __isl_take isl_aff *aff);
4859 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4860 __isl_take isl_aff *aff);
4861 __isl_give isl_set *isl_pw_aff_pos_set(
4862 __isl_take isl_pw_aff *pa);
4863 __isl_give isl_set *isl_pw_aff_nonneg_set(
4864 __isl_take isl_pw_aff *pwaff);
4865 __isl_give isl_set *isl_pw_aff_zero_set(
4866 __isl_take isl_pw_aff *pwaff);
4867 __isl_give isl_set *isl_pw_aff_non_zero_set(
4868 __isl_take isl_pw_aff *pwaff);
4869 __isl_give isl_union_set *
4870 isl_union_pw_aff_zero_union_set(
4871 __isl_take isl_union_pw_aff *upa);
4872 __isl_give isl_union_set *
4873 isl_multi_union_pw_aff_zero_union_set(
4874 __isl_take isl_multi_union_pw_aff *mupa);
4876 The function C<isl_aff_neg_basic_set> returns a basic set
4877 containing those elements in the domain space
4878 of C<aff> where C<aff> is negative.
4879 The function C<isl_pw_aff_nonneg_set> returns a set
4880 containing those elements in the domain
4881 of C<pwaff> where C<pwaff> is non-negative.
4882 The function C<isl_multi_union_pw_aff_zero_union_set>
4883 returns a union set containing those elements
4884 in the domains of its elements where they are all zero.
4888 __isl_give isl_map *isl_set_identity(
4889 __isl_take isl_set *set);
4890 __isl_give isl_union_map *isl_union_set_identity(
4891 __isl_take isl_union_set *uset);
4892 __isl_give isl_union_pw_multi_aff *
4893 isl_union_set_identity_union_pw_multi_aff(
4894 __isl_take isl_union_set *uset);
4896 Construct an identity relation on the given (union) set.
4898 =item * Function Extraction
4900 A piecewise quasi affine expression that is equal to 1 on a set
4901 and 0 outside the set can be created using the following function.
4903 #include <isl/aff.h>
4904 __isl_give isl_pw_aff *isl_set_indicator_function(
4905 __isl_take isl_set *set);
4907 A piecewise multiple quasi affine expression can be extracted
4908 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4909 and the C<isl_map> is single-valued.
4910 In case of a conversion from an C<isl_union_map>
4911 to an C<isl_union_pw_multi_aff>, these properties need to hold
4912 in each domain space.
4913 A conversion to a C<isl_multi_union_pw_aff> additionally
4914 requires that the input is non-empty and involves only a single
4917 #include <isl/aff.h>
4918 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4919 __isl_take isl_set *set);
4920 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4921 __isl_take isl_map *map);
4923 __isl_give isl_union_pw_multi_aff *
4924 isl_union_pw_multi_aff_from_union_set(
4925 __isl_take isl_union_set *uset);
4926 __isl_give isl_union_pw_multi_aff *
4927 isl_union_pw_multi_aff_from_union_map(
4928 __isl_take isl_union_map *umap);
4930 __isl_give isl_multi_union_pw_aff *
4931 isl_multi_union_pw_aff_from_union_map(
4932 __isl_take isl_union_map *umap);
4936 __isl_give isl_basic_set *isl_basic_map_deltas(
4937 __isl_take isl_basic_map *bmap);
4938 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
4939 __isl_give isl_union_set *isl_union_map_deltas(
4940 __isl_take isl_union_map *umap);
4942 These functions return a (basic) set containing the differences
4943 between image elements and corresponding domain elements in the input.
4945 __isl_give isl_basic_map *isl_basic_map_deltas_map(
4946 __isl_take isl_basic_map *bmap);
4947 __isl_give isl_map *isl_map_deltas_map(
4948 __isl_take isl_map *map);
4949 __isl_give isl_union_map *isl_union_map_deltas_map(
4950 __isl_take isl_union_map *umap);
4952 The functions above construct a (basic, regular or union) relation
4953 that maps (a wrapped version of) the input relation to its delta set.
4957 Simplify the representation of a set, relation or functions by trying
4958 to combine pairs of basic sets or relations into a single
4959 basic set or relation.
4961 #include <isl/set.h>
4962 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
4964 #include <isl/map.h>
4965 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
4967 #include <isl/union_set.h>
4968 __isl_give isl_union_set *isl_union_set_coalesce(
4969 __isl_take isl_union_set *uset);
4971 #include <isl/union_map.h>
4972 __isl_give isl_union_map *isl_union_map_coalesce(
4973 __isl_take isl_union_map *umap);
4975 #include <isl/aff.h>
4976 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4977 __isl_take isl_pw_aff *pwqp);
4978 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4979 __isl_take isl_pw_multi_aff *pma);
4980 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4981 __isl_take isl_multi_pw_aff *mpa);
4982 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
4983 __isl_take isl_union_pw_aff *upa);
4984 __isl_give isl_union_pw_multi_aff *
4985 isl_union_pw_multi_aff_coalesce(
4986 __isl_take isl_union_pw_multi_aff *upma);
4987 __isl_give isl_multi_union_pw_aff *
4988 isl_multi_union_pw_aff_coalesce(
4989 __isl_take isl_multi_union_pw_aff *aff);
4991 #include <isl/polynomial.h>
4992 __isl_give isl_pw_qpolynomial_fold *
4993 isl_pw_qpolynomial_fold_coalesce(
4994 __isl_take isl_pw_qpolynomial_fold *pwf);
4995 __isl_give isl_union_pw_qpolynomial *
4996 isl_union_pw_qpolynomial_coalesce(
4997 __isl_take isl_union_pw_qpolynomial *upwqp);
4998 __isl_give isl_union_pw_qpolynomial_fold *
4999 isl_union_pw_qpolynomial_fold_coalesce(
5000 __isl_take isl_union_pw_qpolynomial_fold *upwf);
5002 One of the methods for combining pairs of basic sets or relations
5003 can result in coefficients that are much larger than those that appear
5004 in the constraints of the input. By default, the coefficients are
5005 not allowed to grow larger, but this can be changed by unsetting
5006 the following option.
5008 isl_stat isl_options_set_coalesce_bounded_wrapping(
5009 isl_ctx *ctx, int val);
5010 int isl_options_get_coalesce_bounded_wrapping(
5013 =item * Detecting equalities
5015 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
5016 __isl_take isl_basic_set *bset);
5017 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
5018 __isl_take isl_basic_map *bmap);
5019 __isl_give isl_set *isl_set_detect_equalities(
5020 __isl_take isl_set *set);
5021 __isl_give isl_map *isl_map_detect_equalities(
5022 __isl_take isl_map *map);
5023 __isl_give isl_union_set *isl_union_set_detect_equalities(
5024 __isl_take isl_union_set *uset);
5025 __isl_give isl_union_map *isl_union_map_detect_equalities(
5026 __isl_take isl_union_map *umap);
5028 Simplify the representation of a set or relation by detecting implicit
5031 =item * Removing redundant constraints
5033 #include <isl/set.h>
5034 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
5035 __isl_take isl_basic_set *bset);
5036 __isl_give isl_set *isl_set_remove_redundancies(
5037 __isl_take isl_set *set);
5039 #include <isl/union_set.h>
5040 __isl_give isl_union_set *
5041 isl_union_set_remove_redundancies(
5042 __isl_take isl_union_set *uset);
5044 #include <isl/map.h>
5045 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
5046 __isl_take isl_basic_map *bmap);
5047 __isl_give isl_map *isl_map_remove_redundancies(
5048 __isl_take isl_map *map);
5050 #include <isl/union_map.h>
5051 __isl_give isl_union_map *
5052 isl_union_map_remove_redundancies(
5053 __isl_take isl_union_map *umap);
5057 __isl_give isl_basic_set *isl_set_convex_hull(
5058 __isl_take isl_set *set);
5059 __isl_give isl_basic_map *isl_map_convex_hull(
5060 __isl_take isl_map *map);
5062 If the input set or relation has any existentially quantified
5063 variables, then the result of these operations is currently undefined.
5067 #include <isl/set.h>
5068 __isl_give isl_basic_set *
5069 isl_set_unshifted_simple_hull(
5070 __isl_take isl_set *set);
5071 __isl_give isl_basic_set *isl_set_simple_hull(
5072 __isl_take isl_set *set);
5073 __isl_give isl_basic_set *
5074 isl_set_plain_unshifted_simple_hull(
5075 __isl_take isl_set *set);
5076 __isl_give isl_basic_set *
5077 isl_set_unshifted_simple_hull_from_set_list(
5078 __isl_take isl_set *set,
5079 __isl_take isl_set_list *list);
5081 #include <isl/map.h>
5082 __isl_give isl_basic_map *
5083 isl_map_unshifted_simple_hull(
5084 __isl_take isl_map *map);
5085 __isl_give isl_basic_map *isl_map_simple_hull(
5086 __isl_take isl_map *map);
5087 __isl_give isl_basic_map *
5088 isl_map_plain_unshifted_simple_hull(
5089 __isl_take isl_map *map);
5090 __isl_give isl_basic_map *
5091 isl_map_unshifted_simple_hull_from_map_list(
5092 __isl_take isl_map *map,
5093 __isl_take isl_map_list *list);
5095 #include <isl/union_map.h>
5096 __isl_give isl_union_map *isl_union_map_simple_hull(
5097 __isl_take isl_union_map *umap);
5099 These functions compute a single basic set or relation
5100 that contains the whole input set or relation.
5101 In particular, the output is described by translates
5102 of the constraints describing the basic sets or relations in the input.
5103 In case of C<isl_set_unshifted_simple_hull>, only the original
5104 constraints are used, without any translation.
5105 In case of C<isl_set_plain_unshifted_simple_hull> and
5106 C<isl_map_plain_unshifted_simple_hull>, the result is described
5107 by original constraints that are obviously satisfied
5108 by the entire input set or relation.
5109 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
5110 C<isl_map_unshifted_simple_hull_from_map_list>, the
5111 constraints are taken from the elements of the second argument.
5115 (See \autoref{s:simple hull}.)
5121 __isl_give isl_basic_set *isl_basic_set_affine_hull(
5122 __isl_take isl_basic_set *bset);
5123 __isl_give isl_basic_set *isl_set_affine_hull(
5124 __isl_take isl_set *set);
5125 __isl_give isl_union_set *isl_union_set_affine_hull(
5126 __isl_take isl_union_set *uset);
5127 __isl_give isl_basic_map *isl_basic_map_affine_hull(
5128 __isl_take isl_basic_map *bmap);
5129 __isl_give isl_basic_map *isl_map_affine_hull(
5130 __isl_take isl_map *map);
5131 __isl_give isl_union_map *isl_union_map_affine_hull(
5132 __isl_take isl_union_map *umap);
5134 In case of union sets and relations, the affine hull is computed
5137 =item * Polyhedral hull
5139 __isl_give isl_basic_set *isl_set_polyhedral_hull(
5140 __isl_take isl_set *set);
5141 __isl_give isl_basic_map *isl_map_polyhedral_hull(
5142 __isl_take isl_map *map);
5143 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
5144 __isl_take isl_union_set *uset);
5145 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
5146 __isl_take isl_union_map *umap);
5148 These functions compute a single basic set or relation
5149 not involving any existentially quantified variables
5150 that contains the whole input set or relation.
5151 In case of union sets and relations, the polyhedral hull is computed
5154 =item * Other approximations
5156 #include <isl/set.h>
5157 __isl_give isl_basic_set *
5158 isl_basic_set_drop_constraints_involving_dims(
5159 __isl_take isl_basic_set *bset,
5160 enum isl_dim_type type,
5161 unsigned first, unsigned n);
5162 __isl_give isl_basic_set *
5163 isl_basic_set_drop_constraints_not_involving_dims(
5164 __isl_take isl_basic_set *bset,
5165 enum isl_dim_type type,
5166 unsigned first, unsigned n);
5167 __isl_give isl_set *
5168 isl_set_drop_constraints_involving_dims(
5169 __isl_take isl_set *set,
5170 enum isl_dim_type type,
5171 unsigned first, unsigned n);
5172 __isl_give isl_set *
5173 isl_set_drop_constraints_not_involving_dims(
5174 __isl_take isl_set *set,
5175 enum isl_dim_type type,
5176 unsigned first, unsigned n);
5178 #include <isl/map.h>
5179 __isl_give isl_basic_map *
5180 isl_basic_map_drop_constraints_involving_dims(
5181 __isl_take isl_basic_map *bmap,
5182 enum isl_dim_type type,
5183 unsigned first, unsigned n);
5184 __isl_give isl_basic_map *
5185 isl_basic_map_drop_constraints_not_involving_dims(
5186 __isl_take isl_basic_map *bmap,
5187 enum isl_dim_type type,
5188 unsigned first, unsigned n);
5189 __isl_give isl_map *
5190 isl_map_drop_constraints_involving_dims(
5191 __isl_take isl_map *map,
5192 enum isl_dim_type type,
5193 unsigned first, unsigned n);
5194 __isl_give isl_map *
5195 isl_map_drop_constraints_not_involving_dims(
5196 __isl_take isl_map *map,
5197 enum isl_dim_type type,
5198 unsigned first, unsigned n);
5200 These functions drop any constraints (not) involving the specified dimensions.
5201 Note that the result depends on the representation of the input.
5203 #include <isl/polynomial.h>
5204 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5205 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5206 __isl_give isl_union_pw_qpolynomial *
5207 isl_union_pw_qpolynomial_to_polynomial(
5208 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5210 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5211 the polynomial will be an overapproximation. If C<sign> is negative,
5212 it will be an underapproximation. If C<sign> is zero, the approximation
5213 will lie somewhere in between.
5217 __isl_give isl_basic_set *isl_basic_set_sample(
5218 __isl_take isl_basic_set *bset);
5219 __isl_give isl_basic_set *isl_set_sample(
5220 __isl_take isl_set *set);
5221 __isl_give isl_basic_map *isl_basic_map_sample(
5222 __isl_take isl_basic_map *bmap);
5223 __isl_give isl_basic_map *isl_map_sample(
5224 __isl_take isl_map *map);
5226 If the input (basic) set or relation is non-empty, then return
5227 a singleton subset of the input. Otherwise, return an empty set.
5229 =item * Optimization
5231 #include <isl/ilp.h>
5232 __isl_give isl_val *isl_basic_set_max_val(
5233 __isl_keep isl_basic_set *bset,
5234 __isl_keep isl_aff *obj);
5235 __isl_give isl_val *isl_set_min_val(
5236 __isl_keep isl_set *set,
5237 __isl_keep isl_aff *obj);
5238 __isl_give isl_val *isl_set_max_val(
5239 __isl_keep isl_set *set,
5240 __isl_keep isl_aff *obj);
5241 __isl_give isl_multi_val *
5242 isl_union_set_min_multi_union_pw_aff(
5243 __isl_keep isl_union_set *set,
5244 __isl_keep isl_multi_union_pw_aff *obj);
5246 Compute the minimum or maximum of the integer affine expression C<obj>
5247 over the points in C<set>, returning the result in C<opt>.
5248 The result is C<NULL> in case of an error, the optimal value in case
5249 there is one, negative infinity or infinity if the problem is unbounded and
5250 NaN if the problem is empty.
5252 #include <isl/ilp.h>
5253 __isl_give isl_val *isl_basic_set_dim_max_val(
5254 __isl_take isl_basic_set *bset, int pos);
5256 Return the maximal value attained by the given set dimension,
5257 independently of the parameter values and of any other dimensions.
5258 The result is C<NULL> in case of an error, the optimal value in case
5259 there is one, infinity if the problem is unbounded and
5260 NaN if the input is empty.
5262 =item * Parametric optimization
5264 __isl_give isl_pw_aff *isl_set_dim_min(
5265 __isl_take isl_set *set, int pos);
5266 __isl_give isl_pw_aff *isl_set_dim_max(
5267 __isl_take isl_set *set, int pos);
5268 __isl_give isl_pw_aff *isl_map_dim_min(
5269 __isl_take isl_map *map, int pos);
5270 __isl_give isl_pw_aff *isl_map_dim_max(
5271 __isl_take isl_map *map, int pos);
5273 Compute the minimum or maximum of the given set or output dimension
5274 as a function of the parameters (and input dimensions), but independently
5275 of the other set or output dimensions.
5276 For lexicographic optimization, see L<"Lexicographic Optimization">.
5280 The following functions compute either the set of (rational) coefficient
5281 values of valid constraints for the given set or the set of (rational)
5282 values satisfying the constraints with coefficients from the given set.
5283 Internally, these two sets of functions perform essentially the
5284 same operations, except that the set of coefficients is assumed to
5285 be a cone, while the set of values may be any polyhedron.
5286 The current implementation is based on the Farkas lemma and
5287 Fourier-Motzkin elimination, but this may change or be made optional
5288 in future. In particular, future implementations may use different
5289 dualization algorithms or skip the elimination step.
5291 #include <isl/set.h>
5292 __isl_give isl_basic_set *isl_basic_set_coefficients(
5293 __isl_take isl_basic_set *bset);
5294 __isl_give isl_basic_set_list *
5295 isl_basic_set_list_coefficients(
5296 __isl_take isl_basic_set_list *list);
5297 __isl_give isl_basic_set *isl_set_coefficients(
5298 __isl_take isl_set *set);
5299 __isl_give isl_union_set *isl_union_set_coefficients(
5300 __isl_take isl_union_set *bset);
5301 __isl_give isl_basic_set *isl_basic_set_solutions(
5302 __isl_take isl_basic_set *bset);
5303 __isl_give isl_basic_set *isl_set_solutions(
5304 __isl_take isl_set *set);
5305 __isl_give isl_union_set *isl_union_set_solutions(
5306 __isl_take isl_union_set *bset);
5310 __isl_give isl_map *isl_map_fixed_power_val(
5311 __isl_take isl_map *map,
5312 __isl_take isl_val *exp);
5313 __isl_give isl_union_map *
5314 isl_union_map_fixed_power_val(
5315 __isl_take isl_union_map *umap,
5316 __isl_take isl_val *exp);
5318 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
5319 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
5320 of C<map> is computed.
5322 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
5324 __isl_give isl_union_map *isl_union_map_power(
5325 __isl_take isl_union_map *umap, int *exact);
5327 Compute a parametric representation for all positive powers I<k> of C<map>.
5328 The result maps I<k> to a nested relation corresponding to the
5329 I<k>th power of C<map>.
5330 The result may be an overapproximation. If the result is known to be exact,
5331 then C<*exact> is set to C<1>.
5333 =item * Transitive closure
5335 __isl_give isl_map *isl_map_transitive_closure(
5336 __isl_take isl_map *map, int *exact);
5337 __isl_give isl_union_map *isl_union_map_transitive_closure(
5338 __isl_take isl_union_map *umap, int *exact);
5340 Compute the transitive closure of C<map>.
5341 The result may be an overapproximation. If the result is known to be exact,
5342 then C<*exact> is set to C<1>.
5344 =item * Reaching path lengths
5346 __isl_give isl_map *isl_map_reaching_path_lengths(
5347 __isl_take isl_map *map, int *exact);
5349 Compute a relation that maps each element in the range of C<map>
5350 to the lengths of all paths composed of edges in C<map> that
5351 end up in the given element.
5352 The result may be an overapproximation. If the result is known to be exact,
5353 then C<*exact> is set to C<1>.
5354 To compute the I<maximal> path length, the resulting relation
5355 should be postprocessed by C<isl_map_lexmax>.
5356 In particular, if the input relation is a dependence relation
5357 (mapping sources to sinks), then the maximal path length corresponds
5358 to the free schedule.
5359 Note, however, that C<isl_map_lexmax> expects the maximum to be
5360 finite, so if the path lengths are unbounded (possibly due to
5361 the overapproximation), then you will get an error message.
5365 #include <isl/space.h>
5366 __isl_give isl_space *isl_space_wrap(
5367 __isl_take isl_space *space);
5368 __isl_give isl_space *isl_space_unwrap(
5369 __isl_take isl_space *space);
5371 #include <isl/local_space.h>
5372 __isl_give isl_local_space *isl_local_space_wrap(
5373 __isl_take isl_local_space *ls);
5375 #include <isl/set.h>
5376 __isl_give isl_basic_map *isl_basic_set_unwrap(
5377 __isl_take isl_basic_set *bset);
5378 __isl_give isl_map *isl_set_unwrap(
5379 __isl_take isl_set *set);
5381 #include <isl/map.h>
5382 __isl_give isl_basic_set *isl_basic_map_wrap(
5383 __isl_take isl_basic_map *bmap);
5384 __isl_give isl_set *isl_map_wrap(
5385 __isl_take isl_map *map);
5387 #include <isl/union_set.h>
5388 __isl_give isl_union_map *isl_union_set_unwrap(
5389 __isl_take isl_union_set *uset);
5391 #include <isl/union_map.h>
5392 __isl_give isl_union_set *isl_union_map_wrap(
5393 __isl_take isl_union_map *umap);
5395 The input to C<isl_space_unwrap> should
5396 be the space of a set, while that of
5397 C<isl_space_wrap> should be the space of a relation.
5398 Conversely, the output of C<isl_space_unwrap> is the space
5399 of a relation, while that of C<isl_space_wrap> is the space of a set.
5403 Remove any internal structure of domain (and range) of the given
5404 set or relation. If there is any such internal structure in the input,
5405 then the name of the space is also removed.
5407 #include <isl/space.h>
5408 __isl_give isl_space *isl_space_flatten_domain(
5409 __isl_take isl_space *space);
5410 __isl_give isl_space *isl_space_flatten_range(
5411 __isl_take isl_space *space);
5413 #include <isl/local_space.h>
5414 __isl_give isl_local_space *
5415 isl_local_space_flatten_domain(
5416 __isl_take isl_local_space *ls);
5417 __isl_give isl_local_space *
5418 isl_local_space_flatten_range(
5419 __isl_take isl_local_space *ls);
5421 #include <isl/set.h>
5422 __isl_give isl_basic_set *isl_basic_set_flatten(
5423 __isl_take isl_basic_set *bset);
5424 __isl_give isl_set *isl_set_flatten(
5425 __isl_take isl_set *set);
5427 #include <isl/map.h>
5428 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
5429 __isl_take isl_basic_map *bmap);
5430 __isl_give isl_basic_map *isl_basic_map_flatten_range(
5431 __isl_take isl_basic_map *bmap);
5432 __isl_give isl_map *isl_map_flatten_range(
5433 __isl_take isl_map *map);
5434 __isl_give isl_map *isl_map_flatten_domain(
5435 __isl_take isl_map *map);
5436 __isl_give isl_basic_map *isl_basic_map_flatten(
5437 __isl_take isl_basic_map *bmap);
5438 __isl_give isl_map *isl_map_flatten(
5439 __isl_take isl_map *map);
5441 #include <isl/val.h>
5442 __isl_give isl_multi_val *isl_multi_val_flatten_range(
5443 __isl_take isl_multi_val *mv);
5445 #include <isl/aff.h>
5446 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
5447 __isl_take isl_multi_aff *ma);
5448 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
5449 __isl_take isl_multi_aff *ma);
5450 __isl_give isl_multi_pw_aff *
5451 isl_multi_pw_aff_flatten_range(
5452 __isl_take isl_multi_pw_aff *mpa);
5453 __isl_give isl_multi_union_pw_aff *
5454 isl_multi_union_pw_aff_flatten_range(
5455 __isl_take isl_multi_union_pw_aff *mupa);
5457 #include <isl/map.h>
5458 __isl_give isl_map *isl_set_flatten_map(
5459 __isl_take isl_set *set);
5461 The function above constructs a relation
5462 that maps the input set to a flattened version of the set.
5466 Lift the input set to a space with extra dimensions corresponding
5467 to the existentially quantified variables in the input.
5468 In particular, the result lives in a wrapped map where the domain
5469 is the original space and the range corresponds to the original
5470 existentially quantified variables.
5472 #include <isl/set.h>
5473 __isl_give isl_basic_set *isl_basic_set_lift(
5474 __isl_take isl_basic_set *bset);
5475 __isl_give isl_set *isl_set_lift(
5476 __isl_take isl_set *set);
5477 __isl_give isl_union_set *isl_union_set_lift(
5478 __isl_take isl_union_set *uset);
5480 Given a local space that contains the existentially quantified
5481 variables of a set, a basic relation that, when applied to
5482 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
5483 can be constructed using the following function.
5485 #include <isl/local_space.h>
5486 __isl_give isl_basic_map *isl_local_space_lifting(
5487 __isl_take isl_local_space *ls);
5489 #include <isl/aff.h>
5490 __isl_give isl_multi_aff *isl_multi_aff_lift(
5491 __isl_take isl_multi_aff *maff,
5492 __isl_give isl_local_space **ls);
5494 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
5495 then it is assigned the local space that lies at the basis of
5496 the lifting applied.
5498 =item * Internal Product
5500 #include <isl/space.h>
5501 __isl_give isl_space *isl_space_zip(
5502 __isl_take isl_space *space);
5504 #include <isl/map.h>
5505 __isl_give isl_basic_map *isl_basic_map_zip(
5506 __isl_take isl_basic_map *bmap);
5507 __isl_give isl_map *isl_map_zip(
5508 __isl_take isl_map *map);
5510 #include <isl/union_map.h>
5511 __isl_give isl_union_map *isl_union_map_zip(
5512 __isl_take isl_union_map *umap);
5514 Given a relation with nested relations for domain and range,
5515 interchange the range of the domain with the domain of the range.
5519 #include <isl/space.h>
5520 __isl_give isl_space *isl_space_curry(
5521 __isl_take isl_space *space);
5522 __isl_give isl_space *isl_space_uncurry(
5523 __isl_take isl_space *space);
5525 #include <isl/map.h>
5526 __isl_give isl_basic_map *isl_basic_map_curry(
5527 __isl_take isl_basic_map *bmap);
5528 __isl_give isl_basic_map *isl_basic_map_uncurry(
5529 __isl_take isl_basic_map *bmap);
5530 __isl_give isl_map *isl_map_curry(
5531 __isl_take isl_map *map);
5532 __isl_give isl_map *isl_map_uncurry(
5533 __isl_take isl_map *map);
5535 #include <isl/union_map.h>
5536 __isl_give isl_union_map *isl_union_map_curry(
5537 __isl_take isl_union_map *umap);
5538 __isl_give isl_union_map *isl_union_map_uncurry(
5539 __isl_take isl_union_map *umap);
5541 Given a relation with a nested relation for domain,
5542 the C<curry> functions
5543 move the range of the nested relation out of the domain
5544 and use it as the domain of a nested relation in the range,
5545 with the original range as range of this nested relation.
5546 The C<uncurry> functions perform the inverse operation.
5548 #include <isl/space.h>
5549 __isl_give isl_space *isl_space_range_curry(
5550 __isl_take isl_space *space);
5552 #include <isl/map.h>
5553 __isl_give isl_map *isl_map_range_curry(
5554 __isl_take isl_map *map);
5556 #include <isl/union_map.h>
5557 __isl_give isl_union_map *isl_union_map_range_curry(
5558 __isl_take isl_union_map *umap);
5560 These functions apply the currying to the relation that
5561 is nested inside the range of the input.
5563 =item * Aligning parameters
5565 Change the order of the parameters of the given set, relation
5567 such that the first parameters match those of C<model>.
5568 This may involve the introduction of extra parameters.
5569 All parameters need to be named.
5571 #include <isl/space.h>
5572 __isl_give isl_space *isl_space_align_params(
5573 __isl_take isl_space *space1,
5574 __isl_take isl_space *space2)
5576 #include <isl/set.h>
5577 __isl_give isl_basic_set *isl_basic_set_align_params(
5578 __isl_take isl_basic_set *bset,
5579 __isl_take isl_space *model);
5580 __isl_give isl_set *isl_set_align_params(
5581 __isl_take isl_set *set,
5582 __isl_take isl_space *model);
5584 #include <isl/map.h>
5585 __isl_give isl_basic_map *isl_basic_map_align_params(
5586 __isl_take isl_basic_map *bmap,
5587 __isl_take isl_space *model);
5588 __isl_give isl_map *isl_map_align_params(
5589 __isl_take isl_map *map,
5590 __isl_take isl_space *model);
5592 #include <isl/val.h>
5593 __isl_give isl_multi_val *isl_multi_val_align_params(
5594 __isl_take isl_multi_val *mv,
5595 __isl_take isl_space *model);
5597 #include <isl/aff.h>
5598 __isl_give isl_aff *isl_aff_align_params(
5599 __isl_take isl_aff *aff,
5600 __isl_take isl_space *model);
5601 __isl_give isl_multi_aff *isl_multi_aff_align_params(
5602 __isl_take isl_multi_aff *multi,
5603 __isl_take isl_space *model);
5604 __isl_give isl_pw_aff *isl_pw_aff_align_params(
5605 __isl_take isl_pw_aff *pwaff,
5606 __isl_take isl_space *model);
5607 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
5608 __isl_take isl_pw_multi_aff *pma,
5609 __isl_take isl_space *model);
5610 __isl_give isl_union_pw_aff *
5611 isl_union_pw_aff_align_params(
5612 __isl_take isl_union_pw_aff *upa,
5613 __isl_take isl_space *model);
5614 __isl_give isl_union_pw_multi_aff *
5615 isl_union_pw_multi_aff_align_params(
5616 __isl_take isl_union_pw_multi_aff *upma,
5617 __isl_take isl_space *model);
5618 __isl_give isl_multi_union_pw_aff *
5619 isl_multi_union_pw_aff_align_params(
5620 __isl_take isl_multi_union_pw_aff *mupa,
5621 __isl_take isl_space *model);
5623 #include <isl/polynomial.h>
5624 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5625 __isl_take isl_qpolynomial *qp,
5626 __isl_take isl_space *model);
5628 =item * Unary Arithmetic Operations
5630 #include <isl/set.h>
5631 __isl_give isl_set *isl_set_neg(
5632 __isl_take isl_set *set);
5633 #include <isl/map.h>
5634 __isl_give isl_map *isl_map_neg(
5635 __isl_take isl_map *map);
5637 C<isl_set_neg> constructs a set containing the opposites of
5638 the elements in its argument.
5639 The domain of the result of C<isl_map_neg> is the same
5640 as the domain of its argument. The corresponding range
5641 elements are the opposites of the corresponding range
5642 elements in the argument.
5644 #include <isl/val.h>
5645 __isl_give isl_multi_val *isl_multi_val_neg(
5646 __isl_take isl_multi_val *mv);
5648 #include <isl/aff.h>
5649 __isl_give isl_aff *isl_aff_neg(
5650 __isl_take isl_aff *aff);
5651 __isl_give isl_multi_aff *isl_multi_aff_neg(
5652 __isl_take isl_multi_aff *ma);
5653 __isl_give isl_pw_aff *isl_pw_aff_neg(
5654 __isl_take isl_pw_aff *pwaff);
5655 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
5656 __isl_take isl_pw_multi_aff *pma);
5657 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
5658 __isl_take isl_multi_pw_aff *mpa);
5659 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
5660 __isl_take isl_union_pw_aff *upa);
5661 __isl_give isl_union_pw_multi_aff *
5662 isl_union_pw_multi_aff_neg(
5663 __isl_take isl_union_pw_multi_aff *upma);
5664 __isl_give isl_multi_union_pw_aff *
5665 isl_multi_union_pw_aff_neg(
5666 __isl_take isl_multi_union_pw_aff *mupa);
5667 __isl_give isl_aff *isl_aff_ceil(
5668 __isl_take isl_aff *aff);
5669 __isl_give isl_pw_aff *isl_pw_aff_ceil(
5670 __isl_take isl_pw_aff *pwaff);
5671 __isl_give isl_aff *isl_aff_floor(
5672 __isl_take isl_aff *aff);
5673 __isl_give isl_multi_aff *isl_multi_aff_floor(
5674 __isl_take isl_multi_aff *ma);
5675 __isl_give isl_pw_aff *isl_pw_aff_floor(
5676 __isl_take isl_pw_aff *pwaff);
5677 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
5678 __isl_take isl_union_pw_aff *upa);
5679 __isl_give isl_multi_union_pw_aff *
5680 isl_multi_union_pw_aff_floor(
5681 __isl_take isl_multi_union_pw_aff *mupa);
5683 #include <isl/aff.h>
5684 __isl_give isl_pw_aff *isl_pw_aff_list_min(
5685 __isl_take isl_pw_aff_list *list);
5686 __isl_give isl_pw_aff *isl_pw_aff_list_max(
5687 __isl_take isl_pw_aff_list *list);
5689 #include <isl/polynomial.h>
5690 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5691 __isl_take isl_qpolynomial *qp);
5692 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5693 __isl_take isl_pw_qpolynomial *pwqp);
5694 __isl_give isl_union_pw_qpolynomial *
5695 isl_union_pw_qpolynomial_neg(
5696 __isl_take isl_union_pw_qpolynomial *upwqp);
5697 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5698 __isl_take isl_qpolynomial *qp,
5700 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5701 __isl_take isl_pw_qpolynomial *pwqp,
5706 The following functions evaluate a function in a point.
5708 #include <isl/polynomial.h>
5709 __isl_give isl_val *isl_pw_qpolynomial_eval(
5710 __isl_take isl_pw_qpolynomial *pwqp,
5711 __isl_take isl_point *pnt);
5712 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5713 __isl_take isl_pw_qpolynomial_fold *pwf,
5714 __isl_take isl_point *pnt);
5715 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5716 __isl_take isl_union_pw_qpolynomial *upwqp,
5717 __isl_take isl_point *pnt);
5718 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5719 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5720 __isl_take isl_point *pnt);
5722 =item * Dimension manipulation
5724 It is usually not advisable to directly change the (input or output)
5725 space of a set or a relation as this removes the name and the internal
5726 structure of the space. However, the functions below can be useful
5727 to add new parameters, assuming
5728 C<isl_set_align_params> and C<isl_map_align_params>
5731 #include <isl/space.h>
5732 __isl_give isl_space *isl_space_add_dims(
5733 __isl_take isl_space *space,
5734 enum isl_dim_type type, unsigned n);
5735 __isl_give isl_space *isl_space_insert_dims(
5736 __isl_take isl_space *space,
5737 enum isl_dim_type type, unsigned pos, unsigned n);
5738 __isl_give isl_space *isl_space_drop_dims(
5739 __isl_take isl_space *space,
5740 enum isl_dim_type type, unsigned first, unsigned n);
5741 __isl_give isl_space *isl_space_move_dims(
5742 __isl_take isl_space *space,
5743 enum isl_dim_type dst_type, unsigned dst_pos,
5744 enum isl_dim_type src_type, unsigned src_pos,
5747 #include <isl/local_space.h>
5748 __isl_give isl_local_space *isl_local_space_add_dims(
5749 __isl_take isl_local_space *ls,
5750 enum isl_dim_type type, unsigned n);
5751 __isl_give isl_local_space *isl_local_space_insert_dims(
5752 __isl_take isl_local_space *ls,
5753 enum isl_dim_type type, unsigned first, unsigned n);
5754 __isl_give isl_local_space *isl_local_space_drop_dims(
5755 __isl_take isl_local_space *ls,
5756 enum isl_dim_type type, unsigned first, unsigned n);
5758 #include <isl/set.h>
5759 __isl_give isl_basic_set *isl_basic_set_add_dims(
5760 __isl_take isl_basic_set *bset,
5761 enum isl_dim_type type, unsigned n);
5762 __isl_give isl_set *isl_set_add_dims(
5763 __isl_take isl_set *set,
5764 enum isl_dim_type type, unsigned n);
5765 __isl_give isl_basic_set *isl_basic_set_insert_dims(
5766 __isl_take isl_basic_set *bset,
5767 enum isl_dim_type type, unsigned pos,
5769 __isl_give isl_set *isl_set_insert_dims(
5770 __isl_take isl_set *set,
5771 enum isl_dim_type type, unsigned pos, unsigned n);
5772 __isl_give isl_basic_set *isl_basic_set_move_dims(
5773 __isl_take isl_basic_set *bset,
5774 enum isl_dim_type dst_type, unsigned dst_pos,
5775 enum isl_dim_type src_type, unsigned src_pos,
5777 __isl_give isl_set *isl_set_move_dims(
5778 __isl_take isl_set *set,
5779 enum isl_dim_type dst_type, unsigned dst_pos,
5780 enum isl_dim_type src_type, unsigned src_pos,
5783 #include <isl/map.h>
5784 __isl_give isl_basic_map *isl_basic_map_add_dims(
5785 __isl_take isl_basic_map *bmap,
5786 enum isl_dim_type type, unsigned n);
5787 __isl_give isl_map *isl_map_add_dims(
5788 __isl_take isl_map *map,
5789 enum isl_dim_type type, unsigned n);
5790 __isl_give isl_basic_map *isl_basic_map_insert_dims(
5791 __isl_take isl_basic_map *bmap,
5792 enum isl_dim_type type, unsigned pos,
5794 __isl_give isl_map *isl_map_insert_dims(
5795 __isl_take isl_map *map,
5796 enum isl_dim_type type, unsigned pos, unsigned n);
5797 __isl_give isl_basic_map *isl_basic_map_move_dims(
5798 __isl_take isl_basic_map *bmap,
5799 enum isl_dim_type dst_type, unsigned dst_pos,
5800 enum isl_dim_type src_type, unsigned src_pos,
5802 __isl_give isl_map *isl_map_move_dims(
5803 __isl_take isl_map *map,
5804 enum isl_dim_type dst_type, unsigned dst_pos,
5805 enum isl_dim_type src_type, unsigned src_pos,
5808 #include <isl/val.h>
5809 __isl_give isl_multi_val *isl_multi_val_insert_dims(
5810 __isl_take isl_multi_val *mv,
5811 enum isl_dim_type type, unsigned first, unsigned n);
5812 __isl_give isl_multi_val *isl_multi_val_add_dims(
5813 __isl_take isl_multi_val *mv,
5814 enum isl_dim_type type, unsigned n);
5815 __isl_give isl_multi_val *isl_multi_val_drop_dims(
5816 __isl_take isl_multi_val *mv,
5817 enum isl_dim_type type, unsigned first, unsigned n);
5819 #include <isl/aff.h>
5820 __isl_give isl_aff *isl_aff_insert_dims(
5821 __isl_take isl_aff *aff,
5822 enum isl_dim_type type, unsigned first, unsigned n);
5823 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
5824 __isl_take isl_multi_aff *ma,
5825 enum isl_dim_type type, unsigned first, unsigned n);
5826 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
5827 __isl_take isl_pw_aff *pwaff,
5828 enum isl_dim_type type, unsigned first, unsigned n);
5829 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
5830 __isl_take isl_multi_pw_aff *mpa,
5831 enum isl_dim_type type, unsigned first, unsigned n);
5832 __isl_give isl_aff *isl_aff_add_dims(
5833 __isl_take isl_aff *aff,
5834 enum isl_dim_type type, unsigned n);
5835 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
5836 __isl_take isl_multi_aff *ma,
5837 enum isl_dim_type type, unsigned n);
5838 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
5839 __isl_take isl_pw_aff *pwaff,
5840 enum isl_dim_type type, unsigned n);
5841 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
5842 __isl_take isl_multi_pw_aff *mpa,
5843 enum isl_dim_type type, unsigned n);
5844 __isl_give isl_aff *isl_aff_drop_dims(
5845 __isl_take isl_aff *aff,
5846 enum isl_dim_type type, unsigned first, unsigned n);
5847 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
5848 __isl_take isl_multi_aff *maff,
5849 enum isl_dim_type type, unsigned first, unsigned n);
5850 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
5851 __isl_take isl_pw_aff *pwaff,
5852 enum isl_dim_type type, unsigned first, unsigned n);
5853 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
5854 __isl_take isl_pw_multi_aff *pma,
5855 enum isl_dim_type type, unsigned first, unsigned n);
5856 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
5857 __isl_take isl_union_pw_aff *upa,
5858 enum isl_dim_type type, unsigned first, unsigned n);
5859 __isl_give isl_union_pw_multi_aff *
5860 isl_union_pw_multi_aff_drop_dims(
5861 __isl_take isl_union_pw_multi_aff *upma,
5862 enum isl_dim_type type,
5863 unsigned first, unsigned n);
5864 __isl_give isl_multi_union_pw_aff *
5865 isl_multi_union_pw_aff_drop_dims(
5866 __isl_take isl_multi_union_pw_aff *mupa,
5867 enum isl_dim_type type, unsigned first,
5869 __isl_give isl_aff *isl_aff_move_dims(
5870 __isl_take isl_aff *aff,
5871 enum isl_dim_type dst_type, unsigned dst_pos,
5872 enum isl_dim_type src_type, unsigned src_pos,
5874 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
5875 __isl_take isl_multi_aff *ma,
5876 enum isl_dim_type dst_type, unsigned dst_pos,
5877 enum isl_dim_type src_type, unsigned src_pos,
5879 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
5880 __isl_take isl_pw_aff *pa,
5881 enum isl_dim_type dst_type, unsigned dst_pos,
5882 enum isl_dim_type src_type, unsigned src_pos,
5884 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
5885 __isl_take isl_multi_pw_aff *pma,
5886 enum isl_dim_type dst_type, unsigned dst_pos,
5887 enum isl_dim_type src_type, unsigned src_pos,
5890 #include <isl/polynomial.h>
5891 __isl_give isl_union_pw_qpolynomial *
5892 isl_union_pw_qpolynomial_drop_dims(
5893 __isl_take isl_union_pw_qpolynomial *upwqp,
5894 enum isl_dim_type type,
5895 unsigned first, unsigned n);
5896 __isl_give isl_union_pw_qpolynomial_fold *
5897 isl_union_pw_qpolynomial_fold_drop_dims(
5898 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5899 enum isl_dim_type type,
5900 unsigned first, unsigned n);
5902 The operations on union expressions can only manipulate parameters.
5906 =head2 Binary Operations
5908 The two arguments of a binary operation not only need to live
5909 in the same C<isl_ctx>, they currently also need to have
5910 the same (number of) parameters.
5912 =head3 Basic Operations
5916 =item * Intersection
5918 #include <isl/local_space.h>
5919 __isl_give isl_local_space *isl_local_space_intersect(
5920 __isl_take isl_local_space *ls1,
5921 __isl_take isl_local_space *ls2);
5923 #include <isl/set.h>
5924 __isl_give isl_basic_set *isl_basic_set_intersect_params(
5925 __isl_take isl_basic_set *bset1,
5926 __isl_take isl_basic_set *bset2);
5927 __isl_give isl_basic_set *isl_basic_set_intersect(
5928 __isl_take isl_basic_set *bset1,
5929 __isl_take isl_basic_set *bset2);
5930 __isl_give isl_basic_set *isl_basic_set_list_intersect(
5931 __isl_take struct isl_basic_set_list *list);
5932 __isl_give isl_set *isl_set_intersect_params(
5933 __isl_take isl_set *set,
5934 __isl_take isl_set *params);
5935 __isl_give isl_set *isl_set_intersect(
5936 __isl_take isl_set *set1,
5937 __isl_take isl_set *set2);
5939 #include <isl/map.h>
5940 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
5941 __isl_take isl_basic_map *bmap,
5942 __isl_take isl_basic_set *bset);
5943 __isl_give isl_basic_map *isl_basic_map_intersect_range(
5944 __isl_take isl_basic_map *bmap,
5945 __isl_take isl_basic_set *bset);
5946 __isl_give isl_basic_map *isl_basic_map_intersect(
5947 __isl_take isl_basic_map *bmap1,
5948 __isl_take isl_basic_map *bmap2);
5949 __isl_give isl_basic_map *isl_basic_map_list_intersect(
5950 __isl_take isl_basic_map_list *list);
5951 __isl_give isl_map *isl_map_intersect_params(
5952 __isl_take isl_map *map,
5953 __isl_take isl_set *params);
5954 __isl_give isl_map *isl_map_intersect_domain(
5955 __isl_take isl_map *map,
5956 __isl_take isl_set *set);
5957 __isl_give isl_map *isl_map_intersect_range(
5958 __isl_take isl_map *map,
5959 __isl_take isl_set *set);
5960 __isl_give isl_map *isl_map_intersect(
5961 __isl_take isl_map *map1,
5962 __isl_take isl_map *map2);
5963 __isl_give isl_map *
5964 isl_map_intersect_domain_factor_range(
5965 __isl_take isl_map *map,
5966 __isl_take isl_map *factor);
5967 __isl_give isl_map *
5968 isl_map_intersect_range_factor_range(
5969 __isl_take isl_map *map,
5970 __isl_take isl_map *factor);
5972 #include <isl/union_set.h>
5973 __isl_give isl_union_set *isl_union_set_intersect_params(
5974 __isl_take isl_union_set *uset,
5975 __isl_take isl_set *set);
5976 __isl_give isl_union_set *isl_union_set_intersect(
5977 __isl_take isl_union_set *uset1,
5978 __isl_take isl_union_set *uset2);
5980 #include <isl/union_map.h>
5981 __isl_give isl_union_map *isl_union_map_intersect_params(
5982 __isl_take isl_union_map *umap,
5983 __isl_take isl_set *set);
5984 __isl_give isl_union_map *isl_union_map_intersect_domain(
5985 __isl_take isl_union_map *umap,
5986 __isl_take isl_union_set *uset);
5987 __isl_give isl_union_map *isl_union_map_intersect_range(
5988 __isl_take isl_union_map *umap,
5989 __isl_take isl_union_set *uset);
5990 __isl_give isl_union_map *isl_union_map_intersect(
5991 __isl_take isl_union_map *umap1,
5992 __isl_take isl_union_map *umap2);
5993 __isl_give isl_union_map *
5994 isl_union_map_intersect_range_factor_range(
5995 __isl_take isl_union_map *umap,
5996 __isl_take isl_union_map *factor);
5998 #include <isl/aff.h>
5999 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
6000 __isl_take isl_pw_aff *pa,
6001 __isl_take isl_set *set);
6002 __isl_give isl_multi_pw_aff *
6003 isl_multi_pw_aff_intersect_domain(
6004 __isl_take isl_multi_pw_aff *mpa,
6005 __isl_take isl_set *domain);
6006 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
6007 __isl_take isl_pw_multi_aff *pma,
6008 __isl_take isl_set *set);
6009 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
6010 __isl_take isl_union_pw_aff *upa,
6011 __isl_take isl_union_set *uset);
6012 __isl_give isl_union_pw_multi_aff *
6013 isl_union_pw_multi_aff_intersect_domain(
6014 __isl_take isl_union_pw_multi_aff *upma,
6015 __isl_take isl_union_set *uset);
6016 __isl_give isl_multi_union_pw_aff *
6017 isl_multi_union_pw_aff_intersect_domain(
6018 __isl_take isl_multi_union_pw_aff *mupa,
6019 __isl_take isl_union_set *uset);
6020 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
6021 __isl_take isl_pw_aff *pa,
6022 __isl_take isl_set *set);
6023 __isl_give isl_multi_pw_aff *
6024 isl_multi_pw_aff_intersect_params(
6025 __isl_take isl_multi_pw_aff *mpa,
6026 __isl_take isl_set *set);
6027 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
6028 __isl_take isl_pw_multi_aff *pma,
6029 __isl_take isl_set *set);
6030 __isl_give isl_union_pw_aff *
6031 isl_union_pw_aff_intersect_params(
6032 __isl_take isl_union_pw_aff *upa,
6033 __isl_give isl_union_pw_multi_aff *
6034 isl_union_pw_multi_aff_intersect_params(
6035 __isl_take isl_union_pw_multi_aff *upma,
6036 __isl_take isl_set *set);
6037 __isl_give isl_multi_union_pw_aff *
6038 isl_multi_union_pw_aff_intersect_params(
6039 __isl_take isl_multi_union_pw_aff *mupa,
6040 __isl_take isl_set *params);
6041 isl_multi_union_pw_aff_intersect_range(
6042 __isl_take isl_multi_union_pw_aff *mupa,
6043 __isl_take isl_set *set);
6045 #include <isl/polynomial.h>
6046 __isl_give isl_pw_qpolynomial *
6047 isl_pw_qpolynomial_intersect_domain(
6048 __isl_take isl_pw_qpolynomial *pwpq,
6049 __isl_take isl_set *set);
6050 __isl_give isl_union_pw_qpolynomial *
6051 isl_union_pw_qpolynomial_intersect_domain(
6052 __isl_take isl_union_pw_qpolynomial *upwpq,
6053 __isl_take isl_union_set *uset);
6054 __isl_give isl_union_pw_qpolynomial_fold *
6055 isl_union_pw_qpolynomial_fold_intersect_domain(
6056 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6057 __isl_take isl_union_set *uset);
6058 __isl_give isl_pw_qpolynomial *
6059 isl_pw_qpolynomial_intersect_params(
6060 __isl_take isl_pw_qpolynomial *pwpq,
6061 __isl_take isl_set *set);
6062 __isl_give isl_pw_qpolynomial_fold *
6063 isl_pw_qpolynomial_fold_intersect_params(
6064 __isl_take isl_pw_qpolynomial_fold *pwf,
6065 __isl_take isl_set *set);
6066 __isl_give isl_union_pw_qpolynomial *
6067 isl_union_pw_qpolynomial_intersect_params(
6068 __isl_take isl_union_pw_qpolynomial *upwpq,
6069 __isl_take isl_set *set);
6070 __isl_give isl_union_pw_qpolynomial_fold *
6071 isl_union_pw_qpolynomial_fold_intersect_params(
6072 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6073 __isl_take isl_set *set);
6075 The second argument to the C<_params> functions needs to be
6076 a parametric (basic) set. For the other functions, a parametric set
6077 for either argument is only allowed if the other argument is
6078 a parametric set as well.
6079 The list passed to C<isl_basic_set_list_intersect> needs to have
6080 at least one element and all elements need to live in the same space.
6081 The function C<isl_multi_union_pw_aff_intersect_range>
6082 restricts the input function to those shared domain elements
6083 that map to the specified range.
6087 #include <isl/set.h>
6088 __isl_give isl_set *isl_basic_set_union(
6089 __isl_take isl_basic_set *bset1,
6090 __isl_take isl_basic_set *bset2);
6091 __isl_give isl_set *isl_set_union(
6092 __isl_take isl_set *set1,
6093 __isl_take isl_set *set2);
6094 __isl_give isl_set *isl_set_list_union(
6095 __isl_take isl_set_list *list);
6097 #include <isl/map.h>
6098 __isl_give isl_map *isl_basic_map_union(
6099 __isl_take isl_basic_map *bmap1,
6100 __isl_take isl_basic_map *bmap2);
6101 __isl_give isl_map *isl_map_union(
6102 __isl_take isl_map *map1,
6103 __isl_take isl_map *map2);
6105 #include <isl/union_set.h>
6106 __isl_give isl_union_set *isl_union_set_union(
6107 __isl_take isl_union_set *uset1,
6108 __isl_take isl_union_set *uset2);
6109 __isl_give isl_union_set *isl_union_set_list_union(
6110 __isl_take isl_union_set_list *list);
6112 #include <isl/union_map.h>
6113 __isl_give isl_union_map *isl_union_map_union(
6114 __isl_take isl_union_map *umap1,
6115 __isl_take isl_union_map *umap2);
6117 The list passed to C<isl_set_list_union> needs to have
6118 at least one element and all elements need to live in the same space.
6120 =item * Set difference
6122 #include <isl/set.h>
6123 __isl_give isl_set *isl_set_subtract(
6124 __isl_take isl_set *set1,
6125 __isl_take isl_set *set2);
6127 #include <isl/map.h>
6128 __isl_give isl_map *isl_map_subtract(
6129 __isl_take isl_map *map1,
6130 __isl_take isl_map *map2);
6131 __isl_give isl_map *isl_map_subtract_domain(
6132 __isl_take isl_map *map,
6133 __isl_take isl_set *dom);
6134 __isl_give isl_map *isl_map_subtract_range(
6135 __isl_take isl_map *map,
6136 __isl_take isl_set *dom);
6138 #include <isl/union_set.h>
6139 __isl_give isl_union_set *isl_union_set_subtract(
6140 __isl_take isl_union_set *uset1,
6141 __isl_take isl_union_set *uset2);
6143 #include <isl/union_map.h>
6144 __isl_give isl_union_map *isl_union_map_subtract(
6145 __isl_take isl_union_map *umap1,
6146 __isl_take isl_union_map *umap2);
6147 __isl_give isl_union_map *isl_union_map_subtract_domain(
6148 __isl_take isl_union_map *umap,
6149 __isl_take isl_union_set *dom);
6150 __isl_give isl_union_map *isl_union_map_subtract_range(
6151 __isl_take isl_union_map *umap,
6152 __isl_take isl_union_set *dom);
6154 #include <isl/aff.h>
6155 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
6156 __isl_take isl_pw_aff *pa,
6157 __isl_take isl_set *set);
6158 __isl_give isl_pw_multi_aff *
6159 isl_pw_multi_aff_subtract_domain(
6160 __isl_take isl_pw_multi_aff *pma,
6161 __isl_take isl_set *set);
6162 __isl_give isl_union_pw_aff *
6163 isl_union_pw_aff_subtract_domain(
6164 __isl_take isl_union_pw_aff *upa,
6165 __isl_take isl_union_set *uset);
6166 __isl_give isl_union_pw_multi_aff *
6167 isl_union_pw_multi_aff_subtract_domain(
6168 __isl_take isl_union_pw_multi_aff *upma,
6169 __isl_take isl_set *set);
6171 #include <isl/polynomial.h>
6172 __isl_give isl_pw_qpolynomial *
6173 isl_pw_qpolynomial_subtract_domain(
6174 __isl_take isl_pw_qpolynomial *pwpq,
6175 __isl_take isl_set *set);
6176 __isl_give isl_pw_qpolynomial_fold *
6177 isl_pw_qpolynomial_fold_subtract_domain(
6178 __isl_take isl_pw_qpolynomial_fold *pwf,
6179 __isl_take isl_set *set);
6180 __isl_give isl_union_pw_qpolynomial *
6181 isl_union_pw_qpolynomial_subtract_domain(
6182 __isl_take isl_union_pw_qpolynomial *upwpq,
6183 __isl_take isl_union_set *uset);
6184 __isl_give isl_union_pw_qpolynomial_fold *
6185 isl_union_pw_qpolynomial_fold_subtract_domain(
6186 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6187 __isl_take isl_union_set *uset);
6191 #include <isl/space.h>
6192 __isl_give isl_space *isl_space_join(
6193 __isl_take isl_space *left,
6194 __isl_take isl_space *right);
6196 #include <isl/map.h>
6197 __isl_give isl_basic_set *isl_basic_set_apply(
6198 __isl_take isl_basic_set *bset,
6199 __isl_take isl_basic_map *bmap);
6200 __isl_give isl_set *isl_set_apply(
6201 __isl_take isl_set *set,
6202 __isl_take isl_map *map);
6203 __isl_give isl_union_set *isl_union_set_apply(
6204 __isl_take isl_union_set *uset,
6205 __isl_take isl_union_map *umap);
6206 __isl_give isl_basic_map *isl_basic_map_apply_domain(
6207 __isl_take isl_basic_map *bmap1,
6208 __isl_take isl_basic_map *bmap2);
6209 __isl_give isl_basic_map *isl_basic_map_apply_range(
6210 __isl_take isl_basic_map *bmap1,
6211 __isl_take isl_basic_map *bmap2);
6212 __isl_give isl_map *isl_map_apply_domain(
6213 __isl_take isl_map *map1,
6214 __isl_take isl_map *map2);
6215 __isl_give isl_map *isl_map_apply_range(
6216 __isl_take isl_map *map1,
6217 __isl_take isl_map *map2);
6219 #include <isl/union_map.h>
6220 __isl_give isl_union_map *isl_union_map_apply_domain(
6221 __isl_take isl_union_map *umap1,
6222 __isl_take isl_union_map *umap2);
6223 __isl_give isl_union_map *isl_union_map_apply_range(
6224 __isl_take isl_union_map *umap1,
6225 __isl_take isl_union_map *umap2);
6227 #include <isl/aff.h>
6228 __isl_give isl_union_pw_aff *
6229 isl_multi_union_pw_aff_apply_aff(
6230 __isl_take isl_multi_union_pw_aff *mupa,
6231 __isl_take isl_aff *aff);
6232 __isl_give isl_union_pw_aff *
6233 isl_multi_union_pw_aff_apply_pw_aff(
6234 __isl_take isl_multi_union_pw_aff *mupa,
6235 __isl_take isl_pw_aff *pa);
6236 __isl_give isl_multi_union_pw_aff *
6237 isl_multi_union_pw_aff_apply_multi_aff(
6238 __isl_take isl_multi_union_pw_aff *mupa,
6239 __isl_take isl_multi_aff *ma);
6240 __isl_give isl_multi_union_pw_aff *
6241 isl_multi_union_pw_aff_apply_pw_multi_aff(
6242 __isl_take isl_multi_union_pw_aff *mupa,
6243 __isl_take isl_pw_multi_aff *pma);
6245 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
6246 over the shared domain of the elements of the input. The dimension is
6247 required to be greater than zero.
6248 The C<isl_multi_union_pw_aff> argument of
6249 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
6250 but only if the range of the C<isl_multi_aff> argument
6251 is also zero-dimensional.
6252 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
6254 #include <isl/polynomial.h>
6255 __isl_give isl_pw_qpolynomial_fold *
6256 isl_set_apply_pw_qpolynomial_fold(
6257 __isl_take isl_set *set,
6258 __isl_take isl_pw_qpolynomial_fold *pwf,
6260 __isl_give isl_pw_qpolynomial_fold *
6261 isl_map_apply_pw_qpolynomial_fold(
6262 __isl_take isl_map *map,
6263 __isl_take isl_pw_qpolynomial_fold *pwf,
6265 __isl_give isl_union_pw_qpolynomial_fold *
6266 isl_union_set_apply_union_pw_qpolynomial_fold(
6267 __isl_take isl_union_set *uset,
6268 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6270 __isl_give isl_union_pw_qpolynomial_fold *
6271 isl_union_map_apply_union_pw_qpolynomial_fold(
6272 __isl_take isl_union_map *umap,
6273 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6276 The functions taking a map
6277 compose the given map with the given piecewise quasipolynomial reduction.
6278 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
6279 over all elements in the intersection of the range of the map
6280 and the domain of the piecewise quasipolynomial reduction
6281 as a function of an element in the domain of the map.
6282 The functions taking a set compute a bound over all elements in the
6283 intersection of the set and the domain of the
6284 piecewise quasipolynomial reduction.
6288 #include <isl/set.h>
6289 __isl_give isl_basic_set *
6290 isl_basic_set_preimage_multi_aff(
6291 __isl_take isl_basic_set *bset,
6292 __isl_take isl_multi_aff *ma);
6293 __isl_give isl_set *isl_set_preimage_multi_aff(
6294 __isl_take isl_set *set,
6295 __isl_take isl_multi_aff *ma);
6296 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
6297 __isl_take isl_set *set,
6298 __isl_take isl_pw_multi_aff *pma);
6299 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
6300 __isl_take isl_set *set,
6301 __isl_take isl_multi_pw_aff *mpa);
6303 #include <isl/union_set.h>
6304 __isl_give isl_union_set *
6305 isl_union_set_preimage_multi_aff(
6306 __isl_take isl_union_set *uset,
6307 __isl_take isl_multi_aff *ma);
6308 __isl_give isl_union_set *
6309 isl_union_set_preimage_pw_multi_aff(
6310 __isl_take isl_union_set *uset,
6311 __isl_take isl_pw_multi_aff *pma);
6312 __isl_give isl_union_set *
6313 isl_union_set_preimage_union_pw_multi_aff(
6314 __isl_take isl_union_set *uset,
6315 __isl_take isl_union_pw_multi_aff *upma);
6317 #include <isl/map.h>
6318 __isl_give isl_basic_map *
6319 isl_basic_map_preimage_domain_multi_aff(
6320 __isl_take isl_basic_map *bmap,
6321 __isl_take isl_multi_aff *ma);
6322 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
6323 __isl_take isl_map *map,
6324 __isl_take isl_multi_aff *ma);
6325 __isl_give isl_map *isl_map_preimage_range_multi_aff(
6326 __isl_take isl_map *map,
6327 __isl_take isl_multi_aff *ma);
6328 __isl_give isl_map *
6329 isl_map_preimage_domain_pw_multi_aff(
6330 __isl_take isl_map *map,
6331 __isl_take isl_pw_multi_aff *pma);
6332 __isl_give isl_map *
6333 isl_map_preimage_range_pw_multi_aff(
6334 __isl_take isl_map *map,
6335 __isl_take isl_pw_multi_aff *pma);
6336 __isl_give isl_map *
6337 isl_map_preimage_domain_multi_pw_aff(
6338 __isl_take isl_map *map,
6339 __isl_take isl_multi_pw_aff *mpa);
6340 __isl_give isl_basic_map *
6341 isl_basic_map_preimage_range_multi_aff(
6342 __isl_take isl_basic_map *bmap,
6343 __isl_take isl_multi_aff *ma);
6345 #include <isl/union_map.h>
6346 __isl_give isl_union_map *
6347 isl_union_map_preimage_domain_multi_aff(
6348 __isl_take isl_union_map *umap,
6349 __isl_take isl_multi_aff *ma);
6350 __isl_give isl_union_map *
6351 isl_union_map_preimage_range_multi_aff(
6352 __isl_take isl_union_map *umap,
6353 __isl_take isl_multi_aff *ma);
6354 __isl_give isl_union_map *
6355 isl_union_map_preimage_domain_pw_multi_aff(
6356 __isl_take isl_union_map *umap,
6357 __isl_take isl_pw_multi_aff *pma);
6358 __isl_give isl_union_map *
6359 isl_union_map_preimage_range_pw_multi_aff(
6360 __isl_take isl_union_map *umap,
6361 __isl_take isl_pw_multi_aff *pma);
6362 __isl_give isl_union_map *
6363 isl_union_map_preimage_domain_union_pw_multi_aff(
6364 __isl_take isl_union_map *umap,
6365 __isl_take isl_union_pw_multi_aff *upma);
6366 __isl_give isl_union_map *
6367 isl_union_map_preimage_range_union_pw_multi_aff(
6368 __isl_take isl_union_map *umap,
6369 __isl_take isl_union_pw_multi_aff *upma);
6371 These functions compute the preimage of the given set or map domain/range under
6372 the given function. In other words, the expression is plugged
6373 into the set description or into the domain/range of the map.
6377 #include <isl/aff.h>
6378 __isl_give isl_aff *isl_aff_pullback_aff(
6379 __isl_take isl_aff *aff1,
6380 __isl_take isl_aff *aff2);
6381 __isl_give isl_aff *isl_aff_pullback_multi_aff(
6382 __isl_take isl_aff *aff,
6383 __isl_take isl_multi_aff *ma);
6384 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
6385 __isl_take isl_pw_aff *pa,
6386 __isl_take isl_multi_aff *ma);
6387 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
6388 __isl_take isl_pw_aff *pa,
6389 __isl_take isl_pw_multi_aff *pma);
6390 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
6391 __isl_take isl_pw_aff *pa,
6392 __isl_take isl_multi_pw_aff *mpa);
6393 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
6394 __isl_take isl_multi_aff *ma1,
6395 __isl_take isl_multi_aff *ma2);
6396 __isl_give isl_pw_multi_aff *
6397 isl_pw_multi_aff_pullback_multi_aff(
6398 __isl_take isl_pw_multi_aff *pma,
6399 __isl_take isl_multi_aff *ma);
6400 __isl_give isl_multi_pw_aff *
6401 isl_multi_pw_aff_pullback_multi_aff(
6402 __isl_take isl_multi_pw_aff *mpa,
6403 __isl_take isl_multi_aff *ma);
6404 __isl_give isl_pw_multi_aff *
6405 isl_pw_multi_aff_pullback_pw_multi_aff(
6406 __isl_take isl_pw_multi_aff *pma1,
6407 __isl_take isl_pw_multi_aff *pma2);
6408 __isl_give isl_multi_pw_aff *
6409 isl_multi_pw_aff_pullback_pw_multi_aff(
6410 __isl_take isl_multi_pw_aff *mpa,
6411 __isl_take isl_pw_multi_aff *pma);
6412 __isl_give isl_multi_pw_aff *
6413 isl_multi_pw_aff_pullback_multi_pw_aff(
6414 __isl_take isl_multi_pw_aff *mpa1,
6415 __isl_take isl_multi_pw_aff *mpa2);
6416 __isl_give isl_union_pw_aff *
6417 isl_union_pw_aff_pullback_union_pw_multi_aff(
6418 __isl_take isl_union_pw_aff *upa,
6419 __isl_take isl_union_pw_multi_aff *upma);
6420 __isl_give isl_union_pw_multi_aff *
6421 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
6422 __isl_take isl_union_pw_multi_aff *upma1,
6423 __isl_take isl_union_pw_multi_aff *upma2);
6424 __isl_give isl_multi_union_pw_aff *
6425 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
6426 __isl_take isl_multi_union_pw_aff *mupa,
6427 __isl_take isl_union_pw_multi_aff *upma);
6429 These functions precompose the first expression by the second function.
6430 In other words, the second function is plugged
6431 into the first expression.
6435 #include <isl/aff.h>
6436 __isl_give isl_basic_set *isl_aff_eq_basic_set(
6437 __isl_take isl_aff *aff1,
6438 __isl_take isl_aff *aff2);
6439 __isl_give isl_set *isl_aff_eq_set(
6440 __isl_take isl_aff *aff1,
6441 __isl_take isl_aff *aff2);
6442 __isl_give isl_set *isl_aff_ne_set(
6443 __isl_take isl_aff *aff1,
6444 __isl_take isl_aff *aff2);
6445 __isl_give isl_basic_set *isl_aff_le_basic_set(
6446 __isl_take isl_aff *aff1,
6447 __isl_take isl_aff *aff2);
6448 __isl_give isl_set *isl_aff_le_set(
6449 __isl_take isl_aff *aff1,
6450 __isl_take isl_aff *aff2);
6451 __isl_give isl_basic_set *isl_aff_lt_basic_set(
6452 __isl_take isl_aff *aff1,
6453 __isl_take isl_aff *aff2);
6454 __isl_give isl_set *isl_aff_lt_set(
6455 __isl_take isl_aff *aff1,
6456 __isl_take isl_aff *aff2);
6457 __isl_give isl_basic_set *isl_aff_ge_basic_set(
6458 __isl_take isl_aff *aff1,
6459 __isl_take isl_aff *aff2);
6460 __isl_give isl_set *isl_aff_ge_set(
6461 __isl_take isl_aff *aff1,
6462 __isl_take isl_aff *aff2);
6463 __isl_give isl_basic_set *isl_aff_gt_basic_set(
6464 __isl_take isl_aff *aff1,
6465 __isl_take isl_aff *aff2);
6466 __isl_give isl_set *isl_aff_gt_set(
6467 __isl_take isl_aff *aff1,
6468 __isl_take isl_aff *aff2);
6469 __isl_give isl_set *isl_pw_aff_eq_set(
6470 __isl_take isl_pw_aff *pwaff1,
6471 __isl_take isl_pw_aff *pwaff2);
6472 __isl_give isl_set *isl_pw_aff_ne_set(
6473 __isl_take isl_pw_aff *pwaff1,
6474 __isl_take isl_pw_aff *pwaff2);
6475 __isl_give isl_set *isl_pw_aff_le_set(
6476 __isl_take isl_pw_aff *pwaff1,
6477 __isl_take isl_pw_aff *pwaff2);
6478 __isl_give isl_set *isl_pw_aff_lt_set(
6479 __isl_take isl_pw_aff *pwaff1,
6480 __isl_take isl_pw_aff *pwaff2);
6481 __isl_give isl_set *isl_pw_aff_ge_set(
6482 __isl_take isl_pw_aff *pwaff1,
6483 __isl_take isl_pw_aff *pwaff2);
6484 __isl_give isl_set *isl_pw_aff_gt_set(
6485 __isl_take isl_pw_aff *pwaff1,
6486 __isl_take isl_pw_aff *pwaff2);
6488 __isl_give isl_set *isl_multi_aff_lex_le_set(
6489 __isl_take isl_multi_aff *ma1,
6490 __isl_take isl_multi_aff *ma2);
6491 __isl_give isl_set *isl_multi_aff_lex_lt_set(
6492 __isl_take isl_multi_aff *ma1,
6493 __isl_take isl_multi_aff *ma2);
6494 __isl_give isl_set *isl_multi_aff_lex_ge_set(
6495 __isl_take isl_multi_aff *ma1,
6496 __isl_take isl_multi_aff *ma2);
6497 __isl_give isl_set *isl_multi_aff_lex_gt_set(
6498 __isl_take isl_multi_aff *ma1,
6499 __isl_take isl_multi_aff *ma2);
6501 __isl_give isl_set *isl_pw_aff_list_eq_set(
6502 __isl_take isl_pw_aff_list *list1,
6503 __isl_take isl_pw_aff_list *list2);
6504 __isl_give isl_set *isl_pw_aff_list_ne_set(
6505 __isl_take isl_pw_aff_list *list1,
6506 __isl_take isl_pw_aff_list *list2);
6507 __isl_give isl_set *isl_pw_aff_list_le_set(
6508 __isl_take isl_pw_aff_list *list1,
6509 __isl_take isl_pw_aff_list *list2);
6510 __isl_give isl_set *isl_pw_aff_list_lt_set(
6511 __isl_take isl_pw_aff_list *list1,
6512 __isl_take isl_pw_aff_list *list2);
6513 __isl_give isl_set *isl_pw_aff_list_ge_set(
6514 __isl_take isl_pw_aff_list *list1,
6515 __isl_take isl_pw_aff_list *list2);
6516 __isl_give isl_set *isl_pw_aff_list_gt_set(
6517 __isl_take isl_pw_aff_list *list1,
6518 __isl_take isl_pw_aff_list *list2);
6520 The function C<isl_aff_ge_basic_set> returns a basic set
6521 containing those elements in the shared space
6522 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
6523 The function C<isl_pw_aff_ge_set> returns a set
6524 containing those elements in the shared domain
6525 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
6526 greater than or equal to C<pwaff2>.
6527 The function C<isl_multi_aff_lex_le_set> returns a set
6528 containing those elements in the shared domain space
6529 where C<ma1> is lexicographically smaller than or
6531 The functions operating on C<isl_pw_aff_list> apply the corresponding
6532 C<isl_pw_aff> function to each pair of elements in the two lists.
6534 #include <isl/aff.h>
6535 __isl_give isl_map *isl_pw_aff_eq_map(
6536 __isl_take isl_pw_aff *pa1,
6537 __isl_take isl_pw_aff *pa2);
6538 __isl_give isl_map *isl_pw_aff_lt_map(
6539 __isl_take isl_pw_aff *pa1,
6540 __isl_take isl_pw_aff *pa2);
6541 __isl_give isl_map *isl_pw_aff_gt_map(
6542 __isl_take isl_pw_aff *pa1,
6543 __isl_take isl_pw_aff *pa2);
6545 __isl_give isl_map *isl_multi_pw_aff_eq_map(
6546 __isl_take isl_multi_pw_aff *mpa1,
6547 __isl_take isl_multi_pw_aff *mpa2);
6548 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
6549 __isl_take isl_multi_pw_aff *mpa1,
6550 __isl_take isl_multi_pw_aff *mpa2);
6551 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
6552 __isl_take isl_multi_pw_aff *mpa1,
6553 __isl_take isl_multi_pw_aff *mpa2);
6555 These functions return a map between domain elements of the arguments
6556 where the function values satisfy the given relation.
6558 #include <isl/union_map.h>
6559 __isl_give isl_union_map *
6560 isl_union_map_eq_at_multi_union_pw_aff(
6561 __isl_take isl_union_map *umap,
6562 __isl_take isl_multi_union_pw_aff *mupa);
6563 __isl_give isl_union_map *
6564 isl_union_map_lex_lt_at_multi_union_pw_aff(
6565 __isl_take isl_union_map *umap,
6566 __isl_take isl_multi_union_pw_aff *mupa);
6567 __isl_give isl_union_map *
6568 isl_union_map_lex_gt_at_multi_union_pw_aff(
6569 __isl_take isl_union_map *umap,
6570 __isl_take isl_multi_union_pw_aff *mupa);
6572 These functions select the subset of elements in the union map
6573 that have an equal or lexicographically smaller function value.
6575 =item * Cartesian Product
6577 #include <isl/space.h>
6578 __isl_give isl_space *isl_space_product(
6579 __isl_take isl_space *space1,
6580 __isl_take isl_space *space2);
6581 __isl_give isl_space *isl_space_domain_product(
6582 __isl_take isl_space *space1,
6583 __isl_take isl_space *space2);
6584 __isl_give isl_space *isl_space_range_product(
6585 __isl_take isl_space *space1,
6586 __isl_take isl_space *space2);
6589 C<isl_space_product>, C<isl_space_domain_product>
6590 and C<isl_space_range_product> take pairs or relation spaces and
6591 produce a single relations space, where either the domain, the range
6592 or both domain and range are wrapped spaces of relations between
6593 the domains and/or ranges of the input spaces.
6594 If the product is only constructed over the domain or the range
6595 then the ranges or the domains of the inputs should be the same.
6596 The function C<isl_space_product> also accepts a pair of set spaces,
6597 in which case it returns a wrapped space of a relation between the
6600 #include <isl/set.h>
6601 __isl_give isl_set *isl_set_product(
6602 __isl_take isl_set *set1,
6603 __isl_take isl_set *set2);
6605 #include <isl/map.h>
6606 __isl_give isl_basic_map *isl_basic_map_domain_product(
6607 __isl_take isl_basic_map *bmap1,
6608 __isl_take isl_basic_map *bmap2);
6609 __isl_give isl_basic_map *isl_basic_map_range_product(
6610 __isl_take isl_basic_map *bmap1,
6611 __isl_take isl_basic_map *bmap2);
6612 __isl_give isl_basic_map *isl_basic_map_product(
6613 __isl_take isl_basic_map *bmap1,
6614 __isl_take isl_basic_map *bmap2);
6615 __isl_give isl_map *isl_map_domain_product(
6616 __isl_take isl_map *map1,
6617 __isl_take isl_map *map2);
6618 __isl_give isl_map *isl_map_range_product(
6619 __isl_take isl_map *map1,
6620 __isl_take isl_map *map2);
6621 __isl_give isl_map *isl_map_product(
6622 __isl_take isl_map *map1,
6623 __isl_take isl_map *map2);
6625 #include <isl/union_set.h>
6626 __isl_give isl_union_set *isl_union_set_product(
6627 __isl_take isl_union_set *uset1,
6628 __isl_take isl_union_set *uset2);
6630 #include <isl/union_map.h>
6631 __isl_give isl_union_map *isl_union_map_domain_product(
6632 __isl_take isl_union_map *umap1,
6633 __isl_take isl_union_map *umap2);
6634 __isl_give isl_union_map *isl_union_map_range_product(
6635 __isl_take isl_union_map *umap1,
6636 __isl_take isl_union_map *umap2);
6637 __isl_give isl_union_map *isl_union_map_product(
6638 __isl_take isl_union_map *umap1,
6639 __isl_take isl_union_map *umap2);
6641 #include <isl/val.h>
6642 __isl_give isl_multi_val *isl_multi_val_range_product(
6643 __isl_take isl_multi_val *mv1,
6644 __isl_take isl_multi_val *mv2);
6645 __isl_give isl_multi_val *isl_multi_val_product(
6646 __isl_take isl_multi_val *mv1,
6647 __isl_take isl_multi_val *mv2);
6649 #include <isl/aff.h>
6650 __isl_give isl_multi_aff *isl_multi_aff_range_product(
6651 __isl_take isl_multi_aff *ma1,
6652 __isl_take isl_multi_aff *ma2);
6653 __isl_give isl_multi_aff *isl_multi_aff_product(
6654 __isl_take isl_multi_aff *ma1,
6655 __isl_take isl_multi_aff *ma2);
6656 __isl_give isl_multi_pw_aff *
6657 isl_multi_pw_aff_range_product(
6658 __isl_take isl_multi_pw_aff *mpa1,
6659 __isl_take isl_multi_pw_aff *mpa2);
6660 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
6661 __isl_take isl_multi_pw_aff *mpa1,
6662 __isl_take isl_multi_pw_aff *mpa2);
6663 __isl_give isl_pw_multi_aff *
6664 isl_pw_multi_aff_range_product(
6665 __isl_take isl_pw_multi_aff *pma1,
6666 __isl_take isl_pw_multi_aff *pma2);
6667 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
6668 __isl_take isl_pw_multi_aff *pma1,
6669 __isl_take isl_pw_multi_aff *pma2);
6670 __isl_give isl_multi_union_pw_aff *
6671 isl_multi_union_pw_aff_range_product(
6672 __isl_take isl_multi_union_pw_aff *mupa1,
6673 __isl_take isl_multi_union_pw_aff *mupa2);
6675 The above functions compute the cross product of the given
6676 sets, relations or functions. The domains and ranges of the results
6677 are wrapped maps between domains and ranges of the inputs.
6678 To obtain a ``flat'' product, use the following functions
6681 #include <isl/set.h>
6682 __isl_give isl_basic_set *isl_basic_set_flat_product(
6683 __isl_take isl_basic_set *bset1,
6684 __isl_take isl_basic_set *bset2);
6685 __isl_give isl_set *isl_set_flat_product(
6686 __isl_take isl_set *set1,
6687 __isl_take isl_set *set2);
6689 #include <isl/map.h>
6690 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
6691 __isl_take isl_basic_map *bmap1,
6692 __isl_take isl_basic_map *bmap2);
6693 __isl_give isl_map *isl_map_flat_domain_product(
6694 __isl_take isl_map *map1,
6695 __isl_take isl_map *map2);
6696 __isl_give isl_map *isl_map_flat_range_product(
6697 __isl_take isl_map *map1,
6698 __isl_take isl_map *map2);
6699 __isl_give isl_basic_map *isl_basic_map_flat_product(
6700 __isl_take isl_basic_map *bmap1,
6701 __isl_take isl_basic_map *bmap2);
6702 __isl_give isl_map *isl_map_flat_product(
6703 __isl_take isl_map *map1,
6704 __isl_take isl_map *map2);
6706 #include <isl/union_map.h>
6707 __isl_give isl_union_map *
6708 isl_union_map_flat_domain_product(
6709 __isl_take isl_union_map *umap1,
6710 __isl_take isl_union_map *umap2);
6711 __isl_give isl_union_map *
6712 isl_union_map_flat_range_product(
6713 __isl_take isl_union_map *umap1,
6714 __isl_take isl_union_map *umap2);
6716 #include <isl/val.h>
6717 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
6718 __isl_take isl_multi_val *mv1,
6719 __isl_take isl_multi_aff *mv2);
6721 #include <isl/aff.h>
6722 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
6723 __isl_take isl_multi_aff *ma1,
6724 __isl_take isl_multi_aff *ma2);
6725 __isl_give isl_pw_multi_aff *
6726 isl_pw_multi_aff_flat_range_product(
6727 __isl_take isl_pw_multi_aff *pma1,
6728 __isl_take isl_pw_multi_aff *pma2);
6729 __isl_give isl_multi_pw_aff *
6730 isl_multi_pw_aff_flat_range_product(
6731 __isl_take isl_multi_pw_aff *mpa1,
6732 __isl_take isl_multi_pw_aff *mpa2);
6733 __isl_give isl_union_pw_multi_aff *
6734 isl_union_pw_multi_aff_flat_range_product(
6735 __isl_take isl_union_pw_multi_aff *upma1,
6736 __isl_take isl_union_pw_multi_aff *upma2);
6737 __isl_give isl_multi_union_pw_aff *
6738 isl_multi_union_pw_aff_flat_range_product(
6739 __isl_take isl_multi_union_pw_aff *mupa1,
6740 __isl_take isl_multi_union_pw_aff *mupa2);
6742 #include <isl/space.h>
6743 __isl_give isl_space *isl_space_factor_domain(
6744 __isl_take isl_space *space);
6745 __isl_give isl_space *isl_space_factor_range(
6746 __isl_take isl_space *space);
6747 __isl_give isl_space *isl_space_domain_factor_domain(
6748 __isl_take isl_space *space);
6749 __isl_give isl_space *isl_space_domain_factor_range(
6750 __isl_take isl_space *space);
6751 __isl_give isl_space *isl_space_range_factor_domain(
6752 __isl_take isl_space *space);
6753 __isl_give isl_space *isl_space_range_factor_range(
6754 __isl_take isl_space *space);
6756 The functions C<isl_space_range_factor_domain> and
6757 C<isl_space_range_factor_range> extract the two arguments from
6758 the result of a call to C<isl_space_range_product>.
6760 The arguments of a call to a product can be extracted
6761 from the result using the following functions.
6763 #include <isl/map.h>
6764 __isl_give isl_map *isl_map_factor_domain(
6765 __isl_take isl_map *map);
6766 __isl_give isl_map *isl_map_factor_range(
6767 __isl_take isl_map *map);
6768 __isl_give isl_map *isl_map_domain_factor_domain(
6769 __isl_take isl_map *map);
6770 __isl_give isl_map *isl_map_domain_factor_range(
6771 __isl_take isl_map *map);
6772 __isl_give isl_map *isl_map_range_factor_domain(
6773 __isl_take isl_map *map);
6774 __isl_give isl_map *isl_map_range_factor_range(
6775 __isl_take isl_map *map);
6777 #include <isl/union_map.h>
6778 __isl_give isl_union_map *isl_union_map_factor_domain(
6779 __isl_take isl_union_map *umap);
6780 __isl_give isl_union_map *isl_union_map_factor_range(
6781 __isl_take isl_union_map *umap);
6782 __isl_give isl_union_map *
6783 isl_union_map_domain_factor_domain(
6784 __isl_take isl_union_map *umap);
6785 __isl_give isl_union_map *
6786 isl_union_map_domain_factor_range(
6787 __isl_take isl_union_map *umap);
6788 __isl_give isl_union_map *
6789 isl_union_map_range_factor_domain(
6790 __isl_take isl_union_map *umap);
6791 __isl_give isl_union_map *
6792 isl_union_map_range_factor_range(
6793 __isl_take isl_union_map *umap);
6795 #include <isl/val.h>
6796 __isl_give isl_multi_val *isl_multi_val_factor_range(
6797 __isl_take isl_multi_val *mv);
6798 __isl_give isl_multi_val *
6799 isl_multi_val_range_factor_domain(
6800 __isl_take isl_multi_val *mv);
6801 __isl_give isl_multi_val *
6802 isl_multi_val_range_factor_range(
6803 __isl_take isl_multi_val *mv);
6805 #include <isl/aff.h>
6806 __isl_give isl_multi_aff *isl_multi_aff_factor_range(
6807 __isl_take isl_multi_aff *ma);
6808 __isl_give isl_multi_aff *
6809 isl_multi_aff_range_factor_domain(
6810 __isl_take isl_multi_aff *ma);
6811 __isl_give isl_multi_aff *
6812 isl_multi_aff_range_factor_range(
6813 __isl_take isl_multi_aff *ma);
6814 __isl_give isl_multi_pw_aff *
6815 isl_multi_pw_aff_factor_range(
6816 __isl_take isl_multi_pw_aff *mpa);
6817 __isl_give isl_multi_pw_aff *
6818 isl_multi_pw_aff_range_factor_domain(
6819 __isl_take isl_multi_pw_aff *mpa);
6820 __isl_give isl_multi_pw_aff *
6821 isl_multi_pw_aff_range_factor_range(
6822 __isl_take isl_multi_pw_aff *mpa);
6823 __isl_give isl_multi_union_pw_aff *
6824 isl_multi_union_pw_aff_factor_range(
6825 __isl_take isl_multi_union_pw_aff *mupa);
6826 __isl_give isl_multi_union_pw_aff *
6827 isl_multi_union_pw_aff_range_factor_domain(
6828 __isl_take isl_multi_union_pw_aff *mupa);
6829 __isl_give isl_multi_union_pw_aff *
6830 isl_multi_union_pw_aff_range_factor_range(
6831 __isl_take isl_multi_union_pw_aff *mupa);
6833 The splice functions are a generalization of the flat product functions,
6834 where the second argument may be inserted at any position inside
6835 the first argument rather than being placed at the end.
6836 The functions C<isl_multi_val_factor_range>,
6837 C<isl_multi_aff_factor_range>,
6838 C<isl_multi_pw_aff_factor_range> and
6839 C<isl_multi_union_pw_aff_factor_range>
6840 take functions that live in a set space.
6842 #include <isl/val.h>
6843 __isl_give isl_multi_val *isl_multi_val_range_splice(
6844 __isl_take isl_multi_val *mv1, unsigned pos,
6845 __isl_take isl_multi_val *mv2);
6847 #include <isl/aff.h>
6848 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
6849 __isl_take isl_multi_aff *ma1, unsigned pos,
6850 __isl_take isl_multi_aff *ma2);
6851 __isl_give isl_multi_aff *isl_multi_aff_splice(
6852 __isl_take isl_multi_aff *ma1,
6853 unsigned in_pos, unsigned out_pos,
6854 __isl_take isl_multi_aff *ma2);
6855 __isl_give isl_multi_pw_aff *
6856 isl_multi_pw_aff_range_splice(
6857 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
6858 __isl_take isl_multi_pw_aff *mpa2);
6859 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
6860 __isl_take isl_multi_pw_aff *mpa1,
6861 unsigned in_pos, unsigned out_pos,
6862 __isl_take isl_multi_pw_aff *mpa2);
6863 __isl_give isl_multi_union_pw_aff *
6864 isl_multi_union_pw_aff_range_splice(
6865 __isl_take isl_multi_union_pw_aff *mupa1,
6867 __isl_take isl_multi_union_pw_aff *mupa2);
6869 =item * Simplification
6871 When applied to a set or relation,
6872 the gist operation returns a set or relation that has the
6873 same intersection with the context as the input set or relation.
6874 Any implicit equality in the intersection is made explicit in the result,
6875 while all inequalities that are redundant with respect to the intersection
6877 In case of union sets and relations, the gist operation is performed
6880 When applied to a function,
6881 the gist operation applies the set gist operation to each of
6882 the cells in the domain of the input piecewise expression.
6883 The context is also exploited
6884 to simplify the expression associated to each cell.
6886 #include <isl/set.h>
6887 __isl_give isl_basic_set *isl_basic_set_gist(
6888 __isl_take isl_basic_set *bset,
6889 __isl_take isl_basic_set *context);
6890 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
6891 __isl_take isl_set *context);
6892 __isl_give isl_set *isl_set_gist_params(
6893 __isl_take isl_set *set,
6894 __isl_take isl_set *context);
6896 #include <isl/map.h>
6897 __isl_give isl_basic_map *isl_basic_map_gist(
6898 __isl_take isl_basic_map *bmap,
6899 __isl_take isl_basic_map *context);
6900 __isl_give isl_basic_map *isl_basic_map_gist_domain(
6901 __isl_take isl_basic_map *bmap,
6902 __isl_take isl_basic_set *context);
6903 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
6904 __isl_take isl_map *context);
6905 __isl_give isl_map *isl_map_gist_params(
6906 __isl_take isl_map *map,
6907 __isl_take isl_set *context);
6908 __isl_give isl_map *isl_map_gist_domain(
6909 __isl_take isl_map *map,
6910 __isl_take isl_set *context);
6911 __isl_give isl_map *isl_map_gist_range(
6912 __isl_take isl_map *map,
6913 __isl_take isl_set *context);
6915 #include <isl/union_set.h>
6916 __isl_give isl_union_set *isl_union_set_gist(
6917 __isl_take isl_union_set *uset,
6918 __isl_take isl_union_set *context);
6919 __isl_give isl_union_set *isl_union_set_gist_params(
6920 __isl_take isl_union_set *uset,
6921 __isl_take isl_set *set);
6923 #include <isl/union_map.h>
6924 __isl_give isl_union_map *isl_union_map_gist(
6925 __isl_take isl_union_map *umap,
6926 __isl_take isl_union_map *context);
6927 __isl_give isl_union_map *isl_union_map_gist_params(
6928 __isl_take isl_union_map *umap,
6929 __isl_take isl_set *set);
6930 __isl_give isl_union_map *isl_union_map_gist_domain(
6931 __isl_take isl_union_map *umap,
6932 __isl_take isl_union_set *uset);
6933 __isl_give isl_union_map *isl_union_map_gist_range(
6934 __isl_take isl_union_map *umap,
6935 __isl_take isl_union_set *uset);
6937 #include <isl/aff.h>
6938 __isl_give isl_aff *isl_aff_gist_params(
6939 __isl_take isl_aff *aff,
6940 __isl_take isl_set *context);
6941 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
6942 __isl_take isl_set *context);
6943 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
6944 __isl_take isl_multi_aff *maff,
6945 __isl_take isl_set *context);
6946 __isl_give isl_multi_aff *isl_multi_aff_gist(
6947 __isl_take isl_multi_aff *maff,
6948 __isl_take isl_set *context);
6949 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
6950 __isl_take isl_pw_aff *pwaff,
6951 __isl_take isl_set *context);
6952 __isl_give isl_pw_aff *isl_pw_aff_gist(
6953 __isl_take isl_pw_aff *pwaff,
6954 __isl_take isl_set *context);
6955 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
6956 __isl_take isl_pw_multi_aff *pma,
6957 __isl_take isl_set *set);
6958 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
6959 __isl_take isl_pw_multi_aff *pma,
6960 __isl_take isl_set *set);
6961 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
6962 __isl_take isl_multi_pw_aff *mpa,
6963 __isl_take isl_set *set);
6964 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
6965 __isl_take isl_multi_pw_aff *mpa,
6966 __isl_take isl_set *set);
6967 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
6968 __isl_take isl_union_pw_aff *upa,
6969 __isl_take isl_union_set *context);
6970 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
6971 __isl_take isl_union_pw_aff *upa,
6972 __isl_take isl_set *context);
6973 __isl_give isl_union_pw_multi_aff *
6974 isl_union_pw_multi_aff_gist_params(
6975 __isl_take isl_union_pw_multi_aff *upma,
6976 __isl_take isl_set *context);
6977 __isl_give isl_union_pw_multi_aff *
6978 isl_union_pw_multi_aff_gist(
6979 __isl_take isl_union_pw_multi_aff *upma,
6980 __isl_take isl_union_set *context);
6981 __isl_give isl_multi_union_pw_aff *
6982 isl_multi_union_pw_aff_gist_params(
6983 __isl_take isl_multi_union_pw_aff *aff,
6984 __isl_take isl_set *context);
6985 __isl_give isl_multi_union_pw_aff *
6986 isl_multi_union_pw_aff_gist(
6987 __isl_take isl_multi_union_pw_aff *aff,
6988 __isl_take isl_union_set *context);
6990 #include <isl/polynomial.h>
6991 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
6992 __isl_take isl_qpolynomial *qp,
6993 __isl_take isl_set *context);
6994 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
6995 __isl_take isl_qpolynomial *qp,
6996 __isl_take isl_set *context);
6997 __isl_give isl_qpolynomial_fold *
6998 isl_qpolynomial_fold_gist_params(
6999 __isl_take isl_qpolynomial_fold *fold,
7000 __isl_take isl_set *context);
7001 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
7002 __isl_take isl_qpolynomial_fold *fold,
7003 __isl_take isl_set *context);
7004 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
7005 __isl_take isl_pw_qpolynomial *pwqp,
7006 __isl_take isl_set *context);
7007 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
7008 __isl_take isl_pw_qpolynomial *pwqp,
7009 __isl_take isl_set *context);
7010 __isl_give isl_pw_qpolynomial_fold *
7011 isl_pw_qpolynomial_fold_gist(
7012 __isl_take isl_pw_qpolynomial_fold *pwf,
7013 __isl_take isl_set *context);
7014 __isl_give isl_pw_qpolynomial_fold *
7015 isl_pw_qpolynomial_fold_gist_params(
7016 __isl_take isl_pw_qpolynomial_fold *pwf,
7017 __isl_take isl_set *context);
7018 __isl_give isl_union_pw_qpolynomial *
7019 isl_union_pw_qpolynomial_gist_params(
7020 __isl_take isl_union_pw_qpolynomial *upwqp,
7021 __isl_take isl_set *context);
7022 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
7023 __isl_take isl_union_pw_qpolynomial *upwqp,
7024 __isl_take isl_union_set *context);
7025 __isl_give isl_union_pw_qpolynomial_fold *
7026 isl_union_pw_qpolynomial_fold_gist(
7027 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7028 __isl_take isl_union_set *context);
7029 __isl_give isl_union_pw_qpolynomial_fold *
7030 isl_union_pw_qpolynomial_fold_gist_params(
7031 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7032 __isl_take isl_set *context);
7034 =item * Binary Arithmetic Operations
7036 #include <isl/set.h>
7037 __isl_give isl_set *isl_set_sum(
7038 __isl_take isl_set *set1,
7039 __isl_take isl_set *set2);
7040 #include <isl/map.h>
7041 __isl_give isl_map *isl_map_sum(
7042 __isl_take isl_map *map1,
7043 __isl_take isl_map *map2);
7045 C<isl_set_sum> computes the Minkowski sum of its two arguments,
7046 i.e., the set containing the sums of pairs of elements from
7047 C<set1> and C<set2>.
7048 The domain of the result of C<isl_map_sum> is the intersection
7049 of the domains of its two arguments. The corresponding range
7050 elements are the sums of the corresponding range elements
7051 in the two arguments.
7053 #include <isl/val.h>
7054 __isl_give isl_multi_val *isl_multi_val_add(
7055 __isl_take isl_multi_val *mv1,
7056 __isl_take isl_multi_val *mv2);
7057 __isl_give isl_multi_val *isl_multi_val_sub(
7058 __isl_take isl_multi_val *mv1,
7059 __isl_take isl_multi_val *mv2);
7061 #include <isl/aff.h>
7062 __isl_give isl_aff *isl_aff_add(
7063 __isl_take isl_aff *aff1,
7064 __isl_take isl_aff *aff2);
7065 __isl_give isl_multi_aff *isl_multi_aff_add(
7066 __isl_take isl_multi_aff *maff1,
7067 __isl_take isl_multi_aff *maff2);
7068 __isl_give isl_pw_aff *isl_pw_aff_add(
7069 __isl_take isl_pw_aff *pwaff1,
7070 __isl_take isl_pw_aff *pwaff2);
7071 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add(
7072 __isl_take isl_multi_pw_aff *mpa1,
7073 __isl_take isl_multi_pw_aff *mpa2);
7074 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
7075 __isl_take isl_pw_multi_aff *pma1,
7076 __isl_take isl_pw_multi_aff *pma2);
7077 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
7078 __isl_take isl_union_pw_aff *upa1,
7079 __isl_take isl_union_pw_aff *upa2);
7080 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
7081 __isl_take isl_union_pw_multi_aff *upma1,
7082 __isl_take isl_union_pw_multi_aff *upma2);
7083 __isl_give isl_multi_union_pw_aff *
7084 isl_multi_union_pw_aff_add(
7085 __isl_take isl_multi_union_pw_aff *mupa1,
7086 __isl_take isl_multi_union_pw_aff *mupa2);
7087 __isl_give isl_pw_aff *isl_pw_aff_min(
7088 __isl_take isl_pw_aff *pwaff1,
7089 __isl_take isl_pw_aff *pwaff2);
7090 __isl_give isl_pw_aff *isl_pw_aff_max(
7091 __isl_take isl_pw_aff *pwaff1,
7092 __isl_take isl_pw_aff *pwaff2);
7093 __isl_give isl_aff *isl_aff_sub(
7094 __isl_take isl_aff *aff1,
7095 __isl_take isl_aff *aff2);
7096 __isl_give isl_multi_aff *isl_multi_aff_sub(
7097 __isl_take isl_multi_aff *ma1,
7098 __isl_take isl_multi_aff *ma2);
7099 __isl_give isl_pw_aff *isl_pw_aff_sub(
7100 __isl_take isl_pw_aff *pwaff1,
7101 __isl_take isl_pw_aff *pwaff2);
7102 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
7103 __isl_take isl_multi_pw_aff *mpa1,
7104 __isl_take isl_multi_pw_aff *mpa2);
7105 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
7106 __isl_take isl_pw_multi_aff *pma1,
7107 __isl_take isl_pw_multi_aff *pma2);
7108 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
7109 __isl_take isl_union_pw_aff *upa1,
7110 __isl_take isl_union_pw_aff *upa2);
7111 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
7112 __isl_take isl_union_pw_multi_aff *upma1,
7113 __isl_take isl_union_pw_multi_aff *upma2);
7114 __isl_give isl_multi_union_pw_aff *
7115 isl_multi_union_pw_aff_sub(
7116 __isl_take isl_multi_union_pw_aff *mupa1,
7117 __isl_take isl_multi_union_pw_aff *mupa2);
7119 C<isl_aff_sub> subtracts the second argument from the first.
7121 #include <isl/polynomial.h>
7122 __isl_give isl_qpolynomial *isl_qpolynomial_add(
7123 __isl_take isl_qpolynomial *qp1,
7124 __isl_take isl_qpolynomial *qp2);
7125 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
7126 __isl_take isl_pw_qpolynomial *pwqp1,
7127 __isl_take isl_pw_qpolynomial *pwqp2);
7128 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
7129 __isl_take isl_pw_qpolynomial *pwqp1,
7130 __isl_take isl_pw_qpolynomial *pwqp2);
7131 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
7132 __isl_take isl_pw_qpolynomial_fold *pwf1,
7133 __isl_take isl_pw_qpolynomial_fold *pwf2);
7134 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
7135 __isl_take isl_union_pw_qpolynomial *upwqp1,
7136 __isl_take isl_union_pw_qpolynomial *upwqp2);
7137 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
7138 __isl_take isl_qpolynomial *qp1,
7139 __isl_take isl_qpolynomial *qp2);
7140 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
7141 __isl_take isl_pw_qpolynomial *pwqp1,
7142 __isl_take isl_pw_qpolynomial *pwqp2);
7143 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
7144 __isl_take isl_union_pw_qpolynomial *upwqp1,
7145 __isl_take isl_union_pw_qpolynomial *upwqp2);
7146 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
7147 __isl_take isl_pw_qpolynomial_fold *pwf1,
7148 __isl_take isl_pw_qpolynomial_fold *pwf2);
7149 __isl_give isl_union_pw_qpolynomial_fold *
7150 isl_union_pw_qpolynomial_fold_fold(
7151 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
7152 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
7154 #include <isl/aff.h>
7155 __isl_give isl_pw_aff *isl_pw_aff_union_add(
7156 __isl_take isl_pw_aff *pwaff1,
7157 __isl_take isl_pw_aff *pwaff2);
7158 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
7159 __isl_take isl_pw_multi_aff *pma1,
7160 __isl_take isl_pw_multi_aff *pma2);
7161 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
7162 __isl_take isl_union_pw_aff *upa1,
7163 __isl_take isl_union_pw_aff *upa2);
7164 __isl_give isl_union_pw_multi_aff *
7165 isl_union_pw_multi_aff_union_add(
7166 __isl_take isl_union_pw_multi_aff *upma1,
7167 __isl_take isl_union_pw_multi_aff *upma2);
7168 __isl_give isl_multi_union_pw_aff *
7169 isl_multi_union_pw_aff_union_add(
7170 __isl_take isl_multi_union_pw_aff *mupa1,
7171 __isl_take isl_multi_union_pw_aff *mupa2);
7172 __isl_give isl_pw_aff *isl_pw_aff_union_min(
7173 __isl_take isl_pw_aff *pwaff1,
7174 __isl_take isl_pw_aff *pwaff2);
7175 __isl_give isl_pw_aff *isl_pw_aff_union_max(
7176 __isl_take isl_pw_aff *pwaff1,
7177 __isl_take isl_pw_aff *pwaff2);
7179 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
7180 expression with a domain that is the union of those of C<pwaff1> and
7181 C<pwaff2> and such that on each cell, the quasi-affine expression is
7182 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
7183 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
7184 associated expression is the defined one.
7185 This in contrast to the C<isl_pw_aff_max> function, which is
7186 only defined on the shared definition domain of the arguments.
7188 #include <isl/val.h>
7189 __isl_give isl_multi_val *isl_multi_val_add_val(
7190 __isl_take isl_multi_val *mv,
7191 __isl_take isl_val *v);
7192 __isl_give isl_multi_val *isl_multi_val_mod_val(
7193 __isl_take isl_multi_val *mv,
7194 __isl_take isl_val *v);
7195 __isl_give isl_multi_val *isl_multi_val_scale_val(
7196 __isl_take isl_multi_val *mv,
7197 __isl_take isl_val *v);
7198 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
7199 __isl_take isl_multi_val *mv,
7200 __isl_take isl_val *v);
7202 #include <isl/aff.h>
7203 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
7204 __isl_take isl_val *mod);
7205 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
7206 __isl_take isl_pw_aff *pa,
7207 __isl_take isl_val *mod);
7208 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
7209 __isl_take isl_union_pw_aff *upa,
7210 __isl_take isl_val *f);
7211 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
7212 __isl_take isl_val *v);
7213 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
7214 __isl_take isl_multi_aff *ma,
7215 __isl_take isl_val *v);
7216 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
7217 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
7218 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
7219 __isl_take isl_multi_pw_aff *mpa,
7220 __isl_take isl_val *v);
7221 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
7222 __isl_take isl_pw_multi_aff *pma,
7223 __isl_take isl_val *v);
7224 __isl_give isl_union_pw_multi_aff *
7225 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
7226 __isl_take isl_union_pw_aff *upa,
7227 __isl_take isl_val *f);
7228 isl_union_pw_multi_aff_scale_val(
7229 __isl_take isl_union_pw_multi_aff *upma,
7230 __isl_take isl_val *val);
7231 __isl_give isl_multi_union_pw_aff *
7232 isl_multi_union_pw_aff_scale_val(
7233 __isl_take isl_multi_union_pw_aff *mupa,
7234 __isl_take isl_val *v);
7235 __isl_give isl_aff *isl_aff_scale_down_ui(
7236 __isl_take isl_aff *aff, unsigned f);
7237 __isl_give isl_aff *isl_aff_scale_down_val(
7238 __isl_take isl_aff *aff, __isl_take isl_val *v);
7239 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
7240 __isl_take isl_multi_aff *ma,
7241 __isl_take isl_val *v);
7242 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
7243 __isl_take isl_pw_aff *pa,
7244 __isl_take isl_val *f);
7245 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
7246 __isl_take isl_multi_pw_aff *mpa,
7247 __isl_take isl_val *v);
7248 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
7249 __isl_take isl_pw_multi_aff *pma,
7250 __isl_take isl_val *v);
7251 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
7252 __isl_take isl_union_pw_aff *upa,
7253 __isl_take isl_val *v);
7254 __isl_give isl_union_pw_multi_aff *
7255 isl_union_pw_multi_aff_scale_down_val(
7256 __isl_take isl_union_pw_multi_aff *upma,
7257 __isl_take isl_val *val);
7258 __isl_give isl_multi_union_pw_aff *
7259 isl_multi_union_pw_aff_scale_down_val(
7260 __isl_take isl_multi_union_pw_aff *mupa,
7261 __isl_take isl_val *v);
7263 #include <isl/polynomial.h>
7264 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
7265 __isl_take isl_qpolynomial *qp,
7266 __isl_take isl_val *v);
7267 __isl_give isl_qpolynomial_fold *
7268 isl_qpolynomial_fold_scale_val(
7269 __isl_take isl_qpolynomial_fold *fold,
7270 __isl_take isl_val *v);
7271 __isl_give isl_pw_qpolynomial *
7272 isl_pw_qpolynomial_scale_val(
7273 __isl_take isl_pw_qpolynomial *pwqp,
7274 __isl_take isl_val *v);
7275 __isl_give isl_pw_qpolynomial_fold *
7276 isl_pw_qpolynomial_fold_scale_val(
7277 __isl_take isl_pw_qpolynomial_fold *pwf,
7278 __isl_take isl_val *v);
7279 __isl_give isl_union_pw_qpolynomial *
7280 isl_union_pw_qpolynomial_scale_val(
7281 __isl_take isl_union_pw_qpolynomial *upwqp,
7282 __isl_take isl_val *v);
7283 __isl_give isl_union_pw_qpolynomial_fold *
7284 isl_union_pw_qpolynomial_fold_scale_val(
7285 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7286 __isl_take isl_val *v);
7287 __isl_give isl_qpolynomial *
7288 isl_qpolynomial_scale_down_val(
7289 __isl_take isl_qpolynomial *qp,
7290 __isl_take isl_val *v);
7291 __isl_give isl_qpolynomial_fold *
7292 isl_qpolynomial_fold_scale_down_val(
7293 __isl_take isl_qpolynomial_fold *fold,
7294 __isl_take isl_val *v);
7295 __isl_give isl_pw_qpolynomial *
7296 isl_pw_qpolynomial_scale_down_val(
7297 __isl_take isl_pw_qpolynomial *pwqp,
7298 __isl_take isl_val *v);
7299 __isl_give isl_pw_qpolynomial_fold *
7300 isl_pw_qpolynomial_fold_scale_down_val(
7301 __isl_take isl_pw_qpolynomial_fold *pwf,
7302 __isl_take isl_val *v);
7303 __isl_give isl_union_pw_qpolynomial *
7304 isl_union_pw_qpolynomial_scale_down_val(
7305 __isl_take isl_union_pw_qpolynomial *upwqp,
7306 __isl_take isl_val *v);
7307 __isl_give isl_union_pw_qpolynomial_fold *
7308 isl_union_pw_qpolynomial_fold_scale_down_val(
7309 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7310 __isl_take isl_val *v);
7312 #include <isl/val.h>
7313 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
7314 __isl_take isl_multi_val *mv1,
7315 __isl_take isl_multi_val *mv2);
7316 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
7317 __isl_take isl_multi_val *mv1,
7318 __isl_take isl_multi_val *mv2);
7319 __isl_give isl_multi_val *
7320 isl_multi_val_scale_down_multi_val(
7321 __isl_take isl_multi_val *mv1,
7322 __isl_take isl_multi_val *mv2);
7324 #include <isl/aff.h>
7325 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
7326 __isl_take isl_multi_aff *ma,
7327 __isl_take isl_multi_val *mv);
7328 __isl_give isl_multi_union_pw_aff *
7329 isl_multi_union_pw_aff_mod_multi_val(
7330 __isl_take isl_multi_union_pw_aff *upma,
7331 __isl_take isl_multi_val *mv);
7332 __isl_give isl_multi_pw_aff *
7333 isl_multi_pw_aff_mod_multi_val(
7334 __isl_take isl_multi_pw_aff *mpa,
7335 __isl_take isl_multi_val *mv);
7336 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
7337 __isl_take isl_multi_aff *ma,
7338 __isl_take isl_multi_val *mv);
7339 __isl_give isl_pw_multi_aff *
7340 isl_pw_multi_aff_scale_multi_val(
7341 __isl_take isl_pw_multi_aff *pma,
7342 __isl_take isl_multi_val *mv);
7343 __isl_give isl_multi_pw_aff *
7344 isl_multi_pw_aff_scale_multi_val(
7345 __isl_take isl_multi_pw_aff *mpa,
7346 __isl_take isl_multi_val *mv);
7347 __isl_give isl_multi_union_pw_aff *
7348 isl_multi_union_pw_aff_scale_multi_val(
7349 __isl_take isl_multi_union_pw_aff *mupa,
7350 __isl_take isl_multi_val *mv);
7351 __isl_give isl_union_pw_multi_aff *
7352 isl_union_pw_multi_aff_scale_multi_val(
7353 __isl_take isl_union_pw_multi_aff *upma,
7354 __isl_take isl_multi_val *mv);
7355 __isl_give isl_multi_aff *
7356 isl_multi_aff_scale_down_multi_val(
7357 __isl_take isl_multi_aff *ma,
7358 __isl_take isl_multi_val *mv);
7359 __isl_give isl_multi_pw_aff *
7360 isl_multi_pw_aff_scale_down_multi_val(
7361 __isl_take isl_multi_pw_aff *mpa,
7362 __isl_take isl_multi_val *mv);
7363 __isl_give isl_multi_union_pw_aff *
7364 isl_multi_union_pw_aff_scale_down_multi_val(
7365 __isl_take isl_multi_union_pw_aff *mupa,
7366 __isl_take isl_multi_val *mv);
7368 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
7369 by the corresponding elements of C<mv>.
7371 #include <isl/aff.h>
7372 __isl_give isl_aff *isl_aff_mul(
7373 __isl_take isl_aff *aff1,
7374 __isl_take isl_aff *aff2);
7375 __isl_give isl_aff *isl_aff_div(
7376 __isl_take isl_aff *aff1,
7377 __isl_take isl_aff *aff2);
7378 __isl_give isl_pw_aff *isl_pw_aff_mul(
7379 __isl_take isl_pw_aff *pwaff1,
7380 __isl_take isl_pw_aff *pwaff2);
7381 __isl_give isl_pw_aff *isl_pw_aff_div(
7382 __isl_take isl_pw_aff *pa1,
7383 __isl_take isl_pw_aff *pa2);
7384 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
7385 __isl_take isl_pw_aff *pa1,
7386 __isl_take isl_pw_aff *pa2);
7387 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
7388 __isl_take isl_pw_aff *pa1,
7389 __isl_take isl_pw_aff *pa2);
7391 When multiplying two affine expressions, at least one of the two needs
7392 to be a constant. Similarly, when dividing an affine expression by another,
7393 the second expression needs to be a constant.
7394 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
7395 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
7398 #include <isl/polynomial.h>
7399 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
7400 __isl_take isl_qpolynomial *qp1,
7401 __isl_take isl_qpolynomial *qp2);
7402 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
7403 __isl_take isl_pw_qpolynomial *pwqp1,
7404 __isl_take isl_pw_qpolynomial *pwqp2);
7405 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
7406 __isl_take isl_union_pw_qpolynomial *upwqp1,
7407 __isl_take isl_union_pw_qpolynomial *upwqp2);
7411 =head3 Lexicographic Optimization
7413 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
7414 the following functions
7415 compute a set that contains the lexicographic minimum or maximum
7416 of the elements in C<set> (or C<bset>) for those values of the parameters
7417 that satisfy C<dom>.
7418 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7419 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
7421 In other words, the union of the parameter values
7422 for which the result is non-empty and of C<*empty>
7425 #include <isl/set.h>
7426 __isl_give isl_set *isl_basic_set_partial_lexmin(
7427 __isl_take isl_basic_set *bset,
7428 __isl_take isl_basic_set *dom,
7429 __isl_give isl_set **empty);
7430 __isl_give isl_set *isl_basic_set_partial_lexmax(
7431 __isl_take isl_basic_set *bset,
7432 __isl_take isl_basic_set *dom,
7433 __isl_give isl_set **empty);
7434 __isl_give isl_set *isl_set_partial_lexmin(
7435 __isl_take isl_set *set, __isl_take isl_set *dom,
7436 __isl_give isl_set **empty);
7437 __isl_give isl_set *isl_set_partial_lexmax(
7438 __isl_take isl_set *set, __isl_take isl_set *dom,
7439 __isl_give isl_set **empty);
7441 Given a (basic) set C<set> (or C<bset>), the following functions simply
7442 return a set containing the lexicographic minimum or maximum
7443 of the elements in C<set> (or C<bset>).
7444 In case of union sets, the optimum is computed per space.
7446 #include <isl/set.h>
7447 __isl_give isl_set *isl_basic_set_lexmin(
7448 __isl_take isl_basic_set *bset);
7449 __isl_give isl_set *isl_basic_set_lexmax(
7450 __isl_take isl_basic_set *bset);
7451 __isl_give isl_set *isl_set_lexmin(
7452 __isl_take isl_set *set);
7453 __isl_give isl_set *isl_set_lexmax(
7454 __isl_take isl_set *set);
7455 __isl_give isl_union_set *isl_union_set_lexmin(
7456 __isl_take isl_union_set *uset);
7457 __isl_give isl_union_set *isl_union_set_lexmax(
7458 __isl_take isl_union_set *uset);
7460 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
7461 the following functions
7462 compute a relation that maps each element of C<dom>
7463 to the single lexicographic minimum or maximum
7464 of the elements that are associated to that same
7465 element in C<map> (or C<bmap>).
7466 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7467 that contains the elements in C<dom> that do not map
7468 to any elements in C<map> (or C<bmap>).
7469 In other words, the union of the domain of the result and of C<*empty>
7472 #include <isl/map.h>
7473 __isl_give isl_map *isl_basic_map_partial_lexmax(
7474 __isl_take isl_basic_map *bmap,
7475 __isl_take isl_basic_set *dom,
7476 __isl_give isl_set **empty);
7477 __isl_give isl_map *isl_basic_map_partial_lexmin(
7478 __isl_take isl_basic_map *bmap,
7479 __isl_take isl_basic_set *dom,
7480 __isl_give isl_set **empty);
7481 __isl_give isl_map *isl_map_partial_lexmax(
7482 __isl_take isl_map *map, __isl_take isl_set *dom,
7483 __isl_give isl_set **empty);
7484 __isl_give isl_map *isl_map_partial_lexmin(
7485 __isl_take isl_map *map, __isl_take isl_set *dom,
7486 __isl_give isl_set **empty);
7488 Given a (basic) map C<map> (or C<bmap>), the following functions simply
7489 return a map mapping each element in the domain of
7490 C<map> (or C<bmap>) to the lexicographic minimum or maximum
7491 of all elements associated to that element.
7492 In case of union relations, the optimum is computed per space.
7494 #include <isl/map.h>
7495 __isl_give isl_map *isl_basic_map_lexmin(
7496 __isl_take isl_basic_map *bmap);
7497 __isl_give isl_map *isl_basic_map_lexmax(
7498 __isl_take isl_basic_map *bmap);
7499 __isl_give isl_map *isl_map_lexmin(
7500 __isl_take isl_map *map);
7501 __isl_give isl_map *isl_map_lexmax(
7502 __isl_take isl_map *map);
7503 __isl_give isl_union_map *isl_union_map_lexmin(
7504 __isl_take isl_union_map *umap);
7505 __isl_give isl_union_map *isl_union_map_lexmax(
7506 __isl_take isl_union_map *umap);
7508 The following functions return their result in the form of
7509 a piecewise multi-affine expression,
7510 but are otherwise equivalent to the corresponding functions
7511 returning a basic set or relation.
7513 #include <isl/set.h>
7514 __isl_give isl_pw_multi_aff *
7515 isl_basic_set_partial_lexmin_pw_multi_aff(
7516 __isl_take isl_basic_set *bset,
7517 __isl_take isl_basic_set *dom,
7518 __isl_give isl_set **empty);
7519 __isl_give isl_pw_multi_aff *
7520 isl_basic_set_partial_lexmax_pw_multi_aff(
7521 __isl_take isl_basic_set *bset,
7522 __isl_take isl_basic_set *dom,
7523 __isl_give isl_set **empty);
7524 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
7525 __isl_take isl_set *set);
7526 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
7527 __isl_take isl_set *set);
7529 #include <isl/map.h>
7530 __isl_give isl_pw_multi_aff *
7531 isl_basic_map_lexmin_pw_multi_aff(
7532 __isl_take isl_basic_map *bmap);
7533 __isl_give isl_pw_multi_aff *
7534 isl_basic_map_partial_lexmin_pw_multi_aff(
7535 __isl_take isl_basic_map *bmap,
7536 __isl_take isl_basic_set *dom,
7537 __isl_give isl_set **empty);
7538 __isl_give isl_pw_multi_aff *
7539 isl_basic_map_partial_lexmax_pw_multi_aff(
7540 __isl_take isl_basic_map *bmap,
7541 __isl_take isl_basic_set *dom,
7542 __isl_give isl_set **empty);
7543 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
7544 __isl_take isl_map *map);
7545 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
7546 __isl_take isl_map *map);
7548 The following functions return the lexicographic minimum or maximum
7549 on the shared domain of the inputs and the single defined function
7550 on those parts of the domain where only a single function is defined.
7552 #include <isl/aff.h>
7553 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
7554 __isl_take isl_pw_multi_aff *pma1,
7555 __isl_take isl_pw_multi_aff *pma2);
7556 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
7557 __isl_take isl_pw_multi_aff *pma1,
7558 __isl_take isl_pw_multi_aff *pma2);
7560 If the input to a lexicographic optimization problem has
7561 multiple constraints with the same coefficients for the optimized
7562 variables, then, by default, this symmetry is exploited by
7563 replacing those constraints by a single constraint with
7564 an abstract bound, which is in turn bounded by the corresponding terms
7565 in the original constraints.
7566 Without this optimization, the solver would typically consider
7567 all possible orderings of those original bounds, resulting in a needless
7568 decomposition of the domain.
7569 However, the optimization can also result in slowdowns since
7570 an extra parameter is introduced that may get used in additional
7572 The following option determines whether symmetry detection is applied
7573 during lexicographic optimization.
7575 #include <isl/options.h>
7576 isl_stat isl_options_set_pip_symmetry(isl_ctx *ctx,
7578 int isl_options_get_pip_symmetry(isl_ctx *ctx);
7582 See also \autoref{s:offline}.
7586 =head2 Ternary Operations
7588 #include <isl/aff.h>
7589 __isl_give isl_pw_aff *isl_pw_aff_cond(
7590 __isl_take isl_pw_aff *cond,
7591 __isl_take isl_pw_aff *pwaff_true,
7592 __isl_take isl_pw_aff *pwaff_false);
7594 The function C<isl_pw_aff_cond> performs a conditional operator
7595 and returns an expression that is equal to C<pwaff_true>
7596 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
7597 where C<cond> is zero.
7601 Lists are defined over several element types, including
7602 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_union_pw_aff>,
7603 C<isl_union_pw_multi_aff>, C<isl_constraint>,
7604 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
7605 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
7606 Here we take lists of C<isl_set>s as an example.
7607 Lists can be created, copied, modified and freed using the following functions.
7609 #include <isl/set.h>
7610 __isl_give isl_set_list *isl_set_list_from_set(
7611 __isl_take isl_set *el);
7612 __isl_give isl_set_list *isl_set_list_alloc(
7613 isl_ctx *ctx, int n);
7614 __isl_give isl_set_list *isl_set_list_copy(
7615 __isl_keep isl_set_list *list);
7616 __isl_give isl_set_list *isl_set_list_insert(
7617 __isl_take isl_set_list *list, unsigned pos,
7618 __isl_take isl_set *el);
7619 __isl_give isl_set_list *isl_set_list_add(
7620 __isl_take isl_set_list *list,
7621 __isl_take isl_set *el);
7622 __isl_give isl_set_list *isl_set_list_drop(
7623 __isl_take isl_set_list *list,
7624 unsigned first, unsigned n);
7625 __isl_give isl_set_list *isl_set_list_set_set(
7626 __isl_take isl_set_list *list, int index,
7627 __isl_take isl_set *set);
7628 __isl_give isl_set_list *isl_set_list_concat(
7629 __isl_take isl_set_list *list1,
7630 __isl_take isl_set_list *list2);
7631 __isl_give isl_set_list *isl_set_list_map(
7632 __isl_take isl_set_list *list,
7633 __isl_give isl_set *(*fn)(__isl_take isl_set *el,
7636 __isl_give isl_set_list *isl_set_list_sort(
7637 __isl_take isl_set_list *list,
7638 int (*cmp)(__isl_keep isl_set *a,
7639 __isl_keep isl_set *b, void *user),
7641 __isl_null isl_set_list *isl_set_list_free(
7642 __isl_take isl_set_list *list);
7644 C<isl_set_list_alloc> creates an empty list with an initial capacity
7645 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
7646 add elements to a list, increasing its capacity as needed.
7647 C<isl_set_list_from_set> creates a list with a single element.
7649 Lists can be inspected using the following functions.
7651 #include <isl/set.h>
7652 int isl_set_list_n_set(__isl_keep isl_set_list *list);
7653 __isl_give isl_set *isl_set_list_get_set(
7654 __isl_keep isl_set_list *list, int index);
7655 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list,
7656 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7658 isl_stat isl_set_list_foreach_scc(
7659 __isl_keep isl_set_list *list,
7660 isl_bool (*follows)(__isl_keep isl_set *a,
7661 __isl_keep isl_set *b, void *user),
7663 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7666 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
7667 strongly connected components of the graph with as vertices the elements
7668 of C<list> and a directed edge from vertex C<b> to vertex C<a>
7669 iff C<follows(a, b)> returns C<isl_bool_true>. The callbacks C<follows> and
7670 C<fn> should return C<isl_bool_error> or C<isl_stat_error> on error.
7672 Lists can be printed using
7674 #include <isl/set.h>
7675 __isl_give isl_printer *isl_printer_print_set_list(
7676 __isl_take isl_printer *p,
7677 __isl_keep isl_set_list *list);
7679 =head2 Associative arrays
7681 Associative arrays map isl objects of a specific type to isl objects
7682 of some (other) specific type. They are defined for several pairs
7683 of types, including (C<isl_map>, C<isl_basic_set>),
7684 (C<isl_id>, C<isl_ast_expr>),
7685 (C<isl_id>, C<isl_id>) and
7686 (C<isl_id>, C<isl_pw_aff>).
7687 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
7690 Associative arrays can be created, copied and freed using
7691 the following functions.
7693 #include <isl/id_to_ast_expr.h>
7694 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
7695 isl_ctx *ctx, int min_size);
7696 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
7697 __isl_keep isl_id_to_ast_expr *id2expr);
7698 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
7699 __isl_take isl_id_to_ast_expr *id2expr);
7701 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
7702 to specify the expected size of the associative array.
7703 The associative array will be grown automatically as needed.
7705 Associative arrays can be inspected using the following functions.
7707 #include <isl/id_to_ast_expr.h>
7708 __isl_give isl_maybe_isl_ast_expr
7709 isl_id_to_ast_expr_try_get(
7710 __isl_keep isl_id_to_ast_expr *id2expr,
7711 __isl_keep isl_id *key);
7712 isl_bool isl_id_to_ast_expr_has(
7713 __isl_keep isl_id_to_ast_expr *id2expr,
7714 __isl_keep isl_id *key);
7715 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
7716 __isl_keep isl_id_to_ast_expr *id2expr,
7717 __isl_take isl_id *key);
7718 isl_stat isl_id_to_ast_expr_foreach(
7719 __isl_keep isl_id_to_ast_expr *id2expr,
7720 isl_stat (*fn)(__isl_take isl_id *key,
7721 __isl_take isl_ast_expr *val, void *user),
7724 The function C<isl_id_to_ast_expr_try_get> returns a structure
7725 containing two elements, C<valid> and C<value>.
7726 If there is a value associated to the key, then C<valid>
7727 is set to C<isl_bool_true> and C<value> contains a copy of
7728 the associated value. Otherwise C<value> is C<NULL> and
7729 C<valid> may be C<isl_bool_error> or C<isl_bool_false> depending
7730 on whether some error has occurred or there simply is no associated value.
7731 The function C<isl_id_to_ast_expr_has> returns the C<valid> field
7732 in the structure and
7733 the function C<isl_id_to_ast_expr_get> returns the C<value> field.
7735 Associative arrays can be modified using the following functions.
7737 #include <isl/id_to_ast_expr.h>
7738 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
7739 __isl_take isl_id_to_ast_expr *id2expr,
7740 __isl_take isl_id *key,
7741 __isl_take isl_ast_expr *val);
7742 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
7743 __isl_take isl_id_to_ast_expr *id2expr,
7744 __isl_take isl_id *key);
7746 Associative arrays can be printed using the following function.
7748 #include <isl/id_to_ast_expr.h>
7749 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
7750 __isl_take isl_printer *p,
7751 __isl_keep isl_id_to_ast_expr *id2expr);
7755 Vectors can be created, copied and freed using the following functions.
7757 #include <isl/vec.h>
7758 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
7760 __isl_give isl_vec *isl_vec_zero(isl_ctx *ctx,
7762 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
7763 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
7765 Note that the elements of a vector created by C<isl_vec_alloc>
7766 may have arbitrary values.
7767 A vector created by C<isl_vec_zero> has elements with value zero.
7768 The elements can be changed and inspected using the following functions.
7770 int isl_vec_size(__isl_keep isl_vec *vec);
7771 __isl_give isl_val *isl_vec_get_element_val(
7772 __isl_keep isl_vec *vec, int pos);
7773 __isl_give isl_vec *isl_vec_set_element_si(
7774 __isl_take isl_vec *vec, int pos, int v);
7775 __isl_give isl_vec *isl_vec_set_element_val(
7776 __isl_take isl_vec *vec, int pos,
7777 __isl_take isl_val *v);
7778 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
7780 __isl_give isl_vec *isl_vec_set_val(
7781 __isl_take isl_vec *vec, __isl_take isl_val *v);
7782 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
7783 __isl_keep isl_vec *vec2, int pos);
7785 C<isl_vec_get_element> will return a negative value if anything went wrong.
7786 In that case, the value of C<*v> is undefined.
7788 The following function can be used to concatenate two vectors.
7790 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
7791 __isl_take isl_vec *vec2);
7795 Matrices can be created, copied and freed using the following functions.
7797 #include <isl/mat.h>
7798 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
7799 unsigned n_row, unsigned n_col);
7800 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
7801 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
7803 Note that the elements of a newly created matrix may have arbitrary values.
7804 The elements can be changed and inspected using the following functions.
7806 int isl_mat_rows(__isl_keep isl_mat *mat);
7807 int isl_mat_cols(__isl_keep isl_mat *mat);
7808 __isl_give isl_val *isl_mat_get_element_val(
7809 __isl_keep isl_mat *mat, int row, int col);
7810 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
7811 int row, int col, int v);
7812 __isl_give isl_mat *isl_mat_set_element_val(
7813 __isl_take isl_mat *mat, int row, int col,
7814 __isl_take isl_val *v);
7816 The following function computes the rank of a matrix.
7817 The return value may be -1 if some error occurred.
7819 #include <isl/mat.h>
7820 int isl_mat_rank(__isl_keep isl_mat *mat);
7822 The following function can be used to compute the (right) inverse
7823 of a matrix, i.e., a matrix such that the product of the original
7824 and the inverse (in that order) is a multiple of the identity matrix.
7825 The input matrix is assumed to be of full row-rank.
7827 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
7829 The following function can be used to compute the (right) kernel
7830 (or null space) of a matrix, i.e., a matrix such that the product of
7831 the original and the kernel (in that order) is the zero matrix.
7833 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
7835 The following function computes a basis for the space spanned
7836 by the rows of a matrix.
7838 __isl_give isl_mat *isl_mat_row_basis(
7839 __isl_take isl_mat *mat);
7841 The following function computes rows that extend a basis of C<mat1>
7842 to a basis that also covers C<mat2>.
7844 __isl_give isl_mat *isl_mat_row_basis_extension(
7845 __isl_take isl_mat *mat1,
7846 __isl_take isl_mat *mat2);
7848 The following function checks whether there is no linear dependence
7849 among the combined rows of "mat1" and "mat2" that is not already present
7850 in "mat1" or "mat2" individually.
7851 If "mat1" and "mat2" have linearly independent rows by themselves,
7852 then this means that there is no linear dependence among all rows together.
7854 isl_bool isl_mat_has_linearly_independent_rows(
7855 __isl_keep isl_mat *mat1,
7856 __isl_keep isl_mat *mat2);
7858 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
7860 The following functions determine
7861 an upper or lower bound on a quasipolynomial over its domain.
7863 __isl_give isl_pw_qpolynomial_fold *
7864 isl_pw_qpolynomial_bound(
7865 __isl_take isl_pw_qpolynomial *pwqp,
7866 enum isl_fold type, int *tight);
7868 __isl_give isl_union_pw_qpolynomial_fold *
7869 isl_union_pw_qpolynomial_bound(
7870 __isl_take isl_union_pw_qpolynomial *upwqp,
7871 enum isl_fold type, int *tight);
7873 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
7874 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
7875 is the returned bound is known be tight, i.e., for each value
7876 of the parameters there is at least
7877 one element in the domain that reaches the bound.
7878 If the domain of C<pwqp> is not wrapping, then the bound is computed
7879 over all elements in that domain and the result has a purely parametric
7880 domain. If the domain of C<pwqp> is wrapping, then the bound is
7881 computed over the range of the wrapped relation. The domain of the
7882 wrapped relation becomes the domain of the result.
7884 =head2 Parametric Vertex Enumeration
7886 The parametric vertex enumeration described in this section
7887 is mainly intended to be used internally and by the C<barvinok>
7890 #include <isl/vertices.h>
7891 __isl_give isl_vertices *isl_basic_set_compute_vertices(
7892 __isl_keep isl_basic_set *bset);
7894 The function C<isl_basic_set_compute_vertices> performs the
7895 actual computation of the parametric vertices and the chamber
7896 decomposition and stores the result in an C<isl_vertices> object.
7897 This information can be queried by either iterating over all
7898 the vertices or iterating over all the chambers or cells
7899 and then iterating over all vertices that are active on the chamber.
7901 isl_stat isl_vertices_foreach_vertex(
7902 __isl_keep isl_vertices *vertices,
7903 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7904 void *user), void *user);
7906 isl_stat isl_vertices_foreach_cell(
7907 __isl_keep isl_vertices *vertices,
7908 isl_stat (*fn)(__isl_take isl_cell *cell,
7909 void *user), void *user);
7910 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
7911 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7912 void *user), void *user);
7914 Other operations that can be performed on an C<isl_vertices> object are
7917 int isl_vertices_get_n_vertices(
7918 __isl_keep isl_vertices *vertices);
7919 __isl_null isl_vertices *isl_vertices_free(
7920 __isl_take isl_vertices *vertices);
7922 Vertices can be inspected and destroyed using the following functions.
7924 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
7925 __isl_give isl_basic_set *isl_vertex_get_domain(
7926 __isl_keep isl_vertex *vertex);
7927 __isl_give isl_multi_aff *isl_vertex_get_expr(
7928 __isl_keep isl_vertex *vertex);
7929 void isl_vertex_free(__isl_take isl_vertex *vertex);
7931 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
7932 describing the vertex in terms of the parameters,
7933 while C<isl_vertex_get_domain> returns the activity domain
7936 Chambers can be inspected and destroyed using the following functions.
7938 __isl_give isl_basic_set *isl_cell_get_domain(
7939 __isl_keep isl_cell *cell);
7940 void isl_cell_free(__isl_take isl_cell *cell);
7942 =head1 Polyhedral Compilation Library
7944 This section collects functionality in C<isl> that has been specifically
7945 designed for use during polyhedral compilation.
7947 =head2 Schedule Trees
7949 A schedule tree is a structured representation of a schedule,
7950 assigning a relative order to a set of domain elements.
7951 The relative order expressed by the schedule tree is
7952 defined recursively. In particular, the order between
7953 two domain elements is determined by the node that is closest
7954 to the root that refers to both elements and that orders them apart.
7955 Each node in the tree is of one of several types.
7956 The root node is always of type C<isl_schedule_node_domain>
7957 (or C<isl_schedule_node_extension>)
7958 and it describes the (extra) domain elements to which the schedule applies.
7959 The other types of nodes are as follows.
7963 =item C<isl_schedule_node_band>
7965 A band of schedule dimensions. Each schedule dimension is represented
7966 by a union piecewise quasi-affine expression. If this expression
7967 assigns a different value to two domain elements, while all previous
7968 schedule dimensions in the same band assign them the same value,
7969 then the two domain elements are ordered according to these two
7971 Each expression is required to be total in the domain elements
7972 that reach the band node.
7974 =item C<isl_schedule_node_expansion>
7976 An expansion node maps each of the domain elements that reach the node
7977 to one or more domain elements. The image of this mapping forms
7978 the set of domain elements that reach the child of the expansion node.
7979 The function that maps each of the expanded domain elements
7980 to the original domain element from which it was expanded
7981 is called the contraction.
7983 =item C<isl_schedule_node_filter>
7985 A filter node does not impose any ordering, but rather intersects
7986 the set of domain elements that the current subtree refers to
7987 with a given union set. The subtree of the filter node only
7988 refers to domain elements in the intersection.
7989 A filter node is typically only used as a child of a sequence or
7992 =item C<isl_schedule_node_leaf>
7994 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
7996 =item C<isl_schedule_node_mark>
7998 A mark node can be used to attach any kind of information to a subtree
7999 of the schedule tree.
8001 =item C<isl_schedule_node_sequence>
8003 A sequence node has one or more children, each of which is a filter node.
8004 The filters on these filter nodes form a partition of
8005 the domain elements that the current subtree refers to.
8006 If two domain elements appear in distinct filters then the sequence
8007 node orders them according to the child positions of the corresponding
8010 =item C<isl_schedule_node_set>
8012 A set node is similar to a sequence node, except that
8013 it expresses that domain elements appearing in distinct filters
8014 may have any order. The order of the children of a set node
8015 is therefore also immaterial.
8019 The following node types are only supported by the AST generator.
8023 =item C<isl_schedule_node_context>
8025 The context describes constraints on the parameters and
8026 the schedule dimensions of outer
8027 bands that the AST generator may assume to hold. It is also the only
8028 kind of node that may introduce additional parameters.
8029 The space of the context is that of the flat product of the outer
8030 band nodes. In particular, if there are no outer band nodes, then
8031 this space is the unnamed zero-dimensional space.
8032 Since a context node references the outer band nodes, any tree
8033 containing a context node is considered to be anchored.
8035 =item C<isl_schedule_node_extension>
8037 An extension node instructs the AST generator to add additional
8038 domain elements that need to be scheduled.
8039 The additional domain elements are described by the range of
8040 the extension map in terms of the outer schedule dimensions,
8041 i.e., the flat product of the outer band nodes.
8042 Note that domain elements are added whenever the AST generator
8043 reaches the extension node, meaning that there are still some
8044 active domain elements for which an AST needs to be generated.
8045 The conditions under which some domain elements are still active
8046 may however not be completely described by the outer AST nodes
8047 generated at that point.
8048 Since an extension node references the outer band nodes, any tree
8049 containing an extension node is considered to be anchored.
8051 An extension node may also appear as the root of a schedule tree,
8052 when it is intended to be inserted into another tree
8053 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
8054 In this case, the domain of the extension node should
8055 correspond to the flat product of the outer band nodes
8056 in this other schedule tree at the point where the extension tree
8059 =item C<isl_schedule_node_guard>
8061 The guard describes constraints on the parameters and
8062 the schedule dimensions of outer
8063 bands that need to be enforced by the outer nodes
8064 in the generated AST.
8065 That is, the part of the AST that is generated from descendants
8066 of the guard node can assume that these constraints are satisfied.
8067 The space of the guard is that of the flat product of the outer
8068 band nodes. In particular, if there are no outer band nodes, then
8069 this space is the unnamed zero-dimensional space.
8070 Since a guard node references the outer band nodes, any tree
8071 containing a guard node is considered to be anchored.
8075 Except for the C<isl_schedule_node_context> nodes,
8076 none of the nodes may introduce any parameters that were not
8077 already present in the root domain node.
8079 A schedule tree is encapsulated in an C<isl_schedule> object.
8080 The simplest such objects, those with a tree consisting of single domain node,
8081 can be created using the following functions with either an empty
8082 domain or a given domain.
8084 #include <isl/schedule.h>
8085 __isl_give isl_schedule *isl_schedule_empty(
8086 __isl_take isl_space *space);
8087 __isl_give isl_schedule *isl_schedule_from_domain(
8088 __isl_take isl_union_set *domain);
8090 The function C<isl_schedule_constraints_compute_schedule> described
8091 in L</"Scheduling"> can also be used to construct schedules.
8093 C<isl_schedule> objects may be copied and freed using the following functions.
8095 #include <isl/schedule.h>
8096 __isl_give isl_schedule *isl_schedule_copy(
8097 __isl_keep isl_schedule *sched);
8098 __isl_null isl_schedule *isl_schedule_free(
8099 __isl_take isl_schedule *sched);
8101 The following functions checks whether two C<isl_schedule> objects
8102 are obviously the same.
8104 #include <isl/schedule.h>
8105 isl_bool isl_schedule_plain_is_equal(
8106 __isl_keep isl_schedule *schedule1,
8107 __isl_keep isl_schedule *schedule2);
8109 The domain of the schedule, i.e., the domain described by the root node,
8110 can be obtained using the following function.
8112 #include <isl/schedule.h>
8113 __isl_give isl_union_set *isl_schedule_get_domain(
8114 __isl_keep isl_schedule *schedule);
8116 An extra top-level band node (right underneath the domain node) can
8117 be introduced into the schedule using the following function.
8118 The schedule tree is assumed not to have any anchored nodes.
8120 #include <isl/schedule.h>
8121 __isl_give isl_schedule *
8122 isl_schedule_insert_partial_schedule(
8123 __isl_take isl_schedule *schedule,
8124 __isl_take isl_multi_union_pw_aff *partial);
8126 A top-level context node (right underneath the domain node) can
8127 be introduced into the schedule using the following function.
8129 #include <isl/schedule.h>
8130 __isl_give isl_schedule *isl_schedule_insert_context(
8131 __isl_take isl_schedule *schedule,
8132 __isl_take isl_set *context)
8134 A top-level guard node (right underneath the domain node) can
8135 be introduced into the schedule using the following function.
8137 #include <isl/schedule.h>
8138 __isl_give isl_schedule *isl_schedule_insert_guard(
8139 __isl_take isl_schedule *schedule,
8140 __isl_take isl_set *guard)
8142 A schedule that combines two schedules either in the given
8143 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
8144 or an C<isl_schedule_node_set> node,
8145 can be created using the following functions.
8147 #include <isl/schedule.h>
8148 __isl_give isl_schedule *isl_schedule_sequence(
8149 __isl_take isl_schedule *schedule1,
8150 __isl_take isl_schedule *schedule2);
8151 __isl_give isl_schedule *isl_schedule_set(
8152 __isl_take isl_schedule *schedule1,
8153 __isl_take isl_schedule *schedule2);
8155 The domains of the two input schedules need to be disjoint.
8157 The following function can be used to restrict the domain
8158 of a schedule with a domain node as root to be a subset of the given union set.
8159 This operation may remove nodes in the tree that have become
8162 #include <isl/schedule.h>
8163 __isl_give isl_schedule *isl_schedule_intersect_domain(
8164 __isl_take isl_schedule *schedule,
8165 __isl_take isl_union_set *domain);
8167 The following function can be used to simplify the domain
8168 of a schedule with a domain node as root with respect to the given
8171 #include <isl/schedule.h>
8172 __isl_give isl_schedule *isl_schedule_gist_domain_params(
8173 __isl_take isl_schedule *schedule,
8174 __isl_take isl_set *context);
8176 The following function resets the user pointers on all parameter
8177 and tuple identifiers referenced by the nodes of the given schedule.
8179 #include <isl/schedule.h>
8180 __isl_give isl_schedule *isl_schedule_reset_user(
8181 __isl_take isl_schedule *schedule);
8183 The following function aligns the parameters of all nodes
8184 in the given schedule to the given space.
8186 #include <isl/schedule.h>
8187 __isl_give isl_schedule *isl_schedule_align_params(
8188 __isl_take isl_schedule *schedule,
8189 __isl_take isl_space *space);
8191 The following function allows the user to plug in a given function
8192 in the iteration domains. The input schedule is not allowed to contain
8193 any expansion nodes.
8195 #include <isl/schedule.h>
8196 __isl_give isl_schedule *
8197 isl_schedule_pullback_union_pw_multi_aff(
8198 __isl_take isl_schedule *schedule,
8199 __isl_take isl_union_pw_multi_aff *upma);
8201 The following function can be used to plug in the schedule C<expansion>
8202 in the leaves of C<schedule>, where C<contraction> describes how
8203 the domain elements of C<expansion> map to the domain elements
8204 at the original leaves of C<schedule>.
8205 The resulting schedule will contain expansion nodes, unless
8206 C<contraction> is an identity function.
8208 #include <isl/schedule.h>
8209 __isl_give isl_schedule *isl_schedule_expand(
8210 __isl_take isl_schedule *schedule,
8211 __isl_take isl_union_pw_multi_aff *contraction,
8212 __isl_take isl_schedule *expansion);
8214 An C<isl_union_map> representation of the schedule can be obtained
8215 from an C<isl_schedule> using the following function.
8217 #include <isl/schedule.h>
8218 __isl_give isl_union_map *isl_schedule_get_map(
8219 __isl_keep isl_schedule *sched);
8221 The resulting relation encodes the same relative ordering as
8222 the schedule by mapping the domain elements to a common schedule space.
8223 If the schedule_separate_components option is set, then the order
8224 of the children of a set node is explicitly encoded in the result.
8225 If the tree contains any expansion nodes, then the relation
8226 is formulated in terms of the expanded domain elements.
8228 Schedules can be read from input using the following functions.
8230 #include <isl/schedule.h>
8231 __isl_give isl_schedule *isl_schedule_read_from_file(
8232 isl_ctx *ctx, FILE *input);
8233 __isl_give isl_schedule *isl_schedule_read_from_str(
8234 isl_ctx *ctx, const char *str);
8236 A representation of the schedule can be printed using
8238 #include <isl/schedule.h>
8239 __isl_give isl_printer *isl_printer_print_schedule(
8240 __isl_take isl_printer *p,
8241 __isl_keep isl_schedule *schedule);
8242 __isl_give char *isl_schedule_to_str(
8243 __isl_keep isl_schedule *schedule);
8245 C<isl_schedule_to_str> prints the schedule in flow format.
8247 The schedule tree can be traversed through the use of
8248 C<isl_schedule_node> objects that point to a particular
8249 position in the schedule tree. Whenever a C<isl_schedule_node>
8250 is used to modify a node in the schedule tree, the original schedule
8251 tree is left untouched and the modifications are performed to a copy
8252 of the tree. The returned C<isl_schedule_node> then points to
8253 this modified copy of the tree.
8255 The root of the schedule tree can be obtained using the following function.
8257 #include <isl/schedule.h>
8258 __isl_give isl_schedule_node *isl_schedule_get_root(
8259 __isl_keep isl_schedule *schedule);
8261 A pointer to a newly created schedule tree with a single domain
8262 node can be created using the following functions.
8264 #include <isl/schedule_node.h>
8265 __isl_give isl_schedule_node *
8266 isl_schedule_node_from_domain(
8267 __isl_take isl_union_set *domain);
8268 __isl_give isl_schedule_node *
8269 isl_schedule_node_from_extension(
8270 __isl_take isl_union_map *extension);
8272 C<isl_schedule_node_from_extension> creates a tree with an extension
8275 Schedule nodes can be copied and freed using the following functions.
8277 #include <isl/schedule_node.h>
8278 __isl_give isl_schedule_node *isl_schedule_node_copy(
8279 __isl_keep isl_schedule_node *node);
8280 __isl_null isl_schedule_node *isl_schedule_node_free(
8281 __isl_take isl_schedule_node *node);
8283 The following functions can be used to check if two schedule
8284 nodes point to the same position in the same schedule.
8286 #include <isl/schedule_node.h>
8287 isl_bool isl_schedule_node_is_equal(
8288 __isl_keep isl_schedule_node *node1,
8289 __isl_keep isl_schedule_node *node2);
8291 The following properties can be obtained from a schedule node.
8293 #include <isl/schedule_node.h>
8294 enum isl_schedule_node_type isl_schedule_node_get_type(
8295 __isl_keep isl_schedule_node *node);
8296 enum isl_schedule_node_type
8297 isl_schedule_node_get_parent_type(
8298 __isl_keep isl_schedule_node *node);
8299 __isl_give isl_schedule *isl_schedule_node_get_schedule(
8300 __isl_keep isl_schedule_node *node);
8302 The function C<isl_schedule_node_get_type> returns the type of
8303 the node, while C<isl_schedule_node_get_parent_type> returns
8304 type of the parent of the node, which is required to exist.
8305 The function C<isl_schedule_node_get_schedule> returns a copy
8306 to the schedule to which the node belongs.
8308 The following functions can be used to move the schedule node
8309 to a different position in the tree or to check if such a position
8312 #include <isl/schedule_node.h>
8313 isl_bool isl_schedule_node_has_parent(
8314 __isl_keep isl_schedule_node *node);
8315 __isl_give isl_schedule_node *isl_schedule_node_parent(
8316 __isl_take isl_schedule_node *node);
8317 __isl_give isl_schedule_node *isl_schedule_node_root(
8318 __isl_take isl_schedule_node *node);
8319 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
8320 __isl_take isl_schedule_node *node,
8322 int isl_schedule_node_n_children(
8323 __isl_keep isl_schedule_node *node);
8324 __isl_give isl_schedule_node *isl_schedule_node_child(
8325 __isl_take isl_schedule_node *node, int pos);
8326 isl_bool isl_schedule_node_has_children(
8327 __isl_keep isl_schedule_node *node);
8328 __isl_give isl_schedule_node *isl_schedule_node_first_child(
8329 __isl_take isl_schedule_node *node);
8330 isl_bool isl_schedule_node_has_previous_sibling(
8331 __isl_keep isl_schedule_node *node);
8332 __isl_give isl_schedule_node *
8333 isl_schedule_node_previous_sibling(
8334 __isl_take isl_schedule_node *node);
8335 isl_bool isl_schedule_node_has_next_sibling(
8336 __isl_keep isl_schedule_node *node);
8337 __isl_give isl_schedule_node *
8338 isl_schedule_node_next_sibling(
8339 __isl_take isl_schedule_node *node);
8341 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
8342 is the node itself, the ancestor of generation 1 is its parent and so on.
8344 It is also possible to query the number of ancestors of a node,
8345 the position of the current node
8346 within the children of its parent, the position of the subtree
8347 containing a node within the children of an ancestor
8348 or to obtain a copy of a given
8349 child without destroying the current node.
8350 Given two nodes that point to the same schedule, their closest
8351 shared ancestor can be obtained using
8352 C<isl_schedule_node_get_shared_ancestor>.
8354 #include <isl/schedule_node.h>
8355 int isl_schedule_node_get_tree_depth(
8356 __isl_keep isl_schedule_node *node);
8357 int isl_schedule_node_get_child_position(
8358 __isl_keep isl_schedule_node *node);
8359 int isl_schedule_node_get_ancestor_child_position(
8360 __isl_keep isl_schedule_node *node,
8361 __isl_keep isl_schedule_node *ancestor);
8362 __isl_give isl_schedule_node *isl_schedule_node_get_child(
8363 __isl_keep isl_schedule_node *node, int pos);
8364 __isl_give isl_schedule_node *
8365 isl_schedule_node_get_shared_ancestor(
8366 __isl_keep isl_schedule_node *node1,
8367 __isl_keep isl_schedule_node *node2);
8369 All nodes in a schedule tree or
8370 all descendants of a specific node (including the node) can be visited
8371 in depth-first pre-order using the following functions.
8373 #include <isl/schedule.h>
8374 isl_stat isl_schedule_foreach_schedule_node_top_down(
8375 __isl_keep isl_schedule *sched,
8376 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8377 void *user), void *user);
8379 #include <isl/schedule_node.h>
8380 isl_stat isl_schedule_node_foreach_descendant_top_down(
8381 __isl_keep isl_schedule_node *node,
8382 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8383 void *user), void *user);
8385 The callback function is slightly different from the usual
8386 callbacks in that it not only indicates success (non-negative result)
8387 or failure (negative result), but also indicates whether the children
8388 of the given node should be visited. In particular, if the callback
8389 returns a positive value, then the children are visited, but if
8390 the callback returns zero, then the children are not visited.
8392 The following functions checks whether
8393 all descendants of a specific node (including the node itself)
8394 satisfy a user-specified test.
8396 #include <isl/schedule_node.h>
8397 isl_bool isl_schedule_node_every_descendant(
8398 __isl_keep isl_schedule_node *node,
8399 isl_bool (*test)(__isl_keep isl_schedule_node *node,
8400 void *user), void *user)
8402 The ancestors of a node in a schedule tree can be visited from
8403 the root down to and including the parent of the node using
8404 the following function.
8406 #include <isl/schedule_node.h>
8407 isl_stat isl_schedule_node_foreach_ancestor_top_down(
8408 __isl_keep isl_schedule_node *node,
8409 isl_stat (*fn)(__isl_keep isl_schedule_node *node,
8410 void *user), void *user);
8412 The following functions allows for a depth-first post-order
8413 traversal of the nodes in a schedule tree or
8414 of the descendants of a specific node (including the node
8415 itself), where the user callback is allowed to modify the
8418 #include <isl/schedule.h>
8419 __isl_give isl_schedule *
8420 isl_schedule_map_schedule_node_bottom_up(
8421 __isl_take isl_schedule *schedule,
8422 __isl_give isl_schedule_node *(*fn)(
8423 __isl_take isl_schedule_node *node,
8424 void *user), void *user);
8426 #include <isl/schedule_node.h>
8427 __isl_give isl_schedule_node *
8428 isl_schedule_node_map_descendant_bottom_up(
8429 __isl_take isl_schedule_node *node,
8430 __isl_give isl_schedule_node *(*fn)(
8431 __isl_take isl_schedule_node *node,
8432 void *user), void *user);
8434 The traversal continues from the node returned by the callback function.
8435 It is the responsibility of the user to ensure that this does not
8436 lead to an infinite loop. It is safest to always return a pointer
8437 to the same position (same ancestors and child positions) as the input node.
8439 The following function removes a node (along with its descendants)
8440 from a schedule tree and returns a pointer to the leaf at the
8441 same position in the updated tree.
8442 It is not allowed to remove the root of a schedule tree or
8443 a child of a set or sequence node.
8445 #include <isl/schedule_node.h>
8446 __isl_give isl_schedule_node *isl_schedule_node_cut(
8447 __isl_take isl_schedule_node *node);
8449 The following function removes a single node
8450 from a schedule tree and returns a pointer to the child
8451 of the node, now located at the position of the original node
8452 or to a leaf node at that position if there was no child.
8453 It is not allowed to remove the root of a schedule tree,
8454 a set or sequence node, a child of a set or sequence node or
8455 a band node with an anchored subtree.
8457 #include <isl/schedule_node.h>
8458 __isl_give isl_schedule_node *isl_schedule_node_delete(
8459 __isl_take isl_schedule_node *node);
8461 Most nodes in a schedule tree only contain local information.
8462 In some cases, however, a node may also refer to the schedule dimensions
8463 of its outer band nodes.
8464 This means that the position of the node within the tree should
8465 not be changed, or at least that no changes are performed to the
8466 outer band nodes. The following function can be used to test
8467 whether the subtree rooted at a given node contains any such nodes.
8469 #include <isl/schedule_node.h>
8470 isl_bool isl_schedule_node_is_subtree_anchored(
8471 __isl_keep isl_schedule_node *node);
8473 The following function resets the user pointers on all parameter
8474 and tuple identifiers referenced by the given schedule node.
8476 #include <isl/schedule_node.h>
8477 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
8478 __isl_take isl_schedule_node *node);
8480 The following function aligns the parameters of the given schedule
8481 node to the given space.
8483 #include <isl/schedule_node.h>
8484 __isl_give isl_schedule_node *
8485 isl_schedule_node_align_params(
8486 __isl_take isl_schedule_node *node,
8487 __isl_take isl_space *space);
8489 Several node types have their own functions for querying
8490 (and in some cases setting) some node type specific properties.
8492 #include <isl/schedule_node.h>
8493 __isl_give isl_space *isl_schedule_node_band_get_space(
8494 __isl_keep isl_schedule_node *node);
8495 __isl_give isl_multi_union_pw_aff *
8496 isl_schedule_node_band_get_partial_schedule(
8497 __isl_keep isl_schedule_node *node);
8498 __isl_give isl_union_map *
8499 isl_schedule_node_band_get_partial_schedule_union_map(
8500 __isl_keep isl_schedule_node *node);
8501 unsigned isl_schedule_node_band_n_member(
8502 __isl_keep isl_schedule_node *node);
8503 isl_bool isl_schedule_node_band_member_get_coincident(
8504 __isl_keep isl_schedule_node *node, int pos);
8505 __isl_give isl_schedule_node *
8506 isl_schedule_node_band_member_set_coincident(
8507 __isl_take isl_schedule_node *node, int pos,
8509 isl_bool isl_schedule_node_band_get_permutable(
8510 __isl_keep isl_schedule_node *node);
8511 __isl_give isl_schedule_node *
8512 isl_schedule_node_band_set_permutable(
8513 __isl_take isl_schedule_node *node, int permutable);
8514 enum isl_ast_loop_type
8515 isl_schedule_node_band_member_get_ast_loop_type(
8516 __isl_keep isl_schedule_node *node, int pos);
8517 __isl_give isl_schedule_node *
8518 isl_schedule_node_band_member_set_ast_loop_type(
8519 __isl_take isl_schedule_node *node, int pos,
8520 enum isl_ast_loop_type type);
8521 __isl_give isl_union_set *
8522 enum isl_ast_loop_type
8523 isl_schedule_node_band_member_get_isolate_ast_loop_type(
8524 __isl_keep isl_schedule_node *node, int pos);
8525 __isl_give isl_schedule_node *
8526 isl_schedule_node_band_member_set_isolate_ast_loop_type(
8527 __isl_take isl_schedule_node *node, int pos,
8528 enum isl_ast_loop_type type);
8529 isl_schedule_node_band_get_ast_build_options(
8530 __isl_keep isl_schedule_node *node);
8531 __isl_give isl_schedule_node *
8532 isl_schedule_node_band_set_ast_build_options(
8533 __isl_take isl_schedule_node *node,
8534 __isl_take isl_union_set *options);
8535 __isl_give isl_set *
8536 isl_schedule_node_band_get_ast_isolate_option(
8537 __isl_keep isl_schedule_node *node);
8539 The function C<isl_schedule_node_band_get_space> returns the space
8540 of the partial schedule of the band.
8541 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
8542 returns a representation of the partial schedule of the band node
8543 in the form of an C<isl_union_map>.
8544 The coincident and permutable properties are set by
8545 C<isl_schedule_constraints_compute_schedule> on the schedule tree
8547 A scheduling dimension is considered to be ``coincident''
8548 if it satisfies the coincidence constraints within its band.
8549 That is, if the dependence distances of the coincidence
8550 constraints are all zero in that direction (for fixed
8551 iterations of outer bands).
8552 A band is marked permutable if it was produced using the Pluto-like scheduler.
8553 Note that the scheduler may have to resort to a Feautrier style scheduling
8554 step even if the default scheduler is used.
8555 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
8556 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
8557 For the meaning of these loop AST generation types and the difference
8558 between the regular loop AST generation type and the isolate
8559 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
8560 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
8561 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
8562 may return C<isl_ast_loop_error> if an error occurs.
8563 The AST build options govern how an AST is generated for
8564 the individual schedule dimensions during AST generation.
8565 See L</"AST Generation Options (Schedule Tree)">.
8566 The isolate option for the given node can be extracted from these
8567 AST build options using the function
8568 C<isl_schedule_node_band_get_ast_isolate_option>.
8570 #include <isl/schedule_node.h>
8571 __isl_give isl_set *
8572 isl_schedule_node_context_get_context(
8573 __isl_keep isl_schedule_node *node);
8575 #include <isl/schedule_node.h>
8576 __isl_give isl_union_set *
8577 isl_schedule_node_domain_get_domain(
8578 __isl_keep isl_schedule_node *node);
8580 #include <isl/schedule_node.h>
8581 __isl_give isl_union_map *
8582 isl_schedule_node_expansion_get_expansion(
8583 __isl_keep isl_schedule_node *node);
8584 __isl_give isl_union_pw_multi_aff *
8585 isl_schedule_node_expansion_get_contraction(
8586 __isl_keep isl_schedule_node *node);
8588 #include <isl/schedule_node.h>
8589 __isl_give isl_union_map *
8590 isl_schedule_node_extension_get_extension(
8591 __isl_keep isl_schedule_node *node);
8593 #include <isl/schedule_node.h>
8594 __isl_give isl_union_set *
8595 isl_schedule_node_filter_get_filter(
8596 __isl_keep isl_schedule_node *node);
8598 #include <isl/schedule_node.h>
8599 __isl_give isl_set *isl_schedule_node_guard_get_guard(
8600 __isl_keep isl_schedule_node *node);
8602 #include <isl/schedule_node.h>
8603 __isl_give isl_id *isl_schedule_node_mark_get_id(
8604 __isl_keep isl_schedule_node *node);
8606 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
8607 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
8608 partial schedules related to the node.
8610 #include <isl/schedule_node.h>
8611 __isl_give isl_multi_union_pw_aff *
8612 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
8613 __isl_keep isl_schedule_node *node);
8614 __isl_give isl_union_pw_multi_aff *
8615 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
8616 __isl_keep isl_schedule_node *node);
8617 __isl_give isl_union_map *
8618 isl_schedule_node_get_prefix_schedule_union_map(
8619 __isl_keep isl_schedule_node *node);
8620 __isl_give isl_union_map *
8621 isl_schedule_node_get_prefix_schedule_relation(
8622 __isl_keep isl_schedule_node *node);
8623 __isl_give isl_union_map *
8624 isl_schedule_node_get_subtree_schedule_union_map(
8625 __isl_keep isl_schedule_node *node);
8627 In particular, the functions
8628 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
8629 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
8630 and C<isl_schedule_node_get_prefix_schedule_union_map>
8631 return a relative ordering on the domain elements that reach the given
8632 node determined by its ancestors.
8633 The function C<isl_schedule_node_get_prefix_schedule_relation>
8634 additionally includes the domain constraints in the result.
8635 The function C<isl_schedule_node_get_subtree_schedule_union_map>
8636 returns a representation of the partial schedule defined by the
8637 subtree rooted at the given node.
8638 If the tree contains any expansion nodes, then the subtree schedule
8639 is formulated in terms of the expanded domain elements.
8640 The tree passed to functions returning a prefix schedule
8641 may only contain extension nodes if these would not affect
8642 the result of these functions. That is, if one of the ancestors
8643 is an extension node, then all of the domain elements that were
8644 added by the extension node need to have been filtered out
8645 by filter nodes between the extension node and the input node.
8646 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
8647 may not contain in extension nodes in the selected subtree.
8649 The expansion/contraction defined by an entire subtree, combining
8650 the expansions/contractions
8651 on the expansion nodes in the subtree, can be obtained using
8652 the following functions.
8654 #include <isl/schedule_node.h>
8655 __isl_give isl_union_map *
8656 isl_schedule_node_get_subtree_expansion(
8657 __isl_keep isl_schedule_node *node);
8658 __isl_give isl_union_pw_multi_aff *
8659 isl_schedule_node_get_subtree_contraction(
8660 __isl_keep isl_schedule_node *node);
8662 The total number of outer band members of given node, i.e.,
8663 the shared output dimension of the maps in the result
8664 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
8665 using the following function.
8667 #include <isl/schedule_node.h>
8668 int isl_schedule_node_get_schedule_depth(
8669 __isl_keep isl_schedule_node *node);
8671 The following functions return the elements that reach the given node
8672 or the union of universes in the spaces that contain these elements.
8674 #include <isl/schedule_node.h>
8675 __isl_give isl_union_set *
8676 isl_schedule_node_get_domain(
8677 __isl_keep isl_schedule_node *node);
8678 __isl_give isl_union_set *
8679 isl_schedule_node_get_universe_domain(
8680 __isl_keep isl_schedule_node *node);
8682 The input tree of C<isl_schedule_node_get_domain>
8683 may only contain extension nodes if these would not affect
8684 the result of this function. That is, if one of the ancestors
8685 is an extension node, then all of the domain elements that were
8686 added by the extension node need to have been filtered out
8687 by filter nodes between the extension node and the input node.
8689 The following functions can be used to introduce additional nodes
8690 in the schedule tree. The new node is introduced at the point
8691 in the tree where the C<isl_schedule_node> points to and
8692 the results points to the new node.
8694 #include <isl/schedule_node.h>
8695 __isl_give isl_schedule_node *
8696 isl_schedule_node_insert_partial_schedule(
8697 __isl_take isl_schedule_node *node,
8698 __isl_take isl_multi_union_pw_aff *schedule);
8700 This function inserts a new band node with (the greatest integer
8701 part of) the given partial schedule.
8702 The subtree rooted at the given node is assumed not to have
8705 #include <isl/schedule_node.h>
8706 __isl_give isl_schedule_node *
8707 isl_schedule_node_insert_context(
8708 __isl_take isl_schedule_node *node,
8709 __isl_take isl_set *context);
8711 This function inserts a new context node with the given context constraints.
8713 #include <isl/schedule_node.h>
8714 __isl_give isl_schedule_node *
8715 isl_schedule_node_insert_filter(
8716 __isl_take isl_schedule_node *node,
8717 __isl_take isl_union_set *filter);
8719 This function inserts a new filter node with the given filter.
8720 If the original node already pointed to a filter node, then the
8721 two filter nodes are merged into one.
8723 #include <isl/schedule_node.h>
8724 __isl_give isl_schedule_node *
8725 isl_schedule_node_insert_guard(
8726 __isl_take isl_schedule_node *node,
8727 __isl_take isl_set *guard);
8729 This function inserts a new guard node with the given guard constraints.
8731 #include <isl/schedule_node.h>
8732 __isl_give isl_schedule_node *
8733 isl_schedule_node_insert_mark(
8734 __isl_take isl_schedule_node *node,
8735 __isl_take isl_id *mark);
8737 This function inserts a new mark node with the give mark identifier.
8739 #include <isl/schedule_node.h>
8740 __isl_give isl_schedule_node *
8741 isl_schedule_node_insert_sequence(
8742 __isl_take isl_schedule_node *node,
8743 __isl_take isl_union_set_list *filters);
8744 __isl_give isl_schedule_node *
8745 isl_schedule_node_insert_set(
8746 __isl_take isl_schedule_node *node,
8747 __isl_take isl_union_set_list *filters);
8749 These functions insert a new sequence or set node with the given
8750 filters as children.
8752 #include <isl/schedule_node.h>
8753 __isl_give isl_schedule_node *isl_schedule_node_group(
8754 __isl_take isl_schedule_node *node,
8755 __isl_take isl_id *group_id);
8757 This function introduces an expansion node in between the current
8758 node and its parent that expands instances of a space with tuple
8759 identifier C<group_id> to the original domain elements that reach
8760 the node. The group instances are identified by the prefix schedule
8761 of those domain elements. The ancestors of the node are adjusted
8762 to refer to the group instances instead of the original domain
8763 elements. The return value points to the same node in the updated
8764 schedule tree as the input node, i.e., to the child of the newly
8765 introduced expansion node. Grouping instances of different statements
8766 ensures that they will be treated as a single statement by the
8767 AST generator up to the point of the expansion node.
8769 The following function can be used to flatten a nested
8772 #include <isl/schedule_node.h>
8773 __isl_give isl_schedule_node *
8774 isl_schedule_node_sequence_splice_child(
8775 __isl_take isl_schedule_node *node, int pos);
8777 That is, given a sequence node C<node> that has another sequence node
8778 in its child at position C<pos> (in particular, the child of that filter
8779 node is a sequence node), attach the children of that other sequence
8780 node as children of C<node>, replacing the original child at position
8783 The partial schedule of a band node can be scaled (down) or reduced using
8784 the following functions.
8786 #include <isl/schedule_node.h>
8787 __isl_give isl_schedule_node *
8788 isl_schedule_node_band_scale(
8789 __isl_take isl_schedule_node *node,
8790 __isl_take isl_multi_val *mv);
8791 __isl_give isl_schedule_node *
8792 isl_schedule_node_band_scale_down(
8793 __isl_take isl_schedule_node *node,
8794 __isl_take isl_multi_val *mv);
8795 __isl_give isl_schedule_node *
8796 isl_schedule_node_band_mod(
8797 __isl_take isl_schedule_node *node,
8798 __isl_take isl_multi_val *mv);
8800 The spaces of the two arguments need to match.
8801 After scaling, the partial schedule is replaced by its greatest
8802 integer part to ensure that the schedule remains integral.
8804 The partial schedule of a band node can be shifted by an
8805 C<isl_multi_union_pw_aff> with a domain that is a superset
8806 of the domain of the partial schedule using
8807 the following function.
8809 #include <isl/schedule_node.h>
8810 __isl_give isl_schedule_node *
8811 isl_schedule_node_band_shift(
8812 __isl_take isl_schedule_node *node,
8813 __isl_take isl_multi_union_pw_aff *shift);
8815 A band node can be tiled using the following function.
8817 #include <isl/schedule_node.h>
8818 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
8819 __isl_take isl_schedule_node *node,
8820 __isl_take isl_multi_val *sizes);
8822 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
8824 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
8825 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
8827 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
8829 The C<isl_schedule_node_band_tile> function tiles
8830 the band using the given tile sizes inside its schedule.
8831 A new child band node is created to represent the point loops and it is
8832 inserted between the modified band and its children.
8833 The subtree rooted at the given node is assumed not to have
8835 The C<tile_scale_tile_loops> option specifies whether the tile
8836 loops iterators should be scaled by the tile sizes.
8837 If the C<tile_shift_point_loops> option is set, then the point loops
8838 are shifted to start at zero.
8840 A band node can be split into two nested band nodes
8841 using the following function.
8843 #include <isl/schedule_node.h>
8844 __isl_give isl_schedule_node *isl_schedule_node_band_split(
8845 __isl_take isl_schedule_node *node, int pos);
8847 The resulting outer band node contains the first C<pos> dimensions of
8848 the schedule of C<node> while the inner band contains the remaining dimensions.
8849 The schedules of the two band nodes live in anonymous spaces.
8850 The loop AST generation type options and the isolate option
8851 are split over the two band nodes.
8853 A band node can be moved down to the leaves of the subtree rooted
8854 at the band node using the following function.
8856 #include <isl/schedule_node.h>
8857 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
8858 __isl_take isl_schedule_node *node);
8860 The subtree rooted at the given node is assumed not to have
8862 The result points to the node in the resulting tree that is in the same
8863 position as the node pointed to by C<node> in the original tree.
8865 #include <isl/schedule_node.h>
8866 __isl_give isl_schedule_node *
8867 isl_schedule_node_order_before(
8868 __isl_take isl_schedule_node *node,
8869 __isl_take isl_union_set *filter);
8870 __isl_give isl_schedule_node *
8871 isl_schedule_node_order_after(
8872 __isl_take isl_schedule_node *node,
8873 __isl_take isl_union_set *filter);
8875 These functions split the domain elements that reach C<node>
8876 into those that satisfy C<filter> and those that do not and
8877 arranges for the elements that do satisfy the filter to be
8878 executed before (in case of C<isl_schedule_node_order_before>)
8879 or after (in case of C<isl_schedule_node_order_after>)
8880 those that do not. The order is imposed by
8881 a sequence node, possibly reusing the grandparent of C<node>
8882 on two copies of the subtree attached to the original C<node>.
8883 Both copies are simplified with respect to their filter.
8885 Return a pointer to the copy of the subtree that does not
8886 satisfy C<filter>. If there is no such copy (because all
8887 reaching domain elements satisfy the filter), then return
8888 the original pointer.
8890 #include <isl/schedule_node.h>
8891 __isl_give isl_schedule_node *
8892 isl_schedule_node_graft_before(
8893 __isl_take isl_schedule_node *node,
8894 __isl_take isl_schedule_node *graft);
8895 __isl_give isl_schedule_node *
8896 isl_schedule_node_graft_after(
8897 __isl_take isl_schedule_node *node,
8898 __isl_take isl_schedule_node *graft);
8900 This function inserts the C<graft> tree into the tree containing C<node>
8901 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
8902 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
8903 The root node of C<graft>
8904 should be an extension node where the domain of the extension
8905 is the flat product of all outer band nodes of C<node>.
8906 The root node may also be a domain node.
8907 The elements of the domain or the range of the extension may not
8908 intersect with the domain elements that reach "node".
8909 The schedule tree of C<graft> may not be anchored.
8911 The schedule tree of C<node> is modified to include an extension node
8912 corresponding to the root node of C<graft> as a child of the original
8913 parent of C<node>. The original node that C<node> points to and the
8914 child of the root node of C<graft> are attached to this extension node
8915 through a sequence, with appropriate filters and with the child
8916 of C<graft> appearing before or after the original C<node>.
8918 If C<node> already appears inside a sequence that is the child of
8919 an extension node and if the spaces of the new domain elements
8920 do not overlap with those of the original domain elements,
8921 then that extension node is extended with the new extension
8922 rather than introducing a new segment of extension and sequence nodes.
8924 Return a pointer to the same node in the modified tree that
8925 C<node> pointed to in the original tree.
8927 A representation of the schedule node can be printed using
8929 #include <isl/schedule_node.h>
8930 __isl_give isl_printer *isl_printer_print_schedule_node(
8931 __isl_take isl_printer *p,
8932 __isl_keep isl_schedule_node *node);
8933 __isl_give char *isl_schedule_node_to_str(
8934 __isl_keep isl_schedule_node *node);
8936 C<isl_schedule_node_to_str> prints the schedule node in block format.
8938 =head2 Dependence Analysis
8940 C<isl> contains specialized functionality for performing
8941 array dataflow analysis. That is, given a I<sink> access relation,
8942 a collection of possible I<source> accesses and
8943 a collection of I<kill> accesses,
8944 C<isl> can compute relations that describe
8945 for each iteration of the sink access, which iterations
8946 of which of the source access relations may have
8947 accessed the same data element before the given iteration
8948 of the sink access without any intermediate kill of that data element.
8949 The resulting dependence relations map source iterations
8950 to either the corresponding sink iterations or
8951 pairs of corresponding sink iterations and accessed data elements.
8952 To compute standard flow dependences, the sink should be
8953 a read, while the sources should be writes.
8954 If no kills are specified,
8955 then memory based dependence analysis is performed.
8956 If, on the other hand, all sources are also kills,
8957 then value based dependence analysis is performed.
8958 If any of the source accesses are marked as being I<must>
8959 accesses, then they are also treated as kills.
8960 Furthermore, the specification of must-sources results
8961 in the computation of must-dependences.
8962 Only dependences originating in a must access not coscheduled
8963 with any other access to the same element and without
8964 any may accesses between the must access and the sink access
8965 are considered to be must dependences.
8967 =head3 High-level Interface
8969 A high-level interface to dependence analysis is provided
8970 by the following function.
8972 #include <isl/flow.h>
8973 __isl_give isl_union_flow *
8974 isl_union_access_info_compute_flow(
8975 __isl_take isl_union_access_info *access);
8977 The input C<isl_union_access_info> object describes the sink
8978 access relations, the source access relations and a schedule,
8979 while the output C<isl_union_flow> object describes
8980 the resulting dependence relations and the subsets of the
8981 sink relations for which no source was found.
8983 An C<isl_union_access_info> is created, modified, copied and freed using
8984 the following functions.
8986 #include <isl/flow.h>
8987 __isl_give isl_union_access_info *
8988 isl_union_access_info_from_sink(
8989 __isl_take isl_union_map *sink);
8990 __isl_give isl_union_access_info *
8991 isl_union_access_info_set_kill(
8992 __isl_take isl_union_access_info *access,
8993 __isl_take isl_union_map *kill);
8994 __isl_give isl_union_access_info *
8995 isl_union_access_info_set_may_source(
8996 __isl_take isl_union_access_info *access,
8997 __isl_take isl_union_map *may_source);
8998 __isl_give isl_union_access_info *
8999 isl_union_access_info_set_must_source(
9000 __isl_take isl_union_access_info *access,
9001 __isl_take isl_union_map *must_source);
9002 __isl_give isl_union_access_info *
9003 isl_union_access_info_set_schedule(
9004 __isl_take isl_union_access_info *access,
9005 __isl_take isl_schedule *schedule);
9006 __isl_give isl_union_access_info *
9007 isl_union_access_info_set_schedule_map(
9008 __isl_take isl_union_access_info *access,
9009 __isl_take isl_union_map *schedule_map);
9010 __isl_give isl_union_access_info *
9011 isl_union_access_info_copy(
9012 __isl_keep isl_union_access_info *access);
9013 __isl_null isl_union_access_info *
9014 isl_union_access_info_free(
9015 __isl_take isl_union_access_info *access);
9017 The may sources set by C<isl_union_access_info_set_may_source>
9018 do not need to include the must sources set by
9019 C<isl_union_access_info_set_must_source> as a subset.
9020 The kills set by C<isl_union_access_info_set_kill> may overlap
9021 with the may-sources and/or must-sources.
9022 The user is free not to call one (or more) of these functions,
9023 in which case the corresponding set is kept to its empty default.
9024 Similarly, the default schedule initialized by
9025 C<isl_union_access_info_from_sink> is empty.
9026 The current schedule is determined by the last call to either
9027 C<isl_union_access_info_set_schedule> or
9028 C<isl_union_access_info_set_schedule_map>.
9029 The domain of the schedule corresponds to the domains of
9030 the access relations. In particular, the domains of the access
9031 relations are effectively intersected with the domain of the schedule
9032 and only the resulting accesses are considered by the dependence analysis.
9034 An C<isl_union_access_info> object can be read from input
9035 using the following function.
9037 #include <isl/flow.h>
9038 __isl_give isl_union_access_info *
9039 isl_union_access_info_read_from_file(isl_ctx *ctx,
9042 A representation of the information contained in an object
9043 of type C<isl_union_access_info> can be obtained using
9045 #include <isl/flow.h>
9046 __isl_give isl_printer *
9047 isl_printer_print_union_access_info(
9048 __isl_take isl_printer *p,
9049 __isl_keep isl_union_access_info *access);
9050 __isl_give char *isl_union_access_info_to_str(
9051 __isl_keep isl_union_access_info *access);
9053 C<isl_union_access_info_to_str> prints the information in flow format.
9055 The output of C<isl_union_access_info_compute_flow> can be examined,
9056 copied, and freed using the following functions.
9058 #include <isl/flow.h>
9059 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
9060 __isl_keep isl_union_flow *flow);
9061 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
9062 __isl_keep isl_union_flow *flow);
9063 __isl_give isl_union_map *
9064 isl_union_flow_get_full_must_dependence(
9065 __isl_keep isl_union_flow *flow);
9066 __isl_give isl_union_map *
9067 isl_union_flow_get_full_may_dependence(
9068 __isl_keep isl_union_flow *flow);
9069 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
9070 __isl_keep isl_union_flow *flow);
9071 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
9072 __isl_keep isl_union_flow *flow);
9073 __isl_give isl_union_flow *isl_union_flow_copy(
9074 __isl_keep isl_union_flow *flow);
9075 __isl_null isl_union_flow *isl_union_flow_free(
9076 __isl_take isl_union_flow *flow);
9078 The relation returned by C<isl_union_flow_get_must_dependence>
9079 relates domain elements of must sources to domain elements of the sink.
9080 The relation returned by C<isl_union_flow_get_may_dependence>
9081 relates domain elements of must or may sources to domain elements of the sink
9082 and includes the previous relation as a subset.
9083 The relation returned by C<isl_union_flow_get_full_must_dependence>
9084 relates domain elements of must sources to pairs of domain elements of the sink
9085 and accessed data elements.
9086 The relation returned by C<isl_union_flow_get_full_may_dependence>
9087 relates domain elements of must or may sources to pairs of
9088 domain elements of the sink and accessed data elements.
9089 This relation includes the previous relation as a subset.
9090 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
9091 of the sink relation for which no dependences have been found.
9092 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
9093 of the sink relation for which no definite dependences have been found.
9094 That is, it contains those sink access that do not contribute to any
9095 of the elements in the relation returned
9096 by C<isl_union_flow_get_must_dependence>.
9098 A representation of the information contained in an object
9099 of type C<isl_union_flow> can be obtained using
9101 #include <isl/flow.h>
9102 __isl_give isl_printer *isl_printer_print_union_flow(
9103 __isl_take isl_printer *p,
9104 __isl_keep isl_union_flow *flow);
9105 __isl_give char *isl_union_flow_to_str(
9106 __isl_keep isl_union_flow *flow);
9108 C<isl_union_flow_to_str> prints the information in flow format.
9110 =head3 Low-level Interface
9112 A lower-level interface is provided by the following functions.
9114 #include <isl/flow.h>
9116 typedef int (*isl_access_level_before)(void *first, void *second);
9118 __isl_give isl_access_info *isl_access_info_alloc(
9119 __isl_take isl_map *sink,
9120 void *sink_user, isl_access_level_before fn,
9122 __isl_give isl_access_info *isl_access_info_add_source(
9123 __isl_take isl_access_info *acc,
9124 __isl_take isl_map *source, int must,
9126 __isl_null isl_access_info *isl_access_info_free(
9127 __isl_take isl_access_info *acc);
9129 __isl_give isl_flow *isl_access_info_compute_flow(
9130 __isl_take isl_access_info *acc);
9132 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,
9133 isl_stat (*fn)(__isl_take isl_map *dep, int must,
9134 void *dep_user, void *user),
9136 __isl_give isl_map *isl_flow_get_no_source(
9137 __isl_keep isl_flow *deps, int must);
9138 void isl_flow_free(__isl_take isl_flow *deps);
9140 The function C<isl_access_info_compute_flow> performs the actual
9141 dependence analysis. The other functions are used to construct
9142 the input for this function or to read off the output.
9144 The input is collected in an C<isl_access_info>, which can
9145 be created through a call to C<isl_access_info_alloc>.
9146 The arguments to this functions are the sink access relation
9147 C<sink>, a token C<sink_user> used to identify the sink
9148 access to the user, a callback function for specifying the
9149 relative order of source and sink accesses, and the number
9150 of source access relations that will be added.
9152 The callback function has type C<int (*)(void *first, void *second)>.
9153 The function is called with two user supplied tokens identifying
9154 either a source or the sink and it should return the shared nesting
9155 level and the relative order of the two accesses.
9156 In particular, let I<n> be the number of loops shared by
9157 the two accesses. If C<first> precedes C<second> textually,
9158 then the function should return I<2 * n + 1>; otherwise,
9159 it should return I<2 * n>.
9160 The low-level interface assumes that no sources are coscheduled.
9161 If the information returned by the callback does not allow
9162 the relative order to be determined, then one of the sources
9163 is arbitrarily taken to be executed after the other(s).
9165 The sources can be added to the C<isl_access_info> object by performing
9166 (at most) C<max_source> calls to C<isl_access_info_add_source>.
9167 C<must> indicates whether the source is a I<must> access
9168 or a I<may> access. Note that a multi-valued access relation
9169 should only be marked I<must> if every iteration in the domain
9170 of the relation accesses I<all> elements in its image.
9171 The C<source_user> token is again used to identify
9172 the source access. The range of the source access relation
9173 C<source> should have the same dimension as the range
9174 of the sink access relation.
9175 The C<isl_access_info_free> function should usually not be
9176 called explicitly, because it is already called implicitly by
9177 C<isl_access_info_compute_flow>.
9179 The result of the dependence analysis is collected in an
9180 C<isl_flow>. There may be elements of
9181 the sink access for which no preceding source access could be
9182 found or for which all preceding sources are I<may> accesses.
9183 The relations containing these elements can be obtained through
9184 calls to C<isl_flow_get_no_source>, the first with C<must> set
9185 and the second with C<must> unset.
9186 In the case of standard flow dependence analysis,
9187 with the sink a read and the sources I<must> writes,
9188 the first relation corresponds to the reads from uninitialized
9189 array elements and the second relation is empty.
9190 The actual flow dependences can be extracted using
9191 C<isl_flow_foreach>. This function will call the user-specified
9192 callback function C<fn> for each B<non-empty> dependence between
9193 a source and the sink. The callback function is called
9194 with four arguments, the actual flow dependence relation
9195 mapping source iterations to sink iterations, a boolean that
9196 indicates whether it is a I<must> or I<may> dependence, a token
9197 identifying the source and an additional C<void *> with value
9198 equal to the third argument of the C<isl_flow_foreach> call.
9199 A dependence is marked I<must> if it originates from a I<must>
9200 source and if it is not followed by any I<may> sources.
9202 After finishing with an C<isl_flow>, the user should call
9203 C<isl_flow_free> to free all associated memory.
9205 =head3 Interaction with the Low-level Interface
9207 During the dependence analysis, we frequently need to perform
9208 the following operation. Given a relation between sink iterations
9209 and potential source iterations from a particular source domain,
9210 what is the last potential source iteration corresponding to each
9211 sink iteration. It can sometimes be convenient to adjust
9212 the set of potential source iterations before or after each such operation.
9213 The prototypical example is fuzzy array dataflow analysis,
9214 where we need to analyze if, based on data-dependent constraints,
9215 the sink iteration can ever be executed without one or more of
9216 the corresponding potential source iterations being executed.
9217 If so, we can introduce extra parameters and select an unknown
9218 but fixed source iteration from the potential source iterations.
9219 To be able to perform such manipulations, C<isl> provides the following
9222 #include <isl/flow.h>
9224 typedef __isl_give isl_restriction *(*isl_access_restrict)(
9225 __isl_keep isl_map *source_map,
9226 __isl_keep isl_set *sink, void *source_user,
9228 __isl_give isl_access_info *isl_access_info_set_restrict(
9229 __isl_take isl_access_info *acc,
9230 isl_access_restrict fn, void *user);
9232 The function C<isl_access_info_set_restrict> should be called
9233 before calling C<isl_access_info_compute_flow> and registers a callback function
9234 that will be called any time C<isl> is about to compute the last
9235 potential source. The first argument is the (reverse) proto-dependence,
9236 mapping sink iterations to potential source iterations.
9237 The second argument represents the sink iterations for which
9238 we want to compute the last source iteration.
9239 The third argument is the token corresponding to the source
9240 and the final argument is the token passed to C<isl_access_info_set_restrict>.
9241 The callback is expected to return a restriction on either the input or
9242 the output of the operation computing the last potential source.
9243 If the input needs to be restricted then restrictions are needed
9244 for both the source and the sink iterations. The sink iterations
9245 and the potential source iterations will be intersected with these sets.
9246 If the output needs to be restricted then only a restriction on the source
9247 iterations is required.
9248 If any error occurs, the callback should return C<NULL>.
9249 An C<isl_restriction> object can be created, freed and inspected
9250 using the following functions.
9252 #include <isl/flow.h>
9254 __isl_give isl_restriction *isl_restriction_input(
9255 __isl_take isl_set *source_restr,
9256 __isl_take isl_set *sink_restr);
9257 __isl_give isl_restriction *isl_restriction_output(
9258 __isl_take isl_set *source_restr);
9259 __isl_give isl_restriction *isl_restriction_none(
9260 __isl_take isl_map *source_map);
9261 __isl_give isl_restriction *isl_restriction_empty(
9262 __isl_take isl_map *source_map);
9263 __isl_null isl_restriction *isl_restriction_free(
9264 __isl_take isl_restriction *restr);
9266 C<isl_restriction_none> and C<isl_restriction_empty> are special
9267 cases of C<isl_restriction_input>. C<isl_restriction_none>
9268 is essentially equivalent to
9270 isl_restriction_input(isl_set_universe(
9271 isl_space_range(isl_map_get_space(source_map))),
9273 isl_space_domain(isl_map_get_space(source_map))));
9275 whereas C<isl_restriction_empty> is essentially equivalent to
9277 isl_restriction_input(isl_set_empty(
9278 isl_space_range(isl_map_get_space(source_map))),
9280 isl_space_domain(isl_map_get_space(source_map))));
9284 #include <isl/schedule.h>
9285 __isl_give isl_schedule *
9286 isl_schedule_constraints_compute_schedule(
9287 __isl_take isl_schedule_constraints *sc);
9289 The function C<isl_schedule_constraints_compute_schedule> can be
9290 used to compute a schedule that satisfies the given schedule constraints.
9291 These schedule constraints include the iteration domain for which
9292 a schedule should be computed and dependences between pairs of
9293 iterations. In particular, these dependences include
9294 I<validity> dependences and I<proximity> dependences.
9295 By default, the algorithm used to construct the schedule is similar
9296 to that of C<Pluto>.
9297 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
9299 The generated schedule respects all validity dependences.
9300 That is, all dependence distances over these dependences in the
9301 scheduled space are lexicographically positive.
9303 The default algorithm tries to ensure that the dependence distances
9304 over coincidence constraints are zero and to minimize the
9305 dependence distances over proximity dependences.
9306 Moreover, it tries to obtain sequences (bands) of schedule dimensions
9307 for groups of domains where the dependence distances over validity
9308 dependences have only non-negative values.
9309 Note that when minimizing the maximal dependence distance
9310 over proximity dependences, a single affine expression in the parameters
9311 is constructed that bounds all dependence distances. If no such expression
9312 exists, then the algorithm will fail and resort to an alternative
9313 scheduling algorithm. In particular, this means that adding proximity
9314 dependences may eliminate valid solutions. A typical example where this
9315 phenomenon may occur is when some subset of the proximity dependences
9316 has no restriction on some parameter, forcing the coefficient of that
9317 parameter to be zero, while some other subset forces the dependence
9318 distance to depend on that parameter, requiring the same coefficient
9320 When using Feautrier's algorithm, the coincidence and proximity constraints
9321 are only taken into account during the extension to a
9322 full-dimensional schedule.
9324 An C<isl_schedule_constraints> object can be constructed
9325 and manipulated using the following functions.
9327 #include <isl/schedule.h>
9328 __isl_give isl_schedule_constraints *
9329 isl_schedule_constraints_copy(
9330 __isl_keep isl_schedule_constraints *sc);
9331 __isl_give isl_schedule_constraints *
9332 isl_schedule_constraints_on_domain(
9333 __isl_take isl_union_set *domain);
9334 __isl_give isl_schedule_constraints *
9335 isl_schedule_constraints_set_context(
9336 __isl_take isl_schedule_constraints *sc,
9337 __isl_take isl_set *context);
9338 __isl_give isl_schedule_constraints *
9339 isl_schedule_constraints_set_validity(
9340 __isl_take isl_schedule_constraints *sc,
9341 __isl_take isl_union_map *validity);
9342 __isl_give isl_schedule_constraints *
9343 isl_schedule_constraints_set_coincidence(
9344 __isl_take isl_schedule_constraints *sc,
9345 __isl_take isl_union_map *coincidence);
9346 __isl_give isl_schedule_constraints *
9347 isl_schedule_constraints_set_proximity(
9348 __isl_take isl_schedule_constraints *sc,
9349 __isl_take isl_union_map *proximity);
9350 __isl_give isl_schedule_constraints *
9351 isl_schedule_constraints_set_conditional_validity(
9352 __isl_take isl_schedule_constraints *sc,
9353 __isl_take isl_union_map *condition,
9354 __isl_take isl_union_map *validity);
9355 __isl_give isl_schedule_constraints *
9356 isl_schedule_constraints_apply(
9357 __isl_take isl_schedule_constraints *sc,
9358 __isl_take isl_union_map *umap);
9359 __isl_null isl_schedule_constraints *
9360 isl_schedule_constraints_free(
9361 __isl_take isl_schedule_constraints *sc);
9363 The initial C<isl_schedule_constraints> object created by
9364 C<isl_schedule_constraints_on_domain> does not impose any constraints.
9365 That is, it has an empty set of dependences.
9366 The function C<isl_schedule_constraints_set_context> allows the user
9367 to specify additional constraints on the parameters that may
9368 be assumed to hold during the construction of the schedule.
9369 The function C<isl_schedule_constraints_set_validity> replaces the
9370 validity dependences, mapping domain elements I<i> to domain
9371 elements that should be scheduled after I<i>.
9372 The function C<isl_schedule_constraints_set_coincidence> replaces the
9373 coincidence dependences, mapping domain elements I<i> to domain
9374 elements that should be scheduled together with I<I>, if possible.
9375 The function C<isl_schedule_constraints_set_proximity> replaces the
9376 proximity dependences, mapping domain elements I<i> to domain
9377 elements that should be scheduled either before I<I>
9378 or as early as possible after I<i>.
9380 The function C<isl_schedule_constraints_set_conditional_validity>
9381 replaces the conditional validity constraints.
9382 A conditional validity constraint is only imposed when any of the corresponding
9383 conditions is satisfied, i.e., when any of them is non-zero.
9384 That is, the scheduler ensures that within each band if the dependence
9385 distances over the condition constraints are not all zero
9386 then all corresponding conditional validity constraints are respected.
9387 A conditional validity constraint corresponds to a condition
9388 if the two are adjacent, i.e., if the domain of one relation intersect
9389 the range of the other relation.
9390 The typical use case of conditional validity constraints is
9391 to allow order constraints between live ranges to be violated
9392 as long as the live ranges themselves are local to the band.
9393 To allow more fine-grained control over which conditions correspond
9394 to which conditional validity constraints, the domains and ranges
9395 of these relations may include I<tags>. That is, the domains and
9396 ranges of those relation may themselves be wrapped relations
9397 where the iteration domain appears in the domain of those wrapped relations
9398 and the range of the wrapped relations can be arbitrarily chosen
9399 by the user. Conditions and conditional validity constraints are only
9400 considered adjacent to each other if the entire wrapped relation matches.
9401 In particular, a relation with a tag will never be considered adjacent
9402 to a relation without a tag.
9404 The function C<isl_schedule_constraints_apply> takes
9405 schedule constraints that are defined on some set of domain elements
9406 and transforms them to schedule constraints on the elements
9407 to which these domain elements are mapped by the given transformation.
9409 An C<isl_schedule_constraints> object can be inspected
9410 using the following functions.
9412 #include <isl/schedule.h>
9413 __isl_give isl_union_set *
9414 isl_schedule_constraints_get_domain(
9415 __isl_keep isl_schedule_constraints *sc);
9416 __isl_give isl_set *isl_schedule_constraints_get_context(
9417 __isl_keep isl_schedule_constraints *sc);
9418 __isl_give isl_union_map *
9419 isl_schedule_constraints_get_validity(
9420 __isl_keep isl_schedule_constraints *sc);
9421 __isl_give isl_union_map *
9422 isl_schedule_constraints_get_coincidence(
9423 __isl_keep isl_schedule_constraints *sc);
9424 __isl_give isl_union_map *
9425 isl_schedule_constraints_get_proximity(
9426 __isl_keep isl_schedule_constraints *sc);
9427 __isl_give isl_union_map *
9428 isl_schedule_constraints_get_conditional_validity(
9429 __isl_keep isl_schedule_constraints *sc);
9430 __isl_give isl_union_map *
9431 isl_schedule_constraints_get_conditional_validity_condition(
9432 __isl_keep isl_schedule_constraints *sc);
9434 An C<isl_schedule_constraints> object can be read from input
9435 using the following functions.
9437 #include <isl/schedule.h>
9438 __isl_give isl_schedule_constraints *
9439 isl_schedule_constraints_read_from_str(isl_ctx *ctx,
9441 __isl_give isl_schedule_constraints *
9442 isl_schedule_constraints_read_from_file(isl_ctx *ctx,
9445 The contents of an C<isl_schedule_constraints> object can be printed
9446 using the following functions.
9448 #include <isl/schedule.h>
9449 __isl_give isl_printer *
9450 isl_printer_print_schedule_constraints(
9451 __isl_take isl_printer *p,
9452 __isl_keep isl_schedule_constraints *sc);
9453 __isl_give char *isl_schedule_constraints_to_str(
9454 __isl_keep isl_schedule_constraints *sc);
9456 The following function computes a schedule directly from
9457 an iteration domain and validity and proximity dependences
9458 and is implemented in terms of the functions described above.
9459 The use of C<isl_union_set_compute_schedule> is discouraged.
9461 #include <isl/schedule.h>
9462 __isl_give isl_schedule *isl_union_set_compute_schedule(
9463 __isl_take isl_union_set *domain,
9464 __isl_take isl_union_map *validity,
9465 __isl_take isl_union_map *proximity);
9467 The generated schedule represents a schedule tree.
9468 For more information on schedule trees, see
9469 L</"Schedule Trees">.
9473 #include <isl/schedule.h>
9474 isl_stat isl_options_set_schedule_max_coefficient(
9475 isl_ctx *ctx, int val);
9476 int isl_options_get_schedule_max_coefficient(
9478 isl_stat isl_options_set_schedule_max_constant_term(
9479 isl_ctx *ctx, int val);
9480 int isl_options_get_schedule_max_constant_term(
9482 isl_stat isl_options_set_schedule_serialize_sccs(
9483 isl_ctx *ctx, int val);
9484 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx);
9485 isl_stat isl_options_set_schedule_whole_component(
9486 isl_ctx *ctx, int val);
9487 int isl_options_get_schedule_whole_component(
9489 isl_stat isl_options_set_schedule_maximize_band_depth(
9490 isl_ctx *ctx, int val);
9491 int isl_options_get_schedule_maximize_band_depth(
9493 isl_stat isl_options_set_schedule_maximize_coincidence(
9494 isl_ctx *ctx, int val);
9495 int isl_options_get_schedule_maximize_coincidence(
9497 isl_stat isl_options_set_schedule_outer_coincidence(
9498 isl_ctx *ctx, int val);
9499 int isl_options_get_schedule_outer_coincidence(
9501 isl_stat isl_options_set_schedule_split_scaled(
9502 isl_ctx *ctx, int val);
9503 int isl_options_get_schedule_split_scaled(
9505 isl_stat isl_options_set_schedule_treat_coalescing(
9506 isl_ctx *ctx, int val);
9507 int isl_options_get_schedule_treat_coalescing(
9509 isl_stat isl_options_set_schedule_algorithm(
9510 isl_ctx *ctx, int val);
9511 int isl_options_get_schedule_algorithm(
9513 isl_stat isl_options_set_schedule_carry_self_first(
9514 isl_ctx *ctx, int val);
9515 int isl_options_get_schedule_carry_self_first(
9517 isl_stat isl_options_set_schedule_separate_components(
9518 isl_ctx *ctx, int val);
9519 int isl_options_get_schedule_separate_components(
9524 =item * schedule_max_coefficient
9526 This option enforces that the coefficients for variable and parameter
9527 dimensions in the calculated schedule are not larger than the specified value.
9528 This option can significantly increase the speed of the scheduling calculation
9529 and may also prevent fusing of unrelated dimensions. A value of -1 means that
9530 this option does not introduce bounds on the variable or parameter
9533 =item * schedule_max_constant_term
9535 This option enforces that the constant coefficients in the calculated schedule
9536 are not larger than the maximal constant term. This option can significantly
9537 increase the speed of the scheduling calculation and may also prevent fusing of
9538 unrelated dimensions. A value of -1 means that this option does not introduce
9539 bounds on the constant coefficients.
9541 =item * schedule_serialize_sccs
9543 If this option is set, then all strongly connected components
9544 in the dependence graph are serialized as soon as they are detected.
9545 This means in particular that instances of statements will only
9546 appear in the same band node if these statements belong
9547 to the same strongly connected component at the point where
9548 the band node is constructed.
9550 =item * schedule_whole_component
9552 If this option is set, then entire (weakly) connected
9553 components in the dependence graph are scheduled together
9555 Otherwise, each strongly connected component within
9556 such a weakly connected component is first scheduled separately
9557 and then combined with other strongly connected components.
9558 This option has no effect if C<schedule_serialize_sccs> is set.
9560 =item * schedule_maximize_band_depth
9562 If this option is set, then the scheduler tries to maximize
9563 the width of the bands. Wider bands give more possibilities for tiling.
9564 In particular, if the C<schedule_whole_component> option is set,
9565 then bands are split if this might result in wider bands.
9566 Otherwise, the effect of this option is to only allow
9567 strongly connected components to be combined if this does
9568 not reduce the width of the bands.
9569 Note that if the C<schedule_serialize_sccs> options is set, then
9570 the C<schedule_maximize_band_depth> option therefore has no effect.
9572 =item * schedule_maximize_coincidence
9574 This option is only effective if the C<schedule_whole_component>
9575 option is turned off.
9576 If the C<schedule_maximize_coincidence> option is set, then (clusters of)
9577 strongly connected components are only combined with each other
9578 if this does not reduce the number of coincident band members.
9580 =item * schedule_outer_coincidence
9582 If this option is set, then we try to construct schedules
9583 where the outermost scheduling dimension in each band
9584 satisfies the coincidence constraints.
9586 =item * schedule_algorithm
9588 Selects the scheduling algorithm to be used.
9589 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
9590 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
9592 =item * schedule_split_scaled
9594 If this option is set, then we try to construct schedules in which the
9595 constant term is split off from the linear part if the linear parts of
9596 the scheduling rows for all nodes in the graph have a common non-trivial
9598 The constant term is then dropped and the linear
9600 This option is only effective when the Feautrier style scheduler is
9601 being used, either as the main scheduler or as a fallback for the
9602 Pluto-like scheduler.
9604 =item * schedule_treat_coalescing
9606 If this option is set, then the scheduler will try and avoid
9607 producing schedules that perform loop coalescing.
9608 In particular, for the Pluto-like scheduler, this option places
9609 bounds on the schedule coefficients based on the sizes of the instance sets.
9610 For the Feautrier style scheduler, this option detects potentially
9611 coalescing schedules and then tries to adjust the schedule to avoid
9614 =item * schedule_carry_self_first
9616 If this option is set, then the Feautrier style scheduler
9617 (when used as a fallback for the Pluto-like scheduler) will
9618 first try to only carry self-dependences.
9620 =item * schedule_separate_components
9622 If this option is set then the function C<isl_schedule_get_map>
9623 will treat set nodes in the same way as sequence nodes.
9627 =head2 AST Generation
9629 This section describes the C<isl> functionality for generating
9630 ASTs that visit all the elements
9631 in a domain in an order specified by a schedule tree or
9633 In case the schedule given as a C<isl_union_map>, an AST is generated
9634 that visits all the elements in the domain of the C<isl_union_map>
9635 according to the lexicographic order of the corresponding image
9636 element(s). If the range of the C<isl_union_map> consists of
9637 elements in more than one space, then each of these spaces is handled
9638 separately in an arbitrary order.
9639 It should be noted that the schedule tree or the image elements
9640 in a schedule map only specify the I<order>
9641 in which the corresponding domain elements should be visited.
9642 No direct relation between the partial schedule values
9643 or the image elements on the one hand and the loop iterators
9644 in the generated AST on the other hand should be assumed.
9646 Each AST is generated within a build. The initial build
9647 simply specifies the constraints on the parameters (if any)
9648 and can be created, inspected, copied and freed using the following functions.
9650 #include <isl/ast_build.h>
9651 __isl_give isl_ast_build *isl_ast_build_alloc(
9653 __isl_give isl_ast_build *isl_ast_build_from_context(
9654 __isl_take isl_set *set);
9655 __isl_give isl_ast_build *isl_ast_build_copy(
9656 __isl_keep isl_ast_build *build);
9657 __isl_null isl_ast_build *isl_ast_build_free(
9658 __isl_take isl_ast_build *build);
9660 The C<set> argument is usually a parameter set with zero or more parameters.
9661 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
9662 this set is required to be a parameter set.
9663 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
9664 specify any parameter constraints.
9665 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
9666 and L</"Fine-grained Control over AST Generation">.
9667 Finally, the AST itself can be constructed using one of the following
9670 #include <isl/ast_build.h>
9671 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
9672 __isl_keep isl_ast_build *build,
9673 __isl_take isl_schedule *schedule);
9674 __isl_give isl_ast_node *
9675 isl_ast_build_node_from_schedule_map(
9676 __isl_keep isl_ast_build *build,
9677 __isl_take isl_union_map *schedule);
9679 =head3 Inspecting the AST
9681 The basic properties of an AST node can be obtained as follows.
9683 #include <isl/ast.h>
9684 enum isl_ast_node_type isl_ast_node_get_type(
9685 __isl_keep isl_ast_node *node);
9687 The type of an AST node is one of
9688 C<isl_ast_node_for>,
9690 C<isl_ast_node_block>,
9691 C<isl_ast_node_mark> or
9692 C<isl_ast_node_user>.
9693 An C<isl_ast_node_for> represents a for node.
9694 An C<isl_ast_node_if> represents an if node.
9695 An C<isl_ast_node_block> represents a compound node.
9696 An C<isl_ast_node_mark> introduces a mark in the AST.
9697 An C<isl_ast_node_user> represents an expression statement.
9698 An expression statement typically corresponds to a domain element, i.e.,
9699 one of the elements that is visited by the AST.
9701 Each type of node has its own additional properties.
9703 #include <isl/ast.h>
9704 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
9705 __isl_keep isl_ast_node *node);
9706 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
9707 __isl_keep isl_ast_node *node);
9708 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
9709 __isl_keep isl_ast_node *node);
9710 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
9711 __isl_keep isl_ast_node *node);
9712 __isl_give isl_ast_node *isl_ast_node_for_get_body(
9713 __isl_keep isl_ast_node *node);
9714 isl_bool isl_ast_node_for_is_degenerate(
9715 __isl_keep isl_ast_node *node);
9717 An C<isl_ast_for> is considered degenerate if it is known to execute
9720 #include <isl/ast.h>
9721 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
9722 __isl_keep isl_ast_node *node);
9723 __isl_give isl_ast_node *isl_ast_node_if_get_then(
9724 __isl_keep isl_ast_node *node);
9725 isl_bool isl_ast_node_if_has_else(
9726 __isl_keep isl_ast_node *node);
9727 __isl_give isl_ast_node *isl_ast_node_if_get_else(
9728 __isl_keep isl_ast_node *node);
9730 __isl_give isl_ast_node_list *
9731 isl_ast_node_block_get_children(
9732 __isl_keep isl_ast_node *node);
9734 __isl_give isl_id *isl_ast_node_mark_get_id(
9735 __isl_keep isl_ast_node *node);
9736 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
9737 __isl_keep isl_ast_node *node);
9739 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
9740 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
9742 #include <isl/ast.h>
9743 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
9744 __isl_keep isl_ast_node *node);
9746 All descendants of a specific node in the AST (including the node itself)
9748 in depth-first pre-order using the following function.
9750 #include <isl/ast.h>
9751 isl_stat isl_ast_node_foreach_descendant_top_down(
9752 __isl_keep isl_ast_node *node,
9753 isl_bool (*fn)(__isl_keep isl_ast_node *node,
9754 void *user), void *user);
9756 The callback function should return C<isl_bool_true> if the children
9757 of the given node should be visited and C<isl_bool_false> if they should not.
9758 It should return C<isl_bool_error> in case of failure, in which case
9759 the entire traversal is aborted.
9761 Each of the returned C<isl_ast_expr>s can in turn be inspected using
9762 the following functions.
9764 #include <isl/ast.h>
9765 enum isl_ast_expr_type isl_ast_expr_get_type(
9766 __isl_keep isl_ast_expr *expr);
9768 The type of an AST expression is one of
9770 C<isl_ast_expr_id> or
9771 C<isl_ast_expr_int>.
9772 An C<isl_ast_expr_op> represents the result of an operation.
9773 An C<isl_ast_expr_id> represents an identifier.
9774 An C<isl_ast_expr_int> represents an integer value.
9776 Each type of expression has its own additional properties.
9778 #include <isl/ast.h>
9779 enum isl_ast_op_type isl_ast_expr_get_op_type(
9780 __isl_keep isl_ast_expr *expr);
9781 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
9782 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
9783 __isl_keep isl_ast_expr *expr, int pos);
9784 isl_stat isl_ast_expr_foreach_ast_op_type(
9785 __isl_keep isl_ast_expr *expr,
9786 isl_stat (*fn)(enum isl_ast_op_type type,
9787 void *user), void *user);
9788 isl_stat isl_ast_node_foreach_ast_op_type(
9789 __isl_keep isl_ast_node *node,
9790 isl_stat (*fn)(enum isl_ast_op_type type,
9791 void *user), void *user);
9793 C<isl_ast_expr_get_op_type> returns the type of the operation
9794 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
9795 arguments. C<isl_ast_expr_get_op_arg> returns the specified
9797 C<isl_ast_expr_foreach_ast_op_type> calls C<fn> for each distinct
9798 C<isl_ast_op_type> that appears in C<expr>.
9799 C<isl_ast_node_foreach_ast_op_type> does the same for each distinct
9800 C<isl_ast_op_type> that appears in C<node>.
9801 The operation type is one of the following.
9805 =item C<isl_ast_op_and>
9807 Logical I<and> of two arguments.
9808 Both arguments can be evaluated.
9810 =item C<isl_ast_op_and_then>
9812 Logical I<and> of two arguments.
9813 The second argument can only be evaluated if the first evaluates to true.
9815 =item C<isl_ast_op_or>
9817 Logical I<or> of two arguments.
9818 Both arguments can be evaluated.
9820 =item C<isl_ast_op_or_else>
9822 Logical I<or> of two arguments.
9823 The second argument can only be evaluated if the first evaluates to false.
9825 =item C<isl_ast_op_max>
9827 Maximum of two or more arguments.
9829 =item C<isl_ast_op_min>
9831 Minimum of two or more arguments.
9833 =item C<isl_ast_op_minus>
9837 =item C<isl_ast_op_add>
9839 Sum of two arguments.
9841 =item C<isl_ast_op_sub>
9843 Difference of two arguments.
9845 =item C<isl_ast_op_mul>
9847 Product of two arguments.
9849 =item C<isl_ast_op_div>
9851 Exact division. That is, the result is known to be an integer.
9853 =item C<isl_ast_op_fdiv_q>
9855 Result of integer division, rounded towards negative
9858 =item C<isl_ast_op_pdiv_q>
9860 Result of integer division, where dividend is known to be non-negative.
9862 =item C<isl_ast_op_pdiv_r>
9864 Remainder of integer division, where dividend is known to be non-negative.
9866 =item C<isl_ast_op_zdiv_r>
9868 Equal to zero iff the remainder on integer division is zero.
9870 =item C<isl_ast_op_cond>
9872 Conditional operator defined on three arguments.
9873 If the first argument evaluates to true, then the result
9874 is equal to the second argument. Otherwise, the result
9875 is equal to the third argument.
9876 The second and third argument may only be evaluated if
9877 the first argument evaluates to true and false, respectively.
9878 Corresponds to C<a ? b : c> in C.
9880 =item C<isl_ast_op_select>
9882 Conditional operator defined on three arguments.
9883 If the first argument evaluates to true, then the result
9884 is equal to the second argument. Otherwise, the result
9885 is equal to the third argument.
9886 The second and third argument may be evaluated independently
9887 of the value of the first argument.
9888 Corresponds to C<a * b + (1 - a) * c> in C.
9890 =item C<isl_ast_op_eq>
9894 =item C<isl_ast_op_le>
9896 Less than or equal relation.
9898 =item C<isl_ast_op_lt>
9902 =item C<isl_ast_op_ge>
9904 Greater than or equal relation.
9906 =item C<isl_ast_op_gt>
9908 Greater than relation.
9910 =item C<isl_ast_op_call>
9913 The number of arguments of the C<isl_ast_expr> is one more than
9914 the number of arguments in the function call, the first argument
9915 representing the function being called.
9917 =item C<isl_ast_op_access>
9920 The number of arguments of the C<isl_ast_expr> is one more than
9921 the number of index expressions in the array access, the first argument
9922 representing the array being accessed.
9924 =item C<isl_ast_op_member>
9927 This operation has two arguments, a structure and the name of
9928 the member of the structure being accessed.
9932 #include <isl/ast.h>
9933 __isl_give isl_id *isl_ast_expr_get_id(
9934 __isl_keep isl_ast_expr *expr);
9936 Return the identifier represented by the AST expression.
9938 #include <isl/ast.h>
9939 __isl_give isl_val *isl_ast_expr_get_val(
9940 __isl_keep isl_ast_expr *expr);
9942 Return the integer represented by the AST expression.
9944 =head3 Properties of ASTs
9946 #include <isl/ast.h>
9947 isl_bool isl_ast_expr_is_equal(
9948 __isl_keep isl_ast_expr *expr1,
9949 __isl_keep isl_ast_expr *expr2);
9951 Check if two C<isl_ast_expr>s are equal to each other.
9953 =head3 Manipulating and printing the AST
9955 AST nodes can be copied and freed using the following functions.
9957 #include <isl/ast.h>
9958 __isl_give isl_ast_node *isl_ast_node_copy(
9959 __isl_keep isl_ast_node *node);
9960 __isl_null isl_ast_node *isl_ast_node_free(
9961 __isl_take isl_ast_node *node);
9963 AST expressions can be copied and freed using the following functions.
9965 #include <isl/ast.h>
9966 __isl_give isl_ast_expr *isl_ast_expr_copy(
9967 __isl_keep isl_ast_expr *expr);
9968 __isl_null isl_ast_expr *isl_ast_expr_free(
9969 __isl_take isl_ast_expr *expr);
9971 New AST expressions can be created either directly or within
9972 the context of an C<isl_ast_build>.
9974 #include <isl/ast.h>
9975 __isl_give isl_ast_expr *isl_ast_expr_from_val(
9976 __isl_take isl_val *v);
9977 __isl_give isl_ast_expr *isl_ast_expr_from_id(
9978 __isl_take isl_id *id);
9979 __isl_give isl_ast_expr *isl_ast_expr_neg(
9980 __isl_take isl_ast_expr *expr);
9981 __isl_give isl_ast_expr *isl_ast_expr_address_of(
9982 __isl_take isl_ast_expr *expr);
9983 __isl_give isl_ast_expr *isl_ast_expr_add(
9984 __isl_take isl_ast_expr *expr1,
9985 __isl_take isl_ast_expr *expr2);
9986 __isl_give isl_ast_expr *isl_ast_expr_sub(
9987 __isl_take isl_ast_expr *expr1,
9988 __isl_take isl_ast_expr *expr2);
9989 __isl_give isl_ast_expr *isl_ast_expr_mul(
9990 __isl_take isl_ast_expr *expr1,
9991 __isl_take isl_ast_expr *expr2);
9992 __isl_give isl_ast_expr *isl_ast_expr_div(
9993 __isl_take isl_ast_expr *expr1,
9994 __isl_take isl_ast_expr *expr2);
9995 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
9996 __isl_take isl_ast_expr *expr1,
9997 __isl_take isl_ast_expr *expr2);
9998 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
9999 __isl_take isl_ast_expr *expr1,
10000 __isl_take isl_ast_expr *expr2);
10001 __isl_give isl_ast_expr *isl_ast_expr_and(
10002 __isl_take isl_ast_expr *expr1,
10003 __isl_take isl_ast_expr *expr2)
10004 __isl_give isl_ast_expr *isl_ast_expr_and_then(
10005 __isl_take isl_ast_expr *expr1,
10006 __isl_take isl_ast_expr *expr2)
10007 __isl_give isl_ast_expr *isl_ast_expr_or(
10008 __isl_take isl_ast_expr *expr1,
10009 __isl_take isl_ast_expr *expr2)
10010 __isl_give isl_ast_expr *isl_ast_expr_or_else(
10011 __isl_take isl_ast_expr *expr1,
10012 __isl_take isl_ast_expr *expr2)
10013 __isl_give isl_ast_expr *isl_ast_expr_eq(
10014 __isl_take isl_ast_expr *expr1,
10015 __isl_take isl_ast_expr *expr2);
10016 __isl_give isl_ast_expr *isl_ast_expr_le(
10017 __isl_take isl_ast_expr *expr1,
10018 __isl_take isl_ast_expr *expr2);
10019 __isl_give isl_ast_expr *isl_ast_expr_lt(
10020 __isl_take isl_ast_expr *expr1,
10021 __isl_take isl_ast_expr *expr2);
10022 __isl_give isl_ast_expr *isl_ast_expr_ge(
10023 __isl_take isl_ast_expr *expr1,
10024 __isl_take isl_ast_expr *expr2);
10025 __isl_give isl_ast_expr *isl_ast_expr_gt(
10026 __isl_take isl_ast_expr *expr1,
10027 __isl_take isl_ast_expr *expr2);
10028 __isl_give isl_ast_expr *isl_ast_expr_access(
10029 __isl_take isl_ast_expr *array,
10030 __isl_take isl_ast_expr_list *indices);
10031 __isl_give isl_ast_expr *isl_ast_expr_call(
10032 __isl_take isl_ast_expr *function,
10033 __isl_take isl_ast_expr_list *arguments);
10035 The function C<isl_ast_expr_address_of> can be applied to an
10036 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
10037 to represent the address of the C<isl_ast_expr_access>. The function
10038 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
10039 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
10041 #include <isl/ast_build.h>
10042 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
10043 __isl_keep isl_ast_build *build,
10044 __isl_take isl_set *set);
10045 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
10046 __isl_keep isl_ast_build *build,
10047 __isl_take isl_pw_aff *pa);
10048 __isl_give isl_ast_expr *
10049 isl_ast_build_access_from_pw_multi_aff(
10050 __isl_keep isl_ast_build *build,
10051 __isl_take isl_pw_multi_aff *pma);
10052 __isl_give isl_ast_expr *
10053 isl_ast_build_access_from_multi_pw_aff(
10054 __isl_keep isl_ast_build *build,
10055 __isl_take isl_multi_pw_aff *mpa);
10056 __isl_give isl_ast_expr *
10057 isl_ast_build_call_from_pw_multi_aff(
10058 __isl_keep isl_ast_build *build,
10059 __isl_take isl_pw_multi_aff *pma);
10060 __isl_give isl_ast_expr *
10061 isl_ast_build_call_from_multi_pw_aff(
10062 __isl_keep isl_ast_build *build,
10063 __isl_take isl_multi_pw_aff *mpa);
10066 the domains of C<pa>, C<mpa> and C<pma> should correspond
10067 to the schedule space of C<build>.
10068 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
10069 the function being called.
10070 If the accessed space is a nested relation, then it is taken
10071 to represent an access of the member specified by the range
10072 of this nested relation of the structure specified by the domain
10073 of the nested relation.
10075 The following functions can be used to modify an C<isl_ast_expr>.
10077 #include <isl/ast.h>
10078 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
10079 __isl_take isl_ast_expr *expr, int pos,
10080 __isl_take isl_ast_expr *arg);
10082 Replace the argument of C<expr> at position C<pos> by C<arg>.
10084 #include <isl/ast.h>
10085 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
10086 __isl_take isl_ast_expr *expr,
10087 __isl_take isl_id_to_ast_expr *id2expr);
10089 The function C<isl_ast_expr_substitute_ids> replaces the
10090 subexpressions of C<expr> of type C<isl_ast_expr_id>
10091 by the corresponding expression in C<id2expr>, if there is any.
10094 User specified data can be attached to an C<isl_ast_node> and obtained
10095 from the same C<isl_ast_node> using the following functions.
10097 #include <isl/ast.h>
10098 __isl_give isl_ast_node *isl_ast_node_set_annotation(
10099 __isl_take isl_ast_node *node,
10100 __isl_take isl_id *annotation);
10101 __isl_give isl_id *isl_ast_node_get_annotation(
10102 __isl_keep isl_ast_node *node);
10104 Basic printing can be performed using the following functions.
10106 #include <isl/ast.h>
10107 __isl_give isl_printer *isl_printer_print_ast_expr(
10108 __isl_take isl_printer *p,
10109 __isl_keep isl_ast_expr *expr);
10110 __isl_give isl_printer *isl_printer_print_ast_node(
10111 __isl_take isl_printer *p,
10112 __isl_keep isl_ast_node *node);
10113 __isl_give char *isl_ast_expr_to_str(
10114 __isl_keep isl_ast_expr *expr);
10115 __isl_give char *isl_ast_node_to_str(
10116 __isl_keep isl_ast_node *node);
10117 __isl_give char *isl_ast_expr_to_C_str(
10118 __isl_keep isl_ast_expr *expr);
10119 __isl_give char *isl_ast_node_to_C_str(
10120 __isl_keep isl_ast_node *node);
10122 The functions C<isl_ast_expr_to_C_str> and
10123 C<isl_ast_node_to_C_str> are convenience functions
10124 that return a string representation of the input in C format.
10126 More advanced printing can be performed using the following functions.
10128 #include <isl/ast.h>
10129 __isl_give isl_printer *isl_ast_op_type_set_print_name(
10130 __isl_take isl_printer *p,
10131 enum isl_ast_op_type type,
10132 __isl_keep const char *name);
10133 isl_stat isl_options_set_ast_print_macro_once(
10134 isl_ctx *ctx, int val);
10135 int isl_options_get_ast_print_macro_once(isl_ctx *ctx);
10136 __isl_give isl_printer *isl_ast_op_type_print_macro(
10137 enum isl_ast_op_type type,
10138 __isl_take isl_printer *p);
10139 __isl_give isl_printer *isl_ast_expr_print_macros(
10140 __isl_keep isl_ast_expr *expr,
10141 __isl_take isl_printer *p);
10142 __isl_give isl_printer *isl_ast_node_print_macros(
10143 __isl_keep isl_ast_node *node,
10144 __isl_take isl_printer *p);
10145 __isl_give isl_printer *isl_ast_node_print(
10146 __isl_keep isl_ast_node *node,
10147 __isl_take isl_printer *p,
10148 __isl_take isl_ast_print_options *options);
10149 __isl_give isl_printer *isl_ast_node_for_print(
10150 __isl_keep isl_ast_node *node,
10151 __isl_take isl_printer *p,
10152 __isl_take isl_ast_print_options *options);
10153 __isl_give isl_printer *isl_ast_node_if_print(
10154 __isl_keep isl_ast_node *node,
10155 __isl_take isl_printer *p,
10156 __isl_take isl_ast_print_options *options);
10158 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
10159 C<isl> may print out an AST that makes use of macros such
10160 as C<floord>, C<min> and C<max>.
10161 The names of these macros may be modified by a call
10162 to C<isl_ast_op_type_set_print_name>. The user-specified
10163 names are associated to the printer object.
10164 C<isl_ast_op_type_print_macro> prints out the macro
10165 corresponding to a specific C<isl_ast_op_type>.
10166 If the print-macro-once option is set, then a given macro definition
10167 is only printed once to any given printer object.
10168 C<isl_ast_expr_print_macros> scans the C<isl_ast_expr>
10169 for subexpressions where these macros would be used and prints
10170 out the required macro definitions.
10171 Essentially, C<isl_ast_expr_print_macros> calls
10172 C<isl_ast_expr_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
10173 as function argument.
10174 C<isl_ast_node_print_macros> does the same
10175 for expressions in its C<isl_ast_node> argument.
10176 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
10177 C<isl_ast_node_if_print> print an C<isl_ast_node>
10178 in C<ISL_FORMAT_C>, but allow for some extra control
10179 through an C<isl_ast_print_options> object.
10180 This object can be created using the following functions.
10182 #include <isl/ast.h>
10183 __isl_give isl_ast_print_options *
10184 isl_ast_print_options_alloc(isl_ctx *ctx);
10185 __isl_give isl_ast_print_options *
10186 isl_ast_print_options_copy(
10187 __isl_keep isl_ast_print_options *options);
10188 __isl_null isl_ast_print_options *
10189 isl_ast_print_options_free(
10190 __isl_take isl_ast_print_options *options);
10192 __isl_give isl_ast_print_options *
10193 isl_ast_print_options_set_print_user(
10194 __isl_take isl_ast_print_options *options,
10195 __isl_give isl_printer *(*print_user)(
10196 __isl_take isl_printer *p,
10197 __isl_take isl_ast_print_options *options,
10198 __isl_keep isl_ast_node *node, void *user),
10200 __isl_give isl_ast_print_options *
10201 isl_ast_print_options_set_print_for(
10202 __isl_take isl_ast_print_options *options,
10203 __isl_give isl_printer *(*print_for)(
10204 __isl_take isl_printer *p,
10205 __isl_take isl_ast_print_options *options,
10206 __isl_keep isl_ast_node *node, void *user),
10209 The callback set by C<isl_ast_print_options_set_print_user>
10210 is called whenever a node of type C<isl_ast_node_user> needs to
10212 The callback set by C<isl_ast_print_options_set_print_for>
10213 is called whenever a node of type C<isl_ast_node_for> needs to
10215 Note that C<isl_ast_node_for_print> will I<not> call the
10216 callback set by C<isl_ast_print_options_set_print_for> on the node
10217 on which C<isl_ast_node_for_print> is called, but only on nested
10218 nodes of type C<isl_ast_node_for>. It is therefore safe to
10219 call C<isl_ast_node_for_print> from within the callback set by
10220 C<isl_ast_print_options_set_print_for>.
10222 The following option determines the type to be used for iterators
10223 while printing the AST.
10225 isl_stat isl_options_set_ast_iterator_type(
10226 isl_ctx *ctx, const char *val);
10227 const char *isl_options_get_ast_iterator_type(
10230 The AST printer only prints body nodes as blocks if these
10231 blocks cannot be safely omitted.
10232 For example, a C<for> node with one body node will not be
10233 surrounded with braces in C<ISL_FORMAT_C>.
10234 A block will always be printed by setting the following option.
10236 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx,
10238 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
10242 #include <isl/ast_build.h>
10243 isl_stat isl_options_set_ast_build_atomic_upper_bound(
10244 isl_ctx *ctx, int val);
10245 int isl_options_get_ast_build_atomic_upper_bound(
10247 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
10249 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
10250 isl_stat isl_options_set_ast_build_detect_min_max(
10251 isl_ctx *ctx, int val);
10252 int isl_options_get_ast_build_detect_min_max(
10254 isl_stat isl_options_set_ast_build_exploit_nested_bounds(
10255 isl_ctx *ctx, int val);
10256 int isl_options_get_ast_build_exploit_nested_bounds(
10258 isl_stat isl_options_set_ast_build_group_coscheduled(
10259 isl_ctx *ctx, int val);
10260 int isl_options_get_ast_build_group_coscheduled(
10262 isl_stat isl_options_set_ast_build_scale_strides(
10263 isl_ctx *ctx, int val);
10264 int isl_options_get_ast_build_scale_strides(
10266 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx,
10268 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
10269 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx,
10271 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
10275 =item * ast_build_atomic_upper_bound
10277 Generate loop upper bounds that consist of the current loop iterator,
10278 an operator and an expression not involving the iterator.
10279 If this option is not set, then the current loop iterator may appear
10280 several times in the upper bound.
10281 For example, when this option is turned off, AST generation
10284 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
10288 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
10291 When the option is turned on, the following AST is generated
10293 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
10296 =item * ast_build_prefer_pdiv
10298 If this option is turned off, then the AST generation will
10299 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
10300 operators, but no C<isl_ast_op_pdiv_q> or
10301 C<isl_ast_op_pdiv_r> operators.
10302 If this option is turned on, then C<isl> will try to convert
10303 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
10304 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
10306 =item * ast_build_detect_min_max
10308 If this option is turned on, then C<isl> will try and detect
10309 min or max-expressions when building AST expressions from
10310 piecewise affine expressions.
10312 =item * ast_build_exploit_nested_bounds
10314 Simplify conditions based on bounds of nested for loops.
10315 In particular, remove conditions that are implied by the fact
10316 that one or more nested loops have at least one iteration,
10317 meaning that the upper bound is at least as large as the lower bound.
10318 For example, when this option is turned off, AST generation
10321 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
10327 for (int c0 = 0; c0 <= N; c0 += 1)
10328 for (int c1 = 0; c1 <= M; c1 += 1)
10331 When the option is turned on, the following AST is generated
10333 for (int c0 = 0; c0 <= N; c0 += 1)
10334 for (int c1 = 0; c1 <= M; c1 += 1)
10337 =item * ast_build_group_coscheduled
10339 If two domain elements are assigned the same schedule point, then
10340 they may be executed in any order and they may even appear in different
10341 loops. If this options is set, then the AST generator will make
10342 sure that coscheduled domain elements do not appear in separate parts
10343 of the AST. This is useful in case of nested AST generation
10344 if the outer AST generation is given only part of a schedule
10345 and the inner AST generation should handle the domains that are
10346 coscheduled by this initial part of the schedule together.
10347 For example if an AST is generated for a schedule
10349 { A[i] -> [0]; B[i] -> [0] }
10351 then the C<isl_ast_build_set_create_leaf> callback described
10352 below may get called twice, once for each domain.
10353 Setting this option ensures that the callback is only called once
10354 on both domains together.
10356 =item * ast_build_separation_bounds
10358 This option specifies which bounds to use during separation.
10359 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
10360 then all (possibly implicit) bounds on the current dimension will
10361 be used during separation.
10362 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
10363 then only those bounds that are explicitly available will
10364 be used during separation.
10366 =item * ast_build_scale_strides
10368 This option specifies whether the AST generator is allowed
10369 to scale down iterators of strided loops.
10371 =item * ast_build_allow_else
10373 This option specifies whether the AST generator is allowed
10374 to construct if statements with else branches.
10376 =item * ast_build_allow_or
10378 This option specifies whether the AST generator is allowed
10379 to construct if conditions with disjunctions.
10383 =head3 AST Generation Options (Schedule Tree)
10385 In case of AST construction from a schedule tree, the options
10386 that control how an AST is created from the individual schedule
10387 dimensions are stored in the band nodes of the tree
10388 (see L</"Schedule Trees">).
10390 In particular, a schedule dimension can be handled in four
10391 different ways, atomic, separate, unroll or the default.
10392 This loop AST generation type can be set using
10393 C<isl_schedule_node_band_member_set_ast_loop_type>.
10395 the first three can be selected by including a one-dimensional
10396 element with as value the position of the schedule dimension
10397 within the band and as name one of C<atomic>, C<separate>
10398 or C<unroll> in the options
10399 set by C<isl_schedule_node_band_set_ast_build_options>.
10400 Only one of these three may be specified for
10401 any given schedule dimension within a band node.
10402 If none of these is specified, then the default
10403 is used. The meaning of the options is as follows.
10409 When this option is specified, the AST generator will make
10410 sure that a given domains space only appears in a single
10411 loop at the specified level.
10413 For example, for the schedule tree
10415 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10417 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10418 options: "{ atomic[x] }"
10420 the following AST will be generated
10422 for (int c0 = 0; c0 <= 10; c0 += 1) {
10429 On the other hand, for the schedule tree
10431 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10433 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10434 options: "{ separate[x] }"
10436 the following AST will be generated
10440 for (int c0 = 1; c0 <= 9; c0 += 1) {
10447 If neither C<atomic> nor C<separate> is specified, then the AST generator
10448 may produce either of these two results or some intermediate form.
10452 When this option is specified, the AST generator will
10453 split the domain of the specified schedule dimension
10454 into pieces with a fixed set of statements for which
10455 instances need to be executed by the iterations in
10456 the schedule domain part. This option tends to avoid
10457 the generation of guards inside the corresponding loops.
10458 See also the C<atomic> option.
10462 When this option is specified, the AST generator will
10463 I<completely> unroll the corresponding schedule dimension.
10464 It is the responsibility of the user to ensure that such
10465 unrolling is possible.
10466 To obtain a partial unrolling, the user should apply an additional
10467 strip-mining to the schedule and fully unroll the inner schedule
10472 The C<isolate> option is a bit more involved. It allows the user
10473 to isolate a range of schedule dimension values from smaller and
10474 greater values. Additionally, the user may specify a different
10475 atomic/separate/unroll choice for the isolated part and the remaining
10476 parts. The typical use case of the C<isolate> option is to isolate
10477 full tiles from partial tiles.
10478 The part that needs to be isolated may depend on outer schedule dimensions.
10479 The option therefore needs to be able to reference those outer schedule
10480 dimensions. In particular, the space of the C<isolate> option is that
10481 of a wrapped map with as domain the flat product of all outer band nodes
10482 and as range the space of the current band node.
10483 The atomic/separate/unroll choice for the isolated part is determined
10484 by an option that lives in an unnamed wrapped space with as domain
10485 a zero-dimensional C<isolate> space and as range the regular
10486 C<atomic>, C<separate> or C<unroll> space.
10487 This option may also be set directly using
10488 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
10489 The atomic/separate/unroll choice for the remaining part is determined
10490 by the regular C<atomic>, C<separate> or C<unroll> option.
10491 Since the C<isolate> option references outer schedule dimensions,
10492 its use in a band node causes any tree containing the node
10493 to be considered anchored.
10495 As an example, consider the isolation of full tiles from partial tiles
10496 in a tiling of a triangular domain. The original schedule is as follows.
10498 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10500 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10501 { A[i,j] -> [floor(j/10)] }, \
10502 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10506 for (int c0 = 0; c0 <= 10; c0 += 1)
10507 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10508 for (int c2 = 10 * c0;
10509 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10510 for (int c3 = 10 * c1;
10511 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10514 Isolating the full tiles, we have the following input
10516 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10518 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10519 { A[i,j] -> [floor(j/10)] }, \
10520 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10521 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10522 10a+9+10b+9 <= 100 }"
10527 for (int c0 = 0; c0 <= 8; c0 += 1) {
10528 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10529 for (int c2 = 10 * c0;
10530 c2 <= 10 * c0 + 9; c2 += 1)
10531 for (int c3 = 10 * c1;
10532 c3 <= 10 * c1 + 9; c3 += 1)
10534 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10535 for (int c2 = 10 * c0;
10536 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10537 for (int c3 = 10 * c1;
10538 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10541 for (int c0 = 9; c0 <= 10; c0 += 1)
10542 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10543 for (int c2 = 10 * c0;
10544 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10545 for (int c3 = 10 * c1;
10546 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10550 We may then additionally unroll the innermost loop of the isolated part
10552 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10554 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10555 { A[i,j] -> [floor(j/10)] }, \
10556 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10557 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10558 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
10563 for (int c0 = 0; c0 <= 8; c0 += 1) {
10564 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10565 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
10567 A(c2, 10 * c1 + 1);
10568 A(c2, 10 * c1 + 2);
10569 A(c2, 10 * c1 + 3);
10570 A(c2, 10 * c1 + 4);
10571 A(c2, 10 * c1 + 5);
10572 A(c2, 10 * c1 + 6);
10573 A(c2, 10 * c1 + 7);
10574 A(c2, 10 * c1 + 8);
10575 A(c2, 10 * c1 + 9);
10577 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10578 for (int c2 = 10 * c0;
10579 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10580 for (int c3 = 10 * c1;
10581 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10584 for (int c0 = 9; c0 <= 10; c0 += 1)
10585 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10586 for (int c2 = 10 * c0;
10587 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10588 for (int c3 = 10 * c1;
10589 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10594 =head3 AST Generation Options (Schedule Map)
10596 In case of AST construction using
10597 C<isl_ast_build_node_from_schedule_map>, the options
10598 that control how an AST is created from the individual schedule
10599 dimensions are stored in the C<isl_ast_build>.
10600 They can be set using the following function.
10602 #include <isl/ast_build.h>
10603 __isl_give isl_ast_build *
10604 isl_ast_build_set_options(
10605 __isl_take isl_ast_build *build,
10606 __isl_take isl_union_map *options);
10608 The options are encoded in an C<isl_union_map>.
10609 The domain of this union relation refers to the schedule domain,
10610 i.e., the range of the schedule passed
10611 to C<isl_ast_build_node_from_schedule_map>.
10612 In the case of nested AST generation (see L</"Nested AST Generation">),
10613 the domain of C<options> should refer to the extra piece of the schedule.
10614 That is, it should be equal to the range of the wrapped relation in the
10615 range of the schedule.
10616 The range of the options can consist of elements in one or more spaces,
10617 the names of which determine the effect of the option.
10618 The values of the range typically also refer to the schedule dimension
10619 to which the option applies. In case of nested AST generation
10620 (see L</"Nested AST Generation">), these values refer to the position
10621 of the schedule dimension within the innermost AST generation.
10622 The constraints on the domain elements of
10623 the option should only refer to this dimension and earlier dimensions.
10624 We consider the following spaces.
10628 =item C<separation_class>
10630 B<This option has been deprecated. Use the isolate option on
10631 schedule trees instead.>
10633 This space is a wrapped relation between two one dimensional spaces.
10634 The input space represents the schedule dimension to which the option
10635 applies and the output space represents the separation class.
10636 While constructing a loop corresponding to the specified schedule
10637 dimension(s), the AST generator will try to generate separate loops
10638 for domain elements that are assigned different classes.
10639 If only some of the elements are assigned a class, then those elements
10640 that are not assigned any class will be treated as belonging to a class
10641 that is separate from the explicitly assigned classes.
10642 The typical use case for this option is to separate full tiles from
10644 The other options, described below, are applied after the separation
10647 As an example, consider the separation into full and partial tiles
10648 of a tiling of a triangular domain.
10649 Take, for example, the domain
10651 { A[i,j] : 0 <= i,j and i + j <= 100 }
10653 and a tiling into tiles of 10 by 10. The input to the AST generator
10654 is then the schedule
10656 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
10659 Without any options, the following AST is generated
10661 for (int c0 = 0; c0 <= 10; c0 += 1)
10662 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10663 for (int c2 = 10 * c0;
10664 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10666 for (int c3 = 10 * c1;
10667 c3 <= min(10 * c1 + 9, -c2 + 100);
10671 Separation into full and partial tiles can be obtained by assigning
10672 a class, say C<0>, to the full tiles. The full tiles are represented by those
10673 values of the first and second schedule dimensions for which there are
10674 values of the third and fourth dimensions to cover an entire tile.
10675 That is, we need to specify the following option
10677 { [a,b,c,d] -> separation_class[[0]->[0]] :
10678 exists b': 0 <= 10a,10b' and
10679 10a+9+10b'+9 <= 100;
10680 [a,b,c,d] -> separation_class[[1]->[0]] :
10681 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
10683 which simplifies to
10685 { [a, b, c, d] -> separation_class[[1] -> [0]] :
10686 a >= 0 and b >= 0 and b <= 8 - a;
10687 [a, b, c, d] -> separation_class[[0] -> [0]] :
10688 a >= 0 and a <= 8 }
10690 With this option, the generated AST is as follows
10693 for (int c0 = 0; c0 <= 8; c0 += 1) {
10694 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10695 for (int c2 = 10 * c0;
10696 c2 <= 10 * c0 + 9; c2 += 1)
10697 for (int c3 = 10 * c1;
10698 c3 <= 10 * c1 + 9; c3 += 1)
10700 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10701 for (int c2 = 10 * c0;
10702 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10704 for (int c3 = 10 * c1;
10705 c3 <= min(-c2 + 100, 10 * c1 + 9);
10709 for (int c0 = 9; c0 <= 10; c0 += 1)
10710 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10711 for (int c2 = 10 * c0;
10712 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10714 for (int c3 = 10 * c1;
10715 c3 <= min(10 * c1 + 9, -c2 + 100);
10722 This is a single-dimensional space representing the schedule dimension(s)
10723 to which ``separation'' should be applied. Separation tries to split
10724 a loop into several pieces if this can avoid the generation of guards
10726 See also the C<atomic> option.
10730 This is a single-dimensional space representing the schedule dimension(s)
10731 for which the domains should be considered ``atomic''. That is, the
10732 AST generator will make sure that any given domain space will only appear
10733 in a single loop at the specified level.
10735 Consider the following schedule
10737 { a[i] -> [i] : 0 <= i < 10;
10738 b[i] -> [i+1] : 0 <= i < 10 }
10740 If the following option is specified
10742 { [i] -> separate[x] }
10744 then the following AST will be generated
10748 for (int c0 = 1; c0 <= 9; c0 += 1) {
10755 If, on the other hand, the following option is specified
10757 { [i] -> atomic[x] }
10759 then the following AST will be generated
10761 for (int c0 = 0; c0 <= 10; c0 += 1) {
10768 If neither C<atomic> nor C<separate> is specified, then the AST generator
10769 may produce either of these two results or some intermediate form.
10773 This is a single-dimensional space representing the schedule dimension(s)
10774 that should be I<completely> unrolled.
10775 To obtain a partial unrolling, the user should apply an additional
10776 strip-mining to the schedule and fully unroll the inner loop.
10780 =head3 Fine-grained Control over AST Generation
10782 Besides specifying the constraints on the parameters,
10783 an C<isl_ast_build> object can be used to control
10784 various aspects of the AST generation process.
10785 In case of AST construction using
10786 C<isl_ast_build_node_from_schedule_map>,
10787 the most prominent way of control is through ``options'',
10788 as explained above.
10790 Additional control is available through the following functions.
10792 #include <isl/ast_build.h>
10793 __isl_give isl_ast_build *
10794 isl_ast_build_set_iterators(
10795 __isl_take isl_ast_build *build,
10796 __isl_take isl_id_list *iterators);
10798 The function C<isl_ast_build_set_iterators> allows the user to
10799 specify a list of iterator C<isl_id>s to be used as iterators.
10800 If the input schedule is injective, then
10801 the number of elements in this list should be as large as the dimension
10802 of the schedule space, but no direct correspondence should be assumed
10803 between dimensions and elements.
10804 If the input schedule is not injective, then an additional number
10805 of C<isl_id>s equal to the largest dimension of the input domains
10807 If the number of provided C<isl_id>s is insufficient, then additional
10808 names are automatically generated.
10810 #include <isl/ast_build.h>
10811 __isl_give isl_ast_build *
10812 isl_ast_build_set_create_leaf(
10813 __isl_take isl_ast_build *build,
10814 __isl_give isl_ast_node *(*fn)(
10815 __isl_take isl_ast_build *build,
10816 void *user), void *user);
10819 C<isl_ast_build_set_create_leaf> function allows for the
10820 specification of a callback that should be called whenever the AST
10821 generator arrives at an element of the schedule domain.
10822 The callback should return an AST node that should be inserted
10823 at the corresponding position of the AST. The default action (when
10824 the callback is not set) is to continue generating parts of the AST to scan
10825 all the domain elements associated to the schedule domain element
10826 and to insert user nodes, ``calling'' the domain element, for each of them.
10827 The C<build> argument contains the current state of the C<isl_ast_build>.
10828 To ease nested AST generation (see L</"Nested AST Generation">),
10829 all control information that is
10830 specific to the current AST generation such as the options and
10831 the callbacks has been removed from this C<isl_ast_build>.
10832 The callback would typically return the result of a nested
10833 AST generation or a
10834 user defined node created using the following function.
10836 #include <isl/ast.h>
10837 __isl_give isl_ast_node *isl_ast_node_alloc_user(
10838 __isl_take isl_ast_expr *expr);
10840 #include <isl/ast_build.h>
10841 __isl_give isl_ast_build *
10842 isl_ast_build_set_at_each_domain(
10843 __isl_take isl_ast_build *build,
10844 __isl_give isl_ast_node *(*fn)(
10845 __isl_take isl_ast_node *node,
10846 __isl_keep isl_ast_build *build,
10847 void *user), void *user);
10848 __isl_give isl_ast_build *
10849 isl_ast_build_set_before_each_for(
10850 __isl_take isl_ast_build *build,
10851 __isl_give isl_id *(*fn)(
10852 __isl_keep isl_ast_build *build,
10853 void *user), void *user);
10854 __isl_give isl_ast_build *
10855 isl_ast_build_set_after_each_for(
10856 __isl_take isl_ast_build *build,
10857 __isl_give isl_ast_node *(*fn)(
10858 __isl_take isl_ast_node *node,
10859 __isl_keep isl_ast_build *build,
10860 void *user), void *user);
10861 __isl_give isl_ast_build *
10862 isl_ast_build_set_before_each_mark(
10863 __isl_take isl_ast_build *build,
10864 isl_stat (*fn)(__isl_keep isl_id *mark,
10865 __isl_keep isl_ast_build *build,
10866 void *user), void *user);
10867 __isl_give isl_ast_build *
10868 isl_ast_build_set_after_each_mark(
10869 __isl_take isl_ast_build *build,
10870 __isl_give isl_ast_node *(*fn)(
10871 __isl_take isl_ast_node *node,
10872 __isl_keep isl_ast_build *build,
10873 void *user), void *user);
10875 The callback set by C<isl_ast_build_set_at_each_domain> will
10876 be called for each domain AST node.
10877 The callbacks set by C<isl_ast_build_set_before_each_for>
10878 and C<isl_ast_build_set_after_each_for> will be called
10879 for each for AST node. The first will be called in depth-first
10880 pre-order, while the second will be called in depth-first post-order.
10881 Since C<isl_ast_build_set_before_each_for> is called before the for
10882 node is actually constructed, it is only passed an C<isl_ast_build>.
10883 The returned C<isl_id> will be added as an annotation (using
10884 C<isl_ast_node_set_annotation>) to the constructed for node.
10885 In particular, if the user has also specified an C<after_each_for>
10886 callback, then the annotation can be retrieved from the node passed to
10887 that callback using C<isl_ast_node_get_annotation>.
10888 The callbacks set by C<isl_ast_build_set_before_each_mark>
10889 and C<isl_ast_build_set_after_each_mark> will be called for each
10890 mark AST node that is created, i.e., for each mark schedule node
10891 in the input schedule tree. The first will be called in depth-first
10892 pre-order, while the second will be called in depth-first post-order.
10893 Since the callback set by C<isl_ast_build_set_before_each_mark>
10894 is called before the mark AST node is actually constructed, it is passed
10895 the identifier of the mark node.
10896 All callbacks should C<NULL> (or C<isl_stat_error>) on failure.
10897 The given C<isl_ast_build> can be used to create new
10898 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
10899 or C<isl_ast_build_call_from_pw_multi_aff>.
10901 =head3 Nested AST Generation
10903 C<isl> allows the user to create an AST within the context
10904 of another AST. These nested ASTs are created using the
10905 same C<isl_ast_build_node_from_schedule_map> function that is used to create
10906 the outer AST. The C<build> argument should be an C<isl_ast_build>
10907 passed to a callback set by
10908 C<isl_ast_build_set_create_leaf>.
10909 The space of the range of the C<schedule> argument should refer
10910 to this build. In particular, the space should be a wrapped
10911 relation and the domain of this wrapped relation should be the
10912 same as that of the range of the schedule returned by
10913 C<isl_ast_build_get_schedule> below.
10914 In practice, the new schedule is typically
10915 created by calling C<isl_union_map_range_product> on the old schedule
10916 and some extra piece of the schedule.
10917 The space of the schedule domain is also available from
10918 the C<isl_ast_build>.
10920 #include <isl/ast_build.h>
10921 __isl_give isl_union_map *isl_ast_build_get_schedule(
10922 __isl_keep isl_ast_build *build);
10923 __isl_give isl_space *isl_ast_build_get_schedule_space(
10924 __isl_keep isl_ast_build *build);
10925 __isl_give isl_ast_build *isl_ast_build_restrict(
10926 __isl_take isl_ast_build *build,
10927 __isl_take isl_set *set);
10929 The C<isl_ast_build_get_schedule> function returns a (partial)
10930 schedule for the domains elements for which part of the AST still needs to
10931 be generated in the current build.
10932 In particular, the domain elements are mapped to those iterations of the loops
10933 enclosing the current point of the AST generation inside which
10934 the domain elements are executed.
10935 No direct correspondence between
10936 the input schedule and this schedule should be assumed.
10937 The space obtained from C<isl_ast_build_get_schedule_space> can be used
10938 to create a set for C<isl_ast_build_restrict> to intersect
10939 with the current build. In particular, the set passed to
10940 C<isl_ast_build_restrict> can have additional parameters.
10941 The ids of the set dimensions in the space returned by
10942 C<isl_ast_build_get_schedule_space> correspond to the
10943 iterators of the already generated loops.
10944 The user should not rely on the ids of the output dimensions
10945 of the relations in the union relation returned by
10946 C<isl_ast_build_get_schedule> having any particular value.
10948 =head1 Applications
10950 Although C<isl> is mainly meant to be used as a library,
10951 it also contains some basic applications that use some
10952 of the functionality of C<isl>.
10953 For applications that take one or more polytopes or polyhedra
10954 as input, this input may be specified in either the L<isl format>
10955 or the L<PolyLib format>.
10957 =head2 C<isl_polyhedron_sample>
10959 C<isl_polyhedron_sample> takes a polyhedron as input and prints
10960 an integer element of the polyhedron, if there is any.
10961 The first column in the output is the denominator and is always
10962 equal to 1. If the polyhedron contains no integer points,
10963 then a vector of length zero is printed.
10967 C<isl_pip> takes the same input as the C<example> program
10968 from the C<piplib> distribution, i.e., a set of constraints
10969 on the parameters, a line containing only -1 and finally a set
10970 of constraints on a parametric polyhedron.
10971 The coefficients of the parameters appear in the last columns
10972 (but before the final constant column).
10973 The output is the lexicographic minimum of the parametric polyhedron.
10974 As C<isl> currently does not have its own output format, the output
10975 is just a dump of the internal state.
10977 =head2 C<isl_polyhedron_minimize>
10979 C<isl_polyhedron_minimize> computes the minimum of some linear
10980 or affine objective function over the integer points in a polyhedron.
10981 If an affine objective function
10982 is given, then the constant should appear in the last column.
10984 =head2 C<isl_polytope_scan>
10986 Given a polytope, C<isl_polytope_scan> prints
10987 all integer points in the polytope.
10991 Given an C<isl_union_access_info> object as input,
10992 C<isl_flow> prints out the corresponding dependences,
10993 as computed by C<isl_union_access_info_compute_flow>.
10995 =head2 C<isl_codegen>
10997 Given either a schedule tree or a sequence consisting of
10998 a schedule map, a context set and an options relation,
10999 C<isl_codegen> prints out an AST that scans the domain elements
11000 of the schedule in the order of their image(s) taking into account
11001 the constraints in the context set.
11003 =head2 C<isl_schedule>
11005 Given an C<isl_schedule_constraints> object as input,
11006 C<isl_schedule> prints out a schedule that satisfies the given