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 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);
2867 Multiple expressions can be copied and freed using
2868 the following functions.
2870 #include <isl/val.h>
2871 __isl_give isl_multi_val *isl_multi_val_copy(
2872 __isl_keep isl_multi_val *mv);
2873 __isl_null isl_multi_val *isl_multi_val_free(
2874 __isl_take isl_multi_val *mv);
2876 #include <isl/aff.h>
2877 __isl_give isl_multi_aff *isl_multi_aff_copy(
2878 __isl_keep isl_multi_aff *maff);
2879 __isl_null isl_multi_aff *isl_multi_aff_free(
2880 __isl_take isl_multi_aff *maff);
2881 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
2882 __isl_keep isl_multi_pw_aff *mpa);
2883 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
2884 __isl_take isl_multi_pw_aff *mpa);
2885 __isl_give isl_multi_union_pw_aff *
2886 isl_multi_union_pw_aff_copy(
2887 __isl_keep isl_multi_union_pw_aff *mupa);
2888 __isl_null isl_multi_union_pw_aff *
2889 isl_multi_union_pw_aff_free(
2890 __isl_take isl_multi_union_pw_aff *mupa);
2892 The base expression at a given position of a multiple
2893 expression can be extracted using the following functions.
2895 #include <isl/val.h>
2896 __isl_give isl_val *isl_multi_val_get_val(
2897 __isl_keep isl_multi_val *mv, int pos);
2899 #include <isl/aff.h>
2900 __isl_give isl_aff *isl_multi_aff_get_aff(
2901 __isl_keep isl_multi_aff *multi, int pos);
2902 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
2903 __isl_keep isl_multi_pw_aff *mpa, int pos);
2904 __isl_give isl_union_pw_aff *
2905 isl_multi_union_pw_aff_get_union_pw_aff(
2906 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
2908 It can be replaced using the following functions.
2910 #include <isl/val.h>
2911 __isl_give isl_multi_val *isl_multi_val_set_val(
2912 __isl_take isl_multi_val *mv, int pos,
2913 __isl_take isl_val *val);
2915 #include <isl/aff.h>
2916 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
2917 __isl_take isl_multi_aff *multi, int pos,
2918 __isl_take isl_aff *aff);
2919 __isl_give isl_multi_union_pw_aff *
2920 isl_multi_union_pw_aff_set_union_pw_aff(
2921 __isl_take isl_multi_union_pw_aff *mupa, int pos,
2922 __isl_take isl_union_pw_aff *upa);
2924 As a convenience, a sequence of base expressions that have
2925 their domains in a given space can be extracted from a sequence
2926 of union expressions using the following function.
2928 #include <isl/aff.h>
2929 __isl_give isl_multi_pw_aff *
2930 isl_multi_union_pw_aff_extract_multi_pw_aff(
2931 __isl_keep isl_multi_union_pw_aff *mupa,
2932 __isl_take isl_space *space);
2934 Note that there is a difference between C<isl_multi_union_pw_aff>
2935 and C<isl_union_pw_multi_aff> objects. The first is a sequence
2936 of unions of piecewise expressions, while the second is a union
2937 of piecewise sequences. In particular, multiple affine expressions
2938 in an C<isl_union_pw_multi_aff> may live in different spaces,
2939 while there is only a single multiple expression in
2940 an C<isl_multi_union_pw_aff>, which can therefore only live
2941 in a single space. This means that not every
2942 C<isl_union_pw_multi_aff> can be converted to
2943 an C<isl_multi_union_pw_aff>. Conversely, a zero-dimensional
2944 C<isl_multi_union_pw_aff> carries no information
2945 about any possible domain and therefore cannot be converted
2946 to an C<isl_union_pw_multi_aff>. Moreover, the elements
2947 of an C<isl_multi_union_pw_aff> may be defined over different domains,
2948 while each multiple expression inside an C<isl_union_pw_multi_aff>
2949 has a single domain. The conversion of an C<isl_union_pw_multi_aff>
2950 of dimension greater than one may therefore not be exact.
2951 The following functions can
2952 be used to perform these conversions when they are possible.
2954 #include <isl/aff.h>
2955 __isl_give isl_multi_union_pw_aff *
2956 isl_multi_union_pw_aff_from_union_pw_multi_aff(
2957 __isl_take isl_union_pw_multi_aff *upma);
2958 __isl_give isl_union_pw_multi_aff *
2959 isl_union_pw_multi_aff_from_multi_union_pw_aff(
2960 __isl_take isl_multi_union_pw_aff *mupa);
2962 =head3 Piecewise Expressions
2964 A piecewise expression is an expression that is described
2965 using zero or more base expression defined over the same
2966 number of cells in the domain space of the base expressions.
2967 All base expressions are defined over the same
2968 domain space and the cells are disjoint.
2969 The space of a piecewise expression is the same as
2970 that of the base expressions.
2971 If the union of the cells is a strict subset of the domain
2972 space, then the value of the piecewise expression outside
2973 this union is different for types derived from quasi-affine
2974 expressions and those derived from quasipolynomials.
2975 Piecewise expressions derived from quasi-affine expressions
2976 are considered to be undefined outside the union of their cells.
2977 Piecewise expressions derived from quasipolynomials
2978 are considered to be zero outside the union of their cells.
2980 Piecewise quasipolynomials are mainly used by the C<barvinok>
2981 library for representing the number of elements in a parametric set or map.
2982 For example, the piecewise quasipolynomial
2984 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2986 represents the number of points in the map
2988 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2990 The piecewise expression types defined by C<isl>
2991 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
2992 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
2994 A piecewise expression with no cells can be created using
2995 the following functions.
2997 #include <isl/aff.h>
2998 __isl_give isl_pw_aff *isl_pw_aff_empty(
2999 __isl_take isl_space *space);
3000 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3001 __isl_take isl_space *space);
3003 A piecewise expression with a single universe cell can be
3004 created using the following functions.
3006 #include <isl/aff.h>
3007 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3008 __isl_take isl_aff *aff);
3009 __isl_give isl_pw_multi_aff *
3010 isl_pw_multi_aff_from_multi_aff(
3011 __isl_take isl_multi_aff *ma);
3013 #include <isl/polynomial.h>
3014 __isl_give isl_pw_qpolynomial *
3015 isl_pw_qpolynomial_from_qpolynomial(
3016 __isl_take isl_qpolynomial *qp);
3018 A piecewise expression with a single specified cell can be
3019 created using the following functions.
3021 #include <isl/aff.h>
3022 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3023 __isl_take isl_set *set, __isl_take isl_aff *aff);
3024 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3025 __isl_take isl_set *set,
3026 __isl_take isl_multi_aff *maff);
3028 #include <isl/polynomial.h>
3029 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3030 __isl_take isl_set *set,
3031 __isl_take isl_qpolynomial *qp);
3033 The following convenience functions first create a base expression and
3034 then create a piecewise expression over a universe domain.
3036 #include <isl/aff.h>
3037 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3038 __isl_take isl_local_space *ls);
3039 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3040 __isl_take isl_local_space *ls,
3041 enum isl_dim_type type, unsigned pos);
3042 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3043 __isl_take isl_local_space *ls);
3044 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
3045 __isl_take isl_space *space);
3046 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3047 __isl_take isl_space *space);
3048 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
3049 __isl_take isl_space *space);
3050 __isl_give isl_pw_multi_aff *
3051 isl_pw_multi_aff_project_out_map(
3052 __isl_take isl_space *space,
3053 enum isl_dim_type type,
3054 unsigned first, unsigned n);
3056 #include <isl/polynomial.h>
3057 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3058 __isl_take isl_space *space);
3060 The following convenience functions first create a base expression and
3061 then create a piecewise expression over a given domain.
3063 #include <isl/aff.h>
3064 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
3065 __isl_take isl_set *domain,
3066 __isl_take isl_val *v);
3067 __isl_give isl_pw_multi_aff *
3068 isl_pw_multi_aff_multi_val_on_domain(
3069 __isl_take isl_set *domain,
3070 __isl_take isl_multi_val *mv);
3072 As a convenience, a piecewise multiple expression can
3073 also be created from a piecewise expression.
3074 Each multiple expression in the result is derived
3075 from the corresponding base expression.
3077 #include <isl/aff.h>
3078 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
3079 __isl_take isl_pw_aff *pa);
3081 Similarly, a piecewise quasipolynomial can be
3082 created from a piecewise quasi-affine expression using
3083 the following function.
3085 #include <isl/polynomial.h>
3086 __isl_give isl_pw_qpolynomial *
3087 isl_pw_qpolynomial_from_pw_aff(
3088 __isl_take isl_pw_aff *pwaff);
3090 Piecewise expressions can be copied and freed using the following functions.
3092 #include <isl/aff.h>
3093 __isl_give isl_pw_aff *isl_pw_aff_copy(
3094 __isl_keep isl_pw_aff *pwaff);
3095 __isl_null isl_pw_aff *isl_pw_aff_free(
3096 __isl_take isl_pw_aff *pwaff);
3097 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3098 __isl_keep isl_pw_multi_aff *pma);
3099 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
3100 __isl_take isl_pw_multi_aff *pma);
3102 #include <isl/polynomial.h>
3103 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3104 __isl_keep isl_pw_qpolynomial *pwqp);
3105 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
3106 __isl_take isl_pw_qpolynomial *pwqp);
3107 __isl_give isl_pw_qpolynomial_fold *
3108 isl_pw_qpolynomial_fold_copy(
3109 __isl_keep isl_pw_qpolynomial_fold *pwf);
3110 __isl_null isl_pw_qpolynomial_fold *
3111 isl_pw_qpolynomial_fold_free(
3112 __isl_take isl_pw_qpolynomial_fold *pwf);
3114 To iterate over the different cells of a piecewise expression,
3115 use the following functions.
3117 #include <isl/aff.h>
3118 isl_bool isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3119 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3120 isl_stat isl_pw_aff_foreach_piece(
3121 __isl_keep isl_pw_aff *pwaff,
3122 isl_stat (*fn)(__isl_take isl_set *set,
3123 __isl_take isl_aff *aff,
3124 void *user), void *user);
3125 int isl_pw_multi_aff_n_piece(
3126 __isl_keep isl_pw_multi_aff *pma);
3127 isl_stat isl_pw_multi_aff_foreach_piece(
3128 __isl_keep isl_pw_multi_aff *pma,
3129 isl_stat (*fn)(__isl_take isl_set *set,
3130 __isl_take isl_multi_aff *maff,
3131 void *user), void *user);
3133 #include <isl/polynomial.h>
3134 int isl_pw_qpolynomial_n_piece(
3135 __isl_keep isl_pw_qpolynomial *pwqp);
3136 isl_stat isl_pw_qpolynomial_foreach_piece(
3137 __isl_keep isl_pw_qpolynomial *pwqp,
3138 isl_stat (*fn)(__isl_take isl_set *set,
3139 __isl_take isl_qpolynomial *qp,
3140 void *user), void *user);
3141 isl_stat isl_pw_qpolynomial_foreach_lifted_piece(
3142 __isl_keep isl_pw_qpolynomial *pwqp,
3143 isl_stat (*fn)(__isl_take isl_set *set,
3144 __isl_take isl_qpolynomial *qp,
3145 void *user), void *user);
3146 int isl_pw_qpolynomial_fold_n_piece(
3147 __isl_keep isl_pw_qpolynomial_fold *pwf);
3148 isl_stat isl_pw_qpolynomial_fold_foreach_piece(
3149 __isl_keep isl_pw_qpolynomial_fold *pwf,
3150 isl_stat (*fn)(__isl_take isl_set *set,
3151 __isl_take isl_qpolynomial_fold *fold,
3152 void *user), void *user);
3153 isl_stat isl_pw_qpolynomial_fold_foreach_lifted_piece(
3154 __isl_keep isl_pw_qpolynomial_fold *pwf,
3155 isl_stat (*fn)(__isl_take isl_set *set,
3156 __isl_take isl_qpolynomial_fold *fold,
3157 void *user), void *user);
3159 As usual, the function C<fn> should return C<isl_stat_ok> on success
3160 and C<isl_stat_error> on failure. The difference between
3161 C<isl_pw_qpolynomial_foreach_piece> and
3162 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3163 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3164 compute unique representations for all existentially quantified
3165 variables and then turn these existentially quantified variables
3166 into extra set variables, adapting the associated quasipolynomial
3167 accordingly. This means that the C<set> passed to C<fn>
3168 will not have any existentially quantified variables, but that
3169 the dimensions of the sets may be different for different
3170 invocations of C<fn>.
3171 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
3172 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
3174 A piecewise expression consisting of the expressions at a given
3175 position of a piecewise multiple expression can be extracted
3176 using the following function.
3178 #include <isl/aff.h>
3179 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3180 __isl_keep isl_pw_multi_aff *pma, int pos);
3182 These expressions can be replaced using the following function.
3184 #include <isl/aff.h>
3185 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3186 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3187 __isl_take isl_pw_aff *pa);
3189 Note that there is a difference between C<isl_multi_pw_aff> and
3190 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
3191 affine expressions, while the second is a piecewise sequence
3192 of affine expressions. In particular, each of the piecewise
3193 affine expressions in an C<isl_multi_pw_aff> may have a different
3194 domain, while all multiple expressions associated to a cell
3195 in an C<isl_pw_multi_aff> have the same domain.
3196 It is possible to convert between the two, but when converting
3197 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
3198 of the result is the intersection of the domains of the input.
3199 The reverse conversion is exact.
3201 #include <isl/aff.h>
3202 __isl_give isl_pw_multi_aff *
3203 isl_pw_multi_aff_from_multi_pw_aff(
3204 __isl_take isl_multi_pw_aff *mpa);
3205 __isl_give isl_multi_pw_aff *
3206 isl_multi_pw_aff_from_pw_multi_aff(
3207 __isl_take isl_pw_multi_aff *pma);
3209 =head3 Union Expressions
3211 A union expression collects base expressions defined
3212 over different domains. The space of a union expression
3213 is that of the shared parameter space.
3215 The union expression types defined by C<isl>
3216 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
3217 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
3219 C<isl_union_pw_aff>,
3220 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>,
3221 there can be at most one base expression for a given domain space.
3223 C<isl_union_pw_multi_aff>,
3224 there can be multiple such expressions for a given domain space,
3225 but the domains of these expressions need to be disjoint.
3227 An empty union expression can be created using the following functions.
3229 #include <isl/aff.h>
3230 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
3231 __isl_take isl_space *space);
3232 __isl_give isl_union_pw_multi_aff *
3233 isl_union_pw_multi_aff_empty(
3234 __isl_take isl_space *space);
3236 #include <isl/polynomial.h>
3237 __isl_give isl_union_pw_qpolynomial *
3238 isl_union_pw_qpolynomial_zero(
3239 __isl_take isl_space *space);
3241 A union expression containing a single base expression
3242 can be created using the following functions.
3244 #include <isl/aff.h>
3245 __isl_give isl_union_pw_aff *
3246 isl_union_pw_aff_from_pw_aff(
3247 __isl_take isl_pw_aff *pa);
3248 __isl_give isl_union_pw_multi_aff *
3249 isl_union_pw_multi_aff_from_aff(
3250 __isl_take isl_aff *aff);
3251 __isl_give isl_union_pw_multi_aff *
3252 isl_union_pw_multi_aff_from_pw_multi_aff(
3253 __isl_take isl_pw_multi_aff *pma);
3255 #include <isl/polynomial.h>
3256 __isl_give isl_union_pw_qpolynomial *
3257 isl_union_pw_qpolynomial_from_pw_qpolynomial(
3258 __isl_take isl_pw_qpolynomial *pwqp);
3260 The following functions create a base expression on each
3261 of the sets in the union set and collect the results.
3263 #include <isl/aff.h>
3264 __isl_give isl_union_pw_multi_aff *
3265 isl_union_pw_multi_aff_from_union_pw_aff(
3266 __isl_take isl_union_pw_aff *upa);
3267 __isl_give isl_union_pw_aff *
3268 isl_union_pw_multi_aff_get_union_pw_aff(
3269 __isl_keep isl_union_pw_multi_aff *upma, int pos);
3270 __isl_give isl_union_pw_aff *
3271 isl_union_pw_aff_val_on_domain(
3272 __isl_take isl_union_set *domain,
3273 __isl_take isl_val *v);
3274 __isl_give isl_union_pw_multi_aff *
3275 isl_union_pw_multi_aff_multi_val_on_domain(
3276 __isl_take isl_union_set *domain,
3277 __isl_take isl_multi_val *mv);
3279 An C<isl_union_pw_aff> that is equal to a (parametric) affine
3280 expression on a given domain can be created using the following
3283 #include <isl/aff.h>
3284 __isl_give isl_union_pw_aff *
3285 isl_union_pw_aff_aff_on_domain(
3286 __isl_take isl_union_set *domain,
3287 __isl_take isl_aff *aff);
3289 A base expression can be added to a union expression using
3290 the following functions.
3292 #include <isl/aff.h>
3293 __isl_give isl_union_pw_aff *
3294 isl_union_pw_aff_add_pw_aff(
3295 __isl_take isl_union_pw_aff *upa,
3296 __isl_take isl_pw_aff *pa);
3297 __isl_give isl_union_pw_multi_aff *
3298 isl_union_pw_multi_aff_add_pw_multi_aff(
3299 __isl_take isl_union_pw_multi_aff *upma,
3300 __isl_take isl_pw_multi_aff *pma);
3302 #include <isl/polynomial.h>
3303 __isl_give isl_union_pw_qpolynomial *
3304 isl_union_pw_qpolynomial_add_pw_qpolynomial(
3305 __isl_take isl_union_pw_qpolynomial *upwqp,
3306 __isl_take isl_pw_qpolynomial *pwqp);
3308 Union expressions can be copied and freed using
3309 the following functions.
3311 #include <isl/aff.h>
3312 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
3313 __isl_keep isl_union_pw_aff *upa);
3314 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
3315 __isl_take isl_union_pw_aff *upa);
3316 __isl_give isl_union_pw_multi_aff *
3317 isl_union_pw_multi_aff_copy(
3318 __isl_keep isl_union_pw_multi_aff *upma);
3319 __isl_null isl_union_pw_multi_aff *
3320 isl_union_pw_multi_aff_free(
3321 __isl_take isl_union_pw_multi_aff *upma);
3323 #include <isl/polynomial.h>
3324 __isl_give isl_union_pw_qpolynomial *
3325 isl_union_pw_qpolynomial_copy(
3326 __isl_keep isl_union_pw_qpolynomial *upwqp);
3327 __isl_null isl_union_pw_qpolynomial *
3328 isl_union_pw_qpolynomial_free(
3329 __isl_take isl_union_pw_qpolynomial *upwqp);
3330 __isl_give isl_union_pw_qpolynomial_fold *
3331 isl_union_pw_qpolynomial_fold_copy(
3332 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3333 __isl_null isl_union_pw_qpolynomial_fold *
3334 isl_union_pw_qpolynomial_fold_free(
3335 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3337 To iterate over the base expressions in a union expression,
3338 use the following functions.
3340 #include <isl/aff.h>
3341 int isl_union_pw_aff_n_pw_aff(
3342 __isl_keep isl_union_pw_aff *upa);
3343 isl_stat isl_union_pw_aff_foreach_pw_aff(
3344 __isl_keep isl_union_pw_aff *upa,
3345 isl_stat (*fn)(__isl_take isl_pw_aff *pa,
3346 void *user), void *user);
3347 int isl_union_pw_multi_aff_n_pw_multi_aff(
3348 __isl_keep isl_union_pw_multi_aff *upma);
3349 isl_stat isl_union_pw_multi_aff_foreach_pw_multi_aff(
3350 __isl_keep isl_union_pw_multi_aff *upma,
3351 isl_stat (*fn)(__isl_take isl_pw_multi_aff *pma,
3352 void *user), void *user);
3354 #include <isl/polynomial.h>
3355 int isl_union_pw_qpolynomial_n_pw_qpolynomial(
3356 __isl_keep isl_union_pw_qpolynomial *upwqp);
3357 isl_stat isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3358 __isl_keep isl_union_pw_qpolynomial *upwqp,
3359 isl_stat (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
3360 void *user), void *user);
3361 int isl_union_pw_qpolynomial_fold_n_pw_qpolynomial_fold(
3362 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3363 isl_stat isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3364 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3365 isl_stat (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3366 void *user), void *user);
3368 To extract the base expression in a given space from a union, use
3369 the following functions.
3371 #include <isl/aff.h>
3372 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
3373 __isl_keep isl_union_pw_aff *upa,
3374 __isl_take isl_space *space);
3375 __isl_give isl_pw_multi_aff *
3376 isl_union_pw_multi_aff_extract_pw_multi_aff(
3377 __isl_keep isl_union_pw_multi_aff *upma,
3378 __isl_take isl_space *space);
3380 #include <isl/polynomial.h>
3381 __isl_give isl_pw_qpolynomial *
3382 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3383 __isl_keep isl_union_pw_qpolynomial *upwqp,
3384 __isl_take isl_space *space);
3386 =head2 Input and Output
3388 For set and relation,
3389 C<isl> supports its own input/output format, which is similar
3390 to the C<Omega> format, but also supports the C<PolyLib> format
3392 For other object types, typically only an C<isl> format is supported.
3394 =head3 C<isl> format
3396 The C<isl> format is similar to that of C<Omega>, but has a different
3397 syntax for describing the parameters and allows for the definition
3398 of an existentially quantified variable as the integer division
3399 of an affine expression.
3400 For example, the set of integers C<i> between C<0> and C<n>
3401 such that C<i % 10 <= 6> can be described as
3403 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
3406 A set or relation can have several disjuncts, separated
3407 by the keyword C<or>. Each disjunct is either a conjunction
3408 of constraints or a projection (C<exists>) of a conjunction
3409 of constraints. The constraints are separated by the keyword
3412 =head3 C<PolyLib> format
3414 If the represented set is a union, then the first line
3415 contains a single number representing the number of disjuncts.
3416 Otherwise, a line containing the number C<1> is optional.
3418 Each disjunct is represented by a matrix of constraints.
3419 The first line contains two numbers representing
3420 the number of rows and columns,
3421 where the number of rows is equal to the number of constraints
3422 and the number of columns is equal to two plus the number of variables.
3423 The following lines contain the actual rows of the constraint matrix.
3424 In each row, the first column indicates whether the constraint
3425 is an equality (C<0>) or inequality (C<1>). The final column
3426 corresponds to the constant term.
3428 If the set is parametric, then the coefficients of the parameters
3429 appear in the last columns before the constant column.
3430 The coefficients of any existentially quantified variables appear
3431 between those of the set variables and those of the parameters.
3433 =head3 Extended C<PolyLib> format
3435 The extended C<PolyLib> format is nearly identical to the
3436 C<PolyLib> format. The only difference is that the line
3437 containing the number of rows and columns of a constraint matrix
3438 also contains four additional numbers:
3439 the number of output dimensions, the number of input dimensions,
3440 the number of local dimensions (i.e., the number of existentially
3441 quantified variables) and the number of parameters.
3442 For sets, the number of ``output'' dimensions is equal
3443 to the number of set dimensions, while the number of ``input''
3448 Objects can be read from input using the following functions.
3450 #include <isl/val.h>
3451 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
3453 __isl_give isl_multi_val *isl_multi_val_read_from_str(
3454 isl_ctx *ctx, const char *str);
3456 #include <isl/set.h>
3457 __isl_give isl_basic_set *isl_basic_set_read_from_file(
3458 isl_ctx *ctx, FILE *input);
3459 __isl_give isl_basic_set *isl_basic_set_read_from_str(
3460 isl_ctx *ctx, const char *str);
3461 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
3463 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
3466 #include <isl/map.h>
3467 __isl_give isl_basic_map *isl_basic_map_read_from_file(
3468 isl_ctx *ctx, FILE *input);
3469 __isl_give isl_basic_map *isl_basic_map_read_from_str(
3470 isl_ctx *ctx, const char *str);
3471 __isl_give isl_map *isl_map_read_from_file(
3472 isl_ctx *ctx, FILE *input);
3473 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
3476 #include <isl/union_set.h>
3477 __isl_give isl_union_set *isl_union_set_read_from_file(
3478 isl_ctx *ctx, FILE *input);
3479 __isl_give isl_union_set *isl_union_set_read_from_str(
3480 isl_ctx *ctx, const char *str);
3482 #include <isl/union_map.h>
3483 __isl_give isl_union_map *isl_union_map_read_from_file(
3484 isl_ctx *ctx, FILE *input);
3485 __isl_give isl_union_map *isl_union_map_read_from_str(
3486 isl_ctx *ctx, const char *str);
3488 #include <isl/aff.h>
3489 __isl_give isl_aff *isl_aff_read_from_str(
3490 isl_ctx *ctx, const char *str);
3491 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3492 isl_ctx *ctx, const char *str);
3493 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3494 isl_ctx *ctx, const char *str);
3495 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3496 isl_ctx *ctx, const char *str);
3497 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
3498 isl_ctx *ctx, const char *str);
3499 __isl_give isl_union_pw_aff *
3500 isl_union_pw_aff_read_from_str(
3501 isl_ctx *ctx, const char *str);
3502 __isl_give isl_union_pw_multi_aff *
3503 isl_union_pw_multi_aff_read_from_str(
3504 isl_ctx *ctx, const char *str);
3505 __isl_give isl_multi_union_pw_aff *
3506 isl_multi_union_pw_aff_read_from_str(
3507 isl_ctx *ctx, const char *str);
3509 #include <isl/polynomial.h>
3510 __isl_give isl_union_pw_qpolynomial *
3511 isl_union_pw_qpolynomial_read_from_str(
3512 isl_ctx *ctx, const char *str);
3514 For sets and relations,
3515 the input format is autodetected and may be either the C<PolyLib> format
3516 or the C<isl> format.
3520 Before anything can be printed, an C<isl_printer> needs to
3523 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
3525 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
3526 __isl_null isl_printer *isl_printer_free(
3527 __isl_take isl_printer *printer);
3529 C<isl_printer_to_file> prints to the given file, while
3530 C<isl_printer_to_str> prints to a string that can be extracted
3531 using the following function.
3533 #include <isl/printer.h>
3534 __isl_give char *isl_printer_get_str(
3535 __isl_keep isl_printer *printer);
3537 The printer can be inspected using the following functions.
3539 FILE *isl_printer_get_file(
3540 __isl_keep isl_printer *printer);
3541 int isl_printer_get_output_format(
3542 __isl_keep isl_printer *p);
3543 int isl_printer_get_yaml_style(__isl_keep isl_printer *p);
3545 The behavior of the printer can be modified in various ways
3547 __isl_give isl_printer *isl_printer_set_output_format(
3548 __isl_take isl_printer *p, int output_format);
3549 __isl_give isl_printer *isl_printer_set_indent(
3550 __isl_take isl_printer *p, int indent);
3551 __isl_give isl_printer *isl_printer_set_indent_prefix(
3552 __isl_take isl_printer *p, const char *prefix);
3553 __isl_give isl_printer *isl_printer_indent(
3554 __isl_take isl_printer *p, int indent);
3555 __isl_give isl_printer *isl_printer_set_prefix(
3556 __isl_take isl_printer *p, const char *prefix);
3557 __isl_give isl_printer *isl_printer_set_suffix(
3558 __isl_take isl_printer *p, const char *suffix);
3559 __isl_give isl_printer *isl_printer_set_yaml_style(
3560 __isl_take isl_printer *p, int yaml_style);
3562 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
3563 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
3564 and defaults to C<ISL_FORMAT_ISL>.
3565 Each line in the output is prefixed by C<indent_prefix>,
3566 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
3567 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
3568 In the C<PolyLib> format output,
3569 the coefficients of the existentially quantified variables
3570 appear between those of the set variables and those
3572 The function C<isl_printer_indent> increases the indentation
3573 by the specified amount (which may be negative).
3574 The YAML style may be either C<ISL_YAML_STYLE_BLOCK> or
3575 C<ISL_YAML_STYLE_FLOW> and when we are printing something
3578 To actually print something, use
3580 #include <isl/printer.h>
3581 __isl_give isl_printer *isl_printer_print_double(
3582 __isl_take isl_printer *p, double d);
3584 #include <isl/val.h>
3585 __isl_give isl_printer *isl_printer_print_val(
3586 __isl_take isl_printer *p, __isl_keep isl_val *v);
3588 #include <isl/set.h>
3589 __isl_give isl_printer *isl_printer_print_basic_set(
3590 __isl_take isl_printer *printer,
3591 __isl_keep isl_basic_set *bset);
3592 __isl_give isl_printer *isl_printer_print_set(
3593 __isl_take isl_printer *printer,
3594 __isl_keep isl_set *set);
3596 #include <isl/map.h>
3597 __isl_give isl_printer *isl_printer_print_basic_map(
3598 __isl_take isl_printer *printer,
3599 __isl_keep isl_basic_map *bmap);
3600 __isl_give isl_printer *isl_printer_print_map(
3601 __isl_take isl_printer *printer,
3602 __isl_keep isl_map *map);
3604 #include <isl/union_set.h>
3605 __isl_give isl_printer *isl_printer_print_union_set(
3606 __isl_take isl_printer *p,
3607 __isl_keep isl_union_set *uset);
3609 #include <isl/union_map.h>
3610 __isl_give isl_printer *isl_printer_print_union_map(
3611 __isl_take isl_printer *p,
3612 __isl_keep isl_union_map *umap);
3614 #include <isl/val.h>
3615 __isl_give isl_printer *isl_printer_print_multi_val(
3616 __isl_take isl_printer *p,
3617 __isl_keep isl_multi_val *mv);
3619 #include <isl/aff.h>
3620 __isl_give isl_printer *isl_printer_print_aff(
3621 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3622 __isl_give isl_printer *isl_printer_print_multi_aff(
3623 __isl_take isl_printer *p,
3624 __isl_keep isl_multi_aff *maff);
3625 __isl_give isl_printer *isl_printer_print_pw_aff(
3626 __isl_take isl_printer *p,
3627 __isl_keep isl_pw_aff *pwaff);
3628 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3629 __isl_take isl_printer *p,
3630 __isl_keep isl_pw_multi_aff *pma);
3631 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3632 __isl_take isl_printer *p,
3633 __isl_keep isl_multi_pw_aff *mpa);
3634 __isl_give isl_printer *isl_printer_print_union_pw_aff(
3635 __isl_take isl_printer *p,
3636 __isl_keep isl_union_pw_aff *upa);
3637 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3638 __isl_take isl_printer *p,
3639 __isl_keep isl_union_pw_multi_aff *upma);
3640 __isl_give isl_printer *
3641 isl_printer_print_multi_union_pw_aff(
3642 __isl_take isl_printer *p,
3643 __isl_keep isl_multi_union_pw_aff *mupa);
3645 #include <isl/polynomial.h>
3646 __isl_give isl_printer *isl_printer_print_qpolynomial(
3647 __isl_take isl_printer *p,
3648 __isl_keep isl_qpolynomial *qp);
3649 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3650 __isl_take isl_printer *p,
3651 __isl_keep isl_pw_qpolynomial *pwqp);
3652 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3653 __isl_take isl_printer *p,
3654 __isl_keep isl_union_pw_qpolynomial *upwqp);
3656 __isl_give isl_printer *
3657 isl_printer_print_pw_qpolynomial_fold(
3658 __isl_take isl_printer *p,
3659 __isl_keep isl_pw_qpolynomial_fold *pwf);
3660 __isl_give isl_printer *
3661 isl_printer_print_union_pw_qpolynomial_fold(
3662 __isl_take isl_printer *p,
3663 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3665 For C<isl_printer_print_qpolynomial>,
3666 C<isl_printer_print_pw_qpolynomial> and
3667 C<isl_printer_print_pw_qpolynomial_fold>,
3668 the output format of the printer
3669 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3670 For C<isl_printer_print_union_pw_qpolynomial> and
3671 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
3673 In case of printing in C<ISL_FORMAT_C>, the user may want
3674 to set the names of all dimensions first.
3676 C<isl> also provides limited support for printing YAML documents,
3677 just enough for the internal use for printing such documents.
3679 #include <isl/printer.h>
3680 __isl_give isl_printer *isl_printer_yaml_start_mapping(
3681 __isl_take isl_printer *p);
3682 __isl_give isl_printer *isl_printer_yaml_end_mapping(
3683 __isl_take isl_printer *p);
3684 __isl_give isl_printer *isl_printer_yaml_start_sequence(
3685 __isl_take isl_printer *p);
3686 __isl_give isl_printer *isl_printer_yaml_end_sequence(
3687 __isl_take isl_printer *p);
3688 __isl_give isl_printer *isl_printer_yaml_next(
3689 __isl_take isl_printer *p);
3691 A document is started by a call to either
3692 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3693 Anything printed to the printer after such a call belong to the
3694 first key of the mapping or the first element in the sequence.
3695 The function C<isl_printer_yaml_next> moves to the value if
3696 we are currently printing a mapping key, the next key if we
3697 are printing a value or the next element if we are printing
3698 an element in a sequence.
3699 Nested mappings and sequences are initiated by the same
3700 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3701 Each call to these functions needs to have a corresponding call to
3702 C<isl_printer_yaml_end_mapping> or C<isl_printer_yaml_end_sequence>.
3704 When called on a file printer, the following function flushes
3705 the file. When called on a string printer, the buffer is cleared.
3707 __isl_give isl_printer *isl_printer_flush(
3708 __isl_take isl_printer *p);
3710 The following functions allow the user to attach
3711 notes to a printer in order to keep track of additional state.
3713 #include <isl/printer.h>
3714 isl_bool isl_printer_has_note(__isl_keep isl_printer *p,
3715 __isl_keep isl_id *id);
3716 __isl_give isl_id *isl_printer_get_note(
3717 __isl_keep isl_printer *p, __isl_take isl_id *id);
3718 __isl_give isl_printer *isl_printer_set_note(
3719 __isl_take isl_printer *p,
3720 __isl_take isl_id *id, __isl_take isl_id *note);
3722 C<isl_printer_set_note> associates the given note to the given
3723 identifier in the printer.
3724 C<isl_printer_get_note> retrieves a note associated to an
3726 C<isl_printer_has_note> checks if there is such a note.
3727 C<isl_printer_get_note> fails if the requested note does not exist.
3729 Alternatively, a string representation can be obtained
3730 directly using the following functions, which always print
3734 __isl_give char *isl_id_to_str(
3735 __isl_keep isl_id *id);
3737 #include <isl/space.h>
3738 __isl_give char *isl_space_to_str(
3739 __isl_keep isl_space *space);
3741 #include <isl/val.h>
3742 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
3743 __isl_give char *isl_multi_val_to_str(
3744 __isl_keep isl_multi_val *mv);
3746 #include <isl/set.h>
3747 __isl_give char *isl_basic_set_to_str(
3748 __isl_keep isl_basic_set *bset);
3749 __isl_give char *isl_set_to_str(
3750 __isl_keep isl_set *set);
3752 #include <isl/union_set.h>
3753 __isl_give char *isl_union_set_to_str(
3754 __isl_keep isl_union_set *uset);
3756 #include <isl/map.h>
3757 __isl_give char *isl_basic_map_to_str(
3758 __isl_keep isl_basic_map *bmap);
3759 __isl_give char *isl_map_to_str(
3760 __isl_keep isl_map *map);
3762 #include <isl/union_map.h>
3763 __isl_give char *isl_union_map_to_str(
3764 __isl_keep isl_union_map *umap);
3766 #include <isl/aff.h>
3767 __isl_give char *isl_aff_to_str(__isl_keep isl_aff *aff);
3768 __isl_give char *isl_pw_aff_to_str(
3769 __isl_keep isl_pw_aff *pa);
3770 __isl_give char *isl_multi_aff_to_str(
3771 __isl_keep isl_multi_aff *ma);
3772 __isl_give char *isl_pw_multi_aff_to_str(
3773 __isl_keep isl_pw_multi_aff *pma);
3774 __isl_give char *isl_multi_pw_aff_to_str(
3775 __isl_keep isl_multi_pw_aff *mpa);
3776 __isl_give char *isl_union_pw_aff_to_str(
3777 __isl_keep isl_union_pw_aff *upa);
3778 __isl_give char *isl_union_pw_multi_aff_to_str(
3779 __isl_keep isl_union_pw_multi_aff *upma);
3780 __isl_give char *isl_multi_union_pw_aff_to_str(
3781 __isl_keep isl_multi_union_pw_aff *mupa);
3783 #include <isl/point.h>
3784 __isl_give char *isl_point_to_str(
3785 __isl_keep isl_point *pnt);
3787 #include <isl/polynomial.h>
3788 __isl_give char *isl_pw_qpolynomial_to_str(
3789 __isl_keep isl_pw_qpolynomial *pwqp);
3790 __isl_give char *isl_union_pw_qpolynomial_to_str(
3791 __isl_keep isl_union_pw_qpolynomial *upwqp);
3795 =head3 Unary Properties
3801 The following functions test whether the given set or relation
3802 contains any integer points. The ``plain'' variants do not perform
3803 any computations, but simply check if the given set or relation
3804 is already known to be empty.
3806 #include <isl/set.h>
3807 isl_bool isl_basic_set_plain_is_empty(
3808 __isl_keep isl_basic_set *bset);
3809 isl_bool isl_basic_set_is_empty(
3810 __isl_keep isl_basic_set *bset);
3811 isl_bool isl_set_plain_is_empty(
3812 __isl_keep isl_set *set);
3813 isl_bool isl_set_is_empty(__isl_keep isl_set *set);
3815 #include <isl/union_set.h>
3816 isl_bool isl_union_set_is_empty(
3817 __isl_keep isl_union_set *uset);
3819 #include <isl/map.h>
3820 isl_bool isl_basic_map_plain_is_empty(
3821 __isl_keep isl_basic_map *bmap);
3822 isl_bool isl_basic_map_is_empty(
3823 __isl_keep isl_basic_map *bmap);
3824 isl_bool isl_map_plain_is_empty(
3825 __isl_keep isl_map *map);
3826 isl_bool isl_map_is_empty(__isl_keep isl_map *map);
3828 #include <isl/union_map.h>
3829 isl_bool isl_union_map_plain_is_empty(
3830 __isl_keep isl_union_map *umap);
3831 isl_bool isl_union_map_is_empty(
3832 __isl_keep isl_union_map *umap);
3834 =item * Universality
3836 isl_bool isl_basic_set_plain_is_universe(
3837 __isl_keep isl_basic_set *bset);
3838 isl_bool isl_basic_set_is_universe(
3839 __isl_keep isl_basic_set *bset);
3840 isl_bool isl_basic_map_plain_is_universe(
3841 __isl_keep isl_basic_map *bmap);
3842 isl_bool isl_basic_map_is_universe(
3843 __isl_keep isl_basic_map *bmap);
3844 isl_bool isl_set_plain_is_universe(
3845 __isl_keep isl_set *set);
3846 isl_bool isl_map_plain_is_universe(
3847 __isl_keep isl_map *map);
3849 =item * Single-valuedness
3851 #include <isl/set.h>
3852 isl_bool isl_set_is_singleton(__isl_keep isl_set *set);
3854 #include <isl/map.h>
3855 isl_bool isl_basic_map_is_single_valued(
3856 __isl_keep isl_basic_map *bmap);
3857 isl_bool isl_map_plain_is_single_valued(
3858 __isl_keep isl_map *map);
3859 isl_bool isl_map_is_single_valued(__isl_keep isl_map *map);
3861 #include <isl/union_map.h>
3862 isl_bool isl_union_map_is_single_valued(
3863 __isl_keep isl_union_map *umap);
3867 isl_bool isl_map_plain_is_injective(
3868 __isl_keep isl_map *map);
3869 isl_bool isl_map_is_injective(
3870 __isl_keep isl_map *map);
3871 isl_bool isl_union_map_plain_is_injective(
3872 __isl_keep isl_union_map *umap);
3873 isl_bool isl_union_map_is_injective(
3874 __isl_keep isl_union_map *umap);
3878 isl_bool isl_map_is_bijective(
3879 __isl_keep isl_map *map);
3880 isl_bool isl_union_map_is_bijective(
3881 __isl_keep isl_union_map *umap);
3885 The following functions test whether the given relation
3886 only maps elements to themselves.
3888 #include <isl/map.h>
3889 isl_bool isl_map_is_identity(
3890 __isl_keep isl_map *map);
3892 #include <isl/union_map.h>
3893 isl_bool isl_union_map_is_identity(
3894 __isl_keep isl_union_map *umap);
3898 __isl_give isl_val *
3899 isl_basic_map_plain_get_val_if_fixed(
3900 __isl_keep isl_basic_map *bmap,
3901 enum isl_dim_type type, unsigned pos);
3902 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
3903 __isl_keep isl_set *set,
3904 enum isl_dim_type type, unsigned pos);
3905 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
3906 __isl_keep isl_map *map,
3907 enum isl_dim_type type, unsigned pos);
3909 If the set or relation obviously lies on a hyperplane where the given dimension
3910 has a fixed value, then return that value.
3911 Otherwise return NaN.
3915 isl_stat isl_set_dim_residue_class_val(
3916 __isl_keep isl_set *set,
3917 int pos, __isl_give isl_val **modulo,
3918 __isl_give isl_val **residue);
3920 Check if the values of the given set dimension are equal to a fixed
3921 value modulo some integer value. If so, assign the modulo to C<*modulo>
3922 and the fixed value to C<*residue>. If the given dimension attains only
3923 a single value, then assign C<0> to C<*modulo> and the fixed value to
3925 If the dimension does not attain only a single value and if no modulo
3926 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
3928 #include <isl/set.h>
3929 __isl_give isl_stride_info *isl_set_get_stride_info(
3930 __isl_keep isl_set *set, int pos);
3931 __isl_give isl_val *isl_set_get_stride(
3932 __isl_keep isl_set *set, int pos);
3934 Check if the values of the given set dimension are equal to
3935 some affine expression of the other dimensions (the offset)
3936 modulo some integer stride.
3937 If no more specific information can be found, then the stride
3938 is taken to be one and the offset is taken to be the zero expression.
3939 The function C<isl_set_get_stride_info> performs the same
3940 computation but only returns the stride.
3942 the stride and offset can be extracted from the returned object
3943 using the following functions.
3945 #include <isl/set.h>
3946 __isl_give isl_val *isl_stride_info_get_stride(
3947 __isl_keep isl_stride_info *si);
3948 __isl_give isl_aff *isl_stride_info_get_offset(
3949 __isl_keep isl_stride_info *si);
3951 The stride info object can be released using the following function.
3953 #include <isl/set.h>
3954 __isl_null isl_stride_info *isl_stride_info_free(
3955 __isl_take isl_stride_info *si);
3959 To check whether the description of a set, relation or function depends
3960 on one or more given dimensions,
3961 the following functions can be used.
3963 #include <isl/constraint.h>
3964 isl_bool isl_constraint_involves_dims(
3965 __isl_keep isl_constraint *constraint,
3966 enum isl_dim_type type, unsigned first, unsigned n);
3968 #include <isl/set.h>
3969 isl_bool isl_basic_set_involves_dims(
3970 __isl_keep isl_basic_set *bset,
3971 enum isl_dim_type type, unsigned first, unsigned n);
3972 isl_bool isl_set_involves_dims(__isl_keep isl_set *set,
3973 enum isl_dim_type type, unsigned first, unsigned n);
3975 #include <isl/map.h>
3976 isl_bool isl_basic_map_involves_dims(
3977 __isl_keep isl_basic_map *bmap,
3978 enum isl_dim_type type, unsigned first, unsigned n);
3979 isl_bool isl_map_involves_dims(__isl_keep isl_map *map,
3980 enum isl_dim_type type, unsigned first, unsigned n);
3982 #include <isl/union_map.h>
3983 isl_bool isl_union_map_involves_dims(
3984 __isl_keep isl_union_map *umap,
3985 enum isl_dim_type type, unsigned first, unsigned n);
3987 #include <isl/aff.h>
3988 isl_bool isl_aff_involves_dims(__isl_keep isl_aff *aff,
3989 enum isl_dim_type type, unsigned first, unsigned n);
3990 isl_bool isl_pw_aff_involves_dims(
3991 __isl_keep isl_pw_aff *pwaff,
3992 enum isl_dim_type type, unsigned first, unsigned n);
3993 isl_bool isl_multi_aff_involves_dims(
3994 __isl_keep isl_multi_aff *ma,
3995 enum isl_dim_type type, unsigned first, unsigned n);
3996 isl_bool isl_multi_pw_aff_involves_dims(
3997 __isl_keep isl_multi_pw_aff *mpa,
3998 enum isl_dim_type type, unsigned first, unsigned n);
4000 #include <isl/polynomial.h>
4001 isl_bool isl_qpolynomial_involves_dims(
4002 __isl_keep isl_qpolynomial *qp,
4003 enum isl_dim_type type, unsigned first, unsigned n);
4005 Similarly, the following functions can be used to check whether
4006 a given dimension is involved in any lower or upper bound.
4008 #include <isl/set.h>
4009 isl_bool isl_set_dim_has_any_lower_bound(
4010 __isl_keep isl_set *set,
4011 enum isl_dim_type type, unsigned pos);
4012 isl_bool isl_set_dim_has_any_upper_bound(
4013 __isl_keep isl_set *set,
4014 enum isl_dim_type type, unsigned pos);
4016 Note that these functions return true even if there is a bound on
4017 the dimension on only some of the basic sets of C<set>.
4018 To check if they have a bound for all of the basic sets in C<set>,
4019 use the following functions instead.
4021 #include <isl/set.h>
4022 isl_bool isl_set_dim_has_lower_bound(
4023 __isl_keep isl_set *set,
4024 enum isl_dim_type type, unsigned pos);
4025 isl_bool isl_set_dim_has_upper_bound(
4026 __isl_keep isl_set *set,
4027 enum isl_dim_type type, unsigned pos);
4031 To check whether a set is a parameter domain, use this function:
4033 isl_bool isl_set_is_params(__isl_keep isl_set *set);
4034 isl_bool isl_union_set_is_params(
4035 __isl_keep isl_union_set *uset);
4039 The following functions check whether the space of the given
4040 (basic) set or relation domain and/or range is a wrapped relation.
4042 #include <isl/space.h>
4043 isl_bool isl_space_is_wrapping(
4044 __isl_keep isl_space *space);
4045 isl_bool isl_space_domain_is_wrapping(
4046 __isl_keep isl_space *space);
4047 isl_bool isl_space_range_is_wrapping(
4048 __isl_keep isl_space *space);
4049 isl_bool isl_space_is_product(
4050 __isl_keep isl_space *space);
4052 #include <isl/set.h>
4053 isl_bool isl_basic_set_is_wrapping(
4054 __isl_keep isl_basic_set *bset);
4055 isl_bool isl_set_is_wrapping(__isl_keep isl_set *set);
4057 #include <isl/map.h>
4058 isl_bool isl_map_domain_is_wrapping(
4059 __isl_keep isl_map *map);
4060 isl_bool isl_map_range_is_wrapping(
4061 __isl_keep isl_map *map);
4062 isl_bool isl_map_is_product(__isl_keep isl_map *map);
4064 #include <isl/val.h>
4065 isl_bool isl_multi_val_range_is_wrapping(
4066 __isl_keep isl_multi_val *mv);
4068 #include <isl/aff.h>
4069 isl_bool isl_multi_aff_range_is_wrapping(
4070 __isl_keep isl_multi_aff *ma);
4071 isl_bool isl_multi_pw_aff_range_is_wrapping(
4072 __isl_keep isl_multi_pw_aff *mpa);
4073 isl_bool isl_multi_union_pw_aff_range_is_wrapping(
4074 __isl_keep isl_multi_union_pw_aff *mupa);
4076 The input to C<isl_space_is_wrapping> should
4077 be the space of a set, while that of
4078 C<isl_space_domain_is_wrapping> and
4079 C<isl_space_range_is_wrapping> should be the space of a relation.
4080 The input to C<isl_space_is_product> can be either the space
4081 of a set or that of a binary relation.
4082 In case the input is the space of a binary relation, it checks
4083 whether both domain and range are wrapping.
4085 =item * Internal Product
4087 isl_bool isl_basic_map_can_zip(
4088 __isl_keep isl_basic_map *bmap);
4089 isl_bool isl_map_can_zip(__isl_keep isl_map *map);
4091 Check whether the product of domain and range of the given relation
4093 i.e., whether both domain and range are nested relations.
4097 #include <isl/space.h>
4098 isl_bool isl_space_can_curry(
4099 __isl_keep isl_space *space);
4101 #include <isl/map.h>
4102 isl_bool isl_basic_map_can_curry(
4103 __isl_keep isl_basic_map *bmap);
4104 isl_bool isl_map_can_curry(__isl_keep isl_map *map);
4106 Check whether the domain of the (basic) relation is a wrapped relation.
4108 #include <isl/space.h>
4109 __isl_give isl_space *isl_space_uncurry(
4110 __isl_take isl_space *space);
4112 #include <isl/map.h>
4113 isl_bool isl_basic_map_can_uncurry(
4114 __isl_keep isl_basic_map *bmap);
4115 isl_bool isl_map_can_uncurry(__isl_keep isl_map *map);
4117 Check whether the range of the (basic) relation is a wrapped relation.
4119 #include <isl/space.h>
4120 isl_bool isl_space_can_range_curry(
4121 __isl_keep isl_space *space);
4123 #include <isl/map.h>
4124 isl_bool isl_map_can_range_curry(
4125 __isl_keep isl_map *map);
4127 Check whether the domain of the relation wrapped in the range of
4128 the input is itself a wrapped relation.
4130 =item * Special Values
4132 #include <isl/aff.h>
4133 isl_bool isl_aff_is_cst(__isl_keep isl_aff *aff);
4134 isl_bool isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
4135 isl_bool isl_multi_pw_aff_is_cst(
4136 __isl_keep isl_multi_pw_aff *mpa);
4138 Check whether the given expression is a constant.
4140 #include <isl/val.h>
4141 isl_bool isl_multi_val_involves_nan(
4142 __isl_keep isl_multi_val *mv);
4144 #include <isl/aff.h>
4145 isl_bool isl_aff_is_nan(__isl_keep isl_aff *aff);
4146 isl_bool isl_multi_aff_involves_nan(
4147 __isl_keep isl_multi_aff *ma);
4148 isl_bool isl_pw_aff_involves_nan(
4149 __isl_keep isl_pw_aff *pa);
4150 isl_bool isl_pw_multi_aff_involves_nan(
4151 __isl_keep isl_pw_multi_aff *pma);
4152 isl_bool isl_multi_pw_aff_involves_nan(
4153 __isl_keep isl_multi_pw_aff *mpa);
4154 isl_bool isl_union_pw_aff_involves_nan(
4155 __isl_keep isl_union_pw_aff *upa);
4156 isl_bool isl_union_pw_multi_aff_involves_nan(
4157 __isl_keep isl_union_pw_multi_aff *upma);
4158 isl_bool isl_multi_union_pw_aff_involves_nan(
4159 __isl_keep isl_multi_union_pw_aff *mupa);
4161 #include <isl/polynomial.h>
4162 isl_bool isl_qpolynomial_is_nan(
4163 __isl_keep isl_qpolynomial *qp);
4164 isl_bool isl_qpolynomial_fold_is_nan(
4165 __isl_keep isl_qpolynomial_fold *fold);
4166 isl_bool isl_pw_qpolynomial_involves_nan(
4167 __isl_keep isl_pw_qpolynomial *pwqp);
4168 isl_bool isl_pw_qpolynomial_fold_involves_nan(
4169 __isl_keep isl_pw_qpolynomial_fold *pwf);
4170 isl_bool isl_union_pw_qpolynomial_involves_nan(
4171 __isl_keep isl_union_pw_qpolynomial *upwqp);
4172 isl_bool isl_union_pw_qpolynomial_fold_involves_nan(
4173 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4175 Check whether the given expression is equal to or involves NaN.
4177 #include <isl/aff.h>
4178 isl_bool isl_aff_plain_is_zero(
4179 __isl_keep isl_aff *aff);
4181 Check whether the affine expression is obviously zero.
4185 =head3 Binary Properties
4191 The following functions check whether two objects
4192 represent the same set, relation or function.
4193 The C<plain> variants only return true if the objects
4194 are obviously the same. That is, they may return false
4195 even if the objects are the same, but they will never
4196 return true if the objects are not the same.
4198 #include <isl/set.h>
4199 isl_bool isl_basic_set_plain_is_equal(
4200 __isl_keep isl_basic_set *bset1,
4201 __isl_keep isl_basic_set *bset2);
4202 isl_bool isl_basic_set_is_equal(
4203 __isl_keep isl_basic_set *bset1,
4204 __isl_keep isl_basic_set *bset2);
4205 isl_bool isl_set_plain_is_equal(
4206 __isl_keep isl_set *set1,
4207 __isl_keep isl_set *set2);
4208 isl_bool isl_set_is_equal(__isl_keep isl_set *set1,
4209 __isl_keep isl_set *set2);
4211 #include <isl/map.h>
4212 isl_bool isl_basic_map_is_equal(
4213 __isl_keep isl_basic_map *bmap1,
4214 __isl_keep isl_basic_map *bmap2);
4215 isl_bool isl_map_is_equal(__isl_keep isl_map *map1,
4216 __isl_keep isl_map *map2);
4217 isl_bool isl_map_plain_is_equal(
4218 __isl_keep isl_map *map1,
4219 __isl_keep isl_map *map2);
4221 #include <isl/union_set.h>
4222 isl_bool isl_union_set_is_equal(
4223 __isl_keep isl_union_set *uset1,
4224 __isl_keep isl_union_set *uset2);
4226 #include <isl/union_map.h>
4227 isl_bool isl_union_map_is_equal(
4228 __isl_keep isl_union_map *umap1,
4229 __isl_keep isl_union_map *umap2);
4231 #include <isl/aff.h>
4232 isl_bool isl_aff_plain_is_equal(
4233 __isl_keep isl_aff *aff1,
4234 __isl_keep isl_aff *aff2);
4235 isl_bool isl_multi_aff_plain_is_equal(
4236 __isl_keep isl_multi_aff *maff1,
4237 __isl_keep isl_multi_aff *maff2);
4238 isl_bool isl_pw_aff_plain_is_equal(
4239 __isl_keep isl_pw_aff *pwaff1,
4240 __isl_keep isl_pw_aff *pwaff2);
4241 isl_bool isl_pw_aff_is_equal(
4242 __isl_keep isl_pw_aff *pa1,
4243 __isl_keep isl_pw_aff *pa2);
4244 isl_bool isl_pw_multi_aff_plain_is_equal(
4245 __isl_keep isl_pw_multi_aff *pma1,
4246 __isl_keep isl_pw_multi_aff *pma2);
4247 isl_bool isl_pw_multi_aff_is_equal(
4248 __isl_keep isl_pw_multi_aff *pma1,
4249 __isl_keep isl_pw_multi_aff *pma2);
4250 isl_bool isl_multi_pw_aff_plain_is_equal(
4251 __isl_keep isl_multi_pw_aff *mpa1,
4252 __isl_keep isl_multi_pw_aff *mpa2);
4253 isl_bool isl_multi_pw_aff_is_equal(
4254 __isl_keep isl_multi_pw_aff *mpa1,
4255 __isl_keep isl_multi_pw_aff *mpa2);
4256 isl_bool isl_union_pw_aff_plain_is_equal(
4257 __isl_keep isl_union_pw_aff *upa1,
4258 __isl_keep isl_union_pw_aff *upa2);
4259 isl_bool isl_union_pw_multi_aff_plain_is_equal(
4260 __isl_keep isl_union_pw_multi_aff *upma1,
4261 __isl_keep isl_union_pw_multi_aff *upma2);
4262 isl_bool isl_multi_union_pw_aff_plain_is_equal(
4263 __isl_keep isl_multi_union_pw_aff *mupa1,
4264 __isl_keep isl_multi_union_pw_aff *mupa2);
4266 #include <isl/polynomial.h>
4267 isl_bool isl_union_pw_qpolynomial_plain_is_equal(
4268 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4269 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4270 isl_bool isl_union_pw_qpolynomial_fold_plain_is_equal(
4271 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4272 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4274 =item * Disjointness
4276 #include <isl/set.h>
4277 isl_bool isl_basic_set_is_disjoint(
4278 __isl_keep isl_basic_set *bset1,
4279 __isl_keep isl_basic_set *bset2);
4280 isl_bool isl_set_plain_is_disjoint(
4281 __isl_keep isl_set *set1,
4282 __isl_keep isl_set *set2);
4283 isl_bool isl_set_is_disjoint(__isl_keep isl_set *set1,
4284 __isl_keep isl_set *set2);
4286 #include <isl/map.h>
4287 isl_bool isl_basic_map_is_disjoint(
4288 __isl_keep isl_basic_map *bmap1,
4289 __isl_keep isl_basic_map *bmap2);
4290 isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1,
4291 __isl_keep isl_map *map2);
4293 #include <isl/union_set.h>
4294 isl_bool isl_union_set_is_disjoint(
4295 __isl_keep isl_union_set *uset1,
4296 __isl_keep isl_union_set *uset2);
4298 #include <isl/union_map.h>
4299 isl_bool isl_union_map_is_disjoint(
4300 __isl_keep isl_union_map *umap1,
4301 __isl_keep isl_union_map *umap2);
4305 isl_bool isl_basic_set_is_subset(
4306 __isl_keep isl_basic_set *bset1,
4307 __isl_keep isl_basic_set *bset2);
4308 isl_bool isl_set_is_subset(__isl_keep isl_set *set1,
4309 __isl_keep isl_set *set2);
4310 isl_bool isl_set_is_strict_subset(
4311 __isl_keep isl_set *set1,
4312 __isl_keep isl_set *set2);
4313 isl_bool isl_union_set_is_subset(
4314 __isl_keep isl_union_set *uset1,
4315 __isl_keep isl_union_set *uset2);
4316 isl_bool isl_union_set_is_strict_subset(
4317 __isl_keep isl_union_set *uset1,
4318 __isl_keep isl_union_set *uset2);
4319 isl_bool isl_basic_map_is_subset(
4320 __isl_keep isl_basic_map *bmap1,
4321 __isl_keep isl_basic_map *bmap2);
4322 isl_bool isl_basic_map_is_strict_subset(
4323 __isl_keep isl_basic_map *bmap1,
4324 __isl_keep isl_basic_map *bmap2);
4325 isl_bool isl_map_is_subset(
4326 __isl_keep isl_map *map1,
4327 __isl_keep isl_map *map2);
4328 isl_bool isl_map_is_strict_subset(
4329 __isl_keep isl_map *map1,
4330 __isl_keep isl_map *map2);
4331 isl_bool isl_union_map_is_subset(
4332 __isl_keep isl_union_map *umap1,
4333 __isl_keep isl_union_map *umap2);
4334 isl_bool isl_union_map_is_strict_subset(
4335 __isl_keep isl_union_map *umap1,
4336 __isl_keep isl_union_map *umap2);
4338 Check whether the first argument is a (strict) subset of the
4343 Every comparison function returns a negative value if the first
4344 argument is considered smaller than the second, a positive value
4345 if the first argument is considered greater and zero if the two
4346 constraints are considered the same by the comparison criterion.
4348 #include <isl/constraint.h>
4349 int isl_constraint_plain_cmp(
4350 __isl_keep isl_constraint *c1,
4351 __isl_keep isl_constraint *c2);
4353 This function is useful for sorting C<isl_constraint>s.
4354 The order depends on the internal representation of the inputs.
4355 The order is fixed over different calls to the function (assuming
4356 the internal representation of the inputs has not changed), but may
4357 change over different versions of C<isl>.
4359 #include <isl/constraint.h>
4360 int isl_constraint_cmp_last_non_zero(
4361 __isl_keep isl_constraint *c1,
4362 __isl_keep isl_constraint *c2);
4364 This function can be used to sort constraints that live in the same
4365 local space. Constraints that involve ``earlier'' dimensions or
4366 that have a smaller coefficient for the shared latest dimension
4367 are considered smaller than other constraints.
4368 This function only defines a B<partial> order.
4370 #include <isl/set.h>
4371 int isl_set_plain_cmp(__isl_keep isl_set *set1,
4372 __isl_keep isl_set *set2);
4374 This function is useful for sorting C<isl_set>s.
4375 The order depends on the internal representation of the inputs.
4376 The order is fixed over different calls to the function (assuming
4377 the internal representation of the inputs has not changed), but may
4378 change over different versions of C<isl>.
4380 #include <isl/aff.h>
4381 int isl_multi_aff_plain_cmp(
4382 __isl_keep isl_multi_aff *ma1,
4383 __isl_keep isl_multi_aff *ma2);
4384 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4385 __isl_keep isl_pw_aff *pa2);
4387 The functions C<isl_multi_aff_plain_cmp> and
4388 C<isl_pw_aff_plain_cmp> can be used to sort C<isl_multi_aff>s and
4389 C<isl_pw_aff>s. The order is not strictly defined.
4390 The current order sorts expressions that only involve
4391 earlier dimensions before those that involve later dimensions.
4395 =head2 Unary Operations
4401 __isl_give isl_set *isl_set_complement(
4402 __isl_take isl_set *set);
4403 __isl_give isl_map *isl_map_complement(
4404 __isl_take isl_map *map);
4408 #include <isl/space.h>
4409 __isl_give isl_space *isl_space_reverse(
4410 __isl_take isl_space *space);
4412 #include <isl/map.h>
4413 __isl_give isl_basic_map *isl_basic_map_reverse(
4414 __isl_take isl_basic_map *bmap);
4415 __isl_give isl_map *isl_map_reverse(
4416 __isl_take isl_map *map);
4418 #include <isl/union_map.h>
4419 __isl_give isl_union_map *isl_union_map_reverse(
4420 __isl_take isl_union_map *umap);
4424 #include <isl/space.h>
4425 __isl_give isl_space *isl_space_domain(
4426 __isl_take isl_space *space);
4427 __isl_give isl_space *isl_space_range(
4428 __isl_take isl_space *space);
4429 __isl_give isl_space *isl_space_params(
4430 __isl_take isl_space *space);
4432 #include <isl/local_space.h>
4433 __isl_give isl_local_space *isl_local_space_domain(
4434 __isl_take isl_local_space *ls);
4435 __isl_give isl_local_space *isl_local_space_range(
4436 __isl_take isl_local_space *ls);
4438 #include <isl/set.h>
4439 __isl_give isl_basic_set *isl_basic_set_project_out(
4440 __isl_take isl_basic_set *bset,
4441 enum isl_dim_type type, unsigned first, unsigned n);
4442 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
4443 enum isl_dim_type type, unsigned first, unsigned n);
4444 __isl_give isl_map *isl_set_project_onto_map(
4445 __isl_take isl_set *set,
4446 enum isl_dim_type type, unsigned first,
4448 __isl_give isl_basic_set *isl_basic_set_params(
4449 __isl_take isl_basic_set *bset);
4450 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
4452 The function C<isl_set_project_onto_map> returns a relation
4453 that projects the input set onto the given set dimensions.
4455 #include <isl/map.h>
4456 __isl_give isl_basic_map *isl_basic_map_project_out(
4457 __isl_take isl_basic_map *bmap,
4458 enum isl_dim_type type, unsigned first, unsigned n);
4459 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
4460 enum isl_dim_type type, unsigned first, unsigned n);
4461 __isl_give isl_basic_set *isl_basic_map_domain(
4462 __isl_take isl_basic_map *bmap);
4463 __isl_give isl_basic_set *isl_basic_map_range(
4464 __isl_take isl_basic_map *bmap);
4465 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
4466 __isl_give isl_set *isl_map_domain(
4467 __isl_take isl_map *bmap);
4468 __isl_give isl_set *isl_map_range(
4469 __isl_take isl_map *map);
4471 #include <isl/union_set.h>
4472 __isl_give isl_union_set *isl_union_set_project_out(
4473 __isl_take isl_union_set *uset,
4474 enum isl_dim_type type,
4475 unsigned first, unsigned n);
4476 __isl_give isl_set *isl_union_set_params(
4477 __isl_take isl_union_set *uset);
4479 The function C<isl_union_set_project_out> can only project out
4482 #include <isl/union_map.h>
4483 __isl_give isl_union_map *isl_union_map_project_out(
4484 __isl_take isl_union_map *umap,
4485 enum isl_dim_type type, unsigned first, unsigned n);
4486 __isl_give isl_union_map *
4487 isl_union_map_project_out_all_params(
4488 __isl_take isl_union_map *umap);
4489 __isl_give isl_set *isl_union_map_params(
4490 __isl_take isl_union_map *umap);
4491 __isl_give isl_union_set *isl_union_map_domain(
4492 __isl_take isl_union_map *umap);
4493 __isl_give isl_union_set *isl_union_map_range(
4494 __isl_take isl_union_map *umap);
4496 The function C<isl_union_map_project_out> can only project out
4499 #include <isl/aff.h>
4500 __isl_give isl_aff *isl_aff_project_domain_on_params(
4501 __isl_take isl_aff *aff);
4502 __isl_give isl_multi_aff *
4503 isl_multi_aff_project_domain_on_params(
4504 __isl_take isl_multi_aff *ma);
4505 __isl_give isl_pw_aff *
4506 isl_pw_aff_project_domain_on_params(
4507 __isl_take isl_pw_aff *pa);
4508 __isl_give isl_multi_pw_aff *
4509 isl_multi_pw_aff_project_domain_on_params(
4510 __isl_take isl_multi_pw_aff *mpa);
4511 __isl_give isl_pw_multi_aff *
4512 isl_pw_multi_aff_project_domain_on_params(
4513 __isl_take isl_pw_multi_aff *pma);
4514 __isl_give isl_set *isl_pw_aff_domain(
4515 __isl_take isl_pw_aff *pwaff);
4516 __isl_give isl_set *isl_pw_multi_aff_domain(
4517 __isl_take isl_pw_multi_aff *pma);
4518 __isl_give isl_set *isl_multi_pw_aff_domain(
4519 __isl_take isl_multi_pw_aff *mpa);
4520 __isl_give isl_union_set *isl_union_pw_aff_domain(
4521 __isl_take isl_union_pw_aff *upa);
4522 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4523 __isl_take isl_union_pw_multi_aff *upma);
4524 __isl_give isl_union_set *
4525 isl_multi_union_pw_aff_domain(
4526 __isl_take isl_multi_union_pw_aff *mupa);
4527 __isl_give isl_set *isl_pw_aff_params(
4528 __isl_take isl_pw_aff *pwa);
4530 The function C<isl_multi_union_pw_aff_domain> requires its
4531 input to have at least one set dimension.
4533 #include <isl/polynomial.h>
4534 __isl_give isl_qpolynomial *
4535 isl_qpolynomial_project_domain_on_params(
4536 __isl_take isl_qpolynomial *qp);
4537 __isl_give isl_pw_qpolynomial *
4538 isl_pw_qpolynomial_project_domain_on_params(
4539 __isl_take isl_pw_qpolynomial *pwqp);
4540 __isl_give isl_pw_qpolynomial_fold *
4541 isl_pw_qpolynomial_fold_project_domain_on_params(
4542 __isl_take isl_pw_qpolynomial_fold *pwf);
4543 __isl_give isl_set *isl_pw_qpolynomial_domain(
4544 __isl_take isl_pw_qpolynomial *pwqp);
4545 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4546 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4547 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4548 __isl_take isl_union_pw_qpolynomial *upwqp);
4550 #include <isl/space.h>
4551 __isl_give isl_space *isl_space_domain_map(
4552 __isl_take isl_space *space);
4553 __isl_give isl_space *isl_space_range_map(
4554 __isl_take isl_space *space);
4556 #include <isl/map.h>
4557 __isl_give isl_map *isl_set_wrapped_domain_map(
4558 __isl_take isl_set *set);
4559 __isl_give isl_basic_map *isl_basic_map_domain_map(
4560 __isl_take isl_basic_map *bmap);
4561 __isl_give isl_basic_map *isl_basic_map_range_map(
4562 __isl_take isl_basic_map *bmap);
4563 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
4564 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
4566 #include <isl/union_map.h>
4567 __isl_give isl_union_map *isl_union_map_domain_map(
4568 __isl_take isl_union_map *umap);
4569 __isl_give isl_union_pw_multi_aff *
4570 isl_union_map_domain_map_union_pw_multi_aff(
4571 __isl_take isl_union_map *umap);
4572 __isl_give isl_union_map *isl_union_map_range_map(
4573 __isl_take isl_union_map *umap);
4574 __isl_give isl_union_map *
4575 isl_union_set_wrapped_domain_map(
4576 __isl_take isl_union_set *uset);
4578 The functions above construct a (basic, regular or union) relation
4579 that maps (a wrapped version of) the input relation to its domain or range.
4580 C<isl_set_wrapped_domain_map> maps the input set to the domain
4581 of its wrapped relation.
4585 __isl_give isl_basic_set *isl_basic_set_eliminate(
4586 __isl_take isl_basic_set *bset,
4587 enum isl_dim_type type,
4588 unsigned first, unsigned n);
4589 __isl_give isl_set *isl_set_eliminate(
4590 __isl_take isl_set *set, enum isl_dim_type type,
4591 unsigned first, unsigned n);
4592 __isl_give isl_basic_map *isl_basic_map_eliminate(
4593 __isl_take isl_basic_map *bmap,
4594 enum isl_dim_type type,
4595 unsigned first, unsigned n);
4596 __isl_give isl_map *isl_map_eliminate(
4597 __isl_take isl_map *map, enum isl_dim_type type,
4598 unsigned first, unsigned n);
4600 Eliminate the coefficients for the given dimensions from the constraints,
4601 without removing the dimensions.
4603 =item * Constructing a set from a parameter domain
4605 A zero-dimensional (local) space or (basic) set can be constructed
4606 on a given parameter domain using the following functions.
4608 #include <isl/space.h>
4609 __isl_give isl_space *isl_space_set_from_params(
4610 __isl_take isl_space *space);
4612 #include <isl/local_space.h>
4613 __isl_give isl_local_space *
4614 isl_local_space_set_from_params(
4615 __isl_take isl_local_space *ls);
4617 #include <isl/set.h>
4618 __isl_give isl_basic_set *isl_basic_set_from_params(
4619 __isl_take isl_basic_set *bset);
4620 __isl_give isl_set *isl_set_from_params(
4621 __isl_take isl_set *set);
4623 =item * Constructing a relation from one or two sets
4625 Create a relation with the given set(s) as domain and/or range.
4626 If only the domain or the range is specified, then
4627 the range or domain of the created relation is a zero-dimensional
4628 flat anonymous space.
4630 #include <isl/space.h>
4631 __isl_give isl_space *isl_space_from_domain(
4632 __isl_take isl_space *space);
4633 __isl_give isl_space *isl_space_from_range(
4634 __isl_take isl_space *space);
4635 __isl_give isl_space *isl_space_map_from_set(
4636 __isl_take isl_space *space);
4637 __isl_give isl_space *isl_space_map_from_domain_and_range(
4638 __isl_take isl_space *domain,
4639 __isl_take isl_space *range);
4641 #include <isl/local_space.h>
4642 __isl_give isl_local_space *isl_local_space_from_domain(
4643 __isl_take isl_local_space *ls);
4645 #include <isl/map.h>
4646 __isl_give isl_map *isl_map_from_domain(
4647 __isl_take isl_set *set);
4648 __isl_give isl_map *isl_map_from_range(
4649 __isl_take isl_set *set);
4651 #include <isl/union_map.h>
4652 __isl_give isl_union_map *isl_union_map_from_domain(
4653 __isl_take isl_union_set *uset);
4654 __isl_give isl_union_map *isl_union_map_from_range(
4655 __isl_take isl_union_set *uset);
4656 __isl_give isl_union_map *
4657 isl_union_map_from_domain_and_range(
4658 __isl_take isl_union_set *domain,
4659 __isl_take isl_union_set *range);
4661 #include <isl/val.h>
4662 __isl_give isl_multi_val *isl_multi_val_from_range(
4663 __isl_take isl_multi_val *mv);
4665 #include <isl/aff.h>
4666 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4667 __isl_take isl_multi_aff *ma);
4668 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4669 __isl_take isl_pw_aff *pwa);
4670 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4671 __isl_take isl_multi_pw_aff *mpa);
4672 __isl_give isl_multi_union_pw_aff *
4673 isl_multi_union_pw_aff_from_range(
4674 __isl_take isl_multi_union_pw_aff *mupa);
4675 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4676 __isl_take isl_set *set);
4677 __isl_give isl_union_pw_multi_aff *
4678 isl_union_pw_multi_aff_from_domain(
4679 __isl_take isl_union_set *uset);
4681 #include <isl/polynomial.h>
4682 __isl_give isl_pw_qpolynomial *
4683 isl_pw_qpolynomial_from_range(
4684 __isl_take isl_pw_qpolynomial *pwqp);
4685 __isl_give isl_pw_qpolynomial_fold *
4686 isl_pw_qpolynomial_fold_from_range(
4687 __isl_take isl_pw_qpolynomial_fold *pwf);
4691 #include <isl/set.h>
4692 __isl_give isl_basic_set *isl_basic_set_fix_si(
4693 __isl_take isl_basic_set *bset,
4694 enum isl_dim_type type, unsigned pos, int value);
4695 __isl_give isl_basic_set *isl_basic_set_fix_val(
4696 __isl_take isl_basic_set *bset,
4697 enum isl_dim_type type, unsigned pos,
4698 __isl_take isl_val *v);
4699 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
4700 enum isl_dim_type type, unsigned pos, int value);
4701 __isl_give isl_set *isl_set_fix_val(
4702 __isl_take isl_set *set,
4703 enum isl_dim_type type, unsigned pos,
4704 __isl_take isl_val *v);
4706 #include <isl/map.h>
4707 __isl_give isl_basic_map *isl_basic_map_fix_si(
4708 __isl_take isl_basic_map *bmap,
4709 enum isl_dim_type type, unsigned pos, int value);
4710 __isl_give isl_basic_map *isl_basic_map_fix_val(
4711 __isl_take isl_basic_map *bmap,
4712 enum isl_dim_type type, unsigned pos,
4713 __isl_take isl_val *v);
4714 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
4715 enum isl_dim_type type, unsigned pos, int value);
4716 __isl_give isl_map *isl_map_fix_val(
4717 __isl_take isl_map *map,
4718 enum isl_dim_type type, unsigned pos,
4719 __isl_take isl_val *v);
4721 #include <isl/aff.h>
4722 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4723 __isl_take isl_pw_multi_aff *pma,
4724 enum isl_dim_type type, unsigned pos, int value);
4726 #include <isl/polynomial.h>
4727 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4728 __isl_take isl_pw_qpolynomial *pwqp,
4729 enum isl_dim_type type, unsigned n,
4730 __isl_take isl_val *v);
4731 __isl_give isl_pw_qpolynomial_fold *
4732 isl_pw_qpolynomial_fold_fix_val(
4733 __isl_take isl_pw_qpolynomial_fold *pwf,
4734 enum isl_dim_type type, unsigned n,
4735 __isl_take isl_val *v);
4737 Intersect the set, relation or function domain
4738 with the hyperplane where the given
4739 dimension has the fixed given value.
4741 #include <isl/set.h>
4742 __isl_give isl_basic_set *
4743 isl_basic_set_lower_bound_val(
4744 __isl_take isl_basic_set *bset,
4745 enum isl_dim_type type, unsigned pos,
4746 __isl_take isl_val *value);
4747 __isl_give isl_basic_set *
4748 isl_basic_set_upper_bound_val(
4749 __isl_take isl_basic_set *bset,
4750 enum isl_dim_type type, unsigned pos,
4751 __isl_take isl_val *value);
4752 __isl_give isl_set *isl_set_lower_bound_si(
4753 __isl_take isl_set *set,
4754 enum isl_dim_type type, unsigned pos, int value);
4755 __isl_give isl_set *isl_set_lower_bound_val(
4756 __isl_take isl_set *set,
4757 enum isl_dim_type type, unsigned pos,
4758 __isl_take isl_val *value);
4759 __isl_give isl_set *isl_set_upper_bound_si(
4760 __isl_take isl_set *set,
4761 enum isl_dim_type type, unsigned pos, int value);
4762 __isl_give isl_set *isl_set_upper_bound_val(
4763 __isl_take isl_set *set,
4764 enum isl_dim_type type, unsigned pos,
4765 __isl_take isl_val *value);
4767 #include <isl/map.h>
4768 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
4769 __isl_take isl_basic_map *bmap,
4770 enum isl_dim_type type, unsigned pos, int value);
4771 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
4772 __isl_take isl_basic_map *bmap,
4773 enum isl_dim_type type, unsigned pos, int value);
4774 __isl_give isl_map *isl_map_lower_bound_si(
4775 __isl_take isl_map *map,
4776 enum isl_dim_type type, unsigned pos, int value);
4777 __isl_give isl_map *isl_map_upper_bound_si(
4778 __isl_take isl_map *map,
4779 enum isl_dim_type type, unsigned pos, int value);
4781 Intersect the set or relation with the half-space where the given
4782 dimension has a value bounded by the fixed given integer value.
4784 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
4785 enum isl_dim_type type1, int pos1,
4786 enum isl_dim_type type2, int pos2);
4787 __isl_give isl_basic_map *isl_basic_map_equate(
4788 __isl_take isl_basic_map *bmap,
4789 enum isl_dim_type type1, int pos1,
4790 enum isl_dim_type type2, int pos2);
4791 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
4792 enum isl_dim_type type1, int pos1,
4793 enum isl_dim_type type2, int pos2);
4795 Intersect the set or relation with the hyperplane where the given
4796 dimensions are equal to each other.
4798 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
4799 enum isl_dim_type type1, int pos1,
4800 enum isl_dim_type type2, int pos2);
4802 Intersect the relation with the hyperplane where the given
4803 dimensions have opposite values.
4805 __isl_give isl_map *isl_map_order_le(
4806 __isl_take isl_map *map,
4807 enum isl_dim_type type1, int pos1,
4808 enum isl_dim_type type2, int pos2);
4809 __isl_give isl_basic_map *isl_basic_map_order_ge(
4810 __isl_take isl_basic_map *bmap,
4811 enum isl_dim_type type1, int pos1,
4812 enum isl_dim_type type2, int pos2);
4813 __isl_give isl_map *isl_map_order_ge(
4814 __isl_take isl_map *map,
4815 enum isl_dim_type type1, int pos1,
4816 enum isl_dim_type type2, int pos2);
4817 __isl_give isl_map *isl_map_order_lt(__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_gt(
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_gt(__isl_take isl_map *map,
4825 enum isl_dim_type type1, int pos1,
4826 enum isl_dim_type type2, int pos2);
4828 Intersect the relation with the half-space where the given
4829 dimensions satisfy the given ordering.
4831 #include <isl/union_set.h>
4832 __isl_give isl_union_map *isl_union_map_remove_map_if(
4833 __isl_take isl_union_map *umap,
4834 isl_bool (*fn)(__isl_keep isl_map *map,
4835 void *user), void *user);
4837 This function calls the callback function once for each
4838 pair of spaces for which there are elements in the input.
4839 If the callback returns C<isl_bool_true>, then all those elements
4840 are removed from the result. The only remaining elements in the output
4841 are then those for which the callback returns C<isl_bool_false>.
4845 #include <isl/aff.h>
4846 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4847 __isl_take isl_aff *aff);
4848 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4849 __isl_take isl_aff *aff);
4850 __isl_give isl_set *isl_pw_aff_pos_set(
4851 __isl_take isl_pw_aff *pa);
4852 __isl_give isl_set *isl_pw_aff_nonneg_set(
4853 __isl_take isl_pw_aff *pwaff);
4854 __isl_give isl_set *isl_pw_aff_zero_set(
4855 __isl_take isl_pw_aff *pwaff);
4856 __isl_give isl_set *isl_pw_aff_non_zero_set(
4857 __isl_take isl_pw_aff *pwaff);
4858 __isl_give isl_union_set *
4859 isl_union_pw_aff_zero_union_set(
4860 __isl_take isl_union_pw_aff *upa);
4861 __isl_give isl_union_set *
4862 isl_multi_union_pw_aff_zero_union_set(
4863 __isl_take isl_multi_union_pw_aff *mupa);
4865 The function C<isl_aff_neg_basic_set> returns a basic set
4866 containing those elements in the domain space
4867 of C<aff> where C<aff> is negative.
4868 The function C<isl_pw_aff_nonneg_set> returns a set
4869 containing those elements in the domain
4870 of C<pwaff> where C<pwaff> is non-negative.
4871 The function C<isl_multi_union_pw_aff_zero_union_set>
4872 returns a union set containing those elements
4873 in the domains of its elements where they are all zero.
4877 __isl_give isl_map *isl_set_identity(
4878 __isl_take isl_set *set);
4879 __isl_give isl_union_map *isl_union_set_identity(
4880 __isl_take isl_union_set *uset);
4881 __isl_give isl_union_pw_multi_aff *
4882 isl_union_set_identity_union_pw_multi_aff(
4883 __isl_take isl_union_set *uset);
4885 Construct an identity relation on the given (union) set.
4887 =item * Function Extraction
4889 A piecewise quasi affine expression that is equal to 1 on a set
4890 and 0 outside the set can be created using the following function.
4892 #include <isl/aff.h>
4893 __isl_give isl_pw_aff *isl_set_indicator_function(
4894 __isl_take isl_set *set);
4896 A piecewise multiple quasi affine expression can be extracted
4897 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4898 and the C<isl_map> is single-valued.
4899 In case of a conversion from an C<isl_union_map>
4900 to an C<isl_union_pw_multi_aff>, these properties need to hold
4901 in each domain space.
4902 A conversion to a C<isl_multi_union_pw_aff> additionally
4903 requires that the input is non-empty and involves only a single
4906 #include <isl/aff.h>
4907 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4908 __isl_take isl_set *set);
4909 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4910 __isl_take isl_map *map);
4912 __isl_give isl_union_pw_multi_aff *
4913 isl_union_pw_multi_aff_from_union_set(
4914 __isl_take isl_union_set *uset);
4915 __isl_give isl_union_pw_multi_aff *
4916 isl_union_pw_multi_aff_from_union_map(
4917 __isl_take isl_union_map *umap);
4919 __isl_give isl_multi_union_pw_aff *
4920 isl_multi_union_pw_aff_from_union_map(
4921 __isl_take isl_union_map *umap);
4925 __isl_give isl_basic_set *isl_basic_map_deltas(
4926 __isl_take isl_basic_map *bmap);
4927 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
4928 __isl_give isl_union_set *isl_union_map_deltas(
4929 __isl_take isl_union_map *umap);
4931 These functions return a (basic) set containing the differences
4932 between image elements and corresponding domain elements in the input.
4934 __isl_give isl_basic_map *isl_basic_map_deltas_map(
4935 __isl_take isl_basic_map *bmap);
4936 __isl_give isl_map *isl_map_deltas_map(
4937 __isl_take isl_map *map);
4938 __isl_give isl_union_map *isl_union_map_deltas_map(
4939 __isl_take isl_union_map *umap);
4941 The functions above construct a (basic, regular or union) relation
4942 that maps (a wrapped version of) the input relation to its delta set.
4946 Simplify the representation of a set, relation or functions by trying
4947 to combine pairs of basic sets or relations into a single
4948 basic set or relation.
4950 #include <isl/set.h>
4951 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
4953 #include <isl/map.h>
4954 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
4956 #include <isl/union_set.h>
4957 __isl_give isl_union_set *isl_union_set_coalesce(
4958 __isl_take isl_union_set *uset);
4960 #include <isl/union_map.h>
4961 __isl_give isl_union_map *isl_union_map_coalesce(
4962 __isl_take isl_union_map *umap);
4964 #include <isl/aff.h>
4965 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4966 __isl_take isl_pw_aff *pwqp);
4967 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4968 __isl_take isl_pw_multi_aff *pma);
4969 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4970 __isl_take isl_multi_pw_aff *mpa);
4971 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
4972 __isl_take isl_union_pw_aff *upa);
4973 __isl_give isl_union_pw_multi_aff *
4974 isl_union_pw_multi_aff_coalesce(
4975 __isl_take isl_union_pw_multi_aff *upma);
4976 __isl_give isl_multi_union_pw_aff *
4977 isl_multi_union_pw_aff_coalesce(
4978 __isl_take isl_multi_union_pw_aff *aff);
4980 #include <isl/polynomial.h>
4981 __isl_give isl_pw_qpolynomial_fold *
4982 isl_pw_qpolynomial_fold_coalesce(
4983 __isl_take isl_pw_qpolynomial_fold *pwf);
4984 __isl_give isl_union_pw_qpolynomial *
4985 isl_union_pw_qpolynomial_coalesce(
4986 __isl_take isl_union_pw_qpolynomial *upwqp);
4987 __isl_give isl_union_pw_qpolynomial_fold *
4988 isl_union_pw_qpolynomial_fold_coalesce(
4989 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4991 One of the methods for combining pairs of basic sets or relations
4992 can result in coefficients that are much larger than those that appear
4993 in the constraints of the input. By default, the coefficients are
4994 not allowed to grow larger, but this can be changed by unsetting
4995 the following option.
4997 isl_stat isl_options_set_coalesce_bounded_wrapping(
4998 isl_ctx *ctx, int val);
4999 int isl_options_get_coalesce_bounded_wrapping(
5002 =item * Detecting equalities
5004 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
5005 __isl_take isl_basic_set *bset);
5006 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
5007 __isl_take isl_basic_map *bmap);
5008 __isl_give isl_set *isl_set_detect_equalities(
5009 __isl_take isl_set *set);
5010 __isl_give isl_map *isl_map_detect_equalities(
5011 __isl_take isl_map *map);
5012 __isl_give isl_union_set *isl_union_set_detect_equalities(
5013 __isl_take isl_union_set *uset);
5014 __isl_give isl_union_map *isl_union_map_detect_equalities(
5015 __isl_take isl_union_map *umap);
5017 Simplify the representation of a set or relation by detecting implicit
5020 =item * Removing redundant constraints
5022 #include <isl/set.h>
5023 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
5024 __isl_take isl_basic_set *bset);
5025 __isl_give isl_set *isl_set_remove_redundancies(
5026 __isl_take isl_set *set);
5028 #include <isl/union_set.h>
5029 __isl_give isl_union_set *
5030 isl_union_set_remove_redundancies(
5031 __isl_take isl_union_set *uset);
5033 #include <isl/map.h>
5034 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
5035 __isl_take isl_basic_map *bmap);
5036 __isl_give isl_map *isl_map_remove_redundancies(
5037 __isl_take isl_map *map);
5039 #include <isl/union_map.h>
5040 __isl_give isl_union_map *
5041 isl_union_map_remove_redundancies(
5042 __isl_take isl_union_map *umap);
5046 __isl_give isl_basic_set *isl_set_convex_hull(
5047 __isl_take isl_set *set);
5048 __isl_give isl_basic_map *isl_map_convex_hull(
5049 __isl_take isl_map *map);
5051 If the input set or relation has any existentially quantified
5052 variables, then the result of these operations is currently undefined.
5056 #include <isl/set.h>
5057 __isl_give isl_basic_set *
5058 isl_set_unshifted_simple_hull(
5059 __isl_take isl_set *set);
5060 __isl_give isl_basic_set *isl_set_simple_hull(
5061 __isl_take isl_set *set);
5062 __isl_give isl_basic_set *
5063 isl_set_plain_unshifted_simple_hull(
5064 __isl_take isl_set *set);
5065 __isl_give isl_basic_set *
5066 isl_set_unshifted_simple_hull_from_set_list(
5067 __isl_take isl_set *set,
5068 __isl_take isl_set_list *list);
5070 #include <isl/map.h>
5071 __isl_give isl_basic_map *
5072 isl_map_unshifted_simple_hull(
5073 __isl_take isl_map *map);
5074 __isl_give isl_basic_map *isl_map_simple_hull(
5075 __isl_take isl_map *map);
5076 __isl_give isl_basic_map *
5077 isl_map_plain_unshifted_simple_hull(
5078 __isl_take isl_map *map);
5079 __isl_give isl_basic_map *
5080 isl_map_unshifted_simple_hull_from_map_list(
5081 __isl_take isl_map *map,
5082 __isl_take isl_map_list *list);
5084 #include <isl/union_map.h>
5085 __isl_give isl_union_map *isl_union_map_simple_hull(
5086 __isl_take isl_union_map *umap);
5088 These functions compute a single basic set or relation
5089 that contains the whole input set or relation.
5090 In particular, the output is described by translates
5091 of the constraints describing the basic sets or relations in the input.
5092 In case of C<isl_set_unshifted_simple_hull>, only the original
5093 constraints are used, without any translation.
5094 In case of C<isl_set_plain_unshifted_simple_hull> and
5095 C<isl_map_plain_unshifted_simple_hull>, the result is described
5096 by original constraints that are obviously satisfied
5097 by the entire input set or relation.
5098 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
5099 C<isl_map_unshifted_simple_hull_from_map_list>, the
5100 constraints are taken from the elements of the second argument.
5104 (See \autoref{s:simple hull}.)
5110 __isl_give isl_basic_set *isl_basic_set_affine_hull(
5111 __isl_take isl_basic_set *bset);
5112 __isl_give isl_basic_set *isl_set_affine_hull(
5113 __isl_take isl_set *set);
5114 __isl_give isl_union_set *isl_union_set_affine_hull(
5115 __isl_take isl_union_set *uset);
5116 __isl_give isl_basic_map *isl_basic_map_affine_hull(
5117 __isl_take isl_basic_map *bmap);
5118 __isl_give isl_basic_map *isl_map_affine_hull(
5119 __isl_take isl_map *map);
5120 __isl_give isl_union_map *isl_union_map_affine_hull(
5121 __isl_take isl_union_map *umap);
5123 In case of union sets and relations, the affine hull is computed
5126 =item * Polyhedral hull
5128 __isl_give isl_basic_set *isl_set_polyhedral_hull(
5129 __isl_take isl_set *set);
5130 __isl_give isl_basic_map *isl_map_polyhedral_hull(
5131 __isl_take isl_map *map);
5132 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
5133 __isl_take isl_union_set *uset);
5134 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
5135 __isl_take isl_union_map *umap);
5137 These functions compute a single basic set or relation
5138 not involving any existentially quantified variables
5139 that contains the whole input set or relation.
5140 In case of union sets and relations, the polyhedral hull is computed
5143 =item * Other approximations
5145 #include <isl/set.h>
5146 __isl_give isl_basic_set *
5147 isl_basic_set_drop_constraints_involving_dims(
5148 __isl_take isl_basic_set *bset,
5149 enum isl_dim_type type,
5150 unsigned first, unsigned n);
5151 __isl_give isl_basic_set *
5152 isl_basic_set_drop_constraints_not_involving_dims(
5153 __isl_take isl_basic_set *bset,
5154 enum isl_dim_type type,
5155 unsigned first, unsigned n);
5156 __isl_give isl_set *
5157 isl_set_drop_constraints_involving_dims(
5158 __isl_take isl_set *set,
5159 enum isl_dim_type type,
5160 unsigned first, unsigned n);
5161 __isl_give isl_set *
5162 isl_set_drop_constraints_not_involving_dims(
5163 __isl_take isl_set *set,
5164 enum isl_dim_type type,
5165 unsigned first, unsigned n);
5167 #include <isl/map.h>
5168 __isl_give isl_basic_map *
5169 isl_basic_map_drop_constraints_involving_dims(
5170 __isl_take isl_basic_map *bmap,
5171 enum isl_dim_type type,
5172 unsigned first, unsigned n);
5173 __isl_give isl_basic_map *
5174 isl_basic_map_drop_constraints_not_involving_dims(
5175 __isl_take isl_basic_map *bmap,
5176 enum isl_dim_type type,
5177 unsigned first, unsigned n);
5178 __isl_give isl_map *
5179 isl_map_drop_constraints_involving_dims(
5180 __isl_take isl_map *map,
5181 enum isl_dim_type type,
5182 unsigned first, unsigned n);
5183 __isl_give isl_map *
5184 isl_map_drop_constraints_not_involving_dims(
5185 __isl_take isl_map *map,
5186 enum isl_dim_type type,
5187 unsigned first, unsigned n);
5189 These functions drop any constraints (not) involving the specified dimensions.
5190 Note that the result depends on the representation of the input.
5192 #include <isl/polynomial.h>
5193 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5194 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5195 __isl_give isl_union_pw_qpolynomial *
5196 isl_union_pw_qpolynomial_to_polynomial(
5197 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5199 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5200 the polynomial will be an overapproximation. If C<sign> is negative,
5201 it will be an underapproximation. If C<sign> is zero, the approximation
5202 will lie somewhere in between.
5206 __isl_give isl_basic_set *isl_basic_set_sample(
5207 __isl_take isl_basic_set *bset);
5208 __isl_give isl_basic_set *isl_set_sample(
5209 __isl_take isl_set *set);
5210 __isl_give isl_basic_map *isl_basic_map_sample(
5211 __isl_take isl_basic_map *bmap);
5212 __isl_give isl_basic_map *isl_map_sample(
5213 __isl_take isl_map *map);
5215 If the input (basic) set or relation is non-empty, then return
5216 a singleton subset of the input. Otherwise, return an empty set.
5218 =item * Optimization
5220 #include <isl/ilp.h>
5221 __isl_give isl_val *isl_basic_set_max_val(
5222 __isl_keep isl_basic_set *bset,
5223 __isl_keep isl_aff *obj);
5224 __isl_give isl_val *isl_set_min_val(
5225 __isl_keep isl_set *set,
5226 __isl_keep isl_aff *obj);
5227 __isl_give isl_val *isl_set_max_val(
5228 __isl_keep isl_set *set,
5229 __isl_keep isl_aff *obj);
5230 __isl_give isl_multi_val *
5231 isl_union_set_min_multi_union_pw_aff(
5232 __isl_keep isl_union_set *set,
5233 __isl_keep isl_multi_union_pw_aff *obj);
5235 Compute the minimum or maximum of the integer affine expression C<obj>
5236 over the points in C<set>, returning the result in C<opt>.
5237 The result is C<NULL> in case of an error, the optimal value in case
5238 there is one, negative infinity or infinity if the problem is unbounded and
5239 NaN if the problem is empty.
5241 #include <isl/ilp.h>
5242 __isl_give isl_val *isl_basic_set_dim_max_val(
5243 __isl_take isl_basic_set *bset, int pos);
5245 Return the maximal value attained by the given set dimension,
5246 independently of the parameter values and of any other dimensions.
5247 The result is C<NULL> in case of an error, the optimal value in case
5248 there is one, infinity if the problem is unbounded and
5249 NaN if the input is empty.
5251 =item * Parametric optimization
5253 __isl_give isl_pw_aff *isl_set_dim_min(
5254 __isl_take isl_set *set, int pos);
5255 __isl_give isl_pw_aff *isl_set_dim_max(
5256 __isl_take isl_set *set, int pos);
5257 __isl_give isl_pw_aff *isl_map_dim_min(
5258 __isl_take isl_map *map, int pos);
5259 __isl_give isl_pw_aff *isl_map_dim_max(
5260 __isl_take isl_map *map, int pos);
5262 Compute the minimum or maximum of the given set or output dimension
5263 as a function of the parameters (and input dimensions), but independently
5264 of the other set or output dimensions.
5265 For lexicographic optimization, see L<"Lexicographic Optimization">.
5269 The following functions compute either the set of (rational) coefficient
5270 values of valid constraints for the given set or the set of (rational)
5271 values satisfying the constraints with coefficients from the given set.
5272 Internally, these two sets of functions perform essentially the
5273 same operations, except that the set of coefficients is assumed to
5274 be a cone, while the set of values may be any polyhedron.
5275 The current implementation is based on the Farkas lemma and
5276 Fourier-Motzkin elimination, but this may change or be made optional
5277 in future. In particular, future implementations may use different
5278 dualization algorithms or skip the elimination step.
5280 #include <isl/set.h>
5281 __isl_give isl_basic_set *isl_basic_set_coefficients(
5282 __isl_take isl_basic_set *bset);
5283 __isl_give isl_basic_set_list *
5284 isl_basic_set_list_coefficients(
5285 __isl_take isl_basic_set_list *list);
5286 __isl_give isl_basic_set *isl_set_coefficients(
5287 __isl_take isl_set *set);
5288 __isl_give isl_union_set *isl_union_set_coefficients(
5289 __isl_take isl_union_set *bset);
5290 __isl_give isl_basic_set *isl_basic_set_solutions(
5291 __isl_take isl_basic_set *bset);
5292 __isl_give isl_basic_set *isl_set_solutions(
5293 __isl_take isl_set *set);
5294 __isl_give isl_union_set *isl_union_set_solutions(
5295 __isl_take isl_union_set *bset);
5299 __isl_give isl_map *isl_map_fixed_power_val(
5300 __isl_take isl_map *map,
5301 __isl_take isl_val *exp);
5302 __isl_give isl_union_map *
5303 isl_union_map_fixed_power_val(
5304 __isl_take isl_union_map *umap,
5305 __isl_take isl_val *exp);
5307 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
5308 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
5309 of C<map> is computed.
5311 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
5313 __isl_give isl_union_map *isl_union_map_power(
5314 __isl_take isl_union_map *umap, int *exact);
5316 Compute a parametric representation for all positive powers I<k> of C<map>.
5317 The result maps I<k> to a nested relation corresponding to the
5318 I<k>th power of C<map>.
5319 The result may be an overapproximation. If the result is known to be exact,
5320 then C<*exact> is set to C<1>.
5322 =item * Transitive closure
5324 __isl_give isl_map *isl_map_transitive_closure(
5325 __isl_take isl_map *map, int *exact);
5326 __isl_give isl_union_map *isl_union_map_transitive_closure(
5327 __isl_take isl_union_map *umap, int *exact);
5329 Compute the transitive closure 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 * Reaching path lengths
5335 __isl_give isl_map *isl_map_reaching_path_lengths(
5336 __isl_take isl_map *map, int *exact);
5338 Compute a relation that maps each element in the range of C<map>
5339 to the lengths of all paths composed of edges in C<map> that
5340 end up in the given element.
5341 The result may be an overapproximation. If the result is known to be exact,
5342 then C<*exact> is set to C<1>.
5343 To compute the I<maximal> path length, the resulting relation
5344 should be postprocessed by C<isl_map_lexmax>.
5345 In particular, if the input relation is a dependence relation
5346 (mapping sources to sinks), then the maximal path length corresponds
5347 to the free schedule.
5348 Note, however, that C<isl_map_lexmax> expects the maximum to be
5349 finite, so if the path lengths are unbounded (possibly due to
5350 the overapproximation), then you will get an error message.
5354 #include <isl/space.h>
5355 __isl_give isl_space *isl_space_wrap(
5356 __isl_take isl_space *space);
5357 __isl_give isl_space *isl_space_unwrap(
5358 __isl_take isl_space *space);
5360 #include <isl/local_space.h>
5361 __isl_give isl_local_space *isl_local_space_wrap(
5362 __isl_take isl_local_space *ls);
5364 #include <isl/set.h>
5365 __isl_give isl_basic_map *isl_basic_set_unwrap(
5366 __isl_take isl_basic_set *bset);
5367 __isl_give isl_map *isl_set_unwrap(
5368 __isl_take isl_set *set);
5370 #include <isl/map.h>
5371 __isl_give isl_basic_set *isl_basic_map_wrap(
5372 __isl_take isl_basic_map *bmap);
5373 __isl_give isl_set *isl_map_wrap(
5374 __isl_take isl_map *map);
5376 #include <isl/union_set.h>
5377 __isl_give isl_union_map *isl_union_set_unwrap(
5378 __isl_take isl_union_set *uset);
5380 #include <isl/union_map.h>
5381 __isl_give isl_union_set *isl_union_map_wrap(
5382 __isl_take isl_union_map *umap);
5384 The input to C<isl_space_unwrap> should
5385 be the space of a set, while that of
5386 C<isl_space_wrap> should be the space of a relation.
5387 Conversely, the output of C<isl_space_unwrap> is the space
5388 of a relation, while that of C<isl_space_wrap> is the space of a set.
5392 Remove any internal structure of domain (and range) of the given
5393 set or relation. If there is any such internal structure in the input,
5394 then the name of the space is also removed.
5396 #include <isl/space.h>
5397 __isl_give isl_space *isl_space_flatten_domain(
5398 __isl_take isl_space *space);
5399 __isl_give isl_space *isl_space_flatten_range(
5400 __isl_take isl_space *space);
5402 #include <isl/local_space.h>
5403 __isl_give isl_local_space *
5404 isl_local_space_flatten_domain(
5405 __isl_take isl_local_space *ls);
5406 __isl_give isl_local_space *
5407 isl_local_space_flatten_range(
5408 __isl_take isl_local_space *ls);
5410 #include <isl/set.h>
5411 __isl_give isl_basic_set *isl_basic_set_flatten(
5412 __isl_take isl_basic_set *bset);
5413 __isl_give isl_set *isl_set_flatten(
5414 __isl_take isl_set *set);
5416 #include <isl/map.h>
5417 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
5418 __isl_take isl_basic_map *bmap);
5419 __isl_give isl_basic_map *isl_basic_map_flatten_range(
5420 __isl_take isl_basic_map *bmap);
5421 __isl_give isl_map *isl_map_flatten_range(
5422 __isl_take isl_map *map);
5423 __isl_give isl_map *isl_map_flatten_domain(
5424 __isl_take isl_map *map);
5425 __isl_give isl_basic_map *isl_basic_map_flatten(
5426 __isl_take isl_basic_map *bmap);
5427 __isl_give isl_map *isl_map_flatten(
5428 __isl_take isl_map *map);
5430 #include <isl/val.h>
5431 __isl_give isl_multi_val *isl_multi_val_flatten_range(
5432 __isl_take isl_multi_val *mv);
5434 #include <isl/aff.h>
5435 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
5436 __isl_take isl_multi_aff *ma);
5437 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
5438 __isl_take isl_multi_aff *ma);
5439 __isl_give isl_multi_pw_aff *
5440 isl_multi_pw_aff_flatten_range(
5441 __isl_take isl_multi_pw_aff *mpa);
5442 __isl_give isl_multi_union_pw_aff *
5443 isl_multi_union_pw_aff_flatten_range(
5444 __isl_take isl_multi_union_pw_aff *mupa);
5446 #include <isl/map.h>
5447 __isl_give isl_map *isl_set_flatten_map(
5448 __isl_take isl_set *set);
5450 The function above constructs a relation
5451 that maps the input set to a flattened version of the set.
5455 Lift the input set to a space with extra dimensions corresponding
5456 to the existentially quantified variables in the input.
5457 In particular, the result lives in a wrapped map where the domain
5458 is the original space and the range corresponds to the original
5459 existentially quantified variables.
5461 #include <isl/set.h>
5462 __isl_give isl_basic_set *isl_basic_set_lift(
5463 __isl_take isl_basic_set *bset);
5464 __isl_give isl_set *isl_set_lift(
5465 __isl_take isl_set *set);
5466 __isl_give isl_union_set *isl_union_set_lift(
5467 __isl_take isl_union_set *uset);
5469 Given a local space that contains the existentially quantified
5470 variables of a set, a basic relation that, when applied to
5471 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
5472 can be constructed using the following function.
5474 #include <isl/local_space.h>
5475 __isl_give isl_basic_map *isl_local_space_lifting(
5476 __isl_take isl_local_space *ls);
5478 #include <isl/aff.h>
5479 __isl_give isl_multi_aff *isl_multi_aff_lift(
5480 __isl_take isl_multi_aff *maff,
5481 __isl_give isl_local_space **ls);
5483 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
5484 then it is assigned the local space that lies at the basis of
5485 the lifting applied.
5487 =item * Internal Product
5489 #include <isl/space.h>
5490 __isl_give isl_space *isl_space_zip(
5491 __isl_take isl_space *space);
5493 #include <isl/map.h>
5494 __isl_give isl_basic_map *isl_basic_map_zip(
5495 __isl_take isl_basic_map *bmap);
5496 __isl_give isl_map *isl_map_zip(
5497 __isl_take isl_map *map);
5499 #include <isl/union_map.h>
5500 __isl_give isl_union_map *isl_union_map_zip(
5501 __isl_take isl_union_map *umap);
5503 Given a relation with nested relations for domain and range,
5504 interchange the range of the domain with the domain of the range.
5508 #include <isl/space.h>
5509 __isl_give isl_space *isl_space_curry(
5510 __isl_take isl_space *space);
5511 __isl_give isl_space *isl_space_uncurry(
5512 __isl_take isl_space *space);
5514 #include <isl/map.h>
5515 __isl_give isl_basic_map *isl_basic_map_curry(
5516 __isl_take isl_basic_map *bmap);
5517 __isl_give isl_basic_map *isl_basic_map_uncurry(
5518 __isl_take isl_basic_map *bmap);
5519 __isl_give isl_map *isl_map_curry(
5520 __isl_take isl_map *map);
5521 __isl_give isl_map *isl_map_uncurry(
5522 __isl_take isl_map *map);
5524 #include <isl/union_map.h>
5525 __isl_give isl_union_map *isl_union_map_curry(
5526 __isl_take isl_union_map *umap);
5527 __isl_give isl_union_map *isl_union_map_uncurry(
5528 __isl_take isl_union_map *umap);
5530 Given a relation with a nested relation for domain,
5531 the C<curry> functions
5532 move the range of the nested relation out of the domain
5533 and use it as the domain of a nested relation in the range,
5534 with the original range as range of this nested relation.
5535 The C<uncurry> functions perform the inverse operation.
5537 #include <isl/space.h>
5538 __isl_give isl_space *isl_space_range_curry(
5539 __isl_take isl_space *space);
5541 #include <isl/map.h>
5542 __isl_give isl_map *isl_map_range_curry(
5543 __isl_take isl_map *map);
5545 #include <isl/union_map.h>
5546 __isl_give isl_union_map *isl_union_map_range_curry(
5547 __isl_take isl_union_map *umap);
5549 These functions apply the currying to the relation that
5550 is nested inside the range of the input.
5552 =item * Aligning parameters
5554 Change the order of the parameters of the given set, relation
5556 such that the first parameters match those of C<model>.
5557 This may involve the introduction of extra parameters.
5558 All parameters need to be named.
5560 #include <isl/space.h>
5561 __isl_give isl_space *isl_space_align_params(
5562 __isl_take isl_space *space1,
5563 __isl_take isl_space *space2)
5565 #include <isl/set.h>
5566 __isl_give isl_basic_set *isl_basic_set_align_params(
5567 __isl_take isl_basic_set *bset,
5568 __isl_take isl_space *model);
5569 __isl_give isl_set *isl_set_align_params(
5570 __isl_take isl_set *set,
5571 __isl_take isl_space *model);
5573 #include <isl/map.h>
5574 __isl_give isl_basic_map *isl_basic_map_align_params(
5575 __isl_take isl_basic_map *bmap,
5576 __isl_take isl_space *model);
5577 __isl_give isl_map *isl_map_align_params(
5578 __isl_take isl_map *map,
5579 __isl_take isl_space *model);
5581 #include <isl/val.h>
5582 __isl_give isl_multi_val *isl_multi_val_align_params(
5583 __isl_take isl_multi_val *mv,
5584 __isl_take isl_space *model);
5586 #include <isl/aff.h>
5587 __isl_give isl_aff *isl_aff_align_params(
5588 __isl_take isl_aff *aff,
5589 __isl_take isl_space *model);
5590 __isl_give isl_multi_aff *isl_multi_aff_align_params(
5591 __isl_take isl_multi_aff *multi,
5592 __isl_take isl_space *model);
5593 __isl_give isl_pw_aff *isl_pw_aff_align_params(
5594 __isl_take isl_pw_aff *pwaff,
5595 __isl_take isl_space *model);
5596 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
5597 __isl_take isl_pw_multi_aff *pma,
5598 __isl_take isl_space *model);
5599 __isl_give isl_union_pw_aff *
5600 isl_union_pw_aff_align_params(
5601 __isl_take isl_union_pw_aff *upa,
5602 __isl_take isl_space *model);
5603 __isl_give isl_union_pw_multi_aff *
5604 isl_union_pw_multi_aff_align_params(
5605 __isl_take isl_union_pw_multi_aff *upma,
5606 __isl_take isl_space *model);
5607 __isl_give isl_multi_union_pw_aff *
5608 isl_multi_union_pw_aff_align_params(
5609 __isl_take isl_multi_union_pw_aff *mupa,
5610 __isl_take isl_space *model);
5612 #include <isl/polynomial.h>
5613 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5614 __isl_take isl_qpolynomial *qp,
5615 __isl_take isl_space *model);
5617 =item * Unary Arithmetic Operations
5619 #include <isl/set.h>
5620 __isl_give isl_set *isl_set_neg(
5621 __isl_take isl_set *set);
5622 #include <isl/map.h>
5623 __isl_give isl_map *isl_map_neg(
5624 __isl_take isl_map *map);
5626 C<isl_set_neg> constructs a set containing the opposites of
5627 the elements in its argument.
5628 The domain of the result of C<isl_map_neg> is the same
5629 as the domain of its argument. The corresponding range
5630 elements are the opposites of the corresponding range
5631 elements in the argument.
5633 #include <isl/val.h>
5634 __isl_give isl_multi_val *isl_multi_val_neg(
5635 __isl_take isl_multi_val *mv);
5637 #include <isl/aff.h>
5638 __isl_give isl_aff *isl_aff_neg(
5639 __isl_take isl_aff *aff);
5640 __isl_give isl_multi_aff *isl_multi_aff_neg(
5641 __isl_take isl_multi_aff *ma);
5642 __isl_give isl_pw_aff *isl_pw_aff_neg(
5643 __isl_take isl_pw_aff *pwaff);
5644 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
5645 __isl_take isl_pw_multi_aff *pma);
5646 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
5647 __isl_take isl_multi_pw_aff *mpa);
5648 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
5649 __isl_take isl_union_pw_aff *upa);
5650 __isl_give isl_union_pw_multi_aff *
5651 isl_union_pw_multi_aff_neg(
5652 __isl_take isl_union_pw_multi_aff *upma);
5653 __isl_give isl_multi_union_pw_aff *
5654 isl_multi_union_pw_aff_neg(
5655 __isl_take isl_multi_union_pw_aff *mupa);
5656 __isl_give isl_aff *isl_aff_ceil(
5657 __isl_take isl_aff *aff);
5658 __isl_give isl_pw_aff *isl_pw_aff_ceil(
5659 __isl_take isl_pw_aff *pwaff);
5660 __isl_give isl_aff *isl_aff_floor(
5661 __isl_take isl_aff *aff);
5662 __isl_give isl_multi_aff *isl_multi_aff_floor(
5663 __isl_take isl_multi_aff *ma);
5664 __isl_give isl_pw_aff *isl_pw_aff_floor(
5665 __isl_take isl_pw_aff *pwaff);
5666 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
5667 __isl_take isl_union_pw_aff *upa);
5668 __isl_give isl_multi_union_pw_aff *
5669 isl_multi_union_pw_aff_floor(
5670 __isl_take isl_multi_union_pw_aff *mupa);
5672 #include <isl/aff.h>
5673 __isl_give isl_pw_aff *isl_pw_aff_list_min(
5674 __isl_take isl_pw_aff_list *list);
5675 __isl_give isl_pw_aff *isl_pw_aff_list_max(
5676 __isl_take isl_pw_aff_list *list);
5678 #include <isl/polynomial.h>
5679 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5680 __isl_take isl_qpolynomial *qp);
5681 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5682 __isl_take isl_pw_qpolynomial *pwqp);
5683 __isl_give isl_union_pw_qpolynomial *
5684 isl_union_pw_qpolynomial_neg(
5685 __isl_take isl_union_pw_qpolynomial *upwqp);
5686 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5687 __isl_take isl_qpolynomial *qp,
5689 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5690 __isl_take isl_pw_qpolynomial *pwqp,
5695 The following functions evaluate a function in a point.
5697 #include <isl/polynomial.h>
5698 __isl_give isl_val *isl_pw_qpolynomial_eval(
5699 __isl_take isl_pw_qpolynomial *pwqp,
5700 __isl_take isl_point *pnt);
5701 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5702 __isl_take isl_pw_qpolynomial_fold *pwf,
5703 __isl_take isl_point *pnt);
5704 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5705 __isl_take isl_union_pw_qpolynomial *upwqp,
5706 __isl_take isl_point *pnt);
5707 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5708 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5709 __isl_take isl_point *pnt);
5711 =item * Dimension manipulation
5713 It is usually not advisable to directly change the (input or output)
5714 space of a set or a relation as this removes the name and the internal
5715 structure of the space. However, the functions below can be useful
5716 to add new parameters, assuming
5717 C<isl_set_align_params> and C<isl_map_align_params>
5720 #include <isl/space.h>
5721 __isl_give isl_space *isl_space_add_dims(
5722 __isl_take isl_space *space,
5723 enum isl_dim_type type, unsigned n);
5724 __isl_give isl_space *isl_space_insert_dims(
5725 __isl_take isl_space *space,
5726 enum isl_dim_type type, unsigned pos, unsigned n);
5727 __isl_give isl_space *isl_space_drop_dims(
5728 __isl_take isl_space *space,
5729 enum isl_dim_type type, unsigned first, unsigned n);
5730 __isl_give isl_space *isl_space_move_dims(
5731 __isl_take isl_space *space,
5732 enum isl_dim_type dst_type, unsigned dst_pos,
5733 enum isl_dim_type src_type, unsigned src_pos,
5736 #include <isl/local_space.h>
5737 __isl_give isl_local_space *isl_local_space_add_dims(
5738 __isl_take isl_local_space *ls,
5739 enum isl_dim_type type, unsigned n);
5740 __isl_give isl_local_space *isl_local_space_insert_dims(
5741 __isl_take isl_local_space *ls,
5742 enum isl_dim_type type, unsigned first, unsigned n);
5743 __isl_give isl_local_space *isl_local_space_drop_dims(
5744 __isl_take isl_local_space *ls,
5745 enum isl_dim_type type, unsigned first, unsigned n);
5747 #include <isl/set.h>
5748 __isl_give isl_basic_set *isl_basic_set_add_dims(
5749 __isl_take isl_basic_set *bset,
5750 enum isl_dim_type type, unsigned n);
5751 __isl_give isl_set *isl_set_add_dims(
5752 __isl_take isl_set *set,
5753 enum isl_dim_type type, unsigned n);
5754 __isl_give isl_basic_set *isl_basic_set_insert_dims(
5755 __isl_take isl_basic_set *bset,
5756 enum isl_dim_type type, unsigned pos,
5758 __isl_give isl_set *isl_set_insert_dims(
5759 __isl_take isl_set *set,
5760 enum isl_dim_type type, unsigned pos, unsigned n);
5761 __isl_give isl_basic_set *isl_basic_set_move_dims(
5762 __isl_take isl_basic_set *bset,
5763 enum isl_dim_type dst_type, unsigned dst_pos,
5764 enum isl_dim_type src_type, unsigned src_pos,
5766 __isl_give isl_set *isl_set_move_dims(
5767 __isl_take isl_set *set,
5768 enum isl_dim_type dst_type, unsigned dst_pos,
5769 enum isl_dim_type src_type, unsigned src_pos,
5772 #include <isl/map.h>
5773 __isl_give isl_basic_map *isl_basic_map_add_dims(
5774 __isl_take isl_basic_map *bmap,
5775 enum isl_dim_type type, unsigned n);
5776 __isl_give isl_map *isl_map_add_dims(
5777 __isl_take isl_map *map,
5778 enum isl_dim_type type, unsigned n);
5779 __isl_give isl_basic_map *isl_basic_map_insert_dims(
5780 __isl_take isl_basic_map *bmap,
5781 enum isl_dim_type type, unsigned pos,
5783 __isl_give isl_map *isl_map_insert_dims(
5784 __isl_take isl_map *map,
5785 enum isl_dim_type type, unsigned pos, unsigned n);
5786 __isl_give isl_basic_map *isl_basic_map_move_dims(
5787 __isl_take isl_basic_map *bmap,
5788 enum isl_dim_type dst_type, unsigned dst_pos,
5789 enum isl_dim_type src_type, unsigned src_pos,
5791 __isl_give isl_map *isl_map_move_dims(
5792 __isl_take isl_map *map,
5793 enum isl_dim_type dst_type, unsigned dst_pos,
5794 enum isl_dim_type src_type, unsigned src_pos,
5797 #include <isl/val.h>
5798 __isl_give isl_multi_val *isl_multi_val_insert_dims(
5799 __isl_take isl_multi_val *mv,
5800 enum isl_dim_type type, unsigned first, unsigned n);
5801 __isl_give isl_multi_val *isl_multi_val_add_dims(
5802 __isl_take isl_multi_val *mv,
5803 enum isl_dim_type type, unsigned n);
5804 __isl_give isl_multi_val *isl_multi_val_drop_dims(
5805 __isl_take isl_multi_val *mv,
5806 enum isl_dim_type type, unsigned first, unsigned n);
5808 #include <isl/aff.h>
5809 __isl_give isl_aff *isl_aff_insert_dims(
5810 __isl_take isl_aff *aff,
5811 enum isl_dim_type type, unsigned first, unsigned n);
5812 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
5813 __isl_take isl_multi_aff *ma,
5814 enum isl_dim_type type, unsigned first, unsigned n);
5815 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
5816 __isl_take isl_pw_aff *pwaff,
5817 enum isl_dim_type type, unsigned first, unsigned n);
5818 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
5819 __isl_take isl_multi_pw_aff *mpa,
5820 enum isl_dim_type type, unsigned first, unsigned n);
5821 __isl_give isl_aff *isl_aff_add_dims(
5822 __isl_take isl_aff *aff,
5823 enum isl_dim_type type, unsigned n);
5824 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
5825 __isl_take isl_multi_aff *ma,
5826 enum isl_dim_type type, unsigned n);
5827 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
5828 __isl_take isl_pw_aff *pwaff,
5829 enum isl_dim_type type, unsigned n);
5830 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
5831 __isl_take isl_multi_pw_aff *mpa,
5832 enum isl_dim_type type, unsigned n);
5833 __isl_give isl_aff *isl_aff_drop_dims(
5834 __isl_take isl_aff *aff,
5835 enum isl_dim_type type, unsigned first, unsigned n);
5836 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
5837 __isl_take isl_multi_aff *maff,
5838 enum isl_dim_type type, unsigned first, unsigned n);
5839 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
5840 __isl_take isl_pw_aff *pwaff,
5841 enum isl_dim_type type, unsigned first, unsigned n);
5842 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
5843 __isl_take isl_pw_multi_aff *pma,
5844 enum isl_dim_type type, unsigned first, unsigned n);
5845 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
5846 __isl_take isl_union_pw_aff *upa,
5847 enum isl_dim_type type, unsigned first, unsigned n);
5848 __isl_give isl_union_pw_multi_aff *
5849 isl_union_pw_multi_aff_drop_dims(
5850 __isl_take isl_union_pw_multi_aff *upma,
5851 enum isl_dim_type type,
5852 unsigned first, unsigned n);
5853 __isl_give isl_multi_union_pw_aff *
5854 isl_multi_union_pw_aff_drop_dims(
5855 __isl_take isl_multi_union_pw_aff *mupa,
5856 enum isl_dim_type type, unsigned first,
5858 __isl_give isl_aff *isl_aff_move_dims(
5859 __isl_take isl_aff *aff,
5860 enum isl_dim_type dst_type, unsigned dst_pos,
5861 enum isl_dim_type src_type, unsigned src_pos,
5863 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
5864 __isl_take isl_multi_aff *ma,
5865 enum isl_dim_type dst_type, unsigned dst_pos,
5866 enum isl_dim_type src_type, unsigned src_pos,
5868 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
5869 __isl_take isl_pw_aff *pa,
5870 enum isl_dim_type dst_type, unsigned dst_pos,
5871 enum isl_dim_type src_type, unsigned src_pos,
5873 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
5874 __isl_take isl_multi_pw_aff *pma,
5875 enum isl_dim_type dst_type, unsigned dst_pos,
5876 enum isl_dim_type src_type, unsigned src_pos,
5879 #include <isl/polynomial.h>
5880 __isl_give isl_union_pw_qpolynomial *
5881 isl_union_pw_qpolynomial_drop_dims(
5882 __isl_take isl_union_pw_qpolynomial *upwqp,
5883 enum isl_dim_type type,
5884 unsigned first, unsigned n);
5885 __isl_give isl_union_pw_qpolynomial_fold *
5886 isl_union_pw_qpolynomial_fold_drop_dims(
5887 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5888 enum isl_dim_type type,
5889 unsigned first, unsigned n);
5891 The operations on union expressions can only manipulate parameters.
5895 =head2 Binary Operations
5897 The two arguments of a binary operation not only need to live
5898 in the same C<isl_ctx>, they currently also need to have
5899 the same (number of) parameters.
5901 =head3 Basic Operations
5905 =item * Intersection
5907 #include <isl/local_space.h>
5908 __isl_give isl_local_space *isl_local_space_intersect(
5909 __isl_take isl_local_space *ls1,
5910 __isl_take isl_local_space *ls2);
5912 #include <isl/set.h>
5913 __isl_give isl_basic_set *isl_basic_set_intersect_params(
5914 __isl_take isl_basic_set *bset1,
5915 __isl_take isl_basic_set *bset2);
5916 __isl_give isl_basic_set *isl_basic_set_intersect(
5917 __isl_take isl_basic_set *bset1,
5918 __isl_take isl_basic_set *bset2);
5919 __isl_give isl_basic_set *isl_basic_set_list_intersect(
5920 __isl_take struct isl_basic_set_list *list);
5921 __isl_give isl_set *isl_set_intersect_params(
5922 __isl_take isl_set *set,
5923 __isl_take isl_set *params);
5924 __isl_give isl_set *isl_set_intersect(
5925 __isl_take isl_set *set1,
5926 __isl_take isl_set *set2);
5928 #include <isl/map.h>
5929 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
5930 __isl_take isl_basic_map *bmap,
5931 __isl_take isl_basic_set *bset);
5932 __isl_give isl_basic_map *isl_basic_map_intersect_range(
5933 __isl_take isl_basic_map *bmap,
5934 __isl_take isl_basic_set *bset);
5935 __isl_give isl_basic_map *isl_basic_map_intersect(
5936 __isl_take isl_basic_map *bmap1,
5937 __isl_take isl_basic_map *bmap2);
5938 __isl_give isl_basic_map *isl_basic_map_list_intersect(
5939 __isl_take isl_basic_map_list *list);
5940 __isl_give isl_map *isl_map_intersect_params(
5941 __isl_take isl_map *map,
5942 __isl_take isl_set *params);
5943 __isl_give isl_map *isl_map_intersect_domain(
5944 __isl_take isl_map *map,
5945 __isl_take isl_set *set);
5946 __isl_give isl_map *isl_map_intersect_range(
5947 __isl_take isl_map *map,
5948 __isl_take isl_set *set);
5949 __isl_give isl_map *isl_map_intersect(
5950 __isl_take isl_map *map1,
5951 __isl_take isl_map *map2);
5952 __isl_give isl_map *
5953 isl_map_intersect_domain_factor_range(
5954 __isl_take isl_map *map,
5955 __isl_take isl_map *factor);
5956 __isl_give isl_map *
5957 isl_map_intersect_range_factor_range(
5958 __isl_take isl_map *map,
5959 __isl_take isl_map *factor);
5961 #include <isl/union_set.h>
5962 __isl_give isl_union_set *isl_union_set_intersect_params(
5963 __isl_take isl_union_set *uset,
5964 __isl_take isl_set *set);
5965 __isl_give isl_union_set *isl_union_set_intersect(
5966 __isl_take isl_union_set *uset1,
5967 __isl_take isl_union_set *uset2);
5969 #include <isl/union_map.h>
5970 __isl_give isl_union_map *isl_union_map_intersect_params(
5971 __isl_take isl_union_map *umap,
5972 __isl_take isl_set *set);
5973 __isl_give isl_union_map *isl_union_map_intersect_domain(
5974 __isl_take isl_union_map *umap,
5975 __isl_take isl_union_set *uset);
5976 __isl_give isl_union_map *isl_union_map_intersect_range(
5977 __isl_take isl_union_map *umap,
5978 __isl_take isl_union_set *uset);
5979 __isl_give isl_union_map *isl_union_map_intersect(
5980 __isl_take isl_union_map *umap1,
5981 __isl_take isl_union_map *umap2);
5982 __isl_give isl_union_map *
5983 isl_union_map_intersect_range_factor_range(
5984 __isl_take isl_union_map *umap,
5985 __isl_take isl_union_map *factor);
5987 #include <isl/aff.h>
5988 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
5989 __isl_take isl_pw_aff *pa,
5990 __isl_take isl_set *set);
5991 __isl_give isl_multi_pw_aff *
5992 isl_multi_pw_aff_intersect_domain(
5993 __isl_take isl_multi_pw_aff *mpa,
5994 __isl_take isl_set *domain);
5995 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
5996 __isl_take isl_pw_multi_aff *pma,
5997 __isl_take isl_set *set);
5998 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
5999 __isl_take isl_union_pw_aff *upa,
6000 __isl_take isl_union_set *uset);
6001 __isl_give isl_union_pw_multi_aff *
6002 isl_union_pw_multi_aff_intersect_domain(
6003 __isl_take isl_union_pw_multi_aff *upma,
6004 __isl_take isl_union_set *uset);
6005 __isl_give isl_multi_union_pw_aff *
6006 isl_multi_union_pw_aff_intersect_domain(
6007 __isl_take isl_multi_union_pw_aff *mupa,
6008 __isl_take isl_union_set *uset);
6009 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
6010 __isl_take isl_pw_aff *pa,
6011 __isl_take isl_set *set);
6012 __isl_give isl_multi_pw_aff *
6013 isl_multi_pw_aff_intersect_params(
6014 __isl_take isl_multi_pw_aff *mpa,
6015 __isl_take isl_set *set);
6016 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
6017 __isl_take isl_pw_multi_aff *pma,
6018 __isl_take isl_set *set);
6019 __isl_give isl_union_pw_aff *
6020 isl_union_pw_aff_intersect_params(
6021 __isl_take isl_union_pw_aff *upa,
6022 __isl_give isl_union_pw_multi_aff *
6023 isl_union_pw_multi_aff_intersect_params(
6024 __isl_take isl_union_pw_multi_aff *upma,
6025 __isl_take isl_set *set);
6026 __isl_give isl_multi_union_pw_aff *
6027 isl_multi_union_pw_aff_intersect_params(
6028 __isl_take isl_multi_union_pw_aff *mupa,
6029 __isl_take isl_set *params);
6030 isl_multi_union_pw_aff_intersect_range(
6031 __isl_take isl_multi_union_pw_aff *mupa,
6032 __isl_take isl_set *set);
6034 #include <isl/polynomial.h>
6035 __isl_give isl_pw_qpolynomial *
6036 isl_pw_qpolynomial_intersect_domain(
6037 __isl_take isl_pw_qpolynomial *pwpq,
6038 __isl_take isl_set *set);
6039 __isl_give isl_union_pw_qpolynomial *
6040 isl_union_pw_qpolynomial_intersect_domain(
6041 __isl_take isl_union_pw_qpolynomial *upwpq,
6042 __isl_take isl_union_set *uset);
6043 __isl_give isl_union_pw_qpolynomial_fold *
6044 isl_union_pw_qpolynomial_fold_intersect_domain(
6045 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6046 __isl_take isl_union_set *uset);
6047 __isl_give isl_pw_qpolynomial *
6048 isl_pw_qpolynomial_intersect_params(
6049 __isl_take isl_pw_qpolynomial *pwpq,
6050 __isl_take isl_set *set);
6051 __isl_give isl_pw_qpolynomial_fold *
6052 isl_pw_qpolynomial_fold_intersect_params(
6053 __isl_take isl_pw_qpolynomial_fold *pwf,
6054 __isl_take isl_set *set);
6055 __isl_give isl_union_pw_qpolynomial *
6056 isl_union_pw_qpolynomial_intersect_params(
6057 __isl_take isl_union_pw_qpolynomial *upwpq,
6058 __isl_take isl_set *set);
6059 __isl_give isl_union_pw_qpolynomial_fold *
6060 isl_union_pw_qpolynomial_fold_intersect_params(
6061 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6062 __isl_take isl_set *set);
6064 The second argument to the C<_params> functions needs to be
6065 a parametric (basic) set. For the other functions, a parametric set
6066 for either argument is only allowed if the other argument is
6067 a parametric set as well.
6068 The list passed to C<isl_basic_set_list_intersect> needs to have
6069 at least one element and all elements need to live in the same space.
6070 The function C<isl_multi_union_pw_aff_intersect_range>
6071 restricts the input function to those shared domain elements
6072 that map to the specified range.
6076 #include <isl/set.h>
6077 __isl_give isl_set *isl_basic_set_union(
6078 __isl_take isl_basic_set *bset1,
6079 __isl_take isl_basic_set *bset2);
6080 __isl_give isl_set *isl_set_union(
6081 __isl_take isl_set *set1,
6082 __isl_take isl_set *set2);
6083 __isl_give isl_set *isl_set_list_union(
6084 __isl_take isl_set_list *list);
6086 #include <isl/map.h>
6087 __isl_give isl_map *isl_basic_map_union(
6088 __isl_take isl_basic_map *bmap1,
6089 __isl_take isl_basic_map *bmap2);
6090 __isl_give isl_map *isl_map_union(
6091 __isl_take isl_map *map1,
6092 __isl_take isl_map *map2);
6094 #include <isl/union_set.h>
6095 __isl_give isl_union_set *isl_union_set_union(
6096 __isl_take isl_union_set *uset1,
6097 __isl_take isl_union_set *uset2);
6098 __isl_give isl_union_set *isl_union_set_list_union(
6099 __isl_take isl_union_set_list *list);
6101 #include <isl/union_map.h>
6102 __isl_give isl_union_map *isl_union_map_union(
6103 __isl_take isl_union_map *umap1,
6104 __isl_take isl_union_map *umap2);
6106 The list passed to C<isl_set_list_union> needs to have
6107 at least one element and all elements need to live in the same space.
6109 =item * Set difference
6111 #include <isl/set.h>
6112 __isl_give isl_set *isl_set_subtract(
6113 __isl_take isl_set *set1,
6114 __isl_take isl_set *set2);
6116 #include <isl/map.h>
6117 __isl_give isl_map *isl_map_subtract(
6118 __isl_take isl_map *map1,
6119 __isl_take isl_map *map2);
6120 __isl_give isl_map *isl_map_subtract_domain(
6121 __isl_take isl_map *map,
6122 __isl_take isl_set *dom);
6123 __isl_give isl_map *isl_map_subtract_range(
6124 __isl_take isl_map *map,
6125 __isl_take isl_set *dom);
6127 #include <isl/union_set.h>
6128 __isl_give isl_union_set *isl_union_set_subtract(
6129 __isl_take isl_union_set *uset1,
6130 __isl_take isl_union_set *uset2);
6132 #include <isl/union_map.h>
6133 __isl_give isl_union_map *isl_union_map_subtract(
6134 __isl_take isl_union_map *umap1,
6135 __isl_take isl_union_map *umap2);
6136 __isl_give isl_union_map *isl_union_map_subtract_domain(
6137 __isl_take isl_union_map *umap,
6138 __isl_take isl_union_set *dom);
6139 __isl_give isl_union_map *isl_union_map_subtract_range(
6140 __isl_take isl_union_map *umap,
6141 __isl_take isl_union_set *dom);
6143 #include <isl/aff.h>
6144 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
6145 __isl_take isl_pw_aff *pa,
6146 __isl_take isl_set *set);
6147 __isl_give isl_pw_multi_aff *
6148 isl_pw_multi_aff_subtract_domain(
6149 __isl_take isl_pw_multi_aff *pma,
6150 __isl_take isl_set *set);
6151 __isl_give isl_union_pw_aff *
6152 isl_union_pw_aff_subtract_domain(
6153 __isl_take isl_union_pw_aff *upa,
6154 __isl_take isl_union_set *uset);
6155 __isl_give isl_union_pw_multi_aff *
6156 isl_union_pw_multi_aff_subtract_domain(
6157 __isl_take isl_union_pw_multi_aff *upma,
6158 __isl_take isl_set *set);
6160 #include <isl/polynomial.h>
6161 __isl_give isl_pw_qpolynomial *
6162 isl_pw_qpolynomial_subtract_domain(
6163 __isl_take isl_pw_qpolynomial *pwpq,
6164 __isl_take isl_set *set);
6165 __isl_give isl_pw_qpolynomial_fold *
6166 isl_pw_qpolynomial_fold_subtract_domain(
6167 __isl_take isl_pw_qpolynomial_fold *pwf,
6168 __isl_take isl_set *set);
6169 __isl_give isl_union_pw_qpolynomial *
6170 isl_union_pw_qpolynomial_subtract_domain(
6171 __isl_take isl_union_pw_qpolynomial *upwpq,
6172 __isl_take isl_union_set *uset);
6173 __isl_give isl_union_pw_qpolynomial_fold *
6174 isl_union_pw_qpolynomial_fold_subtract_domain(
6175 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6176 __isl_take isl_union_set *uset);
6180 #include <isl/space.h>
6181 __isl_give isl_space *isl_space_join(
6182 __isl_take isl_space *left,
6183 __isl_take isl_space *right);
6185 #include <isl/map.h>
6186 __isl_give isl_basic_set *isl_basic_set_apply(
6187 __isl_take isl_basic_set *bset,
6188 __isl_take isl_basic_map *bmap);
6189 __isl_give isl_set *isl_set_apply(
6190 __isl_take isl_set *set,
6191 __isl_take isl_map *map);
6192 __isl_give isl_union_set *isl_union_set_apply(
6193 __isl_take isl_union_set *uset,
6194 __isl_take isl_union_map *umap);
6195 __isl_give isl_basic_map *isl_basic_map_apply_domain(
6196 __isl_take isl_basic_map *bmap1,
6197 __isl_take isl_basic_map *bmap2);
6198 __isl_give isl_basic_map *isl_basic_map_apply_range(
6199 __isl_take isl_basic_map *bmap1,
6200 __isl_take isl_basic_map *bmap2);
6201 __isl_give isl_map *isl_map_apply_domain(
6202 __isl_take isl_map *map1,
6203 __isl_take isl_map *map2);
6204 __isl_give isl_map *isl_map_apply_range(
6205 __isl_take isl_map *map1,
6206 __isl_take isl_map *map2);
6208 #include <isl/union_map.h>
6209 __isl_give isl_union_map *isl_union_map_apply_domain(
6210 __isl_take isl_union_map *umap1,
6211 __isl_take isl_union_map *umap2);
6212 __isl_give isl_union_map *isl_union_map_apply_range(
6213 __isl_take isl_union_map *umap1,
6214 __isl_take isl_union_map *umap2);
6216 #include <isl/aff.h>
6217 __isl_give isl_union_pw_aff *
6218 isl_multi_union_pw_aff_apply_aff(
6219 __isl_take isl_multi_union_pw_aff *mupa,
6220 __isl_take isl_aff *aff);
6221 __isl_give isl_union_pw_aff *
6222 isl_multi_union_pw_aff_apply_pw_aff(
6223 __isl_take isl_multi_union_pw_aff *mupa,
6224 __isl_take isl_pw_aff *pa);
6225 __isl_give isl_multi_union_pw_aff *
6226 isl_multi_union_pw_aff_apply_multi_aff(
6227 __isl_take isl_multi_union_pw_aff *mupa,
6228 __isl_take isl_multi_aff *ma);
6229 __isl_give isl_multi_union_pw_aff *
6230 isl_multi_union_pw_aff_apply_pw_multi_aff(
6231 __isl_take isl_multi_union_pw_aff *mupa,
6232 __isl_take isl_pw_multi_aff *pma);
6234 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
6235 over the shared domain of the elements of the input. The dimension is
6236 required to be greater than zero.
6237 The C<isl_multi_union_pw_aff> argument of
6238 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
6239 but only if the range of the C<isl_multi_aff> argument
6240 is also zero-dimensional.
6241 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
6243 #include <isl/polynomial.h>
6244 __isl_give isl_pw_qpolynomial_fold *
6245 isl_set_apply_pw_qpolynomial_fold(
6246 __isl_take isl_set *set,
6247 __isl_take isl_pw_qpolynomial_fold *pwf,
6249 __isl_give isl_pw_qpolynomial_fold *
6250 isl_map_apply_pw_qpolynomial_fold(
6251 __isl_take isl_map *map,
6252 __isl_take isl_pw_qpolynomial_fold *pwf,
6254 __isl_give isl_union_pw_qpolynomial_fold *
6255 isl_union_set_apply_union_pw_qpolynomial_fold(
6256 __isl_take isl_union_set *uset,
6257 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6259 __isl_give isl_union_pw_qpolynomial_fold *
6260 isl_union_map_apply_union_pw_qpolynomial_fold(
6261 __isl_take isl_union_map *umap,
6262 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6265 The functions taking a map
6266 compose the given map with the given piecewise quasipolynomial reduction.
6267 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
6268 over all elements in the intersection of the range of the map
6269 and the domain of the piecewise quasipolynomial reduction
6270 as a function of an element in the domain of the map.
6271 The functions taking a set compute a bound over all elements in the
6272 intersection of the set and the domain of the
6273 piecewise quasipolynomial reduction.
6277 #include <isl/set.h>
6278 __isl_give isl_basic_set *
6279 isl_basic_set_preimage_multi_aff(
6280 __isl_take isl_basic_set *bset,
6281 __isl_take isl_multi_aff *ma);
6282 __isl_give isl_set *isl_set_preimage_multi_aff(
6283 __isl_take isl_set *set,
6284 __isl_take isl_multi_aff *ma);
6285 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
6286 __isl_take isl_set *set,
6287 __isl_take isl_pw_multi_aff *pma);
6288 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
6289 __isl_take isl_set *set,
6290 __isl_take isl_multi_pw_aff *mpa);
6292 #include <isl/union_set.h>
6293 __isl_give isl_union_set *
6294 isl_union_set_preimage_multi_aff(
6295 __isl_take isl_union_set *uset,
6296 __isl_take isl_multi_aff *ma);
6297 __isl_give isl_union_set *
6298 isl_union_set_preimage_pw_multi_aff(
6299 __isl_take isl_union_set *uset,
6300 __isl_take isl_pw_multi_aff *pma);
6301 __isl_give isl_union_set *
6302 isl_union_set_preimage_union_pw_multi_aff(
6303 __isl_take isl_union_set *uset,
6304 __isl_take isl_union_pw_multi_aff *upma);
6306 #include <isl/map.h>
6307 __isl_give isl_basic_map *
6308 isl_basic_map_preimage_domain_multi_aff(
6309 __isl_take isl_basic_map *bmap,
6310 __isl_take isl_multi_aff *ma);
6311 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
6312 __isl_take isl_map *map,
6313 __isl_take isl_multi_aff *ma);
6314 __isl_give isl_map *isl_map_preimage_range_multi_aff(
6315 __isl_take isl_map *map,
6316 __isl_take isl_multi_aff *ma);
6317 __isl_give isl_map *
6318 isl_map_preimage_domain_pw_multi_aff(
6319 __isl_take isl_map *map,
6320 __isl_take isl_pw_multi_aff *pma);
6321 __isl_give isl_map *
6322 isl_map_preimage_range_pw_multi_aff(
6323 __isl_take isl_map *map,
6324 __isl_take isl_pw_multi_aff *pma);
6325 __isl_give isl_map *
6326 isl_map_preimage_domain_multi_pw_aff(
6327 __isl_take isl_map *map,
6328 __isl_take isl_multi_pw_aff *mpa);
6329 __isl_give isl_basic_map *
6330 isl_basic_map_preimage_range_multi_aff(
6331 __isl_take isl_basic_map *bmap,
6332 __isl_take isl_multi_aff *ma);
6334 #include <isl/union_map.h>
6335 __isl_give isl_union_map *
6336 isl_union_map_preimage_domain_multi_aff(
6337 __isl_take isl_union_map *umap,
6338 __isl_take isl_multi_aff *ma);
6339 __isl_give isl_union_map *
6340 isl_union_map_preimage_range_multi_aff(
6341 __isl_take isl_union_map *umap,
6342 __isl_take isl_multi_aff *ma);
6343 __isl_give isl_union_map *
6344 isl_union_map_preimage_domain_pw_multi_aff(
6345 __isl_take isl_union_map *umap,
6346 __isl_take isl_pw_multi_aff *pma);
6347 __isl_give isl_union_map *
6348 isl_union_map_preimage_range_pw_multi_aff(
6349 __isl_take isl_union_map *umap,
6350 __isl_take isl_pw_multi_aff *pma);
6351 __isl_give isl_union_map *
6352 isl_union_map_preimage_domain_union_pw_multi_aff(
6353 __isl_take isl_union_map *umap,
6354 __isl_take isl_union_pw_multi_aff *upma);
6355 __isl_give isl_union_map *
6356 isl_union_map_preimage_range_union_pw_multi_aff(
6357 __isl_take isl_union_map *umap,
6358 __isl_take isl_union_pw_multi_aff *upma);
6360 These functions compute the preimage of the given set or map domain/range under
6361 the given function. In other words, the expression is plugged
6362 into the set description or into the domain/range of the map.
6366 #include <isl/aff.h>
6367 __isl_give isl_aff *isl_aff_pullback_aff(
6368 __isl_take isl_aff *aff1,
6369 __isl_take isl_aff *aff2);
6370 __isl_give isl_aff *isl_aff_pullback_multi_aff(
6371 __isl_take isl_aff *aff,
6372 __isl_take isl_multi_aff *ma);
6373 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
6374 __isl_take isl_pw_aff *pa,
6375 __isl_take isl_multi_aff *ma);
6376 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
6377 __isl_take isl_pw_aff *pa,
6378 __isl_take isl_pw_multi_aff *pma);
6379 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
6380 __isl_take isl_pw_aff *pa,
6381 __isl_take isl_multi_pw_aff *mpa);
6382 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
6383 __isl_take isl_multi_aff *ma1,
6384 __isl_take isl_multi_aff *ma2);
6385 __isl_give isl_pw_multi_aff *
6386 isl_pw_multi_aff_pullback_multi_aff(
6387 __isl_take isl_pw_multi_aff *pma,
6388 __isl_take isl_multi_aff *ma);
6389 __isl_give isl_multi_pw_aff *
6390 isl_multi_pw_aff_pullback_multi_aff(
6391 __isl_take isl_multi_pw_aff *mpa,
6392 __isl_take isl_multi_aff *ma);
6393 __isl_give isl_pw_multi_aff *
6394 isl_pw_multi_aff_pullback_pw_multi_aff(
6395 __isl_take isl_pw_multi_aff *pma1,
6396 __isl_take isl_pw_multi_aff *pma2);
6397 __isl_give isl_multi_pw_aff *
6398 isl_multi_pw_aff_pullback_pw_multi_aff(
6399 __isl_take isl_multi_pw_aff *mpa,
6400 __isl_take isl_pw_multi_aff *pma);
6401 __isl_give isl_multi_pw_aff *
6402 isl_multi_pw_aff_pullback_multi_pw_aff(
6403 __isl_take isl_multi_pw_aff *mpa1,
6404 __isl_take isl_multi_pw_aff *mpa2);
6405 __isl_give isl_union_pw_aff *
6406 isl_union_pw_aff_pullback_union_pw_multi_aff(
6407 __isl_take isl_union_pw_aff *upa,
6408 __isl_take isl_union_pw_multi_aff *upma);
6409 __isl_give isl_union_pw_multi_aff *
6410 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
6411 __isl_take isl_union_pw_multi_aff *upma1,
6412 __isl_take isl_union_pw_multi_aff *upma2);
6413 __isl_give isl_multi_union_pw_aff *
6414 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
6415 __isl_take isl_multi_union_pw_aff *mupa,
6416 __isl_take isl_union_pw_multi_aff *upma);
6418 These functions precompose the first expression by the second function.
6419 In other words, the second function is plugged
6420 into the first expression.
6424 #include <isl/aff.h>
6425 __isl_give isl_basic_set *isl_aff_eq_basic_set(
6426 __isl_take isl_aff *aff1,
6427 __isl_take isl_aff *aff2);
6428 __isl_give isl_set *isl_aff_eq_set(
6429 __isl_take isl_aff *aff1,
6430 __isl_take isl_aff *aff2);
6431 __isl_give isl_set *isl_aff_ne_set(
6432 __isl_take isl_aff *aff1,
6433 __isl_take isl_aff *aff2);
6434 __isl_give isl_basic_set *isl_aff_le_basic_set(
6435 __isl_take isl_aff *aff1,
6436 __isl_take isl_aff *aff2);
6437 __isl_give isl_set *isl_aff_le_set(
6438 __isl_take isl_aff *aff1,
6439 __isl_take isl_aff *aff2);
6440 __isl_give isl_basic_set *isl_aff_lt_basic_set(
6441 __isl_take isl_aff *aff1,
6442 __isl_take isl_aff *aff2);
6443 __isl_give isl_set *isl_aff_lt_set(
6444 __isl_take isl_aff *aff1,
6445 __isl_take isl_aff *aff2);
6446 __isl_give isl_basic_set *isl_aff_ge_basic_set(
6447 __isl_take isl_aff *aff1,
6448 __isl_take isl_aff *aff2);
6449 __isl_give isl_set *isl_aff_ge_set(
6450 __isl_take isl_aff *aff1,
6451 __isl_take isl_aff *aff2);
6452 __isl_give isl_basic_set *isl_aff_gt_basic_set(
6453 __isl_take isl_aff *aff1,
6454 __isl_take isl_aff *aff2);
6455 __isl_give isl_set *isl_aff_gt_set(
6456 __isl_take isl_aff *aff1,
6457 __isl_take isl_aff *aff2);
6458 __isl_give isl_set *isl_pw_aff_eq_set(
6459 __isl_take isl_pw_aff *pwaff1,
6460 __isl_take isl_pw_aff *pwaff2);
6461 __isl_give isl_set *isl_pw_aff_ne_set(
6462 __isl_take isl_pw_aff *pwaff1,
6463 __isl_take isl_pw_aff *pwaff2);
6464 __isl_give isl_set *isl_pw_aff_le_set(
6465 __isl_take isl_pw_aff *pwaff1,
6466 __isl_take isl_pw_aff *pwaff2);
6467 __isl_give isl_set *isl_pw_aff_lt_set(
6468 __isl_take isl_pw_aff *pwaff1,
6469 __isl_take isl_pw_aff *pwaff2);
6470 __isl_give isl_set *isl_pw_aff_ge_set(
6471 __isl_take isl_pw_aff *pwaff1,
6472 __isl_take isl_pw_aff *pwaff2);
6473 __isl_give isl_set *isl_pw_aff_gt_set(
6474 __isl_take isl_pw_aff *pwaff1,
6475 __isl_take isl_pw_aff *pwaff2);
6477 __isl_give isl_set *isl_multi_aff_lex_le_set(
6478 __isl_take isl_multi_aff *ma1,
6479 __isl_take isl_multi_aff *ma2);
6480 __isl_give isl_set *isl_multi_aff_lex_lt_set(
6481 __isl_take isl_multi_aff *ma1,
6482 __isl_take isl_multi_aff *ma2);
6483 __isl_give isl_set *isl_multi_aff_lex_ge_set(
6484 __isl_take isl_multi_aff *ma1,
6485 __isl_take isl_multi_aff *ma2);
6486 __isl_give isl_set *isl_multi_aff_lex_gt_set(
6487 __isl_take isl_multi_aff *ma1,
6488 __isl_take isl_multi_aff *ma2);
6490 __isl_give isl_set *isl_pw_aff_list_eq_set(
6491 __isl_take isl_pw_aff_list *list1,
6492 __isl_take isl_pw_aff_list *list2);
6493 __isl_give isl_set *isl_pw_aff_list_ne_set(
6494 __isl_take isl_pw_aff_list *list1,
6495 __isl_take isl_pw_aff_list *list2);
6496 __isl_give isl_set *isl_pw_aff_list_le_set(
6497 __isl_take isl_pw_aff_list *list1,
6498 __isl_take isl_pw_aff_list *list2);
6499 __isl_give isl_set *isl_pw_aff_list_lt_set(
6500 __isl_take isl_pw_aff_list *list1,
6501 __isl_take isl_pw_aff_list *list2);
6502 __isl_give isl_set *isl_pw_aff_list_ge_set(
6503 __isl_take isl_pw_aff_list *list1,
6504 __isl_take isl_pw_aff_list *list2);
6505 __isl_give isl_set *isl_pw_aff_list_gt_set(
6506 __isl_take isl_pw_aff_list *list1,
6507 __isl_take isl_pw_aff_list *list2);
6509 The function C<isl_aff_ge_basic_set> returns a basic set
6510 containing those elements in the shared space
6511 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
6512 The function C<isl_pw_aff_ge_set> returns a set
6513 containing those elements in the shared domain
6514 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
6515 greater than or equal to C<pwaff2>.
6516 The function C<isl_multi_aff_lex_le_set> returns a set
6517 containing those elements in the shared domain space
6518 where C<ma1> is lexicographically smaller than or
6520 The functions operating on C<isl_pw_aff_list> apply the corresponding
6521 C<isl_pw_aff> function to each pair of elements in the two lists.
6523 #include <isl/aff.h>
6524 __isl_give isl_map *isl_pw_aff_eq_map(
6525 __isl_take isl_pw_aff *pa1,
6526 __isl_take isl_pw_aff *pa2);
6527 __isl_give isl_map *isl_pw_aff_lt_map(
6528 __isl_take isl_pw_aff *pa1,
6529 __isl_take isl_pw_aff *pa2);
6530 __isl_give isl_map *isl_pw_aff_gt_map(
6531 __isl_take isl_pw_aff *pa1,
6532 __isl_take isl_pw_aff *pa2);
6534 __isl_give isl_map *isl_multi_pw_aff_eq_map(
6535 __isl_take isl_multi_pw_aff *mpa1,
6536 __isl_take isl_multi_pw_aff *mpa2);
6537 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
6538 __isl_take isl_multi_pw_aff *mpa1,
6539 __isl_take isl_multi_pw_aff *mpa2);
6540 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
6541 __isl_take isl_multi_pw_aff *mpa1,
6542 __isl_take isl_multi_pw_aff *mpa2);
6544 These functions return a map between domain elements of the arguments
6545 where the function values satisfy the given relation.
6547 #include <isl/union_map.h>
6548 __isl_give isl_union_map *
6549 isl_union_map_eq_at_multi_union_pw_aff(
6550 __isl_take isl_union_map *umap,
6551 __isl_take isl_multi_union_pw_aff *mupa);
6552 __isl_give isl_union_map *
6553 isl_union_map_lex_lt_at_multi_union_pw_aff(
6554 __isl_take isl_union_map *umap,
6555 __isl_take isl_multi_union_pw_aff *mupa);
6556 __isl_give isl_union_map *
6557 isl_union_map_lex_gt_at_multi_union_pw_aff(
6558 __isl_take isl_union_map *umap,
6559 __isl_take isl_multi_union_pw_aff *mupa);
6561 These functions select the subset of elements in the union map
6562 that have an equal or lexicographically smaller function value.
6564 =item * Cartesian Product
6566 #include <isl/space.h>
6567 __isl_give isl_space *isl_space_product(
6568 __isl_take isl_space *space1,
6569 __isl_take isl_space *space2);
6570 __isl_give isl_space *isl_space_domain_product(
6571 __isl_take isl_space *space1,
6572 __isl_take isl_space *space2);
6573 __isl_give isl_space *isl_space_range_product(
6574 __isl_take isl_space *space1,
6575 __isl_take isl_space *space2);
6578 C<isl_space_product>, C<isl_space_domain_product>
6579 and C<isl_space_range_product> take pairs or relation spaces and
6580 produce a single relations space, where either the domain, the range
6581 or both domain and range are wrapped spaces of relations between
6582 the domains and/or ranges of the input spaces.
6583 If the product is only constructed over the domain or the range
6584 then the ranges or the domains of the inputs should be the same.
6585 The function C<isl_space_product> also accepts a pair of set spaces,
6586 in which case it returns a wrapped space of a relation between the
6589 #include <isl/set.h>
6590 __isl_give isl_set *isl_set_product(
6591 __isl_take isl_set *set1,
6592 __isl_take isl_set *set2);
6594 #include <isl/map.h>
6595 __isl_give isl_basic_map *isl_basic_map_domain_product(
6596 __isl_take isl_basic_map *bmap1,
6597 __isl_take isl_basic_map *bmap2);
6598 __isl_give isl_basic_map *isl_basic_map_range_product(
6599 __isl_take isl_basic_map *bmap1,
6600 __isl_take isl_basic_map *bmap2);
6601 __isl_give isl_basic_map *isl_basic_map_product(
6602 __isl_take isl_basic_map *bmap1,
6603 __isl_take isl_basic_map *bmap2);
6604 __isl_give isl_map *isl_map_domain_product(
6605 __isl_take isl_map *map1,
6606 __isl_take isl_map *map2);
6607 __isl_give isl_map *isl_map_range_product(
6608 __isl_take isl_map *map1,
6609 __isl_take isl_map *map2);
6610 __isl_give isl_map *isl_map_product(
6611 __isl_take isl_map *map1,
6612 __isl_take isl_map *map2);
6614 #include <isl/union_set.h>
6615 __isl_give isl_union_set *isl_union_set_product(
6616 __isl_take isl_union_set *uset1,
6617 __isl_take isl_union_set *uset2);
6619 #include <isl/union_map.h>
6620 __isl_give isl_union_map *isl_union_map_domain_product(
6621 __isl_take isl_union_map *umap1,
6622 __isl_take isl_union_map *umap2);
6623 __isl_give isl_union_map *isl_union_map_range_product(
6624 __isl_take isl_union_map *umap1,
6625 __isl_take isl_union_map *umap2);
6626 __isl_give isl_union_map *isl_union_map_product(
6627 __isl_take isl_union_map *umap1,
6628 __isl_take isl_union_map *umap2);
6630 #include <isl/val.h>
6631 __isl_give isl_multi_val *isl_multi_val_range_product(
6632 __isl_take isl_multi_val *mv1,
6633 __isl_take isl_multi_val *mv2);
6634 __isl_give isl_multi_val *isl_multi_val_product(
6635 __isl_take isl_multi_val *mv1,
6636 __isl_take isl_multi_val *mv2);
6638 #include <isl/aff.h>
6639 __isl_give isl_multi_aff *isl_multi_aff_range_product(
6640 __isl_take isl_multi_aff *ma1,
6641 __isl_take isl_multi_aff *ma2);
6642 __isl_give isl_multi_aff *isl_multi_aff_product(
6643 __isl_take isl_multi_aff *ma1,
6644 __isl_take isl_multi_aff *ma2);
6645 __isl_give isl_multi_pw_aff *
6646 isl_multi_pw_aff_range_product(
6647 __isl_take isl_multi_pw_aff *mpa1,
6648 __isl_take isl_multi_pw_aff *mpa2);
6649 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
6650 __isl_take isl_multi_pw_aff *mpa1,
6651 __isl_take isl_multi_pw_aff *mpa2);
6652 __isl_give isl_pw_multi_aff *
6653 isl_pw_multi_aff_range_product(
6654 __isl_take isl_pw_multi_aff *pma1,
6655 __isl_take isl_pw_multi_aff *pma2);
6656 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
6657 __isl_take isl_pw_multi_aff *pma1,
6658 __isl_take isl_pw_multi_aff *pma2);
6659 __isl_give isl_multi_union_pw_aff *
6660 isl_multi_union_pw_aff_range_product(
6661 __isl_take isl_multi_union_pw_aff *mupa1,
6662 __isl_take isl_multi_union_pw_aff *mupa2);
6664 The above functions compute the cross product of the given
6665 sets, relations or functions. The domains and ranges of the results
6666 are wrapped maps between domains and ranges of the inputs.
6667 To obtain a ``flat'' product, use the following functions
6670 #include <isl/set.h>
6671 __isl_give isl_basic_set *isl_basic_set_flat_product(
6672 __isl_take isl_basic_set *bset1,
6673 __isl_take isl_basic_set *bset2);
6674 __isl_give isl_set *isl_set_flat_product(
6675 __isl_take isl_set *set1,
6676 __isl_take isl_set *set2);
6678 #include <isl/map.h>
6679 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
6680 __isl_take isl_basic_map *bmap1,
6681 __isl_take isl_basic_map *bmap2);
6682 __isl_give isl_map *isl_map_flat_domain_product(
6683 __isl_take isl_map *map1,
6684 __isl_take isl_map *map2);
6685 __isl_give isl_map *isl_map_flat_range_product(
6686 __isl_take isl_map *map1,
6687 __isl_take isl_map *map2);
6688 __isl_give isl_basic_map *isl_basic_map_flat_product(
6689 __isl_take isl_basic_map *bmap1,
6690 __isl_take isl_basic_map *bmap2);
6691 __isl_give isl_map *isl_map_flat_product(
6692 __isl_take isl_map *map1,
6693 __isl_take isl_map *map2);
6695 #include <isl/union_map.h>
6696 __isl_give isl_union_map *
6697 isl_union_map_flat_domain_product(
6698 __isl_take isl_union_map *umap1,
6699 __isl_take isl_union_map *umap2);
6700 __isl_give isl_union_map *
6701 isl_union_map_flat_range_product(
6702 __isl_take isl_union_map *umap1,
6703 __isl_take isl_union_map *umap2);
6705 #include <isl/val.h>
6706 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
6707 __isl_take isl_multi_val *mv1,
6708 __isl_take isl_multi_aff *mv2);
6710 #include <isl/aff.h>
6711 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
6712 __isl_take isl_multi_aff *ma1,
6713 __isl_take isl_multi_aff *ma2);
6714 __isl_give isl_pw_multi_aff *
6715 isl_pw_multi_aff_flat_range_product(
6716 __isl_take isl_pw_multi_aff *pma1,
6717 __isl_take isl_pw_multi_aff *pma2);
6718 __isl_give isl_multi_pw_aff *
6719 isl_multi_pw_aff_flat_range_product(
6720 __isl_take isl_multi_pw_aff *mpa1,
6721 __isl_take isl_multi_pw_aff *mpa2);
6722 __isl_give isl_union_pw_multi_aff *
6723 isl_union_pw_multi_aff_flat_range_product(
6724 __isl_take isl_union_pw_multi_aff *upma1,
6725 __isl_take isl_union_pw_multi_aff *upma2);
6726 __isl_give isl_multi_union_pw_aff *
6727 isl_multi_union_pw_aff_flat_range_product(
6728 __isl_take isl_multi_union_pw_aff *mupa1,
6729 __isl_take isl_multi_union_pw_aff *mupa2);
6731 #include <isl/space.h>
6732 __isl_give isl_space *isl_space_factor_domain(
6733 __isl_take isl_space *space);
6734 __isl_give isl_space *isl_space_factor_range(
6735 __isl_take isl_space *space);
6736 __isl_give isl_space *isl_space_domain_factor_domain(
6737 __isl_take isl_space *space);
6738 __isl_give isl_space *isl_space_domain_factor_range(
6739 __isl_take isl_space *space);
6740 __isl_give isl_space *isl_space_range_factor_domain(
6741 __isl_take isl_space *space);
6742 __isl_give isl_space *isl_space_range_factor_range(
6743 __isl_take isl_space *space);
6745 The functions C<isl_space_range_factor_domain> and
6746 C<isl_space_range_factor_range> extract the two arguments from
6747 the result of a call to C<isl_space_range_product>.
6749 The arguments of a call to a product can be extracted
6750 from the result using the following functions.
6752 #include <isl/map.h>
6753 __isl_give isl_map *isl_map_factor_domain(
6754 __isl_take isl_map *map);
6755 __isl_give isl_map *isl_map_factor_range(
6756 __isl_take isl_map *map);
6757 __isl_give isl_map *isl_map_domain_factor_domain(
6758 __isl_take isl_map *map);
6759 __isl_give isl_map *isl_map_domain_factor_range(
6760 __isl_take isl_map *map);
6761 __isl_give isl_map *isl_map_range_factor_domain(
6762 __isl_take isl_map *map);
6763 __isl_give isl_map *isl_map_range_factor_range(
6764 __isl_take isl_map *map);
6766 #include <isl/union_map.h>
6767 __isl_give isl_union_map *isl_union_map_factor_domain(
6768 __isl_take isl_union_map *umap);
6769 __isl_give isl_union_map *isl_union_map_factor_range(
6770 __isl_take isl_union_map *umap);
6771 __isl_give isl_union_map *
6772 isl_union_map_domain_factor_domain(
6773 __isl_take isl_union_map *umap);
6774 __isl_give isl_union_map *
6775 isl_union_map_domain_factor_range(
6776 __isl_take isl_union_map *umap);
6777 __isl_give isl_union_map *
6778 isl_union_map_range_factor_domain(
6779 __isl_take isl_union_map *umap);
6780 __isl_give isl_union_map *
6781 isl_union_map_range_factor_range(
6782 __isl_take isl_union_map *umap);
6784 #include <isl/val.h>
6785 __isl_give isl_multi_val *isl_multi_val_factor_range(
6786 __isl_take isl_multi_val *mv);
6787 __isl_give isl_multi_val *
6788 isl_multi_val_range_factor_domain(
6789 __isl_take isl_multi_val *mv);
6790 __isl_give isl_multi_val *
6791 isl_multi_val_range_factor_range(
6792 __isl_take isl_multi_val *mv);
6794 #include <isl/aff.h>
6795 __isl_give isl_multi_aff *isl_multi_aff_factor_range(
6796 __isl_take isl_multi_aff *ma);
6797 __isl_give isl_multi_aff *
6798 isl_multi_aff_range_factor_domain(
6799 __isl_take isl_multi_aff *ma);
6800 __isl_give isl_multi_aff *
6801 isl_multi_aff_range_factor_range(
6802 __isl_take isl_multi_aff *ma);
6803 __isl_give isl_multi_pw_aff *
6804 isl_multi_pw_aff_factor_range(
6805 __isl_take isl_multi_pw_aff *mpa);
6806 __isl_give isl_multi_pw_aff *
6807 isl_multi_pw_aff_range_factor_domain(
6808 __isl_take isl_multi_pw_aff *mpa);
6809 __isl_give isl_multi_pw_aff *
6810 isl_multi_pw_aff_range_factor_range(
6811 __isl_take isl_multi_pw_aff *mpa);
6812 __isl_give isl_multi_union_pw_aff *
6813 isl_multi_union_pw_aff_factor_range(
6814 __isl_take isl_multi_union_pw_aff *mupa);
6815 __isl_give isl_multi_union_pw_aff *
6816 isl_multi_union_pw_aff_range_factor_domain(
6817 __isl_take isl_multi_union_pw_aff *mupa);
6818 __isl_give isl_multi_union_pw_aff *
6819 isl_multi_union_pw_aff_range_factor_range(
6820 __isl_take isl_multi_union_pw_aff *mupa);
6822 The splice functions are a generalization of the flat product functions,
6823 where the second argument may be inserted at any position inside
6824 the first argument rather than being placed at the end.
6825 The functions C<isl_multi_val_factor_range>,
6826 C<isl_multi_aff_factor_range>,
6827 C<isl_multi_pw_aff_factor_range> and
6828 C<isl_multi_union_pw_aff_factor_range>
6829 take functions that live in a set space.
6831 #include <isl/val.h>
6832 __isl_give isl_multi_val *isl_multi_val_range_splice(
6833 __isl_take isl_multi_val *mv1, unsigned pos,
6834 __isl_take isl_multi_val *mv2);
6836 #include <isl/aff.h>
6837 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
6838 __isl_take isl_multi_aff *ma1, unsigned pos,
6839 __isl_take isl_multi_aff *ma2);
6840 __isl_give isl_multi_aff *isl_multi_aff_splice(
6841 __isl_take isl_multi_aff *ma1,
6842 unsigned in_pos, unsigned out_pos,
6843 __isl_take isl_multi_aff *ma2);
6844 __isl_give isl_multi_pw_aff *
6845 isl_multi_pw_aff_range_splice(
6846 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
6847 __isl_take isl_multi_pw_aff *mpa2);
6848 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
6849 __isl_take isl_multi_pw_aff *mpa1,
6850 unsigned in_pos, unsigned out_pos,
6851 __isl_take isl_multi_pw_aff *mpa2);
6852 __isl_give isl_multi_union_pw_aff *
6853 isl_multi_union_pw_aff_range_splice(
6854 __isl_take isl_multi_union_pw_aff *mupa1,
6856 __isl_take isl_multi_union_pw_aff *mupa2);
6858 =item * Simplification
6860 When applied to a set or relation,
6861 the gist operation returns a set or relation that has the
6862 same intersection with the context as the input set or relation.
6863 Any implicit equality in the intersection is made explicit in the result,
6864 while all inequalities that are redundant with respect to the intersection
6866 In case of union sets and relations, the gist operation is performed
6869 When applied to a function,
6870 the gist operation applies the set gist operation to each of
6871 the cells in the domain of the input piecewise expression.
6872 The context is also exploited
6873 to simplify the expression associated to each cell.
6875 #include <isl/set.h>
6876 __isl_give isl_basic_set *isl_basic_set_gist(
6877 __isl_take isl_basic_set *bset,
6878 __isl_take isl_basic_set *context);
6879 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
6880 __isl_take isl_set *context);
6881 __isl_give isl_set *isl_set_gist_params(
6882 __isl_take isl_set *set,
6883 __isl_take isl_set *context);
6885 #include <isl/map.h>
6886 __isl_give isl_basic_map *isl_basic_map_gist(
6887 __isl_take isl_basic_map *bmap,
6888 __isl_take isl_basic_map *context);
6889 __isl_give isl_basic_map *isl_basic_map_gist_domain(
6890 __isl_take isl_basic_map *bmap,
6891 __isl_take isl_basic_set *context);
6892 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
6893 __isl_take isl_map *context);
6894 __isl_give isl_map *isl_map_gist_params(
6895 __isl_take isl_map *map,
6896 __isl_take isl_set *context);
6897 __isl_give isl_map *isl_map_gist_domain(
6898 __isl_take isl_map *map,
6899 __isl_take isl_set *context);
6900 __isl_give isl_map *isl_map_gist_range(
6901 __isl_take isl_map *map,
6902 __isl_take isl_set *context);
6904 #include <isl/union_set.h>
6905 __isl_give isl_union_set *isl_union_set_gist(
6906 __isl_take isl_union_set *uset,
6907 __isl_take isl_union_set *context);
6908 __isl_give isl_union_set *isl_union_set_gist_params(
6909 __isl_take isl_union_set *uset,
6910 __isl_take isl_set *set);
6912 #include <isl/union_map.h>
6913 __isl_give isl_union_map *isl_union_map_gist(
6914 __isl_take isl_union_map *umap,
6915 __isl_take isl_union_map *context);
6916 __isl_give isl_union_map *isl_union_map_gist_params(
6917 __isl_take isl_union_map *umap,
6918 __isl_take isl_set *set);
6919 __isl_give isl_union_map *isl_union_map_gist_domain(
6920 __isl_take isl_union_map *umap,
6921 __isl_take isl_union_set *uset);
6922 __isl_give isl_union_map *isl_union_map_gist_range(
6923 __isl_take isl_union_map *umap,
6924 __isl_take isl_union_set *uset);
6926 #include <isl/aff.h>
6927 __isl_give isl_aff *isl_aff_gist_params(
6928 __isl_take isl_aff *aff,
6929 __isl_take isl_set *context);
6930 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
6931 __isl_take isl_set *context);
6932 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
6933 __isl_take isl_multi_aff *maff,
6934 __isl_take isl_set *context);
6935 __isl_give isl_multi_aff *isl_multi_aff_gist(
6936 __isl_take isl_multi_aff *maff,
6937 __isl_take isl_set *context);
6938 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
6939 __isl_take isl_pw_aff *pwaff,
6940 __isl_take isl_set *context);
6941 __isl_give isl_pw_aff *isl_pw_aff_gist(
6942 __isl_take isl_pw_aff *pwaff,
6943 __isl_take isl_set *context);
6944 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
6945 __isl_take isl_pw_multi_aff *pma,
6946 __isl_take isl_set *set);
6947 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
6948 __isl_take isl_pw_multi_aff *pma,
6949 __isl_take isl_set *set);
6950 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
6951 __isl_take isl_multi_pw_aff *mpa,
6952 __isl_take isl_set *set);
6953 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
6954 __isl_take isl_multi_pw_aff *mpa,
6955 __isl_take isl_set *set);
6956 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
6957 __isl_take isl_union_pw_aff *upa,
6958 __isl_take isl_union_set *context);
6959 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
6960 __isl_take isl_union_pw_aff *upa,
6961 __isl_take isl_set *context);
6962 __isl_give isl_union_pw_multi_aff *
6963 isl_union_pw_multi_aff_gist_params(
6964 __isl_take isl_union_pw_multi_aff *upma,
6965 __isl_take isl_set *context);
6966 __isl_give isl_union_pw_multi_aff *
6967 isl_union_pw_multi_aff_gist(
6968 __isl_take isl_union_pw_multi_aff *upma,
6969 __isl_take isl_union_set *context);
6970 __isl_give isl_multi_union_pw_aff *
6971 isl_multi_union_pw_aff_gist_params(
6972 __isl_take isl_multi_union_pw_aff *aff,
6973 __isl_take isl_set *context);
6974 __isl_give isl_multi_union_pw_aff *
6975 isl_multi_union_pw_aff_gist(
6976 __isl_take isl_multi_union_pw_aff *aff,
6977 __isl_take isl_union_set *context);
6979 #include <isl/polynomial.h>
6980 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
6981 __isl_take isl_qpolynomial *qp,
6982 __isl_take isl_set *context);
6983 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
6984 __isl_take isl_qpolynomial *qp,
6985 __isl_take isl_set *context);
6986 __isl_give isl_qpolynomial_fold *
6987 isl_qpolynomial_fold_gist_params(
6988 __isl_take isl_qpolynomial_fold *fold,
6989 __isl_take isl_set *context);
6990 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
6991 __isl_take isl_qpolynomial_fold *fold,
6992 __isl_take isl_set *context);
6993 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
6994 __isl_take isl_pw_qpolynomial *pwqp,
6995 __isl_take isl_set *context);
6996 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
6997 __isl_take isl_pw_qpolynomial *pwqp,
6998 __isl_take isl_set *context);
6999 __isl_give isl_pw_qpolynomial_fold *
7000 isl_pw_qpolynomial_fold_gist(
7001 __isl_take isl_pw_qpolynomial_fold *pwf,
7002 __isl_take isl_set *context);
7003 __isl_give isl_pw_qpolynomial_fold *
7004 isl_pw_qpolynomial_fold_gist_params(
7005 __isl_take isl_pw_qpolynomial_fold *pwf,
7006 __isl_take isl_set *context);
7007 __isl_give isl_union_pw_qpolynomial *
7008 isl_union_pw_qpolynomial_gist_params(
7009 __isl_take isl_union_pw_qpolynomial *upwqp,
7010 __isl_take isl_set *context);
7011 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
7012 __isl_take isl_union_pw_qpolynomial *upwqp,
7013 __isl_take isl_union_set *context);
7014 __isl_give isl_union_pw_qpolynomial_fold *
7015 isl_union_pw_qpolynomial_fold_gist(
7016 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7017 __isl_take isl_union_set *context);
7018 __isl_give isl_union_pw_qpolynomial_fold *
7019 isl_union_pw_qpolynomial_fold_gist_params(
7020 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7021 __isl_take isl_set *context);
7023 =item * Binary Arithmetic Operations
7025 #include <isl/set.h>
7026 __isl_give isl_set *isl_set_sum(
7027 __isl_take isl_set *set1,
7028 __isl_take isl_set *set2);
7029 #include <isl/map.h>
7030 __isl_give isl_map *isl_map_sum(
7031 __isl_take isl_map *map1,
7032 __isl_take isl_map *map2);
7034 C<isl_set_sum> computes the Minkowski sum of its two arguments,
7035 i.e., the set containing the sums of pairs of elements from
7036 C<set1> and C<set2>.
7037 The domain of the result of C<isl_map_sum> is the intersection
7038 of the domains of its two arguments. The corresponding range
7039 elements are the sums of the corresponding range elements
7040 in the two arguments.
7042 #include <isl/val.h>
7043 __isl_give isl_multi_val *isl_multi_val_add(
7044 __isl_take isl_multi_val *mv1,
7045 __isl_take isl_multi_val *mv2);
7046 __isl_give isl_multi_val *isl_multi_val_sub(
7047 __isl_take isl_multi_val *mv1,
7048 __isl_take isl_multi_val *mv2);
7050 #include <isl/aff.h>
7051 __isl_give isl_aff *isl_aff_add(
7052 __isl_take isl_aff *aff1,
7053 __isl_take isl_aff *aff2);
7054 __isl_give isl_multi_aff *isl_multi_aff_add(
7055 __isl_take isl_multi_aff *maff1,
7056 __isl_take isl_multi_aff *maff2);
7057 __isl_give isl_pw_aff *isl_pw_aff_add(
7058 __isl_take isl_pw_aff *pwaff1,
7059 __isl_take isl_pw_aff *pwaff2);
7060 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add(
7061 __isl_take isl_multi_pw_aff *mpa1,
7062 __isl_take isl_multi_pw_aff *mpa2);
7063 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
7064 __isl_take isl_pw_multi_aff *pma1,
7065 __isl_take isl_pw_multi_aff *pma2);
7066 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
7067 __isl_take isl_union_pw_aff *upa1,
7068 __isl_take isl_union_pw_aff *upa2);
7069 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
7070 __isl_take isl_union_pw_multi_aff *upma1,
7071 __isl_take isl_union_pw_multi_aff *upma2);
7072 __isl_give isl_multi_union_pw_aff *
7073 isl_multi_union_pw_aff_add(
7074 __isl_take isl_multi_union_pw_aff *mupa1,
7075 __isl_take isl_multi_union_pw_aff *mupa2);
7076 __isl_give isl_pw_aff *isl_pw_aff_min(
7077 __isl_take isl_pw_aff *pwaff1,
7078 __isl_take isl_pw_aff *pwaff2);
7079 __isl_give isl_pw_aff *isl_pw_aff_max(
7080 __isl_take isl_pw_aff *pwaff1,
7081 __isl_take isl_pw_aff *pwaff2);
7082 __isl_give isl_aff *isl_aff_sub(
7083 __isl_take isl_aff *aff1,
7084 __isl_take isl_aff *aff2);
7085 __isl_give isl_multi_aff *isl_multi_aff_sub(
7086 __isl_take isl_multi_aff *ma1,
7087 __isl_take isl_multi_aff *ma2);
7088 __isl_give isl_pw_aff *isl_pw_aff_sub(
7089 __isl_take isl_pw_aff *pwaff1,
7090 __isl_take isl_pw_aff *pwaff2);
7091 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
7092 __isl_take isl_multi_pw_aff *mpa1,
7093 __isl_take isl_multi_pw_aff *mpa2);
7094 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
7095 __isl_take isl_pw_multi_aff *pma1,
7096 __isl_take isl_pw_multi_aff *pma2);
7097 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
7098 __isl_take isl_union_pw_aff *upa1,
7099 __isl_take isl_union_pw_aff *upa2);
7100 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
7101 __isl_take isl_union_pw_multi_aff *upma1,
7102 __isl_take isl_union_pw_multi_aff *upma2);
7103 __isl_give isl_multi_union_pw_aff *
7104 isl_multi_union_pw_aff_sub(
7105 __isl_take isl_multi_union_pw_aff *mupa1,
7106 __isl_take isl_multi_union_pw_aff *mupa2);
7108 C<isl_aff_sub> subtracts the second argument from the first.
7110 #include <isl/polynomial.h>
7111 __isl_give isl_qpolynomial *isl_qpolynomial_add(
7112 __isl_take isl_qpolynomial *qp1,
7113 __isl_take isl_qpolynomial *qp2);
7114 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
7115 __isl_take isl_pw_qpolynomial *pwqp1,
7116 __isl_take isl_pw_qpolynomial *pwqp2);
7117 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
7118 __isl_take isl_pw_qpolynomial *pwqp1,
7119 __isl_take isl_pw_qpolynomial *pwqp2);
7120 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
7121 __isl_take isl_pw_qpolynomial_fold *pwf1,
7122 __isl_take isl_pw_qpolynomial_fold *pwf2);
7123 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
7124 __isl_take isl_union_pw_qpolynomial *upwqp1,
7125 __isl_take isl_union_pw_qpolynomial *upwqp2);
7126 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
7127 __isl_take isl_qpolynomial *qp1,
7128 __isl_take isl_qpolynomial *qp2);
7129 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
7130 __isl_take isl_pw_qpolynomial *pwqp1,
7131 __isl_take isl_pw_qpolynomial *pwqp2);
7132 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
7133 __isl_take isl_union_pw_qpolynomial *upwqp1,
7134 __isl_take isl_union_pw_qpolynomial *upwqp2);
7135 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
7136 __isl_take isl_pw_qpolynomial_fold *pwf1,
7137 __isl_take isl_pw_qpolynomial_fold *pwf2);
7138 __isl_give isl_union_pw_qpolynomial_fold *
7139 isl_union_pw_qpolynomial_fold_fold(
7140 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
7141 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
7143 #include <isl/aff.h>
7144 __isl_give isl_pw_aff *isl_pw_aff_union_add(
7145 __isl_take isl_pw_aff *pwaff1,
7146 __isl_take isl_pw_aff *pwaff2);
7147 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
7148 __isl_take isl_pw_multi_aff *pma1,
7149 __isl_take isl_pw_multi_aff *pma2);
7150 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
7151 __isl_take isl_union_pw_aff *upa1,
7152 __isl_take isl_union_pw_aff *upa2);
7153 __isl_give isl_union_pw_multi_aff *
7154 isl_union_pw_multi_aff_union_add(
7155 __isl_take isl_union_pw_multi_aff *upma1,
7156 __isl_take isl_union_pw_multi_aff *upma2);
7157 __isl_give isl_multi_union_pw_aff *
7158 isl_multi_union_pw_aff_union_add(
7159 __isl_take isl_multi_union_pw_aff *mupa1,
7160 __isl_take isl_multi_union_pw_aff *mupa2);
7161 __isl_give isl_pw_aff *isl_pw_aff_union_min(
7162 __isl_take isl_pw_aff *pwaff1,
7163 __isl_take isl_pw_aff *pwaff2);
7164 __isl_give isl_pw_aff *isl_pw_aff_union_max(
7165 __isl_take isl_pw_aff *pwaff1,
7166 __isl_take isl_pw_aff *pwaff2);
7168 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
7169 expression with a domain that is the union of those of C<pwaff1> and
7170 C<pwaff2> and such that on each cell, the quasi-affine expression is
7171 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
7172 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
7173 associated expression is the defined one.
7174 This in contrast to the C<isl_pw_aff_max> function, which is
7175 only defined on the shared definition domain of the arguments.
7177 #include <isl/val.h>
7178 __isl_give isl_multi_val *isl_multi_val_add_val(
7179 __isl_take isl_multi_val *mv,
7180 __isl_take isl_val *v);
7181 __isl_give isl_multi_val *isl_multi_val_mod_val(
7182 __isl_take isl_multi_val *mv,
7183 __isl_take isl_val *v);
7184 __isl_give isl_multi_val *isl_multi_val_scale_val(
7185 __isl_take isl_multi_val *mv,
7186 __isl_take isl_val *v);
7187 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
7188 __isl_take isl_multi_val *mv,
7189 __isl_take isl_val *v);
7191 #include <isl/aff.h>
7192 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
7193 __isl_take isl_val *mod);
7194 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
7195 __isl_take isl_pw_aff *pa,
7196 __isl_take isl_val *mod);
7197 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
7198 __isl_take isl_union_pw_aff *upa,
7199 __isl_take isl_val *f);
7200 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
7201 __isl_take isl_val *v);
7202 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
7203 __isl_take isl_multi_aff *ma,
7204 __isl_take isl_val *v);
7205 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
7206 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
7207 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
7208 __isl_take isl_multi_pw_aff *mpa,
7209 __isl_take isl_val *v);
7210 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
7211 __isl_take isl_pw_multi_aff *pma,
7212 __isl_take isl_val *v);
7213 __isl_give isl_union_pw_multi_aff *
7214 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
7215 __isl_take isl_union_pw_aff *upa,
7216 __isl_take isl_val *f);
7217 isl_union_pw_multi_aff_scale_val(
7218 __isl_take isl_union_pw_multi_aff *upma,
7219 __isl_take isl_val *val);
7220 __isl_give isl_multi_union_pw_aff *
7221 isl_multi_union_pw_aff_scale_val(
7222 __isl_take isl_multi_union_pw_aff *mupa,
7223 __isl_take isl_val *v);
7224 __isl_give isl_aff *isl_aff_scale_down_ui(
7225 __isl_take isl_aff *aff, unsigned f);
7226 __isl_give isl_aff *isl_aff_scale_down_val(
7227 __isl_take isl_aff *aff, __isl_take isl_val *v);
7228 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
7229 __isl_take isl_multi_aff *ma,
7230 __isl_take isl_val *v);
7231 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
7232 __isl_take isl_pw_aff *pa,
7233 __isl_take isl_val *f);
7234 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
7235 __isl_take isl_multi_pw_aff *mpa,
7236 __isl_take isl_val *v);
7237 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
7238 __isl_take isl_pw_multi_aff *pma,
7239 __isl_take isl_val *v);
7240 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
7241 __isl_take isl_union_pw_aff *upa,
7242 __isl_take isl_val *v);
7243 __isl_give isl_union_pw_multi_aff *
7244 isl_union_pw_multi_aff_scale_down_val(
7245 __isl_take isl_union_pw_multi_aff *upma,
7246 __isl_take isl_val *val);
7247 __isl_give isl_multi_union_pw_aff *
7248 isl_multi_union_pw_aff_scale_down_val(
7249 __isl_take isl_multi_union_pw_aff *mupa,
7250 __isl_take isl_val *v);
7252 #include <isl/polynomial.h>
7253 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
7254 __isl_take isl_qpolynomial *qp,
7255 __isl_take isl_val *v);
7256 __isl_give isl_qpolynomial_fold *
7257 isl_qpolynomial_fold_scale_val(
7258 __isl_take isl_qpolynomial_fold *fold,
7259 __isl_take isl_val *v);
7260 __isl_give isl_pw_qpolynomial *
7261 isl_pw_qpolynomial_scale_val(
7262 __isl_take isl_pw_qpolynomial *pwqp,
7263 __isl_take isl_val *v);
7264 __isl_give isl_pw_qpolynomial_fold *
7265 isl_pw_qpolynomial_fold_scale_val(
7266 __isl_take isl_pw_qpolynomial_fold *pwf,
7267 __isl_take isl_val *v);
7268 __isl_give isl_union_pw_qpolynomial *
7269 isl_union_pw_qpolynomial_scale_val(
7270 __isl_take isl_union_pw_qpolynomial *upwqp,
7271 __isl_take isl_val *v);
7272 __isl_give isl_union_pw_qpolynomial_fold *
7273 isl_union_pw_qpolynomial_fold_scale_val(
7274 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7275 __isl_take isl_val *v);
7276 __isl_give isl_qpolynomial *
7277 isl_qpolynomial_scale_down_val(
7278 __isl_take isl_qpolynomial *qp,
7279 __isl_take isl_val *v);
7280 __isl_give isl_qpolynomial_fold *
7281 isl_qpolynomial_fold_scale_down_val(
7282 __isl_take isl_qpolynomial_fold *fold,
7283 __isl_take isl_val *v);
7284 __isl_give isl_pw_qpolynomial *
7285 isl_pw_qpolynomial_scale_down_val(
7286 __isl_take isl_pw_qpolynomial *pwqp,
7287 __isl_take isl_val *v);
7288 __isl_give isl_pw_qpolynomial_fold *
7289 isl_pw_qpolynomial_fold_scale_down_val(
7290 __isl_take isl_pw_qpolynomial_fold *pwf,
7291 __isl_take isl_val *v);
7292 __isl_give isl_union_pw_qpolynomial *
7293 isl_union_pw_qpolynomial_scale_down_val(
7294 __isl_take isl_union_pw_qpolynomial *upwqp,
7295 __isl_take isl_val *v);
7296 __isl_give isl_union_pw_qpolynomial_fold *
7297 isl_union_pw_qpolynomial_fold_scale_down_val(
7298 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7299 __isl_take isl_val *v);
7301 #include <isl/val.h>
7302 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
7303 __isl_take isl_multi_val *mv1,
7304 __isl_take isl_multi_val *mv2);
7305 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
7306 __isl_take isl_multi_val *mv1,
7307 __isl_take isl_multi_val *mv2);
7308 __isl_give isl_multi_val *
7309 isl_multi_val_scale_down_multi_val(
7310 __isl_take isl_multi_val *mv1,
7311 __isl_take isl_multi_val *mv2);
7313 #include <isl/aff.h>
7314 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
7315 __isl_take isl_multi_aff *ma,
7316 __isl_take isl_multi_val *mv);
7317 __isl_give isl_multi_union_pw_aff *
7318 isl_multi_union_pw_aff_mod_multi_val(
7319 __isl_take isl_multi_union_pw_aff *upma,
7320 __isl_take isl_multi_val *mv);
7321 __isl_give isl_multi_pw_aff *
7322 isl_multi_pw_aff_mod_multi_val(
7323 __isl_take isl_multi_pw_aff *mpa,
7324 __isl_take isl_multi_val *mv);
7325 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
7326 __isl_take isl_multi_aff *ma,
7327 __isl_take isl_multi_val *mv);
7328 __isl_give isl_pw_multi_aff *
7329 isl_pw_multi_aff_scale_multi_val(
7330 __isl_take isl_pw_multi_aff *pma,
7331 __isl_take isl_multi_val *mv);
7332 __isl_give isl_multi_pw_aff *
7333 isl_multi_pw_aff_scale_multi_val(
7334 __isl_take isl_multi_pw_aff *mpa,
7335 __isl_take isl_multi_val *mv);
7336 __isl_give isl_multi_union_pw_aff *
7337 isl_multi_union_pw_aff_scale_multi_val(
7338 __isl_take isl_multi_union_pw_aff *mupa,
7339 __isl_take isl_multi_val *mv);
7340 __isl_give isl_union_pw_multi_aff *
7341 isl_union_pw_multi_aff_scale_multi_val(
7342 __isl_take isl_union_pw_multi_aff *upma,
7343 __isl_take isl_multi_val *mv);
7344 __isl_give isl_multi_aff *
7345 isl_multi_aff_scale_down_multi_val(
7346 __isl_take isl_multi_aff *ma,
7347 __isl_take isl_multi_val *mv);
7348 __isl_give isl_multi_pw_aff *
7349 isl_multi_pw_aff_scale_down_multi_val(
7350 __isl_take isl_multi_pw_aff *mpa,
7351 __isl_take isl_multi_val *mv);
7352 __isl_give isl_multi_union_pw_aff *
7353 isl_multi_union_pw_aff_scale_down_multi_val(
7354 __isl_take isl_multi_union_pw_aff *mupa,
7355 __isl_take isl_multi_val *mv);
7357 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
7358 by the corresponding elements of C<mv>.
7360 #include <isl/aff.h>
7361 __isl_give isl_aff *isl_aff_mul(
7362 __isl_take isl_aff *aff1,
7363 __isl_take isl_aff *aff2);
7364 __isl_give isl_aff *isl_aff_div(
7365 __isl_take isl_aff *aff1,
7366 __isl_take isl_aff *aff2);
7367 __isl_give isl_pw_aff *isl_pw_aff_mul(
7368 __isl_take isl_pw_aff *pwaff1,
7369 __isl_take isl_pw_aff *pwaff2);
7370 __isl_give isl_pw_aff *isl_pw_aff_div(
7371 __isl_take isl_pw_aff *pa1,
7372 __isl_take isl_pw_aff *pa2);
7373 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
7374 __isl_take isl_pw_aff *pa1,
7375 __isl_take isl_pw_aff *pa2);
7376 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
7377 __isl_take isl_pw_aff *pa1,
7378 __isl_take isl_pw_aff *pa2);
7380 When multiplying two affine expressions, at least one of the two needs
7381 to be a constant. Similarly, when dividing an affine expression by another,
7382 the second expression needs to be a constant.
7383 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
7384 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
7387 #include <isl/polynomial.h>
7388 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
7389 __isl_take isl_qpolynomial *qp1,
7390 __isl_take isl_qpolynomial *qp2);
7391 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
7392 __isl_take isl_pw_qpolynomial *pwqp1,
7393 __isl_take isl_pw_qpolynomial *pwqp2);
7394 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
7395 __isl_take isl_union_pw_qpolynomial *upwqp1,
7396 __isl_take isl_union_pw_qpolynomial *upwqp2);
7400 =head3 Lexicographic Optimization
7402 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
7403 the following functions
7404 compute a set that contains the lexicographic minimum or maximum
7405 of the elements in C<set> (or C<bset>) for those values of the parameters
7406 that satisfy C<dom>.
7407 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7408 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
7410 In other words, the union of the parameter values
7411 for which the result is non-empty and of C<*empty>
7414 #include <isl/set.h>
7415 __isl_give isl_set *isl_basic_set_partial_lexmin(
7416 __isl_take isl_basic_set *bset,
7417 __isl_take isl_basic_set *dom,
7418 __isl_give isl_set **empty);
7419 __isl_give isl_set *isl_basic_set_partial_lexmax(
7420 __isl_take isl_basic_set *bset,
7421 __isl_take isl_basic_set *dom,
7422 __isl_give isl_set **empty);
7423 __isl_give isl_set *isl_set_partial_lexmin(
7424 __isl_take isl_set *set, __isl_take isl_set *dom,
7425 __isl_give isl_set **empty);
7426 __isl_give isl_set *isl_set_partial_lexmax(
7427 __isl_take isl_set *set, __isl_take isl_set *dom,
7428 __isl_give isl_set **empty);
7430 Given a (basic) set C<set> (or C<bset>), the following functions simply
7431 return a set containing the lexicographic minimum or maximum
7432 of the elements in C<set> (or C<bset>).
7433 In case of union sets, the optimum is computed per space.
7435 #include <isl/set.h>
7436 __isl_give isl_set *isl_basic_set_lexmin(
7437 __isl_take isl_basic_set *bset);
7438 __isl_give isl_set *isl_basic_set_lexmax(
7439 __isl_take isl_basic_set *bset);
7440 __isl_give isl_set *isl_set_lexmin(
7441 __isl_take isl_set *set);
7442 __isl_give isl_set *isl_set_lexmax(
7443 __isl_take isl_set *set);
7444 __isl_give isl_union_set *isl_union_set_lexmin(
7445 __isl_take isl_union_set *uset);
7446 __isl_give isl_union_set *isl_union_set_lexmax(
7447 __isl_take isl_union_set *uset);
7449 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
7450 the following functions
7451 compute a relation that maps each element of C<dom>
7452 to the single lexicographic minimum or maximum
7453 of the elements that are associated to that same
7454 element in C<map> (or C<bmap>).
7455 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7456 that contains the elements in C<dom> that do not map
7457 to any elements in C<map> (or C<bmap>).
7458 In other words, the union of the domain of the result and of C<*empty>
7461 #include <isl/map.h>
7462 __isl_give isl_map *isl_basic_map_partial_lexmax(
7463 __isl_take isl_basic_map *bmap,
7464 __isl_take isl_basic_set *dom,
7465 __isl_give isl_set **empty);
7466 __isl_give isl_map *isl_basic_map_partial_lexmin(
7467 __isl_take isl_basic_map *bmap,
7468 __isl_take isl_basic_set *dom,
7469 __isl_give isl_set **empty);
7470 __isl_give isl_map *isl_map_partial_lexmax(
7471 __isl_take isl_map *map, __isl_take isl_set *dom,
7472 __isl_give isl_set **empty);
7473 __isl_give isl_map *isl_map_partial_lexmin(
7474 __isl_take isl_map *map, __isl_take isl_set *dom,
7475 __isl_give isl_set **empty);
7477 Given a (basic) map C<map> (or C<bmap>), the following functions simply
7478 return a map mapping each element in the domain of
7479 C<map> (or C<bmap>) to the lexicographic minimum or maximum
7480 of all elements associated to that element.
7481 In case of union relations, the optimum is computed per space.
7483 #include <isl/map.h>
7484 __isl_give isl_map *isl_basic_map_lexmin(
7485 __isl_take isl_basic_map *bmap);
7486 __isl_give isl_map *isl_basic_map_lexmax(
7487 __isl_take isl_basic_map *bmap);
7488 __isl_give isl_map *isl_map_lexmin(
7489 __isl_take isl_map *map);
7490 __isl_give isl_map *isl_map_lexmax(
7491 __isl_take isl_map *map);
7492 __isl_give isl_union_map *isl_union_map_lexmin(
7493 __isl_take isl_union_map *umap);
7494 __isl_give isl_union_map *isl_union_map_lexmax(
7495 __isl_take isl_union_map *umap);
7497 The following functions return their result in the form of
7498 a piecewise multi-affine expression,
7499 but are otherwise equivalent to the corresponding functions
7500 returning a basic set or relation.
7502 #include <isl/set.h>
7503 __isl_give isl_pw_multi_aff *
7504 isl_basic_set_partial_lexmin_pw_multi_aff(
7505 __isl_take isl_basic_set *bset,
7506 __isl_take isl_basic_set *dom,
7507 __isl_give isl_set **empty);
7508 __isl_give isl_pw_multi_aff *
7509 isl_basic_set_partial_lexmax_pw_multi_aff(
7510 __isl_take isl_basic_set *bset,
7511 __isl_take isl_basic_set *dom,
7512 __isl_give isl_set **empty);
7513 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
7514 __isl_take isl_set *set);
7515 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
7516 __isl_take isl_set *set);
7518 #include <isl/map.h>
7519 __isl_give isl_pw_multi_aff *
7520 isl_basic_map_lexmin_pw_multi_aff(
7521 __isl_take isl_basic_map *bmap);
7522 __isl_give isl_pw_multi_aff *
7523 isl_basic_map_partial_lexmin_pw_multi_aff(
7524 __isl_take isl_basic_map *bmap,
7525 __isl_take isl_basic_set *dom,
7526 __isl_give isl_set **empty);
7527 __isl_give isl_pw_multi_aff *
7528 isl_basic_map_partial_lexmax_pw_multi_aff(
7529 __isl_take isl_basic_map *bmap,
7530 __isl_take isl_basic_set *dom,
7531 __isl_give isl_set **empty);
7532 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
7533 __isl_take isl_map *map);
7534 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
7535 __isl_take isl_map *map);
7537 The following functions return the lexicographic minimum or maximum
7538 on the shared domain of the inputs and the single defined function
7539 on those parts of the domain where only a single function is defined.
7541 #include <isl/aff.h>
7542 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
7543 __isl_take isl_pw_multi_aff *pma1,
7544 __isl_take isl_pw_multi_aff *pma2);
7545 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
7546 __isl_take isl_pw_multi_aff *pma1,
7547 __isl_take isl_pw_multi_aff *pma2);
7549 If the input to a lexicographic optimization problem has
7550 multiple constraints with the same coefficients for the optimized
7551 variables, then, by default, this symmetry is exploited by
7552 replacing those constraints by a single constraint with
7553 an abstract bound, which is in turn bounded by the corresponding terms
7554 in the original constraints.
7555 Without this optimization, the solver would typically consider
7556 all possible orderings of those original bounds, resulting in a needless
7557 decomposition of the domain.
7558 However, the optimization can also result in slowdowns since
7559 an extra parameter is introduced that may get used in additional
7561 The following option determines whether symmetry detection is applied
7562 during lexicographic optimization.
7564 #include <isl/options.h>
7565 isl_stat isl_options_set_pip_symmetry(isl_ctx *ctx,
7567 int isl_options_get_pip_symmetry(isl_ctx *ctx);
7571 See also \autoref{s:offline}.
7575 =head2 Ternary Operations
7577 #include <isl/aff.h>
7578 __isl_give isl_pw_aff *isl_pw_aff_cond(
7579 __isl_take isl_pw_aff *cond,
7580 __isl_take isl_pw_aff *pwaff_true,
7581 __isl_take isl_pw_aff *pwaff_false);
7583 The function C<isl_pw_aff_cond> performs a conditional operator
7584 and returns an expression that is equal to C<pwaff_true>
7585 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
7586 where C<cond> is zero.
7590 Lists are defined over several element types, including
7591 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_union_pw_aff>,
7592 C<isl_union_pw_multi_aff>, C<isl_constraint>,
7593 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
7594 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
7595 Here we take lists of C<isl_set>s as an example.
7596 Lists can be created, copied, modified and freed using the following functions.
7598 #include <isl/set.h>
7599 __isl_give isl_set_list *isl_set_list_from_set(
7600 __isl_take isl_set *el);
7601 __isl_give isl_set_list *isl_set_list_alloc(
7602 isl_ctx *ctx, int n);
7603 __isl_give isl_set_list *isl_set_list_copy(
7604 __isl_keep isl_set_list *list);
7605 __isl_give isl_set_list *isl_set_list_insert(
7606 __isl_take isl_set_list *list, unsigned pos,
7607 __isl_take isl_set *el);
7608 __isl_give isl_set_list *isl_set_list_add(
7609 __isl_take isl_set_list *list,
7610 __isl_take isl_set *el);
7611 __isl_give isl_set_list *isl_set_list_drop(
7612 __isl_take isl_set_list *list,
7613 unsigned first, unsigned n);
7614 __isl_give isl_set_list *isl_set_list_set_set(
7615 __isl_take isl_set_list *list, int index,
7616 __isl_take isl_set *set);
7617 __isl_give isl_set_list *isl_set_list_concat(
7618 __isl_take isl_set_list *list1,
7619 __isl_take isl_set_list *list2);
7620 __isl_give isl_set_list *isl_set_list_map(
7621 __isl_take isl_set_list *list,
7622 __isl_give isl_set *(*fn)(__isl_take isl_set *el,
7625 __isl_give isl_set_list *isl_set_list_sort(
7626 __isl_take isl_set_list *list,
7627 int (*cmp)(__isl_keep isl_set *a,
7628 __isl_keep isl_set *b, void *user),
7630 __isl_null isl_set_list *isl_set_list_free(
7631 __isl_take isl_set_list *list);
7633 C<isl_set_list_alloc> creates an empty list with an initial capacity
7634 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
7635 add elements to a list, increasing its capacity as needed.
7636 C<isl_set_list_from_set> creates a list with a single element.
7638 Lists can be inspected using the following functions.
7640 #include <isl/set.h>
7641 int isl_set_list_n_set(__isl_keep isl_set_list *list);
7642 __isl_give isl_set *isl_set_list_get_set(
7643 __isl_keep isl_set_list *list, int index);
7644 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list,
7645 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7647 isl_stat isl_set_list_foreach_scc(
7648 __isl_keep isl_set_list *list,
7649 isl_bool (*follows)(__isl_keep isl_set *a,
7650 __isl_keep isl_set *b, void *user),
7652 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7655 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
7656 strongly connected components of the graph with as vertices the elements
7657 of C<list> and a directed edge from vertex C<b> to vertex C<a>
7658 iff C<follows(a, b)> returns C<isl_bool_true>. The callbacks C<follows> and
7659 C<fn> should return C<isl_bool_error> or C<isl_stat_error> on error.
7661 Lists can be printed using
7663 #include <isl/set.h>
7664 __isl_give isl_printer *isl_printer_print_set_list(
7665 __isl_take isl_printer *p,
7666 __isl_keep isl_set_list *list);
7668 =head2 Associative arrays
7670 Associative arrays map isl objects of a specific type to isl objects
7671 of some (other) specific type. They are defined for several pairs
7672 of types, including (C<isl_map>, C<isl_basic_set>),
7673 (C<isl_id>, C<isl_ast_expr>),
7674 (C<isl_id>, C<isl_id>) and
7675 (C<isl_id>, C<isl_pw_aff>).
7676 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
7679 Associative arrays can be created, copied and freed using
7680 the following functions.
7682 #include <isl/id_to_ast_expr.h>
7683 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
7684 isl_ctx *ctx, int min_size);
7685 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
7686 __isl_keep isl_id_to_ast_expr *id2expr);
7687 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
7688 __isl_take isl_id_to_ast_expr *id2expr);
7690 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
7691 to specify the expected size of the associative array.
7692 The associative array will be grown automatically as needed.
7694 Associative arrays can be inspected using the following functions.
7696 #include <isl/id_to_ast_expr.h>
7697 __isl_give isl_maybe_isl_ast_expr
7698 isl_id_to_ast_expr_try_get(
7699 __isl_keep isl_id_to_ast_expr *id2expr,
7700 __isl_keep isl_id *key);
7701 isl_bool isl_id_to_ast_expr_has(
7702 __isl_keep isl_id_to_ast_expr *id2expr,
7703 __isl_keep isl_id *key);
7704 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
7705 __isl_keep isl_id_to_ast_expr *id2expr,
7706 __isl_take isl_id *key);
7707 isl_stat isl_id_to_ast_expr_foreach(
7708 __isl_keep isl_id_to_ast_expr *id2expr,
7709 isl_stat (*fn)(__isl_take isl_id *key,
7710 __isl_take isl_ast_expr *val, void *user),
7713 The function C<isl_id_to_ast_expr_try_get> returns a structure
7714 containing two elements, C<valid> and C<value>.
7715 If there is a value associated to the key, then C<valid>
7716 is set to C<isl_bool_true> and C<value> contains a copy of
7717 the associated value. Otherwise C<value> is C<NULL> and
7718 C<valid> may be C<isl_bool_error> or C<isl_bool_false> depending
7719 on whether some error has occurred or there simply is no associated value.
7720 The function C<isl_id_to_ast_expr_has> returns the C<valid> field
7721 in the structure and
7722 the function C<isl_id_to_ast_expr_get> returns the C<value> field.
7724 Associative arrays can be modified using the following functions.
7726 #include <isl/id_to_ast_expr.h>
7727 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
7728 __isl_take isl_id_to_ast_expr *id2expr,
7729 __isl_take isl_id *key,
7730 __isl_take isl_ast_expr *val);
7731 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
7732 __isl_take isl_id_to_ast_expr *id2expr,
7733 __isl_take isl_id *key);
7735 Associative arrays can be printed using the following function.
7737 #include <isl/id_to_ast_expr.h>
7738 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
7739 __isl_take isl_printer *p,
7740 __isl_keep isl_id_to_ast_expr *id2expr);
7744 Vectors can be created, copied and freed using the following functions.
7746 #include <isl/vec.h>
7747 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
7749 __isl_give isl_vec *isl_vec_zero(isl_ctx *ctx,
7751 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
7752 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
7754 Note that the elements of a vector created by C<isl_vec_alloc>
7755 may have arbitrary values.
7756 A vector created by C<isl_vec_zero> has elements with value zero.
7757 The elements can be changed and inspected using the following functions.
7759 int isl_vec_size(__isl_keep isl_vec *vec);
7760 __isl_give isl_val *isl_vec_get_element_val(
7761 __isl_keep isl_vec *vec, int pos);
7762 __isl_give isl_vec *isl_vec_set_element_si(
7763 __isl_take isl_vec *vec, int pos, int v);
7764 __isl_give isl_vec *isl_vec_set_element_val(
7765 __isl_take isl_vec *vec, int pos,
7766 __isl_take isl_val *v);
7767 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
7769 __isl_give isl_vec *isl_vec_set_val(
7770 __isl_take isl_vec *vec, __isl_take isl_val *v);
7771 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
7772 __isl_keep isl_vec *vec2, int pos);
7774 C<isl_vec_get_element> will return a negative value if anything went wrong.
7775 In that case, the value of C<*v> is undefined.
7777 The following function can be used to concatenate two vectors.
7779 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
7780 __isl_take isl_vec *vec2);
7784 Matrices can be created, copied and freed using the following functions.
7786 #include <isl/mat.h>
7787 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
7788 unsigned n_row, unsigned n_col);
7789 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
7790 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
7792 Note that the elements of a newly created matrix may have arbitrary values.
7793 The elements can be changed and inspected using the following functions.
7795 int isl_mat_rows(__isl_keep isl_mat *mat);
7796 int isl_mat_cols(__isl_keep isl_mat *mat);
7797 __isl_give isl_val *isl_mat_get_element_val(
7798 __isl_keep isl_mat *mat, int row, int col);
7799 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
7800 int row, int col, int v);
7801 __isl_give isl_mat *isl_mat_set_element_val(
7802 __isl_take isl_mat *mat, int row, int col,
7803 __isl_take isl_val *v);
7805 The following function computes the rank of a matrix.
7806 The return value may be -1 if some error occurred.
7808 #include <isl/mat.h>
7809 int isl_mat_rank(__isl_keep isl_mat *mat);
7811 The following function can be used to compute the (right) inverse
7812 of a matrix, i.e., a matrix such that the product of the original
7813 and the inverse (in that order) is a multiple of the identity matrix.
7814 The input matrix is assumed to be of full row-rank.
7816 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
7818 The following function can be used to compute the (right) kernel
7819 (or null space) of a matrix, i.e., a matrix such that the product of
7820 the original and the kernel (in that order) is the zero matrix.
7822 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
7824 The following function computes a basis for the space spanned
7825 by the rows of a matrix.
7827 __isl_give isl_mat *isl_mat_row_basis(
7828 __isl_take isl_mat *mat);
7830 The following function computes rows that extend a basis of C<mat1>
7831 to a basis that also covers C<mat2>.
7833 __isl_give isl_mat *isl_mat_row_basis_extension(
7834 __isl_take isl_mat *mat1,
7835 __isl_take isl_mat *mat2);
7837 The following function checks whether there is no linear dependence
7838 among the combined rows of "mat1" and "mat2" that is not already present
7839 in "mat1" or "mat2" individually.
7840 If "mat1" and "mat2" have linearly independent rows by themselves,
7841 then this means that there is no linear dependence among all rows together.
7843 isl_bool isl_mat_has_linearly_independent_rows(
7844 __isl_keep isl_mat *mat1,
7845 __isl_keep isl_mat *mat2);
7847 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
7849 The following functions determine
7850 an upper or lower bound on a quasipolynomial over its domain.
7852 __isl_give isl_pw_qpolynomial_fold *
7853 isl_pw_qpolynomial_bound(
7854 __isl_take isl_pw_qpolynomial *pwqp,
7855 enum isl_fold type, int *tight);
7857 __isl_give isl_union_pw_qpolynomial_fold *
7858 isl_union_pw_qpolynomial_bound(
7859 __isl_take isl_union_pw_qpolynomial *upwqp,
7860 enum isl_fold type, int *tight);
7862 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
7863 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
7864 is the returned bound is known be tight, i.e., for each value
7865 of the parameters there is at least
7866 one element in the domain that reaches the bound.
7867 If the domain of C<pwqp> is not wrapping, then the bound is computed
7868 over all elements in that domain and the result has a purely parametric
7869 domain. If the domain of C<pwqp> is wrapping, then the bound is
7870 computed over the range of the wrapped relation. The domain of the
7871 wrapped relation becomes the domain of the result.
7873 =head2 Parametric Vertex Enumeration
7875 The parametric vertex enumeration described in this section
7876 is mainly intended to be used internally and by the C<barvinok>
7879 #include <isl/vertices.h>
7880 __isl_give isl_vertices *isl_basic_set_compute_vertices(
7881 __isl_keep isl_basic_set *bset);
7883 The function C<isl_basic_set_compute_vertices> performs the
7884 actual computation of the parametric vertices and the chamber
7885 decomposition and stores the result in an C<isl_vertices> object.
7886 This information can be queried by either iterating over all
7887 the vertices or iterating over all the chambers or cells
7888 and then iterating over all vertices that are active on the chamber.
7890 isl_stat isl_vertices_foreach_vertex(
7891 __isl_keep isl_vertices *vertices,
7892 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7893 void *user), void *user);
7895 isl_stat isl_vertices_foreach_cell(
7896 __isl_keep isl_vertices *vertices,
7897 isl_stat (*fn)(__isl_take isl_cell *cell,
7898 void *user), void *user);
7899 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
7900 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7901 void *user), void *user);
7903 Other operations that can be performed on an C<isl_vertices> object are
7906 int isl_vertices_get_n_vertices(
7907 __isl_keep isl_vertices *vertices);
7908 __isl_null isl_vertices *isl_vertices_free(
7909 __isl_take isl_vertices *vertices);
7911 Vertices can be inspected and destroyed using the following functions.
7913 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
7914 __isl_give isl_basic_set *isl_vertex_get_domain(
7915 __isl_keep isl_vertex *vertex);
7916 __isl_give isl_multi_aff *isl_vertex_get_expr(
7917 __isl_keep isl_vertex *vertex);
7918 void isl_vertex_free(__isl_take isl_vertex *vertex);
7920 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
7921 describing the vertex in terms of the parameters,
7922 while C<isl_vertex_get_domain> returns the activity domain
7925 Chambers can be inspected and destroyed using the following functions.
7927 __isl_give isl_basic_set *isl_cell_get_domain(
7928 __isl_keep isl_cell *cell);
7929 void isl_cell_free(__isl_take isl_cell *cell);
7931 =head1 Polyhedral Compilation Library
7933 This section collects functionality in C<isl> that has been specifically
7934 designed for use during polyhedral compilation.
7936 =head2 Schedule Trees
7938 A schedule tree is a structured representation of a schedule,
7939 assigning a relative order to a set of domain elements.
7940 The relative order expressed by the schedule tree is
7941 defined recursively. In particular, the order between
7942 two domain elements is determined by the node that is closest
7943 to the root that refers to both elements and that orders them apart.
7944 Each node in the tree is of one of several types.
7945 The root node is always of type C<isl_schedule_node_domain>
7946 (or C<isl_schedule_node_extension>)
7947 and it describes the (extra) domain elements to which the schedule applies.
7948 The other types of nodes are as follows.
7952 =item C<isl_schedule_node_band>
7954 A band of schedule dimensions. Each schedule dimension is represented
7955 by a union piecewise quasi-affine expression. If this expression
7956 assigns a different value to two domain elements, while all previous
7957 schedule dimensions in the same band assign them the same value,
7958 then the two domain elements are ordered according to these two
7960 Each expression is required to be total in the domain elements
7961 that reach the band node.
7963 =item C<isl_schedule_node_expansion>
7965 An expansion node maps each of the domain elements that reach the node
7966 to one or more domain elements. The image of this mapping forms
7967 the set of domain elements that reach the child of the expansion node.
7968 The function that maps each of the expanded domain elements
7969 to the original domain element from which it was expanded
7970 is called the contraction.
7972 =item C<isl_schedule_node_filter>
7974 A filter node does not impose any ordering, but rather intersects
7975 the set of domain elements that the current subtree refers to
7976 with a given union set. The subtree of the filter node only
7977 refers to domain elements in the intersection.
7978 A filter node is typically only used as a child of a sequence or
7981 =item C<isl_schedule_node_leaf>
7983 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
7985 =item C<isl_schedule_node_mark>
7987 A mark node can be used to attach any kind of information to a subtree
7988 of the schedule tree.
7990 =item C<isl_schedule_node_sequence>
7992 A sequence node has one or more children, each of which is a filter node.
7993 The filters on these filter nodes form a partition of
7994 the domain elements that the current subtree refers to.
7995 If two domain elements appear in distinct filters then the sequence
7996 node orders them according to the child positions of the corresponding
7999 =item C<isl_schedule_node_set>
8001 A set node is similar to a sequence node, except that
8002 it expresses that domain elements appearing in distinct filters
8003 may have any order. The order of the children of a set node
8004 is therefore also immaterial.
8008 The following node types are only supported by the AST generator.
8012 =item C<isl_schedule_node_context>
8014 The context describes constraints on the parameters and
8015 the schedule dimensions of outer
8016 bands that the AST generator may assume to hold. It is also the only
8017 kind of node that may introduce additional parameters.
8018 The space of the context is that of the flat product of the outer
8019 band nodes. In particular, if there are no outer band nodes, then
8020 this space is the unnamed zero-dimensional space.
8021 Since a context node references the outer band nodes, any tree
8022 containing a context node is considered to be anchored.
8024 =item C<isl_schedule_node_extension>
8026 An extension node instructs the AST generator to add additional
8027 domain elements that need to be scheduled.
8028 The additional domain elements are described by the range of
8029 the extension map in terms of the outer schedule dimensions,
8030 i.e., the flat product of the outer band nodes.
8031 Note that domain elements are added whenever the AST generator
8032 reaches the extension node, meaning that there are still some
8033 active domain elements for which an AST needs to be generated.
8034 The conditions under which some domain elements are still active
8035 may however not be completely described by the outer AST nodes
8036 generated at that point.
8037 Since an extension node references the outer band nodes, any tree
8038 containing an extension node is considered to be anchored.
8040 An extension node may also appear as the root of a schedule tree,
8041 when it is intended to be inserted into another tree
8042 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
8043 In this case, the domain of the extension node should
8044 correspond to the flat product of the outer band nodes
8045 in this other schedule tree at the point where the extension tree
8048 =item C<isl_schedule_node_guard>
8050 The guard describes constraints on the parameters and
8051 the schedule dimensions of outer
8052 bands that need to be enforced by the outer nodes
8053 in the generated AST.
8054 That is, the part of the AST that is generated from descendants
8055 of the guard node can assume that these constraints are satisfied.
8056 The space of the guard is that of the flat product of the outer
8057 band nodes. In particular, if there are no outer band nodes, then
8058 this space is the unnamed zero-dimensional space.
8059 Since a guard node references the outer band nodes, any tree
8060 containing a guard node is considered to be anchored.
8064 Except for the C<isl_schedule_node_context> nodes,
8065 none of the nodes may introduce any parameters that were not
8066 already present in the root domain node.
8068 A schedule tree is encapsulated in an C<isl_schedule> object.
8069 The simplest such objects, those with a tree consisting of single domain node,
8070 can be created using the following functions with either an empty
8071 domain or a given domain.
8073 #include <isl/schedule.h>
8074 __isl_give isl_schedule *isl_schedule_empty(
8075 __isl_take isl_space *space);
8076 __isl_give isl_schedule *isl_schedule_from_domain(
8077 __isl_take isl_union_set *domain);
8079 The function C<isl_schedule_constraints_compute_schedule> described
8080 in L</"Scheduling"> can also be used to construct schedules.
8082 C<isl_schedule> objects may be copied and freed using the following functions.
8084 #include <isl/schedule.h>
8085 __isl_give isl_schedule *isl_schedule_copy(
8086 __isl_keep isl_schedule *sched);
8087 __isl_null isl_schedule *isl_schedule_free(
8088 __isl_take isl_schedule *sched);
8090 The following functions checks whether two C<isl_schedule> objects
8091 are obviously the same.
8093 #include <isl/schedule.h>
8094 isl_bool isl_schedule_plain_is_equal(
8095 __isl_keep isl_schedule *schedule1,
8096 __isl_keep isl_schedule *schedule2);
8098 The domain of the schedule, i.e., the domain described by the root node,
8099 can be obtained using the following function.
8101 #include <isl/schedule.h>
8102 __isl_give isl_union_set *isl_schedule_get_domain(
8103 __isl_keep isl_schedule *schedule);
8105 An extra top-level band node (right underneath the domain node) can
8106 be introduced into the schedule using the following function.
8107 The schedule tree is assumed not to have any anchored nodes.
8109 #include <isl/schedule.h>
8110 __isl_give isl_schedule *
8111 isl_schedule_insert_partial_schedule(
8112 __isl_take isl_schedule *schedule,
8113 __isl_take isl_multi_union_pw_aff *partial);
8115 A top-level context node (right underneath the domain node) can
8116 be introduced into the schedule using the following function.
8118 #include <isl/schedule.h>
8119 __isl_give isl_schedule *isl_schedule_insert_context(
8120 __isl_take isl_schedule *schedule,
8121 __isl_take isl_set *context)
8123 A top-level guard node (right underneath the domain node) can
8124 be introduced into the schedule using the following function.
8126 #include <isl/schedule.h>
8127 __isl_give isl_schedule *isl_schedule_insert_guard(
8128 __isl_take isl_schedule *schedule,
8129 __isl_take isl_set *guard)
8131 A schedule that combines two schedules either in the given
8132 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
8133 or an C<isl_schedule_node_set> node,
8134 can be created using the following functions.
8136 #include <isl/schedule.h>
8137 __isl_give isl_schedule *isl_schedule_sequence(
8138 __isl_take isl_schedule *schedule1,
8139 __isl_take isl_schedule *schedule2);
8140 __isl_give isl_schedule *isl_schedule_set(
8141 __isl_take isl_schedule *schedule1,
8142 __isl_take isl_schedule *schedule2);
8144 The domains of the two input schedules need to be disjoint.
8146 The following function can be used to restrict the domain
8147 of a schedule with a domain node as root to be a subset of the given union set.
8148 This operation may remove nodes in the tree that have become
8151 #include <isl/schedule.h>
8152 __isl_give isl_schedule *isl_schedule_intersect_domain(
8153 __isl_take isl_schedule *schedule,
8154 __isl_take isl_union_set *domain);
8156 The following function can be used to simplify the domain
8157 of a schedule with a domain node as root with respect to the given
8160 #include <isl/schedule.h>
8161 __isl_give isl_schedule *isl_schedule_gist_domain_params(
8162 __isl_take isl_schedule *schedule,
8163 __isl_take isl_set *context);
8165 The following function resets the user pointers on all parameter
8166 and tuple identifiers referenced by the nodes of the given schedule.
8168 #include <isl/schedule.h>
8169 __isl_give isl_schedule *isl_schedule_reset_user(
8170 __isl_take isl_schedule *schedule);
8172 The following function aligns the parameters of all nodes
8173 in the given schedule to the given space.
8175 #include <isl/schedule.h>
8176 __isl_give isl_schedule *isl_schedule_align_params(
8177 __isl_take isl_schedule *schedule,
8178 __isl_take isl_space *space);
8180 The following function allows the user to plug in a given function
8181 in the iteration domains. The input schedule is not allowed to contain
8182 any expansion nodes.
8184 #include <isl/schedule.h>
8185 __isl_give isl_schedule *
8186 isl_schedule_pullback_union_pw_multi_aff(
8187 __isl_take isl_schedule *schedule,
8188 __isl_take isl_union_pw_multi_aff *upma);
8190 The following function can be used to plug in the schedule C<expansion>
8191 in the leaves of C<schedule>, where C<contraction> describes how
8192 the domain elements of C<expansion> map to the domain elements
8193 at the original leaves of C<schedule>.
8194 The resulting schedule will contain expansion nodes, unless
8195 C<contraction> is an identity function.
8197 #include <isl/schedule.h>
8198 __isl_give isl_schedule *isl_schedule_expand(
8199 __isl_take isl_schedule *schedule,
8200 __isl_take isl_union_pw_multi_aff *contraction,
8201 __isl_take isl_schedule *expansion);
8203 An C<isl_union_map> representation of the schedule can be obtained
8204 from an C<isl_schedule> using the following function.
8206 #include <isl/schedule.h>
8207 __isl_give isl_union_map *isl_schedule_get_map(
8208 __isl_keep isl_schedule *sched);
8210 The resulting relation encodes the same relative ordering as
8211 the schedule by mapping the domain elements to a common schedule space.
8212 If the schedule_separate_components option is set, then the order
8213 of the children of a set node is explicitly encoded in the result.
8214 If the tree contains any expansion nodes, then the relation
8215 is formulated in terms of the expanded domain elements.
8217 Schedules can be read from input using the following functions.
8219 #include <isl/schedule.h>
8220 __isl_give isl_schedule *isl_schedule_read_from_file(
8221 isl_ctx *ctx, FILE *input);
8222 __isl_give isl_schedule *isl_schedule_read_from_str(
8223 isl_ctx *ctx, const char *str);
8225 A representation of the schedule can be printed using
8227 #include <isl/schedule.h>
8228 __isl_give isl_printer *isl_printer_print_schedule(
8229 __isl_take isl_printer *p,
8230 __isl_keep isl_schedule *schedule);
8231 __isl_give char *isl_schedule_to_str(
8232 __isl_keep isl_schedule *schedule);
8234 C<isl_schedule_to_str> prints the schedule in flow format.
8236 The schedule tree can be traversed through the use of
8237 C<isl_schedule_node> objects that point to a particular
8238 position in the schedule tree. Whenever a C<isl_schedule_node>
8239 is used to modify a node in the schedule tree, the original schedule
8240 tree is left untouched and the modifications are performed to a copy
8241 of the tree. The returned C<isl_schedule_node> then points to
8242 this modified copy of the tree.
8244 The root of the schedule tree can be obtained using the following function.
8246 #include <isl/schedule.h>
8247 __isl_give isl_schedule_node *isl_schedule_get_root(
8248 __isl_keep isl_schedule *schedule);
8250 A pointer to a newly created schedule tree with a single domain
8251 node can be created using the following functions.
8253 #include <isl/schedule_node.h>
8254 __isl_give isl_schedule_node *
8255 isl_schedule_node_from_domain(
8256 __isl_take isl_union_set *domain);
8257 __isl_give isl_schedule_node *
8258 isl_schedule_node_from_extension(
8259 __isl_take isl_union_map *extension);
8261 C<isl_schedule_node_from_extension> creates a tree with an extension
8264 Schedule nodes can be copied and freed using the following functions.
8266 #include <isl/schedule_node.h>
8267 __isl_give isl_schedule_node *isl_schedule_node_copy(
8268 __isl_keep isl_schedule_node *node);
8269 __isl_null isl_schedule_node *isl_schedule_node_free(
8270 __isl_take isl_schedule_node *node);
8272 The following functions can be used to check if two schedule
8273 nodes point to the same position in the same schedule.
8275 #include <isl/schedule_node.h>
8276 isl_bool isl_schedule_node_is_equal(
8277 __isl_keep isl_schedule_node *node1,
8278 __isl_keep isl_schedule_node *node2);
8280 The following properties can be obtained from a schedule node.
8282 #include <isl/schedule_node.h>
8283 enum isl_schedule_node_type isl_schedule_node_get_type(
8284 __isl_keep isl_schedule_node *node);
8285 enum isl_schedule_node_type
8286 isl_schedule_node_get_parent_type(
8287 __isl_keep isl_schedule_node *node);
8288 __isl_give isl_schedule *isl_schedule_node_get_schedule(
8289 __isl_keep isl_schedule_node *node);
8291 The function C<isl_schedule_node_get_type> returns the type of
8292 the node, while C<isl_schedule_node_get_parent_type> returns
8293 type of the parent of the node, which is required to exist.
8294 The function C<isl_schedule_node_get_schedule> returns a copy
8295 to the schedule to which the node belongs.
8297 The following functions can be used to move the schedule node
8298 to a different position in the tree or to check if such a position
8301 #include <isl/schedule_node.h>
8302 isl_bool isl_schedule_node_has_parent(
8303 __isl_keep isl_schedule_node *node);
8304 __isl_give isl_schedule_node *isl_schedule_node_parent(
8305 __isl_take isl_schedule_node *node);
8306 __isl_give isl_schedule_node *isl_schedule_node_root(
8307 __isl_take isl_schedule_node *node);
8308 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
8309 __isl_take isl_schedule_node *node,
8311 int isl_schedule_node_n_children(
8312 __isl_keep isl_schedule_node *node);
8313 __isl_give isl_schedule_node *isl_schedule_node_child(
8314 __isl_take isl_schedule_node *node, int pos);
8315 isl_bool isl_schedule_node_has_children(
8316 __isl_keep isl_schedule_node *node);
8317 __isl_give isl_schedule_node *isl_schedule_node_first_child(
8318 __isl_take isl_schedule_node *node);
8319 isl_bool isl_schedule_node_has_previous_sibling(
8320 __isl_keep isl_schedule_node *node);
8321 __isl_give isl_schedule_node *
8322 isl_schedule_node_previous_sibling(
8323 __isl_take isl_schedule_node *node);
8324 isl_bool isl_schedule_node_has_next_sibling(
8325 __isl_keep isl_schedule_node *node);
8326 __isl_give isl_schedule_node *
8327 isl_schedule_node_next_sibling(
8328 __isl_take isl_schedule_node *node);
8330 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
8331 is the node itself, the ancestor of generation 1 is its parent and so on.
8333 It is also possible to query the number of ancestors of a node,
8334 the position of the current node
8335 within the children of its parent, the position of the subtree
8336 containing a node within the children of an ancestor
8337 or to obtain a copy of a given
8338 child without destroying the current node.
8339 Given two nodes that point to the same schedule, their closest
8340 shared ancestor can be obtained using
8341 C<isl_schedule_node_get_shared_ancestor>.
8343 #include <isl/schedule_node.h>
8344 int isl_schedule_node_get_tree_depth(
8345 __isl_keep isl_schedule_node *node);
8346 int isl_schedule_node_get_child_position(
8347 __isl_keep isl_schedule_node *node);
8348 int isl_schedule_node_get_ancestor_child_position(
8349 __isl_keep isl_schedule_node *node,
8350 __isl_keep isl_schedule_node *ancestor);
8351 __isl_give isl_schedule_node *isl_schedule_node_get_child(
8352 __isl_keep isl_schedule_node *node, int pos);
8353 __isl_give isl_schedule_node *
8354 isl_schedule_node_get_shared_ancestor(
8355 __isl_keep isl_schedule_node *node1,
8356 __isl_keep isl_schedule_node *node2);
8358 All nodes in a schedule tree or
8359 all descendants of a specific node (including the node) can be visited
8360 in depth-first pre-order using the following functions.
8362 #include <isl/schedule.h>
8363 isl_stat isl_schedule_foreach_schedule_node_top_down(
8364 __isl_keep isl_schedule *sched,
8365 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8366 void *user), void *user);
8368 #include <isl/schedule_node.h>
8369 isl_stat isl_schedule_node_foreach_descendant_top_down(
8370 __isl_keep isl_schedule_node *node,
8371 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8372 void *user), void *user);
8374 The callback function is slightly different from the usual
8375 callbacks in that it not only indicates success (non-negative result)
8376 or failure (negative result), but also indicates whether the children
8377 of the given node should be visited. In particular, if the callback
8378 returns a positive value, then the children are visited, but if
8379 the callback returns zero, then the children are not visited.
8381 The following functions checks whether
8382 all descendants of a specific node (including the node itself)
8383 satisfy a user-specified test.
8385 #include <isl/schedule_node.h>
8386 isl_bool isl_schedule_node_every_descendant(
8387 __isl_keep isl_schedule_node *node,
8388 isl_bool (*test)(__isl_keep isl_schedule_node *node,
8389 void *user), void *user)
8391 The ancestors of a node in a schedule tree can be visited from
8392 the root down to and including the parent of the node using
8393 the following function.
8395 #include <isl/schedule_node.h>
8396 isl_stat isl_schedule_node_foreach_ancestor_top_down(
8397 __isl_keep isl_schedule_node *node,
8398 isl_stat (*fn)(__isl_keep isl_schedule_node *node,
8399 void *user), void *user);
8401 The following functions allows for a depth-first post-order
8402 traversal of the nodes in a schedule tree or
8403 of the descendants of a specific node (including the node
8404 itself), where the user callback is allowed to modify the
8407 #include <isl/schedule.h>
8408 __isl_give isl_schedule *
8409 isl_schedule_map_schedule_node_bottom_up(
8410 __isl_take isl_schedule *schedule,
8411 __isl_give isl_schedule_node *(*fn)(
8412 __isl_take isl_schedule_node *node,
8413 void *user), void *user);
8415 #include <isl/schedule_node.h>
8416 __isl_give isl_schedule_node *
8417 isl_schedule_node_map_descendant_bottom_up(
8418 __isl_take isl_schedule_node *node,
8419 __isl_give isl_schedule_node *(*fn)(
8420 __isl_take isl_schedule_node *node,
8421 void *user), void *user);
8423 The traversal continues from the node returned by the callback function.
8424 It is the responsibility of the user to ensure that this does not
8425 lead to an infinite loop. It is safest to always return a pointer
8426 to the same position (same ancestors and child positions) as the input node.
8428 The following function removes a node (along with its descendants)
8429 from a schedule tree and returns a pointer to the leaf at the
8430 same position in the updated tree.
8431 It is not allowed to remove the root of a schedule tree or
8432 a child of a set or sequence node.
8434 #include <isl/schedule_node.h>
8435 __isl_give isl_schedule_node *isl_schedule_node_cut(
8436 __isl_take isl_schedule_node *node);
8438 The following function removes a single node
8439 from a schedule tree and returns a pointer to the child
8440 of the node, now located at the position of the original node
8441 or to a leaf node at that position if there was no child.
8442 It is not allowed to remove the root of a schedule tree,
8443 a set or sequence node, a child of a set or sequence node or
8444 a band node with an anchored subtree.
8446 #include <isl/schedule_node.h>
8447 __isl_give isl_schedule_node *isl_schedule_node_delete(
8448 __isl_take isl_schedule_node *node);
8450 Most nodes in a schedule tree only contain local information.
8451 In some cases, however, a node may also refer to the schedule dimensions
8452 of its outer band nodes.
8453 This means that the position of the node within the tree should
8454 not be changed, or at least that no changes are performed to the
8455 outer band nodes. The following function can be used to test
8456 whether the subtree rooted at a given node contains any such nodes.
8458 #include <isl/schedule_node.h>
8459 isl_bool isl_schedule_node_is_subtree_anchored(
8460 __isl_keep isl_schedule_node *node);
8462 The following function resets the user pointers on all parameter
8463 and tuple identifiers referenced by the given schedule node.
8465 #include <isl/schedule_node.h>
8466 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
8467 __isl_take isl_schedule_node *node);
8469 The following function aligns the parameters of the given schedule
8470 node to the given space.
8472 #include <isl/schedule_node.h>
8473 __isl_give isl_schedule_node *
8474 isl_schedule_node_align_params(
8475 __isl_take isl_schedule_node *node,
8476 __isl_take isl_space *space);
8478 Several node types have their own functions for querying
8479 (and in some cases setting) some node type specific properties.
8481 #include <isl/schedule_node.h>
8482 __isl_give isl_space *isl_schedule_node_band_get_space(
8483 __isl_keep isl_schedule_node *node);
8484 __isl_give isl_multi_union_pw_aff *
8485 isl_schedule_node_band_get_partial_schedule(
8486 __isl_keep isl_schedule_node *node);
8487 __isl_give isl_union_map *
8488 isl_schedule_node_band_get_partial_schedule_union_map(
8489 __isl_keep isl_schedule_node *node);
8490 unsigned isl_schedule_node_band_n_member(
8491 __isl_keep isl_schedule_node *node);
8492 isl_bool isl_schedule_node_band_member_get_coincident(
8493 __isl_keep isl_schedule_node *node, int pos);
8494 __isl_give isl_schedule_node *
8495 isl_schedule_node_band_member_set_coincident(
8496 __isl_take isl_schedule_node *node, int pos,
8498 isl_bool isl_schedule_node_band_get_permutable(
8499 __isl_keep isl_schedule_node *node);
8500 __isl_give isl_schedule_node *
8501 isl_schedule_node_band_set_permutable(
8502 __isl_take isl_schedule_node *node, int permutable);
8503 enum isl_ast_loop_type
8504 isl_schedule_node_band_member_get_ast_loop_type(
8505 __isl_keep isl_schedule_node *node, int pos);
8506 __isl_give isl_schedule_node *
8507 isl_schedule_node_band_member_set_ast_loop_type(
8508 __isl_take isl_schedule_node *node, int pos,
8509 enum isl_ast_loop_type type);
8510 __isl_give isl_union_set *
8511 enum isl_ast_loop_type
8512 isl_schedule_node_band_member_get_isolate_ast_loop_type(
8513 __isl_keep isl_schedule_node *node, int pos);
8514 __isl_give isl_schedule_node *
8515 isl_schedule_node_band_member_set_isolate_ast_loop_type(
8516 __isl_take isl_schedule_node *node, int pos,
8517 enum isl_ast_loop_type type);
8518 isl_schedule_node_band_get_ast_build_options(
8519 __isl_keep isl_schedule_node *node);
8520 __isl_give isl_schedule_node *
8521 isl_schedule_node_band_set_ast_build_options(
8522 __isl_take isl_schedule_node *node,
8523 __isl_take isl_union_set *options);
8524 __isl_give isl_set *
8525 isl_schedule_node_band_get_ast_isolate_option(
8526 __isl_keep isl_schedule_node *node);
8528 The function C<isl_schedule_node_band_get_space> returns the space
8529 of the partial schedule of the band.
8530 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
8531 returns a representation of the partial schedule of the band node
8532 in the form of an C<isl_union_map>.
8533 The coincident and permutable properties are set by
8534 C<isl_schedule_constraints_compute_schedule> on the schedule tree
8536 A scheduling dimension is considered to be ``coincident''
8537 if it satisfies the coincidence constraints within its band.
8538 That is, if the dependence distances of the coincidence
8539 constraints are all zero in that direction (for fixed
8540 iterations of outer bands).
8541 A band is marked permutable if it was produced using the Pluto-like scheduler.
8542 Note that the scheduler may have to resort to a Feautrier style scheduling
8543 step even if the default scheduler is used.
8544 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
8545 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
8546 For the meaning of these loop AST generation types and the difference
8547 between the regular loop AST generation type and the isolate
8548 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
8549 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
8550 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
8551 may return C<isl_ast_loop_error> if an error occurs.
8552 The AST build options govern how an AST is generated for
8553 the individual schedule dimensions during AST generation.
8554 See L</"AST Generation Options (Schedule Tree)">.
8555 The isolate option for the given node can be extracted from these
8556 AST build options using the function
8557 C<isl_schedule_node_band_get_ast_isolate_option>.
8559 #include <isl/schedule_node.h>
8560 __isl_give isl_set *
8561 isl_schedule_node_context_get_context(
8562 __isl_keep isl_schedule_node *node);
8564 #include <isl/schedule_node.h>
8565 __isl_give isl_union_set *
8566 isl_schedule_node_domain_get_domain(
8567 __isl_keep isl_schedule_node *node);
8569 #include <isl/schedule_node.h>
8570 __isl_give isl_union_map *
8571 isl_schedule_node_expansion_get_expansion(
8572 __isl_keep isl_schedule_node *node);
8573 __isl_give isl_union_pw_multi_aff *
8574 isl_schedule_node_expansion_get_contraction(
8575 __isl_keep isl_schedule_node *node);
8577 #include <isl/schedule_node.h>
8578 __isl_give isl_union_map *
8579 isl_schedule_node_extension_get_extension(
8580 __isl_keep isl_schedule_node *node);
8582 #include <isl/schedule_node.h>
8583 __isl_give isl_union_set *
8584 isl_schedule_node_filter_get_filter(
8585 __isl_keep isl_schedule_node *node);
8587 #include <isl/schedule_node.h>
8588 __isl_give isl_set *isl_schedule_node_guard_get_guard(
8589 __isl_keep isl_schedule_node *node);
8591 #include <isl/schedule_node.h>
8592 __isl_give isl_id *isl_schedule_node_mark_get_id(
8593 __isl_keep isl_schedule_node *node);
8595 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
8596 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
8597 partial schedules related to the node.
8599 #include <isl/schedule_node.h>
8600 __isl_give isl_multi_union_pw_aff *
8601 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
8602 __isl_keep isl_schedule_node *node);
8603 __isl_give isl_union_pw_multi_aff *
8604 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
8605 __isl_keep isl_schedule_node *node);
8606 __isl_give isl_union_map *
8607 isl_schedule_node_get_prefix_schedule_union_map(
8608 __isl_keep isl_schedule_node *node);
8609 __isl_give isl_union_map *
8610 isl_schedule_node_get_prefix_schedule_relation(
8611 __isl_keep isl_schedule_node *node);
8612 __isl_give isl_union_map *
8613 isl_schedule_node_get_subtree_schedule_union_map(
8614 __isl_keep isl_schedule_node *node);
8616 In particular, the functions
8617 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
8618 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
8619 and C<isl_schedule_node_get_prefix_schedule_union_map>
8620 return a relative ordering on the domain elements that reach the given
8621 node determined by its ancestors.
8622 The function C<isl_schedule_node_get_prefix_schedule_relation>
8623 additionally includes the domain constraints in the result.
8624 The function C<isl_schedule_node_get_subtree_schedule_union_map>
8625 returns a representation of the partial schedule defined by the
8626 subtree rooted at the given node.
8627 If the tree contains any expansion nodes, then the subtree schedule
8628 is formulated in terms of the expanded domain elements.
8629 The tree passed to functions returning a prefix schedule
8630 may only contain extension nodes if these would not affect
8631 the result of these functions. That is, if one of the ancestors
8632 is an extension node, then all of the domain elements that were
8633 added by the extension node need to have been filtered out
8634 by filter nodes between the extension node and the input node.
8635 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
8636 may not contain in extension nodes in the selected subtree.
8638 The expansion/contraction defined by an entire subtree, combining
8639 the expansions/contractions
8640 on the expansion nodes in the subtree, can be obtained using
8641 the following functions.
8643 #include <isl/schedule_node.h>
8644 __isl_give isl_union_map *
8645 isl_schedule_node_get_subtree_expansion(
8646 __isl_keep isl_schedule_node *node);
8647 __isl_give isl_union_pw_multi_aff *
8648 isl_schedule_node_get_subtree_contraction(
8649 __isl_keep isl_schedule_node *node);
8651 The total number of outer band members of given node, i.e.,
8652 the shared output dimension of the maps in the result
8653 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
8654 using the following function.
8656 #include <isl/schedule_node.h>
8657 int isl_schedule_node_get_schedule_depth(
8658 __isl_keep isl_schedule_node *node);
8660 The following functions return the elements that reach the given node
8661 or the union of universes in the spaces that contain these elements.
8663 #include <isl/schedule_node.h>
8664 __isl_give isl_union_set *
8665 isl_schedule_node_get_domain(
8666 __isl_keep isl_schedule_node *node);
8667 __isl_give isl_union_set *
8668 isl_schedule_node_get_universe_domain(
8669 __isl_keep isl_schedule_node *node);
8671 The input tree of C<isl_schedule_node_get_domain>
8672 may only contain extension nodes if these would not affect
8673 the result of this function. That is, if one of the ancestors
8674 is an extension node, then all of the domain elements that were
8675 added by the extension node need to have been filtered out
8676 by filter nodes between the extension node and the input node.
8678 The following functions can be used to introduce additional nodes
8679 in the schedule tree. The new node is introduced at the point
8680 in the tree where the C<isl_schedule_node> points to and
8681 the results points to the new node.
8683 #include <isl/schedule_node.h>
8684 __isl_give isl_schedule_node *
8685 isl_schedule_node_insert_partial_schedule(
8686 __isl_take isl_schedule_node *node,
8687 __isl_take isl_multi_union_pw_aff *schedule);
8689 This function inserts a new band node with (the greatest integer
8690 part of) the given partial schedule.
8691 The subtree rooted at the given node is assumed not to have
8694 #include <isl/schedule_node.h>
8695 __isl_give isl_schedule_node *
8696 isl_schedule_node_insert_context(
8697 __isl_take isl_schedule_node *node,
8698 __isl_take isl_set *context);
8700 This function inserts a new context node with the given context constraints.
8702 #include <isl/schedule_node.h>
8703 __isl_give isl_schedule_node *
8704 isl_schedule_node_insert_filter(
8705 __isl_take isl_schedule_node *node,
8706 __isl_take isl_union_set *filter);
8708 This function inserts a new filter node with the given filter.
8709 If the original node already pointed to a filter node, then the
8710 two filter nodes are merged into one.
8712 #include <isl/schedule_node.h>
8713 __isl_give isl_schedule_node *
8714 isl_schedule_node_insert_guard(
8715 __isl_take isl_schedule_node *node,
8716 __isl_take isl_set *guard);
8718 This function inserts a new guard node with the given guard constraints.
8720 #include <isl/schedule_node.h>
8721 __isl_give isl_schedule_node *
8722 isl_schedule_node_insert_mark(
8723 __isl_take isl_schedule_node *node,
8724 __isl_take isl_id *mark);
8726 This function inserts a new mark node with the give mark identifier.
8728 #include <isl/schedule_node.h>
8729 __isl_give isl_schedule_node *
8730 isl_schedule_node_insert_sequence(
8731 __isl_take isl_schedule_node *node,
8732 __isl_take isl_union_set_list *filters);
8733 __isl_give isl_schedule_node *
8734 isl_schedule_node_insert_set(
8735 __isl_take isl_schedule_node *node,
8736 __isl_take isl_union_set_list *filters);
8738 These functions insert a new sequence or set node with the given
8739 filters as children.
8741 #include <isl/schedule_node.h>
8742 __isl_give isl_schedule_node *isl_schedule_node_group(
8743 __isl_take isl_schedule_node *node,
8744 __isl_take isl_id *group_id);
8746 This function introduces an expansion node in between the current
8747 node and its parent that expands instances of a space with tuple
8748 identifier C<group_id> to the original domain elements that reach
8749 the node. The group instances are identified by the prefix schedule
8750 of those domain elements. The ancestors of the node are adjusted
8751 to refer to the group instances instead of the original domain
8752 elements. The return value points to the same node in the updated
8753 schedule tree as the input node, i.e., to the child of the newly
8754 introduced expansion node. Grouping instances of different statements
8755 ensures that they will be treated as a single statement by the
8756 AST generator up to the point of the expansion node.
8758 The following function can be used to flatten a nested
8761 #include <isl/schedule_node.h>
8762 __isl_give isl_schedule_node *
8763 isl_schedule_node_sequence_splice_child(
8764 __isl_take isl_schedule_node *node, int pos);
8766 That is, given a sequence node C<node> that has another sequence node
8767 in its child at position C<pos> (in particular, the child of that filter
8768 node is a sequence node), attach the children of that other sequence
8769 node as children of C<node>, replacing the original child at position
8772 The partial schedule of a band node can be scaled (down) or reduced using
8773 the following functions.
8775 #include <isl/schedule_node.h>
8776 __isl_give isl_schedule_node *
8777 isl_schedule_node_band_scale(
8778 __isl_take isl_schedule_node *node,
8779 __isl_take isl_multi_val *mv);
8780 __isl_give isl_schedule_node *
8781 isl_schedule_node_band_scale_down(
8782 __isl_take isl_schedule_node *node,
8783 __isl_take isl_multi_val *mv);
8784 __isl_give isl_schedule_node *
8785 isl_schedule_node_band_mod(
8786 __isl_take isl_schedule_node *node,
8787 __isl_take isl_multi_val *mv);
8789 The spaces of the two arguments need to match.
8790 After scaling, the partial schedule is replaced by its greatest
8791 integer part to ensure that the schedule remains integral.
8793 The partial schedule of a band node can be shifted by an
8794 C<isl_multi_union_pw_aff> with a domain that is a superset
8795 of the domain of the partial schedule using
8796 the following function.
8798 #include <isl/schedule_node.h>
8799 __isl_give isl_schedule_node *
8800 isl_schedule_node_band_shift(
8801 __isl_take isl_schedule_node *node,
8802 __isl_take isl_multi_union_pw_aff *shift);
8804 A band node can be tiled using the following function.
8806 #include <isl/schedule_node.h>
8807 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
8808 __isl_take isl_schedule_node *node,
8809 __isl_take isl_multi_val *sizes);
8811 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
8813 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
8814 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
8816 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
8818 The C<isl_schedule_node_band_tile> function tiles
8819 the band using the given tile sizes inside its schedule.
8820 A new child band node is created to represent the point loops and it is
8821 inserted between the modified band and its children.
8822 The subtree rooted at the given node is assumed not to have
8824 The C<tile_scale_tile_loops> option specifies whether the tile
8825 loops iterators should be scaled by the tile sizes.
8826 If the C<tile_shift_point_loops> option is set, then the point loops
8827 are shifted to start at zero.
8829 A band node can be split into two nested band nodes
8830 using the following function.
8832 #include <isl/schedule_node.h>
8833 __isl_give isl_schedule_node *isl_schedule_node_band_split(
8834 __isl_take isl_schedule_node *node, int pos);
8836 The resulting outer band node contains the first C<pos> dimensions of
8837 the schedule of C<node> while the inner band contains the remaining dimensions.
8838 The schedules of the two band nodes live in anonymous spaces.
8839 The loop AST generation type options and the isolate option
8840 are split over the two band nodes.
8842 A band node can be moved down to the leaves of the subtree rooted
8843 at the band node using the following function.
8845 #include <isl/schedule_node.h>
8846 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
8847 __isl_take isl_schedule_node *node);
8849 The subtree rooted at the given node is assumed not to have
8851 The result points to the node in the resulting tree that is in the same
8852 position as the node pointed to by C<node> in the original tree.
8854 #include <isl/schedule_node.h>
8855 __isl_give isl_schedule_node *
8856 isl_schedule_node_order_before(
8857 __isl_take isl_schedule_node *node,
8858 __isl_take isl_union_set *filter);
8859 __isl_give isl_schedule_node *
8860 isl_schedule_node_order_after(
8861 __isl_take isl_schedule_node *node,
8862 __isl_take isl_union_set *filter);
8864 These functions split the domain elements that reach C<node>
8865 into those that satisfy C<filter> and those that do not and
8866 arranges for the elements that do satisfy the filter to be
8867 executed before (in case of C<isl_schedule_node_order_before>)
8868 or after (in case of C<isl_schedule_node_order_after>)
8869 those that do not. The order is imposed by
8870 a sequence node, possibly reusing the grandparent of C<node>
8871 on two copies of the subtree attached to the original C<node>.
8872 Both copies are simplified with respect to their filter.
8874 Return a pointer to the copy of the subtree that does not
8875 satisfy C<filter>. If there is no such copy (because all
8876 reaching domain elements satisfy the filter), then return
8877 the original pointer.
8879 #include <isl/schedule_node.h>
8880 __isl_give isl_schedule_node *
8881 isl_schedule_node_graft_before(
8882 __isl_take isl_schedule_node *node,
8883 __isl_take isl_schedule_node *graft);
8884 __isl_give isl_schedule_node *
8885 isl_schedule_node_graft_after(
8886 __isl_take isl_schedule_node *node,
8887 __isl_take isl_schedule_node *graft);
8889 This function inserts the C<graft> tree into the tree containing C<node>
8890 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
8891 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
8892 The root node of C<graft>
8893 should be an extension node where the domain of the extension
8894 is the flat product of all outer band nodes of C<node>.
8895 The root node may also be a domain node.
8896 The elements of the domain or the range of the extension may not
8897 intersect with the domain elements that reach "node".
8898 The schedule tree of C<graft> may not be anchored.
8900 The schedule tree of C<node> is modified to include an extension node
8901 corresponding to the root node of C<graft> as a child of the original
8902 parent of C<node>. The original node that C<node> points to and the
8903 child of the root node of C<graft> are attached to this extension node
8904 through a sequence, with appropriate filters and with the child
8905 of C<graft> appearing before or after the original C<node>.
8907 If C<node> already appears inside a sequence that is the child of
8908 an extension node and if the spaces of the new domain elements
8909 do not overlap with those of the original domain elements,
8910 then that extension node is extended with the new extension
8911 rather than introducing a new segment of extension and sequence nodes.
8913 Return a pointer to the same node in the modified tree that
8914 C<node> pointed to in the original tree.
8916 A representation of the schedule node can be printed using
8918 #include <isl/schedule_node.h>
8919 __isl_give isl_printer *isl_printer_print_schedule_node(
8920 __isl_take isl_printer *p,
8921 __isl_keep isl_schedule_node *node);
8922 __isl_give char *isl_schedule_node_to_str(
8923 __isl_keep isl_schedule_node *node);
8925 C<isl_schedule_node_to_str> prints the schedule node in block format.
8927 =head2 Dependence Analysis
8929 C<isl> contains specialized functionality for performing
8930 array dataflow analysis. That is, given a I<sink> access relation,
8931 a collection of possible I<source> accesses and
8932 a collection of I<kill> accesses,
8933 C<isl> can compute relations that describe
8934 for each iteration of the sink access, which iterations
8935 of which of the source access relations may have
8936 accessed the same data element before the given iteration
8937 of the sink access without any intermediate kill of that data element.
8938 The resulting dependence relations map source iterations
8939 to either the corresponding sink iterations or
8940 pairs of corresponding sink iterations and accessed data elements.
8941 To compute standard flow dependences, the sink should be
8942 a read, while the sources should be writes.
8943 If no kills are specified,
8944 then memory based dependence analysis is performed.
8945 If, on the other hand, all sources are also kills,
8946 then value based dependence analysis is performed.
8947 If any of the source accesses are marked as being I<must>
8948 accesses, then they are also treated as kills.
8949 Furthermore, the specification of must-sources results
8950 in the computation of must-dependences.
8951 Only dependences originating in a must access not coscheduled
8952 with any other access to the same element and without
8953 any may accesses between the must access and the sink access
8954 are considered to be must dependences.
8956 =head3 High-level Interface
8958 A high-level interface to dependence analysis is provided
8959 by the following function.
8961 #include <isl/flow.h>
8962 __isl_give isl_union_flow *
8963 isl_union_access_info_compute_flow(
8964 __isl_take isl_union_access_info *access);
8966 The input C<isl_union_access_info> object describes the sink
8967 access relations, the source access relations and a schedule,
8968 while the output C<isl_union_flow> object describes
8969 the resulting dependence relations and the subsets of the
8970 sink relations for which no source was found.
8972 An C<isl_union_access_info> is created, modified, copied and freed using
8973 the following functions.
8975 #include <isl/flow.h>
8976 __isl_give isl_union_access_info *
8977 isl_union_access_info_from_sink(
8978 __isl_take isl_union_map *sink);
8979 __isl_give isl_union_access_info *
8980 isl_union_access_info_set_kill(
8981 __isl_take isl_union_access_info *access,
8982 __isl_take isl_union_map *kill);
8983 __isl_give isl_union_access_info *
8984 isl_union_access_info_set_may_source(
8985 __isl_take isl_union_access_info *access,
8986 __isl_take isl_union_map *may_source);
8987 __isl_give isl_union_access_info *
8988 isl_union_access_info_set_must_source(
8989 __isl_take isl_union_access_info *access,
8990 __isl_take isl_union_map *must_source);
8991 __isl_give isl_union_access_info *
8992 isl_union_access_info_set_schedule(
8993 __isl_take isl_union_access_info *access,
8994 __isl_take isl_schedule *schedule);
8995 __isl_give isl_union_access_info *
8996 isl_union_access_info_set_schedule_map(
8997 __isl_take isl_union_access_info *access,
8998 __isl_take isl_union_map *schedule_map);
8999 __isl_give isl_union_access_info *
9000 isl_union_access_info_copy(
9001 __isl_keep isl_union_access_info *access);
9002 __isl_null isl_union_access_info *
9003 isl_union_access_info_free(
9004 __isl_take isl_union_access_info *access);
9006 The may sources set by C<isl_union_access_info_set_may_source>
9007 do not need to include the must sources set by
9008 C<isl_union_access_info_set_must_source> as a subset.
9009 The kills set by C<isl_union_access_info_set_kill> may overlap
9010 with the may-sources and/or must-sources.
9011 The user is free not to call one (or more) of these functions,
9012 in which case the corresponding set is kept to its empty default.
9013 Similarly, the default schedule initialized by
9014 C<isl_union_access_info_from_sink> is empty.
9015 The current schedule is determined by the last call to either
9016 C<isl_union_access_info_set_schedule> or
9017 C<isl_union_access_info_set_schedule_map>.
9018 The domain of the schedule corresponds to the domains of
9019 the access relations. In particular, the domains of the access
9020 relations are effectively intersected with the domain of the schedule
9021 and only the resulting accesses are considered by the dependence analysis.
9023 An C<isl_union_access_info> object can be read from input
9024 using the following function.
9026 #include <isl/flow.h>
9027 __isl_give isl_union_access_info *
9028 isl_union_access_info_read_from_file(isl_ctx *ctx,
9031 A representation of the information contained in an object
9032 of type C<isl_union_access_info> can be obtained using
9034 #include <isl/flow.h>
9035 __isl_give isl_printer *
9036 isl_printer_print_union_access_info(
9037 __isl_take isl_printer *p,
9038 __isl_keep isl_union_access_info *access);
9039 __isl_give char *isl_union_access_info_to_str(
9040 __isl_keep isl_union_access_info *access);
9042 C<isl_union_access_info_to_str> prints the information in flow format.
9044 The output of C<isl_union_access_info_compute_flow> can be examined,
9045 copied, and freed using the following functions.
9047 #include <isl/flow.h>
9048 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
9049 __isl_keep isl_union_flow *flow);
9050 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
9051 __isl_keep isl_union_flow *flow);
9052 __isl_give isl_union_map *
9053 isl_union_flow_get_full_must_dependence(
9054 __isl_keep isl_union_flow *flow);
9055 __isl_give isl_union_map *
9056 isl_union_flow_get_full_may_dependence(
9057 __isl_keep isl_union_flow *flow);
9058 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
9059 __isl_keep isl_union_flow *flow);
9060 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
9061 __isl_keep isl_union_flow *flow);
9062 __isl_give isl_union_flow *isl_union_flow_copy(
9063 __isl_keep isl_union_flow *flow);
9064 __isl_null isl_union_flow *isl_union_flow_free(
9065 __isl_take isl_union_flow *flow);
9067 The relation returned by C<isl_union_flow_get_must_dependence>
9068 relates domain elements of must sources to domain elements of the sink.
9069 The relation returned by C<isl_union_flow_get_may_dependence>
9070 relates domain elements of must or may sources to domain elements of the sink
9071 and includes the previous relation as a subset.
9072 The relation returned by C<isl_union_flow_get_full_must_dependence>
9073 relates domain elements of must sources to pairs of domain elements of the sink
9074 and accessed data elements.
9075 The relation returned by C<isl_union_flow_get_full_may_dependence>
9076 relates domain elements of must or may sources to pairs of
9077 domain elements of the sink and accessed data elements.
9078 This relation includes the previous relation as a subset.
9079 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
9080 of the sink relation for which no dependences have been found.
9081 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
9082 of the sink relation for which no definite dependences have been found.
9083 That is, it contains those sink access that do not contribute to any
9084 of the elements in the relation returned
9085 by C<isl_union_flow_get_must_dependence>.
9087 A representation of the information contained in an object
9088 of type C<isl_union_flow> can be obtained using
9090 #include <isl/flow.h>
9091 __isl_give isl_printer *isl_printer_print_union_flow(
9092 __isl_take isl_printer *p,
9093 __isl_keep isl_union_flow *flow);
9094 __isl_give char *isl_union_flow_to_str(
9095 __isl_keep isl_union_flow *flow);
9097 C<isl_union_flow_to_str> prints the information in flow format.
9099 =head3 Low-level Interface
9101 A lower-level interface is provided by the following functions.
9103 #include <isl/flow.h>
9105 typedef int (*isl_access_level_before)(void *first, void *second);
9107 __isl_give isl_access_info *isl_access_info_alloc(
9108 __isl_take isl_map *sink,
9109 void *sink_user, isl_access_level_before fn,
9111 __isl_give isl_access_info *isl_access_info_add_source(
9112 __isl_take isl_access_info *acc,
9113 __isl_take isl_map *source, int must,
9115 __isl_null isl_access_info *isl_access_info_free(
9116 __isl_take isl_access_info *acc);
9118 __isl_give isl_flow *isl_access_info_compute_flow(
9119 __isl_take isl_access_info *acc);
9121 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,
9122 isl_stat (*fn)(__isl_take isl_map *dep, int must,
9123 void *dep_user, void *user),
9125 __isl_give isl_map *isl_flow_get_no_source(
9126 __isl_keep isl_flow *deps, int must);
9127 void isl_flow_free(__isl_take isl_flow *deps);
9129 The function C<isl_access_info_compute_flow> performs the actual
9130 dependence analysis. The other functions are used to construct
9131 the input for this function or to read off the output.
9133 The input is collected in an C<isl_access_info>, which can
9134 be created through a call to C<isl_access_info_alloc>.
9135 The arguments to this functions are the sink access relation
9136 C<sink>, a token C<sink_user> used to identify the sink
9137 access to the user, a callback function for specifying the
9138 relative order of source and sink accesses, and the number
9139 of source access relations that will be added.
9141 The callback function has type C<int (*)(void *first, void *second)>.
9142 The function is called with two user supplied tokens identifying
9143 either a source or the sink and it should return the shared nesting
9144 level and the relative order of the two accesses.
9145 In particular, let I<n> be the number of loops shared by
9146 the two accesses. If C<first> precedes C<second> textually,
9147 then the function should return I<2 * n + 1>; otherwise,
9148 it should return I<2 * n>.
9149 The low-level interface assumes that no sources are coscheduled.
9150 If the information returned by the callback does not allow
9151 the relative order to be determined, then one of the sources
9152 is arbitrarily taken to be executed after the other(s).
9154 The sources can be added to the C<isl_access_info> object by performing
9155 (at most) C<max_source> calls to C<isl_access_info_add_source>.
9156 C<must> indicates whether the source is a I<must> access
9157 or a I<may> access. Note that a multi-valued access relation
9158 should only be marked I<must> if every iteration in the domain
9159 of the relation accesses I<all> elements in its image.
9160 The C<source_user> token is again used to identify
9161 the source access. The range of the source access relation
9162 C<source> should have the same dimension as the range
9163 of the sink access relation.
9164 The C<isl_access_info_free> function should usually not be
9165 called explicitly, because it is already called implicitly by
9166 C<isl_access_info_compute_flow>.
9168 The result of the dependence analysis is collected in an
9169 C<isl_flow>. There may be elements of
9170 the sink access for which no preceding source access could be
9171 found or for which all preceding sources are I<may> accesses.
9172 The relations containing these elements can be obtained through
9173 calls to C<isl_flow_get_no_source>, the first with C<must> set
9174 and the second with C<must> unset.
9175 In the case of standard flow dependence analysis,
9176 with the sink a read and the sources I<must> writes,
9177 the first relation corresponds to the reads from uninitialized
9178 array elements and the second relation is empty.
9179 The actual flow dependences can be extracted using
9180 C<isl_flow_foreach>. This function will call the user-specified
9181 callback function C<fn> for each B<non-empty> dependence between
9182 a source and the sink. The callback function is called
9183 with four arguments, the actual flow dependence relation
9184 mapping source iterations to sink iterations, a boolean that
9185 indicates whether it is a I<must> or I<may> dependence, a token
9186 identifying the source and an additional C<void *> with value
9187 equal to the third argument of the C<isl_flow_foreach> call.
9188 A dependence is marked I<must> if it originates from a I<must>
9189 source and if it is not followed by any I<may> sources.
9191 After finishing with an C<isl_flow>, the user should call
9192 C<isl_flow_free> to free all associated memory.
9194 =head3 Interaction with the Low-level Interface
9196 During the dependence analysis, we frequently need to perform
9197 the following operation. Given a relation between sink iterations
9198 and potential source iterations from a particular source domain,
9199 what is the last potential source iteration corresponding to each
9200 sink iteration. It can sometimes be convenient to adjust
9201 the set of potential source iterations before or after each such operation.
9202 The prototypical example is fuzzy array dataflow analysis,
9203 where we need to analyze if, based on data-dependent constraints,
9204 the sink iteration can ever be executed without one or more of
9205 the corresponding potential source iterations being executed.
9206 If so, we can introduce extra parameters and select an unknown
9207 but fixed source iteration from the potential source iterations.
9208 To be able to perform such manipulations, C<isl> provides the following
9211 #include <isl/flow.h>
9213 typedef __isl_give isl_restriction *(*isl_access_restrict)(
9214 __isl_keep isl_map *source_map,
9215 __isl_keep isl_set *sink, void *source_user,
9217 __isl_give isl_access_info *isl_access_info_set_restrict(
9218 __isl_take isl_access_info *acc,
9219 isl_access_restrict fn, void *user);
9221 The function C<isl_access_info_set_restrict> should be called
9222 before calling C<isl_access_info_compute_flow> and registers a callback function
9223 that will be called any time C<isl> is about to compute the last
9224 potential source. The first argument is the (reverse) proto-dependence,
9225 mapping sink iterations to potential source iterations.
9226 The second argument represents the sink iterations for which
9227 we want to compute the last source iteration.
9228 The third argument is the token corresponding to the source
9229 and the final argument is the token passed to C<isl_access_info_set_restrict>.
9230 The callback is expected to return a restriction on either the input or
9231 the output of the operation computing the last potential source.
9232 If the input needs to be restricted then restrictions are needed
9233 for both the source and the sink iterations. The sink iterations
9234 and the potential source iterations will be intersected with these sets.
9235 If the output needs to be restricted then only a restriction on the source
9236 iterations is required.
9237 If any error occurs, the callback should return C<NULL>.
9238 An C<isl_restriction> object can be created, freed and inspected
9239 using the following functions.
9241 #include <isl/flow.h>
9243 __isl_give isl_restriction *isl_restriction_input(
9244 __isl_take isl_set *source_restr,
9245 __isl_take isl_set *sink_restr);
9246 __isl_give isl_restriction *isl_restriction_output(
9247 __isl_take isl_set *source_restr);
9248 __isl_give isl_restriction *isl_restriction_none(
9249 __isl_take isl_map *source_map);
9250 __isl_give isl_restriction *isl_restriction_empty(
9251 __isl_take isl_map *source_map);
9252 __isl_null isl_restriction *isl_restriction_free(
9253 __isl_take isl_restriction *restr);
9255 C<isl_restriction_none> and C<isl_restriction_empty> are special
9256 cases of C<isl_restriction_input>. C<isl_restriction_none>
9257 is essentially equivalent to
9259 isl_restriction_input(isl_set_universe(
9260 isl_space_range(isl_map_get_space(source_map))),
9262 isl_space_domain(isl_map_get_space(source_map))));
9264 whereas C<isl_restriction_empty> is essentially equivalent to
9266 isl_restriction_input(isl_set_empty(
9267 isl_space_range(isl_map_get_space(source_map))),
9269 isl_space_domain(isl_map_get_space(source_map))));
9273 #include <isl/schedule.h>
9274 __isl_give isl_schedule *
9275 isl_schedule_constraints_compute_schedule(
9276 __isl_take isl_schedule_constraints *sc);
9278 The function C<isl_schedule_constraints_compute_schedule> can be
9279 used to compute a schedule that satisfies the given schedule constraints.
9280 These schedule constraints include the iteration domain for which
9281 a schedule should be computed and dependences between pairs of
9282 iterations. In particular, these dependences include
9283 I<validity> dependences and I<proximity> dependences.
9284 By default, the algorithm used to construct the schedule is similar
9285 to that of C<Pluto>.
9286 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
9288 The generated schedule respects all validity dependences.
9289 That is, all dependence distances over these dependences in the
9290 scheduled space are lexicographically positive.
9292 The default algorithm tries to ensure that the dependence distances
9293 over coincidence constraints are zero and to minimize the
9294 dependence distances over proximity dependences.
9295 Moreover, it tries to obtain sequences (bands) of schedule dimensions
9296 for groups of domains where the dependence distances over validity
9297 dependences have only non-negative values.
9298 Note that when minimizing the maximal dependence distance
9299 over proximity dependences, a single affine expression in the parameters
9300 is constructed that bounds all dependence distances. If no such expression
9301 exists, then the algorithm will fail and resort to an alternative
9302 scheduling algorithm. In particular, this means that adding proximity
9303 dependences may eliminate valid solutions. A typical example where this
9304 phenomenon may occur is when some subset of the proximity dependences
9305 has no restriction on some parameter, forcing the coefficient of that
9306 parameter to be zero, while some other subset forces the dependence
9307 distance to depend on that parameter, requiring the same coefficient
9309 When using Feautrier's algorithm, the coincidence and proximity constraints
9310 are only taken into account during the extension to a
9311 full-dimensional schedule.
9313 An C<isl_schedule_constraints> object can be constructed
9314 and manipulated using the following functions.
9316 #include <isl/schedule.h>
9317 __isl_give isl_schedule_constraints *
9318 isl_schedule_constraints_copy(
9319 __isl_keep isl_schedule_constraints *sc);
9320 __isl_give isl_schedule_constraints *
9321 isl_schedule_constraints_on_domain(
9322 __isl_take isl_union_set *domain);
9323 __isl_give isl_schedule_constraints *
9324 isl_schedule_constraints_set_context(
9325 __isl_take isl_schedule_constraints *sc,
9326 __isl_take isl_set *context);
9327 __isl_give isl_schedule_constraints *
9328 isl_schedule_constraints_set_validity(
9329 __isl_take isl_schedule_constraints *sc,
9330 __isl_take isl_union_map *validity);
9331 __isl_give isl_schedule_constraints *
9332 isl_schedule_constraints_set_coincidence(
9333 __isl_take isl_schedule_constraints *sc,
9334 __isl_take isl_union_map *coincidence);
9335 __isl_give isl_schedule_constraints *
9336 isl_schedule_constraints_set_proximity(
9337 __isl_take isl_schedule_constraints *sc,
9338 __isl_take isl_union_map *proximity);
9339 __isl_give isl_schedule_constraints *
9340 isl_schedule_constraints_set_conditional_validity(
9341 __isl_take isl_schedule_constraints *sc,
9342 __isl_take isl_union_map *condition,
9343 __isl_take isl_union_map *validity);
9344 __isl_give isl_schedule_constraints *
9345 isl_schedule_constraints_apply(
9346 __isl_take isl_schedule_constraints *sc,
9347 __isl_take isl_union_map *umap);
9348 __isl_null isl_schedule_constraints *
9349 isl_schedule_constraints_free(
9350 __isl_take isl_schedule_constraints *sc);
9352 The initial C<isl_schedule_constraints> object created by
9353 C<isl_schedule_constraints_on_domain> does not impose any constraints.
9354 That is, it has an empty set of dependences.
9355 The function C<isl_schedule_constraints_set_context> allows the user
9356 to specify additional constraints on the parameters that may
9357 be assumed to hold during the construction of the schedule.
9358 The function C<isl_schedule_constraints_set_validity> replaces the
9359 validity dependences, mapping domain elements I<i> to domain
9360 elements that should be scheduled after I<i>.
9361 The function C<isl_schedule_constraints_set_coincidence> replaces the
9362 coincidence dependences, mapping domain elements I<i> to domain
9363 elements that should be scheduled together with I<I>, if possible.
9364 The function C<isl_schedule_constraints_set_proximity> replaces the
9365 proximity dependences, mapping domain elements I<i> to domain
9366 elements that should be scheduled either before I<I>
9367 or as early as possible after I<i>.
9369 The function C<isl_schedule_constraints_set_conditional_validity>
9370 replaces the conditional validity constraints.
9371 A conditional validity constraint is only imposed when any of the corresponding
9372 conditions is satisfied, i.e., when any of them is non-zero.
9373 That is, the scheduler ensures that within each band if the dependence
9374 distances over the condition constraints are not all zero
9375 then all corresponding conditional validity constraints are respected.
9376 A conditional validity constraint corresponds to a condition
9377 if the two are adjacent, i.e., if the domain of one relation intersect
9378 the range of the other relation.
9379 The typical use case of conditional validity constraints is
9380 to allow order constraints between live ranges to be violated
9381 as long as the live ranges themselves are local to the band.
9382 To allow more fine-grained control over which conditions correspond
9383 to which conditional validity constraints, the domains and ranges
9384 of these relations may include I<tags>. That is, the domains and
9385 ranges of those relation may themselves be wrapped relations
9386 where the iteration domain appears in the domain of those wrapped relations
9387 and the range of the wrapped relations can be arbitrarily chosen
9388 by the user. Conditions and conditional validity constraints are only
9389 considered adjacent to each other if the entire wrapped relation matches.
9390 In particular, a relation with a tag will never be considered adjacent
9391 to a relation without a tag.
9393 The function C<isl_schedule_constraints_apply> takes
9394 schedule constraints that are defined on some set of domain elements
9395 and transforms them to schedule constraints on the elements
9396 to which these domain elements are mapped by the given transformation.
9398 An C<isl_schedule_constraints> object can be inspected
9399 using the following functions.
9401 #include <isl/schedule.h>
9402 __isl_give isl_union_set *
9403 isl_schedule_constraints_get_domain(
9404 __isl_keep isl_schedule_constraints *sc);
9405 __isl_give isl_set *isl_schedule_constraints_get_context(
9406 __isl_keep isl_schedule_constraints *sc);
9407 __isl_give isl_union_map *
9408 isl_schedule_constraints_get_validity(
9409 __isl_keep isl_schedule_constraints *sc);
9410 __isl_give isl_union_map *
9411 isl_schedule_constraints_get_coincidence(
9412 __isl_keep isl_schedule_constraints *sc);
9413 __isl_give isl_union_map *
9414 isl_schedule_constraints_get_proximity(
9415 __isl_keep isl_schedule_constraints *sc);
9416 __isl_give isl_union_map *
9417 isl_schedule_constraints_get_conditional_validity(
9418 __isl_keep isl_schedule_constraints *sc);
9419 __isl_give isl_union_map *
9420 isl_schedule_constraints_get_conditional_validity_condition(
9421 __isl_keep isl_schedule_constraints *sc);
9423 An C<isl_schedule_constraints> object can be read from input
9424 using the following functions.
9426 #include <isl/schedule.h>
9427 __isl_give isl_schedule_constraints *
9428 isl_schedule_constraints_read_from_str(isl_ctx *ctx,
9430 __isl_give isl_schedule_constraints *
9431 isl_schedule_constraints_read_from_file(isl_ctx *ctx,
9434 The contents of an C<isl_schedule_constraints> object can be printed
9435 using the following functions.
9437 #include <isl/schedule.h>
9438 __isl_give isl_printer *
9439 isl_printer_print_schedule_constraints(
9440 __isl_take isl_printer *p,
9441 __isl_keep isl_schedule_constraints *sc);
9442 __isl_give char *isl_schedule_constraints_to_str(
9443 __isl_keep isl_schedule_constraints *sc);
9445 The following function computes a schedule directly from
9446 an iteration domain and validity and proximity dependences
9447 and is implemented in terms of the functions described above.
9448 The use of C<isl_union_set_compute_schedule> is discouraged.
9450 #include <isl/schedule.h>
9451 __isl_give isl_schedule *isl_union_set_compute_schedule(
9452 __isl_take isl_union_set *domain,
9453 __isl_take isl_union_map *validity,
9454 __isl_take isl_union_map *proximity);
9456 The generated schedule represents a schedule tree.
9457 For more information on schedule trees, see
9458 L</"Schedule Trees">.
9462 #include <isl/schedule.h>
9463 isl_stat isl_options_set_schedule_max_coefficient(
9464 isl_ctx *ctx, int val);
9465 int isl_options_get_schedule_max_coefficient(
9467 isl_stat isl_options_set_schedule_max_constant_term(
9468 isl_ctx *ctx, int val);
9469 int isl_options_get_schedule_max_constant_term(
9471 isl_stat isl_options_set_schedule_serialize_sccs(
9472 isl_ctx *ctx, int val);
9473 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx);
9474 isl_stat isl_options_set_schedule_whole_component(
9475 isl_ctx *ctx, int val);
9476 int isl_options_get_schedule_whole_component(
9478 isl_stat isl_options_set_schedule_maximize_band_depth(
9479 isl_ctx *ctx, int val);
9480 int isl_options_get_schedule_maximize_band_depth(
9482 isl_stat isl_options_set_schedule_maximize_coincidence(
9483 isl_ctx *ctx, int val);
9484 int isl_options_get_schedule_maximize_coincidence(
9486 isl_stat isl_options_set_schedule_outer_coincidence(
9487 isl_ctx *ctx, int val);
9488 int isl_options_get_schedule_outer_coincidence(
9490 isl_stat isl_options_set_schedule_split_scaled(
9491 isl_ctx *ctx, int val);
9492 int isl_options_get_schedule_split_scaled(
9494 isl_stat isl_options_set_schedule_treat_coalescing(
9495 isl_ctx *ctx, int val);
9496 int isl_options_get_schedule_treat_coalescing(
9498 isl_stat isl_options_set_schedule_algorithm(
9499 isl_ctx *ctx, int val);
9500 int isl_options_get_schedule_algorithm(
9502 isl_stat isl_options_set_schedule_carry_self_first(
9503 isl_ctx *ctx, int val);
9504 int isl_options_get_schedule_carry_self_first(
9506 isl_stat isl_options_set_schedule_separate_components(
9507 isl_ctx *ctx, int val);
9508 int isl_options_get_schedule_separate_components(
9513 =item * schedule_max_coefficient
9515 This option enforces that the coefficients for variable and parameter
9516 dimensions in the calculated schedule are not larger than the specified value.
9517 This option can significantly increase the speed of the scheduling calculation
9518 and may also prevent fusing of unrelated dimensions. A value of -1 means that
9519 this option does not introduce bounds on the variable or parameter
9522 =item * schedule_max_constant_term
9524 This option enforces that the constant coefficients in the calculated schedule
9525 are not larger than the maximal constant term. This option can significantly
9526 increase the speed of the scheduling calculation and may also prevent fusing of
9527 unrelated dimensions. A value of -1 means that this option does not introduce
9528 bounds on the constant coefficients.
9530 =item * schedule_serialize_sccs
9532 If this option is set, then all strongly connected components
9533 in the dependence graph are serialized as soon as they are detected.
9534 This means in particular that instances of statements will only
9535 appear in the same band node if these statements belong
9536 to the same strongly connected component at the point where
9537 the band node is constructed.
9539 =item * schedule_whole_component
9541 If this option is set, then entire (weakly) connected
9542 components in the dependence graph are scheduled together
9544 Otherwise, each strongly connected component within
9545 such a weakly connected component is first scheduled separately
9546 and then combined with other strongly connected components.
9547 This option has no effect if C<schedule_serialize_sccs> is set.
9549 =item * schedule_maximize_band_depth
9551 If this option is set, then the scheduler tries to maximize
9552 the width of the bands. Wider bands give more possibilities for tiling.
9553 In particular, if the C<schedule_whole_component> option is set,
9554 then bands are split if this might result in wider bands.
9555 Otherwise, the effect of this option is to only allow
9556 strongly connected components to be combined if this does
9557 not reduce the width of the bands.
9558 Note that if the C<schedule_serialize_sccs> options is set, then
9559 the C<schedule_maximize_band_depth> option therefore has no effect.
9561 =item * schedule_maximize_coincidence
9563 This option is only effective if the C<schedule_whole_component>
9564 option is turned off.
9565 If the C<schedule_maximize_coincidence> option is set, then (clusters of)
9566 strongly connected components are only combined with each other
9567 if this does not reduce the number of coincident band members.
9569 =item * schedule_outer_coincidence
9571 If this option is set, then we try to construct schedules
9572 where the outermost scheduling dimension in each band
9573 satisfies the coincidence constraints.
9575 =item * schedule_algorithm
9577 Selects the scheduling algorithm to be used.
9578 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
9579 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
9581 =item * schedule_split_scaled
9583 If this option is set, then we try to construct schedules in which the
9584 constant term is split off from the linear part if the linear parts of
9585 the scheduling rows for all nodes in the graph have a common non-trivial
9587 The constant term is then dropped and the linear
9589 This option is only effective when the Feautrier style scheduler is
9590 being used, either as the main scheduler or as a fallback for the
9591 Pluto-like scheduler.
9593 =item * schedule_treat_coalescing
9595 If this option is set, then the scheduler will try and avoid
9596 producing schedules that perform loop coalescing.
9597 In particular, for the Pluto-like scheduler, this option places
9598 bounds on the schedule coefficients based on the sizes of the instance sets.
9599 For the Feautrier style scheduler, this option detects potentially
9600 coalescing schedules and then tries to adjust the schedule to avoid
9603 =item * schedule_carry_self_first
9605 If this option is set, then the Feautrier style scheduler
9606 (when used as a fallback for the Pluto-like scheduler) will
9607 first try to only carry self-dependences.
9609 =item * schedule_separate_components
9611 If this option is set then the function C<isl_schedule_get_map>
9612 will treat set nodes in the same way as sequence nodes.
9616 =head2 AST Generation
9618 This section describes the C<isl> functionality for generating
9619 ASTs that visit all the elements
9620 in a domain in an order specified by a schedule tree or
9622 In case the schedule given as a C<isl_union_map>, an AST is generated
9623 that visits all the elements in the domain of the C<isl_union_map>
9624 according to the lexicographic order of the corresponding image
9625 element(s). If the range of the C<isl_union_map> consists of
9626 elements in more than one space, then each of these spaces is handled
9627 separately in an arbitrary order.
9628 It should be noted that the schedule tree or the image elements
9629 in a schedule map only specify the I<order>
9630 in which the corresponding domain elements should be visited.
9631 No direct relation between the partial schedule values
9632 or the image elements on the one hand and the loop iterators
9633 in the generated AST on the other hand should be assumed.
9635 Each AST is generated within a build. The initial build
9636 simply specifies the constraints on the parameters (if any)
9637 and can be created, inspected, copied and freed using the following functions.
9639 #include <isl/ast_build.h>
9640 __isl_give isl_ast_build *isl_ast_build_alloc(
9642 __isl_give isl_ast_build *isl_ast_build_from_context(
9643 __isl_take isl_set *set);
9644 __isl_give isl_ast_build *isl_ast_build_copy(
9645 __isl_keep isl_ast_build *build);
9646 __isl_null isl_ast_build *isl_ast_build_free(
9647 __isl_take isl_ast_build *build);
9649 The C<set> argument is usually a parameter set with zero or more parameters.
9650 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
9651 this set is required to be a parameter set.
9652 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
9653 specify any parameter constraints.
9654 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
9655 and L</"Fine-grained Control over AST Generation">.
9656 Finally, the AST itself can be constructed using one of the following
9659 #include <isl/ast_build.h>
9660 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
9661 __isl_keep isl_ast_build *build,
9662 __isl_take isl_schedule *schedule);
9663 __isl_give isl_ast_node *
9664 isl_ast_build_node_from_schedule_map(
9665 __isl_keep isl_ast_build *build,
9666 __isl_take isl_union_map *schedule);
9668 =head3 Inspecting the AST
9670 The basic properties of an AST node can be obtained as follows.
9672 #include <isl/ast.h>
9673 enum isl_ast_node_type isl_ast_node_get_type(
9674 __isl_keep isl_ast_node *node);
9676 The type of an AST node is one of
9677 C<isl_ast_node_for>,
9679 C<isl_ast_node_block>,
9680 C<isl_ast_node_mark> or
9681 C<isl_ast_node_user>.
9682 An C<isl_ast_node_for> represents a for node.
9683 An C<isl_ast_node_if> represents an if node.
9684 An C<isl_ast_node_block> represents a compound node.
9685 An C<isl_ast_node_mark> introduces a mark in the AST.
9686 An C<isl_ast_node_user> represents an expression statement.
9687 An expression statement typically corresponds to a domain element, i.e.,
9688 one of the elements that is visited by the AST.
9690 Each type of node has its own additional properties.
9692 #include <isl/ast.h>
9693 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
9694 __isl_keep isl_ast_node *node);
9695 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
9696 __isl_keep isl_ast_node *node);
9697 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
9698 __isl_keep isl_ast_node *node);
9699 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
9700 __isl_keep isl_ast_node *node);
9701 __isl_give isl_ast_node *isl_ast_node_for_get_body(
9702 __isl_keep isl_ast_node *node);
9703 isl_bool isl_ast_node_for_is_degenerate(
9704 __isl_keep isl_ast_node *node);
9706 An C<isl_ast_for> is considered degenerate if it is known to execute
9709 #include <isl/ast.h>
9710 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
9711 __isl_keep isl_ast_node *node);
9712 __isl_give isl_ast_node *isl_ast_node_if_get_then(
9713 __isl_keep isl_ast_node *node);
9714 isl_bool isl_ast_node_if_has_else(
9715 __isl_keep isl_ast_node *node);
9716 __isl_give isl_ast_node *isl_ast_node_if_get_else(
9717 __isl_keep isl_ast_node *node);
9719 __isl_give isl_ast_node_list *
9720 isl_ast_node_block_get_children(
9721 __isl_keep isl_ast_node *node);
9723 __isl_give isl_id *isl_ast_node_mark_get_id(
9724 __isl_keep isl_ast_node *node);
9725 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
9726 __isl_keep isl_ast_node *node);
9728 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
9729 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
9731 #include <isl/ast.h>
9732 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
9733 __isl_keep isl_ast_node *node);
9735 All descendants of a specific node in the AST (including the node itself)
9737 in depth-first pre-order using the following function.
9739 #include <isl/ast.h>
9740 isl_stat isl_ast_node_foreach_descendant_top_down(
9741 __isl_keep isl_ast_node *node,
9742 isl_bool (*fn)(__isl_keep isl_ast_node *node,
9743 void *user), void *user);
9745 The callback function should return C<isl_bool_true> if the children
9746 of the given node should be visited and C<isl_bool_false> if they should not.
9747 It should return C<isl_bool_error> in case of failure, in which case
9748 the entire traversal is aborted.
9750 Each of the returned C<isl_ast_expr>s can in turn be inspected using
9751 the following functions.
9753 #include <isl/ast.h>
9754 enum isl_ast_expr_type isl_ast_expr_get_type(
9755 __isl_keep isl_ast_expr *expr);
9757 The type of an AST expression is one of
9759 C<isl_ast_expr_id> or
9760 C<isl_ast_expr_int>.
9761 An C<isl_ast_expr_op> represents the result of an operation.
9762 An C<isl_ast_expr_id> represents an identifier.
9763 An C<isl_ast_expr_int> represents an integer value.
9765 Each type of expression has its own additional properties.
9767 #include <isl/ast.h>
9768 enum isl_ast_op_type isl_ast_expr_get_op_type(
9769 __isl_keep isl_ast_expr *expr);
9770 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
9771 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
9772 __isl_keep isl_ast_expr *expr, int pos);
9773 isl_stat isl_ast_expr_foreach_ast_op_type(
9774 __isl_keep isl_ast_expr *expr,
9775 isl_stat (*fn)(enum isl_ast_op_type type,
9776 void *user), void *user);
9777 isl_stat isl_ast_node_foreach_ast_op_type(
9778 __isl_keep isl_ast_node *node,
9779 isl_stat (*fn)(enum isl_ast_op_type type,
9780 void *user), void *user);
9782 C<isl_ast_expr_get_op_type> returns the type of the operation
9783 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
9784 arguments. C<isl_ast_expr_get_op_arg> returns the specified
9786 C<isl_ast_expr_foreach_ast_op_type> calls C<fn> for each distinct
9787 C<isl_ast_op_type> that appears in C<expr>.
9788 C<isl_ast_node_foreach_ast_op_type> does the same for each distinct
9789 C<isl_ast_op_type> that appears in C<node>.
9790 The operation type is one of the following.
9794 =item C<isl_ast_op_and>
9796 Logical I<and> of two arguments.
9797 Both arguments can be evaluated.
9799 =item C<isl_ast_op_and_then>
9801 Logical I<and> of two arguments.
9802 The second argument can only be evaluated if the first evaluates to true.
9804 =item C<isl_ast_op_or>
9806 Logical I<or> of two arguments.
9807 Both arguments can be evaluated.
9809 =item C<isl_ast_op_or_else>
9811 Logical I<or> of two arguments.
9812 The second argument can only be evaluated if the first evaluates to false.
9814 =item C<isl_ast_op_max>
9816 Maximum of two or more arguments.
9818 =item C<isl_ast_op_min>
9820 Minimum of two or more arguments.
9822 =item C<isl_ast_op_minus>
9826 =item C<isl_ast_op_add>
9828 Sum of two arguments.
9830 =item C<isl_ast_op_sub>
9832 Difference of two arguments.
9834 =item C<isl_ast_op_mul>
9836 Product of two arguments.
9838 =item C<isl_ast_op_div>
9840 Exact division. That is, the result is known to be an integer.
9842 =item C<isl_ast_op_fdiv_q>
9844 Result of integer division, rounded towards negative
9847 =item C<isl_ast_op_pdiv_q>
9849 Result of integer division, where dividend is known to be non-negative.
9851 =item C<isl_ast_op_pdiv_r>
9853 Remainder of integer division, where dividend is known to be non-negative.
9855 =item C<isl_ast_op_zdiv_r>
9857 Equal to zero iff the remainder on integer division is zero.
9859 =item C<isl_ast_op_cond>
9861 Conditional operator defined on three arguments.
9862 If the first argument evaluates to true, then the result
9863 is equal to the second argument. Otherwise, the result
9864 is equal to the third argument.
9865 The second and third argument may only be evaluated if
9866 the first argument evaluates to true and false, respectively.
9867 Corresponds to C<a ? b : c> in C.
9869 =item C<isl_ast_op_select>
9871 Conditional operator defined on three arguments.
9872 If the first argument evaluates to true, then the result
9873 is equal to the second argument. Otherwise, the result
9874 is equal to the third argument.
9875 The second and third argument may be evaluated independently
9876 of the value of the first argument.
9877 Corresponds to C<a * b + (1 - a) * c> in C.
9879 =item C<isl_ast_op_eq>
9883 =item C<isl_ast_op_le>
9885 Less than or equal relation.
9887 =item C<isl_ast_op_lt>
9891 =item C<isl_ast_op_ge>
9893 Greater than or equal relation.
9895 =item C<isl_ast_op_gt>
9897 Greater than relation.
9899 =item C<isl_ast_op_call>
9902 The number of arguments of the C<isl_ast_expr> is one more than
9903 the number of arguments in the function call, the first argument
9904 representing the function being called.
9906 =item C<isl_ast_op_access>
9909 The number of arguments of the C<isl_ast_expr> is one more than
9910 the number of index expressions in the array access, the first argument
9911 representing the array being accessed.
9913 =item C<isl_ast_op_member>
9916 This operation has two arguments, a structure and the name of
9917 the member of the structure being accessed.
9921 #include <isl/ast.h>
9922 __isl_give isl_id *isl_ast_expr_get_id(
9923 __isl_keep isl_ast_expr *expr);
9925 Return the identifier represented by the AST expression.
9927 #include <isl/ast.h>
9928 __isl_give isl_val *isl_ast_expr_get_val(
9929 __isl_keep isl_ast_expr *expr);
9931 Return the integer represented by the AST expression.
9933 =head3 Properties of ASTs
9935 #include <isl/ast.h>
9936 isl_bool isl_ast_expr_is_equal(
9937 __isl_keep isl_ast_expr *expr1,
9938 __isl_keep isl_ast_expr *expr2);
9940 Check if two C<isl_ast_expr>s are equal to each other.
9942 =head3 Manipulating and printing the AST
9944 AST nodes can be copied and freed using the following functions.
9946 #include <isl/ast.h>
9947 __isl_give isl_ast_node *isl_ast_node_copy(
9948 __isl_keep isl_ast_node *node);
9949 __isl_null isl_ast_node *isl_ast_node_free(
9950 __isl_take isl_ast_node *node);
9952 AST expressions can be copied and freed using the following functions.
9954 #include <isl/ast.h>
9955 __isl_give isl_ast_expr *isl_ast_expr_copy(
9956 __isl_keep isl_ast_expr *expr);
9957 __isl_null isl_ast_expr *isl_ast_expr_free(
9958 __isl_take isl_ast_expr *expr);
9960 New AST expressions can be created either directly or within
9961 the context of an C<isl_ast_build>.
9963 #include <isl/ast.h>
9964 __isl_give isl_ast_expr *isl_ast_expr_from_val(
9965 __isl_take isl_val *v);
9966 __isl_give isl_ast_expr *isl_ast_expr_from_id(
9967 __isl_take isl_id *id);
9968 __isl_give isl_ast_expr *isl_ast_expr_neg(
9969 __isl_take isl_ast_expr *expr);
9970 __isl_give isl_ast_expr *isl_ast_expr_address_of(
9971 __isl_take isl_ast_expr *expr);
9972 __isl_give isl_ast_expr *isl_ast_expr_add(
9973 __isl_take isl_ast_expr *expr1,
9974 __isl_take isl_ast_expr *expr2);
9975 __isl_give isl_ast_expr *isl_ast_expr_sub(
9976 __isl_take isl_ast_expr *expr1,
9977 __isl_take isl_ast_expr *expr2);
9978 __isl_give isl_ast_expr *isl_ast_expr_mul(
9979 __isl_take isl_ast_expr *expr1,
9980 __isl_take isl_ast_expr *expr2);
9981 __isl_give isl_ast_expr *isl_ast_expr_div(
9982 __isl_take isl_ast_expr *expr1,
9983 __isl_take isl_ast_expr *expr2);
9984 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
9985 __isl_take isl_ast_expr *expr1,
9986 __isl_take isl_ast_expr *expr2);
9987 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
9988 __isl_take isl_ast_expr *expr1,
9989 __isl_take isl_ast_expr *expr2);
9990 __isl_give isl_ast_expr *isl_ast_expr_and(
9991 __isl_take isl_ast_expr *expr1,
9992 __isl_take isl_ast_expr *expr2)
9993 __isl_give isl_ast_expr *isl_ast_expr_and_then(
9994 __isl_take isl_ast_expr *expr1,
9995 __isl_take isl_ast_expr *expr2)
9996 __isl_give isl_ast_expr *isl_ast_expr_or(
9997 __isl_take isl_ast_expr *expr1,
9998 __isl_take isl_ast_expr *expr2)
9999 __isl_give isl_ast_expr *isl_ast_expr_or_else(
10000 __isl_take isl_ast_expr *expr1,
10001 __isl_take isl_ast_expr *expr2)
10002 __isl_give isl_ast_expr *isl_ast_expr_eq(
10003 __isl_take isl_ast_expr *expr1,
10004 __isl_take isl_ast_expr *expr2);
10005 __isl_give isl_ast_expr *isl_ast_expr_le(
10006 __isl_take isl_ast_expr *expr1,
10007 __isl_take isl_ast_expr *expr2);
10008 __isl_give isl_ast_expr *isl_ast_expr_lt(
10009 __isl_take isl_ast_expr *expr1,
10010 __isl_take isl_ast_expr *expr2);
10011 __isl_give isl_ast_expr *isl_ast_expr_ge(
10012 __isl_take isl_ast_expr *expr1,
10013 __isl_take isl_ast_expr *expr2);
10014 __isl_give isl_ast_expr *isl_ast_expr_gt(
10015 __isl_take isl_ast_expr *expr1,
10016 __isl_take isl_ast_expr *expr2);
10017 __isl_give isl_ast_expr *isl_ast_expr_access(
10018 __isl_take isl_ast_expr *array,
10019 __isl_take isl_ast_expr_list *indices);
10020 __isl_give isl_ast_expr *isl_ast_expr_call(
10021 __isl_take isl_ast_expr *function,
10022 __isl_take isl_ast_expr_list *arguments);
10024 The function C<isl_ast_expr_address_of> can be applied to an
10025 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
10026 to represent the address of the C<isl_ast_expr_access>. The function
10027 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
10028 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
10030 #include <isl/ast_build.h>
10031 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
10032 __isl_keep isl_ast_build *build,
10033 __isl_take isl_set *set);
10034 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
10035 __isl_keep isl_ast_build *build,
10036 __isl_take isl_pw_aff *pa);
10037 __isl_give isl_ast_expr *
10038 isl_ast_build_access_from_pw_multi_aff(
10039 __isl_keep isl_ast_build *build,
10040 __isl_take isl_pw_multi_aff *pma);
10041 __isl_give isl_ast_expr *
10042 isl_ast_build_access_from_multi_pw_aff(
10043 __isl_keep isl_ast_build *build,
10044 __isl_take isl_multi_pw_aff *mpa);
10045 __isl_give isl_ast_expr *
10046 isl_ast_build_call_from_pw_multi_aff(
10047 __isl_keep isl_ast_build *build,
10048 __isl_take isl_pw_multi_aff *pma);
10049 __isl_give isl_ast_expr *
10050 isl_ast_build_call_from_multi_pw_aff(
10051 __isl_keep isl_ast_build *build,
10052 __isl_take isl_multi_pw_aff *mpa);
10055 the domains of C<pa>, C<mpa> and C<pma> should correspond
10056 to the schedule space of C<build>.
10057 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
10058 the function being called.
10059 If the accessed space is a nested relation, then it is taken
10060 to represent an access of the member specified by the range
10061 of this nested relation of the structure specified by the domain
10062 of the nested relation.
10064 The following functions can be used to modify an C<isl_ast_expr>.
10066 #include <isl/ast.h>
10067 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
10068 __isl_take isl_ast_expr *expr, int pos,
10069 __isl_take isl_ast_expr *arg);
10071 Replace the argument of C<expr> at position C<pos> by C<arg>.
10073 #include <isl/ast.h>
10074 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
10075 __isl_take isl_ast_expr *expr,
10076 __isl_take isl_id_to_ast_expr *id2expr);
10078 The function C<isl_ast_expr_substitute_ids> replaces the
10079 subexpressions of C<expr> of type C<isl_ast_expr_id>
10080 by the corresponding expression in C<id2expr>, if there is any.
10083 User specified data can be attached to an C<isl_ast_node> and obtained
10084 from the same C<isl_ast_node> using the following functions.
10086 #include <isl/ast.h>
10087 __isl_give isl_ast_node *isl_ast_node_set_annotation(
10088 __isl_take isl_ast_node *node,
10089 __isl_take isl_id *annotation);
10090 __isl_give isl_id *isl_ast_node_get_annotation(
10091 __isl_keep isl_ast_node *node);
10093 Basic printing can be performed using the following functions.
10095 #include <isl/ast.h>
10096 __isl_give isl_printer *isl_printer_print_ast_expr(
10097 __isl_take isl_printer *p,
10098 __isl_keep isl_ast_expr *expr);
10099 __isl_give isl_printer *isl_printer_print_ast_node(
10100 __isl_take isl_printer *p,
10101 __isl_keep isl_ast_node *node);
10102 __isl_give char *isl_ast_expr_to_str(
10103 __isl_keep isl_ast_expr *expr);
10104 __isl_give char *isl_ast_node_to_str(
10105 __isl_keep isl_ast_node *node);
10106 __isl_give char *isl_ast_expr_to_C_str(
10107 __isl_keep isl_ast_expr *expr);
10108 __isl_give char *isl_ast_node_to_C_str(
10109 __isl_keep isl_ast_node *node);
10111 The functions C<isl_ast_expr_to_C_str> and
10112 C<isl_ast_node_to_C_str> are convenience functions
10113 that return a string representation of the input in C format.
10115 More advanced printing can be performed using the following functions.
10117 #include <isl/ast.h>
10118 __isl_give isl_printer *isl_ast_op_type_set_print_name(
10119 __isl_take isl_printer *p,
10120 enum isl_ast_op_type type,
10121 __isl_keep const char *name);
10122 isl_stat isl_options_set_ast_print_macro_once(
10123 isl_ctx *ctx, int val);
10124 int isl_options_get_ast_print_macro_once(isl_ctx *ctx);
10125 __isl_give isl_printer *isl_ast_op_type_print_macro(
10126 enum isl_ast_op_type type,
10127 __isl_take isl_printer *p);
10128 __isl_give isl_printer *isl_ast_expr_print_macros(
10129 __isl_keep isl_ast_expr *expr,
10130 __isl_take isl_printer *p);
10131 __isl_give isl_printer *isl_ast_node_print_macros(
10132 __isl_keep isl_ast_node *node,
10133 __isl_take isl_printer *p);
10134 __isl_give isl_printer *isl_ast_node_print(
10135 __isl_keep isl_ast_node *node,
10136 __isl_take isl_printer *p,
10137 __isl_take isl_ast_print_options *options);
10138 __isl_give isl_printer *isl_ast_node_for_print(
10139 __isl_keep isl_ast_node *node,
10140 __isl_take isl_printer *p,
10141 __isl_take isl_ast_print_options *options);
10142 __isl_give isl_printer *isl_ast_node_if_print(
10143 __isl_keep isl_ast_node *node,
10144 __isl_take isl_printer *p,
10145 __isl_take isl_ast_print_options *options);
10147 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
10148 C<isl> may print out an AST that makes use of macros such
10149 as C<floord>, C<min> and C<max>.
10150 The names of these macros may be modified by a call
10151 to C<isl_ast_op_type_set_print_name>. The user-specified
10152 names are associated to the printer object.
10153 C<isl_ast_op_type_print_macro> prints out the macro
10154 corresponding to a specific C<isl_ast_op_type>.
10155 If the print-macro-once option is set, then a given macro definition
10156 is only printed once to any given printer object.
10157 C<isl_ast_expr_print_macros> scans the C<isl_ast_expr>
10158 for subexpressions where these macros would be used and prints
10159 out the required macro definitions.
10160 Essentially, C<isl_ast_expr_print_macros> calls
10161 C<isl_ast_expr_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
10162 as function argument.
10163 C<isl_ast_node_print_macros> does the same
10164 for expressions in its C<isl_ast_node> argument.
10165 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
10166 C<isl_ast_node_if_print> print an C<isl_ast_node>
10167 in C<ISL_FORMAT_C>, but allow for some extra control
10168 through an C<isl_ast_print_options> object.
10169 This object can be created using the following functions.
10171 #include <isl/ast.h>
10172 __isl_give isl_ast_print_options *
10173 isl_ast_print_options_alloc(isl_ctx *ctx);
10174 __isl_give isl_ast_print_options *
10175 isl_ast_print_options_copy(
10176 __isl_keep isl_ast_print_options *options);
10177 __isl_null isl_ast_print_options *
10178 isl_ast_print_options_free(
10179 __isl_take isl_ast_print_options *options);
10181 __isl_give isl_ast_print_options *
10182 isl_ast_print_options_set_print_user(
10183 __isl_take isl_ast_print_options *options,
10184 __isl_give isl_printer *(*print_user)(
10185 __isl_take isl_printer *p,
10186 __isl_take isl_ast_print_options *options,
10187 __isl_keep isl_ast_node *node, void *user),
10189 __isl_give isl_ast_print_options *
10190 isl_ast_print_options_set_print_for(
10191 __isl_take isl_ast_print_options *options,
10192 __isl_give isl_printer *(*print_for)(
10193 __isl_take isl_printer *p,
10194 __isl_take isl_ast_print_options *options,
10195 __isl_keep isl_ast_node *node, void *user),
10198 The callback set by C<isl_ast_print_options_set_print_user>
10199 is called whenever a node of type C<isl_ast_node_user> needs to
10201 The callback set by C<isl_ast_print_options_set_print_for>
10202 is called whenever a node of type C<isl_ast_node_for> needs to
10204 Note that C<isl_ast_node_for_print> will I<not> call the
10205 callback set by C<isl_ast_print_options_set_print_for> on the node
10206 on which C<isl_ast_node_for_print> is called, but only on nested
10207 nodes of type C<isl_ast_node_for>. It is therefore safe to
10208 call C<isl_ast_node_for_print> from within the callback set by
10209 C<isl_ast_print_options_set_print_for>.
10211 The following option determines the type to be used for iterators
10212 while printing the AST.
10214 isl_stat isl_options_set_ast_iterator_type(
10215 isl_ctx *ctx, const char *val);
10216 const char *isl_options_get_ast_iterator_type(
10219 The AST printer only prints body nodes as blocks if these
10220 blocks cannot be safely omitted.
10221 For example, a C<for> node with one body node will not be
10222 surrounded with braces in C<ISL_FORMAT_C>.
10223 A block will always be printed by setting the following option.
10225 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx,
10227 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
10231 #include <isl/ast_build.h>
10232 isl_stat isl_options_set_ast_build_atomic_upper_bound(
10233 isl_ctx *ctx, int val);
10234 int isl_options_get_ast_build_atomic_upper_bound(
10236 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
10238 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
10239 isl_stat isl_options_set_ast_build_detect_min_max(
10240 isl_ctx *ctx, int val);
10241 int isl_options_get_ast_build_detect_min_max(
10243 isl_stat isl_options_set_ast_build_exploit_nested_bounds(
10244 isl_ctx *ctx, int val);
10245 int isl_options_get_ast_build_exploit_nested_bounds(
10247 isl_stat isl_options_set_ast_build_group_coscheduled(
10248 isl_ctx *ctx, int val);
10249 int isl_options_get_ast_build_group_coscheduled(
10251 isl_stat isl_options_set_ast_build_scale_strides(
10252 isl_ctx *ctx, int val);
10253 int isl_options_get_ast_build_scale_strides(
10255 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx,
10257 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
10258 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx,
10260 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
10264 =item * ast_build_atomic_upper_bound
10266 Generate loop upper bounds that consist of the current loop iterator,
10267 an operator and an expression not involving the iterator.
10268 If this option is not set, then the current loop iterator may appear
10269 several times in the upper bound.
10270 For example, when this option is turned off, AST generation
10273 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
10277 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
10280 When the option is turned on, the following AST is generated
10282 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
10285 =item * ast_build_prefer_pdiv
10287 If this option is turned off, then the AST generation will
10288 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
10289 operators, but no C<isl_ast_op_pdiv_q> or
10290 C<isl_ast_op_pdiv_r> operators.
10291 If this option is turned on, then C<isl> will try to convert
10292 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
10293 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
10295 =item * ast_build_detect_min_max
10297 If this option is turned on, then C<isl> will try and detect
10298 min or max-expressions when building AST expressions from
10299 piecewise affine expressions.
10301 =item * ast_build_exploit_nested_bounds
10303 Simplify conditions based on bounds of nested for loops.
10304 In particular, remove conditions that are implied by the fact
10305 that one or more nested loops have at least one iteration,
10306 meaning that the upper bound is at least as large as the lower bound.
10307 For example, when this option is turned off, AST generation
10310 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
10316 for (int c0 = 0; c0 <= N; c0 += 1)
10317 for (int c1 = 0; c1 <= M; c1 += 1)
10320 When the option is turned on, the following AST is generated
10322 for (int c0 = 0; c0 <= N; c0 += 1)
10323 for (int c1 = 0; c1 <= M; c1 += 1)
10326 =item * ast_build_group_coscheduled
10328 If two domain elements are assigned the same schedule point, then
10329 they may be executed in any order and they may even appear in different
10330 loops. If this options is set, then the AST generator will make
10331 sure that coscheduled domain elements do not appear in separate parts
10332 of the AST. This is useful in case of nested AST generation
10333 if the outer AST generation is given only part of a schedule
10334 and the inner AST generation should handle the domains that are
10335 coscheduled by this initial part of the schedule together.
10336 For example if an AST is generated for a schedule
10338 { A[i] -> [0]; B[i] -> [0] }
10340 then the C<isl_ast_build_set_create_leaf> callback described
10341 below may get called twice, once for each domain.
10342 Setting this option ensures that the callback is only called once
10343 on both domains together.
10345 =item * ast_build_separation_bounds
10347 This option specifies which bounds to use during separation.
10348 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
10349 then all (possibly implicit) bounds on the current dimension will
10350 be used during separation.
10351 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
10352 then only those bounds that are explicitly available will
10353 be used during separation.
10355 =item * ast_build_scale_strides
10357 This option specifies whether the AST generator is allowed
10358 to scale down iterators of strided loops.
10360 =item * ast_build_allow_else
10362 This option specifies whether the AST generator is allowed
10363 to construct if statements with else branches.
10365 =item * ast_build_allow_or
10367 This option specifies whether the AST generator is allowed
10368 to construct if conditions with disjunctions.
10372 =head3 AST Generation Options (Schedule Tree)
10374 In case of AST construction from a schedule tree, the options
10375 that control how an AST is created from the individual schedule
10376 dimensions are stored in the band nodes of the tree
10377 (see L</"Schedule Trees">).
10379 In particular, a schedule dimension can be handled in four
10380 different ways, atomic, separate, unroll or the default.
10381 This loop AST generation type can be set using
10382 C<isl_schedule_node_band_member_set_ast_loop_type>.
10384 the first three can be selected by including a one-dimensional
10385 element with as value the position of the schedule dimension
10386 within the band and as name one of C<atomic>, C<separate>
10387 or C<unroll> in the options
10388 set by C<isl_schedule_node_band_set_ast_build_options>.
10389 Only one of these three may be specified for
10390 any given schedule dimension within a band node.
10391 If none of these is specified, then the default
10392 is used. The meaning of the options is as follows.
10398 When this option is specified, the AST generator will make
10399 sure that a given domains space only appears in a single
10400 loop at the specified level.
10402 For example, for the schedule tree
10404 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10406 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10407 options: "{ atomic[x] }"
10409 the following AST will be generated
10411 for (int c0 = 0; c0 <= 10; c0 += 1) {
10418 On the other hand, for the schedule tree
10420 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10422 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10423 options: "{ separate[x] }"
10425 the following AST will be generated
10429 for (int c0 = 1; c0 <= 9; c0 += 1) {
10436 If neither C<atomic> nor C<separate> is specified, then the AST generator
10437 may produce either of these two results or some intermediate form.
10441 When this option is specified, the AST generator will
10442 split the domain of the specified schedule dimension
10443 into pieces with a fixed set of statements for which
10444 instances need to be executed by the iterations in
10445 the schedule domain part. This option tends to avoid
10446 the generation of guards inside the corresponding loops.
10447 See also the C<atomic> option.
10451 When this option is specified, the AST generator will
10452 I<completely> unroll the corresponding schedule dimension.
10453 It is the responsibility of the user to ensure that such
10454 unrolling is possible.
10455 To obtain a partial unrolling, the user should apply an additional
10456 strip-mining to the schedule and fully unroll the inner schedule
10461 The C<isolate> option is a bit more involved. It allows the user
10462 to isolate a range of schedule dimension values from smaller and
10463 greater values. Additionally, the user may specify a different
10464 atomic/separate/unroll choice for the isolated part and the remaining
10465 parts. The typical use case of the C<isolate> option is to isolate
10466 full tiles from partial tiles.
10467 The part that needs to be isolated may depend on outer schedule dimensions.
10468 The option therefore needs to be able to reference those outer schedule
10469 dimensions. In particular, the space of the C<isolate> option is that
10470 of a wrapped map with as domain the flat product of all outer band nodes
10471 and as range the space of the current band node.
10472 The atomic/separate/unroll choice for the isolated part is determined
10473 by an option that lives in an unnamed wrapped space with as domain
10474 a zero-dimensional C<isolate> space and as range the regular
10475 C<atomic>, C<separate> or C<unroll> space.
10476 This option may also be set directly using
10477 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
10478 The atomic/separate/unroll choice for the remaining part is determined
10479 by the regular C<atomic>, C<separate> or C<unroll> option.
10480 Since the C<isolate> option references outer schedule dimensions,
10481 its use in a band node causes any tree containing the node
10482 to be considered anchored.
10484 As an example, consider the isolation of full tiles from partial tiles
10485 in a tiling of a triangular domain. The original schedule is as follows.
10487 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10489 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10490 { A[i,j] -> [floor(j/10)] }, \
10491 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10495 for (int c0 = 0; c0 <= 10; c0 += 1)
10496 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10497 for (int c2 = 10 * c0;
10498 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10499 for (int c3 = 10 * c1;
10500 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10503 Isolating the full tiles, we have the following input
10505 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10507 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10508 { A[i,j] -> [floor(j/10)] }, \
10509 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10510 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10511 10a+9+10b+9 <= 100 }"
10516 for (int c0 = 0; c0 <= 8; c0 += 1) {
10517 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10518 for (int c2 = 10 * c0;
10519 c2 <= 10 * c0 + 9; c2 += 1)
10520 for (int c3 = 10 * c1;
10521 c3 <= 10 * c1 + 9; c3 += 1)
10523 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10524 for (int c2 = 10 * c0;
10525 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10526 for (int c3 = 10 * c1;
10527 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10530 for (int c0 = 9; c0 <= 10; c0 += 1)
10531 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10532 for (int c2 = 10 * c0;
10533 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10534 for (int c3 = 10 * c1;
10535 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10539 We may then additionally unroll the innermost loop of the isolated part
10541 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10543 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10544 { A[i,j] -> [floor(j/10)] }, \
10545 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10546 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10547 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
10552 for (int c0 = 0; c0 <= 8; c0 += 1) {
10553 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10554 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
10556 A(c2, 10 * c1 + 1);
10557 A(c2, 10 * c1 + 2);
10558 A(c2, 10 * c1 + 3);
10559 A(c2, 10 * c1 + 4);
10560 A(c2, 10 * c1 + 5);
10561 A(c2, 10 * c1 + 6);
10562 A(c2, 10 * c1 + 7);
10563 A(c2, 10 * c1 + 8);
10564 A(c2, 10 * c1 + 9);
10566 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10567 for (int c2 = 10 * c0;
10568 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10569 for (int c3 = 10 * c1;
10570 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10573 for (int c0 = 9; c0 <= 10; c0 += 1)
10574 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10575 for (int c2 = 10 * c0;
10576 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10577 for (int c3 = 10 * c1;
10578 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10583 =head3 AST Generation Options (Schedule Map)
10585 In case of AST construction using
10586 C<isl_ast_build_node_from_schedule_map>, the options
10587 that control how an AST is created from the individual schedule
10588 dimensions are stored in the C<isl_ast_build>.
10589 They can be set using the following function.
10591 #include <isl/ast_build.h>
10592 __isl_give isl_ast_build *
10593 isl_ast_build_set_options(
10594 __isl_take isl_ast_build *build,
10595 __isl_take isl_union_map *options);
10597 The options are encoded in an C<isl_union_map>.
10598 The domain of this union relation refers to the schedule domain,
10599 i.e., the range of the schedule passed
10600 to C<isl_ast_build_node_from_schedule_map>.
10601 In the case of nested AST generation (see L</"Nested AST Generation">),
10602 the domain of C<options> should refer to the extra piece of the schedule.
10603 That is, it should be equal to the range of the wrapped relation in the
10604 range of the schedule.
10605 The range of the options can consist of elements in one or more spaces,
10606 the names of which determine the effect of the option.
10607 The values of the range typically also refer to the schedule dimension
10608 to which the option applies. In case of nested AST generation
10609 (see L</"Nested AST Generation">), these values refer to the position
10610 of the schedule dimension within the innermost AST generation.
10611 The constraints on the domain elements of
10612 the option should only refer to this dimension and earlier dimensions.
10613 We consider the following spaces.
10617 =item C<separation_class>
10619 B<This option has been deprecated. Use the isolate option on
10620 schedule trees instead.>
10622 This space is a wrapped relation between two one dimensional spaces.
10623 The input space represents the schedule dimension to which the option
10624 applies and the output space represents the separation class.
10625 While constructing a loop corresponding to the specified schedule
10626 dimension(s), the AST generator will try to generate separate loops
10627 for domain elements that are assigned different classes.
10628 If only some of the elements are assigned a class, then those elements
10629 that are not assigned any class will be treated as belonging to a class
10630 that is separate from the explicitly assigned classes.
10631 The typical use case for this option is to separate full tiles from
10633 The other options, described below, are applied after the separation
10636 As an example, consider the separation into full and partial tiles
10637 of a tiling of a triangular domain.
10638 Take, for example, the domain
10640 { A[i,j] : 0 <= i,j and i + j <= 100 }
10642 and a tiling into tiles of 10 by 10. The input to the AST generator
10643 is then the schedule
10645 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
10648 Without any options, the following AST is generated
10650 for (int c0 = 0; c0 <= 10; c0 += 1)
10651 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10652 for (int c2 = 10 * c0;
10653 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10655 for (int c3 = 10 * c1;
10656 c3 <= min(10 * c1 + 9, -c2 + 100);
10660 Separation into full and partial tiles can be obtained by assigning
10661 a class, say C<0>, to the full tiles. The full tiles are represented by those
10662 values of the first and second schedule dimensions for which there are
10663 values of the third and fourth dimensions to cover an entire tile.
10664 That is, we need to specify the following option
10666 { [a,b,c,d] -> separation_class[[0]->[0]] :
10667 exists b': 0 <= 10a,10b' and
10668 10a+9+10b'+9 <= 100;
10669 [a,b,c,d] -> separation_class[[1]->[0]] :
10670 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
10672 which simplifies to
10674 { [a, b, c, d] -> separation_class[[1] -> [0]] :
10675 a >= 0 and b >= 0 and b <= 8 - a;
10676 [a, b, c, d] -> separation_class[[0] -> [0]] :
10677 a >= 0 and a <= 8 }
10679 With this option, the generated AST is as follows
10682 for (int c0 = 0; c0 <= 8; c0 += 1) {
10683 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10684 for (int c2 = 10 * c0;
10685 c2 <= 10 * c0 + 9; c2 += 1)
10686 for (int c3 = 10 * c1;
10687 c3 <= 10 * c1 + 9; c3 += 1)
10689 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10690 for (int c2 = 10 * c0;
10691 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10693 for (int c3 = 10 * c1;
10694 c3 <= min(-c2 + 100, 10 * c1 + 9);
10698 for (int c0 = 9; c0 <= 10; c0 += 1)
10699 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10700 for (int c2 = 10 * c0;
10701 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10703 for (int c3 = 10 * c1;
10704 c3 <= min(10 * c1 + 9, -c2 + 100);
10711 This is a single-dimensional space representing the schedule dimension(s)
10712 to which ``separation'' should be applied. Separation tries to split
10713 a loop into several pieces if this can avoid the generation of guards
10715 See also the C<atomic> option.
10719 This is a single-dimensional space representing the schedule dimension(s)
10720 for which the domains should be considered ``atomic''. That is, the
10721 AST generator will make sure that any given domain space will only appear
10722 in a single loop at the specified level.
10724 Consider the following schedule
10726 { a[i] -> [i] : 0 <= i < 10;
10727 b[i] -> [i+1] : 0 <= i < 10 }
10729 If the following option is specified
10731 { [i] -> separate[x] }
10733 then the following AST will be generated
10737 for (int c0 = 1; c0 <= 9; c0 += 1) {
10744 If, on the other hand, the following option is specified
10746 { [i] -> atomic[x] }
10748 then the following AST will be generated
10750 for (int c0 = 0; c0 <= 10; c0 += 1) {
10757 If neither C<atomic> nor C<separate> is specified, then the AST generator
10758 may produce either of these two results or some intermediate form.
10762 This is a single-dimensional space representing the schedule dimension(s)
10763 that should be I<completely> unrolled.
10764 To obtain a partial unrolling, the user should apply an additional
10765 strip-mining to the schedule and fully unroll the inner loop.
10769 =head3 Fine-grained Control over AST Generation
10771 Besides specifying the constraints on the parameters,
10772 an C<isl_ast_build> object can be used to control
10773 various aspects of the AST generation process.
10774 In case of AST construction using
10775 C<isl_ast_build_node_from_schedule_map>,
10776 the most prominent way of control is through ``options'',
10777 as explained above.
10779 Additional control is available through the following functions.
10781 #include <isl/ast_build.h>
10782 __isl_give isl_ast_build *
10783 isl_ast_build_set_iterators(
10784 __isl_take isl_ast_build *build,
10785 __isl_take isl_id_list *iterators);
10787 The function C<isl_ast_build_set_iterators> allows the user to
10788 specify a list of iterator C<isl_id>s to be used as iterators.
10789 If the input schedule is injective, then
10790 the number of elements in this list should be as large as the dimension
10791 of the schedule space, but no direct correspondence should be assumed
10792 between dimensions and elements.
10793 If the input schedule is not injective, then an additional number
10794 of C<isl_id>s equal to the largest dimension of the input domains
10796 If the number of provided C<isl_id>s is insufficient, then additional
10797 names are automatically generated.
10799 #include <isl/ast_build.h>
10800 __isl_give isl_ast_build *
10801 isl_ast_build_set_create_leaf(
10802 __isl_take isl_ast_build *build,
10803 __isl_give isl_ast_node *(*fn)(
10804 __isl_take isl_ast_build *build,
10805 void *user), void *user);
10808 C<isl_ast_build_set_create_leaf> function allows for the
10809 specification of a callback that should be called whenever the AST
10810 generator arrives at an element of the schedule domain.
10811 The callback should return an AST node that should be inserted
10812 at the corresponding position of the AST. The default action (when
10813 the callback is not set) is to continue generating parts of the AST to scan
10814 all the domain elements associated to the schedule domain element
10815 and to insert user nodes, ``calling'' the domain element, for each of them.
10816 The C<build> argument contains the current state of the C<isl_ast_build>.
10817 To ease nested AST generation (see L</"Nested AST Generation">),
10818 all control information that is
10819 specific to the current AST generation such as the options and
10820 the callbacks has been removed from this C<isl_ast_build>.
10821 The callback would typically return the result of a nested
10822 AST generation or a
10823 user defined node created using the following function.
10825 #include <isl/ast.h>
10826 __isl_give isl_ast_node *isl_ast_node_alloc_user(
10827 __isl_take isl_ast_expr *expr);
10829 #include <isl/ast_build.h>
10830 __isl_give isl_ast_build *
10831 isl_ast_build_set_at_each_domain(
10832 __isl_take isl_ast_build *build,
10833 __isl_give isl_ast_node *(*fn)(
10834 __isl_take isl_ast_node *node,
10835 __isl_keep isl_ast_build *build,
10836 void *user), void *user);
10837 __isl_give isl_ast_build *
10838 isl_ast_build_set_before_each_for(
10839 __isl_take isl_ast_build *build,
10840 __isl_give isl_id *(*fn)(
10841 __isl_keep isl_ast_build *build,
10842 void *user), void *user);
10843 __isl_give isl_ast_build *
10844 isl_ast_build_set_after_each_for(
10845 __isl_take isl_ast_build *build,
10846 __isl_give isl_ast_node *(*fn)(
10847 __isl_take isl_ast_node *node,
10848 __isl_keep isl_ast_build *build,
10849 void *user), void *user);
10850 __isl_give isl_ast_build *
10851 isl_ast_build_set_before_each_mark(
10852 __isl_take isl_ast_build *build,
10853 isl_stat (*fn)(__isl_keep isl_id *mark,
10854 __isl_keep isl_ast_build *build,
10855 void *user), void *user);
10856 __isl_give isl_ast_build *
10857 isl_ast_build_set_after_each_mark(
10858 __isl_take isl_ast_build *build,
10859 __isl_give isl_ast_node *(*fn)(
10860 __isl_take isl_ast_node *node,
10861 __isl_keep isl_ast_build *build,
10862 void *user), void *user);
10864 The callback set by C<isl_ast_build_set_at_each_domain> will
10865 be called for each domain AST node.
10866 The callbacks set by C<isl_ast_build_set_before_each_for>
10867 and C<isl_ast_build_set_after_each_for> will be called
10868 for each for AST node. The first will be called in depth-first
10869 pre-order, while the second will be called in depth-first post-order.
10870 Since C<isl_ast_build_set_before_each_for> is called before the for
10871 node is actually constructed, it is only passed an C<isl_ast_build>.
10872 The returned C<isl_id> will be added as an annotation (using
10873 C<isl_ast_node_set_annotation>) to the constructed for node.
10874 In particular, if the user has also specified an C<after_each_for>
10875 callback, then the annotation can be retrieved from the node passed to
10876 that callback using C<isl_ast_node_get_annotation>.
10877 The callbacks set by C<isl_ast_build_set_before_each_mark>
10878 and C<isl_ast_build_set_after_each_mark> will be called for each
10879 mark AST node that is created, i.e., for each mark schedule node
10880 in the input schedule tree. The first will be called in depth-first
10881 pre-order, while the second will be called in depth-first post-order.
10882 Since the callback set by C<isl_ast_build_set_before_each_mark>
10883 is called before the mark AST node is actually constructed, it is passed
10884 the identifier of the mark node.
10885 All callbacks should C<NULL> (or C<isl_stat_error>) on failure.
10886 The given C<isl_ast_build> can be used to create new
10887 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
10888 or C<isl_ast_build_call_from_pw_multi_aff>.
10890 =head3 Nested AST Generation
10892 C<isl> allows the user to create an AST within the context
10893 of another AST. These nested ASTs are created using the
10894 same C<isl_ast_build_node_from_schedule_map> function that is used to create
10895 the outer AST. The C<build> argument should be an C<isl_ast_build>
10896 passed to a callback set by
10897 C<isl_ast_build_set_create_leaf>.
10898 The space of the range of the C<schedule> argument should refer
10899 to this build. In particular, the space should be a wrapped
10900 relation and the domain of this wrapped relation should be the
10901 same as that of the range of the schedule returned by
10902 C<isl_ast_build_get_schedule> below.
10903 In practice, the new schedule is typically
10904 created by calling C<isl_union_map_range_product> on the old schedule
10905 and some extra piece of the schedule.
10906 The space of the schedule domain is also available from
10907 the C<isl_ast_build>.
10909 #include <isl/ast_build.h>
10910 __isl_give isl_union_map *isl_ast_build_get_schedule(
10911 __isl_keep isl_ast_build *build);
10912 __isl_give isl_space *isl_ast_build_get_schedule_space(
10913 __isl_keep isl_ast_build *build);
10914 __isl_give isl_ast_build *isl_ast_build_restrict(
10915 __isl_take isl_ast_build *build,
10916 __isl_take isl_set *set);
10918 The C<isl_ast_build_get_schedule> function returns a (partial)
10919 schedule for the domains elements for which part of the AST still needs to
10920 be generated in the current build.
10921 In particular, the domain elements are mapped to those iterations of the loops
10922 enclosing the current point of the AST generation inside which
10923 the domain elements are executed.
10924 No direct correspondence between
10925 the input schedule and this schedule should be assumed.
10926 The space obtained from C<isl_ast_build_get_schedule_space> can be used
10927 to create a set for C<isl_ast_build_restrict> to intersect
10928 with the current build. In particular, the set passed to
10929 C<isl_ast_build_restrict> can have additional parameters.
10930 The ids of the set dimensions in the space returned by
10931 C<isl_ast_build_get_schedule_space> correspond to the
10932 iterators of the already generated loops.
10933 The user should not rely on the ids of the output dimensions
10934 of the relations in the union relation returned by
10935 C<isl_ast_build_get_schedule> having any particular value.
10937 =head1 Applications
10939 Although C<isl> is mainly meant to be used as a library,
10940 it also contains some basic applications that use some
10941 of the functionality of C<isl>.
10942 For applications that take one or more polytopes or polyhedra
10943 as input, this input may be specified in either the L<isl format>
10944 or the L<PolyLib format>.
10946 =head2 C<isl_polyhedron_sample>
10948 C<isl_polyhedron_sample> takes a polyhedron as input and prints
10949 an integer element of the polyhedron, if there is any.
10950 The first column in the output is the denominator and is always
10951 equal to 1. If the polyhedron contains no integer points,
10952 then a vector of length zero is printed.
10956 C<isl_pip> takes the same input as the C<example> program
10957 from the C<piplib> distribution, i.e., a set of constraints
10958 on the parameters, a line containing only -1 and finally a set
10959 of constraints on a parametric polyhedron.
10960 The coefficients of the parameters appear in the last columns
10961 (but before the final constant column).
10962 The output is the lexicographic minimum of the parametric polyhedron.
10963 As C<isl> currently does not have its own output format, the output
10964 is just a dump of the internal state.
10966 =head2 C<isl_polyhedron_minimize>
10968 C<isl_polyhedron_minimize> computes the minimum of some linear
10969 or affine objective function over the integer points in a polyhedron.
10970 If an affine objective function
10971 is given, then the constant should appear in the last column.
10973 =head2 C<isl_polytope_scan>
10975 Given a polytope, C<isl_polytope_scan> prints
10976 all integer points in the polytope.
10980 Given an C<isl_union_access_info> object as input,
10981 C<isl_flow> prints out the corresponding dependences,
10982 as computed by C<isl_union_access_info_compute_flow>.
10984 =head2 C<isl_codegen>
10986 Given either a schedule tree or a sequence consisting of
10987 a schedule map, a context set and an options relation,
10988 C<isl_codegen> prints out an AST that scans the domain elements
10989 of the schedule in the order of their image(s) taking into account
10990 the constraints in the context set.
10992 =head2 C<isl_schedule>
10994 Given an C<isl_schedule_constraints> object as input,
10995 C<isl_schedule> prints out a schedule that satisfies the given