3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
8 using C<GMP> or C<imath>.
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
171 =head3 Changes since isl-0.10
175 =item * The functions C<isl_set_dim_has_lower_bound> and
176 C<isl_set_dim_has_upper_bound> have been renamed to
177 C<isl_set_dim_has_any_lower_bound> and
178 C<isl_set_dim_has_any_upper_bound>.
179 The new C<isl_set_dim_has_lower_bound> and
180 C<isl_set_dim_has_upper_bound> have slightly different meanings.
184 =head3 Changes since isl-0.12
188 =item * C<isl_int> has been replaced by C<isl_val>.
189 Some of the old functions are still available in C<isl/deprecated/*.h>
190 but they will be removed in the future.
192 =item * The functions C<isl_pw_qpolynomial_eval>,
193 C<isl_union_pw_qpolynomial_eval>, C<isl_pw_qpolynomial_fold_eval>
194 and C<isl_union_pw_qpolynomial_fold_eval> have been changed to return
195 an C<isl_val> instead of an C<isl_qpolynomial>.
197 =item * The function C<isl_band_member_is_zero_distance>
198 has been removed. Essentially the same functionality is available
199 through C<isl_band_member_is_coincident>, except that it requires
200 setting up coincidence constraints.
201 The option C<schedule_outer_zero_distance> has accordingly been
202 replaced by the option C<schedule_outer_coincidence>.
204 =item * The function C<isl_vertex_get_expr> has been changed
205 to return an C<isl_multi_aff> instead of a rational C<isl_basic_set>.
206 The function C<isl_vertex_get_domain> has been changed to return
207 a regular basic set, rather than a rational basic set.
211 =head3 Changes since isl-0.14
215 =item * The function C<isl_union_pw_multi_aff_add> now consistently
216 computes the sum on the shared definition domain.
217 The function C<isl_union_pw_multi_aff_union_add> has been added
218 to compute the sum on the union of definition domains.
219 The original behavior of C<isl_union_pw_multi_aff_add> was
220 confused and is no longer available.
222 =item * Band forests have been replaced by schedule trees.
224 =item * The function C<isl_union_map_compute_flow> has been
225 replaced by the function C<isl_union_access_info_compute_flow>.
226 Note that the may dependence relation returned by
227 C<isl_union_flow_get_may_dependence> is the union of
228 the two dependence relations returned by
229 C<isl_union_map_compute_flow>. Similarly for the no source relations.
230 The function C<isl_union_map_compute_flow> is still available
231 for backward compatibility, but it will be removed in the future.
233 =item * The function C<isl_basic_set_drop_constraint> has been
236 =item * The function C<isl_ast_build_ast_from_schedule> has been
237 renamed to C<isl_ast_build_node_from_schedule_map>.
238 The original name is still available
239 for backward compatibility, but it will be removed in the future.
241 =item * The C<separation_class> AST generation option has been
244 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
245 have been renamed to C<isl_constraint_alloc_equality> and
246 C<isl_constraint_alloc_inequality>. The original names have been
247 kept for backward compatibility, but they will be removed in the future.
249 =item * The C<schedule_fuse> option has been replaced
250 by the C<schedule_serialize_sccs> option. The effect
251 of setting the C<schedule_fuse> option to C<ISL_SCHEDULE_FUSE_MIN>
252 is now obtained by turning on the C<schedule_serialize_sccs> option.
256 =head3 Changes since isl-0.17
260 =item * The function C<isl_printer_print_ast_expr> no longer prints
261 in C format by default. To print in C format, the output format
262 of the printer needs to have been explicitly set to C<ISL_FORMAT_C>.
263 As a result, the function C<isl_ast_expr_to_str> no longer prints
264 the expression in C format. Use C<isl_ast_expr_to_C_str> instead.
266 =item * The functions C<isl_set_align_divs> and C<isl_map_align_divs>
267 have been deprecated. The function C<isl_set_lift> has an effect
268 that is similar to C<isl_set_align_divs> and could in some cases
269 be used as an alternative.
275 C<isl> is released under the MIT license.
279 Permission is hereby granted, free of charge, to any person obtaining a copy of
280 this software and associated documentation files (the "Software"), to deal in
281 the Software without restriction, including without limitation the rights to
282 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
283 of the Software, and to permit persons to whom the Software is furnished to do
284 so, subject to the following conditions:
286 The above copyright notice and this permission notice shall be included in all
287 copies or substantial portions of the Software.
289 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
290 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
291 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
292 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
293 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
294 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
299 Note that by default C<isl> requires C<GMP>, which is released
300 under the GNU Lesser General Public License (LGPL). This means
301 that code linked against C<isl> is also linked against LGPL code.
303 When configuring with C<--with-int=imath> or C<--with-int=imath-32>, C<isl>
304 will link against C<imath>, a library for exact integer arithmetic released
305 under the MIT license.
309 The source of C<isl> can be obtained either as a tarball
310 or from the git repository. Both are available from
311 L<http://isl.gforge.inria.fr/>.
312 The installation process depends on how you obtained
315 =head2 Installation from the git repository
319 =item 1 Clone or update the repository
321 The first time the source is obtained, you need to clone
324 git clone git://repo.or.cz/isl.git
326 To obtain updates, you need to pull in the latest changes
330 =item 2 Optionally get C<imath> submodule
332 To build C<isl> with C<imath>, you need to obtain the C<imath>
333 submodule by running in the git source tree of C<isl>
338 This will fetch the required version of C<imath> in a subdirectory of C<isl>.
340 =item 2 Generate C<configure>
346 After performing the above steps, continue
347 with the L<Common installation instructions>.
349 =head2 Common installation instructions
353 =item 1 Obtain C<GMP>
355 By default, building C<isl> requires C<GMP>, including its headers files.
356 Your distribution may not provide these header files by default
357 and you may need to install a package called C<gmp-devel> or something
358 similar. Alternatively, C<GMP> can be built from
359 source, available from L<http://gmplib.org/>.
360 C<GMP> is not needed if you build C<isl> with C<imath>.
364 C<isl> uses the standard C<autoconf> C<configure> script.
369 optionally followed by some configure options.
370 A complete list of options can be obtained by running
374 Below we discuss some of the more common options.
380 Installation prefix for C<isl>
382 =item C<--with-int=[gmp|imath|imath-32]>
384 Select the integer library to be used by C<isl>, the default is C<gmp>.
385 With C<imath-32>, C<isl> will use 32 bit integers, but fall back to C<imath>
386 for values out of the 32 bit range. In most applications, C<isl> will run
387 fastest with the C<imath-32> option, followed by C<gmp> and C<imath>, the
390 =item C<--with-gmp-prefix>
392 Installation prefix for C<GMP> (architecture-independent files).
394 =item C<--with-gmp-exec-prefix>
396 Installation prefix for C<GMP> (architecture-dependent files).
404 =item 4 Install (optional)
410 =head1 Integer Set Library
412 =head2 Memory Management
414 Since a high-level operation on isl objects usually involves
415 several substeps and since the user is usually not interested in
416 the intermediate results, most functions that return a new object
417 will also release all the objects passed as arguments.
418 If the user still wants to use one or more of these arguments
419 after the function call, she should pass along a copy of the
420 object rather than the object itself.
421 The user is then responsible for making sure that the original
422 object gets used somewhere else or is explicitly freed.
424 The arguments and return values of all documented functions are
425 annotated to make clear which arguments are released and which
426 arguments are preserved. In particular, the following annotations
433 C<__isl_give> means that a new object is returned.
434 The user should make sure that the returned pointer is
435 used exactly once as a value for an C<__isl_take> argument.
436 In between, it can be used as a value for as many
437 C<__isl_keep> arguments as the user likes.
438 There is one exception, and that is the case where the
439 pointer returned is C<NULL>. Is this case, the user
440 is free to use it as an C<__isl_take> argument or not.
441 When applied to a C<char *>, the returned pointer needs to be
446 C<__isl_null> means that a C<NULL> value is returned.
450 C<__isl_take> means that the object the argument points to
451 is taken over by the function and may no longer be used
452 by the user as an argument to any other function.
453 The pointer value must be one returned by a function
454 returning an C<__isl_give> pointer.
455 If the user passes in a C<NULL> value, then this will
456 be treated as an error in the sense that the function will
457 not perform its usual operation. However, it will still
458 make sure that all the other C<__isl_take> arguments
463 C<__isl_keep> means that the function will only use the object
464 temporarily. After the function has finished, the user
465 can still use it as an argument to other functions.
466 A C<NULL> value will be treated in the same way as
467 a C<NULL> value for an C<__isl_take> argument.
468 This annotation may also be used on return values of
469 type C<const char *>, in which case the returned pointer should
470 not be freed by the user and is only valid until the object
471 from which it was derived is updated or freed.
475 =head2 Initialization
477 All manipulations of integer sets and relations occur within
478 the context of an C<isl_ctx>.
479 A given C<isl_ctx> can only be used within a single thread.
480 All arguments of a function are required to have been allocated
481 within the same context.
482 There are currently no functions available for moving an object
483 from one C<isl_ctx> to another C<isl_ctx>. This means that
484 there is currently no way of safely moving an object from one
485 thread to another, unless the whole C<isl_ctx> is moved.
487 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
488 freed using C<isl_ctx_free>.
489 All objects allocated within an C<isl_ctx> should be freed
490 before the C<isl_ctx> itself is freed.
492 isl_ctx *isl_ctx_alloc();
493 void isl_ctx_free(isl_ctx *ctx);
495 The user can impose a bound on the number of low-level I<operations>
496 that can be performed by an C<isl_ctx>. This bound can be set and
497 retrieved using the following functions. A bound of zero means that
498 no bound is imposed. The number of operations performed can be
499 reset using C<isl_ctx_reset_operations>. Note that the number
500 of low-level operations needed to perform a high-level computation
501 may differ significantly across different versions
502 of C<isl>, but it should be the same across different platforms
503 for the same version of C<isl>.
505 Warning: This feature is experimental. C<isl> has good support to abort and
506 bail out during the computation, but this feature may exercise error code paths
507 that are normally not used that much. Consequently, it is not unlikely that
508 hidden bugs will be exposed.
510 void isl_ctx_set_max_operations(isl_ctx *ctx,
511 unsigned long max_operations);
512 unsigned long isl_ctx_get_max_operations(isl_ctx *ctx);
513 void isl_ctx_reset_operations(isl_ctx *ctx);
515 In order to be able to create an object in the same context
516 as another object, most object types (described later in
517 this document) provide a function to obtain the context
518 in which the object was created.
521 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
522 isl_ctx *isl_multi_val_get_ctx(
523 __isl_keep isl_multi_val *mv);
526 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
528 #include <isl/local_space.h>
529 isl_ctx *isl_local_space_get_ctx(
530 __isl_keep isl_local_space *ls);
533 isl_ctx *isl_set_list_get_ctx(
534 __isl_keep isl_set_list *list);
537 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
538 isl_ctx *isl_multi_aff_get_ctx(
539 __isl_keep isl_multi_aff *maff);
540 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pa);
541 isl_ctx *isl_pw_multi_aff_get_ctx(
542 __isl_keep isl_pw_multi_aff *pma);
543 isl_ctx *isl_multi_pw_aff_get_ctx(
544 __isl_keep isl_multi_pw_aff *mpa);
545 isl_ctx *isl_union_pw_aff_get_ctx(
546 __isl_keep isl_union_pw_aff *upa);
547 isl_ctx *isl_union_pw_multi_aff_get_ctx(
548 __isl_keep isl_union_pw_multi_aff *upma);
549 isl_ctx *isl_multi_union_pw_aff_get_ctx(
550 __isl_keep isl_multi_union_pw_aff *mupa);
552 #include <isl/id_to_ast_expr.h>
553 isl_ctx *isl_id_to_ast_expr_get_ctx(
554 __isl_keep isl_id_to_ast_expr *id2expr);
556 #include <isl/point.h>
557 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
560 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
563 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
565 #include <isl/vertices.h>
566 isl_ctx *isl_vertices_get_ctx(
567 __isl_keep isl_vertices *vertices);
568 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
569 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
571 #include <isl/flow.h>
572 isl_ctx *isl_restriction_get_ctx(
573 __isl_keep isl_restriction *restr);
574 isl_ctx *isl_union_access_info_get_ctx(
575 __isl_keep isl_union_access_info *access);
576 isl_ctx *isl_union_flow_get_ctx(
577 __isl_keep isl_union_flow *flow);
579 #include <isl/schedule.h>
580 isl_ctx *isl_schedule_get_ctx(
581 __isl_keep isl_schedule *sched);
582 isl_ctx *isl_schedule_constraints_get_ctx(
583 __isl_keep isl_schedule_constraints *sc);
585 #include <isl/schedule_node.h>
586 isl_ctx *isl_schedule_node_get_ctx(
587 __isl_keep isl_schedule_node *node);
589 #include <isl/band.h>
590 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
592 #include <isl/ast_build.h>
593 isl_ctx *isl_ast_build_get_ctx(
594 __isl_keep isl_ast_build *build);
597 isl_ctx *isl_ast_expr_get_ctx(
598 __isl_keep isl_ast_expr *expr);
599 isl_ctx *isl_ast_node_get_ctx(
600 __isl_keep isl_ast_node *node);
604 C<isl> uses two special return types for functions that either return
605 a boolean or that in principle do not return anything.
606 In particular, the C<isl_bool> type has three possible values:
607 C<isl_bool_true> (a positive integer value), indicating I<true> or I<yes>;
608 C<isl_bool_false> (the integer value zero), indicating I<false> or I<no>; and
609 C<isl_bool_error> (a negative integer value), indicating that something
610 went wrong. The following function can be used to negate an C<isl_bool>,
611 where the negation of C<isl_bool_error> is C<isl_bool_error> again.
614 isl_bool isl_bool_not(isl_bool b);
616 The C<isl_stat> type has two possible values:
617 C<isl_stat_ok> (the integer value zero), indicating a successful
619 C<isl_stat_error> (a negative integer value), indicating that something
621 See L</"Error Handling"> for more information on
622 C<isl_bool_error> and C<isl_stat_error>.
626 An C<isl_val> represents an integer value, a rational value
627 or one of three special values, infinity, negative infinity and NaN.
628 Some predefined values can be created using the following functions.
631 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
632 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
633 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
634 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
635 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
636 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
638 Specific integer values can be created using the following functions.
641 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
643 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
645 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
646 size_t n, size_t size, const void *chunks);
648 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
649 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
650 The least significant digit is assumed to be stored first.
652 Value objects can be copied and freed using the following functions.
655 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
656 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
658 They can be inspected using the following functions.
661 long isl_val_get_num_si(__isl_keep isl_val *v);
662 long isl_val_get_den_si(__isl_keep isl_val *v);
663 __isl_give isl_val *isl_val_get_den_val(
664 __isl_keep isl_val *v);
665 double isl_val_get_d(__isl_keep isl_val *v);
666 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
668 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
669 size_t size, void *chunks);
671 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
672 of C<size> bytes needed to store the absolute value of the
674 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
675 which is assumed to have been preallocated by the caller.
676 The least significant digit is stored first.
677 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
678 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
679 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
681 An C<isl_val> can be modified using the following function.
684 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
687 The following unary properties are defined on C<isl_val>s.
690 int isl_val_sgn(__isl_keep isl_val *v);
691 isl_bool isl_val_is_zero(__isl_keep isl_val *v);
692 isl_bool isl_val_is_one(__isl_keep isl_val *v);
693 isl_bool isl_val_is_negone(__isl_keep isl_val *v);
694 isl_bool isl_val_is_nonneg(__isl_keep isl_val *v);
695 isl_bool isl_val_is_nonpos(__isl_keep isl_val *v);
696 isl_bool isl_val_is_pos(__isl_keep isl_val *v);
697 isl_bool isl_val_is_neg(__isl_keep isl_val *v);
698 isl_bool isl_val_is_int(__isl_keep isl_val *v);
699 isl_bool isl_val_is_rat(__isl_keep isl_val *v);
700 isl_bool isl_val_is_nan(__isl_keep isl_val *v);
701 isl_bool isl_val_is_infty(__isl_keep isl_val *v);
702 isl_bool isl_val_is_neginfty(__isl_keep isl_val *v);
704 Note that the sign of NaN is undefined.
706 The following binary properties are defined on pairs of C<isl_val>s.
709 isl_bool isl_val_lt(__isl_keep isl_val *v1,
710 __isl_keep isl_val *v2);
711 isl_bool isl_val_le(__isl_keep isl_val *v1,
712 __isl_keep isl_val *v2);
713 isl_bool isl_val_gt(__isl_keep isl_val *v1,
714 __isl_keep isl_val *v2);
715 isl_bool isl_val_ge(__isl_keep isl_val *v1,
716 __isl_keep isl_val *v2);
717 isl_bool isl_val_eq(__isl_keep isl_val *v1,
718 __isl_keep isl_val *v2);
719 isl_bool isl_val_ne(__isl_keep isl_val *v1,
720 __isl_keep isl_val *v2);
721 isl_bool isl_val_abs_eq(__isl_keep isl_val *v1,
722 __isl_keep isl_val *v2);
724 The function C<isl_val_abs_eq> checks whether its two arguments
725 are equal in absolute value.
727 For integer C<isl_val>s we additionally have the following binary property.
730 isl_bool isl_val_is_divisible_by(__isl_keep isl_val *v1,
731 __isl_keep isl_val *v2);
733 An C<isl_val> can also be compared to an integer using the following
734 function. The result is undefined for NaN.
737 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
739 The following unary operations are available on C<isl_val>s.
742 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
743 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
744 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
745 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
746 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
747 __isl_give isl_val *isl_val_inv(__isl_take isl_val *v);
748 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
750 The following binary operations are available on C<isl_val>s.
753 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
754 __isl_take isl_val *v2);
755 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
756 __isl_take isl_val *v2);
757 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
758 __isl_take isl_val *v2);
759 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
761 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
762 __isl_take isl_val *v2);
763 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
765 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
766 __isl_take isl_val *v2);
767 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
769 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
770 __isl_take isl_val *v2);
772 On integer values, we additionally have the following operations.
775 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
776 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
777 __isl_take isl_val *v2);
778 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
779 __isl_take isl_val *v2);
780 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
781 __isl_take isl_val *v2, __isl_give isl_val **x,
782 __isl_give isl_val **y);
784 The function C<isl_val_gcdext> returns the greatest common divisor g
785 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
786 that C<*x> * C<v1> + C<*y> * C<v2> = g.
788 =head3 GMP specific functions
790 These functions are only available if C<isl> has been compiled with C<GMP>
793 Specific integer and rational values can be created from C<GMP> values using
794 the following functions.
796 #include <isl/val_gmp.h>
797 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
799 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
800 const mpz_t n, const mpz_t d);
802 The numerator and denominator of a rational value can be extracted as
803 C<GMP> values using the following functions.
805 #include <isl/val_gmp.h>
806 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
807 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
809 =head2 Sets and Relations
811 C<isl> uses six types of objects for representing sets and relations,
812 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
813 C<isl_union_set> and C<isl_union_map>.
814 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
815 can be described as a conjunction of affine constraints, while
816 C<isl_set> and C<isl_map> represent unions of
817 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
818 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
819 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
820 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
821 where spaces are considered different if they have a different number
822 of dimensions and/or different names (see L<"Spaces">).
823 The difference between sets and relations (maps) is that sets have
824 one set of variables, while relations have two sets of variables,
825 input variables and output variables.
827 =head2 Error Handling
829 C<isl> supports different ways to react in case a runtime error is triggered.
830 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
831 with two maps that have incompatible spaces. There are three possible ways
832 to react on error: to warn, to continue or to abort.
834 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
835 the last error in the corresponding C<isl_ctx> and the function in which the
836 error was triggered returns a value indicating that some error has
837 occurred. In case of functions returning a pointer, this value is
838 C<NULL>. In case of functions returning an C<isl_bool> or an
839 C<isl_stat>, this valus is C<isl_bool_error> or C<isl_stat_error>.
840 An error does not corrupt internal state,
841 such that isl can continue to be used. C<isl> also provides functions to
842 read the last error and to reset the memory that stores the last error. The
843 last error is only stored for information purposes. Its presence does not
844 change the behavior of C<isl>. Hence, resetting an error is not required to
845 continue to use isl, but only to observe new errors.
848 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
849 void isl_ctx_reset_error(isl_ctx *ctx);
851 Another option is to continue on error. This is similar to warn on error mode,
852 except that C<isl> does not print any warning. This allows a program to
853 implement its own error reporting.
855 The last option is to directly abort the execution of the program from within
856 the isl library. This makes it obviously impossible to recover from an error,
857 but it allows to directly spot the error location. By aborting on error,
858 debuggers break at the location the error occurred and can provide a stack
859 trace. Other tools that automatically provide stack traces on abort or that do
860 not want to continue execution after an error was triggered may also prefer to
863 The on error behavior of isl can be specified by calling
864 C<isl_options_set_on_error> or by setting the command line option
865 C<--isl-on-error>. Valid arguments for the function call are
866 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
867 choices for the command line option are C<warn>, C<continue> and C<abort>.
868 It is also possible to query the current error mode.
870 #include <isl/options.h>
871 isl_stat isl_options_set_on_error(isl_ctx *ctx, int val);
872 int isl_options_get_on_error(isl_ctx *ctx);
876 Identifiers are used to identify both individual dimensions
877 and tuples of dimensions. They consist of an optional name and an optional
878 user pointer. The name and the user pointer cannot both be C<NULL>, however.
879 Identifiers with the same name but different pointer values
880 are considered to be distinct.
881 Similarly, identifiers with different names but the same pointer value
882 are also considered to be distinct.
883 Equal identifiers are represented using the same object.
884 Pairs of identifiers can therefore be tested for equality using the
886 Identifiers can be constructed, copied, freed, inspected and printed
887 using the following functions.
890 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
891 __isl_keep const char *name, void *user);
892 __isl_give isl_id *isl_id_set_free_user(
893 __isl_take isl_id *id,
894 void (*free_user)(void *user));
895 __isl_give isl_id *isl_id_copy(isl_id *id);
896 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
898 void *isl_id_get_user(__isl_keep isl_id *id);
899 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
901 __isl_give isl_printer *isl_printer_print_id(
902 __isl_take isl_printer *p, __isl_keep isl_id *id);
904 The callback set by C<isl_id_set_free_user> is called on the user
905 pointer when the last reference to the C<isl_id> is freed.
906 Note that C<isl_id_get_name> returns a pointer to some internal
907 data structure, so the result can only be used while the
908 corresponding C<isl_id> is alive.
912 Whenever a new set, relation or similar object is created from scratch,
913 the space in which it lives needs to be specified using an C<isl_space>.
914 Each space involves zero or more parameters and zero, one or two
915 tuples of set or input/output dimensions. The parameters and dimensions
916 are identified by an C<isl_dim_type> and a position.
917 The type C<isl_dim_param> refers to parameters,
918 the type C<isl_dim_set> refers to set dimensions (for spaces
919 with a single tuple of dimensions) and the types C<isl_dim_in>
920 and C<isl_dim_out> refer to input and output dimensions
921 (for spaces with two tuples of dimensions).
922 Local spaces (see L</"Local Spaces">) also contain dimensions
923 of type C<isl_dim_div>.
924 Note that parameters are only identified by their position within
925 a given object. Across different objects, parameters are (usually)
926 identified by their names or identifiers. Only unnamed parameters
927 are identified by their positions across objects. The use of unnamed
928 parameters is discouraged.
930 #include <isl/space.h>
931 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
932 unsigned nparam, unsigned n_in, unsigned n_out);
933 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
935 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
936 unsigned nparam, unsigned dim);
937 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
938 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
940 The space used for creating a parameter domain
941 needs to be created using C<isl_space_params_alloc>.
942 For other sets, the space
943 needs to be created using C<isl_space_set_alloc>, while
944 for a relation, the space
945 needs to be created using C<isl_space_alloc>.
947 To check whether a given space is that of a set or a map
948 or whether it is a parameter space, use these functions:
950 #include <isl/space.h>
951 isl_bool isl_space_is_params(__isl_keep isl_space *space);
952 isl_bool isl_space_is_set(__isl_keep isl_space *space);
953 isl_bool isl_space_is_map(__isl_keep isl_space *space);
955 Spaces can be compared using the following functions:
957 #include <isl/space.h>
958 isl_bool isl_space_is_equal(__isl_keep isl_space *space1,
959 __isl_keep isl_space *space2);
960 isl_bool isl_space_has_equal_tuples(
961 __isl_keep isl_space *space1,
962 __isl_keep isl_space *space2);
963 isl_bool isl_space_is_domain(__isl_keep isl_space *space1,
964 __isl_keep isl_space *space2);
965 isl_bool isl_space_is_range(__isl_keep isl_space *space1,
966 __isl_keep isl_space *space2);
967 isl_bool isl_space_tuple_is_equal(
968 __isl_keep isl_space *space1,
969 enum isl_dim_type type1,
970 __isl_keep isl_space *space2,
971 enum isl_dim_type type2);
973 C<isl_space_is_domain> checks whether the first argument is equal
974 to the domain of the second argument. This requires in particular that
975 the first argument is a set space and that the second argument
976 is a map space. C<isl_space_tuple_is_equal> checks whether the given
977 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
978 spaces are the same. That is, it checks if they have the same
979 identifier (if any), the same dimension and the same internal structure
981 C<isl_space_is_equal> checks whether two spaces are identical.
982 In particular, it checks whether they have the same type
983 (parameter, set or map space), the same tuples
984 (if they are not parameter spaces) in the sense
985 of C<isl_space_tuple_is_equal> and the same parameters
987 C<isl_space_has_equal_tuples> check whether two spaces have
988 the same tuples. In contrast to C<isl_space_is_equal>, it does not check the
989 parameters. This is useful because many C<isl> functions align the
990 parameters before they perform their operations, such that equivalence
993 It is often useful to create objects that live in the
994 same space as some other object. This can be accomplished
995 by creating the new objects
996 (see L</"Creating New Sets and Relations"> or
997 L</"Functions">) based on the space
998 of the original object.
1000 #include <isl/set.h>
1001 __isl_give isl_space *isl_basic_set_get_space(
1002 __isl_keep isl_basic_set *bset);
1003 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
1005 #include <isl/union_set.h>
1006 __isl_give isl_space *isl_union_set_get_space(
1007 __isl_keep isl_union_set *uset);
1009 #include <isl/map.h>
1010 __isl_give isl_space *isl_basic_map_get_space(
1011 __isl_keep isl_basic_map *bmap);
1012 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
1014 #include <isl/union_map.h>
1015 __isl_give isl_space *isl_union_map_get_space(
1016 __isl_keep isl_union_map *umap);
1018 #include <isl/constraint.h>
1019 __isl_give isl_space *isl_constraint_get_space(
1020 __isl_keep isl_constraint *constraint);
1022 #include <isl/polynomial.h>
1023 __isl_give isl_space *isl_qpolynomial_get_domain_space(
1024 __isl_keep isl_qpolynomial *qp);
1025 __isl_give isl_space *isl_qpolynomial_get_space(
1026 __isl_keep isl_qpolynomial *qp);
1027 __isl_give isl_space *
1028 isl_qpolynomial_fold_get_domain_space(
1029 __isl_keep isl_qpolynomial_fold *fold);
1030 __isl_give isl_space *isl_qpolynomial_fold_get_space(
1031 __isl_keep isl_qpolynomial_fold *fold);
1032 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
1033 __isl_keep isl_pw_qpolynomial *pwqp);
1034 __isl_give isl_space *isl_pw_qpolynomial_get_space(
1035 __isl_keep isl_pw_qpolynomial *pwqp);
1036 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
1037 __isl_keep isl_pw_qpolynomial_fold *pwf);
1038 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
1039 __isl_keep isl_pw_qpolynomial_fold *pwf);
1040 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
1041 __isl_keep isl_union_pw_qpolynomial *upwqp);
1042 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
1043 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1045 #include <isl/val.h>
1046 __isl_give isl_space *isl_multi_val_get_space(
1047 __isl_keep isl_multi_val *mv);
1049 #include <isl/aff.h>
1050 __isl_give isl_space *isl_aff_get_domain_space(
1051 __isl_keep isl_aff *aff);
1052 __isl_give isl_space *isl_aff_get_space(
1053 __isl_keep isl_aff *aff);
1054 __isl_give isl_space *isl_pw_aff_get_domain_space(
1055 __isl_keep isl_pw_aff *pwaff);
1056 __isl_give isl_space *isl_pw_aff_get_space(
1057 __isl_keep isl_pw_aff *pwaff);
1058 __isl_give isl_space *isl_multi_aff_get_domain_space(
1059 __isl_keep isl_multi_aff *maff);
1060 __isl_give isl_space *isl_multi_aff_get_space(
1061 __isl_keep isl_multi_aff *maff);
1062 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
1063 __isl_keep isl_pw_multi_aff *pma);
1064 __isl_give isl_space *isl_pw_multi_aff_get_space(
1065 __isl_keep isl_pw_multi_aff *pma);
1066 __isl_give isl_space *isl_union_pw_aff_get_space(
1067 __isl_keep isl_union_pw_aff *upa);
1068 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
1069 __isl_keep isl_union_pw_multi_aff *upma);
1070 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
1071 __isl_keep isl_multi_pw_aff *mpa);
1072 __isl_give isl_space *isl_multi_pw_aff_get_space(
1073 __isl_keep isl_multi_pw_aff *mpa);
1074 __isl_give isl_space *
1075 isl_multi_union_pw_aff_get_domain_space(
1076 __isl_keep isl_multi_union_pw_aff *mupa);
1077 __isl_give isl_space *
1078 isl_multi_union_pw_aff_get_space(
1079 __isl_keep isl_multi_union_pw_aff *mupa);
1081 #include <isl/point.h>
1082 __isl_give isl_space *isl_point_get_space(
1083 __isl_keep isl_point *pnt);
1085 The number of dimensions of a given type of space
1086 may be read off from a space or an object that lives
1087 in a space using the following functions.
1088 In case of C<isl_space_dim>, type may be
1089 C<isl_dim_param>, C<isl_dim_in> (only for relations),
1090 C<isl_dim_out> (only for relations), C<isl_dim_set>
1091 (only for sets) or C<isl_dim_all>.
1093 #include <isl/space.h>
1094 unsigned isl_space_dim(__isl_keep isl_space *space,
1095 enum isl_dim_type type);
1097 #include <isl/local_space.h>
1098 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1099 enum isl_dim_type type);
1101 #include <isl/set.h>
1102 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1103 enum isl_dim_type type);
1104 unsigned isl_set_dim(__isl_keep isl_set *set,
1105 enum isl_dim_type type);
1107 #include <isl/union_set.h>
1108 unsigned isl_union_set_dim(__isl_keep isl_union_set *uset,
1109 enum isl_dim_type type);
1111 #include <isl/map.h>
1112 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1113 enum isl_dim_type type);
1114 unsigned isl_map_dim(__isl_keep isl_map *map,
1115 enum isl_dim_type type);
1117 #include <isl/union_map.h>
1118 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1119 enum isl_dim_type type);
1121 #include <isl/val.h>
1122 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
1123 enum isl_dim_type type);
1125 #include <isl/aff.h>
1126 int isl_aff_dim(__isl_keep isl_aff *aff,
1127 enum isl_dim_type type);
1128 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1129 enum isl_dim_type type);
1130 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1131 enum isl_dim_type type);
1132 unsigned isl_pw_multi_aff_dim(
1133 __isl_keep isl_pw_multi_aff *pma,
1134 enum isl_dim_type type);
1135 unsigned isl_multi_pw_aff_dim(
1136 __isl_keep isl_multi_pw_aff *mpa,
1137 enum isl_dim_type type);
1138 unsigned isl_union_pw_aff_dim(
1139 __isl_keep isl_union_pw_aff *upa,
1140 enum isl_dim_type type);
1141 unsigned isl_union_pw_multi_aff_dim(
1142 __isl_keep isl_union_pw_multi_aff *upma,
1143 enum isl_dim_type type);
1144 unsigned isl_multi_union_pw_aff_dim(
1145 __isl_keep isl_multi_union_pw_aff *mupa,
1146 enum isl_dim_type type);
1148 #include <isl/polynomial.h>
1149 unsigned isl_union_pw_qpolynomial_dim(
1150 __isl_keep isl_union_pw_qpolynomial *upwqp,
1151 enum isl_dim_type type);
1152 unsigned isl_union_pw_qpolynomial_fold_dim(
1153 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1154 enum isl_dim_type type);
1156 Note that an C<isl_union_set>, an C<isl_union_map>,
1157 an C<isl_union_pw_multi_aff>,
1158 an C<isl_union_pw_qpolynomial> and
1159 an C<isl_union_pw_qpolynomial_fold>
1160 only have parameters.
1162 The identifiers or names of the individual dimensions of spaces
1163 may be set or read off using the following functions on spaces
1164 or objects that live in spaces.
1165 These functions are mostly useful to obtain the identifiers, positions
1166 or names of the parameters. Identifiers of individual dimensions are
1167 essentially only useful for printing. They are ignored by all other
1168 operations and may not be preserved across those operations.
1170 #include <isl/space.h>
1171 __isl_give isl_space *isl_space_set_dim_id(
1172 __isl_take isl_space *space,
1173 enum isl_dim_type type, unsigned pos,
1174 __isl_take isl_id *id);
1175 isl_bool isl_space_has_dim_id(__isl_keep isl_space *space,
1176 enum isl_dim_type type, unsigned pos);
1177 __isl_give isl_id *isl_space_get_dim_id(
1178 __isl_keep isl_space *space,
1179 enum isl_dim_type type, unsigned pos);
1180 __isl_give isl_space *isl_space_set_dim_name(
1181 __isl_take isl_space *space,
1182 enum isl_dim_type type, unsigned pos,
1183 __isl_keep const char *name);
1184 isl_bool isl_space_has_dim_name(__isl_keep isl_space *space,
1185 enum isl_dim_type type, unsigned pos);
1186 __isl_keep const char *isl_space_get_dim_name(
1187 __isl_keep isl_space *space,
1188 enum isl_dim_type type, unsigned pos);
1190 #include <isl/local_space.h>
1191 __isl_give isl_local_space *isl_local_space_set_dim_id(
1192 __isl_take isl_local_space *ls,
1193 enum isl_dim_type type, unsigned pos,
1194 __isl_take isl_id *id);
1195 isl_bool isl_local_space_has_dim_id(
1196 __isl_keep isl_local_space *ls,
1197 enum isl_dim_type type, unsigned pos);
1198 __isl_give isl_id *isl_local_space_get_dim_id(
1199 __isl_keep isl_local_space *ls,
1200 enum isl_dim_type type, unsigned pos);
1201 __isl_give isl_local_space *isl_local_space_set_dim_name(
1202 __isl_take isl_local_space *ls,
1203 enum isl_dim_type type, unsigned pos, const char *s);
1204 isl_bool isl_local_space_has_dim_name(
1205 __isl_keep isl_local_space *ls,
1206 enum isl_dim_type type, unsigned pos)
1207 const char *isl_local_space_get_dim_name(
1208 __isl_keep isl_local_space *ls,
1209 enum isl_dim_type type, unsigned pos);
1211 #include <isl/constraint.h>
1212 const char *isl_constraint_get_dim_name(
1213 __isl_keep isl_constraint *constraint,
1214 enum isl_dim_type type, unsigned pos);
1216 #include <isl/set.h>
1217 __isl_give isl_id *isl_basic_set_get_dim_id(
1218 __isl_keep isl_basic_set *bset,
1219 enum isl_dim_type type, unsigned pos);
1220 __isl_give isl_set *isl_set_set_dim_id(
1221 __isl_take isl_set *set, enum isl_dim_type type,
1222 unsigned pos, __isl_take isl_id *id);
1223 isl_bool isl_set_has_dim_id(__isl_keep isl_set *set,
1224 enum isl_dim_type type, unsigned pos);
1225 __isl_give isl_id *isl_set_get_dim_id(
1226 __isl_keep isl_set *set, enum isl_dim_type type,
1228 const char *isl_basic_set_get_dim_name(
1229 __isl_keep isl_basic_set *bset,
1230 enum isl_dim_type type, unsigned pos);
1231 isl_bool isl_set_has_dim_name(__isl_keep isl_set *set,
1232 enum isl_dim_type type, unsigned pos);
1233 const char *isl_set_get_dim_name(
1234 __isl_keep isl_set *set,
1235 enum isl_dim_type type, unsigned pos);
1237 #include <isl/map.h>
1238 __isl_give isl_map *isl_map_set_dim_id(
1239 __isl_take isl_map *map, enum isl_dim_type type,
1240 unsigned pos, __isl_take isl_id *id);
1241 isl_bool isl_basic_map_has_dim_id(
1242 __isl_keep isl_basic_map *bmap,
1243 enum isl_dim_type type, unsigned pos);
1244 isl_bool isl_map_has_dim_id(__isl_keep isl_map *map,
1245 enum isl_dim_type type, unsigned pos);
1246 __isl_give isl_id *isl_map_get_dim_id(
1247 __isl_keep isl_map *map, enum isl_dim_type type,
1249 __isl_give isl_id *isl_union_map_get_dim_id(
1250 __isl_keep isl_union_map *umap,
1251 enum isl_dim_type type, unsigned pos);
1252 const char *isl_basic_map_get_dim_name(
1253 __isl_keep isl_basic_map *bmap,
1254 enum isl_dim_type type, unsigned pos);
1255 isl_bool isl_map_has_dim_name(__isl_keep isl_map *map,
1256 enum isl_dim_type type, unsigned pos);
1257 const char *isl_map_get_dim_name(
1258 __isl_keep isl_map *map,
1259 enum isl_dim_type type, unsigned pos);
1261 #include <isl/val.h>
1262 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1263 __isl_take isl_multi_val *mv,
1264 enum isl_dim_type type, unsigned pos,
1265 __isl_take isl_id *id);
1266 __isl_give isl_id *isl_multi_val_get_dim_id(
1267 __isl_keep isl_multi_val *mv,
1268 enum isl_dim_type type, unsigned pos);
1269 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1270 __isl_take isl_multi_val *mv,
1271 enum isl_dim_type type, unsigned pos, const char *s);
1273 #include <isl/aff.h>
1274 __isl_give isl_aff *isl_aff_set_dim_id(
1275 __isl_take isl_aff *aff, enum isl_dim_type type,
1276 unsigned pos, __isl_take isl_id *id);
1277 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1278 __isl_take isl_multi_aff *maff,
1279 enum isl_dim_type type, unsigned pos,
1280 __isl_take isl_id *id);
1281 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1282 __isl_take isl_pw_aff *pma,
1283 enum isl_dim_type type, unsigned pos,
1284 __isl_take isl_id *id);
1285 __isl_give isl_multi_pw_aff *
1286 isl_multi_pw_aff_set_dim_id(
1287 __isl_take isl_multi_pw_aff *mpa,
1288 enum isl_dim_type type, unsigned pos,
1289 __isl_take isl_id *id);
1290 __isl_give isl_multi_union_pw_aff *
1291 isl_multi_union_pw_aff_set_dim_id(
1292 __isl_take isl_multi_union_pw_aff *mupa,
1293 enum isl_dim_type type, unsigned pos,
1294 __isl_take isl_id *id);
1295 __isl_give isl_id *isl_multi_aff_get_dim_id(
1296 __isl_keep isl_multi_aff *ma,
1297 enum isl_dim_type type, unsigned pos);
1298 isl_bool isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1299 enum isl_dim_type type, unsigned pos);
1300 __isl_give isl_id *isl_pw_aff_get_dim_id(
1301 __isl_keep isl_pw_aff *pa,
1302 enum isl_dim_type type, unsigned pos);
1303 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1304 __isl_keep isl_pw_multi_aff *pma,
1305 enum isl_dim_type type, unsigned pos);
1306 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1307 __isl_keep isl_multi_pw_aff *mpa,
1308 enum isl_dim_type type, unsigned pos);
1309 __isl_give isl_id *isl_multi_union_pw_aff_get_dim_id(
1310 __isl_keep isl_multi_union_pw_aff *mupa,
1311 enum isl_dim_type type, unsigned pos);
1312 __isl_give isl_aff *isl_aff_set_dim_name(
1313 __isl_take isl_aff *aff, enum isl_dim_type type,
1314 unsigned pos, const char *s);
1315 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1316 __isl_take isl_multi_aff *maff,
1317 enum isl_dim_type type, unsigned pos, const char *s);
1318 __isl_give isl_multi_pw_aff *
1319 isl_multi_pw_aff_set_dim_name(
1320 __isl_take isl_multi_pw_aff *mpa,
1321 enum isl_dim_type type, unsigned pos, const char *s);
1322 __isl_give isl_union_pw_aff *
1323 isl_union_pw_aff_set_dim_name(
1324 __isl_take isl_union_pw_aff *upa,
1325 enum isl_dim_type type, unsigned pos,
1327 __isl_give isl_union_pw_multi_aff *
1328 isl_union_pw_multi_aff_set_dim_name(
1329 __isl_take isl_union_pw_multi_aff *upma,
1330 enum isl_dim_type type, unsigned pos,
1332 __isl_give isl_multi_union_pw_aff *
1333 isl_multi_union_pw_aff_set_dim_name(
1334 __isl_take isl_multi_union_pw_aff *mupa,
1335 enum isl_dim_type type, unsigned pos,
1336 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1337 enum isl_dim_type type, unsigned pos);
1338 const char *isl_pw_aff_get_dim_name(
1339 __isl_keep isl_pw_aff *pa,
1340 enum isl_dim_type type, unsigned pos);
1341 const char *isl_pw_multi_aff_get_dim_name(
1342 __isl_keep isl_pw_multi_aff *pma,
1343 enum isl_dim_type type, unsigned pos);
1345 #include <isl/polynomial.h>
1346 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1347 __isl_take isl_qpolynomial *qp,
1348 enum isl_dim_type type, unsigned pos,
1350 __isl_give isl_pw_qpolynomial *
1351 isl_pw_qpolynomial_set_dim_name(
1352 __isl_take isl_pw_qpolynomial *pwqp,
1353 enum isl_dim_type type, unsigned pos,
1355 __isl_give isl_pw_qpolynomial_fold *
1356 isl_pw_qpolynomial_fold_set_dim_name(
1357 __isl_take isl_pw_qpolynomial_fold *pwf,
1358 enum isl_dim_type type, unsigned pos,
1360 __isl_give isl_union_pw_qpolynomial *
1361 isl_union_pw_qpolynomial_set_dim_name(
1362 __isl_take isl_union_pw_qpolynomial *upwqp,
1363 enum isl_dim_type type, unsigned pos,
1365 __isl_give isl_union_pw_qpolynomial_fold *
1366 isl_union_pw_qpolynomial_fold_set_dim_name(
1367 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1368 enum isl_dim_type type, unsigned pos,
1371 Note that C<isl_space_get_name> returns a pointer to some internal
1372 data structure, so the result can only be used while the
1373 corresponding C<isl_space> is alive.
1374 Also note that every function that operates on two sets or relations
1375 requires that both arguments have the same parameters. This also
1376 means that if one of the arguments has named parameters, then the
1377 other needs to have named parameters too and the names need to match.
1378 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1379 arguments may have different parameters (as long as they are named),
1380 in which case the result will have as parameters the union of the parameters of
1383 Given the identifier or name of a dimension (typically a parameter),
1384 its position can be obtained from the following functions.
1386 #include <isl/space.h>
1387 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1388 enum isl_dim_type type, __isl_keep isl_id *id);
1389 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1390 enum isl_dim_type type, const char *name);
1392 #include <isl/local_space.h>
1393 int isl_local_space_find_dim_by_name(
1394 __isl_keep isl_local_space *ls,
1395 enum isl_dim_type type, const char *name);
1397 #include <isl/val.h>
1398 int isl_multi_val_find_dim_by_id(
1399 __isl_keep isl_multi_val *mv,
1400 enum isl_dim_type type, __isl_keep isl_id *id);
1401 int isl_multi_val_find_dim_by_name(
1402 __isl_keep isl_multi_val *mv,
1403 enum isl_dim_type type, const char *name);
1405 #include <isl/set.h>
1406 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1407 enum isl_dim_type type, __isl_keep isl_id *id);
1408 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1409 enum isl_dim_type type, const char *name);
1411 #include <isl/map.h>
1412 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1413 enum isl_dim_type type, __isl_keep isl_id *id);
1414 int isl_basic_map_find_dim_by_name(
1415 __isl_keep isl_basic_map *bmap,
1416 enum isl_dim_type type, const char *name);
1417 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1418 enum isl_dim_type type, const char *name);
1419 int isl_union_map_find_dim_by_name(
1420 __isl_keep isl_union_map *umap,
1421 enum isl_dim_type type, const char *name);
1423 #include <isl/aff.h>
1424 int isl_multi_aff_find_dim_by_id(
1425 __isl_keep isl_multi_aff *ma,
1426 enum isl_dim_type type, __isl_keep isl_id *id);
1427 int isl_multi_pw_aff_find_dim_by_id(
1428 __isl_keep isl_multi_pw_aff *mpa,
1429 enum isl_dim_type type, __isl_keep isl_id *id);
1430 int isl_multi_union_pw_aff_find_dim_by_id(
1431 __isl_keep isl_union_multi_pw_aff *mupa,
1432 enum isl_dim_type type, __isl_keep isl_id *id);
1433 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff,
1434 enum isl_dim_type type, const char *name);
1435 int isl_multi_aff_find_dim_by_name(
1436 __isl_keep isl_multi_aff *ma,
1437 enum isl_dim_type type, const char *name);
1438 int isl_pw_aff_find_dim_by_name(__isl_keep isl_pw_aff *pa,
1439 enum isl_dim_type type, const char *name);
1440 int isl_multi_pw_aff_find_dim_by_name(
1441 __isl_keep isl_multi_pw_aff *mpa,
1442 enum isl_dim_type type, const char *name);
1443 int isl_pw_multi_aff_find_dim_by_name(
1444 __isl_keep isl_pw_multi_aff *pma,
1445 enum isl_dim_type type, const char *name);
1446 int isl_union_pw_aff_find_dim_by_name(
1447 __isl_keep isl_union_pw_aff *upa,
1448 enum isl_dim_type type, const char *name);
1449 int isl_union_pw_multi_aff_find_dim_by_name(
1450 __isl_keep isl_union_pw_multi_aff *upma,
1451 enum isl_dim_type type, const char *name);
1452 int isl_multi_union_pw_aff_find_dim_by_name(
1453 __isl_keep isl_multi_union_pw_aff *mupa,
1454 enum isl_dim_type type, const char *name);
1456 #include <isl/polynomial.h>
1457 int isl_pw_qpolynomial_find_dim_by_name(
1458 __isl_keep isl_pw_qpolynomial *pwqp,
1459 enum isl_dim_type type, const char *name);
1460 int isl_pw_qpolynomial_fold_find_dim_by_name(
1461 __isl_keep isl_pw_qpolynomial_fold *pwf,
1462 enum isl_dim_type type, const char *name);
1463 int isl_union_pw_qpolynomial_find_dim_by_name(
1464 __isl_keep isl_union_pw_qpolynomial *upwqp,
1465 enum isl_dim_type type, const char *name);
1466 int isl_union_pw_qpolynomial_fold_find_dim_by_name(
1467 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1468 enum isl_dim_type type, const char *name);
1470 The identifiers or names of entire spaces may be set or read off
1471 using the following functions.
1473 #include <isl/space.h>
1474 __isl_give isl_space *isl_space_set_tuple_id(
1475 __isl_take isl_space *space,
1476 enum isl_dim_type type, __isl_take isl_id *id);
1477 __isl_give isl_space *isl_space_reset_tuple_id(
1478 __isl_take isl_space *space, enum isl_dim_type type);
1479 isl_bool isl_space_has_tuple_id(
1480 __isl_keep isl_space *space,
1481 enum isl_dim_type type);
1482 __isl_give isl_id *isl_space_get_tuple_id(
1483 __isl_keep isl_space *space, enum isl_dim_type type);
1484 __isl_give isl_space *isl_space_set_tuple_name(
1485 __isl_take isl_space *space,
1486 enum isl_dim_type type, const char *s);
1487 isl_bool isl_space_has_tuple_name(
1488 __isl_keep isl_space *space,
1489 enum isl_dim_type type);
1490 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
1491 enum isl_dim_type type);
1493 #include <isl/local_space.h>
1494 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1495 __isl_take isl_local_space *ls,
1496 enum isl_dim_type type, __isl_take isl_id *id);
1498 #include <isl/set.h>
1499 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1500 __isl_take isl_basic_set *bset,
1501 __isl_take isl_id *id);
1502 __isl_give isl_set *isl_set_set_tuple_id(
1503 __isl_take isl_set *set, __isl_take isl_id *id);
1504 __isl_give isl_set *isl_set_reset_tuple_id(
1505 __isl_take isl_set *set);
1506 isl_bool isl_set_has_tuple_id(__isl_keep isl_set *set);
1507 __isl_give isl_id *isl_set_get_tuple_id(
1508 __isl_keep isl_set *set);
1509 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1510 __isl_take isl_basic_set *set, const char *s);
1511 __isl_give isl_set *isl_set_set_tuple_name(
1512 __isl_take isl_set *set, const char *s);
1513 const char *isl_basic_set_get_tuple_name(
1514 __isl_keep isl_basic_set *bset);
1515 isl_bool isl_set_has_tuple_name(__isl_keep isl_set *set);
1516 const char *isl_set_get_tuple_name(
1517 __isl_keep isl_set *set);
1519 #include <isl/map.h>
1520 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1521 __isl_take isl_basic_map *bmap,
1522 enum isl_dim_type type, __isl_take isl_id *id);
1523 __isl_give isl_map *isl_map_set_tuple_id(
1524 __isl_take isl_map *map, enum isl_dim_type type,
1525 __isl_take isl_id *id);
1526 __isl_give isl_map *isl_map_reset_tuple_id(
1527 __isl_take isl_map *map, enum isl_dim_type type);
1528 isl_bool isl_map_has_tuple_id(__isl_keep isl_map *map,
1529 enum isl_dim_type type);
1530 __isl_give isl_id *isl_map_get_tuple_id(
1531 __isl_keep isl_map *map, enum isl_dim_type type);
1532 __isl_give isl_map *isl_map_set_tuple_name(
1533 __isl_take isl_map *map,
1534 enum isl_dim_type type, const char *s);
1535 const char *isl_basic_map_get_tuple_name(
1536 __isl_keep isl_basic_map *bmap,
1537 enum isl_dim_type type);
1538 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1539 __isl_take isl_basic_map *bmap,
1540 enum isl_dim_type type, const char *s);
1541 isl_bool isl_map_has_tuple_name(__isl_keep isl_map *map,
1542 enum isl_dim_type type);
1543 const char *isl_map_get_tuple_name(
1544 __isl_keep isl_map *map,
1545 enum isl_dim_type type);
1547 #include <isl/val.h>
1548 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1549 __isl_take isl_multi_val *mv,
1550 enum isl_dim_type type, __isl_take isl_id *id);
1551 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1552 __isl_take isl_multi_val *mv,
1553 enum isl_dim_type type);
1554 isl_bool isl_multi_val_has_tuple_id(
1555 __isl_keep isl_multi_val *mv,
1556 enum isl_dim_type type);
1557 __isl_give isl_id *isl_multi_val_get_tuple_id(
1558 __isl_keep isl_multi_val *mv,
1559 enum isl_dim_type type);
1560 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1561 __isl_take isl_multi_val *mv,
1562 enum isl_dim_type type, const char *s);
1563 const char *isl_multi_val_get_tuple_name(
1564 __isl_keep isl_multi_val *mv,
1565 enum isl_dim_type type);
1567 #include <isl/aff.h>
1568 __isl_give isl_aff *isl_aff_set_tuple_id(
1569 __isl_take isl_aff *aff,
1570 enum isl_dim_type type, __isl_take isl_id *id);
1571 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1572 __isl_take isl_multi_aff *maff,
1573 enum isl_dim_type type, __isl_take isl_id *id);
1574 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1575 __isl_take isl_pw_aff *pwaff,
1576 enum isl_dim_type type, __isl_take isl_id *id);
1577 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1578 __isl_take isl_pw_multi_aff *pma,
1579 enum isl_dim_type type, __isl_take isl_id *id);
1580 __isl_give isl_multi_union_pw_aff *
1581 isl_multi_union_pw_aff_set_tuple_id(
1582 __isl_take isl_multi_union_pw_aff *mupa,
1583 enum isl_dim_type type, __isl_take isl_id *id);
1584 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1585 __isl_take isl_multi_aff *ma,
1586 enum isl_dim_type type);
1587 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1588 __isl_take isl_pw_aff *pa,
1589 enum isl_dim_type type);
1590 __isl_give isl_multi_pw_aff *
1591 isl_multi_pw_aff_reset_tuple_id(
1592 __isl_take isl_multi_pw_aff *mpa,
1593 enum isl_dim_type type);
1594 __isl_give isl_pw_multi_aff *
1595 isl_pw_multi_aff_reset_tuple_id(
1596 __isl_take isl_pw_multi_aff *pma,
1597 enum isl_dim_type type);
1598 __isl_give isl_multi_union_pw_aff *
1599 isl_multi_union_pw_aff_reset_tuple_id(
1600 __isl_take isl_multi_union_pw_aff *mupa,
1601 enum isl_dim_type type);
1602 isl_bool isl_multi_aff_has_tuple_id(
1603 __isl_keep isl_multi_aff *ma,
1604 enum isl_dim_type type);
1605 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1606 __isl_keep isl_multi_aff *ma,
1607 enum isl_dim_type type);
1608 isl_bool isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1609 enum isl_dim_type type);
1610 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1611 __isl_keep isl_pw_aff *pa,
1612 enum isl_dim_type type);
1613 isl_bool isl_pw_multi_aff_has_tuple_id(
1614 __isl_keep isl_pw_multi_aff *pma,
1615 enum isl_dim_type type);
1616 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1617 __isl_keep isl_pw_multi_aff *pma,
1618 enum isl_dim_type type);
1619 isl_bool isl_multi_pw_aff_has_tuple_id(
1620 __isl_keep isl_multi_pw_aff *mpa,
1621 enum isl_dim_type type);
1622 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1623 __isl_keep isl_multi_pw_aff *mpa,
1624 enum isl_dim_type type);
1625 isl_bool isl_multi_union_pw_aff_has_tuple_id(
1626 __isl_keep isl_multi_union_pw_aff *mupa,
1627 enum isl_dim_type type);
1628 __isl_give isl_id *isl_multi_union_pw_aff_get_tuple_id(
1629 __isl_keep isl_multi_union_pw_aff *mupa,
1630 enum isl_dim_type type);
1631 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1632 __isl_take isl_multi_aff *maff,
1633 enum isl_dim_type type, const char *s);
1634 __isl_give isl_multi_pw_aff *
1635 isl_multi_pw_aff_set_tuple_name(
1636 __isl_take isl_multi_pw_aff *mpa,
1637 enum isl_dim_type type, const char *s);
1638 __isl_give isl_multi_union_pw_aff *
1639 isl_multi_union_pw_aff_set_tuple_name(
1640 __isl_take isl_multi_union_pw_aff *mupa,
1641 enum isl_dim_type type, const char *s);
1642 const char *isl_multi_aff_get_tuple_name(
1643 __isl_keep isl_multi_aff *multi,
1644 enum isl_dim_type type);
1645 isl_bool isl_pw_multi_aff_has_tuple_name(
1646 __isl_keep isl_pw_multi_aff *pma,
1647 enum isl_dim_type type);
1648 const char *isl_pw_multi_aff_get_tuple_name(
1649 __isl_keep isl_pw_multi_aff *pma,
1650 enum isl_dim_type type);
1651 const char *isl_multi_union_pw_aff_get_tuple_name(
1652 __isl_keep isl_multi_union_pw_aff *mupa,
1653 enum isl_dim_type type);
1655 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1656 or C<isl_dim_set>. As with C<isl_space_get_name>,
1657 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1659 Binary operations require the corresponding spaces of their arguments
1660 to have the same name.
1662 To keep the names of all parameters and tuples, but reset the user pointers
1663 of all the corresponding identifiers, use the following function.
1665 #include <isl/space.h>
1666 __isl_give isl_space *isl_space_reset_user(
1667 __isl_take isl_space *space);
1669 #include <isl/set.h>
1670 __isl_give isl_set *isl_set_reset_user(
1671 __isl_take isl_set *set);
1673 #include <isl/map.h>
1674 __isl_give isl_map *isl_map_reset_user(
1675 __isl_take isl_map *map);
1677 #include <isl/union_set.h>
1678 __isl_give isl_union_set *isl_union_set_reset_user(
1679 __isl_take isl_union_set *uset);
1681 #include <isl/union_map.h>
1682 __isl_give isl_union_map *isl_union_map_reset_user(
1683 __isl_take isl_union_map *umap);
1685 #include <isl/val.h>
1686 __isl_give isl_multi_val *isl_multi_val_reset_user(
1687 __isl_take isl_multi_val *mv);
1689 #include <isl/aff.h>
1690 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1691 __isl_take isl_multi_aff *ma);
1692 __isl_give isl_pw_aff *isl_pw_aff_reset_user(
1693 __isl_take isl_pw_aff *pa);
1694 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1695 __isl_take isl_multi_pw_aff *mpa);
1696 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_reset_user(
1697 __isl_take isl_pw_multi_aff *pma);
1698 __isl_give isl_union_pw_aff *isl_union_pw_aff_reset_user(
1699 __isl_take isl_union_pw_aff *upa);
1700 __isl_give isl_multi_union_pw_aff *
1701 isl_multi_union_pw_aff_reset_user(
1702 __isl_take isl_multi_union_pw_aff *mupa);
1703 __isl_give isl_union_pw_multi_aff *
1704 isl_union_pw_multi_aff_reset_user(
1705 __isl_take isl_union_pw_multi_aff *upma);
1707 #include <isl/polynomial.h>
1708 __isl_give isl_pw_qpolynomial *
1709 isl_pw_qpolynomial_reset_user(
1710 __isl_take isl_pw_qpolynomial *pwqp);
1711 __isl_give isl_union_pw_qpolynomial *
1712 isl_union_pw_qpolynomial_reset_user(
1713 __isl_take isl_union_pw_qpolynomial *upwqp);
1714 __isl_give isl_pw_qpolynomial_fold *
1715 isl_pw_qpolynomial_fold_reset_user(
1716 __isl_take isl_pw_qpolynomial_fold *pwf);
1717 __isl_give isl_union_pw_qpolynomial_fold *
1718 isl_union_pw_qpolynomial_fold_reset_user(
1719 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1721 Spaces can be nested. In particular, the domain of a set or
1722 the domain or range of a relation can be a nested relation.
1723 This process is also called I<wrapping>.
1724 The functions for detecting, constructing and deconstructing
1725 such nested spaces can be found in the wrapping properties
1726 of L</"Unary Properties">, the wrapping operations
1727 of L</"Unary Operations"> and the Cartesian product operations
1728 of L</"Basic Operations">.
1730 Spaces can be created from other spaces
1731 using the functions described in L</"Unary Operations">
1732 and L</"Binary Operations">.
1736 A local space is essentially a space with
1737 zero or more existentially quantified variables.
1738 The local space of various objects can be obtained
1739 using the following functions.
1741 #include <isl/constraint.h>
1742 __isl_give isl_local_space *isl_constraint_get_local_space(
1743 __isl_keep isl_constraint *constraint);
1745 #include <isl/set.h>
1746 __isl_give isl_local_space *isl_basic_set_get_local_space(
1747 __isl_keep isl_basic_set *bset);
1749 #include <isl/map.h>
1750 __isl_give isl_local_space *isl_basic_map_get_local_space(
1751 __isl_keep isl_basic_map *bmap);
1753 #include <isl/aff.h>
1754 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1755 __isl_keep isl_aff *aff);
1756 __isl_give isl_local_space *isl_aff_get_local_space(
1757 __isl_keep isl_aff *aff);
1759 A new local space can be created from a space using
1761 #include <isl/local_space.h>
1762 __isl_give isl_local_space *isl_local_space_from_space(
1763 __isl_take isl_space *space);
1765 They can be inspected, modified, copied and freed using the following functions.
1767 #include <isl/local_space.h>
1768 isl_bool isl_local_space_is_params(
1769 __isl_keep isl_local_space *ls);
1770 isl_bool isl_local_space_is_set(
1771 __isl_keep isl_local_space *ls);
1772 __isl_give isl_space *isl_local_space_get_space(
1773 __isl_keep isl_local_space *ls);
1774 __isl_give isl_aff *isl_local_space_get_div(
1775 __isl_keep isl_local_space *ls, int pos);
1776 __isl_give isl_local_space *isl_local_space_copy(
1777 __isl_keep isl_local_space *ls);
1778 __isl_null isl_local_space *isl_local_space_free(
1779 __isl_take isl_local_space *ls);
1781 Note that C<isl_local_space_get_div> can only be used on local spaces
1784 Two local spaces can be compared using
1786 isl_bool isl_local_space_is_equal(
1787 __isl_keep isl_local_space *ls1,
1788 __isl_keep isl_local_space *ls2);
1790 Local spaces can be created from other local spaces
1791 using the functions described in L</"Unary Operations">
1792 and L</"Binary Operations">.
1794 =head2 Creating New Sets and Relations
1796 C<isl> has functions for creating some standard sets and relations.
1800 =item * Empty sets and relations
1802 __isl_give isl_basic_set *isl_basic_set_empty(
1803 __isl_take isl_space *space);
1804 __isl_give isl_basic_map *isl_basic_map_empty(
1805 __isl_take isl_space *space);
1806 __isl_give isl_set *isl_set_empty(
1807 __isl_take isl_space *space);
1808 __isl_give isl_map *isl_map_empty(
1809 __isl_take isl_space *space);
1810 __isl_give isl_union_set *isl_union_set_empty(
1811 __isl_take isl_space *space);
1812 __isl_give isl_union_map *isl_union_map_empty(
1813 __isl_take isl_space *space);
1815 For C<isl_union_set>s and C<isl_union_map>s, the space
1816 is only used to specify the parameters.
1818 =item * Universe sets and relations
1820 __isl_give isl_basic_set *isl_basic_set_universe(
1821 __isl_take isl_space *space);
1822 __isl_give isl_basic_map *isl_basic_map_universe(
1823 __isl_take isl_space *space);
1824 __isl_give isl_set *isl_set_universe(
1825 __isl_take isl_space *space);
1826 __isl_give isl_map *isl_map_universe(
1827 __isl_take isl_space *space);
1828 __isl_give isl_union_set *isl_union_set_universe(
1829 __isl_take isl_union_set *uset);
1830 __isl_give isl_union_map *isl_union_map_universe(
1831 __isl_take isl_union_map *umap);
1833 The sets and relations constructed by the functions above
1834 contain all integer values, while those constructed by the
1835 functions below only contain non-negative values.
1837 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1838 __isl_take isl_space *space);
1839 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1840 __isl_take isl_space *space);
1841 __isl_give isl_set *isl_set_nat_universe(
1842 __isl_take isl_space *space);
1843 __isl_give isl_map *isl_map_nat_universe(
1844 __isl_take isl_space *space);
1846 =item * Identity relations
1848 __isl_give isl_basic_map *isl_basic_map_identity(
1849 __isl_take isl_space *space);
1850 __isl_give isl_map *isl_map_identity(
1851 __isl_take isl_space *space);
1853 The number of input and output dimensions in C<space> needs
1856 =item * Lexicographic order
1858 __isl_give isl_map *isl_map_lex_lt(
1859 __isl_take isl_space *set_space);
1860 __isl_give isl_map *isl_map_lex_le(
1861 __isl_take isl_space *set_space);
1862 __isl_give isl_map *isl_map_lex_gt(
1863 __isl_take isl_space *set_space);
1864 __isl_give isl_map *isl_map_lex_ge(
1865 __isl_take isl_space *set_space);
1866 __isl_give isl_map *isl_map_lex_lt_first(
1867 __isl_take isl_space *space, unsigned n);
1868 __isl_give isl_map *isl_map_lex_le_first(
1869 __isl_take isl_space *space, unsigned n);
1870 __isl_give isl_map *isl_map_lex_gt_first(
1871 __isl_take isl_space *space, unsigned n);
1872 __isl_give isl_map *isl_map_lex_ge_first(
1873 __isl_take isl_space *space, unsigned n);
1875 The first four functions take a space for a B<set>
1876 and return relations that express that the elements in the domain
1877 are lexicographically less
1878 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1879 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1880 than the elements in the range.
1881 The last four functions take a space for a map
1882 and return relations that express that the first C<n> dimensions
1883 in the domain are lexicographically less
1884 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1885 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1886 than the first C<n> dimensions in the range.
1890 A basic set or relation can be converted to a set or relation
1891 using the following functions.
1893 __isl_give isl_set *isl_set_from_basic_set(
1894 __isl_take isl_basic_set *bset);
1895 __isl_give isl_map *isl_map_from_basic_map(
1896 __isl_take isl_basic_map *bmap);
1898 Sets and relations can be converted to union sets and relations
1899 using the following functions.
1901 __isl_give isl_union_set *isl_union_set_from_basic_set(
1902 __isl_take isl_basic_set *bset);
1903 __isl_give isl_union_map *isl_union_map_from_basic_map(
1904 __isl_take isl_basic_map *bmap);
1905 __isl_give isl_union_set *isl_union_set_from_set(
1906 __isl_take isl_set *set);
1907 __isl_give isl_union_map *isl_union_map_from_map(
1908 __isl_take isl_map *map);
1910 The inverse conversions below can only be used if the input
1911 union set or relation is known to contain elements in exactly one
1914 __isl_give isl_set *isl_set_from_union_set(
1915 __isl_take isl_union_set *uset);
1916 __isl_give isl_map *isl_map_from_union_map(
1917 __isl_take isl_union_map *umap);
1919 Sets and relations can be copied and freed again using the following
1922 __isl_give isl_basic_set *isl_basic_set_copy(
1923 __isl_keep isl_basic_set *bset);
1924 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1925 __isl_give isl_union_set *isl_union_set_copy(
1926 __isl_keep isl_union_set *uset);
1927 __isl_give isl_basic_map *isl_basic_map_copy(
1928 __isl_keep isl_basic_map *bmap);
1929 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1930 __isl_give isl_union_map *isl_union_map_copy(
1931 __isl_keep isl_union_map *umap);
1932 __isl_null isl_basic_set *isl_basic_set_free(
1933 __isl_take isl_basic_set *bset);
1934 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1935 __isl_null isl_union_set *isl_union_set_free(
1936 __isl_take isl_union_set *uset);
1937 __isl_null isl_basic_map *isl_basic_map_free(
1938 __isl_take isl_basic_map *bmap);
1939 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1940 __isl_null isl_union_map *isl_union_map_free(
1941 __isl_take isl_union_map *umap);
1943 Other sets and relations can be constructed by starting
1944 from a universe set or relation, adding equality and/or
1945 inequality constraints and then projecting out the
1946 existentially quantified variables, if any.
1947 Constraints can be constructed, manipulated and
1948 added to (or removed from) (basic) sets and relations
1949 using the following functions.
1951 #include <isl/constraint.h>
1952 __isl_give isl_constraint *isl_constraint_alloc_equality(
1953 __isl_take isl_local_space *ls);
1954 __isl_give isl_constraint *isl_constraint_alloc_inequality(
1955 __isl_take isl_local_space *ls);
1956 __isl_give isl_constraint *isl_constraint_set_constant_si(
1957 __isl_take isl_constraint *constraint, int v);
1958 __isl_give isl_constraint *isl_constraint_set_constant_val(
1959 __isl_take isl_constraint *constraint,
1960 __isl_take isl_val *v);
1961 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1962 __isl_take isl_constraint *constraint,
1963 enum isl_dim_type type, int pos, int v);
1964 __isl_give isl_constraint *
1965 isl_constraint_set_coefficient_val(
1966 __isl_take isl_constraint *constraint,
1967 enum isl_dim_type type, int pos,
1968 __isl_take isl_val *v);
1969 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1970 __isl_take isl_basic_map *bmap,
1971 __isl_take isl_constraint *constraint);
1972 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1973 __isl_take isl_basic_set *bset,
1974 __isl_take isl_constraint *constraint);
1975 __isl_give isl_map *isl_map_add_constraint(
1976 __isl_take isl_map *map,
1977 __isl_take isl_constraint *constraint);
1978 __isl_give isl_set *isl_set_add_constraint(
1979 __isl_take isl_set *set,
1980 __isl_take isl_constraint *constraint);
1982 For example, to create a set containing the even integers
1983 between 10 and 42, you would use the following code.
1986 isl_local_space *ls;
1988 isl_basic_set *bset;
1990 space = isl_space_set_alloc(ctx, 0, 2);
1991 bset = isl_basic_set_universe(isl_space_copy(space));
1992 ls = isl_local_space_from_space(space);
1994 c = isl_constraint_alloc_equality(isl_local_space_copy(ls));
1995 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1996 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1997 bset = isl_basic_set_add_constraint(bset, c);
1999 c = isl_constraint_alloc_inequality(isl_local_space_copy(ls));
2000 c = isl_constraint_set_constant_si(c, -10);
2001 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
2002 bset = isl_basic_set_add_constraint(bset, c);
2004 c = isl_constraint_alloc_inequality(ls);
2005 c = isl_constraint_set_constant_si(c, 42);
2006 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
2007 bset = isl_basic_set_add_constraint(bset, c);
2009 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
2013 isl_basic_set *bset;
2014 bset = isl_basic_set_read_from_str(ctx,
2015 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
2017 A basic set or relation can also be constructed from two matrices
2018 describing the equalities and the inequalities.
2020 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
2021 __isl_take isl_space *space,
2022 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2023 enum isl_dim_type c1,
2024 enum isl_dim_type c2, enum isl_dim_type c3,
2025 enum isl_dim_type c4);
2026 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
2027 __isl_take isl_space *space,
2028 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
2029 enum isl_dim_type c1,
2030 enum isl_dim_type c2, enum isl_dim_type c3,
2031 enum isl_dim_type c4, enum isl_dim_type c5);
2033 The C<isl_dim_type> arguments indicate the order in which
2034 different kinds of variables appear in the input matrices
2035 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
2036 C<isl_dim_set> and C<isl_dim_div> for sets and
2037 of C<isl_dim_cst>, C<isl_dim_param>,
2038 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
2040 A (basic or union) set or relation can also be constructed from a
2041 (union) (piecewise) (multiple) affine expression
2042 or a list of affine expressions
2043 (See L</"Functions">), provided these affine expressions do not
2046 __isl_give isl_basic_map *isl_basic_map_from_aff(
2047 __isl_take isl_aff *aff);
2048 __isl_give isl_map *isl_map_from_aff(
2049 __isl_take isl_aff *aff);
2050 __isl_give isl_set *isl_set_from_pw_aff(
2051 __isl_take isl_pw_aff *pwaff);
2052 __isl_give isl_map *isl_map_from_pw_aff(
2053 __isl_take isl_pw_aff *pwaff);
2054 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
2055 __isl_take isl_space *domain_space,
2056 __isl_take isl_aff_list *list);
2057 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
2058 __isl_take isl_multi_aff *maff)
2059 __isl_give isl_map *isl_map_from_multi_aff(
2060 __isl_take isl_multi_aff *maff)
2061 __isl_give isl_set *isl_set_from_pw_multi_aff(
2062 __isl_take isl_pw_multi_aff *pma);
2063 __isl_give isl_map *isl_map_from_pw_multi_aff(
2064 __isl_take isl_pw_multi_aff *pma);
2065 __isl_give isl_set *isl_set_from_multi_pw_aff(
2066 __isl_take isl_multi_pw_aff *mpa);
2067 __isl_give isl_map *isl_map_from_multi_pw_aff(
2068 __isl_take isl_multi_pw_aff *mpa);
2069 __isl_give isl_union_map *isl_union_map_from_union_pw_aff(
2070 __isl_take isl_union_pw_aff *upa);
2071 __isl_give isl_union_map *
2072 isl_union_map_from_union_pw_multi_aff(
2073 __isl_take isl_union_pw_multi_aff *upma);
2074 __isl_give isl_union_map *
2075 isl_union_map_from_multi_union_pw_aff(
2076 __isl_take isl_multi_union_pw_aff *mupa);
2078 The C<domain_space> argument describes the domain of the resulting
2079 basic relation. It is required because the C<list> may consist
2080 of zero affine expressions.
2081 The C<mupa> passed to C<isl_union_map_from_multi_union_pw_aff>
2082 is not allowed to be zero-dimensional. The domain of the result
2083 is the shared domain of the union piecewise affine elements.
2085 =head2 Inspecting Sets and Relations
2087 Usually, the user should not have to care about the actual constraints
2088 of the sets and maps, but should instead apply the abstract operations
2089 explained in the following sections.
2090 Occasionally, however, it may be required to inspect the individual
2091 coefficients of the constraints. This section explains how to do so.
2092 In these cases, it may also be useful to have C<isl> compute
2093 an explicit representation of the existentially quantified variables.
2095 __isl_give isl_set *isl_set_compute_divs(
2096 __isl_take isl_set *set);
2097 __isl_give isl_map *isl_map_compute_divs(
2098 __isl_take isl_map *map);
2099 __isl_give isl_union_set *isl_union_set_compute_divs(
2100 __isl_take isl_union_set *uset);
2101 __isl_give isl_union_map *isl_union_map_compute_divs(
2102 __isl_take isl_union_map *umap);
2104 This explicit representation defines the existentially quantified
2105 variables as integer divisions of the other variables, possibly
2106 including earlier existentially quantified variables.
2107 An explicitly represented existentially quantified variable therefore
2108 has a unique value when the values of the other variables are known.
2110 Alternatively, the existentially quantified variables can be removed
2111 using the following functions, which compute an overapproximation.
2113 __isl_give isl_basic_set *isl_basic_set_remove_divs(
2114 __isl_take isl_basic_set *bset);
2115 __isl_give isl_basic_map *isl_basic_map_remove_divs(
2116 __isl_take isl_basic_map *bmap);
2117 __isl_give isl_set *isl_set_remove_divs(
2118 __isl_take isl_set *set);
2119 __isl_give isl_map *isl_map_remove_divs(
2120 __isl_take isl_map *map);
2122 It is also possible to only remove those divs that are defined
2123 in terms of a given range of dimensions or only those for which
2124 no explicit representation is known.
2126 __isl_give isl_basic_set *
2127 isl_basic_set_remove_divs_involving_dims(
2128 __isl_take isl_basic_set *bset,
2129 enum isl_dim_type type,
2130 unsigned first, unsigned n);
2131 __isl_give isl_basic_map *
2132 isl_basic_map_remove_divs_involving_dims(
2133 __isl_take isl_basic_map *bmap,
2134 enum isl_dim_type type,
2135 unsigned first, unsigned n);
2136 __isl_give isl_set *isl_set_remove_divs_involving_dims(
2137 __isl_take isl_set *set, enum isl_dim_type type,
2138 unsigned first, unsigned n);
2139 __isl_give isl_map *isl_map_remove_divs_involving_dims(
2140 __isl_take isl_map *map, enum isl_dim_type type,
2141 unsigned first, unsigned n);
2143 __isl_give isl_basic_set *
2144 isl_basic_set_remove_unknown_divs(
2145 __isl_take isl_basic_set *bset);
2146 __isl_give isl_set *isl_set_remove_unknown_divs(
2147 __isl_take isl_set *set);
2148 __isl_give isl_map *isl_map_remove_unknown_divs(
2149 __isl_take isl_map *map);
2151 To iterate over all the sets or maps in a union set or map, use
2153 isl_stat isl_union_set_foreach_set(
2154 __isl_keep isl_union_set *uset,
2155 isl_stat (*fn)(__isl_take isl_set *set, void *user),
2157 isl_stat isl_union_map_foreach_map(
2158 __isl_keep isl_union_map *umap,
2159 isl_stat (*fn)(__isl_take isl_map *map, void *user),
2162 These functions call the callback function once for each
2163 (pair of) space(s) for which there are elements in the input.
2164 The argument to the callback contains all elements in the input
2165 with that (pair of) space(s).
2167 The number of sets or maps in a union set or map can be obtained
2170 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
2171 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
2173 To extract the set or map in a given space from a union, use
2175 __isl_give isl_set *isl_union_set_extract_set(
2176 __isl_keep isl_union_set *uset,
2177 __isl_take isl_space *space);
2178 __isl_give isl_map *isl_union_map_extract_map(
2179 __isl_keep isl_union_map *umap,
2180 __isl_take isl_space *space);
2182 To iterate over all the basic sets or maps in a set or map, use
2184 isl_stat isl_set_foreach_basic_set(__isl_keep isl_set *set,
2185 isl_stat (*fn)(__isl_take isl_basic_set *bset,
2188 isl_stat isl_map_foreach_basic_map(__isl_keep isl_map *map,
2189 isl_stat (*fn)(__isl_take isl_basic_map *bmap,
2193 The callback function C<fn> should return 0 if successful and
2194 -1 if an error occurs. In the latter case, or if any other error
2195 occurs, the above functions will return -1.
2197 It should be noted that C<isl> does not guarantee that
2198 the basic sets or maps passed to C<fn> are disjoint.
2199 If this is required, then the user should call one of
2200 the following functions first.
2202 __isl_give isl_set *isl_set_make_disjoint(
2203 __isl_take isl_set *set);
2204 __isl_give isl_map *isl_map_make_disjoint(
2205 __isl_take isl_map *map);
2207 The number of basic sets in a set can be obtained
2208 or the number of basic maps in a map can be obtained
2211 #include <isl/set.h>
2212 int isl_set_n_basic_set(__isl_keep isl_set *set);
2214 #include <isl/map.h>
2215 int isl_map_n_basic_map(__isl_keep isl_map *map);
2217 It is also possible to obtain a list of basic sets from a set
2219 #include <isl/set.h>
2220 __isl_give isl_basic_set_list *isl_set_get_basic_set_list(
2221 __isl_keep isl_set *set);
2223 The returned list can be manipulated using the functions in L<"Lists">.
2225 To iterate over the constraints of a basic set or map, use
2227 #include <isl/constraint.h>
2229 int isl_basic_set_n_constraint(
2230 __isl_keep isl_basic_set *bset);
2231 isl_stat isl_basic_set_foreach_constraint(
2232 __isl_keep isl_basic_set *bset,
2233 isl_stat (*fn)(__isl_take isl_constraint *c,
2236 int isl_basic_map_n_constraint(
2237 __isl_keep isl_basic_map *bmap);
2238 isl_stat isl_basic_map_foreach_constraint(
2239 __isl_keep isl_basic_map *bmap,
2240 isl_stat (*fn)(__isl_take isl_constraint *c,
2243 __isl_null isl_constraint *isl_constraint_free(
2244 __isl_take isl_constraint *c);
2246 Again, the callback function C<fn> should return 0 if successful and
2247 -1 if an error occurs. In the latter case, or if any other error
2248 occurs, the above functions will return -1.
2249 The constraint C<c> represents either an equality or an inequality.
2250 Use the following function to find out whether a constraint
2251 represents an equality. If not, it represents an inequality.
2253 isl_bool isl_constraint_is_equality(
2254 __isl_keep isl_constraint *constraint);
2256 It is also possible to obtain a list of constraints from a basic
2259 #include <isl/constraint.h>
2260 __isl_give isl_constraint_list *
2261 isl_basic_map_get_constraint_list(
2262 __isl_keep isl_basic_map *bmap);
2263 __isl_give isl_constraint_list *
2264 isl_basic_set_get_constraint_list(
2265 __isl_keep isl_basic_set *bset);
2267 These functions require that all existentially quantified variables
2268 have an explicit representation.
2269 The returned list can be manipulated using the functions in L<"Lists">.
2271 The coefficients of the constraints can be inspected using
2272 the following functions.
2274 isl_bool isl_constraint_is_lower_bound(
2275 __isl_keep isl_constraint *constraint,
2276 enum isl_dim_type type, unsigned pos);
2277 isl_bool isl_constraint_is_upper_bound(
2278 __isl_keep isl_constraint *constraint,
2279 enum isl_dim_type type, unsigned pos);
2280 __isl_give isl_val *isl_constraint_get_constant_val(
2281 __isl_keep isl_constraint *constraint);
2282 __isl_give isl_val *isl_constraint_get_coefficient_val(
2283 __isl_keep isl_constraint *constraint,
2284 enum isl_dim_type type, int pos);
2286 The explicit representations of the existentially quantified
2287 variables can be inspected using the following function.
2288 Note that the user is only allowed to use this function
2289 if the inspected set or map is the result of a call
2290 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2291 The existentially quantified variable is equal to the floor
2292 of the returned affine expression. The affine expression
2293 itself can be inspected using the functions in
2296 __isl_give isl_aff *isl_constraint_get_div(
2297 __isl_keep isl_constraint *constraint, int pos);
2299 To obtain the constraints of a basic set or map in matrix
2300 form, use the following functions.
2302 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2303 __isl_keep isl_basic_set *bset,
2304 enum isl_dim_type c1, enum isl_dim_type c2,
2305 enum isl_dim_type c3, enum isl_dim_type c4);
2306 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2307 __isl_keep isl_basic_set *bset,
2308 enum isl_dim_type c1, enum isl_dim_type c2,
2309 enum isl_dim_type c3, enum isl_dim_type c4);
2310 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2311 __isl_keep isl_basic_map *bmap,
2312 enum isl_dim_type c1,
2313 enum isl_dim_type c2, enum isl_dim_type c3,
2314 enum isl_dim_type c4, enum isl_dim_type c5);
2315 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2316 __isl_keep isl_basic_map *bmap,
2317 enum isl_dim_type c1,
2318 enum isl_dim_type c2, enum isl_dim_type c3,
2319 enum isl_dim_type c4, enum isl_dim_type c5);
2321 The C<isl_dim_type> arguments dictate the order in which
2322 different kinds of variables appear in the resulting matrix.
2323 For set inputs, they should be a permutation of
2324 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
2325 For map inputs, they should be a permutation of
2326 C<isl_dim_cst>, C<isl_dim_param>,
2327 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2331 Points are elements of a set. They can be used to construct
2332 simple sets (boxes) or they can be used to represent the
2333 individual elements of a set.
2334 The zero point (the origin) can be created using
2336 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2338 The coordinates of a point can be inspected, set and changed
2341 __isl_give isl_val *isl_point_get_coordinate_val(
2342 __isl_keep isl_point *pnt,
2343 enum isl_dim_type type, int pos);
2344 __isl_give isl_point *isl_point_set_coordinate_val(
2345 __isl_take isl_point *pnt,
2346 enum isl_dim_type type, int pos,
2347 __isl_take isl_val *v);
2349 __isl_give isl_point *isl_point_add_ui(
2350 __isl_take isl_point *pnt,
2351 enum isl_dim_type type, int pos, unsigned val);
2352 __isl_give isl_point *isl_point_sub_ui(
2353 __isl_take isl_point *pnt,
2354 enum isl_dim_type type, int pos, unsigned val);
2356 Points can be copied or freed using
2358 __isl_give isl_point *isl_point_copy(
2359 __isl_keep isl_point *pnt);
2360 void isl_point_free(__isl_take isl_point *pnt);
2362 A singleton set can be created from a point using
2364 __isl_give isl_basic_set *isl_basic_set_from_point(
2365 __isl_take isl_point *pnt);
2366 __isl_give isl_set *isl_set_from_point(
2367 __isl_take isl_point *pnt);
2368 __isl_give isl_union_set *isl_union_set_from_point(
2369 __isl_take isl_point *pnt);
2371 and a box can be created from two opposite extremal points using
2373 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2374 __isl_take isl_point *pnt1,
2375 __isl_take isl_point *pnt2);
2376 __isl_give isl_set *isl_set_box_from_points(
2377 __isl_take isl_point *pnt1,
2378 __isl_take isl_point *pnt2);
2380 All elements of a B<bounded> (union) set can be enumerated using
2381 the following functions.
2383 isl_stat isl_set_foreach_point(__isl_keep isl_set *set,
2384 isl_stat (*fn)(__isl_take isl_point *pnt,
2387 isl_stat isl_union_set_foreach_point(
2388 __isl_keep isl_union_set *uset,
2389 isl_stat (*fn)(__isl_take isl_point *pnt,
2393 The function C<fn> is called for each integer point in
2394 C<set> with as second argument the last argument of
2395 the C<isl_set_foreach_point> call. The function C<fn>
2396 should return C<0> on success and C<-1> on failure.
2397 In the latter case, C<isl_set_foreach_point> will stop
2398 enumerating and return C<-1> as well.
2399 If the enumeration is performed successfully and to completion,
2400 then C<isl_set_foreach_point> returns C<0>.
2402 To obtain a single point of a (basic or union) set, use
2404 __isl_give isl_point *isl_basic_set_sample_point(
2405 __isl_take isl_basic_set *bset);
2406 __isl_give isl_point *isl_set_sample_point(
2407 __isl_take isl_set *set);
2408 __isl_give isl_point *isl_union_set_sample_point(
2409 __isl_take isl_union_set *uset);
2411 If C<set> does not contain any (integer) points, then the
2412 resulting point will be ``void'', a property that can be
2415 isl_bool isl_point_is_void(__isl_keep isl_point *pnt);
2419 Besides sets and relation, C<isl> also supports various types of functions.
2420 Each of these types is derived from the value type (see L</"Values">)
2421 or from one of two primitive function types
2422 through the application of zero or more type constructors.
2423 We first describe the primitive type and then we describe
2424 the types derived from these primitive types.
2426 =head3 Primitive Functions
2428 C<isl> support two primitive function types, quasi-affine
2429 expressions and quasipolynomials.
2430 A quasi-affine expression is defined either over a parameter
2431 space or over a set and is composed of integer constants,
2432 parameters and set variables, addition, subtraction and
2433 integer division by an integer constant.
2434 For example, the quasi-affine expression
2436 [n] -> { [x] -> [2*floor((4 n + x)/9] }
2438 maps C<x> to C<2*floor((4 n + x)/9>.
2439 A quasipolynomial is a polynomial expression in quasi-affine
2440 expression. That is, it additionally allows for multiplication.
2441 Note, though, that it is not allowed to construct an integer
2442 division of an expression involving multiplications.
2443 Here is an example of a quasipolynomial that is not
2444 quasi-affine expression
2446 [n] -> { [x] -> (n*floor((4 n + x)/9) }
2448 Note that the external representations of quasi-affine expressions
2449 and quasipolynomials are different. Quasi-affine expressions
2450 use a notation with square brackets just like binary relations,
2451 while quasipolynomials do not. This might change at some point.
2453 If a primitive function is defined over a parameter space,
2454 then the space of the function itself is that of a set.
2455 If it is defined over a set, then the space of the function
2456 is that of a relation. In both cases, the set space (or
2457 the output space) is single-dimensional, anonymous and unstructured.
2458 To create functions with multiple dimensions or with other kinds
2459 of set or output spaces, use multiple expressions
2460 (see L</"Multiple Expressions">).
2464 =item * Quasi-affine Expressions
2466 Besides the expressions described above, a quasi-affine
2467 expression can also be set to NaN. Such expressions
2468 typically represent a failure to represent a result
2469 as a quasi-affine expression.
2471 The zero quasi affine expression or the quasi affine expression
2472 that is equal to a given value or
2473 a specified dimension on a given domain can be created using
2475 #include <isl/aff.h>
2476 __isl_give isl_aff *isl_aff_zero_on_domain(
2477 __isl_take isl_local_space *ls);
2478 __isl_give isl_aff *isl_aff_val_on_domain(
2479 __isl_take isl_local_space *ls,
2480 __isl_take isl_val *val);
2481 __isl_give isl_aff *isl_aff_var_on_domain(
2482 __isl_take isl_local_space *ls,
2483 enum isl_dim_type type, unsigned pos);
2484 __isl_give isl_aff *isl_aff_nan_on_domain(
2485 __isl_take isl_local_space *ls);
2487 Quasi affine expressions can be copied and freed using
2489 #include <isl/aff.h>
2490 __isl_give isl_aff *isl_aff_copy(
2491 __isl_keep isl_aff *aff);
2492 __isl_null isl_aff *isl_aff_free(
2493 __isl_take isl_aff *aff);
2495 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2496 using the following function. The constraint is required to have
2497 a non-zero coefficient for the specified dimension.
2499 #include <isl/constraint.h>
2500 __isl_give isl_aff *isl_constraint_get_bound(
2501 __isl_keep isl_constraint *constraint,
2502 enum isl_dim_type type, int pos);
2504 The entire affine expression of the constraint can also be extracted
2505 using the following function.
2507 #include <isl/constraint.h>
2508 __isl_give isl_aff *isl_constraint_get_aff(
2509 __isl_keep isl_constraint *constraint);
2511 Conversely, an equality constraint equating
2512 the affine expression to zero or an inequality constraint enforcing
2513 the affine expression to be non-negative, can be constructed using
2515 __isl_give isl_constraint *isl_equality_from_aff(
2516 __isl_take isl_aff *aff);
2517 __isl_give isl_constraint *isl_inequality_from_aff(
2518 __isl_take isl_aff *aff);
2520 The coefficients and the integer divisions of an affine expression
2521 can be inspected using the following functions.
2523 #include <isl/aff.h>
2524 __isl_give isl_val *isl_aff_get_constant_val(
2525 __isl_keep isl_aff *aff);
2526 __isl_give isl_val *isl_aff_get_coefficient_val(
2527 __isl_keep isl_aff *aff,
2528 enum isl_dim_type type, int pos);
2529 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2530 enum isl_dim_type type, int pos);
2531 __isl_give isl_val *isl_aff_get_denominator_val(
2532 __isl_keep isl_aff *aff);
2533 __isl_give isl_aff *isl_aff_get_div(
2534 __isl_keep isl_aff *aff, int pos);
2536 They can be modified using the following functions.
2538 #include <isl/aff.h>
2539 __isl_give isl_aff *isl_aff_set_constant_si(
2540 __isl_take isl_aff *aff, int v);
2541 __isl_give isl_aff *isl_aff_set_constant_val(
2542 __isl_take isl_aff *aff, __isl_take isl_val *v);
2543 __isl_give isl_aff *isl_aff_set_coefficient_si(
2544 __isl_take isl_aff *aff,
2545 enum isl_dim_type type, int pos, int v);
2546 __isl_give isl_aff *isl_aff_set_coefficient_val(
2547 __isl_take isl_aff *aff,
2548 enum isl_dim_type type, int pos,
2549 __isl_take isl_val *v);
2551 __isl_give isl_aff *isl_aff_add_constant_si(
2552 __isl_take isl_aff *aff, int v);
2553 __isl_give isl_aff *isl_aff_add_constant_val(
2554 __isl_take isl_aff *aff, __isl_take isl_val *v);
2555 __isl_give isl_aff *isl_aff_add_constant_num_si(
2556 __isl_take isl_aff *aff, int v);
2557 __isl_give isl_aff *isl_aff_add_coefficient_si(
2558 __isl_take isl_aff *aff,
2559 enum isl_dim_type type, int pos, int v);
2560 __isl_give isl_aff *isl_aff_add_coefficient_val(
2561 __isl_take isl_aff *aff,
2562 enum isl_dim_type type, int pos,
2563 __isl_take isl_val *v);
2565 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
2566 set the I<numerator> of the constant or coefficient, while
2567 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
2568 the constant or coefficient as a whole.
2569 The C<add_constant> and C<add_coefficient> functions add an integer
2570 or rational value to
2571 the possibly rational constant or coefficient.
2572 The C<add_constant_num> functions add an integer value to
2575 =item * Quasipolynomials
2577 Some simple quasipolynomials can be created using the following functions.
2579 #include <isl/polynomial.h>
2580 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2581 __isl_take isl_space *domain);
2582 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2583 __isl_take isl_space *domain);
2584 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2585 __isl_take isl_space *domain);
2586 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2587 __isl_take isl_space *domain);
2588 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2589 __isl_take isl_space *domain);
2590 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2591 __isl_take isl_space *domain,
2592 __isl_take isl_val *val);
2593 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2594 __isl_take isl_space *domain,
2595 enum isl_dim_type type, unsigned pos);
2596 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2597 __isl_take isl_aff *aff);
2599 Recall that the space in which a quasipolynomial lives is a map space
2600 with a one-dimensional range. The C<domain> argument in some of
2601 the functions above corresponds to the domain of this map space.
2603 Quasipolynomials can be copied and freed again using the following
2606 #include <isl/polynomial.h>
2607 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2608 __isl_keep isl_qpolynomial *qp);
2609 __isl_null isl_qpolynomial *isl_qpolynomial_free(
2610 __isl_take isl_qpolynomial *qp);
2612 The constant term of a quasipolynomial can be extracted using
2614 __isl_give isl_val *isl_qpolynomial_get_constant_val(
2615 __isl_keep isl_qpolynomial *qp);
2617 To iterate over all terms in a quasipolynomial,
2620 isl_stat isl_qpolynomial_foreach_term(
2621 __isl_keep isl_qpolynomial *qp,
2622 isl_stat (*fn)(__isl_take isl_term *term,
2623 void *user), void *user);
2625 The terms themselves can be inspected and freed using
2628 unsigned isl_term_dim(__isl_keep isl_term *term,
2629 enum isl_dim_type type);
2630 __isl_give isl_val *isl_term_get_coefficient_val(
2631 __isl_keep isl_term *term);
2632 int isl_term_get_exp(__isl_keep isl_term *term,
2633 enum isl_dim_type type, unsigned pos);
2634 __isl_give isl_aff *isl_term_get_div(
2635 __isl_keep isl_term *term, unsigned pos);
2636 void isl_term_free(__isl_take isl_term *term);
2638 Each term is a product of parameters, set variables and
2639 integer divisions. The function C<isl_term_get_exp>
2640 returns the exponent of a given dimensions in the given term.
2646 A reduction represents a maximum or a minimum of its
2648 The only reduction type defined by C<isl> is
2649 C<isl_qpolynomial_fold>.
2651 There are currently no functions to directly create such
2652 objects, but they do appear in the piecewise quasipolynomial
2653 reductions returned by the C<isl_pw_qpolynomial_bound> function.
2655 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
2657 Reductions can be copied and freed using
2658 the following functions.
2660 #include <isl/polynomial.h>
2661 __isl_give isl_qpolynomial_fold *
2662 isl_qpolynomial_fold_copy(
2663 __isl_keep isl_qpolynomial_fold *fold);
2664 void isl_qpolynomial_fold_free(
2665 __isl_take isl_qpolynomial_fold *fold);
2667 To iterate over all quasipolynomials in a reduction, use
2669 isl_stat isl_qpolynomial_fold_foreach_qpolynomial(
2670 __isl_keep isl_qpolynomial_fold *fold,
2671 isl_stat (*fn)(__isl_take isl_qpolynomial *qp,
2672 void *user), void *user);
2674 =head3 Multiple Expressions
2676 A multiple expression represents a sequence of zero or
2677 more base expressions, all defined on the same domain space.
2678 The domain space of the multiple expression is the same
2679 as that of the base expressions, but the range space
2680 can be any space. In case the base expressions have
2681 a set space, the corresponding multiple expression
2682 also has a set space.
2683 Objects of the value type do not have an associated space.
2684 The space of a multiple value is therefore always a set space.
2685 Similarly, the space of a multiple union piecewise
2686 affine expression is always a set space.
2688 The multiple expression types defined by C<isl>
2689 are C<isl_multi_val>, C<isl_multi_aff>, C<isl_multi_pw_aff>,
2690 C<isl_multi_union_pw_aff>.
2692 A multiple expression with the value zero for
2693 each output (or set) dimension can be created
2694 using the following functions.
2696 #include <isl/val.h>
2697 __isl_give isl_multi_val *isl_multi_val_zero(
2698 __isl_take isl_space *space);
2700 #include <isl/aff.h>
2701 __isl_give isl_multi_aff *isl_multi_aff_zero(
2702 __isl_take isl_space *space);
2703 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
2704 __isl_take isl_space *space);
2705 __isl_give isl_multi_union_pw_aff *
2706 isl_multi_union_pw_aff_zero(
2707 __isl_take isl_space *space);
2709 Since there is no canonical way of representing a zero
2710 value of type C<isl_union_pw_aff>, the space passed
2711 to C<isl_multi_union_pw_aff_zero> needs to be zero-dimensional.
2713 An identity function can be created using the following
2714 functions. The space needs to be that of a relation
2715 with the same number of input and output dimensions.
2717 #include <isl/aff.h>
2718 __isl_give isl_multi_aff *isl_multi_aff_identity(
2719 __isl_take isl_space *space);
2720 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
2721 __isl_take isl_space *space);
2723 A function that performs a projection on a universe
2724 relation or set can be created using the following functions.
2725 See also the corresponding
2726 projection operations in L</"Unary Operations">.
2728 #include <isl/aff.h>
2729 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
2730 __isl_take isl_space *space);
2731 __isl_give isl_multi_aff *isl_multi_aff_range_map(
2732 __isl_take isl_space *space);
2733 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
2734 __isl_take isl_space *space,
2735 enum isl_dim_type type,
2736 unsigned first, unsigned n);
2738 A multiple expression can be created from a single
2739 base expression using the following functions.
2740 The space of the created multiple expression is the same
2741 as that of the base expression, except for
2742 C<isl_multi_union_pw_aff_from_union_pw_aff> where the input
2743 lives in a parameter space and the output lives
2744 in a single-dimensional set space.
2746 #include <isl/aff.h>
2747 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
2748 __isl_take isl_aff *aff);
2749 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
2750 __isl_take isl_pw_aff *pa);
2751 __isl_give isl_multi_union_pw_aff *
2752 isl_multi_union_pw_aff_from_union_pw_aff(
2753 __isl_take isl_union_pw_aff *upa);
2755 A multiple expression can be created from a list
2756 of base expression in a specified space.
2757 The domain of this space needs to be the same
2758 as the domains of the base expressions in the list.
2759 If the base expressions have a set space (or no associated space),
2760 then this space also needs to be a set space.
2762 #include <isl/val.h>
2763 __isl_give isl_multi_val *isl_multi_val_from_val_list(
2764 __isl_take isl_space *space,
2765 __isl_take isl_val_list *list);
2767 #include <isl/aff.h>
2768 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2769 __isl_take isl_space *space,
2770 __isl_take isl_aff_list *list);
2771 __isl_give isl_multi_pw_aff *
2772 isl_multi_pw_aff_from_pw_aff_list(
2773 __isl_take isl_space *space,
2774 __isl_take isl_pw_aff_list *list);
2775 __isl_give isl_multi_union_pw_aff *
2776 isl_multi_union_pw_aff_from_union_pw_aff_list(
2777 __isl_take isl_space *space,
2778 __isl_take isl_union_pw_aff_list *list);
2780 As a convenience, a multiple piecewise expression can
2781 also be created from a multiple expression.
2782 Each piecewise expression in the result has a single
2785 #include <isl/aff.h>
2786 __isl_give isl_multi_pw_aff *
2787 isl_multi_pw_aff_from_multi_aff(
2788 __isl_take isl_multi_aff *ma);
2790 Similarly, a multiple union expression can be
2791 created from a multiple expression.
2793 #include <isl/aff.h>
2794 __isl_give isl_multi_union_pw_aff *
2795 isl_multi_union_pw_aff_from_multi_aff(
2796 __isl_take isl_multi_aff *ma);
2797 __isl_give isl_multi_union_pw_aff *
2798 isl_multi_union_pw_aff_from_multi_pw_aff(
2799 __isl_take isl_multi_pw_aff *mpa);
2801 A multiple quasi-affine expression can be created from
2802 a multiple value with a given domain space using the following
2805 #include <isl/aff.h>
2806 __isl_give isl_multi_aff *
2807 isl_multi_aff_multi_val_on_space(
2808 __isl_take isl_space *space,
2809 __isl_take isl_multi_val *mv);
2812 a multiple union piecewise affine expression can be created from
2813 a multiple value with a given domain or
2814 a multiple affine expression with a given domain
2815 using the following functions.
2817 #include <isl/aff.h>
2818 __isl_give isl_multi_union_pw_aff *
2819 isl_multi_union_pw_aff_multi_val_on_domain(
2820 __isl_take isl_union_set *domain,
2821 __isl_take isl_multi_val *mv);
2822 __isl_give isl_multi_union_pw_aff *
2823 isl_multi_union_pw_aff_multi_aff_on_domain(
2824 __isl_take isl_union_set *domain,
2825 __isl_take isl_multi_aff *ma);
2827 Multiple expressions can be copied and freed using
2828 the following functions.
2830 #include <isl/val.h>
2831 __isl_give isl_multi_val *isl_multi_val_copy(
2832 __isl_keep isl_multi_val *mv);
2833 __isl_null isl_multi_val *isl_multi_val_free(
2834 __isl_take isl_multi_val *mv);
2836 #include <isl/aff.h>
2837 __isl_give isl_multi_aff *isl_multi_aff_copy(
2838 __isl_keep isl_multi_aff *maff);
2839 __isl_null isl_multi_aff *isl_multi_aff_free(
2840 __isl_take isl_multi_aff *maff);
2841 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
2842 __isl_keep isl_multi_pw_aff *mpa);
2843 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
2844 __isl_take isl_multi_pw_aff *mpa);
2845 __isl_give isl_multi_union_pw_aff *
2846 isl_multi_union_pw_aff_copy(
2847 __isl_keep isl_multi_union_pw_aff *mupa);
2848 __isl_null isl_multi_union_pw_aff *
2849 isl_multi_union_pw_aff_free(
2850 __isl_take isl_multi_union_pw_aff *mupa);
2852 The base expression at a given position of a multiple
2853 expression can be extracted using the following functions.
2855 #include <isl/val.h>
2856 __isl_give isl_val *isl_multi_val_get_val(
2857 __isl_keep isl_multi_val *mv, int pos);
2859 #include <isl/aff.h>
2860 __isl_give isl_aff *isl_multi_aff_get_aff(
2861 __isl_keep isl_multi_aff *multi, int pos);
2862 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
2863 __isl_keep isl_multi_pw_aff *mpa, int pos);
2864 __isl_give isl_union_pw_aff *
2865 isl_multi_union_pw_aff_get_union_pw_aff(
2866 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
2868 It can be replaced using the following functions.
2870 #include <isl/val.h>
2871 __isl_give isl_multi_val *isl_multi_val_set_val(
2872 __isl_take isl_multi_val *mv, int pos,
2873 __isl_take isl_val *val);
2875 #include <isl/aff.h>
2876 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
2877 __isl_take isl_multi_aff *multi, int pos,
2878 __isl_take isl_aff *aff);
2879 __isl_give isl_multi_union_pw_aff *
2880 isl_multi_union_pw_aff_set_union_pw_aff(
2881 __isl_take isl_multi_union_pw_aff *mupa, int pos,
2882 __isl_take isl_union_pw_aff *upa);
2884 As a convenience, a sequence of base expressions that have
2885 their domains in a given space can be extracted from a sequence
2886 of union expressions using the following function.
2888 #include <isl/aff.h>
2889 __isl_give isl_multi_pw_aff *
2890 isl_multi_union_pw_aff_extract_multi_pw_aff(
2891 __isl_keep isl_multi_union_pw_aff *mupa,
2892 __isl_take isl_space *space);
2894 Note that there is a difference between C<isl_multi_union_pw_aff>
2895 and C<isl_union_pw_multi_aff> objects. The first is a sequence
2896 of unions of piecewise expressions, while the second is a union
2897 of piecewise sequences. In particular, multiple affine expressions
2898 in an C<isl_union_pw_multi_aff> may live in different spaces,
2899 while there is only a single multiple expression in
2900 an C<isl_multi_union_pw_aff>, which can therefore only live
2901 in a single space. This means that not every
2902 C<isl_union_pw_multi_aff> can be converted to
2903 an C<isl_multi_union_pw_aff>. Conversely, a zero-dimensional
2904 C<isl_multi_union_pw_aff> carries no information
2905 about any possible domain and therefore cannot be converted
2906 to an C<isl_union_pw_multi_aff>. Moreover, the elements
2907 of an C<isl_multi_union_pw_aff> may be defined over different domains,
2908 while each multiple expression inside an C<isl_union_pw_multi_aff>
2909 has a single domain. The conversion of an C<isl_union_pw_multi_aff>
2910 of dimension greater than one may therefore not be exact.
2911 The following functions can
2912 be used to perform these conversions when they are possible.
2914 #include <isl/aff.h>
2915 __isl_give isl_multi_union_pw_aff *
2916 isl_multi_union_pw_aff_from_union_pw_multi_aff(
2917 __isl_take isl_union_pw_multi_aff *upma);
2918 __isl_give isl_union_pw_multi_aff *
2919 isl_union_pw_multi_aff_from_multi_union_pw_aff(
2920 __isl_take isl_multi_union_pw_aff *mupa);
2922 =head3 Piecewise Expressions
2924 A piecewise expression is an expression that is described
2925 using zero or more base expression defined over the same
2926 number of cells in the domain space of the base expressions.
2927 All base expressions are defined over the same
2928 domain space and the cells are disjoint.
2929 The space of a piecewise expression is the same as
2930 that of the base expressions.
2931 If the union of the cells is a strict subset of the domain
2932 space, then the value of the piecewise expression outside
2933 this union is different for types derived from quasi-affine
2934 expressions and those derived from quasipolynomials.
2935 Piecewise expressions derived from quasi-affine expressions
2936 are considered to be undefined outside the union of their cells.
2937 Piecewise expressions derived from quasipolynomials
2938 are considered to be zero outside the union of their cells.
2940 Piecewise quasipolynomials are mainly used by the C<barvinok>
2941 library for representing the number of elements in a parametric set or map.
2942 For example, the piecewise quasipolynomial
2944 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2946 represents the number of points in the map
2948 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2950 The piecewise expression types defined by C<isl>
2951 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
2952 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
2954 A piecewise expression with no cells can be created using
2955 the following functions.
2957 #include <isl/aff.h>
2958 __isl_give isl_pw_aff *isl_pw_aff_empty(
2959 __isl_take isl_space *space);
2960 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
2961 __isl_take isl_space *space);
2963 A piecewise expression with a single universe cell can be
2964 created using the following functions.
2966 #include <isl/aff.h>
2967 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2968 __isl_take isl_aff *aff);
2969 __isl_give isl_pw_multi_aff *
2970 isl_pw_multi_aff_from_multi_aff(
2971 __isl_take isl_multi_aff *ma);
2973 #include <isl/polynomial.h>
2974 __isl_give isl_pw_qpolynomial *
2975 isl_pw_qpolynomial_from_qpolynomial(
2976 __isl_take isl_qpolynomial *qp);
2978 A piecewise expression with a single specified cell can be
2979 created using the following functions.
2981 #include <isl/aff.h>
2982 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2983 __isl_take isl_set *set, __isl_take isl_aff *aff);
2984 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
2985 __isl_take isl_set *set,
2986 __isl_take isl_multi_aff *maff);
2988 #include <isl/polynomial.h>
2989 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2990 __isl_take isl_set *set,
2991 __isl_take isl_qpolynomial *qp);
2993 The following convenience functions first create a base expression and
2994 then create a piecewise expression over a universe domain.
2996 #include <isl/aff.h>
2997 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
2998 __isl_take isl_local_space *ls);
2999 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3000 __isl_take isl_local_space *ls,
3001 enum isl_dim_type type, unsigned pos);
3002 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
3003 __isl_take isl_local_space *ls);
3004 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
3005 __isl_take isl_space *space);
3006 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3007 __isl_take isl_space *space);
3008 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
3009 __isl_take isl_space *space);
3010 __isl_give isl_pw_multi_aff *
3011 isl_pw_multi_aff_project_out_map(
3012 __isl_take isl_space *space,
3013 enum isl_dim_type type,
3014 unsigned first, unsigned n);
3016 #include <isl/polynomial.h>
3017 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3018 __isl_take isl_space *space);
3020 The following convenience functions first create a base expression and
3021 then create a piecewise expression over a given domain.
3023 #include <isl/aff.h>
3024 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
3025 __isl_take isl_set *domain,
3026 __isl_take isl_val *v);
3027 __isl_give isl_pw_multi_aff *
3028 isl_pw_multi_aff_multi_val_on_domain(
3029 __isl_take isl_set *domain,
3030 __isl_take isl_multi_val *mv);
3032 As a convenience, a piecewise multiple expression can
3033 also be created from a piecewise expression.
3034 Each multiple expression in the result is derived
3035 from the corresponding base expression.
3037 #include <isl/aff.h>
3038 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
3039 __isl_take isl_pw_aff *pa);
3041 Similarly, a piecewise quasipolynomial can be
3042 created from a piecewise quasi-affine expression using
3043 the following function.
3045 #include <isl/polynomial.h>
3046 __isl_give isl_pw_qpolynomial *
3047 isl_pw_qpolynomial_from_pw_aff(
3048 __isl_take isl_pw_aff *pwaff);
3050 Piecewise expressions can be copied and freed using the following functions.
3052 #include <isl/aff.h>
3053 __isl_give isl_pw_aff *isl_pw_aff_copy(
3054 __isl_keep isl_pw_aff *pwaff);
3055 __isl_null isl_pw_aff *isl_pw_aff_free(
3056 __isl_take isl_pw_aff *pwaff);
3057 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3058 __isl_keep isl_pw_multi_aff *pma);
3059 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
3060 __isl_take isl_pw_multi_aff *pma);
3062 #include <isl/polynomial.h>
3063 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3064 __isl_keep isl_pw_qpolynomial *pwqp);
3065 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
3066 __isl_take isl_pw_qpolynomial *pwqp);
3067 __isl_give isl_pw_qpolynomial_fold *
3068 isl_pw_qpolynomial_fold_copy(
3069 __isl_keep isl_pw_qpolynomial_fold *pwf);
3070 __isl_null isl_pw_qpolynomial_fold *
3071 isl_pw_qpolynomial_fold_free(
3072 __isl_take isl_pw_qpolynomial_fold *pwf);
3074 To iterate over the different cells of a piecewise expression,
3075 use the following functions.
3077 #include <isl/aff.h>
3078 isl_bool isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3079 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3080 isl_stat isl_pw_aff_foreach_piece(
3081 __isl_keep isl_pw_aff *pwaff,
3082 isl_stat (*fn)(__isl_take isl_set *set,
3083 __isl_take isl_aff *aff,
3084 void *user), void *user);
3085 int isl_pw_multi_aff_n_piece(
3086 __isl_keep isl_pw_multi_aff *pma);
3087 isl_stat isl_pw_multi_aff_foreach_piece(
3088 __isl_keep isl_pw_multi_aff *pma,
3089 isl_stat (*fn)(__isl_take isl_set *set,
3090 __isl_take isl_multi_aff *maff,
3091 void *user), void *user);
3093 #include <isl/polynomial.h>
3094 int isl_pw_qpolynomial_n_piece(
3095 __isl_keep isl_pw_qpolynomial *pwqp);
3096 isl_stat isl_pw_qpolynomial_foreach_piece(
3097 __isl_keep isl_pw_qpolynomial *pwqp,
3098 isl_stat (*fn)(__isl_take isl_set *set,
3099 __isl_take isl_qpolynomial *qp,
3100 void *user), void *user);
3101 isl_stat isl_pw_qpolynomial_foreach_lifted_piece(
3102 __isl_keep isl_pw_qpolynomial *pwqp,
3103 isl_stat (*fn)(__isl_take isl_set *set,
3104 __isl_take isl_qpolynomial *qp,
3105 void *user), void *user);
3106 int isl_pw_qpolynomial_fold_n_piece(
3107 __isl_keep isl_pw_qpolynomial_fold *pwf);
3108 isl_stat isl_pw_qpolynomial_fold_foreach_piece(
3109 __isl_keep isl_pw_qpolynomial_fold *pwf,
3110 isl_stat (*fn)(__isl_take isl_set *set,
3111 __isl_take isl_qpolynomial_fold *fold,
3112 void *user), void *user);
3113 isl_stat isl_pw_qpolynomial_fold_foreach_lifted_piece(
3114 __isl_keep isl_pw_qpolynomial_fold *pwf,
3115 isl_stat (*fn)(__isl_take isl_set *set,
3116 __isl_take isl_qpolynomial_fold *fold,
3117 void *user), void *user);
3119 As usual, the function C<fn> should return C<0> on success
3120 and C<-1> on failure. The difference between
3121 C<isl_pw_qpolynomial_foreach_piece> and
3122 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3123 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3124 compute unique representations for all existentially quantified
3125 variables and then turn these existentially quantified variables
3126 into extra set variables, adapting the associated quasipolynomial
3127 accordingly. This means that the C<set> passed to C<fn>
3128 will not have any existentially quantified variables, but that
3129 the dimensions of the sets may be different for different
3130 invocations of C<fn>.
3131 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
3132 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
3134 A piecewise expression consisting of the expressions at a given
3135 position of a piecewise multiple expression can be extracted
3136 using the following function.
3138 #include <isl/aff.h>
3139 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3140 __isl_keep isl_pw_multi_aff *pma, int pos);
3142 These expressions can be replaced using the following function.
3144 #include <isl/aff.h>
3145 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3146 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3147 __isl_take isl_pw_aff *pa);
3149 Note that there is a difference between C<isl_multi_pw_aff> and
3150 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
3151 affine expressions, while the second is a piecewise sequence
3152 of affine expressions. In particular, each of the piecewise
3153 affine expressions in an C<isl_multi_pw_aff> may have a different
3154 domain, while all multiple expressions associated to a cell
3155 in an C<isl_pw_multi_aff> have the same domain.
3156 It is possible to convert between the two, but when converting
3157 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
3158 of the result is the intersection of the domains of the input.
3159 The reverse conversion is exact.
3161 #include <isl/aff.h>
3162 __isl_give isl_pw_multi_aff *
3163 isl_pw_multi_aff_from_multi_pw_aff(
3164 __isl_take isl_multi_pw_aff *mpa);
3165 __isl_give isl_multi_pw_aff *
3166 isl_multi_pw_aff_from_pw_multi_aff(
3167 __isl_take isl_pw_multi_aff *pma);
3169 =head3 Union Expressions
3171 A union expression collects base expressions defined
3172 over different domains. The space of a union expression
3173 is that of the shared parameter space.
3175 The union expression types defined by C<isl>
3176 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
3177 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
3179 C<isl_union_pw_aff>,
3180 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>,
3181 there can be at most one base expression for a given domain space.
3183 C<isl_union_pw_multi_aff>,
3184 there can be multiple such expressions for a given domain space,
3185 but the domains of these expressions need to be disjoint.
3187 An empty union expression can be created using the following functions.
3189 #include <isl/aff.h>
3190 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
3191 __isl_take isl_space *space);
3192 __isl_give isl_union_pw_multi_aff *
3193 isl_union_pw_multi_aff_empty(
3194 __isl_take isl_space *space);
3196 #include <isl/polynomial.h>
3197 __isl_give isl_union_pw_qpolynomial *
3198 isl_union_pw_qpolynomial_zero(
3199 __isl_take isl_space *space);
3201 A union expression containing a single base expression
3202 can be created using the following functions.
3204 #include <isl/aff.h>
3205 __isl_give isl_union_pw_aff *
3206 isl_union_pw_aff_from_pw_aff(
3207 __isl_take isl_pw_aff *pa);
3208 __isl_give isl_union_pw_multi_aff *
3209 isl_union_pw_multi_aff_from_aff(
3210 __isl_take isl_aff *aff);
3211 __isl_give isl_union_pw_multi_aff *
3212 isl_union_pw_multi_aff_from_pw_multi_aff(
3213 __isl_take isl_pw_multi_aff *pma);
3215 #include <isl/polynomial.h>
3216 __isl_give isl_union_pw_qpolynomial *
3217 isl_union_pw_qpolynomial_from_pw_qpolynomial(
3218 __isl_take isl_pw_qpolynomial *pwqp);
3220 The following functions create a base expression on each
3221 of the sets in the union set and collect the results.
3223 #include <isl/aff.h>
3224 __isl_give isl_union_pw_multi_aff *
3225 isl_union_pw_multi_aff_from_union_pw_aff(
3226 __isl_take isl_union_pw_aff *upa);
3227 __isl_give isl_union_pw_aff *
3228 isl_union_pw_multi_aff_get_union_pw_aff(
3229 __isl_keep isl_union_pw_multi_aff *upma, int pos);
3230 __isl_give isl_union_pw_aff *
3231 isl_union_pw_aff_val_on_domain(
3232 __isl_take isl_union_set *domain,
3233 __isl_take isl_val *v);
3234 __isl_give isl_union_pw_multi_aff *
3235 isl_union_pw_multi_aff_multi_val_on_domain(
3236 __isl_take isl_union_set *domain,
3237 __isl_take isl_multi_val *mv);
3239 An C<isl_union_pw_aff> that is equal to a (parametric) affine
3240 expression on a given domain can be created using the following
3243 #include <isl/aff.h>
3244 __isl_give isl_union_pw_aff *
3245 isl_union_pw_aff_aff_on_domain(
3246 __isl_take isl_union_set *domain,
3247 __isl_take isl_aff *aff);
3249 A base expression can be added to a union expression using
3250 the following functions.
3252 #include <isl/aff.h>
3253 __isl_give isl_union_pw_aff *
3254 isl_union_pw_aff_add_pw_aff(
3255 __isl_take isl_union_pw_aff *upa,
3256 __isl_take isl_pw_aff *pa);
3257 __isl_give isl_union_pw_multi_aff *
3258 isl_union_pw_multi_aff_add_pw_multi_aff(
3259 __isl_take isl_union_pw_multi_aff *upma,
3260 __isl_take isl_pw_multi_aff *pma);
3262 #include <isl/polynomial.h>
3263 __isl_give isl_union_pw_qpolynomial *
3264 isl_union_pw_qpolynomial_add_pw_qpolynomial(
3265 __isl_take isl_union_pw_qpolynomial *upwqp,
3266 __isl_take isl_pw_qpolynomial *pwqp);
3268 Union expressions can be copied and freed using
3269 the following functions.
3271 #include <isl/aff.h>
3272 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
3273 __isl_keep isl_union_pw_aff *upa);
3274 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
3275 __isl_take isl_union_pw_aff *upa);
3276 __isl_give isl_union_pw_multi_aff *
3277 isl_union_pw_multi_aff_copy(
3278 __isl_keep isl_union_pw_multi_aff *upma);
3279 __isl_null isl_union_pw_multi_aff *
3280 isl_union_pw_multi_aff_free(
3281 __isl_take isl_union_pw_multi_aff *upma);
3283 #include <isl/polynomial.h>
3284 __isl_give isl_union_pw_qpolynomial *
3285 isl_union_pw_qpolynomial_copy(
3286 __isl_keep isl_union_pw_qpolynomial *upwqp);
3287 __isl_null isl_union_pw_qpolynomial *
3288 isl_union_pw_qpolynomial_free(
3289 __isl_take isl_union_pw_qpolynomial *upwqp);
3290 __isl_give isl_union_pw_qpolynomial_fold *
3291 isl_union_pw_qpolynomial_fold_copy(
3292 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3293 __isl_null isl_union_pw_qpolynomial_fold *
3294 isl_union_pw_qpolynomial_fold_free(
3295 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3297 To iterate over the base expressions in a union expression,
3298 use the following functions.
3300 #include <isl/aff.h>
3301 int isl_union_pw_aff_n_pw_aff(
3302 __isl_keep isl_union_pw_aff *upa);
3303 isl_stat isl_union_pw_aff_foreach_pw_aff(
3304 __isl_keep isl_union_pw_aff *upa,
3305 isl_stat (*fn)(__isl_take isl_pw_aff *pa,
3306 void *user), void *user);
3307 int isl_union_pw_multi_aff_n_pw_multi_aff(
3308 __isl_keep isl_union_pw_multi_aff *upma);
3309 isl_stat isl_union_pw_multi_aff_foreach_pw_multi_aff(
3310 __isl_keep isl_union_pw_multi_aff *upma,
3311 isl_stat (*fn)(__isl_take isl_pw_multi_aff *pma,
3312 void *user), void *user);
3314 #include <isl/polynomial.h>
3315 int isl_union_pw_qpolynomial_n_pw_qpolynomial(
3316 __isl_keep isl_union_pw_qpolynomial *upwqp);
3317 isl_stat isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3318 __isl_keep isl_union_pw_qpolynomial *upwqp,
3319 isl_stat (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
3320 void *user), void *user);
3321 int isl_union_pw_qpolynomial_fold_n_pw_qpolynomial_fold(
3322 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3323 isl_stat isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3324 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3325 isl_stat (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3326 void *user), void *user);
3328 To extract the base expression in a given space from a union, use
3329 the following functions.
3331 #include <isl/aff.h>
3332 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
3333 __isl_keep isl_union_pw_aff *upa,
3334 __isl_take isl_space *space);
3335 __isl_give isl_pw_multi_aff *
3336 isl_union_pw_multi_aff_extract_pw_multi_aff(
3337 __isl_keep isl_union_pw_multi_aff *upma,
3338 __isl_take isl_space *space);
3340 #include <isl/polynomial.h>
3341 __isl_give isl_pw_qpolynomial *
3342 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3343 __isl_keep isl_union_pw_qpolynomial *upwqp,
3344 __isl_take isl_space *space);
3346 =head2 Input and Output
3348 For set and relation,
3349 C<isl> supports its own input/output format, which is similar
3350 to the C<Omega> format, but also supports the C<PolyLib> format
3352 For other object types, typically only an C<isl> format is supported.
3354 =head3 C<isl> format
3356 The C<isl> format is similar to that of C<Omega>, but has a different
3357 syntax for describing the parameters and allows for the definition
3358 of an existentially quantified variable as the integer division
3359 of an affine expression.
3360 For example, the set of integers C<i> between C<0> and C<n>
3361 such that C<i % 10 <= 6> can be described as
3363 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
3366 A set or relation can have several disjuncts, separated
3367 by the keyword C<or>. Each disjunct is either a conjunction
3368 of constraints or a projection (C<exists>) of a conjunction
3369 of constraints. The constraints are separated by the keyword
3372 =head3 C<PolyLib> format
3374 If the represented set is a union, then the first line
3375 contains a single number representing the number of disjuncts.
3376 Otherwise, a line containing the number C<1> is optional.
3378 Each disjunct is represented by a matrix of constraints.
3379 The first line contains two numbers representing
3380 the number of rows and columns,
3381 where the number of rows is equal to the number of constraints
3382 and the number of columns is equal to two plus the number of variables.
3383 The following lines contain the actual rows of the constraint matrix.
3384 In each row, the first column indicates whether the constraint
3385 is an equality (C<0>) or inequality (C<1>). The final column
3386 corresponds to the constant term.
3388 If the set is parametric, then the coefficients of the parameters
3389 appear in the last columns before the constant column.
3390 The coefficients of any existentially quantified variables appear
3391 between those of the set variables and those of the parameters.
3393 =head3 Extended C<PolyLib> format
3395 The extended C<PolyLib> format is nearly identical to the
3396 C<PolyLib> format. The only difference is that the line
3397 containing the number of rows and columns of a constraint matrix
3398 also contains four additional numbers:
3399 the number of output dimensions, the number of input dimensions,
3400 the number of local dimensions (i.e., the number of existentially
3401 quantified variables) and the number of parameters.
3402 For sets, the number of ``output'' dimensions is equal
3403 to the number of set dimensions, while the number of ``input''
3408 Objects can be read from input using the following functions.
3410 #include <isl/val.h>
3411 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
3413 __isl_give isl_multi_val *isl_multi_val_read_from_str(
3414 isl_ctx *ctx, const char *str);
3416 #include <isl/set.h>
3417 __isl_give isl_basic_set *isl_basic_set_read_from_file(
3418 isl_ctx *ctx, FILE *input);
3419 __isl_give isl_basic_set *isl_basic_set_read_from_str(
3420 isl_ctx *ctx, const char *str);
3421 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
3423 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
3426 #include <isl/map.h>
3427 __isl_give isl_basic_map *isl_basic_map_read_from_file(
3428 isl_ctx *ctx, FILE *input);
3429 __isl_give isl_basic_map *isl_basic_map_read_from_str(
3430 isl_ctx *ctx, const char *str);
3431 __isl_give isl_map *isl_map_read_from_file(
3432 isl_ctx *ctx, FILE *input);
3433 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
3436 #include <isl/union_set.h>
3437 __isl_give isl_union_set *isl_union_set_read_from_file(
3438 isl_ctx *ctx, FILE *input);
3439 __isl_give isl_union_set *isl_union_set_read_from_str(
3440 isl_ctx *ctx, const char *str);
3442 #include <isl/union_map.h>
3443 __isl_give isl_union_map *isl_union_map_read_from_file(
3444 isl_ctx *ctx, FILE *input);
3445 __isl_give isl_union_map *isl_union_map_read_from_str(
3446 isl_ctx *ctx, const char *str);
3448 #include <isl/aff.h>
3449 __isl_give isl_aff *isl_aff_read_from_str(
3450 isl_ctx *ctx, const char *str);
3451 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3452 isl_ctx *ctx, const char *str);
3453 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3454 isl_ctx *ctx, const char *str);
3455 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3456 isl_ctx *ctx, const char *str);
3457 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
3458 isl_ctx *ctx, const char *str);
3459 __isl_give isl_union_pw_aff *
3460 isl_union_pw_aff_read_from_str(
3461 isl_ctx *ctx, const char *str);
3462 __isl_give isl_union_pw_multi_aff *
3463 isl_union_pw_multi_aff_read_from_str(
3464 isl_ctx *ctx, const char *str);
3465 __isl_give isl_multi_union_pw_aff *
3466 isl_multi_union_pw_aff_read_from_str(
3467 isl_ctx *ctx, const char *str);
3469 #include <isl/polynomial.h>
3470 __isl_give isl_union_pw_qpolynomial *
3471 isl_union_pw_qpolynomial_read_from_str(
3472 isl_ctx *ctx, const char *str);
3474 For sets and relations,
3475 the input format is autodetected and may be either the C<PolyLib> format
3476 or the C<isl> format.
3480 Before anything can be printed, an C<isl_printer> needs to
3483 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
3485 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
3486 __isl_null isl_printer *isl_printer_free(
3487 __isl_take isl_printer *printer);
3489 C<isl_printer_to_file> prints to the given file, while
3490 C<isl_printer_to_str> prints to a string that can be extracted
3491 using the following function.
3493 #include <isl/printer.h>
3494 __isl_give char *isl_printer_get_str(
3495 __isl_keep isl_printer *printer);
3497 The printer can be inspected using the following functions.
3499 FILE *isl_printer_get_file(
3500 __isl_keep isl_printer *printer);
3501 int isl_printer_get_output_format(
3502 __isl_keep isl_printer *p);
3503 int isl_printer_get_yaml_style(__isl_keep isl_printer *p);
3505 The behavior of the printer can be modified in various ways
3507 __isl_give isl_printer *isl_printer_set_output_format(
3508 __isl_take isl_printer *p, int output_format);
3509 __isl_give isl_printer *isl_printer_set_indent(
3510 __isl_take isl_printer *p, int indent);
3511 __isl_give isl_printer *isl_printer_set_indent_prefix(
3512 __isl_take isl_printer *p, const char *prefix);
3513 __isl_give isl_printer *isl_printer_indent(
3514 __isl_take isl_printer *p, int indent);
3515 __isl_give isl_printer *isl_printer_set_prefix(
3516 __isl_take isl_printer *p, const char *prefix);
3517 __isl_give isl_printer *isl_printer_set_suffix(
3518 __isl_take isl_printer *p, const char *suffix);
3519 __isl_give isl_printer *isl_printer_set_yaml_style(
3520 __isl_take isl_printer *p, int yaml_style);
3522 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
3523 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
3524 and defaults to C<ISL_FORMAT_ISL>.
3525 Each line in the output is prefixed by C<indent_prefix>,
3526 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
3527 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
3528 In the C<PolyLib> format output,
3529 the coefficients of the existentially quantified variables
3530 appear between those of the set variables and those
3532 The function C<isl_printer_indent> increases the indentation
3533 by the specified amount (which may be negative).
3534 The YAML style may be either C<ISL_YAML_STYLE_BLOCK> or
3535 C<ISL_YAML_STYLE_FLOW> and when we are printing something
3538 To actually print something, use
3540 #include <isl/printer.h>
3541 __isl_give isl_printer *isl_printer_print_double(
3542 __isl_take isl_printer *p, double d);
3544 #include <isl/val.h>
3545 __isl_give isl_printer *isl_printer_print_val(
3546 __isl_take isl_printer *p, __isl_keep isl_val *v);
3548 #include <isl/set.h>
3549 __isl_give isl_printer *isl_printer_print_basic_set(
3550 __isl_take isl_printer *printer,
3551 __isl_keep isl_basic_set *bset);
3552 __isl_give isl_printer *isl_printer_print_set(
3553 __isl_take isl_printer *printer,
3554 __isl_keep isl_set *set);
3556 #include <isl/map.h>
3557 __isl_give isl_printer *isl_printer_print_basic_map(
3558 __isl_take isl_printer *printer,
3559 __isl_keep isl_basic_map *bmap);
3560 __isl_give isl_printer *isl_printer_print_map(
3561 __isl_take isl_printer *printer,
3562 __isl_keep isl_map *map);
3564 #include <isl/union_set.h>
3565 __isl_give isl_printer *isl_printer_print_union_set(
3566 __isl_take isl_printer *p,
3567 __isl_keep isl_union_set *uset);
3569 #include <isl/union_map.h>
3570 __isl_give isl_printer *isl_printer_print_union_map(
3571 __isl_take isl_printer *p,
3572 __isl_keep isl_union_map *umap);
3574 #include <isl/val.h>
3575 __isl_give isl_printer *isl_printer_print_multi_val(
3576 __isl_take isl_printer *p,
3577 __isl_keep isl_multi_val *mv);
3579 #include <isl/aff.h>
3580 __isl_give isl_printer *isl_printer_print_aff(
3581 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3582 __isl_give isl_printer *isl_printer_print_multi_aff(
3583 __isl_take isl_printer *p,
3584 __isl_keep isl_multi_aff *maff);
3585 __isl_give isl_printer *isl_printer_print_pw_aff(
3586 __isl_take isl_printer *p,
3587 __isl_keep isl_pw_aff *pwaff);
3588 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3589 __isl_take isl_printer *p,
3590 __isl_keep isl_pw_multi_aff *pma);
3591 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3592 __isl_take isl_printer *p,
3593 __isl_keep isl_multi_pw_aff *mpa);
3594 __isl_give isl_printer *isl_printer_print_union_pw_aff(
3595 __isl_take isl_printer *p,
3596 __isl_keep isl_union_pw_aff *upa);
3597 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3598 __isl_take isl_printer *p,
3599 __isl_keep isl_union_pw_multi_aff *upma);
3600 __isl_give isl_printer *
3601 isl_printer_print_multi_union_pw_aff(
3602 __isl_take isl_printer *p,
3603 __isl_keep isl_multi_union_pw_aff *mupa);
3605 #include <isl/polynomial.h>
3606 __isl_give isl_printer *isl_printer_print_qpolynomial(
3607 __isl_take isl_printer *p,
3608 __isl_keep isl_qpolynomial *qp);
3609 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3610 __isl_take isl_printer *p,
3611 __isl_keep isl_pw_qpolynomial *pwqp);
3612 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3613 __isl_take isl_printer *p,
3614 __isl_keep isl_union_pw_qpolynomial *upwqp);
3616 __isl_give isl_printer *
3617 isl_printer_print_pw_qpolynomial_fold(
3618 __isl_take isl_printer *p,
3619 __isl_keep isl_pw_qpolynomial_fold *pwf);
3620 __isl_give isl_printer *
3621 isl_printer_print_union_pw_qpolynomial_fold(
3622 __isl_take isl_printer *p,
3623 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3625 For C<isl_printer_print_qpolynomial>,
3626 C<isl_printer_print_pw_qpolynomial> and
3627 C<isl_printer_print_pw_qpolynomial_fold>,
3628 the output format of the printer
3629 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3630 For C<isl_printer_print_union_pw_qpolynomial> and
3631 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
3633 In case of printing in C<ISL_FORMAT_C>, the user may want
3634 to set the names of all dimensions first.
3636 C<isl> also provides limited support for printing YAML documents,
3637 just enough for the internal use for printing such documents.
3639 #include <isl/printer.h>
3640 __isl_give isl_printer *isl_printer_yaml_start_mapping(
3641 __isl_take isl_printer *p);
3642 __isl_give isl_printer *isl_printer_yaml_end_mapping(
3643 __isl_take isl_printer *p);
3644 __isl_give isl_printer *isl_printer_yaml_start_sequence(
3645 __isl_take isl_printer *p);
3646 __isl_give isl_printer *isl_printer_yaml_end_sequence(
3647 __isl_take isl_printer *p);
3648 __isl_give isl_printer *isl_printer_yaml_next(
3649 __isl_take isl_printer *p);
3651 A document is started by a call to either
3652 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3653 Anything printed to the printer after such a call belong to the
3654 first key of the mapping or the first element in the sequence.
3655 The function C<isl_printer_yaml_next> moves to the value if
3656 we are currently printing a mapping key, the next key if we
3657 are printing a value or the next element if we are printing
3658 an element in a sequence.
3659 Nested mappings and sequences are initiated by the same
3660 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3661 Each call to these functions needs to have a corresponding call to
3662 C<isl_printer_yaml_end_mapping> or C<isl_printer_yaml_end_sequence>.
3664 When called on a file printer, the following function flushes
3665 the file. When called on a string printer, the buffer is cleared.
3667 __isl_give isl_printer *isl_printer_flush(
3668 __isl_take isl_printer *p);
3670 The following functions allow the user to attach
3671 notes to a printer in order to keep track of additional state.
3673 #include <isl/printer.h>
3674 isl_bool isl_printer_has_note(__isl_keep isl_printer *p,
3675 __isl_keep isl_id *id);
3676 __isl_give isl_id *isl_printer_get_note(
3677 __isl_keep isl_printer *p, __isl_take isl_id *id);
3678 __isl_give isl_printer *isl_printer_set_note(
3679 __isl_take isl_printer *p,
3680 __isl_take isl_id *id, __isl_take isl_id *note);
3682 C<isl_printer_set_note> associates the given note to the given
3683 identifier in the printer.
3684 C<isl_printer_get_note> retrieves a note associated to an
3686 C<isl_printer_has_note> checks if there is such a note.
3687 C<isl_printer_get_note> fails if the requested note does not exist.
3689 Alternatively, a string representation can be obtained
3690 directly using the following functions, which always print
3694 __isl_give char *isl_id_to_str(
3695 __isl_keep isl_id *id);
3697 #include <isl/space.h>
3698 __isl_give char *isl_space_to_str(
3699 __isl_keep isl_space *space);
3701 #include <isl/val.h>
3702 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
3703 __isl_give char *isl_multi_val_to_str(
3704 __isl_keep isl_multi_val *mv);
3706 #include <isl/set.h>
3707 __isl_give char *isl_basic_set_to_str(
3708 __isl_keep isl_basic_set *bset);
3709 __isl_give char *isl_set_to_str(
3710 __isl_keep isl_set *set);
3712 #include <isl/union_set.h>
3713 __isl_give char *isl_union_set_to_str(
3714 __isl_keep isl_union_set *uset);
3716 #include <isl/map.h>
3717 __isl_give char *isl_basic_map_to_str(
3718 __isl_keep isl_basic_map *bmap);
3719 __isl_give char *isl_map_to_str(
3720 __isl_keep isl_map *map);
3722 #include <isl/union_map.h>
3723 __isl_give char *isl_union_map_to_str(
3724 __isl_keep isl_union_map *umap);
3726 #include <isl/aff.h>
3727 __isl_give char *isl_aff_to_str(__isl_keep isl_aff *aff);
3728 __isl_give char *isl_pw_aff_to_str(
3729 __isl_keep isl_pw_aff *pa);
3730 __isl_give char *isl_multi_aff_to_str(
3731 __isl_keep isl_multi_aff *ma);
3732 __isl_give char *isl_pw_multi_aff_to_str(
3733 __isl_keep isl_pw_multi_aff *pma);
3734 __isl_give char *isl_multi_pw_aff_to_str(
3735 __isl_keep isl_multi_pw_aff *mpa);
3736 __isl_give char *isl_union_pw_aff_to_str(
3737 __isl_keep isl_union_pw_aff *upa);
3738 __isl_give char *isl_union_pw_multi_aff_to_str(
3739 __isl_keep isl_union_pw_multi_aff *upma);
3740 __isl_give char *isl_multi_union_pw_aff_to_str(
3741 __isl_keep isl_multi_union_pw_aff *mupa);
3743 #include <isl/point.h>
3744 __isl_give char *isl_point_to_str(
3745 __isl_keep isl_point *pnt);
3747 #include <isl/polynomial.h>
3748 __isl_give char *isl_pw_qpolynomial_to_str(
3749 __isl_keep isl_pw_qpolynomial *pwqp);
3750 __isl_give char *isl_union_pw_qpolynomial_to_str(
3751 __isl_keep isl_union_pw_qpolynomial *upwqp);
3755 =head3 Unary Properties
3761 The following functions test whether the given set or relation
3762 contains any integer points. The ``plain'' variants do not perform
3763 any computations, but simply check if the given set or relation
3764 is already known to be empty.
3766 isl_bool isl_basic_set_plain_is_empty(
3767 __isl_keep isl_basic_set *bset);
3768 isl_bool isl_basic_set_is_empty(
3769 __isl_keep isl_basic_set *bset);
3770 isl_bool isl_set_plain_is_empty(
3771 __isl_keep isl_set *set);
3772 isl_bool isl_set_is_empty(__isl_keep isl_set *set);
3773 isl_bool isl_union_set_is_empty(
3774 __isl_keep isl_union_set *uset);
3775 isl_bool isl_basic_map_plain_is_empty(
3776 __isl_keep isl_basic_map *bmap);
3777 isl_bool isl_basic_map_is_empty(
3778 __isl_keep isl_basic_map *bmap);
3779 isl_bool isl_map_plain_is_empty(
3780 __isl_keep isl_map *map);
3781 isl_bool isl_map_is_empty(__isl_keep isl_map *map);
3782 isl_bool isl_union_map_is_empty(
3783 __isl_keep isl_union_map *umap);
3785 =item * Universality
3787 isl_bool isl_basic_set_plain_is_universe(
3788 __isl_keep isl_basic_set *bset);
3789 isl_bool isl_basic_set_is_universe(
3790 __isl_keep isl_basic_set *bset);
3791 isl_bool isl_basic_map_plain_is_universe(
3792 __isl_keep isl_basic_map *bmap);
3793 isl_bool isl_basic_map_is_universe(
3794 __isl_keep isl_basic_map *bmap);
3795 isl_bool isl_set_plain_is_universe(
3796 __isl_keep isl_set *set);
3797 isl_bool isl_map_plain_is_universe(
3798 __isl_keep isl_map *map);
3800 =item * Single-valuedness
3802 #include <isl/set.h>
3803 isl_bool isl_set_is_singleton(__isl_keep isl_set *set);
3805 #include <isl/map.h>
3806 isl_bool isl_basic_map_is_single_valued(
3807 __isl_keep isl_basic_map *bmap);
3808 isl_bool isl_map_plain_is_single_valued(
3809 __isl_keep isl_map *map);
3810 isl_bool isl_map_is_single_valued(__isl_keep isl_map *map);
3812 #include <isl/union_map.h>
3813 isl_bool isl_union_map_is_single_valued(
3814 __isl_keep isl_union_map *umap);
3818 isl_bool isl_map_plain_is_injective(
3819 __isl_keep isl_map *map);
3820 isl_bool isl_map_is_injective(
3821 __isl_keep isl_map *map);
3822 isl_bool isl_union_map_plain_is_injective(
3823 __isl_keep isl_union_map *umap);
3824 isl_bool isl_union_map_is_injective(
3825 __isl_keep isl_union_map *umap);
3829 isl_bool isl_map_is_bijective(
3830 __isl_keep isl_map *map);
3831 isl_bool isl_union_map_is_bijective(
3832 __isl_keep isl_union_map *umap);
3836 The following functions test whether the given relation
3837 only maps elements to themselves.
3839 #include <isl/map.h>
3840 isl_bool isl_map_is_identity(
3841 __isl_keep isl_map *map);
3843 #include <isl/union_map.h>
3844 isl_bool isl_union_map_is_identity(
3845 __isl_keep isl_union_map *umap);
3849 __isl_give isl_val *
3850 isl_basic_map_plain_get_val_if_fixed(
3851 __isl_keep isl_basic_map *bmap,
3852 enum isl_dim_type type, unsigned pos);
3853 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
3854 __isl_keep isl_set *set,
3855 enum isl_dim_type type, unsigned pos);
3856 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
3857 __isl_keep isl_map *map,
3858 enum isl_dim_type type, unsigned pos);
3860 If the set or relation obviously lies on a hyperplane where the given dimension
3861 has a fixed value, then return that value.
3862 Otherwise return NaN.
3866 isl_stat isl_set_dim_residue_class_val(
3867 __isl_keep isl_set *set,
3868 int pos, __isl_give isl_val **modulo,
3869 __isl_give isl_val **residue);
3871 Check if the values of the given set dimension are equal to a fixed
3872 value modulo some integer value. If so, assign the modulo to C<*modulo>
3873 and the fixed value to C<*residue>. If the given dimension attains only
3874 a single value, then assign C<0> to C<*modulo> and the fixed value to
3876 If the dimension does not attain only a single value and if no modulo
3877 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
3881 To check whether the description of a set, relation or function depends
3882 on one or more given dimensions,
3883 the following functions can be used.
3885 #include <isl/constraint.h>
3886 isl_bool isl_constraint_involves_dims(
3887 __isl_keep isl_constraint *constraint,
3888 enum isl_dim_type type, unsigned first, unsigned n);
3890 #include <isl/set.h>
3891 isl_bool isl_basic_set_involves_dims(
3892 __isl_keep isl_basic_set *bset,
3893 enum isl_dim_type type, unsigned first, unsigned n);
3894 isl_bool isl_set_involves_dims(__isl_keep isl_set *set,
3895 enum isl_dim_type type, unsigned first, unsigned n);
3897 #include <isl/map.h>
3898 isl_bool isl_basic_map_involves_dims(
3899 __isl_keep isl_basic_map *bmap,
3900 enum isl_dim_type type, unsigned first, unsigned n);
3901 isl_bool isl_map_involves_dims(__isl_keep isl_map *map,
3902 enum isl_dim_type type, unsigned first, unsigned n);
3904 #include <isl/union_map.h>
3905 isl_bool isl_union_map_involves_dims(
3906 __isl_keep isl_union_map *umap,
3907 enum isl_dim_type type, unsigned first, unsigned n);
3909 #include <isl/aff.h>
3910 isl_bool isl_aff_involves_dims(__isl_keep isl_aff *aff,
3911 enum isl_dim_type type, unsigned first, unsigned n);
3912 isl_bool isl_pw_aff_involves_dims(
3913 __isl_keep isl_pw_aff *pwaff,
3914 enum isl_dim_type type, unsigned first, unsigned n);
3915 isl_bool isl_multi_aff_involves_dims(
3916 __isl_keep isl_multi_aff *ma,
3917 enum isl_dim_type type, unsigned first, unsigned n);
3918 isl_bool isl_multi_pw_aff_involves_dims(
3919 __isl_keep isl_multi_pw_aff *mpa,
3920 enum isl_dim_type type, unsigned first, unsigned n);
3922 #include <isl/polynomial.h>
3923 isl_bool isl_qpolynomial_involves_dims(
3924 __isl_keep isl_qpolynomial *qp,
3925 enum isl_dim_type type, unsigned first, unsigned n);
3927 Similarly, the following functions can be used to check whether
3928 a given dimension is involved in any lower or upper bound.
3930 #include <isl/set.h>
3931 isl_bool isl_set_dim_has_any_lower_bound(
3932 __isl_keep isl_set *set,
3933 enum isl_dim_type type, unsigned pos);
3934 isl_bool isl_set_dim_has_any_upper_bound(
3935 __isl_keep isl_set *set,
3936 enum isl_dim_type type, unsigned pos);
3938 Note that these functions return true even if there is a bound on
3939 the dimension on only some of the basic sets of C<set>.
3940 To check if they have a bound for all of the basic sets in C<set>,
3941 use the following functions instead.
3943 #include <isl/set.h>
3944 isl_bool isl_set_dim_has_lower_bound(
3945 __isl_keep isl_set *set,
3946 enum isl_dim_type type, unsigned pos);
3947 isl_bool isl_set_dim_has_upper_bound(
3948 __isl_keep isl_set *set,
3949 enum isl_dim_type type, unsigned pos);
3953 To check whether a set is a parameter domain, use this function:
3955 isl_bool isl_set_is_params(__isl_keep isl_set *set);
3956 isl_bool isl_union_set_is_params(
3957 __isl_keep isl_union_set *uset);
3961 The following functions check whether the space of the given
3962 (basic) set or relation range is a wrapped relation.
3964 #include <isl/space.h>
3965 isl_bool isl_space_is_wrapping(
3966 __isl_keep isl_space *space);
3967 isl_bool isl_space_domain_is_wrapping(
3968 __isl_keep isl_space *space);
3969 isl_bool isl_space_range_is_wrapping(
3970 __isl_keep isl_space *space);
3972 #include <isl/set.h>
3973 isl_bool isl_basic_set_is_wrapping(
3974 __isl_keep isl_basic_set *bset);
3975 isl_bool isl_set_is_wrapping(__isl_keep isl_set *set);
3977 #include <isl/map.h>
3978 isl_bool isl_map_domain_is_wrapping(
3979 __isl_keep isl_map *map);
3980 isl_bool isl_map_range_is_wrapping(
3981 __isl_keep isl_map *map);
3983 #include <isl/val.h>
3984 isl_bool isl_multi_val_range_is_wrapping(
3985 __isl_keep isl_multi_val *mv);
3987 #include <isl/aff.h>
3988 isl_bool isl_multi_aff_range_is_wrapping(
3989 __isl_keep isl_multi_aff *ma);
3990 isl_bool isl_multi_pw_aff_range_is_wrapping(
3991 __isl_keep isl_multi_pw_aff *mpa);
3992 isl_bool isl_multi_union_pw_aff_range_is_wrapping(
3993 __isl_keep isl_multi_union_pw_aff *mupa);
3995 The input to C<isl_space_is_wrapping> should
3996 be the space of a set, while that of
3997 C<isl_space_domain_is_wrapping> and
3998 C<isl_space_range_is_wrapping> should be the space of a relation.
4000 =item * Internal Product
4002 isl_bool isl_basic_map_can_zip(
4003 __isl_keep isl_basic_map *bmap);
4004 isl_bool isl_map_can_zip(__isl_keep isl_map *map);
4006 Check whether the product of domain and range of the given relation
4008 i.e., whether both domain and range are nested relations.
4012 #include <isl/space.h>
4013 isl_bool isl_space_can_curry(
4014 __isl_keep isl_space *space);
4016 #include <isl/map.h>
4017 isl_bool isl_basic_map_can_curry(
4018 __isl_keep isl_basic_map *bmap);
4019 isl_bool isl_map_can_curry(__isl_keep isl_map *map);
4021 Check whether the domain of the (basic) relation is a wrapped relation.
4023 #include <isl/space.h>
4024 __isl_give isl_space *isl_space_uncurry(
4025 __isl_take isl_space *space);
4027 #include <isl/map.h>
4028 isl_bool isl_basic_map_can_uncurry(
4029 __isl_keep isl_basic_map *bmap);
4030 isl_bool isl_map_can_uncurry(__isl_keep isl_map *map);
4032 Check whether the range of the (basic) relation is a wrapped relation.
4034 #include <isl/space.h>
4035 isl_bool isl_space_can_range_curry(
4036 __isl_keep isl_space *space);
4038 #include <isl/map.h>
4039 isl_bool isl_map_can_range_curry(
4040 __isl_keep isl_map *map);
4042 Check whether the domain of the relation wrapped in the range of
4043 the input is itself a wrapped relation.
4045 =item * Special Values
4047 #include <isl/aff.h>
4048 isl_bool isl_aff_is_cst(__isl_keep isl_aff *aff);
4049 isl_bool isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
4050 isl_bool isl_multi_pw_aff_is_cst(
4051 __isl_keep isl_multi_pw_aff *mpa);
4053 Check whether the given expression is a constant.
4055 #include <isl/val.h>
4056 isl_bool isl_multi_val_involves_nan(
4057 __isl_keep isl_multi_val *mv);
4059 #include <isl/aff.h>
4060 isl_bool isl_aff_is_nan(__isl_keep isl_aff *aff);
4061 isl_bool isl_multi_aff_involves_nan(
4062 __isl_keep isl_multi_aff *ma);
4063 isl_bool isl_pw_aff_involves_nan(
4064 __isl_keep isl_pw_aff *pa);
4065 isl_bool isl_pw_multi_aff_involves_nan(
4066 __isl_keep isl_pw_multi_aff *pma);
4067 isl_bool isl_multi_pw_aff_involves_nan(
4068 __isl_keep isl_multi_pw_aff *mpa);
4069 isl_bool isl_union_pw_aff_involves_nan(
4070 __isl_keep isl_union_pw_aff *upa);
4071 isl_bool isl_union_pw_multi_aff_involves_nan(
4072 __isl_keep isl_union_pw_multi_aff *upma);
4073 isl_bool isl_multi_union_pw_aff_involves_nan(
4074 __isl_keep isl_multi_union_pw_aff *mupa);
4076 #include <isl/polynomial.h>
4077 isl_bool isl_qpolynomial_is_nan(
4078 __isl_keep isl_qpolynomial *qp);
4079 isl_bool isl_qpolynomial_fold_is_nan(
4080 __isl_keep isl_qpolynomial_fold *fold);
4081 isl_bool isl_pw_qpolynomial_involves_nan(
4082 __isl_keep isl_pw_qpolynomial *pwqp);
4083 isl_bool isl_pw_qpolynomial_fold_involves_nan(
4084 __isl_keep isl_pw_qpolynomial_fold *pwf);
4085 isl_bool isl_union_pw_qpolynomial_involves_nan(
4086 __isl_keep isl_union_pw_qpolynomial *upwqp);
4087 isl_bool isl_union_pw_qpolynomial_fold_involves_nan(
4088 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4090 Check whether the given expression is equal to or involves NaN.
4092 #include <isl/aff.h>
4093 isl_bool isl_aff_plain_is_zero(
4094 __isl_keep isl_aff *aff);
4096 Check whether the affine expression is obviously zero.
4100 =head3 Binary Properties
4106 The following functions check whether two objects
4107 represent the same set, relation or function.
4108 The C<plain> variants only return true if the objects
4109 are obviously the same. That is, they may return false
4110 even if the objects are the same, but they will never
4111 return true if the objects are not the same.
4113 #include <isl/set.h>
4114 isl_bool isl_basic_set_plain_is_equal(
4115 __isl_keep isl_basic_set *bset1,
4116 __isl_keep isl_basic_set *bset2);
4117 isl_bool isl_basic_set_is_equal(
4118 __isl_keep isl_basic_set *bset1,
4119 __isl_keep isl_basic_set *bset2);
4120 isl_bool isl_set_plain_is_equal(
4121 __isl_keep isl_set *set1,
4122 __isl_keep isl_set *set2);
4123 isl_bool isl_set_is_equal(__isl_keep isl_set *set1,
4124 __isl_keep isl_set *set2);
4126 #include <isl/map.h>
4127 isl_bool isl_basic_map_is_equal(
4128 __isl_keep isl_basic_map *bmap1,
4129 __isl_keep isl_basic_map *bmap2);
4130 isl_bool isl_map_is_equal(__isl_keep isl_map *map1,
4131 __isl_keep isl_map *map2);
4132 isl_bool isl_map_plain_is_equal(
4133 __isl_keep isl_map *map1,
4134 __isl_keep isl_map *map2);
4136 #include <isl/union_set.h>
4137 isl_bool isl_union_set_is_equal(
4138 __isl_keep isl_union_set *uset1,
4139 __isl_keep isl_union_set *uset2);
4141 #include <isl/union_map.h>
4142 isl_bool isl_union_map_is_equal(
4143 __isl_keep isl_union_map *umap1,
4144 __isl_keep isl_union_map *umap2);
4146 #include <isl/aff.h>
4147 isl_bool isl_aff_plain_is_equal(
4148 __isl_keep isl_aff *aff1,
4149 __isl_keep isl_aff *aff2);
4150 isl_bool isl_multi_aff_plain_is_equal(
4151 __isl_keep isl_multi_aff *maff1,
4152 __isl_keep isl_multi_aff *maff2);
4153 isl_bool isl_pw_aff_plain_is_equal(
4154 __isl_keep isl_pw_aff *pwaff1,
4155 __isl_keep isl_pw_aff *pwaff2);
4156 isl_bool isl_pw_aff_is_equal(
4157 __isl_keep isl_pw_aff *pa1,
4158 __isl_keep isl_pw_aff *pa2);
4159 isl_bool isl_pw_multi_aff_plain_is_equal(
4160 __isl_keep isl_pw_multi_aff *pma1,
4161 __isl_keep isl_pw_multi_aff *pma2);
4162 isl_bool isl_pw_multi_aff_is_equal(
4163 __isl_keep isl_pw_multi_aff *pma1,
4164 __isl_keep isl_pw_multi_aff *pma2);
4165 isl_bool isl_multi_pw_aff_plain_is_equal(
4166 __isl_keep isl_multi_pw_aff *mpa1,
4167 __isl_keep isl_multi_pw_aff *mpa2);
4168 isl_bool isl_multi_pw_aff_is_equal(
4169 __isl_keep isl_multi_pw_aff *mpa1,
4170 __isl_keep isl_multi_pw_aff *mpa2);
4171 isl_bool isl_union_pw_aff_plain_is_equal(
4172 __isl_keep isl_union_pw_aff *upa1,
4173 __isl_keep isl_union_pw_aff *upa2);
4174 isl_bool isl_union_pw_multi_aff_plain_is_equal(
4175 __isl_keep isl_union_pw_multi_aff *upma1,
4176 __isl_keep isl_union_pw_multi_aff *upma2);
4177 isl_bool isl_multi_union_pw_aff_plain_is_equal(
4178 __isl_keep isl_multi_union_pw_aff *mupa1,
4179 __isl_keep isl_multi_union_pw_aff *mupa2);
4181 #include <isl/polynomial.h>
4182 isl_bool isl_union_pw_qpolynomial_plain_is_equal(
4183 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4184 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4185 isl_bool isl_union_pw_qpolynomial_fold_plain_is_equal(
4186 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4187 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4189 =item * Disjointness
4191 #include <isl/set.h>
4192 isl_bool isl_basic_set_is_disjoint(
4193 __isl_keep isl_basic_set *bset1,
4194 __isl_keep isl_basic_set *bset2);
4195 isl_bool isl_set_plain_is_disjoint(
4196 __isl_keep isl_set *set1,
4197 __isl_keep isl_set *set2);
4198 isl_bool isl_set_is_disjoint(__isl_keep isl_set *set1,
4199 __isl_keep isl_set *set2);
4201 #include <isl/map.h>
4202 isl_bool isl_basic_map_is_disjoint(
4203 __isl_keep isl_basic_map *bmap1,
4204 __isl_keep isl_basic_map *bmap2);
4205 isl_bool isl_map_is_disjoint(__isl_keep isl_map *map1,
4206 __isl_keep isl_map *map2);
4208 #include <isl/union_set.h>
4209 isl_bool isl_union_set_is_disjoint(
4210 __isl_keep isl_union_set *uset1,
4211 __isl_keep isl_union_set *uset2);
4213 #include <isl/union_map.h>
4214 isl_bool isl_union_map_is_disjoint(
4215 __isl_keep isl_union_map *umap1,
4216 __isl_keep isl_union_map *umap2);
4220 isl_bool isl_basic_set_is_subset(
4221 __isl_keep isl_basic_set *bset1,
4222 __isl_keep isl_basic_set *bset2);
4223 isl_bool isl_set_is_subset(__isl_keep isl_set *set1,
4224 __isl_keep isl_set *set2);
4225 isl_bool isl_set_is_strict_subset(
4226 __isl_keep isl_set *set1,
4227 __isl_keep isl_set *set2);
4228 isl_bool isl_union_set_is_subset(
4229 __isl_keep isl_union_set *uset1,
4230 __isl_keep isl_union_set *uset2);
4231 isl_bool isl_union_set_is_strict_subset(
4232 __isl_keep isl_union_set *uset1,
4233 __isl_keep isl_union_set *uset2);
4234 isl_bool isl_basic_map_is_subset(
4235 __isl_keep isl_basic_map *bmap1,
4236 __isl_keep isl_basic_map *bmap2);
4237 isl_bool isl_basic_map_is_strict_subset(
4238 __isl_keep isl_basic_map *bmap1,
4239 __isl_keep isl_basic_map *bmap2);
4240 isl_bool isl_map_is_subset(
4241 __isl_keep isl_map *map1,
4242 __isl_keep isl_map *map2);
4243 isl_bool isl_map_is_strict_subset(
4244 __isl_keep isl_map *map1,
4245 __isl_keep isl_map *map2);
4246 isl_bool isl_union_map_is_subset(
4247 __isl_keep isl_union_map *umap1,
4248 __isl_keep isl_union_map *umap2);
4249 isl_bool isl_union_map_is_strict_subset(
4250 __isl_keep isl_union_map *umap1,
4251 __isl_keep isl_union_map *umap2);
4253 Check whether the first argument is a (strict) subset of the
4258 Every comparison function returns a negative value if the first
4259 argument is considered smaller than the second, a positive value
4260 if the first argument is considered greater and zero if the two
4261 constraints are considered the same by the comparison criterion.
4263 #include <isl/constraint.h>
4264 int isl_constraint_plain_cmp(
4265 __isl_keep isl_constraint *c1,
4266 __isl_keep isl_constraint *c2);
4268 This function is useful for sorting C<isl_constraint>s.
4269 The order depends on the internal representation of the inputs.
4270 The order is fixed over different calls to the function (assuming
4271 the internal representation of the inputs has not changed), but may
4272 change over different versions of C<isl>.
4274 #include <isl/constraint.h>
4275 int isl_constraint_cmp_last_non_zero(
4276 __isl_keep isl_constraint *c1,
4277 __isl_keep isl_constraint *c2);
4279 This function can be used to sort constraints that live in the same
4280 local space. Constraints that involve ``earlier'' dimensions or
4281 that have a smaller coefficient for the shared latest dimension
4282 are considered smaller than other constraints.
4283 This function only defines a B<partial> order.
4285 #include <isl/set.h>
4286 int isl_set_plain_cmp(__isl_keep isl_set *set1,
4287 __isl_keep isl_set *set2);
4289 This function is useful for sorting C<isl_set>s.
4290 The order depends on the internal representation of the inputs.
4291 The order is fixed over different calls to the function (assuming
4292 the internal representation of the inputs has not changed), but may
4293 change over different versions of C<isl>.
4295 #include <isl/aff.h>
4296 int isl_multi_aff_plain_cmp(
4297 __isl_keep isl_multi_aff *ma1,
4298 __isl_keep isl_multi_aff *ma2);
4299 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4300 __isl_keep isl_pw_aff *pa2);
4302 The functions C<isl_multi_aff_plain_cmp> and
4303 C<isl_pw_aff_plain_cmp> can be used to sort C<isl_multi_aff>s and
4304 C<isl_pw_aff>s. The order is not strictly defined.
4305 The current order sorts expressions that only involve
4306 earlier dimensions before those that involve later dimensions.
4310 =head2 Unary Operations
4316 __isl_give isl_set *isl_set_complement(
4317 __isl_take isl_set *set);
4318 __isl_give isl_map *isl_map_complement(
4319 __isl_take isl_map *map);
4323 #include <isl/space.h>
4324 __isl_give isl_space *isl_space_reverse(
4325 __isl_take isl_space *space);
4327 #include <isl/map.h>
4328 __isl_give isl_basic_map *isl_basic_map_reverse(
4329 __isl_take isl_basic_map *bmap);
4330 __isl_give isl_map *isl_map_reverse(
4331 __isl_take isl_map *map);
4333 #include <isl/union_map.h>
4334 __isl_give isl_union_map *isl_union_map_reverse(
4335 __isl_take isl_union_map *umap);
4339 #include <isl/space.h>
4340 __isl_give isl_space *isl_space_domain(
4341 __isl_take isl_space *space);
4342 __isl_give isl_space *isl_space_range(
4343 __isl_take isl_space *space);
4344 __isl_give isl_space *isl_space_params(
4345 __isl_take isl_space *space);
4347 #include <isl/local_space.h>
4348 __isl_give isl_local_space *isl_local_space_domain(
4349 __isl_take isl_local_space *ls);
4350 __isl_give isl_local_space *isl_local_space_range(
4351 __isl_take isl_local_space *ls);
4353 #include <isl/set.h>
4354 __isl_give isl_basic_set *isl_basic_set_project_out(
4355 __isl_take isl_basic_set *bset,
4356 enum isl_dim_type type, unsigned first, unsigned n);
4357 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
4358 enum isl_dim_type type, unsigned first, unsigned n);
4359 __isl_give isl_map *isl_set_project_onto_map(
4360 __isl_take isl_set *set,
4361 enum isl_dim_type type, unsigned first,
4363 __isl_give isl_basic_set *isl_basic_set_params(
4364 __isl_take isl_basic_set *bset);
4365 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
4367 The function C<isl_set_project_onto_map> returns a relation
4368 that projects the input set onto the given set dimensions.
4370 #include <isl/map.h>
4371 __isl_give isl_basic_map *isl_basic_map_project_out(
4372 __isl_take isl_basic_map *bmap,
4373 enum isl_dim_type type, unsigned first, unsigned n);
4374 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
4375 enum isl_dim_type type, unsigned first, unsigned n);
4376 __isl_give isl_basic_set *isl_basic_map_domain(
4377 __isl_take isl_basic_map *bmap);
4378 __isl_give isl_basic_set *isl_basic_map_range(
4379 __isl_take isl_basic_map *bmap);
4380 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
4381 __isl_give isl_set *isl_map_domain(
4382 __isl_take isl_map *bmap);
4383 __isl_give isl_set *isl_map_range(
4384 __isl_take isl_map *map);
4386 #include <isl/union_set.h>
4387 __isl_give isl_union_set *isl_union_set_project_out(
4388 __isl_take isl_union_set *uset,
4389 enum isl_dim_type type,
4390 unsigned first, unsigned n);
4391 __isl_give isl_set *isl_union_set_params(
4392 __isl_take isl_union_set *uset);
4394 The function C<isl_union_set_project_out> can only project out
4397 #include <isl/union_map.h>
4398 __isl_give isl_union_map *isl_union_map_project_out(
4399 __isl_take isl_union_map *umap,
4400 enum isl_dim_type type, unsigned first, unsigned n);
4401 __isl_give isl_set *isl_union_map_params(
4402 __isl_take isl_union_map *umap);
4403 __isl_give isl_union_set *isl_union_map_domain(
4404 __isl_take isl_union_map *umap);
4405 __isl_give isl_union_set *isl_union_map_range(
4406 __isl_take isl_union_map *umap);
4408 The function C<isl_union_map_project_out> can only project out
4411 #include <isl/aff.h>
4412 __isl_give isl_aff *isl_aff_project_domain_on_params(
4413 __isl_take isl_aff *aff);
4414 __isl_give isl_pw_aff *
4415 isl_pw_aff_project_domain_on_params(
4416 __isl_take isl_pw_aff *pa);
4417 __isl_give isl_pw_multi_aff *
4418 isl_pw_multi_aff_project_domain_on_params(
4419 __isl_take isl_pw_multi_aff *pma);
4420 __isl_give isl_set *isl_pw_aff_domain(
4421 __isl_take isl_pw_aff *pwaff);
4422 __isl_give isl_set *isl_pw_multi_aff_domain(
4423 __isl_take isl_pw_multi_aff *pma);
4424 __isl_give isl_set *isl_multi_pw_aff_domain(
4425 __isl_take isl_multi_pw_aff *mpa);
4426 __isl_give isl_union_set *isl_union_pw_aff_domain(
4427 __isl_take isl_union_pw_aff *upa);
4428 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4429 __isl_take isl_union_pw_multi_aff *upma);
4430 __isl_give isl_union_set *
4431 isl_multi_union_pw_aff_domain(
4432 __isl_take isl_multi_union_pw_aff *mupa);
4433 __isl_give isl_set *isl_pw_aff_params(
4434 __isl_take isl_pw_aff *pwa);
4436 The function C<isl_multi_union_pw_aff_domain> requires its
4437 input to have at least one set dimension.
4439 #include <isl/polynomial.h>
4440 __isl_give isl_qpolynomial *
4441 isl_qpolynomial_project_domain_on_params(
4442 __isl_take isl_qpolynomial *qp);
4443 __isl_give isl_pw_qpolynomial *
4444 isl_pw_qpolynomial_project_domain_on_params(
4445 __isl_take isl_pw_qpolynomial *pwqp);
4446 __isl_give isl_pw_qpolynomial_fold *
4447 isl_pw_qpolynomial_fold_project_domain_on_params(
4448 __isl_take isl_pw_qpolynomial_fold *pwf);
4449 __isl_give isl_set *isl_pw_qpolynomial_domain(
4450 __isl_take isl_pw_qpolynomial *pwqp);
4451 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4452 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4453 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4454 __isl_take isl_union_pw_qpolynomial *upwqp);
4456 #include <isl/space.h>
4457 __isl_give isl_space *isl_space_domain_map(
4458 __isl_take isl_space *space);
4459 __isl_give isl_space *isl_space_range_map(
4460 __isl_take isl_space *space);
4462 #include <isl/map.h>
4463 __isl_give isl_map *isl_set_wrapped_domain_map(
4464 __isl_take isl_set *set);
4465 __isl_give isl_basic_map *isl_basic_map_domain_map(
4466 __isl_take isl_basic_map *bmap);
4467 __isl_give isl_basic_map *isl_basic_map_range_map(
4468 __isl_take isl_basic_map *bmap);
4469 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
4470 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
4472 #include <isl/union_map.h>
4473 __isl_give isl_union_map *isl_union_map_domain_map(
4474 __isl_take isl_union_map *umap);
4475 __isl_give isl_union_pw_multi_aff *
4476 isl_union_map_domain_map_union_pw_multi_aff(
4477 __isl_take isl_union_map *umap);
4478 __isl_give isl_union_map *isl_union_map_range_map(
4479 __isl_take isl_union_map *umap);
4480 __isl_give isl_union_map *
4481 isl_union_set_wrapped_domain_map(
4482 __isl_take isl_union_set *uset);
4484 The functions above construct a (basic, regular or union) relation
4485 that maps (a wrapped version of) the input relation to its domain or range.
4486 C<isl_set_wrapped_domain_map> maps the input set to the domain
4487 of its wrapped relation.
4491 __isl_give isl_basic_set *isl_basic_set_eliminate(
4492 __isl_take isl_basic_set *bset,
4493 enum isl_dim_type type,
4494 unsigned first, unsigned n);
4495 __isl_give isl_set *isl_set_eliminate(
4496 __isl_take isl_set *set, enum isl_dim_type type,
4497 unsigned first, unsigned n);
4498 __isl_give isl_basic_map *isl_basic_map_eliminate(
4499 __isl_take isl_basic_map *bmap,
4500 enum isl_dim_type type,
4501 unsigned first, unsigned n);
4502 __isl_give isl_map *isl_map_eliminate(
4503 __isl_take isl_map *map, enum isl_dim_type type,
4504 unsigned first, unsigned n);
4506 Eliminate the coefficients for the given dimensions from the constraints,
4507 without removing the dimensions.
4509 =item * Constructing a set from a parameter domain
4511 A zero-dimensional space or (basic) set can be constructed
4512 on a given parameter domain using the following functions.
4514 #include <isl/space.h>
4515 __isl_give isl_space *isl_space_set_from_params(
4516 __isl_take isl_space *space);
4518 #include <isl/set.h>
4519 __isl_give isl_basic_set *isl_basic_set_from_params(
4520 __isl_take isl_basic_set *bset);
4521 __isl_give isl_set *isl_set_from_params(
4522 __isl_take isl_set *set);
4524 =item * Constructing a relation from one or two sets
4526 Create a relation with the given set(s) as domain and/or range.
4527 If only the domain or the range is specified, then
4528 the range or domain of the created relation is a zero-dimensional
4529 flat anonymous space.
4531 #include <isl/space.h>
4532 __isl_give isl_space *isl_space_from_domain(
4533 __isl_take isl_space *space);
4534 __isl_give isl_space *isl_space_from_range(
4535 __isl_take isl_space *space);
4536 __isl_give isl_space *isl_space_map_from_set(
4537 __isl_take isl_space *space);
4538 __isl_give isl_space *isl_space_map_from_domain_and_range(
4539 __isl_take isl_space *domain,
4540 __isl_take isl_space *range);
4542 #include <isl/local_space.h>
4543 __isl_give isl_local_space *isl_local_space_from_domain(
4544 __isl_take isl_local_space *ls);
4546 #include <isl/map.h>
4547 __isl_give isl_map *isl_map_from_domain(
4548 __isl_take isl_set *set);
4549 __isl_give isl_map *isl_map_from_range(
4550 __isl_take isl_set *set);
4552 #include <isl/union_map.h>
4553 __isl_give isl_union_map *
4554 isl_union_map_from_domain_and_range(
4555 __isl_take isl_union_set *domain,
4556 __isl_take isl_union_set *range);
4558 #include <isl/val.h>
4559 __isl_give isl_multi_val *isl_multi_val_from_range(
4560 __isl_take isl_multi_val *mv);
4562 #include <isl/aff.h>
4563 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4564 __isl_take isl_multi_aff *ma);
4565 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4566 __isl_take isl_pw_aff *pwa);
4567 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4568 __isl_take isl_multi_pw_aff *mpa);
4569 __isl_give isl_multi_union_pw_aff *
4570 isl_multi_union_pw_aff_from_range(
4571 __isl_take isl_multi_union_pw_aff *mupa);
4572 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4573 __isl_take isl_set *set);
4574 __isl_give isl_union_pw_multi_aff *
4575 isl_union_pw_multi_aff_from_domain(
4576 __isl_take isl_union_set *uset);
4578 #include <isl/polynomial.h>
4579 __isl_give isl_pw_qpolynomial *
4580 isl_pw_qpolynomial_from_range(
4581 __isl_take isl_pw_qpolynomial *pwqp);
4582 __isl_give isl_pw_qpolynomial_fold *
4583 isl_pw_qpolynomial_fold_from_range(
4584 __isl_take isl_pw_qpolynomial_fold *pwf);
4588 #include <isl/set.h>
4589 __isl_give isl_basic_set *isl_basic_set_fix_si(
4590 __isl_take isl_basic_set *bset,
4591 enum isl_dim_type type, unsigned pos, int value);
4592 __isl_give isl_basic_set *isl_basic_set_fix_val(
4593 __isl_take isl_basic_set *bset,
4594 enum isl_dim_type type, unsigned pos,
4595 __isl_take isl_val *v);
4596 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
4597 enum isl_dim_type type, unsigned pos, int value);
4598 __isl_give isl_set *isl_set_fix_val(
4599 __isl_take isl_set *set,
4600 enum isl_dim_type type, unsigned pos,
4601 __isl_take isl_val *v);
4603 #include <isl/map.h>
4604 __isl_give isl_basic_map *isl_basic_map_fix_si(
4605 __isl_take isl_basic_map *bmap,
4606 enum isl_dim_type type, unsigned pos, int value);
4607 __isl_give isl_basic_map *isl_basic_map_fix_val(
4608 __isl_take isl_basic_map *bmap,
4609 enum isl_dim_type type, unsigned pos,
4610 __isl_take isl_val *v);
4611 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
4612 enum isl_dim_type type, unsigned pos, int value);
4613 __isl_give isl_map *isl_map_fix_val(
4614 __isl_take isl_map *map,
4615 enum isl_dim_type type, unsigned pos,
4616 __isl_take isl_val *v);
4618 #include <isl/aff.h>
4619 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4620 __isl_take isl_pw_multi_aff *pma,
4621 enum isl_dim_type type, unsigned pos, int value);
4623 #include <isl/polynomial.h>
4624 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4625 __isl_take isl_pw_qpolynomial *pwqp,
4626 enum isl_dim_type type, unsigned n,
4627 __isl_take isl_val *v);
4629 Intersect the set, relation or function domain
4630 with the hyperplane where the given
4631 dimension has the fixed given value.
4633 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
4634 __isl_take isl_basic_map *bmap,
4635 enum isl_dim_type type, unsigned pos, int value);
4636 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
4637 __isl_take isl_basic_map *bmap,
4638 enum isl_dim_type type, unsigned pos, int value);
4639 __isl_give isl_set *isl_set_lower_bound_si(
4640 __isl_take isl_set *set,
4641 enum isl_dim_type type, unsigned pos, int value);
4642 __isl_give isl_set *isl_set_lower_bound_val(
4643 __isl_take isl_set *set,
4644 enum isl_dim_type type, unsigned pos,
4645 __isl_take isl_val *value);
4646 __isl_give isl_map *isl_map_lower_bound_si(
4647 __isl_take isl_map *map,
4648 enum isl_dim_type type, unsigned pos, int value);
4649 __isl_give isl_set *isl_set_upper_bound_si(
4650 __isl_take isl_set *set,
4651 enum isl_dim_type type, unsigned pos, int value);
4652 __isl_give isl_set *isl_set_upper_bound_val(
4653 __isl_take isl_set *set,
4654 enum isl_dim_type type, unsigned pos,
4655 __isl_take isl_val *value);
4656 __isl_give isl_map *isl_map_upper_bound_si(
4657 __isl_take isl_map *map,
4658 enum isl_dim_type type, unsigned pos, int value);
4660 Intersect the set or relation with the half-space where the given
4661 dimension has a value bounded by the fixed given integer value.
4663 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
4664 enum isl_dim_type type1, int pos1,
4665 enum isl_dim_type type2, int pos2);
4666 __isl_give isl_basic_map *isl_basic_map_equate(
4667 __isl_take isl_basic_map *bmap,
4668 enum isl_dim_type type1, int pos1,
4669 enum isl_dim_type type2, int pos2);
4670 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
4671 enum isl_dim_type type1, int pos1,
4672 enum isl_dim_type type2, int pos2);
4674 Intersect the set or relation with the hyperplane where the given
4675 dimensions are equal to each other.
4677 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
4678 enum isl_dim_type type1, int pos1,
4679 enum isl_dim_type type2, int pos2);
4681 Intersect the relation with the hyperplane where the given
4682 dimensions have opposite values.
4684 __isl_give isl_map *isl_map_order_le(
4685 __isl_take isl_map *map,
4686 enum isl_dim_type type1, int pos1,
4687 enum isl_dim_type type2, int pos2);
4688 __isl_give isl_basic_map *isl_basic_map_order_ge(
4689 __isl_take isl_basic_map *bmap,
4690 enum isl_dim_type type1, int pos1,
4691 enum isl_dim_type type2, int pos2);
4692 __isl_give isl_map *isl_map_order_ge(
4693 __isl_take isl_map *map,
4694 enum isl_dim_type type1, int pos1,
4695 enum isl_dim_type type2, int pos2);
4696 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
4697 enum isl_dim_type type1, int pos1,
4698 enum isl_dim_type type2, int pos2);
4699 __isl_give isl_basic_map *isl_basic_map_order_gt(
4700 __isl_take isl_basic_map *bmap,
4701 enum isl_dim_type type1, int pos1,
4702 enum isl_dim_type type2, int pos2);
4703 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
4704 enum isl_dim_type type1, int pos1,
4705 enum isl_dim_type type2, int pos2);
4707 Intersect the relation with the half-space where the given
4708 dimensions satisfy the given ordering.
4712 #include <isl/aff.h>
4713 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4714 __isl_take isl_aff *aff);
4715 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4716 __isl_take isl_aff *aff);
4717 __isl_give isl_set *isl_pw_aff_pos_set(
4718 __isl_take isl_pw_aff *pa);
4719 __isl_give isl_set *isl_pw_aff_nonneg_set(
4720 __isl_take isl_pw_aff *pwaff);
4721 __isl_give isl_set *isl_pw_aff_zero_set(
4722 __isl_take isl_pw_aff *pwaff);
4723 __isl_give isl_set *isl_pw_aff_non_zero_set(
4724 __isl_take isl_pw_aff *pwaff);
4725 __isl_give isl_union_set *
4726 isl_union_pw_aff_zero_union_set(
4727 __isl_take isl_union_pw_aff *upa);
4728 __isl_give isl_union_set *
4729 isl_multi_union_pw_aff_zero_union_set(
4730 __isl_take isl_multi_union_pw_aff *mupa);
4732 The function C<isl_aff_neg_basic_set> returns a basic set
4733 containing those elements in the domain space
4734 of C<aff> where C<aff> is negative.
4735 The function C<isl_pw_aff_nonneg_set> returns a set
4736 containing those elements in the domain
4737 of C<pwaff> where C<pwaff> is non-negative.
4738 The function C<isl_multi_union_pw_aff_zero_union_set>
4739 returns a union set containing those elements
4740 in the domains of its elements where they are all zero.
4744 __isl_give isl_map *isl_set_identity(
4745 __isl_take isl_set *set);
4746 __isl_give isl_union_map *isl_union_set_identity(
4747 __isl_take isl_union_set *uset);
4748 __isl_give isl_union_pw_multi_aff *
4749 isl_union_set_identity_union_pw_multi_aff(
4750 __isl_take isl_union_set *uset);
4752 Construct an identity relation on the given (union) set.
4754 =item * Function Extraction
4756 A piecewise quasi affine expression that is equal to 1 on a set
4757 and 0 outside the set can be created using the following function.
4759 #include <isl/aff.h>
4760 __isl_give isl_pw_aff *isl_set_indicator_function(
4761 __isl_take isl_set *set);
4763 A piecewise multiple quasi affine expression can be extracted
4764 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4765 and the C<isl_map> is single-valued.
4766 In case of a conversion from an C<isl_union_map>
4767 to an C<isl_union_pw_multi_aff>, these properties need to hold
4768 in each domain space.
4769 A conversion to a C<isl_multi_union_pw_aff> additionally
4770 requires that the input is non-empty and involves only a single
4773 #include <isl/aff.h>
4774 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4775 __isl_take isl_set *set);
4776 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4777 __isl_take isl_map *map);
4779 __isl_give isl_union_pw_multi_aff *
4780 isl_union_pw_multi_aff_from_union_set(
4781 __isl_take isl_union_set *uset);
4782 __isl_give isl_union_pw_multi_aff *
4783 isl_union_pw_multi_aff_from_union_map(
4784 __isl_take isl_union_map *umap);
4786 __isl_give isl_multi_union_pw_aff *
4787 isl_multi_union_pw_aff_from_union_map(
4788 __isl_take isl_union_map *umap);
4792 __isl_give isl_basic_set *isl_basic_map_deltas(
4793 __isl_take isl_basic_map *bmap);
4794 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
4795 __isl_give isl_union_set *isl_union_map_deltas(
4796 __isl_take isl_union_map *umap);
4798 These functions return a (basic) set containing the differences
4799 between image elements and corresponding domain elements in the input.
4801 __isl_give isl_basic_map *isl_basic_map_deltas_map(
4802 __isl_take isl_basic_map *bmap);
4803 __isl_give isl_map *isl_map_deltas_map(
4804 __isl_take isl_map *map);
4805 __isl_give isl_union_map *isl_union_map_deltas_map(
4806 __isl_take isl_union_map *umap);
4808 The functions above construct a (basic, regular or union) relation
4809 that maps (a wrapped version of) the input relation to its delta set.
4813 Simplify the representation of a set, relation or functions by trying
4814 to combine pairs of basic sets or relations into a single
4815 basic set or relation.
4817 #include <isl/set.h>
4818 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
4820 #include <isl/map.h>
4821 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
4823 #include <isl/union_set.h>
4824 __isl_give isl_union_set *isl_union_set_coalesce(
4825 __isl_take isl_union_set *uset);
4827 #include <isl/union_map.h>
4828 __isl_give isl_union_map *isl_union_map_coalesce(
4829 __isl_take isl_union_map *umap);
4831 #include <isl/aff.h>
4832 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4833 __isl_take isl_pw_aff *pwqp);
4834 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4835 __isl_take isl_pw_multi_aff *pma);
4836 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4837 __isl_take isl_multi_pw_aff *mpa);
4838 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
4839 __isl_take isl_union_pw_aff *upa);
4840 __isl_give isl_union_pw_multi_aff *
4841 isl_union_pw_multi_aff_coalesce(
4842 __isl_take isl_union_pw_multi_aff *upma);
4843 __isl_give isl_multi_union_pw_aff *
4844 isl_multi_union_pw_aff_coalesce(
4845 __isl_take isl_multi_union_pw_aff *aff);
4847 #include <isl/polynomial.h>
4848 __isl_give isl_pw_qpolynomial_fold *
4849 isl_pw_qpolynomial_fold_coalesce(
4850 __isl_take isl_pw_qpolynomial_fold *pwf);
4851 __isl_give isl_union_pw_qpolynomial *
4852 isl_union_pw_qpolynomial_coalesce(
4853 __isl_take isl_union_pw_qpolynomial *upwqp);
4854 __isl_give isl_union_pw_qpolynomial_fold *
4855 isl_union_pw_qpolynomial_fold_coalesce(
4856 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4858 One of the methods for combining pairs of basic sets or relations
4859 can result in coefficients that are much larger than those that appear
4860 in the constraints of the input. By default, the coefficients are
4861 not allowed to grow larger, but this can be changed by unsetting
4862 the following option.
4864 isl_stat isl_options_set_coalesce_bounded_wrapping(
4865 isl_ctx *ctx, int val);
4866 int isl_options_get_coalesce_bounded_wrapping(
4869 =item * Detecting equalities
4871 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
4872 __isl_take isl_basic_set *bset);
4873 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
4874 __isl_take isl_basic_map *bmap);
4875 __isl_give isl_set *isl_set_detect_equalities(
4876 __isl_take isl_set *set);
4877 __isl_give isl_map *isl_map_detect_equalities(
4878 __isl_take isl_map *map);
4879 __isl_give isl_union_set *isl_union_set_detect_equalities(
4880 __isl_take isl_union_set *uset);
4881 __isl_give isl_union_map *isl_union_map_detect_equalities(
4882 __isl_take isl_union_map *umap);
4884 Simplify the representation of a set or relation by detecting implicit
4887 =item * Removing redundant constraints
4889 #include <isl/set.h>
4890 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
4891 __isl_take isl_basic_set *bset);
4892 __isl_give isl_set *isl_set_remove_redundancies(
4893 __isl_take isl_set *set);
4895 #include <isl/union_set.h>
4896 __isl_give isl_union_set *
4897 isl_union_set_remove_redundancies(
4898 __isl_take isl_union_set *uset);
4900 #include <isl/map.h>
4901 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
4902 __isl_take isl_basic_map *bmap);
4903 __isl_give isl_map *isl_map_remove_redundancies(
4904 __isl_take isl_map *map);
4906 #include <isl/union_map.h>
4907 __isl_give isl_union_map *
4908 isl_union_map_remove_redundancies(
4909 __isl_take isl_union_map *umap);
4913 __isl_give isl_basic_set *isl_set_convex_hull(
4914 __isl_take isl_set *set);
4915 __isl_give isl_basic_map *isl_map_convex_hull(
4916 __isl_take isl_map *map);
4918 If the input set or relation has any existentially quantified
4919 variables, then the result of these operations is currently undefined.
4923 #include <isl/set.h>
4924 __isl_give isl_basic_set *
4925 isl_set_unshifted_simple_hull(
4926 __isl_take isl_set *set);
4927 __isl_give isl_basic_set *isl_set_simple_hull(
4928 __isl_take isl_set *set);
4929 __isl_give isl_basic_set *
4930 isl_set_plain_unshifted_simple_hull(
4931 __isl_take isl_set *set);
4932 __isl_give isl_basic_set *
4933 isl_set_unshifted_simple_hull_from_set_list(
4934 __isl_take isl_set *set,
4935 __isl_take isl_set_list *list);
4937 #include <isl/map.h>
4938 __isl_give isl_basic_map *
4939 isl_map_unshifted_simple_hull(
4940 __isl_take isl_map *map);
4941 __isl_give isl_basic_map *isl_map_simple_hull(
4942 __isl_take isl_map *map);
4943 __isl_give isl_basic_map *
4944 isl_map_plain_unshifted_simple_hull(
4945 __isl_take isl_map *map);
4946 __isl_give isl_basic_map *
4947 isl_map_unshifted_simple_hull_from_map_list(
4948 __isl_take isl_map *map,
4949 __isl_take isl_map_list *list);
4951 #include <isl/union_map.h>
4952 __isl_give isl_union_map *isl_union_map_simple_hull(
4953 __isl_take isl_union_map *umap);
4955 These functions compute a single basic set or relation
4956 that contains the whole input set or relation.
4957 In particular, the output is described by translates
4958 of the constraints describing the basic sets or relations in the input.
4959 In case of C<isl_set_unshifted_simple_hull>, only the original
4960 constraints are used, without any translation.
4961 In case of C<isl_set_plain_unshifted_simple_hull> and
4962 C<isl_map_plain_unshifted_simple_hull>, the result is described
4963 by original constraints that are obviously satisfied
4964 by the entire input set or relation.
4965 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
4966 C<isl_map_unshifted_simple_hull_from_map_list>, the
4967 constraints are taken from the elements of the second argument.
4971 (See \autoref{s:simple hull}.)
4977 __isl_give isl_basic_set *isl_basic_set_affine_hull(
4978 __isl_take isl_basic_set *bset);
4979 __isl_give isl_basic_set *isl_set_affine_hull(
4980 __isl_take isl_set *set);
4981 __isl_give isl_union_set *isl_union_set_affine_hull(
4982 __isl_take isl_union_set *uset);
4983 __isl_give isl_basic_map *isl_basic_map_affine_hull(
4984 __isl_take isl_basic_map *bmap);
4985 __isl_give isl_basic_map *isl_map_affine_hull(
4986 __isl_take isl_map *map);
4987 __isl_give isl_union_map *isl_union_map_affine_hull(
4988 __isl_take isl_union_map *umap);
4990 In case of union sets and relations, the affine hull is computed
4993 =item * Polyhedral hull
4995 __isl_give isl_basic_set *isl_set_polyhedral_hull(
4996 __isl_take isl_set *set);
4997 __isl_give isl_basic_map *isl_map_polyhedral_hull(
4998 __isl_take isl_map *map);
4999 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
5000 __isl_take isl_union_set *uset);
5001 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
5002 __isl_take isl_union_map *umap);
5004 These functions compute a single basic set or relation
5005 not involving any existentially quantified variables
5006 that contains the whole input set or relation.
5007 In case of union sets and relations, the polyhedral hull is computed
5010 =item * Other approximations
5012 #include <isl/set.h>
5013 __isl_give isl_basic_set *
5014 isl_basic_set_drop_constraints_involving_dims(
5015 __isl_take isl_basic_set *bset,
5016 enum isl_dim_type type,
5017 unsigned first, unsigned n);
5018 __isl_give isl_basic_set *
5019 isl_basic_set_drop_constraints_not_involving_dims(
5020 __isl_take isl_basic_set *bset,
5021 enum isl_dim_type type,
5022 unsigned first, unsigned n);
5023 __isl_give isl_set *
5024 isl_set_drop_constraints_involving_dims(
5025 __isl_take isl_set *set,
5026 enum isl_dim_type type,
5027 unsigned first, unsigned n);
5028 __isl_give isl_set *
5029 isl_set_drop_constraints_not_involving_dims(
5030 __isl_take isl_set *set,
5031 enum isl_dim_type type,
5032 unsigned first, unsigned n);
5034 #include <isl/map.h>
5035 __isl_give isl_basic_map *
5036 isl_basic_map_drop_constraints_involving_dims(
5037 __isl_take isl_basic_map *bmap,
5038 enum isl_dim_type type,
5039 unsigned first, unsigned n);
5040 __isl_give isl_basic_map *
5041 isl_basic_map_drop_constraints_not_involving_dims(
5042 __isl_take isl_basic_map *bmap,
5043 enum isl_dim_type type,
5044 unsigned first, unsigned n);
5045 __isl_give isl_map *
5046 isl_map_drop_constraints_involving_dims(
5047 __isl_take isl_map *map,
5048 enum isl_dim_type type,
5049 unsigned first, unsigned n);
5050 __isl_give isl_map *
5051 isl_map_drop_constraints_not_involving_dims(
5052 __isl_take isl_map *map,
5053 enum isl_dim_type type,
5054 unsigned first, unsigned n);
5056 These functions drop any constraints (not) involving the specified dimensions.
5057 Note that the result depends on the representation of the input.
5059 #include <isl/polynomial.h>
5060 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
5061 __isl_take isl_pw_qpolynomial *pwqp, int sign);
5062 __isl_give isl_union_pw_qpolynomial *
5063 isl_union_pw_qpolynomial_to_polynomial(
5064 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
5066 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
5067 the polynomial will be an overapproximation. If C<sign> is negative,
5068 it will be an underapproximation. If C<sign> is zero, the approximation
5069 will lie somewhere in between.
5073 __isl_give isl_basic_set *isl_basic_set_sample(
5074 __isl_take isl_basic_set *bset);
5075 __isl_give isl_basic_set *isl_set_sample(
5076 __isl_take isl_set *set);
5077 __isl_give isl_basic_map *isl_basic_map_sample(
5078 __isl_take isl_basic_map *bmap);
5079 __isl_give isl_basic_map *isl_map_sample(
5080 __isl_take isl_map *map);
5082 If the input (basic) set or relation is non-empty, then return
5083 a singleton subset of the input. Otherwise, return an empty set.
5085 =item * Optimization
5087 #include <isl/ilp.h>
5088 __isl_give isl_val *isl_basic_set_max_val(
5089 __isl_keep isl_basic_set *bset,
5090 __isl_keep isl_aff *obj);
5091 __isl_give isl_val *isl_set_min_val(
5092 __isl_keep isl_set *set,
5093 __isl_keep isl_aff *obj);
5094 __isl_give isl_val *isl_set_max_val(
5095 __isl_keep isl_set *set,
5096 __isl_keep isl_aff *obj);
5097 __isl_give isl_multi_val *
5098 isl_union_set_min_multi_union_pw_aff(
5099 __isl_keep isl_union_set *set,
5100 __isl_keep isl_multi_union_pw_aff *obj);
5102 Compute the minimum or maximum of the integer affine expression C<obj>
5103 over the points in C<set>, returning the result in C<opt>.
5104 The result is C<NULL> in case of an error, the optimal value in case
5105 there is one, negative infinity or infinity if the problem is unbounded and
5106 NaN if the problem is empty.
5108 =item * Parametric optimization
5110 __isl_give isl_pw_aff *isl_set_dim_min(
5111 __isl_take isl_set *set, int pos);
5112 __isl_give isl_pw_aff *isl_set_dim_max(
5113 __isl_take isl_set *set, int pos);
5114 __isl_give isl_pw_aff *isl_map_dim_min(
5115 __isl_take isl_map *map, int pos);
5116 __isl_give isl_pw_aff *isl_map_dim_max(
5117 __isl_take isl_map *map, int pos);
5119 Compute the minimum or maximum of the given set or output dimension
5120 as a function of the parameters (and input dimensions), but independently
5121 of the other set or output dimensions.
5122 For lexicographic optimization, see L<"Lexicographic Optimization">.
5126 The following functions compute either the set of (rational) coefficient
5127 values of valid constraints for the given set or the set of (rational)
5128 values satisfying the constraints with coefficients from the given set.
5129 Internally, these two sets of functions perform essentially the
5130 same operations, except that the set of coefficients is assumed to
5131 be a cone, while the set of values may be any polyhedron.
5132 The current implementation is based on the Farkas lemma and
5133 Fourier-Motzkin elimination, but this may change or be made optional
5134 in future. In particular, future implementations may use different
5135 dualization algorithms or skip the elimination step.
5137 __isl_give isl_basic_set *isl_basic_set_coefficients(
5138 __isl_take isl_basic_set *bset);
5139 __isl_give isl_basic_set *isl_set_coefficients(
5140 __isl_take isl_set *set);
5141 __isl_give isl_union_set *isl_union_set_coefficients(
5142 __isl_take isl_union_set *bset);
5143 __isl_give isl_basic_set *isl_basic_set_solutions(
5144 __isl_take isl_basic_set *bset);
5145 __isl_give isl_basic_set *isl_set_solutions(
5146 __isl_take isl_set *set);
5147 __isl_give isl_union_set *isl_union_set_solutions(
5148 __isl_take isl_union_set *bset);
5152 __isl_give isl_map *isl_map_fixed_power_val(
5153 __isl_take isl_map *map,
5154 __isl_take isl_val *exp);
5155 __isl_give isl_union_map *
5156 isl_union_map_fixed_power_val(
5157 __isl_take isl_union_map *umap,
5158 __isl_take isl_val *exp);
5160 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
5161 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
5162 of C<map> is computed.
5164 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
5166 __isl_give isl_union_map *isl_union_map_power(
5167 __isl_take isl_union_map *umap, int *exact);
5169 Compute a parametric representation for all positive powers I<k> of C<map>.
5170 The result maps I<k> to a nested relation corresponding to the
5171 I<k>th power of C<map>.
5172 The result may be an overapproximation. If the result is known to be exact,
5173 then C<*exact> is set to C<1>.
5175 =item * Transitive closure
5177 __isl_give isl_map *isl_map_transitive_closure(
5178 __isl_take isl_map *map, int *exact);
5179 __isl_give isl_union_map *isl_union_map_transitive_closure(
5180 __isl_take isl_union_map *umap, int *exact);
5182 Compute the transitive closure of C<map>.
5183 The result may be an overapproximation. If the result is known to be exact,
5184 then C<*exact> is set to C<1>.
5186 =item * Reaching path lengths
5188 __isl_give isl_map *isl_map_reaching_path_lengths(
5189 __isl_take isl_map *map, int *exact);
5191 Compute a relation that maps each element in the range of C<map>
5192 to the lengths of all paths composed of edges in C<map> that
5193 end up in the given element.
5194 The result may be an overapproximation. If the result is known to be exact,
5195 then C<*exact> is set to C<1>.
5196 To compute the I<maximal> path length, the resulting relation
5197 should be postprocessed by C<isl_map_lexmax>.
5198 In particular, if the input relation is a dependence relation
5199 (mapping sources to sinks), then the maximal path length corresponds
5200 to the free schedule.
5201 Note, however, that C<isl_map_lexmax> expects the maximum to be
5202 finite, so if the path lengths are unbounded (possibly due to
5203 the overapproximation), then you will get an error message.
5207 #include <isl/space.h>
5208 __isl_give isl_space *isl_space_wrap(
5209 __isl_take isl_space *space);
5210 __isl_give isl_space *isl_space_unwrap(
5211 __isl_take isl_space *space);
5213 #include <isl/local_space.h>
5214 __isl_give isl_local_space *isl_local_space_wrap(
5215 __isl_take isl_local_space *ls);
5217 #include <isl/set.h>
5218 __isl_give isl_basic_map *isl_basic_set_unwrap(
5219 __isl_take isl_basic_set *bset);
5220 __isl_give isl_map *isl_set_unwrap(
5221 __isl_take isl_set *set);
5223 #include <isl/map.h>
5224 __isl_give isl_basic_set *isl_basic_map_wrap(
5225 __isl_take isl_basic_map *bmap);
5226 __isl_give isl_set *isl_map_wrap(
5227 __isl_take isl_map *map);
5229 #include <isl/union_set.h>
5230 __isl_give isl_union_map *isl_union_set_unwrap(
5231 __isl_take isl_union_set *uset);
5233 #include <isl/union_map.h>
5234 __isl_give isl_union_set *isl_union_map_wrap(
5235 __isl_take isl_union_map *umap);
5237 The input to C<isl_space_unwrap> should
5238 be the space of a set, while that of
5239 C<isl_space_wrap> should be the space of a relation.
5240 Conversely, the output of C<isl_space_unwrap> is the space
5241 of a relation, while that of C<isl_space_wrap> is the space of a set.
5245 Remove any internal structure of domain (and range) of the given
5246 set or relation. If there is any such internal structure in the input,
5247 then the name of the space is also removed.
5249 #include <isl/local_space.h>
5250 __isl_give isl_local_space *
5251 isl_local_space_flatten_domain(
5252 __isl_take isl_local_space *ls);
5253 __isl_give isl_local_space *
5254 isl_local_space_flatten_range(
5255 __isl_take isl_local_space *ls);
5257 #include <isl/set.h>
5258 __isl_give isl_basic_set *isl_basic_set_flatten(
5259 __isl_take isl_basic_set *bset);
5260 __isl_give isl_set *isl_set_flatten(
5261 __isl_take isl_set *set);
5263 #include <isl/map.h>
5264 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
5265 __isl_take isl_basic_map *bmap);
5266 __isl_give isl_basic_map *isl_basic_map_flatten_range(
5267 __isl_take isl_basic_map *bmap);
5268 __isl_give isl_map *isl_map_flatten_range(
5269 __isl_take isl_map *map);
5270 __isl_give isl_map *isl_map_flatten_domain(
5271 __isl_take isl_map *map);
5272 __isl_give isl_basic_map *isl_basic_map_flatten(
5273 __isl_take isl_basic_map *bmap);
5274 __isl_give isl_map *isl_map_flatten(
5275 __isl_take isl_map *map);
5277 #include <isl/val.h>
5278 __isl_give isl_multi_val *isl_multi_val_flatten_range(
5279 __isl_take isl_multi_val *mv);
5281 #include <isl/aff.h>
5282 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
5283 __isl_take isl_multi_aff *ma);
5284 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
5285 __isl_take isl_multi_aff *ma);
5286 __isl_give isl_multi_pw_aff *
5287 isl_multi_pw_aff_flatten_range(
5288 __isl_take isl_multi_pw_aff *mpa);
5289 __isl_give isl_multi_union_pw_aff *
5290 isl_multi_union_pw_aff_flatten_range(
5291 __isl_take isl_multi_union_pw_aff *mupa);
5293 #include <isl/map.h>
5294 __isl_give isl_map *isl_set_flatten_map(
5295 __isl_take isl_set *set);
5297 The function above constructs a relation
5298 that maps the input set to a flattened version of the set.
5302 Lift the input set to a space with extra dimensions corresponding
5303 to the existentially quantified variables in the input.
5304 In particular, the result lives in a wrapped map where the domain
5305 is the original space and the range corresponds to the original
5306 existentially quantified variables.
5308 #include <isl/set.h>
5309 __isl_give isl_basic_set *isl_basic_set_lift(
5310 __isl_take isl_basic_set *bset);
5311 __isl_give isl_set *isl_set_lift(
5312 __isl_take isl_set *set);
5313 __isl_give isl_union_set *isl_union_set_lift(
5314 __isl_take isl_union_set *uset);
5316 Given a local space that contains the existentially quantified
5317 variables of a set, a basic relation that, when applied to
5318 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
5319 can be constructed using the following function.
5321 #include <isl/local_space.h>
5322 __isl_give isl_basic_map *isl_local_space_lifting(
5323 __isl_take isl_local_space *ls);
5325 #include <isl/aff.h>
5326 __isl_give isl_multi_aff *isl_multi_aff_lift(
5327 __isl_take isl_multi_aff *maff,
5328 __isl_give isl_local_space **ls);
5330 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
5331 then it is assigned the local space that lies at the basis of
5332 the lifting applied.
5334 =item * Internal Product
5336 #include <isl/space.h>
5337 __isl_give isl_space *isl_space_zip(
5338 __isl_take isl_space *space);
5340 #include <isl/map.h>
5341 __isl_give isl_basic_map *isl_basic_map_zip(
5342 __isl_take isl_basic_map *bmap);
5343 __isl_give isl_map *isl_map_zip(
5344 __isl_take isl_map *map);
5346 #include <isl/union_map.h>
5347 __isl_give isl_union_map *isl_union_map_zip(
5348 __isl_take isl_union_map *umap);
5350 Given a relation with nested relations for domain and range,
5351 interchange the range of the domain with the domain of the range.
5355 #include <isl/space.h>
5356 __isl_give isl_space *isl_space_curry(
5357 __isl_take isl_space *space);
5358 __isl_give isl_space *isl_space_uncurry(
5359 __isl_take isl_space *space);
5361 #include <isl/map.h>
5362 __isl_give isl_basic_map *isl_basic_map_curry(
5363 __isl_take isl_basic_map *bmap);
5364 __isl_give isl_basic_map *isl_basic_map_uncurry(
5365 __isl_take isl_basic_map *bmap);
5366 __isl_give isl_map *isl_map_curry(
5367 __isl_take isl_map *map);
5368 __isl_give isl_map *isl_map_uncurry(
5369 __isl_take isl_map *map);
5371 #include <isl/union_map.h>
5372 __isl_give isl_union_map *isl_union_map_curry(
5373 __isl_take isl_union_map *umap);
5374 __isl_give isl_union_map *isl_union_map_uncurry(
5375 __isl_take isl_union_map *umap);
5377 Given a relation with a nested relation for domain,
5378 the C<curry> functions
5379 move the range of the nested relation out of the domain
5380 and use it as the domain of a nested relation in the range,
5381 with the original range as range of this nested relation.
5382 The C<uncurry> functions perform the inverse operation.
5384 #include <isl/space.h>
5385 __isl_give isl_space *isl_space_range_curry(
5386 __isl_take isl_space *space);
5388 #include <isl/map.h>
5389 __isl_give isl_map *isl_map_range_curry(
5390 __isl_take isl_map *map);
5392 #include <isl/union_map.h>
5393 __isl_give isl_union_map *isl_union_map_range_curry(
5394 __isl_take isl_union_map *umap);
5396 These functions apply the currying to the relation that
5397 is nested inside the range of the input.
5399 =item * Aligning parameters
5401 Change the order of the parameters of the given set, relation
5403 such that the first parameters match those of C<model>.
5404 This may involve the introduction of extra parameters.
5405 All parameters need to be named.
5407 #include <isl/space.h>
5408 __isl_give isl_space *isl_space_align_params(
5409 __isl_take isl_space *space1,
5410 __isl_take isl_space *space2)
5412 #include <isl/set.h>
5413 __isl_give isl_basic_set *isl_basic_set_align_params(
5414 __isl_take isl_basic_set *bset,
5415 __isl_take isl_space *model);
5416 __isl_give isl_set *isl_set_align_params(
5417 __isl_take isl_set *set,
5418 __isl_take isl_space *model);
5420 #include <isl/map.h>
5421 __isl_give isl_basic_map *isl_basic_map_align_params(
5422 __isl_take isl_basic_map *bmap,
5423 __isl_take isl_space *model);
5424 __isl_give isl_map *isl_map_align_params(
5425 __isl_take isl_map *map,
5426 __isl_take isl_space *model);
5428 #include <isl/val.h>
5429 __isl_give isl_multi_val *isl_multi_val_align_params(
5430 __isl_take isl_multi_val *mv,
5431 __isl_take isl_space *model);
5433 #include <isl/aff.h>
5434 __isl_give isl_aff *isl_aff_align_params(
5435 __isl_take isl_aff *aff,
5436 __isl_take isl_space *model);
5437 __isl_give isl_multi_aff *isl_multi_aff_align_params(
5438 __isl_take isl_multi_aff *multi,
5439 __isl_take isl_space *model);
5440 __isl_give isl_pw_aff *isl_pw_aff_align_params(
5441 __isl_take isl_pw_aff *pwaff,
5442 __isl_take isl_space *model);
5443 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
5444 __isl_take isl_pw_multi_aff *pma,
5445 __isl_take isl_space *model);
5446 __isl_give isl_union_pw_aff *
5447 isl_union_pw_aff_align_params(
5448 __isl_take isl_union_pw_aff *upa,
5449 __isl_take isl_space *model);
5450 __isl_give isl_union_pw_multi_aff *
5451 isl_union_pw_multi_aff_align_params(
5452 __isl_take isl_union_pw_multi_aff *upma,
5453 __isl_take isl_space *model);
5454 __isl_give isl_multi_union_pw_aff *
5455 isl_multi_union_pw_aff_align_params(
5456 __isl_take isl_multi_union_pw_aff *mupa,
5457 __isl_take isl_space *model);
5459 #include <isl/polynomial.h>
5460 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5461 __isl_take isl_qpolynomial *qp,
5462 __isl_take isl_space *model);
5464 =item * Unary Arithmetic Operations
5466 #include <isl/set.h>
5467 __isl_give isl_set *isl_set_neg(
5468 __isl_take isl_set *set);
5469 #include <isl/map.h>
5470 __isl_give isl_map *isl_map_neg(
5471 __isl_take isl_map *map);
5473 C<isl_set_neg> constructs a set containing the opposites of
5474 the elements in its argument.
5475 The domain of the result of C<isl_map_neg> is the same
5476 as the domain of its argument. The corresponding range
5477 elements are the opposites of the corresponding range
5478 elements in the argument.
5480 #include <isl/val.h>
5481 __isl_give isl_multi_val *isl_multi_val_neg(
5482 __isl_take isl_multi_val *mv);
5484 #include <isl/aff.h>
5485 __isl_give isl_aff *isl_aff_neg(
5486 __isl_take isl_aff *aff);
5487 __isl_give isl_multi_aff *isl_multi_aff_neg(
5488 __isl_take isl_multi_aff *ma);
5489 __isl_give isl_pw_aff *isl_pw_aff_neg(
5490 __isl_take isl_pw_aff *pwaff);
5491 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
5492 __isl_take isl_pw_multi_aff *pma);
5493 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
5494 __isl_take isl_multi_pw_aff *mpa);
5495 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
5496 __isl_take isl_union_pw_aff *upa);
5497 __isl_give isl_union_pw_multi_aff *
5498 isl_union_pw_multi_aff_neg(
5499 __isl_take isl_union_pw_multi_aff *upma);
5500 __isl_give isl_multi_union_pw_aff *
5501 isl_multi_union_pw_aff_neg(
5502 __isl_take isl_multi_union_pw_aff *mupa);
5503 __isl_give isl_aff *isl_aff_ceil(
5504 __isl_take isl_aff *aff);
5505 __isl_give isl_pw_aff *isl_pw_aff_ceil(
5506 __isl_take isl_pw_aff *pwaff);
5507 __isl_give isl_aff *isl_aff_floor(
5508 __isl_take isl_aff *aff);
5509 __isl_give isl_multi_aff *isl_multi_aff_floor(
5510 __isl_take isl_multi_aff *ma);
5511 __isl_give isl_pw_aff *isl_pw_aff_floor(
5512 __isl_take isl_pw_aff *pwaff);
5513 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
5514 __isl_take isl_union_pw_aff *upa);
5515 __isl_give isl_multi_union_pw_aff *
5516 isl_multi_union_pw_aff_floor(
5517 __isl_take isl_multi_union_pw_aff *mupa);
5519 #include <isl/aff.h>
5520 __isl_give isl_pw_aff *isl_pw_aff_list_min(
5521 __isl_take isl_pw_aff_list *list);
5522 __isl_give isl_pw_aff *isl_pw_aff_list_max(
5523 __isl_take isl_pw_aff_list *list);
5525 #include <isl/polynomial.h>
5526 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5527 __isl_take isl_qpolynomial *qp);
5528 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5529 __isl_take isl_pw_qpolynomial *pwqp);
5530 __isl_give isl_union_pw_qpolynomial *
5531 isl_union_pw_qpolynomial_neg(
5532 __isl_take isl_union_pw_qpolynomial *upwqp);
5533 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5534 __isl_take isl_qpolynomial *qp,
5536 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5537 __isl_take isl_pw_qpolynomial *pwqp,
5542 The following functions evaluate a function in a point.
5544 #include <isl/polynomial.h>
5545 __isl_give isl_val *isl_pw_qpolynomial_eval(
5546 __isl_take isl_pw_qpolynomial *pwqp,
5547 __isl_take isl_point *pnt);
5548 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5549 __isl_take isl_pw_qpolynomial_fold *pwf,
5550 __isl_take isl_point *pnt);
5551 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5552 __isl_take isl_union_pw_qpolynomial *upwqp,
5553 __isl_take isl_point *pnt);
5554 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5555 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5556 __isl_take isl_point *pnt);
5558 =item * Dimension manipulation
5560 It is usually not advisable to directly change the (input or output)
5561 space of a set or a relation as this removes the name and the internal
5562 structure of the space. However, the functions below can be useful
5563 to add new parameters, assuming
5564 C<isl_set_align_params> and C<isl_map_align_params>
5567 #include <isl/space.h>
5568 __isl_give isl_space *isl_space_add_dims(
5569 __isl_take isl_space *space,
5570 enum isl_dim_type type, unsigned n);
5571 __isl_give isl_space *isl_space_insert_dims(
5572 __isl_take isl_space *space,
5573 enum isl_dim_type type, unsigned pos, unsigned n);
5574 __isl_give isl_space *isl_space_drop_dims(
5575 __isl_take isl_space *space,
5576 enum isl_dim_type type, unsigned first, unsigned n);
5577 __isl_give isl_space *isl_space_move_dims(
5578 __isl_take isl_space *space,
5579 enum isl_dim_type dst_type, unsigned dst_pos,
5580 enum isl_dim_type src_type, unsigned src_pos,
5583 #include <isl/local_space.h>
5584 __isl_give isl_local_space *isl_local_space_add_dims(
5585 __isl_take isl_local_space *ls,
5586 enum isl_dim_type type, unsigned n);
5587 __isl_give isl_local_space *isl_local_space_insert_dims(
5588 __isl_take isl_local_space *ls,
5589 enum isl_dim_type type, unsigned first, unsigned n);
5590 __isl_give isl_local_space *isl_local_space_drop_dims(
5591 __isl_take isl_local_space *ls,
5592 enum isl_dim_type type, unsigned first, unsigned n);
5594 #include <isl/set.h>
5595 __isl_give isl_basic_set *isl_basic_set_add_dims(
5596 __isl_take isl_basic_set *bset,
5597 enum isl_dim_type type, unsigned n);
5598 __isl_give isl_set *isl_set_add_dims(
5599 __isl_take isl_set *set,
5600 enum isl_dim_type type, unsigned n);
5601 __isl_give isl_basic_set *isl_basic_set_insert_dims(
5602 __isl_take isl_basic_set *bset,
5603 enum isl_dim_type type, unsigned pos,
5605 __isl_give isl_set *isl_set_insert_dims(
5606 __isl_take isl_set *set,
5607 enum isl_dim_type type, unsigned pos, unsigned n);
5608 __isl_give isl_basic_set *isl_basic_set_move_dims(
5609 __isl_take isl_basic_set *bset,
5610 enum isl_dim_type dst_type, unsigned dst_pos,
5611 enum isl_dim_type src_type, unsigned src_pos,
5613 __isl_give isl_set *isl_set_move_dims(
5614 __isl_take isl_set *set,
5615 enum isl_dim_type dst_type, unsigned dst_pos,
5616 enum isl_dim_type src_type, unsigned src_pos,
5619 #include <isl/map.h>
5620 __isl_give isl_basic_map *isl_basic_map_add_dims(
5621 __isl_take isl_basic_map *bmap,
5622 enum isl_dim_type type, unsigned n);
5623 __isl_give isl_map *isl_map_add_dims(
5624 __isl_take isl_map *map,
5625 enum isl_dim_type type, unsigned n);
5626 __isl_give isl_basic_map *isl_basic_map_insert_dims(
5627 __isl_take isl_basic_map *bmap,
5628 enum isl_dim_type type, unsigned pos,
5630 __isl_give isl_map *isl_map_insert_dims(
5631 __isl_take isl_map *map,
5632 enum isl_dim_type type, unsigned pos, unsigned n);
5633 __isl_give isl_basic_map *isl_basic_map_move_dims(
5634 __isl_take isl_basic_map *bmap,
5635 enum isl_dim_type dst_type, unsigned dst_pos,
5636 enum isl_dim_type src_type, unsigned src_pos,
5638 __isl_give isl_map *isl_map_move_dims(
5639 __isl_take isl_map *map,
5640 enum isl_dim_type dst_type, unsigned dst_pos,
5641 enum isl_dim_type src_type, unsigned src_pos,
5644 #include <isl/val.h>
5645 __isl_give isl_multi_val *isl_multi_val_insert_dims(
5646 __isl_take isl_multi_val *mv,
5647 enum isl_dim_type type, unsigned first, unsigned n);
5648 __isl_give isl_multi_val *isl_multi_val_add_dims(
5649 __isl_take isl_multi_val *mv,
5650 enum isl_dim_type type, unsigned n);
5651 __isl_give isl_multi_val *isl_multi_val_drop_dims(
5652 __isl_take isl_multi_val *mv,
5653 enum isl_dim_type type, unsigned first, unsigned n);
5655 #include <isl/aff.h>
5656 __isl_give isl_aff *isl_aff_insert_dims(
5657 __isl_take isl_aff *aff,
5658 enum isl_dim_type type, unsigned first, unsigned n);
5659 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
5660 __isl_take isl_multi_aff *ma,
5661 enum isl_dim_type type, unsigned first, unsigned n);
5662 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
5663 __isl_take isl_pw_aff *pwaff,
5664 enum isl_dim_type type, unsigned first, unsigned n);
5665 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
5666 __isl_take isl_multi_pw_aff *mpa,
5667 enum isl_dim_type type, unsigned first, unsigned n);
5668 __isl_give isl_aff *isl_aff_add_dims(
5669 __isl_take isl_aff *aff,
5670 enum isl_dim_type type, unsigned n);
5671 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
5672 __isl_take isl_multi_aff *ma,
5673 enum isl_dim_type type, unsigned n);
5674 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
5675 __isl_take isl_pw_aff *pwaff,
5676 enum isl_dim_type type, unsigned n);
5677 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
5678 __isl_take isl_multi_pw_aff *mpa,
5679 enum isl_dim_type type, unsigned n);
5680 __isl_give isl_aff *isl_aff_drop_dims(
5681 __isl_take isl_aff *aff,
5682 enum isl_dim_type type, unsigned first, unsigned n);
5683 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
5684 __isl_take isl_multi_aff *maff,
5685 enum isl_dim_type type, unsigned first, unsigned n);
5686 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
5687 __isl_take isl_pw_aff *pwaff,
5688 enum isl_dim_type type, unsigned first, unsigned n);
5689 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
5690 __isl_take isl_pw_multi_aff *pma,
5691 enum isl_dim_type type, unsigned first, unsigned n);
5692 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
5693 __isl_take isl_union_pw_aff *upa,
5694 enum isl_dim_type type, unsigned first, unsigned n);
5695 __isl_give isl_union_pw_multi_aff *
5696 isl_union_pw_multi_aff_drop_dims(
5697 __isl_take isl_union_pw_multi_aff *upma,
5698 enum isl_dim_type type,
5699 unsigned first, unsigned n);
5700 __isl_give isl_multi_union_pw_aff *
5701 isl_multi_union_pw_aff_drop_dims(
5702 __isl_take isl_multi_union_pw_aff *mupa,
5703 enum isl_dim_type type, unsigned first,
5705 __isl_give isl_aff *isl_aff_move_dims(
5706 __isl_take isl_aff *aff,
5707 enum isl_dim_type dst_type, unsigned dst_pos,
5708 enum isl_dim_type src_type, unsigned src_pos,
5710 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
5711 __isl_take isl_multi_aff *ma,
5712 enum isl_dim_type dst_type, unsigned dst_pos,
5713 enum isl_dim_type src_type, unsigned src_pos,
5715 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
5716 __isl_take isl_pw_aff *pa,
5717 enum isl_dim_type dst_type, unsigned dst_pos,
5718 enum isl_dim_type src_type, unsigned src_pos,
5720 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
5721 __isl_take isl_multi_pw_aff *pma,
5722 enum isl_dim_type dst_type, unsigned dst_pos,
5723 enum isl_dim_type src_type, unsigned src_pos,
5726 #include <isl/polynomial.h>
5727 __isl_give isl_union_pw_qpolynomial *
5728 isl_union_pw_qpolynomial_drop_dims(
5729 __isl_take isl_union_pw_qpolynomial *upwqp,
5730 enum isl_dim_type type,
5731 unsigned first, unsigned n);
5732 __isl_give isl_union_pw_qpolynomial_fold *
5733 isl_union_pw_qpolynomial_fold_drop_dims(
5734 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5735 enum isl_dim_type type,
5736 unsigned first, unsigned n);
5738 The operations on union expressions can only manipulate parameters.
5742 =head2 Binary Operations
5744 The two arguments of a binary operation not only need to live
5745 in the same C<isl_ctx>, they currently also need to have
5746 the same (number of) parameters.
5748 =head3 Basic Operations
5752 =item * Intersection
5754 #include <isl/local_space.h>
5755 __isl_give isl_local_space *isl_local_space_intersect(
5756 __isl_take isl_local_space *ls1,
5757 __isl_take isl_local_space *ls2);
5759 #include <isl/set.h>
5760 __isl_give isl_basic_set *isl_basic_set_intersect_params(
5761 __isl_take isl_basic_set *bset1,
5762 __isl_take isl_basic_set *bset2);
5763 __isl_give isl_basic_set *isl_basic_set_intersect(
5764 __isl_take isl_basic_set *bset1,
5765 __isl_take isl_basic_set *bset2);
5766 __isl_give isl_basic_set *isl_basic_set_list_intersect(
5767 __isl_take struct isl_basic_set_list *list);
5768 __isl_give isl_set *isl_set_intersect_params(
5769 __isl_take isl_set *set,
5770 __isl_take isl_set *params);
5771 __isl_give isl_set *isl_set_intersect(
5772 __isl_take isl_set *set1,
5773 __isl_take isl_set *set2);
5775 #include <isl/map.h>
5776 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
5777 __isl_take isl_basic_map *bmap,
5778 __isl_take isl_basic_set *bset);
5779 __isl_give isl_basic_map *isl_basic_map_intersect_range(
5780 __isl_take isl_basic_map *bmap,
5781 __isl_take isl_basic_set *bset);
5782 __isl_give isl_basic_map *isl_basic_map_intersect(
5783 __isl_take isl_basic_map *bmap1,
5784 __isl_take isl_basic_map *bmap2);
5785 __isl_give isl_basic_map *isl_basic_map_list_intersect(
5786 __isl_take isl_basic_map_list *list);
5787 __isl_give isl_map *isl_map_intersect_params(
5788 __isl_take isl_map *map,
5789 __isl_take isl_set *params);
5790 __isl_give isl_map *isl_map_intersect_domain(
5791 __isl_take isl_map *map,
5792 __isl_take isl_set *set);
5793 __isl_give isl_map *isl_map_intersect_range(
5794 __isl_take isl_map *map,
5795 __isl_take isl_set *set);
5796 __isl_give isl_map *isl_map_intersect(
5797 __isl_take isl_map *map1,
5798 __isl_take isl_map *map2);
5800 #include <isl/union_set.h>
5801 __isl_give isl_union_set *isl_union_set_intersect_params(
5802 __isl_take isl_union_set *uset,
5803 __isl_take isl_set *set);
5804 __isl_give isl_union_set *isl_union_set_intersect(
5805 __isl_take isl_union_set *uset1,
5806 __isl_take isl_union_set *uset2);
5808 #include <isl/union_map.h>
5809 __isl_give isl_union_map *isl_union_map_intersect_params(
5810 __isl_take isl_union_map *umap,
5811 __isl_take isl_set *set);
5812 __isl_give isl_union_map *isl_union_map_intersect_domain(
5813 __isl_take isl_union_map *umap,
5814 __isl_take isl_union_set *uset);
5815 __isl_give isl_union_map *isl_union_map_intersect_range(
5816 __isl_take isl_union_map *umap,
5817 __isl_take isl_union_set *uset);
5818 __isl_give isl_union_map *isl_union_map_intersect(
5819 __isl_take isl_union_map *umap1,
5820 __isl_take isl_union_map *umap2);
5822 #include <isl/aff.h>
5823 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
5824 __isl_take isl_pw_aff *pa,
5825 __isl_take isl_set *set);
5826 __isl_give isl_multi_pw_aff *
5827 isl_multi_pw_aff_intersect_domain(
5828 __isl_take isl_multi_pw_aff *mpa,
5829 __isl_take isl_set *domain);
5830 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
5831 __isl_take isl_pw_multi_aff *pma,
5832 __isl_take isl_set *set);
5833 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
5834 __isl_take isl_union_pw_aff *upa,
5835 __isl_take isl_union_set *uset);
5836 __isl_give isl_union_pw_multi_aff *
5837 isl_union_pw_multi_aff_intersect_domain(
5838 __isl_take isl_union_pw_multi_aff *upma,
5839 __isl_take isl_union_set *uset);
5840 __isl_give isl_multi_union_pw_aff *
5841 isl_multi_union_pw_aff_intersect_domain(
5842 __isl_take isl_multi_union_pw_aff *mupa,
5843 __isl_take isl_union_set *uset);
5844 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
5845 __isl_take isl_pw_aff *pa,
5846 __isl_take isl_set *set);
5847 __isl_give isl_multi_pw_aff *
5848 isl_multi_pw_aff_intersect_params(
5849 __isl_take isl_multi_pw_aff *mpa,
5850 __isl_take isl_set *set);
5851 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
5852 __isl_take isl_pw_multi_aff *pma,
5853 __isl_take isl_set *set);
5854 __isl_give isl_union_pw_aff *
5855 isl_union_pw_aff_intersect_params(
5856 __isl_take isl_union_pw_aff *upa,
5857 __isl_give isl_union_pw_multi_aff *
5858 isl_union_pw_multi_aff_intersect_params(
5859 __isl_take isl_union_pw_multi_aff *upma,
5860 __isl_take isl_set *set);
5861 __isl_give isl_multi_union_pw_aff *
5862 isl_multi_union_pw_aff_intersect_params(
5863 __isl_take isl_multi_union_pw_aff *mupa,
5864 __isl_take isl_set *params);
5865 isl_multi_union_pw_aff_intersect_range(
5866 __isl_take isl_multi_union_pw_aff *mupa,
5867 __isl_take isl_set *set);
5869 #include <isl/polynomial.h>
5870 __isl_give isl_pw_qpolynomial *
5871 isl_pw_qpolynomial_intersect_domain(
5872 __isl_take isl_pw_qpolynomial *pwpq,
5873 __isl_take isl_set *set);
5874 __isl_give isl_union_pw_qpolynomial *
5875 isl_union_pw_qpolynomial_intersect_domain(
5876 __isl_take isl_union_pw_qpolynomial *upwpq,
5877 __isl_take isl_union_set *uset);
5878 __isl_give isl_union_pw_qpolynomial_fold *
5879 isl_union_pw_qpolynomial_fold_intersect_domain(
5880 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5881 __isl_take isl_union_set *uset);
5882 __isl_give isl_pw_qpolynomial *
5883 isl_pw_qpolynomial_intersect_params(
5884 __isl_take isl_pw_qpolynomial *pwpq,
5885 __isl_take isl_set *set);
5886 __isl_give isl_pw_qpolynomial_fold *
5887 isl_pw_qpolynomial_fold_intersect_params(
5888 __isl_take isl_pw_qpolynomial_fold *pwf,
5889 __isl_take isl_set *set);
5890 __isl_give isl_union_pw_qpolynomial *
5891 isl_union_pw_qpolynomial_intersect_params(
5892 __isl_take isl_union_pw_qpolynomial *upwpq,
5893 __isl_take isl_set *set);
5894 __isl_give isl_union_pw_qpolynomial_fold *
5895 isl_union_pw_qpolynomial_fold_intersect_params(
5896 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5897 __isl_take isl_set *set);
5899 The second argument to the C<_params> functions needs to be
5900 a parametric (basic) set. For the other functions, a parametric set
5901 for either argument is only allowed if the other argument is
5902 a parametric set as well.
5903 The list passed to C<isl_basic_set_list_intersect> needs to have
5904 at least one element and all elements need to live in the same space.
5905 The function C<isl_multi_union_pw_aff_intersect_range>
5906 restricts the input function to those shared domain elements
5907 that map to the specified range.
5911 #include <isl/set.h>
5912 __isl_give isl_set *isl_basic_set_union(
5913 __isl_take isl_basic_set *bset1,
5914 __isl_take isl_basic_set *bset2);
5915 __isl_give isl_set *isl_set_union(
5916 __isl_take isl_set *set1,
5917 __isl_take isl_set *set2);
5918 __isl_give isl_set *isl_set_list_union(
5919 __isl_take isl_set_list *list);
5921 #include <isl/map.h>
5922 __isl_give isl_map *isl_basic_map_union(
5923 __isl_take isl_basic_map *bmap1,
5924 __isl_take isl_basic_map *bmap2);
5925 __isl_give isl_map *isl_map_union(
5926 __isl_take isl_map *map1,
5927 __isl_take isl_map *map2);
5929 #include <isl/union_set.h>
5930 __isl_give isl_union_set *isl_union_set_union(
5931 __isl_take isl_union_set *uset1,
5932 __isl_take isl_union_set *uset2);
5933 __isl_give isl_union_set *isl_union_set_list_union(
5934 __isl_take isl_union_set_list *list);
5936 #include <isl/union_map.h>
5937 __isl_give isl_union_map *isl_union_map_union(
5938 __isl_take isl_union_map *umap1,
5939 __isl_take isl_union_map *umap2);
5941 The list passed to C<isl_set_list_union> needs to have
5942 at least one element and all elements need to live in the same space.
5944 =item * Set difference
5946 #include <isl/set.h>
5947 __isl_give isl_set *isl_set_subtract(
5948 __isl_take isl_set *set1,
5949 __isl_take isl_set *set2);
5951 #include <isl/map.h>
5952 __isl_give isl_map *isl_map_subtract(
5953 __isl_take isl_map *map1,
5954 __isl_take isl_map *map2);
5955 __isl_give isl_map *isl_map_subtract_domain(
5956 __isl_take isl_map *map,
5957 __isl_take isl_set *dom);
5958 __isl_give isl_map *isl_map_subtract_range(
5959 __isl_take isl_map *map,
5960 __isl_take isl_set *dom);
5962 #include <isl/union_set.h>
5963 __isl_give isl_union_set *isl_union_set_subtract(
5964 __isl_take isl_union_set *uset1,
5965 __isl_take isl_union_set *uset2);
5967 #include <isl/union_map.h>
5968 __isl_give isl_union_map *isl_union_map_subtract(
5969 __isl_take isl_union_map *umap1,
5970 __isl_take isl_union_map *umap2);
5971 __isl_give isl_union_map *isl_union_map_subtract_domain(
5972 __isl_take isl_union_map *umap,
5973 __isl_take isl_union_set *dom);
5974 __isl_give isl_union_map *isl_union_map_subtract_range(
5975 __isl_take isl_union_map *umap,
5976 __isl_take isl_union_set *dom);
5978 #include <isl/aff.h>
5979 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
5980 __isl_take isl_pw_aff *pa,
5981 __isl_take isl_set *set);
5982 __isl_give isl_pw_multi_aff *
5983 isl_pw_multi_aff_subtract_domain(
5984 __isl_take isl_pw_multi_aff *pma,
5985 __isl_take isl_set *set);
5986 __isl_give isl_union_pw_aff *
5987 isl_union_pw_aff_subtract_domain(
5988 __isl_take isl_union_pw_aff *upa,
5989 __isl_take isl_union_set *uset);
5990 __isl_give isl_union_pw_multi_aff *
5991 isl_union_pw_multi_aff_subtract_domain(
5992 __isl_take isl_union_pw_multi_aff *upma,
5993 __isl_take isl_set *set);
5995 #include <isl/polynomial.h>
5996 __isl_give isl_pw_qpolynomial *
5997 isl_pw_qpolynomial_subtract_domain(
5998 __isl_take isl_pw_qpolynomial *pwpq,
5999 __isl_take isl_set *set);
6000 __isl_give isl_pw_qpolynomial_fold *
6001 isl_pw_qpolynomial_fold_subtract_domain(
6002 __isl_take isl_pw_qpolynomial_fold *pwf,
6003 __isl_take isl_set *set);
6004 __isl_give isl_union_pw_qpolynomial *
6005 isl_union_pw_qpolynomial_subtract_domain(
6006 __isl_take isl_union_pw_qpolynomial *upwpq,
6007 __isl_take isl_union_set *uset);
6008 __isl_give isl_union_pw_qpolynomial_fold *
6009 isl_union_pw_qpolynomial_fold_subtract_domain(
6010 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6011 __isl_take isl_union_set *uset);
6015 #include <isl/space.h>
6016 __isl_give isl_space *isl_space_join(
6017 __isl_take isl_space *left,
6018 __isl_take isl_space *right);
6020 #include <isl/map.h>
6021 __isl_give isl_basic_set *isl_basic_set_apply(
6022 __isl_take isl_basic_set *bset,
6023 __isl_take isl_basic_map *bmap);
6024 __isl_give isl_set *isl_set_apply(
6025 __isl_take isl_set *set,
6026 __isl_take isl_map *map);
6027 __isl_give isl_union_set *isl_union_set_apply(
6028 __isl_take isl_union_set *uset,
6029 __isl_take isl_union_map *umap);
6030 __isl_give isl_basic_map *isl_basic_map_apply_domain(
6031 __isl_take isl_basic_map *bmap1,
6032 __isl_take isl_basic_map *bmap2);
6033 __isl_give isl_basic_map *isl_basic_map_apply_range(
6034 __isl_take isl_basic_map *bmap1,
6035 __isl_take isl_basic_map *bmap2);
6036 __isl_give isl_map *isl_map_apply_domain(
6037 __isl_take isl_map *map1,
6038 __isl_take isl_map *map2);
6039 __isl_give isl_map *isl_map_apply_range(
6040 __isl_take isl_map *map1,
6041 __isl_take isl_map *map2);
6043 #include <isl/union_map.h>
6044 __isl_give isl_union_map *isl_union_map_apply_domain(
6045 __isl_take isl_union_map *umap1,
6046 __isl_take isl_union_map *umap2);
6047 __isl_give isl_union_map *isl_union_map_apply_range(
6048 __isl_take isl_union_map *umap1,
6049 __isl_take isl_union_map *umap2);
6051 #include <isl/aff.h>
6052 __isl_give isl_union_pw_aff *
6053 isl_multi_union_pw_aff_apply_aff(
6054 __isl_take isl_multi_union_pw_aff *mupa,
6055 __isl_take isl_aff *aff);
6056 __isl_give isl_union_pw_aff *
6057 isl_multi_union_pw_aff_apply_pw_aff(
6058 __isl_take isl_multi_union_pw_aff *mupa,
6059 __isl_take isl_pw_aff *pa);
6060 __isl_give isl_multi_union_pw_aff *
6061 isl_multi_union_pw_aff_apply_multi_aff(
6062 __isl_take isl_multi_union_pw_aff *mupa,
6063 __isl_take isl_multi_aff *ma);
6064 __isl_give isl_multi_union_pw_aff *
6065 isl_multi_union_pw_aff_apply_pw_multi_aff(
6066 __isl_take isl_multi_union_pw_aff *mupa,
6067 __isl_take isl_pw_multi_aff *pma);
6069 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
6070 over the shared domain of the elements of the input. The dimension is
6071 required to be greater than zero.
6072 The C<isl_multi_union_pw_aff> argument of
6073 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
6074 but only if the range of the C<isl_multi_aff> argument
6075 is also zero-dimensional.
6076 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
6078 #include <isl/polynomial.h>
6079 __isl_give isl_pw_qpolynomial_fold *
6080 isl_set_apply_pw_qpolynomial_fold(
6081 __isl_take isl_set *set,
6082 __isl_take isl_pw_qpolynomial_fold *pwf,
6084 __isl_give isl_pw_qpolynomial_fold *
6085 isl_map_apply_pw_qpolynomial_fold(
6086 __isl_take isl_map *map,
6087 __isl_take isl_pw_qpolynomial_fold *pwf,
6089 __isl_give isl_union_pw_qpolynomial_fold *
6090 isl_union_set_apply_union_pw_qpolynomial_fold(
6091 __isl_take isl_union_set *uset,
6092 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6094 __isl_give isl_union_pw_qpolynomial_fold *
6095 isl_union_map_apply_union_pw_qpolynomial_fold(
6096 __isl_take isl_union_map *umap,
6097 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6100 The functions taking a map
6101 compose the given map with the given piecewise quasipolynomial reduction.
6102 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
6103 over all elements in the intersection of the range of the map
6104 and the domain of the piecewise quasipolynomial reduction
6105 as a function of an element in the domain of the map.
6106 The functions taking a set compute a bound over all elements in the
6107 intersection of the set and the domain of the
6108 piecewise quasipolynomial reduction.
6112 #include <isl/set.h>
6113 __isl_give isl_basic_set *
6114 isl_basic_set_preimage_multi_aff(
6115 __isl_take isl_basic_set *bset,
6116 __isl_take isl_multi_aff *ma);
6117 __isl_give isl_set *isl_set_preimage_multi_aff(
6118 __isl_take isl_set *set,
6119 __isl_take isl_multi_aff *ma);
6120 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
6121 __isl_take isl_set *set,
6122 __isl_take isl_pw_multi_aff *pma);
6123 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
6124 __isl_take isl_set *set,
6125 __isl_take isl_multi_pw_aff *mpa);
6127 #include <isl/union_set.h>
6128 __isl_give isl_union_set *
6129 isl_union_set_preimage_multi_aff(
6130 __isl_take isl_union_set *uset,
6131 __isl_take isl_multi_aff *ma);
6132 __isl_give isl_union_set *
6133 isl_union_set_preimage_pw_multi_aff(
6134 __isl_take isl_union_set *uset,
6135 __isl_take isl_pw_multi_aff *pma);
6136 __isl_give isl_union_set *
6137 isl_union_set_preimage_union_pw_multi_aff(
6138 __isl_take isl_union_set *uset,
6139 __isl_take isl_union_pw_multi_aff *upma);
6141 #include <isl/map.h>
6142 __isl_give isl_basic_map *
6143 isl_basic_map_preimage_domain_multi_aff(
6144 __isl_take isl_basic_map *bmap,
6145 __isl_take isl_multi_aff *ma);
6146 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
6147 __isl_take isl_map *map,
6148 __isl_take isl_multi_aff *ma);
6149 __isl_give isl_map *isl_map_preimage_range_multi_aff(
6150 __isl_take isl_map *map,
6151 __isl_take isl_multi_aff *ma);
6152 __isl_give isl_map *
6153 isl_map_preimage_domain_pw_multi_aff(
6154 __isl_take isl_map *map,
6155 __isl_take isl_pw_multi_aff *pma);
6156 __isl_give isl_map *
6157 isl_map_preimage_range_pw_multi_aff(
6158 __isl_take isl_map *map,
6159 __isl_take isl_pw_multi_aff *pma);
6160 __isl_give isl_map *
6161 isl_map_preimage_domain_multi_pw_aff(
6162 __isl_take isl_map *map,
6163 __isl_take isl_multi_pw_aff *mpa);
6164 __isl_give isl_basic_map *
6165 isl_basic_map_preimage_range_multi_aff(
6166 __isl_take isl_basic_map *bmap,
6167 __isl_take isl_multi_aff *ma);
6169 #include <isl/union_map.h>
6170 __isl_give isl_union_map *
6171 isl_union_map_preimage_domain_multi_aff(
6172 __isl_take isl_union_map *umap,
6173 __isl_take isl_multi_aff *ma);
6174 __isl_give isl_union_map *
6175 isl_union_map_preimage_range_multi_aff(
6176 __isl_take isl_union_map *umap,
6177 __isl_take isl_multi_aff *ma);
6178 __isl_give isl_union_map *
6179 isl_union_map_preimage_domain_pw_multi_aff(
6180 __isl_take isl_union_map *umap,
6181 __isl_take isl_pw_multi_aff *pma);
6182 __isl_give isl_union_map *
6183 isl_union_map_preimage_range_pw_multi_aff(
6184 __isl_take isl_union_map *umap,
6185 __isl_take isl_pw_multi_aff *pma);
6186 __isl_give isl_union_map *
6187 isl_union_map_preimage_domain_union_pw_multi_aff(
6188 __isl_take isl_union_map *umap,
6189 __isl_take isl_union_pw_multi_aff *upma);
6190 __isl_give isl_union_map *
6191 isl_union_map_preimage_range_union_pw_multi_aff(
6192 __isl_take isl_union_map *umap,
6193 __isl_take isl_union_pw_multi_aff *upma);
6195 These functions compute the preimage of the given set or map domain/range under
6196 the given function. In other words, the expression is plugged
6197 into the set description or into the domain/range of the map.
6201 #include <isl/aff.h>
6202 __isl_give isl_aff *isl_aff_pullback_aff(
6203 __isl_take isl_aff *aff1,
6204 __isl_take isl_aff *aff2);
6205 __isl_give isl_aff *isl_aff_pullback_multi_aff(
6206 __isl_take isl_aff *aff,
6207 __isl_take isl_multi_aff *ma);
6208 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
6209 __isl_take isl_pw_aff *pa,
6210 __isl_take isl_multi_aff *ma);
6211 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
6212 __isl_take isl_pw_aff *pa,
6213 __isl_take isl_pw_multi_aff *pma);
6214 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
6215 __isl_take isl_pw_aff *pa,
6216 __isl_take isl_multi_pw_aff *mpa);
6217 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
6218 __isl_take isl_multi_aff *ma1,
6219 __isl_take isl_multi_aff *ma2);
6220 __isl_give isl_pw_multi_aff *
6221 isl_pw_multi_aff_pullback_multi_aff(
6222 __isl_take isl_pw_multi_aff *pma,
6223 __isl_take isl_multi_aff *ma);
6224 __isl_give isl_multi_pw_aff *
6225 isl_multi_pw_aff_pullback_multi_aff(
6226 __isl_take isl_multi_pw_aff *mpa,
6227 __isl_take isl_multi_aff *ma);
6228 __isl_give isl_pw_multi_aff *
6229 isl_pw_multi_aff_pullback_pw_multi_aff(
6230 __isl_take isl_pw_multi_aff *pma1,
6231 __isl_take isl_pw_multi_aff *pma2);
6232 __isl_give isl_multi_pw_aff *
6233 isl_multi_pw_aff_pullback_pw_multi_aff(
6234 __isl_take isl_multi_pw_aff *mpa,
6235 __isl_take isl_pw_multi_aff *pma);
6236 __isl_give isl_multi_pw_aff *
6237 isl_multi_pw_aff_pullback_multi_pw_aff(
6238 __isl_take isl_multi_pw_aff *mpa1,
6239 __isl_take isl_multi_pw_aff *mpa2);
6240 __isl_give isl_union_pw_aff *
6241 isl_union_pw_aff_pullback_union_pw_multi_aff(
6242 __isl_take isl_union_pw_aff *upa,
6243 __isl_take isl_union_pw_multi_aff *upma);
6244 __isl_give isl_union_pw_multi_aff *
6245 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
6246 __isl_take isl_union_pw_multi_aff *upma1,
6247 __isl_take isl_union_pw_multi_aff *upma2);
6248 __isl_give isl_multi_union_pw_aff *
6249 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
6250 __isl_take isl_multi_union_pw_aff *mupa,
6251 __isl_take isl_union_pw_multi_aff *upma);
6253 These functions precompose the first expression by the second function.
6254 In other words, the second function is plugged
6255 into the first expression.
6259 #include <isl/aff.h>
6260 __isl_give isl_basic_set *isl_aff_eq_basic_set(
6261 __isl_take isl_aff *aff1,
6262 __isl_take isl_aff *aff2);
6263 __isl_give isl_set *isl_aff_eq_set(
6264 __isl_take isl_aff *aff1,
6265 __isl_take isl_aff *aff2);
6266 __isl_give isl_basic_set *isl_aff_le_basic_set(
6267 __isl_take isl_aff *aff1,
6268 __isl_take isl_aff *aff2);
6269 __isl_give isl_set *isl_aff_le_set(
6270 __isl_take isl_aff *aff1,
6271 __isl_take isl_aff *aff2);
6272 __isl_give isl_basic_set *isl_aff_ge_basic_set(
6273 __isl_take isl_aff *aff1,
6274 __isl_take isl_aff *aff2);
6275 __isl_give isl_set *isl_aff_ge_set(
6276 __isl_take isl_aff *aff1,
6277 __isl_take isl_aff *aff2);
6278 __isl_give isl_set *isl_pw_aff_eq_set(
6279 __isl_take isl_pw_aff *pwaff1,
6280 __isl_take isl_pw_aff *pwaff2);
6281 __isl_give isl_set *isl_pw_aff_ne_set(
6282 __isl_take isl_pw_aff *pwaff1,
6283 __isl_take isl_pw_aff *pwaff2);
6284 __isl_give isl_set *isl_pw_aff_le_set(
6285 __isl_take isl_pw_aff *pwaff1,
6286 __isl_take isl_pw_aff *pwaff2);
6287 __isl_give isl_set *isl_pw_aff_lt_set(
6288 __isl_take isl_pw_aff *pwaff1,
6289 __isl_take isl_pw_aff *pwaff2);
6290 __isl_give isl_set *isl_pw_aff_ge_set(
6291 __isl_take isl_pw_aff *pwaff1,
6292 __isl_take isl_pw_aff *pwaff2);
6293 __isl_give isl_set *isl_pw_aff_gt_set(
6294 __isl_take isl_pw_aff *pwaff1,
6295 __isl_take isl_pw_aff *pwaff2);
6297 __isl_give isl_set *isl_multi_aff_lex_le_set(
6298 __isl_take isl_multi_aff *ma1,
6299 __isl_take isl_multi_aff *ma2);
6300 __isl_give isl_set *isl_multi_aff_lex_lt_set(
6301 __isl_take isl_multi_aff *ma1,
6302 __isl_take isl_multi_aff *ma2);
6303 __isl_give isl_set *isl_multi_aff_lex_ge_set(
6304 __isl_take isl_multi_aff *ma1,
6305 __isl_take isl_multi_aff *ma2);
6306 __isl_give isl_set *isl_multi_aff_lex_gt_set(
6307 __isl_take isl_multi_aff *ma1,
6308 __isl_take isl_multi_aff *ma2);
6310 __isl_give isl_set *isl_pw_aff_list_eq_set(
6311 __isl_take isl_pw_aff_list *list1,
6312 __isl_take isl_pw_aff_list *list2);
6313 __isl_give isl_set *isl_pw_aff_list_ne_set(
6314 __isl_take isl_pw_aff_list *list1,
6315 __isl_take isl_pw_aff_list *list2);
6316 __isl_give isl_set *isl_pw_aff_list_le_set(
6317 __isl_take isl_pw_aff_list *list1,
6318 __isl_take isl_pw_aff_list *list2);
6319 __isl_give isl_set *isl_pw_aff_list_lt_set(
6320 __isl_take isl_pw_aff_list *list1,
6321 __isl_take isl_pw_aff_list *list2);
6322 __isl_give isl_set *isl_pw_aff_list_ge_set(
6323 __isl_take isl_pw_aff_list *list1,
6324 __isl_take isl_pw_aff_list *list2);
6325 __isl_give isl_set *isl_pw_aff_list_gt_set(
6326 __isl_take isl_pw_aff_list *list1,
6327 __isl_take isl_pw_aff_list *list2);
6329 The function C<isl_aff_ge_basic_set> returns a basic set
6330 containing those elements in the shared space
6331 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
6332 The function C<isl_pw_aff_ge_set> returns a set
6333 containing those elements in the shared domain
6334 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
6335 greater than or equal to C<pwaff2>.
6336 The function C<isl_multi_aff_lex_le_set> returns a set
6337 containing those elements in the shared domain space
6338 where C<ma1> is lexicographically smaller than or
6340 The functions operating on C<isl_pw_aff_list> apply the corresponding
6341 C<isl_pw_aff> function to each pair of elements in the two lists.
6343 #include <isl/aff.h>
6344 __isl_give isl_map *isl_pw_aff_eq_map(
6345 __isl_take isl_pw_aff *pa1,
6346 __isl_take isl_pw_aff *pa2);
6347 __isl_give isl_map *isl_pw_aff_lt_map(
6348 __isl_take isl_pw_aff *pa1,
6349 __isl_take isl_pw_aff *pa2);
6350 __isl_give isl_map *isl_pw_aff_gt_map(
6351 __isl_take isl_pw_aff *pa1,
6352 __isl_take isl_pw_aff *pa2);
6354 __isl_give isl_map *isl_multi_pw_aff_eq_map(
6355 __isl_take isl_multi_pw_aff *mpa1,
6356 __isl_take isl_multi_pw_aff *mpa2);
6357 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
6358 __isl_take isl_multi_pw_aff *mpa1,
6359 __isl_take isl_multi_pw_aff *mpa2);
6360 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
6361 __isl_take isl_multi_pw_aff *mpa1,
6362 __isl_take isl_multi_pw_aff *mpa2);
6364 These functions return a map between domain elements of the arguments
6365 where the function values satisfy the given relation.
6367 #include <isl/union_map.h>
6368 __isl_give isl_union_map *
6369 isl_union_map_eq_at_multi_union_pw_aff(
6370 __isl_take isl_union_map *umap,
6371 __isl_take isl_multi_union_pw_aff *mupa);
6372 __isl_give isl_union_map *
6373 isl_union_map_lex_lt_at_multi_union_pw_aff(
6374 __isl_take isl_union_map *umap,
6375 __isl_take isl_multi_union_pw_aff *mupa);
6376 __isl_give isl_union_map *
6377 isl_union_map_lex_gt_at_multi_union_pw_aff(
6378 __isl_take isl_union_map *umap,
6379 __isl_take isl_multi_union_pw_aff *mupa);
6381 These functions select the subset of elements in the union map
6382 that have an equal or lexicographically smaller function value.
6384 =item * Cartesian Product
6386 #include <isl/space.h>
6387 __isl_give isl_space *isl_space_product(
6388 __isl_take isl_space *space1,
6389 __isl_take isl_space *space2);
6390 __isl_give isl_space *isl_space_domain_product(
6391 __isl_take isl_space *space1,
6392 __isl_take isl_space *space2);
6393 __isl_give isl_space *isl_space_range_product(
6394 __isl_take isl_space *space1,
6395 __isl_take isl_space *space2);
6398 C<isl_space_product>, C<isl_space_domain_product>
6399 and C<isl_space_range_product> take pairs or relation spaces and
6400 produce a single relations space, where either the domain, the range
6401 or both domain and range are wrapped spaces of relations between
6402 the domains and/or ranges of the input spaces.
6403 If the product is only constructed over the domain or the range
6404 then the ranges or the domains of the inputs should be the same.
6405 The function C<isl_space_product> also accepts a pair of set spaces,
6406 in which case it returns a wrapped space of a relation between the
6409 #include <isl/set.h>
6410 __isl_give isl_set *isl_set_product(
6411 __isl_take isl_set *set1,
6412 __isl_take isl_set *set2);
6414 #include <isl/map.h>
6415 __isl_give isl_basic_map *isl_basic_map_domain_product(
6416 __isl_take isl_basic_map *bmap1,
6417 __isl_take isl_basic_map *bmap2);
6418 __isl_give isl_basic_map *isl_basic_map_range_product(
6419 __isl_take isl_basic_map *bmap1,
6420 __isl_take isl_basic_map *bmap2);
6421 __isl_give isl_basic_map *isl_basic_map_product(
6422 __isl_take isl_basic_map *bmap1,
6423 __isl_take isl_basic_map *bmap2);
6424 __isl_give isl_map *isl_map_domain_product(
6425 __isl_take isl_map *map1,
6426 __isl_take isl_map *map2);
6427 __isl_give isl_map *isl_map_range_product(
6428 __isl_take isl_map *map1,
6429 __isl_take isl_map *map2);
6430 __isl_give isl_map *isl_map_product(
6431 __isl_take isl_map *map1,
6432 __isl_take isl_map *map2);
6434 #include <isl/union_set.h>
6435 __isl_give isl_union_set *isl_union_set_product(
6436 __isl_take isl_union_set *uset1,
6437 __isl_take isl_union_set *uset2);
6439 #include <isl/union_map.h>
6440 __isl_give isl_union_map *isl_union_map_domain_product(
6441 __isl_take isl_union_map *umap1,
6442 __isl_take isl_union_map *umap2);
6443 __isl_give isl_union_map *isl_union_map_range_product(
6444 __isl_take isl_union_map *umap1,
6445 __isl_take isl_union_map *umap2);
6446 __isl_give isl_union_map *isl_union_map_product(
6447 __isl_take isl_union_map *umap1,
6448 __isl_take isl_union_map *umap2);
6450 #include <isl/val.h>
6451 __isl_give isl_multi_val *isl_multi_val_range_product(
6452 __isl_take isl_multi_val *mv1,
6453 __isl_take isl_multi_val *mv2);
6454 __isl_give isl_multi_val *isl_multi_val_product(
6455 __isl_take isl_multi_val *mv1,
6456 __isl_take isl_multi_val *mv2);
6458 #include <isl/aff.h>
6459 __isl_give isl_multi_aff *isl_multi_aff_range_product(
6460 __isl_take isl_multi_aff *ma1,
6461 __isl_take isl_multi_aff *ma2);
6462 __isl_give isl_multi_aff *isl_multi_aff_product(
6463 __isl_take isl_multi_aff *ma1,
6464 __isl_take isl_multi_aff *ma2);
6465 __isl_give isl_multi_pw_aff *
6466 isl_multi_pw_aff_range_product(
6467 __isl_take isl_multi_pw_aff *mpa1,
6468 __isl_take isl_multi_pw_aff *mpa2);
6469 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
6470 __isl_take isl_multi_pw_aff *mpa1,
6471 __isl_take isl_multi_pw_aff *mpa2);
6472 __isl_give isl_pw_multi_aff *
6473 isl_pw_multi_aff_range_product(
6474 __isl_take isl_pw_multi_aff *pma1,
6475 __isl_take isl_pw_multi_aff *pma2);
6476 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
6477 __isl_take isl_pw_multi_aff *pma1,
6478 __isl_take isl_pw_multi_aff *pma2);
6479 __isl_give isl_multi_union_pw_aff *
6480 isl_multi_union_pw_aff_range_product(
6481 __isl_take isl_multi_union_pw_aff *mupa1,
6482 __isl_take isl_multi_union_pw_aff *mupa2);
6484 The above functions compute the cross product of the given
6485 sets, relations or functions. The domains and ranges of the results
6486 are wrapped maps between domains and ranges of the inputs.
6487 To obtain a ``flat'' product, use the following functions
6490 #include <isl/set.h>
6491 __isl_give isl_basic_set *isl_basic_set_flat_product(
6492 __isl_take isl_basic_set *bset1,
6493 __isl_take isl_basic_set *bset2);
6494 __isl_give isl_set *isl_set_flat_product(
6495 __isl_take isl_set *set1,
6496 __isl_take isl_set *set2);
6498 #include <isl/map.h>
6499 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
6500 __isl_take isl_basic_map *bmap1,
6501 __isl_take isl_basic_map *bmap2);
6502 __isl_give isl_map *isl_map_flat_domain_product(
6503 __isl_take isl_map *map1,
6504 __isl_take isl_map *map2);
6505 __isl_give isl_map *isl_map_flat_range_product(
6506 __isl_take isl_map *map1,
6507 __isl_take isl_map *map2);
6508 __isl_give isl_basic_map *isl_basic_map_flat_product(
6509 __isl_take isl_basic_map *bmap1,
6510 __isl_take isl_basic_map *bmap2);
6511 __isl_give isl_map *isl_map_flat_product(
6512 __isl_take isl_map *map1,
6513 __isl_take isl_map *map2);
6515 #include <isl/union_map.h>
6516 __isl_give isl_union_map *
6517 isl_union_map_flat_domain_product(
6518 __isl_take isl_union_map *umap1,
6519 __isl_take isl_union_map *umap2);
6520 __isl_give isl_union_map *
6521 isl_union_map_flat_range_product(
6522 __isl_take isl_union_map *umap1,
6523 __isl_take isl_union_map *umap2);
6525 #include <isl/val.h>
6526 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
6527 __isl_take isl_multi_val *mv1,
6528 __isl_take isl_multi_aff *mv2);
6530 #include <isl/aff.h>
6531 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
6532 __isl_take isl_multi_aff *ma1,
6533 __isl_take isl_multi_aff *ma2);
6534 __isl_give isl_pw_multi_aff *
6535 isl_pw_multi_aff_flat_range_product(
6536 __isl_take isl_pw_multi_aff *pma1,
6537 __isl_take isl_pw_multi_aff *pma2);
6538 __isl_give isl_multi_pw_aff *
6539 isl_multi_pw_aff_flat_range_product(
6540 __isl_take isl_multi_pw_aff *mpa1,
6541 __isl_take isl_multi_pw_aff *mpa2);
6542 __isl_give isl_union_pw_multi_aff *
6543 isl_union_pw_multi_aff_flat_range_product(
6544 __isl_take isl_union_pw_multi_aff *upma1,
6545 __isl_take isl_union_pw_multi_aff *upma2);
6546 __isl_give isl_multi_union_pw_aff *
6547 isl_multi_union_pw_aff_flat_range_product(
6548 __isl_take isl_multi_union_pw_aff *mupa1,
6549 __isl_take isl_multi_union_pw_aff *mupa2);
6551 #include <isl/space.h>
6552 __isl_give isl_space *isl_space_factor_domain(
6553 __isl_take isl_space *space);
6554 __isl_give isl_space *isl_space_factor_range(
6555 __isl_take isl_space *space);
6556 __isl_give isl_space *isl_space_domain_factor_domain(
6557 __isl_take isl_space *space);
6558 __isl_give isl_space *isl_space_domain_factor_range(
6559 __isl_take isl_space *space);
6560 __isl_give isl_space *isl_space_range_factor_domain(
6561 __isl_take isl_space *space);
6562 __isl_give isl_space *isl_space_range_factor_range(
6563 __isl_take isl_space *space);
6565 The functions C<isl_space_range_factor_domain> and
6566 C<isl_space_range_factor_range> extract the two arguments from
6567 the result of a call to C<isl_space_range_product>.
6569 The arguments of a call to a product can be extracted
6570 from the result using the following functions.
6572 #include <isl/map.h>
6573 __isl_give isl_map *isl_map_factor_domain(
6574 __isl_take isl_map *map);
6575 __isl_give isl_map *isl_map_factor_range(
6576 __isl_take isl_map *map);
6577 __isl_give isl_map *isl_map_domain_factor_domain(
6578 __isl_take isl_map *map);
6579 __isl_give isl_map *isl_map_domain_factor_range(
6580 __isl_take isl_map *map);
6581 __isl_give isl_map *isl_map_range_factor_domain(
6582 __isl_take isl_map *map);
6583 __isl_give isl_map *isl_map_range_factor_range(
6584 __isl_take isl_map *map);
6586 #include <isl/union_map.h>
6587 __isl_give isl_union_map *isl_union_map_factor_domain(
6588 __isl_take isl_union_map *umap);
6589 __isl_give isl_union_map *isl_union_map_factor_range(
6590 __isl_take isl_union_map *umap);
6591 __isl_give isl_union_map *
6592 isl_union_map_domain_factor_domain(
6593 __isl_take isl_union_map *umap);
6594 __isl_give isl_union_map *
6595 isl_union_map_domain_factor_range(
6596 __isl_take isl_union_map *umap);
6597 __isl_give isl_union_map *
6598 isl_union_map_range_factor_domain(
6599 __isl_take isl_union_map *umap);
6600 __isl_give isl_union_map *
6601 isl_union_map_range_factor_range(
6602 __isl_take isl_union_map *umap);
6604 #include <isl/val.h>
6605 __isl_give isl_multi_val *isl_multi_val_factor_range(
6606 __isl_take isl_multi_val *mv);
6607 __isl_give isl_multi_val *
6608 isl_multi_val_range_factor_domain(
6609 __isl_take isl_multi_val *mv);
6610 __isl_give isl_multi_val *
6611 isl_multi_val_range_factor_range(
6612 __isl_take isl_multi_val *mv);
6614 #include <isl/aff.h>
6615 __isl_give isl_multi_aff *isl_multi_aff_factor_range(
6616 __isl_take isl_multi_aff *ma);
6617 __isl_give isl_multi_aff *
6618 isl_multi_aff_range_factor_domain(
6619 __isl_take isl_multi_aff *ma);
6620 __isl_give isl_multi_aff *
6621 isl_multi_aff_range_factor_range(
6622 __isl_take isl_multi_aff *ma);
6623 __isl_give isl_multi_pw_aff *
6624 isl_multi_pw_aff_factor_range(
6625 __isl_take isl_multi_pw_aff *mpa);
6626 __isl_give isl_multi_pw_aff *
6627 isl_multi_pw_aff_range_factor_domain(
6628 __isl_take isl_multi_pw_aff *mpa);
6629 __isl_give isl_multi_pw_aff *
6630 isl_multi_pw_aff_range_factor_range(
6631 __isl_take isl_multi_pw_aff *mpa);
6632 __isl_give isl_multi_union_pw_aff *
6633 isl_multi_union_pw_aff_factor_range(
6634 __isl_take isl_multi_union_pw_aff *mupa);
6635 __isl_give isl_multi_union_pw_aff *
6636 isl_multi_union_pw_aff_range_factor_domain(
6637 __isl_take isl_multi_union_pw_aff *mupa);
6638 __isl_give isl_multi_union_pw_aff *
6639 isl_multi_union_pw_aff_range_factor_range(
6640 __isl_take isl_multi_union_pw_aff *mupa);
6642 The splice functions are a generalization of the flat product functions,
6643 where the second argument may be inserted at any position inside
6644 the first argument rather than being placed at the end.
6645 The functions C<isl_multi_val_factor_range>,
6646 C<isl_multi_aff_factor_range>,
6647 C<isl_multi_pw_aff_factor_range> and
6648 C<isl_multi_union_pw_aff_factor_range>
6649 take functions that live in a set space.
6651 #include <isl/val.h>
6652 __isl_give isl_multi_val *isl_multi_val_range_splice(
6653 __isl_take isl_multi_val *mv1, unsigned pos,
6654 __isl_take isl_multi_val *mv2);
6656 #include <isl/aff.h>
6657 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
6658 __isl_take isl_multi_aff *ma1, unsigned pos,
6659 __isl_take isl_multi_aff *ma2);
6660 __isl_give isl_multi_aff *isl_multi_aff_splice(
6661 __isl_take isl_multi_aff *ma1,
6662 unsigned in_pos, unsigned out_pos,
6663 __isl_take isl_multi_aff *ma2);
6664 __isl_give isl_multi_pw_aff *
6665 isl_multi_pw_aff_range_splice(
6666 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
6667 __isl_take isl_multi_pw_aff *mpa2);
6668 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
6669 __isl_take isl_multi_pw_aff *mpa1,
6670 unsigned in_pos, unsigned out_pos,
6671 __isl_take isl_multi_pw_aff *mpa2);
6672 __isl_give isl_multi_union_pw_aff *
6673 isl_multi_union_pw_aff_range_splice(
6674 __isl_take isl_multi_union_pw_aff *mupa1,
6676 __isl_take isl_multi_union_pw_aff *mupa2);
6678 =item * Simplification
6680 When applied to a set or relation,
6681 the gist operation returns a set or relation that has the
6682 same intersection with the context as the input set or relation.
6683 Any implicit equality in the intersection is made explicit in the result,
6684 while all inequalities that are redundant with respect to the intersection
6686 In case of union sets and relations, the gist operation is performed
6689 When applied to a function,
6690 the gist operation applies the set gist operation to each of
6691 the cells in the domain of the input piecewise expression.
6692 The context is also exploited
6693 to simplify the expression associated to each cell.
6695 #include <isl/set.h>
6696 __isl_give isl_basic_set *isl_basic_set_gist(
6697 __isl_take isl_basic_set *bset,
6698 __isl_take isl_basic_set *context);
6699 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
6700 __isl_take isl_set *context);
6701 __isl_give isl_set *isl_set_gist_params(
6702 __isl_take isl_set *set,
6703 __isl_take isl_set *context);
6705 #include <isl/map.h>
6706 __isl_give isl_basic_map *isl_basic_map_gist(
6707 __isl_take isl_basic_map *bmap,
6708 __isl_take isl_basic_map *context);
6709 __isl_give isl_basic_map *isl_basic_map_gist_domain(
6710 __isl_take isl_basic_map *bmap,
6711 __isl_take isl_basic_set *context);
6712 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
6713 __isl_take isl_map *context);
6714 __isl_give isl_map *isl_map_gist_params(
6715 __isl_take isl_map *map,
6716 __isl_take isl_set *context);
6717 __isl_give isl_map *isl_map_gist_domain(
6718 __isl_take isl_map *map,
6719 __isl_take isl_set *context);
6720 __isl_give isl_map *isl_map_gist_range(
6721 __isl_take isl_map *map,
6722 __isl_take isl_set *context);
6724 #include <isl/union_set.h>
6725 __isl_give isl_union_set *isl_union_set_gist(
6726 __isl_take isl_union_set *uset,
6727 __isl_take isl_union_set *context);
6728 __isl_give isl_union_set *isl_union_set_gist_params(
6729 __isl_take isl_union_set *uset,
6730 __isl_take isl_set *set);
6732 #include <isl/union_map.h>
6733 __isl_give isl_union_map *isl_union_map_gist(
6734 __isl_take isl_union_map *umap,
6735 __isl_take isl_union_map *context);
6736 __isl_give isl_union_map *isl_union_map_gist_params(
6737 __isl_take isl_union_map *umap,
6738 __isl_take isl_set *set);
6739 __isl_give isl_union_map *isl_union_map_gist_domain(
6740 __isl_take isl_union_map *umap,
6741 __isl_take isl_union_set *uset);
6742 __isl_give isl_union_map *isl_union_map_gist_range(
6743 __isl_take isl_union_map *umap,
6744 __isl_take isl_union_set *uset);
6746 #include <isl/aff.h>
6747 __isl_give isl_aff *isl_aff_gist_params(
6748 __isl_take isl_aff *aff,
6749 __isl_take isl_set *context);
6750 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
6751 __isl_take isl_set *context);
6752 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
6753 __isl_take isl_multi_aff *maff,
6754 __isl_take isl_set *context);
6755 __isl_give isl_multi_aff *isl_multi_aff_gist(
6756 __isl_take isl_multi_aff *maff,
6757 __isl_take isl_set *context);
6758 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
6759 __isl_take isl_pw_aff *pwaff,
6760 __isl_take isl_set *context);
6761 __isl_give isl_pw_aff *isl_pw_aff_gist(
6762 __isl_take isl_pw_aff *pwaff,
6763 __isl_take isl_set *context);
6764 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
6765 __isl_take isl_pw_multi_aff *pma,
6766 __isl_take isl_set *set);
6767 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
6768 __isl_take isl_pw_multi_aff *pma,
6769 __isl_take isl_set *set);
6770 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
6771 __isl_take isl_multi_pw_aff *mpa,
6772 __isl_take isl_set *set);
6773 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
6774 __isl_take isl_multi_pw_aff *mpa,
6775 __isl_take isl_set *set);
6776 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
6777 __isl_take isl_union_pw_aff *upa,
6778 __isl_take isl_union_set *context);
6779 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
6780 __isl_take isl_union_pw_aff *upa,
6781 __isl_take isl_set *context);
6782 __isl_give isl_union_pw_multi_aff *
6783 isl_union_pw_multi_aff_gist_params(
6784 __isl_take isl_union_pw_multi_aff *upma,
6785 __isl_take isl_set *context);
6786 __isl_give isl_union_pw_multi_aff *
6787 isl_union_pw_multi_aff_gist(
6788 __isl_take isl_union_pw_multi_aff *upma,
6789 __isl_take isl_union_set *context);
6790 __isl_give isl_multi_union_pw_aff *
6791 isl_multi_union_pw_aff_gist_params(
6792 __isl_take isl_multi_union_pw_aff *aff,
6793 __isl_take isl_set *context);
6794 __isl_give isl_multi_union_pw_aff *
6795 isl_multi_union_pw_aff_gist(
6796 __isl_take isl_multi_union_pw_aff *aff,
6797 __isl_take isl_union_set *context);
6799 #include <isl/polynomial.h>
6800 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
6801 __isl_take isl_qpolynomial *qp,
6802 __isl_take isl_set *context);
6803 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
6804 __isl_take isl_qpolynomial *qp,
6805 __isl_take isl_set *context);
6806 __isl_give isl_qpolynomial_fold *
6807 isl_qpolynomial_fold_gist_params(
6808 __isl_take isl_qpolynomial_fold *fold,
6809 __isl_take isl_set *context);
6810 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
6811 __isl_take isl_qpolynomial_fold *fold,
6812 __isl_take isl_set *context);
6813 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
6814 __isl_take isl_pw_qpolynomial *pwqp,
6815 __isl_take isl_set *context);
6816 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
6817 __isl_take isl_pw_qpolynomial *pwqp,
6818 __isl_take isl_set *context);
6819 __isl_give isl_pw_qpolynomial_fold *
6820 isl_pw_qpolynomial_fold_gist(
6821 __isl_take isl_pw_qpolynomial_fold *pwf,
6822 __isl_take isl_set *context);
6823 __isl_give isl_pw_qpolynomial_fold *
6824 isl_pw_qpolynomial_fold_gist_params(
6825 __isl_take isl_pw_qpolynomial_fold *pwf,
6826 __isl_take isl_set *context);
6827 __isl_give isl_union_pw_qpolynomial *
6828 isl_union_pw_qpolynomial_gist_params(
6829 __isl_take isl_union_pw_qpolynomial *upwqp,
6830 __isl_take isl_set *context);
6831 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
6832 __isl_take isl_union_pw_qpolynomial *upwqp,
6833 __isl_take isl_union_set *context);
6834 __isl_give isl_union_pw_qpolynomial_fold *
6835 isl_union_pw_qpolynomial_fold_gist(
6836 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6837 __isl_take isl_union_set *context);
6838 __isl_give isl_union_pw_qpolynomial_fold *
6839 isl_union_pw_qpolynomial_fold_gist_params(
6840 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6841 __isl_take isl_set *context);
6843 =item * Binary Arithmetic Operations
6845 #include <isl/set.h>
6846 __isl_give isl_set *isl_set_sum(
6847 __isl_take isl_set *set1,
6848 __isl_take isl_set *set2);
6849 #include <isl/map.h>
6850 __isl_give isl_map *isl_map_sum(
6851 __isl_take isl_map *map1,
6852 __isl_take isl_map *map2);
6854 C<isl_set_sum> computes the Minkowski sum of its two arguments,
6855 i.e., the set containing the sums of pairs of elements from
6856 C<set1> and C<set2>.
6857 The domain of the result of C<isl_map_sum> is the intersection
6858 of the domains of its two arguments. The corresponding range
6859 elements are the sums of the corresponding range elements
6860 in the two arguments.
6862 #include <isl/val.h>
6863 __isl_give isl_multi_val *isl_multi_val_add(
6864 __isl_take isl_multi_val *mv1,
6865 __isl_take isl_multi_val *mv2);
6866 __isl_give isl_multi_val *isl_multi_val_sub(
6867 __isl_take isl_multi_val *mv1,
6868 __isl_take isl_multi_val *mv2);
6870 #include <isl/aff.h>
6871 __isl_give isl_aff *isl_aff_add(
6872 __isl_take isl_aff *aff1,
6873 __isl_take isl_aff *aff2);
6874 __isl_give isl_multi_aff *isl_multi_aff_add(
6875 __isl_take isl_multi_aff *maff1,
6876 __isl_take isl_multi_aff *maff2);
6877 __isl_give isl_pw_aff *isl_pw_aff_add(
6878 __isl_take isl_pw_aff *pwaff1,
6879 __isl_take isl_pw_aff *pwaff2);
6880 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add(
6881 __isl_take isl_multi_pw_aff *mpa1,
6882 __isl_take isl_multi_pw_aff *mpa2);
6883 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
6884 __isl_take isl_pw_multi_aff *pma1,
6885 __isl_take isl_pw_multi_aff *pma2);
6886 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
6887 __isl_take isl_union_pw_aff *upa1,
6888 __isl_take isl_union_pw_aff *upa2);
6889 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
6890 __isl_take isl_union_pw_multi_aff *upma1,
6891 __isl_take isl_union_pw_multi_aff *upma2);
6892 __isl_give isl_multi_union_pw_aff *
6893 isl_multi_union_pw_aff_add(
6894 __isl_take isl_multi_union_pw_aff *mupa1,
6895 __isl_take isl_multi_union_pw_aff *mupa2);
6896 __isl_give isl_pw_aff *isl_pw_aff_min(
6897 __isl_take isl_pw_aff *pwaff1,
6898 __isl_take isl_pw_aff *pwaff2);
6899 __isl_give isl_pw_aff *isl_pw_aff_max(
6900 __isl_take isl_pw_aff *pwaff1,
6901 __isl_take isl_pw_aff *pwaff2);
6902 __isl_give isl_aff *isl_aff_sub(
6903 __isl_take isl_aff *aff1,
6904 __isl_take isl_aff *aff2);
6905 __isl_give isl_multi_aff *isl_multi_aff_sub(
6906 __isl_take isl_multi_aff *ma1,
6907 __isl_take isl_multi_aff *ma2);
6908 __isl_give isl_pw_aff *isl_pw_aff_sub(
6909 __isl_take isl_pw_aff *pwaff1,
6910 __isl_take isl_pw_aff *pwaff2);
6911 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
6912 __isl_take isl_multi_pw_aff *mpa1,
6913 __isl_take isl_multi_pw_aff *mpa2);
6914 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
6915 __isl_take isl_pw_multi_aff *pma1,
6916 __isl_take isl_pw_multi_aff *pma2);
6917 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
6918 __isl_take isl_union_pw_aff *upa1,
6919 __isl_take isl_union_pw_aff *upa2);
6920 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
6921 __isl_take isl_union_pw_multi_aff *upma1,
6922 __isl_take isl_union_pw_multi_aff *upma2);
6923 __isl_give isl_multi_union_pw_aff *
6924 isl_multi_union_pw_aff_sub(
6925 __isl_take isl_multi_union_pw_aff *mupa1,
6926 __isl_take isl_multi_union_pw_aff *mupa2);
6928 C<isl_aff_sub> subtracts the second argument from the first.
6930 #include <isl/polynomial.h>
6931 __isl_give isl_qpolynomial *isl_qpolynomial_add(
6932 __isl_take isl_qpolynomial *qp1,
6933 __isl_take isl_qpolynomial *qp2);
6934 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
6935 __isl_take isl_pw_qpolynomial *pwqp1,
6936 __isl_take isl_pw_qpolynomial *pwqp2);
6937 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
6938 __isl_take isl_pw_qpolynomial *pwqp1,
6939 __isl_take isl_pw_qpolynomial *pwqp2);
6940 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
6941 __isl_take isl_pw_qpolynomial_fold *pwf1,
6942 __isl_take isl_pw_qpolynomial_fold *pwf2);
6943 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
6944 __isl_take isl_union_pw_qpolynomial *upwqp1,
6945 __isl_take isl_union_pw_qpolynomial *upwqp2);
6946 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
6947 __isl_take isl_qpolynomial *qp1,
6948 __isl_take isl_qpolynomial *qp2);
6949 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
6950 __isl_take isl_pw_qpolynomial *pwqp1,
6951 __isl_take isl_pw_qpolynomial *pwqp2);
6952 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
6953 __isl_take isl_union_pw_qpolynomial *upwqp1,
6954 __isl_take isl_union_pw_qpolynomial *upwqp2);
6955 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
6956 __isl_take isl_pw_qpolynomial_fold *pwf1,
6957 __isl_take isl_pw_qpolynomial_fold *pwf2);
6958 __isl_give isl_union_pw_qpolynomial_fold *
6959 isl_union_pw_qpolynomial_fold_fold(
6960 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
6961 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
6963 #include <isl/aff.h>
6964 __isl_give isl_pw_aff *isl_pw_aff_union_add(
6965 __isl_take isl_pw_aff *pwaff1,
6966 __isl_take isl_pw_aff *pwaff2);
6967 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
6968 __isl_take isl_pw_multi_aff *pma1,
6969 __isl_take isl_pw_multi_aff *pma2);
6970 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
6971 __isl_take isl_union_pw_aff *upa1,
6972 __isl_take isl_union_pw_aff *upa2);
6973 __isl_give isl_union_pw_multi_aff *
6974 isl_union_pw_multi_aff_union_add(
6975 __isl_take isl_union_pw_multi_aff *upma1,
6976 __isl_take isl_union_pw_multi_aff *upma2);
6977 __isl_give isl_multi_union_pw_aff *
6978 isl_multi_union_pw_aff_union_add(
6979 __isl_take isl_multi_union_pw_aff *mupa1,
6980 __isl_take isl_multi_union_pw_aff *mupa2);
6981 __isl_give isl_pw_aff *isl_pw_aff_union_min(
6982 __isl_take isl_pw_aff *pwaff1,
6983 __isl_take isl_pw_aff *pwaff2);
6984 __isl_give isl_pw_aff *isl_pw_aff_union_max(
6985 __isl_take isl_pw_aff *pwaff1,
6986 __isl_take isl_pw_aff *pwaff2);
6988 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
6989 expression with a domain that is the union of those of C<pwaff1> and
6990 C<pwaff2> and such that on each cell, the quasi-affine expression is
6991 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
6992 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
6993 associated expression is the defined one.
6994 This in contrast to the C<isl_pw_aff_max> function, which is
6995 only defined on the shared definition domain of the arguments.
6997 #include <isl/val.h>
6998 __isl_give isl_multi_val *isl_multi_val_add_val(
6999 __isl_take isl_multi_val *mv,
7000 __isl_take isl_val *v);
7001 __isl_give isl_multi_val *isl_multi_val_mod_val(
7002 __isl_take isl_multi_val *mv,
7003 __isl_take isl_val *v);
7004 __isl_give isl_multi_val *isl_multi_val_scale_val(
7005 __isl_take isl_multi_val *mv,
7006 __isl_take isl_val *v);
7007 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
7008 __isl_take isl_multi_val *mv,
7009 __isl_take isl_val *v);
7011 #include <isl/aff.h>
7012 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
7013 __isl_take isl_val *mod);
7014 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
7015 __isl_take isl_pw_aff *pa,
7016 __isl_take isl_val *mod);
7017 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
7018 __isl_take isl_union_pw_aff *upa,
7019 __isl_take isl_val *f);
7020 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
7021 __isl_take isl_val *v);
7022 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
7023 __isl_take isl_multi_aff *ma,
7024 __isl_take isl_val *v);
7025 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
7026 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
7027 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
7028 __isl_take isl_multi_pw_aff *mpa,
7029 __isl_take isl_val *v);
7030 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
7031 __isl_take isl_pw_multi_aff *pma,
7032 __isl_take isl_val *v);
7033 __isl_give isl_union_pw_multi_aff *
7034 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
7035 __isl_take isl_union_pw_aff *upa,
7036 __isl_take isl_val *f);
7037 isl_union_pw_multi_aff_scale_val(
7038 __isl_take isl_union_pw_multi_aff *upma,
7039 __isl_take isl_val *val);
7040 __isl_give isl_multi_union_pw_aff *
7041 isl_multi_union_pw_aff_scale_val(
7042 __isl_take isl_multi_union_pw_aff *mupa,
7043 __isl_take isl_val *v);
7044 __isl_give isl_aff *isl_aff_scale_down_ui(
7045 __isl_take isl_aff *aff, unsigned f);
7046 __isl_give isl_aff *isl_aff_scale_down_val(
7047 __isl_take isl_aff *aff, __isl_take isl_val *v);
7048 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
7049 __isl_take isl_multi_aff *ma,
7050 __isl_take isl_val *v);
7051 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
7052 __isl_take isl_pw_aff *pa,
7053 __isl_take isl_val *f);
7054 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
7055 __isl_take isl_multi_pw_aff *mpa,
7056 __isl_take isl_val *v);
7057 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
7058 __isl_take isl_pw_multi_aff *pma,
7059 __isl_take isl_val *v);
7060 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
7061 __isl_take isl_union_pw_aff *upa,
7062 __isl_take isl_val *v);
7063 __isl_give isl_union_pw_multi_aff *
7064 isl_union_pw_multi_aff_scale_down_val(
7065 __isl_take isl_union_pw_multi_aff *upma,
7066 __isl_take isl_val *val);
7067 __isl_give isl_multi_union_pw_aff *
7068 isl_multi_union_pw_aff_scale_down_val(
7069 __isl_take isl_multi_union_pw_aff *mupa,
7070 __isl_take isl_val *v);
7072 #include <isl/polynomial.h>
7073 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
7074 __isl_take isl_qpolynomial *qp,
7075 __isl_take isl_val *v);
7076 __isl_give isl_qpolynomial_fold *
7077 isl_qpolynomial_fold_scale_val(
7078 __isl_take isl_qpolynomial_fold *fold,
7079 __isl_take isl_val *v);
7080 __isl_give isl_pw_qpolynomial *
7081 isl_pw_qpolynomial_scale_val(
7082 __isl_take isl_pw_qpolynomial *pwqp,
7083 __isl_take isl_val *v);
7084 __isl_give isl_pw_qpolynomial_fold *
7085 isl_pw_qpolynomial_fold_scale_val(
7086 __isl_take isl_pw_qpolynomial_fold *pwf,
7087 __isl_take isl_val *v);
7088 __isl_give isl_union_pw_qpolynomial *
7089 isl_union_pw_qpolynomial_scale_val(
7090 __isl_take isl_union_pw_qpolynomial *upwqp,
7091 __isl_take isl_val *v);
7092 __isl_give isl_union_pw_qpolynomial_fold *
7093 isl_union_pw_qpolynomial_fold_scale_val(
7094 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7095 __isl_take isl_val *v);
7096 __isl_give isl_qpolynomial *
7097 isl_qpolynomial_scale_down_val(
7098 __isl_take isl_qpolynomial *qp,
7099 __isl_take isl_val *v);
7100 __isl_give isl_qpolynomial_fold *
7101 isl_qpolynomial_fold_scale_down_val(
7102 __isl_take isl_qpolynomial_fold *fold,
7103 __isl_take isl_val *v);
7104 __isl_give isl_pw_qpolynomial *
7105 isl_pw_qpolynomial_scale_down_val(
7106 __isl_take isl_pw_qpolynomial *pwqp,
7107 __isl_take isl_val *v);
7108 __isl_give isl_pw_qpolynomial_fold *
7109 isl_pw_qpolynomial_fold_scale_down_val(
7110 __isl_take isl_pw_qpolynomial_fold *pwf,
7111 __isl_take isl_val *v);
7112 __isl_give isl_union_pw_qpolynomial *
7113 isl_union_pw_qpolynomial_scale_down_val(
7114 __isl_take isl_union_pw_qpolynomial *upwqp,
7115 __isl_take isl_val *v);
7116 __isl_give isl_union_pw_qpolynomial_fold *
7117 isl_union_pw_qpolynomial_fold_scale_down_val(
7118 __isl_take isl_union_pw_qpolynomial_fold *upwf,
7119 __isl_take isl_val *v);
7121 #include <isl/val.h>
7122 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
7123 __isl_take isl_multi_val *mv1,
7124 __isl_take isl_multi_val *mv2);
7125 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
7126 __isl_take isl_multi_val *mv1,
7127 __isl_take isl_multi_val *mv2);
7128 __isl_give isl_multi_val *
7129 isl_multi_val_scale_down_multi_val(
7130 __isl_take isl_multi_val *mv1,
7131 __isl_take isl_multi_val *mv2);
7133 #include <isl/aff.h>
7134 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
7135 __isl_take isl_multi_aff *ma,
7136 __isl_take isl_multi_val *mv);
7137 __isl_give isl_multi_union_pw_aff *
7138 isl_multi_union_pw_aff_mod_multi_val(
7139 __isl_take isl_multi_union_pw_aff *upma,
7140 __isl_take isl_multi_val *mv);
7141 __isl_give isl_multi_pw_aff *
7142 isl_multi_pw_aff_mod_multi_val(
7143 __isl_take isl_multi_pw_aff *mpa,
7144 __isl_take isl_multi_val *mv);
7145 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
7146 __isl_take isl_multi_aff *ma,
7147 __isl_take isl_multi_val *mv);
7148 __isl_give isl_pw_multi_aff *
7149 isl_pw_multi_aff_scale_multi_val(
7150 __isl_take isl_pw_multi_aff *pma,
7151 __isl_take isl_multi_val *mv);
7152 __isl_give isl_multi_pw_aff *
7153 isl_multi_pw_aff_scale_multi_val(
7154 __isl_take isl_multi_pw_aff *mpa,
7155 __isl_take isl_multi_val *mv);
7156 __isl_give isl_multi_union_pw_aff *
7157 isl_multi_union_pw_aff_scale_multi_val(
7158 __isl_take isl_multi_union_pw_aff *mupa,
7159 __isl_take isl_multi_val *mv);
7160 __isl_give isl_union_pw_multi_aff *
7161 isl_union_pw_multi_aff_scale_multi_val(
7162 __isl_take isl_union_pw_multi_aff *upma,
7163 __isl_take isl_multi_val *mv);
7164 __isl_give isl_multi_aff *
7165 isl_multi_aff_scale_down_multi_val(
7166 __isl_take isl_multi_aff *ma,
7167 __isl_take isl_multi_val *mv);
7168 __isl_give isl_multi_pw_aff *
7169 isl_multi_pw_aff_scale_down_multi_val(
7170 __isl_take isl_multi_pw_aff *mpa,
7171 __isl_take isl_multi_val *mv);
7172 __isl_give isl_multi_union_pw_aff *
7173 isl_multi_union_pw_aff_scale_down_multi_val(
7174 __isl_take isl_multi_union_pw_aff *mupa,
7175 __isl_take isl_multi_val *mv);
7177 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
7178 by the corresponding elements of C<mv>.
7180 #include <isl/aff.h>
7181 __isl_give isl_aff *isl_aff_mul(
7182 __isl_take isl_aff *aff1,
7183 __isl_take isl_aff *aff2);
7184 __isl_give isl_aff *isl_aff_div(
7185 __isl_take isl_aff *aff1,
7186 __isl_take isl_aff *aff2);
7187 __isl_give isl_pw_aff *isl_pw_aff_mul(
7188 __isl_take isl_pw_aff *pwaff1,
7189 __isl_take isl_pw_aff *pwaff2);
7190 __isl_give isl_pw_aff *isl_pw_aff_div(
7191 __isl_take isl_pw_aff *pa1,
7192 __isl_take isl_pw_aff *pa2);
7193 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
7194 __isl_take isl_pw_aff *pa1,
7195 __isl_take isl_pw_aff *pa2);
7196 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
7197 __isl_take isl_pw_aff *pa1,
7198 __isl_take isl_pw_aff *pa2);
7200 When multiplying two affine expressions, at least one of the two needs
7201 to be a constant. Similarly, when dividing an affine expression by another,
7202 the second expression needs to be a constant.
7203 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
7204 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
7207 #include <isl/polynomial.h>
7208 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
7209 __isl_take isl_qpolynomial *qp1,
7210 __isl_take isl_qpolynomial *qp2);
7211 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
7212 __isl_take isl_pw_qpolynomial *pwqp1,
7213 __isl_take isl_pw_qpolynomial *pwqp2);
7214 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
7215 __isl_take isl_union_pw_qpolynomial *upwqp1,
7216 __isl_take isl_union_pw_qpolynomial *upwqp2);
7220 =head3 Lexicographic Optimization
7222 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
7223 the following functions
7224 compute a set that contains the lexicographic minimum or maximum
7225 of the elements in C<set> (or C<bset>) for those values of the parameters
7226 that satisfy C<dom>.
7227 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7228 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
7230 In other words, the union of the parameter values
7231 for which the result is non-empty and of C<*empty>
7234 #include <isl/set.h>
7235 __isl_give isl_set *isl_basic_set_partial_lexmin(
7236 __isl_take isl_basic_set *bset,
7237 __isl_take isl_basic_set *dom,
7238 __isl_give isl_set **empty);
7239 __isl_give isl_set *isl_basic_set_partial_lexmax(
7240 __isl_take isl_basic_set *bset,
7241 __isl_take isl_basic_set *dom,
7242 __isl_give isl_set **empty);
7243 __isl_give isl_set *isl_set_partial_lexmin(
7244 __isl_take isl_set *set, __isl_take isl_set *dom,
7245 __isl_give isl_set **empty);
7246 __isl_give isl_set *isl_set_partial_lexmax(
7247 __isl_take isl_set *set, __isl_take isl_set *dom,
7248 __isl_give isl_set **empty);
7250 Given a (basic) set C<set> (or C<bset>), the following functions simply
7251 return a set containing the lexicographic minimum or maximum
7252 of the elements in C<set> (or C<bset>).
7253 In case of union sets, the optimum is computed per space.
7255 #include <isl/set.h>
7256 __isl_give isl_set *isl_basic_set_lexmin(
7257 __isl_take isl_basic_set *bset);
7258 __isl_give isl_set *isl_basic_set_lexmax(
7259 __isl_take isl_basic_set *bset);
7260 __isl_give isl_set *isl_set_lexmin(
7261 __isl_take isl_set *set);
7262 __isl_give isl_set *isl_set_lexmax(
7263 __isl_take isl_set *set);
7264 __isl_give isl_union_set *isl_union_set_lexmin(
7265 __isl_take isl_union_set *uset);
7266 __isl_give isl_union_set *isl_union_set_lexmax(
7267 __isl_take isl_union_set *uset);
7269 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
7270 the following functions
7271 compute a relation that maps each element of C<dom>
7272 to the single lexicographic minimum or maximum
7273 of the elements that are associated to that same
7274 element in C<map> (or C<bmap>).
7275 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
7276 that contains the elements in C<dom> that do not map
7277 to any elements in C<map> (or C<bmap>).
7278 In other words, the union of the domain of the result and of C<*empty>
7281 #include <isl/map.h>
7282 __isl_give isl_map *isl_basic_map_partial_lexmax(
7283 __isl_take isl_basic_map *bmap,
7284 __isl_take isl_basic_set *dom,
7285 __isl_give isl_set **empty);
7286 __isl_give isl_map *isl_basic_map_partial_lexmin(
7287 __isl_take isl_basic_map *bmap,
7288 __isl_take isl_basic_set *dom,
7289 __isl_give isl_set **empty);
7290 __isl_give isl_map *isl_map_partial_lexmax(
7291 __isl_take isl_map *map, __isl_take isl_set *dom,
7292 __isl_give isl_set **empty);
7293 __isl_give isl_map *isl_map_partial_lexmin(
7294 __isl_take isl_map *map, __isl_take isl_set *dom,
7295 __isl_give isl_set **empty);
7297 Given a (basic) map C<map> (or C<bmap>), the following functions simply
7298 return a map mapping each element in the domain of
7299 C<map> (or C<bmap>) to the lexicographic minimum or maximum
7300 of all elements associated to that element.
7301 In case of union relations, the optimum is computed per space.
7303 #include <isl/map.h>
7304 __isl_give isl_map *isl_basic_map_lexmin(
7305 __isl_take isl_basic_map *bmap);
7306 __isl_give isl_map *isl_basic_map_lexmax(
7307 __isl_take isl_basic_map *bmap);
7308 __isl_give isl_map *isl_map_lexmin(
7309 __isl_take isl_map *map);
7310 __isl_give isl_map *isl_map_lexmax(
7311 __isl_take isl_map *map);
7312 __isl_give isl_union_map *isl_union_map_lexmin(
7313 __isl_take isl_union_map *umap);
7314 __isl_give isl_union_map *isl_union_map_lexmax(
7315 __isl_take isl_union_map *umap);
7317 The following functions return their result in the form of
7318 a piecewise multi-affine expression,
7319 but are otherwise equivalent to the corresponding functions
7320 returning a basic set or relation.
7322 #include <isl/set.h>
7323 __isl_give isl_pw_multi_aff *
7324 isl_basic_set_partial_lexmin_pw_multi_aff(
7325 __isl_take isl_basic_set *bset,
7326 __isl_take isl_basic_set *dom,
7327 __isl_give isl_set **empty);
7328 __isl_give isl_pw_multi_aff *
7329 isl_basic_set_partial_lexmax_pw_multi_aff(
7330 __isl_take isl_basic_set *bset,
7331 __isl_take isl_basic_set *dom,
7332 __isl_give isl_set **empty);
7333 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
7334 __isl_take isl_set *set);
7335 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
7336 __isl_take isl_set *set);
7338 #include <isl/map.h>
7339 __isl_give isl_pw_multi_aff *
7340 isl_basic_map_lexmin_pw_multi_aff(
7341 __isl_take isl_basic_map *bmap);
7342 __isl_give isl_pw_multi_aff *
7343 isl_basic_map_partial_lexmin_pw_multi_aff(
7344 __isl_take isl_basic_map *bmap,
7345 __isl_take isl_basic_set *dom,
7346 __isl_give isl_set **empty);
7347 __isl_give isl_pw_multi_aff *
7348 isl_basic_map_partial_lexmax_pw_multi_aff(
7349 __isl_take isl_basic_map *bmap,
7350 __isl_take isl_basic_set *dom,
7351 __isl_give isl_set **empty);
7352 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
7353 __isl_take isl_map *map);
7354 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
7355 __isl_take isl_map *map);
7357 The following functions return the lexicographic minimum or maximum
7358 on the shared domain of the inputs and the single defined function
7359 on those parts of the domain where only a single function is defined.
7361 #include <isl/aff.h>
7362 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
7363 __isl_take isl_pw_multi_aff *pma1,
7364 __isl_take isl_pw_multi_aff *pma2);
7365 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
7366 __isl_take isl_pw_multi_aff *pma1,
7367 __isl_take isl_pw_multi_aff *pma2);
7369 If the input to a lexicographic optimization problem has
7370 multiple constraints with the same coefficients for the optimized
7371 variables, then, by default, this symmetry is exploited by
7372 replacing those constraints by a single constraint with
7373 an abstract bound, which is in turn bounded by the corresponding terms
7374 in the original constraints.
7375 Without this optimization, the solver would typically consider
7376 all possible orderings of those original bounds, resulting in a needless
7377 decomposition of the domain.
7378 However, the optimization can also result in slowdowns since
7379 an extra parameter is introduced that may get used in additional
7381 The following option determines whether symmetry detection is applied
7382 during lexicographic optimization.
7384 #include <isl/options.h>
7385 isl_stat isl_options_set_pip_symmetry(isl_ctx *ctx,
7387 int isl_options_get_pip_symmetry(isl_ctx *ctx);
7391 See also \autoref{s:offline}.
7395 =head2 Ternary Operations
7397 #include <isl/aff.h>
7398 __isl_give isl_pw_aff *isl_pw_aff_cond(
7399 __isl_take isl_pw_aff *cond,
7400 __isl_take isl_pw_aff *pwaff_true,
7401 __isl_take isl_pw_aff *pwaff_false);
7403 The function C<isl_pw_aff_cond> performs a conditional operator
7404 and returns an expression that is equal to C<pwaff_true>
7405 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
7406 where C<cond> is zero.
7410 Lists are defined over several element types, including
7411 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_union_pw_aff>,
7412 C<isl_union_pw_multi_aff>, C<isl_constraint>,
7413 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
7414 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
7415 Here we take lists of C<isl_set>s as an example.
7416 Lists can be created, copied, modified and freed using the following functions.
7418 #include <isl/set.h>
7419 __isl_give isl_set_list *isl_set_list_from_set(
7420 __isl_take isl_set *el);
7421 __isl_give isl_set_list *isl_set_list_alloc(
7422 isl_ctx *ctx, int n);
7423 __isl_give isl_set_list *isl_set_list_copy(
7424 __isl_keep isl_set_list *list);
7425 __isl_give isl_set_list *isl_set_list_insert(
7426 __isl_take isl_set_list *list, unsigned pos,
7427 __isl_take isl_set *el);
7428 __isl_give isl_set_list *isl_set_list_add(
7429 __isl_take isl_set_list *list,
7430 __isl_take isl_set *el);
7431 __isl_give isl_set_list *isl_set_list_drop(
7432 __isl_take isl_set_list *list,
7433 unsigned first, unsigned n);
7434 __isl_give isl_set_list *isl_set_list_set_set(
7435 __isl_take isl_set_list *list, int index,
7436 __isl_take isl_set *set);
7437 __isl_give isl_set_list *isl_set_list_concat(
7438 __isl_take isl_set_list *list1,
7439 __isl_take isl_set_list *list2);
7440 __isl_give isl_set_list *isl_set_list_sort(
7441 __isl_take isl_set_list *list,
7442 int (*cmp)(__isl_keep isl_set *a,
7443 __isl_keep isl_set *b, void *user),
7445 __isl_null isl_set_list *isl_set_list_free(
7446 __isl_take isl_set_list *list);
7448 C<isl_set_list_alloc> creates an empty list with an initial capacity
7449 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
7450 add elements to a list, increasing its capacity as needed.
7451 C<isl_set_list_from_set> creates a list with a single element.
7453 Lists can be inspected using the following functions.
7455 #include <isl/set.h>
7456 int isl_set_list_n_set(__isl_keep isl_set_list *list);
7457 __isl_give isl_set *isl_set_list_get_set(
7458 __isl_keep isl_set_list *list, int index);
7459 isl_stat isl_set_list_foreach(__isl_keep isl_set_list *list,
7460 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7462 isl_stat isl_set_list_foreach_scc(
7463 __isl_keep isl_set_list *list,
7464 isl_bool (*follows)(__isl_keep isl_set *a,
7465 __isl_keep isl_set *b, void *user),
7467 isl_stat (*fn)(__isl_take isl_set *el, void *user),
7470 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
7471 strongly connected components of the graph with as vertices the elements
7472 of C<list> and a directed edge from vertex C<b> to vertex C<a>
7473 iff C<follows(a, b)> returns C<isl_bool_true>. The callbacks C<follows> and
7474 C<fn> should return C<isl_bool_error> or C<isl_stat_error> on error.
7476 Lists can be printed using
7478 #include <isl/set.h>
7479 __isl_give isl_printer *isl_printer_print_set_list(
7480 __isl_take isl_printer *p,
7481 __isl_keep isl_set_list *list);
7483 =head2 Associative arrays
7485 Associative arrays map isl objects of a specific type to isl objects
7486 of some (other) specific type. They are defined for several pairs
7487 of types, including (C<isl_map>, C<isl_basic_set>),
7488 (C<isl_id>, C<isl_ast_expr>),
7489 (C<isl_id>, C<isl_id>) and
7490 (C<isl_id>, C<isl_pw_aff>).
7491 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
7494 Associative arrays can be created, copied and freed using
7495 the following functions.
7497 #include <isl/id_to_ast_expr.h>
7498 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
7499 isl_ctx *ctx, int min_size);
7500 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
7501 __isl_keep isl_id_to_ast_expr *id2expr);
7502 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
7503 __isl_take isl_id_to_ast_expr *id2expr);
7505 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
7506 to specify the expected size of the associative array.
7507 The associative array will be grown automatically as needed.
7509 Associative arrays can be inspected using the following functions.
7511 #include <isl/id_to_ast_expr.h>
7512 __isl_give isl_maybe_isl_ast_expr
7513 isl_id_to_ast_expr_try_get(
7514 __isl_keep isl_id_to_ast_expr *id2expr,
7515 __isl_keep isl_id *key);
7516 isl_bool isl_id_to_ast_expr_has(
7517 __isl_keep isl_id_to_ast_expr *id2expr,
7518 __isl_keep isl_id *key);
7519 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
7520 __isl_keep isl_id_to_ast_expr *id2expr,
7521 __isl_take isl_id *key);
7522 isl_stat isl_id_to_ast_expr_foreach(
7523 __isl_keep isl_id_to_ast_expr *id2expr,
7524 isl_stat (*fn)(__isl_take isl_id *key,
7525 __isl_take isl_ast_expr *val, void *user),
7528 The function C<isl_id_to_ast_expr_try_get> returns a structure
7529 containing two elements, C<valid> and C<value>.
7530 If there is a value associated to the key, then C<valid>
7531 is set to C<isl_bool_true> and C<value> contains a copy of
7532 the associated value. Otherwise C<value> is C<NULL> and
7533 C<valid> may be C<isl_bool_error> or C<isl_bool_false> depending
7534 on whether some error has occurred or there simply is no associated value.
7535 The function C<isl_id_to_ast_expr_has> returns the C<valid> field
7536 in the structure and
7537 the function C<isl_id_to_ast_expr_get> returns the C<value> field.
7539 Associative arrays can be modified using the following functions.
7541 #include <isl/id_to_ast_expr.h>
7542 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
7543 __isl_take isl_id_to_ast_expr *id2expr,
7544 __isl_take isl_id *key,
7545 __isl_take isl_ast_expr *val);
7546 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
7547 __isl_take isl_id_to_ast_expr *id2expr,
7548 __isl_take isl_id *key);
7550 Associative arrays can be printed using the following function.
7552 #include <isl/id_to_ast_expr.h>
7553 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
7554 __isl_take isl_printer *p,
7555 __isl_keep isl_id_to_ast_expr *id2expr);
7559 Vectors can be created, copied and freed using the following functions.
7561 #include <isl/vec.h>
7562 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
7564 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
7565 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
7567 Note that the elements of a newly created vector may have arbitrary values.
7568 The elements can be changed and inspected using the following functions.
7570 int isl_vec_size(__isl_keep isl_vec *vec);
7571 __isl_give isl_val *isl_vec_get_element_val(
7572 __isl_keep isl_vec *vec, int pos);
7573 __isl_give isl_vec *isl_vec_set_element_si(
7574 __isl_take isl_vec *vec, int pos, int v);
7575 __isl_give isl_vec *isl_vec_set_element_val(
7576 __isl_take isl_vec *vec, int pos,
7577 __isl_take isl_val *v);
7578 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
7580 __isl_give isl_vec *isl_vec_set_val(
7581 __isl_take isl_vec *vec, __isl_take isl_val *v);
7582 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
7583 __isl_keep isl_vec *vec2, int pos);
7585 C<isl_vec_get_element> will return a negative value if anything went wrong.
7586 In that case, the value of C<*v> is undefined.
7588 The following function can be used to concatenate two vectors.
7590 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
7591 __isl_take isl_vec *vec2);
7595 Matrices can be created, copied and freed using the following functions.
7597 #include <isl/mat.h>
7598 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
7599 unsigned n_row, unsigned n_col);
7600 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
7601 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
7603 Note that the elements of a newly created matrix may have arbitrary values.
7604 The elements can be changed and inspected using the following functions.
7606 int isl_mat_rows(__isl_keep isl_mat *mat);
7607 int isl_mat_cols(__isl_keep isl_mat *mat);
7608 __isl_give isl_val *isl_mat_get_element_val(
7609 __isl_keep isl_mat *mat, int row, int col);
7610 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
7611 int row, int col, int v);
7612 __isl_give isl_mat *isl_mat_set_element_val(
7613 __isl_take isl_mat *mat, int row, int col,
7614 __isl_take isl_val *v);
7616 C<isl_mat_get_element> will return a negative value if anything went wrong.
7617 In that case, the value of C<*v> is undefined.
7619 The following function can be used to compute the (right) inverse
7620 of a matrix, i.e., a matrix such that the product of the original
7621 and the inverse (in that order) is a multiple of the identity matrix.
7622 The input matrix is assumed to be of full row-rank.
7624 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
7626 The following function can be used to compute the (right) kernel
7627 (or null space) of a matrix, i.e., a matrix such that the product of
7628 the original and the kernel (in that order) is the zero matrix.
7630 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
7632 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
7634 The following functions determine
7635 an upper or lower bound on a quasipolynomial over its domain.
7637 __isl_give isl_pw_qpolynomial_fold *
7638 isl_pw_qpolynomial_bound(
7639 __isl_take isl_pw_qpolynomial *pwqp,
7640 enum isl_fold type, int *tight);
7642 __isl_give isl_union_pw_qpolynomial_fold *
7643 isl_union_pw_qpolynomial_bound(
7644 __isl_take isl_union_pw_qpolynomial *upwqp,
7645 enum isl_fold type, int *tight);
7647 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
7648 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
7649 is the returned bound is known be tight, i.e., for each value
7650 of the parameters there is at least
7651 one element in the domain that reaches the bound.
7652 If the domain of C<pwqp> is not wrapping, then the bound is computed
7653 over all elements in that domain and the result has a purely parametric
7654 domain. If the domain of C<pwqp> is wrapping, then the bound is
7655 computed over the range of the wrapped relation. The domain of the
7656 wrapped relation becomes the domain of the result.
7658 =head2 Parametric Vertex Enumeration
7660 The parametric vertex enumeration described in this section
7661 is mainly intended to be used internally and by the C<barvinok>
7664 #include <isl/vertices.h>
7665 __isl_give isl_vertices *isl_basic_set_compute_vertices(
7666 __isl_keep isl_basic_set *bset);
7668 The function C<isl_basic_set_compute_vertices> performs the
7669 actual computation of the parametric vertices and the chamber
7670 decomposition and stores the result in an C<isl_vertices> object.
7671 This information can be queried by either iterating over all
7672 the vertices or iterating over all the chambers or cells
7673 and then iterating over all vertices that are active on the chamber.
7675 isl_stat isl_vertices_foreach_vertex(
7676 __isl_keep isl_vertices *vertices,
7677 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7678 void *user), void *user);
7680 isl_stat isl_vertices_foreach_cell(
7681 __isl_keep isl_vertices *vertices,
7682 isl_stat (*fn)(__isl_take isl_cell *cell,
7683 void *user), void *user);
7684 isl_stat isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
7685 isl_stat (*fn)(__isl_take isl_vertex *vertex,
7686 void *user), void *user);
7688 Other operations that can be performed on an C<isl_vertices> object are
7691 int isl_vertices_get_n_vertices(
7692 __isl_keep isl_vertices *vertices);
7693 void isl_vertices_free(__isl_take isl_vertices *vertices);
7695 Vertices can be inspected and destroyed using the following functions.
7697 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
7698 __isl_give isl_basic_set *isl_vertex_get_domain(
7699 __isl_keep isl_vertex *vertex);
7700 __isl_give isl_multi_aff *isl_vertex_get_expr(
7701 __isl_keep isl_vertex *vertex);
7702 void isl_vertex_free(__isl_take isl_vertex *vertex);
7704 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
7705 describing the vertex in terms of the parameters,
7706 while C<isl_vertex_get_domain> returns the activity domain
7709 Chambers can be inspected and destroyed using the following functions.
7711 __isl_give isl_basic_set *isl_cell_get_domain(
7712 __isl_keep isl_cell *cell);
7713 void isl_cell_free(__isl_take isl_cell *cell);
7715 =head1 Polyhedral Compilation Library
7717 This section collects functionality in C<isl> that has been specifically
7718 designed for use during polyhedral compilation.
7720 =head2 Schedule Trees
7722 A schedule tree is a structured representation of a schedule,
7723 assigning a relative order to a set of domain elements.
7724 The relative order expressed by the schedule tree is
7725 defined recursively. In particular, the order between
7726 two domain elements is determined by the node that is closest
7727 to the root that refers to both elements and that orders them apart.
7728 Each node in the tree is of one of several types.
7729 The root node is always of type C<isl_schedule_node_domain>
7730 (or C<isl_schedule_node_extension>)
7731 and it describes the (extra) domain elements to which the schedule applies.
7732 The other types of nodes are as follows.
7736 =item C<isl_schedule_node_band>
7738 A band of schedule dimensions. Each schedule dimension is represented
7739 by a union piecewise quasi-affine expression. If this expression
7740 assigns a different value to two domain elements, while all previous
7741 schedule dimensions in the same band assign them the same value,
7742 then the two domain elements are ordered according to these two
7744 Each expression is required to be total in the domain elements
7745 that reach the band node.
7747 =item C<isl_schedule_node_expansion>
7749 An expansion node maps each of the domain elements that reach the node
7750 to one or more domain elements. The image of this mapping forms
7751 the set of domain elements that reach the child of the expansion node.
7752 The function that maps each of the expanded domain elements
7753 to the original domain element from which it was expanded
7754 is called the contraction.
7756 =item C<isl_schedule_node_filter>
7758 A filter node does not impose any ordering, but rather intersects
7759 the set of domain elements that the current subtree refers to
7760 with a given union set. The subtree of the filter node only
7761 refers to domain elements in the intersection.
7762 A filter node is typically only used as a child of a sequence or
7765 =item C<isl_schedule_node_leaf>
7767 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
7769 =item C<isl_schedule_node_mark>
7771 A mark node can be used to attach any kind of information to a subtree
7772 of the schedule tree.
7774 =item C<isl_schedule_node_sequence>
7776 A sequence node has one or more children, each of which is a filter node.
7777 The filters on these filter nodes form a partition of
7778 the domain elements that the current subtree refers to.
7779 If two domain elements appear in distinct filters then the sequence
7780 node orders them according to the child positions of the corresponding
7783 =item C<isl_schedule_node_set>
7785 A set node is similar to a sequence node, except that
7786 it expresses that domain elements appearing in distinct filters
7787 may have any order. The order of the children of a set node
7788 is therefore also immaterial.
7792 The following node types are only supported by the AST generator.
7796 =item C<isl_schedule_node_context>
7798 The context describes constraints on the parameters and
7799 the schedule dimensions of outer
7800 bands that the AST generator may assume to hold. It is also the only
7801 kind of node that may introduce additional parameters.
7802 The space of the context is that of the flat product of the outer
7803 band nodes. In particular, if there are no outer band nodes, then
7804 this space is the unnamed zero-dimensional space.
7805 Since a context node references the outer band nodes, any tree
7806 containing a context node is considered to be anchored.
7808 =item C<isl_schedule_node_extension>
7810 An extension node instructs the AST generator to add additional
7811 domain elements that need to be scheduled.
7812 The additional domain elements are described by the range of
7813 the extension map in terms of the outer schedule dimensions,
7814 i.e., the flat product of the outer band nodes.
7815 Note that domain elements are added whenever the AST generator
7816 reaches the extension node, meaning that there are still some
7817 active domain elements for which an AST needs to be generated.
7818 The conditions under which some domain elements are still active
7819 may however not be completely described by the outer AST nodes
7820 generated at that point.
7822 An extension node may also appear as the root of a schedule tree,
7823 when it is intended to be inserted into another tree
7824 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
7825 In this case, the domain of the extension node should
7826 correspond to the flat product of the outer band nodes
7827 in this other schedule tree at the point where the extension tree
7830 =item C<isl_schedule_node_guard>
7832 The guard describes constraints on the parameters and
7833 the schedule dimensions of outer
7834 bands that need to be enforced by the outer nodes
7835 in the generated AST.
7836 The space of the guard is that of the flat product of the outer
7837 band nodes. In particular, if there are no outer band nodes, then
7838 this space is the unnamed zero-dimensional space.
7839 Since a guard node references the outer band nodes, any tree
7840 containing a guard node is considered to be anchored.
7844 Except for the C<isl_schedule_node_context> nodes,
7845 none of the nodes may introduce any parameters that were not
7846 already present in the root domain node.
7848 A schedule tree is encapsulated in an C<isl_schedule> object.
7849 The simplest such objects, those with a tree consisting of single domain node,
7850 can be created using the following functions with either an empty
7851 domain or a given domain.
7853 #include <isl/schedule.h>
7854 __isl_give isl_schedule *isl_schedule_empty(
7855 __isl_take isl_space *space);
7856 __isl_give isl_schedule *isl_schedule_from_domain(
7857 __isl_take isl_union_set *domain);
7859 The function C<isl_schedule_constraints_compute_schedule> described
7860 in L</"Scheduling"> can also be used to construct schedules.
7862 C<isl_schedule> objects may be copied and freed using the following functions.
7864 #include <isl/schedule.h>
7865 __isl_give isl_schedule *isl_schedule_copy(
7866 __isl_keep isl_schedule *sched);
7867 __isl_null isl_schedule *isl_schedule_free(
7868 __isl_take isl_schedule *sched);
7870 The following functions checks whether two C<isl_schedule> objects
7871 are obviously the same.
7873 #include <isl/schedule.h>
7874 isl_bool isl_schedule_plain_is_equal(
7875 __isl_keep isl_schedule *schedule1,
7876 __isl_keep isl_schedule *schedule2);
7878 The domain of the schedule, i.e., the domain described by the root node,
7879 can be obtained using the following function.
7881 #include <isl/schedule.h>
7882 __isl_give isl_union_set *isl_schedule_get_domain(
7883 __isl_keep isl_schedule *schedule);
7885 An extra top-level band node (right underneath the domain node) can
7886 be introduced into the schedule using the following function.
7887 The schedule tree is assumed not to have any anchored nodes.
7889 #include <isl/schedule.h>
7890 __isl_give isl_schedule *
7891 isl_schedule_insert_partial_schedule(
7892 __isl_take isl_schedule *schedule,
7893 __isl_take isl_multi_union_pw_aff *partial);
7895 A top-level context node (right underneath the domain node) can
7896 be introduced into the schedule using the following function.
7898 #include <isl/schedule.h>
7899 __isl_give isl_schedule *isl_schedule_insert_context(
7900 __isl_take isl_schedule *schedule,
7901 __isl_take isl_set *context)
7903 A top-level guard node (right underneath the domain node) can
7904 be introduced into the schedule using the following function.
7906 #include <isl/schedule.h>
7907 __isl_give isl_schedule *isl_schedule_insert_guard(
7908 __isl_take isl_schedule *schedule,
7909 __isl_take isl_set *guard)
7911 A schedule that combines two schedules either in the given
7912 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
7913 or an C<isl_schedule_node_set> node,
7914 can be created using the following functions.
7916 #include <isl/schedule.h>
7917 __isl_give isl_schedule *isl_schedule_sequence(
7918 __isl_take isl_schedule *schedule1,
7919 __isl_take isl_schedule *schedule2);
7920 __isl_give isl_schedule *isl_schedule_set(
7921 __isl_take isl_schedule *schedule1,
7922 __isl_take isl_schedule *schedule2);
7924 The domains of the two input schedules need to be disjoint.
7926 The following function can be used to restrict the domain
7927 of a schedule with a domain node as root to be a subset of the given union set.
7928 This operation may remove nodes in the tree that have become
7931 #include <isl/schedule.h>
7932 __isl_give isl_schedule *isl_schedule_intersect_domain(
7933 __isl_take isl_schedule *schedule,
7934 __isl_take isl_union_set *domain);
7936 The following function can be used to simplify the domain
7937 of a schedule with a domain node as root with respect to the given
7940 #include <isl/schedule.h>
7941 __isl_give isl_schedule *isl_schedule_gist_domain_params(
7942 __isl_take isl_schedule *schedule,
7943 __isl_take isl_set *context);
7945 The following function resets the user pointers on all parameter
7946 and tuple identifiers referenced by the nodes of the given schedule.
7948 #include <isl/schedule.h>
7949 __isl_give isl_schedule *isl_schedule_reset_user(
7950 __isl_take isl_schedule *schedule);
7952 The following function aligns the parameters of all nodes
7953 in the given schedule to the given space.
7955 #include <isl/schedule.h>
7956 __isl_give isl_schedule *isl_schedule_align_params(
7957 __isl_take isl_schedule *schedule,
7958 __isl_take isl_space *space);
7960 The following function allows the user to plug in a given function
7961 in the iteration domains. The input schedule is not allowed to contain
7962 any expansion nodes.
7964 #include <isl/schedule.h>
7965 __isl_give isl_schedule *
7966 isl_schedule_pullback_union_pw_multi_aff(
7967 __isl_take isl_schedule *schedule,
7968 __isl_take isl_union_pw_multi_aff *upma);
7970 The following function can be used to plug in the schedule C<expansion>
7971 in the leaves of C<schedule>, where C<contraction> describes how
7972 the domain elements of C<expansion> map to the domain elements
7973 at the original leaves of C<schedule>.
7974 The resulting schedule will contain expansion nodes, unless
7975 C<contraction> is an identity function.
7977 #include <isl/schedule.h>
7978 __isl_give isl_schedule *isl_schedule_expand(
7979 __isl_take isl_schedule *schedule,
7980 __isl_take isl_union_pw_multi_aff *contraction,
7981 __isl_take isl_schedule *expansion);
7983 An C<isl_union_map> representation of the schedule can be obtained
7984 from an C<isl_schedule> using the following function.
7986 #include <isl/schedule.h>
7987 __isl_give isl_union_map *isl_schedule_get_map(
7988 __isl_keep isl_schedule *sched);
7990 The resulting relation encodes the same relative ordering as
7991 the schedule by mapping the domain elements to a common schedule space.
7992 If the schedule_separate_components option is set, then the order
7993 of the children of a set node is explicitly encoded in the result.
7994 If the tree contains any expansion nodes, then the relation
7995 is formulated in terms of the expanded domain elements.
7997 Schedules can be read from input using the following functions.
7999 #include <isl/schedule.h>
8000 __isl_give isl_schedule *isl_schedule_read_from_file(
8001 isl_ctx *ctx, FILE *input);
8002 __isl_give isl_schedule *isl_schedule_read_from_str(
8003 isl_ctx *ctx, const char *str);
8005 A representation of the schedule can be printed using
8007 #include <isl/schedule.h>
8008 __isl_give isl_printer *isl_printer_print_schedule(
8009 __isl_take isl_printer *p,
8010 __isl_keep isl_schedule *schedule);
8011 __isl_give char *isl_schedule_to_str(
8012 __isl_keep isl_schedule *schedule);
8014 C<isl_schedule_to_str> prints the schedule in flow format.
8016 The schedule tree can be traversed through the use of
8017 C<isl_schedule_node> objects that point to a particular
8018 position in the schedule tree. Whenever a C<isl_schedule_node>
8019 is use to modify a node in the schedule tree, the original schedule
8020 tree is left untouched and the modifications are performed to a copy
8021 of the tree. The returned C<isl_schedule_node> then points to
8022 this modified copy of the tree.
8024 The root of the schedule tree can be obtained using the following function.
8026 #include <isl/schedule.h>
8027 __isl_give isl_schedule_node *isl_schedule_get_root(
8028 __isl_keep isl_schedule *schedule);
8030 A pointer to a newly created schedule tree with a single domain
8031 node can be created using the following functions.
8033 #include <isl/schedule_node.h>
8034 __isl_give isl_schedule_node *
8035 isl_schedule_node_from_domain(
8036 __isl_take isl_union_set *domain);
8037 __isl_give isl_schedule_node *
8038 isl_schedule_node_from_extension(
8039 __isl_take isl_union_map *extension);
8041 C<isl_schedule_node_from_extension> creates a tree with an extension
8044 Schedule nodes can be copied and freed using the following functions.
8046 #include <isl/schedule_node.h>
8047 __isl_give isl_schedule_node *isl_schedule_node_copy(
8048 __isl_keep isl_schedule_node *node);
8049 __isl_null isl_schedule_node *isl_schedule_node_free(
8050 __isl_take isl_schedule_node *node);
8052 The following functions can be used to check if two schedule
8053 nodes point to the same position in the same schedule.
8055 #include <isl/schedule_node.h>
8056 isl_bool isl_schedule_node_is_equal(
8057 __isl_keep isl_schedule_node *node1,
8058 __isl_keep isl_schedule_node *node2);
8060 The following properties can be obtained from a schedule node.
8062 #include <isl/schedule_node.h>
8063 enum isl_schedule_node_type isl_schedule_node_get_type(
8064 __isl_keep isl_schedule_node *node);
8065 enum isl_schedule_node_type
8066 isl_schedule_node_get_parent_type(
8067 __isl_keep isl_schedule_node *node);
8068 __isl_give isl_schedule *isl_schedule_node_get_schedule(
8069 __isl_keep isl_schedule_node *node);
8071 The function C<isl_schedule_node_get_type> returns the type of
8072 the node, while C<isl_schedule_node_get_parent_type> returns
8073 type of the parent of the node, which is required to exist.
8074 The function C<isl_schedule_node_get_schedule> returns a copy
8075 to the schedule to which the node belongs.
8077 The following functions can be used to move the schedule node
8078 to a different position in the tree or to check if such a position
8081 #include <isl/schedule_node.h>
8082 isl_bool isl_schedule_node_has_parent(
8083 __isl_keep isl_schedule_node *node);
8084 __isl_give isl_schedule_node *isl_schedule_node_parent(
8085 __isl_take isl_schedule_node *node);
8086 __isl_give isl_schedule_node *isl_schedule_node_root(
8087 __isl_take isl_schedule_node *node);
8088 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
8089 __isl_take isl_schedule_node *node,
8091 int isl_schedule_node_n_children(
8092 __isl_keep isl_schedule_node *node);
8093 __isl_give isl_schedule_node *isl_schedule_node_child(
8094 __isl_take isl_schedule_node *node, int pos);
8095 isl_bool isl_schedule_node_has_children(
8096 __isl_keep isl_schedule_node *node);
8097 __isl_give isl_schedule_node *isl_schedule_node_first_child(
8098 __isl_take isl_schedule_node *node);
8099 isl_bool isl_schedule_node_has_previous_sibling(
8100 __isl_keep isl_schedule_node *node);
8101 __isl_give isl_schedule_node *
8102 isl_schedule_node_previous_sibling(
8103 __isl_take isl_schedule_node *node);
8104 isl_bool isl_schedule_node_has_next_sibling(
8105 __isl_keep isl_schedule_node *node);
8106 __isl_give isl_schedule_node *
8107 isl_schedule_node_next_sibling(
8108 __isl_take isl_schedule_node *node);
8110 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
8111 is the node itself, the ancestor of generation 1 is its parent and so on.
8113 It is also possible to query the number of ancestors of a node,
8114 the position of the current node
8115 within the children of its parent, the position of the subtree
8116 containing a node within the children of an ancestor
8117 or to obtain a copy of a given
8118 child without destroying the current node.
8119 Given two nodes that point to the same schedule, their closest
8120 shared ancestor can be obtained using
8121 C<isl_schedule_node_get_shared_ancestor>.
8123 #include <isl/schedule_node.h>
8124 int isl_schedule_node_get_tree_depth(
8125 __isl_keep isl_schedule_node *node);
8126 int isl_schedule_node_get_child_position(
8127 __isl_keep isl_schedule_node *node);
8128 int isl_schedule_node_get_ancestor_child_position(
8129 __isl_keep isl_schedule_node *node,
8130 __isl_keep isl_schedule_node *ancestor);
8131 __isl_give isl_schedule_node *isl_schedule_node_get_child(
8132 __isl_keep isl_schedule_node *node, int pos);
8133 __isl_give isl_schedule_node *
8134 isl_schedule_node_get_shared_ancestor(
8135 __isl_keep isl_schedule_node *node1,
8136 __isl_keep isl_schedule_node *node2);
8138 All nodes in a schedule tree or
8139 all descendants of a specific node (including the node) can be visited
8140 in depth-first pre-order using the following functions.
8142 #include <isl/schedule.h>
8143 isl_stat isl_schedule_foreach_schedule_node_top_down(
8144 __isl_keep isl_schedule *sched,
8145 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8146 void *user), void *user);
8148 #include <isl/schedule_node.h>
8149 isl_stat isl_schedule_node_foreach_descendant_top_down(
8150 __isl_keep isl_schedule_node *node,
8151 isl_bool (*fn)(__isl_keep isl_schedule_node *node,
8152 void *user), void *user);
8154 The callback function is slightly different from the usual
8155 callbacks in that it not only indicates success (non-negative result)
8156 or failure (negative result), but also indicates whether the children
8157 of the given node should be visited. In particular, if the callback
8158 returns a positive value, then the children are visited, but if
8159 the callback returns zero, then the children are not visited.
8161 The ancestors of a node in a schedule tree can be visited from
8162 the root down to and including the parent of the node using
8163 the following function.
8165 #include <isl/schedule_node.h>
8166 isl_stat isl_schedule_node_foreach_ancestor_top_down(
8167 __isl_keep isl_schedule_node *node,
8168 isl_stat (*fn)(__isl_keep isl_schedule_node *node,
8169 void *user), void *user);
8171 The following functions allows for a depth-first post-order
8172 traversal of the nodes in a schedule tree or
8173 of the descendants of a specific node (including the node
8174 itself), where the user callback is allowed to modify the
8177 #include <isl/schedule.h>
8178 __isl_give isl_schedule *
8179 isl_schedule_map_schedule_node_bottom_up(
8180 __isl_take isl_schedule *schedule,
8181 __isl_give isl_schedule_node *(*fn)(
8182 __isl_take isl_schedule_node *node,
8183 void *user), void *user);
8185 #include <isl/schedule_node.h>
8186 __isl_give isl_schedule_node *
8187 isl_schedule_node_map_descendant_bottom_up(
8188 __isl_take isl_schedule_node *node,
8189 __isl_give isl_schedule_node *(*fn)(
8190 __isl_take isl_schedule_node *node,
8191 void *user), void *user);
8193 The traversal continues from the node returned by the callback function.
8194 It is the responsibility of the user to ensure that this does not
8195 lead to an infinite loop. It is safest to always return a pointer
8196 to the same position (same ancestors and child positions) as the input node.
8198 The following function removes a node (along with its descendants)
8199 from a schedule tree and returns a pointer to the leaf at the
8200 same position in the updated tree.
8201 It is not allowed to remove the root of a schedule tree or
8202 a child of a set or sequence node.
8204 #include <isl/schedule_node.h>
8205 __isl_give isl_schedule_node *isl_schedule_node_cut(
8206 __isl_take isl_schedule_node *node);
8208 The following function removes a single node
8209 from a schedule tree and returns a pointer to the child
8210 of the node, now located at the position of the original node
8211 or to a leaf node at that position if there was no child.
8212 It is not allowed to remove the root of a schedule tree,
8213 a set or sequence node, a child of a set or sequence node or
8214 a band node with an anchored subtree.
8216 #include <isl/schedule_node.h>
8217 __isl_give isl_schedule_node *isl_schedule_node_delete(
8218 __isl_take isl_schedule_node *node);
8220 Most nodes in a schedule tree only contain local information.
8221 In some cases, however, a node may also refer to the schedule dimensions
8222 of its outer band nodes.
8223 This means that the position of the node within the tree should
8224 not be changed, or at least that no changes are performed to the
8225 outer band nodes. The following function can be used to test
8226 whether the subtree rooted at a given node contains any such nodes.
8228 #include <isl/schedule_node.h>
8229 isl_bool isl_schedule_node_is_subtree_anchored(
8230 __isl_keep isl_schedule_node *node);
8232 The following function resets the user pointers on all parameter
8233 and tuple identifiers referenced by the given schedule node.
8235 #include <isl/schedule_node.h>
8236 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
8237 __isl_take isl_schedule_node *node);
8239 The following function aligns the parameters of the given schedule
8240 node to the given space.
8242 #include <isl/schedule_node.h>
8243 __isl_give isl_schedule_node *
8244 isl_schedule_node_align_params(
8245 __isl_take isl_schedule_node *node,
8246 __isl_take isl_space *space);
8248 Several node types have their own functions for querying
8249 (and in some cases setting) some node type specific properties.
8251 #include <isl/schedule_node.h>
8252 __isl_give isl_space *isl_schedule_node_band_get_space(
8253 __isl_keep isl_schedule_node *node);
8254 __isl_give isl_multi_union_pw_aff *
8255 isl_schedule_node_band_get_partial_schedule(
8256 __isl_keep isl_schedule_node *node);
8257 __isl_give isl_union_map *
8258 isl_schedule_node_band_get_partial_schedule_union_map(
8259 __isl_keep isl_schedule_node *node);
8260 unsigned isl_schedule_node_band_n_member(
8261 __isl_keep isl_schedule_node *node);
8262 isl_bool isl_schedule_node_band_member_get_coincident(
8263 __isl_keep isl_schedule_node *node, int pos);
8264 __isl_give isl_schedule_node *
8265 isl_schedule_node_band_member_set_coincident(
8266 __isl_take isl_schedule_node *node, int pos,
8268 isl_bool isl_schedule_node_band_get_permutable(
8269 __isl_keep isl_schedule_node *node);
8270 __isl_give isl_schedule_node *
8271 isl_schedule_node_band_set_permutable(
8272 __isl_take isl_schedule_node *node, int permutable);
8273 enum isl_ast_loop_type
8274 isl_schedule_node_band_member_get_ast_loop_type(
8275 __isl_keep isl_schedule_node *node, int pos);
8276 __isl_give isl_schedule_node *
8277 isl_schedule_node_band_member_set_ast_loop_type(
8278 __isl_take isl_schedule_node *node, int pos,
8279 enum isl_ast_loop_type type);
8280 __isl_give isl_union_set *
8281 enum isl_ast_loop_type
8282 isl_schedule_node_band_member_get_isolate_ast_loop_type(
8283 __isl_keep isl_schedule_node *node, int pos);
8284 __isl_give isl_schedule_node *
8285 isl_schedule_node_band_member_set_isolate_ast_loop_type(
8286 __isl_take isl_schedule_node *node, int pos,
8287 enum isl_ast_loop_type type);
8288 isl_schedule_node_band_get_ast_build_options(
8289 __isl_keep isl_schedule_node *node);
8290 __isl_give isl_schedule_node *
8291 isl_schedule_node_band_set_ast_build_options(
8292 __isl_take isl_schedule_node *node,
8293 __isl_take isl_union_set *options);
8294 __isl_give isl_set *
8295 isl_schedule_node_band_get_ast_isolate_option(
8296 __isl_keep isl_schedule_node *node);
8298 The function C<isl_schedule_node_band_get_space> returns the space
8299 of the partial schedule of the band.
8300 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
8301 returns a representation of the partial schedule of the band node
8302 in the form of an C<isl_union_map>.
8303 The coincident and permutable properties are set by
8304 C<isl_schedule_constraints_compute_schedule> on the schedule tree
8306 A scheduling dimension is considered to be ``coincident''
8307 if it satisfies the coincidence constraints within its band.
8308 That is, if the dependence distances of the coincidence
8309 constraints are all zero in that direction (for fixed
8310 iterations of outer bands).
8311 A band is marked permutable if it was produced using the Pluto-like scheduler.
8312 Note that the scheduler may have to resort to a Feautrier style scheduling
8313 step even if the default scheduler is used.
8314 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
8315 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
8316 For the meaning of these loop AST generation types and the difference
8317 between the regular loop AST generation type and the isolate
8318 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
8319 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
8320 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
8321 may return C<isl_ast_loop_error> if an error occurs.
8322 The AST build options govern how an AST is generated for
8323 the individual schedule dimensions during AST generation.
8324 See L</"AST Generation Options (Schedule Tree)">.
8325 The isolate option for the given node can be extracted from these
8326 AST build options using the function
8327 C<isl_schedule_node_band_get_ast_isolate_option>.
8329 #include <isl/schedule_node.h>
8330 __isl_give isl_set *
8331 isl_schedule_node_context_get_context(
8332 __isl_keep isl_schedule_node *node);
8334 #include <isl/schedule_node.h>
8335 __isl_give isl_union_set *
8336 isl_schedule_node_domain_get_domain(
8337 __isl_keep isl_schedule_node *node);
8339 #include <isl/schedule_node.h>
8340 __isl_give isl_union_map *
8341 isl_schedule_node_expansion_get_expansion(
8342 __isl_keep isl_schedule_node *node);
8343 __isl_give isl_union_pw_multi_aff *
8344 isl_schedule_node_expansion_get_contraction(
8345 __isl_keep isl_schedule_node *node);
8347 #include <isl/schedule_node.h>
8348 __isl_give isl_union_map *
8349 isl_schedule_node_extension_get_extension(
8350 __isl_keep isl_schedule_node *node);
8352 #include <isl/schedule_node.h>
8353 __isl_give isl_union_set *
8354 isl_schedule_node_filter_get_filter(
8355 __isl_keep isl_schedule_node *node);
8357 #include <isl/schedule_node.h>
8358 __isl_give isl_set *isl_schedule_node_guard_get_guard(
8359 __isl_keep isl_schedule_node *node);
8361 #include <isl/schedule_node.h>
8362 __isl_give isl_id *isl_schedule_node_mark_get_id(
8363 __isl_keep isl_schedule_node *node);
8365 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
8366 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
8367 partial schedules related to the node.
8369 #include <isl/schedule_node.h>
8370 __isl_give isl_multi_union_pw_aff *
8371 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
8372 __isl_keep isl_schedule_node *node);
8373 __isl_give isl_union_pw_multi_aff *
8374 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
8375 __isl_keep isl_schedule_node *node);
8376 __isl_give isl_union_map *
8377 isl_schedule_node_get_prefix_schedule_union_map(
8378 __isl_keep isl_schedule_node *node);
8379 __isl_give isl_union_map *
8380 isl_schedule_node_get_prefix_schedule_relation(
8381 __isl_keep isl_schedule_node *node);
8382 __isl_give isl_union_map *
8383 isl_schedule_node_get_subtree_schedule_union_map(
8384 __isl_keep isl_schedule_node *node);
8386 In particular, the functions
8387 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
8388 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
8389 and C<isl_schedule_node_get_prefix_schedule_union_map>
8390 return a relative ordering on the domain elements that reach the given
8391 node determined by its ancestors.
8392 The function C<isl_schedule_node_get_prefix_schedule_relation>
8393 additionally includes the domain constraints in the result.
8394 The function C<isl_schedule_node_get_subtree_schedule_union_map>
8395 returns a representation of the partial schedule defined by the
8396 subtree rooted at the given node.
8397 If the tree contains any expansion nodes, then the subtree schedule
8398 is formulated in terms of the expanded domain elements.
8399 The tree passed to functions returning a prefix schedule
8400 may only contain extension nodes if these would not affect
8401 the result of these functions. That is, if one of the ancestors
8402 is an extension node, then all of the domain elements that were
8403 added by the extension node need to have been filtered out
8404 by filter nodes between the extension node and the input node.
8405 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
8406 may not contain in extension nodes in the selected subtree.
8408 The expansion/contraction defined by an entire subtree, combining
8409 the expansions/contractions
8410 on the expansion nodes in the subtree, can be obtained using
8411 the following functions.
8413 #include <isl/schedule_node.h>
8414 __isl_give isl_union_map *
8415 isl_schedule_node_get_subtree_expansion(
8416 __isl_keep isl_schedule_node *node);
8417 __isl_give isl_union_pw_multi_aff *
8418 isl_schedule_node_get_subtree_contraction(
8419 __isl_keep isl_schedule_node *node);
8421 The total number of outer band members of given node, i.e.,
8422 the shared output dimension of the maps in the result
8423 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
8424 using the following function.
8426 #include <isl/schedule_node.h>
8427 int isl_schedule_node_get_schedule_depth(
8428 __isl_keep isl_schedule_node *node);
8430 The following functions return the elements that reach the given node
8431 or the union of universes in the spaces that contain these elements.
8433 #include <isl/schedule_node.h>
8434 __isl_give isl_union_set *
8435 isl_schedule_node_get_domain(
8436 __isl_keep isl_schedule_node *node);
8437 __isl_give isl_union_set *
8438 isl_schedule_node_get_universe_domain(
8439 __isl_keep isl_schedule_node *node);
8441 The input tree of C<isl_schedule_node_get_domain>
8442 may only contain extension nodes if these would not affect
8443 the result of this function. That is, if one of the ancestors
8444 is an extension node, then all of the domain elements that were
8445 added by the extension node need to have been filtered out
8446 by filter nodes between the extension node and the input node.
8448 The following functions can be used to introduce additional nodes
8449 in the schedule tree. The new node is introduced at the point
8450 in the tree where the C<isl_schedule_node> points to and
8451 the results points to the new node.
8453 #include <isl/schedule_node.h>
8454 __isl_give isl_schedule_node *
8455 isl_schedule_node_insert_partial_schedule(
8456 __isl_take isl_schedule_node *node,
8457 __isl_take isl_multi_union_pw_aff *schedule);
8459 This function inserts a new band node with (the greatest integer
8460 part of) the given partial schedule.
8461 The subtree rooted at the given node is assumed not to have
8464 #include <isl/schedule_node.h>
8465 __isl_give isl_schedule_node *
8466 isl_schedule_node_insert_context(
8467 __isl_take isl_schedule_node *node,
8468 __isl_take isl_set *context);
8470 This function inserts a new context node with the given context constraints.
8472 #include <isl/schedule_node.h>
8473 __isl_give isl_schedule_node *
8474 isl_schedule_node_insert_filter(
8475 __isl_take isl_schedule_node *node,
8476 __isl_take isl_union_set *filter);
8478 This function inserts a new filter node with the given filter.
8479 If the original node already pointed to a filter node, then the
8480 two filter nodes are merged into one.
8482 #include <isl/schedule_node.h>
8483 __isl_give isl_schedule_node *
8484 isl_schedule_node_insert_guard(
8485 __isl_take isl_schedule_node *node,
8486 __isl_take isl_set *guard);
8488 This function inserts a new guard node with the given guard constraints.
8490 #include <isl/schedule_node.h>
8491 __isl_give isl_schedule_node *
8492 isl_schedule_node_insert_mark(
8493 __isl_take isl_schedule_node *node,
8494 __isl_take isl_id *mark);
8496 This function inserts a new mark node with the give mark identifier.
8498 #include <isl/schedule_node.h>
8499 __isl_give isl_schedule_node *
8500 isl_schedule_node_insert_sequence(
8501 __isl_take isl_schedule_node *node,
8502 __isl_take isl_union_set_list *filters);
8503 __isl_give isl_schedule_node *
8504 isl_schedule_node_insert_set(
8505 __isl_take isl_schedule_node *node,
8506 __isl_take isl_union_set_list *filters);
8508 These functions insert a new sequence or set node with the given
8509 filters as children.
8511 #include <isl/schedule_node.h>
8512 __isl_give isl_schedule_node *isl_schedule_node_group(
8513 __isl_take isl_schedule_node *node,
8514 __isl_take isl_id *group_id);
8516 This function introduces an expansion node in between the current
8517 node and its parent that expands instances of a space with tuple
8518 identifier C<group_id> to the original domain elements that reach
8519 the node. The group instances are identified by the prefix schedule
8520 of those domain elements. The ancestors of the node are adjusted
8521 to refer to the group instances instead of the original domain
8522 elements. The return value points to the same node in the updated
8523 schedule tree as the input node, i.e., to the child of the newly
8524 introduced expansion node. Grouping instances of different statements
8525 ensures that they will be treated as a single statement by the
8526 AST generator up to the point of the expansion node.
8528 The following function can be used to flatten a nested
8531 #include <isl/schedule_node.h>
8532 __isl_give isl_schedule_node *
8533 isl_schedule_node_sequence_splice_child(
8534 __isl_take isl_schedule_node *node, int pos);
8536 That is, given a sequence node C<node> that has another sequence node
8537 in its child at position C<pos> (in particular, the child of that filter
8538 node is a sequence node), attach the children of that other sequence
8539 node as children of C<node>, replacing the original child at position
8542 The partial schedule of a band node can be scaled (down) or reduced using
8543 the following functions.
8545 #include <isl/schedule_node.h>
8546 __isl_give isl_schedule_node *
8547 isl_schedule_node_band_scale(
8548 __isl_take isl_schedule_node *node,
8549 __isl_take isl_multi_val *mv);
8550 __isl_give isl_schedule_node *
8551 isl_schedule_node_band_scale_down(
8552 __isl_take isl_schedule_node *node,
8553 __isl_take isl_multi_val *mv);
8554 __isl_give isl_schedule_node *
8555 isl_schedule_node_band_mod(
8556 __isl_take isl_schedule_node *node,
8557 __isl_take isl_multi_val *mv);
8559 The spaces of the two arguments need to match.
8560 After scaling, the partial schedule is replaced by its greatest
8561 integer part to ensure that the schedule remains integral.
8563 The partial schedule of a band node can be shifted by an
8564 C<isl_multi_union_pw_aff> with a domain that is a superset
8565 of the domain of the partial schedule using
8566 the following function.
8568 #include <isl/schedule_node.h>
8569 __isl_give isl_schedule_node *
8570 isl_schedule_node_band_shift(
8571 __isl_take isl_schedule_node *node,
8572 __isl_take isl_multi_union_pw_aff *shift);
8574 A band node can be tiled using the following function.
8576 #include <isl/schedule_node.h>
8577 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
8578 __isl_take isl_schedule_node *node,
8579 __isl_take isl_multi_val *sizes);
8581 isl_stat isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
8583 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
8584 isl_stat isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
8586 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
8588 The C<isl_schedule_node_band_tile> function tiles
8589 the band using the given tile sizes inside its schedule.
8590 A new child band node is created to represent the point loops and it is
8591 inserted between the modified band and its children.
8592 The subtree rooted at the given node is assumed not to have
8594 The C<tile_scale_tile_loops> option specifies whether the tile
8595 loops iterators should be scaled by the tile sizes.
8596 If the C<tile_shift_point_loops> option is set, then the point loops
8597 are shifted to start at zero.
8599 A band node can be split into two nested band nodes
8600 using the following function.
8602 #include <isl/schedule_node.h>
8603 __isl_give isl_schedule_node *isl_schedule_node_band_split(
8604 __isl_take isl_schedule_node *node, int pos);
8606 The resulting outer band node contains the first C<pos> dimensions of
8607 the schedule of C<node> while the inner band contains the remaining dimensions.
8608 The schedules of the two band nodes live in anonymous spaces.
8609 The loop AST generation type options and the isolate option
8610 are split over the the two band nodes.
8612 A band node can be moved down to the leaves of the subtree rooted
8613 at the band node using the following function.
8615 #include <isl/schedule_node.h>
8616 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
8617 __isl_take isl_schedule_node *node);
8619 The subtree rooted at the given node is assumed not to have
8621 The result points to the node in the resulting tree that is in the same
8622 position as the node pointed to by C<node> in the original tree.
8624 #include <isl/schedule_node.h>
8625 __isl_give isl_schedule_node *
8626 isl_schedule_node_order_before(
8627 __isl_take isl_schedule_node *node,
8628 __isl_take isl_union_set *filter);
8629 __isl_give isl_schedule_node *
8630 isl_schedule_node_order_after(
8631 __isl_take isl_schedule_node *node,
8632 __isl_take isl_union_set *filter);
8634 These functions split the domain elements that reach C<node>
8635 into those that satisfy C<filter> and those that do not and
8636 arranges for the elements that do satisfy the filter to be
8637 executed before (in case of C<isl_schedule_node_order_before>)
8638 or after (in case of C<isl_schedule_node_order_after>)
8639 those that do not. The order is imposed by
8640 a sequence node, possibly reusing the grandparent of C<node>
8641 on two copies of the subtree attached to the original C<node>.
8642 Both copies are simplified with respect to their filter.
8644 Return a pointer to the copy of the subtree that does not
8645 satisfy C<filter>. If there is no such copy (because all
8646 reaching domain elements satisfy the filter), then return
8647 the original pointer.
8649 #include <isl/schedule_node.h>
8650 __isl_give isl_schedule_node *
8651 isl_schedule_node_graft_before(
8652 __isl_take isl_schedule_node *node,
8653 __isl_take isl_schedule_node *graft);
8654 __isl_give isl_schedule_node *
8655 isl_schedule_node_graft_after(
8656 __isl_take isl_schedule_node *node,
8657 __isl_take isl_schedule_node *graft);
8659 This function inserts the C<graft> tree into the tree containing C<node>
8660 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
8661 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
8662 The root node of C<graft>
8663 should be an extension node where the domain of the extension
8664 is the flat product of all outer band nodes of C<node>.
8665 The root node may also be a domain node.
8666 The elements of the domain or the range of the extension may not
8667 intersect with the domain elements that reach "node".
8668 The schedule tree of C<graft> may not be anchored.
8670 The schedule tree of C<node> is modified to include an extension node
8671 corresponding to the root node of C<graft> as a child of the original
8672 parent of C<node>. The original node that C<node> points to and the
8673 child of the root node of C<graft> are attached to this extension node
8674 through a sequence, with appropriate filters and with the child
8675 of C<graft> appearing before or after the original C<node>.
8677 If C<node> already appears inside a sequence that is the child of
8678 an extension node and if the spaces of the new domain elements
8679 do not overlap with those of the original domain elements,
8680 then that extension node is extended with the new extension
8681 rather than introducing a new segment of extension and sequence nodes.
8683 Return a pointer to the same node in the modified tree that
8684 C<node> pointed to in the original tree.
8686 A representation of the schedule node can be printed using
8688 #include <isl/schedule_node.h>
8689 __isl_give isl_printer *isl_printer_print_schedule_node(
8690 __isl_take isl_printer *p,
8691 __isl_keep isl_schedule_node *node);
8692 __isl_give char *isl_schedule_node_to_str(
8693 __isl_keep isl_schedule_node *node);
8695 C<isl_schedule_node_to_str> prints the schedule node in block format.
8697 =head2 Dependence Analysis
8699 C<isl> contains specialized functionality for performing
8700 array dataflow analysis. That is, given a I<sink> access relation
8701 and a collection of possible I<source> access relations,
8702 C<isl> can compute relations that describe
8703 for each iteration of the sink access, which iteration
8704 of which of the source access relations was the last
8705 to access the same data element before the given iteration
8707 The resulting dependence relations map source iterations
8708 to either the corresponding sink iterations or
8709 pairs of corresponding sink iterations and accessed data elements.
8710 To compute standard flow dependences, the sink should be
8711 a read, while the sources should be writes.
8712 If any of the source accesses are marked as being I<may>
8713 accesses, then there will be a dependence from the last
8714 I<must> access B<and> from any I<may> access that follows
8715 this last I<must> access.
8716 In particular, if I<all> sources are I<may> accesses,
8717 then memory based dependence analysis is performed.
8718 If, on the other hand, all sources are I<must> accesses,
8719 then value based dependence analysis is performed.
8721 =head3 High-level Interface
8723 A high-level interface to dependence analysis is provided
8724 by the following function.
8726 #include <isl/flow.h>
8727 __isl_give isl_union_flow *
8728 isl_union_access_info_compute_flow(
8729 __isl_take isl_union_access_info *access);
8731 The input C<isl_union_access_info> object describes the sink
8732 access relations, the source access relations and a schedule,
8733 while the output C<isl_union_flow> object describes
8734 the resulting dependence relations and the subsets of the
8735 sink relations for which no source was found.
8737 An C<isl_union_access_info> is created, modified, copied and freed using
8738 the following functions.
8740 #include <isl/flow.h>
8741 __isl_give isl_union_access_info *
8742 isl_union_access_info_from_sink(
8743 __isl_take isl_union_map *sink);
8744 __isl_give isl_union_access_info *
8745 isl_union_access_info_set_must_source(
8746 __isl_take isl_union_access_info *access,
8747 __isl_take isl_union_map *must_source);
8748 __isl_give isl_union_access_info *
8749 isl_union_access_info_set_may_source(
8750 __isl_take isl_union_access_info *access,
8751 __isl_take isl_union_map *may_source);
8752 __isl_give isl_union_access_info *
8753 isl_union_access_info_set_schedule(
8754 __isl_take isl_union_access_info *access,
8755 __isl_take isl_schedule *schedule);
8756 __isl_give isl_union_access_info *
8757 isl_union_access_info_set_schedule_map(
8758 __isl_take isl_union_access_info *access,
8759 __isl_take isl_union_map *schedule_map);
8760 __isl_give isl_union_access_info *
8761 isl_union_access_info_copy(
8762 __isl_keep isl_union_access_info *access);
8763 __isl_null isl_union_access_info *
8764 isl_union_access_info_free(
8765 __isl_take isl_union_access_info *access);
8767 The may sources set by C<isl_union_access_info_set_may_source>
8768 do not need to include the must sources set by
8769 C<isl_union_access_info_set_must_source> as a subset.
8770 The user is free not to call one (or both) of these functions,
8771 in which case the corresponding set is kept to its empty default.
8772 Similarly, the default schedule initialized by
8773 C<isl_union_access_info_from_sink> is empty.
8774 The current schedule is determined by the last call to either
8775 C<isl_union_access_info_set_schedule> or
8776 C<isl_union_access_info_set_schedule_map>.
8777 The domain of the schedule corresponds to the domains of
8778 the access relations. In particular, the domains of the access
8779 relations are effectively intersected with the domain of the schedule
8780 and only the resulting accesses are considered by the dependence analysis.
8782 A representation of the information contained in an object
8783 of type C<isl_union_access_info> can be obtained using
8785 #include <isl/flow.h>
8786 __isl_give isl_printer *
8787 isl_printer_print_union_access_info(
8788 __isl_take isl_printer *p,
8789 __isl_keep isl_union_access_info *access);
8790 __isl_give char *isl_union_access_info_to_str(
8791 __isl_keep isl_union_access_info *access);
8793 C<isl_union_access_info_to_str> prints the information in flow format.
8795 The output of C<isl_union_access_info_compute_flow> can be examined,
8796 copied, and freed using the following functions.
8798 #include <isl/flow.h>
8799 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
8800 __isl_keep isl_union_flow *flow);
8801 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
8802 __isl_keep isl_union_flow *flow);
8803 __isl_give isl_union_map *
8804 isl_union_flow_get_full_must_dependence(
8805 __isl_keep isl_union_flow *flow);
8806 __isl_give isl_union_map *
8807 isl_union_flow_get_full_may_dependence(
8808 __isl_keep isl_union_flow *flow);
8809 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
8810 __isl_keep isl_union_flow *flow);
8811 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
8812 __isl_keep isl_union_flow *flow);
8813 __isl_give isl_union_flow *isl_union_flow_copy(
8814 __isl_keep isl_union_flow *flow);
8815 __isl_null isl_union_flow *isl_union_flow_free(
8816 __isl_take isl_union_flow *flow);
8818 The relation returned by C<isl_union_flow_get_must_dependence>
8819 relates domain elements of must sources to domain elements of the sink.
8820 The relation returned by C<isl_union_flow_get_may_dependence>
8821 relates domain elements of must or may sources to domain elements of the sink
8822 and includes the previous relation as a subset.
8823 The relation returned by C<isl_union_flow_get_full_must_dependence>
8824 relates domain elements of must sources to pairs of domain elements of the sink
8825 and accessed data elements.
8826 The relation returned by C<isl_union_flow_get_full_may_dependence>
8827 relates domain elements of must or may sources to pairs of
8828 domain elements of the sink and accessed data elements.
8829 This relation includes the previous relation as a subset.
8830 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
8831 of the sink relation for which no dependences have been found.
8832 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
8833 of the sink relation for which no definite dependences have been found.
8834 That is, it contains those sink access that do not contribute to any
8835 of the elements in the relation returned
8836 by C<isl_union_flow_get_must_dependence>.
8838 A representation of the information contained in an object
8839 of type C<isl_union_flow> can be obtained using
8841 #include <isl/flow.h>
8842 __isl_give isl_printer *isl_printer_print_union_flow(
8843 __isl_take isl_printer *p,
8844 __isl_keep isl_union_flow *flow);
8845 __isl_give char *isl_union_flow_to_str(
8846 __isl_keep isl_union_flow *flow);
8848 C<isl_union_flow_to_str> prints the information in flow format.
8850 =head3 Low-level Interface
8852 A lower-level interface is provided by the following functions.
8854 #include <isl/flow.h>
8856 typedef int (*isl_access_level_before)(void *first, void *second);
8858 __isl_give isl_access_info *isl_access_info_alloc(
8859 __isl_take isl_map *sink,
8860 void *sink_user, isl_access_level_before fn,
8862 __isl_give isl_access_info *isl_access_info_add_source(
8863 __isl_take isl_access_info *acc,
8864 __isl_take isl_map *source, int must,
8866 __isl_null isl_access_info *isl_access_info_free(
8867 __isl_take isl_access_info *acc);
8869 __isl_give isl_flow *isl_access_info_compute_flow(
8870 __isl_take isl_access_info *acc);
8872 isl_stat isl_flow_foreach(__isl_keep isl_flow *deps,
8873 isl_stat (*fn)(__isl_take isl_map *dep, int must,
8874 void *dep_user, void *user),
8876 __isl_give isl_map *isl_flow_get_no_source(
8877 __isl_keep isl_flow *deps, int must);
8878 void isl_flow_free(__isl_take isl_flow *deps);
8880 The function C<isl_access_info_compute_flow> performs the actual
8881 dependence analysis. The other functions are used to construct
8882 the input for this function or to read off the output.
8884 The input is collected in an C<isl_access_info>, which can
8885 be created through a call to C<isl_access_info_alloc>.
8886 The arguments to this functions are the sink access relation
8887 C<sink>, a token C<sink_user> used to identify the sink
8888 access to the user, a callback function for specifying the
8889 relative order of source and sink accesses, and the number
8890 of source access relations that will be added.
8891 The callback function has type C<int (*)(void *first, void *second)>.
8892 The function is called with two user supplied tokens identifying
8893 either a source or the sink and it should return the shared nesting
8894 level and the relative order of the two accesses.
8895 In particular, let I<n> be the number of loops shared by
8896 the two accesses. If C<first> precedes C<second> textually,
8897 then the function should return I<2 * n + 1>; otherwise,
8898 it should return I<2 * n>.
8899 The sources can be added to the C<isl_access_info> by performing
8900 (at most) C<max_source> calls to C<isl_access_info_add_source>.
8901 C<must> indicates whether the source is a I<must> access
8902 or a I<may> access. Note that a multi-valued access relation
8903 should only be marked I<must> if every iteration in the domain
8904 of the relation accesses I<all> elements in its image.
8905 The C<source_user> token is again used to identify
8906 the source access. The range of the source access relation
8907 C<source> should have the same dimension as the range
8908 of the sink access relation.
8909 The C<isl_access_info_free> function should usually not be
8910 called explicitly, because it is called implicitly by
8911 C<isl_access_info_compute_flow>.
8913 The result of the dependence analysis is collected in an
8914 C<isl_flow>. There may be elements of
8915 the sink access for which no preceding source access could be
8916 found or for which all preceding sources are I<may> accesses.
8917 The relations containing these elements can be obtained through
8918 calls to C<isl_flow_get_no_source>, the first with C<must> set
8919 and the second with C<must> unset.
8920 In the case of standard flow dependence analysis,
8921 with the sink a read and the sources I<must> writes,
8922 the first relation corresponds to the reads from uninitialized
8923 array elements and the second relation is empty.
8924 The actual flow dependences can be extracted using
8925 C<isl_flow_foreach>. This function will call the user-specified
8926 callback function C<fn> for each B<non-empty> dependence between
8927 a source and the sink. The callback function is called
8928 with four arguments, the actual flow dependence relation
8929 mapping source iterations to sink iterations, a boolean that
8930 indicates whether it is a I<must> or I<may> dependence, a token
8931 identifying the source and an additional C<void *> with value
8932 equal to the third argument of the C<isl_flow_foreach> call.
8933 A dependence is marked I<must> if it originates from a I<must>
8934 source and if it is not followed by any I<may> sources.
8936 After finishing with an C<isl_flow>, the user should call
8937 C<isl_flow_free> to free all associated memory.
8939 =head3 Interaction with the Low-level Interface
8941 During the dependence analysis, we frequently need to perform
8942 the following operation. Given a relation between sink iterations
8943 and potential source iterations from a particular source domain,
8944 what is the last potential source iteration corresponding to each
8945 sink iteration. It can sometimes be convenient to adjust
8946 the set of potential source iterations before or after each such operation.
8947 The prototypical example is fuzzy array dataflow analysis,
8948 where we need to analyze if, based on data-dependent constraints,
8949 the sink iteration can ever be executed without one or more of
8950 the corresponding potential source iterations being executed.
8951 If so, we can introduce extra parameters and select an unknown
8952 but fixed source iteration from the potential source iterations.
8953 To be able to perform such manipulations, C<isl> provides the following
8956 #include <isl/flow.h>
8958 typedef __isl_give isl_restriction *(*isl_access_restrict)(
8959 __isl_keep isl_map *source_map,
8960 __isl_keep isl_set *sink, void *source_user,
8962 __isl_give isl_access_info *isl_access_info_set_restrict(
8963 __isl_take isl_access_info *acc,
8964 isl_access_restrict fn, void *user);
8966 The function C<isl_access_info_set_restrict> should be called
8967 before calling C<isl_access_info_compute_flow> and registers a callback function
8968 that will be called any time C<isl> is about to compute the last
8969 potential source. The first argument is the (reverse) proto-dependence,
8970 mapping sink iterations to potential source iterations.
8971 The second argument represents the sink iterations for which
8972 we want to compute the last source iteration.
8973 The third argument is the token corresponding to the source
8974 and the final argument is the token passed to C<isl_access_info_set_restrict>.
8975 The callback is expected to return a restriction on either the input or
8976 the output of the operation computing the last potential source.
8977 If the input needs to be restricted then restrictions are needed
8978 for both the source and the sink iterations. The sink iterations
8979 and the potential source iterations will be intersected with these sets.
8980 If the output needs to be restricted then only a restriction on the source
8981 iterations is required.
8982 If any error occurs, the callback should return C<NULL>.
8983 An C<isl_restriction> object can be created, freed and inspected
8984 using the following functions.
8986 #include <isl/flow.h>
8988 __isl_give isl_restriction *isl_restriction_input(
8989 __isl_take isl_set *source_restr,
8990 __isl_take isl_set *sink_restr);
8991 __isl_give isl_restriction *isl_restriction_output(
8992 __isl_take isl_set *source_restr);
8993 __isl_give isl_restriction *isl_restriction_none(
8994 __isl_take isl_map *source_map);
8995 __isl_give isl_restriction *isl_restriction_empty(
8996 __isl_take isl_map *source_map);
8997 __isl_null isl_restriction *isl_restriction_free(
8998 __isl_take isl_restriction *restr);
9000 C<isl_restriction_none> and C<isl_restriction_empty> are special
9001 cases of C<isl_restriction_input>. C<isl_restriction_none>
9002 is essentially equivalent to
9004 isl_restriction_input(isl_set_universe(
9005 isl_space_range(isl_map_get_space(source_map))),
9007 isl_space_domain(isl_map_get_space(source_map))));
9009 whereas C<isl_restriction_empty> is essentially equivalent to
9011 isl_restriction_input(isl_set_empty(
9012 isl_space_range(isl_map_get_space(source_map))),
9014 isl_space_domain(isl_map_get_space(source_map))));
9018 #include <isl/schedule.h>
9019 __isl_give isl_schedule *
9020 isl_schedule_constraints_compute_schedule(
9021 __isl_take isl_schedule_constraints *sc);
9023 The function C<isl_schedule_constraints_compute_schedule> can be
9024 used to compute a schedule that satisfies the given schedule constraints.
9025 These schedule constraints include the iteration domain for which
9026 a schedule should be computed and dependences between pairs of
9027 iterations. In particular, these dependences include
9028 I<validity> dependences and I<proximity> dependences.
9029 By default, the algorithm used to construct the schedule is similar
9030 to that of C<Pluto>.
9031 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
9033 The generated schedule respects all validity dependences.
9034 That is, all dependence distances over these dependences in the
9035 scheduled space are lexicographically positive.
9037 The default algorithm tries to ensure that the dependence distances
9038 over coincidence constraints are zero and to minimize the
9039 dependence distances over proximity dependences.
9040 Moreover, it tries to obtain sequences (bands) of schedule dimensions
9041 for groups of domains where the dependence distances over validity
9042 dependences have only non-negative values.
9043 Note that when minimizing the maximal dependence distance
9044 over proximity dependences, a single affine expression in the parameters
9045 is constructed that bounds all dependence distances. If no such expression
9046 exists, then the algorithm will fail and resort to an alternative
9047 scheduling algorithm. In particular, this means that adding proximity
9048 dependences may eliminate valid solutions. A typical example where this
9049 phenomenon may occur is when some subset of the proximity dependences
9050 has no restriction on some parameter, forcing the coefficient of that
9051 parameter to be zero, while some other subset forces the dependence
9052 distance to depend on that parameter, requiring the same coefficient
9054 When using Feautrier's algorithm, the coincidence and proximity constraints
9055 are only taken into account during the extension to a
9056 full-dimensional schedule.
9058 An C<isl_schedule_constraints> object can be constructed
9059 and manipulated using the following functions.
9061 #include <isl/schedule.h>
9062 __isl_give isl_schedule_constraints *
9063 isl_schedule_constraints_copy(
9064 __isl_keep isl_schedule_constraints *sc);
9065 __isl_give isl_schedule_constraints *
9066 isl_schedule_constraints_on_domain(
9067 __isl_take isl_union_set *domain);
9068 __isl_give isl_schedule_constraints *
9069 isl_schedule_constraints_set_context(
9070 __isl_take isl_schedule_constraints *sc,
9071 __isl_take isl_set *context);
9072 __isl_give isl_schedule_constraints *
9073 isl_schedule_constraints_set_validity(
9074 __isl_take isl_schedule_constraints *sc,
9075 __isl_take isl_union_map *validity);
9076 __isl_give isl_schedule_constraints *
9077 isl_schedule_constraints_set_coincidence(
9078 __isl_take isl_schedule_constraints *sc,
9079 __isl_take isl_union_map *coincidence);
9080 __isl_give isl_schedule_constraints *
9081 isl_schedule_constraints_set_proximity(
9082 __isl_take isl_schedule_constraints *sc,
9083 __isl_take isl_union_map *proximity);
9084 __isl_give isl_schedule_constraints *
9085 isl_schedule_constraints_set_conditional_validity(
9086 __isl_take isl_schedule_constraints *sc,
9087 __isl_take isl_union_map *condition,
9088 __isl_take isl_union_map *validity);
9089 __isl_give isl_schedule_constraints *
9090 isl_schedule_constraints_apply(
9091 __isl_take isl_schedule_constraints *sc,
9092 __isl_take isl_union_map *umap);
9093 __isl_null isl_schedule_constraints *
9094 isl_schedule_constraints_free(
9095 __isl_take isl_schedule_constraints *sc);
9097 The initial C<isl_schedule_constraints> object created by
9098 C<isl_schedule_constraints_on_domain> does not impose any constraints.
9099 That is, it has an empty set of dependences.
9100 The function C<isl_schedule_constraints_set_context> allows the user
9101 to specify additional constraints on the parameters that may
9102 be assumed to hold during the construction of the schedule.
9103 The function C<isl_schedule_constraints_set_validity> replaces the
9104 validity dependences, mapping domain elements I<i> to domain
9105 elements that should be scheduled after I<i>.
9106 The function C<isl_schedule_constraints_set_coincidence> replaces the
9107 coincidence dependences, mapping domain elements I<i> to domain
9108 elements that should be scheduled together with I<I>, if possible.
9109 The function C<isl_schedule_constraints_set_proximity> replaces the
9110 proximity dependences, mapping domain elements I<i> to domain
9111 elements that should be scheduled either before I<I>
9112 or as early as possible after I<i>.
9114 The function C<isl_schedule_constraints_set_conditional_validity>
9115 replaces the conditional validity constraints.
9116 A conditional validity constraint is only imposed when any of the corresponding
9117 conditions is satisfied, i.e., when any of them is non-zero.
9118 That is, the scheduler ensures that within each band if the dependence
9119 distances over the condition constraints are not all zero
9120 then all corresponding conditional validity constraints are respected.
9121 A conditional validity constraint corresponds to a condition
9122 if the two are adjacent, i.e., if the domain of one relation intersect
9123 the range of the other relation.
9124 The typical use case of conditional validity constraints is
9125 to allow order constraints between live ranges to be violated
9126 as long as the live ranges themselves are local to the band.
9127 To allow more fine-grained control over which conditions correspond
9128 to which conditional validity constraints, the domains and ranges
9129 of these relations may include I<tags>. That is, the domains and
9130 ranges of those relation may themselves be wrapped relations
9131 where the iteration domain appears in the domain of those wrapped relations
9132 and the range of the wrapped relations can be arbitrarily chosen
9133 by the user. Conditions and conditional validity constraints are only
9134 considered adjacent to each other if the entire wrapped relation matches.
9135 In particular, a relation with a tag will never be considered adjacent
9136 to a relation without a tag.
9138 The function C<isl_schedule_constraints_compute_schedule> takes
9139 schedule constraints that are defined on some set of domain elements
9140 and transforms them to schedule constraints on the elements
9141 to which these domain elements are mapped by the given transformation.
9143 An C<isl_schedule_constraints> object can be inspected
9144 using the following functions.
9146 #include <isl/schedule.h>
9147 __isl_give isl_union_set *
9148 isl_schedule_constraints_get_domain(
9149 __isl_keep isl_schedule_constraints *sc);
9150 __isl_give isl_set *isl_schedule_constraints_get_context(
9151 __isl_keep isl_schedule_constraints *sc);
9152 __isl_give isl_union_map *
9153 isl_schedule_constraints_get_validity(
9154 __isl_keep isl_schedule_constraints *sc);
9155 __isl_give isl_union_map *
9156 isl_schedule_constraints_get_coincidence(
9157 __isl_keep isl_schedule_constraints *sc);
9158 __isl_give isl_union_map *
9159 isl_schedule_constraints_get_proximity(
9160 __isl_keep isl_schedule_constraints *sc);
9161 __isl_give isl_union_map *
9162 isl_schedule_constraints_get_conditional_validity(
9163 __isl_keep isl_schedule_constraints *sc);
9164 __isl_give isl_union_map *
9165 isl_schedule_constraints_get_conditional_validity_condition(
9166 __isl_keep isl_schedule_constraints *sc);
9168 An C<isl_schedule_constraints> object can be read from input
9169 using the following functions.
9171 #include <isl/schedule.h>
9172 __isl_give isl_schedule_constraints *
9173 isl_schedule_constraints_read_from_str(isl_ctx *ctx,
9175 __isl_give isl_schedule_constraints *
9176 isl_schedule_constraints_read_from_file(isl_ctx *ctx,
9179 The contents of an C<isl_schedule_constraints> object can be printed
9180 using the following functions.
9182 #include <isl/schedule.h>
9183 __isl_give isl_printer *
9184 isl_printer_print_schedule_constraints(
9185 __isl_take isl_printer *p,
9186 __isl_keep isl_schedule_constraints *sc);
9187 __isl_give char *isl_schedule_constraints_to_str(
9188 __isl_keep isl_schedule_constraints *sc);
9190 The following function computes a schedule directly from
9191 an iteration domain and validity and proximity dependences
9192 and is implemented in terms of the functions described above.
9193 The use of C<isl_union_set_compute_schedule> is discouraged.
9195 #include <isl/schedule.h>
9196 __isl_give isl_schedule *isl_union_set_compute_schedule(
9197 __isl_take isl_union_set *domain,
9198 __isl_take isl_union_map *validity,
9199 __isl_take isl_union_map *proximity);
9201 The generated schedule represents a schedule tree.
9202 For more information on schedule trees, see
9203 L</"Schedule Trees">.
9207 #include <isl/schedule.h>
9208 isl_stat isl_options_set_schedule_max_coefficient(
9209 isl_ctx *ctx, int val);
9210 int isl_options_get_schedule_max_coefficient(
9212 isl_stat isl_options_set_schedule_max_constant_term(
9213 isl_ctx *ctx, int val);
9214 int isl_options_get_schedule_max_constant_term(
9216 isl_stat isl_options_set_schedule_serialize_sccs(
9217 isl_ctx *ctx, int val);
9218 int isl_options_get_schedule_serialize_sccs(isl_ctx *ctx);
9219 isl_stat isl_options_set_schedule_whole_component(
9220 isl_ctx *ctx, int val);
9221 int isl_options_get_schedule_whole_component(
9223 isl_stat isl_options_set_schedule_maximize_band_depth(
9224 isl_ctx *ctx, int val);
9225 int isl_options_get_schedule_maximize_band_depth(
9227 isl_stat isl_options_set_schedule_maximize_coincidence(
9228 isl_ctx *ctx, int val);
9229 int isl_options_get_schedule_maximize_coincidence(
9231 isl_stat isl_options_set_schedule_outer_coincidence(
9232 isl_ctx *ctx, int val);
9233 int isl_options_get_schedule_outer_coincidence(
9235 isl_stat isl_options_set_schedule_split_scaled(
9236 isl_ctx *ctx, int val);
9237 int isl_options_get_schedule_split_scaled(
9239 isl_stat isl_options_set_schedule_treat_coalescing(
9240 isl_ctx *ctx, int val);
9241 int isl_options_get_schedule_treat_coalescing(
9243 isl_stat isl_options_set_schedule_algorithm(
9244 isl_ctx *ctx, int val);
9245 int isl_options_get_schedule_algorithm(
9247 isl_stat isl_options_set_schedule_separate_components(
9248 isl_ctx *ctx, int val);
9249 int isl_options_get_schedule_separate_components(
9254 =item * schedule_max_coefficient
9256 This option enforces that the coefficients for variable and parameter
9257 dimensions in the calculated schedule are not larger than the specified value.
9258 This option can significantly increase the speed of the scheduling calculation
9259 and may also prevent fusing of unrelated dimensions. A value of -1 means that
9260 this option does not introduce bounds on the variable or parameter
9263 =item * schedule_max_constant_term
9265 This option enforces that the constant coefficients in the calculated schedule
9266 are not larger than the maximal constant term. This option can significantly
9267 increase the speed of the scheduling calculation and may also prevent fusing of
9268 unrelated dimensions. A value of -1 means that this option does not introduce
9269 bounds on the constant coefficients.
9271 =item * schedule_serialize_sccs
9273 If this option is set, then all strongly connected components
9274 in the dependence graph are serialized as soon as they are detected.
9275 This means in particular that instances of statements will only
9276 appear in the same band node if these statements belong
9277 to the same strongly connected component at the point where
9278 the band node is constructed.
9280 =item * schedule_whole_component
9282 If this option is set, then entire (weakly) connected
9283 components in the dependence graph are scheduled together
9285 Otherwise, each strongly connected component within
9286 such a weakly connected component is first scheduled separately
9287 and then combined with other strongly connected components.
9288 This option has no effect if C<schedule_serialize_sccs> is set.
9290 =item * schedule_maximize_band_depth
9292 If this option is set, then the scheduler tries to maximize
9293 the width of the bands. Wider bands give more possibilities for tiling.
9294 In particular, if the C<schedule_whole_component> option is set,
9295 then bands are split if this might result in wider bands.
9296 Otherwise, the effect of this option is to only allow
9297 strongly connected components to be combined if this does
9298 not reduce the width of the bands.
9299 Note that if the C<schedule_serialize_sccs> options is set, then
9300 the C<schedule_maximize_band_depth> option therefore has no effect.
9302 =item * schedule_maximize_coincidence
9304 This option is only effective if the C<schedule_whole_component>
9305 option is turned off.
9306 If the C<schedule_maximize_coincidence> option is set, then (clusters of)
9307 strongly connected components are only combined with each other
9308 if this does not reduce the number of coincident band members.
9310 =item * schedule_outer_coincidence
9312 If this option is set, then we try to construct schedules
9313 where the outermost scheduling dimension in each band
9314 satisfies the coincidence constraints.
9316 =item * schedule_algorithm
9318 Selects the scheduling algorithm to be used.
9319 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
9320 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
9322 =item * schedule_split_scaled
9324 If this option is set, then we try to construct schedules in which the
9325 constant term is split off from the linear part if the linear parts of
9326 the scheduling rows for all nodes in the graphs have a common non-trivial
9328 The constant term is then placed in a separate band and the linear
9330 This option is only effective when the Feautrier style scheduler is
9331 being used, either as the main scheduler or as a fallback for the
9332 Pluto-like scheduler.
9334 =item * schedule_treat_coalescing
9336 If this option is set, then the scheduler will try and avoid
9337 producing schedules that perform loop coalescing.
9338 In particular, for the Pluto-like scheduler, this option places
9339 bounds on the schedule coefficients based on the sizes of the instance sets.
9340 For the Feautrier style scheduler, this option detects potentially
9341 coalescing schedules and then tries to adjust the schedule to avoid
9344 =item * schedule_separate_components
9346 If this option is set then the function C<isl_schedule_get_map>
9347 will treat set nodes in the same way as sequence nodes.
9351 =head2 AST Generation
9353 This section describes the C<isl> functionality for generating
9354 ASTs that visit all the elements
9355 in a domain in an order specified by a schedule tree or
9357 In case the schedule given as a C<isl_union_map>, an AST is generated
9358 that visits all the elements in the domain of the C<isl_union_map>
9359 according to the lexicographic order of the corresponding image
9360 element(s). If the range of the C<isl_union_map> consists of
9361 elements in more than one space, then each of these spaces is handled
9362 separately in an arbitrary order.
9363 It should be noted that the schedule tree or the image elements
9364 in a schedule map only specify the I<order>
9365 in which the corresponding domain elements should be visited.
9366 No direct relation between the partial schedule values
9367 or the image elements on the one hand and the loop iterators
9368 in the generated AST on the other hand should be assumed.
9370 Each AST is generated within a build. The initial build
9371 simply specifies the constraints on the parameters (if any)
9372 and can be created, inspected, copied and freed using the following functions.
9374 #include <isl/ast_build.h>
9375 __isl_give isl_ast_build *isl_ast_build_alloc(
9377 __isl_give isl_ast_build *isl_ast_build_from_context(
9378 __isl_take isl_set *set);
9379 __isl_give isl_ast_build *isl_ast_build_copy(
9380 __isl_keep isl_ast_build *build);
9381 __isl_null isl_ast_build *isl_ast_build_free(
9382 __isl_take isl_ast_build *build);
9384 The C<set> argument is usually a parameter set with zero or more parameters.
9385 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
9386 this set is required to be a parameter set.
9387 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
9388 specify any parameter constraints.
9389 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
9390 and L</"Fine-grained Control over AST Generation">.
9391 Finally, the AST itself can be constructed using one of the following
9394 #include <isl/ast_build.h>
9395 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
9396 __isl_keep isl_ast_build *build,
9397 __isl_take isl_schedule *schedule);
9398 __isl_give isl_ast_node *
9399 isl_ast_build_node_from_schedule_map(
9400 __isl_keep isl_ast_build *build,
9401 __isl_take isl_union_map *schedule);
9403 =head3 Inspecting the AST
9405 The basic properties of an AST node can be obtained as follows.
9407 #include <isl/ast.h>
9408 enum isl_ast_node_type isl_ast_node_get_type(
9409 __isl_keep isl_ast_node *node);
9411 The type of an AST node is one of
9412 C<isl_ast_node_for>,
9414 C<isl_ast_node_block>,
9415 C<isl_ast_node_mark> or
9416 C<isl_ast_node_user>.
9417 An C<isl_ast_node_for> represents a for node.
9418 An C<isl_ast_node_if> represents an if node.
9419 An C<isl_ast_node_block> represents a compound node.
9420 An C<isl_ast_node_mark> introduces a mark in the AST.
9421 An C<isl_ast_node_user> represents an expression statement.
9422 An expression statement typically corresponds to a domain element, i.e.,
9423 one of the elements that is visited by the AST.
9425 Each type of node has its own additional properties.
9427 #include <isl/ast.h>
9428 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
9429 __isl_keep isl_ast_node *node);
9430 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
9431 __isl_keep isl_ast_node *node);
9432 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
9433 __isl_keep isl_ast_node *node);
9434 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
9435 __isl_keep isl_ast_node *node);
9436 __isl_give isl_ast_node *isl_ast_node_for_get_body(
9437 __isl_keep isl_ast_node *node);
9438 isl_bool isl_ast_node_for_is_degenerate(
9439 __isl_keep isl_ast_node *node);
9441 An C<isl_ast_for> is considered degenerate if it is known to execute
9444 #include <isl/ast.h>
9445 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
9446 __isl_keep isl_ast_node *node);
9447 __isl_give isl_ast_node *isl_ast_node_if_get_then(
9448 __isl_keep isl_ast_node *node);
9449 isl_bool isl_ast_node_if_has_else(
9450 __isl_keep isl_ast_node *node);
9451 __isl_give isl_ast_node *isl_ast_node_if_get_else(
9452 __isl_keep isl_ast_node *node);
9454 __isl_give isl_ast_node_list *
9455 isl_ast_node_block_get_children(
9456 __isl_keep isl_ast_node *node);
9458 __isl_give isl_id *isl_ast_node_mark_get_id(
9459 __isl_keep isl_ast_node *node);
9460 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
9461 __isl_keep isl_ast_node *node);
9463 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
9464 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
9466 #include <isl/ast.h>
9467 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
9468 __isl_keep isl_ast_node *node);
9470 All descendants of a specific node in the AST (including the node itself)
9472 in depth-first pre-order using the following function.
9474 #include <isl/ast.h>
9475 isl_stat isl_ast_node_foreach_descendant_top_down(
9476 __isl_keep isl_ast_node *node,
9477 isl_bool (*fn)(__isl_keep isl_ast_node *node,
9478 void *user), void *user);
9480 The callback function should return C<isl_bool_true> if the children
9481 of the given node should be visited and C<isl_bool_false> if they should not.
9482 It should return C<isl_bool_error> in case of failure, in which case
9483 the entire traversal is aborted.
9485 Each of the returned C<isl_ast_expr>s can in turn be inspected using
9486 the following functions.
9488 #include <isl/ast.h>
9489 enum isl_ast_expr_type isl_ast_expr_get_type(
9490 __isl_keep isl_ast_expr *expr);
9492 The type of an AST expression is one of
9494 C<isl_ast_expr_id> or
9495 C<isl_ast_expr_int>.
9496 An C<isl_ast_expr_op> represents the result of an operation.
9497 An C<isl_ast_expr_id> represents an identifier.
9498 An C<isl_ast_expr_int> represents an integer value.
9500 Each type of expression has its own additional properties.
9502 #include <isl/ast.h>
9503 enum isl_ast_op_type isl_ast_expr_get_op_type(
9504 __isl_keep isl_ast_expr *expr);
9505 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
9506 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
9507 __isl_keep isl_ast_expr *expr, int pos);
9508 isl_stat isl_ast_expr_foreach_ast_op_type(
9509 __isl_keep isl_ast_expr *expr,
9510 isl_stat (*fn)(enum isl_ast_op_type type,
9511 void *user), void *user);
9512 isl_stat isl_ast_node_foreach_ast_op_type(
9513 __isl_keep isl_ast_node *node,
9514 isl_stat (*fn)(enum isl_ast_op_type type,
9515 void *user), void *user);
9517 C<isl_ast_expr_get_op_type> returns the type of the operation
9518 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
9519 arguments. C<isl_ast_expr_get_op_arg> returns the specified
9521 C<isl_ast_expr_foreach_ast_op_type> calls C<fn> for each distinct
9522 C<isl_ast_op_type> that appears in C<expr>.
9523 C<isl_ast_node_foreach_ast_op_type> does the same for each distinct
9524 C<isl_ast_op_type> that appears in C<node>.
9525 The operation type is one of the following.
9529 =item C<isl_ast_op_and>
9531 Logical I<and> of two arguments.
9532 Both arguments can be evaluated.
9534 =item C<isl_ast_op_and_then>
9536 Logical I<and> of two arguments.
9537 The second argument can only be evaluated if the first evaluates to true.
9539 =item C<isl_ast_op_or>
9541 Logical I<or> of two arguments.
9542 Both arguments can be evaluated.
9544 =item C<isl_ast_op_or_else>
9546 Logical I<or> of two arguments.
9547 The second argument can only be evaluated if the first evaluates to false.
9549 =item C<isl_ast_op_max>
9551 Maximum of two or more arguments.
9553 =item C<isl_ast_op_min>
9555 Minimum of two or more arguments.
9557 =item C<isl_ast_op_minus>
9561 =item C<isl_ast_op_add>
9563 Sum of two arguments.
9565 =item C<isl_ast_op_sub>
9567 Difference of two arguments.
9569 =item C<isl_ast_op_mul>
9571 Product of two arguments.
9573 =item C<isl_ast_op_div>
9575 Exact division. That is, the result is known to be an integer.
9577 =item C<isl_ast_op_fdiv_q>
9579 Result of integer division, rounded towards negative
9582 =item C<isl_ast_op_pdiv_q>
9584 Result of integer division, where dividend is known to be non-negative.
9586 =item C<isl_ast_op_pdiv_r>
9588 Remainder of integer division, where dividend is known to be non-negative.
9590 =item C<isl_ast_op_zdiv_r>
9592 Equal to zero iff the remainder on integer division is zero.
9594 =item C<isl_ast_op_cond>
9596 Conditional operator defined on three arguments.
9597 If the first argument evaluates to true, then the result
9598 is equal to the second argument. Otherwise, the result
9599 is equal to the third argument.
9600 The second and third argument may only be evaluated if
9601 the first argument evaluates to true and false, respectively.
9602 Corresponds to C<a ? b : c> in C.
9604 =item C<isl_ast_op_select>
9606 Conditional operator defined on three arguments.
9607 If the first argument evaluates to true, then the result
9608 is equal to the second argument. Otherwise, the result
9609 is equal to the third argument.
9610 The second and third argument may be evaluated independently
9611 of the value of the first argument.
9612 Corresponds to C<a * b + (1 - a) * c> in C.
9614 =item C<isl_ast_op_eq>
9618 =item C<isl_ast_op_le>
9620 Less than or equal relation.
9622 =item C<isl_ast_op_lt>
9626 =item C<isl_ast_op_ge>
9628 Greater than or equal relation.
9630 =item C<isl_ast_op_gt>
9632 Greater than relation.
9634 =item C<isl_ast_op_call>
9637 The number of arguments of the C<isl_ast_expr> is one more than
9638 the number of arguments in the function call, the first argument
9639 representing the function being called.
9641 =item C<isl_ast_op_access>
9644 The number of arguments of the C<isl_ast_expr> is one more than
9645 the number of index expressions in the array access, the first argument
9646 representing the array being accessed.
9648 =item C<isl_ast_op_member>
9651 This operation has two arguments, a structure and the name of
9652 the member of the structure being accessed.
9656 #include <isl/ast.h>
9657 __isl_give isl_id *isl_ast_expr_get_id(
9658 __isl_keep isl_ast_expr *expr);
9660 Return the identifier represented by the AST expression.
9662 #include <isl/ast.h>
9663 __isl_give isl_val *isl_ast_expr_get_val(
9664 __isl_keep isl_ast_expr *expr);
9666 Return the integer represented by the AST expression.
9668 =head3 Properties of ASTs
9670 #include <isl/ast.h>
9671 isl_bool isl_ast_expr_is_equal(
9672 __isl_keep isl_ast_expr *expr1,
9673 __isl_keep isl_ast_expr *expr2);
9675 Check if two C<isl_ast_expr>s are equal to each other.
9677 =head3 Manipulating and printing the AST
9679 AST nodes can be copied and freed using the following functions.
9681 #include <isl/ast.h>
9682 __isl_give isl_ast_node *isl_ast_node_copy(
9683 __isl_keep isl_ast_node *node);
9684 __isl_null isl_ast_node *isl_ast_node_free(
9685 __isl_take isl_ast_node *node);
9687 AST expressions can be copied and freed using the following functions.
9689 #include <isl/ast.h>
9690 __isl_give isl_ast_expr *isl_ast_expr_copy(
9691 __isl_keep isl_ast_expr *expr);
9692 __isl_null isl_ast_expr *isl_ast_expr_free(
9693 __isl_take isl_ast_expr *expr);
9695 New AST expressions can be created either directly or within
9696 the context of an C<isl_ast_build>.
9698 #include <isl/ast.h>
9699 __isl_give isl_ast_expr *isl_ast_expr_from_val(
9700 __isl_take isl_val *v);
9701 __isl_give isl_ast_expr *isl_ast_expr_from_id(
9702 __isl_take isl_id *id);
9703 __isl_give isl_ast_expr *isl_ast_expr_neg(
9704 __isl_take isl_ast_expr *expr);
9705 __isl_give isl_ast_expr *isl_ast_expr_address_of(
9706 __isl_take isl_ast_expr *expr);
9707 __isl_give isl_ast_expr *isl_ast_expr_add(
9708 __isl_take isl_ast_expr *expr1,
9709 __isl_take isl_ast_expr *expr2);
9710 __isl_give isl_ast_expr *isl_ast_expr_sub(
9711 __isl_take isl_ast_expr *expr1,
9712 __isl_take isl_ast_expr *expr2);
9713 __isl_give isl_ast_expr *isl_ast_expr_mul(
9714 __isl_take isl_ast_expr *expr1,
9715 __isl_take isl_ast_expr *expr2);
9716 __isl_give isl_ast_expr *isl_ast_expr_div(
9717 __isl_take isl_ast_expr *expr1,
9718 __isl_take isl_ast_expr *expr2);
9719 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
9720 __isl_take isl_ast_expr *expr1,
9721 __isl_take isl_ast_expr *expr2);
9722 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
9723 __isl_take isl_ast_expr *expr1,
9724 __isl_take isl_ast_expr *expr2);
9725 __isl_give isl_ast_expr *isl_ast_expr_and(
9726 __isl_take isl_ast_expr *expr1,
9727 __isl_take isl_ast_expr *expr2)
9728 __isl_give isl_ast_expr *isl_ast_expr_and_then(
9729 __isl_take isl_ast_expr *expr1,
9730 __isl_take isl_ast_expr *expr2)
9731 __isl_give isl_ast_expr *isl_ast_expr_or(
9732 __isl_take isl_ast_expr *expr1,
9733 __isl_take isl_ast_expr *expr2)
9734 __isl_give isl_ast_expr *isl_ast_expr_or_else(
9735 __isl_take isl_ast_expr *expr1,
9736 __isl_take isl_ast_expr *expr2)
9737 __isl_give isl_ast_expr *isl_ast_expr_eq(
9738 __isl_take isl_ast_expr *expr1,
9739 __isl_take isl_ast_expr *expr2);
9740 __isl_give isl_ast_expr *isl_ast_expr_le(
9741 __isl_take isl_ast_expr *expr1,
9742 __isl_take isl_ast_expr *expr2);
9743 __isl_give isl_ast_expr *isl_ast_expr_lt(
9744 __isl_take isl_ast_expr *expr1,
9745 __isl_take isl_ast_expr *expr2);
9746 __isl_give isl_ast_expr *isl_ast_expr_ge(
9747 __isl_take isl_ast_expr *expr1,
9748 __isl_take isl_ast_expr *expr2);
9749 __isl_give isl_ast_expr *isl_ast_expr_gt(
9750 __isl_take isl_ast_expr *expr1,
9751 __isl_take isl_ast_expr *expr2);
9752 __isl_give isl_ast_expr *isl_ast_expr_access(
9753 __isl_take isl_ast_expr *array,
9754 __isl_take isl_ast_expr_list *indices);
9755 __isl_give isl_ast_expr *isl_ast_expr_call(
9756 __isl_take isl_ast_expr *function,
9757 __isl_take isl_ast_expr_list *arguments);
9759 The function C<isl_ast_expr_address_of> can be applied to an
9760 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
9761 to represent the address of the C<isl_ast_expr_access>. The function
9762 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
9763 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
9765 #include <isl/ast_build.h>
9766 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
9767 __isl_keep isl_ast_build *build,
9768 __isl_take isl_set *set);
9769 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
9770 __isl_keep isl_ast_build *build,
9771 __isl_take isl_pw_aff *pa);
9772 __isl_give isl_ast_expr *
9773 isl_ast_build_access_from_pw_multi_aff(
9774 __isl_keep isl_ast_build *build,
9775 __isl_take isl_pw_multi_aff *pma);
9776 __isl_give isl_ast_expr *
9777 isl_ast_build_access_from_multi_pw_aff(
9778 __isl_keep isl_ast_build *build,
9779 __isl_take isl_multi_pw_aff *mpa);
9780 __isl_give isl_ast_expr *
9781 isl_ast_build_call_from_pw_multi_aff(
9782 __isl_keep isl_ast_build *build,
9783 __isl_take isl_pw_multi_aff *pma);
9784 __isl_give isl_ast_expr *
9785 isl_ast_build_call_from_multi_pw_aff(
9786 __isl_keep isl_ast_build *build,
9787 __isl_take isl_multi_pw_aff *mpa);
9790 the domains of C<pa>, C<mpa> and C<pma> should correspond
9791 to the schedule space of C<build>.
9792 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
9793 the function being called.
9794 If the accessed space is a nested relation, then it is taken
9795 to represent an access of the member specified by the range
9796 of this nested relation of the structure specified by the domain
9797 of the nested relation.
9799 The following functions can be used to modify an C<isl_ast_expr>.
9801 #include <isl/ast.h>
9802 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
9803 __isl_take isl_ast_expr *expr, int pos,
9804 __isl_take isl_ast_expr *arg);
9806 Replace the argument of C<expr> at position C<pos> by C<arg>.
9808 #include <isl/ast.h>
9809 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
9810 __isl_take isl_ast_expr *expr,
9811 __isl_take isl_id_to_ast_expr *id2expr);
9813 The function C<isl_ast_expr_substitute_ids> replaces the
9814 subexpressions of C<expr> of type C<isl_ast_expr_id>
9815 by the corresponding expression in C<id2expr>, if there is any.
9818 User specified data can be attached to an C<isl_ast_node> and obtained
9819 from the same C<isl_ast_node> using the following functions.
9821 #include <isl/ast.h>
9822 __isl_give isl_ast_node *isl_ast_node_set_annotation(
9823 __isl_take isl_ast_node *node,
9824 __isl_take isl_id *annotation);
9825 __isl_give isl_id *isl_ast_node_get_annotation(
9826 __isl_keep isl_ast_node *node);
9828 Basic printing can be performed using the following functions.
9830 #include <isl/ast.h>
9831 __isl_give isl_printer *isl_printer_print_ast_expr(
9832 __isl_take isl_printer *p,
9833 __isl_keep isl_ast_expr *expr);
9834 __isl_give isl_printer *isl_printer_print_ast_node(
9835 __isl_take isl_printer *p,
9836 __isl_keep isl_ast_node *node);
9837 __isl_give char *isl_ast_expr_to_str(
9838 __isl_keep isl_ast_expr *expr);
9839 __isl_give char *isl_ast_node_to_str(
9840 __isl_keep isl_ast_node *node);
9841 __isl_give char *isl_ast_expr_to_C_str(
9842 __isl_keep isl_ast_expr *expr);
9843 __isl_give char *isl_ast_node_to_C_str(
9844 __isl_keep isl_ast_node *node);
9846 The functions C<isl_ast_expr_to_C_str> and
9847 C<isl_ast_node_to_C_str> are convenience functions
9848 that return a string representation of the input in C format.
9850 More advanced printing can be performed using the following functions.
9852 #include <isl/ast.h>
9853 __isl_give isl_printer *isl_ast_op_type_set_print_name(
9854 __isl_take isl_printer *p,
9855 enum isl_ast_op_type type,
9856 __isl_keep const char *name);
9857 isl_stat isl_options_set_ast_print_macro_once(
9858 isl_ctx *ctx, int val);
9859 int isl_options_get_ast_print_macro_once(isl_ctx *ctx);
9860 __isl_give isl_printer *isl_ast_op_type_print_macro(
9861 enum isl_ast_op_type type,
9862 __isl_take isl_printer *p);
9863 __isl_give isl_printer *isl_ast_expr_print_macros(
9864 __isl_keep isl_ast_expr *expr,
9865 __isl_take isl_printer *p);
9866 __isl_give isl_printer *isl_ast_node_print_macros(
9867 __isl_keep isl_ast_node *node,
9868 __isl_take isl_printer *p);
9869 __isl_give isl_printer *isl_ast_node_print(
9870 __isl_keep isl_ast_node *node,
9871 __isl_take isl_printer *p,
9872 __isl_take isl_ast_print_options *options);
9873 __isl_give isl_printer *isl_ast_node_for_print(
9874 __isl_keep isl_ast_node *node,
9875 __isl_take isl_printer *p,
9876 __isl_take isl_ast_print_options *options);
9877 __isl_give isl_printer *isl_ast_node_if_print(
9878 __isl_keep isl_ast_node *node,
9879 __isl_take isl_printer *p,
9880 __isl_take isl_ast_print_options *options);
9882 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
9883 C<isl> may print out an AST that makes use of macros such
9884 as C<floord>, C<min> and C<max>.
9885 The names of these macros may be modified by a call
9886 to C<isl_ast_op_type_set_print_name>. The user-specified
9887 names are associated to the printer object.
9888 C<isl_ast_op_type_print_macro> prints out the macro
9889 corresponding to a specific C<isl_ast_op_type>.
9890 If the print-macro-once option is set, then a given macro definition
9891 is only printed once to any given printer object.
9892 C<isl_ast_expr_print_macros> scans the C<isl_ast_expr>
9893 for subexpressions where these macros would be used and prints
9894 out the required macro definitions.
9895 Essentially, C<isl_ast_expr_print_macros> calls
9896 C<isl_ast_expr_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
9897 as function argument.
9898 C<isl_ast_node_print_macros> does the same
9899 for expressions in its C<isl_ast_node> argument.
9900 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
9901 C<isl_ast_node_if_print> print an C<isl_ast_node>
9902 in C<ISL_FORMAT_C>, but allow for some extra control
9903 through an C<isl_ast_print_options> object.
9904 This object can be created using the following functions.
9906 #include <isl/ast.h>
9907 __isl_give isl_ast_print_options *
9908 isl_ast_print_options_alloc(isl_ctx *ctx);
9909 __isl_give isl_ast_print_options *
9910 isl_ast_print_options_copy(
9911 __isl_keep isl_ast_print_options *options);
9912 __isl_null isl_ast_print_options *
9913 isl_ast_print_options_free(
9914 __isl_take isl_ast_print_options *options);
9916 __isl_give isl_ast_print_options *
9917 isl_ast_print_options_set_print_user(
9918 __isl_take isl_ast_print_options *options,
9919 __isl_give isl_printer *(*print_user)(
9920 __isl_take isl_printer *p,
9921 __isl_take isl_ast_print_options *options,
9922 __isl_keep isl_ast_node *node, void *user),
9924 __isl_give isl_ast_print_options *
9925 isl_ast_print_options_set_print_for(
9926 __isl_take isl_ast_print_options *options,
9927 __isl_give isl_printer *(*print_for)(
9928 __isl_take isl_printer *p,
9929 __isl_take isl_ast_print_options *options,
9930 __isl_keep isl_ast_node *node, void *user),
9933 The callback set by C<isl_ast_print_options_set_print_user>
9934 is called whenever a node of type C<isl_ast_node_user> needs to
9936 The callback set by C<isl_ast_print_options_set_print_for>
9937 is called whenever a node of type C<isl_ast_node_for> needs to
9939 Note that C<isl_ast_node_for_print> will I<not> call the
9940 callback set by C<isl_ast_print_options_set_print_for> on the node
9941 on which C<isl_ast_node_for_print> is called, but only on nested
9942 nodes of type C<isl_ast_node_for>. It is therefore safe to
9943 call C<isl_ast_node_for_print> from within the callback set by
9944 C<isl_ast_print_options_set_print_for>.
9946 The following option determines the type to be used for iterators
9947 while printing the AST.
9949 isl_stat isl_options_set_ast_iterator_type(
9950 isl_ctx *ctx, const char *val);
9951 const char *isl_options_get_ast_iterator_type(
9954 The AST printer only prints body nodes as blocks if these
9955 blocks cannot be safely omitted.
9956 For example, a C<for> node with one body node will not be
9957 surrounded with braces in C<ISL_FORMAT_C>.
9958 A block will always be printed by setting the following option.
9960 isl_stat isl_options_set_ast_always_print_block(isl_ctx *ctx,
9962 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
9966 #include <isl/ast_build.h>
9967 isl_stat isl_options_set_ast_build_atomic_upper_bound(
9968 isl_ctx *ctx, int val);
9969 int isl_options_get_ast_build_atomic_upper_bound(
9971 isl_stat isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
9973 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
9974 isl_stat isl_options_set_ast_build_detect_min_max(
9975 isl_ctx *ctx, int val);
9976 int isl_options_get_ast_build_detect_min_max(
9978 isl_stat isl_options_set_ast_build_exploit_nested_bounds(
9979 isl_ctx *ctx, int val);
9980 int isl_options_get_ast_build_exploit_nested_bounds(
9982 isl_stat isl_options_set_ast_build_group_coscheduled(
9983 isl_ctx *ctx, int val);
9984 int isl_options_get_ast_build_group_coscheduled(
9986 isl_stat isl_options_set_ast_build_scale_strides(
9987 isl_ctx *ctx, int val);
9988 int isl_options_get_ast_build_scale_strides(
9990 isl_stat isl_options_set_ast_build_allow_else(isl_ctx *ctx,
9992 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
9993 isl_stat isl_options_set_ast_build_allow_or(isl_ctx *ctx,
9995 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
9999 =item * ast_build_atomic_upper_bound
10001 Generate loop upper bounds that consist of the current loop iterator,
10002 an operator and an expression not involving the iterator.
10003 If this option is not set, then the current loop iterator may appear
10004 several times in the upper bound.
10005 For example, when this option is turned off, AST generation
10008 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
10012 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
10015 When the option is turned on, the following AST is generated
10017 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
10020 =item * ast_build_prefer_pdiv
10022 If this option is turned off, then the AST generation will
10023 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
10024 operators, but no C<isl_ast_op_pdiv_q> or
10025 C<isl_ast_op_pdiv_r> operators.
10026 If this option is turned on, then C<isl> will try to convert
10027 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
10028 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
10030 =item * ast_build_detect_min_max
10032 If this option is turned on, then C<isl> will try and detect
10033 min or max-expressions when building AST expressions from
10034 piecewise affine expressions.
10036 =item * ast_build_exploit_nested_bounds
10038 Simplify conditions based on bounds of nested for loops.
10039 In particular, remove conditions that are implied by the fact
10040 that one or more nested loops have at least one iteration,
10041 meaning that the upper bound is at least as large as the lower bound.
10042 For example, when this option is turned off, AST generation
10045 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
10051 for (int c0 = 0; c0 <= N; c0 += 1)
10052 for (int c1 = 0; c1 <= M; c1 += 1)
10055 When the option is turned on, the following AST is generated
10057 for (int c0 = 0; c0 <= N; c0 += 1)
10058 for (int c1 = 0; c1 <= M; c1 += 1)
10061 =item * ast_build_group_coscheduled
10063 If two domain elements are assigned the same schedule point, then
10064 they may be executed in any order and they may even appear in different
10065 loops. If this options is set, then the AST generator will make
10066 sure that coscheduled domain elements do not appear in separate parts
10067 of the AST. This is useful in case of nested AST generation
10068 if the outer AST generation is given only part of a schedule
10069 and the inner AST generation should handle the domains that are
10070 coscheduled by this initial part of the schedule together.
10071 For example if an AST is generated for a schedule
10073 { A[i] -> [0]; B[i] -> [0] }
10075 then the C<isl_ast_build_set_create_leaf> callback described
10076 below may get called twice, once for each domain.
10077 Setting this option ensures that the callback is only called once
10078 on both domains together.
10080 =item * ast_build_separation_bounds
10082 This option specifies which bounds to use during separation.
10083 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
10084 then all (possibly implicit) bounds on the current dimension will
10085 be used during separation.
10086 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
10087 then only those bounds that are explicitly available will
10088 be used during separation.
10090 =item * ast_build_scale_strides
10092 This option specifies whether the AST generator is allowed
10093 to scale down iterators of strided loops.
10095 =item * ast_build_allow_else
10097 This option specifies whether the AST generator is allowed
10098 to construct if statements with else branches.
10100 =item * ast_build_allow_or
10102 This option specifies whether the AST generator is allowed
10103 to construct if conditions with disjunctions.
10107 =head3 AST Generation Options (Schedule Tree)
10109 In case of AST construction from a schedule tree, the options
10110 that control how an AST is created from the individual schedule
10111 dimensions are stored in the band nodes of the tree
10112 (see L</"Schedule Trees">).
10114 In particular, a schedule dimension can be handled in four
10115 different ways, atomic, separate, unroll or the default.
10116 This loop AST generation type can be set using
10117 C<isl_schedule_node_band_member_set_ast_loop_type>.
10119 the first three can be selected by including a one-dimensional
10120 element with as value the position of the schedule dimension
10121 within the band and as name one of C<atomic>, C<separate>
10122 or C<unroll> in the options
10123 set by C<isl_schedule_node_band_set_ast_build_options>.
10124 Only one of these three may be specified for
10125 any given schedule dimension within a band node.
10126 If none of these is specified, then the default
10127 is used. The meaning of the options is as follows.
10133 When this option is specified, the AST generator will make
10134 sure that a given domains space only appears in a single
10135 loop at the specified level.
10137 For example, for the schedule tree
10139 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10141 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10142 options: "{ atomic[x] }"
10144 the following AST will be generated
10146 for (int c0 = 0; c0 <= 10; c0 += 1) {
10153 On the other hand, for the schedule tree
10155 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
10157 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
10158 options: "{ separate[x] }"
10160 the following AST will be generated
10164 for (int c0 = 1; c0 <= 9; c0 += 1) {
10171 If neither C<atomic> nor C<separate> is specified, then the AST generator
10172 may produce either of these two results or some intermediate form.
10176 When this option is specified, the AST generator will
10177 split the domain of the specified schedule dimension
10178 into pieces with a fixed set of statements for which
10179 instances need to be executed by the iterations in
10180 the schedule domain part. This option tends to avoid
10181 the generation of guards inside the corresponding loops.
10182 See also the C<atomic> option.
10186 When this option is specified, the AST generator will
10187 I<completely> unroll the corresponding schedule dimension.
10188 It is the responsibility of the user to ensure that such
10189 unrolling is possible.
10190 To obtain a partial unrolling, the user should apply an additional
10191 strip-mining to the schedule and fully unroll the inner schedule
10196 The C<isolate> option is a bit more involved. It allows the user
10197 to isolate a range of schedule dimension values from smaller and
10198 greater values. Additionally, the user may specify a different
10199 atomic/separate/unroll choice for the isolated part and the remaining
10200 parts. The typical use case of the C<isolate> option is to isolate
10201 full tiles from partial tiles.
10202 The part that needs to be isolated may depend on outer schedule dimensions.
10203 The option therefore needs to be able to reference those outer schedule
10204 dimensions. In particular, the space of the C<isolate> option is that
10205 of a wrapped map with as domain the flat product of all outer band nodes
10206 and as range the space of the current band node.
10207 The atomic/separate/unroll choice for the isolated part is determined
10208 by an option that lives in an unnamed wrapped space with as domain
10209 a zero-dimensional C<isolate> space and as range the regular
10210 C<atomic>, C<separate> or C<unroll> space.
10211 This option may also be set directly using
10212 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
10213 The atomic/separate/unroll choice for the remaining part is determined
10214 by the regular C<atomic>, C<separate> or C<unroll> option.
10215 Since the C<isolate> option references outer schedule dimensions,
10216 its use in a band node causes any tree containing the node
10217 to be considered anchored.
10219 As an example, consider the isolation of full tiles from partial tiles
10220 in a tiling of a triangular domain. The original schedule is as follows.
10222 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10224 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10225 { A[i,j] -> [floor(j/10)] }, \
10226 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10230 for (int c0 = 0; c0 <= 10; c0 += 1)
10231 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10232 for (int c2 = 10 * c0;
10233 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10234 for (int c3 = 10 * c1;
10235 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10238 Isolating the full tiles, we have the following input
10240 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10242 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10243 { A[i,j] -> [floor(j/10)] }, \
10244 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10245 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10246 10a+9+10b+9 <= 100 }"
10251 for (int c0 = 0; c0 <= 8; c0 += 1) {
10252 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10253 for (int c2 = 10 * c0;
10254 c2 <= 10 * c0 + 9; c2 += 1)
10255 for (int c3 = 10 * c1;
10256 c3 <= 10 * c1 + 9; c3 += 1)
10258 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10259 for (int c2 = 10 * c0;
10260 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10261 for (int c3 = 10 * c1;
10262 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10265 for (int c0 = 9; c0 <= 10; c0 += 1)
10266 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10267 for (int c2 = 10 * c0;
10268 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10269 for (int c3 = 10 * c1;
10270 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10274 We may then additionally unroll the innermost loop of the isolated part
10276 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
10278 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
10279 { A[i,j] -> [floor(j/10)] }, \
10280 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
10281 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
10282 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
10287 for (int c0 = 0; c0 <= 8; c0 += 1) {
10288 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10289 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
10291 A(c2, 10 * c1 + 1);
10292 A(c2, 10 * c1 + 2);
10293 A(c2, 10 * c1 + 3);
10294 A(c2, 10 * c1 + 4);
10295 A(c2, 10 * c1 + 5);
10296 A(c2, 10 * c1 + 6);
10297 A(c2, 10 * c1 + 7);
10298 A(c2, 10 * c1 + 8);
10299 A(c2, 10 * c1 + 9);
10301 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10302 for (int c2 = 10 * c0;
10303 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10304 for (int c3 = 10 * c1;
10305 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10308 for (int c0 = 9; c0 <= 10; c0 += 1)
10309 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10310 for (int c2 = 10 * c0;
10311 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
10312 for (int c3 = 10 * c1;
10313 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
10318 =head3 AST Generation Options (Schedule Map)
10320 In case of AST construction using
10321 C<isl_ast_build_node_from_schedule_map>, the options
10322 that control how an AST is created from the individual schedule
10323 dimensions are stored in the C<isl_ast_build>.
10324 They can be set using the following function.
10326 #include <isl/ast_build.h>
10327 __isl_give isl_ast_build *
10328 isl_ast_build_set_options(
10329 __isl_take isl_ast_build *control,
10330 __isl_take isl_union_map *options);
10332 The options are encoded in an C<isl_union_map>.
10333 The domain of this union relation refers to the schedule domain,
10334 i.e., the range of the schedule passed
10335 to C<isl_ast_build_node_from_schedule_map>.
10336 In the case of nested AST generation (see L</"Nested AST Generation">),
10337 the domain of C<options> should refer to the extra piece of the schedule.
10338 That is, it should be equal to the range of the wrapped relation in the
10339 range of the schedule.
10340 The range of the options can consist of elements in one or more spaces,
10341 the names of which determine the effect of the option.
10342 The values of the range typically also refer to the schedule dimension
10343 to which the option applies. In case of nested AST generation
10344 (see L</"Nested AST Generation">), these values refer to the position
10345 of the schedule dimension within the innermost AST generation.
10346 The constraints on the domain elements of
10347 the option should only refer to this dimension and earlier dimensions.
10348 We consider the following spaces.
10352 =item C<separation_class>
10354 B<This option has been deprecated. Use the isolate option on
10355 schedule trees instead.>
10357 This space is a wrapped relation between two one dimensional spaces.
10358 The input space represents the schedule dimension to which the option
10359 applies and the output space represents the separation class.
10360 While constructing a loop corresponding to the specified schedule
10361 dimension(s), the AST generator will try to generate separate loops
10362 for domain elements that are assigned different classes.
10363 If only some of the elements are assigned a class, then those elements
10364 that are not assigned any class will be treated as belonging to a class
10365 that is separate from the explicitly assigned classes.
10366 The typical use case for this option is to separate full tiles from
10368 The other options, described below, are applied after the separation
10371 As an example, consider the separation into full and partial tiles
10372 of a tiling of a triangular domain.
10373 Take, for example, the domain
10375 { A[i,j] : 0 <= i,j and i + j <= 100 }
10377 and a tiling into tiles of 10 by 10. The input to the AST generator
10378 is then the schedule
10380 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
10383 Without any options, the following AST is generated
10385 for (int c0 = 0; c0 <= 10; c0 += 1)
10386 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10387 for (int c2 = 10 * c0;
10388 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10390 for (int c3 = 10 * c1;
10391 c3 <= min(10 * c1 + 9, -c2 + 100);
10395 Separation into full and partial tiles can be obtained by assigning
10396 a class, say C<0>, to the full tiles. The full tiles are represented by those
10397 values of the first and second schedule dimensions for which there are
10398 values of the third and fourth dimensions to cover an entire tile.
10399 That is, we need to specify the following option
10401 { [a,b,c,d] -> separation_class[[0]->[0]] :
10402 exists b': 0 <= 10a,10b' and
10403 10a+9+10b'+9 <= 100;
10404 [a,b,c,d] -> separation_class[[1]->[0]] :
10405 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
10407 which simplifies to
10409 { [a, b, c, d] -> separation_class[[1] -> [0]] :
10410 a >= 0 and b >= 0 and b <= 8 - a;
10411 [a, b, c, d] -> separation_class[[0] -> [0]] :
10412 a >= 0 and a <= 8 }
10414 With this option, the generated AST is as follows
10417 for (int c0 = 0; c0 <= 8; c0 += 1) {
10418 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
10419 for (int c2 = 10 * c0;
10420 c2 <= 10 * c0 + 9; c2 += 1)
10421 for (int c3 = 10 * c1;
10422 c3 <= 10 * c1 + 9; c3 += 1)
10424 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
10425 for (int c2 = 10 * c0;
10426 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10428 for (int c3 = 10 * c1;
10429 c3 <= min(-c2 + 100, 10 * c1 + 9);
10433 for (int c0 = 9; c0 <= 10; c0 += 1)
10434 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
10435 for (int c2 = 10 * c0;
10436 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
10438 for (int c3 = 10 * c1;
10439 c3 <= min(10 * c1 + 9, -c2 + 100);
10446 This is a single-dimensional space representing the schedule dimension(s)
10447 to which ``separation'' should be applied. Separation tries to split
10448 a loop into several pieces if this can avoid the generation of guards
10450 See also the C<atomic> option.
10454 This is a single-dimensional space representing the schedule dimension(s)
10455 for which the domains should be considered ``atomic''. That is, the
10456 AST generator will make sure that any given domain space will only appear
10457 in a single loop at the specified level.
10459 Consider the following schedule
10461 { a[i] -> [i] : 0 <= i < 10;
10462 b[i] -> [i+1] : 0 <= i < 10 }
10464 If the following option is specified
10466 { [i] -> separate[x] }
10468 then the following AST will be generated
10472 for (int c0 = 1; c0 <= 9; c0 += 1) {
10479 If, on the other hand, the following option is specified
10481 { [i] -> atomic[x] }
10483 then the following AST will be generated
10485 for (int c0 = 0; c0 <= 10; c0 += 1) {
10492 If neither C<atomic> nor C<separate> is specified, then the AST generator
10493 may produce either of these two results or some intermediate form.
10497 This is a single-dimensional space representing the schedule dimension(s)
10498 that should be I<completely> unrolled.
10499 To obtain a partial unrolling, the user should apply an additional
10500 strip-mining to the schedule and fully unroll the inner loop.
10504 =head3 Fine-grained Control over AST Generation
10506 Besides specifying the constraints on the parameters,
10507 an C<isl_ast_build> object can be used to control
10508 various aspects of the AST generation process.
10509 In case of AST construction using
10510 C<isl_ast_build_node_from_schedule_map>,
10511 the most prominent way of control is through ``options'',
10512 as explained above.
10514 Additional control is available through the following functions.
10516 #include <isl/ast_build.h>
10517 __isl_give isl_ast_build *
10518 isl_ast_build_set_iterators(
10519 __isl_take isl_ast_build *control,
10520 __isl_take isl_id_list *iterators);
10522 The function C<isl_ast_build_set_iterators> allows the user to
10523 specify a list of iterator C<isl_id>s to be used as iterators.
10524 If the input schedule is injective, then
10525 the number of elements in this list should be as large as the dimension
10526 of the schedule space, but no direct correspondence should be assumed
10527 between dimensions and elements.
10528 If the input schedule is not injective, then an additional number
10529 of C<isl_id>s equal to the largest dimension of the input domains
10531 If the number of provided C<isl_id>s is insufficient, then additional
10532 names are automatically generated.
10534 #include <isl/ast_build.h>
10535 __isl_give isl_ast_build *
10536 isl_ast_build_set_create_leaf(
10537 __isl_take isl_ast_build *control,
10538 __isl_give isl_ast_node *(*fn)(
10539 __isl_take isl_ast_build *build,
10540 void *user), void *user);
10543 C<isl_ast_build_set_create_leaf> function allows for the
10544 specification of a callback that should be called whenever the AST
10545 generator arrives at an element of the schedule domain.
10546 The callback should return an AST node that should be inserted
10547 at the corresponding position of the AST. The default action (when
10548 the callback is not set) is to continue generating parts of the AST to scan
10549 all the domain elements associated to the schedule domain element
10550 and to insert user nodes, ``calling'' the domain element, for each of them.
10551 The C<build> argument contains the current state of the C<isl_ast_build>.
10552 To ease nested AST generation (see L</"Nested AST Generation">),
10553 all control information that is
10554 specific to the current AST generation such as the options and
10555 the callbacks has been removed from this C<isl_ast_build>.
10556 The callback would typically return the result of a nested
10557 AST generation or a
10558 user defined node created using the following function.
10560 #include <isl/ast.h>
10561 __isl_give isl_ast_node *isl_ast_node_alloc_user(
10562 __isl_take isl_ast_expr *expr);
10564 #include <isl/ast_build.h>
10565 __isl_give isl_ast_build *
10566 isl_ast_build_set_at_each_domain(
10567 __isl_take isl_ast_build *build,
10568 __isl_give isl_ast_node *(*fn)(
10569 __isl_take isl_ast_node *node,
10570 __isl_keep isl_ast_build *build,
10571 void *user), void *user);
10572 __isl_give isl_ast_build *
10573 isl_ast_build_set_before_each_for(
10574 __isl_take isl_ast_build *build,
10575 __isl_give isl_id *(*fn)(
10576 __isl_keep isl_ast_build *build,
10577 void *user), void *user);
10578 __isl_give isl_ast_build *
10579 isl_ast_build_set_after_each_for(
10580 __isl_take isl_ast_build *build,
10581 __isl_give isl_ast_node *(*fn)(
10582 __isl_take isl_ast_node *node,
10583 __isl_keep isl_ast_build *build,
10584 void *user), void *user);
10585 __isl_give isl_ast_build *
10586 isl_ast_build_set_before_each_mark(
10587 __isl_take isl_ast_build *build,
10588 isl_stat (*fn)(__isl_keep isl_id *mark,
10589 __isl_keep isl_ast_build *build,
10590 void *user), void *user);
10591 __isl_give isl_ast_build *
10592 isl_ast_build_set_after_each_mark(
10593 __isl_take isl_ast_build *build,
10594 __isl_give isl_ast_node *(*fn)(
10595 __isl_take isl_ast_node *node,
10596 __isl_keep isl_ast_build *build,
10597 void *user), void *user);
10599 The callback set by C<isl_ast_build_set_at_each_domain> will
10600 be called for each domain AST node.
10601 The callbacks set by C<isl_ast_build_set_before_each_for>
10602 and C<isl_ast_build_set_after_each_for> will be called
10603 for each for AST node. The first will be called in depth-first
10604 pre-order, while the second will be called in depth-first post-order.
10605 Since C<isl_ast_build_set_before_each_for> is called before the for
10606 node is actually constructed, it is only passed an C<isl_ast_build>.
10607 The returned C<isl_id> will be added as an annotation (using
10608 C<isl_ast_node_set_annotation>) to the constructed for node.
10609 In particular, if the user has also specified an C<after_each_for>
10610 callback, then the annotation can be retrieved from the node passed to
10611 that callback using C<isl_ast_node_get_annotation>.
10612 The callbacks set by C<isl_ast_build_set_before_each_mark>
10613 and C<isl_ast_build_set_after_each_mark> will be called for each
10614 mark AST node that is created, i.e., for each mark schedule node
10615 in the input schedule tree. The first will be called in depth-first
10616 pre-order, while the second will be called in depth-first post-order.
10617 Since the callback set by C<isl_ast_build_set_before_each_mark>
10618 is called before the mark AST node is actually constructed, it is passed
10619 the identifier of the mark node.
10620 All callbacks should C<NULL> (or -1) on failure.
10621 The given C<isl_ast_build> can be used to create new
10622 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
10623 or C<isl_ast_build_call_from_pw_multi_aff>.
10625 =head3 Nested AST Generation
10627 C<isl> allows the user to create an AST within the context
10628 of another AST. These nested ASTs are created using the
10629 same C<isl_ast_build_node_from_schedule_map> function that is used to create
10630 the outer AST. The C<build> argument should be an C<isl_ast_build>
10631 passed to a callback set by
10632 C<isl_ast_build_set_create_leaf>.
10633 The space of the range of the C<schedule> argument should refer
10634 to this build. In particular, the space should be a wrapped
10635 relation and the domain of this wrapped relation should be the
10636 same as that of the range of the schedule returned by
10637 C<isl_ast_build_get_schedule> below.
10638 In practice, the new schedule is typically
10639 created by calling C<isl_union_map_range_product> on the old schedule
10640 and some extra piece of the schedule.
10641 The space of the schedule domain is also available from
10642 the C<isl_ast_build>.
10644 #include <isl/ast_build.h>
10645 __isl_give isl_union_map *isl_ast_build_get_schedule(
10646 __isl_keep isl_ast_build *build);
10647 __isl_give isl_space *isl_ast_build_get_schedule_space(
10648 __isl_keep isl_ast_build *build);
10649 __isl_give isl_ast_build *isl_ast_build_restrict(
10650 __isl_take isl_ast_build *build,
10651 __isl_take isl_set *set);
10653 The C<isl_ast_build_get_schedule> function returns a (partial)
10654 schedule for the domains elements for which part of the AST still needs to
10655 be generated in the current build.
10656 In particular, the domain elements are mapped to those iterations of the loops
10657 enclosing the current point of the AST generation inside which
10658 the domain elements are executed.
10659 No direct correspondence between
10660 the input schedule and this schedule should be assumed.
10661 The space obtained from C<isl_ast_build_get_schedule_space> can be used
10662 to create a set for C<isl_ast_build_restrict> to intersect
10663 with the current build. In particular, the set passed to
10664 C<isl_ast_build_restrict> can have additional parameters.
10665 The ids of the set dimensions in the space returned by
10666 C<isl_ast_build_get_schedule_space> correspond to the
10667 iterators of the already generated loops.
10668 The user should not rely on the ids of the output dimensions
10669 of the relations in the union relation returned by
10670 C<isl_ast_build_get_schedule> having any particular value.
10672 =head1 Applications
10674 Although C<isl> is mainly meant to be used as a library,
10675 it also contains some basic applications that use some
10676 of the functionality of C<isl>.
10677 For applications that take one or more polytopes or polyhedra
10678 as input, this input may be specified in either the L<isl format>
10679 or the L<PolyLib format>.
10681 =head2 C<isl_polyhedron_sample>
10683 C<isl_polyhedron_sample> takes a polyhedron as input and prints
10684 an integer element of the polyhedron, if there is any.
10685 The first column in the output is the denominator and is always
10686 equal to 1. If the polyhedron contains no integer points,
10687 then a vector of length zero is printed.
10691 C<isl_pip> takes the same input as the C<example> program
10692 from the C<piplib> distribution, i.e., a set of constraints
10693 on the parameters, a line containing only -1 and finally a set
10694 of constraints on a parametric polyhedron.
10695 The coefficients of the parameters appear in the last columns
10696 (but before the final constant column).
10697 The output is the lexicographic minimum of the parametric polyhedron.
10698 As C<isl> currently does not have its own output format, the output
10699 is just a dump of the internal state.
10701 =head2 C<isl_polyhedron_minimize>
10703 C<isl_polyhedron_minimize> computes the minimum of some linear
10704 or affine objective function over the integer points in a polyhedron.
10705 If an affine objective function
10706 is given, then the constant should appear in the last column.
10708 =head2 C<isl_polytope_scan>
10710 Given a polytope, C<isl_polytope_scan> prints
10711 all integer points in the polytope.
10713 =head2 C<isl_codegen>
10715 Given either a schedule tree or a sequence consisting of
10716 a schedule map, a context set and an options relation,
10717 C<isl_codegen> prints out an AST that scans the domain elements
10718 of the schedule in the order of their image(s) taking into account
10719 the constraints in the context set.
10721 =head2 C<isl_schedule>
10723 Given an C<isl_schedule_constraints> object as input,
10724 C<isl_schedule> prints out a schedule that satisfies the given